LMFDB - Embedded newform 35.10.k.a.3.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,10,Mod(3,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("35.3");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	35.k (of order $12$, degree $4$, 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:	$18.0262542657$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$34$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			3.18
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.78516 + 0.746280i) q^{2} +(-58.8948 - 219.798i) q^{3} +(-436.205 - 251.843i) q^{4} +(332.404 + 1357.44i) q^{5} -656.125i q^{6} +(-4609.57 + 4370.98i) q^{7} +(-2070.86 - 2070.86i) q^{8} +(-27796.8 + 16048.5i) q^{9} +(-87.2304 + 4028.74i) q^{10} +(-1797.21 + 3112.86i) q^{11} +(-29664.5 + 110709. i) q^{12} +(85773.0 - 85773.0i) q^{13} +(-16100.3 + 8733.84i) q^{14} +(278785. - 153008. i) q^{15} +(124721. + 216024. i) q^{16} +(283380. - 75931.3i) q^{17} +(-89395.0 + 23953.3i) q^{18} +(-212428. - 367937. i) q^{19} +(196864. - 675834. i) q^{20} +(1.23221e6 + 755748. i) q^{21} +(-7328.58 + 7328.58i) q^{22} +(-389878. + 1.45505e6i) q^{23} +(-333208. + 577134. i) q^{24} +(-1.73214e6 + 902435. i) q^{25} +(302902. - 174880. i) q^{26} +(1.99745e6 + 1.99745e6i) q^{27} +(3.11152e6 - 745757. i) q^{28} +2.16272e6i q^{29} +(890647. - 218099. i) q^{30} +(3.45039e6 + 1.99208e6i) q^{31} +(574243. + 2.14310e6i) q^{32} +(790048. + 211693. i) q^{33} +845922. q^{34} +(-7.46557e6 - 4.80426e6i) q^{35} +1.61668e7 q^{36} +(6.63470e6 + 1.77776e6i) q^{37} +(-317062. - 1.18329e6i) q^{38} +(-2.39044e7 - 1.38012e7i) q^{39} +(2.12269e6 - 3.49942e6i) q^{40} +3.63281e6i q^{41} +(2.86791e6 + 3.02445e6i) q^{42} +(2.77832e7 + 2.77832e7i) q^{43} +(1.56790e6 - 905230. i) q^{44} +(-3.10245e7 - 3.23978e7i) q^{45} +(-2.17174e6 + 3.76157e6i) q^{46} +(-1.59307e7 + 5.94543e7i) q^{47} +(4.01362e7 - 4.01362e7i) q^{48} +(2.14263e6 - 4.02967e7i) q^{49} +(-5.49775e6 + 1.22076e6i) q^{50} +(-3.33792e7 - 5.78144e7i) q^{51} +(-5.90159e7 + 1.58133e7i) q^{52} +(-5.92787e7 + 1.58837e7i) q^{53} +(4.07255e6 + 7.05387e6i) q^{54} +(-4.82291e6 - 1.40487e6i) q^{55} +(1.85974e7 + 494076. i) q^{56} +(-6.83610e7 + 6.83610e7i) q^{57} +(-1.61399e6 + 6.02351e6i) q^{58} +(-4.55948e7 + 7.89725e7i) q^{59} +(-1.60142e8 - 3.46739e6i) q^{60} +(1.20833e8 - 6.97631e7i) q^{61} +(8.12322e6 + 8.12322e6i) q^{62} +(5.79835e7 - 1.95476e8i) q^{63} -1.21317e8i q^{64} +(1.44943e8 + 8.79201e7i) q^{65} +(2.04243e6 + 1.17919e6i) q^{66} +(-7.19519e7 - 2.68528e8i) q^{67} +(-1.42734e8 - 3.82455e7i) q^{68} +3.42779e8 q^{69} +(-1.72074e7 - 1.89520e7i) q^{70} -6.36797e7 q^{71} +(9.07973e7 + 2.43291e7i) q^{72} +(1.04439e8 + 3.89772e8i) q^{73} +(1.71520e7 + 9.90268e6i) q^{74} +(3.00368e8 + 3.27573e8i) q^{75} +2.13994e8i q^{76} +(-5.32189e6 - 2.22045e7i) q^{77} +(-5.62778e7 - 5.62778e7i) q^{78} +(-1.14647e8 + 6.61912e7i) q^{79} +(-2.51781e8 + 2.41109e8i) q^{80} +(5.51488e6 - 9.55206e6i) q^{81} +(-2.71110e6 + 1.01180e7i) q^{82} +(-2.53316e8 + 2.53316e8i) q^{83} +(-3.47168e8 - 6.39985e8i) q^{84} +(1.97268e8 + 3.59430e8i) q^{85} +(5.66464e7 + 9.81144e7i) q^{86} +(4.75362e8 - 1.27373e8i) q^{87} +(1.01681e7 - 2.72452e6i) q^{88} +(1.71855e8 + 2.97662e8i) q^{89} +(-6.22304e7 - 1.13386e8i) q^{90} +(-2.04642e7 + 7.70289e8i) q^{91} +(5.36510e8 - 5.36510e8i) q^{92} +(2.34647e8 - 8.75714e8i) q^{93} +(-8.87390e7 + 1.53701e8i) q^{94} +(4.28838e8 - 4.10661e8i) q^{95} +(4.37231e8 - 2.52435e8i) q^{96} +(1.08286e8 + 1.08286e8i) q^{97} +(3.60402e7 - 1.10634e8i) q^{98} -1.15370e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) $ 136 * q - 2 * q^2 - 6 * q^3 - 1710 * q^5 + 5940 * q^7 - 3484 * q^8 + 153786 * q^10 - 87752 * q^11 + 3066 * q^12 - 318872 * q^15 + 3132804 * q^16 - 1578678 * q^17 - 239036 * q^18 - 5745396 * q^21 + 2132088 * q^22 + 312550 * q^23 + 4308518 * q^25 + 2294580 * q^26 - 9559382 * q^28 + 21412708 * q^30 + 8900220 * q^31 + 17154282 * q^32 - 13729410 * q^33 + 6034552 * q^35 - 114903056 * q^36 + 26817310 * q^37 - 20958672 * q^38 + 143985558 * q^40 - 38052106 * q^42 + 46427728 * q^43 - 96332286 * q^45 + 2421124 * q^46 + 147698754 * q^47 - 11742092 * q^50 - 138178540 * q^51 - 126665976 * q^52 - 16288570 * q^53 + 501495076 * q^56 - 71567164 * q^57 - 681848346 * q^58 + 254653694 * q^60 - 575844240 * q^61 + 491512776 * q^63 + 833960586 * q^65 + 260439612 * q^66 + 22092746 * q^67 - 2824755312 * q^68 - 1044240840 * q^70 + 355056144 * q^71 + 98662792 * q^72 + 1852831146 * q^73 + 2937834474 * q^75 + 1226263510 * q^77 + 2595615712 * q^78 - 3778385244 * q^80 + 1504403888 * q^81 - 3707543946 * q^82 - 1726556112 * q^85 + 1771746456 * q^86 + 30331668 * q^87 - 1182712628 * q^88 - 4378590056 * q^91 + 2593806924 * q^92 - 4305536726 * q^93 + 861804818 * q^95 + 15624596040 * q^96 + 5117393178 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.78516	+	0.746280i	0.123088	+	0.0329812i	0.319837	−	0.947473i	$-0.396372\pi$
$2$	2.78516	+	0.746280i	0.123088	+	0.0329812i	−0.196749	+	0.980454i	$0.563039\pi$
$3$	−58.8948	−	219.798i	−0.419789	−	1.56668i	−0.775045	−	0.631906i	$-0.782273\pi$
$3$	−58.8948	−	219.798i	−0.419789	−	1.56668i	0.355256	−	0.934769i	$-0.384394\pi$
$4$	−436.205	−	251.843i	−0.851963	−	0.491881i
$5$	332.404	+	1357.44i	0.237849	+	0.971302i
$5$	332.404	+	1357.44i	0.237849	+	0.971302i
$6$		−	656.125i		−	0.206684i
$7$	−4609.57	+	4370.98i	−0.725636	+	0.688078i
$7$	−4609.57	+	4370.98i	−0.725636	+	0.688078i
$8$	−2070.86	−	2070.86i	−0.178750	−	0.178750i
$9$	−27796.8	+	16048.5i	−1.41222	+	0.815347i
$10$	−87.2304	+	4028.74i	−0.00275847	+	0.127400i
$11$	−1797.21	+	3112.86i	−0.0370111	+	0.0641051i	−0.883938	−	0.467605i	$-0.845117\pi$
$11$	−1797.21	+	3112.86i	−0.0370111	+	0.0641051i	0.846927	+	0.531710i	$0.178450\pi$
$12$	−29664.5	+	110709.i	−0.412973	+	1.54124i
$13$	85773.0	−	85773.0i	0.832924	−	0.832924i	−0.154991	−	0.987916i	$-0.549535\pi$
$13$	85773.0	−	85773.0i	0.832924	−	0.832924i	0.987916	+	0.154991i	$0.0495350\pi$
$14$	−16100.3	+	8733.84i	−0.112011	+	0.0607616i
$15$	278785.	−	153008.i	1.42187	−	0.780374i
$16$	124721.	+	216024.i	0.475774	+	0.824065i
$17$	283380.	−	75931.3i	0.822902	−	0.220496i	0.177287	−	0.984159i	$-0.443268\pi$
$17$	283380.	−	75931.3i	0.822902	−	0.220496i	0.645615	+	0.763663i	$0.276601\pi$
$18$	−89395.0	+	23953.3i	−0.200718	+	0.0537823i
$19$	−212428.	−	367937.i	−0.373957	−	0.647712i	0.616214	−	0.787579i	$-0.288666\pi$
$19$	−212428.	−	367937.i	−0.373957	−	0.647712i	−0.990170	+	0.139867i	$0.955332\pi$
$20$	196864.	−	675834.i	0.275126	−	0.944506i
$21$	1.23221e6	+	755748.i	1.38261	+	0.847989i
$22$	−7328.58	+	7328.58i	−0.00666987	+	0.00666987i
$23$	−389878.	+	1.45505e6i	−0.290505	+	1.08418i	0.654217	+	0.756307i	$0.272998\pi$
$23$	−389878.	+	1.45505e6i	−0.290505	+	1.08418i	−0.944722	+	0.327873i	$0.893668\pi$
$24$	−333208.	+	577134.i	−0.205005	+	0.355080i
$25$	−1.73214e6	+	902435.i	−0.886856	+	0.462047i
$26$	302902.	−	174880.i	0.129994	−	0.0750518i
$27$	1.99745e6	+	1.99745e6i	0.723334	+	0.723334i
$28$	3.11152e6	−	745757.i	0.956668	−	0.229290i
$29$			2.16272e6i			0.567818i	0.958851	+	0.283909i	$0.0916314\pi$
$29$			2.16272e6i			0.567818i	−0.958851	+	0.283909i	$0.908369\pi$
$30$	890647.	−	218099.i	0.200752	−	0.0491595i
$31$	3.45039e6	+	1.99208e6i	0.671028	+	0.387418i	0.796466	−	0.604683i	$-0.206700\pi$
$31$	3.45039e6	+	1.99208e6i	0.671028	+	0.387418i	−0.125438	+	0.992101i	$0.540034\pi$
$32$	574243.	+	2.14310e6i	0.0968102	+	0.361300i
$33$	790048.	+	211693.i	0.115969	+	0.0310737i
$34$	845922.			0.108561
$35$	−7.46557e6	−	4.80426e6i	−0.840924	−	0.541153i
$36$	1.61668e7			1.60421
$37$	6.63470e6	+	1.77776e6i	0.581987	+	0.155943i	0.537788	−	0.843080i	$-0.319260\pi$
$37$	6.63470e6	+	1.77776e6i	0.581987	+	0.155943i	0.0441986	+	0.999023i	$0.485927\pi$
$38$	−317062.	−	1.18329e6i	−0.0246671	−	0.0920589i
$39$	−2.39044e7	−	1.38012e7i	−1.65457	−	0.955269i
$40$	2.12269e6	−	3.49942e6i	0.131104	−	0.216135i
$41$			3.63281e6i			0.200778i	0.994948	+	0.100389i	$0.0320087\pi$
$41$			3.63281e6i			0.200778i	−0.994948	+	0.100389i	$0.967991\pi$
$42$	2.86791e6	+	3.02445e6i	0.142214	+	0.149977i
$43$	2.77832e7	+	2.77832e7i	1.23929	+	1.23929i	0.960291	+	0.279001i	$0.0900033\pi$
$43$	2.77832e7	+	2.77832e7i	1.23929	+	1.23929i	0.279001	+	0.960291i	$0.409997\pi$
$44$	1.56790e6	−	905230.i	0.0630641	−	0.0364101i
$45$	−3.10245e7	−	3.23978e7i	−1.12784	−	1.17777i
$46$	−2.17174e6	+	3.76157e6i	−0.0715152	+	0.123868i
$47$	−1.59307e7	+	5.94543e7i	−0.476206	+	1.77723i	0.140552	+	0.990073i	$0.455112\pi$
$47$	−1.59307e7	+	5.94543e7i	−0.476206	+	1.77723i	−0.616759	+	0.787152i	$0.711555\pi$
$48$	4.01362e7	−	4.01362e7i	1.09132	−	1.09132i
$49$	2.14263e6	−	4.02967e7i	0.0530963	−	0.998589i
$50$	−5.49775e6	+	1.22076e6i	−0.124400	+	0.0276226i
$51$	−3.33792e7	−	5.78144e7i	−0.690891	−	1.19666i
$52$	−5.90159e7	+	1.58133e7i	−1.11932	+	0.299921i
$53$	−5.92787e7	+	1.58837e7i	−1.03195	+	0.276509i	−0.734772	−	0.678314i	$-0.762711\pi$
$53$	−5.92787e7	+	1.58837e7i	−1.03195	+	0.276509i	−0.297175	+	0.954823i	$0.596044\pi$
$54$	4.07255e6	+	7.05387e6i	0.0651771	+	0.112890i
$55$	−4.82291e6	−	1.40487e6i	−0.0710685	−	0.0207016i
$56$	1.85974e7	+	494076.i	0.252701	+	0.00671348i
$57$	−6.83610e7	+	6.83610e7i	−0.857771	+	0.857771i
$58$	−1.61399e6	+	6.02351e6i	−0.0187273	+	0.0698914i
$59$	−4.55948e7	+	7.89725e7i	−0.489871	+	0.848481i	−0.999932	−	0.0116572i	$-0.996289\pi$
$59$	−4.55948e7	+	7.89725e7i	−0.489871	+	0.848481i	0.510061	+	0.860138i	$0.329623\pi$
$60$	−1.60142e8	−	3.46739e6i	−1.59523	−	0.0345400i
$61$	1.20833e8	−	6.97631e7i	1.11738	−	0.645122i	0.176652	−	0.984273i	$-0.443473\pi$
$61$	1.20833e8	−	6.97631e7i	1.11738	−	0.645122i	0.940732	+	0.339152i	$0.110140\pi$
$62$	8.12322e6	+	8.12322e6i	0.0698178	+	0.0698178i
$63$	5.79835e7	−	1.95476e8i	0.463737	−	1.56337i
$64$		−	1.21317e8i		−	0.903884i
$65$	1.44943e8	+	8.79201e7i	1.00713	+	0.610911i
$66$	2.04243e6	+	1.17919e6i	0.0132495	+	0.00764958i
$67$	−7.19519e7	−	2.68528e8i	−0.436220	−	1.62800i	−0.738129	−	0.674660i	$-0.764290\pi$
$67$	−7.19519e7	−	2.68528e8i	−0.436220	−	1.62800i	0.301909	−	0.953337i	$-0.402376\pi$
$68$	−1.42734e8	−	3.82455e7i	−0.809540	−	0.216916i
