LMFDB - Embedded newform 71.7.h.a.7.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,7,Mod(7,71)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("71.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	71.h (of order $70$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.3338399370$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$35$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			7.14
Character	$\chi$	$=$	71.7
Dual form			71.7.h.a.61.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.94555 - 1.36489i) q^{2} +(18.2494 + 42.6966i) q^{3} +(-32.3451 - 19.3253i) q^{4} +(49.7071 + 152.983i) q^{5} +(-31.9774 - 236.067i) q^{6} +(-399.783 - 17.9543i) q^{7} +(360.497 + 377.050i) q^{8} +(-986.173 + 1031.46i) q^{9} +O(q^{10})$	\(q+(-4.94555 - 1.36489i) q^{2} +(18.2494 + 42.6966i) q^{3} +(-32.3451 - 19.3253i) q^{4} +(49.7071 + 152.983i) q^{5} +(-31.9774 - 236.067i) q^{6} +(-399.783 - 17.9543i) q^{7} +(360.497 + 377.050i) q^{8} +(-986.173 + 1031.46i) q^{9} +(-37.0251 - 824.428i) q^{10} +(26.3785 + 145.357i) q^{11} +(234.846 - 1733.70i) q^{12} +(-360.563 + 1986.87i) q^{13} +(1952.64 + 634.451i) q^{14} +(-5624.71 + 4914.16i) q^{15} +(-125.526 - 233.266i) q^{16} +(4913.05 - 6762.23i) q^{17} +(6284.99 - 3755.11i) q^{18} +(-1866.49 - 1630.70i) q^{19} +(1348.66 - 5908.85i) q^{20} +(-6529.21 - 17397.0i) q^{21} +(67.9401 - 754.876i) q^{22} +(7814.11 + 6231.54i) q^{23} +(-9519.91 + 22272.9i) q^{24} +(-8292.01 + 6024.50i) q^{25} +(4495.03 - 9334.02i) q^{26} +(-30345.4 - 11388.8i) q^{27} +(12584.0 + 8306.66i) q^{28} +(-21242.5 + 1911.86i) q^{29} +(34524.6 - 16626.2i) q^{30} +(-42832.9 - 23049.4i) q^{31} +(-7126.67 - 31224.0i) q^{32} +(-5724.87 + 3778.95i) q^{33} +(-33527.4 + 26737.2i) q^{34} +(-17125.3 - 62052.3i) q^{35} +(51831.1 - 14304.5i) q^{36} +(16711.2 + 20955.2i) q^{37} +(7005.10 + 10612.3i) q^{38} +(-91412.4 + 20864.3i) q^{39} +(-39762.9 + 73891.8i) q^{40} +(-46351.3 - 96249.5i) q^{41} +(8545.61 + 94949.4i) q^{42} +(-34583.0 + 52391.0i) q^{43} +(1955.86 - 5211.37i) q^{44} +(-206815. - 99596.7i) q^{45} +(-30139.7 - 41483.8i) q^{46} +(102594. + 43850.8i) q^{47} +(7668.88 - 9616.47i) q^{48} +(42328.4 + 3809.62i) q^{49} +(49231.3 - 18476.8i) q^{50} +(378384. + 86363.7i) q^{51} +(50059.3 - 57297.4i) q^{52} +(56732.4 + 94954.0i) q^{53} +(134530. + 97742.0i) q^{54} +(-20926.0 + 11260.7i) q^{55} +(-137351. - 157211. i) q^{56} +(35563.1 - 109452. i) q^{57} +(107666. + 19538.4i) q^{58} +(371920. + 50380.0i) q^{59} +(276900. - 50249.9i) q^{60} +(-140329. + 6302.16i) q^{61} +(180373. + 172454. i) q^{62} +(412774. - 394652. i) q^{63} +(-8132.45 + 181083. i) q^{64} +(-321878. + 43601.4i) q^{65} +(33470.5 - 10875.2i) q^{66} +(1383.69 - 2315.91i) q^{67} +(-289595. + 123779. i) q^{68} +(-123463. + 447358. i) q^{69} +330257. i q^{70} +(-288322. + 212063. i) q^{71} -744423. q^{72} +(99583.2 + 27483.2i) q^{73} +(-54044.6 - 126444. i) q^{74} +(-408550. - 244097. i) q^{75} +(28858.0 + 88815.7i) q^{76} +(-7935.87 - 58584.9i) q^{77} +(480562. + 21582.1i) q^{78} +(-455110. - 476007. i) q^{79} +(29446.1 - 30798.2i) q^{80} +(-20848.1 - 464220. i) q^{81} +(97863.3 + 539271. i) q^{82} +(-142850. + 1.05456e6i) q^{83} +(-125015. + 688887. i) q^{84} +(1.27872e6 + 415480. i) q^{85} +(242540. - 211901. i) q^{86} +(-469294. - 872094. i) q^{87} +(-45297.7 + 62346.9i) q^{88} +(-627718. + 375044. i) q^{89} +(886875. + 774840. i) q^{90} +(179819. - 787840. i) q^{91} +(-132322. - 352570. i) q^{92} +(202455. - 2.24946e6i) q^{93} +(-447534. - 356896. i) q^{94} +(156691. - 366598. i) q^{95} +(1.20310e6 - 874103. i) q^{96} +(-23159.2 + 48090.6i) q^{97} +(-204138. - 76614.1i) q^{98} +(-175943. - 116139. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 10 q^{2} + 55 q^{3} + 1198 q^{4} + 126 q^{5} - 918 q^{6} - 23 q^{7} + 131 q^{8} + 7546 q^{9}+O(q^{10}) $ 840 * q - 10 * q^2 + 55 * q^3 + 1198 * q^4 + 126 * q^5 - 918 * q^6 - 23 * q^7 + 131 * q^8 + 7546 * q^9	\( 840 q - 10 q^{2} + 55 q^{3} + 1198 q^{4} + 126 q^{5} - 918 q^{6} - 23 q^{7} + 131 q^{8} + 7546 q^{9} - 2738 q^{10} - 1463 q^{11} + 3287 q^{12} - 23 q^{13} - 18290 q^{14} + 5228 q^{15} + 68462 q^{16} + 2570 q^{17} - 26745 q^{18} - 6745 q^{19} - 52864 q^{20} + 15937 q^{21} - 19928 q^{22} - 28 q^{23} - 35893 q^{24} - 571092 q^{25} + 66997 q^{26} + 198565 q^{27} + 128154 q^{28} - 40961 q^{29} + 407435 q^{30} - 128519 q^{31} + 401320 q^{32} + 75353 q^{33} - 476 q^{34} + 131968 q^{35} - 200068 q^{36} - 21044 q^{37} + 145205 q^{38} + 123396 q^{39} - 149980 q^{40} - 34188 q^{41} + 509224 q^{42} + 516743 q^{43} - 350483 q^{44} - 1812421 q^{45} + 839500 q^{46} - 397055 q^{47} + 132073 q^{48} - 516660 q^{49} - 275587 q^{50} - 883071 q^{51} + 391433 q^{52} + 251317 q^{53} + 404299 q^{54} - 435352 q^{55} + 2535081 q^{56} + 1392540 q^{57} - 3191058 q^{58} - 1813895 q^{59} - 7905336 q^{60} + 934381 q^{61} - 239618 q^{62} - 1259119 q^{63} + 5909363 q^{64} + 910632 q^{65} + 12964425 q^{66} + 2624713 q^{67} + 2922405 q^{68} + 2751764 q^{69} - 300728 q^{71} - 7000676 q^{72} - 4735993 q^{73} - 2407708 q^{74} - 5888351 q^{75} - 8042728 q^{76} - 7609131 q^{77} - 868580 q^{78} - 602041 q^{79} + 1791625 q^{80} + 5757840 q^{81} + 2634308 q^{82} + 3040503 q^{83} + 20965752 q^{84} + 700170 q^{85} + 5182335 q^{86} - 9283491 q^{87} - 15723405 q^{88} + 5631815 q^{89} + 10615935 q^{90} + 8939142 q^{91} - 12987536 q^{92} - 4837027 q^{93} + 4628120 q^{94} - 5586244 q^{95} + 6473670 q^{96} - 5779648 q^{97} + 8628336 q^{98} + 2652449 q^{99}+O(q^{100}) \) 840 * q - 10 * q^2 + 55 * q^3 + 1198 * q^4 + 126 * q^5 - 918 * q^6 - 23 * q^7 + 131 * q^8 + 7546 * q^9 - 2738 * q^10 - 1463 * q^11 + 3287 * q^12 - 23 * q^13 - 18290 * q^14 + 5228 * q^15 + 68462 * q^16 + 2570 * q^17 - 26745 * q^18 - 6745 * q^19 - 52864 * q^20 + 15937 * q^21 - 19928 * q^22 - 28 * q^23 - 35893 * q^24 - 571092 * q^25 + 66997 * q^26 + 198565 * q^27 + 128154 * q^28 - 40961 * q^29 + 407435 * q^30 - 128519 * q^31 + 401320 * q^32 + 75353 * q^33 - 476 * q^34 + 131968 * q^35 - 200068 * q^36 - 21044 * q^37 + 145205 * q^38 + 123396 * q^39 - 149980 * q^40 - 34188 * q^41 + 509224 * q^42 + 516743 * q^43 - 350483 * q^44 - 1812421 * q^45 + 839500 * q^46 - 397055 * q^47 + 132073 * q^48 - 516660 * q^49 - 275587 * q^50 - 883071 * q^51 + 391433 * q^52 + 251317 * q^53 + 404299 * q^54 - 435352 * q^55 + 2535081 * q^56 + 1392540 * q^57 - 3191058 * q^58 - 1813895 * q^59 - 7905336 * q^60 + 934381 * q^61 - 239618 * q^62 - 1259119 * q^63 + 5909363 * q^64 + 910632 * q^65 + 12964425 * q^66 + 2624713 * q^67 + 2922405 * q^68 + 2751764 * q^69 - 300728 * q^71 - 7000676 * q^72 - 4735993 * q^73 - 2407708 * q^74 - 5888351 * q^75 - 8042728 * q^76 - 7609131 * q^77 - 868580 * q^78 - 602041 * q^79 + 1791625 * q^80 + 5757840 * q^81 + 2634308 * q^82 + 3040503 * q^83 + 20965752 * q^84 + 700170 * q^85 + 5182335 * q^86 - 9283491 * q^87 - 15723405 * q^88 + 5631815 * q^89 + 10615935 * q^90 + 8939142 * q^91 - 12987536 * q^92 - 4837027 * q^93 + 4628120 * q^94 - 5586244 * q^95 + 6473670 * q^96 - 5779648 * q^97 + 8628336 * q^98 + 2652449 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{70}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−4.94555	−	1.36489i	−0.618194	−	0.170611i	−0.0571078	−	0.998368i	$-0.518188\pi$
$2$	−4.94555	−	1.36489i	−0.618194	−	0.170611i	−0.561086	+	0.827757i	$0.689616\pi$
$3$	18.2494	+	42.6966i	0.675904	+	1.58136i	0.807377	+	0.590035i	$0.200886\pi$
$3$	18.2494	+	42.6966i	0.675904	+	1.58136i	−0.131474	+	0.991320i	$0.541971\pi$
$4$	−32.3451	−	19.3253i	−0.505393	−	0.301958i
$5$	49.7071	+	152.983i	0.397657	+	1.22386i	0.926873	+	0.375374i	$0.122486\pi$
$5$	49.7071	+	152.983i	0.397657	+	1.22386i	−0.529217	+	0.848487i	$0.677514\pi$
$6$	−31.9774	−	236.067i	−0.148043	−	1.09290i
$7$	−399.783	−	17.9543i	−1.16555	−	0.0523448i	−0.546334	−	0.837568i	$-0.683977\pi$
$7$	−399.783	−	17.9543i	−1.16555	−	0.0523448i	−0.619213	+	0.785223i	$0.712548\pi$
$8$	360.497	+	377.050i	0.704096	+	0.736426i
$9$	−986.173	+	1031.46i	−1.35278	+	1.41489i
$10$	−37.0251	−	824.428i	−0.0370251	−	0.824428i
$11$	26.3785	+	145.357i	0.0198185	+	0.109209i	0.992323	−	0.123677i	$-0.0394687\pi$
$11$	26.3785	+	145.357i	0.0198185	+	0.109209i	−0.972504	+	0.232886i	$0.925183\pi$
$12$	234.846	−	1733.70i	0.135906	−	1.00330i
$13$	−360.563	+	1986.87i	−0.164116	+	0.904354i	0.791815	+	0.610761i	$0.209137\pi$
$13$	−360.563	+	1986.87i	−0.164116	+	0.904354i	−0.955931	+	0.293592i	$0.905149\pi$
$14$	1952.64	+	634.451i	0.711604	+	0.231214i
$15$	−5624.71	+	4914.16i	−1.66658	+	1.45605i
$16$	−125.526	−	233.266i	−0.0306459	−	0.0569496i
$17$	4913.05	−	6762.23i	1.00001	−	1.37639i	0.0746899	−	0.997207i	$-0.476203\pi$
$17$	4913.05	−	6762.23i	1.00001	−	1.37639i	0.925320	−	0.379188i	$-0.123797\pi$
$18$	6284.99	−	3755.11i	1.07767	−	0.643880i
$19$	−1866.49	−	1630.70i	−0.272123	−	0.237746i	0.511050	−	0.859551i	$-0.329257\pi$
$19$	−1866.49	−	1630.70i	−0.272123	−	0.237746i	−0.783172	+	0.621805i	$0.786400\pi$
$20$	1348.66	−	5908.85i	0.168582	−	0.738606i
$21$	−6529.21	−	17397.0i	−0.705022	−	1.87852i
$22$	67.9401	−	754.876i	0.00638055	−	0.0708937i
$23$	7814.11	+	6231.54i	0.642238	+	0.512168i	0.889591	−	0.456758i	$-0.150989\pi$
$23$	7814.11	+	6231.54i	0.642238	+	0.512168i	−0.247353	+	0.968925i	$0.579561\pi$
$24$	−9519.91	+	22272.9i	−0.688651	+	1.61118i
$25$	−8292.01	+	6024.50i	−0.530689	+	0.385568i
$26$	4495.03	−	9334.02i	0.255748	−	0.531066i
$27$	−30345.4	−	11388.8i	−1.54171	−	0.578612i
$28$	12584.0	+	8306.66i	0.573253	+	0.378401i
$29$	−21242.5	+	1911.86i	−0.870989	+	0.0783904i	−0.516110	−	0.856522i	$-0.672621\pi$
$29$	−21242.5	+	1911.86i	−0.870989	+	0.0783904i	−0.354878	+	0.934913i	$0.615478\pi$
$30$	34524.6	−	16626.2i	1.27869	−	0.615784i
$31$	−42832.9	−	23049.4i	−1.43778	−	0.773702i	−0.445215	−	0.895424i	$-0.646873\pi$
$31$	−42832.9	−	23049.4i	−1.43778	−	0.773702i	−0.992564	+	0.121721i	$0.961159\pi$
$32$	−7126.67	−	31224.0i	−0.217489	−	0.952880i
$33$	−5724.87	+	3778.95i	−0.159303	+	0.105155i
$34$	−33527.4	+	26737.2i	−0.853028	+	0.680267i
$35$	−17125.3	−	62052.3i	−0.399425	−	1.44728i
$36$	51831.1	−	14304.5i	1.11092	−	0.306595i
$37$	16711.2	+	20955.2i	0.329915	+	0.413700i	0.918929	−	0.394422i	$-0.129055\pi$
$37$	16711.2	+	20955.2i	0.329915	+	0.413700i	−0.589014	+	0.808123i	$0.700484\pi$
$38$	7005.10	+	10612.3i	0.127662	+	0.193400i
$39$	−91412.4	+	20864.3i	−1.54103	+	0.351730i
$40$	−39762.9	+	73891.8i	−0.621295	+	1.15456i
$41$	−46351.3	−	96249.5i	−0.672528	−	1.39652i	−0.905631	−	0.424067i	$-0.860602\pi$
$41$	−46351.3	−	96249.5i	−0.672528	−	1.39652i	0.233103	−	0.972452i	$-0.425112\pi$
$42$	8545.61	+	94949.4i	0.115344	+	1.28158i
