LMFDB - Embedded newform 35.10.k.a.3.10

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			3.10
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-22.3519 - 5.98917i) q^{2} +(-10.0261 - 37.4181i) q^{3} +(20.3322 + 11.7388i) q^{4} +(-924.440 + 1048.11i) q^{5} +896.413i q^{6} +(-6331.22 - 518.872i) q^{7} +(7993.56 + 7993.56i) q^{8} +(15746.4 - 9091.18i) q^{9} +(26940.3 - 17890.6i) q^{10} +(-30456.2 + 52751.6i) q^{11} +(235.390 - 878.486i) q^{12} +(-117199. + 117199. i) q^{13} +(138407. + 49516.6i) q^{14} +(48486.8 + 24082.3i) q^{15} +(-136807. - 236956. i) q^{16} +(315442. - 84522.3i) q^{17} +(-406410. + 108897. i) q^{18} +(-144650. - 250541. i) q^{19} +(-31099.4 + 10458.6i) q^{20} +(44062.6 + 242104. i) q^{21} +(996692. - 996692. i) q^{22} +(143682. - 536228. i) q^{23} +(218959. - 379248. i) q^{24} +(-243946. - 1.93783e6i) q^{25} +(3.32153e6 - 1.91769e6i) q^{26} +(-1.03721e6 - 1.03721e6i) q^{27} +(-122637. - 84870.7i) q^{28} -5.36320e6i q^{29} +(-939540. - 828680. i) q^{30} +(-885940. - 511497. i) q^{31} +(140685. + 525043. i) q^{32} +(2.27922e6 + 610716. i) q^{33} -7.55694e6 q^{34} +(6.39667e6 - 6.15616e6i) q^{35} +426878. q^{36} +(1.12669e7 + 3.01894e6i) q^{37} +(1.73267e6 + 6.46641e6i) q^{38} +(5.56039e6 + 3.21029e6i) q^{39} +(-1.57677e7 + 988567. i) q^{40} -2.35954e6i q^{41} +(465124. - 5.67539e6i) q^{42} +(-9.45901e6 - 9.45901e6i) q^{43} +(-1.23848e6 + 715037. i) q^{44} +(-5.02803e6 + 2.49082e7i) q^{45} +(-6.42312e6 + 1.11252e7i) q^{46} +(-1.13449e7 + 4.23397e7i) q^{47} +(-7.49480e6 + 7.49480e6i) q^{48} +(3.98152e7 + 6.57019e6i) q^{49} +(-6.15334e6 + 4.47752e7i) q^{50} +(-6.32533e6 - 1.09558e7i) q^{51} +(-3.75867e6 + 1.00713e6i) q^{52} +(5.23150e6 - 1.40178e6i) q^{53} +(1.69715e7 + 2.93955e7i) q^{54} +(-2.71346e7 - 8.06871e7i) q^{55} +(-4.64614e7 - 5.47566e7i) q^{56} +(-7.92449e6 + 7.92449e6i) q^{57} +(-3.21211e7 + 1.19878e8i) q^{58} +(4.55608e7 - 7.89137e7i) q^{59} +(703147. + 1.05882e6i) q^{60} +(1.10097e8 - 6.35646e7i) q^{61} +(1.67390e7 + 1.67390e7i) q^{62} +(-1.04411e8 + 4.93879e7i) q^{63} +1.27512e8i q^{64} +(-1.44940e7 - 2.31180e8i) q^{65} +(-4.72872e7 - 2.73013e7i) q^{66} +(5.87933e7 + 2.19419e8i) q^{67} +(7.40581e6 + 1.98438e6i) q^{68} -2.15052e7 q^{69} +(-1.79848e8 + 9.92910e7i) q^{70} -3.71610e7 q^{71} +(1.98541e8 + 5.31988e7i) q^{72} +(2.94824e7 + 1.10030e8i) q^{73} +(-2.33755e8 - 1.34958e8i) q^{74} +(-7.00640e7 + 2.85570e7i) q^{75} -6.79207e6i q^{76} +(2.20196e8 - 3.18179e8i) q^{77} +(-1.05058e8 - 1.05058e8i) q^{78} +(4.88106e8 - 2.81808e8i) q^{79} +(3.74826e8 + 7.56632e7i) q^{80} +(1.50531e8 - 2.60727e8i) q^{81} +(-1.41317e7 + 5.27402e7i) q^{82} +(-1.58033e8 + 1.58033e8i) q^{83} +(-1.94613e6 + 5.43975e6i) q^{84} +(-2.03018e8 + 4.08754e8i) q^{85} +(1.54775e8 + 2.68078e8i) q^{86} +(-2.00681e8 + 5.37722e7i) q^{87} +(-6.65126e8 + 1.78220e8i) q^{88} +(-2.79946e8 - 4.84880e8i) q^{89} +(2.61566e8 - 5.26632e8i) q^{90} +(8.02821e8 - 6.81199e8i) q^{91} +(9.21603e6 - 9.21603e6i) q^{92} +(-1.02567e7 + 3.82785e7i) q^{93} +(5.07159e8 - 8.78425e8i) q^{94} +(3.96316e8 + 8.00012e7i) q^{95} +(1.82356e7 - 1.05283e7i) q^{96} +(-9.93544e8 - 9.93544e8i) q^{97} +(-8.50594e8 - 3.85316e8i) q^{98} +1.10753e9i 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 $

$2$	−22.3519	−	5.98917i	−0.987824	−	0.264687i	−0.271488	−	0.962442i	$-0.587516\pi$
$2$	−22.3519	−	5.98917i	−0.987824	−	0.264687i	−0.716336	+	0.697755i	$0.754182\pi$
$3$	−10.0261	−	37.4181i	−0.0714641	−	0.266708i	0.920944	−	0.389695i	$-0.127419\pi$
$3$	−10.0261	−	37.4181i	−0.0714641	−	0.266708i	−0.992408	+	0.122987i	$0.960753\pi$
$4$	20.3322	+	11.7388i	0.0397113	+	0.0229273i
$5$	−924.440	+	1048.11i	−0.661475	+	0.749967i
$5$	−924.440	+	1048.11i	−0.661475	+	0.749967i
$6$			896.413i			0.282376i
$7$	−6331.22	−	518.872i	−0.996659	−	0.0816806i
$7$	−6331.22	−	518.872i	−0.996659	−	0.0816806i
$8$	7993.56	+	7993.56i	0.689978	+	0.689978i
$9$	15746.4	−	9091.18i	0.799999	−	0.461880i
$10$	26940.3	−	17890.6i	0.851927	−	0.565751i
$11$	−30456.2	+	52751.6i	−0.627203	+	1.08635i	0.360908	+	0.932602i	$0.382467\pi$
$11$	−30456.2	+	52751.6i	−0.627203	+	1.08635i	−0.988110	+	0.153746i	$0.950866\pi$
$12$	235.390	−	878.486i	0.00327696	−	0.0122298i
$13$	−117199.	+	117199.i	−1.13809	+	1.13809i	−0.149299	+	0.988792i	$0.547702\pi$
$13$	−117199.	+	117199.i	−1.13809	+	1.13809i	−0.988792	+	0.149299i	$0.952298\pi$
$14$	138407.	+	49516.6i	0.962903	+	0.344488i
$15$	48486.8	+	24082.3i	0.247294	+	0.122825i
$16$	−136807.	−	236956.i	−0.521876	−	0.903916i
