LMFDB - Embedded newform 27.7.f.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, 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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.9309 - 2.28007i) q^{2} +(19.5181 + 18.6559i) q^{3} +(101.870 + 37.0775i) q^{4} +(-78.6006 - 93.6725i) q^{5} +(-209.851 - 285.740i) q^{6} +(149.932 - 54.5707i) q^{7} +(-504.967 - 291.543i) q^{8} +(32.9160 + 728.257i) q^{9} +O(q^{10})$	\(q+(-12.9309 - 2.28007i) q^{2} +(19.5181 + 18.6559i) q^{3} +(101.870 + 37.0775i) q^{4} +(-78.6006 - 93.6725i) q^{5} +(-209.851 - 285.740i) q^{6} +(149.932 - 54.5707i) q^{7} +(-504.967 - 291.543i) q^{8} +(32.9160 + 728.257i) q^{9} +(802.798 + 1390.49i) q^{10} +(-771.586 + 919.541i) q^{11} +(1296.59 + 2624.15i) q^{12} +(595.843 + 3379.19i) q^{13} +(-2063.18 + 363.795i) q^{14} +(213.406 - 3294.68i) q^{15} +(550.080 + 461.572i) q^{16} +(194.413 - 112.244i) q^{17} +(1234.84 - 9492.07i) q^{18} +(-4509.62 + 7810.89i) q^{19} +(-4533.86 - 12456.7i) q^{20} +(3944.46 + 1731.99i) q^{21} +(12073.9 - 10131.2i) q^{22} +(-4908.20 + 13485.2i) q^{23} +(-4417.03 - 15111.0i) q^{24} +(116.762 - 662.190i) q^{25} -45054.6i q^{26} +(-12943.8 + 14828.3i) q^{27} +17296.8 q^{28} +(-8347.98 - 1471.97i) q^{29} +(-10271.6 + 42116.6i) q^{30} +(53068.2 + 19315.3i) q^{31} +(17926.6 + 21364.1i) q^{32} +(-32214.8 + 3553.10i) q^{33} +(-2769.86 + 1008.15i) q^{34} +(-16896.5 - 9755.21i) q^{35} +(-23648.8 + 75407.6i) q^{36} +(-44133.5 - 76441.5i) q^{37} +(76122.8 - 90719.7i) q^{38} +(-51412.1 + 77071.6i) q^{39} +(12381.1 + 70217.0i) q^{40} +(93692.0 - 16520.4i) q^{41} +(-47056.4 - 31389.9i) q^{42} +(-54840.2 - 46016.4i) q^{43} +(-112695. + 65064.7i) q^{44} +(65630.4 - 60324.7i) q^{45} +(94214.7 - 163185. i) q^{46} +(31800.7 + 87371.7i) q^{47} +(2125.51 + 19271.2i) q^{48} +(-70622.8 + 59259.5i) q^{49} +(-3019.68 + 8296.50i) q^{50} +(5888.59 + 1436.14i) q^{51} +(-64593.8 + 366329. i) q^{52} +76273.2i q^{53} +(201185. - 162231. i) q^{54} +146783. q^{55} +(-91620.4 - 16155.1i) q^{56} +(-233738. + 68323.1i) q^{57} +(104591. + 38068.0i) q^{58} +(45458.9 + 54175.9i) q^{59} +(143898. - 327715. i) q^{60} +(22675.9 - 8253.36i) q^{61} +(-642181. - 370763. i) q^{62} +(44676.6 + 107393. i) q^{63} +(-206074. - 356931. i) q^{64} +(269704. - 321421. i) q^{65} +(424668. + 27507.0i) q^{66} +(-15960.5 - 90516.5i) q^{67} +(23966.5 - 4225.94i) q^{68} +(-347377. + 171639. i) q^{69} +(196245. + 164669. i) q^{70} +(-38826.1 + 22416.3i) q^{71} +(195696. - 377342. i) q^{72} +(141448. - 244995. i) q^{73} +(396395. + 1.08909e6i) q^{74} +(14632.7 - 10746.4i) q^{75} +(-749001. + 628486. i) q^{76} +(-65505.4 + 179974. i) q^{77} +(840534. - 879383. i) q^{78} +(42870.5 - 243131. i) q^{79} -87807.2i q^{80} +(-529274. + 47942.5i) q^{81} -1.24919e6 q^{82} +(-440070. - 77596.3i) q^{83} +(337602. + 322688. i) q^{84} +(-25795.2 - 9388.67i) q^{85} +(604214. + 720074. i) q^{86} +(-135476. - 184469. i) q^{87} +(657711. - 239387. i) q^{88} +(775996. + 448022. i) q^{89} +(-986206. + 630412. i) q^{90} +(273741. + 474133. i) q^{91} +(-999993. + 1.19174e6i) q^{92} +(675450. + 1.36703e6i) q^{93} +(-211999. - 1.20230e6i) q^{94} +(1.08612e6 - 191513. i) q^{95} +(-48672.0 + 751424. i) q^{96} +(-390147. - 327373. i) q^{97} +(1.04833e6 - 605255. i) q^{98} +(-695059. - 531645. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−12.9309	−	2.28007i	−1.61636	−	0.285009i	−0.708954	−	0.705254i	$-0.750833\pi$
$2$	−12.9309	−	2.28007i	−1.61636	−	0.285009i	−0.907410	+	0.420246i	$0.861944\pi$
$3$	19.5181	+	18.6559i	0.722894	+	0.690959i
$3$	19.5181	+	18.6559i	0.722894	+	0.690959i
$4$	101.870	+	37.0775i	1.59171	+	0.579336i
$5$	−78.6006	−	93.6725i	−0.628805	−	0.749380i	0.353753	−	0.935339i	$-0.384905\pi$
$5$	−78.6006	−	93.6725i	−0.628805	−	0.749380i	−0.982558	+	0.185959i	$0.940461\pi$
$6$	−209.851	−	285.740i	−0.971531	−	1.32287i
$7$	149.932	−	54.5707i	0.437119	−	0.159098i	−0.114081	−	0.993471i	$-0.536392\pi$
$7$	149.932	−	54.5707i	0.437119	−	0.159098i	0.551200	+	0.834373i	$0.314170\pi$
$8$	−504.967	−	291.543i	−0.986264	−	0.569420i
$9$	32.9160	+	728.257i	0.0451522	+	0.998980i
$10$	802.798	+	1390.49i	0.802798	+	1.39049i
$11$	−771.586	+	919.541i	−0.579704	+	0.690865i	−0.973592	−	0.228294i	$-0.926685\pi$
$11$	−771.586	+	919.541i	−0.579704	+	0.690865i	0.393888	+	0.919158i	$0.371130\pi$
$12$	1296.59	+	2624.15i	0.750342	+	1.51861i
$13$	595.843	+	3379.19i	0.271208	+	1.53809i	0.750756	+	0.660580i	$0.229689\pi$
$13$	595.843	+	3379.19i	0.271208	+	1.53809i	−0.479548	+	0.877515i	$0.659200\pi$
$14$	−2063.18	+	363.795i	−0.751888	+	0.132578i
$15$	213.406	−	3294.68i	0.0632315	−	0.976201i
$16$	550.080	+	461.572i	0.134297	+	0.112688i
$17$	194.413	−	112.244i	0.0395711	−	0.0228464i	−0.480084	−	0.877223i	$-0.659394\pi$
$17$	194.413	−	112.244i	0.0395711	−	0.0228464i	0.519655	+	0.854376i	$0.326060\pi$
$18$	1234.84	−	9492.07i	0.211736	−	1.62758i
$19$	−4509.62	+	7810.89i	−0.657474	+	1.13878i	0.323793	+	0.946128i	$0.395042\pi$
$19$	−4509.62	+	7810.89i	−0.657474	+	1.13878i	−0.981267	+	0.192651i	$0.938291\pi$
$20$	−4533.86	−	12456.7i	−0.566733	−	1.55709i
$21$	3944.46	+	1731.99i	0.425921	+	0.187020i
$22$	12073.9	−	10131.2i	1.13392	−	0.951468i
$23$	−4908.20	+	13485.2i	−0.403403	+	1.10834i	0.557191	+	0.830384i	$0.311879\pi$
$23$	−4908.20	+	13485.2i	−0.403403	+	1.10834i	−0.960594	+	0.277956i	$0.910343\pi$
$24$	−4417.03	−	15111.0i	−0.319519	−	1.09310i
$25$	116.762	−	662.190i	0.00747277	−	0.0423802i
$26$		−	45054.6i		−	2.56342i
$27$	−12943.8	+	14828.3i	−0.657614	+	0.753355i
$28$	17296.8			0.787939
$29$	−8347.98	−	1471.97i	−0.342285	−	0.0603540i	−0.000136405	−	1.00000i	$-0.500043\pi$
$29$	−8347.98	−	1471.97i	−0.342285	−	0.0603540i	−0.342148	+	0.939646i	$0.611155\pi$
$30$	−10271.6	+	42116.6i	−0.380431	+	1.55987i
$31$	53068.2	+	19315.3i	1.78135	+	0.648359i	0.999696	+	0.0246482i	$0.00784656\pi$
$31$	53068.2	+	19315.3i	1.78135	+	0.648359i	0.781655	+	0.623711i	$0.214376\pi$
$32$	17926.6	+	21364.1i	0.547076	+	0.651980i
$33$	−32214.8	+	3553.10i	−0.896424	+	0.0988704i
$34$	−2769.86	+	1008.15i	−0.0704727	+	0.0256500i
$35$	−16896.5	−	9755.21i	−0.394088	−	0.227527i
$36$	−23648.8	+	75407.6i	−0.506876	+	1.61625i
$37$	−44133.5	−	76441.5i	−0.871291	−	1.50912i	−0.860662	−	0.509176i	$-0.829950\pi$
$37$	−44133.5	−	76441.5i	−0.871291	−	1.50912i	−0.0106286	−	0.999944i	$-0.503383\pi$
$38$	76122.8	−	90719.7i	1.38728	−	1.65330i
$39$	−51412.1	+	77071.6i	−0.866706	+	1.29927i
$40$	12381.1	+	70217.0i	0.193455	+	1.09714i
$41$	93692.0	−	16520.4i	1.35941	−	0.239701i	0.554049	−	0.832484i	$-0.313082\pi$
$41$	93692.0	−	16520.4i	1.35941	−	0.239701i	0.805362	+	0.592783i	$0.201971\pi$
$42$	−47056.4	−	31389.9i	−0.635142	−	0.423684i
$43$	−54840.2	−	46016.4i	−0.689754	−	0.578772i	0.229085	−	0.973407i	$-0.426427\pi$
$43$	−54840.2	−	46016.4i	−0.689754	−	0.578772i	−0.918838	+	0.394635i	$0.870871\pi$
$44$	−112695.	+	65064.7i	−1.32296	+	0.763814i
$45$	65630.4	−	60324.7i	0.720224	−	0.662000i
$46$	94214.7	−	163185.i	0.967932	−	1.67651i
$47$	31800.7	+	87371.7i	0.306297	+	0.841545i	0.993370	+	0.114957i	$0.0366730\pi$
$47$	31800.7	+	87371.7i	0.306297	+	0.841545i	−0.687073	+	0.726588i	$0.741105\pi$
$48$	2125.51	+	19271.2i	0.0192194	+	0.174255i
$49$	−70622.8	+	59259.5i	−0.600284	+	0.503698i
$50$	−3019.68	+	8296.50i	−0.0241574	+	0.0663720i
$51$	5888.59	+	1436.14i	0.0443916	+	0.0108265i
$52$	−64593.8	+	366329.i	−0.459389	+	2.60532i
$53$			76273.2i			0.512324i	0.966634	+	0.256162i	$0.0824580\pi$
$53$			76273.2i			0.512324i	−0.966634	+	0.256162i	$0.917542\pi$
