LMFDB - Embedded newform 43.7.d.a.37.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, 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:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.19
Character	$\chi$	$=$	43.37
Dual form			43.7.d.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+12.4749i q^{2} +(3.88212 + 2.24134i) q^{3} -91.6224 q^{4} +(-151.098 - 87.2364i) q^{5} +(-27.9605 + 48.4289i) q^{6} +(378.610 - 218.590i) q^{7} -344.585i q^{8} +(-354.453 - 613.930i) q^{9} +O(q^{10})$	\(q+12.4749i q^{2} +(3.88212 + 2.24134i) q^{3} -91.6224 q^{4} +(-151.098 - 87.2364i) q^{5} +(-27.9605 + 48.4289i) q^{6} +(378.610 - 218.590i) q^{7} -344.585i q^{8} +(-354.453 - 613.930i) q^{9} +(1088.26 - 1884.93i) q^{10} -420.318 q^{11} +(-355.689 - 205.357i) q^{12} +(-379.357 - 657.066i) q^{13} +(2726.89 + 4723.11i) q^{14} +(-391.053 - 677.324i) q^{15} -1565.17 q^{16} +(-92.2559 - 159.792i) q^{17} +(7658.70 - 4421.75i) q^{18} +(-703.023 - 405.891i) q^{19} +(13844.0 + 7992.81i) q^{20} +1959.74 q^{21} -5243.41i q^{22} +(6480.89 - 11225.2i) q^{23} +(772.334 - 1337.72i) q^{24} +(7407.89 + 12830.8i) q^{25} +(8196.81 - 4732.43i) q^{26} -6445.68i q^{27} +(-34689.1 + 20027.8i) q^{28} +(-30832.9 + 17801.4i) q^{29} +(8449.53 - 4878.34i) q^{30} +(13582.6 - 23525.7i) q^{31} -41578.8i q^{32} +(-1631.72 - 942.077i) q^{33} +(1993.38 - 1150.88i) q^{34} -76276.2 q^{35} +(32475.8 + 56249.7i) q^{36} +(-60406.5 - 34875.7i) q^{37} +(5063.43 - 8770.12i) q^{38} -3401.08i q^{39} +(-30060.4 + 52066.2i) q^{40} -111493. q^{41} +24447.6i q^{42} +(40434.4 - 68457.4i) q^{43} +38510.5 q^{44} +123685. i q^{45} +(140033. + 80848.3i) q^{46} +135508. q^{47} +(-6076.19 - 3508.09i) q^{48} +(36739.1 - 63634.0i) q^{49} +(-160063. + 92412.4i) q^{50} -827.108i q^{51} +(34757.6 + 60201.9i) q^{52} +(-75410.1 + 130614. i) q^{53} +80409.0 q^{54} +(63509.2 + 36667.0i) q^{55} +(-75323.1 - 130463. i) q^{56} +(-1819.48 - 3151.43i) q^{57} +(-222070. - 384637. i) q^{58} -61299.5 q^{59} +(35829.2 + 62058.1i) q^{60} +(76693.0 - 44278.7i) q^{61} +(293480. + 169441. i) q^{62} +(-268399. - 154960. i) q^{63} +418519. q^{64} +132375. i q^{65} +(11752.3 - 20355.5i) q^{66} +(117617. - 203719. i) q^{67} +(8452.70 + 14640.5i) q^{68} +(50319.2 - 29051.8i) q^{69} -951536. i q^{70} +(-105906. + 61144.9i) q^{71} +(-211551. + 122139. i) q^{72} +(-297679. + 171865. i) q^{73} +(435070. - 753563. i) q^{74} +66414.5i q^{75} +(64412.6 + 37188.7i) q^{76} +(-159137. + 91877.5i) q^{77} +42428.0 q^{78} +(435438. + 754200. i) q^{79} +(236494. + 136540. i) q^{80} +(-243949. + 422532. i) q^{81} -1.39086e6i q^{82} +(-420483. + 728298. i) q^{83} -179556. q^{84} +32192.3i q^{85} +(853998. + 504414. i) q^{86} -159596. q^{87} +144835. i q^{88} +(672657. + 388359. i) q^{89} -1.54295e6 q^{90} +(-287257. - 165848. i) q^{91} +(-593795. + 1.02848e6i) q^{92} +(105458. - 60886.4i) q^{93} +1.69045e6i q^{94} +(70816.9 + 122658. i) q^{95} +(93192.3 - 161414. i) q^{96} +1.04611e6 q^{97} +(793826. + 458315. i) q^{98} +(148983. + 258046. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			12.4749i			1.55936i	0.626179	+	0.779679i	$0.284618\pi$
$2$			12.4749i			1.55936i	−0.626179	+	0.779679i	$0.715382\pi$
$3$	3.88212	+	2.24134i	0.143782	+	0.0830127i	0.570165	−	0.821530i	$-0.306879\pi$
$3$	3.88212	+	2.24134i	0.143782	+	0.0830127i	−0.426383	+	0.904543i	$0.640212\pi$
$4$	−91.6224			−1.43160
$5$	−151.098	−	87.2364i	−1.20878	−	0.697891i	−0.246290	−	0.969196i	$-0.579212\pi$
$5$	−151.098	−	87.2364i	−1.20878	−	0.697891i	−0.962493	+	0.271305i	$0.912545\pi$
$6$	−27.9605	+	48.4289i	−0.129447	+	0.224208i
$7$	378.610	−	218.590i	1.10382	−	0.637290i	0.166597	−	0.986025i	$-0.446722\pi$
$7$	378.610	−	218.590i	1.10382	−	0.637290i	0.937221	+	0.348735i	$0.113389\pi$
$8$		−	344.585i		−	0.673019i
$9$	−354.453	−	613.930i	−0.486218	−	0.842154i
$10$	1088.26	−	1884.93i	1.08826	−	1.88493i
$11$	−420.318			−0.315791			−0.157896	−	0.987456i	$-0.550471\pi$
$11$	−420.318			−0.315791			−0.157896	+	0.987456i	$0.550471\pi$
$12$	−355.689	−	205.357i	−0.205839	−	0.118841i
$13$	−379.357	−	657.066i	−0.172670	−	0.299074i	0.766682	−	0.642027i	$-0.221906\pi$
$13$	−379.357	−	657.066i	−0.172670	−	0.299074i	−0.939353	+	0.342953i	$0.888573\pi$
$14$	2726.89	+	4723.11i	0.993764	+	1.72125i
$15$	−391.053	−	677.324i	−0.115868	−	0.200689i
$16$	−1565.17			−0.382122
$17$	−92.2559	−	159.792i	−0.0187779	−	0.0325243i	0.856484	−	0.516174i	$-0.172644\pi$
$17$	−92.2559	−	159.792i	−0.0187779	−	0.0325243i	−0.875262	+	0.483650i	$0.839311\pi$
$18$	7658.70	−	4421.75i	1.31322	−	0.758188i
$19$	−703.023	−	405.891i	−0.102496	−	0.0591763i	0.447876	−	0.894096i	$-0.352181\pi$
$19$	−703.023	−	405.891i	−0.102496	−	0.0591763i	−0.550372	+	0.834920i	$0.685514\pi$
$20$	13844.0	+	7992.81i	1.73049	+	0.999101i
$21$	1959.74			0.211613
$22$		−	5243.41i		−	0.492432i
$23$	6480.89	−	11225.2i	0.532661	−	0.922597i	−0.466611	−	0.884463i	$-0.654525\pi$
$23$	6480.89	−	11225.2i	0.532661	−	0.922597i	0.999273	−	0.0381342i	$-0.0121414\pi$
$24$	772.334	−	1337.72i	0.0558691	−	0.0967681i
$25$	7407.89	+	12830.8i	0.474105	+	0.821174i
$26$	8196.81	−	4732.43i	0.466364	−	0.269255i
$27$		−	6445.68i		−	0.327474i
$28$	−34689.1	+	20027.8i	−1.58023	+	0.912344i
$29$	−30832.9	+	17801.4i	−1.26422	+	0.729895i	−0.973887	−	0.227032i	$-0.927098\pi$
$29$	−30832.9	+	17801.4i	−1.26422	+	0.729895i	−0.290328	+	0.956927i	$0.593764\pi$
$30$	8449.53	−	4878.34i	0.312946	−	0.180679i
$31$	13582.6	−	23525.7i	0.455929	−	0.789692i	−0.542812	−	0.839854i	$-0.682641\pi$
$31$	13582.6	−	23525.7i	0.455929	−	0.789692i	0.998741	+	0.0501623i	$0.0159739\pi$
$32$		−	41578.8i		−	1.26888i
$33$	−1631.72	−	942.077i	−0.0454051	−	0.0262147i
$34$	1993.38	−	1150.88i	0.0507171	−	0.0292815i
$35$	−76276.2			−1.77904
$36$	32475.8	+	56249.7i	0.696069	+	1.20563i
$37$	−60406.5	−	34875.7i	−1.19255	−	0.688522i	−0.233669	−	0.972316i	$-0.575073\pi$
$37$	−60406.5	−	34875.7i	−1.19255	−	0.688522i	−0.958885	+	0.283794i	$0.908407\pi$
$38$	5063.43	−	8770.12i	0.0922771	−	0.159829i
$39$		−	3401.08i		−	0.0573353i
$40$	−30060.4	+	52066.2i	−0.469694	+	0.813534i
$41$	−111493.			−1.61769			−0.808843	−	0.588024i	$-0.799906\pi$
$41$	−111493.			−1.61769			−0.808843	+	0.588024i	$0.799906\pi$
$42$			24447.6i			0.329980i
$43$	40434.4	−	68457.4i	0.508564	−	0.861024i
$43$	40434.4	−	68457.4i	0.508564	−	0.861024i
$44$	38510.5			0.452086
$45$			123685.i			1.35731i
$46$	140033.	+	80848.3i	1.43866	+	0.830610i
$47$	135508.			1.30518			0.652592	−	0.757709i	$-0.273681\pi$
$47$	135508.			1.30518			0.652592	+	0.757709i	$0.273681\pi$
$48$	−6076.19	−	3508.09i	−0.0549424	−	0.0317210i
$49$	36739.1	−	63634.0i	0.312277	−	0.540880i
$50$	−160063.	+	92412.4i	−1.28050	+	0.739300i
$51$		−	827.108i		−	0.00623522i
$52$	34757.6	+	60201.9i	0.247195	+	0.428154i
$53$	−75410.1	+	130614.i	−0.506526	+	0.877330i	0.493445	+	0.869777i	$0.335737\pi$
$53$	−75410.1	+	130614.i	−0.506526	+	0.877330i	−0.999971	+	0.00755259i	$0.997596\pi$
$54$	80409.0			0.510650
$55$	63509.2	+	36667.0i	0.381723	+	0.220388i
$56$	−75323.1	−	130463.i	−0.428908	−	0.742890i
$57$	−1819.48	−	3151.43i	−0.00982477	−	0.0170170i
$58$	−222070.	−	384637.i	−1.13817	−	1.97137i
$59$	−61299.5			−0.298470			−0.149235	−	0.988802i	$-0.547681\pi$
$59$	−61299.5			−0.298470			−0.149235	+	0.988802i	$0.547681\pi$
$60$	35829.2	+	62058.1i	0.165876	+	0.287306i
$61$	76693.0	−	44278.7i	0.337883	−	0.195077i	−0.321452	−	0.946926i	$-0.604171\pi$
$61$	76693.0	−	44278.7i	0.337883	−	0.195077i	0.659336	+	0.751849i	$0.270838\pi$
$62$	293480.	+	169441.i	1.23141	+	0.710956i
$63$	−268399.	−	154960.i	−1.07339	−	0.619724i
$64$	418519.			1.59652
$65$			132375.i			0.482021i
$66$	11752.3	−	20355.5i	0.0408781	−	0.0708029i
$67$	117617.	−	203719.i	0.391062	−	0.677340i	−0.601527	−	0.798852i	$-0.705441\pi$
$67$	117617.	−	203719.i	0.391062	−	0.677340i	0.992590	+	0.121512i	$0.0387743\pi$
$68$	8452.70	+	14640.5i	0.0268825	+	0.0465618i
$69$	50319.2	−	29051.8i	0.153174	−	0.0884353i
$70$		−	951536.i		−	2.77416i
$71$	−105906.	+	61144.9i	−0.295901	+	0.170838i	−0.640600	−	0.767875i	$-0.721314\pi$
$71$	−105906.	+	61144.9i	−0.295901	+	0.170838i	0.344699	+	0.938713i	$0.387981\pi$
$72$	−211551.	+	122139.i	−0.566785	+	0.327234i
$73$	−297679.	+	171865.i	−0.765208	+	0.441793i	−0.831162	−	0.556030i	$-0.812324\pi$
$73$	−297679.	+	171865.i	−0.765208	+	0.441793i	0.0659546	+	0.997823i	$0.478991\pi$
$74$	435070.	−	753563.i	1.07365	−	1.85962i
$75$			66414.5i			0.157427i
$76$	64412.6	+	37188.7i	0.146734	+	0.0847168i
$77$	−159137.	+	91877.5i	−0.348576	+	0.201251i
$78$	42428.0			0.0894064
$79$	435438.	+	754200.i	0.883171	+	1.52970i	0.847796	+	0.530323i	$0.177929\pi$
$79$	435438.	+	754200.i	0.883171	+	1.52970i	0.0353750	+	0.999374i	$0.488737\pi$
$80$	236494.	+	136540.i	0.461903	+	0.266680i