$69$	3.42779e8			1.82051
$70$	−1.72074e7	−	1.89520e7i	−0.0856594	−	0.0943440i
$71$	−6.36797e7			−0.297398			−0.148699	−	0.988882i	$-0.547509\pi$
$71$	−6.36797e7			−0.297398			−0.148699	+	0.988882i	$0.547509\pi$
$72$	9.07973e7	+	2.43291e7i	0.398177	+	0.106691i
$73$	1.04439e8	+	3.89772e8i	0.430438	+	1.60642i	0.751753	+	0.659445i	$0.229209\pi$
$73$	1.04439e8	+	3.89772e8i	0.430438	+	1.60642i	−0.321315	+	0.946972i	$0.604125\pi$
$74$	1.71520e7	+	9.90268e6i	0.0664922	+	0.0383893i
$75$	3.00368e8	+	3.27573e8i	1.09617	+	1.19545i
$76$			2.13994e8i			0.735768i
$77$	−5.32189e6	−	2.22045e7i	−0.0172527	−	0.0719835i
$78$	−5.62778e7	−	5.62778e7i	−0.172152	−	0.172152i
$79$	−1.14647e8	+	6.61912e7i	−0.331161	+	0.191196i	−0.656356	−	0.754451i	$-0.727903\pi$
$79$	−1.14647e8	+	6.61912e7i	−0.331161	+	0.191196i	0.325196	+	0.945647i	$0.394570\pi$
$80$	−2.51781e8	+	2.41109e8i	−0.687254	+	0.658124i
$81$	5.51488e6	−	9.55206e6i	0.0142349	−	0.0246555i
$82$	−2.71110e6	+	1.01180e7i	−0.00662190	+	0.0247133i
$83$	−2.53316e8	+	2.53316e8i	−0.585885	+	0.585885i	−0.936514	−	0.350630i	$-0.885968\pi$
$83$	−2.53316e8	+	2.53316e8i	−0.585885	+	0.585885i	0.350630	+	0.936514i	$0.385968\pi$
$84$	−3.47168e8	−	6.39985e8i	−0.760823	−	1.40253i
$85$	1.97268e8	+	3.59430e8i	0.409895	+	0.746842i
$86$	5.66464e7	+	9.81144e7i	0.111668	+	0.193415i
$87$	4.75362e8	−	1.27373e8i	0.889587	−	0.238364i
$88$	1.01681e7	−	2.72452e6i	0.0180745	−	0.00484304i
$89$	1.71855e8	+	2.97662e8i	0.290341	+	0.502885i	0.973890	−	0.227019i	$-0.0728980\pi$
$89$	1.71855e8	+	2.97662e8i	0.290341	+	0.502885i	−0.683550	+	0.729904i	$0.739565\pi$
$90$	−6.22304e7	−	1.13386e8i	−0.0999795	−	0.182166i
$91$	−2.04642e7	+	7.70289e8i	−0.0312830	+	1.17752i
$92$	5.36510e8	−	5.36510e8i	0.780787	−	0.780787i
$93$	2.34647e8	−	8.75714e8i	0.325268	−	1.21392i
$94$	−8.87390e7	+	1.53701e8i	−0.117230	+	0.203049i
$95$	4.28838e8	−	4.10661e8i	0.540179	−	0.517282i
$96$	4.37231e8	−	2.52435e8i	0.525401	−	0.303340i
$97$	1.08286e8	+	1.08286e8i	0.124193	+	0.124193i	0.766472	−	0.642278i	$-0.222011\pi$
$97$	1.08286e8	+	1.08286e8i	0.124193	+	0.124193i	−0.642278	+	0.766472i	$0.722011\pi$
$98$	3.60402e7	−	1.10634e8i	0.0394702	−	0.121163i
$99$		−	1.15370e8i		−	0.120708i
$100$	9.82840e8	+	4.25810e7i	0.982840	+	0.0425810i
$101$	8.67069e8	+	5.00603e8i	0.829101	+	0.478682i	0.853545	−	0.521019i	$-0.174448\pi$
$101$	8.67069e8	+	5.00603e8i	0.829101	+	0.478682i	−0.0244437	+	0.999701i	$0.507781\pi$
$102$	−4.98204e7	−	1.85932e8i	−0.0455729	−	0.170080i
$103$	−1.98231e9	−	5.31158e8i	−1.73542	−	0.465004i	−0.753997	−	0.656878i	$-0.771877\pi$
$103$	−1.98231e9	−	5.31158e8i	−1.73542	−	0.465004i	−0.981420	+	0.191874i	$0.938543\pi$
$104$	−3.55247e8			−0.297770
$105$	−6.16286e8	+	1.92387e9i	−0.494801	+	1.54463i
$106$	−1.76954e8			−0.136140
$107$	−1.16344e9	−	3.11742e8i	−0.858055	−	0.229915i	−0.197140	−	0.980375i	$-0.563165\pi$
$107$	−1.16344e9	−	3.11742e8i	−0.858055	−	0.229915i	−0.660916	+	0.750460i	$0.729832\pi$
$108$	−3.68254e8	−	1.37434e9i	−0.260460	−	0.972048i
$109$	7.84896e8	+	4.53160e8i	0.532590	+	0.307491i	0.742071	−	0.670322i	$-0.233844\pi$
$109$	7.84896e8	+	4.53160e8i	0.532590	+	0.307491i	−0.209480	+	0.977813i	$0.567177\pi$
$110$	−1.23841e7	−	7.51203e6i	−0.00806489	−	0.00489204i
$111$		−	1.56300e9i		−	0.977248i
$112$	−1.51915e9	−	4.50621e8i	−0.912261	−	0.270602i
$113$	−7.67819e8	−	7.67819e8i	−0.443002	−	0.443002i	0.450018	−	0.893020i	$-0.351418\pi$
$113$	−7.67819e8	−	7.67819e8i	−0.443002	−	0.443002i	−0.893020	+	0.450018i	$0.851418\pi$
$114$	−2.41412e8	+	1.39379e8i	−0.133871	+	0.0772907i
$115$	−2.10473e9	−	4.55717e7i	−1.12216	−	0.0242971i
$116$	5.44666e8	−	9.43389e8i	0.279299	−	0.483760i
$117$	−1.00769e9	+	3.76074e9i	−0.497152	+	1.85540i
$118$	−1.85924e8	+	1.85924e8i	−0.0882809	+	0.0882809i
$119$	−9.74363e8	+	1.58866e9i	−0.445409	+	0.726221i
$120$	−8.94182e8	−	2.60467e8i	−0.393650	−	0.114667i
$121$	1.17251e9	+	2.03085e9i	0.497260	+	0.861280i
$122$	3.88602e8	−	1.04126e8i	0.158813	−	0.0425538i
$123$	7.98487e8	−	2.13954e8i	0.314554	−	0.0842844i
$124$	−1.00339e9	−	1.73791e9i	−0.381127	−	0.660132i
$125$	−1.80077e9	−	2.05130e9i	−0.659725	−	0.751508i
$126$	3.07373e8	−	5.01159e8i	0.108642	−	0.177136i
$127$	−4.25719e8	+	4.25719e8i	−0.145213	+	0.145213i	−0.775976	−	0.630763i	$-0.782742\pi$
$127$	−4.25719e8	+	4.25719e8i	−0.145213	+	0.145213i	0.630763	+	0.775976i	$0.282742\pi$
$128$	3.84549e8	−	1.43516e9i	0.126621	−	0.472557i
$129$	4.47041e9	−	7.74298e9i	1.42133	−	2.46181i
$130$	3.38075e8	+	3.53039e8i	0.103817	+	0.108412i
$131$	1.10332e9	−	6.37004e8i	0.327327	−	0.188982i	−0.327327	−	0.944911i	$-0.606148\pi$
$131$	1.10332e9	−	6.37004e8i	0.327327	−	0.188982i	0.654654	+	0.755929i	$0.272814\pi$
$132$	−2.91310e8	−	2.91310e8i	−0.0835165	−	0.0835165i
$133$	2.58745e9	+	7.67508e8i	0.717033	+	0.212692i
$134$		−	8.01589e8i		−	0.214773i
$135$	−2.04745e9	+	3.37537e9i	−0.530532	+	0.874621i
$136$	−7.44081e8	−	4.29596e8i	−0.186507	−	0.107680i
$137$	1.62417e9	+	6.06148e9i	0.393902	+	1.47006i	0.823642	+	0.567110i	$0.191939\pi$
$137$	1.62417e9	+	6.06148e9i	0.393902	+	1.47006i	−0.429739	+	0.902953i	$0.641395\pi$
$138$	9.54691e8	+	2.55809e8i	0.224082	+	0.0600426i
$139$	−3.00434e9			−0.682627			−0.341313	−	0.939950i	$-0.610872\pi$
$139$	−3.00434e9			−0.682627			−0.341313	+	0.939950i	$0.610872\pi$
$140$	2.04660e9	+	3.97579e9i	0.450253	+	0.874677i
$141$	1.40062e10			2.98424
$142$	−1.77358e8	−	4.75229e7i	−0.0366061	−	0.00980856i
$143$	1.12847e8	+	4.21152e8i	0.0225673	+	0.0842221i
$144$	−6.93371e9	−	4.00318e9i	−1.34380	−	0.775843i
$145$	−2.93575e9	+	7.18897e8i	−0.551523	+	0.135055i
$146$			1.16352e9i			0.211926i
$147$	−8.98334e9	+	1.90232e9i	−1.58675	+	0.336013i
$148$	−2.44637e9	−	2.44637e9i	−0.419126	−	0.419126i
$149$	9.83035e9	−	5.67555e9i	1.63392	−	0.943344i	0.651052	−	0.759033i	$-0.274328\pi$
$149$	9.83035e9	−	5.67555e9i	1.63392	−	0.943344i	0.982868	−	0.184311i	$-0.0590052\pi$
$150$	5.92110e8	+	1.13650e9i	0.0954974	+	0.183298i
$151$	3.97790e9	−	6.88992e9i	0.622669	−	1.07849i	−0.366317	−	0.930490i	$-0.619382\pi$
$151$	3.97790e9	−	6.88992e9i	0.622669	−	1.07849i	0.988987	−	0.148005i	$-0.0472851\pi$
$152$	−3.22035e8	+	1.20185e9i	−0.0489336	+	0.182623i
$153$	−6.65846e9	+	6.65846e9i	−0.982341	+	0.982341i
$154$	1.74849e6	−	6.58147e7i	0.000250507	−	0.00942930i
$155$	−1.55720e9	+	5.34586e9i	−0.216697	+	0.743918i
$156$	6.95147e9	+	1.20403e10i	0.939757	+	1.62771i
$157$	−2.58308e8	+	6.92135e7i	−0.0339305	+	0.00909164i	−0.275744	−	0.961231i	$-0.588924\pi$
$157$	−2.58308e8	+	6.92135e7i	−0.0339305	+	0.00909164i	0.241814	+	0.970323i	$0.422258\pi$
$158$	−3.68706e8	+	9.87943e7i	−0.0470677	+	0.0126117i
$159$	6.98242e9	+	1.20939e10i	0.866401	+	1.50065i
$160$	−2.71825e9	+	1.49188e9i	−0.327906	+	0.179967i
$161$	−4.56281e9	−	8.41128e9i	−0.535200	−	0.986611i
$162$	2.24883e7	−	2.24883e7i	0.00256531	−	0.00256531i
$163$	1.80599e8	−	6.74003e8i	0.0200387	−	0.0747856i	−0.955182	−	0.296018i	$-0.904341\pi$
$163$	1.80599e8	−	6.74003e8i	0.0200387	−	0.0747856i	0.975221	+	0.221232i	$0.0710079\pi$
$164$	9.14899e8	−	1.58465e9i	0.0987588	−	0.171055i
$165$	−2.47441e7	+	1.14281e9i	−0.00259893	+	0.120032i
$166$	−8.94571e8	+	5.16481e8i	−0.0914383	+	0.0527919i
$167$	3.72851e9	+	3.72851e9i	0.370946	+	0.370946i	0.867822	−	0.496876i	$-0.165519\pi$
$167$	3.72851e9	+	3.72851e9i	0.370946	+	0.370946i	−0.496876	+	0.867822i	$0.665519\pi$
$168$	−9.86695e8	−	4.11679e9i	−0.0955634	−	0.398719i
$169$		−	4.10952e9i		−	0.387526i
$170$	2.81188e8	+	1.14829e9i	0.0258212	+	0.105446i
$171$	1.18096e10	+	6.81830e9i	1.05622	+	0.609809i
$172$	−5.12215e9	−	1.91161e10i	−0.446246	−	1.66541i
$173$	9.22167e8	+	2.47094e8i	0.0782712	+	0.0209727i	0.297742	−	0.954646i	$-0.403766\pi$
$173$	9.22167e8	+	2.47094e8i	0.0782712	+	0.0209727i	−0.219471	+	0.975619i	$0.570433\pi$
$174$	1.41901e9			0.117359
$175$	4.03989e9	−	1.17310e10i	0.325611	−	0.945504i
$176$	−8.96603e8			−0.0704357
$177$	2.00433e10	+	5.37060e9i	1.53494	+	0.411285i
$178$	2.56504e8	+	9.57288e8i	0.0191516	+	0.0714747i
$179$	−1.21512e10	−	7.01548e9i	−0.884667	−	0.510763i	−0.0124724	−	0.999922i	$-0.503970\pi$
$179$	−1.21512e10	−	7.01548e9i	−0.884667	−	0.510763i	−0.872194	+	0.489160i	$0.837304\pi$
$180$	5.37391e9	+	2.19454e10i	0.381561	+	1.55818i
$181$			4.59071e8i			0.0317926i	0.999874	+	0.0158963i	$0.00506016\pi$
$181$			4.59071e8i			0.0317926i	−0.999874	+	0.0158963i	$0.994940\pi$
$182$	−6.31847e8	+	2.13010e9i	−0.0426865	+	0.143906i
$183$	−2.24503e10	−	2.24503e10i	−1.47976	−	1.47976i
$184$	3.82057e9	−	2.20581e9i	0.245724	−	0.141869i
$185$	−2.07797e8	+	9.59711e9i	−0.0130427	+	0.602376i
$186$	1.30706e9	−	2.26389e9i	0.0800730	−	0.138690i
$187$	−2.72929e8	+	1.01859e9i	−0.0163216	+	0.0609130i
$188$	2.19222e10	−	2.19222e10i	1.27989	−	1.27989i
$189$	−1.79382e10	−	4.76562e8i	−1.02259	−	0.0271670i
$190$	1.50085e9	−	8.23722e8i	0.0835499	−	0.0458553i
$191$	−8.61997e9	−	1.49302e10i	−0.468658	−	0.811739i	0.530700	−	0.847559i	$-0.321929\pi$
$191$	−8.61997e9	−	1.49302e10i	−0.468658	−	0.811739i	−0.999358	+	0.0358204i	$0.988596\pi$
$192$	−2.66653e10	+	7.14496e9i	−1.41609	+	0.379441i
$193$	−2.29586e10	+	6.15174e9i	−1.19107	+	0.319146i	−0.799309	−	0.600921i	$-0.794801\pi$
$193$	−2.29586e10	+	6.15174e9i	−1.19107	+	0.319146i	−0.391761	+	0.920067i	$0.628134\pi$
$194$	2.20781e8	+	3.82404e8i	0.0111906	+	0.0193827i
$195$	1.07883e10	−	3.70362e10i	0.534316	−	1.83430i
$196$	−1.10831e10	+	1.70380e10i	−0.536423	+	0.824644i
$197$	8.18874e9	−	8.18874e9i	0.387364	−	0.387364i	−0.486382	−	0.873746i	$-0.661684\pi$
$197$	8.18874e9	−	8.18874e9i	0.387364	−	0.387364i	0.873746	+	0.486382i	$0.161684\pi$
$198$	8.60983e7	−	3.21323e8i	0.00398108	−	0.0148576i
$199$	−9.73716e9	+	1.68652e10i	−0.440142	+	0.762349i	−0.997700	−	0.0677894i	$-0.978405\pi$
$199$	−9.73716e9	+	1.68652e10i	−0.440142	+	0.762349i	0.557557	+	0.830139i	$0.311739\pi$
$200$	5.45583e9	+	1.71820e9i	0.241116	+	0.0759345i
$201$	−5.47845e10	+	3.16298e10i	−2.36742	+	1.36683i
$202$	2.04133e9	+	2.04133e9i	0.0862646	+	0.0862646i
$203$	−9.45321e9	−	9.96920e9i	−0.390703	−	0.412029i
$204$			3.36252e10i			1.35935i
$205$	−4.93131e9	+	1.20756e9i	−0.195016	+	0.0477548i