$54$	201185.	−	162231.i	1.27766	−	1.03027i
$55$	146783.			0.882241
$56$	−91620.4	−	16155.1i	−0.521708	−	0.0919913i
$57$	−233738.	+	68323.1i	−1.26213	+	0.368929i
$58$	104591.	+	38068.0i	0.536055	+	0.195108i
$59$	45458.9	+	54175.9i	0.221342	+	0.263785i	0.865276	−	0.501296i	$-0.167143\pi$
$59$	45458.9	+	54175.9i	0.221342	+	0.263785i	−0.643934	+	0.765081i	$0.722699\pi$
$60$	143898.	−	327715.i	0.666194	−	1.51720i
$61$	22675.9	−	8253.36i	0.0999022	−	0.0363614i	−0.291585	−	0.956545i	$-0.594183\pi$
$61$	22675.9	−	8253.36i	0.0999022	−	0.0363614i	0.391488	+	0.920183i	$0.371961\pi$
$62$	−642181.	−	370763.i	−2.69453	−	1.55568i
$63$	44676.6	+	107393.i	0.178673	+	0.429490i
$64$	−206074.	−	356931.i	−0.786111	−	1.36158i
$65$	269704.	−	321421.i	0.982081	−	1.17040i
$66$	424668.	+	27507.0i	1.47713	+	0.0956780i
$67$	−15960.5	−	90516.5i	−0.0530667	−	0.300956i	0.946710	−	0.322087i	$-0.104384\pi$
$67$	−15960.5	−	90516.5i	−0.0530667	−	0.300956i	−0.999777	+	0.0211310i	$0.993273\pi$
$68$	23966.5	−	4225.94i	0.0762215	−	0.0134399i
$69$	−347377.	+	171639.i	−1.05743	+	0.522478i
$70$	196245.	+	164669.i	0.572142	+	0.480084i
$71$	−38826.1	+	22416.3i	−0.108480	+	0.0626309i	−0.553258	−	0.833010i	$-0.686616\pi$
$71$	−38826.1	+	22416.3i	−0.108480	+	0.0626309i	0.444778	+	0.895641i	$0.353282\pi$
$72$	195696.	−	377342.i	0.524307	−	1.01097i
$73$	141448.	−	244995.i	0.363603	−	0.629779i	−0.624948	−	0.780667i	$-0.714880\pi$
$73$	141448.	−	244995.i	0.363603	−	0.629779i	0.988551	+	0.150887i	$0.0482131\pi$
$74$	396395.	+	1.08909e6i	0.978211	+	2.68761i
$75$	14632.7	−	10746.4i	0.0346850	−	0.0254730i
$76$	−749001.	+	628486.i	−1.70625	+	1.43171i
$77$	−65505.4	+	179974.i	−0.143484	+	0.394220i
$78$	840534.	−	879383.i	1.77122	−	1.85308i
$79$	42870.5	−	243131.i	0.0869515	−	0.493127i	−0.909967	−	0.414681i	$-0.863893\pi$
$79$	42870.5	−	243131.i	0.0869515	−	0.493127i	0.996918	−	0.0784457i	$-0.0249957\pi$
$80$		−	87807.2i		−	0.171498i
$81$	−529274.	+	47942.5i	−0.995923	+	0.0902123i
$82$	−1.24919e6			−2.26562
$83$	−440070.	−	77596.3i	−0.769640	−	0.135708i	−0.224978	−	0.974364i	$-0.572231\pi$
$83$	−440070.	−	77596.3i	−0.769640	−	0.135708i	−0.544662	+	0.838655i	$0.683342\pi$
$84$	337602.	+	322688.i	0.569597	+	0.544433i
$85$	−25795.2	−	9388.67i	−0.0420031	−	0.0152879i
$86$	604214.	+	720074.i	0.949938	+	1.13209i
$87$	−135476.	−	184469.i	−0.205734	−	0.280134i
$88$	657711.	−	239387.i	0.965133	−	0.351280i
$89$	775996.	+	448022.i	1.10075	+	0.635520i	0.936419	−	0.350885i	$-0.114119\pi$
$89$	775996.	+	448022.i	1.10075	+	0.635520i	0.164334	+	0.986405i	$0.447453\pi$
$90$	−986206.	+	630412.i	−1.35282	+	0.864763i
$91$	273741.	+	474133.i	0.363258	+	0.629182i
$92$	−999993.	+	1.19174e6i	−1.28420	+	1.53045i
$93$	675450.	+	1.36703e6i	0.839740	+	1.69954i
$94$	−211999.	−	1.20230e6i	−0.255241	−	1.44754i
$95$	1.08612e6	−	191513.i	1.26680	−	0.223371i
$96$	−48672.0	+	751424.i	−0.0550130	+	0.849320i
$97$	−390147.	−	327373.i	−0.427478	−	0.358696i	0.403521	−	0.914970i	$-0.367786\pi$
$97$	−390147.	−	327373.i	−0.427478	−	0.358696i	−0.830999	+	0.556274i	$0.812231\pi$
$98$	1.04833e6	−	605255.i	1.11384	−	0.643073i
$99$	−695059.	−	531645.i	−0.716335	−	0.547919i
$100$	36446.8	−	63127.8i	0.0364468	−	0.0631278i
$101$	−81898.4	−	225014.i	−0.0794898	−	0.218396i	0.893581	−	0.448901i	$-0.148184\pi$
$101$	−81898.4	−	225014.i	−0.0794898	−	0.218396i	−0.973071	+	0.230505i	$0.925962\pi$
$102$	−72870.4	−	31997.0i	−0.0686674	−	0.0301515i
$103$	−633486.	+	531558.i	−0.579730	+	0.486451i	−0.884858	−	0.465860i	$-0.845745\pi$
$103$	−633486.	+	531558.i	−0.579730	+	0.486451i	0.305129	+	0.952311i	$0.401301\pi$
$104$	684299.	−	1.88010e6i	0.608339	−	1.67140i
$105$	−147797.	−	505623.i	−0.127672	−	0.436776i
$106$	173908.	−	986283.i	0.146017	−	0.828102i
$107$		−	1.25451e6i		−	1.02405i	−0.858970	−	0.512026i	$-0.828895\pi$
$107$		−	1.25451e6i		−	1.02405i	0.858970	−	0.512026i	$-0.171105\pi$
$108$	−1.86838e6	+	1.03063e6i	−1.48318	+	0.818145i
$109$	1.71372e6			1.32331			0.661653	−	0.749810i	$-0.269855\pi$
$109$	1.71372e6			1.32331			0.661653	+	0.749810i	$0.269855\pi$
$110$	−1.89804e6	−	334675.i	−1.42602	−	0.251446i
$111$	564679.	−	2.31534e6i	0.412888	−	1.69296i
$112$	107663.	+	39186.0i	0.0766322	+	0.0278919i
$113$	−1.30575e6	−	1.55613e6i	−0.904947	−	1.07847i	−0.996576	−	0.0826810i	$-0.973652\pi$
$113$	−1.30575e6	−	1.55613e6i	−0.904947	−	1.07847i	0.0916287	−	0.995793i	$-0.470793\pi$
$114$	3.17823e6	−	350541.i	2.14522	−	0.236605i
$115$	1.64898e6	−	600179.i	1.08423	−	0.394627i
$116$	−795828.	−	459472.i	−0.509853	−	0.294364i
$117$	−2.44131e6	+	545156.i	−1.52428	+	0.340379i
$118$	−464301.	−	804193.i	−0.282588	−	0.489457i
$119$	23023.4	−	27438.2i	0.0136625	−	0.0162823i
$120$	−1.06830e6	+	1.60149e6i	−0.618231	+	0.926786i
$121$	57418.6	+	325637.i	0.0324113	+	0.183814i
$122$	−312039.	+	55020.8i	−0.171842	+	0.0303003i
$123$	2.13690e6	+	1.42546e6i	1.14833	+	0.766019i
$124$	4.68988e6	+	3.93527e6i	2.45978	+	2.06400i
$125$	−1.72587e6	+	996430.i	−0.883644	+	0.510172i
$126$	−332847.	−	1.49055e6i	−0.166392	−	0.745135i
$127$	−549915.	+	952481.i	−0.268463	+	0.464991i	−0.968465	−	0.249149i	$-0.919849\pi$
$127$	−549915.	+	952481.i	−0.268463	+	0.464991i	0.700002	+	0.714141i	$0.253182\pi$
$128$	1.24043e6	+	3.40807e6i	0.591485	+	1.62509i
$129$	−211903.	−	1.92125e6i	−0.0987114	−	0.894982i
$130$	−4.22038e6	+	3.54132e6i	−1.92098	+	1.61189i
$131$	864346.	−	2.37477e6i	0.384480	−	1.05635i	−0.584968	−	0.811056i	$-0.698893\pi$
$131$	864346.	−	2.37477e6i	0.384480	−	1.05635i	0.969449	−	0.245295i	$-0.0788847\pi$
$132$	−3.41345e6	−	832490.i	−1.48413	−	0.361957i
$133$	−249889.	+	1.41719e6i	−0.106217	+	0.602385i
$134$			1.20685e6i			0.501579i
$135$	2.40639e6	+	46967.0i	0.978060	+	0.0190894i
$136$	−130896.			−0.0520367
$137$	1.08435e6	+	191200.i	0.421703	+	0.0743576i	0.380473	−	0.924792i	$-0.375761\pi$
$137$	1.08435e6	+	191200.i	0.421703	+	0.0743576i	0.0412300	+	0.999150i	$0.486872\pi$
$138$	4.88325e6	−	1.42740e6i	1.85811	−	0.543137i
$139$	3.00005e6	+	1.09193e6i	1.11708	+	0.406584i	0.833586	−	0.552390i	$-0.186284\pi$
$139$	3.00005e6	+	1.09193e6i	1.11708	+	0.406584i	0.283494	+	0.958974i	$0.408506\pi$
$140$	−1.35954e6	−	1.62024e6i	−0.495460	−	0.590466i
$141$	−1.00931e6	+	2.29860e6i	−0.360052	+	0.819987i
$142$	553168.	−	201337.i	0.193193	−	0.0703166i
$143$	−3.56705e6	−	2.05944e6i	−1.21984	−	0.704272i
$144$	−318036.	+	415792.i	−0.106510	+	0.139248i
$145$	518273.	+	897675.i	0.170002	+	0.294452i
$146$	−2.38765e6	+	2.84550e6i	−0.767208	+	0.914323i
$147$	−2.48396e6	−	160894.i	−0.781976	−	0.0506509i
$148$	−1.66160e6	−	9.42342e6i	−0.512557	−	2.90685i
$149$	1.56457e6	−	275877.i	0.472974	−	0.0833981i	0.0679200	−	0.997691i	$-0.478364\pi$
$149$	1.56457e6	−	275877.i	0.472974	−	0.0833981i	0.405054	+	0.914293i	$0.367253\pi$
$150$	−213717.	+	105598.i	−0.0633236	+	0.0312882i
$151$	462785.	+	388323.i	0.134415	+	0.112788i	0.707517	−	0.706697i	$-0.249815\pi$
$151$	462785.	+	388323.i	0.134415	+	0.112788i	−0.573101	+	0.819484i	$0.694260\pi$
$152$	4.55442e6	−	2.62949e6i	1.29689	−	0.748758i
$153$	88141.9	+	137888.i	0.0246098	+	0.0384992i
$154$	1.25740e6	−	2.17788e6i	0.344279	−	0.596309i
$155$	−2.36189e6	−	6.48923e6i	−0.634255	−	1.74260i
$156$	−8.09495e6	+	5.94502e6i	−2.13226	+	1.56596i
$157$	−5.06563e6	+	4.25057e6i	−1.30899	+	1.09837i	−0.320469	+	0.947259i	$0.603840\pi$
$157$	−5.06563e6	+	4.25057e6i	−1.30899	+	1.09837i	−0.988517	+	0.151110i	$0.951715\pi$
$158$	−1.10871e6	+	3.04615e6i	−0.281091	+	0.772291i