$17$	315442.	−	84522.3i	0.916007	−	0.245443i	0.230129	−	0.973160i	$-0.426085\pi$
$17$	315442.	−	84522.3i	0.916007	−	0.245443i	0.685878	+	0.727717i	$0.259418\pi$
$18$	−406410.	+	108897.i	−0.912512	+	0.244507i
$19$	−144650.	−	250541.i	−0.254641	−	0.441051i	0.710157	−	0.704043i	$-0.248624\pi$
$19$	−144650.	−	250541.i	−0.254641	−	0.441051i	−0.964798	+	0.262993i	$0.915291\pi$
$20$	−31099.4	+	10458.6i	−0.0434628	+	0.0146163i
$21$	44062.6	+	242104.i	0.0494405	+	0.271654i
$22$	996692.	−	996692.i	0.907107	−	0.907107i
$23$	143682.	−	536228.i	0.107060	−	0.399553i	−0.891511	−	0.452999i	$-0.850354\pi$
$23$	143682.	−	536228.i	0.107060	−	0.399553i	0.998571	+	0.0534467i	$0.0170207\pi$
$24$	218959.	−	379248.i	0.134714	−	0.233331i
$25$	−243946.	−	1.93783e6i	−0.124901	−	0.992169i
$26$	3.32153e6	−	1.91769e6i	1.42547	−	0.822996i
$27$	−1.03721e6	−	1.03721e6i	−0.375602	−	0.375602i
$28$	−122637.	−	84870.7i	−0.0377059	−	0.0260944i
$29$		−	5.36320e6i		−	1.40810i	−0.710151	−	0.704049i	$-0.751373\pi$
$29$		−	5.36320e6i		−	1.40810i	0.710151	−	0.704049i	$-0.248627\pi$
$30$	−939540.	−	828680.i	−0.211773	−	0.186785i
$31$	−885940.	−	511497.i	−0.172297	−	0.0994754i	0.411372	−	0.911468i	$-0.365050\pi$
$31$	−885940.	−	511497.i	−0.172297	−	0.0994754i	−0.583668	+	0.811992i	$0.698383\pi$
$32$	140685.	+	525043.i	0.0237177	+	0.0885156i
$33$	2.27922e6	+	610716.i	0.334560	+	0.0896450i
$34$	−7.55694e6			−0.969819
$35$	6.39667e6	−	6.15616e6i	0.720523	−	0.693431i
$36$	426878.			0.0423587
$37$	1.12669e7	+	3.01894e6i	0.988314	+	0.264818i	0.716542	−	0.697544i	$-0.245724\pi$
$37$	1.12669e7	+	3.01894e6i	0.988314	+	0.264818i	0.271772	+	0.962362i	$0.412390\pi$
$38$	1.73267e6	+	6.46641e6i	0.134800	+	0.503080i
$39$	5.56039e6	+	3.21029e6i	0.384871	+	0.222205i
$40$	−1.57677e7	+	988567.i	−0.973864	+	0.0610571i
$41$		−	2.35954e6i		−	0.130407i	−0.997872	−	0.0652034i	$-0.979230\pi$
$41$		−	2.35954e6i		−	0.130407i	0.997872	−	0.0652034i	$-0.0207696\pi$
$42$	465124.	−	5.67539e6i	0.0230646	−	0.281432i
$43$	−9.45901e6	−	9.45901e6i	−0.421927	−	0.421927i	0.463940	−	0.885867i	$-0.346435\pi$
$43$	−9.45901e6	−	9.45901e6i	−0.421927	−	0.421927i	−0.885867	+	0.463940i	$0.846435\pi$
$44$	−1.23848e6	+	715037.i	−0.0498141	+	0.0287602i
$45$	−5.02803e6	+	2.49082e7i	−0.182785	+	0.905495i
$46$	−6.42312e6	+	1.11252e7i	−0.211512	+	0.366350i
$47$	−1.13449e7	+	4.23397e7i	−0.339125	+	1.26563i	0.560203	+	0.828355i	$0.310723\pi$
$47$	−1.13449e7	+	4.23397e7i	−0.339125	+	1.26563i	−0.899328	+	0.437275i	$0.855944\pi$
$48$	−7.49480e6	+	7.49480e6i	−0.203786	+	0.203786i
$49$	3.98152e7	+	6.57019e6i	0.986657	+	0.162815i
$50$	−6.15334e6	+	4.47752e7i	−0.139234	+	1.01315i
$51$	−6.32533e6	−	1.09558e7i	−0.130923	−	0.226766i
$52$	−3.75867e6	+	1.00713e6i	−0.0712885	+	0.0191017i
$53$	5.23150e6	−	1.40178e6i	0.0910719	−	0.0244026i	−0.212995	−	0.977053i	$-0.568322\pi$
$53$	5.23150e6	−	1.40178e6i	0.0910719	−	0.0244026i	0.304067	+	0.952651i	$0.401655\pi$
$54$	1.69715e7	+	2.93955e7i	0.271612	+	0.470445i
$55$	−2.71346e7	−	8.06871e7i	−0.399845	−	1.18897i
$56$	−4.64614e7	−	5.47566e7i	−0.631315	−	0.744030i
$57$	−7.92449e6	+	7.92449e6i	−0.0994340	+	0.0994340i
$58$	−3.21211e7	+	1.19878e8i	−0.372705	+	1.39095i
$59$	4.55608e7	−	7.89137e7i	0.489506	−	0.847849i	−0.510421	−	0.859924i	$-0.670511\pi$
$59$	4.55608e7	−	7.89137e7i	0.489506	−	0.847849i	0.999927	+	0.0120758i	$0.00384394\pi$
$60$	703147.	+	1.05882e6i	0.00700431	+	0.0105473i
$61$	1.10097e8	−	6.35646e7i	1.01810	−	0.587802i	0.104549	−	0.994520i	$-0.466660\pi$
$61$	1.10097e8	−	6.35646e7i	1.01810	−	0.587802i	0.913554	+	0.406718i	$0.133327\pi$
$62$	1.67390e7	+	1.67390e7i	0.143869	+	0.143869i
$63$	−1.04411e8	+	4.93879e7i	−0.835053	+	0.394992i
$64$			1.27512e8i			0.950036i
$65$	−1.44940e7	−	2.31180e8i	−0.100711	−	1.60635i
$66$	−4.72872e7	−	2.73013e7i	−0.306758	−	0.177107i
$67$	5.87933e7	+	2.19419e8i	0.356444	+	1.33027i	0.878658	+	0.477452i	$0.158439\pi$
$67$	5.87933e7	+	2.19419e8i	0.356444	+	1.33027i	−0.522214	+	0.852814i	$0.674894\pi$
$68$	7.40581e6	+	1.98438e6i	0.0420032	+	0.0112547i
$69$	−2.15052e7			−0.114215
$70$	−1.79848e8	+	9.92910e7i	−0.895291	+	0.494275i
$71$	−3.71610e7			−0.173550			−0.0867750	−	0.996228i	$-0.527656\pi$
$71$	−3.71610e7			−0.173550			−0.0867750	+	0.996228i	$0.527656\pi$
$72$	1.98541e8	+	5.31988e7i	0.870669	+	0.233295i
$73$	2.94824e7	+	1.10030e8i	0.121510	+	0.453480i	0.999691	−	0.0248473i	$-0.00790996\pi$
$73$	2.94824e7	+	1.10030e8i	0.121510	+	0.453480i	−0.878182	+	0.478327i	$0.841243\pi$
$74$	−2.33755e8	−	1.34958e8i	−0.906186	−	0.523187i
$75$	−7.00640e7	+	2.85570e7i	−0.255693	+	0.104216i