$206$	−5.12464e9	−	2.95872e9i	−0.198272	−	0.114472i
$207$	−1.25139e10	−	4.67025e10i	−0.473725	−	1.76797i
$208$	2.92267e10	+	7.83128e9i	1.08267	+	0.290100i
$209$	1.52711e9			0.0553622
$210$	−3.15219e9	+	4.89834e9i	−0.111847	+	0.173805i
$211$	2.23812e10			0.777341			0.388671	−	0.921377i	$-0.372934\pi$
$211$	2.23812e10			0.777341			0.388671	+	0.921377i	$0.372934\pi$
$212$	2.98579e10	+	8.00039e9i	1.01519	+	0.272019i
$213$	3.75041e9	+	1.39967e10i	0.124845	+	0.465927i
$214$	−3.00770e9	−	1.73650e9i	−0.0980331	−	0.0565994i
$215$	−2.84786e10	+	4.69491e10i	−0.908962	+	1.49849i
$216$		−	8.27287e9i		−	0.258592i
$217$	−2.46122e10	+	5.89895e9i	−0.753497	+	0.180595i
$218$	1.84787e9	+	1.84787e9i	0.0554138	+	0.0554138i
$219$	7.95205e10	−	4.59112e10i	2.33604	−	1.34871i
$220$	1.74997e9	+	1.82743e9i	0.0503650	+	0.0525942i
$221$	1.77935e10	−	3.08192e10i	0.501759	−	0.869072i
$222$	1.16643e9	−	4.35319e9i	0.0322308	−	0.120287i
$223$	−2.88495e10	+	2.88495e10i	−0.781209	+	0.781209i	−0.980035	−	0.198826i	$-0.936287\pi$
$223$	−2.88495e10	+	2.88495e10i	−0.781209	+	0.781209i	0.198826	+	0.980035i	$0.436287\pi$
$224$	−1.20145e10	−	7.36878e9i	−0.318852	−	0.195560i
$225$	3.36652e10	−	5.28830e10i	0.875709	−	1.37561i
$226$	−1.56549e9	−	2.71150e9i	−0.0399173	−	0.0691388i
$227$	5.77033e10	−	1.54616e10i	1.44240	−	0.386489i	0.549024	−	0.835806i	$-0.314999\pi$
$227$	5.77033e10	−	1.54616e10i	1.44240	−	0.386489i	0.893372	+	0.449317i	$0.148333\pi$
$228$	4.70356e10	−	1.26032e10i	1.15271	−	0.308868i
$229$	−1.74028e10	−	3.01426e10i	−0.418177	−	0.724304i	0.577579	−	0.816335i	$-0.303998\pi$
$229$	−1.74028e10	−	3.01426e10i	−0.418177	−	0.724304i	−0.995756	+	0.0920308i	$0.970664\pi$
$230$	−5.82799e9	−	1.69764e9i	−0.137323	−	0.0400010i
$231$	−4.56709e9	+	2.47748e9i	−0.105532	+	0.0572474i
$232$	4.47868e9	−	4.47868e9i	0.101497	−	0.101497i
$233$	−1.77311e10	+	6.61734e10i	−0.394125	+	1.47089i	0.429140	+	0.903238i	$0.358817\pi$
$233$	−1.77311e10	+	6.61734e10i	−0.394125	+	1.47089i	−0.823265	+	0.567657i	$0.807850\pi$
$234$	−5.61313e9	+	9.72223e9i	−0.122387	+	0.211980i
$235$	−8.60008e10	−	1.86209e9i	−1.83949	−	0.0398287i
$236$	3.97774e10	−	2.29655e10i	0.834703	−	0.481916i
$237$	2.13008e10	+	2.13008e10i	0.438559	+	0.438559i
$238$	−3.89934e9	+	3.69751e9i	−0.0787761	+	0.0746987i
$239$			6.94608e10i			1.37705i	0.725213	+	0.688524i	$0.241741\pi$
$239$			6.94608e10i			1.37705i	−0.725213	+	0.688524i	$0.758259\pi$
$240$	6.78238e10	+	4.11409e10i	1.31957	+	0.800430i
$241$	−8.26375e9	−	4.77108e9i	−0.157798	−	0.0911045i	0.419022	−	0.907976i	$-0.362373\pi$
$241$	−8.26375e9	−	4.77108e9i	−0.157798	−	0.0911045i	−0.576820	+	0.816872i	$0.695706\pi$
$242$	1.75005e9	+	6.53127e9i	0.0328005	+	0.122413i
$243$	5.12821e10	+	1.37410e10i	0.943490	+	0.252807i
$244$	−7.02774e10			−1.26929
$245$	5.54124e10	−	1.04863e10i	0.982561	−	0.185941i
$246$	2.38358e9			0.0414975
$247$	−4.97796e10	−	1.33384e10i	−0.850973	−	0.228017i
$248$	−3.01995e9	−	1.12706e10i	−0.0506952	−	0.189197i
$249$	7.05976e10	+	4.07595e10i	1.16384	+	0.671943i
$250$	−3.48458e9	−	7.05706e9i	−0.0564183	−	0.114260i
$251$			3.44213e10i			0.547388i	0.961817	+	0.273694i	$0.0882456\pi$
$251$			3.44213e10i			0.547388i	−0.961817	+	0.273694i	$0.911754\pi$
$252$	−7.45219e10	+	7.06647e10i	−1.16408	+	1.10383i
$253$	−3.82866e9	−	3.82866e9i	−0.0587495	−	0.0587495i
$254$	−1.50340e9	+	8.67987e8i	−0.0226633	+	0.0130846i
$255$	6.73840e10	−	6.45278e10i	0.997990	−	0.955688i
$256$	−2.89152e10	+	5.00825e10i	−0.420771	+	0.728797i
$257$	−2.46633e10	+	9.20446e10i	−0.352656	+	1.31613i	0.530752	+	0.847527i	$0.321910\pi$
$257$	−2.46633e10	+	9.20446e10i	−0.352656	+	1.31613i	−0.883408	+	0.468604i	$0.844757\pi$
$258$	1.82292e10	−	1.82292e10i	0.256141	−	0.256141i
$259$	−3.83536e10	+	2.08054e10i	−0.529612	+	0.287295i
$260$	−4.10826e10	−	7.48540e10i	−0.557543	−	1.01586i
$261$	−3.47084e10	−	6.01166e10i	−0.462969	−	0.801886i
$262$	3.54831e9	−	9.50766e8i	0.0465228	−	0.0124657i
$263$	2.92929e10	−	7.84902e9i	0.377539	−	0.101161i	−0.0650589	−	0.997881i	$-0.520724\pi$
$263$	2.92929e10	−	7.84902e9i	0.377539	−	0.101161i	0.442598	+	0.896720i	$0.354057\pi$
$264$	−1.19769e9	−	2.07446e9i	−0.0151750	−	0.0262838i
$265$	−4.12656e10	−	7.51873e10i	−0.514022	−	0.936565i
$266$	6.63367e9	+	4.06859e9i	0.0812431	+	0.0498284i
$267$	5.53043e10	−	5.53043e10i	0.665975	−	0.665975i
$268$	−3.62412e10	+	1.35254e11i	−0.429137	+	1.60156i
$269$	6.62194e10	−	1.14695e11i	0.771081	−	1.33555i	−0.165890	−	0.986144i	$-0.553050\pi$
$269$	6.62194e10	−	1.14695e11i	0.771081	−	1.33555i	0.936971	−	0.349408i	$-0.113617\pi$
$270$	−8.22144e9	+	7.87296e9i	−0.0941480	+	0.0901574i
$271$	−1.91531e10	+	1.10581e10i	−0.215714	+	0.124542i	−0.603964	−	0.797012i	$-0.706413\pi$
$271$	−1.91531e10	+	1.10581e10i	−0.215714	+	0.124542i	0.388250	+	0.921554i	$0.373080\pi$
$272$	5.17465e10	+	5.17465e10i	0.573219	+	0.573219i
$273$	1.70514e11	−	4.08680e10i	1.85792	−	0.445299i
$274$			1.80942e10i			0.193938i
$275$	3.03868e8	−	7.01378e9i	0.00320396	−	0.0739528i
$276$	−1.49522e11	−	8.63264e10i	−1.55101	−	0.895473i
$277$	−1.62717e10	−	6.07267e10i	−0.166063	−	0.619756i	−0.997902	−	0.0647393i	$-0.979378\pi$
$277$	−1.62717e10	−	6.07267e10i	−0.166063	−	0.619756i	0.831839	−	0.555017i	$-0.187288\pi$
$278$	−8.36757e9	−	2.24208e9i	−0.0840229	−	0.0225139i
$279$	−1.27880e11			−1.26352
$280$	5.51119e9	+	2.54091e10i	0.0535839	+	0.247046i
$281$	2.03609e10			0.194813			0.0974065	−	0.995245i	$-0.468945\pi$
$281$	2.03609e10			0.194813			0.0974065	+	0.995245i	$0.468945\pi$
$282$	3.90094e10	+	1.04525e10i	0.367323	+	0.0984240i
$283$	2.27252e10	+	8.48117e10i	0.210605	+	0.785989i	0.987668	+	0.156566i	$0.0500423\pi$
$283$	2.27252e10	+	8.48117e10i	0.210605	+	0.785989i	−0.777062	+	0.629424i	$0.783291\pi$
$284$	2.77774e10	+	1.60373e10i	0.253372	+	0.146285i
$285$	−1.15519e11	−	7.00722e10i	−1.03717	−	0.629135i
$286$			1.25719e9i			0.0111110i
$287$	−1.58790e10	−	1.67457e10i	−0.138151	−	0.145692i
$288$	−5.03557e10	−	5.03557e10i	−0.431303	−	0.431303i
$289$	−2.81617e10	+	1.62592e10i	−0.237475	+	0.137106i
$290$	−8.71303e9	−	1.88655e8i	−0.0723399	−	0.00156631i
$291$	1.74236e10	−	3.01785e10i	0.142436	−	0.246706i
$292$	5.26046e10	−	1.96323e11i	0.423449	−	1.58033i
$293$	−9.03487e10	+	9.03487e10i	−0.716172	+	0.716172i	−0.967819	−	0.251647i	$-0.919028\pi$
$293$	−9.03487e10	+	9.03487e10i	−0.716172	+	0.716172i	0.251647	+	0.967819i	$0.419028\pi$
$294$	−2.64397e10	−	1.40583e9i	−0.206392	−	0.0109741i
$295$	−1.22356e11	−	3.56412e10i	−0.940646	−	0.274002i
$296$	−1.00580e10	−	1.74210e10i	−0.0761552	−	0.131905i
$297$	−9.80763e9	+	2.62795e9i	−0.0731408	+	0.0195980i
$298$	3.16146e10	−	8.47111e9i	0.232228	−	0.0622253i
$299$	9.13626e10	+	1.58245e11i	0.661071	+	1.14501i
$300$	−4.85249e10	−	2.18534e11i	−0.345875	−	1.55767i
$301$	−2.49508e11	−	6.62865e9i	−1.75201	−	0.0465453i
$302$	1.62209e10	−	1.62209e10i	0.112213	−	0.112213i
$303$	5.89658e10	−	2.20063e11i	0.401891	−	1.49988i
$304$	5.29887e10	−	9.17791e10i	0.355838	−	0.616329i
$305$	1.34864e11	+	1.40834e11i	0.892377	+	0.931875i
$306$	−2.35139e10	+	1.35758e10i	−0.153313	+	0.0885152i
$307$	1.34142e11	+	1.34142e11i	0.861870	+	0.861870i	0.991555	−	0.129686i	$-0.0413968\pi$
$307$	1.34142e11	+	1.34142e11i	0.861870	+	0.861870i	−0.129686	+	0.991555i	$0.541397\pi$
$308$	−3.27062e9	+	1.10260e10i	−0.0207086	+	0.0698136i
$309$			4.66991e11i			2.91404i
$310$	−8.32656e9	+	1.37270e10i	−0.0512080	+	0.0844202i
$311$	−7.69553e10	−	4.44302e10i	−0.466463	−	0.269312i	0.248295	−	0.968684i	$-0.420130\pi$
$311$	−7.69553e10	−	4.44302e10i	−0.466463	−	0.269312i	−0.714758	+	0.699372i	$0.753463\pi$
$312$	2.09222e10	+	7.80828e10i	0.125001	+	0.466509i
$313$	−7.26320e10	−	1.94617e10i	−0.427738	−	0.114612i	0.0385259	−	0.999258i	$-0.487734\pi$
$313$	−7.26320e10	−	1.94617e10i	−0.427738	−	0.114612i	−0.466264	+	0.884645i	$0.654400\pi$
$314$	−7.71081e8			−0.00447628
$315$	2.84620e11	+	1.37320e10i	1.62880	+	0.0785842i
$316$	6.66792e10			0.376182
$317$	−3.25498e11	−	8.72170e10i	−1.81043	−	0.485104i	−0.814906	−	0.579593i	$-0.803211\pi$
$317$	−3.25498e11	−	8.72170e10i	−1.81043	−	0.485104i	−0.995526	+	0.0944898i	$0.969878\pi$
$318$	1.04217e10	+	3.88942e10i	0.0571499	+	0.213286i
$319$	−6.73224e9	−	3.88686e9i	−0.0364000	−	0.0210156i
$320$	1.64680e11	−	4.03264e10i	0.877945	−	0.214988i
$321$			2.74081e11i			1.44081i
$322$	−6.43096e9	−	2.68319e10i	−0.0333368	−	0.139091i
$323$	−8.81358e10	−	8.81358e10i	−0.450548	−	0.450548i
$324$	−4.81124e9	+	2.77777e9i	−0.0242552	+	0.0140037i
$325$	−7.11663e10	+	2.25975e11i	−0.353834	+	1.12353i
$326$	1.00599e9	−	1.74243e9i	0.00493304	−	0.00854428i
$327$	5.33776e10	−	1.99208e11i	0.258163	−	0.963477i
$328$	7.52304e9	−	7.52304e9i	0.0358890	−	0.0358890i
$329$	−1.86440e11	−	3.43691e11i	−0.877318	−	1.61729i
$330$	−9.21771e8	+	3.16443e9i	−0.00427868	+	0.0146887i
$331$	−5.82989e10	−	1.00977e11i	−0.266953	−	0.462375i	0.701121	−	0.713043i	$-0.252683\pi$
$331$	−5.82989e10	−	1.00977e11i	−0.266953	−	0.462375i	−0.968073	+	0.250667i	$0.919350\pi$
$332$	1.74294e11	−	4.67019e10i	0.787337	−	0.210966i
$333$	−2.12954e11	+	5.70607e10i	−0.949043	+	0.254295i
$334$	7.60196e9	+	1.31670e10i	0.0334246	+	0.0578931i
$335$	3.40593e11	−	1.86930e11i	1.47752	−	0.810919i
$336$	−9.57591e9	+	3.60446e11i	−0.0409877	+	1.54281i
$337$	2.40951e11	−	2.40951e11i	1.01764	−	1.01764i	0.0177991	−	0.999842i	$-0.494334\pi$
$337$	2.40951e11	−	2.40951e11i	1.01764	−	1.01764i	0.999842	−	0.0177991i	$-0.00566592\pi$
$338$	3.06685e9	−	1.14457e10i	0.0127811	−	0.0476997i
$339$	−1.23545e11	+	2.13986e11i	−0.508073	+	0.880008i
$340$	4.47041e9	−	2.06466e11i	0.0181423	−	0.837901i
$341$	−1.24022e10	+	7.16039e9i	−0.0496710	+	0.0286776i
$342$	2.78033e10	+	2.78033e10i	0.109895	+	0.109895i
$343$	1.66260e11	+	1.95116e11i	0.648579	+	0.761147i
$344$		−	1.15070e11i		−	0.443046i
$345$	1.13941e11	+	4.65300e11i	0.433006	+	1.76826i
$346$	2.38398e9	+	1.37639e9i	0.00894252	+	0.00516296i
$347$	5.50176e9	+	2.05329e10i	0.0203713	+	0.0760268i	0.975363	−	0.220605i	$-0.0708032\pi$
$347$	5.50176e9	+	2.05329e10i	0.0203713	+	0.0760268i	−0.954992	+	0.296632i	$0.904137\pi$
$348$	−2.39433e11	−	6.41560e10i	−0.875141	−	0.234493i