$159$	−1.42294e6	+	1.48871e6i	−0.353995	+	0.370356i
$160$	592187.	−	3.35846e6i	0.144577	−	0.819936i
$161$			2.28970e6i			0.548657i
$162$	6.95331e6	+	586841.i	1.63549	+	0.138031i
$163$	3.90233e6			0.901076			0.450538	−	0.892757i	$-0.351232\pi$
$163$	3.90233e6			0.901076			0.450538	+	0.892757i	$0.351232\pi$
$164$	1.01569e7	+	1.79094e6i	2.30266	+	0.406021i
$165$	2.86493e6	+	2.73836e6i	0.637767	+	0.609592i
$166$	5.51359e6	+	2.00678e6i	1.20534	+	0.438708i
$167$	3.60932e6	+	4.30142e6i	0.774955	+	0.923555i	0.998694	−	0.0510938i	$-0.0162707\pi$
$167$	3.60932e6	+	4.30142e6i	0.774955	+	0.923555i	−0.223739	+	0.974649i	$0.571826\pi$
$168$	−1.48687e6	−	2.02458e6i	−0.313578	−	0.426979i
$169$	−6.52821e6	+	2.37607e6i	−1.35249	+	0.492266i
$170$	312148.	+	180219.i	0.0635352	+	0.0366820i
$171$	−5.83677e6	−	3.02705e6i	−1.16730	−	0.605385i
$172$	−3.88038e6	−	6.72101e6i	−0.762586	−	1.32084i
$173$	377611.	−	450019.i	0.0729299	−	0.0869145i	−0.728346	−	0.685210i	$-0.759711\pi$
$173$	377611.	−	450019.i	0.0729299	−	0.0869145i	0.801276	+	0.598295i	$0.204155\pi$
$174$	1.33123e6	+	2.69425e6i	0.252700	+	0.511435i
$175$	−18629.9	−	105655.i	−0.00347613	−	0.0197141i
$176$	−848868.	+	149678.i	−0.155705	+	0.0274550i
$177$	−123424.	+	1.90549e6i	−0.0222577	+	0.343626i
$178$	−9.01282e6	−	7.56266e6i	−1.59809	−	1.34096i
$179$	−301502.	+	174072.i	−0.0525691	+	0.0303508i	−0.526054	−	0.850451i	$-0.676329\pi$
$179$	−301502.	+	174072.i	−0.0525691	+	0.0303508i	0.473485	+	0.880802i	$0.342996\pi$
$180$	8.92243e6	−	3.71184e6i	1.52991	−	0.636461i
$181$	−371178.	+	642900.i	−0.0625961	+	0.108420i	−0.895625	−	0.444810i	$-0.853271\pi$
$181$	−371178.	+	642900.i	−0.0625961	+	0.108420i	0.833029	+	0.553229i	$0.186605\pi$
$182$	−2.45867e6	−	6.75513e6i	−0.407836	−	1.12052i
$183$	596565.	+	261949.i	0.0973430	+	0.0427428i
$184$	6.40999e6	−	5.37862e6i	1.02897	−	0.863410i
$185$	−3.69155e6	+	1.01424e7i	−0.583033	+	1.60187i
$186$	−5.61726e6	−	1.92171e7i	−0.872943	−	2.98640i
$187$	−46793.0	+	265377.i	−0.00715577	+	0.0405824i
$188$			1.00796e7i			1.51695i
$189$	−1.13150e6	+	2.92959e6i	−0.167598	+	0.433931i
$190$	−1.44812e7			−2.11128
$191$	6.33450e6	+	1.11694e6i	0.909101	+	0.160299i	0.608595	−	0.793481i	$-0.291733\pi$
$191$	6.33450e6	+	1.11694e6i	0.909101	+	0.160299i	0.300506	+	0.953780i	$0.402845\pi$
$192$	2.63668e6	−	1.08111e7i	0.372523	−	1.52745i
$193$	1.05983e7	+	3.85746e6i	1.47422	+	0.536573i	0.949244	−	0.314542i	$-0.101851\pi$
$193$	1.05983e7	+	3.85746e6i	1.47422	+	0.536573i	0.524979	+	0.851115i	$0.324073\pi$
$194$	4.29853e6	+	5.12279e6i	0.588728	+	0.701619i
$195$	1.12605e7	−	1.24197e6i	1.51864	−	0.167497i
$196$	−9.39150e6	+	3.41823e6i	−1.24729	+	0.453976i
$197$	−9.90910e6	−	5.72102e6i	−1.29609	−	0.748299i	−0.316365	−	0.948638i	$-0.602462\pi$
$197$	−9.90910e6	−	5.72102e6i	−1.29609	−	0.748299i	−0.979727	+	0.200339i	$0.935796\pi$
$198$	7.77556e6	+	8.45944e6i	1.00170	+	1.08980i
$199$	2.17553e6	+	3.76813e6i	0.276062	+	0.478153i	0.970402	−	0.241493i	$-0.0776372\pi$
$199$	2.17553e6	+	3.76813e6i	0.276062	+	0.478153i	−0.694341	+	0.719646i	$0.744304\pi$
$200$	−252018.	+	300343.i	−0.0315022	+	0.0375429i
$201$	1.37715e6	−	2.06447e6i	0.169587	−	0.254226i
$202$	545974.	+	3.09637e6i	0.0662396	+	0.375663i
$203$	−1.33196e6	+	234860.i	−0.159221	+	0.0280750i
$204$	546620.	+	364633.i	0.0643865	+	0.0429503i
$205$	−8.91176e6	−	7.47785e6i	−1.03443	−	0.867991i
$206$	9.40355e6	−	5.42914e6i	1.07570	−	0.621054i
$207$	−9.98222e6	−	3.13055e6i	−1.12542	−	0.352947i
$208$	−1.23198e6	+	2.13385e6i	−0.136903	+	0.237123i
$209$	−3.70287e6	−	1.01735e7i	−0.405601	−	1.11438i
$210$	758290.	+	6.87515e6i	0.0818799	+	0.742377i
$211$	1.21112e6	−	1.01625e6i	0.128925	−	0.108181i	−0.576045	−	0.817418i	$-0.695405\pi$
$211$	1.21112e6	−	1.01625e6i	0.128925	−	0.108181i	0.704970	+	0.709237i	$0.250960\pi$
$212$	−2.82802e6	+	7.76992e6i	−0.296807	+	0.815472i
$213$	−1.17601e6	−	286812.i	−0.121695	−	0.0296796i
$214$	−2.86037e6	+	1.62219e7i	−0.291864	+	1.65524i
$215$			8.75394e6i			0.880822i
$216$	1.08593e7	−	3.71412e6i	1.07756	−	0.368549i
$217$	9.01067e6			0.881816
$218$	−2.21600e7	−	3.90740e6i	−2.13894	−	0.377154i
$219$	7.33139e6	−	2.14301e6i	0.697998	−	0.204029i
$220$	1.49527e7	+	5.44234e6i	1.40427	+	0.511114i
$221$	495135.	+	590079.i	0.0458719	+	0.0546680i
$222$	−1.25810e7	+	2.86520e7i	−1.14989	+	2.61876i
$223$	2.59042e6	−	942835.i	0.233591	−	0.0850200i	−0.222573	−	0.974916i	$-0.571445\pi$
$223$	2.59042e6	−	942835.i	0.233591	−	0.0850200i	0.456163	+	0.889896i	$0.349223\pi$
$224$	3.85362e6	+	2.22489e6i	0.342867	+	0.197954i
$225$	486088.	+	63236.0i	0.0426744	+	0.00555159i
$226$	1.33364e7	+	2.30993e7i	1.15535	+	2.00113i
$227$	1.26828e7	−	1.51148e7i	1.08427	−	1.29218i	0.130566	−	0.991440i	$-0.458321\pi$
$227$	1.26828e7	−	1.51148e7i	1.08427	−	1.29218i	0.953705	−	0.300744i	$-0.0972350\pi$
$228$	−2.63441e7	−	1.70639e6i	−2.22269	−	0.143970i
$229$	−269055.	−	1.52589e6i	−0.0224044	−	0.127062i	0.971554	−	0.236817i	$-0.0761043\pi$
$229$	−269055.	−	1.52589e6i	−0.0224044	−	0.127062i	−0.993959	+	0.109756i	$0.964993\pi$
$230$	−2.26912e7	+	4.00108e6i	−1.86498	+	0.328847i
$231$	−4.63613e6	+	2.29071e6i	−0.376114	+	0.185838i
$232$	3.78631e6	+	3.17709e6i	0.303216	+	0.254429i
$233$	−1.16623e7	+	6.73323e6i	−0.921969	+	0.532299i	−0.884263	−	0.466990i	$-0.845338\pi$
$233$	−1.16623e7	+	6.73323e6i	−0.921969	+	0.532299i	−0.0377061	+	0.999289i	$0.512005\pi$
$234$	3.28113e7	−	1.48302e6i	2.56080	−	0.115744i
$235$	5.68478e6	−	9.84632e6i	0.438036	−	0.758701i
$236$	2.62218e6	+	7.20437e6i	0.199492	+	0.548101i
$237$	5.37257e6	−	3.94567e6i	0.403587	−	0.296399i
$238$	−360275.	+	302307.i	−0.0267241	+	0.0224242i
$239$	6.19108e6	−	1.70098e7i	0.453495	−	1.24597i	−0.476753	−	0.879037i	$-0.658187\pi$
$239$	6.19108e6	−	1.70098e7i	0.453495	−	1.24597i	0.930248	−	0.366930i	$-0.119591\pi$
$240$	1.63812e6	−	1.71383e6i	0.118498	−	0.123975i
$241$	1.41936e6	−	8.04961e6i	0.101401	−	0.575074i	−0.891196	−	0.453619i	$-0.850133\pi$
$241$	1.41936e6	−	8.04961e6i	0.101401	−	0.575074i	0.992597	−	0.121455i	$-0.0387561\pi$
$242$		−	4.34171e6i		−	0.306347i
$243$	−1.12249e7	−	8.93833e6i	−0.782280	−	0.622927i
$244$	2.61600e6			0.180081
$245$	1.11020e7	+	1.95758e6i	0.754922	+	0.133113i
$246$	−2.43819e7	−	2.33048e7i	−1.63780	−	1.56545i
$247$	−2.90815e7	−	1.05848e7i	−1.92986	−	0.702412i
$248$	−2.11665e7	−	2.52252e7i	−1.38769	−	1.65379i
$249$	−7.14173e6	−	9.72444e6i	−0.462600	−	0.629892i
$250$	2.45890e7	−	8.94965e6i	1.57369	−	0.572778i
$251$	1.60397e7	+	9.26055e6i	1.01432	+	0.585619i	0.912454	−	0.409178i	$-0.134185\pi$
$251$	1.60397e7	+	9.26055e6i	1.01432	+	0.585619i	0.101868	+	0.994798i	$0.467518\pi$
$252$	569342.	+	1.25965e7i	0.0355772	+	0.787135i
$253$	−8.61306e6	−	1.49183e7i	−0.531859	−	0.921206i
$254$	9.28263e6	−	1.10626e7i	0.566461	−	0.675081i
$255$	−328320.	−	664481.i	−0.0198005	−	0.0400739i
$256$	−3.68892e6	−	2.09209e7i	−0.219877	−	1.24698i
$257$	1.08807e7	−	1.91856e6i	0.640998	−	0.113025i	0.156304	−	0.987709i	$-0.450042\pi$
$257$	1.08807e7	−	1.91856e6i	0.640998	−	0.113025i	0.484694	+	0.874684i	$0.338931\pi$
$258$	−1.64048e6	+	2.53267e7i	−0.0955241	+	1.47475i
$259$	−1.07885e7	−	9.05261e6i	−0.620956	−	0.521044i
$260$	3.93921e7	−	2.27430e7i	2.24124	−	1.29398i
$261$	797193.	−	6.12792e6i	0.0448376	−	0.344661i
$262$	−1.65914e7	+	2.87372e7i	−0.922529	+	1.59787i
$263$	1.06253e7	+	2.91928e7i	0.584082	+	1.60475i	0.781136	+	0.624360i	$0.214640\pi$
$263$	1.06253e7	+	2.91928e7i	0.584082	+	1.60475i	−0.197054	+	0.980393i	$0.563137\pi$
$264$	1.73033e7	+	7.59779e6i	0.940409	+	0.412929i