$43$	−34583.0	+	52391.0i	−0.434968	+	0.658948i	−0.984269	−	0.176676i	$-0.943465\pi$
$43$	−34583.0	+	52391.0i	−0.434968	+	0.658948i	0.549301	+	0.835624i	$0.314894\pi$
$44$	1955.86	−	5211.37i	0.0229604	−	0.0611779i
$45$	−206815.	−	99596.7i	−2.26957	−	1.09297i
$46$	−30139.7	−	41483.8i	−0.309646	−	0.426192i
$47$	102594.	+	43850.8i	0.988164	+	0.422362i	0.825551	−	0.564328i	$-0.190865\pi$
$47$	102594.	+	43850.8i	0.988164	+	0.422362i	0.162614	+	0.986690i	$0.448008\pi$
$48$	7668.88	−	9616.47i	0.0693439	−	0.0869545i
$49$	42328.4	+	3809.62i	0.359785	+	0.0323813i
$50$	49231.3	−	18476.8i	0.393851	−	0.147815i
$51$	378384.	+	86363.7i	2.85248	+	0.651060i
$52$	50059.3	−	57297.4i	0.356020	−	0.407498i
$53$	56732.4	+	94954.0i	0.381069	+	0.637802i	0.987552	−	0.157295i	$-0.0502773\pi$
$53$	56732.4	+	94954.0i	0.381069	+	0.637802i	−0.606483	+	0.795097i	$0.707420\pi$
$54$	134530.	+	97742.0i	0.854356	+	0.620726i
$55$	−20926.0	+	11260.7i	−0.125776	+	0.0676829i
$56$	−137351.	−	157211.i	−0.782108	−	0.895195i
$57$	35563.1	−	109452.i	0.192033	−	0.591016i
$58$	107666.	+	19538.4i	0.551814	+	0.100140i
$59$	371920.	+	50380.0i	1.81090	+	0.245303i	0.959994	−	0.280020i	$-0.0903411\pi$
$59$	371920.	+	50380.0i	1.81090	+	0.245303i	0.850903	+	0.525323i	$0.176055\pi$
$60$	276900.	−	50249.9i	1.28194	−	0.232638i
$61$	−140329.	+	6302.16i	−0.618239	+	0.0277652i	−0.351783	−	0.936082i	$-0.614424\pi$
$61$	−140329.	+	6302.16i	−0.618239	+	0.0277652i	−0.266457	+	0.963847i	$0.585853\pi$
$62$	180373.	+	172454.i	0.756825	+	0.723599i
$63$	412774.	−	394652.i	1.65079	−	1.57831i
$64$	−8132.45	+	181083.i	−0.0310228	+	0.690777i
$65$	−321878.	+	43601.4i	−1.17207	+	0.158767i
$66$	33470.5	−	10875.2i	0.116421	−	0.0378274i
$67$	1383.69	−	2315.91i	0.00460061	−	0.00770013i	−0.856140	−	0.516744i	$-0.827144\pi$
$67$	1383.69	−	2315.91i	0.00460061	−	0.00770013i	0.860740	+	0.509044i	$0.170001\pi$
$68$	−289595.	+	123779.i	−0.921011	+	0.393659i
$69$	−123463.	+	447358.i	−0.375828	+	1.36178i
$70$			330257.i			0.962848i
$71$	−288322.	+	212063.i	−0.805570	+	0.592501i
$71$	−288322.	+	212063.i	−0.805570	+	0.592501i
$72$	−744423.			−1.99445
$73$	99583.2	+	27483.2i	0.255987	+	0.0706478i	0.391675	−	0.920104i	$-0.371896\pi$
$73$	99583.2	+	27483.2i	0.255987	+	0.0706478i	−0.135688	+	0.990752i	$0.543324\pi$
$74$	−54044.6	−	126444.i	−0.133370	−	0.312034i
$75$	−408550.	−	244097.i	−0.968414	−	0.578600i
$76$	28858.0	+	88815.7i	0.0657393	+	0.202325i
$77$	−7935.87	−	58584.9i	−0.0173829	−	0.128326i
$78$	480562.	+	21582.1i	1.01267	+	0.0454789i
$79$	−455110.	−	476007.i	−0.923070	−	0.965456i	0.0764296	−	0.997075i	$-0.475648\pi$
$79$	−455110.	−	476007.i	−0.923070	−	0.965456i	−0.999500	+	0.0316191i	$0.989934\pi$
$80$	29446.1	−	30798.2i	0.0575119	−	0.0601527i
$81$	−20848.1	−	464220.i	−0.0392294	−	0.873511i
$82$	97863.3	+	539271.i	0.177492	+	0.978061i
$83$	−142850.	+	1.05456e6i	−0.249830	+	1.84432i	0.237857	+	0.971300i	$0.423555\pi$
$83$	−142850.	+	1.05456e6i	−0.249830	+	1.84432i	−0.487687	+	0.873019i	$0.662159\pi$
$84$	−125015.	+	688887.i	−0.210923	+	1.16228i
$85$	1.27872e6	+	415480.i	2.08218	+	0.676540i
$86$	242540.	−	211901.i	0.381318	−	0.333148i
$87$	−469294.	−	872094.i	−0.712667	−	1.32436i
$88$	−45297.7	+	62346.9i	−0.0664703	+	0.0914885i
$89$	−627718.	+	375044.i	−0.890419	+	0.532000i	−0.883740	−	0.467977i	$-0.844983\pi$
$89$	−627718.	+	375044.i	−0.890419	+	0.532000i	−0.00667815	+	0.999978i	$0.502126\pi$
$90$	886875.	+	774840.i	1.21656	+	1.06288i
$91$	179819.	−	787840.i	0.238623	−	1.04548i
$92$	−132322.	−	352570.i	−0.169929	−	0.452775i
$93$	202455.	−	2.24946e6i	0.251697	−	2.79659i
$94$	−447534.	−	356896.i	−0.538818	−	0.429693i
$95$	156691.	−	366598.i	0.182757	−	0.427582i
$96$	1.20310e6	−	874103.i	1.35984	−	0.987982i
$97$	−23159.2	+	48090.6i	−0.0253752	+	0.0526921i	−0.913271	−	0.407352i	$-0.866452\pi$
$97$	−23159.2	+	48090.6i	−0.0253752	+	0.0526921i	0.887896	+	0.460044i	$0.152166\pi$
$98$	−204138.	−	76614.1i	−0.216893	−	0.0814011i
$99$	−175943.	−	116139.i	−0.181329	−	0.119694i
$100$	384631.	−	34617.5i	0.384631	−	0.0346175i
$101$	−608887.	+	293225.i	−0.590980	+	0.284601i	−0.705375	−	0.708834i	$-0.749221\pi$
$101$	−608887.	+	293225.i	−0.590980	+	0.284601i	0.114395	+	0.993435i	$0.463507\pi$
$102$	−1.75344e6	−	943568.i	−1.65231	−	0.889145i
$103$	367357.	+	1.60950e6i	0.336184	+	1.47292i	0.806929	+	0.590649i	$0.201128\pi$
$103$	367357.	+	1.60950e6i	0.336184	+	1.47292i	−0.470745	+	0.882269i	$0.656015\pi$
$104$	−879130.	+	580308.i	−0.781543	+	0.515892i
$105$	2.33689e6	−	1.86361e6i	2.01870	−	1.60986i
$106$	−150972.	−	547033.i	−0.126759	−	0.459300i
$107$	−745888.	+	205852.i	−0.608866	+	0.168036i	−0.556855	−	0.830610i	$-0.687992\pi$
$107$	−745888.	+	205852.i	−0.608866	+	0.168036i	−0.0520119	+	0.998646i	$0.516563\pi$
$108$	761433.	+	954807.i	0.604450	+	0.757957i
$109$	234789.	+	355690.i	0.181300	+	0.274658i	0.913847	−	0.406059i	$-0.133097\pi$
$109$	234789.	+	355690.i	0.181300	+	0.274658i	−0.732547	+	0.680717i	$0.761669\pi$
$110$	118860.	−	27129.0i	0.0893013	−	0.0203824i
$111$	−589745.	+	1.09593e6i	−0.431216	+	0.801334i
$112$	45994.8	+	95509.2i	0.0327382	+	0.0679816i
$113$	66215.7	+	735716.i	0.0458908	+	0.509888i	0.985737	+	0.168291i	$0.0538249\pi$
$113$	66215.7	+	735716.i	0.0458908	+	0.509888i	−0.939847	+	0.341597i	$0.889032\pi$
$114$	−325269.	+	492761.i	−0.219547	+	0.332600i
$115$	−564901.	+	1.50517e6i	−0.371432	+	0.989677i
$116$	724040.	+	348679.i	0.463862	+	0.223384i
$117$	−1.69379e6	−	2.33130e6i	−1.05755	−	1.45559i
$118$	−1.77059e6	−	756786.i	−1.07763	−	0.460603i
$119$	−2.08556e6	+	2.61521e6i	−1.23760	+	1.55191i
$120$	−3.88058e6	−	349258.i	−2.24570	−	0.202117i
$121$	1.63816e6	−	614813.i	0.924701	−	0.347046i
$122$	702604.	+	160365.i	0.386929	+	0.0883140i
$123$	3.26364e6	−	3.73554e6i	1.75383	−	2.00742i
$124$	939999.	+	1.57329e6i	0.493018	+	0.825173i
$125$	699541.	+	508247.i	0.358165	+	0.260222i
$126$	−2.58005e6	+	1.38838e6i	−1.28978	+	0.694062i
$127$	−2.29674e6	−	2.62883e6i	−1.12125	−	1.28337i	−0.954777	−	0.297324i	$-0.903906\pi$
$127$	−2.29674e6	−	2.62883e6i	−1.12125	−	1.28337i	−0.166471	−	0.986046i	$-0.553237\pi$
$128$	−346022.	+	1.06495e6i	−0.164996	+	0.507807i
$129$	−2.86803e6	−	520471.i	−1.33603	−	0.242453i
$130$	1.65138e6	+	223694.i	0.751651	+	0.101818i
$131$	−1.52249e6	+	276290.i	−0.677235	+	0.122900i	−0.506267	−	0.862377i	$-0.668975\pi$
$131$	−1.52249e6	+	276290.i	−0.677235	+	0.122900i	−0.170968	+	0.985277i	$0.554689\pi$
$132$	258201.	−	11595.8i	0.112263	−	0.00504173i
$133$	716911.	+	685438.i	0.304727	+	0.291349i
$134$	−10004.1	+	9564.89i	−0.00415780	+	0.00397526i
$135$	233911.	−	5.20842e6i	0.0950711	−	2.11692i
$136$	4.32084e6	−	585297.i	1.71772	−	0.232680i
$137$	2.68701e6	−	873062.i	1.04498	−	0.339534i	0.264283	−	0.964445i	$-0.414865\pi$
$137$	2.68701e6	−	873062.i	1.04498	−	0.339534i	0.780696	+	0.624911i	$0.214865\pi$
$138$	1.22118e6	−	2.04392e6i	0.464669	−	0.777725i
$139$	−77823.6	+	33263.4i	−0.0289779	+	0.0123857i	−0.407465	−	0.913221i	$-0.633587\pi$
$139$	−77823.6	+	33263.4i	−0.0289779	+	0.0123857i	0.378487	+	0.925606i	$0.376444\pi$
$140$	−645258.	+	2.33804e6i	−0.235152	+	0.852056i
$141$			5.18067e6i			1.84811i
$142$	1.71535e6	−	655241.i	0.599086	−	0.228842i
$143$	−298316.			−0.102016
$144$	364393.	+	100566.i	0.122035	+	0.0336794i
$145$	−1.34839e6	−	3.15471e6i	−0.442293	−	1.03480i
$146$	−454982.	−	271839.i	−0.146196	−	0.0873482i
$147$	609809.	+	1.87680e6i	0.191974	+	0.590835i
$148$	−135560.	−	1.00075e6i	−0.0418165	−	0.308701i
$149$	1.48907e6	+	66874.2i	0.450149	+	0.0202162i	0.268786	−	0.963200i	$-0.413378\pi$
$149$	1.48907e6	+	66874.2i	0.450149	+	0.0202162i	0.181363	+	0.983416i	$0.441949\pi$
$150$	1.68734e6	+	1.76482e6i	0.499952	+	0.522909i
$151$	−4.53976e6	+	4.74822e6i	−1.31857	+	1.37911i	−0.442619	+	0.896710i	$0.645951\pi$
$151$	−4.53976e6	+	4.74822e6i	−1.31857	+	1.37911i	−0.875949	+	0.482404i	$0.839764\pi$
$152$	−58006.8	−	1.29162e6i	−0.0165177	−	0.367794i
$153$	2.12983e6	+	1.17363e7i	0.594662	+	3.27686i
$154$	−40714.5	+	300566.i	−0.0111477	+	0.0822959i
$155$	1.39705e6	−	7.69841e6i	0.375162	−	2.06731i
$156$	3.35996e6	+	1.09172e6i	0.885034	+	0.287565i
$157$	1.41709e6	−	1.23808e6i	0.366184	−	0.319925i	−0.455105	−	0.890438i	$-0.650398\pi$
$157$	1.41709e6	−	1.23808e6i	0.366184	−	0.319925i	0.821289	+	0.570513i	$0.193255\pi$
$158$	1.60107e6	+	2.97529e6i	0.405920	+	0.754325i
$159$	−3.01888e6	+	4.15513e6i	−0.751025	+	1.03370i
$160$	4.42248e6	−	2.64231e6i	1.07971	−	0.645095i
$161$	−3.01206e6	−	2.63156e6i	−0.721749	−	0.630573i
$162$	−530501.	+	2.32428e6i	−0.124779	+	0.546693i
$163$	−2.52602e6	−	6.73057e6i	−0.583277	−	1.55414i	−0.813847	−	0.581080i	$-0.802630\pi$
$163$	−2.52602e6	−	6.73057e6i	−0.583277	−	1.55414i	0.230570	−	0.973056i	$-0.425941\pi$
$164$	−360813.	+	4.00896e6i	−0.0817994	+	0.908866i
$165$	−862681.	−	687965.i	−0.192043	−	0.153149i
$166$	2.14582e6	−	5.02040e6i	0.469104	−	1.09752i
$167$	−1.31020e6	+	951919.i	−0.281313	+	0.204386i	−0.719490	−	0.694503i	$-0.755624\pi$
$167$	−1.31020e6	+	951919.i	−0.281313	+	0.204386i	0.438177	+	0.898889i	$0.355624\pi$
$168$	4.20579e6	−	8.73340e6i	0.886991	−	1.84186i
$169$	701400.	+	263240.i	0.145313	+	0.0545370i
$170$	−5.75688e6	−	3.80008e6i	−1.17176	−	0.773475i
$171$	3.52268e6	−	317047.i	0.704506	−	0.0634067i
$172$	2.13106e6	−	1.02627e6i	0.418804	−	0.201685i
$173$	−8.34948e6	−	4.49305e6i	−1.61258	−	0.867766i	−0.996808	−	0.0798423i	$-0.974558\pi$
$173$	−8.34948e6	−	4.49305e6i	−1.61258	−	0.867766i	−0.615772	−	0.787924i	$-0.711156\pi$
$174$	1.13061e6	+	4.95352e6i	0.214617	+	0.940299i
$175$	3.42317e6	−	2.25961e6i	0.638725	−	0.421619i
$176$	30595.7	−	24399.2i	0.00561206	−	0.00447547i
$177$	4.63627e6	+	1.67991e7i	0.836081	+	3.02947i
$178$	3.61630e6	−	998036.i	0.641217	−	0.176965i
$179$	−1.25836e6	−	1.57793e6i	−0.219404	−	0.275124i	0.659933	−	0.751325i	$-0.270585\pi$
$179$	−1.25836e6	−	1.57793e6i	−0.219404	−	0.275124i	−0.879336	+	0.476201i	$0.842013\pi$
$180$	4.76471e6	+	7.21823e6i	0.816994	+	1.23769i
$181$	5.26329e6	−	1.20131e6i	0.887609	−	0.202591i	0.245676	−	0.969352i	$-0.420990\pi$
$181$	5.26329e6	−	1.20131e6i	0.887609	−	0.202591i	0.641933	+	0.766761i	$0.278133\pi$
$182$	−1.96462e6	+	3.65087e6i	−0.325885	+	0.605596i
$183$	−2.82999e6	−	5.87654e6i	−0.461777	−	0.958889i
$184$	467357.	+	5.19276e6i	0.0750232	+	0.833576i
$185$	−2.37511e6	+	3.59814e6i	−0.375119	+	0.568281i
$186$	−4.07150e6	+	1.08485e7i	−0.632726	+	1.68589i
$187$	1.11254e6	+	535770.i	0.170134	+	0.0819320i
$188$	−2.47099e6	−	3.40103e6i	−0.371875	−	0.511843i
$189$	1.19271e7	+	5.09788e6i	1.76664	+	0.755099i
$190$	−1.27529e6	+	1.59916e6i	−0.185929	+	0.233148i
$191$	7.83374e6	+	705050.i	1.12427	+	0.101186i	0.636130	−	0.771582i	$-0.280534\pi$