$76$		−	6.79207e6i		−	0.0233529i
$77$	2.20196e8	−	3.18179e8i	0.713841	−	1.03149i
$78$	−1.05058e8	−	1.05058e8i	−0.321370	−	0.321370i
$79$	4.88106e8	−	2.81808e8i	1.40991	−	0.814014i	0.414534	−	0.910034i	$-0.363944\pi$
$79$	4.88106e8	−	2.81808e8i	1.40991	−	0.814014i	0.995379	+	0.0960196i	$0.0306111\pi$
$80$	3.74826e8	+	7.56632e7i	1.02311	+	0.206528i
$81$	1.50531e8	−	2.60727e8i	0.388546	−	0.672981i
$82$	−1.41317e7	+	5.27402e7i	−0.0345169	+	0.128819i
$83$	−1.58033e8	+	1.58033e8i	−0.365507	+	0.365507i	−0.865836	−	0.500329i	$-0.833212\pi$
$83$	−1.58033e8	+	1.58033e8i	−0.365507	+	0.365507i	0.500329	+	0.865836i	$0.333212\pi$
$84$	−1.94613e6	+	5.43975e6i	−0.00426495	+	0.0119213i
$85$	−2.03018e8	+	4.08754e8i	−0.421842	+	0.849330i
$86$	1.54775e8	+	2.68078e8i	0.305111	+	0.528468i
$87$	−2.00681e8	+	5.37722e7i	−0.375551	+	0.100629i
$88$	−6.65126e8	+	1.78220e8i	−1.18231	+	0.316800i
$89$	−2.79946e8	−	4.84880e8i	−0.472954	−	0.819180i	0.526567	−	0.850134i	$-0.323479\pi$
$89$	−2.79946e8	−	4.84880e8i	−0.472954	−	0.819180i	−0.999521	+	0.0309536i	$0.990146\pi$
$90$	2.61566e8	−	5.26632e8i	0.420232	−	0.846089i
$91$	8.02821e8	−	6.81199e8i	1.22725	−	1.04133i
$92$	9.21603e6	−	9.21603e6i	0.0134122	−	0.0134122i
$93$	−1.02567e7	+	3.82785e7i	−0.0142179	+	0.0530618i
$94$	5.07159e8	−	8.78425e8i	0.669991	−	1.16046i
$95$	3.96316e8	+	8.00012e7i	0.499212	+	0.100772i
$96$	1.82356e7	−	1.05283e7i	0.0219128	−	0.0126514i
$97$	−9.93544e8	−	9.93544e8i	−1.13950	−	1.13950i	−0.988540	−	0.150960i	$-0.951764\pi$
$97$	−9.93544e8	−	9.93544e8i	−1.13950	−	1.13950i	−0.150960	−	0.988540i	$-0.548236\pi$
$98$	−8.50594e8	−	3.85316e8i	−0.931548	−	0.421988i
$99$			1.10753e9i			1.15877i
$100$	1.77878e7	−	4.22640e7i	0.0177878	−	0.0422640i
$101$	−9.77608e7	−	5.64422e7i	−0.0934800	−	0.0539707i	0.452531	−	0.891749i	$-0.350521\pi$
$101$	−9.77608e7	−	5.64422e7i	−0.0934800	−	0.0539707i	−0.546011	+	0.837778i	$0.683854\pi$
$102$	7.57670e7	+	2.82766e8i	0.0693073	+	0.258658i
$103$	1.24533e9	+	3.33685e8i	1.09023	+	0.292126i	0.758779	−	0.651348i	$-0.225796\pi$
$103$	1.24533e9	+	3.33685e8i	1.09023	+	0.292126i	0.331448	+	0.943473i	$0.392463\pi$
$104$	−1.87367e9			−1.57052
$105$	−2.94485e8	−	1.77629e8i	−0.236435	−	0.142614i
$106$	−1.25329e8			−0.0964220
$107$	1.76606e9	+	4.73214e8i	1.30250	+	0.349004i	0.842396	−	0.538860i	$-0.181145\pi$
$107$	1.76606e9	+	4.73214e8i	1.30250	+	0.349004i	0.460106	+	0.887864i	$0.347811\pi$
$108$	−8.91311e6	−	3.32642e7i	−0.00630409	−	0.0235272i
$109$	9.71246e8	+	5.60749e8i	0.659038	+	0.380496i	0.791910	−	0.610638i	$-0.209087\pi$
$109$	9.71246e8	+	5.60749e8i	0.659038	+	0.380496i	−0.132873	+	0.991133i	$0.542420\pi$
$110$	1.23261e8	+	1.96602e9i	0.0802712	+	1.28033i
$111$		−	4.51852e8i		−	0.282516i
$112$	7.43204e8	+	1.57121e9i	0.446300	+	0.943523i
$113$	−1.16486e9	−	1.16486e9i	−0.672077	−	0.672077i	0.286117	−	0.958195i	$-0.407635\pi$
$113$	−1.16486e9	−	1.16486e9i	−0.672077	−	0.672077i	−0.958195	+	0.286117i	$0.907635\pi$
$114$	2.24589e8	−	1.29666e8i	0.124542	−	0.0719044i
$115$	4.29201e8	+	6.46305e8i	0.228834	+	0.344585i
$116$	6.29575e7	−	1.09046e8i	0.0322839	−	0.0559174i
$117$	−7.79981e8	+	2.91093e9i	−0.384811	+	1.43613i
$118$	−1.49100e9	+	1.49100e9i	−0.707959	+	0.707959i
$119$	−2.04099e9	+	3.71456e8i	−0.932994	+	0.169803i
$120$	1.95079e8	+	5.80085e8i	0.0858808	+	0.255374i
$121$	−6.76182e8	−	1.17118e9i	−0.286767	−	0.496695i
$122$	−2.84158e9	+	7.61399e8i	−1.16129	+	0.311167i
$123$	−8.82895e7	+	2.36571e7i	−0.0347805	+	0.00931941i
$124$	−1.20087e7	−	2.07997e7i	−0.00456141	−	0.00790060i
$125$	2.25657e9	+	1.53573e9i	0.826713	+	0.562624i
$126$	2.62958e9	−	4.78578e8i	0.929434	−	0.169155i
$127$	−1.78977e9	+	1.78977e9i	−0.610492	+	0.610492i	−0.943074	−	0.332582i	$-0.892080\pi$
$127$	−1.78977e9	+	1.78977e9i	−0.610492	+	0.610492i	0.332582	+	0.943074i	$0.392080\pi$
$128$	8.35720e8	−	3.11895e9i	0.275180	−	1.02698i
$129$	−2.59101e8	+	4.48775e8i	−0.0823786	+	0.142684i
$130$	−1.06061e9	+	5.25412e9i	−0.325694	+	1.61345i
$131$	1.93710e9	−	1.11838e9i	0.574686	−	0.331795i	−0.184333	−	0.982864i	$-0.559012\pi$
$131$	1.93710e9	−	1.11838e9i	0.574686	−	0.331795i	0.759019	+	0.651069i	$0.225679\pi$
$132$	3.91725e7	+	3.91725e7i	0.0112305	+	0.0112305i
$133$	7.85814e8	+	1.66129e9i	0.217765	+	0.460376i
$134$		−	5.25656e9i		−	1.40841i
$135$	2.04594e9	−	1.28272e8i	0.530140	−	0.0332375i
$136$	3.19714e9	+	1.84587e9i	0.801375	+	0.462674i
$137$	−1.74290e9	−	6.50457e9i	−0.422697	−	1.57753i	−0.768902	−	0.639366i	$-0.779197\pi$
$137$	−1.74290e9	−	6.50457e9i	−0.422697	−	1.57753i	0.346206	−	0.938159i	$-0.387470\pi$