$265$	7.14470e6	−	5.99512e6i	0.383925	−	0.322152i
$266$	6.46260e6	−	1.77558e7i	0.343370	−	0.943401i
$267$	6.78777e6	+	2.32215e7i	0.356610	+	1.21999i
$268$	1.73023e6	−	9.81265e6i	0.0898878	−	0.509779i
$269$			2.72611e7i			1.40051i	0.713893	+	0.700254i	$0.246930\pi$
$269$			2.72611e7i			1.40051i	−0.713893	+	0.700254i	$0.753070\pi$
$270$	−3.10098e7	−	6.09407e6i	−1.57546	−	0.309611i
$271$	2.15342e7			1.08199			0.540993	−	0.841027i	$-0.318048\pi$
$271$	2.15342e7			1.08199			0.540993	+	0.841027i	$0.318048\pi$
$272$	158751.	+	27992.1i	0.00788879	+	0.00139101i
$273$	−3.50246e6	+	1.43611e7i	−0.172141	+	0.705829i
$274$	−1.35857e7	−	4.94477e6i	−0.660433	−	0.240378i
$275$	518819.	+	618304.i	0.0249470	+	0.0297306i
$276$	−4.17511e7	+	4.60490e6i	−1.98582	+	0.219025i
$277$	−2.04068e6	+	742746.i	−0.0960141	+	0.0349463i	−0.389581	−	0.920992i	$-0.627380\pi$
$277$	−2.04068e6	+	742746.i	−0.0960141	+	0.0349463i	0.293566	+	0.955939i	$0.405158\pi$
$278$	−3.63037e7	−	2.09600e7i	−1.68973	−	0.975565i
$279$	−1.23197e7	+	3.92831e7i	−0.567266	+	1.80881i
$280$	5.68812e6	+	9.85211e6i	0.259116	+	0.448803i
$281$	−4.93973e6	+	5.88694e6i	−0.222630	+	0.265320i	−0.865785	−	0.500416i	$-0.833181\pi$
$281$	−4.93973e6	+	5.88694e6i	−0.222630	+	0.265320i	0.643155	+	0.765736i	$0.277625\pi$
$282$	1.82922e7	−	2.74218e7i	0.815679	−	1.22278i
$283$	−1.03182e6	−	5.85175e6i	−0.0455245	−	0.258182i	0.953548	−	0.301241i	$-0.0974009\pi$
$283$	−1.03182e6	−	5.85175e6i	−0.0455245	−	0.258182i	−0.999073	+	0.0430586i	$0.986290\pi$
$284$	−4.78634e6	+	843961.i	−0.208953	+	0.0368441i
$285$	2.47720e7	+	1.65246e7i	1.07010	+	0.713834i
$286$	4.14296e7	+	3.47635e7i	1.77098	+	1.48602i
$287$	1.31459e7	−	7.58978e6i	0.556089	−	0.321058i
$288$	−1.49685e7	+	1.37584e7i	−0.626614	+	0.575957i
$289$	−1.20436e7	+	2.08601e7i	−0.498956	+	0.864217i
$290$	−4.65498e6	−	1.27895e7i	−0.190864	−	0.524394i
$291$	−1.50753e6	−	1.36682e7i	−0.0611768	−	0.554669i
$292$	2.34930e7	−	1.97130e7i	0.943605	−	0.791778i
$293$	−348489.	+	957466.i	−0.0138544	+	0.0380645i	−0.946427	−	0.322918i	$-0.895336\pi$
$293$	−348489.	+	957466.i	−0.0138544	+	0.0380645i	0.932573	+	0.360982i	$0.117559\pi$
$294$	3.17531e7	+	7.74412e6i	1.24952	+	0.304740i
$295$	1.50169e6	−	8.51651e6i	0.0584944	−	0.331738i
$296$			5.14672e7i			1.98452i
$297$	−3.64795e6	−	2.33437e7i	−0.139245	−	0.891045i
$298$	−2.08604e7			−0.788268
$299$	−4.84935e7	−	8.55072e6i	−1.81414	−	0.319881i
$300$	1.88908e6	−	552189.i	0.0699659	−	0.0204514i
$301$	−1.07335e7	−	3.90666e6i	−0.393586	−	0.143254i
$302$	−5.09883e6	−	6.07655e6i	−0.185119	−	0.220616i
$303$	2.59933e6	−	5.91974e6i	0.0934402	−	0.212802i
$304$	−6.08593e6	+	2.21510e6i	−0.216624	+	0.0788446i
$305$	−2.55545e6	−	1.47539e6i	−0.0900675	−	0.0520005i
$306$	−825362.	−	1.98398e6i	−0.0288058	−	0.0692427i
$307$	1.89526e7	+	3.28268e7i	0.655018	+	1.13452i	0.981889	+	0.189455i	$0.0606721\pi$
$307$	1.89526e7	+	3.28268e7i	0.655018	+	1.13452i	−0.326872	+	0.945069i	$0.605995\pi$
$308$	−1.33460e7	+	1.59051e7i	−0.456772	+	0.544359i
$309$	−2.22812e7	−	1.44322e6i	−0.755201	−	0.0489167i
$310$	1.57455e7	+	8.92969e7i	0.528531	+	2.99745i
$311$	−1.88396e7	+	3.32193e6i	−0.626311	+	0.110435i	−0.477790	−	0.878474i	$-0.658562\pi$
$311$	−1.88396e7	+	3.32193e6i	−0.626311	+	0.110435i	−0.148520	+	0.988909i	$0.547451\pi$
$312$	4.84311e7	−	2.39298e7i	1.59463	−	0.787907i
$313$	−2.86596e7	−	2.40482e7i	−0.934623	−	0.784242i	0.0420185	−	0.999117i	$-0.486621\pi$
$313$	−2.86596e7	−	2.40482e7i	−0.934623	−	0.784242i	−0.976642	+	0.214875i	$0.931066\pi$
$314$	7.51949e7	−	4.34138e7i	2.42884	−	1.40229i
$315$	6.54813e6	−	1.26261e7i	0.209501	−	0.403959i
$316$	1.33819e7	−	2.31781e7i	0.424088	−	0.734541i
$317$	3.27787e6	+	9.00588e6i	0.102900	+	0.282715i	0.980449	−	0.196771i	$-0.0630455\pi$
$317$	3.27787e6	+	9.00588e6i	0.102900	+	0.282715i	−0.877550	+	0.479486i	$0.840823\pi$
$318$	2.17943e7	−	1.60060e7i	0.677739	−	0.497739i
$319$	7.79473e6	−	6.54055e6i	0.240120	−	0.201485i
$320$	−1.72371e7	+	4.73585e7i	−0.526034	+	1.44527i
$321$	2.34040e7	−	2.44857e7i	0.707578	−	0.740282i
$322$	5.22068e6	−	2.96079e7i	0.156372	−	0.886830i
$323$			2.02471e6i			0.0600836i
$324$	−5.56945e7	−	1.47403e7i	−1.63748	−	0.433381i
$325$	2.30724e6			0.0672114
$326$	−5.04607e7	−	8.89759e6i	−1.45647	−	0.256814i
$327$	3.34486e7	+	3.19710e7i	0.956610	+	0.914350i
$328$	−5.21278e7	−	1.89730e7i	−1.47723	−	0.537667i
$329$	9.53588e6	+	1.13644e7i	0.267777	+	0.319124i
$330$	−3.08025e7	−	4.19418e7i	−0.857125	−	1.16709i
$331$	−2.50263e7	+	9.10881e6i	−0.690100	+	0.251176i	−0.663178	−	0.748462i	$-0.730793\pi$
$331$	−2.50263e7	+	9.10881e6i	−0.690100	+	0.251176i	−0.0269219	+	0.999638i	$0.508571\pi$
$332$	−4.19527e7	−	2.42214e7i	−1.14642	−	0.661889i
$333$	5.42163e7	−	3.46566e7i	1.46824	−	0.938542i
$334$	−3.68643e7	−	6.38509e7i	−0.989388	−	1.71367i
$335$	−7.22440e6	+	8.60971e6i	−0.192162	+	0.229010i
$336$	1.37033e6	+	2.77338e6i	0.0361249	+	0.0731126i
$337$	1.15210e6	+	6.53388e6i	0.0301023	+	0.170719i	0.996153	−	0.0876352i	$-0.0279310\pi$
$337$	1.15210e6	+	6.53388e6i	0.0301023	+	0.170719i	−0.966050	+	0.258354i	$0.916820\pi$
$338$	8.98334e7	−	1.58400e7i	2.32642	−	0.410210i
$339$	3.54519e6	−	5.47326e7i	0.0909999	−	1.40490i
$340$	−2.27963e6	−	1.91284e6i	−0.0580000	−	0.0486678i
$341$	−5.87079e7	+	3.38950e7i	−1.48059	+	0.854816i
$342$	6.85728e7	+	5.24508e7i	1.71425	+	1.31122i
$343$	−1.67405e7	+	2.89953e7i	−0.414844	+	0.718531i
$344$	1.42768e7	+	3.92251e7i	0.350715	+	0.963581i
$345$	4.33819e7	+	1.90488e7i	1.05645	+	0.463884i
$346$	−5.90893e6	+	4.95818e6i	−0.142653	+	0.119700i
$347$	1.20592e7	−	3.31324e7i	0.288623	−	0.792985i	−0.707637	−	0.706576i	$-0.750239\pi$
$347$	1.20592e7	−	3.31324e7i	0.288623	−	0.792985i	0.996260	−	0.0864087i	$-0.0275391\pi$
$348$	−6.96124e6	−	2.38149e7i	−0.165177	−	0.565082i
$349$	−7.48623e6	+	4.24565e7i	−0.176111	+	0.998776i	0.760742	+	0.649054i	$0.224835\pi$
$349$	−7.48623e6	+	4.24565e7i	−0.176111	+	0.998776i	−0.936854	+	0.349722i	$0.886276\pi$
$350$			1.40870e6i			0.0328559i
$351$	−5.78202e7	−	3.49043e7i	−1.33708	−	0.807157i
$352$	−3.34771e7			−0.767572
$353$	5.45917e7	+	9.62600e6i	1.24109	+	0.218837i	0.755382	−	0.655285i	$-0.227451\pi$
$353$	5.45917e7	+	9.62600e6i	1.24109	+	0.218837i	0.485706	+	0.874122i	$0.338562\pi$
$354$	5.94064e6	−	2.43583e7i	0.133913	−	0.549082i
$355$	5.15155e6	+	1.87501e6i	0.115147	+	0.0419101i
$356$	6.24389e7	+	7.44118e7i	1.38390	+	1.64927i
$357$	961259.	−	106021.i	0.0211269	−	0.00233018i
$358$	4.29559e6	−	1.56347e6i	0.0936211	−	0.0340753i
$359$	−8.33001e6	−	4.80933e6i	−0.180037	−	0.103945i	0.407273	−	0.913306i	$-0.366480\pi$
$359$	−8.33001e6	−	4.80933e6i	−0.180037	−	0.103945i	−0.587310	+	0.809362i	$0.699813\pi$
$360$	−5.07284e7	+	1.13279e7i	−1.08729	+	0.242796i
$361$	−1.71503e7	−	2.97053e7i	−0.364545	−	0.631411i
$362$	6.26553e6	−	7.46697e6i	0.132079	−	0.157405i
$363$	−4.95434e6	+	7.42703e6i	−0.103578	+	0.155273i
$364$	1.03062e7	+	5.84494e7i	0.213695	+	1.21193i
$365$	−3.40672e7	+	6.00696e6i	−0.700579	+	0.123531i
$366$	−7.11688e6	−	4.74745e6i	−0.145160	−	0.0968316i
$367$	9.58685e6	+	8.04432e6i	0.193945	+	0.162739i	0.734589	−	0.678512i	$-0.237375\pi$
$367$	9.58685e6	+	8.04432e6i	0.193945	+	0.162739i	−0.540644	+	0.841251i	$0.681820\pi$
$368$	−8.92427e6	+	5.15243e6i	−0.179073	+	0.103388i
$369$	1.51151e7	+	6.76880e7i	0.300837	+	1.34720i
$370$	7.08605e7	−	1.22734e8i	1.39894	−	2.42304i
$371$	4.16229e6	+	1.14358e7i	0.0815099	+	0.223946i
$372$	1.81217e7	+	1.64303e8i	0.352022	+	3.19166i