$191$	7.83374e6	+	705050.i	1.12427	+	0.101186i	0.488136	+	0.872768i	$0.337677\pi$
$192$	−7.88004e6	+	2.95743e6i	−1.11333	+	0.417841i
$193$	−1.71403e6	−	391216.i	−0.238422	−	0.0544183i	0.101640	−	0.994821i	$-0.467591\pi$
$193$	−1.71403e6	−	391216.i	−0.238422	−	0.0544183i	−0.340062	+	0.940403i	$0.610448\pi$
$194$	180173.	−	206225.i	0.0246766	−	0.0282447i
$195$	−7.73572e6	−	1.29474e7i	−1.04327	−	1.74614i
$196$	−1.29549e6	−	941232.i	−0.172055	−	0.125005i
$197$	114906.	−	61833.7i	0.0150295	−	0.00808773i	−0.466337	−	0.884607i	$-0.654426\pi$
$197$	114906.	−	61833.7i	0.0150295	−	0.00808773i	0.481366	+	0.876520i	$0.340141\pi$
$198$	711621.	+	814516.i	0.0916755	+	0.104931i
$199$	−2.07635e6	+	6.39036e6i	−0.263477	+	0.810898i	0.728564	+	0.684978i	$0.240188\pi$
$199$	−2.07635e6	+	6.39036e6i	−0.263477	+	0.810898i	−0.992040	+	0.125920i	$0.959812\pi$
$200$	−5.26078e6	−	954691.i	−0.657598	−	0.119336i
$201$	124133.	+	16815.0i	0.0152862	+	0.00207066i
$202$	3.41150e6	−	619097.i	0.413896	−	0.0751111i
$203$	8.52672e6	−	382936.i	1.01928	−	0.0457760i
$204$	−1.05699e7	−	1.01058e7i	−1.24503	−	1.19037i
$205$	1.24205e7	−	1.18752e7i	1.44171	−	1.37842i
$206$	379995.	−	8.46126e6i	0.0434687	−	0.967906i
$207$	−1.41336e7	+	1.91453e6i	−1.59347	+	0.215850i
$208$	508727.	−	165295.i	0.0565321	−	0.0183684i
$209$	187799.	−	314323.i	0.0205710	−	0.0344300i
$210$	−1.41008e7	+	6.02699e6i	−1.52260	+	0.650792i
$211$	−1.39586e6	+	5.05778e6i	−0.148592	+	0.538410i	0.851314	+	0.524657i	$0.175806\pi$
$211$	−1.39586e6	+	5.05778e6i	−0.148592	+	0.538410i	−0.999905	+	0.0137529i	$0.995622\pi$
$212$		−	4.16767e6i		−	0.437407i
$213$	−1.43161e7	−	8.44036e6i	−1.48144	−	0.873418i
$214$	3.96979e6			0.405067
$215$	−9.73393e6	−	2.68639e6i	−0.979429	−	0.270305i
$216$	−6.64526e6	−	1.55474e7i	−0.659403	−	1.54275i
$217$	1.67100e7	+	9.98377e6i	1.63530	+	0.977046i
$218$	−675685.	−	2.07955e6i	−0.0652191	−	0.200724i
$219$	643894.	+	4.75341e6i	0.0613030	+	0.452557i
$220$	894470.	+	40170.7i	0.0840036	+	0.00377260i
$221$	1.16642e7	+	1.21998e7i	1.08063	+	1.13025i
$222$	4.41243e6	−	4.61504e6i	0.403291	−	0.421810i
$223$	459349.	+	1.02282e7i	0.0414217	+	0.922327i	0.906891	+	0.421365i	$0.138449\pi$
$223$	459349.	+	1.02282e7i	0.0414217	+	0.922327i	−0.865469	+	0.500962i	$0.832980\pi$
$224$	2.28851e6	+	1.26108e7i	0.203615	+	1.12201i
$225$	1.96335e6	−	1.44940e7i	0.172366	−	1.27245i
$226$	676696.	−	3.72890e6i	0.0586230	−	0.323039i
$227$	−6.63517e6	−	2.15590e6i	−0.567250	−	0.184311i	0.0113307	−	0.999936i	$-0.496393\pi$
$227$	−6.63517e6	−	2.15590e6i	−0.567250	−	0.184311i	−0.578581	+	0.815625i	$0.696393\pi$
$228$	−3.26549e6	+	2.85297e6i	−0.275514	+	0.240709i
$229$	−2.56220e6	−	4.76137e6i	−0.213357	−	0.396484i	0.751313	−	0.659946i	$-0.229421\pi$
$229$	−2.56220e6	−	4.76137e6i	−0.213357	−	0.396484i	−0.964670	+	0.263463i	$0.915135\pi$
$230$	4.84814e6	−	6.67290e6i	0.398467	−	0.548442i
$231$	2.35655e6	−	1.40797e6i	0.191179	−	0.114224i
$232$	−8.37874e6	−	7.32028e6i	−0.670988	−	0.586224i
$233$	5.31250e6	−	2.32756e7i	0.419982	−	1.84006i	−0.112541	−	0.993647i	$-0.535899\pi$
$233$	5.31250e6	−	2.32756e7i	0.419982	−	1.84006i	0.532523	−	0.846415i	$-0.321244\pi$
$234$	5.19476e6	+	1.38414e7i	0.405432	+	1.08027i
$235$	−1.60876e6	+	1.78748e7i	−0.123962	+	1.37733i
$236$	−1.10562e7	−	8.81703e6i	−0.841143	−	0.670789i
$237$	1.20184e7	−	2.81185e7i	0.902822	−	2.11226i
$238$	1.38837e7	−	1.00871e7i	1.02985	−	0.748232i
$239$	5.25776e6	−	1.09178e7i	0.385130	−	0.799730i	−0.614809	−	0.788676i	$-0.710767\pi$
$239$	5.25776e6	−	1.09178e7i	0.385130	−	0.799730i	0.999939	−	0.0110540i	$-0.00351868\pi$
$240$	1.85235e6	+	695199.i	0.133995	+	0.0502893i
$241$	−2.93234e6	−	1.93562e6i	−0.209490	−	0.138283i	0.441796	−	0.897116i	$-0.354341\pi$
$241$	−2.93234e6	−	1.93562e6i	−0.209490	−	0.138283i	−0.651286	+	0.758833i	$0.725770\pi$
$242$	−8.94078e6	+	804685.i	−0.630855	+	0.0567779i
$243$	−1.84838e6	+	890132.i	−0.128817	+	0.0620348i
$244$	4.66074e6	+	2.50805e6i	0.320838	+	0.172650i
$245$	1.52121e6	+	6.66487e6i	0.103441	+	0.453204i
$246$	−2.12391e7	+	1.40198e7i	−1.42669	+	0.941752i
$247$	3.91297e6	−	3.12049e6i	0.259666	−	0.207077i
$248$	−6.75036e6	−	2.44594e7i	−0.442560	−	1.60358i
$249$	−4.76329e7	+	1.31459e7i	−3.08538	+	0.851512i
$250$	−2.76592e6	−	3.46836e6i	−0.177019	−	0.221975i
$251$	−2.00942e6	−	3.04414e6i	−0.127072	−	0.192506i	0.765468	−	0.643474i	$-0.222507\pi$
$251$	−2.00942e6	−	3.04414e6i	−0.127072	−	0.192506i	−0.892540	+	0.450968i	$0.851079\pi$
$252$	−2.09780e7	+	4.78809e6i	−1.31088	+	0.299200i
$253$	−699676.	+	1.30022e6i	−0.0432052	+	0.0802886i
$254$	7.77061e6	+	1.61358e7i	0.474192	+	0.984669i
$255$	5.59622e6	+	6.21791e7i	0.337500	+	3.74994i
$256$	9.55576e6	−	1.44764e7i	0.569568	−	0.862858i
$257$	−1.13409e7	+	3.02177e7i	−0.668111	+	1.78018i	−0.0437454	+	0.999043i	$0.513929\pi$
$257$	−1.13409e7	+	3.02177e7i	−0.668111	+	1.78018i	−0.624366	+	0.781132i	$0.714642\pi$
$258$	1.34736e7	+	6.48856e6i	0.784559	+	0.377824i
$259$	−6.30460e6	−	8.67754e6i	−0.362876	−	0.499456i
$260$	1.12538e7	+	4.81011e6i	0.640294	+	0.273675i
$261$	1.89768e7	−	2.37962e7i	1.06734	−	1.33840i
$262$	7.90664e6	+	711611.i	0.439631	+	0.0395675i
$263$	−6.45437e6	+	2.42236e6i	−0.354802	+	0.133160i	−0.522410	−	0.852694i	$-0.674967\pi$
$263$	−6.45437e6	+	2.42236e6i	−0.354802	+	0.133160i	0.167608	+	0.985854i	$0.446396\pi$
$264$	−3.48865e6	−	796262.i	−0.189603	−	0.0432757i
$265$	−1.17063e7	+	1.33990e7i	−0.629046	+	0.720001i
$266$	−2.60998e6	−	4.36837e6i	−0.138673	−	0.232100i
$267$	−2.74686e7	−	1.99571e7i	−1.44312	−	1.04849i
$268$	−89511.5	+	48168.2i	−0.00465023	+	0.00250240i
$269$	1.30524e7	+	1.49397e7i	0.670555	+	0.767512i	0.983234	−	0.182347i	$-0.0583693\pi$
$269$	1.30524e7	+	1.49397e7i	0.670555	+	0.767512i	−0.312679	+	0.949859i	$0.601226\pi$
$270$	−8.26572e6	+	2.54393e7i	−0.419942	+	1.29245i
$271$	−1.48078e7	−	2.68721e6i	−0.744014	−	0.135019i	−0.206704	−	0.978403i	$-0.566274\pi$
$271$	−1.48078e7	−	2.68721e6i	−0.744014	−	0.135019i	−0.537310	+	0.843385i	$0.680559\pi$
$272$	−2.19411e6	−	297212.i	−0.109031	−	0.0147693i
$273$	3.69197e7	−	6.69994e6i	1.81455	−	0.329293i
$274$	−1.44804e7	+	650314.i	−0.703928	+	0.0316134i
$275$	−1.09444e6	−	1.04639e6i	−0.0526250	−	0.0503146i
$276$	1.26387e7	−	1.20839e7i	0.601142	−	0.574750i
$277$	−1.15946e6	+	2.58173e7i	−0.0545526	+	1.21471i	0.765887	+	0.642975i	$0.222300\pi$
$277$	−1.15946e6	+	2.58173e7i	−0.0545526	+	1.21471i	−0.820440	+	0.571733i	$0.806271\pi$
$278$	430281.	−	58285.6i	0.0200271	−	0.00271286i
$279$	6.60151e7	−	2.14496e7i	3.03970	−	0.987658i
$280$	1.72232e7	−	2.88268e7i	0.784584	−	1.31317i
$281$	−1.83381e7	+	7.83809e6i	−0.826487	+	0.353258i	−0.764343	−	0.644810i	$-0.776937\pi$
$281$	−1.83381e7	+	7.83809e6i	−0.826487	+	0.353258i	−0.0621440	+	0.998067i	$0.519794\pi$
$282$	7.07103e6	−	2.56213e7i	0.315308	−	1.14249i
$283$			6.76351e6i			0.298410i	0.988806	+	0.149205i	$0.0476714\pi$
$283$			6.76351e6i			0.298410i	−0.988806	+	0.149205i	$0.952329\pi$
$284$	1.34240e7	−	1.28728e6i	0.586040	−	0.0561976i
$285$	1.85120e7			0.799685
$286$	1.47534e6	+	407168.i	0.0630658	+	0.0174051i
$287$	1.68024e7	+	3.93111e7i	0.710763	+	1.66291i
$288$	3.92343e7	+	2.34414e7i	1.64244	+	0.981309i
$289$	−1.41308e7	−	4.34901e7i	−0.585427	−	1.80176i
$290$	2.36270e6	+	1.74422e7i	0.0968757	+	0.715165i
$291$	−2.47595e6	−	111195.i	−0.100476	−	0.00451238i
$292$	−2.68991e6	−	2.81342e6i	−0.108041	−	0.113002i
$293$	2.08527e7	−	2.18102e7i	0.829007	−	0.867074i	−0.163837	−	0.986487i	$-0.552387\pi$
$293$	2.08527e7	−	2.18102e7i	0.829007	−	0.867074i	0.992845	+	0.119414i	$0.0381015\pi$
$294$	−454226.	−	1.01141e7i	−0.0178744	−	0.398003i
$295$	1.07798e7	+	5.94016e7i	0.419899	+	2.31383i
$296$	−1.87682e6	+	1.38552e7i	−0.0723680	+	0.534242i
$297$	854983.	−	4.71134e6i	0.0326353	−	0.179836i
$298$	−7.27300e6	−	2.36314e6i	−0.274830	−	0.0892978i
$299$	−1.51987e7	+	1.32787e7i	−0.568582	+	0.496755i
$300$	8.49734e6	+	1.57907e7i	0.314716	+	0.584841i
$301$	1.47663e7	−	2.03241e7i	0.541468	−	0.745266i
$302$	2.89324e7	−	1.72863e7i	1.05042	−	0.627598i
$303$	−2.36315e7	−	2.06462e7i	−0.849501	−	0.742186i
$304$	−146095.	+	640082.i	−0.00520012	+	0.0227832i
$305$	−7.93945e6	−	2.11546e7i	−0.279828	−	0.745598i
$306$	5.48556e6	−	6.09496e7i	0.191451	−	2.12719i
$307$	5.21544e6	+	4.15918e6i	0.180250	+	0.143745i	0.709459	−	0.704747i	$-0.248940\pi$
$307$	5.21544e6	+	4.15918e6i	0.180250	+	0.143745i	−0.529208	+	0.848492i	$0.677511\pi$
$308$	−875486.	+	2.04830e6i	−0.0299638	+	0.0701038i
$309$	−6.20160e7	+	4.50572e7i	−2.10198	+	1.52718i
$310$	−1.74167e7	+	3.61661e7i	−0.584628	+	1.21399i
$311$	−262019.	−	98337.4i	−0.00871067	−	0.00326917i	0.347016	−	0.937859i	$-0.387195\pi$
$311$	−262019.	−	98337.4i	−0.00871067	−	0.00326917i	−0.355726	+	0.934590i	$0.615766\pi$
$312$	−4.08208e7	−	2.69456e7i	−1.34406	−	0.887204i
$313$	4.45408e7	−	4.00874e6i	1.45253	−	0.130730i	0.664924	−	0.746911i	$-0.268464\pi$
$313$	4.45408e7	−	4.00874e6i	1.45253	−	0.130730i	0.787605	+	0.616181i	$0.211321\pi$
$314$	−8.69814e6	+	4.18880e6i	−0.280955	+	0.135301i
$315$	8.08927e7	+	4.35302e7i	2.58808	+	1.39271i
$316$	5.52159e6	+	2.41917e7i	0.174986	+	0.766663i
$317$	9.54693e6	−	6.30188e6i	0.299700	−	0.197830i	−0.392094	−	0.919925i	$-0.628249\pi$
$317$	9.54693e6	−	6.30188e6i	0.299700	−	0.197830i	0.691794	+	0.722095i	$0.256821\pi$
$318$	2.06013e7	−	1.64290e7i	0.640639	−	0.510893i
$319$	−838249.	−	3.03733e6i	−0.0258227	−	0.0935663i
$320$	−2.81068e7	+	7.75699e6i	−0.857752	+	0.236725i
$321$	−2.24012e7	−	2.80902e7i	−0.677260	−	0.849258i
$322$	1.13045e7	+	1.71256e7i	0.338598	+	0.512955i
$323$	−2.01973e7	+	4.60991e6i	−0.599358	+	0.136800i
$324$	−8.29686e6	+	1.54181e7i	−0.243937	+	0.453312i
$325$	−8.98007e6	−	1.86473e7i	−0.261595	−	0.543208i
$326$	3.30613e6	+	3.67341e7i	0.0954261	+	1.06027i
$327$	−1.09020e7	+	1.65158e7i	−0.311790	+	0.472342i
$328$	1.95814e7	−	5.21744e7i	0.554909	−	1.47855i
$329$	−4.02280e7	−	1.93728e7i	−1.12964	−	0.544007i
$330$	3.32744e6	+	4.57983e6i	0.0925910	+	0.127441i
$331$	4.66505e7	+	1.99394e7i	1.28639	+	0.549830i	0.924070	−	0.382224i	$-0.124842\pi$
$331$	4.66505e7	+	1.99394e7i	1.28639	+	0.549830i	0.362321	+	0.932054i	$0.381985\pi$
$332$	2.50001e7	−	3.13492e7i	0.683169	−	0.856667i
$333$	−3.80944e7	−	3.42856e6i	−1.03164	−	0.0928494i
$334$	7.77895e6	−	2.91949e6i	0.208776	−	0.0783551i
$335$	423074.	+	96563.9i	0.0112534	+	0.00256850i
$336$	−3.23854e6	+	3.70681e6i	−0.0853751	+	0.0977197i
$337$	1.73705e7	+	2.90734e7i	0.453862	+	0.759637i	0.996783	−	0.0801467i	$-0.0255389\pi$
$337$	1.73705e7	+	2.90734e7i	0.453862	+	0.759637i	−0.542921	+	0.839784i	$0.682682\pi$
$338$	−3.10952e6	−	2.25920e6i	−0.0805273	−	0.0585065i