$81$	−243949.	+	422532.i	−0.459033	+	0.795069i
$82$		−	1.39086e6i		−	2.52255i
$83$	−420483.	+	728298.i	−0.735385	+	1.27372i	0.219170	+	0.975687i	$0.429665\pi$
$83$	−420483.	+	728298.i	−0.735385	+	1.27372i	−0.954554	+	0.298037i	$0.903668\pi$
$84$	−179556.			−0.302945
$85$			32192.3i			0.0524198i
$86$	853998.	+	504414.i	1.34265	+	0.793034i
$87$	−159596.			−0.242362
$88$			144835.i			0.212533i
$89$	672657.	+	388359.i	0.954166	+	0.550888i	0.894372	−	0.447323i	$-0.147623\pi$
$89$	672657.	+	388359.i	0.954166	+	0.550888i	0.0597931	+	0.998211i	$0.480956\pi$
$90$	−1.54295e6			−2.11653
$91$	−287257.	−	165848.i	−0.381194	−	0.220082i
$92$	−593795.	+	1.02848e6i	−0.762558	+	1.32079i
$93$	105458.	−	60886.4i	0.131109	−	0.0756957i
$94$			1.69045e6i			2.03525i
$95$	70816.9	+	122658.i	0.0825973	+	0.143063i
$96$	93192.3	−	161414.i	0.105333	−	0.182443i
$97$	1.04611e6			1.14621			0.573104	−	0.819482i	$-0.305739\pi$
$97$	1.04611e6			1.14621			0.573104	+	0.819482i	$0.305739\pi$
$98$	793826.	+	458315.i	0.843426	+	0.486952i
$99$	148983.	+	258046.i	0.153543	+	0.265945i
$100$	−678728.	−	1.17559e6i	−0.678728	−	1.17559i
$101$	77737.1	+	134645.i	0.0754509	+	0.130685i	0.901282	−	0.433232i	$-0.142627\pi$
$101$	77737.1	+	134645.i	0.0754509	+	0.130685i	−0.825831	+	0.563917i	$0.809294\pi$
$102$	10318.1			0.00972294
$103$	−776057.	−	1.34417e6i	−0.710202	−	1.23011i	−0.964781	−	0.263054i	$-0.915270\pi$
$103$	−776057.	−	1.34417e6i	−0.710202	−	1.23011i	0.254579	−	0.967052i	$-0.418063\pi$
$104$	−226415.	+	130721.i	−0.201282	+	0.116210i
$105$	−296113.	−	170961.i	−0.255794	−	0.147683i
$106$	−1.62940e6	−	940732.i	−1.36807	−	0.789856i
$107$	−429685.			−0.350751			−0.175376	−	0.984502i	$-0.556114\pi$
$107$	−429685.			−0.350751			−0.175376	+	0.984502i	$0.556114\pi$
$108$			590568.i			0.468812i
$109$	1.00756e6	−	1.74515e6i	0.778023	−	1.34758i	−0.155057	−	0.987906i	$-0.549556\pi$
$109$	1.00756e6	−	1.74515e6i	0.778023	−	1.34758i	0.933080	−	0.359670i	$-0.117111\pi$
$110$	−457417.	+	792269.i	−0.343664	+	0.595243i
$111$	−156337.	−	270783.i	−0.114312	−	0.197994i
$112$	−592590.	+	342132.i	−0.421794	+	0.243523i
$113$		−	1.00027e6i		−	0.693234i	−0.938007	−	0.346617i	$-0.887330\pi$
$113$		−	1.00027e6i		−	0.693234i	0.938007	−	0.346617i	$-0.112670\pi$
$114$	39313.7	−	22697.8i	0.0265356	−	0.0153203i
$115$	−1.95850e6	+	1.13074e6i	−1.28774	+	0.743480i
$116$	2.82499e6	−	1.63101e6i	1.80985	−	1.04492i
$117$	−268928.	+	465797.i	−0.167911	+	0.290830i
$118$		−	764703.i		−	0.465422i
$119$	−69858.0	−	40332.5i	−0.0414548	−	0.0239340i
$120$	−233396.	+	134751.i	−0.135067	+	0.0779811i
$121$	−1.59489e6			−0.900276
$122$	552372.	+	956736.i	0.304195	+	0.526881i
$123$	−432827.	−	249893.i	−0.232595	−	0.134289i
$124$	−1.24447e6	+	2.15548e6i	−0.652707	+	1.13052i
$125$			141187.i			0.0722879i
$126$	1.93311e6	−	3.34824e6i	0.966371	−	1.67380i
$127$	3.35539e6			1.63807			0.819033	−	0.573746i	$-0.194511\pi$
$127$	3.35539e6			1.63807			0.819033	+	0.573746i	$0.194511\pi$
$128$			2.55993e6i			1.22067i
$129$	310408.	−	175133.i	0.144598	−	0.0815826i
$130$	−1.65136e6			−0.751643
$131$		−	755149.i		−	0.335907i	−0.985795	−	0.167953i	$-0.946284\pi$
$131$		−	755149.i		−	0.335907i	0.985795	−	0.167953i	$-0.0537158\pi$
$132$	149502.	+	86315.3i	0.0650020	+	0.0375289i
$133$	−354895.			−0.150850
$134$	2.54137e6	+	1.46726e6i	1.05622	+	0.609807i
$135$	−562298.	+	973928.i	−0.228542	+	0.395846i
$136$	−55062.0	+	31790.0i	−0.0218895	+	0.0126379i
$137$		−	2.97394e6i		−	1.15657i	−0.815836	−	0.578284i	$-0.803723\pi$
$137$		−	2.97394e6i		−	1.15657i	0.815836	−	0.578284i	$-0.196277\pi$
$138$	362417.	+	627725.i	0.137902	+	0.238854i
$139$	995440.	−	1.72415e6i	0.370656	−	0.641995i	−0.619011	−	0.785383i	$-0.712466\pi$
$139$	995440.	−	1.72415e6i	0.370656	−	0.641995i	0.989667	+	0.143388i	$0.0457996\pi$
$140$	6.98861e6			2.54687
$141$	526059.	+	303720.i	0.187662	+	0.108347i
$142$	−762775.	−	1.32117e6i	−0.266398	−	0.461415i
$143$	159451.	+	276176.i	0.0545278	+	0.0944449i
$144$	554780.	+	960907.i	0.185795	+	0.321806i
$145$	6.21173e6			2.03755
$146$	−2.14399e6	−	3.71350e6i	−0.688914	−	1.19323i
$147$	285251.	−	164690.i	0.0897998	−	0.0518459i
$148$	5.53458e6	+	3.19539e6i	1.70726	+	0.985687i
$149$	−2.92354e6	−	1.68791e6i	−0.883792	−	0.510258i	−0.0118854	−	0.999929i	$-0.503783\pi$
$149$	−2.92354e6	−	1.68791e6i	−0.883792	−	0.510258i	−0.871907	+	0.489672i	$0.837117\pi$
$150$	−828512.			−0.245485
$151$			2.88050e6i			0.836638i	0.908300	+	0.418319i	$0.137381\pi$
$151$			2.88050e6i			0.836638i	−0.908300	+	0.418319i	$0.862619\pi$
$152$	−139864.	+	242252.i	−0.0398268	+	0.0689820i
$153$	−65400.7	+	113277.i	−0.0182603	+	0.0316278i
$154$	−1.14616e6	−	1.98521e6i	−0.313822	−	0.543555i
$155$	−4.10460e6	+	2.36979e6i	−1.10224	+	0.636377i
$156$			311615.i			0.0820813i
$157$	−2.33061e6	+	1.34558e6i	−0.602240	+	0.347704i	−0.769922	−	0.638137i	$-0.779705\pi$
$157$	−2.33061e6	+	1.34558e6i	−0.602240	+	0.347704i	0.167682	+	0.985841i	$0.446372\pi$
$158$	−9.40855e6	+	5.43203e6i	−2.38535	+	1.37718i
$159$	−585502.	+	338040.i	−0.145659	+	0.0840962i
$160$	−3.62719e6	+	6.28247e6i	−0.885543	+	1.53381i
$161$		−	5.66665e6i		−	1.35784i
$162$	−5.27103e6	−	3.04323e6i	−1.23980	−	0.715798i
$163$	−2.31373e6	+	1.33583e6i	−0.534256	+	0.308453i	−0.742748	−	0.669571i	$-0.766478\pi$
$163$	−2.31373e6	+	1.33583e6i	−0.534256	+	0.308453i	0.208492	+	0.978024i	$0.433145\pi$
$164$	1.02152e7			2.31588
$165$	164367.	+	284692.i	0.0365900	+	0.0633757i
$166$	−9.08543e6	−	5.24547e6i	−1.98619	−	1.14673i
$167$	4.04438e6	−	7.00507e6i	0.868365	−	1.50405i	0.00469819	−	0.999989i	$-0.498505\pi$
$167$	4.04438e6	−	7.00507e6i	0.868365	−	1.50405i	0.863667	−	0.504063i	$-0.168162\pi$
$168$		−	675299.i		−	0.142419i
$169$	2.12558e6	−	3.68161e6i	0.440370	−	0.762743i
$170$	−401595.			−0.0817412
$171$			575476.i			0.115090i
$172$	−3.70470e6	+	6.27223e6i	−0.728060	+	1.23264i
$173$	2.84826e6			0.550099			0.275050	−	0.961430i	$-0.411306\pi$
$173$	2.84826e6			0.550099			0.275050	+	0.961430i	$0.411306\pi$
$174$		−	1.99094e6i		−	0.377930i
$175$	5.60940e6	+	3.23859e6i	1.04665	+	0.604285i
$176$	657870.			0.120671
$177$	−237972.	−	137393.i	−0.0429147	−	0.0247768i
$178$	−4.84473e6	+	8.39131e6i	−0.859032	+	1.48789i
$179$	1.93207e6	−	1.11548e6i	0.336871	−	0.194493i	−0.322016	−	0.946734i	$-0.604361\pi$
$179$	1.93207e6	−	1.11548e6i	0.336871	−	0.194493i	0.658888	+	0.752241i	$0.271027\pi$
$180$		−	1.13323e7i		−	1.94312i
$181$	−2.90981e6	−	5.03994e6i	−0.490715	−	0.849943i	0.509228	−	0.860632i	$-0.329931\pi$
$181$	−2.90981e6	−	5.03994e6i	−0.490715	−	0.849943i	−0.999943	+	0.0106883i	$0.996598\pi$
$182$	2.06893e6	−	3.58349e6i	0.343187	−	0.594418i
$183$	396975.			0.0647754
$184$	−3.86805e6	−	2.23322e6i	−0.620925	−	0.358491i
$185$	6.08486e6	+	1.05393e7i	0.961027	+	1.66455i
$186$	759550.	+	1.31558e6i	0.118037	+	0.204446i
$187$	38776.8	+	67163.4i	0.00592990	+	0.0102709i
$188$	−1.24156e7			−1.86850
$189$	−1.40896e6	−	2.44040e6i	−0.208696	−	0.361472i
$190$	−1.53015e6	+	883431.i	−0.223086	+	0.128799i
$191$	1.52768e6	+	882005.i	0.219246	+	0.126582i	0.605601	−	0.795768i	$-0.292933\pi$
$191$	1.52768e6	+	882005.i	0.219246	+	0.126582i	−0.386355	+	0.922350i	$0.626266\pi$
$192$	1.62474e6	+	938044.i	0.229552	+	0.132532i
$193$	−2.76583e6			−0.384728			−0.192364	−	0.981324i	$-0.561615\pi$
$193$	−2.76583e6			−0.384728			−0.192364	+	0.981324i	$0.561615\pi$
$194$			1.30501e7i			1.78735i
$195$	−296698.	+	513895.i	−0.0400138	+	0.0693060i
$196$	−3.36612e6	+	5.83030e6i	−0.447056	+	0.774324i
$197$	4.38307e6	+	7.59171e6i	0.573297	+	0.992980i	0.996224	+	0.0868165i	$0.0276694\pi$
$197$	4.38307e6	+	7.59171e6i	0.573297	+	0.992980i	−0.422927	+	0.906164i	$0.638997\pi$
$198$	−3.21909e6	+	1.85854e6i	−0.414703	+	0.239429i
$199$			2.67177e6i			0.339031i	0.985528	+	0.169515i	$0.0542202\pi$
$199$			2.67177e6i			0.339031i	−0.985528	+	0.169515i	$0.945780\pi$
$200$	4.42132e6	−	2.55265e6i	0.552665	−	0.319081i
$201$	913207.	−	527241.i	0.112456	−	0.0649263i
$202$	−1.67967e6	+	969761.i	−0.203784	+	0.117655i
$203$	−7.78244e6	+	1.34796e7i	−0.930310	+	1.61134i
$204$			75781.6i			0.00892634i
$205$	1.68463e7	+	9.72621e6i	1.95543	+	1.12897i
$206$	1.67684e7	−	9.68121e6i	1.91818	−	1.10746i
$207$	−9.18868e6			−1.03596
$208$	593759.	+	1.02842e6i	0.0659812	+	0.114283i
$209$	295493.	+	170603.i	0.0323675	+	0.0186874i
$210$	2.13272e6	−	3.69398e6i	0.230290	−	0.398874i
$211$		−	1.60766e7i		−	1.71138i	−0.517485	−	0.855692i	$-0.673132\pi$
$211$		−	1.60766e7i		−	1.71138i	0.517485	−	0.855692i	$-0.326868\pi$
$212$	6.90926e6	−	1.19672e7i	0.725143	−	1.25598i
$213$	−548187.			−0.0567270
$214$		−	5.36027e6i		−	0.546947i
$215$	−1.20815e7	+	6.81642e6i	−1.21565	+	0.685869i
$216$	−2.22109e6			−0.220396
$217$		−	1.18761e7i		−	1.16224i