$373$	4.05591e7	−	3.40331e7i	0.781560	−	0.655806i	−0.162081	−	0.986777i	$-0.551821\pi$
$373$	4.05591e7	−	3.40331e7i	0.781560	−	0.655806i	0.943641	+	0.330971i	$0.107376\pi$
$374$	1.21015e6	−	3.32487e6i	0.0231327	−	0.0635565i
$375$	−5.22750e7	−	1.27491e7i	−0.991289	−	0.241761i
$376$	9.41429e6	−	5.33911e7i	0.177102	−	1.00440i
$377$		−	2.90865e7i		−	0.542835i
$378$	2.13110e7	−	3.53023e7i	0.394574	−	0.653624i
$379$	−5.99673e6			−0.110153			−0.0550765	−	0.998482i	$-0.517540\pi$
$379$	−5.99673e6			−0.110153			−0.0550765	+	0.998482i	$0.517540\pi$
$380$	1.17744e8	+	2.07614e7i	2.14579	+	0.378361i
$381$	−2.85027e7	+	8.33150e6i	−0.515360	+	0.150643i
$382$	−7.93641e7	−	2.88862e7i	−1.42375	−	0.518203i
$383$	−6.26262e7	−	7.46350e7i	−1.11470	−	1.32845i	−0.938964	−	0.344016i	$-0.888213\pi$
$383$	−6.26262e7	−	7.46350e7i	−1.11470	−	1.32845i	−0.175740	−	0.984437i	$-0.556232\pi$
$384$	−3.93695e7	+	8.96605e7i	−0.695290	+	1.58346i
$385$	2.20074e7	−	8.01005e6i	0.385644	−	0.140363i
$386$	−1.28250e8	−	7.40452e7i	−2.22995	−	1.28746i
$387$	3.17066e7	−	4.14524e7i	0.547038	−	0.715183i
$388$	−2.76060e7	−	4.78150e7i	−0.472616	−	0.818594i
$389$	2.24599e7	−	2.67667e7i	0.381557	−	0.454722i	−0.540748	−	0.841185i	$-0.681859\pi$
$389$	2.24599e7	−	2.67667e7i	0.381557	−	0.454722i	0.922305	+	0.386463i	$0.126303\pi$
$390$	−1.48441e8	−	9.61494e6i	−2.50241	−	0.162089i
$391$	559416.	+	3.17261e6i	0.00935847	+	0.0530745i
$392$	5.29389e7	−	9.33455e6i	0.878853	−	0.154966i
$393$	6.11739e7	−	3.02260e7i	1.00783	−	0.497970i
$394$	1.15089e8	+	9.65715e7i	1.88168	+	1.57892i
$395$	−2.61443e7	+	1.50944e7i	−0.424215	+	0.244921i
$396$	−5.10933e7	−	7.99295e7i	−0.822770	−	1.28713i
$397$	3.61967e7	−	6.26945e7i	0.578492	−	1.00198i	−0.417161	−	0.908833i	$-0.636975\pi$
$397$	3.61967e7	−	6.26945e7i	0.578492	−	1.00198i	0.995653	−	0.0931442i	$-0.0296918\pi$
$398$	−1.95400e7	−	5.36858e7i	−0.309939	−	0.851550i
$399$	−3.13164e7	+	2.29991e7i	−0.493007	+	0.362069i
$400$	369877.	−	310363.i	0.00577932	−	0.00484943i
$401$	−2.12273e7	+	5.83216e7i	−0.329202	+	0.904475i	0.659112	+	0.752045i	$0.270932\pi$
$401$	−2.12273e7	+	5.83216e7i	−0.329202	+	0.904475i	−0.988314	+	0.152430i	$0.951290\pi$
$402$	−2.25149e7	+	2.35555e7i	−0.346571	+	0.362589i
$403$	−3.36497e7	+	1.90837e8i	−0.514121	+	2.91573i
$404$		−	2.59587e7i		−	0.393675i
$405$	4.60922e7	+	4.58101e7i	0.693844	+	0.689599i
$406$	1.77589e7			0.265362
$407$	1.04344e8	+	1.83986e7i	1.54769	+	0.272899i
$408$	−2.55485e6	−	2.44198e6i	−0.0376170	−	0.0359552i
$409$	−5.88018e7	−	2.14021e7i	−0.859450	−	0.312814i	−0.125563	−	0.992086i	$-0.540074\pi$
$409$	−5.88018e7	−	2.14021e7i	−0.859450	−	0.312814i	−0.733887	+	0.679271i	$0.762296\pi$
$410$	9.81872e7	+	1.17015e8i	1.42463	+	1.69781i
$411$	1.75974e7	+	2.39613e7i	0.253469	+	0.345132i
$412$	−8.42418e7	+	3.06615e7i	−1.20458	+	0.438432i
$413$	9.77216e6	+	5.64196e6i	0.138720	+	0.0800903i
$414$	1.21941e8	+	6.32411e7i	1.71850	+	0.891247i
$415$	2.73211e7	+	4.73216e7i	0.382256	+	0.662087i
$416$	−6.15120e7	+	7.33071e7i	−0.854436	+	1.01828i
$417$	3.81845e7	+	7.72811e7i	0.526598	+	1.06577i
$418$	2.46851e7	+	1.39996e8i	0.337992	+	1.91685i
$419$	−5.03798e6	+	888332.i	−0.0684880	+	0.0120763i	−0.207787	−	0.978174i	$-0.566626\pi$
$419$	−5.03798e6	+	888332.i	−0.0684880	+	0.0120763i	0.139299	+	0.990250i	$0.455515\pi$
$420$	3.69125e6	−	5.69875e7i	0.0498226	−	0.769187i
$421$	−3.99711e7	−	3.35398e7i	−0.535674	−	0.449484i	0.334382	−	0.942438i	$-0.391473\pi$
$421$	−3.99711e7	−	3.35398e7i	−0.535674	−	0.449484i	−0.870055	+	0.492954i	$0.835917\pi$
$422$	−1.79780e7	+	1.03796e7i	−0.239223	+	0.138115i
$423$	−6.25823e7	+	2.60350e7i	−0.826857	+	0.343983i
$424$	2.22369e7	−	3.85155e7i	0.291727	−	0.505286i
$425$	−51627.0	−	141844.i	−0.000672528	−	0.00184776i
$426$	1.45529e7	+	6.39012e6i	0.188244	+	0.0826571i
$427$	2.94945e6	−	2.47488e6i	0.0378841	−	0.0317886i
$428$	4.65140e7	−	1.27796e8i	0.593270	−	1.63000i
$429$	−3.12016e7	−	1.06743e8i	−0.395189	−	1.35197i
$430$	1.99596e7	−	1.13196e8i	0.251042	−	1.42373i
$431$			2.86654e7i			0.358036i	0.983846	+	0.179018i	$0.0572920\pi$
$431$			2.86654e7i			0.358036i	−0.983846	+	0.179018i	$0.942708\pi$
$432$	−1.39644e7	+	2.18225e6i	−0.173210	+	0.0270678i
$433$	−1.16501e7			−0.143505			−0.0717524	−	0.997422i	$-0.522859\pi$
$433$	−1.16501e7			−0.143505			−0.0717524	+	0.997422i	$0.522859\pi$
$434$	−1.16516e8	−	2.05449e7i	−1.42534	−	0.251325i
$435$	−6.63119e6	+	2.71898e7i	−0.0805608	+	0.330322i
$436$	1.74576e8	+	6.35404e7i	2.10632	+	0.766638i
$437$	−8.31970e7	−	9.91504e7i	−0.996927	−	1.18809i
$438$	−9.96878e7	+	1.09950e7i	−1.18637	+	0.130850i
$439$	1.03967e8	−	3.78408e7i	1.22886	−	0.447267i	0.355651	−	0.934619i	$-0.384259\pi$
$439$	1.03967e8	−	3.78408e7i	1.22886	−	0.447267i	0.873206	+	0.487352i	$0.162037\pi$
$440$	−7.41205e7	−	4.27935e7i	−0.870122	−	0.502365i
$441$	−4.54808e7	−	4.94809e7i	−0.530288	−	0.576928i
$442$	−5.05713e6	−	8.75920e6i	−0.0585648	−	0.101437i
$443$	−3.01655e7	+	3.59498e7i	−0.346976	+	0.413510i	−0.911103	−	0.412178i	$-0.864768\pi$
$443$	−3.01655e7	+	3.59498e7i	−0.346976	+	0.413510i	0.564127	+	0.825688i	$0.309213\pi$
$444$	1.43371e8	−	2.14926e8i	1.63799	−	2.45550i
$445$	−1.90264e7	−	1.07904e8i	−0.215912	−	1.22450i
$446$	−3.56462e7	+	6.28539e6i	−0.401799	+	0.0708480i
$447$	3.56843e7	+	2.38039e7i	0.399535	+	0.266518i
$448$	−5.03751e7	−	4.22697e7i	−0.560250	−	0.470105i
$449$	1.08401e8	−	6.25852e7i	1.19755	−	0.691405i	0.237541	−	0.971377i	$-0.423659\pi$
$449$	1.08401e8	−	6.25852e7i	1.19755	−	0.691405i	0.960008	+	0.279972i	$0.0903252\pi$
$450$	−6.14138e6	−	1.92601e6i	−0.0673951	−	0.0211360i
$451$	−5.71003e7	+	9.89005e7i	−0.622456	+	1.07812i
$452$	−7.53185e7	−	2.06936e8i	−0.815617	−	2.24089i
$453$	1.78820e6	+	1.62130e7i	0.0192363	+	0.174409i
$454$	−1.98463e8	+	1.66530e8i	−2.12086	+	1.77961i
$455$	2.28971e7	−	6.29092e7i	0.243078	−	0.667851i
$456$	1.37949e8	+	3.36438e7i	1.45487	+	0.354822i
$457$	−4.77310e6	+	2.70696e7i	−0.0500095	+	0.283618i	−0.999549	−	0.0300295i	$-0.990440\pi$
$457$	−4.77310e6	+	2.70696e7i	−0.0500095	+	0.283618i	0.949540	+	0.313647i	$0.101551\pi$
$458$			2.03446e7i			0.211764i
$459$	−852051.	+	4.33568e6i	−0.00881105	+	0.0448352i
$460$	1.90234e8			1.95440
$461$	−3.80147e7	−	6.70301e6i	−0.388015	−	0.0684175i	−0.0237623	−	0.999718i	$-0.507564\pi$
$461$	−3.80147e7	−	6.70301e6i	−0.388015	−	0.0684175i	−0.364253	+	0.931300i	$0.618676\pi$
$462$	6.51723e7	−	1.90503e7i	0.660902	−	0.193186i
$463$	1.43463e8	+	5.22163e7i	1.44543	+	0.526093i	0.941311	−	0.337541i	$-0.109595\pi$
$463$	1.43463e8	+	5.22163e7i	1.44543	+	0.526093i	0.504119	+	0.863634i	$0.331817\pi$
$464$	−3.91263e6	−	4.66289e6i	−0.0391665	−	0.0466769i
$465$	7.49626e7	−	1.70721e8i	0.745566	−	1.69796i
$466$	1.66156e8	−	6.04760e7i	1.64195	−	0.597620i
$467$	−4.83886e7	−	2.79372e7i	−0.475108	−	0.274304i	0.243268	−	0.969959i	$-0.421781\pi$
$467$	−4.83886e7	−	2.79372e7i	−0.475108	−	0.274304i	−0.718375	+	0.695656i	$0.755114\pi$
$468$	−2.68908e8	−	3.49827e7i	−2.62341	−	0.341284i
$469$	−7.33254e6	−	1.27003e7i	−0.0710781	−	0.123111i
$470$	−9.59597e7	+	1.14360e8i	−0.924262	+	1.10149i
$471$	−1.78170e8	−	1.15406e7i	−1.70519	−	0.110450i
$472$	−7.16068e6	−	4.06102e7i	−0.0680971	−	0.386198i
$473$	8.46280e7	−	1.49222e7i	0.799706	−	0.141010i
$474$	−7.84687e7	+	3.87713e7i	−0.736820	+	0.364062i
$475$	4.64574e6	+	3.89824e6i	0.0433485	+	0.0363737i
$476$	3.36273e6	−	1.94147e6i	0.0311796	−	0.0180016i
$477$	−5.55465e7	+	2.51061e6i	−0.511801	+	0.0231326i
$478$	−1.18840e8	+	2.05837e8i	−1.08812	+	1.88469i