$339$	−3.02042e7	+	1.62536e7i	−0.775297	+	0.417205i
$340$	−3.33310e7	−	3.81504e7i	−0.848030	−	0.970649i
$341$	2.22053e6	−	6.83408e6i	0.0560007	−	0.172352i
$342$	−1.78543e7	−	3.24008e6i	−0.446339	−	0.0809987i
$343$	2.98016e7	+	4.03690e6i	0.738511	+	0.100038i
$344$	−3.22211e7	+	5.84726e6i	−0.791525	+	0.143641i
$345$	−7.45749e7	+	3.34916e6i	−1.81608	+	0.0815604i
$346$	3.51603e7	+	3.36167e7i	0.848837	+	0.811572i
$347$	−4.15981e7	+	3.97719e7i	−0.995601	+	0.951892i	−0.998842	−	0.0481031i	$-0.984682\pi$
$347$	−4.15981e7	+	3.97719e7i	−0.995601	+	0.951892i	0.00324175	+	0.999995i	$0.498968\pi$
$348$	−1.67412e6	+	3.72772e7i	−0.0397237	+	0.884516i
$349$	−9.99766e6	+	1.35427e6i	−0.235192	+	0.0318589i	−0.250881	−	0.968018i	$-0.580720\pi$
$349$	−9.99766e6	+	1.35427e6i	−0.235192	+	0.0318589i	0.0156889	+	0.999877i	$0.495006\pi$
$350$	−2.00136e7	+	6.50280e6i	−0.466789	+	0.151669i
$351$	3.35695e7	−	5.61858e7i	0.776288	−	1.29929i
$352$	4.35064e6	−	1.85955e6i	0.0997528	−	0.0426364i
$353$	−7.67394e6	+	2.78059e7i	−0.174459	+	0.632139i	0.823443	+	0.567399i	$0.192050\pi$
$353$	−7.67394e6	+	2.78059e7i	−0.174459	+	0.632139i	−0.997902	+	0.0647400i	$0.979378\pi$
$354$		−	8.94090e7i		−	2.01545i
$355$	−4.67736e7	−	3.35673e7i	−1.04548	−	0.750293i
$356$	2.75514e7			0.610653
$357$	−1.49721e8	−	4.13203e7i	−3.29062	−	0.908153i
$358$	4.06957e6	+	9.52124e6i	0.0886951	+	0.207513i
$359$	7.38992e7	+	4.41527e7i	1.59719	+	0.954276i	0.986756	+	0.162209i	$0.0518618\pi$
$359$	7.38992e7	+	4.41527e7i	1.59719	+	0.954276i	0.610433	+	0.792068i	$0.290995\pi$
$360$	−3.70031e7	−	1.13884e8i	−0.793105	−	2.44093i
$361$	−5.49053e6	−	4.05327e7i	−0.116706	−	0.861558i
$362$	−2.76695e7	−	1.24264e6i	−0.583279	−	0.0261951i
$363$	5.61459e7	+	5.87240e7i	1.17381	+	1.22771i
$364$	−2.10415e7	+	2.20077e7i	−0.436288	+	0.456322i
$365$	745534.	+	1.66006e7i	0.0153317	+	0.341386i
$366$	5.97507e6	+	3.29254e7i	0.121871	+	0.671564i
$367$	−4.84350e6	+	3.57561e7i	−0.0979853	+	0.723356i	0.873596	+	0.486651i	$0.161782\pi$
$367$	−4.84350e6	+	3.57561e7i	−0.0979853	+	0.723356i	−0.971582	+	0.236705i	$0.923933\pi$
$368$	472734.	−	2.60498e6i	0.00948579	−	0.0522710i
$369$	1.44988e8	+	4.71093e7i	2.88570	+	0.937622i
$370$	1.66573e7	−	1.45530e7i	0.328851	−	0.287308i
$371$	−2.09758e7	−	3.89795e7i	−0.410768	−	0.763335i
$372$	−5.00199e7	+	6.88464e7i	−0.971659	+	1.33737i
$373$	−2.21562e6	+	1.32377e6i	−0.0426942	+	0.0255086i	−0.534088	−	0.845429i	$-0.679345\pi$
$373$	−2.21562e6	+	1.32377e6i	−0.0426942	+	0.0255086i	0.491394	+	0.870938i	$0.336488\pi$
$374$	−4.77085e6	−	4.16817e6i	−0.0911971	−	0.0796765i
$375$	−8.93419e6	+	3.91432e7i	−0.169419	+	0.742272i
$376$	2.04509e7	+	5.44912e7i	0.384724	+	1.02509i
$377$	3.86066e6	−	4.28954e7i	0.0720505	−	0.800547i
$378$	−5.20280e7	−	4.14909e7i	−0.963300	−	0.768206i
$379$	2.24750e6	−	5.25829e6i	0.0412840	−	0.0965888i	−0.897617	−	0.440777i	$-0.854703\pi$
$379$	2.24750e6	−	5.25829e6i	0.0412840	−	0.0965888i	0.938901	+	0.344188i	$0.111846\pi$
$380$	−1.21528e7	+	8.82954e6i	−0.221476	+	0.160912i
$381$	7.03281e7	−	1.46038e8i	1.27161	−	2.64052i
$382$	−3.77799e7	−	1.41790e7i	−0.677752	−	0.254364i
$383$	−2.73348e6	−	1.80436e6i	−0.0486542	−	0.0321163i	0.526336	−	0.850277i	$-0.323565\pi$
$383$	−2.73348e6	−	1.80436e6i	−0.0486542	−	0.0321163i	−0.574990	+	0.818160i	$0.694994\pi$
$384$	−5.17843e7	+	4.66067e6i	−0.914544	+	0.0823105i
$385$	8.56801e6	−	4.12614e6i	0.150140	−	0.0723038i
$386$	7.94286e6	+	4.27424e6i	0.138107	+	0.0743184i
$387$	−1.99342e7	−	8.73374e7i	−0.343927	−	1.50684i
$388$	1.67845e6	−	1.10794e6i	0.0287352	−	0.0189680i
$389$	1.41026e7	−	1.12464e7i	0.239580	−	0.191059i	−0.496338	−	0.868129i	$-0.665322\pi$
$389$	1.41026e7	−	1.12464e7i	0.239580	−	0.191059i	0.735918	+	0.677071i	$0.236751\pi$
$390$	2.05857e7	+	7.45905e7i	0.347033	+	1.25745i
$391$	8.05302e7	−	2.22249e7i	1.34719	−	0.371800i
$392$	1.38228e7	+	1.73333e7i	0.229477	+	0.287755i
$393$	−3.95811e7	−	5.99628e7i	−0.652094	−	0.987880i
$394$	−652671.	+	148968.i	−0.0106710	+	0.00243559i
$395$	5.01987e7	−	9.32848e7i	0.814519	−	1.51363i
$396$	3.44649e6	+	7.15670e6i	0.0554998	+	0.115246i
$397$	505813.	+	5.62004e6i	0.00808385	+	0.0898189i	0.999003	−	0.0446387i	$-0.0142137\pi$
$397$	505813.	+	5.62004e6i	0.00808385	+	0.0898189i	−0.990919	+	0.134458i	$0.957071\pi$
$398$	1.89908e7	−	2.87699e7i	0.301228	−	0.456340i
$399$	−1.61826e7	+	4.31185e7i	−0.254760	+	0.678805i
$400$	2.44617e6	+	1.17801e6i	0.0382214	+	0.0184064i
$401$	−2.29393e7	−	3.15732e7i	−0.355752	−	0.489650i	0.593207	−	0.805050i	$-0.297862\pi$
$401$	−2.29393e7	−	3.15732e7i	−0.355752	−	0.489650i	−0.948959	+	0.315399i	$0.897862\pi$
$402$	−590957.	−	252587.i	−0.00909657	−	0.00388806i
$403$	6.12399e7	−	7.67924e7i	0.935663	−	1.17328i
$404$	2.53612e7	+	2.28255e6i	0.384615	+	0.0346159i
$405$	6.99813e7	−	2.62644e7i	1.05346	−	0.395369i
$406$	−4.26920e7	−	9.74418e6i	−0.637924	−	0.145602i
$407$	−2.60517e6	+	2.98186e6i	−0.0386414	+	0.0442286i
$408$	1.03843e8	+	1.73804e8i	1.52896	+	2.55905i
$409$	6.84753e7	+	4.97502e7i	1.00084	+	0.727152i	0.962268	−	0.272104i	$-0.0877194\pi$
$409$	6.84753e7	+	4.97502e7i	1.00084	+	0.727152i	0.0385712	+	0.999256i	$0.487719\pi$
$410$	−7.76347e7	+	4.17770e7i	−1.12643	+	0.606158i
$411$	8.63131e7	+	9.87932e7i	1.24323	+	1.42299i
$412$	1.92218e7	−	5.91587e7i	0.274855	−	0.845915i
$413$	−1.47783e8	−	2.68186e7i	−2.09785	−	0.380703i
$414$	7.25117e7	+	9.82238e6i	1.02190	+	0.138425i
$415$	−1.68430e8	+	3.05655e7i	−2.35654	+	0.427648i
$416$	6.46074e7	−	2.90152e6i	0.897434	−	0.0403038i
$417$	−2.84047e6	−	2.71576e6i	−0.0391725	−	0.0374528i
$418$	−1.35779e6	+	1.29818e6i	−0.0185910	+	0.0177748i
$419$	4.84691e6	−	1.07925e8i	0.0658905	−	1.46717i	−0.645172	−	0.764038i	$-0.723214\pi$
$419$	4.84691e6	−	1.07925e8i	0.0658905	−	1.46717i	0.711062	−	0.703129i	$-0.248214\pi$
$420$	−1.11602e8	+	1.51175e7i	−1.50634	+	0.204048i
$421$	−1.66309e7	+	5.40371e6i	−0.222879	+	0.0724178i	−0.418328	−	0.908296i	$-0.637384\pi$
$421$	−1.66309e7	+	5.40371e6i	−0.222879	+	0.0724178i	0.195449	+	0.980714i	$0.437384\pi$
$422$	1.38066e7	−	2.31084e7i	0.183717	−	0.307491i
$423$	−1.46406e8	+	6.25769e7i	−1.93436	+	0.826785i
$424$	−1.53506e7	+	5.56216e7i	−0.201385	+	0.729702i
$425$			8.56711e7i			1.11601i
$426$	5.92807e7	+	6.12820e7i	0.766805	+	0.792692i
$427$	5.62141e7			0.722040
$428$	2.81040e7	+	7.75621e6i	0.358457	+	0.0989277i
$429$	−5.44410e6	−	1.27371e7i	−0.0689531	−	0.161324i
$430$	4.44731e7	+	2.65714e7i	0.559360	+	0.334202i
$431$	4.09849e7	+	1.26138e8i	0.511908	+	1.57549i	0.788839	+	0.614600i	$0.210683\pi$
$431$	4.09849e7	+	1.26138e8i	0.511908	+	1.57549i	−0.276931	+	0.960890i	$0.589317\pi$
$432$	1.15250e6	+	8.50812e6i	0.0142952	+	0.105532i
$433$	−3.30415e7	−	1.48389e6i	−0.407001	−	0.0182784i	−0.159577	−	0.987186i	$-0.551013\pi$
$433$	−3.30415e7	−	1.48389e6i	−0.407001	−	0.0182784i	−0.247425	+	0.968907i	$0.579584\pi$
$434$	−6.90136e7	−	7.21825e7i	−0.844239	−	0.883004i
$435$	1.10088e8	−	1.15143e8i	1.33743	−	1.39885i
$436$	−720457.	−	1.60422e7i	−0.00869258	−	0.193555i
$437$	−4.42315e6	−	2.43736e7i	−0.0530014	−	0.292062i
$438$	3.30346e6	−	2.43871e7i	0.0393139	−	0.290227i
$439$	−6.28201e6	+	3.46167e7i	−0.0742515	+	0.409159i	0.925301	+	0.379234i	$0.123813\pi$
$439$	−6.28201e6	+	3.46167e7i	−0.0742515	+	0.409159i	−0.999552	+	0.0299250i	$0.990473\pi$
$440$	−1.17896e7	−	3.83067e6i	−0.138402	−	0.0449694i
$441$	−4.56726e7	+	3.99029e7i	−0.532525	+	0.465253i
$442$	−4.10345e7	−	7.62549e7i	−0.475206	−	0.883082i
$443$	−7.50234e7	+	1.03261e8i	−0.862950	+	1.18775i	0.117908	+	0.993025i	$0.462381\pi$
$443$	−7.50234e7	+	1.03261e8i	−0.862950	+	1.18775i	−0.980858	+	0.194725i	$0.937619\pi$
$444$	4.02545e7	−	2.40510e7i	0.459903	−	0.274779i
$445$	−8.85772e7	−	7.73876e7i	−1.00518	−	0.878195i
$446$	1.16886e7	−	5.12111e7i	0.131752	−	0.577244i
$447$	2.43193e7	+	6.47986e7i	0.272288	+	0.725510i
$448$	6.50243e6	−	7.22479e7i	0.0723172	−	0.803509i
$449$	6.10322e7	+	4.86716e7i	0.674249	+	0.537695i	0.899673	−	0.436565i	$-0.143805\pi$
$449$	6.10322e7	+	4.86716e7i	0.674249	+	0.537695i	−0.225424	+	0.974261i	$0.572377\pi$
$450$	−2.94926e7	+	6.90013e7i	−0.323650	+	0.757216i
$451$	1.27679e7	−	9.27642e6i	0.139184	−	0.101123i
$452$	1.20762e7	−	2.50765e7i	0.130772	−	0.271551i
$453$	−2.85581e8	−	1.07180e8i	−3.07209	−	1.15298i
$454$	2.98720e7	+	1.97184e7i	0.319225	+	0.210719i
$455$	1.29464e8	−	1.16520e7i	1.37441	−	0.123699i
$456$	5.40893e7	−	2.60480e7i	0.570449	−	0.274714i
$457$	4.94993e7	+	2.66367e7i	0.518622	+	0.279082i	0.712168	−	0.702009i	$-0.247713\pi$
$457$	4.94993e7	+	2.66367e7i	0.518622	+	0.279082i	−0.193547	+	0.981091i	$0.561999\pi$
$458$	6.17278e6	+	2.70447e7i	0.0642517	+	0.281505i
$459$	−2.26102e8	+	1.49249e8i	−2.33812	+	1.54338i
$460$	4.73598e7	−	3.77682e7i	0.486560	−	0.388019i
$461$	701633.	+	2.54231e6i	0.00716155	+	0.0259493i	0.967456	−	0.253038i	$-0.0814298\pi$
$461$	701633.	+	2.54231e6i	0.00716155	+	0.0259493i	−0.960295	+	0.278987i	$0.910001\pi$
$462$	−1.35762e7	+	3.74679e6i	−0.137674	+	0.0379956i
$463$	−1.51528e7	−	1.90011e7i	−0.152669	−	0.191441i	0.699615	−	0.714520i	$-0.253355\pi$
$463$	−1.51528e7	−	1.90011e7i	−0.152669	−	0.191441i	−0.852284	+	0.523079i	$0.824783\pi$
$464$	3.11245e6	+	4.71516e6i	0.0311565	+	0.0472001i
$465$	3.54191e8	−	8.08418e7i	3.52273	−	0.804039i
$466$	−5.80417e7	+	1.07860e8i	−0.573565	+	1.06586i
$467$	−5.99537e7	−	1.24495e8i	−0.588661	−	1.22237i	−0.956297	−	0.292398i	$-0.905547\pi$
$467$	−5.99537e7	−	1.24495e8i	−0.588661	−	1.22237i	0.367635	−	0.929970i	$-0.380167\pi$
$468$	9.73270e6	+	1.08139e8i	0.0949501	+	1.05498i
$469$	−594757.	+	901019.i	−0.00576529	+	0.00873404i
$470$	3.23533e7	−	8.62051e7i	0.311620	−	0.830309i
$471$	7.87227e7	+	3.79109e7i	0.753420	+	0.362828i
$472$	1.15080e8	+	1.58394e8i	1.09440	+	1.50631i
$473$	−8.52766e6	−	3.64490e6i	−0.0805835	−	0.0344431i
$474$	−9.78162e7	+	1.22658e8i	−0.918493	+	1.15175i
$475$	2.53011e7	+	2.27714e6i	0.236080	+	0.0212476i
$476$	1.17998e8	−	4.42852e7i	1.09409	−	0.410618i
$477$	−1.53889e8	−	3.51241e7i	−1.41792	−	0.323631i
$478$	−4.09041e7	+	4.68186e7i	−0.374527	+	0.428681i
$479$	4.90397e7	+	8.20786e7i	0.446212	+	0.746833i	0.996084	−	0.0884162i	$-0.0281805\pi$
$479$	4.90397e7	+	8.20786e7i	0.446212	+	0.746833i	−0.549872	+	0.835249i	$0.685323\pi$
$480$	1.93525e8	+	1.40604e8i	1.74990	+	1.27138i
$481$	−4.76605e7	+	2.56472e7i	−0.428275	+	0.230465i
$482$	1.18601e7	+	1.35750e7i	0.105913	+	0.121227i
$483$	5.73903e7	−	1.76629e8i	0.509327	−	1.56755i
$484$	−6.48681e7	−	1.17718e7i	−0.572131	−	0.103826i
$485$	−8.50821e6	−	1.15252e6i	−0.0745784	−	0.0101023i
$486$	1.03562e7	−	1.87937e6i	0.0902175	−	0.0163721i
$487$	−1.57423e8	+	7.06988e6i	−1.36296	+	0.0612104i	−0.714283	−	0.699857i	$-0.753247\pi$