$138$	4.80682e8	+	1.28798e8i	0.112824	+	0.0302311i
$139$	−6.73839e9			−1.53105			−0.765525	−	0.643406i	$-0.777521\pi$
$139$	−6.73839e9			−1.53105			−0.765525	+	0.643406i	$0.777521\pi$
$140$	2.02324e8	−	5.00789e7i	0.0445114	−	0.0110174i
$141$	1.69801e9			0.361789
$142$	8.30618e8	+	2.22563e8i	0.171437	+	0.0459363i
$143$	−2.61299e9	−	9.75183e9i	−0.522548	−	1.95018i
$144$	−4.30842e9	−	2.48747e9i	−0.835001	−	0.482088i
$145$	5.62123e9	+	4.95796e9i	1.05603	+	0.931422i
$146$		−	2.63595e9i		−	0.480120i
$147$	−1.53349e8	−	1.55568e9i	−0.0270864	−	0.274784i
$148$	1.93641e8	+	1.93641e8i	0.0331757	+	0.0331757i
$149$	4.23370e9	−	2.44433e9i	0.703691	−	0.406276i	−0.105030	−	0.994469i	$-0.533494\pi$
$149$	4.23370e9	−	2.44433e9i	0.703691	−	0.406276i	0.808721	+	0.588193i	$0.200160\pi$
$150$	1.73710e9	−	2.18677e8i	0.280165	−	0.0352689i
$151$	4.36771e9	−	7.56509e9i	0.683687	−	1.18418i	−0.290160	−	0.956978i	$-0.593709\pi$
$151$	4.36771e9	−	7.56509e9i	0.683687	−	1.18418i	0.973847	−	0.227203i	$-0.0729580\pi$
$152$	8.46448e8	−	3.15899e9i	0.128619	−	0.480012i
$153$	4.19866e9	−	4.19866e9i	0.619440	−	0.619440i
$154$	−6.82743e9	+	5.79312e9i	−0.978169	+	0.829983i
$155$	1.35510e9	−	4.55714e8i	0.188573	−	0.0634161i
$156$	7.53699e7	+	1.30545e8i	0.0101891	+	0.0176481i
$157$	8.20449e9	−	2.19839e9i	1.07771	−	0.288772i	0.324054	−	0.946038i	$-0.394954\pi$
$157$	8.20449e9	−	2.19839e9i	1.07771	−	0.288772i	0.753658	+	0.657266i	$0.228287\pi$
$158$	−1.25979e10	+	3.37560e9i	−1.60820	+	0.430917i
$159$	−1.04903e8	−	1.81698e8i	−0.0130168	−	0.0225457i
$160$	−6.80357e8	−	3.37917e8i	−0.0820724	−	0.0407634i
$161$	−1.18791e9	+	3.32042e9i	−0.139338	+	0.389473i
$162$	−4.92618e9	+	4.92618e9i	−0.561944	+	0.561944i
$163$	−1.02258e9	+	3.81630e9i	−0.113462	+	0.423447i	−0.999167	−	0.0408016i	$-0.987009\pi$
$163$	−1.02258e9	+	3.81630e9i	−0.113462	+	0.423447i	0.885705	+	0.464248i	$0.153676\pi$
$164$	2.76982e7	−	4.79746e7i	0.00298988	−	0.00517862i
$165$	−2.74710e9	+	1.82431e9i	−0.288534	+	0.191611i
$166$	4.47881e9	−	2.58584e9i	0.457801	−	0.264312i
$167$	1.02529e10	+	1.02529e10i	1.02005	+	1.02005i	0.999795	+	0.0202573i	$0.00644854\pi$
$167$	1.02529e10	+	1.02529e10i	1.02005	+	1.02005i	0.0202573	+	0.999795i	$0.493551\pi$
$168$	−1.58306e9	+	2.28749e9i	−0.153322	+	0.221548i
$169$		−	1.68665e10i		−	1.59050i
$170$	6.98594e9	−	7.92051e9i	0.641512	−	0.727332i
$171$	−4.55544e9	−	2.63008e9i	−0.407425	−	0.235227i
$172$	−8.12850e7	−	3.03360e8i	−0.00708161	−	0.0264289i
$173$	−3.96395e9	−	1.06214e9i	−0.336450	−	0.0901515i	0.0866387	−	0.996240i	$-0.472387\pi$
$173$	−3.96395e9	−	1.06214e9i	−0.336450	−	0.0901515i	−0.423089	+	0.906088i	$0.639054\pi$
$174$	4.80764e9			0.397613
$175$	5.38993e8	+	1.23954e10i	0.0434422	+	0.999056i
$176$	1.66664e10			1.30929
$177$	−3.40960e9	−	9.13599e8i	−0.261110	−	0.0699642i
$178$	3.35329e9	+	1.25146e10i	0.250369	+	0.934390i
$179$	−5.18020e9	−	2.99079e9i	−0.377145	−	0.217744i	0.299431	−	0.954118i	$-0.403203\pi$
$179$	−5.18020e9	−	2.99079e9i	−0.377145	−	0.217744i	−0.676575	+	0.736374i	$0.736537\pi$
$180$	−3.94623e8	+	4.47415e8i	−0.0280192	+	0.0317676i
$181$			1.10387e10i			0.764478i	0.924064	+	0.382239i	$0.124847\pi$
$181$			1.10387e10i			0.764478i	−0.924064	+	0.382239i	$0.875153\pi$
$182$	−2.20244e10	+	1.04179e10i	−1.48793	+	0.703813i
$183$	−3.48232e9	−	3.48232e9i	−0.229529	−	0.229529i
$184$	5.43489e9	−	3.13784e9i	0.349551	−	0.201814i
$185$	−1.35797e10	+	9.01808e9i	−0.852350	+	0.566032i
$186$	4.58513e8	−	7.94168e8i	0.0280895	−	0.0486524i
$187$	−5.14845e9	+	1.92143e10i	−0.307886	+	1.14904i
$188$	−7.27682e8	+	7.27682e8i	−0.0424846	+	0.0424846i
$189$	6.02860e9	+	7.10495e9i	0.343667	+	0.405026i
$190$	−8.37926e9	−	4.16178e9i	−0.466460	−	0.231680i
$191$	−1.29060e10	−	2.23539e10i	−0.701685	−	1.21535i	−0.967874	−	0.251434i	$-0.919098\pi$
$191$	−1.29060e10	−	2.23539e10i	−0.701685	−	1.21535i	0.266189	−	0.963921i	$-0.414235\pi$
$192$	4.77124e9	−	1.27845e9i	0.253382	−	0.0678935i
$193$	−2.26612e10	+	6.07206e9i	−1.17564	+	0.315013i	−0.793197	−	0.608965i	$-0.791585\pi$
$193$	−2.26612e10	+	6.07206e9i	−1.17564	+	0.315013i	−0.382446	+	0.923978i	$0.624918\pi$
$194$	1.62571e10	+	2.81581e10i	0.824015	+	1.42724i
$195$	−8.50499e9	+	2.86018e9i	−0.421229	+	0.141657i
$196$	7.32403e8	+	6.00968e8i	0.0354485	+	0.0290870i
$197$	1.81492e10	−	1.81492e10i	0.858537	−	0.858537i	−0.132628	−	0.991166i	$-0.542342\pi$
$197$	1.81492e10	−	1.81492e10i	0.858537	−	0.858537i	0.991166	+	0.132628i	$0.0423417\pi$
$198$	6.63319e9	−	2.47554e10i	0.306711	−	1.14466i