$349$	1.39708e11			0.504087			0.252043	−	0.967716i	$-0.418897\pi$
$349$	1.39708e11			0.504087			0.252043	+	0.967716i	$0.418897\pi$
$350$	2.00063e10	−	2.96577e10i	0.0712625	−	0.105641i
$351$	3.42655e11			1.20497
$352$	−7.70322e9	−	2.06407e9i	−0.0267442	−	0.00716610i
$353$	1.11671e11	+	4.16760e11i	0.382783	+	1.42857i	0.841632	+	0.540051i	$0.181595\pi$
$353$	1.11671e11	+	4.16760e11i	0.382783	+	1.42857i	−0.458849	+	0.888514i	$0.651738\pi$
$354$	5.18158e10	+	2.99159e10i	0.175367	+	0.101248i
$355$	−2.11674e10	−	8.64411e10i	−0.0707359	−	0.288864i
$356$		−	1.73122e11i		−	0.571252i
$357$	4.06569e11	+	1.20600e11i	1.32473	+	0.392952i
$358$	−2.86074e10	−	2.86074e10i	−0.0920459	−	0.0920459i
$359$	3.63148e11	−	2.09663e11i	1.15387	−	0.666189i	0.204045	−	0.978961i	$-0.434591\pi$
$359$	3.63148e11	−	2.09663e11i	1.15387	−	0.666189i	0.949828	+	0.312772i	$0.101258\pi$
$360$	−2.84375e9	+	1.31339e11i	−0.00892340	+	0.412127i
$361$	7.10923e10	−	1.23135e11i	0.220313	−	0.381593i
$362$	−3.42596e8	+	1.27858e9i	−0.00104856	+	0.00391328i
$363$	3.77323e11	−	3.77323e11i	1.14060	−	1.14060i
$364$	2.02918e11	−	3.30850e11i	0.605850	−	0.987813i
$365$	−4.94375e11	+	2.71332e11i	−1.45794	+	0.800170i
$366$	−4.57733e10	−	7.92817e10i	−0.133336	−	0.230945i
$367$	−5.14635e11	+	1.37896e11i	−1.48082	+	0.396784i	−0.906625	−	0.421936i	$-0.861351\pi$
$367$	−5.14635e11	+	1.37896e11i	−1.48082	+	0.396784i	−0.574192	+	0.818720i	$0.694684\pi$
$368$	−3.62951e11	+	9.72523e10i	−1.03165	+	0.276430i
$369$	−5.83011e10	−	1.00981e11i	−0.163704	−	0.283543i
$370$	−7.74088e9	+	2.65744e10i	−0.0214725	+	0.0737149i
$371$	2.03822e11	−	3.32323e11i	0.558558	−	0.910706i
$372$	−3.22897e11	+	3.22897e11i	−0.874219	+	0.874219i
$373$	2.69647e10	−	1.00634e11i	0.0721284	−	0.269187i	−0.920438	−	0.390888i	$-0.872168\pi$
$373$	2.69647e10	−	1.00634e11i	0.0721284	−	0.269187i	0.992567	+	0.121701i	$0.0388348\pi$
$374$	−1.52030e9	+	2.63324e9i	−0.00401797	+	0.00695934i
$375$	−3.44816e11	+	5.16617e11i	−0.900423	+	1.34905i
$376$	1.56111e11	−	9.01310e10i	0.402800	−	0.232557i
$377$	1.85503e11	+	1.85503e11i	0.472950	+	0.472950i
$378$	−4.96050e10	−	1.47142e10i	−0.124972	−	0.0370702i
$379$			3.10212e11i			0.772294i	0.922437	+	0.386147i	$0.126194\pi$
$379$			3.10212e11i			0.772294i	−0.922437	+	0.386147i	$0.873806\pi$
$380$	−2.90484e11	+	7.11326e10i	−0.714653	+	0.175002i
$381$	1.18645e11	+	6.84997e10i	0.288461	+	0.166543i
$382$	−1.28658e10	−	4.80159e10i	−0.0309138	−	0.115372i
$383$	3.55234e11	+	9.51845e10i	0.843567	+	0.226033i	0.654624	−	0.755955i	$-0.272827\pi$
$383$	3.55234e11	+	9.51845e10i	0.843567	+	0.226033i	0.188943	+	0.981988i	$0.439494\pi$
$384$	−3.38093e11			−0.793498
$385$	2.83722e10	−	1.46050e10i	0.0658142	−	0.0338788i
$386$	−6.85341e10			−0.157132
$387$	−1.21816e12	−	3.26405e11i	−2.76061	−	0.739703i
$388$	−1.99638e10	−	7.45058e10i	−0.0447198	−	0.166897i
$389$	2.03491e11	+	1.17486e11i	0.450580	+	0.260143i	0.708075	−	0.706137i	$-0.249564\pi$
$389$	2.03491e11	+	1.17486e11i	0.450580	+	0.260143i	−0.257495	+	0.966280i	$0.582897\pi$
$390$	5.76865e10	−	9.51005e10i	0.126265	−	0.208157i
$391$			4.41934e11i			0.956229i
$392$	−8.78857e10	+	7.90116e10i	−0.187988	+	0.169007i
$393$	−2.04992e11	−	2.04992e11i	−0.433482	−	0.433482i
$394$	2.89180e10	−	1.66958e10i	0.0604555	−	0.0349040i
$395$	−1.27959e11	−	1.33623e11i	−0.264475	−	0.276181i
$396$	−2.90551e10	+	5.03250e10i	−0.0593737	+	0.102838i
$397$	5.19238e10	−	1.93782e11i	0.104908	−	0.391522i	−0.893427	−	0.449209i	$-0.851706\pi$
$397$	5.19238e10	−	1.93782e11i	0.104908	−	0.391522i	0.998335	+	0.0576867i	$0.0183725\pi$
$398$	−3.97057e10	+	3.97057e10i	−0.0793193	+	0.0793193i
$399$	1.63099e10	−	6.13919e11i	0.0322161	−	1.21264i
$400$	−4.10982e11	−	2.61631e11i	−0.802700	−	0.510997i
$401$	2.10386e10	+	3.64398e10i	0.0406318	+	0.0703764i	0.885626	−	0.464399i	$-0.153730\pi$
$401$	2.10386e10	+	3.64398e10i	0.0406318	+	0.0703764i	−0.844994	+	0.534775i	$0.820396\pi$
$402$	−1.76188e11	+	4.72095e10i	−0.336480	+	0.0901596i
$403$	4.66818e11	−	1.25083e11i	0.881606	−	0.236226i
$404$	−2.52146e11	−	4.36730e11i	−0.470909	−	0.815638i
$405$	1.47995e10	+	4.31096e9i	0.0273337	+	0.00796207i
$406$	−1.88888e10	−	3.48205e10i	−0.0345015	−	0.0636016i
$407$	−1.74579e10	+	1.74579e10i	−0.0315367	+	0.0315367i
$408$	−5.06019e10	+	1.88849e11i	−0.0904058	+	0.337399i
$409$	1.75452e11	−	3.03891e11i	0.310029	−	0.536986i	−0.668339	−	0.743856i	$-0.732995\pi$
$409$	1.75452e11	−	3.03891e11i	0.310029	−	0.536986i	0.978368	+	0.206871i	$0.0663279\pi$
$410$	−1.46357e10	−	3.16892e8i	−0.0255791	−	0.000553840i
$411$	1.23665e12	−	7.13979e11i	2.13776	−	1.23423i
$412$	7.30924e11	+	7.30924e11i	1.24978	+	1.24978i
$413$	−1.35015e11	−	5.63323e11i	−0.228353	−	0.952758i
$414$		−	1.39413e11i		−	0.233239i
$415$	−4.28064e11	−	2.59657e11i	−0.708423	−	0.429719i
$416$	2.33075e11	+	1.34566e11i	0.381571	+	0.220300i
$417$	1.76940e11	+	6.60350e11i	0.286559	+	1.06945i
$418$	4.25325e9	+	1.13965e9i	0.00681440	+	0.00182591i
$419$	−9.89534e11			−1.56844			−0.784220	−	0.620483i	$-0.786936\pi$
$419$	−9.89534e11			−1.56844			−0.784220	+	0.620483i	$0.786936\pi$
$420$	7.53339e11	−	6.83993e11i	1.18132	−	1.07258i
$421$	−8.96550e9			−0.0139093			−0.00695465	−	0.999976i	$-0.502214\pi$
$421$	−8.96550e9			−0.0139093			−0.00695465	+	0.999976i	$0.502214\pi$
$422$	6.23350e10	+	1.67026e10i	0.0956811	+	0.0256377i
$423$	−5.11328e11	−	1.90830e12i	−0.776547	−	2.89811i
$424$	1.55651e11	+	8.98649e10i	0.233886	+	0.135034i
$425$	−4.22330e11	+	3.87255e11i	−0.627916	+	0.575767i
$426$			4.17818e10i			0.0614673i
$427$	−2.52056e11	+	8.49738e11i	−0.366920	+	1.23697i
$428$	4.28986e11	+	4.28986e11i	0.617940	+	0.617940i
$429$	8.59224e10	−	4.96073e10i	0.122475	−	0.0707111i
$430$	−1.14355e11	+	1.09507e11i	−0.161304	+	0.154467i
$431$	5.91712e10	−	1.02488e11i	0.0825967	−	0.143062i	−0.821768	−	0.569822i	$-0.807012\pi$
$431$	5.91712e10	−	1.02488e11i	0.0825967	−	0.143062i	0.904365	+	0.426761i	$0.140345\pi$
$432$	−1.82372e11	+	6.80622e11i	−0.251931	+	0.940219i
$433$	−3.16462e11	+	3.16462e11i	−0.432639	+	0.432639i	−0.889525	−	0.456886i	$-0.848965\pi$
$433$	−3.16462e11	+	3.16462e11i	−0.432639	+	0.432639i	0.456886	+	0.889525i	$0.348965\pi$
$434$	−7.29510e10	−	1.93808e9i	−0.0987024	−	0.00262221i
$435$	3.30913e11	+	6.02935e11i	0.443111	+	0.807363i
$436$	−2.28250e11	−	3.95341e11i	−0.302498	−	0.523942i
$437$	6.18186e11	−	1.65642e11i	0.810872	−	0.217273i
$438$	2.55739e11	−	6.85252e10i	0.332020	−	0.0889645i
$439$	−3.66133e11	−	6.34161e11i	−0.470488	−	0.814909i	0.528942	−	0.848658i	$-0.322589\pi$
$439$	−3.66133e11	−	6.34161e11i	−0.470488	−	0.814909i	−0.999430	+	0.0337488i	$0.989255\pi$
$440$	7.07827e9	+	1.28968e10i	0.00900306	+	0.0164039i
$441$	5.87142e11	+	1.15450e12i	0.739213	+	1.45352i
$442$	7.25573e10	−	7.25573e10i	0.0904234	−	0.0904234i
$443$	−3.05460e11	+	1.13999e12i	−0.376823	+	1.40632i	0.473840	+	0.880611i	$0.342867\pi$
$443$	−3.05460e11	+	1.13999e12i	−0.376823	+	1.40632i	−0.850663	+	0.525711i	$0.823799\pi$
$444$	−3.93630e11	+	6.81787e11i	−0.480689	+	0.832579i
$445$	−3.46932e11	+	3.32227e11i	−0.419396	+	0.401619i
$446$	−1.01880e11	+	5.88206e10i	−0.121922	+	0.0703919i
$447$	−1.82643e12	−	1.82643e12i	−2.16382	−	2.16382i
$448$	5.30276e11	+	5.59220e11i	0.621943	+	0.655891i
$449$			2.97276e11i			0.345184i	0.984993	+	0.172592i	$0.0552142\pi$
$449$			2.97276e11i			0.345184i	−0.984993	+	0.172592i	$0.944786\pi$
$450$	1.33228e11	−	1.22164e11i	0.153158	−	0.140438i
$451$	−1.13084e10	−	6.52893e9i	−0.0128709	−	0.00743101i
$452$	1.41557e11	+	5.28296e11i	0.159517	+	0.595325i
$453$	−1.74867e12	−	4.68555e11i	−1.95104	−	0.522780i
$454$	1.72251e11			0.190288
$455$	−1.05242e12	+	2.28268e11i	−1.15117	+	0.249686i
$456$	2.83132e11			0.306653
$457$	1.03511e12	+	2.77356e11i	1.11010	+	0.297450i	0.766871	−	0.641801i	$-0.221813\pi$
$457$	1.03511e12	+	2.77356e11i	1.11010	+	0.297450i	0.343229	+	0.939252i	$0.388479\pi$
$458$	−2.59748e10	−	9.69392e10i	−0.0275840	−	0.102945i
$459$	7.17706e11	+	4.14368e11i	0.754726	+	0.435741i
$460$	9.06616e11	+	5.49940e11i	0.944089	+	0.572670i
$461$			9.82467e11i			1.01313i	0.862203	+	0.506564i	$0.169084\pi$
$461$			9.82467e11i			1.01313i	−0.862203	+	0.506564i	$0.830916\pi$
$462$	−1.45689e10	+	3.49183e9i	−0.0148778	+	0.00356586i
$463$	−2.62714e11	−	2.62714e11i	−0.265686	−	0.265686i	0.561673	−	0.827359i	$-0.310158\pi$
$463$	−2.62714e11	−	2.62714e11i	−0.265686	−	0.265686i	−0.827359	+	0.561673i	$0.810158\pi$
$464$	−4.67199e11	+	2.69737e11i	−0.467919	+	0.270153i
$465$	1.26672e12	+	2.74272e10i	1.25645	+	0.0272046i
$466$	−9.87677e10	+	1.71071e11i	−0.0970238	+	0.168050i
$467$	4.10253e11	−	1.53109e12i	0.399141	−	1.48961i	−0.415470	−	0.909607i	$-0.636383\pi$
$467$	4.10253e11	−	1.53109e12i	0.399141	−	1.48961i	0.814611	−	0.580008i	$-0.196950\pi$
$468$	1.38667e12	−	1.38667e12i	1.33619	−	1.33619i
$469$	1.50540e12	+	9.23299e11i	1.43673	+	0.881180i
$470$	−2.38136e11	−	6.93669e10i	−0.225105	−	0.0655710i
$471$	3.04260e10	+	5.26995e10i	0.0284873	+	0.0493415i
$472$	2.57961e11	−	6.91205e10i	0.239230	−	0.0641014i
$473$	−1.36417e11	+	3.65529e10i	−0.125312	+	0.0335774i
$474$	4.34297e10	+	7.52224e10i	0.0395170	+	0.0684455i
$475$	6.99994e11	+	4.45615e11i	0.630919	+	0.401642i
$476$	8.25114e11	−	4.47594e11i	0.736687	−	0.399625i
$477$	1.39285e12	−	1.39285e12i	1.23189	−	1.23189i
$478$	−5.18372e10	+	1.93459e11i	−0.0454168	+	0.169498i
$479$	6.06716e11	−	1.05086e12i	0.526594	−	0.912087i	−0.472926	−	0.881102i	$-0.656802\pi$
$479$	6.06716e11	−	1.05086e12i	0.526594	−	0.912087i	0.999520	−	0.0309850i	$-0.00986441\pi$
$480$	4.88002e11	+	5.09603e11i	0.419601	+	0.438174i
$481$	7.21562e11	−	4.16594e11i	0.614640	−	0.354862i
$482$	−1.94553e10	−	1.94553e10i	−0.0164182	−	0.0164182i
$483$	−1.58006e12	+	1.49828e12i	−1.32103	+	1.25265i
$484$		−	1.18116e12i		−	0.978371i
$485$	−1.10996e11	+	1.82986e11i	−0.0910901	+	0.150169i
$486$	1.32574e11	+	7.65416e10i	0.107794	+	0.0622350i
$487$	−1.00312e11	−	3.74371e11i	−0.0808116	−	0.301593i	0.913677	−	0.406442i	$-0.133231\pi$
$487$	−1.00312e11	−	3.74371e11i	−0.0808116	−	0.301593i	−0.994488	+	0.104849i	$0.966564\pi$
$488$	−3.94698e11	−	1.05759e11i	−0.315047	−	0.0844166i
$489$	−1.58781e11			−0.125577