$487$	−1.57423e8	+	7.06988e6i	−1.36296	+	0.0612104i	−0.648673	+	0.761068i	$0.724676\pi$
$488$	−5.29643e7	−	5.06390e7i	−0.455747	−	0.435738i
$489$	2.41274e8	−	2.30681e8i	2.06340	−	1.97281i
$490$	1.57355e6	−	3.50378e7i	0.0133749	−	0.297816i
$491$	−1.18678e6	+	160760.i	−0.0100259	+	0.00135810i	−0.139245	−	0.990258i	$-0.544467\pi$
$491$	−1.18678e6	+	160760.i	−0.0100259	+	0.00135810i	0.129219	+	0.991616i	$0.458753\pi$
$492$	−1.77753e8	+	5.77556e7i	−1.49253	+	0.484952i
$493$	−9.14371e7	+	1.53040e8i	−0.763101	+	1.27722i
$494$	−2.36109e7	+	1.00918e7i	−0.195854	+	0.0837119i
$495$	9.02166e6	−	3.26892e7i	0.0743825	−	0.269519i
$496$			1.28847e7i			0.105592i
$497$	1.19074e8	−	7.96024e7i	0.969943	−	0.648421i
$498$	2.53514e8			2.05264
$499$	1.16349e8	+	3.21102e7i	0.936396	+	0.258429i	0.700748	−	0.713409i	$-0.252850\pi$
$499$	1.16349e8	+	3.21102e7i	0.936396	+	0.258429i	0.235649	+	0.971838i	$0.424279\pi$
$500$	−1.28047e7	−	2.99582e7i	−0.102438	−	0.239665i
$501$	−6.45541e7	−	3.85693e7i	−0.513347	−	0.306711i
$502$	5.78279e6	+	1.77976e7i	0.0457116	+	0.140686i
$503$	3.21550e7	+	2.37378e8i	0.252665	+	1.86525i	0.461288	+	0.887250i	$0.347387\pi$
$503$	3.21550e7	+	2.37378e8i	0.252665	+	1.86525i	−0.208624	+	0.977996i	$0.566898\pi$
$504$	2.97607e8	+	1.33656e7i	2.32462	+	0.104399i
$505$	−7.51243e7	−	7.85738e7i	−0.583319	−	0.610104i
$506$	5.23493e6	−	5.47531e6i	0.0404073	−	0.0422627i
$507$	1.56068e6	+	3.47513e7i	0.0119754	+	0.266654i
$508$	2.34854e7	+	1.29415e8i	0.179146	+	0.987176i
$509$	1.93218e7	−	1.42639e8i	0.146519	−	1.08165i	−0.757096	−	0.653303i	$-0.773383\pi$
$509$	1.93218e7	−	1.42639e8i	0.146519	−	1.08165i	0.903616	−	0.428344i	$-0.140903\pi$
$510$	5.71910e7	−	3.15148e8i	0.431139	−	2.37577i
$511$	−3.93182e7	−	1.27752e7i	−0.294666	−	0.0957429i
$512$	−1.30489e7	+	1.14005e7i	−0.0972219	+	0.0849402i
$513$	3.80676e7	+	7.07414e7i	0.281970	+	0.523988i
$514$	9.73309e7	−	1.33964e8i	0.716739	−	0.986507i
$515$	−2.27965e8	+	1.36203e8i	−1.66896	+	0.997158i
$516$	8.27087e7	+	7.22604e7i	0.602008	+	0.525958i
$517$	−3.66777e6	+	1.60695e7i	−0.0265418	+	0.116287i
$518$	1.93359e7	+	5.15203e7i	0.139115	+	0.370672i
$519$	3.94648e7	−	4.38490e8i	0.282298	−	3.13659i
$520$	−1.32476e8	−	1.05646e8i	−0.942166	−	0.751352i
$521$	−1.18462e7	+	2.77155e7i	−0.0837655	+	0.195979i	−0.956174	−	0.292797i	$-0.905414\pi$
$521$	−1.18462e7	+	2.77155e7i	−0.0837655	+	0.195979i	0.872409	+	0.488777i	$0.162557\pi$
$522$	−1.26330e8	+	9.17841e7i	−0.888167	+	0.645291i
$523$	1.05707e8	−	2.19504e8i	0.738925	−	1.53439i	−0.102929	−	0.994689i	$-0.532821\pi$
$523$	1.05707e8	−	2.19504e8i	0.738925	−	1.53439i	0.841854	−	0.539705i	$-0.181464\pi$
$524$	5.45844e7	+	2.04859e7i	0.379380	+	0.142384i
$525$	1.58948e8	+	1.04921e8i	1.09845	+	0.725077i
$526$	3.52267e7	−	3.17046e6i	0.242055	−	0.0217854i
$527$	−3.66305e8	+	1.76403e8i	−2.50271	+	1.20524i
$528$	1.60012e6	+	861060.i	0.0108705	+	0.00584967i
$529$	−1.07129e7	−	4.69364e7i	−0.0723671	−	0.317061i
$530$	7.61823e7	−	5.02875e7i	0.511713	−	0.337779i
$531$	−4.18743e8	+	3.33936e8i	−2.79681	+	2.23038i
$532$	−9.94230e6	−	3.60251e7i	−0.0660316	−	0.239260i
$533$	2.07947e8	−	5.73898e7i	1.37332	−	0.379012i
$534$	1.08608e8	+	1.36190e8i	0.713244	+	0.894380i
$535$	−6.85677e7	−	1.03876e8i	−0.447773	−	0.678347i
$536$	1.37203e6	−	313158.i	0.00890985	−	0.00203361i
$537$	4.44079e7	−	8.25237e7i	0.286773	−	0.532913i
$538$	−4.41605e7	−	9.17002e7i	−0.283588	−	0.588876i
$539$	562801.	+	6.25323e6i	0.00359409	+	0.0399336i
$540$	−1.08220e8	+	1.63947e8i	−0.687270	+	1.04117i
$541$	4.75586e7	−	1.26719e8i	0.300357	−	0.800297i	−0.696236	−	0.717813i	$-0.745143\pi$
$541$	4.75586e7	−	1.26719e8i	0.300357	−	0.800297i	0.996592	−	0.0824841i	$-0.0262854\pi$
$542$	6.95648e7	+	3.35006e7i	0.436910	+	0.210405i
$543$	1.47344e8	+	2.02801e8i	0.920306	+	1.26669i
$544$	−2.46157e8	−	1.05213e8i	−1.52903	−	0.653539i
$545$	−4.27437e7	+	5.35990e7i	−0.264048	+	0.331106i
$546$	−1.91733e8	−	1.72563e7i	−1.17793	−	0.106015i
$547$	−1.48949e8	+	5.59017e7i	−0.910075	+	0.341557i	−0.762119	−	0.647437i	$-0.775841\pi$
$547$	−1.48949e8	+	5.59017e7i	−0.910075	+	0.341557i	−0.147956	+	0.988994i	$0.547269\pi$
$548$	−1.03784e8	−	2.36880e7i	−0.630650	−	0.143942i
$549$	1.31888e8	−	1.50958e8i	0.797054	−	0.912302i
$550$	3.98439e6	+	6.66874e6i	0.0239482	+	0.0400826i
$551$	4.27666e7	+	3.10718e7i	0.255653	+	0.185742i
$552$	−2.13184e8	+	1.14719e8i	−1.26747	+	0.682055i
$553$	1.73399e8	+	1.98471e8i	1.02535	+	1.17360i
$554$	4.09719e7	−	1.26098e8i	0.240966	−	0.741618i
$555$	−1.96973e8	−	3.57453e7i	−1.15220	−	0.209093i
$556$	3.16004e6	+	428056.i	0.0183852	+	0.00249044i
$557$	1.82171e8	−	3.30592e7i	1.05418	−	0.191305i	0.376313	−	0.926493i	$-0.377192\pi$
$557$	1.82171e8	−	3.30592e7i	1.05418	−	0.191305i	0.677864	+	0.735188i	$0.262906\pi$
$558$	−3.55757e8	+	1.59771e7i	−2.04763	+	0.0919591i
$559$	−9.16245e7	−	8.76020e7i	−0.524537	−	0.501509i
$560$	−1.23250e7	+	1.17839e7i	−0.0701815	+	0.0671003i
$561$	−2.57241e6	+	5.72791e7i	−0.0145697	+	0.324420i
$562$	1.01390e8	−	1.37343e7i	0.571199	−	0.0773742i
$563$	−1.48427e8	+	4.82269e7i	−0.831741	+	0.270249i	−0.693779	−	0.720188i	$-0.744055\pi$
$563$	−1.48427e8	+	4.82269e7i	−0.831741	+	0.270249i	−0.137963	+	0.990437i	$0.544055\pi$
$564$	1.00118e8	−	1.67570e8i	0.558053	−	0.934023i
$565$	−1.09260e8	+	4.67001e7i	−0.605784	+	0.258924i
$566$	9.23142e6	−	3.34493e7i	0.0509119	−	0.184475i
$567$			1.85961e8i			1.02017i
$568$	−1.83898e8	−	3.22640e7i	−1.00353	−	0.176065i
$569$	−1.01199e6			−0.00549339			−0.00274669	−	0.999996i	$-0.500874\pi$
$569$	−1.01199e6			−0.00549339			−0.00274669	+	0.999996i	$0.500874\pi$
$570$	−9.15521e7	−	2.52668e7i	−0.494360	−	0.136435i
$571$	−2.86878e7	−	6.71185e7i	−0.154095	−	0.360524i	0.824638	−	0.565661i	$-0.191379\pi$
$571$	−2.86878e7	−	6.71185e7i	−0.154095	−	0.360524i	−0.978733	+	0.205137i	$0.934236\pi$
$572$	9.64909e6	+	5.76506e6i	0.0515582	+	0.0308046i
$573$	1.12858e8	+	3.47341e8i	0.599885	+	1.84626i
$574$	−2.94418e7	−	2.17348e8i	−0.155679	−	1.14927i
$575$	−1.02337e8	−	4.59594e6i	−0.538304	−	0.0241752i
$576$	−1.78759e8	−	1.86968e8i	−0.935408	−	0.978360i
$577$	9.03294e7	−	9.44772e7i	0.470221	−	0.491812i	−0.444568	−	0.895745i	$-0.646643\pi$
$577$	9.03294e7	−	9.44772e7i	0.470221	−	0.491812i	0.914789	+	0.403933i	$0.132357\pi$
$578$	1.05255e7	+	2.34370e8i	0.0545081	+	1.21372i
$579$	−1.45764e7	−	8.03227e7i	−0.0750957	−	0.413811i
$580$	−1.73520e7	+	1.28097e8i	−0.0889334	+	0.656533i
$581$	7.60426e7	−	4.19029e8i	0.387729	−	2.13656i
$582$	1.20932e7	+	3.92931e6i	0.0613438	+	0.0199318i
$583$	−1.23057e7	+	1.07512e7i	−0.0621015	+	0.0542565i
$584$	2.55369e7	+	4.74555e7i	0.128212	+	0.238258i
$585$	2.72455e8	−	3.75002e8i	1.36090	−	1.87312i
$586$	−1.32896e8	+	7.94018e7i	−0.660420	+	0.394582i
$587$	−1.15884e8	−	1.01245e8i	−0.572940	−	0.500562i	0.322006	−	0.946738i	$-0.395643\pi$
$587$	−1.15884e8	−	1.01245e8i	−0.572940	−	0.500562i	−0.894946	+	0.446175i	$0.852786\pi$
$588$	1.65454e7	−	7.24901e7i	0.0813852	−	0.356572i
$589$	4.23605e7	+	1.12869e8i	0.207307	+	0.552369i
$590$	2.77643e7	−	3.08487e8i	0.135186	−	1.50204i
$591$	4.73706e6	+	3.77768e6i	0.0229481	+	0.0183005i
$592$	2.79044e6	−	6.52855e6i	0.0134495	−	0.0314667i
$593$	−1.79693e8	+	1.30554e8i	−0.861720	+	0.626077i	−0.928352	−	0.371701i	$-0.878775\pi$
$593$	−1.79693e8	+	1.30554e8i	−0.861720	+	0.626077i	0.0666320	+	0.997778i	$0.478775\pi$
$594$	−1.06588e7	+	2.21333e7i	−0.0508569	+	0.105605i
$595$	−5.03749e8	−	1.89060e8i	−2.39146	−	0.897530i
$596$	−4.68718e7	−	3.09398e7i	−0.221398	−	0.146143i
$597$	−3.10739e8	+	2.79670e7i	−1.46040	+	0.131439i
$598$	9.32900e7	−	4.49261e7i	0.436246	−	0.210085i
$599$	2.36779e8	+	1.27416e8i	1.10170	+	0.592848i	0.920557	−	0.390609i	$-0.127736\pi$
$599$	2.36779e8	+	1.27416e8i	1.10170	+	0.592848i	0.181140	+	0.983457i	$0.442021\pi$
$600$	−5.52440e7	−	2.42040e8i	−0.255759	−	1.12056i
$601$	−2.85573e7	+	1.88505e7i	−0.131551	+	0.0868361i	−0.614959	−	0.788559i	$-0.710827\pi$
$601$	−2.85573e7	+	1.88505e7i	−0.131551	+	0.0868361i	0.483408	+	0.875395i	$0.339399\pi$
$602$	−1.00768e8	+	8.03595e7i	−0.461883	+	0.368339i
$603$	1.02420e6	+	3.71111e6i	0.00467126	+	0.0169259i
$604$	2.38600e8	−	6.58495e7i	1.08283	−	0.298842i
$605$	1.75484e8	+	2.20050e8i	0.792450	+	0.993701i
$606$	8.86912e7	+	1.34361e8i	0.398531	+	0.603749i
$607$	2.23869e8	−	5.10965e7i	1.00098	−	0.228468i	0.309531	−	0.950889i	$-0.399828\pi$
$607$	2.23869e8	−	5.10965e7i	1.00098	−	0.228468i	0.691453	+	0.722421i	$0.256971\pi$
$608$	−3.76151e7	+	6.99006e7i	−0.167360	+	0.311007i
$609$	1.71958e8	+	3.57074e8i	0.761324	+	1.58091i
$610$	1.03914e7	+	1.15458e8i	0.0457808	+	0.508666i
$611$	−1.24117e8	+	1.88030e8i	−0.544138	+	0.824334i
$612$	1.57919e8	−	4.20772e8i	0.688936	−	1.83566i
$613$	3.88930e8	+	1.87299e8i	1.68846	+	0.813118i	0.995770	+	0.0918803i	$0.0292877\pi$
$613$	3.88930e8	+	1.87299e8i	1.68846	+	0.813118i	0.692687	+	0.721238i	$0.256427\pi$
$614$	−2.01165e7	−	2.76879e7i	−0.0869053	−	0.119615i
$615$	7.33699e8	+	3.13598e8i	3.15422	+	1.34818i
$616$	1.92286e7	−	2.41119e7i	0.0822632	−	0.103155i
$617$	1.59041e8	+	1.43139e7i	0.677100	+	0.0609401i	0.422852	−	0.906199i	$-0.361029\pi$
$617$	1.59041e8	+	1.43139e7i	0.677100	+	0.0609401i	0.254248	+	0.967139i	$0.418172\pi$
$618$	3.68201e8	−	1.38188e8i	1.55998	−	0.585472i
$619$	2.79092e8	+	6.37010e7i	1.17673	+	0.268580i	0.765795	−	0.643085i	$-0.222346\pi$
$619$	2.79092e8	+	6.37010e7i	1.17673	+	0.268580i	0.410933	+	0.911666i	$0.365203\pi$
$620$	−1.93962e8	+	2.22007e8i	−0.813845	+	0.931521i
$621$	−1.66152e8	−	2.78092e8i	−0.693795	−	1.16122i
$622$	1.16161e6	+	843959.i	0.00482713	+	0.00350712i
$623$	2.57684e8	−	1.38666e8i	1.06567	−	0.573463i
$624$	1.63415e7	+	1.87044e7i	0.0672571	+	0.0769820i
$625$	−9.24693e7	+	2.84591e8i	−0.378754	+	1.16569i
$626$	−2.25750e8	−	4.09676e7i	−0.920249	−	0.167001i
$627$	1.68478e7	+	2.28218e6i	0.0683501	+	0.00925865i
$628$	−6.97623e7	+	1.26600e7i	−0.281671	+	0.0511157i
$629$	2.23806e8	−	1.00512e7i	0.899333	−	0.0403891i
$630$	−3.40646e8	−	3.25691e8i	−1.36233	−	1.30252i
$631$	−2.61036e8	+	2.49576e8i	−1.03899	+	0.993380i	−0.999983	−	0.00585901i	$-0.998135\pi$
$631$	−2.61036e8	+	2.49576e8i	−1.03899	+	0.993380i	−0.0390110	+	0.999239i	$0.512421\pi$
$632$	1.54131e7	−	3.43198e8i	0.0610573	−	1.35955i
$633$	−2.41424e8	+	3.27031e7i	−0.951851	+	0.128937i
$634$	−5.58162e7	+	1.81358e7i	−0.219024	+	0.0711654i
$635$	2.88002e8	−	4.82034e8i	1.12480	−	1.88259i
$636$	1.77945e8	−	7.60575e7i	0.691696	−	0.295645i
$637$	−2.28312e7	+	8.27272e7i	−0.0883306	+	0.320059i
$638$			1.61654e7i			0.0622478i
$639$	6.56022e7	−	5.06522e8i	0.251429	−	1.94132i
$640$	−1.80118e8			−0.687097