$479$	−1.37883e7	−	3.78830e7i	−0.125460	−	0.344697i	0.861022	−	0.508567i	$-0.169825\pi$
$479$	−1.37883e7	−	3.78830e7i	−0.125460	−	0.344697i	−0.986482	+	0.163870i	$0.947602\pi$
$480$	7.42134e7	−	5.45031e7i	0.671056	−	0.492831i
$481$	2.32014e8	−	1.94683e8i	2.08487	−	1.74941i
$482$	−3.67074e7	+	1.00853e8i	−0.327802	+	0.900629i
$483$	−4.27164e7	+	4.46907e7i	−0.379100	+	0.396621i
$484$	−6.22460e6	+	3.53014e7i	−0.0549004	+	0.311355i
$485$			6.22778e7i			0.545893i
$486$	1.24768e8	+	1.41174e8i	1.08691	+	1.22983i
$487$	−1.32889e8			−1.15054			−0.575272	−	0.817962i	$-0.695104\pi$
$487$	−1.32889e8			−1.15054			−0.575272	+	0.817962i	$0.695104\pi$
$488$	−1.38568e7	−	2.44333e6i	−0.119235	−	0.0210243i
$489$	7.61663e7	+	7.28014e7i	0.651383	+	0.622606i
$490$	−1.39095e8	−	5.06266e7i	−1.18229	−	0.430319i
$491$	−3.69168e7	−	4.39958e7i	−0.311875	−	0.371678i	0.587224	−	0.809425i	$-0.300221\pi$
$491$	−3.69168e7	−	4.39958e7i	−0.311875	−	0.371678i	−0.899098	+	0.437747i	$0.855776\pi$
$492$	1.64832e8	+	2.24442e8i	1.38404	+	1.88455i
$493$	−1.78817e6	+	650842.i	−0.0149235	+	0.00543169i
$494$	3.51917e8	+	2.03179e8i	2.91917	+	1.68538i
$495$	4.83150e6	+	1.06896e8i	0.0398351	+	0.881341i
$496$	2.02764e7	+	3.51197e7i	0.166167	+	0.287810i
$497$	−4.59800e6	+	5.47969e6i	−0.0374542	+	0.0446361i
$498$	7.01767e7	+	1.42030e8i	0.568205	+	1.14998i
$499$	−2.11665e7	−	1.20041e8i	−0.170352	−	0.966114i	−0.943373	−	0.331734i	$-0.892366\pi$
$499$	−2.11665e7	−	1.20041e8i	−0.170352	−	0.966114i	0.773021	−	0.634380i	$-0.218745\pi$
$500$	−2.12758e8	+	3.75151e7i	−1.70207	+	0.300120i
$501$	−9.79957e6	+	1.51291e8i	−0.0779281	+	1.20309i
$502$	−1.86294e8	−	1.56319e8i	−1.47261	−	1.23567i
$503$	2.13734e8	−	1.23400e8i	1.67946	−	0.969638i	0.717458	−	0.696602i	$-0.245306\pi$
$503$	2.13734e8	−	1.23400e8i	1.67946	−	0.969638i	0.962004	−	0.273035i	$-0.0880276\pi$
$504$	8.74931e6	−	6.72549e7i	0.0683412	−	0.525330i
$505$	−1.46404e7	+	2.53579e7i	−0.113678	+	0.196897i
$506$	7.73601e7	+	2.12545e8i	0.597126	+	1.64059i
$507$	−1.71746e8	−	7.54130e7i	−1.31784	−	0.578658i
$508$	−9.13352e7	+	7.66393e7i	−0.696702	+	0.584602i
$509$	−3.34426e7	+	9.18829e7i	−0.253599	+	0.696757i	0.745929	+	0.666026i	$0.232006\pi$
$509$	−3.34426e7	+	9.18829e7i	−0.253599	+	0.696757i	−0.999528	+	0.0307313i	$0.990216\pi$
$510$	2.73041e6	+	9.34094e6i	0.0205834	+	0.0704174i
$511$	7.83799e6	−	4.44514e7i	0.0587411	−	0.333137i
$512$			4.68232e7i			0.348860i
$513$	−5.74505e7	−	1.67973e8i	−0.425541	−	1.24419i
$514$	−1.45072e8			−1.06830
$515$	9.95848e7	+	1.75595e7i	0.729074	+	0.128555i
$516$	4.96486e7	−	2.03574e8i	0.361375	−	1.48174i
$517$	−1.04879e8	−	3.81728e7i	−0.758955	−	0.276237i
$518$	1.18864e8	+	1.41657e8i	0.855190	+	1.01918i
$519$	1.57658e7	−	1.73887e6i	0.112775	−	0.0124384i
$520$	−2.29900e8	+	8.36766e7i	−1.63504	+	0.595106i
$521$	1.16289e8	+	6.71395e7i	0.822292	+	0.474750i	0.851206	−	0.524832i	$-0.175872\pi$
$521$	1.16289e8	+	6.71395e7i	0.822292	+	0.474750i	−0.0289145	+	0.999582i	$0.509205\pi$
$522$	−2.42805e7	+	7.74220e7i	−0.170705	+	0.544318i
$523$	1.16031e8	+	2.00972e8i	0.811093	+	1.40485i	0.912100	+	0.409969i	$0.134460\pi$
$523$	1.16031e8	+	2.00972e8i	0.811093	+	1.40485i	−0.101006	+	0.994886i	$0.532206\pi$
$524$	1.76101e8	−	2.09869e8i	1.22396	−	1.45866i
$525$	1.60747e6	−	2.40975e6i	0.0111087	−	0.0166531i
$526$	−7.08333e7	−	4.01716e8i	−0.486721	−	2.76033i
$527$	1.24852e7	−	2.20147e6i	0.0853027	−	0.0150412i
$528$	−1.93607e7	−	1.29149e7i	−0.131528	−	0.0877386i
$529$	−4.43574e7	−	3.72203e7i	−0.299639	−	0.251427i
$530$	−1.06057e8	+	6.12320e7i	−0.712379	+	0.411292i
$531$	−3.79576e7	+	3.48890e7i	−0.253522	+	0.233026i
$532$	−7.80021e7	+	1.35104e8i	−0.518050	+	0.897288i
$533$	1.11651e8	+	3.06760e8i	0.737366	+	2.02590i
$534$	−3.48255e7	−	3.15751e8i	−0.228704	−	2.07358i
$535$	−1.17513e8	+	9.86051e7i	−0.767405	+	0.643929i
$536$	−1.83299e7	+	5.03610e7i	−0.119033	+	0.327039i
$537$	−9.13222e6	−	2.22722e6i	−0.0589730	−	0.0143827i
$538$	6.21571e7	−	3.52510e8i	0.399157	−	2.26373i
$539$		−	1.10664e8i		−	0.706710i
$540$	2.43397e8	+	9.40076e7i	1.54573	+	0.597010i
$541$	7.17784e7			0.453317			0.226658	−	0.973974i	$-0.427220\pi$
$541$	7.17784e7			0.453317			0.226658	+	0.973974i	$0.427220\pi$
$542$	−2.78458e8	−	4.90996e7i	−1.74888	−	0.308376i
$543$	−1.92386e7	+	5.62355e6i	−0.120164	+	0.0351246i
$544$	5.88316e6	+	2.14129e6i	0.0365438	+	0.0133009i
$545$	−1.34699e8	−	1.60528e8i	−0.832101	−	0.991659i
$546$	7.80343e7	−	1.77716e8i	0.479410	−	1.09181i
$547$	1.51944e8	−	5.53032e7i	0.928373	−	0.337900i	0.166809	−	0.985989i	$-0.446654\pi$
$547$	1.51944e8	−	5.53032e7i	0.928373	−	0.337900i	0.761564	+	0.648089i	$0.224432\pi$
$548$	1.03373e8	+	5.96823e7i	0.628151	+	0.362663i
$549$	6.75696e6	+	1.62422e7i	0.0408352	+	0.0981586i
$550$	−5.29903e6	−	9.17818e6i	−0.0318499	−	0.0551656i
$551$	4.91436e7	−	5.85671e7i	0.293773	−	0.350105i
$552$	2.25454e8	+	1.46033e7i	1.34042	+	0.0868230i
$553$	−6.84017e6	−	3.87925e7i	−0.0404475	−	0.229389i
$554$	2.80813e7	−	4.95150e6i	0.165154	−	0.0291211i
$555$	−2.61268e8	+	1.29093e8i	−1.52830	+	0.755131i
$556$	2.65128e8	+	2.22469e8i	1.54252	+	1.29433i
$557$	−2.34982e8	+	1.35667e8i	−1.35978	+	0.785070i	−0.989594	−	0.143888i	$-0.954040\pi$
$557$	−2.34982e8	+	1.35667e8i	−1.35978	+	0.785070i	−0.370186	+	0.928958i	$0.620706\pi$
$558$	2.48873e8	−	4.79876e8i	1.43243	−	2.76202i
$559$	1.22822e8	−	2.12734e8i	0.703140	−	1.21787i
$560$	−4.79170e6	−	1.31651e7i	−0.0272851	−	0.0749652i
$561$	−5.86415e6	+	4.30669e6i	−0.0332136	+	0.0243924i
$562$	7.72979e7	−	6.48606e7i	0.435470	−	0.365403i
$563$	7.54154e7	−	2.07202e8i	0.422605	−	1.16110i	−0.527606	−	0.849489i	$-0.676910\pi$
$563$	7.54154e7	−	2.07202e8i	0.422605	−	1.16110i	0.950211	−	0.311608i	$-0.100868\pi$
$564$	−1.88044e8	+	1.96735e8i	−1.04815	+	1.09659i
$565$	−4.31340e7	+	2.44625e8i	−0.239152	+	1.35630i
$566$			7.80212e7i			0.430292i
$567$	−7.67388e7	+	3.60710e7i	−0.420984	+	0.197883i
$568$	2.61412e7			0.142653
$569$	−1.54614e8	−	2.72626e7i	−0.839288	−	0.147989i	−0.262550	−	0.964918i	$-0.584564\pi$
$569$	−1.54614e8	−	2.72626e7i	−0.839288	−	0.147989i	−0.576738	+	0.816929i	$0.695675\pi$
$570$	−2.82647e8	−	2.70160e8i	−1.52623	−	1.45880i
$571$	1.65907e8	+	6.03850e7i	0.891159	+	0.324355i	0.746704	−	0.665156i	$-0.231635\pi$
$571$	1.65907e8	+	6.03850e7i	0.891159	+	0.324355i	0.144455	+	0.989511i	$0.453857\pi$
$572$	−2.87015e8	−	3.42051e8i	−1.53362	−	1.82769i
$573$	1.02800e8	+	1.39976e8i	0.546424	+	0.744030i
$574$	−1.87294e8	+	6.81693e7i	−0.990347	+	0.360457i
$575$	8.35666e6	+	4.82472e6i	0.0439571	+	0.0253786i
$576$	2.53154e8	−	1.61824e8i	1.32470	−	0.846788i
$577$	−2.26946e7	−	3.93082e7i	−0.118140	−	0.204624i	0.800891	−	0.598810i	$-0.204360\pi$
$577$	−2.26946e7	−	3.93082e7i	−0.118140	−	0.204624i	−0.919030	+	0.394187i	$0.871026\pi$
$578$	2.03297e8	−	2.42280e8i	1.05280	−	1.25468i
$579$	1.34894e8	+	2.73011e8i	0.694957	+	1.40651i
$580$	1.95127e7	+	1.10662e8i	0.100008	+	0.567172i
$581$	−7.02150e7	+	1.23808e7i	−0.358015	+	0.0631278i
$582$	−1.16708e7	+	1.80180e8i	−0.0592015	+	0.913983i
$583$	−7.01363e7	−	5.88514e7i	−0.353946	−	0.296996i
$584$	−1.42853e8	+	8.24762e7i	−0.717217	+	0.414085i
$585$	2.42954e8	+	1.85834e8i	1.21355	+	0.928234i
$586$	6.68937e6	−	1.15863e7i	0.0332424	−	0.0575775i
$587$	−1.82275e7	−	5.00795e7i	−0.0901180	−	0.247597i	0.886443	−	0.462838i	$-0.153169\pi$
$587$	−1.82275e7	−	5.00795e7i	−0.0901180	−	0.247597i	−0.976561	+	0.215240i	$0.930947\pi$
$588$	−2.47075e8	−	1.08489e8i	−1.21534	−	0.533648i
$589$	−3.90187e8	+	3.27406e8i	−1.90953	+	1.60229i
$590$	−3.88365e7	+	1.06702e8i	−0.189097	+	0.519538i