$490$	1.62158e11	+	1.21472e10i	0.127074	+	0.00951903i
$491$	−1.14792e12			−0.891343			−0.445672	−	0.895196i	$-0.647035\pi$
$491$	−1.14792e12			−0.891343			−0.445672	+	0.895196i	$0.647035\pi$
$492$	−4.02187e11	−	1.07766e11i	−0.309446	−	0.0829158i
$493$	1.64218e11	+	6.12871e11i	0.125202	+	0.467259i
$494$	−1.28690e11	−	7.42991e10i	−0.0972239	−	0.0561322i
$495$	1.56607e11	−	3.83495e10i	0.117244	−	0.0287102i
$496$			9.93822e11i			0.737295i
$497$	2.93536e11	−	2.78343e11i	0.215803	−	0.204633i
$498$	1.66207e11	+	1.66207e11i	0.121093	+	0.121093i
$499$	6.84559e11	−	3.95230e11i	0.494263	−	0.285363i	−0.232078	−	0.972697i	$-0.574553\pi$
$499$	6.84559e11	−	3.95230e11i	0.494263	−	0.285363i	0.726341	+	0.687334i	$0.241219\pi$
$500$	2.68899e11	+	1.34830e12i	0.192408	+	0.964762i
$501$	5.99930e11	−	1.03911e12i	0.425433	−	0.736871i
$502$	−2.56879e10	+	9.58687e10i	−0.0180535	+	0.0673767i
$503$	−6.08289e11	+	6.08289e11i	−0.423696	+	0.423696i	−0.886474	−	0.462778i	$-0.846853\pi$
$503$	−6.08289e11	+	6.08289e11i	−0.423696	+	0.423696i	0.462778	+	0.886474i	$0.346853\pi$
$504$	−5.24878e11	+	2.84727e11i	−0.362344	+	0.196558i
$505$	−3.91319e11	+	1.34339e12i	−0.267744	+	0.919162i
$506$	−7.80616e9	−	1.35207e10i	−0.00529371	−	0.00916897i
$507$	−9.03266e11	+	2.42029e11i	−0.607127	+	0.162679i
$508$	2.92915e11	−	7.84863e10i	0.195144	−	0.0522886i
$509$	7.14829e11	+	1.23812e12i	0.472033	+	0.817585i	0.999488	−	0.0319978i	$-0.0101870\pi$
$509$	7.14829e11	+	1.23812e12i	0.472033	+	0.817585i	−0.527455	+	0.849583i	$0.676854\pi$
$510$	2.35831e11	−	1.29433e11i	0.154360	−	0.0847185i
$511$	−2.18511e12	−	1.34018e12i	−1.41768	−	0.869499i
$512$	−6.55820e11	+	6.55820e11i	−0.421764	+	0.421764i
$513$	3.10620e11	−	1.15925e12i	0.198017	−	0.739008i
$514$	−1.37382e11	+	2.37953e11i	−0.0868153	+	0.150369i
$515$	6.20855e10	−	2.86742e12i	0.0388917	−	1.79621i
$516$	−3.90003e12	+	2.25168e12i	−2.42183	+	1.39825i
$517$	−1.56442e11	−	1.56442e11i	−0.0963043	−	0.0963043i
$518$	−1.22348e11	+	2.93238e10i	−0.0746640	+	0.0178952i
$519$		−	2.17243e11i		−	0.131430i
$520$	−1.18086e11	−	4.82225e11i	−0.0708243	−	0.289224i
$521$	−1.81856e12	−	1.04995e12i	−1.08133	−	0.624307i	−0.150076	−	0.988675i	$-0.547952\pi$
$521$	−1.81856e12	−	1.04995e12i	−1.08133	−	0.624307i	−0.931255	+	0.364368i	$0.881285\pi$
$522$	−5.18043e10	−	1.93336e11i	−0.0305386	−	0.113971i
$523$	1.41453e12	+	3.79021e11i	0.826711	+	0.221516i	0.647278	−	0.762254i	$-0.275907\pi$
$523$	1.41453e12	+	3.79021e11i	0.826711	+	0.221516i	0.179433	+	0.983770i	$0.442574\pi$
$524$	−6.41700e11			−0.371827
$525$	−2.81638e12	−	1.97067e11i	−1.61799	−	0.113213i
$526$	8.74429e10			0.0498068
$527$	1.12903e12	+	3.02523e11i	0.637615	+	0.170848i
$528$	5.28052e10	+	1.97072e11i	0.0295682	+	0.110350i
$529$	−4.05308e11	−	2.34005e11i	−0.225027	−	0.129919i
$530$	−5.88203e10	−	2.40204e11i	−0.0323807	−	0.132233i
$531$		−	2.92691e12i		−	1.59766i
$532$	−9.35366e11	−	9.86421e11i	−0.506266	−	0.533900i
$533$	3.11597e11	+	3.11597e11i	0.167233	+	0.167233i
$534$	1.95304e11	−	1.12759e11i	0.103938	−	0.0600086i
$535$	3.64385e10	−	1.68291e12i	0.0192295	−	0.888116i
$536$	−4.07081e11	+	7.05086e11i	−0.213030	+	0.368978i
$537$	−8.26351e11	+	3.08399e12i	−0.428825	+	1.60040i
$538$	2.70026e11	−	2.70026e11i	0.138959	−	0.138959i
$539$	1.21587e11	+	7.90913e10i	0.0620495	+	0.0403626i
$540$	1.74317e12	−	9.56718e11i	0.882203	−	0.484186i
$541$	3.77072e11	+	6.53108e11i	0.189250	+	0.327791i	0.945001	−	0.327069i	$-0.106061\pi$
$541$	3.77072e11	+	6.53108e11i	0.189250	+	0.327791i	−0.755750	+	0.654860i	$0.772728\pi$
$542$	−6.15968e10	+	1.65048e10i	−0.0306593	+	0.00821512i
$543$	1.00903e11	−	2.70369e10i	0.0498087	−	0.0133462i
$544$	3.25458e11	+	5.63709e11i	0.159331	+	0.275969i
$545$	−3.54233e11	+	1.21608e12i	−0.171991	+	0.590442i
$546$	5.05406e11	+	1.34270e10i	0.243373	+	0.00646567i
$547$	−1.78037e11	+	1.78037e11i	−0.0850290	+	0.0850290i	−0.748342	−	0.663313i	$-0.769150\pi$
$547$	−1.78037e11	+	1.78037e11i	−0.0850290	+	0.0850290i	0.663313	+	0.748342i	$0.269150\pi$
$548$	8.18071e11	−	3.05308e12i	0.387506	−	1.44619i
$549$	−2.23918e12	+	3.87838e12i	−1.05200	+	1.82211i
$550$	6.08056e9	−	1.93077e10i	0.00283342	−	0.00899701i
$551$	7.95744e11	−	4.59423e11i	0.367783	−	0.212339i
$552$	−7.09845e11	−	7.09845e11i	−0.325415	−	0.325415i
$553$	2.39150e11	−	8.06231e11i	0.108745	−	0.366603i
$554$		−	1.81277e11i		−	0.0817613i
$555$	2.12167e12	−	5.19547e11i	0.949203	−	0.232437i
$556$	1.31051e12	+	7.56623e11i	0.581572	+	0.335771i
$557$	1.32666e11	+	4.95118e11i	0.0584000	+	0.217952i	0.988959	−	0.148191i	$-0.0473450\pi$
$557$	1.32666e11	+	4.95118e11i	0.0584000	+	0.217952i	−0.930559	+	0.366142i	$0.880678\pi$
$558$	−3.56165e11	−	9.54341e10i	−0.155524	−	0.0416725i
$559$	4.76609e12			2.06447
$560$	1.06719e11	−	2.21193e12i	0.0458557	−	0.950443i
$561$	2.39958e11			0.102283
$562$	5.67082e10	+	1.51949e10i	0.0239791	+	0.00642518i
$563$	6.63187e11	+	2.47505e12i	0.278194	+	1.03824i	0.953670	+	0.300853i	$0.0972715\pi$
$563$	6.63187e11	+	2.47505e12i	0.278194	+	1.03824i	−0.675476	+	0.737382i	$0.736062\pi$
$564$	−6.10957e12	−	3.52736e12i	−2.54246	−	1.46789i
$565$	7.87039e11	−	1.29749e12i	0.324921	−	0.535656i
$566$			2.53173e11i			0.103692i
$567$	1.63307e10	+	6.81363e10i	0.00663559	+	0.0276857i
$568$	1.31872e11	+	1.31872e11i	0.0531598	+	0.0531598i
$569$	−6.74524e11	+	3.89437e11i	−0.269769	+	0.155751i	−0.628783	−	0.777581i	$-0.716447\pi$
$569$	−6.74524e11	+	3.89437e11i	−0.269769	+	0.155751i	0.359014	+	0.933332i	$0.383113\pi$
$570$	−2.69445e11	−	2.81372e11i	−0.106914	−	0.111646i
$571$	1.71436e12	−	2.96935e12i	0.674899	−	1.16896i	−0.301599	−	0.953435i	$-0.597520\pi$
$571$	1.71436e12	−	2.96935e12i	0.674899	−	1.16896i	0.976498	−	0.215525i	$-0.0691462\pi$
$572$	5.68396e10	−	2.12128e11i	0.0222008	−	0.0828545i
$573$	−2.77397e12	+	2.77397e12i	−1.07499	+	1.07499i
$574$	−3.17284e10	−	5.84895e10i	−0.0121996	−	0.0224892i
$575$	−6.37760e11	−	2.87218e12i	−0.243305	−	1.09574i
$576$	1.94696e12	+	3.37223e12i	0.736979	+	1.27649i
$577$	1.95817e12	−	5.24690e11i	0.735460	−	0.197066i	0.128401	−	0.991722i	$-0.459016\pi$
$577$	1.95817e12	−	5.24690e11i	0.735460	−	0.197066i	0.607059	+	0.794656i	$0.292349\pi$
$578$	−9.05686e10	+	2.42678e10i	−0.0337522	+	0.00904388i
$579$	2.70428e12	+	4.68396e12i	0.999997	+	1.73205i
$580$	1.46164e12	+	4.25763e11i	0.536308	+	0.156222i
$581$	6.04375e10	−	2.27492e12i	0.0220046	−	0.828274i
$582$	7.10490e10	−	7.10490e10i	0.0256687	−	0.0256687i
$583$	5.70927e10	−	2.13073e11i	0.0204678	−	0.0763870i
$584$	5.90884e11	−	1.02344e12i	0.210206	−	0.364087i
$585$	−5.43992e12	−	1.17786e11i	−1.92040	−	0.0415806i
$586$	−3.19060e11	+	1.84210e11i	−0.111772	+	0.0645317i
$587$	−4.59961e11	−	4.59961e11i	−0.159901	−	0.159901i	0.622622	−	0.782523i	$-0.286067\pi$
$587$	−4.59961e11	−	4.59961e11i	−0.159901	−	0.159901i	−0.782523	+	0.622622i	$0.786067\pi$
$588$	4.39766e12	+	1.43259e12i	1.51713	+	0.494224i
$589$		−	1.69270e12i		−	0.579511i
$590$	−3.14182e11	−	1.90578e11i	−0.106745	−	0.0647499i
$591$	−2.28215e12	−	1.31760e12i	−0.769485	−	0.444262i
$592$	4.43450e11	+	1.65498e12i	0.148387	+	0.553789i
$593$	2.45388e12	+	6.57516e11i	0.814906	+	0.218353i	0.642118	−	0.766606i	$-0.278056\pi$
$593$	2.45388e12	+	6.57516e11i	0.814906	+	0.218353i	0.172788	+	0.984959i	$0.444722\pi$
$594$	−2.92769e10			−0.00964910
$595$	−2.48038e12	−	7.94559e11i	−0.811321	−	0.259896i
$596$	−5.71739e12			−1.85605
$597$	4.28042e12	+	1.14694e12i	1.37912	+	0.369534i
$598$	1.36364e11	+	5.08918e11i	0.0436059	+	0.162739i
$599$	−1.02325e12	−	5.90773e11i	−0.324758	−	0.187499i	0.328753	−	0.944416i	$-0.393372\pi$
$599$	−1.02325e12	−	5.90773e11i	−0.324758	−	0.187499i	−0.653512	+	0.756917i	$0.726705\pi$
$600$	5.63380e10	−	1.30038e12i	0.0177468	−	0.409627i
$601$			4.45303e11i			0.139226i	0.997574	+	0.0696130i	$0.0221764\pi$
$601$			4.45303e11i			0.139226i	−0.997574	+	0.0696130i	$0.977824\pi$
$602$	−6.89972e11	−	2.04665e11i	−0.214115	−	0.0635124i
$603$	6.30950e12	+	6.30950e12i	1.94342	+	1.94342i
$604$	−3.47036e12	+	2.00361e12i	−1.06098	+	0.612558i
$605$	−2.36701e12	+	2.26668e12i	−0.718290	+	0.687845i
$606$	3.28458e11	−	5.68905e11i	0.0989356	−	0.171362i
$607$	−7.90929e11	+	2.95179e12i	−0.236477	+	0.882543i	0.741001	+	0.671504i	$0.234351\pi$
$607$	−7.90929e11	+	2.95179e12i	−0.236477	+	0.882543i	−0.977478	+	0.211039i	$0.932315\pi$
$608$	6.66541e11	−	6.66541e11i	0.197816	−	0.197816i
$609$	−1.63447e12	+	2.66494e12i	−0.481503	+	0.785071i
$610$	2.70517e11	+	4.92891e11i	0.0791061	+	0.144134i
$611$	3.73314e12	+	6.46600e12i	1.08365	+	1.87694i
$612$	4.58134e12	−	1.22757e12i	1.32011	−	0.353723i
$613$	5.76335e11	−	1.54429e11i	0.164855	−	0.0441728i	−0.175447	−	0.984489i	$-0.556137\pi$
$613$	5.76335e11	−	1.54429e11i	0.164855	−	0.0441728i	0.340303	+	0.940316i	$0.389470\pi$
$614$	2.73498e11	+	4.73713e11i	0.0776600	+	0.134511i
$615$	5.55849e11	+	1.01278e12i	0.156682	+	0.285480i
$616$	−3.49615e10	+	5.70033e10i	−0.00978311	+	0.0159509i
$617$	5.07347e11	−	5.07347e11i	0.140936	−	0.140936i	−0.633119	−	0.774055i	$-0.718226\pi$
$617$	5.07347e11	−	5.07347e11i	0.140936	−	0.140936i	0.774055	+	0.633119i	$0.218226\pi$
$618$	−3.48506e11	+	1.30064e12i	−0.0961086	+	0.358682i
$619$	2.50430e11	−	4.33758e11i	0.0685613	−	0.118752i	−0.829707	−	0.558199i	$-0.811492\pi$
$619$	2.50430e11	−	4.33758e11i	0.0685613	−	0.118752i	0.898268	+	0.439448i	$0.144826\pi$
$620$	2.02558e12	−	1.93972e12i	0.550537	−	0.527202i
$621$	−3.68514e12	+	2.12762e12i	−0.994357	+	0.574092i
$622$	−1.81175e11	−	1.81175e11i	−0.0485335	−	0.0485335i
$623$	−2.09326e12	−	6.20917e11i	−0.556706	−	0.165134i
$624$		−	6.88521e12i		−	1.81797i
$625$	2.18592e12	−	3.12629e12i	0.573026	−	0.819537i
$626$	−1.87767e11	−	1.08408e11i	−0.0488693	−	0.0282147i
$627$	−8.99391e10	−	3.35657e11i	−0.0232405	−	0.0867345i
$628$	1.30106e11	+	3.48619e10i	0.0333795	+	0.00894401i
$629$	2.01513e12			0.513303
$630$	7.82463e11	+	2.50652e11i	0.197893	+	0.0633926i
$631$	3.65378e11			0.0917510			0.0458755	−	0.998947i	$-0.485392\pi$
$631$	3.65378e11			0.0917510			0.0458755	+	0.998947i	$0.485392\pi$
$632$	3.74489e11	+	1.00344e11i	0.0933710	+	0.0250187i
$633$	−1.31813e12	−	4.91935e12i	−0.326320	−	1.21784i