$641$	7.97007e7	+	2.19960e7i	0.302613	+	0.0835160i	0.414046	−	0.910256i	$-0.364115\pi$
$641$	7.97007e7	+	2.19960e7i	0.302613	+	0.0835160i	−0.111432	+	0.993772i	$0.535544\pi$
$642$	7.24463e7	+	1.69497e8i	0.273786	+	0.640554i
$643$	2.95704e7	+	1.76675e7i	0.111230	+	0.0664571i	0.567437	−	0.823417i	$-0.307935\pi$
$643$	2.95704e7	+	1.76675e7i	0.111230	+	0.0664571i	−0.456207	+	0.889874i	$0.650792\pi$
$644$	4.65698e7	+	1.43327e8i	0.174360	+	0.536625i
$645$	−6.29385e7	−	4.64631e8i	−0.234551	−	1.73152i
$646$	1.06179e8	+	4.76850e6i	0.393859	+	0.0176882i
$647$	1.21814e8	+	1.27407e8i	0.449762	+	0.470415i	0.908336	−	0.418242i	$-0.137354\pi$
$647$	1.21814e8	+	1.27407e8i	0.449762	+	0.470415i	−0.458573	+	0.888657i	$0.651639\pi$
$648$	1.67518e8	−	1.75211e8i	0.615655	−	0.643925i
$649$	2.48758e6	+	5.53903e7i	0.00910003	+	0.202628i
$650$	1.89600e7	+	1.04478e8i	0.0690395	+	0.380439i
$651$	−1.21325e8	+	8.95658e8i	−0.439752	+	3.24638i
$652$	−4.83658e7	+	2.66517e8i	−0.174500	+	0.961574i
$653$	1.58841e8	+	5.16105e7i	0.570457	+	0.185353i	0.580021	−	0.814602i	$-0.303044\pi$
$653$	1.58841e8	+	5.16105e7i	0.570457	+	0.185353i	−0.00956397	+	0.999954i	$0.503044\pi$
$654$	7.64586e7	−	6.67999e7i	0.273334	−	0.238805i
$655$	−1.17946e8	−	2.19180e8i	−0.419720	−	0.779970i
$656$	−1.66334e7	+	2.28939e7i	−0.0589210	+	0.0810978i
$657$	−1.26554e8	+	7.56125e7i	−0.446252	+	0.266623i
$658$	1.72508e8	+	1.50716e8i	0.605525	+	0.529032i
$659$	8.05480e7	−	3.52904e8i	0.281448	−	1.23311i	−0.614489	−	0.788925i	$-0.710638\pi$
$659$	8.05480e7	−	3.52904e8i	0.281448	−	1.23311i	0.895937	−	0.444181i	$-0.146505\pi$
$660$	1.46084e7	+	3.89239e7i	0.0508125	+	0.135389i
$661$	−4.32979e7	+	4.81079e8i	−0.149921	+	1.66576i	0.471187	+	0.882033i	$0.343826\pi$
$661$	−4.32979e7	+	4.81079e8i	−0.149921	+	1.66576i	−0.621108	+	0.783725i	$0.713317\pi$
$662$	−2.03498e8	−	1.62284e8i	−0.701432	−	0.559374i
$663$	−3.08024e8	+	7.20659e8i	−1.05693	+	2.47280i
$664$	−4.49118e8	+	3.26303e8i	−1.53411	+	1.11460i
$665$	−6.92245e7	+	1.43746e8i	−0.235394	+	0.488800i
$666$	1.83718e8	+	6.89507e7i	0.621914	+	0.233408i
$667$	−1.77905e8	−	1.17434e8i	−0.599531	−	0.395747i
$668$	6.07749e7	−	5.46984e6i	0.203889	−	0.0183504i
$669$	−4.28327e8	+	2.06271e8i	−1.43053	+	0.688906i
$670$	−1.96054e6	−	1.05501e6i	−0.00651854	−	0.00350778i
$671$	−4.61772e6	−	2.02315e7i	−0.0152848	−	0.0669671i
$672$	−4.96672e8	+	3.27850e8i	−1.63667	+	1.08036i
$673$	1.60879e8	−	1.28297e8i	0.527781	−	0.420891i	−0.323010	−	0.946396i	$-0.604695\pi$
$673$	1.60879e8	−	1.28297e8i	0.527781	−	0.420891i	0.850791	+	0.525504i	$0.176123\pi$
$674$	−4.62251e7	−	1.67493e8i	−0.150973	−	0.547037i
$675$	3.20236e8	−	8.83796e7i	1.04126	−	0.287369i
$676$	−1.75997e7	−	2.20693e7i	−0.0569724	−	0.0714411i
$677$	−7.73458e7	−	1.17174e8i	−0.249271	−	0.377629i	0.688299	−	0.725427i	$-0.258358\pi$
$677$	−7.73458e7	−	1.17174e8i	−0.249271	−	0.377629i	−0.937569	+	0.347799i	$0.886929\pi$
$678$	1.71561e8	−	3.91576e7i	0.550463	−	0.125640i
$679$	1.01221e7	−	1.88100e7i	0.0323341	−	0.0600868i
$680$	3.04317e8	+	6.31920e8i	0.967829	+	2.00972i
$681$	−2.90384e7	−	3.22643e8i	−0.0919457	−	1.02160i
$682$	−2.03095e7	+	3.07676e7i	−0.0640244	+	0.0969929i
$683$	1.15161e8	−	3.06845e8i	0.361445	−	0.963067i	−0.622185	−	0.782870i	$-0.713755\pi$
$683$	1.15161e8	−	3.06845e8i	0.361445	−	0.963067i	0.983631	−	0.180197i	$-0.0576736\pi$
$684$	−1.20069e8	−	5.78220e7i	−0.375198	−	0.180686i
$685$	2.67127e8	+	3.67668e8i	0.831085	+	1.14389i
$686$	−1.41875e8	−	6.06405e7i	−0.439476	−	0.187841i
$687$	1.56536e8	−	1.96289e8i	0.482773	−	0.605378i
$688$	1.65621e7	+	1.49061e6i	0.0508568	+	0.00457719i
$689$	−2.09116e8	+	7.84827e7i	−0.639338	+	0.239948i
$690$	3.73386e8	+	8.52228e7i	1.13661	+	0.259423i
$691$	−3.35949e8	+	3.84524e8i	−1.01821	+	1.16544i	−0.0320805	+	0.999485i	$0.510213\pi$
$691$	−3.35949e8	+	3.84524e8i	−1.01821	+	1.16544i	−0.986133	+	0.165954i	$0.946930\pi$
$692$	1.83236e8	+	3.06685e8i	0.552957	+	0.925494i
$693$	6.82539e7	+	4.95894e7i	0.205082	+	0.149001i
$694$	2.60010e8	−	1.39917e8i	0.777878	−	0.418594i
$695$	−8.95710e6	−	1.02522e7i	−0.0266817	−	0.0305396i
$696$	1.59644e8	−	4.91334e8i	0.473506	−	1.45730i
$697$	−8.78587e8	−	1.59440e8i	−2.59470	−	0.470868i
$698$	5.12924e7	+	6.94803e6i	0.150830	+	0.0204313i
$699$	1.09074e9	−	1.97940e8i	3.19366	−	0.579564i
$700$	−1.54390e8	+	6.93368e6i	−0.450118	+	0.0202148i
$701$	1.37292e8	+	1.31264e8i	0.398557	+	0.381060i	0.863557	−	0.504251i	$-0.168231\pi$
$701$	1.37292e8	+	1.31264e8i	0.398557	+	0.381060i	−0.465000	+	0.885311i	$0.653946\pi$
$702$	−2.42707e8	+	2.32051e8i	−0.701569	+	0.670769i
$703$	2.98039e6	−	6.63635e7i	0.00857841	−	0.191013i
$704$	−2.65363e7	+	3.59458e6i	−0.0760540	+	0.0103022i
$705$	−7.92553e8	+	2.57516e8i	−2.26184	+	0.734915i
$706$	7.59038e7	−	1.27042e8i	0.215700	−	0.361020i
$707$	2.48687e8	−	1.06294e8i	0.703712	−	0.300781i
$708$	1.74688e8	−	6.32967e8i	0.492224	−	1.78353i
$709$			6.30649e8i			1.76949i	0.466072	+	0.884747i	$0.345669\pi$
$709$			6.30649e8i			1.76949i	−0.466072	+	0.884747i	$0.654331\pi$
$710$	1.85506e8	+	2.29849e8i	0.518301	+	0.642197i
$711$	9.39798e8			2.61472
$712$	−3.67701e8	−	1.01479e8i	−1.01872	−	0.281149i
$713$	−1.91068e8	−	4.47025e8i	−0.527131	−	1.23328i
$714$	6.84055e8	+	4.08704e8i	1.87930	+	1.12283i
$715$	−1.48284e7	−	4.56372e7i	−0.0405674	−	0.124854i
$716$	1.02077e7	+	7.53564e7i	0.0278093	+	0.205296i
$717$	5.62106e8	+	2.52442e7i	1.52497	+	0.0684864i
$718$	−3.05209e8	−	3.19224e8i	−0.824564	−	0.862426i
$719$	−2.84995e8	+	2.98082e8i	−0.766745	+	0.801953i	−0.984746	−	0.173996i	$-0.944332\pi$
$719$	−2.84995e8	+	2.98082e8i	−0.766745	+	0.801953i	0.218001	+	0.975949i	$0.430046\pi$
$720$	2.72805e6	+	6.07447e7i	0.00730894	+	0.162746i
$721$	−1.17966e8	−	6.50044e8i	−0.314739	−	1.73435i
$722$	−2.81688e7	+	2.07951e8i	−0.0748441	+	0.552521i
$723$	2.91309e7	−	1.60525e8i	0.0770796	−	0.424743i
$724$	−1.93458e8	−	6.28582e7i	−0.509765	−	0.165633i
$725$	1.64625e8	−	1.43829e8i	0.431999	−	0.377426i
$726$	−1.97521e8	−	3.67056e8i	−0.516183	−	0.959229i
$727$	2.75083e8	−	3.78619e8i	0.715913	−	0.985369i	−0.283737	−	0.958902i	$-0.591574\pi$
$727$	2.75083e8	−	3.78619e8i	0.715913	−	0.985369i	0.999650	−	0.0264670i	$-0.00842570\pi$
$728$	3.61880e8	−	2.16213e8i	0.937929	−	0.560387i
$729$	−3.26846e8	−	2.85557e8i	−0.843646	−	0.737071i
$730$	1.89709e7	−	8.31168e7i	0.0487661	−	0.213658i
$731$	1.84372e8	+	4.91257e8i	0.472001	+	1.25764i
$732$	−2.20295e7	+	2.44768e8i	−0.0561658	+	0.624053i
$733$	2.33666e8	+	1.86343e8i	0.593313	+	0.473152i	0.873520	−	0.486788i	$-0.161832\pi$
$733$	2.33666e8	+	1.86343e8i	0.593313	+	0.473152i	−0.280207	+	0.959940i	$0.590403\pi$
$734$	7.27568e7	−	1.70223e8i	0.183986	−	0.430457i
$735$	−2.56806e8	+	1.86581e8i	−0.646760	+	0.469899i
$736$	1.38885e8	−	2.88398e8i	0.348355	−	0.723366i
$737$	373135.	+	140040.i	0.000932101	+	0.000349824i
$738$	−6.52745e8	−	4.30873e8i	−1.62396	−	1.07196i
$739$	−1.28703e8	+	1.15835e7i	−0.318900	+	0.0287016i	−0.247933	−	0.968777i	$-0.579751\pi$
$739$	−1.28703e8	+	1.15835e7i	−0.318900	+	0.0287016i	−0.0709671	+	0.997479i	$0.522609\pi$
$740$	1.46358e8	−	7.04825e7i	0.361179	−	0.173935i
$741$	2.04644e8	+	1.10123e8i	0.502972	+	0.270661i
$742$	5.05342e7	+	2.21405e8i	0.123701	+	0.541971i
$743$	−1.32516e8	+	8.74730e7i	−0.323074	+	0.213259i	−0.702016	−	0.712161i	$-0.747716\pi$
$743$	−1.32516e8	+	8.74730e7i	−0.323074	+	0.213259i	0.378942	+	0.925420i	$0.376288\pi$
$744$	9.21142e8	−	7.34586e8i	2.23670	−	1.78371i
$745$	6.37867e7	+	2.31126e8i	0.154263	+	0.558959i
$746$	1.27643e7	−	3.52272e6i	0.0307454	−	0.00848518i
$747$	−9.46856e8	−	1.18732e9i	−2.27155	−	2.84843i
$748$	−2.56313e7	−	3.88297e7i	−0.0612442	−	0.0927811i
$749$	3.01889e8	−	6.89041e7i	0.718458	−	0.163983i
$750$	9.76105e7	−	1.81391e8i	0.231373	−	0.429963i
$751$	1.45035e8	+	3.01168e8i	0.342415	+	0.711033i	0.999068	−	0.0431602i	$-0.0137426\pi$
$751$	1.45035e8	+	3.01168e8i	0.342415	+	0.711033i	−0.656653	+	0.754193i	$0.728028\pi$
$752$	−2.64930e6	−	2.94361e7i	−0.00622984	−	0.0692192i
$753$	9.33038e7	−	1.41349e8i	0.218532	−	0.331061i
$754$	−7.76404e7	+	2.06872e8i	−0.181123	+	0.482601i
$755$	−9.52054e8	−	4.58485e8i	−2.21218	−	1.06533i
$756$	−2.87265e8	−	3.95386e8i	−0.664840	−	0.915074i
$757$	1.29190e8	+	5.52183e7i	0.297811	+	0.127290i	0.536743	−	0.843746i	$-0.319655\pi$
$757$	1.29190e8	+	5.52183e7i	0.297811	+	0.127290i	−0.238932	+	0.971036i	$0.576797\pi$
$758$	−1.82921e7	+	2.29376e7i	−0.0420006	+	0.0526671i
$759$	−6.82835e7	−	6.14562e6i	−0.156167	−	0.0140553i
$760$	1.94713e8	−	7.30768e7i	0.443561	−	0.166471i
$761$	3.77189e8	+	8.60910e7i	0.855866	+	0.195346i	0.627872	−	0.778317i	$-0.283926\pi$
$761$	3.77189e8	+	8.60910e7i	0.855866	+	0.195346i	0.227994	+	0.973663i	$0.426783\pi$
$762$	−5.47136e8	+	6.26248e8i	−1.23660	+	1.41541i
$763$	−8.74784e7	−	1.46414e8i	−0.196937	−	0.329617i
$764$	−2.39758e8	−	1.74194e8i	−0.537642	−	0.390620i
$765$	−1.68959e9	+	9.09205e8i	−3.77395	+	2.03085i
$766$	1.10558e7	+	1.26544e7i	0.0245983	+	0.0281551i
$767$	−2.34199e8	+	7.20790e8i	−0.519038	+	1.59743i
$768$	7.92478e8	+	1.43814e8i	1.74946	+	0.317480i
$769$	−8.24652e8	−	1.11707e8i	−1.81339	−	0.245641i	−0.852532	−	0.522675i	$-0.824934\pi$
$769$	−8.24652e8	−	1.11707e8i	−1.81339	−	0.245641i	−0.960860	+	0.277035i	$0.910648\pi$
$770$	−4.80053e7	+	8.71167e6i	−0.105152	+	0.0190822i
$771$	−1.49716e9	+	6.72375e7i	−3.26667	+	0.146706i
$772$	4.78801e7	+	4.57781e7i	0.104065	+	0.0994961i
$773$	7.27458e6	−	6.95521e6i	0.0157496	−	0.0150582i	−0.683147	−	0.730281i	$-0.739389\pi$
$773$	7.27458e6	−	6.95521e6i	0.0157496	−	0.0150582i	0.698896	+	0.715223i	$0.253675\pi$
$774$	−2.06200e7	+	4.59140e8i	−0.0444698	+	0.990198i
$775$	4.94032e8	−	6.69211e7i	1.06133	−	0.143767i
$776$	−2.64814e7	+	8.60433e6i	−0.0566704	+	0.0184133i
$777$	2.55446e8	−	4.27545e8i	0.544548	−	0.911420i
$778$	−8.50952e7	+	3.63715e7i	−0.180703	+	0.0772364i
$779$	−7.04400e7	+	2.55234e8i	−0.149007	+	0.539915i
$780$			5.68281e8i			1.19751i
$781$	−3.84304e7	−	3.63159e7i	−0.0806717	−	0.0762330i
$782$	−4.28601e8			−0.896257
$783$	6.66387e8	+	1.83911e8i	1.38817	+	0.383109i
$784$	−4.42464e6	−	1.03520e7i	−0.00918184	−	0.0214820i
$785$	2.59844e8	+	1.55249e8i	0.537159	+	0.320938i
$786$	1.13908e8	+	3.50573e8i	0.234578	+	0.721956i
$787$	7.36550e7	+	5.43743e8i	0.151105	+	1.11550i	0.894635	+	0.446797i	$0.147435\pi$
$787$	7.36550e7	+	5.43743e8i	0.151105	+	1.11550i	−0.743531	+	0.668702i	$0.766850\pi$
$788$	−4.91161e6	−	220581.i	−0.0100380	−	0.000450805i
$789$	−2.21215e8	−	2.31373e8i	−0.450385	−	0.471065i
$790$	−3.75584e8	+	3.92830e8i	−0.761773	+	0.796752i
$791$	−1.32626e7	−	2.95315e8i	−0.0267979	−	0.596701i
$792$	−1.96367e7	−	1.08207e8i	−0.0395270	−	0.217812i