$591$	−8.66766e7	−	2.96527e8i	−0.419894	−	1.43649i
$592$	1.10063e7	−	6.24197e7i	0.0530487	−	0.300854i
$593$			9.61267e7i			0.460978i	0.973075	+	0.230489i	$0.0740325\pi$
$593$			9.61267e7i			0.460978i	−0.973075	+	0.230489i	$0.925967\pi$
$594$	−6.05382e6	+	3.10173e8i	−0.0288848	+	1.47994i
$595$	−4.37986e6			−0.0207926
$596$	1.69611e8	+	2.99071e7i	0.801154	+	0.141265i
$597$	−2.78355e7	+	1.14133e8i	−0.130821	+	0.536401i
$598$	6.07570e8	+	2.21137e8i	2.84114	+	1.03409i
$599$	1.18851e8	+	1.41641e8i	0.552996	+	0.659035i	0.968049	−	0.250762i	$-0.0806813\pi$
$599$	1.18851e8	+	1.41641e8i	0.552996	+	0.659035i	−0.415053	+	0.909797i	$0.636237\pi$
$600$	−1.05221e7	+	1.16053e6i	−0.0487134	+	0.00537280i
$601$	7.26052e7	−	2.64261e7i	0.334460	−	0.121734i	−0.169330	−	0.985559i	$-0.554161\pi$
$601$	7.26052e7	−	2.64261e7i	0.334460	−	0.121734i	0.503791	+	0.863826i	$0.331938\pi$
$602$	1.29886e8	+	7.49897e7i	0.595350	+	0.343726i
$603$	6.53938e7	−	1.46028e7i	0.298253	−	0.0666014i
$604$	3.27457e7	+	5.67172e7i	0.148608	+	0.257397i
$605$	2.59901e7	−	3.09738e7i	0.117366	−	0.139871i
$606$	−4.71091e7	+	7.06210e7i	−0.211684	+	0.317334i
$607$	−3.83411e7	−	2.17443e8i	−0.171435	−	0.972255i	−0.942179	−	0.335110i	$-0.891226\pi$
$607$	−3.83411e7	−	2.17443e8i	−0.171435	−	0.972255i	0.770744	−	0.637145i	$-0.219885\pi$
$608$	−2.47715e8	+	4.36788e7i	−1.10215	+	0.194339i
$609$	−3.03788e7	−	2.02648e7i	−0.134499	−	0.0897201i
$610$	2.96804e7	+	2.49048e7i	0.130761	+	0.109722i
$611$	−2.76298e8	+	1.59521e8i	−1.21131	+	0.699348i
$612$	3.86645e6	+	1.73146e7i	0.0168678	+	0.0755369i
$613$	−5.16939e7	+	8.95364e7i	−0.224418	+	0.388703i	−0.956145	−	0.292895i	$-0.905381\pi$
$613$	−5.16939e7	+	8.95364e7i	−0.224418	+	0.388703i	0.731727	+	0.681598i	$0.238715\pi$
$614$	−1.70227e8	−	4.67694e8i	−0.735398	−	2.02049i
$615$	−3.44350e7	−	3.12210e8i	−0.148039	−	1.34222i
$616$	8.55483e7	−	7.17836e7i	0.365990	−	0.307102i
$617$	−5.82222e7	+	1.59964e8i	−0.247875	+	0.681031i	0.751888	+	0.659290i	$0.229143\pi$
$617$	−5.82222e7	+	1.59964e8i	−0.247875	+	0.681031i	−0.999764	+	0.0217411i	$0.993079\pi$
$618$	2.84825e8	+	6.94648e7i	1.20674	+	0.294306i
$619$	−5.21735e7	+	2.95890e8i	−0.219977	+	1.24755i	0.652080	+	0.758150i	$0.273896\pi$
$619$	−5.21735e7	+	2.95890e8i	−0.219977	+	1.24755i	−0.872058	+	0.489403i	$0.837215\pi$
$620$		−	7.48627e8i		−	3.14116i
$621$	−1.36431e8	−	2.47330e8i	−0.569691	−	1.03277i
$622$	2.51187e8			1.04382
$623$	1.40795e8	+	2.48260e7i	0.582270	+	0.102670i
$624$	−6.38548e7	+	1.86651e7i	−0.262809	+	0.0768206i
$625$	2.19120e8	+	7.97530e7i	0.897514	+	0.326668i
$626$	3.15763e8	+	3.76311e8i	1.28718	+	1.53400i
$627$	1.17523e8	−	2.67649e8i	0.476784	−	1.08583i
$628$	−6.73635e8	+	2.45183e8i	−2.71985	+	0.989945i
$629$	−1.71602e7	−	9.90746e6i	−0.0689559	−	0.0398117i
$630$	−1.13462e8	+	1.48337e8i	−0.453761	+	0.593236i
$631$	8.66785e7	+	1.50132e8i	0.345004	+	0.597564i	0.985354	−	0.170519i	$-0.0545444\pi$
$631$	8.66785e7	+	1.50132e8i	0.345004	+	0.597564i	−0.640351	+	0.768083i	$0.721211\pi$
$632$	−9.25312e7	+	1.10274e8i	−0.366553	+	0.436841i
$633$	4.25977e7	+	2.75918e6i	0.167948	+	0.0108785i
$634$	−2.18519e7	−	1.23928e8i	−0.0857473	−	0.486297i
$635$	1.32445e8	−	2.33536e7i	0.517266	−	0.0912080i
$636$	−2.00152e8	+	9.88952e7i	−0.778018	+	0.384418i
$637$	−2.42330e8	−	2.03339e8i	−0.937536	−	0.786687i
$638$	−1.15706e8	+	6.68028e7i	−0.445547	+	0.257237i
$639$	−1.76028e7	−	2.75375e7i	−0.0674651	−	0.105541i
$640$	2.21743e8	−	3.84071e8i	0.845883	−	1.46511i
$641$	−9.14767e7	−	2.51330e8i	−0.347325	−	0.954268i	−0.983209	−	0.182483i	$-0.941586\pi$
$641$	−9.14767e7	−	2.51330e8i	−0.347325	−	0.954268i	0.635884	−	0.771785i	$-0.280636\pi$
$642$	−3.58464e8	+	2.63260e8i	−1.35469	+	0.994899i
$643$	1.99296e8	−	1.67230e8i	0.749664	−	0.629043i	−0.185750	−	0.982597i	$-0.559471\pi$
$643$	1.99296e8	−	1.67230e8i	0.749664	−	0.629043i	0.935414	+	0.353554i	$0.115027\pi$
$644$	−8.48964e7	+	2.33251e8i	−0.317857	+	0.873304i
$645$	−1.63313e8	+	1.70861e8i	−0.608612	+	0.636741i
$646$	4.61649e6	−	2.61814e7i	0.0171244	−	0.0971171i
$647$			1.66752e7i			0.0615685i	0.999526	+	0.0307842i	$0.00980048\pi$
$647$			1.66752e7i			0.0615685i	−0.999526	+	0.0307842i	$0.990200\pi$
$648$	2.81243e8	+	1.30097e8i	1.03361	+	0.478125i
$649$	−8.48924e7			−0.310552
$650$	−2.98347e7	−	5.26067e6i	−0.108638	−	0.0191558i
$651$	1.75872e8	+	1.68102e8i	0.637459	+	0.609298i
$652$	3.97529e8	+	1.44689e8i	1.43425	+	0.522025i
$653$	9.94259e7	+	1.18491e8i	0.357075	+	0.425546i	0.914440	−	0.404722i	$-0.132632\pi$
$653$	9.94259e7	+	1.18491e8i	0.357075	+	0.425546i	−0.557364	+	0.830268i	$0.688187\pi$
$654$	−3.59625e8	−	4.89679e8i	−1.28563	−	1.75056i
$655$	−2.90389e8	+	1.05693e8i	−1.03337	+	0.376116i
$656$	5.91634e7	+	3.41580e7i	0.209576	+	0.120999i
$657$	1.83075e8	+	9.49460e7i	0.645554	+	0.334796i
$658$	−9.73960e7	−	1.68695e8i	−0.341872	−	0.592140i
$659$	2.77852e8	−	3.31131e8i	0.970860	−	1.15703i	−0.0167121	−	0.999860i	$-0.505320\pi$
$659$	2.77852e8	−	3.31131e8i	0.970860	−	1.15703i	0.987572	−	0.157166i	$-0.0502357\pi$
$660$	1.90317e8	+	3.85180e8i	0.661983	+	1.33978i
$661$	5.89884e7	+	3.34540e8i	0.204250	+	1.15836i	0.898615	+	0.438737i	$0.144574\pi$
$661$	5.89884e7	+	3.34540e8i	0.204250	+	1.15836i	−0.694365	+	0.719623i	$0.744315\pi$
$662$	3.44381e8	−	6.07237e7i	1.18704	−	0.209307i
$663$	−1.34433e6	+	2.07544e7i	−0.00461279	+	0.0712147i
$664$	1.99598e8	+	1.67483e8i	0.681793	+	0.572092i
$665$	1.52394e8	−	8.79845e7i	0.518205	−	0.299186i
$666$	−7.80086e8	+	3.24525e8i	−2.64070	+	1.09857i
$667$	6.08234e7	−	1.05349e8i	0.204971	−	0.355021i
$668$	2.08194e8	+	5.72009e8i	0.698456	+	1.91899i
$669$	6.81496e7	+	2.99242e7i	0.227607	+	0.0999410i
$670$	1.13049e8	−	9.48593e7i	0.375874	−	0.315395i
$671$	−9.90712e6	+	2.72196e7i	−0.0327929	+	0.0900978i
$672$	3.37083e7	+	1.15318e8i	0.111078	+	0.380006i
$673$	8.94903e7	−	5.07524e8i	0.293583	−	1.66499i	−0.379324	−	0.925264i	$-0.623844\pi$
$673$	8.94903e7	−	5.07524e8i	0.293583	−	1.66499i	0.672907	−	0.739727i	$-0.265045\pi$
$674$		−	8.71159e7i		−	0.284523i
$675$	8.30780e6	+	1.03026e7i	0.0270131	+	0.0334994i
$676$	−7.53125e8			−2.43796
$677$	−3.54826e8	−	6.25654e7i	−1.14353	−	0.201636i	−0.430383	−	0.902646i	$-0.641622\pi$
$677$	−3.54826e8	−	6.25654e7i	−1.14353	−	0.201636i	−0.713151	+	0.701010i	$0.752733\pi$
$678$	−1.70637e8	+	6.99659e8i	−0.547499	+	2.24490i
$679$	−7.63605e7	−	2.77929e7i	−0.243927	−	0.0887821i
$680$	1.02885e7	+	1.22614e7i	0.0327209	+	0.0389953i
$681$	5.29524e8	−	5.84035e7i	1.67666	−	0.184926i
$682$	8.36430e8	−	3.04436e8i	2.63680	−	0.959715i
$683$	−1.45212e8	−	8.38384e7i	−0.455766	−	0.263136i	0.254496	−	0.967074i	$-0.418090\pi$
$683$	−1.45212e8	−	8.38384e7i	−0.455766	−	0.263136i	−0.710262	+	0.703937i	$0.751424\pi$
$684$	−4.82353e8	−	5.24777e8i	−1.50729	−	1.63986i
$685$	−6.73202e7	−	1.16602e8i	−0.209447	−	0.362772i
$686$	2.82581e8	−	3.36767e8i	0.875327	−	1.04317i
$687$	2.32153e7	−	3.48019e7i	0.0715985	−	0.107333i
$688$	−8.92662e6	−	5.06254e7i	−0.0274108	−	0.155454i
$689$	−2.57742e8	+	4.54469e7i	−0.788003	+	0.138946i
$690$	−5.17535e8	−	3.45232e8i	−1.57540	−	1.05090i
$691$	−1.95334e8	−	1.63904e8i	−0.592029	−	0.496771i	0.296843	−	0.954926i	$-0.404066\pi$
$691$	−1.95334e8	−	1.63904e8i	−0.592029	−	0.496771i	−0.888872	+	0.458155i	$0.848510\pi$
$692$	5.51526e7	−	3.18424e7i	0.166436	−	0.0960919i
$693$	−1.33224e8	−	4.17807e7i	−0.400297	−	0.125538i
$694$	−2.31481e8	+	4.00937e8i	−0.692527	+	1.19949i
$695$	−1.33522e8	−	3.66849e8i	−0.397739	−	1.09278i
$696$	1.46303e7	+	1.32648e8i	0.0433936	+	0.393435i