$634$	−8.41475e11	−	4.85826e11i	−0.206842	−	0.119421i
$635$	−7.19397e11	−	4.36375e11i	−0.175585	−	0.106507i
$636$		−	7.03389e12i		−	1.70466i
$637$	−3.27259e12	−	3.64015e12i	−0.787524	−	0.875975i
$638$	−1.58497e10	−	1.58497e10i	−0.00378728	−	0.00378728i
$639$	1.77009e12	−	1.02196e12i	0.419993	−	0.242483i
$640$	2.07596e12	+	4.49488e10i	0.489113	+	0.0105903i
$641$	−1.07072e12	+	1.85454e12i	−0.250503	+	0.433884i	−0.963664	−	0.267116i	$-0.913929\pi$
$641$	−1.07072e12	+	1.85454e12i	−0.250503	+	0.433884i	0.713161	+	0.701000i	$0.247263\pi$
$642$	−2.04541e11	+	7.63359e11i	−0.0475197	+	0.177346i
$643$	−5.01088e12	+	5.01088e12i	−1.15602	+	1.15602i	−0.170695	+	0.985324i	$0.554601\pi$
$643$	−5.01088e12	+	5.01088e12i	−1.15602	+	1.15602i	−0.985324	+	0.170695i	$0.945399\pi$
$644$	−1.28003e11	+	4.81815e12i	−0.0293248	+	1.10381i
$645$	1.19966e13	+	3.49450e12i	2.72922	+	0.794998i
$646$	−1.79698e11	−	3.11246e11i	−0.0405972	−	0.0703165i
$647$	6.98646e12	−	1.87202e12i	1.56743	−	0.419991i	0.632423	−	0.774624i	$-0.282061\pi$
$647$	6.98646e12	−	1.87202e12i	1.56743	−	0.419991i	0.935006	+	0.354632i	$0.115394\pi$
$648$	−3.12015e10	+	8.36041e9i	−0.00695165	+	0.00186269i
$649$	−1.63887e11	−	2.83861e11i	−0.0362613	−	0.0628064i
$650$	−3.66850e11	+	5.76267e11i	−0.0806081	+	0.126623i
$651$	2.74611e12	+	5.06230e12i	0.599244	+	1.10467i
$652$	−2.48521e11	+	2.48521e11i	−0.0538579	+	0.0538579i
$653$	1.10214e12	−	4.11325e12i	0.237207	−	0.885270i	−0.739934	−	0.672680i	$-0.765143\pi$
$653$	1.10214e12	−	4.11325e12i	0.237207	−	0.885270i	0.977141	−	0.212591i	$-0.0681901\pi$
$654$	2.97330e11	−	5.14990e11i	0.0635533	−	0.110078i
$655$	1.23144e12	+	1.28595e12i	0.261413	+	0.272984i
$656$	−7.84774e11	+	4.53090e11i	−0.165454	+	0.0955250i
$657$	−9.15833e12	−	9.15833e12i	−1.91766	−	1.91766i
$658$	−2.62774e11	−	1.09637e12i	−0.0546469	−	0.228003i
$659$			4.52254e12i			0.934111i	0.884228	+	0.467056i	$0.154685\pi$
$659$			4.52254e12i			0.934111i	−0.884228	+	0.467056i	$0.845315\pi$
$660$	2.98602e11	−	4.92267e11i	0.0612554	−	0.100984i
$661$	−4.89614e12	−	2.82678e12i	−0.997578	−	0.575952i	−0.0900472	−	0.995938i	$-0.528702\pi$
$661$	−4.89614e12	−	2.82678e12i	−0.997578	−	0.575952i	−0.907531	+	0.419986i	$0.862035\pi$
$662$	−8.70146e10	−	3.24743e11i	−0.0176088	−	0.0657171i
$663$	−7.82195e12	−	2.09589e12i	−1.57219	−	0.421266i
$664$	1.04916e12			0.209453
$665$	−1.81765e11	+	3.76742e12i	−0.0360424	+	0.747044i
$666$	−6.35692e11			−0.125202
$667$	−3.14686e12	−	8.43197e11i	−0.615617	−	0.164954i
$668$	−6.87395e11	−	2.56539e12i	−0.133571	−	0.498494i
$669$	8.04017e12	+	4.64200e12i	1.55184	+	0.895957i
$670$	1.08811e12	−	2.66452e11i	0.208610	−	0.0510836i
$671$			5.01516e11i			0.0955066i
$672$	−9.12055e11	+	3.07475e12i	−0.172528	+	0.581631i
$673$	−5.49933e12	−	5.49933e12i	−1.03334	−	1.03334i	−0.999425	−	0.0339131i	$-0.989203\pi$
$673$	−5.49933e12	−	5.49933e12i	−1.03334	−	1.03334i	−0.0339131	−	0.999425i	$-0.510797\pi$
$674$	8.50903e11	−	4.91269e11i	0.158822	−	0.0916959i
$675$	−5.26243e12	−	1.65730e12i	−0.975707	−	0.307279i
$676$	−1.03495e12	+	1.79259e12i	−0.190617	+	0.330158i
$677$	1.41030e12	−	5.26330e12i	0.258025	−	0.962962i	−0.708358	−	0.705853i	$-0.750564\pi$
$677$	1.41030e12	−	5.26330e12i	0.258025	−	0.962962i	0.966383	−	0.257108i	$-0.0827696\pi$
$678$	−5.03785e11	+	5.03785e11i	−0.0915612	+	0.0915612i
$679$	−9.72466e11	−	2.58354e10i	−0.175574	−	0.00466446i
$680$	3.35813e11	−	1.15284e12i	0.0602292	−	0.206766i
$681$	−6.79686e12	−	1.17725e13i	−1.21101	−	2.09752i
$682$	−3.98856e10	+	1.06873e10i	−0.00705971	+	0.00189164i
$683$	1.06924e13	−	2.86501e12i	1.88010	−	0.503771i	0.880542	−	0.473969i	$-0.157179\pi$
$683$	1.06924e13	−	2.86501e12i	1.88010	−	0.503771i	0.999556	−	0.0298020i	$-0.00948768\pi$
$684$	−3.43428e12	−	5.94835e12i	−0.599907	−	1.03907i
$685$	−7.68819e12	+	4.21957e12i	−1.33419	+	0.732251i
$686$	3.17448e11	+	6.67504e11i	0.0547285	+	0.115079i
$687$	−5.60036e12	+	5.60036e12i	−0.959203	+	0.959203i
$688$	−2.53667e12	+	9.46698e12i	−0.431634	+	1.61088i
$689$	−3.72212e12	+	6.44691e12i	−0.629222	+	1.08985i
$690$	−2.99007e10	+	1.38096e12i	−0.00502182	+	0.231932i
$691$	3.53385e11	−	2.04027e11i	0.0589654	−	0.0340437i	−0.470227	−	0.882545i	$-0.655828\pi$
$691$	3.53385e11	−	2.04027e11i	0.0589654	−	0.0340437i	0.529193	+	0.848502i	$0.322495\pi$
$692$	−3.40025e11	−	3.40025e11i	−0.0563681	−	0.0563681i
$693$	5.04280e11	+	5.31806e11i	0.0830563	+	0.0875898i
$694$			6.12930e10i			0.0100298i
$695$	−9.98657e11	−	4.07821e12i	−0.162362	−	0.663037i
$696$	−1.24818e12	−	7.20636e11i	−0.201621	−	0.116406i
$697$	2.75844e11	+	1.02947e12i	0.0442707	+	0.165221i
$698$	3.89107e11	+	1.04261e11i	0.0620469	+	0.0166254i
$699$	1.55891e13			2.46986
$700$	−4.71659e12	+	4.09970e12i	−0.742483	+	0.645372i
$701$	−3.21644e12			−0.503088			−0.251544	−	0.967846i	$-0.580938\pi$
$701$	−3.21644e12			−0.503088			−0.251544	+	0.967846i	$0.580938\pi$
$702$	9.54347e11	+	2.55716e11i	0.148316	+	0.0397413i
$703$	−7.55294e11	−	2.81879e12i	−0.116632	−	0.435276i
$704$	3.77644e11	+	2.18033e11i	0.0579436	+	0.0334537i
$705$	4.65571e12	+	1.90125e13i	0.709799	+	2.89860i
$706$			1.24408e12i			0.188463i
$707$	−6.18494e12	+	1.48238e12i	−0.930996	+	0.223138i
$708$	−7.39045e12	−	7.39045e12i	−1.10541	−	1.10541i
$709$	−4.07921e12	+	2.35513e12i	−0.606273	+	0.350032i	−0.771505	−	0.636223i	$-0.780496\pi$
$709$	−4.07921e12	+	2.35513e12i	−0.606273	+	0.350032i	0.165233	+	0.986255i	$0.447163\pi$
$710$	5.55481e9	−	2.56549e11i	0.000820364	−	0.0378885i
$711$	2.12454e12	−	3.67980e12i	0.311782	−	0.540022i
$712$	2.60528e11	−	9.72304e11i	0.0379922	−	0.141789i
$713$	−4.24381e12	+	4.24381e12i	−0.614968	+	0.614968i
$714$	1.04236e12	+	6.39304e11i	0.150098	+	0.0920588i
$715$	−5.34175e11	+	2.93175e11i	−0.0764376	+	0.0419518i
$716$	3.53360e12	+	6.12038e12i	0.502469	+	0.870301i
$717$	1.52674e13	−	4.09088e12i	2.15739	−	0.578070i
$718$	1.16789e12	−	3.12935e11i	0.163999	−	0.0439435i
$719$	−5.65326e12	−	9.79173e12i	−0.788894	−	1.36640i	−0.926645	−	0.375938i	$-0.877321\pi$
$719$	−5.65326e12	−	9.79173e12i	−0.788894	−	1.36640i	0.137751	−	0.990467i	$-0.456013\pi$
$720$	3.12926e12	−	1.07427e13i	0.433956	−	1.48977i
$721$	1.14593e13	−	6.21623e12i	1.57924	−	0.856679i
$722$	2.89897e11	−	2.89897e11i	0.0397032	−	0.0397032i
$723$	−5.61984e11	+	2.09735e12i	−0.0764894	+	0.285462i
$724$	1.15614e11	−	2.00249e11i	0.0156382	−	0.0270861i
$725$	−1.95171e12	−	3.74613e12i	−0.262358	−	0.503573i
$726$	1.33249e12	−	7.69315e11i	0.178012	−	0.102776i
$727$	−1.73027e12	−	1.73027e12i	−0.229726	−	0.229726i	0.582852	−	0.812578i	$-0.301937\pi$
$727$	−1.73027e12	−	1.73027e12i	−0.229726	−	0.229726i	−0.812578	+	0.582852i	$0.801937\pi$
$728$	1.63754e12	−	1.55278e12i	0.216073	−	0.204889i
$729$		−	1.22981e13i		−	1.61274i
$730$	−1.57940e12	+	3.86758e11i	−0.205845	+	0.0504065i
$731$	9.98279e12	+	5.76357e12i	1.29308	+	0.746557i
$732$	4.13898e12	+	1.54469e13i	0.532835	+	1.98857i
$733$	2.92217e12	+	7.82992e11i	0.373884	+	0.100182i	0.440868	−	0.897572i	$-0.354671\pi$
$733$	2.92217e12	+	7.82992e11i	0.373884	+	0.100182i	−0.0669835	+	0.997754i	$0.521337\pi$
$734$	−1.53625e12			−0.195357
$735$	−5.56838e12	−	1.15620e13i	−0.703778	−	1.46130i
$736$	−3.34220e12			−0.419838
$737$	9.65204e11	+	2.58626e11i	0.120508	+	0.0322900i
$738$	−8.70180e10	−	3.24755e11i	−0.0107983	−	0.0402998i
$739$	−1.38548e13	−	7.99909e12i	−1.70884	−	0.986599i	−0.936001	−	0.351998i	$-0.885502\pi$
$739$	−1.38548e13	−	7.99909e12i	−1.70884	−	0.986599i	−0.772839	−	0.634602i	$-0.781164\pi$
$740$	2.50761e12	−	4.13397e12i	0.307409	−	0.506786i
$741$			1.17271e13i			1.42892i
$742$	8.15682e11	−	7.73463e11i	0.0987878	−	0.0936747i
$743$	−3.27722e11	−	3.27722e11i	−0.0394508	−	0.0394508i	0.687106	−	0.726557i	$-0.258881\pi$
$743$	−3.27722e11	−	3.27722e11i	−0.0394508	−	0.0394508i	−0.726557	+	0.687106i	$0.758881\pi$
$744$	−2.29940e12	+	1.32756e12i	−0.275129	+	0.158846i
$745$	1.09719e13	+	1.14575e13i	1.30490	+	1.36266i
$746$	1.50202e11	−	2.60157e11i	0.0177562	−	0.0307547i
$747$	2.97604e12	−	1.11067e13i	0.349700	−	1.30510i
$748$	3.75577e11	−	3.75577e11i	0.0438674	−	0.0438674i
$749$	6.72555e12	−	3.64836e12i	0.780836	−	0.423574i
$750$	−1.34591e12	+	1.18153e12i	−0.155324	+	0.136354i
$751$	2.96881e12	+	5.14213e12i	0.340567	+	0.589880i	0.984538	−	0.175170i	$-0.0560475\pi$
$751$	2.96881e12	+	5.14213e12i	0.340567	+	0.589880i	−0.643971	+	0.765050i	$0.722714\pi$
$752$	−1.48304e13	+	3.97380e12i	−1.69112	+	0.453133i
$753$	7.56575e12	−	2.02724e12i	0.857580	−	0.229788i
$754$	3.78217e11	+	6.55092e11i	0.0426158	+	0.0738127i
$755$	1.06749e13	+	3.10950e12i	1.19565	+	0.348281i
$756$	7.70471e12	+	4.72549e12i	0.857844	+	0.526137i
$757$	−7.29132e12	+	7.29132e12i	−0.807003	+	0.807003i	−0.984179	−	0.177177i	$-0.943304\pi$
$757$	−7.29132e12	+	7.29132e12i	−0.807003	+	0.807003i	0.177177	+	0.984179i	$0.443304\pi$
$758$	−2.31505e11	+	8.63990e11i	−0.0254712	+	0.0950598i
$759$	−6.16045e11	+	1.06702e12i	−0.0673790	+	0.116704i
$760$	−1.73848e12	−	3.76418e10i	−0.189021	−	0.00409269i
$761$	4.26009e12	−	2.45957e12i	0.460456	−	0.265844i	−0.251780	−	0.967784i	$-0.581016\pi$
$761$	4.26009e12	−	2.45957e12i	0.460456	−	0.265844i	0.712236	+	0.701940i	$0.247683\pi$
$762$	2.79325e11	+	2.79325e11i	0.0300132	+	0.0300132i
$763$	−5.59879e12	+	1.34190e12i	−0.598045	+	0.143337i
$764$			8.68352e12i			0.922095i
$765$	−1.12517e13	−	6.82513e12i	−1.18780	−	0.720501i
$766$	9.18346e11	+	5.30207e11i	0.0963778	+	0.0556437i
$767$	2.86291e12	+	1.06845e13i	0.298695	+	1.11475i
$768$	1.27110e13	+	3.40591e12i	1.31842	+	0.353270i
$769$	−1.17181e13			−1.20834			−0.604171	−	0.796855i	$-0.706496\pi$
$769$	−1.17181e13			−1.20834			−0.604171	+	0.796855i	$0.706496\pi$
$770$	8.99204e10	−	1.95036e10i	0.00921828	−	0.00199943i
$771$	2.16838e13			2.20999
$772$	1.15639e13	+	3.09854e12i	1.17173	+	0.313964i
$773$	−1.54721e12	−	5.77428e12i	−0.155863	−	0.581688i	−0.999030	−	0.0440366i	$-0.985978\pi$
$773$	−1.54721e12	−	5.77428e12i	−0.155863	−	0.581688i	0.843167	−	0.537652i	$-0.180688\pi$
$774$	−3.14917e12	−	1.81818e12i	−0.315401	−	0.182097i
$775$	−7.77429e12	−	3.36817e11i	−0.774111	−	0.0335379i
$776$		−	4.48489e11i		−	0.0443991i
$777$	6.83183e12	+	7.20474e12i	0.672423	+	0.709127i