$218$	2.17705e7	+	1.25692e7i	2.10135	+	1.21322i
$219$	−1.54083e6			−0.146698
$220$	−5.81886e6	−	3.35952e6i	−0.546475	−	0.315507i
$221$	−69995.8	+	121236.i	−0.00648478	+	0.0112320i
$222$	3.37798e6	−	1.95028e6i	0.308744	−	0.178254i
$223$			1.59793e6i			0.144093i	0.997401	+	0.0720465i	$0.0229530\pi$
$223$			1.59793e6i			0.144093i	−0.997401	+	0.0720465i	$0.977047\pi$
$224$	−9.08873e6	−	1.57421e7i	−0.808647	−	1.40062i
$225$	5.25149e6	−	9.09585e6i	0.461036	−	0.798539i
$226$	1.24782e7			1.08100
$227$	1.86680e7	+	1.07780e7i	1.59595	+	0.921423i	0.992256	+	0.124208i	$0.0396391\pi$
$227$	1.86680e7	+	1.07780e7i	1.59595	+	0.921423i	0.603696	+	0.797215i	$0.293694\pi$
$228$	166705.	+	288742.i	0.0140651	+	0.0243615i
$229$	205052.	+	355160.i	0.0170749	+	0.0295745i	0.874437	−	0.485140i	$-0.161231\pi$
$229$	205052.	+	355160.i	0.0170749	+	0.0295745i	−0.857362	+	0.514714i	$0.827898\pi$
$230$	−1.41058e7	−	2.44320e7i	−1.15935	−	2.00806i
$231$	−823716.			−0.0668254
$232$	6.13411e6	+	1.06246e7i	0.491233	+	0.850840i
$233$	1.44999e7	−	8.37152e6i	1.14630	−	0.661815i	0.198315	−	0.980138i	$-0.436453\pi$
$233$	1.44999e7	−	8.37152e6i	1.14630	−	0.661815i	0.947982	+	0.318323i	$0.103120\pi$
$234$	−5.81076e6	−	3.35484e6i	−0.453509	−	0.261833i
$235$	−2.04750e7	−	1.18213e7i	−1.57769	−	0.910877i
$236$	5.61641e6			0.427290
$237$			3.90386e6i			0.293258i
$238$	503143.	−	871469.i	0.0373216	−	0.0646429i
$239$	2.60933e6	−	4.51949e6i	0.191133	−	0.331052i	−0.754493	−	0.656308i	$-0.772117\pi$
$239$	2.60933e6	−	4.51949e6i	0.191133	−	0.331052i	0.945626	+	0.325256i	$0.105451\pi$
$240$	612066.	+	1.06013e6i	0.0442756	+	0.0766876i
$241$	−1.88006e7	+	1.08545e7i	−1.34314	+	0.775460i	−0.987266	−	0.159076i	$-0.949149\pi$
$241$	−1.88006e7	+	1.08545e7i	−1.34314	+	0.775460i	−0.355870	+	0.934536i	$0.615815\pi$
$242$		−	1.98961e7i		−	1.40385i
$243$	−5.96344e6	+	3.44300e6i	−0.415603	+	0.239948i
$244$	−7.02680e6	+	4.05692e6i	−0.483713	+	0.279272i
$245$	−1.11024e7	+	6.40998e6i	−0.754951	+	0.435871i
$246$	3.11738e6	−	5.39947e6i	0.209404	−	0.362698i
$247$			615910.i			0.0408720i
$248$	−8.10662e6	−	4.68036e6i	−0.531477	−	0.306848i
$249$	−3.26473e6	+	1.88489e6i	−0.211470	+	0.122092i
$250$	−1.76129e6			−0.112723
$251$	596498.	+	1.03316e6i	0.0377214	+	0.0653354i	0.884270	−	0.466976i	$-0.154657\pi$
$251$	596498.	+	1.03316e6i	0.0377214	+	0.0653354i	−0.846548	+	0.532312i	$0.821323\pi$
$252$	2.45913e7	+	1.41978e7i	1.53667	+	0.887196i
$253$	−2.72404e6	+	4.71817e6i	−0.168210	+	0.291348i
$254$			4.18580e7i			2.55433i
$255$	−72154.0	+	124974.i	−0.00435151	+	0.00753703i
$256$	−5.14954e6			−0.306936
$257$		−	1.12769e7i		−	0.664339i	−0.943220	−	0.332169i	$-0.892219\pi$
$257$		−	1.12769e7i		−	0.664339i	0.943220	−	0.332169i	$-0.107781\pi$
$258$	2.18476e6	+	3.87230e6i	0.127217	+	0.225481i
$259$	−3.04940e7			−1.75515
$260$		−	1.21285e7i		−	0.690061i
$261$	2.18576e7	+	1.26195e7i	1.22937	+	0.709776i
$262$	9.42038e6			0.523799
$263$	1.71416e7	+	9.89672e6i	0.942290	+	0.544031i	0.890677	−	0.454636i	$-0.150231\pi$
$263$	1.71416e7	+	9.89672e6i	0.942290	+	0.544031i	0.0516124	+	0.998667i	$0.483564\pi$
$264$	−324626.	+	562269.i	−0.0176430	+	0.0305585i
$265$	2.27886e7	−	1.31570e7i	1.22456	−	0.707001i
$266$		−	4.42727e6i		−	0.235229i
$267$	1.74089e6	+	3.01531e6i	0.0914613	+	0.158416i
$268$	−1.07764e7	+	1.86652e7i	−0.559845	+	0.969680i
$269$	−3.34585e7			−1.71889			−0.859447	−	0.511225i	$-0.829192\pi$
$269$	−3.34585e7			−1.71889			−0.859447	+	0.511225i	$0.829192\pi$
$270$	−1.21496e7	−	7.01459e6i	−0.617265	−	0.356378i
$271$	−1.29591e7	−	2.24458e7i	−0.651128	−	1.12779i	−0.982850	−	0.184409i	$-0.940963\pi$
$271$	−1.29591e7	−	2.24458e7i	−0.651128	−	1.12779i	0.331721	−	0.943377i	$-0.392371\pi$
$272$	144396.	+	250102.i	0.00717546	+	0.0124283i
$273$	−743443.	−	1.28768e6i	−0.0365392	−	0.0632878i
$274$	3.70995e7			1.80350
$275$	−3.11367e6	−	5.39303e6i	−0.149718	−	0.259319i
$276$	−4.61036e6	+	2.66179e6i	−0.219284	+	0.126604i
$277$	1.31443e7	+	7.58885e6i	0.618439	+	0.357056i	0.776261	−	0.630411i	$-0.217114\pi$
$277$	1.31443e7	+	7.58885e6i	0.618439	+	0.357056i	−0.157822	+	0.987468i	$0.550447\pi$
$278$	2.15086e7	+	1.24180e7i	1.00110	+	0.577985i
$279$	−1.92575e7			−0.886723
$280$			2.62837e7i			1.19732i
$281$	1.76300e7	−	3.05361e7i	0.794573	−	1.37624i	−0.128537	−	0.991705i	$-0.541028\pi$
$281$	1.76300e7	−	3.05361e7i	0.794573	−	1.37624i	0.923110	−	0.384536i	$-0.125638\pi$
$282$	−3.78887e6	+	6.56252e6i	−0.168952	+	0.292633i
$283$	5.31097e6	+	9.19887e6i	0.234323	+	0.405859i	0.959076	−	0.283150i	$-0.0913794\pi$
$283$	5.31097e6	+	9.19887e6i	0.234323	+	0.405859i	−0.724753	+	0.689009i	$0.758046\pi$
$284$	9.70337e6	−	5.60224e6i	0.423611	−	0.244572i
$285$			634899.i			0.0274265i
$286$	−3.44527e6	+	1.98912e6i	−0.147273	+	0.0850284i
$287$	−4.22122e7	+	2.43712e7i	−1.78563	+	1.03094i
$288$	−2.55265e7	+	1.47377e7i	−1.06860	+	0.616954i
$289$	1.20518e7	−	2.08743e7i	0.499295	−	0.864804i
$290$			7.74905e7i			3.17727i
$291$	4.06114e6	+	2.34470e6i	0.164804	+	0.0951499i
$292$	2.72740e7	−	1.57467e7i	1.09547	−	0.632471i
$293$	−3.89091e7			−1.54685			−0.773424	−	0.633889i	$-0.781458\pi$
$293$	−3.89091e7			−1.54685			−0.773424	+	0.633889i	$0.781458\pi$
$294$	2.05448e6	+	3.55847e6i	0.0808464	+	0.140030i
$295$	9.26223e6	+	5.34755e6i	0.360786	+	0.208300i
$296$	−1.20177e7	+	2.08152e7i	−0.463388	+	0.802611i
$297$			2.70923e6i			0.103413i
$298$	2.10564e7	−	3.64708e7i	0.795675	−	1.37815i
$299$	−9.83429e6			−0.367900
$300$		−	6.08505e6i		−	0.225372i
$301$	344724.	−	3.47572e7i	0.0126407	−	1.27452i
$302$	−3.59339e7			−1.30462
$303$			696942.i			0.0250535i
$304$	1.10035e6	+	635289.i	0.0391662	+	0.0226126i
$305$	−1.54509e7			−0.544570
$306$	−1.41312e6	−	815865.i	−0.0493191	−	0.0284744i
$307$	−5.02787e6	+	8.70852e6i	−0.173768	+	0.300974i	−0.939734	−	0.341906i	$-0.888927\pi$
$307$	−5.02787e6	+	8.70852e6i	−0.173768	+	0.300974i	0.765967	+	0.642880i	$0.222261\pi$
$308$	1.45805e7	−	8.41804e6i	0.499021	−	0.288110i
$309$		−	6.95764e6i		−	0.235823i
$310$	−2.95628e7	−	5.12043e7i	−0.992341	−	1.71878i
$311$	−2.81457e7	+	4.87498e7i	−0.935687	+	1.62066i	−0.162283	+	0.986744i	$0.551886\pi$
$311$	−2.81457e7	+	4.87498e7i	−0.935687	+	1.62066i	−0.773404	+	0.633913i	$0.781448\pi$
$312$	−1.17196e6			−0.0385877
$313$	7.33929e6	+	4.23734e6i	0.239343	+	0.138185i	0.614875	−	0.788625i	$-0.289207\pi$
$313$	7.33929e6	+	4.23734e6i	0.239343	+	0.138185i	−0.375532	+	0.926810i	$0.622540\pi$
$314$	−1.67859e7	−	2.90740e7i	−0.542195	−	0.939109i
$315$	2.70363e7	+	4.68283e7i	0.864999	+	1.49822i
$316$	−3.98958e7	−	6.91016e7i	−1.26435	−	2.18991i
$317$	1.94298e7			0.609946			0.304973	−	0.952361i	$-0.401353\pi$
$317$	1.94298e7			0.609946			0.304973	+	0.952361i	$0.401353\pi$
$318$	−4.21700e6	−	7.30406e6i	−0.131136	−	0.227135i
$319$	1.29596e7	−	7.48225e6i	0.399228	−	0.230494i
$320$	−6.32374e7	−	3.65101e7i	−1.92985	−	1.11420i
$321$	−1.66809e6	−	963072.i	−0.0504318	−	0.0291168i
$322$	7.06907e7			2.11736
$323$			149783.i			0.00444483i
$324$	2.23512e7	−	3.87134e7i	0.657152	−	1.13822i
$325$	5.62047e6	−	9.73494e6i	0.163728	−	0.283585i
$326$	−1.66643e7	−	2.88635e7i	−0.480989	−	0.833097i
$327$	7.82295e6	−	4.51658e6i	0.223732	−	0.129172i
$328$			3.84187e7i			1.08873i
$329$	5.13047e7	−	2.96208e7i	1.44069	−	0.831781i
$330$	−3.55149e6	+	2.05045e6i	−0.0988255	+	0.0570569i
$331$	5.02910e7	−	2.90355e7i	1.38678	−	0.800656i	0.393826	−	0.919185i	$-0.371151\pi$
$331$	5.02910e7	−	2.90355e7i	1.38678	−	0.800656i	0.992951	+	0.118529i	$0.0378178\pi$
$332$	3.85257e7	−	6.67284e7i	1.05278	−	1.82346i
$333$			4.94471e7i			1.33909i
$334$	8.73873e7	+	5.04531e7i	2.34536	+	1.35409i
$335$	−3.55434e7	+	2.05210e7i	−0.945420	+	0.545838i
$336$	−3.06734e6			−0.0808619
$337$	1.87860e6	+	3.25383e6i	0.0490845	+	0.0850169i	0.889524	−	0.456889i	$-0.151036\pi$
$337$	1.87860e6	+	3.25383e6i	0.0490845	+	0.0850169i	−0.840439	+	0.541906i	$0.817703\pi$
$338$	4.59277e7	+	2.65163e7i	1.18939	+	0.686695i
$339$	2.24194e6	−	3.88315e6i	0.0575472	−	0.0996747i
$340$		−	2.94953e6i		−	0.0750441i
$341$	−5.70900e6	+	9.88828e6i	−0.143978	+	0.249378i
$342$	−7.17899e6			−0.179467
$343$			1.93106e7i			0.478536i
$344$	−2.35894e7	−	1.39331e7i	−0.579485	−	0.342273i
$345$	−1.01375e7			−0.246873
$346$			3.55316e7i			0.857802i
$347$	−4.34447e6	−	2.50828e6i	−0.103980	−	0.0600327i	0.447108	−	0.894480i	$-0.352454\pi$
$347$	−4.34447e6	−	2.50828e6i	−0.103980	−	0.0600327i	−0.551088	+	0.834447i	$0.685787\pi$
$348$	1.46226e7			0.346966
$349$	1.48639e7	+	8.58170e6i	0.349670	+	0.201882i	0.664540	−	0.747253i	$-0.268628\pi$
$349$	1.48639e7	+	8.58170e6i	0.349670	+	0.201882i	−0.314870	+	0.949135i	$0.601961\pi$
$350$	−4.04010e7	+	6.99765e7i	−0.942297	+	1.63211i
$351$	−4.23523e6	+	2.44521e6i	−0.0979391	+	0.0565451i
$352$			1.74763e7i			0.400702i