$199$	−3.03084e9	+	5.24957e9i	−0.137001	+	0.237293i	−0.926360	−	0.376639i	$-0.877080\pi$
$199$	−3.03084e9	+	5.24957e9i	−0.137001	+	0.237293i	0.789359	+	0.613932i	$0.210413\pi$
$200$	1.35402e10	−	1.74402e10i	0.598396	−	0.770754i
$201$	7.62078e9	−	4.39986e9i	0.329319	−	0.190133i
$202$	1.84710e9	+	1.84710e9i	0.0780564	+	0.0780564i
$203$	−2.78281e9	+	3.39556e10i	−0.115014	+	1.40339i
$204$		−	2.97007e8i		−	0.0120069i
$205$	2.47306e9	+	2.18126e9i	0.0978008	+	0.0862609i
$206$	−2.58370e10	−	1.49170e10i	−0.999631	−	0.577137i
$207$	−2.61247e9	−	9.74989e9i	−0.0988975	−	0.369091i
$208$	4.38044e10	+	1.17374e10i	1.62268	+	0.434796i
$209$	1.76220e10			0.638845
$210$	5.51846e9	+	5.73406e9i	0.195808	+	0.203458i
$211$	−8.88326e9			−0.308533			−0.154266	−	0.988029i	$-0.549301\pi$
$211$	−8.88326e9			−0.308533			−0.154266	+	0.988029i	$0.549301\pi$
$212$	1.22823e8	+	3.29103e7i	0.00417607	+	0.00111897i
$213$	3.72581e8	+	1.39049e9i	0.0124026	+	0.0462871i
$214$	−3.66406e10	−	2.11545e10i	−1.19427	−	0.689509i
$215$	1.86584e10	−	1.16980e9i	0.595526	−	0.0373369i
$216$		−	1.65819e10i		−	0.518314i
$217$	5.34368e9	+	3.69809e9i	0.163596	+	0.113216i
$218$	−1.83508e10	−	1.83508e10i	−0.550301	−	0.550301i
$219$	3.82151e9	−	2.20635e9i	0.112263	−	0.0648151i
$220$	3.95463e8	−	1.95907e9i	0.0113816	−	0.0563831i
$221$	−2.70634e10	+	4.68752e10i	−0.763163	+	1.32184i
$222$	−2.70622e9	+	1.00998e10i	−0.0747782	+	0.279076i
$223$	−3.62273e10	+	3.62273e10i	−0.980988	+	0.980988i	−0.999823	−	0.0188344i	$-0.994004\pi$
$223$	−3.62273e10	+	3.62273e10i	−0.980988	+	0.980988i	0.0188344	+	0.999823i	$0.494004\pi$
$224$	−6.18277e8	−	3.39716e9i	−0.0164084	−	0.0901571i
$225$	−2.14584e10	−	2.82961e10i	−0.558183	−	0.736046i
$226$	1.90602e10	+	3.30133e10i	0.486004	+	0.841784i
$227$	−1.45545e9	+	3.89988e8i	−0.0363816	+	0.00974843i	−0.276964	−	0.960880i	$-0.589328\pi$
$227$	−1.45545e9	+	3.89988e8i	−0.0363816	+	0.00974843i	0.240582	+	0.970629i	$0.422662\pi$
$228$	−2.54146e8	+	6.80983e7i	−0.00622841	+	0.00166890i
$229$	2.65942e10	+	4.60625e10i	0.639038	+	1.10685i	0.985644	+	0.168836i	$0.0540008\pi$
$229$	2.65942e10	+	4.60625e10i	0.639038	+	1.10685i	−0.346606	+	0.938011i	$0.612666\pi$
$230$	−5.72262e9	−	1.70167e10i	−0.134840	−	0.400959i
$231$	−1.41134e10	−	5.04920e9i	−0.326120	−	0.116673i
$232$	4.28710e10	−	4.28710e10i	0.971557	−	0.971557i
$233$	3.94319e9	−	1.47162e10i	0.0876488	−	0.327110i	−0.908154	−	0.418637i	$-0.862508\pi$
$233$	3.94319e9	−	1.47162e10i	0.0876488	−	0.327110i	0.995803	+	0.0915269i	$0.0291747\pi$
$234$	3.48681e10	−	6.03933e10i	0.760251	−	1.31679i
$235$	−3.38890e10	−	5.10312e10i	−0.724858	−	1.09152i
$236$	1.85270e9	−	1.06966e9i	0.0388778	−	0.0224461i
$237$	−1.54385e10	−	1.54385e10i	−0.317862	−	0.317862i
$238$	4.78447e10	+	3.92108e9i	0.966579	+	0.0792154i
$239$			7.73103e9i			0.153266i	0.997059	+	0.0766331i	$0.0244170\pi$
$239$			7.73103e9i			0.153266i	−0.997059	+	0.0766331i	$0.975583\pi$
$240$	−9.26885e8	−	1.47839e10i	−0.0180333	−	0.287632i
$241$	6.29437e10	+	3.63405e10i	1.20192	+	0.693928i	0.960982	−	0.276612i	$-0.0892118\pi$
$241$	6.29437e10	+	3.63405e10i	1.20192	+	0.693928i	0.240938	+	0.970541i	$0.422545\pi$
$242$	8.09954e9	+	3.02279e10i	0.151807	+	0.566551i
$243$	−3.91530e10	−	1.04910e10i	−0.720338	−	0.193014i
$244$	2.98469e9			0.0539069
$245$	−4.36930e10	+	3.56569e10i	−0.774755	+	0.632261i
$246$	2.11512e9			0.0368238
$247$	4.63159e10	+	1.24103e10i	0.791760	+	0.212151i
$248$	−2.99313e9	−	1.11705e10i	−0.0502449	−	0.187517i
$249$	7.49773e9	+	4.32882e9i	0.123604	+	0.0713629i
$250$	−4.12410e10	−	4.78414e10i	−0.667727	−	0.774593i
$251$			1.45028e9i			0.0230632i	0.999934	+	0.0115316i	$0.00367071\pi$
$251$			1.45028e9i			0.0230632i	−0.999934	+	0.0115316i	$0.996329\pi$
$252$	−2.70266e9	−	2.21495e8i	−0.0422171	−	0.00345988i
$253$	2.39109e10	+	2.39109e10i	0.366905	+	0.366905i
$254$	5.07239e10	−	2.92855e10i	0.764647	−	0.441469i
$255$	1.73303e10	+	3.49833e9i	0.256669	+	0.0518119i
$256$	−4.71687e9	+	8.16987e9i	−0.0686396	+	0.118887i
$257$	1.59280e10	−	5.94443e10i	0.227753	−	0.849984i	−0.753530	−	0.657413i	$-0.771651\pi$
$257$	1.59280e10	−	5.94443e10i	0.227753	−	0.849984i	0.981283	−	0.192571i	$-0.0616827\pi$
$258$	8.47918e9	−	8.47918e9i	0.119142	−	0.119142i
$259$	−6.97665e10	−	2.49597e10i	−0.963381	−	0.344659i
$260$	2.41908e9	−	4.87054e9i	0.0328299	−	0.0660993i
$261$	−4.87578e10	−	8.44510e10i	−0.650372	−	1.12648i
$262$	−4.99960e10	+	1.33964e10i	−0.655510	+	0.175643i
$263$	1.46476e11	−	3.92481e10i	1.88784	−	0.505846i	0.888991	−	0.457924i	$-0.151407\pi$