$778$	4.79077e11	+	4.79077e11i	0.0468810	+	0.0468810i
$779$	1.33665e12	−	7.71713e11i	0.130046	−	0.0750822i
$780$	−1.40332e13	+	1.34384e13i	−1.35748	+	1.29994i
$781$	1.14446e11	−	1.98226e11i	0.0110070	−	0.0190648i
$782$	−3.29807e11	+	1.23086e12i	−0.0315376	+	0.117700i
$783$	−4.31993e12	+	4.31993e12i	−0.410722	+	0.410722i
$784$	8.97227e12	−	4.56300e12i	0.848165	−	0.431348i
$785$	−1.79816e11	−	3.27630e11i	−0.0169011	−	0.0307943i
$786$	−4.17954e11	−	7.23917e11i	−0.0390595	−	0.0676531i
$787$	−1.09452e13	+	2.93275e12i	−1.01703	+	0.272514i	−0.728566	−	0.684976i	$-0.759813\pi$
$787$	−1.09452e13	+	2.93275e12i	−1.01703	+	0.272514i	−0.288468	+	0.957489i	$0.593146\pi$
$788$	−5.63425e12	+	1.50969e12i	−0.520557	+	0.139483i
$789$	−3.45040e12	−	5.97628e12i	−0.316974	−	0.549015i
$790$	−2.56666e11	−	4.67654e11i	−0.0234448	−	0.0427172i
$791$	6.89544e12	+	1.83190e11i	0.626279	+	0.0166383i
$792$	−2.38915e11	+	2.38915e11i	−0.0215764	+	0.0215764i
$793$	4.38044e12	−	1.63480e13i	0.393358	−	1.46803i
$794$	2.89232e11	−	5.00964e11i	0.0258258	−	0.0447316i
$795$	−1.40957e13	+	1.34982e13i	−1.25151	+	1.19846i
$796$	8.49479e12	−	4.90447e12i	0.749970	−	0.432995i
$797$	9.06472e12	+	9.06472e12i	0.795778	+	0.795778i	0.982427	−	0.186648i	$-0.0597625\pi$
$797$	9.06472e12	+	9.06472e12i	0.795778	+	0.795778i	−0.186648	+	0.982427i	$0.559763\pi$
$798$	5.03581e11	−	1.69769e12i	0.0439599	−	0.148199i
$799$			1.80578e13i			1.56748i
$800$	−2.92868e12	−	3.19394e12i	−0.252794	−	0.275691i
$801$	−9.55405e12	−	5.51603e12i	−0.820052	−	0.473457i
$802$	3.14013e10	+	1.17191e11i	0.00268017	+	0.0100025i
$803$	−1.40101e12	−	3.75399e11i	−0.118911	−	0.0318620i
$804$	3.18630e13			2.68927
$805$	9.90108e12	−	8.98966e12i	0.831000	−	0.754505i
$806$	1.39351e12			0.116306
$807$	−2.91099e13	−	7.79996e12i	−2.41607	−	0.647383i
$808$	−7.58900e11	−	2.83225e12i	−0.0626373	−	0.233766i
$809$	−6.08304e12	−	3.51205e12i	−0.499290	−	0.288265i	0.229130	−	0.973396i	$-0.426412\pi$
$809$	−6.08304e12	−	3.51205e12i	−0.499290	−	0.288265i	−0.728420	+	0.685131i	$0.759745\pi$
$810$	3.80017e10	+	2.30512e10i	0.00310184	+	0.00188153i
$811$			4.35195e12i			0.353256i	0.984278	+	0.176628i	$0.0565190\pi$
$811$			4.35195e12i			0.353256i	−0.984278	+	0.176628i	$0.943481\pi$
$812$	1.61286e12	+	6.72934e12i	0.130195	+	0.543213i
$813$	3.55856e12	+	3.55856e12i	0.285672	+	0.285672i
$814$	−6.16513e10	+	3.55944e10i	−0.00492190	+	0.00284166i
$815$	9.74948e11	+	2.11096e10i	0.0774056	+	0.00167599i
$816$	8.32619e12	−	1.44214e13i	0.657417	−	1.13868i
$817$	4.32051e12	−	1.61244e13i	0.339263	−	1.26615i
$818$	7.15447e11	−	7.15447e11i	0.0558712	−	0.0558712i
$819$	−1.17931e13	−	2.17400e13i	−0.915907	−	1.68842i
$820$	2.45518e12	+	7.15172e11i	0.189636	+	0.0552393i
$821$	−4.43123e12	−	7.67511e12i	−0.340392	−	0.589577i	0.644113	−	0.764930i	$-0.277227\pi$
$821$	−4.43123e12	−	7.67511e12i	−0.340392	−	0.589577i	−0.984506	+	0.175353i	$0.943893\pi$
$822$	3.97709e12	−	1.06566e12i	0.303838	−	0.0814131i
$823$	−8.59164e12	+	2.30212e12i	−0.652795	+	0.174916i	−0.569992	−	0.821650i	$-0.693054\pi$
$823$	−8.59164e12	+	2.30212e12i	−0.652795	+	0.174916i	−0.0828028	+	0.996566i	$0.526387\pi$
$824$	3.00513e12	+	5.20503e12i	0.227086	+	0.393324i
$825$	−1.55951e12	+	3.46285e11i	−0.117205	+	0.0260250i
$826$	4.43588e10	−	1.66970e12i	0.00331565	−	0.124804i
$827$	−1.84872e12	+	1.84872e12i	−0.137434	+	0.137434i	−0.772477	−	0.635043i	$-0.780983\pi$
$827$	−1.84872e12	+	1.84872e12i	−0.137434	+	0.137434i	0.635043	+	0.772477i	$0.280983\pi$
$828$	−6.30308e12	+	2.35234e13i	−0.466033	+	1.73926i
$829$	3.20935e12	−	5.55875e12i	0.236005	−	0.408773i	−0.723559	−	0.690262i	$-0.757495\pi$
$829$	3.20935e12	−	5.55875e12i	0.236005	−	0.408773i	0.959564	+	0.281490i	$0.0908285\pi$
$830$	−9.98448e11	−	1.04264e12i	−0.0730254	−	0.0762577i
$831$	−1.23893e13	+	7.15298e12i	−0.901245	+	0.520334i
$832$	−1.04057e13	−	1.04057e13i	−0.752867	−	0.752867i
$833$	−2.45260e12	−	1.15819e13i	−0.176492	−	0.833449i
$834$			1.97123e12i			0.141088i
$835$	−3.82184e12	+	6.30058e12i	−0.272072	+	0.448530i
$836$	−6.66135e11	−	3.84593e11i	−0.0471665	−	0.0272316i
$837$	2.91290e12	+	1.08711e13i	0.205145	+	0.765611i
$838$	−2.75601e12	−	7.38470e11i	−0.193055	−	0.0517291i
$839$	−1.22883e13			−0.856175			−0.428087	−	0.903737i	$-0.640812\pi$
$839$	−1.22883e13			−0.856175			−0.428087	+	0.903737i	$0.640812\pi$
$840$	5.26029e12	−	2.70781e12i	0.364547	−	0.187656i
$841$	9.82979e12			0.677583
$842$	−2.49703e10	−	6.69078e9i	−0.00171206	−	0.000458746i
$843$	−1.19915e12	−	4.47529e12i	−0.0817805	−	0.305209i
$844$	−9.76277e12	−	5.63654e12i	−0.662266	−	0.382359i
$845$	5.57841e12	−	1.36602e12i	0.376405	−	0.0921727i
$846$		−	5.69651e12i		−	0.382333i
$847$	−1.42816e13	−	4.23632e12i	−0.953458	−	0.282822i
$848$	−1.08246e13	−	1.08246e13i	−0.718836	−	0.718836i
$849$	1.73031e13	−	9.98994e12i	1.14298	−	0.659900i
$850$	−1.46526e12	+	7.63389e11i	−0.0962783	+	0.0501604i
$851$	−5.17345e12	+	8.96067e12i	−0.338140	+	0.585676i
$852$	1.88903e12	−	7.04994e12i	0.122817	−	0.458361i
$853$	4.02727e12	−	4.02727e12i	0.260459	−	0.260459i	−0.564781	−	0.825241i	$-0.691039\pi$
$853$	4.02727e12	−	4.02727e12i	0.260459	−	0.260459i	0.825241	+	0.564781i	$0.191039\pi$
$854$	−1.33616e12	+	2.17855e12i	−0.0859601	+	0.140154i
$855$	−5.32983e12	+	1.82973e13i	−0.341088	+	1.17095i
$856$	1.76374e12	+	3.05488e12i	0.112280	+	0.194474i
$857$	4.25883e12	−	1.14115e12i	0.269697	−	0.0722652i	−0.121436	−	0.992599i	$-0.538750\pi$
$857$	4.25883e12	−	1.14115e12i	0.269697	−	0.0722652i	0.391133	+	0.920334i	$0.372083\pi$
$858$	2.76328e11	−	7.40419e10i	0.0174073	−	0.00466428i
$859$	5.01732e12	+	8.69026e12i	0.314415	+	0.544582i	0.979313	−	0.202352i	$-0.0648584\pi$
$859$	5.01732e12	+	8.69026e12i	0.314415	+	0.544582i	−0.664898	+	0.746934i	$0.731525\pi$
$860$	2.42463e13	−	1.33073e13i	1.51148	−	0.829557i
$861$	−2.74549e12	+	4.47641e12i	−0.170257	+	0.277597i
$862$	2.41285e11	−	2.41285e11i	0.0148850	−	0.0148850i
$863$	3.38278e12	−	1.26247e13i	0.207599	−	0.774770i	−0.781043	−	0.624478i	$-0.785312\pi$
$863$	3.38278e12	−	1.26247e13i	0.207599	−	0.774770i	0.988642	−	0.150292i	$-0.0480214\pi$
$864$	−3.13372e12	+	5.42777e12i	−0.191315	+	0.331367i
$865$	−2.88821e10	+	1.33392e12i	−0.00175411	+	0.0810134i
$866$	−1.11756e12	+	6.45226e11i	−0.0675214	+	0.0389835i
$867$	5.23232e12	+	5.23232e12i	0.314491	+	0.314491i
$868$	1.22216e13	+	3.62525e12i	0.730782	+	0.216770i
$869$		−	4.75838e11i		−	0.0283055i
$870$	4.71686e11	+	1.92622e12i	0.0279136	+	0.113991i
$871$	−2.92040e13	−	1.68609e13i	−1.71934	−	0.992659i
$872$	−6.86978e11	−	2.56384e12i	−0.0402364	−	0.150164i
$873$	−4.74782e12	−	1.27217e12i	−0.276650	−	0.0741280i
$874$	1.84536e12			0.106974
$875$	1.72669e13	+	1.58447e12i	0.995816	+	0.0913790i
$876$	−4.62496e13			−2.65363
$877$	−2.72739e13	−	7.30803e12i	−1.55686	−	0.417159i	−0.625192	−	0.780471i	$-0.714979\pi$
$877$	−2.72739e13	−	7.30803e12i	−1.55686	−	0.417159i	−0.931668	+	0.363311i	$0.881646\pi$
$878$	−5.46475e11	−	2.03947e12i	−0.0310345	−	0.115822i
$879$	2.51796e13	+	1.45374e13i	1.42265	+	0.821368i
$880$	−2.98034e11	−	1.21708e12i	−0.0167531	−	0.0684144i
$881$			7.68542e12i			0.429809i	0.976635	+	0.214905i	$0.0689441\pi$
$881$			7.68542e12i			0.429809i	−0.976635	+	0.214905i	$0.931056\pi$
$882$	7.73699e11	+	3.65365e12i	0.0430491	+	0.203291i
$883$	−1.87038e12	−	1.87038e12i	−0.103539	−	0.103539i	0.653439	−	0.756979i	$-0.273325\pi$
$883$	−1.87038e12	−	1.87038e12i	−0.103539	−	0.103539i	−0.756979	+	0.653439i	$0.773325\pi$
$884$	−1.55232e13	+	8.96232e12i	−0.854960	+	0.493611i
$885$	−6.27753e11	+	2.89928e13i	−0.0343989	+	1.58871i
$886$	−1.70151e12	+	2.94709e12i	−0.0927645	+	0.160673i
$887$	3.18624e12	−	1.18912e13i	0.172831	−	0.645015i	−0.824080	−	0.566474i	$-0.808307\pi$
$887$	3.18624e12	−	1.18912e13i	0.172831	−	0.645015i	0.996911	−	0.0785409i	$-0.0250261\pi$
$888$	−3.23674e12	+	3.23674e12i	−0.174683	+	0.174683i
$889$	1.01570e11	−	3.82319e12i	0.00545391	−	0.205290i
$890$	−1.21419e12	+	6.66395e11i	−0.0648684	+	0.0356022i
$891$	1.98228e10	+	3.43341e10i	0.00105370	+	0.00182506i
$892$	1.98499e13	−	5.31876e12i	1.04982	−	0.281299i
$893$	2.52595e13	−	6.76827e12i	1.32921	−	0.356161i
$894$	−3.72387e12	−	6.44994e12i	−0.194974	−	0.337704i
$895$	5.48397e12	−	1.88264e13i	0.285688	−	0.980763i
$896$	4.50044e12	+	8.29631e12i	0.233275	+	0.430030i
$897$	2.94011e13	−	2.94011e13i	1.51635	−	1.51635i
$898$	−2.21851e11	+	8.27959e11i	−0.0113846	+	0.0424879i
$899$	−4.30832e12	+	7.46223e12i	−0.219983	+	0.381022i
$900$	−2.80031e13	+	1.45895e13i	−1.42271	+	0.741222i
$901$	−1.55923e13	+	9.00222e12i	−0.788222	+	0.455080i
$902$	−2.66234e10	−	2.66234e10i	−0.00133916	−	0.00133916i
$903$	1.32378e13	+	5.52319e13i	0.662552	+	2.76436i
$904$			3.18009e12i			0.158373i
$905$	−6.23159e11	+	1.52597e11i	−0.0308802	+	0.00756184i
$906$	−4.52065e12	−	2.61000e12i	−0.222907	−	0.128695i
$907$	5.89362e12	+	2.19953e13i	0.289167	+	1.07919i	0.945740	+	0.324924i	$0.105339\pi$
$907$	5.89362e12	+	2.19953e13i	0.289167	+	1.07919i	−0.656573	+	0.754263i	$0.727994\pi$
$908$	−2.90644e13	−	7.78777e12i	−1.41897	−	0.380213i
$909$	−3.21356e13			−1.56117
$910$	−3.10151e12	−	1.49637e11i	−0.149929	−	0.00723359i
$911$	2.41062e13			1.15957			0.579785	−	0.814770i	$-0.303137\pi$
$911$	2.41062e13			1.15957			0.579785	+	0.814770i	$0.303137\pi$
$912$	−2.32937e13	−	6.24152e12i	−1.11496	−	0.298754i
$913$	−3.33276e11	−	1.24380e12i	−0.0158740	−	0.0592424i
$914$	2.67595e12	+	1.54496e12i	0.126829	+	0.0732250i
$915$	2.30123e13	−	3.79374e13i	1.08534	−	1.78926i
$916$			1.75311e13i			0.822773i
$917$	−2.30151e12	+	7.75892e12i	−0.107486	+	0.362359i
$918$	1.68969e12	+	1.68969e12i	0.0785262	+	0.0785262i
$919$	2.06338e13	−	1.19129e13i	0.954243	−	0.550932i	0.0598463	−	0.998208i	$-0.480939\pi$
$919$	2.06338e13	−	1.19129e13i	0.954243	−	0.550932i	0.894396	+	0.447275i	$0.147606\pi$
$920$	4.26422e12	+	4.45296e12i	0.196243	+	0.204929i
$921$	2.15839e13	−	3.73844e13i	0.988466	−	1.71207i
$922$	−7.33196e11	+	2.73632e12i	−0.0334142	+	0.124703i
$923$	−5.46200e12	+	5.46200e12i	−0.247710	+	0.247710i
$924$	2.61612e12	+	6.95021e10i	0.118068	+	0.00313671i
$925$	−1.30965e13	+	2.90805e12i	−0.588191	+	0.130606i