$793$	3.80757e7	−	2.81086e8i	0.0763534	−	0.563664i
$794$	5.16919e6	−	2.84846e7i	0.0103267	−	0.0569047i
$795$	−7.85723e8	−	2.55297e8i	−1.56375	−	0.508094i
$796$	1.90656e8	−	1.66571e8i	0.378016	−	0.330263i
$797$	−2.13269e8	−	3.96320e8i	−0.421263	−	0.782837i	0.578191	−	0.815902i	$-0.303759\pi$
$797$	−2.13269e8	−	3.96320e8i	−0.421263	−	0.782837i	−0.999453	+	0.0330647i	$0.989473\pi$
$798$	1.38884e8	−	1.91157e8i	0.273302	−	0.376168i
$799$	8.00579e8	−	4.78324e8i	1.56951	−	0.937738i
$800$	2.47203e8	+	2.15975e8i	0.482819	+	0.421826i
$801$	2.32197e8	−	1.01732e9i	0.451813	−	1.97952i
$802$	7.03537e7	+	1.87457e8i	0.136384	+	0.363394i
$803$	−1.36803e6	+	1.52001e7i	−0.00264211	+	0.0293562i
$804$	−3.69015e6	−	2.94280e6i	−0.00710029	−	0.00566229i
$805$	2.52862e8	−	5.91600e8i	0.484726	−	1.13407i
$806$	−4.07678e8	+	2.96196e8i	−0.778597	+	0.565683i
$807$	−3.99676e8	+	8.29935e8i	−0.760479	+	1.57915i
$808$	−3.30062e8	−	1.23874e8i	−0.625694	−	0.234827i
$809$	6.42145e7	+	4.23876e7i	0.121280	+	0.0800559i	0.610081	−	0.792339i	$-0.291137\pi$
$809$	6.42145e7	+	4.23876e7i	0.121280	+	0.0800559i	−0.488801	+	0.872395i	$0.662566\pi$
$810$	−3.81944e8	+	3.43756e7i	−0.718695	+	0.0646837i
$811$	5.46781e8	−	2.63316e8i	1.02506	−	0.493645i	0.155693	−	0.987805i	$-0.450239\pi$
$811$	5.46781e8	−	2.63316e8i	1.02506	−	0.493645i	0.869371	+	0.494161i	$0.164525\pi$
$812$	−2.83198e8	−	1.52396e8i	−0.528960	−	0.284645i
$813$	−1.55498e8	−	6.81280e8i	−0.289369	−	1.26781i
$814$	1.69539e7	−	1.11912e7i	0.0314338	−	0.0207492i
$815$	9.04099e8	−	7.20995e8i	1.67010	−	1.33186i
$816$	−2.73512e7	−	9.91049e7i	−0.0503392	−	0.182400i
$817$	1.49983e8	−	4.13926e7i	0.275027	−	0.0759026i
$818$	−2.70745e8	−	3.39504e8i	−0.494653	−	0.620275i
$819$	6.35290e8	+	9.62423e8i	1.15643	+	1.75192i
$820$	−6.31236e8	+	1.44075e8i	−1.14485	+	0.261305i
$821$	5.18088e8	−	9.62769e8i	0.936212	−	1.73977i	0.331192	−	0.943563i	$-0.392549\pi$
$821$	5.18088e8	−	9.62769e8i	0.936212	−	1.73977i	0.605020	−	0.796210i	$-0.293165\pi$
$822$	−2.92024e8	−	6.06395e8i	−0.525779	−	1.09179i
$823$	5.18766e7	+	5.76396e8i	0.0930619	+	1.03400i	0.897809	+	0.440385i	$0.145158\pi$
$823$	5.18766e7	+	5.76396e8i	0.0930619	+	1.03400i	−0.804747	+	0.593617i	$0.797699\pi$
$824$	−4.74430e8	+	7.18731e8i	−0.847990	+	1.28465i
$825$	2.47044e7	−	6.58246e7i	0.0439959	−	0.117227i
$826$	6.94263e8	+	3.34339e8i	1.23192	+	0.593263i
$827$	2.15260e8	+	2.96280e8i	0.380581	+	0.523824i	0.955738	−	0.294218i	$-0.0950592\pi$
$827$	2.15260e8	+	2.96280e8i	0.380581	+	0.523824i	−0.575158	+	0.818043i	$0.695059\pi$
$828$	4.94153e8	+	2.11211e8i	0.870503	+	0.372071i
$829$	3.14043e8	−	3.93797e8i	0.551221	−	0.691209i	−0.425687	−	0.904870i	$-0.639968\pi$
$829$	3.14043e8	−	3.93797e8i	0.551221	−	0.691209i	0.976908	+	0.213662i	$0.0685390\pi$
$830$	8.74696e8	+	7.87241e7i	1.52976	+	0.137681i
$831$	−1.12347e9	+	4.21646e8i	−1.95776	+	0.734759i
$832$	−3.56855e8	−	8.14499e7i	−0.619616	−	0.141423i
$833$	2.33723e8	−	2.67517e8i	0.404358	−	0.462825i
$834$	1.03410e7	+	1.73079e7i	0.0178264	+	0.0298363i
$835$	−2.10754e8	−	1.53121e8i	−0.362006	−	0.263013i
$836$	−1.21488e7	+	6.53754e6i	−0.0207929	+	0.0111891i
$837$	1.03728e9	+	1.18726e9i	1.76896	+	2.02474i
$838$	−1.71276e8	+	5.27133e8i	−0.291048	+	0.895752i
$839$	−8.39955e8	−	1.52429e8i	−1.42223	−	0.258097i	−0.587709	−	0.809072i	$-0.699970\pi$
$839$	−8.39955e8	−	1.52429e8i	−1.42223	−	0.258097i	−0.834521	+	0.550975i	$0.814256\pi$
$840$	1.54512e9	+	2.09300e8i	2.60689	+	0.353128i
$841$	−1.37674e8	+	2.49842e7i	−0.231454	+	0.0420026i
$842$	8.96245e7	−	4.02504e6i	0.150138	−	0.00674270i
$843$	−6.69320e8	−	6.39935e8i	−1.11725	−	1.06820i
$844$	1.42893e8	−	1.36619e8i	0.237674	−	0.227240i
$845$	−5.40658e6	+	1.20387e8i	−0.00896092	+	0.199530i
$846$	8.09468e8	−	1.09650e8i	1.33687	−	0.181091i
$847$	−6.65948e8	+	2.16380e8i	−1.09595	+	0.356095i
$848$	1.50281e7	−	2.51529e7i	0.0246444	−	0.0412477i
$849$	−2.88779e8	+	1.23430e8i	−0.471892	+	0.201696i
$850$	1.16931e8	−	4.23691e8i	0.190403	−	0.689910i
$851$			2.67882e8i			0.434665i
$852$	2.99942e8	+	5.49667e8i	0.484974	+	0.888752i
$853$	3.76602e8			0.606785			0.303393	−	0.952866i	$-0.401881\pi$
$853$	3.76602e8			0.606785			0.303393	+	0.952866i	$0.401881\pi$
$854$	−2.78010e8	−	7.67258e7i	−0.446361	−	0.123188i
$855$	2.23605e8	+	5.23149e8i	0.357752	+	0.837004i
$856$	−3.46507e8	−	2.07028e8i	−0.552447	−	0.330071i
$857$	−7.80436e7	−	2.40194e8i	−0.123992	−	0.381609i	0.869724	−	0.493539i	$-0.164297\pi$
$857$	−7.80436e7	−	2.40194e8i	−0.123992	−	0.381609i	−0.993716	+	0.111929i	$0.964297\pi$
$858$	9.53938e6	+	7.04226e7i	0.0151028	+	0.111494i
$859$	3.92121e7	+	1.76102e6i	0.0618644	+	0.00277833i	0.0757755	−	0.997125i	$-0.475857\pi$
$859$	3.92121e7	+	1.76102e6i	0.0618644	+	0.00277833i	−0.0139111	+	0.999903i	$0.504428\pi$
$860$	2.62930e8	+	2.75003e8i	0.413375	+	0.432357i
$861$	−1.37182e9	+	1.43481e9i	−2.14925	+	2.24794i
$862$	−3.05282e7	−	6.79764e8i	−0.0476628	−	1.06130i
$863$	5.22935e7	+	2.88161e8i	0.0813608	+	0.448335i	0.998734	+	0.0503063i	$0.0160198\pi$
$863$	5.22935e7	+	2.88161e8i	0.0813608	+	0.448335i	−0.917373	+	0.398028i	$0.869695\pi$
$864$	−1.39343e8	+	1.02867e9i	−0.216044	+	1.59490i
$865$	2.72330e8	−	1.50066e9i	0.420772	−	2.31865i
$866$	1.61383e8	+	5.24365e7i	0.248487	+	0.0807384i
$867$	1.59900e9	−	1.39700e9i	2.45353	−	2.14358i
$868$	−3.47548e8	−	6.45853e8i	−0.531442	−	0.987584i
$869$	5.71861e7	−	7.87099e7i	0.0871427	−	0.119942i
$870$	−7.01603e8	+	4.19188e8i	−1.06545	+	0.636578i
$871$	4.10250e6	+	3.58425e6i	0.00620860	+	0.00542429i
$872$	−4.94723e7	+	2.16752e8i	−0.0746127	+	0.326900i
$873$	−2.67644e7	−	7.13134e7i	−0.0402267	−	0.107184i
$874$	−1.13922e7	+	1.26578e8i	−0.0170637	+	0.189594i
$875$	−2.70539e8	−	2.15748e8i	−0.403837	−	0.322049i
$876$	7.10344e7	−	1.66193e8i	0.105671	−	0.247230i
$877$	2.68413e8	−	1.95013e8i	0.397928	−	0.289112i	−0.370768	−	0.928725i	$-0.620906\pi$
$877$	2.68413e8	−	1.95013e8i	0.397928	−	0.289112i	0.768697	+	0.639614i	$0.220906\pi$
$878$	7.83159e7	−	1.62625e8i	0.115709	−	0.240272i
$879$	1.31177e9	+	4.92315e8i	1.93148	+	0.724897i
$880$	5.25348e6	+	3.46779e6i	0.00770902	+	0.00508868i
$881$	−5.94909e8	+	5.35428e7i	−0.870008	+	0.0783021i	−0.515641	−	0.856805i	$-0.672446\pi$
$881$	−5.94909e8	+	5.35428e7i	−0.870008	+	0.0783021i	−0.354366	+	0.935107i	$0.615303\pi$
$882$	2.80339e8	−	1.35004e8i	0.408581	−	0.196762i
$883$	6.26561e8	+	3.37167e8i	0.910084	+	0.489737i	0.860740	−	0.509045i	$-0.170001\pi$
$883$	6.26561e8	+	3.37167e8i	0.910084	+	0.489737i	0.0493436	+	0.998782i	$0.484287\pi$
$884$	−1.41515e8	−	6.20017e8i	−0.204854	−	0.897525i
$885$	−2.33952e9	+	1.54430e9i	−3.37518	+	2.22794i
$886$	5.11972e8	−	4.08284e8i	0.736114	−	0.587031i
$887$	−9.30778e7	−	3.37260e8i	−0.133375	−	0.483274i	0.866498	−	0.499180i	$-0.166365\pi$
$887$	−9.30778e7	−	3.37260e8i	−0.133375	−	0.483274i	−0.999873	+	0.0159058i	$0.994937\pi$
$888$	−6.25821e8	+	1.72716e8i	−0.893741	+	0.246657i
$889$	8.70999e8	+	1.09220e9i	1.23969	+	1.55452i
$890$	3.32438e8	+	5.03622e8i	0.471564	+	0.714389i
$891$	6.69278e7	−	1.52758e7i	0.0946179	−	0.0215959i
$892$	1.82806e8	−	3.39710e8i	0.257570	−	0.478645i
$893$	−1.19983e8	−	2.49148e8i	−0.168487	−	0.349866i
$894$	−3.18298e7	−	3.53658e8i	−0.0445473	−	0.494961i
$895$	1.78846e8	−	2.70941e8i	0.249466	−	0.377925i
$896$	1.57454e8	−	4.19535e8i	0.218892	−	0.583236i
$897$	−8.44323e8	−	4.06605e8i	−1.16985	−	0.563372i
$898$	−2.35407e8	−	3.24010e8i	−0.325080	−	0.447434i
$899$	9.53947e8	+	4.07736e8i	1.31294	+	0.561178i
$900$	−3.43607e8	+	4.30869e8i	−0.471340	+	0.591042i
$901$	9.20829e8	+	8.28762e7i	1.25894	+	0.113307i
$902$	−7.58055e7	+	2.84503e7i	−0.103295	+	0.0387674i
$903$	1.13725e9	+	2.59569e8i	1.54451	+	0.352525i
$904$	−2.53531e8	+	2.90190e8i	−0.343184	+	0.392805i
$905$	4.45403e8	+	7.45478e8i	0.600907	+	1.00575i
$906$	1.26607e9	+	9.19851e8i	1.70244	+	1.23690i
$907$	8.03445e8	−	4.32352e8i	1.07680	−	0.579450i	0.163417	−	0.986557i	$-0.447748\pi$
$907$	8.03445e8	−	4.32352e8i	1.07680	−	0.579450i	0.913380	+	0.407107i	$0.133463\pi$
$908$	1.72952e8	+	1.97960e8i	0.231030	+	0.264435i
$909$	2.98020e8	−	9.17211e8i	0.396784	−	1.22117i
$910$	−6.56176e8	−	1.19078e8i	−0.870755	−	0.158019i
$911$	−8.93437e8	−	1.21024e8i	−1.18170	−	0.160073i	−0.483090	−	0.875571i	$-0.660486\pi$
$911$	−8.93437e8	−	1.21024e8i	−1.18170	−	0.160073i	−0.698615	+	0.715498i	$0.746200\pi$
$912$	−2.99955e7	+	5.44337e6i	−0.0395431	+	0.00717602i
$913$	−1.57056e8	+	7.05339e6i	−0.206368	+	0.00926798i
$914$	−2.08445e8	−	1.99294e8i	−0.272994	−	0.261009i
$915$	7.58338e8	−	7.25046e8i	0.989919	−	0.946459i
$916$	−9.14020e6	+	2.03522e8i	−0.0118924	+	0.264805i
$917$	6.13624e8	−	8.31210e7i	0.795782	−	0.107796i
$918$	1.32191e9	−	4.29514e8i	1.70873	−	0.555199i
$919$	−2.84761e8	+	4.76610e8i	−0.366889	+	0.614068i	−0.985108	−	0.171937i	$-0.944997\pi$
$919$	−2.84761e8	+	4.76610e8i	−0.366889	+	0.614068i	0.618219	+	0.786006i	$0.287854\pi$
$920$	−7.71172e8	+	3.29615e8i	−0.990347	+	0.423295i
$921$	−8.24040e7	+	2.98584e8i	−0.105480	+	0.382198i
$922$		−	1.35308e7i		−	0.0172635i
$923$	−3.17382e8	−	6.49319e8i	−0.403624	−	0.825759i
$924$	−1.03433e8			−0.131112
$925$	−2.64813e8	−	7.30839e7i	−0.334591	−	0.0923414i
$926$	4.90049e7	+	1.14653e8i	0.0617173	+	0.144395i
$927$	−2.02240e9	−	1.20833e9i	−2.53880	−	1.51686i
$928$	2.11084e8	+	6.49651e8i	0.264127	+	0.812898i
$929$	−1.16344e8	−	8.58889e8i	−0.145110	−	1.07125i	−0.906275	−	0.422689i	$-0.861086\pi$
$929$	−1.16344e8	−	8.58889e8i	−0.145110	−	1.07125i	0.761164	−	0.648559i	$-0.224628\pi$
$930$	−1.86201e9	−	8.36230e7i	−2.31491	−	0.103963i
$931$	−7.27931e7	−	7.61356e7i	−0.0902071	−	0.0943493i
$932$	−6.21641e8	+	6.50186e8i	−0.767878	+	0.803137i
$933$	−583018.	−	1.29819e7i	−0.000717856	−	0.0159843i
$934$	1.26583e8	+	6.97528e8i	0.155358	+	0.856093i
$935$	−2.66625e7	+	1.96831e8i	−0.0326187	+	0.240801i
$936$	2.68411e8	−	1.47907e9i	0.327321	−	1.80369i
$937$	1.29843e9	+	4.21887e8i	1.57834	+	0.512834i	0.961629	−	0.274353i	$-0.0884638\pi$
$937$	1.29843e9	+	4.21887e8i	1.57834	+	0.512834i	0.616713	+	0.787188i	$0.288464\pi$
$938$	4.17119e6	−	3.64426e6i	0.00505419	−	0.00441571i
$939$	9.84002e8	+	1.82858e9i	1.18850	+	2.20860i
$940$	3.97472e8	−	5.47074e8i	0.478546	−	0.658662i
$941$	4.66629e8	−	2.78798e8i	0.560019	−	0.334596i	−0.204838	−	0.978796i	$-0.565667\pi$
$941$	4.66629e8	−	2.78798e8i	0.560019	−	0.334596i	0.764857	+	0.644200i	$0.222810\pi$
$942$	−3.37583e8	−	2.94938e8i	−0.403858	−	0.352840i
$943$	2.37589e8	−	1.04094e9i	0.283329	−	1.24134i
$944$	−3.49336e7	−	9.30802e7i	−0.0415267	−	0.110647i
$945$	−1.87027e8	+	2.07804e9i	−0.221620	+	2.46240i
$946$	3.71991e7	+	2.96653e7i	0.0439399	+	0.0350409i