$263$	1.46476e11	−	3.92481e10i	1.88784	−	0.505846i	0.998851	−	0.0479214i	$-0.0152597\pi$
$264$	1.33373e10	+	2.31009e10i	0.168986	+	0.292692i
$265$	−3.36699e9	+	6.77904e9i	−0.0419407	+	0.0844427i
$266$	−7.61468e9	−	4.18393e10i	−0.0932576	−	0.512410i
$267$	−1.53365e10	+	1.53365e10i	−0.184682	+	0.184682i
$268$	−1.38032e9	+	5.15144e9i	−0.0163446	+	0.0609989i
$269$	−2.63703e10	+	4.56746e10i	−0.307064	+	0.531851i	−0.977719	−	0.209919i	$-0.932680\pi$
$269$	−2.63703e10	+	4.56746e10i	−0.307064	+	0.531851i	0.670655	+	0.741770i	$0.266013\pi$
$270$	−4.64989e10	−	9.38637e9i	−0.532483	−	0.107488i
$271$	−1.01529e11	+	5.86178e10i	−1.14348	+	0.660188i	−0.947290	−	0.320378i	$-0.896190\pi$
$271$	−1.01529e11	+	5.86178e10i	−1.14348	+	0.660188i	−0.196189	+	0.980566i	$0.562857\pi$
$272$	−6.31826e10	−	6.31826e10i	−0.699902	−	0.699902i
$273$	−3.35383e10	−	2.32102e10i	−0.365435	−	0.252899i
$274$			1.55828e11i			1.67020i
$275$	1.09653e11	+	4.61503e10i	1.15618	+	0.486606i
$276$	−4.37247e8	−	2.52445e8i	−0.00453561	−	0.00261864i
$277$	−1.54616e10	−	5.77036e10i	−0.157796	−	0.588903i	−0.998850	−	0.0479513i	$-0.984731\pi$
$277$	−1.54616e10	−	5.77036e10i	−0.157796	−	0.588903i	0.841054	−	0.540952i	$-0.181936\pi$
$278$	1.50616e11	+	4.03574e10i	1.51241	+	0.405248i
$279$	−1.86005e10			−0.183783
$280$	1.00342e11	+	1.92257e9i	0.975597	+	0.0186927i
$281$	−1.49997e11			−1.43517			−0.717587	−	0.696469i	$-0.754753\pi$
$281$	−1.49997e11			−1.43517			−0.717587	+	0.696469i	$0.754753\pi$
$282$	−3.79538e10	−	1.01697e10i	−0.357384	−	0.0957606i
$283$	−1.54516e10	−	5.76663e10i	−0.143197	−	0.534420i	−0.999829	−	0.0184916i	$-0.994114\pi$
$283$	−1.54516e10	−	5.76663e10i	−0.143197	−	0.534420i	0.856632	−	0.515929i	$-0.172553\pi$
$284$	−7.55563e8	−	4.36225e8i	−0.00689189	−	0.00397904i
$285$	−9.80026e8	−	1.56315e10i	−0.00879905	−	0.140345i
$286$			2.33622e11i			2.06474i
$287$	−1.22430e9	+	1.49388e10i	−0.0106517	+	0.129971i
$288$	6.98854e9	+	6.98854e9i	0.0598577	+	0.0598577i
$289$	−1.03407e10	+	5.97020e9i	−0.0871985	+	0.0503441i
$290$	−9.59510e10	−	1.44486e11i	−0.796634	−	1.19960i
$291$	−2.72151e10	+	4.71379e10i	−0.222480	+	0.385347i
$292$	−6.92176e8	+	2.58324e9i	−0.00557178	+	0.0207942i
$293$	1.48691e11	−	1.48691e11i	1.17864	−	1.17864i	0.198550	−	0.980091i	$-0.436377\pi$
$293$	1.48691e11	−	1.48691e11i	1.17864	−	1.17864i	0.980091	−	0.198550i	$-0.0636232\pi$
$294$	−5.88960e9	+	3.56908e10i	−0.0459751	+	0.278608i
$295$	4.05920e10	+	1.20704e11i	0.312062	+	0.927944i
$296$	6.59302e10	+	1.14194e11i	0.499196	+	0.864633i
$297$	8.63036e10	−	2.31250e10i	0.643613	−	0.172456i
$298$	−1.09271e11	+	2.92790e10i	−0.802659	+	0.215072i
$299$	4.60058e10	+	7.96844e10i	0.332883	+	0.576571i
$300$	−1.75978e9	−	2.41842e8i	−0.0125433	−	0.00172379i
$301$	5.49791e10	+	6.47951e10i	0.386054	+	0.454981i
$302$	−1.42935e11	+	1.42935e11i	−0.988799	+	0.988799i
$303$	−1.13180e9	+	4.22392e9i	−0.00771394	+	0.0287888i
$304$	−3.95782e10	+	6.85515e10i	−0.265782	+	0.460347i
$305$	−3.51555e10	+	1.74156e11i	−0.232618	+	1.15236i
$306$	−1.18995e11	+	6.87015e10i	−0.775855	+	0.447940i
$307$	−1.20986e11	−	1.20986e11i	−0.777346	−	0.777346i	0.202033	−	0.979379i	$-0.435245\pi$
$307$	−1.20986e11	−	1.20986e11i	−0.777346	−	0.777346i	−0.979379	+	0.202033i	$0.935245\pi$
$308$	8.21211e9	−	3.88445e9i	0.0519968	−	0.0245952i
$309$		−	4.99435e10i		−	0.311649i
$310$	−3.30185e10	+	2.07012e9i	−0.203062	+	0.0127312i
$311$	3.49223e10	+	2.01624e10i	0.211681	+	0.122214i	0.602092	−	0.798427i	$-0.294334\pi$
$311$	3.49223e10	+	2.01624e10i	0.211681	+	0.122214i	−0.390412	+	0.920640i	$0.627667\pi$
$312$	1.87856e10	+	7.01090e10i	0.112236	+	0.418869i
$313$	5.22373e10	+	1.39969e10i	0.307632	+	0.0824297i	0.409332	−	0.912385i	$-0.365762\pi$
$313$	5.22373e10	+	1.39969e10i	0.307632	+	0.0824297i	−0.101700	+	0.994815i	$0.532428\pi$
$314$	−1.96552e11			−1.14102
$315$	4.47577e10	−	1.55091e11i	0.256136	−	0.887540i
$316$	1.32324e10			0.0746527
$317$	7.75021e10	+	2.07666e10i	0.431069	+	0.115505i	0.467828	−	0.883820i	$-0.345037\pi$
$317$	7.75021e10	+	2.07666e10i	0.431069	+	0.115505i	−0.0367590	+	0.999324i	$0.511703\pi$
$318$	1.25657e9	+	4.68958e9i	0.00689072	+	0.0257165i
$319$	2.82917e11	+	1.63342e11i	1.52968	+	0.883163i
$320$	−1.33646e11	−	1.17877e11i	−0.712496	−	0.628426i
$321$		−	7.08270e10i		−	0.372329i
$322$	4.64387e10	−	6.71032e10i	0.240729	−	0.347850i
$323$	−6.68050e10	−	6.68050e10i	−0.341506	−	0.341506i
$324$	6.12123e9	−	3.53410e9i	0.0308593	−	0.0178166i
$325$	2.55701e11	+	1.98521e11i	1.27133	+	0.987031i
$326$	4.57130e10	−	7.91773e10i	0.224161	−	0.388259i