$926$	−5.35642e11	−	9.27759e11i	−0.0239401	−	0.0414654i
$927$	6.36261e13	−	1.70486e13i	2.82993	−	0.758279i
$928$	−4.63493e12	+	1.24193e12i	−0.205153	+	0.0549706i
$929$	1.49397e13	+	2.58763e13i	0.658069	+	1.13981i	0.981115	+	0.193425i	$0.0619597\pi$
$929$	1.49397e13	+	2.58763e13i	0.658069	+	1.13981i	−0.323046	+	0.946383i	$0.604707\pi$
$930$	3.50755e12	+	1.02172e12i	0.153756	+	0.0447877i
$931$	−1.52818e13	+	7.77181e12i	−0.666654	+	0.339038i
$932$	2.43997e13	−	2.43997e13i	1.05928	−	1.05928i
$933$	−5.23341e12	+	1.95314e13i	−0.226109	+	0.843850i
$934$	2.28524e12	−	3.95815e12i	0.0982586	−	0.170189i
$935$	−1.47339e12	−	3.19019e10i	−0.0630471	−	0.00136510i
$936$	9.87473e12	−	5.70118e12i	0.420517	−	0.242786i
$937$	−1.15375e13	−	1.15375e13i	−0.488973	−	0.488973i	0.419009	−	0.907982i	$-0.362377\pi$
$937$	−1.15375e13	−	1.15375e13i	−0.488973	−	0.488973i	−0.907982	+	0.419009i	$0.862377\pi$
$938$	3.50373e12	+	3.69498e12i	0.147781	+	0.155847i
$939$			1.71106e13i			0.718240i
$940$	3.70450e13	+	2.24709e13i	1.54758	+	0.938742i
$941$	−4.55384e12	−	2.62916e12i	−0.189332	−	0.109311i	0.402338	−	0.915491i	$-0.368198\pi$
$941$	−4.55384e12	−	2.62916e12i	−0.189332	−	0.109311i	−0.591670	+	0.806180i	$0.701531\pi$
$942$	4.54127e10	+	1.69483e11i	0.00187909	+	0.00701287i
$943$	−5.28591e12	−	1.41636e12i	−0.217679	−	0.0583270i
$944$	−2.27466e13			−0.932271
$945$	−5.31583e12	−	2.45084e13i	−0.216834	−	0.999704i
$946$	−4.07222e11			−0.0165318
$947$	1.17757e13	+	3.15530e12i	0.475788	+	0.127487i	0.488741	−	0.872429i	$-0.337456\pi$
$947$	1.17757e13	+	3.15530e12i	0.475788	+	0.127487i	−0.0129526	+	0.999916i	$0.504123\pi$
$948$	−3.92706e12	−	1.46560e13i	−0.157917	−	0.589355i
$949$	4.23900e13	+	2.44739e13i	1.69655	+	0.979501i
$950$	1.61704e12	+	1.76350e12i	0.0644116	+	0.0702456i
$951$			7.66807e13i			3.04000i
$952$	5.30765e12	−	1.27212e12i	0.209429	−	0.0501950i
$953$	6.16220e11	+	6.16220e11i	0.0242001	+	0.0242001i	0.719103	−	0.694903i	$-0.244553\pi$
$953$	6.16220e11	+	6.16220e11i	0.0242001	+	0.0242001i	−0.694903	+	0.719103i	$0.744553\pi$
$954$	4.91875e12	−	2.83984e12i	0.192259	−	0.111001i
$955$	1.74015e13	−	1.66639e13i	0.676974	−	0.648280i
$956$	1.74932e13	−	3.02991e13i	0.677344	−	1.17319i
$957$	−4.57832e11	+	1.70865e12i	−0.0176442	+	0.0658492i
$958$	2.47404e12	−	2.47404e12i	0.0948989	−	0.0948989i
$959$	−3.39813e13	−	2.08416e13i	−1.29735	−	0.795696i
$960$	−1.85625e13	−	3.38215e13i	−0.705368	−	1.28520i
$961$	−5.28301e12	−	9.15044e12i	−0.199814	−	0.346088i
$962$	2.32056e12	−	6.21792e11i	0.0873584	−	0.0234076i
$963$	3.73427e13	−	1.00060e13i	1.39923	−	0.374921i
$964$	2.40313e12	+	4.16234e12i	0.0896251	+	0.155235i
$965$	−1.59821e13	−	2.91200e13i	−0.593282	−	1.08098i
$966$	−5.51885e12	+	2.99377e12i	−0.203916	+	0.110617i
$967$	−1.50765e13	+	1.50765e13i	−0.554473	+	0.554473i	−0.927728	−	0.373256i	$-0.878241\pi$
$967$	−1.50765e13	+	1.50765e13i	−0.554473	+	0.554473i	0.373256	+	0.927728i	$0.378241\pi$
$968$	1.77750e12	−	6.63372e12i	0.0650684	−	0.242839i
$969$	−1.41814e13	+	2.45628e13i	−0.516727	+	0.894997i
$970$	−4.45701e11	+	4.26809e11i	−0.0161648	+	0.0154796i
$971$	−2.71251e12	+	1.56607e12i	−0.0979229	+	0.0565358i	−0.548162	−	0.836372i	$-0.684672\pi$
$971$	−2.71251e12	+	1.56607e12i	−0.0979229	+	0.0565358i	0.450239	+	0.892908i	$0.351339\pi$
$972$	−1.89089e13	−	1.89089e13i	−0.679467	−	0.679467i
$973$	1.38487e13	−	1.31319e13i	0.495339	−	0.469701i
$974$		−	1.11754e12i		−	0.0397877i
$975$	5.38604e13	+	2.33347e12i	1.90875	+	0.0826954i
$976$	3.01410e13	+	1.74019e13i	1.06324	+	0.613865i
$977$	8.66596e12	+	3.23418e13i	0.304292	+	1.13563i	0.933553	+	0.358440i	$0.116691\pi$
$977$	8.66596e12	+	3.23418e13i	0.304292	+	1.13563i	−0.629260	+	0.777195i	$0.716642\pi$
$978$	−4.42230e11	−	1.18495e11i	−0.0154569	−	0.00414168i
$979$	−1.23544e12			−0.0429833
$980$	−2.68121e13	−	9.38104e12i	−0.928566	−	0.324888i
$981$	−2.90901e13			−1.00285
$982$	−3.19714e12	−	8.56670e11i	−0.109713	−	0.0293976i
$983$	2.91270e12	+	1.08704e13i	0.0994959	+	0.371324i	0.997663	−	0.0683311i	$-0.0217674\pi$
$983$	2.91270e12	+	1.08704e13i	0.0994959	+	0.371324i	−0.898167	+	0.439655i	$0.855101\pi$
$984$	−2.09662e12	−	1.21048e12i	−0.0712922	−	0.0411606i
$985$	1.38377e13	+	8.39372e12i	0.468382	+	0.284113i
$986$			1.82949e12i			0.0616431i
$987$	−6.45625e13	+	6.12208e13i	−2.16547	+	2.05339i
$988$	1.83549e13	+	1.83549e13i	0.612839	+	0.612839i
$989$	−5.12578e13	+	2.95937e13i	−1.70364	+	0.983594i
$990$	4.64795e11	+	1.00638e10i	0.0153781	+	0.000332968i
$991$	−8.46005e12	+	1.46532e13i	−0.278639	+	0.482616i	−0.971047	−	0.238890i	$-0.923217\pi$
$991$	−8.46005e12	+	1.46532e13i	−0.278639	+	0.482616i	0.692408	+	0.721506i	$0.256550\pi$
$992$	−2.28788e12	+	8.53849e12i	−0.0750121	+	0.279949i
$993$	−1.87610e13	+	1.87610e13i	−0.612328	+	0.612328i
$994$	1.02527e12	−	5.56168e11i	0.0333118	−	0.0180704i
$995$	−2.61302e13	−	7.61149e12i	−0.845159	−	0.246187i
$996$	−2.05300e13	−	3.55590e13i	−0.661031	−	1.14494i
$997$	−7.14876e12	+	1.91550e12i	−0.229141	+	0.0613981i	−0.371562	−	0.928408i	$-0.621178\pi$
$997$	−7.14876e12	+	1.91550e12i	−0.229141	+	0.0613981i	0.142422	+	0.989806i	$0.454511\pi$
$998$	2.20155e12	−	5.89905e11i	0.0702493	−	0.0188232i
$999$	9.70149e12	+	1.68035e13i	0.308172	+	0.533770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.18	✓	136
5.2	odd	4	inner	35.10.k.a.17.17	yes	136
7.5	odd	6	inner	35.10.k.a.33.17	yes	136
35.12	even	12	inner	35.10.k.a.12.18	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.18	✓	136	1.1	even	1	trivial
35.10.k.a.12.18	yes	136	35.12	even	12	inner
35.10.k.a.17.17	yes	136	5.2	odd	4	inner
35.10.k.a.33.17	yes	136	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	35.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.78516 + 0.746280i) q^{2} +(-58.8948 - 219.798i) q^{3} +(-436.205 - 251.843i) q^{4} +(332.404 + 1357.44i) q^{5} -656.125i q^{6} +(-4609.57 + 4370.98i) q^{7} +(-2070.86 - 2070.86i) q^{8} +(-27796.8 + 16048.5i) q^{9} +(-87.2304 + 4028.74i) q^{10} +(-1797.21 + 3112.86i) q^{11} +(-29664.5 + 110709. i) q^{12} +(85773.0 - 85773.0i) q^{13} +(-16100.3 + 8733.84i) q^{14} +(278785. - 153008. i) q^{15} +(124721. + 216024. i) q^{16} +(283380. - 75931.3i) q^{17} +(-89395.0 + 23953.3i) q^{18} +(-212428. - 367937. i) q^{19} +(196864. - 675834. i) q^{20} +(1.23221e6 + 755748. i) q^{21} +(-7328.58 + 7328.58i) q^{22} +(-389878. + 1.45505e6i) q^{23} +(-333208. + 577134. i) q^{24} +(-1.73214e6 + 902435. i) q^{25} +(302902. - 174880. i) q^{26} +(1.99745e6 + 1.99745e6i) q^{27} +(3.11152e6 - 745757. i) q^{28} +2.16272e6i q^{29} +(890647. - 218099. i) q^{30} +(3.45039e6 + 1.99208e6i) q^{31} +(574243. + 2.14310e6i) q^{32} +(790048. + 211693. i) q^{33} +845922. q^{34} +(-7.46557e6 - 4.80426e6i) q^{35} +1.61668e7 q^{36} +(6.63470e6 + 1.77776e6i) q^{37} +(-317062. - 1.18329e6i) q^{38} +(-2.39044e7 - 1.38012e7i) q^{39} +(2.12269e6 - 3.49942e6i) q^{40} +3.63281e6i q^{41} +(2.86791e6 + 3.02445e6i) q^{42} +(2.77832e7 + 2.77832e7i) q^{43} +(1.56790e6 - 905230. i) q^{44} +(-3.10245e7 - 3.23978e7i) q^{45} +(-2.17174e6 + 3.76157e6i) q^{46} +(-1.59307e7 + 5.94543e7i) q^{47} +(4.01362e7 - 4.01362e7i) q^{48} +(2.14263e6 - 4.02967e7i) q^{49} +(-5.49775e6 + 1.22076e6i) q^{50} +(-3.33792e7 - 5.78144e7i) q^{51} +(-5.90159e7 + 1.58133e7i) q^{52} +(-5.92787e7 + 1.58837e7i) q^{53} +(4.07255e6 + 7.05387e6i) q^{54} +(-4.82291e6 - 1.40487e6i) q^{55} +(1.85974e7 + 494076. i) q^{56} +(-6.83610e7 + 6.83610e7i) q^{57} +(-1.61399e6 + 6.02351e6i) q^{58} +(-4.55948e7 + 7.89725e7i) q^{59} +(-1.60142e8 - 3.46739e6i) q^{60} +(1.20833e8 - 6.97631e7i) q^{61} +(8.12322e6 + 8.12322e6i) q^{62} +(5.79835e7 - 1.95476e8i) q^{63} -1.21317e8i q^{64} +(1.44943e8 + 8.79201e7i) q^{65} +(2.04243e6 + 1.17919e6i) q^{66} +(-7.19519e7 - 2.68528e8i) q^{67} +(-1.42734e8 - 3.82455e7i) q^{68} +3.42779e8 q^{69} +(-1.72074e7 - 1.89520e7i) q^{70} -6.36797e7 q^{71} +(9.07973e7 + 2.43291e7i) q^{72} +(1.04439e8 + 3.89772e8i) q^{73} +(1.71520e7 + 9.90268e6i) q^{74} +(3.00368e8 + 3.27573e8i) q^{75} +2.13994e8i q^{76} +(-5.32189e6 - 2.22045e7i) q^{77} +(-5.62778e7 - 5.62778e7i) q^{78} +(-1.14647e8 + 6.61912e7i) q^{79} +(-2.51781e8 + 2.41109e8i) q^{80} +(5.51488e6 - 9.55206e6i) q^{81} +(-2.71110e6 + 1.01180e7i) q^{82} +(-2.53316e8 + 2.53316e8i) q^{83} +(-3.47168e8 - 6.39985e8i) q^{84} +(1.97268e8 + 3.59430e8i) q^{85} +(5.66464e7 + 9.81144e7i) q^{86} +(4.75362e8 - 1.27373e8i) q^{87} +(1.01681e7 - 2.72452e6i) q^{88} +(1.71855e8 + 2.97662e8i) q^{89} +(-6.22304e7 - 1.13386e8i) q^{90} +(-2.04642e7 + 7.70289e8i) q^{91} +(5.36510e8 - 5.36510e8i) q^{92} +(2.34647e8 - 8.75714e8i) q^{93} +(-8.87390e7 + 1.53701e8i) q^{94} +(4.28838e8 - 4.10661e8i) q^{95} +(4.37231e8 - 2.52435e8i) q^{96} +(1.08286e8 + 1.08286e8i) q^{97} +(3.60402e7 - 1.10634e8i) q^{98} -1.15370e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) \) 136 * q - 2 * q^2 - 6 * q^3 - 1710 * q^5 + 5940 * q^7 - 3484 * q^8 + 153786 * q^10 - 87752 * q^11 + 3066 * q^12 - 318872 * q^15 + 3132804 * q^16 - 1578678 * q^17 - 239036 * q^18 - 5745396 * q^21 + 2132088 * q^22 + 312550 * q^23 + 4308518 * q^25 + 2294580 * q^26 - 9559382 * q^28 + 21412708 * q^30 + 8900220 * q^31 + 17154282 * q^32 - 13729410 * q^33 + 6034552 * q^35 - 114903056 * q^36 + 26817310 * q^37 - 20958672 * q^38 + 143985558 * q^40 - 38052106 * q^42 + 46427728 * q^43 - 96332286 * q^45 + 2421124 * q^46 + 147698754 * q^47 - 11742092 * q^50 - 138178540 * q^51 - 126665976 * q^52 - 16288570 * q^53 + 501495076 * q^56 - 71567164 * q^57 - 681848346 * q^58 + 254653694 * q^60 - 575844240 * q^61 + 491512776 * q^63 + 833960586 * q^65 + 260439612 * q^66 + 22092746 * q^67 - 2824755312 * q^68 - 1044240840 * q^70 + 355056144 * q^71 + 98662792 * q^72 + 1852831146 * q^73 + 2937834474 * q^75 + 1226263510 * q^77 + 2595615712 * q^78 - 3778385244 * q^80 + 1504403888 * q^81 - 3707543946 * q^82 - 1726556112 * q^85 + 1771746456 * q^86 + 30331668 * q^87 - 1182712628 * q^88 - 4378590056 * q^91 + 2593806924 * q^92 - 4305536726 * q^93 + 861804818 * q^95 + 15624596040 * q^96 + 5117393178 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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