$353$	−3.95359e7	−	6.84783e7i	−0.898810	−	1.55679i	−0.829017	−	0.559224i	$-0.811099\pi$
$353$	−3.95359e7	−	6.84783e7i	−0.898810	−	1.55679i	−0.0697936	−	0.997561i	$-0.522234\pi$
$354$	1.71396e6	−	2.96867e6i	0.0386359	−	0.0669194i
$355$	2.13363e7			0.476906
$356$	−6.16304e7	−	3.55824e7i	−1.36598	−	0.788651i
$357$	−180798.	−	313151.i	−0.00397364	−	0.00688255i
$358$	1.39155e7	+	2.41023e7i	0.303284	+	0.525303i
$359$	−7.98925e6	−	1.38378e7i	−0.172672	−	0.299077i	0.766681	−	0.642028i	$-0.221907\pi$
$359$	−7.98925e6	−	1.38378e7i	−0.172672	−	0.299077i	−0.939353	+	0.342951i	$0.888573\pi$
$360$	4.26200e7			0.913494
$361$	−2.31934e7	−	4.01722e7i	−0.492996	−	0.853895i
$362$	6.28727e7	−	3.62995e7i	1.32537	−	0.765201i
$363$	−6.19157e6	−	3.57470e6i	−0.129444	−	0.0747343i
$364$	2.63191e7	+	1.51954e7i	0.545717	+	0.315070i
$365$	5.99715e7			1.23329
$366$			4.95222e6i			0.101008i
$367$	−2.74362e7	+	4.75209e7i	−0.555041	+	0.961360i	0.442859	+	0.896591i	$0.353964\pi$
$367$	−2.74362e7	+	4.75209e7i	−0.555041	+	0.961360i	−0.997900	+	0.0647686i	$0.979369\pi$
$368$	−1.01437e7	+	1.75694e7i	−0.203542	+	0.352545i
$369$	3.95189e7	+	6.84487e7i	0.786548	+	1.36234i
$370$	−1.31476e8	+	7.59078e7i	−2.59563	+	1.49859i
$371$			6.59358e7i			1.29122i
$372$	−9.66234e6	+	5.57856e6i	−0.187695	+	0.108366i
$373$	6.42697e7	−	3.71062e7i	1.23845	−	0.715022i	0.269676	−	0.962951i	$-0.413083\pi$
$373$	6.42697e7	−	3.71062e7i	1.23845	−	0.715022i	0.968778	+	0.247929i	$0.0797500\pi$
$374$	−837855.	+	483736.i	−0.0160160	+	0.00924684i
$375$	−316449.	+	548106.i	−0.00600081	+	0.0103937i
$376$		−	4.66942e7i		−	0.878413i
$377$	2.33934e7	+	1.35062e7i	0.436585	+	0.252063i
$378$	3.04436e7	−	1.75766e7i	0.563665	−	0.325432i
$379$	1.83114e7			0.336359			0.168179	−	0.985756i	$-0.446211\pi$
$379$	1.83114e7			0.336359			0.168179	+	0.985756i	$0.446211\pi$
$380$	−6.48841e6	−	1.12383e7i	−0.118246	−	0.204809i
$381$	1.30260e7	+	7.52057e6i	0.235525	+	0.135980i
$382$	−1.10029e7	+	1.90576e7i	−0.197386	+	0.341883i
$383$		−	6.34110e7i		−	1.12867i	−0.825545	−	0.564337i	$-0.809132\pi$
$383$		−	6.34110e7i		−	1.12867i	0.825545	−	0.564337i	$-0.190868\pi$
$384$	−5.73767e6	+	9.93794e6i	−0.101331	+	0.175510i
$385$	3.20603e7			0.561804
$386$		−	3.45034e7i		−	0.599929i
$387$	−5.63602e7	−	558983.i	−0.972388	−	0.00964418i
$388$	−9.58474e7			−1.64091
$389$		−	1.07167e7i		−	0.182058i	−0.995848	−	0.0910292i	$-0.970984\pi$
$389$		−	1.07167e7i		−	0.182058i	0.995848	−	0.0910292i	$-0.0290157\pi$
$390$	−6.41078e6	−	3.70126e6i	−0.108073	−	0.0623959i
$391$	−2.39160e6			−0.0400091
$392$	−2.19273e7	−	1.26598e7i	−0.364022	−	0.210168i
$393$	1.69255e6	−	2.93158e6i	0.0278845	−	0.0482974i
$394$	−9.47055e7	+	5.46783e7i	−1.54841	+	0.893976i
$395$		−	1.51944e8i		−	2.46543i
$396$	−1.36502e7	−	2.36428e7i	−0.219812	−	0.380726i
$397$	−9.45321e6	+	1.63734e7i	−0.151080	+	0.261679i	−0.931625	−	0.363421i	$-0.881609\pi$
$397$	−9.45321e6	+	1.63734e7i	−0.151080	+	0.261679i	0.780545	+	0.625100i	$0.214942\pi$
$398$	−3.33299e7			−0.528671
$399$	−1.37775e6	−	795442.i	−0.0216895	−	0.0125225i
$400$	−1.15946e7	−	2.00825e7i	−0.181166	−	0.313789i
$401$	8.42526e6	+	1.45930e7i	0.130662	+	0.226314i	0.923932	−	0.382557i	$-0.124956\pi$
$401$	8.42526e6	+	1.45930e7i	0.130662	+	0.226314i	−0.793270	+	0.608870i	$0.791623\pi$
$402$	6.57726e6	+	1.13921e7i	0.101243	+	0.175359i
$403$	−2.06106e7			−0.314902
$404$	−7.12246e6	−	1.23365e7i	−0.108015	−	0.187088i
$405$	7.37204e7	−	4.25625e7i	1.10974	−	0.640711i
$406$	−1.68156e8	−	9.70849e7i	−2.51266	−	1.45069i
$407$	2.53899e7	+	1.46589e7i	0.376598	+	0.217429i
$408$	−285009.			−0.00419642
$409$			5.05692e7i			0.739123i	0.929206	+	0.369561i	$0.120492\pi$
$409$			5.05692e7i			0.739123i	−0.929206	+	0.369561i	$0.879508\pi$
$410$	−1.21333e8	+	2.10155e8i	−1.76047	+	3.04922i
$411$	6.66562e6	−	1.15452e7i	0.0960097	−	0.166294i
$412$	7.11042e7	+	1.23156e8i	1.01673	+	1.76102i
$413$	−2.32086e7	+	1.33995e7i	−0.329457	+	0.190212i
$414$		−	1.14628e8i		−	1.61543i
$415$	1.27068e8	−	7.33629e7i	1.77784	−	1.02644i
$416$	−2.73200e7	+	1.57732e7i	−0.379490	+	0.219099i
$417$	7.72884e6	−	4.46225e6i	0.106587	−	0.0615383i
$418$	−2.12825e6	+	3.68624e6i	−0.0291403	+	0.0504725i
$419$			1.19850e8i			1.62928i	0.579970	+	0.814638i	$0.303064\pi$
$419$			1.19850e8i			1.62928i	−0.579970	+	0.814638i	$0.696936\pi$
$420$	2.71306e7	+	1.56639e7i	0.366194	+	0.211422i
$421$	−1.27795e8	+	7.37823e7i	−1.71264	+	0.988794i	−0.781678	+	0.623682i	$0.785636\pi$
$421$	−1.27795e8	+	7.37823e7i	−1.71264	+	0.988794i	−0.930963	+	0.365112i	$0.881031\pi$
$422$	2.00554e8			2.66866
$423$	−4.80313e7	−	8.31926e7i	−0.634604	−	1.09917i
$424$	4.50078e7	+	2.59852e7i	0.590459	+	0.340902i
$425$	1.36684e6	−	2.36744e6i	0.0178054	−	0.0308399i
$426$		−	6.83856e6i		−	0.0884577i
$427$	1.93578e7	−	3.35287e7i	0.248641	−	0.430659i
$428$	3.93688e7			0.502135
$429$			1.42953e6i			0.0181060i
$430$	−8.50340e7	−	1.50716e8i	−1.06952	−	1.89563i
$431$	−1.12149e8			−1.40076			−0.700382	−	0.713768i	$-0.746987\pi$
$431$	−1.12149e8			−1.40076			−0.700382	+	0.713768i	$0.746987\pi$
$432$			1.00886e7i			0.125135i
$433$	−3.34651e7	−	1.93211e7i	−0.412219	−	0.237995i	0.279524	−	0.960139i	$-0.409823\pi$
$433$	−3.34651e7	−	1.93211e7i	−0.412219	−	0.237995i	−0.691743	+	0.722144i	$0.743157\pi$
$434$	1.48153e8			1.81234
$435$	2.41147e7	+	1.39226e7i	0.292963	+	0.169142i
$436$	−9.23152e7	+	1.59895e8i	−1.11382	+	1.92919i
$437$	−9.11243e6	+	5.26107e6i	−0.109192	+	0.0630419i
$438$		−	1.92217e7i		−	0.228754i
$439$	8.27483e6	+	1.43324e7i	0.0978060	+	0.169405i	0.910776	−	0.412900i	$-0.135484\pi$
$439$	8.27483e6	+	1.43324e7i	0.0978060	+	0.169405i	−0.812970	+	0.582305i	$0.802151\pi$
$440$	1.26349e7	−	2.18843e7i	0.148325	−	0.256907i
$441$	−5.20891e7			−0.607339
$442$	−1.51241e6	−	873189.i	−0.0175147	−	0.0101121i
$443$	−4.79009e7	−	8.29668e7i	−0.550976	−	0.954318i	−0.998204	−	0.0598984i	$-0.980922\pi$
$443$	−4.79009e7	−	8.29668e7i	−0.550976	−	0.954318i	0.447229	−	0.894420i	$-0.352411\pi$
$444$	1.43239e7	+	2.48098e7i	0.163649	+	0.283449i
$445$	−6.77581e7	−	1.17360e8i	−0.768920	−	1.33181i
$446$	−1.99340e7			−0.224693
$447$	−7.56635e6	−	1.31053e7i	−0.0847157	−	0.146732i
$448$	1.58455e8	−	9.14843e7i	1.76227	−	1.01745i
$449$	9.61523e7	+	5.55136e7i	1.06224	+	0.613282i	0.926050	−	0.377402i	$-0.123182\pi$
$449$	9.61523e7	+	5.55136e7i	1.06224	+	0.613282i	0.136186	+	0.990683i	$0.456516\pi$
$450$	1.13470e8	+	6.55117e7i	1.24521	+	0.718921i
$451$	4.68623e7			0.510851
$452$			9.16467e7i			0.992434i
$453$	−6.45620e6	+	1.11825e7i	−0.0694516	+	0.120294i
$454$	−1.34454e8	+	2.32881e8i	−1.43683	+	2.48866i
$455$	2.89359e7	+	5.01185e7i	0.307187	+	0.532064i
$456$	−1.08594e6	+	626966.i	−0.0114528	+	0.00661225i
$457$			1.71343e8i			1.79522i	0.440787	+	0.897612i	$0.354699\pi$
$457$			1.71343e8i			1.79522i	−0.440787	+	0.897612i	$0.645301\pi$
$458$	−4.43058e6	+	2.55800e6i	−0.0461173	+	0.0266258i
$459$	−1.02997e6	+	594652.i	−0.0106509	+	0.00614928i
$460$	1.79442e8	−	1.03601e8i	1.84353	−	1.06437i
$461$	4.84292e7	−	8.38818e7i	0.494316	−	0.856180i	−0.505663	−	0.862731i	$-0.668752\pi$
$461$	4.84292e7	−	8.38818e7i	0.494316	−	0.856180i	0.999979	+	0.00655104i	$0.00208528\pi$
$462$		−	1.02757e7i		−	0.104205i
$463$	3.82722e7	+	2.20965e7i	0.385603	+	0.222628i	0.680253	−	0.732977i	$-0.261870\pi$
$463$	3.82722e7	+	2.20965e7i	0.385603	+	0.222628i	−0.294650	+	0.955605i	$0.595203\pi$
$464$	4.82589e7	−	2.78623e7i	0.483085	−	0.278909i
$465$	−2.12460e7			−0.211310
$466$	1.04434e8	+	1.80884e8i	1.03201	+	1.78749i
$467$	−6.04778e7	−	3.49168e7i	−0.593807	−	0.342834i	0.172795	−	0.984958i	$-0.444720\pi$
$467$	−6.04778e7	−	3.49168e7i	−0.593807	−	0.342834i	−0.766601	+	0.642123i	$0.778054\pi$
$468$	2.46398e7	−	4.26775e7i	0.240381	−	0.416352i
$469$		−	1.02840e8i		−	0.996881i
$470$	1.47469e8	−	2.55423e8i	1.42038	−	2.46018i
$471$	−1.20636e7			−0.115455
$472$			2.11229e7i			0.200876i
$473$	−1.69953e7	+	2.87739e7i	−0.160600	+	0.271904i
$474$	−4.87001e7			−0.457294
$475$		−	1.20272e7i		−	0.112223i
$476$	6.40055e6	+	3.69536e6i	0.0593467	+	0.0342638i
$477$	1.06917e8			0.985129
$478$	5.63801e7	+	3.25510e7i	0.516228	+	0.298045i
$479$	−4.45443e6	+	7.71530e6i	−0.0405309	+	0.0702015i	−0.885579	−	0.464488i	$-0.846238\pi$
$479$	−4.45443e6	+	7.71530e6i	−0.0405309	+	0.0702015i	0.845048	+	0.534690i	$0.179572\pi$
$480$	−2.81623e7	+	1.62595e7i	−0.254651	+	0.147023i
$481$			5.29213e7i			0.475549i
$482$	−1.35409e8	−	2.34535e8i	−1.20922	−	2.09443i
$483$	1.27009e7	−	2.19986e7i	0.112718	−	0.195233i
$484$	1.46128e8			1.28883
$485$	−1.58066e8	−	9.12592e7i	−1.38552	−	0.799929i
$486$	−4.29509e7	−	7.43932e7i	−0.374166	−	0.648074i
$487$	−1.26590e7	−	2.19260e7i	−0.109600	−	0.189833i	0.806008	−	0.591905i	$-0.201624\pi$