$327$	1.12443e10	−	4.19643e10i	0.0543836	−	0.202962i
$328$	1.88611e10	−	1.88611e10i	0.0899778	−	0.0899778i
$329$	9.37958e10	−	2.62175e11i	0.441369	−	1.23370i
$330$	7.23290e10	−	2.43238e10i	0.335737	−	0.112907i
$331$	−1.67191e11	−	2.89583e11i	−0.765573	−	1.32601i	−0.939943	−	0.341331i	$-0.889122\pi$
$331$	−1.67191e11	−	2.89583e11i	−0.765573	−	1.32601i	0.174370	−	0.984680i	$-0.444211\pi$
$332$	−5.06826e9	+	1.35804e9i	−0.0228948	+	0.00613465i
$333$	2.04858e11	−	5.48916e10i	0.912965	−	0.244628i
$334$	−1.67765e11	−	2.90578e11i	−0.737638	−	1.27763i
$335$	−2.84327e11	−	1.41218e11i	−1.23343	−	0.612617i
$336$	5.13401e10	−	4.35624e10i	0.219750	−	0.186460i
$337$	1.51131e11	−	1.51131e11i	0.638293	−	0.638293i	−0.311841	−	0.950134i	$-0.600946\pi$
$337$	1.51131e11	−	1.51131e11i	0.638293	−	0.638293i	0.950134	+	0.311841i	$0.100946\pi$
$338$	−1.01016e11	+	3.76998e11i	−0.420985	+	1.57114i
$339$	−3.19077e10	+	5.52657e10i	−0.131219	+	0.227278i
$340$	−8.92607e9	+	5.92766e9i	−0.0362248	+	0.0240563i
$341$	5.39646e10	−	3.11565e10i	0.216130	−	0.124783i
$342$	8.60706e10	+	8.60706e10i	0.340202	+	0.340202i
$343$	−2.48669e11	−	6.22563e10i	−0.970061	−	0.242862i
$344$		−	1.51222e11i		−	0.582241i
$345$	1.98802e10	−	2.25398e10i	0.0755502	−	0.0856573i
$346$	8.22404e10	+	4.74815e10i	0.308491	+	0.178108i
$347$	−7.07556e10	−	2.64064e11i	−0.261986	−	0.977746i	−0.964069	−	0.265651i	$-0.914413\pi$
$347$	−7.07556e10	−	2.64064e11i	−0.261986	−	0.977746i	0.702083	−	0.712095i	$-0.252253\pi$
$348$	−4.71149e9	−	1.26244e9i	−0.0172208	−	0.00461429i
$349$	2.89272e11			1.04374			0.521870	−	0.853025i	$-0.325235\pi$
$349$	2.89272e11			1.04374			0.521870	+	0.853025i	$0.325235\pi$
$350$	6.21908e10	−	2.80289e11i	0.221523	−	0.998390i
$351$	2.43118e11			0.854939
$352$	−3.19816e10	−	8.56944e9i	−0.111034	−	0.0297516i
$353$	−4.92003e10	−	1.83618e11i	−0.168648	−	0.629404i	−0.997547	−	0.0700045i	$-0.977699\pi$
$353$	−4.92003e10	−	1.83618e11i	−0.168648	−	0.629404i	0.828899	−	0.559399i	$-0.188968\pi$
$354$	7.07393e10	+	4.08413e10i	0.239412	+	0.138225i
$355$	3.43531e10	−	3.89488e10i	0.114799	−	0.130157i
$356$		−	1.31449e10i		−	0.0433743i
$357$	3.43624e10	+	7.26456e10i	0.111964	+	0.236702i
$358$	9.78749e10	+	9.78749e10i	0.314918	+	0.314918i
$359$	−3.11120e11	+	1.79625e11i	−0.988561	+	0.570746i	−0.904844	−	0.425744i	$-0.860013\pi$
$359$	−3.11120e11	+	1.79625e11i	−0.988561	+	0.570746i	−0.0837171	+	0.996490i	$0.526679\pi$
$360$	−2.39297e11	+	1.58913e11i	−0.750890	+	0.498654i
$361$	1.19497e11	−	2.06974e11i	0.370316	−	0.641407i
$362$	6.61128e10	−	2.46736e11i	0.202347	−	0.755169i
$363$	−3.70438e10	+	3.70438e10i	−0.111979	+	0.111979i
$364$	2.43196e10	−	4.42611e9i	0.0726105	−	0.0132150i
$365$	−1.42578e11	−	7.08152e10i	−0.420470	−	0.208838i
$366$	5.69802e10	+	9.86925e10i	0.165981	+	0.287488i
$367$	−3.53593e11	+	9.47449e10i	−1.01743	+	0.272621i	−0.728732	−	0.684798i	$-0.759890\pi$
$367$	−3.53593e11	+	9.47449e10i	−1.01743	+	0.272621i	−0.288702	+	0.957419i	$0.593224\pi$
$368$	−1.46719e11	+	3.93132e10i	−0.417034	+	0.111744i
$369$	−2.14510e10	−	3.71543e10i	−0.0602323	−	0.104325i
$370$	3.57543e11	−	1.20240e11i	0.991793	−	0.333534i
$371$	−3.38491e10	+	6.16047e9i	−0.0927608	+	0.0168823i
$372$	−6.57884e8	+	6.57884e8i	−0.00178117	+	0.00178117i
$373$	−1.55398e11	+	5.79951e11i	−0.415675	+	1.55132i	0.367804	+	0.929904i	$0.380110\pi$
$373$	−1.55398e11	+	5.79951e11i	−0.415675	+	1.55132i	−0.783479	+	0.621418i	$0.786557\pi$
$374$	2.30155e11	−	3.98641e11i	0.608274	−	1.05356i
$375$	3.48391e10	−	9.98341e10i	0.0909760	−	0.260698i
$376$	−4.29130e11	+	2.47759e11i	−1.10725	+	0.639269i
$377$	6.28559e11	+	6.28559e11i	1.60254	+	1.60254i
$378$	−9.21979e10	−	1.94916e11i	−0.232278	−	0.491059i
$379$			2.29583e11i			0.571562i	0.958295	+	0.285781i	$0.0922530\pi$
$379$			2.29583e11i			0.571562i	−0.958295	+	0.285781i	$0.907747\pi$
$380$	7.11884e9	+	6.27886e9i	0.0175139	+	0.0154474i
$381$	8.49141e10	+	4.90252e10i	0.206451	+	0.119195i
$382$	1.54593e11	+	5.76948e11i	0.371453	+	1.38628i
$383$	−4.54725e11	−	1.21843e11i	−1.07983	−	0.289339i	−0.325303	−	0.945610i	$-0.605466\pi$
$383$	−4.54725e11	−	1.21843e11i	−1.07983	−	0.289339i	−0.754525	+	0.656271i	$0.772133\pi$
$384$	−1.25084e11			−0.293570
$385$	1.29929e11	+	5.24928e11i	0.301393	+	1.21766i
$386$	5.42888e11			1.24471
$387$	−2.34939e11	−	6.29517e10i	−0.532421	−	0.142662i
$388$	−8.53791e9	−	3.18639e10i	−0.0191253	−	0.0713767i
$389$	−1.41271e10	−	8.15630e9i	−0.0312810	−	0.0180601i	0.484278	−	0.874914i	$-0.339082\pi$
$389$	−1.41271e10	−	8.15630e9i	−0.0312810	−	0.0180601i	−0.515559	+	0.856854i	$0.672416\pi$