$697$	1.63606e7	−	1.37282e7i	0.0483171	−	0.0405429i
$698$	1.93608e8	−	5.31932e8i	0.569319	−	1.56419i
$699$	−3.53241e8	−	8.61503e7i	−1.03428	−	0.252246i
$700$	2.01961e6	−	1.14538e7i	0.00588809	−	0.0333930i
$701$		−	9.83379e7i		−	0.285474i	−0.989761	−	0.142737i	$-0.954410\pi$
$701$		−	9.83379e7i		−	0.285474i	0.989761	−	0.142737i	$-0.0455904\pi$
$702$	6.68084e8	+	5.83179e8i	1.93117	+	1.68574i
$703$	7.96101e8			2.29141
$704$	4.87217e8	+	8.59094e7i	1.39638	+	0.246220i
$705$	2.94648e8	−	8.61274e7i	0.840885	−	0.245796i
$706$	−6.83973e8	−	2.48946e8i	−1.94368	−	0.707442i
$707$	−2.45584e7	−	2.92675e7i	−0.0694930	−	0.0828185i
$708$	−8.32239e7	+	1.89535e8i	−0.234503	+	0.534060i
$709$	4.52942e8	−	1.64857e8i	1.27088	−	0.462562i	0.383473	−	0.923552i	$-0.374728\pi$
$709$	4.52942e8	−	1.64857e8i	1.27088	−	0.462562i	0.887405	+	0.460990i	$0.152506\pi$
$710$	−6.23391e7	−	3.59915e7i	−0.174175	−	0.100560i
$711$	1.78473e8	+	2.32178e7i	0.496550	+	0.0645971i
$712$	−2.61235e8	−	4.52472e8i	−0.723755	−	1.25358i
$713$	−5.20939e8	+	6.20831e8i	−1.43720	+	1.71279i
$714$	−1.26717e7	−	820784.i	−0.0348129	−	0.00225494i
$715$	8.74596e7	+	4.96008e8i	0.239270	+	1.35697i
$716$	−3.71680e7	+	6.55372e6i	−0.101258	+	0.0178545i
$717$	4.38172e8	−	2.16501e8i	1.18874	−	0.587356i
$718$	9.67491e7	+	8.11821e7i	0.261381	+	0.219324i
$719$	1.14689e8	−	6.62157e7i	0.308557	−	0.178145i	−0.337724	−	0.941245i	$-0.609657\pi$
$719$	1.14689e8	−	6.62157e7i	0.308557	−	0.178145i	0.646280	+	0.763100i	$0.276324\pi$
$720$	6.39461e7	−	2.89026e6i	0.171323	−	0.00774353i
$721$	−6.59723e7	+	1.14267e8i	−0.176017	+	0.304871i
$722$	1.54040e8	+	4.23220e8i	0.409280	+	1.12449i
$723$	1.77876e8	−	1.30634e8i	0.470655	−	0.345654i
$724$	−6.16489e7	+	5.17296e7i	−0.162446	+	0.136309i
$725$	−1.94945e6	+	5.35608e6i	−0.00511563	+	0.0140551i
$726$	8.09983e7	−	8.47420e7i	0.211673	−	0.221457i
$727$	−8.98469e7	+	5.09547e8i	−0.233830	+	1.32612i	0.611234	+	0.791450i	$0.290673\pi$
$727$	−8.98469e7	+	5.09547e8i	−0.233830	+	1.32612i	−0.845064	+	0.534665i	$0.820438\pi$
$728$		−	3.19229e8i		−	0.827386i
$729$	−5.23360e7	−	3.83869e8i	−0.135088	−	0.990834i
$730$	4.54216e8			1.16760
$731$	−1.58267e7	−	2.79068e6i	−0.0405171	−	0.00714427i
$732$	5.10594e7	+	4.88038e7i	0.130180	+	0.124429i
$733$	−5.85852e8	−	2.13233e8i	−1.48757	−	0.541429i	−0.534758	−	0.845005i	$-0.679597\pi$
$733$	−5.85852e8	−	2.13233e8i	−1.48757	−	0.541429i	−0.952807	+	0.303576i	$0.901819\pi$
$734$	−1.05625e8	−	1.25879e8i	−0.267103	−	0.318321i
$735$	1.80170e8	+	2.45326e8i	0.453753	+	0.617847i
$736$	−3.76086e8	+	1.36884e8i	−0.943308	+	0.343336i
$737$	9.55485e7	+	5.51649e7i	0.238683	+	0.137804i
$738$	−4.11183e7	−	9.09732e8i	−0.102298	−	2.26331i
$739$	−3.08298e8	−	5.33988e8i	−0.763901	−	1.32312i	−0.940825	−	0.338892i	$-0.889948\pi$
$739$	−3.08298e8	−	5.33988e8i	−0.763901	−	1.32312i	0.176924	−	0.984225i	$-0.443385\pi$
$740$	−7.52112e8	+	8.96332e8i	−1.85604	+	2.21194i
$741$	−3.70148e8	−	7.49137e8i	−0.909748	−	1.84123i
$742$	−2.77478e7	−	1.57365e8i	−0.0679229	−	0.385210i
$743$	5.48908e8	−	9.67873e7i	1.33824	−	0.235967i	0.541708	−	0.840567i	$-0.317778\pi$
$743$	5.48908e8	−	9.67873e7i	1.33824	−	0.235967i	0.796530	+	0.604599i	$0.206667\pi$
$744$	5.74685e7	−	8.87229e8i	0.139544	−	2.15435i
$745$	−1.48819e8	−	1.24874e8i	−0.359905	−	0.301996i
$746$	−6.02065e8	+	3.47602e8i	−1.45020	+	0.837271i
$747$	4.20246e7	−	3.23038e8i	0.100819	−	0.774983i
$748$	−1.46063e7	+	2.52988e7i	−0.0349008	+	0.0604499i
$749$	−6.84594e7	−	1.88091e8i	−0.162925	−	0.447633i
$750$	6.46895e8	+	2.84048e8i	1.53338	+	0.673300i
$751$	−3.46980e8	+	2.91150e8i	−0.819189	+	0.687381i	−0.952782	−	0.303655i	$-0.901793\pi$
$751$	−3.46980e8	+	2.91150e8i	−0.819189	+	0.687381i	0.133593	+	0.991036i	$0.457349\pi$
$752$	−2.28354e7	+	6.27397e7i	−0.0536976	+	0.147533i
$753$	1.40302e8	+	4.79984e8i	0.328609	+	1.12420i
$754$	−6.63193e7	+	3.76115e8i	−0.154713	+	0.877419i
$755$		−	7.38727e7i		−	0.171650i
$756$	−2.23887e8	+	2.56483e8i	−0.518160	+	0.593598i
$757$	−6.56644e8			−1.51371			−0.756854	−	0.653583i	$-0.773265\pi$
$757$	−6.56644e8			−1.51371			−0.756854	+	0.653583i	$0.773265\pi$
$758$	7.75432e7	+	1.36730e7i	0.178047	+	0.0313946i
$759$	1.10202e8	−	4.51861e8i	0.252038	−

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.9309 - 2.28007i) q^{2} +(19.5181 + 18.6559i) q^{3} +(101.870 + 37.0775i) q^{4} +(-78.6006 - 93.6725i) q^{5} +(-209.851 - 285.740i) q^{6} +(149.932 - 54.5707i) q^{7} +(-504.967 - 291.543i) q^{8} +(32.9160 + 728.257i) q^{9} +O(q^{10})\)	\(q+(-12.9309 - 2.28007i) q^{2} +(19.5181 + 18.6559i) q^{3} +(101.870 + 37.0775i) q^{4} +(-78.6006 - 93.6725i) q^{5} +(-209.851 - 285.740i) q^{6} +(149.932 - 54.5707i) q^{7} +(-504.967 - 291.543i) q^{8} +(32.9160 + 728.257i) q^{9} +(802.798 + 1390.49i) q^{10} +(-771.586 + 919.541i) q^{11} +(1296.59 + 2624.15i) q^{12} +(595.843 + 3379.19i) q^{13} +(-2063.18 + 363.795i) q^{14} +(213.406 - 3294.68i) q^{15} +(550.080 + 461.572i) q^{16} +(194.413 - 112.244i) q^{17} +(1234.84 - 9492.07i) q^{18} +(-4509.62 + 7810.89i) q^{19} +(-4533.86 - 12456.7i) q^{20} +(3944.46 + 1731.99i) q^{21} +(12073.9 - 10131.2i) q^{22} +(-4908.20 + 13485.2i) q^{23} +(-4417.03 - 15111.0i) q^{24} +(116.762 - 662.190i) q^{25} -45054.6i q^{26} +(-12943.8 + 14828.3i) q^{27} +17296.8 q^{28} +(-8347.98 - 1471.97i) q^{29} +(-10271.6 + 42116.6i) q^{30} +(53068.2 + 19315.3i) q^{31} +(17926.6 + 21364.1i) q^{32} +(-32214.8 + 3553.10i) q^{33} +(-2769.86 + 1008.15i) q^{34} +(-16896.5 - 9755.21i) q^{35} +(-23648.8 + 75407.6i) q^{36} +(-44133.5 - 76441.5i) q^{37} +(76122.8 - 90719.7i) q^{38} +(-51412.1 + 77071.6i) q^{39} +(12381.1 + 70217.0i) q^{40} +(93692.0 - 16520.4i) q^{41} +(-47056.4 - 31389.9i) q^{42} +(-54840.2 - 46016.4i) q^{43} +(-112695. + 65064.7i) q^{44} +(65630.4 - 60324.7i) q^{45} +(94214.7 - 163185. i) q^{46} +(31800.7 + 87371.7i) q^{47} +(2125.51 + 19271.2i) q^{48} +(-70622.8 + 59259.5i) q^{49} +(-3019.68 + 8296.50i) q^{50} +(5888.59 + 1436.14i) q^{51} +(-64593.8 + 366329. i) q^{52} +76273.2i q^{53} +(201185. - 162231. i) q^{54} +146783. q^{55} +(-91620.4 - 16155.1i) q^{56} +(-233738. + 68323.1i) q^{57} +(104591. + 38068.0i) q^{58} +(45458.9 + 54175.9i) q^{59} +(143898. - 327715. i) q^{60} +(22675.9 - 8253.36i) q^{61} +(-642181. - 370763. i) q^{62} +(44676.6 + 107393. i) q^{63} +(-206074. - 356931. i) q^{64} +(269704. - 321421. i) q^{65} +(424668. + 27507.0i) q^{66} +(-15960.5 - 90516.5i) q^{67} +(23966.5 - 4225.94i) q^{68} +(-347377. + 171639. i) q^{69} +(196245. + 164669. i) q^{70} +(-38826.1 + 22416.3i) q^{71} +(195696. - 377342. i) q^{72} +(141448. - 244995. i) q^{73} +(396395. + 1.08909e6i) q^{74} +(14632.7 - 10746.4i) q^{75} +(-749001. + 628486. i) q^{76} +(-65505.4 + 179974. i) q^{77} +(840534. - 879383. i) q^{78} +(42870.5 - 243131. i) q^{79} -87807.2i q^{80} +(-529274. + 47942.5i) q^{81} -1.24919e6 q^{82} +(-440070. - 77596.3i) q^{83} +(337602. + 322688. i) q^{84} +(-25795.2 - 9388.67i) q^{85} +(604214. + 720074. i) q^{86} +(-135476. - 184469. i) q^{87} +(657711. - 239387. i) q^{88} +(775996. + 448022. i) q^{89} +(-986206. + 630412. i) q^{90} +(273741. + 474133. i) q^{91} +(-999993. + 1.19174e6i) q^{92} +(675450. + 1.36703e6i) q^{93} +(-211999. - 1.20230e6i) q^{94} +(1.08612e6 - 191513. i) q^{95} +(-48672.0 + 751424. i) q^{96} +(-390147. - 327373. i) q^{97} +(1.04833e6 - 605255. i) q^{98} +(-695059. - 531645. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

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