$487$	−1.26590e7	−	2.19260e7i	−0.109600	−	0.189833i	−0.915608	+	0.402071i	$0.868290\pi$
$488$	−1.52578e7	−	2.64273e7i	−0.131290	−	0.227402i
$489$	−1.19762e7			−0.102422
$490$	−7.99636e7	−	1.38501e8i	−0.679679	−	1.17724i
$491$	−1.41257e7	+	8.15546e6i	−0.119334	+	0.0688976i	−0.558479	−	0.829519i	$-0.688615\pi$
$491$	−1.41257e7	+	8.15546e6i	−0.119334	+	0.0688976i	0.439145	+	0.898416i	$0.355282\pi$
$492$	3.96567e7	+	2.28958e7i	0.332982	+	0.192247i
$493$	5.68904e6	+	3.28457e6i	0.0474787	+	0.0274118i
$494$	−7.68339e6			−0.0637341
$495$		−	5.19869e7i		−	0.428626i
$496$	−2.12591e7	+	3.68218e7i	−0.174221	+	0.301759i
$497$	−2.67314e7	+	4.63001e7i	−0.217747	+	0.377149i
$498$	−2.35138e7	−	4.07271e7i	−0.190386	−	0.329758i
$499$	9.76647e7	−	5.63867e7i	0.786024	−	0.453811i	−0.0525367	−	0.998619i	$-0.516731\pi$
$499$	9.76647e7	−	5.63867e7i	0.786024	−	0.453811i	0.838561	+	0.544808i	$0.183397\pi$
$500$		−	1.29359e7i		−	0.103487i
$501$	3.14015e7	−	1.81297e7i	0.249711	−	0.144171i
$502$	−1.28886e7	+	7.44123e6i	−0.101881	+	0.0588212i
$503$	1.12952e7	−	6.52129e6i	0.0887545	−	0.0512424i	−0.454966	−	0.890509i	$-0.650349\pi$
$503$	1.12952e7	−	6.52129e6i	0.0887545	−	0.0512424i	0.543720	+	0.839266i	$0.317015\pi$
$504$	−5.33970e7	+	9.24863e7i	−0.417085	+	0.722413i
$505$		−	2.71260e7i		−	0.210626i
$506$	−5.88585e7	−	3.39820e7i	−0.454316	−	0.262299i
$507$	1.65035e7	−	9.52831e6i	0.126635	−	0.0731126i
$508$	−3.07428e8			−2.34505
$509$	−7.65166e7	−	1.32531e8i	−0.580233	−	1.00499i	−0.995451	−	0.0952715i	$-0.969628\pi$
$509$	−7.65166e7	−	1.32531e8i	−0.580233	−	1.00499i	0.415218	−	0.909722i	$-0.363705\pi$
$510$	−1.55904e6	−	900111.i	−0.0117529	−	0.00678556i
$511$	−7.51361e7	+	1.30140e8i	−0.563101	+	0.975319i
$512$			9.95955e7i			0.742044i
$513$	−2.61624e6	+	4.53146e6i	−0.0193787	+	0.0335649i
$514$	1.40678e8			1.03594
$515$			2.70802e8i			1.98258i
$516$	−2.84403e7	+	1.60461e7i	−0.207007	+	0.116794i
$517$	−5.69565e7			−0.412166
$518$		−	3.80408e8i		−	2.73691i
$519$	1.10573e7	+	6.38392e6i	0.0790944	+	0.0456652i
$520$	4.56145e7			0.324409
$521$	−9.54675e7	−	5.51182e7i	−0.675060	−	0.389746i	0.122931	−	0.992415i	$-0.460770\pi$
$521$	−9.54675e7	−	5.51182e7i	−0.675060	−	0.389746i	−0.797991	+	0.602669i	$0.794104\pi$
$522$	−1.57427e8	+	2.72671e8i	−1.10680	+	1.91703i
$523$	1.93354e8	−	1.11633e8i	1.35160	−	0.780345i	0.363125	−	0.931741i	$-0.381710\pi$
$523$	1.93354e8	−	1.11633e8i	1.35160	−	0.780345i	0.988473	+	0.151395i	$0.0483766\pi$
$524$			6.91885e7i			0.480884i
$525$	1.45176e7	+	2.51452e7i	0.100327	+	0.173771i
$526$	−1.23460e8	+	2.13839e8i	−0.848340	+	1.46937i
$527$	−5.01229e6			−0.0342456
$528$	2.55393e6	+	1.47451e6i	0.0173503	+	0.0100172i
$529$	−9.98598e6	−	1.72962e7i	−0.0674565	−	0.116838i
$530$	1.64132e8	+	2.84285e8i	1.10247	+	1.90953i
$531$	2.17278e7	+	3.76336e7i	0.145122	+	0.251358i
$532$	3.25163e7			0.215957
$533$	4.22955e7	+	7.32579e7i	0.279327	+	0.483808i
$534$	−3.76156e7	+	2.17174e7i	−0.247027	+	0.142621i
$535$	6.49245e7	+	3.74842e7i	0.423982	+	0.244786i
$536$	−7.01986e7	−	4.05292e7i	−0.455862	−	0.263192i
$537$	1.00007e7			0.0645815
$538$		−	4.17390e8i		−	2.68037i
$539$	−1.54421e7	+	2.67465e7i	−0.0986144	+	0.170805i
$540$	5.15191e7	−	8.92336e7i	0.327180	−	0.566692i
$541$	−2.79905e7	−	4.84809e7i	−0.176774	−	0.306181i	0.764000	−	0.645216i	$-0.223233\pi$
$541$	−2.79905e7	−	4.84809e7i	−0.176774	−	0.306181i	−0.940774	+	0.339035i	$0.889899\pi$
$542$	2.80008e8	−	1.61663e8i	1.75862	−	1.01534i
$543$		−	2.60876e7i		−	0.162942i
$544$	−6.64395e6	+	3.83589e6i	−0.0412696	+	0.0238270i
$545$	−3.04481e8	+	1.75792e8i	−1.88092	+	1.08595i
$546$	1.60636e7	−	9.27435e6i	0.0986884	−	0.0569778i
$547$	−2.98419e7	+	5.16877e7i	−0.182333	+	0.315809i	−0.942674	−	0.333714i	$-0.891698\pi$
$547$	−2.98419e7	+	5.16877e7i	−0.182333	+	0.315809i	0.760342	+	0.649523i	$0.225031\pi$
$548$			2.72480e8i			1.65574i
$549$	−5.43681e7	−	3.13895e7i	−0.328570	−	0.189700i
$550$	6.72774e7	−	3.88426e7i	0.404372	−	0.233464i
$551$	2.89017e7			0.172770
$552$	−1.00108e7	−	1.73393e7i	−0.0595186	−	0.103089i
$553$	3.29722e8	+	1.90365e8i	1.94972	+	1.12567i
$554$	−9.46699e7	+	1.63973e8i	−0.556779	+	0.964369i
$555$			5.45530e7i			0.319110i
$556$	−9.12046e7	+	1.57971e8i	−0.530631	+	0.919079i
$557$	−9.88185e7			−0.571838			−0.285919	−	0.958254i	$-0.592299\pi$
$557$	−9.88185e7			−0.571838			−0.285919	+	0.958254i	$0.592299\pi$
$558$		−	2.40235e8i		−	1.38272i
$559$	−6.03201e7	−	598257.i	−0.345324	−	0.00342494i
$560$	1.19385e8			0.679810
$561$			347648.i			0.00196903i
$562$	3.80934e8	+	2.19932e8i	2.14605	+	1.23902i
$563$	−1.07791e8			−0.604029			−0.302014	−	0.953303i	$-0.597659\pi$
$563$	−1.07791e8			−0.604029			−0.302014	+	0.953303i	$0.597659\pi$
$564$	−4.81988e7	−	2.78276e7i	−0.268657	−	0.155109i
$565$	−8.72596e7	+	1.51138e8i	−0.483802	+	0.837970i
$566$	−1.14755e8	+	6.62537e7i	−0.632880	+	0.365393i
$567$			2.13300e8i			1.17015i
$568$	2.10697e7	+	3.64937e7i	0.114977	+	0.199147i
$569$	8.87737e7	−	1.53761e8i	0.481889	−	0.834657i	−0.517895	−	0.855444i	$-0.673284\pi$
$569$	8.87737e7	−	1.53761e8i	0.481889	−	0.834657i	0.999784	+	0.0207876i	$0.00661737\pi$
$570$	−7.92029e6			−0.0427678
$571$	−3.56821e7	−	2.06010e7i	−0.191664	−	0.110658i	0.401097	−	0.916036i	$-0.368629\pi$
$571$	−3.56821e7	−	2.06010e7i	−0.191664	−	0.110658i	−0.592762	+	0.805378i	$0.701962\pi$
$572$	−1.46092e7	−	2.53039e7i	−0.0780620	−	0.135207i
$573$	3.95375e6	+	6.84810e6i	0.0210158	+	0.0364004i
$574$	−3.04028e8	−	5.26591e8i	−1.60760	−	2.78444i
$575$	1.92039e8			1.01015
$576$	−1.48345e8	−	2.56941e8i	−0.776258	−	1.34452i
$577$	−2.58188e8	+	1.49065e8i	−1.34403	+	0.775974i	−0.987396	−	0.158271i	$-0.949408\pi$
$577$	−2.58188e8	+	1.49065e8i	−1.34403	+	0.775974i	−0.356631	+	0.934245i	$0.616075\pi$
$578$	2.60404e8	+	1.50344e8i	1.34854	+	0.778580i
$579$	−1.07373e7	−	6.19918e6i	−0.0553171	−	0.0319373i
$580$	−5.69133e8			−2.91696
$581$			3.67655e8i			1.87461i
$582$	−2.92498e7	+	5.06622e7i	−0.148373	+	0.256989i
$583$	3.16962e7	−	5.48995e7i	0.159957	−	0.277053i
$584$	5.92222e7	+	1.02576e8i	0.297335	+	0.514999i
$585$	8.12690e7	−	4.69207e7i	0.405936	−	0.234367i
$586$		−	4.85385e8i		−	2.41209i
$587$	7.04553e7	−	4.06774e7i	0.348337	−	0.201112i	−0.315616	−	0.948887i	$-0.602211\pi$
$587$	7.04553e7	−	4.06774e7i	0.348337	−	0.201112i	0.663952	+	0.747775i	$0.268878\pi$
$588$	−2.61354e7	+	1.50893e7i	−0.128557	+	0.0742226i
$589$	−1.90977e7	+	1.10261e7i	−0.0934621	+	0.0539604i
$590$	−6.67100e7	+	1.15545e8i	−0.324814	+	0.562594i
$591$			3.92959e7i			0.190364i
$592$	9.45466e7	+	5.45865e7i	0.455702	+	0.263099i
$593$	4.52430e7	−	2.61210e7i	0.216964	−	0.125264i	−0.387580	−	0.921836i	$-0.626689\pi$
$593$	4.52430e7	−	2.61210e7i	0.216964	−	0.125264i	0.604544	+	0.796572i	$0.293356\pi$
$594$	−3.37973e7			−0.161259
$595$	7.03693e6	+	1.21883e7i	0.0334066	+	0.0578619i
$596$	2.67862e8	+	1.54650e8i	1.26524	+	0.730485i
$597$	−5.98834e6	+	1.03721e7i	−0.0281438	+	0.0487466i
$598$		−	1.22681e8i		−	0.573687i
$599$	3.50357e7	−	6.06836e7i	0.163016	−	0.282352i	−0.772933	−	0.634488i	$-0.781211\pi$
$599$	3.50357e7	−	6.06836e7i	0.163016	−	0.282352i	0.935949	+	0.352136i	$0.114544\pi$
$600$	2.28855e7			0.105951
$601$		−	1.05336e8i		−	0.485238i	−0.970122	−	0.242619i	$-0.921994\pi$
$601$		−	1.05336e8i		−	0.485238i	0.970122	−	0.242619i	$-0.0780064\pi$
$602$	4.33592e8	+	4.30038e6i	1.98743	+	0.0197114i
$603$	−1.66759e8			−0.760566
$604$		−	2.63919e8i		−	1.19773i
$605$	2.40985e8	+	1.39133e8i	1.08824	+	0.628295i
$606$	−8.69426e6			−0.0390674
$607$	−2.00932e8	−	1.16008e8i	−0.898426	−	0.518706i	−0.0217368	−	0.999764i	$-0.506920\pi$
$607$	−2.00932e8	−	1.16008e8i	−0.898426	−	0.518706i	−0.876689	+	0.481057i	$0.840253\pi$
$608$	−1.68764e7	+	2.92309e7i	−0.0750879	+	0.130056i
$609$	−6.04247e7	+	3.48862e7i	−0.267524	+	0.154455i
$610$		−	1.92748e8i		−	0.849180i
$611$	−5.14060e7	−	8.90378e7i	−0.225367	−	0.390347i
$612$	5.99217e6	−	1.03787e7i	0.0261415	−	0.0452783i
$613$	1.45471e6			0.00631532			0.00315766	−	0.999995i	$-0.498995\pi$
$613$	1.45471e6			0.00631532			0.00315766	+	0.999995i	$0.498995\pi$
$614$	−1.08638e8	−	6.27220e7i	−0.469327	−	0.270966i
$615$	4.35996e7	+	7.55166e7i	0.187438	+	0.324651i
$616$	3.16597e7	+	5.48361e7i	0.135445	+	0.234598i
$617$	−7.33525e7	−	1.27050e8i	−0.312291	−	0.540904i	0.666567	−	0.745445i	$-0.267763\pi$
$617$	−7.33525e7	−	1.27050e8i	−0.312291	−	0.540904i	−0.978858	+	0.204541i	$0.934430\pi$
$618$	8.67957e7			0.367733
$619$	−5.83796e6	−	1.01116e7i	−0.0246144	−	0.0426334i	0.853456	−	0.521165i	$-0.174502\pi$
$619$	−5.83796e6	−	1.01116e7i	−0.0246144	−	0.0426334i	−0.878070	+	0.478532i	$0.841169\pi$
$620$	3.76073e8	−	2.17126e8i	1.57796	−	0.911038i
$621$	−7.23542e7	−	4.17737e7i	−0.302127	−	0.174433i
$622$	−6.08147e8	−	3.51114e8i	−2.52719	−	1.45907i
$623$	3.39566e8			1.40430