$947$	3.38640e8	−	7.92286e8i	0.398738	−	0.932894i	−0.593069	−	0.805151i	$-0.702084\pi$
$947$	3.38640e8	−	7.92286e8i	0.398738	−	0.932894i	0.991807	−	0.127743i	$-0.0407731\pi$
$948$	−9.32136e8	+	6.77236e8i	−1.09409	+	0.794905i
$949$	−9.05114e7	+	1.87949e8i	−0.105902	+	0.219908i
$950$	−1.22020e8	−	4.57948e7i	−0.142318	−	0.0534128i
$951$	4.43294e8	+	2.92616e8i	0.515407	+	0.340217i
$952$	−1.73790e9	+	1.56414e8i	−2.01426	+	0.181286i
$953$	−8.09948e8	+	3.90050e8i	−0.935790	+	0.450653i	−0.838682	−	0.544621i	$-0.816673\pi$
$953$	−8.09948e8	+	3.90050e8i	−0.935790	+	0.450653i	−0.0971076	+	0.995274i	$0.530959\pi$
$954$	7.13125e8	+	3.83749e8i	0.821336	+	0.441980i
$955$	2.81532e8	+	1.23347e9i	0.323235	+	1.41618i
$956$	−3.81054e8	+	2.51531e8i	−0.436127	+	0.287885i
$957$	1.14386e8	−	9.12197e7i	0.130508	−	0.104077i
$958$	−1.30500e8	−	4.72858e8i	−0.148428	−	0.537816i
$959$	−1.08989e9	+	3.00792e8i	−1.23574	+	0.341044i
$960$	−8.44129e8	−	1.05850e9i	−0.954103	−	1.19641i
$961$	8.14461e8	+	1.23386e9i	0.917698	+	1.39025i
$962$	2.70713e8	−	6.17885e7i	0.304077	−	0.0694036i
$963$	5.23247e8	−	9.72356e8i	0.585906	−	1.08880i
$964$	5.74404e7	+	1.19276e8i	0.0641189	+	0.133144i
$965$	−2.53501e7	−	2.81663e8i	−0.0282097	−	0.313435i
$966$	−5.24905e8	+	7.95197e8i	−0.582304	+	0.882152i
$967$	7.58172e7	−	2.02014e8i	0.0838471	−	0.223410i	−0.887623	−	0.460570i	$-0.847645\pi$
$967$	7.58172e7	−	2.02014e8i	0.0838471	−	0.223410i	0.971471	+	0.237160i	$0.0762165\pi$
$968$	8.22369e8	+	3.96032e8i	0.906652	+	0.436620i
$969$	−5.65416e8	−	7.78229e8i	−0.621437	−	0.855334i
$970$	4.05048e7	+	1.73126e7i	0.0443804	+	0.0189691i
$971$	−4.66245e8	+	5.84653e8i	−0.509280	+	0.638617i	−0.968294	−	0.249812i	$-0.919631\pi$
$971$	−4.66245e8	+	5.84653e8i	−0.509280	+	0.638617i	0.459015	+	0.888429i	$0.348203\pi$
$972$	7.69881e7	+	6.92906e6i	0.0838349	+	0.00754528i
$973$	3.17097e7	−	1.19009e7i	0.0344234	−	0.0129193i
$974$	7.88194e8	+	1.79900e8i	0.853014	+	0.194695i
$975$	6.32296e8	−	7.23721e8i	0.682192	−	0.780831i
$976$	1.90849e7	+	3.19427e7i	0.0205277	+	0.0343576i
$977$	−1.21901e9	−	8.85661e8i	−1.30714	−	0.949695i	−0.307144	−	0.951663i	$-0.599373\pi$
$977$	−1.21901e9	−	8.85661e8i	−1.30714	−	0.949695i	−0.999998	+	0.00196833i	$0.999373\pi$
$978$	−1.50809e9	+	8.11536e8i	−1.61217	+	0.867543i
$979$	−7.10736e7	−	8.13503e7i	−0.0757461	−	0.0866984i
$980$	7.95969e7	−	2.44974e8i	0.0845703	−	0.260281i
$981$	−5.98422e8	−	1.08597e8i	−0.633870	−	0.115030i
$982$	6.08869e6	+	824769.i	0.00642968	+	0.000870959i
$983$	−8.63555e8	+	1.56712e8i	−0.909137	+	0.164984i	−0.612928	−	0.790139i	$-0.710008\pi$
$983$	−8.63555e8	+	1.56712e8i	−0.909137	+	0.164984i	−0.296209	+	0.955123i	$0.595723\pi$
$984$	2.58502e9	−	1.16093e8i	2.71318	−	0.121849i
$985$	1.51711e7	+	1.45051e7i	0.0158748	+	0.0151779i
$986$	6.61089e8	−	6.32066e8i	0.689651	−	0.659374i
$987$	9.30151e7	−	2.07114e9i	0.0967391	−	2.15406i
$988$	−1.86870e8	+	2.53133e7i	−0.193762	+	0.0262469i
$989$	−5.96712e8	+	1.93883e8i	−0.616844	+	0.200425i
$990$	−8.92342e7	+	1.49353e8i	−0.0919657	+	0.153925i
$991$	1.63634e8	−	6.99404e7i	0.168133	−	0.0718633i	−0.307313	−	0.951609i	$-0.599430\pi$
$991$	1.63634e8	−	6.99404e7i	0.168133	−	0.0718633i	0.475445	+	0.879745i	$0.342287\pi$
$992$	−4.14437e8	+	1.50168e9i	−0.424545	+	1.53830i
$993$			2.35570e9i			2.40587i
$994$	−6.97533e8	+	2.31156e8i	−0.710241	+	0.235367i
$995$	−1.08082e9			−1.09720
$996$	1.79474e9	+	4.95317e8i	1.81645	+	0.501309i
$997$	1.04316e8	+	2.44059e8i	0.105260	+	0.246269i	0.963876	−	0.266351i	$-0.0858179\pi$
$997$	1.04316e8	+	2.44059e8i	0.105260	+	0.246269i	−0.858616	+	0.512620i	$0.828675\pi$
$998$	−5.31582e8	−	3.17605e8i	−0.534784	−	0.319519i
$999$	−2.68453e8	−	8.26213e8i	−0.269260	−	0.828696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.7.h.a.7.14	✓	840
71.61	odd	70	inner	71.7.h.a.61.14	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.7.h.a.7.14	✓	840	1.1	even	1	trivial
71.7.h.a.61.14	yes	840	71.61	odd	70	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	71.h (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.94555 - 1.36489i) q^{2} +(18.2494 + 42.6966i) q^{3} +(-32.3451 - 19.3253i) q^{4} +(49.7071 + 152.983i) q^{5} +(-31.9774 - 236.067i) q^{6} +(-399.783 - 17.9543i) q^{7} +(360.497 + 377.050i) q^{8} +(-986.173 + 1031.46i) q^{9} +O(q^{10})\)	\(q+(-4.94555 - 1.36489i) q^{2} +(18.2494 + 42.6966i) q^{3} +(-32.3451 - 19.3253i) q^{4} +(49.7071 + 152.983i) q^{5} +(-31.9774 - 236.067i) q^{6} +(-399.783 - 17.9543i) q^{7} +(360.497 + 377.050i) q^{8} +(-986.173 + 1031.46i) q^{9} +(-37.0251 - 824.428i) q^{10} +(26.3785 + 145.357i) q^{11} +(234.846 - 1733.70i) q^{12} +(-360.563 + 1986.87i) q^{13} +(1952.64 + 634.451i) q^{14} +(-5624.71 + 4914.16i) q^{15} +(-125.526 - 233.266i) q^{16} +(4913.05 - 6762.23i) q^{17} +(6284.99 - 3755.11i) q^{18} +(-1866.49 - 1630.70i) q^{19} +(1348.66 - 5908.85i) q^{20} +(-6529.21 - 17397.0i) q^{21} +(67.9401 - 754.876i) q^{22} +(7814.11 + 6231.54i) q^{23} +(-9519.91 + 22272.9i) q^{24} +(-8292.01 + 6024.50i) q^{25} +(4495.03 - 9334.02i) q^{26} +(-30345.4 - 11388.8i) q^{27} +(12584.0 + 8306.66i) q^{28} +(-21242.5 + 1911.86i) q^{29} +(34524.6 - 16626.2i) q^{30} +(-42832.9 - 23049.4i) q^{31} +(-7126.67 - 31224.0i) q^{32} +(-5724.87 + 3778.95i) q^{33} +(-33527.4 + 26737.2i) q^{34} +(-17125.3 - 62052.3i) q^{35} +(51831.1 - 14304.5i) q^{36} +(16711.2 + 20955.2i) q^{37} +(7005.10 + 10612.3i) q^{38} +(-91412.4 + 20864.3i) q^{39} +(-39762.9 + 73891.8i) q^{40} +(-46351.3 - 96249.5i) q^{41} +(8545.61 + 94949.4i) q^{42} +(-34583.0 + 52391.0i) q^{43} +(1955.86 - 5211.37i) q^{44} +(-206815. - 99596.7i) q^{45} +(-30139.7 - 41483.8i) q^{46} +(102594. + 43850.8i) q^{47} +(7668.88 - 9616.47i) q^{48} +(42328.4 + 3809.62i) q^{49} +(49231.3 - 18476.8i) q^{50} +(378384. + 86363.7i) q^{51} +(50059.3 - 57297.4i) q^{52} +(56732.4 + 94954.0i) q^{53} +(134530. + 97742.0i) q^{54} +(-20926.0 + 11260.7i) q^{55} +(-137351. - 157211. i) q^{56} +(35563.1 - 109452. i) q^{57} +(107666. + 19538.4i) q^{58} +(371920. + 50380.0i) q^{59} +(276900. - 50249.9i) q^{60} +(-140329. + 6302.16i) q^{61} +(180373. + 172454. i) q^{62} +(412774. - 394652. i) q^{63} +(-8132.45 + 181083. i) q^{64} +(-321878. + 43601.4i) q^{65} +(33470.5 - 10875.2i) q^{66} +(1383.69 - 2315.91i) q^{67} +(-289595. + 123779. i) q^{68} +(-123463. + 447358. i) q^{69} +330257. i q^{70} +(-288322. + 212063. i) q^{71} -744423. q^{72} +(99583.2 + 27483.2i) q^{73} +(-54044.6 - 126444. i) q^{74} +(-408550. - 244097. i) q^{75} +(28858.0 + 88815.7i) q^{76} +(-7935.87 - 58584.9i) q^{77} +(480562. + 21582.1i) q^{78} +(-455110. - 476007. i) q^{79} +(29446.1 - 30798.2i) q^{80} +(-20848.1 - 464220. i) q^{81} +(97863.3 + 539271. i) q^{82} +(-142850. + 1.05456e6i) q^{83} +(-125015. + 688887. i) q^{84} +(1.27872e6 + 415480. i) q^{85} +(242540. - 211901. i) q^{86} +(-469294. - 872094. i) q^{87} +(-45297.7 + 62346.9i) q^{88} +(-627718. + 375044. i) q^{89} +(886875. + 774840. i) q^{90} +(179819. - 787840. i) q^{91} +(-132322. - 352570. i) q^{92} +(202455. - 2.24946e6i) q^{93} +(-447534. - 356896. i) q^{94} +(156691. - 366598. i) q^{95} +(1.20310e6 - 874103. i) q^{96} +(-23159.2 + 48090.6i) q^{97} +(-204138. - 76614.1i) q^{98} +(-175943. - 116139. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 10 q^{2} + 55 q^{3} + 1198 q^{4} + 126 q^{5} - 918 q^{6} - 23 q^{7} + 131 q^{8} + 7546 q^{9}+O(q^{10}) \) 840 * q - 10 * q^2 + 55 * q^3 + 1198 * q^4 + 126 * q^5 - 918 * q^6 - 23 * q^7 + 131 * q^8 + 7546 * q^9	\( 840 q - 10 q^{2} + 55 q^{3} + 1198 q^{4} + 126 q^{5} - 918 q^{6} - 23 q^{7} + 131 q^{8} + 7546 q^{9} - 2738 q^{10} - 1463 q^{11} + 3287 q^{12} - 23 q^{13} - 18290 q^{14} + 5228 q^{15} + 68462 q^{16} + 2570 q^{17} - 26745 q^{18} - 6745 q^{19} - 52864 q^{20} + 15937 q^{21} - 19928 q^{22} - 28 q^{23} - 35893 q^{24} - 571092 q^{25} + 66997 q^{26} + 198565 q^{27} + 128154 q^{28} - 40961 q^{29} + 407435 q^{30} - 128519 q^{31} + 401320 q^{32} + 75353 q^{33} - 476 q^{34} + 131968 q^{35} - 200068 q^{36} - 21044 q^{37} + 145205 q^{38} + 123396 q^{39} - 149980 q^{40} - 34188 q^{41} + 509224 q^{42} + 516743 q^{43} - 350483 q^{44} - 1812421 q^{45} + 839500 q^{46} - 397055 q^{47} + 132073 q^{48} - 516660 q^{49} - 275587 q^{50} - 883071 q^{51} + 391433 q^{52} + 251317 q^{53} + 404299 q^{54} - 435352 q^{55} + 2535081 q^{56} + 1392540 q^{57} - 3191058 q^{58} - 1813895 q^{59} - 7905336 q^{60} + 934381 q^{61} - 239618 q^{62} - 1259119 q^{63} + 5909363 q^{64} + 910632 q^{65} + 12964425 q^{66} + 2624713 q^{67} + 2922405 q^{68} + 2751764 q^{69} - 300728 q^{71} - 7000676 q^{72} - 4735993 q^{73} - 2407708 q^{74} - 5888351 q^{75} - 8042728 q^{76} - 7609131 q^{77} - 868580 q^{78} - 602041 q^{79} + 1791625 q^{80} + 5757840 q^{81} + 2634308 q^{82} + 3040503 q^{83} + 20965752 q^{84} + 700170 q^{85} + 5182335 q^{86} - 9283491 q^{87} - 15723405 q^{88} + 5631815 q^{89} + 10615935 q^{90} + 8939142 q^{91} - 12987536 q^{92} - 4837027 q^{93} + 4628120 q^{94} - 5586244 q^{95} + 6473670 q^{96} - 5779648 q^{97} + 8628336 q^{98} + 2652449 q^{99}+O(q^{100}) \) 840 * q - 10 * q^2 + 55 * q^3 + 1198 * q^4 + 126 * q^5 - 918 * q^6 - 23 * q^7 + 131 * q^8 + 7546 * q^9 - 2738 * q^10 - 1463 * q^11 + 3287 * q^12 - 23 * q^13 - 18290 * q^14 + 5228 * q^15 + 68462 * q^16 + 2570 * q^17 - 26745 * q^18 - 6745 * q^19 - 52864 * q^20 + 15937 * q^21 - 19928 * q^22 - 28 * q^23 - 35893 * q^24 - 571092 * q^25 + 66997 * q^26 + 198565 * q^27 + 128154 * q^28 - 40961 * q^29 + 407435 * q^30 - 128519 * q^31 + 401320 * q^32 + 75353 * q^33 - 476 * q^34 + 131968 * q^35 - 200068 * q^36 - 21044 * q^37 + 145205 * q^38 + 123396 * q^39 - 149980 * q^40 - 34188 * q^41 + 509224 * q^42 + 516743 * q^43 - 350483 * q^44 - 1812421 * q^45 + 839500 * q^46 - 397055 * q^47 + 132073 * q^48 - 516660 * q^49 - 275587 * q^50 - 883071 * q^51 + 391433 * q^52 + 251317 * q^53 + 404299 * q^54 - 435352 * q^55 + 2535081 * q^56 + 1392540 * q^57 - 3191058 * q^58 - 1813895 * q^59 - 7905336 * q^60 + 934381 * q^61 - 239618 * q^62 - 1259119 * q^63 + 5909363 * q^64 + 910632 * q^65 + 12964425 * q^66 + 2624713 * q^67 + 2922405 * q^68 + 2751764 * q^69 - 300728 * q^71 - 7000676 * q^72 - 4735993 * q^73 - 2407708 * q^74 - 5888351 * q^75 - 8042728 * q^76 - 7609131 * q^77 - 868580 * q^78 - 602041 * q^79 + 1791625 * q^80 + 5757840 * q^81 + 2634308 * q^82 + 3040503 * q^83 + 20965752 * q^84 + 700170 * q^85 + 5182335 * q^86 - 9283491 * q^87 - 15723405 * q^88 + 5631815 * q^89 + 10615935 * q^90 + 8939142 * q^91 - 12987536 * q^92 - 4837027 * q^93 + 4628120 * q^94 - 5586244 * q^95 + 6473670 * q^96 - 5779648 * q^97 + 8628336 * q^98 + 2652449 * q^99

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