$624$			5.32327e6i			0.0219091i
$625$	1.28065e8	−	2.21815e8i	0.524554	−	0.908554i
$626$	−5.28603e7	+	9.15567e7i	−0.215480	+	0.373222i
$627$	764760.	+	1.32460e6i	0.00310258	+	0.00537382i
$628$	2.13536e8	−	1.23285e8i	0.862167	−	0.497772i
$629$			1.28700e7i			0.0517160i
$630$	−5.84177e8	+	3.37274e8i	−2.33627	+	1.34884i
$631$	3.79760e8	−	2.19255e8i	1.51155	−	0.872692i	0.511638	−	0.859201i	$-0.329039\pi$
$631$	3.79760e8	−	2.19255e8i	1.51155	−	0.872692i	0.999909	−	0.0134905i	$-0.00429428\pi$
$632$	2.59886e8	−	1.50046e8i	1.02951	−	0.594390i
$633$	3.60332e7	−	6.24114e7i	0.142067	−	0.246067i
$634$			2.42385e8i			0.951125i
$635$	−5.06992e8	−	2.92712e8i	−1.98007	−	1.14319i
$636$	5.36451e7	−	3.09720e7i	0.208525	−	0.120392i
$637$	−5.57489e7			−0.215684
$638$	9.33401e7	+	1.61670e8i	0.359423	+	0.622540i
$639$	7.50774e7	+	4.33460e7i	0.287744	+	0.166129i
$640$	2.23319e8	−	3.86800e8i	0.851894	−	1.47552i
$641$		−	1.52366e8i		−	0.578513i	−0.957252	−	0.289256i	$-0.906592\pi$
$641$		−	1.52366e8i		−	0.578513i	0.957252	−	0.289256i	$-0.0934080\pi$
$642$	1.20142e7	−	2.08092e7i	0.0454035	−	0.0786412i
$643$	3.97399e7			0.149484			0.0747418	−	0.997203i	$-0.476187\pi$
$643$	3.97399e7			0.149484			0.0747418	+	0.997203i	$0.476187\pi$
$644$			5.19191e8i			1.94388i
$645$	−6.21799e7	−	616703.i	−0.231724	−	0.00229825i
$646$	−1.86853e6			−0.00693109
$647$		−	2.64767e8i		−	0.977577i	−0.872402	−	0.488788i	$-0.837439\pi$
$647$		−	2.64767e8i		−	0.977577i	0.872402	−	0.488788i	$-0.162561\pi$
$648$	1.45598e8	+	8.40613e7i	0.535096	+	0.308938i
$649$	2.57653e7			0.0942542
$650$	1.21442e8	+	7.01146e7i	0.442211	+	0.255310i
$651$	2.66184e7	−	4.61044e7i	0.0964803	−	0.167109i
$652$	2.11989e8	−	1.22392e8i	0.764841	−	0.441581i
$653$			3.33567e7i			0.119796i	0.998204	+	0.0598981i	$0.0190776\pi$
$653$			3.33567e7i			0.119796i	−0.998204	+	0.0598981i	$0.980922\pi$
$654$	5.63438e7	+	9.75903e7i	0.201425	+	0.348878i
$655$	−6.58765e7	+	1.14101e8i	−0.234426	+	0.406038i
$656$	1.74505e8			0.618154
$657$	2.11026e8	+	1.21836e8i	0.744115	+	0.429615i
$658$	3.69516e8	+	6.40020e8i	1.29705	+	2.24655i
$659$	−1.39501e8	−	2.41623e8i	−0.487441	−	0.844273i	0.512455	−	0.858714i	$-0.328736\pi$
$659$	−1.39501e8	−	2.41623e8i	−0.487441	−	0.844273i	−0.999896	+	0.0144416i	$0.995403\pi$
$660$	−1.50597e7	−	2.60841e7i	−0.0523822	−	0.0907286i
$661$	−2.54984e8			−0.882895			−0.441447	−	0.897287i	$-0.645535\pi$
$661$	−2.54984e8			−0.882895			−0.441447	+	0.897287i	$0.645535\pi$
$662$	3.62215e8	+	6.27374e8i	1.24851	+	2.16248i
$663$	−543464.	+	313769.i	−0.00186479	+	0.00107664i
$664$	2.50961e8	+	1.44892e8i	0.857239	+	0.494927i
$665$	5.36239e7	+	3.09598e7i	0.182345	+	0.105277i
$666$	−6.16847e8			−2.08812
$667$			4.61476e8i			1.55515i
$668$	−3.70555e8	+	6.41821e8i	−1.24315	+	2.15320i
$669$	−3.58151e6	+	6.20335e6i	−0.0119616	+	0.0207180i
$670$	−2.55997e8	−	4.43399e8i	−0.851158	−	1.47425i
$671$	−3.22355e7	+	1.86112e7i	−0.106700	+	0.0616036i
$672$		−	8.14838e7i		−	0.268512i
$673$	−2.35511e8	+	1.35972e8i	−0.772621	+	0.446073i	−0.833809	−	0.552053i	$-0.813844\pi$
$673$	−2.35511e8	+	1.35972e8i	−0.772621	+	0.446073i	0.0611879	+	0.998126i	$0.480511\pi$
$674$	−4.05911e7	+	2.34353e7i	−0.132572	+	0.0765404i
$675$	8.27035e7	−	4.77489e7i	0.268913	−	0.155257i
$676$	−1.94751e8	+	3.37318e8i	−0.630433	+	1.09194i
$677$		−	5.92442e8i		−	1.90932i	−0.297692	−	0.954662i	$-0.596217\pi$
$677$		−	5.92442e8i		−	1.90932i	0.297692	−	0.954662i	$-0.403783\pi$
$678$	4.84418e7	+	2.79679e7i	0.155429	+	0.0897368i
$679$	3.96069e8	−	2.28671e8i	1.26521	−	0.730468i
$680$	1.10930e7			0.0352795
$681$	4.83142e7	+	8.36827e7i	0.152980	+	0.264968i
$682$	−1.23355e8	−	7.12190e7i	−0.388869	−	0.224514i
$683$	2.17174e8	−	3.76156e8i	0.681625	−	1.18061i	−0.292860	−	0.956155i	$-0.594607\pi$
$683$	2.17174e8	−	3.76156e8i	0.681625	−	1.18061i	0.974485	−	0.224454i	$-0.0720597\pi$
$684$		−	5.27265e7i		−	0.164763i
$685$	−2.59436e8	+	4.49357e8i	−0.807158	+	1.39804i
$686$	−2.40898e8			−0.746209
$687$			1.83837e6i			0.00566972i
$688$	−6.32869e7	+	1.07148e8i	−0.194334	+	0.329016i
$689$	1.14429e8			0.349849
$690$		−	1.26464e8i		−	0.384964i
$691$	1.98594e8	+	1.14658e8i	0.601911	+	0.347513i	0.769793	−	0.638294i	$-0.220359\pi$
$691$	1.98594e8	+	1.14658e8i	0.601911	+	0.347513i	−0.167882	+	0.985807i	$0.553693\pi$
$692$	−2.60964e8			−0.787522
$693$	1.12813e8	+	6.51325e7i	0.338968	+	0.195703i
$694$	3.12905e7	−	5.41967e7i	0.0936125	−	0.162142i
$695$	−3.00818e8	+	1.73677e8i	−0.896085	+	0.517355i
$696$			5.49945e7i			0.163114i
$697$	1.02858e7	+	1.78156e7i	0.0303768	+	0.0526141i
$698$	−1.07056e8	+	1.85426e8i	−0.314806	+	0.545260i
$699$	7.50538e7			0.219756
$700$	−5.13946e8	−	2.96727e8i	−1.49839	−	0.865094i
$701$	2.84100e8	+	4.92076e8i	0.824741	+	1.42849i	0.902117	+	0.431492i	$0.142013\pi$
$701$	2.84100e8	+	4.92076e8i	0.824741	+	1.42849i	−0.0773758	+	0.997002i	$0.524654\pi$
$702$	−3.05037e7	−	5.28340e7i	−0.0881742	−	0.152722i
$703$	2.83114e7	+	4.90368e7i	0.0814884	+	0.141142i
$704$	−1.75911e8			−0.504168
$705$	−5.29909e7	−	9.17830e7i	−0.151229	−	0.261936i
$706$	8.54258e8	−	4.93206e8i	2.42759	−	1.40157i
$707$	5.88641e7	+	3.39852e7i	0.166568	+	0.0961682i
$708$	2.18036e7	+	1.25883e7i	0.0614367	+	0.0354705i
$709$	−4.00861e8			−1.12475			−0.562374	−	0.826883i	$-0.690112\pi$
$709$	−4.00861e8			−1.12475			−0.562374	+	0.826883i	$0.690112\pi$
$710$			2.66167e8i			0.743668i
$711$	3.08684e8	−	5.34657e8i	0.858827	−	1.48753i
$712$	1.33823e8	−	2.31788e8i	0.370758	−	0.642171i
$713$	−1.76054e8	−	3.04935e8i	−0.485711	−	0.841277i
$714$	3.90652e6	−	2.25543e6i	0.0107324	−	0.00619634i
$715$		−	5.56396e7i		−	0.152218i
$716$	−1.77021e8	+	1.02203e8i	−0.482265	+	0.278436i
$717$	2.02595e7	−	1.16968e7i	0.0549630	−	0.0317329i
$718$	1.72625e8	−	9.96648e7i	0.466368	−	0.269258i
$719$	8.67714e7	−	1.50292e8i	0.233448	−	0.404344i	−0.725373	−	0.688356i	$-0.758333\pi$
$719$	8.67714e7	−	1.50292e8i	0.233448	−	0.404344i	0.958820	+	0.284013i	$0.0916658\pi$
$720$		−	1.93588e8i		−	0.518658i
$721$	−5.87646e8	−	3.39277e8i	−1.56787	−	0.905210i
$722$	5.01143e8	−	2.89335e8i	1.33153	−	0.768758i
$723$	−9.73148e7			−0.257492
$724$	2.66604e8	+	4.61772e8i	0.702507	+	1.21678i
$725$	−4.56814e8	−	2.63742e8i	−1.19874	−	0.692094i
$726$	4.45940e7	−	7.72390e7i	0.116538	−	0.201849i
$727$			1.63476e8i			0.425451i	0.977112	+	0.212726i	$0.0682340\pi$
$727$			1.63476e8i			0.425451i	−0.977112	+	0.212726i	$0.931766\pi$
$728$	−5.71487e7	+	9.89844e7i	−0.148119	+	0.256550i
$729$	3.24810e8			0.838392
$730$			7.48137e8i			1.92315i
$731$	−1.46693e7	−	145490.i	−0.0375540	−	0.000372462i
$732$	−3.63718e7			−0.0927325
$733$			3.73379e8i			0.948064i	0.880508	+	0.474032i	$0.157202\pi$
$733$			3.73379e8i			0.948064i	−0.880508	+	0.474032i	$0.842798\pi$
$734$	−5.92816e8	−	3.42263e8i	−1.49910	−	0.865509i
$735$	−5.74678e7			−0.144731
$736$	−4.66732e8	−	2.69468e8i	−1.17067	−	0.675886i
$737$	−4.94366e7	+	8.56267e7i	−0.123494	+	0.213898i
$738$	−8.53888e8	+	4.92993e8i	−2.12438	+	1.22651i
$739$			1.79925e8i			0.445818i	0.974839	+	0.222909i	$0.0715552\pi$
$739$			1.79925e8i			0.445818i	−0.974839	+	0.222909i	$0.928445\pi$
$740$	−5.57509e8	−	9.65635e8i	−1.37581	−	2.38296i
$741$	−1.38046e6	+	2.39103e6i	−0.00339290	+	0.00587667i
$742$	−8.22540e8			−2.01347
$743$	−5.07460e8	−	2.92982e8i	−1.23719	−	0.714290i	−0.268668	−	0.963233i	$-0.586584\pi$
$743$	−5.07460e8	−	2.92982e8i	−1.23719	−	0.714290i	−0.968518	+	0.248943i	$0.919917\pi$
$744$	−2.09806e7	−	3.63394e7i	−0.0509446	−	0.0882387i
$745$	2.94494e8	+	5.10078e8i	0.712209	+	1.23358i
$746$	4.62894e8	+	8.01757e8i	1.11498	+	1.93119i
$747$	5.96166e8			1.43023
$748$	−3.55282e6	−	6.15367e6i	−0.00848924	−	0.0147038i
$749$	−1.62683e8	+	9.39251e7i	−0.387166	+	0.223530i
$750$	−6.83755e6	−	3.94766e6i	−0.0162075	−	0.00935742i
$751$	2.33553e8	+	1.34842e8i	0.551398	+	0.318350i	0.749686	−	0.661794i	$-0.230205\pi$
$751$	2.33553e8	+	1.34842e8i	0.551398	+	0.318350i	−0.198287	+	0.980144i	$0.563538\pi$
$752$	−2.12094e8			−0.498740
$753$			5.34782e6i			0.0125254i
$754$	−1.68488e8	+	2.91829e8i	−0.393056	+	0.680793i
$755$	2.51285e8	−	4.35238e8i	0.583883	−	1.01131i
$756$	1.29093e8	+	2.23595e8i	0.298769	+	0.517484i
$757$	−2.99492e8	+	1.72912e8i	−0.690396	+	0.398600i	−0.803760	−	0.594953i	$-0.797171\pi$
$757$	−2.99492e8	+	1.72912e8i	−0.690396	+	0.398600i	0.113364	+	0.993553i	$0.463837\pi$
$758$			2.28432e8i			0.524504i
$759$	−2.11501e7	+	1.22110e7i	−0.0483711	+	0.0279271i
$760$	4.22663e7	−	2.44025e7i	0.0962839	−	0.0555895i
$761$	2.41485e8	−	1.39421e8i	0.547943	−	0.316355i	−0.200349	−	0.979725i	$-0.564208\pi$
$761$	2.41485e8	−	1.39421e8i	0.547943	−	0.316355i	0.748292	+	0.663369i	$0.230874\pi$
$762$	−9.38181e7	+	1.62498e8i	−0.212042	+	0.367267i
$763$		−	8.80974e8i		−	1.98330i
$764$	−1.39969e8	−	8.08114e7i	−0.313873	−	0.181214i
$765$	1.97638e7	−	1.14106e7i	0.0441455	−	0.0254874i
$766$	7.91044e8			1.76001
$767$	2.32544e7	+	4.02778e7i	0.0515370	+	0.0892647i
$768$	−1.99911e7	−	1.15419e7i	−0.0441320	−	0.0254796i
$769$	2.77862e8	−	4.81271e8i	0.611013	−	1.05830i	−0.380057	−	0.924963i	$-0.624096\pi$
$769$	2.77862e8	−	4.81271e8i	0.611013	−	1.05830i	0.991070	−	0.133342i	$-0.0425709\pi$
$770$			3.99948e8i			0.876054i
$771$	2.52754e7	−	4.37782e7i	0.0551486	−	0.0955201i
$772$	2.53412e8			0.550777
$773$			7.24323e8i			1.56817i	0.620652	+	0.784086i	$0.286868\pi$
$773$			7.24323e8i			1.56817i	−0.620652	+	0.784086i	$0.713132\pi$
$774$	6.97323e6	−	7.03086e8i	0.0150387	−	1.51630i
$775$	4.02473e8			0.864632
$776$		−	3.60476e8i		−	0.771420i
$777$	−1.18381e8	−	6.83474e7i	−0.252360	−	0.145700i
$778$	1.33689e8			0.283894
$779$	7.83818e7	+	4.52538e7i	0.165807	+	0.0957288i
$780$	2.71841e7	−	4.70843e7i	0.0572838	−	0.0992185i
$781$	4.45142e7	−	2.57003e7i	0.0934428	−	0.0539492i
$782$		−	2.98349e7i		−	0.0623885i
$783$	1.14742e8	+	1.98739e8i	0.239022	+	0.413998i
$784$	−5.75030e7	+	9.95982e7i	−0.119328	+	0.206682i
$785$	4.69533e8			0.970638
$786$	3.65710e7	+	2.11143e7i	0.0753129	+	0.0434819i
$787$	4.52218e8	+	7.83264e8i	0.927733	+	1.60688i	0.787105	+	0.616819i	$0.211579\pi$
$787$	4.52218e8	+	7.83264e8i	0.927733	+	1.60688i	0.140628	+	0.990062i	$0.455088\pi$
$788$	−4.01588e8	−	6.95570e8i	−0.820732	−	1.42155i
$789$	4.43639e7	+	7.68405e7i	0.0903230	+	0.156444i
$790$	1.89548e9			3.84449
$791$	−2.18648e8	−	3.78710e8i	−0.441791	−	0.765205i
$792$	8.89189e7	−	5.13373e7i	0.178986	−	0.103337i
$793$	−5.81881e7	−	3.35949e7i	−0.116685	−	0.0673680i
$794$	−2.04256e8	−	1.17928e8i	−0.408051	−	0.235588i
$795$	1.17958e8			0.234760
$796$		−	2.44793e8i		−	0.485356i
$797$	−2.08180e8	+	3.60579e8i	−0.411211	+	0.712239i	−0.995022	−	0.0996507i	$-0.968227\pi$
$797$	−2.08180e8	+	3.60579e8i	−0.411211	+	0.712239i	0.583811	+	0.811889i	$0.301561\pi$
$798$	9.92303e6	−	1.71872e7i	0.0195270	−	0.0338218i
$799$	−1.25014e7	−	2.16531e7i	−0.0245086	−	0.0424502i
$800$	5.33491e8	−	3.08011e8i	1.04197	−	0.601584i
$801$		−	5.50619e8i		−	1.07141i
$802$	−1.82046e8	+	1.05104e8i	−0.352904	+	0.203749i
$803$	1.25120e8	−	7.22379e7i	0.241646	−	0.139514i
$804$	−8.36702e7	+	4.83070e7i	−0.160991	+	0.0929485i
$805$	−4.94338e8	+	8.56218e8i	−0.947624	+	1.64133i
$806$		−	2.57114e8i		−	0.491045i
$807$	−1.29890e8	−	7.49919e7i	−0.247146	−	0.142690i
$808$	4.63966e7	−	2.67871e7i	0.0879533	−	0.0507798i
$809$	8.29434e8			1.56652			0.783261	−	0.621693i	$-0.213555\pi$
$809$	8.29434e8			1.56652			0.783261	+	0.621693i	$0.213555\pi$
$810$	5.30962e8	+	9.19652e8i	0.999098	+	1.73049i
$811$	7.68570e8	+	4.43734e8i	1.44086	+	0.831880i	0.997907	−	0.0646664i	$-0.0205983\pi$
$811$	7.68570e8	+	4.43734e8i	1.44086	+	0.831880i	0.442951	+	0.896546i	$0.353932\pi$
$812$	7.13045e8	−	1.23503e9i	1.33183	−	2.30680i
$813$		−	1.16183e8i		−	0.216208i
$814$	−1.82868e8	+	3.16736e8i	−0.339050	+	0.587252i
$815$	4.66133e8			0.861067
$816$			1.29457e6i			0.00238262i
$817$	−5.62126e7	+	3.17152e7i	−0.103078	+	0.0581569i
$818$	−6.30845e8			−1.15256
$819$			2.35141e8i			0.428032i
$820$	−1.54350e9	−	8.91139e8i	−2.79940	−	1.61623i
$821$	−4.16723e8			−0.753040			−0.376520	−	0.926409i	$-0.622879\pi$
$821$	−4.16723e8			−0.753040			−0.376520	+	0.926409i	$0.622879\pi$
$822$	1.44025e8	+	8.31528e7i	0.259312	+	0.149714i
$823$	−5.84636e7	+	1.01262e8i	−0.104878	+	0.181655i	−0.913688	−	0.406415i	$-0.866779\pi$
$823$	−5.84636e7	+	1.01262e8i	−0.104878	+	0.181655i	0.808810	+	0.588070i	$0.200112\pi$
$824$	−4.63182e8	+	2.67418e8i	−0.827884	+	0.477979i
$825$		−	2.79152e7i		−	0.0497140i
$826$	−1.67157e8	−	2.89524e8i	−0.296609	−	0.513742i
$827$	1.41648e7	−	2.45341e7i	0.0250434	−	0.0433764i	−0.853232	−	0.521531i	$-0.825361\pi$
$827$	1.41648e7	−	2.45341e7i	0.0250434	−	0.0433764i	0.878275	+	0.478155i	$0.158694\pi$
$828$	8.41889e8			1.48308
$829$	3.51608e8	+	2.03001e8i	0.617156	+	0.356315i	0.775761	−	0.631027i	$-0.217366\pi$
$829$	3.51608e8	+	2.03001e8i	0.617156	+	0.356315i	−0.158605	+	0.987342i	$0.550700\pi$
$830$	9.15193e8	+	1.58516e9i	1.60058	+	2.77229i
$831$	3.40184e7	+	5.89216e7i	0.0592804	+	0.102677i
$832$	−1.58768e8	−	2.74994e8i	−0.275672	−	0.477479i
$833$	−1.35576e7			−0.0234557
$834$	5.56659e7	+	9.64162e7i	0.0959602	+	0.166208i
$835$	−1.22219e9	+	7.05634e8i	−2.09933	+	1.21205i
$836$	−2.70738e7	−	1.56311e7i	−0.0463372	−	0.0267528i
$837$	−1.51639e8	−	8.75489e7i	−0.258604	−	0.149305i
$838$	−1.49511e9			−2.54063
$839$		−	3.67602e8i		−	0.622433i	−0.950339	−	0.311216i	$-0.899264\pi$
$839$		−	3.67602e8i		−	0.622433i	0.950339	−	0.311216i	$-0.100736\pi$
$840$	−5.89107e7	+	1.02036e8i	−0.0993931	+	0.172154i
$841$	3.36369e8	−	5.82608e8i	0.565494	−	0.979464i
$842$	−9.20425e8	−	1.59422e9i	−1.54188	−	2.67062i
$843$	1.36884e8	−	7.90298e7i	0.228491	−	0.131919i
$844$			1.47298e9i			2.45002i
$845$	−6.42342e8	+	3.70856e8i	−1.06462	+	0.614661i
$846$	1.03782e9	−	5.99184e8i	1.71399	−	0.989575i
$847$	−6.03842e8	+	3.48629e8i	−0.993741	+	0.573737i
$848$	1.18030e8	−	2.04434e8i	0.193555	−	0.335247i
$849$			4.76148e7i			0.0778071i
$850$	2.95335e7	+	1.70512e7i	0.0480904	+	0.0277650i
$851$	−7.82976e8	+	4.52051e8i	−1.27046	+	0.733498i
$852$	5.02262e7			0.0812103
$853$	4.40041e7	+	7.62173e7i	0.0708999	+	0.122802i	0.899296	−	0.437341i	$-0.144080\pi$
$853$	4.40041e7	+	7.62173e7i	0.0708999	+	0.122802i	−0.828396	+	0.560143i	$0.810746\pi$
$854$	4.18267e8	+	2.41486e8i	0.671552	+	0.387721i
$855$	5.02025e7	−	8.69532e7i	0.0803206	−	0.139119i
$856$			1.48063e8i			0.236062i
$857$	4.10434e7	−	7.10893e7i	0.0652080	−	0.112944i	−0.831578	−	0.555408i	$-0.812562\pi$
$857$	4.10434e7	−	7.10893e7i	0.0652080	−	0.112944i	0.896786	+	0.442464i	$0.145896\pi$
$858$	−1.78332e7			−0.0282337
$859$		−	8.44333e8i		−	1.33209i	−0.745910	−	0.666046i	$-0.767985\pi$
$859$		−	8.44333e8i		−	1.33209i	0.745910	−	0.666046i	$-0.232015\pi$
$860$	1.10694e9	−	6.24537e8i	1.74032	−	0.981890i
$861$	−2.18497e8			−0.342323
$862$		−	1.39905e9i		−	2.18429i
$863$	−4.77903e8	−	2.75917e8i	−0.743545	−	0.429286i	0.0798121	−	0.996810i	$-0.474568\pi$
$863$	−4.77903e8	−	2.75917e8i	−0.743545	−	0.429286i	−0.823357	+	0.567524i	$0.807901\pi$
$864$	−2.68004e8			−0.415527
$865$	−4.30366e8	−	2.48472e8i	−0.664951	−	0.383909i
$866$	2.41028e8	−	4.17473e8i	0.371119	−	0.642798i
$867$	9.35727e7	−	5.40243e7i	0.143579	−	0.0828956i
$868$			1.08811e9i			1.66386i
$869$	−1.83022e8	−	3.17004e8i	−0.278898	−	0.483065i
$870$	−1.73683e8	+	3.00827e8i	−0.263754	+	0.456835i
$871$	−1.78476e8			−0.270100
$872$	−6.01353e8	−	3.47191e8i	−0.906943	−	0.523624i
$873$	−3.70798e8	−	6.42241e8i	−0.557307	−	0.965284i
$874$	−6.56311e7	−	1.13676e8i	−0.0983050	−	0.170269i
$875$	3.08622e7	+	5.34549e7i	0.0460684	+	0.0797927i
$876$	1.41175e8			0.210012
$877$	4.80167e8	+	8.31674e8i	0.711859	+	1.23298i	0.964159	+	0.265326i	$0.0854797\pi$
$877$	4.80167e8	+	8.31674e8i	0.711859	+	1.23298i	−0.252300	+	0.967649i	$0.581187\pi$
$878$	−1.78795e8	+	1.03227e8i	−0.264163	+	0.152515i
$879$	−1.51050e8	−	8.72085e7i	−0.222409	−	0.128408i
$880$	−9.94028e7	−	5.73903e7i	−0.145865	−	0.0842151i
$881$	5.47293e7			0.0800372			0.0400186	−	0.999199i	$-0.487258\pi$
$881$	5.47293e7			0.0800372			0.0400186	+	0.999199i	$0.487258\pi$
$882$		−	6.49805e8i		−	0.947059i
$883$	−2.26976e8	+	3.93134e8i	−0.329684	+	0.571029i	−0.982449	−	0.186531i	$-0.940276\pi$
$883$	−2.26976e8	+	3.93134e8i	−0.329684	+	0.571029i	0.652765	+	0.757560i	$0.273609\pi$
$884$	6.41318e6	−	1.11080e7i	0.00928361	−	0.0160797i
$885$	2.39714e7	+	4.15196e7i	0.0345830	+	0.0598996i
$886$	1.03500e9	−	5.97557e8i	1.48812	−	0.859169i
$887$			3.00505e8i			0.430607i	0.976547	+	0.215303i	$0.0690740\pi$
$887$			3.00505e8i			0.430607i	−0.976547	+	0.215303i	$0.930926\pi$
$888$	−9.33079e7	+	5.38714e7i	−0.133254	+	0.0769341i
$889$	1.27038e9	−	7.33456e8i	1.80813	−	1.04392i
$890$	1.46406e9	−	8.45273e8i	2.07677	−	1.19902i
$891$	1.02536e8	−	1.77598e8i	0.144959	−	0.251076i
$892$		−	1.46406e8i		−	0.206284i
$893$	−9.52654e7	−	5.50015e7i	−0.133777	−	0.0772361i
$894$	1.63487e8	−	9.43893e7i	0.228808	−	0.132102i
$895$	−3.89243e8			−0.542939
$896$	5.59576e8	+	9.69214e8i	0.777920	+	1.34740i
$897$	−3.81779e7	−	2.20420e7i	−0.0528974	−	0.0305403i
$898$	−6.92524e8	+	1.19949e9i	−0.956326	+	1.65641i
$899$			9.67156e8i			1.33112i
$900$	−4.81154e8	+	8.33384e8i	−0.660020	+	1.14319i
$901$	2.78281e7			0.0380460
$902$			5.84602e8i			0.796600i
$903$	7.92411e7	−	1.34159e8i	0.107619	−	0.182204i
$904$	−3.44677e8			−0.466559
$905$			1.01537e9i			1.36986i
$906$	−1.39500e8	−	8.05402e7i	−0.187581	−	0.108300i
$907$	−8.18971e8			−1.09761			−0.548804	−	0.835951i	$-0.684916\pi$
$907$	−8.18971e8			−1.09761			−0.548804	+	0.835951i	$0.684916\pi$
$908$	−1.71040e9	−	9.87503e8i	−2.28476	−	1.31911i
$909$	5.51083e7	−	9.54503e7i	0.0733711	−	0.127083i
$910$	−6.25221e8	+	3.60972e8i	−0.829678	+	0.479015i
$911$			1.16848e9i			1.54549i	0.634718	+	0.772744i	$0.281116\pi$
$911$			1.16848e9i			1.54549i	−0.634718	+	0.772744i	$0.718884\pi$
$912$	2.84780e6	+	4.93253e6i	0.00375426	+	0.00650258i
$913$	1.76737e8	−	3.06117e8i	0.232228	−	0.402231i
$914$	−2.13748e9			−2.79940
$915$	−5.99822e7	−	3.46307e7i	−0.0782995	−	0.0452062i
$916$	−1.87873e7	−	3.25406e7i	−0.0244444	−	0.0423389i
$917$	−1.65068e8	−	2.85907e8i	−0.214070	−	0.370780i
$918$	−7.41820e6	−	1.28487e7i	−0.00958894	−	0.0166085i
$919$	−1.00059e8			−0.128917			−0.0644586	−	0.997920i	$-0.520532\pi$
$919$	−1.00059e8			−0.128917			−0.0644586	+	0.997920i	$0.520532\pi$
$920$	3.89637e8	+	6.74870e8i	0.500376	+	0.866676i
$921$	−3.90376e7	+	2.25383e7i	−0.0499694	+	0.0288498i
$922$	1.04642e9	+	6.04148e8i	1.33509	+	0.770816i
$923$	8.03524e7	+	4.63915e7i	0.102187	+	0.0589975i
$924$	7.54708e7			0.0956672
$925$		−	1.03342e9i		−	1.30573i
$926$	−2.75651e8	+	4.77441e8i	−0.347157	+	0.601293i
$927$	−5.50151e8	+	9.52890e8i	−0.690626	+	1.19620i
$928$	7.40161e8	+	1.28200e9i	0.926152	+	1.60414i
$929$	9.07638e8	−	5.24025e8i	1.13205	−	0.653589i	0.187600	−	0.982245i	$-0.439929\pi$
$929$	9.07638e8	−	5.24025e8i	1.13205	−	0.653589i	0.944450	+	0.328656i	$0.106596\pi$
$930$		−	2.65042e8i		−	0.329507i
$931$	−5.16569e7	+	2.98241e7i	−0.0640146	+	0.0369588i
$932$	−1.32852e9	+	7.67019e8i	−1.64104	+	0.947454i
$933$	−2.18530e8	+	1.26168e8i	−0.269070	+	0.155348i
$934$	4.35583e8	−	7.54452e8i	0.534602	−	0.925958i
$935$		−	1.35310e7i		−	0.0165537i
$936$	1.60507e8	+	9.26688e7i	0.195734	+	0.113007i
$937$	8.61124e8	−	4.97170e8i	1.04676	−	0.604347i	0.125019	−	0.992154i	$-0.460101\pi$
$937$	8.61124e8	−	4.97170e8i	1.04676	−	0.604347i	0.921740	+	0.387807i	$0.126767\pi$
$938$	1.28291e9			1.55449
$939$	1.89947e7	+	3.28997e7i	0.0229422	+	0.0397370i
$940$	1.87597e9	+	1.08309e9i	2.25861	+	1.30401i
$941$	4.81445e8	−	8.33888e8i	0.577801	−	1.00078i	−0.417930	−	0.908479i	$-0.637244\pi$
$941$	4.81445e8	−	8.33888e8i	0.577801	−	1.00078i	0.995731	−	0.0923011i	$-0.0294222\pi$
$942$		−	1.50492e8i		−	0.180036i
$943$	−7.22571e8	+	1.25153e9i	−0.861679	+	1.49247i
$944$	9.59443e7			0.114052
$945$			4.91652e8i			0.582589i
$946$	−3.58951e8	−	2.12014e8i	−0.423995	−	0.250433i
$947$	−1.07333e8			−0.126382			−0.0631909	−	0.998001i	$-0.520128\pi$
$947$	−1.07333e8			−0.126382			−0.0631909	+	0.998001i	$0.520128\pi$
$948$		−	3.57681e8i		−	0.419827i
$949$	2.25853e8	+	1.30396e8i	0.264258	+	0.152569i
$950$	1.50037e8			0.174996
$951$	7.54290e7	+	4.35489e7i	0.0876994	+	0.0506333i
$952$	−1.38980e7	+	2.40720e7i	−0.0161080	+	0.0278999i
$953$	−6.15803e8	+	3.55534e8i	−0.711480	+	0.410773i	−0.811609	−	0.584201i	$-0.801408\pi$
$953$	−6.15803e8	+	3.55534e8i	−0.711480	+	0.410773i	0.100129	+	0.994974i	$0.468075\pi$
$954$			1.33378e9i			1.53617i
$955$	−1.53886e8	−	2.66538e8i	−0.176681	−	0.306020i
$956$	−2.39073e8	+	4.14086e8i	−0.273626	+	0.473933i
$957$	6.70812e7			0.0765358
$958$	−9.62474e7	−	5.55684e7i	−0.109469	−	0.0632021i
$959$	−6.50075e8	−	1.12596e9i	−0.737069	−	1.27664i
$960$	−1.63663e8	−	2.83473e8i	−0.184985	−	0.320404i
$961$	7.47794e7	+	1.29522e8i	0.0842581	+	0.145939i
$962$	−6.60187e8			−0.741552
$963$	1.52303e8	+	2.63797e8i	0.170541	+	0.295386i
$964$	1.72255e9	−	9.94517e8i	1.92283	−	1.11015i
$965$	4.17912e8	+	2.41281e8i	0.465053	+	0.268498i
$966$	2.74430e8	+	1.58442e8i	0.304438	+	0.175768i
$967$	−1.00608e9			−1.11264			−0.556320	−	0.830968i	$-0.687787\pi$
$967$	−1.00608e9			−1.11264			−0.556320	+	0.830968i	$0.687787\pi$
$968$			5.49577e8i			0.605902i
$969$	−335715.	+	581476.i	−0.000368978	+	0.000639088i
$970$	1.13845e9	−	1.97185e9i	1.24738	−	2.16052i
$971$	−4.21794e8	−	7.30569e8i	−0.460726	−	0.798001i	0.538271	−	0.842772i	$-0.319078\pi$
$971$	−4.21794e8	−	7.30569e8i	−0.460726	−	0.798001i	−0.998997	+	0.0447705i	$0.985744\pi$
$972$	5.46385e8	−	3.15455e8i	0.594977	−	0.343510i
$973$		−	8.70375e8i		−	0.944861i
$974$	2.73524e8	−	1.57919e8i	0.296018	−	0.170906i
$975$	4.36387e7	−	2.51948e7i	0.0470823	−	0.0271830i
$976$	−1.20038e8	+	6.93039e7i	−0.129113	+	0.0745432i
$977$	3.86484e8	−	6.69409e8i	0.414426	−	0.717808i	−0.580942	−	0.813945i	$-0.697316\pi$
$977$	3.86484e8	−	6.69409e8i	0.414426	−	0.717808i	0.995368	+	0.0961376i	$0.0306489\pi$
$978$		−	1.49402e8i		−	0.159713i
$979$	−2.82730e8	−	1.63234e8i	−0.301317	−	0.173965i
$980$	1.01723e9	−	5.87297e8i	1.08079	−	0.623993i
$981$	−1.42853e9			−1.51315
$982$	−1.01738e8	−	1.76216e8i	−0.107436	−	0.186085i
$983$	−3.47037e8	−	2.00362e8i	−0.365355	−	0.210938i	0.306072	−	0.952008i	$-0.400985\pi$
$983$	−3.47037e8	−	2.00362e8i	−0.365355	−	0.210938i	−0.671427	+	0.741070i	$0.734318\pi$
$984$	−8.61095e7	+	1.49146e8i	−0.0903786	+	0.156540i
$985$		−	1.52945e9i		−	1.60040i
$986$	−4.09746e7	+	7.09701e7i	−0.0427448	+	0.0740363i
$987$	2.65561e8			0.276194
$988$		−	5.64311e7i		−	0.0585124i
$989$	−5.06400e8	−	8.97551e8i	−0.523485	−	0.927834i
$990$	6.48530e8			0.668382
$991$		−	3.41860e8i		−	0.351259i	−0.984456	−	0.175630i	$-0.943804\pi$
$991$		−	3.41860e8i		−	0.351259i	0.984456	−	0.175630i	$-0.0561961\pi$
$992$	−9.78170e8	−	5.64747e8i	−1.00203	−	0.578521i
$993$	2.60314e8			0.265858
$994$	−5.77588e8	−	3.33471e8i	−0.588111	−	0.339546i
$995$	2.33075e8	−	4.03698e8i	0.236607	−	0.409815i
$996$	2.99123e8	−	1.72698e8i	0.302741	−	0.174788i
$997$			3.93553e8i			0.397117i	0.980089	+	0.198558i	$0.0636259\pi$
$997$			3.93553e8i			0.397117i	−0.980089	+	0.198558i	$0.936374\pi$
$998$	7.03417e8	+	1.21835e9i	0.707655	+	1.22569i
$999$	−2.24797e8	+	3.89361e8i	−0.225473	+	0.390531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.37.19	yes	42
43.7	odd	6	inner	43.7.d.a.7.3	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.3	✓	42	43.7	odd	6	inner
43.7.d.a.37.19	yes	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+12.4749i q^{2} +(3.88212 + 2.24134i) q^{3} -91.6224 q^{4} +(-151.098 - 87.2364i) q^{5} +(-27.9605 + 48.4289i) q^{6} +(378.610 - 218.590i) q^{7} -344.585i q^{8} +(-354.453 - 613.930i) q^{9} +O(q^{10})\)	\(q+12.4749i q^{2} +(3.88212 + 2.24134i) q^{3} -91.6224 q^{4} +(-151.098 - 87.2364i) q^{5} +(-27.9605 + 48.4289i) q^{6} +(378.610 - 218.590i) q^{7} -344.585i q^{8} +(-354.453 - 613.930i) q^{9} +(1088.26 - 1884.93i) q^{10} -420.318 q^{11} +(-355.689 - 205.357i) q^{12} +(-379.357 - 657.066i) q^{13} +(2726.89 + 4723.11i) q^{14} +(-391.053 - 677.324i) q^{15} -1565.17 q^{16} +(-92.2559 - 159.792i) q^{17} +(7658.70 - 4421.75i) q^{18} +(-703.023 - 405.891i) q^{19} +(13844.0 + 7992.81i) q^{20} +1959.74 q^{21} -5243.41i q^{22} +(6480.89 - 11225.2i) q^{23} +(772.334 - 1337.72i) q^{24} +(7407.89 + 12830.8i) q^{25} +(8196.81 - 4732.43i) q^{26} -6445.68i q^{27} +(-34689.1 + 20027.8i) q^{28} +(-30832.9 + 17801.4i) q^{29} +(8449.53 - 4878.34i) q^{30} +(13582.6 - 23525.7i) q^{31} -41578.8i q^{32} +(-1631.72 - 942.077i) q^{33} +(1993.38 - 1150.88i) q^{34} -76276.2 q^{35} +(32475.8 + 56249.7i) q^{36} +(-60406.5 - 34875.7i) q^{37} +(5063.43 - 8770.12i) q^{38} -3401.08i q^{39} +(-30060.4 + 52066.2i) q^{40} -111493. q^{41} +24447.6i q^{42} +(40434.4 - 68457.4i) q^{43} +38510.5 q^{44} +123685. i q^{45} +(140033. + 80848.3i) q^{46} +135508. q^{47} +(-6076.19 - 3508.09i) q^{48} +(36739.1 - 63634.0i) q^{49} +(-160063. + 92412.4i) q^{50} -827.108i q^{51} +(34757.6 + 60201.9i) q^{52} +(-75410.1 + 130614. i) q^{53} +80409.0 q^{54} +(63509.2 + 36667.0i) q^{55} +(-75323.1 - 130463. i) q^{56} +(-1819.48 - 3151.43i) q^{57} +(-222070. - 384637. i) q^{58} -61299.5 q^{59} +(35829.2 + 62058.1i) q^{60} +(76693.0 - 44278.7i) q^{61} +(293480. + 169441. i) q^{62} +(-268399. - 154960. i) q^{63} +418519. q^{64} +132375. i q^{65} +(11752.3 - 20355.5i) q^{66} +(117617. - 203719. i) q^{67} +(8452.70 + 14640.5i) q^{68} +(50319.2 - 29051.8i) q^{69} -951536. i q^{70} +(-105906. + 61144.9i) q^{71} +(-211551. + 122139. i) q^{72} +(-297679. + 171865. i) q^{73} +(435070. - 753563. i) q^{74} +66414.5i q^{75} +(64412.6 + 37188.7i) q^{76} +(-159137. + 91877.5i) q^{77} +42428.0 q^{78} +(435438. + 754200. i) q^{79} +(236494. + 136540. i) q^{80} +(-243949. + 422532. i) q^{81} -1.39086e6i q^{82} +(-420483. + 728298. i) q^{83} -179556. q^{84} +32192.3i q^{85} +(853998. + 504414. i) q^{86} -159596. q^{87} +144835. i q^{88} +(672657. + 388359. i) q^{89} -1.54295e6 q^{90} +(-287257. - 165848. i) q^{91} +(-593795. + 1.02848e6i) q^{92} +(105458. - 60886.4i) q^{93} +1.69045e6i q^{94} +(70816.9 + 122658. i) q^{95} +(93192.3 - 161414. i) q^{96} +1.04611e6 q^{97} +(793826. + 458315. i) q^{98} +(148983. + 258046. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

L-functions

Modular forms

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