$390$	2.07233e11	−	1.29926e10i	0.453595	−	0.0284384i
$391$		−	1.81293e11i		−	0.392270i
$392$	2.65746e11	+	3.70784e11i	0.568432	+	0.793110i
$393$	−6.12694e10	−	6.12694e10i	−0.129562	−	0.129562i
$394$	−5.14367e11	+	2.96970e11i	−1.07533	+	0.620840i
$395$	−1.55859e11	+	7.72104e11i	−0.322140	+	1.59584i
$396$	−1.30011e10	+	2.25185e10i	−0.0265675	+	0.0460162i
$397$	1.63027e11	−	6.08423e11i	0.329383	−	1.22927i	−0.580449	−	0.814297i	$-0.697123\pi$
$397$	1.63027e11	−	6.08423e11i	0.329383	−	1.22927i	0.909832	−	0.414977i	$-0.136210\pi$
$398$	9.91857e10	−	9.91857e10i	0.198141	−	0.198141i
$399$	5.42835e10	−	4.60599e10i	0.107224	−	0.0909799i
$400$	−4.25807e11	+	3.22913e11i	−0.831655	+	0.630689i
$401$	−3.89262e11	−	6.74222e11i	−0.751783	−	1.30213i	−0.946958	−	0.321358i	$-0.895861\pi$
$401$	−3.89262e11	−	6.74222e11i	−0.751783	−	1.30213i	0.195175	−	0.980768i	$-0.437473\pi$
$402$	−1.96690e11	+	5.27031e10i	−0.375635	+	0.100651i
$403$	1.63778e11	−	4.38841e10i	0.309301	−	0.0828770i
$404$	−1.32513e9	−	2.29519e9i	−0.00247481	−	0.00428649i
$405$	1.34114e11	+	3.98799e11i	0.247700	+	0.736557i
$406$	2.65567e11	−	7.42306e11i	0.485073	−	1.35586i
$407$	−5.02399e11	+	5.02399e11i	−0.907558	+	0.907558i
$408$	3.70139e10	−	1.38138e11i	0.0661292	−	0.246798i
$409$	3.23504e11	−	5.60325e11i	0.571643	−	0.990114i	−0.424755	−	0.905308i	$-0.639640\pi$
$409$	3.23504e11	−	5.60325e11i	0.571643	−	0.990114i	0.996398	−	0.0848056i	$-0.0270269\pi$
$410$	−4.22137e10	−	6.35668e10i	−0.0737778	−	0.111097i
$411$	−2.25914e11	+	1.30432e11i	−0.390531	+	0.225473i
$412$	2.14032e10	+	2.14032e10i	0.0365967	+	0.0365967i
$413$	−3.29402e11	+	4.75980e11i	−0.557123	+	0.805032i
$414$			2.33575e11i			0.390773i
$415$	−1.95440e10	−	3.11727e11i	−0.0323442	−	0.515892i
$416$	−7.80223e10	−	4.50462e10i	−0.127732	−	0.0737459i
$417$	6.75600e10	+	2.52137e11i	0.109415	+	0.408343i
$418$	−3.93884e11	−	1.05541e11i	−0.631067	−	0.169094i
$419$	4.97851e11			0.789107			0.394554	−	0.918873i	$-0.370899\pi$
$419$	4.97851e11			0.789107			0.394554	+	0.918873i	$0.370899\pi$
$420$	−3.90239e9	−	7.06848e9i	−0.00611939	−	0.0110842i
$421$	3.31117e11			0.513703			0.256851	−	0.966451i	$-0.417315\pi$
$421$	3.31117e11			0.513703			0.256851	+	0.966451i	$0.417315\pi$
$422$	1.98558e11	+	5.32034e10i	0.304776	+	0.0816645i
$423$	2.06277e11	+	7.69835e11i	0.313270	+	1.16914i
$424$	5.30234e10	+	3.06131e10i	0.0796749	+	0.0460003i
$425$	−2.40741e11	−	5.90654e11i	−0.357931	−	0.878178i
$426$		−	3.33116e10i		−	0.0490063i
$427$	−7.30031e11	+	3.45315e11i	−1.06271	+	0.502679i
$428$	3.03529e10	+	3.03529e10i	0.0437223	+	0.0437223i
$429$	−3.38696e11	+	1.95546e11i	−0.482784	+	0.278735i
$430$	−4.24056e11	−	8.56010e10i	−0.598157	−	0.120745i
$431$	3.23601e11	−	5.60493e11i	0.451713	−	0.782389i	−0.546780	−	0.837276i	$-0.684147\pi$
$431$	3.23601e11	−	5.60493e11i	0.451713	−	0.782389i	0.998493	+	0.0548873i	$0.0174799\pi$
$432$	−1.03876e11	+	3.87669e11i	−0.143495	+	0.535530i
$433$	−4.79907e8	+	4.79907e8i	−0.000656087	+	0.000656087i	−0.707435	−	0.706779i	$-0.750148\pi$
$433$	−4.79907e8	+	4.79907e8i	−0.000656087	+	0.000656087i	0.706779	+	0.707435i	$0.250148\pi$
$434$	−9.72929e10	−	1.14664e11i	−0.131637	−	0.155139i
$435$	1.29158e11	−	2.60045e11i	0.172950	−	0.348214i
$436$	1.31650e10	+	2.28025e10i	0.0174475	+	0.0302199i
$437$	−1.55131e11	+	4.15672e10i	−0.203485	+	0.0545235i
$438$	−9.86323e10	+	2.64284e10i	−0.128052	+	0.0343114i
$439$	−1.35469e11	−	2.34639e11i	−0.174080	−	0.301516i	0.765762	−	0.643124i	$-0.222362\pi$
$439$	−1.35469e11	−	2.34639e11i	−0.174080	−	0.301516i	−0.939843	+	0.341608i	$0.889029\pi$
$440$	4.28075e11	−	8.61880e11i	0.544481	−	1.09625i
$441$	6.86676e11	−	2.58510e11i	0.864526	−	0.325465i
$442$	8.85662e11	−	8.85662e11i	1.10374	−	1.10374i
$443$	−1.70180e11	+	6.35120e11i	−0.209938	+	0.783500i	0.777949	+	0.628327i	$0.216260\pi$
$443$	−1.70180e11	+	6.35120e11i	−0.209938	+	0.783500i	−0.987887	+	0.155173i	$0.950407\pi$
$444$	5.30420e9	−	9.18715e9i	0.00647734	−	0.0112191i
$445$	7.67001e11	+	1.54829e11i	0.927205	+	0.187168i
$446$	1.02672e12	−	5.92777e11i	1.22870	−	0.709389i
$447$	−1.33910e11	−	1.33910e11i	−0.158646	−	0.158646i
$448$	6.61623e10	−	8.07305e11i	0.0775996	−	0.946862i
$449$		−	1.05911e12i		−	1.22980i	−0.788606	−	0.614898i	$-0.789197\pi$
$449$		−	1.05911e12i		−	1.22980i	0.788606	−	0.614898i	$-0.210803\pi$
$450$	3.10167e11	+	7.60989e11i	0.356565	+	0.874827i
$451$	1.24470e11	+	7.18626e10i	0.141667	+	0.0817916i
$452$	−1.00101e10	−	3.73581e10i	−0.0112801	−	0.0420980i
$453$	−3.26862e11	−	8.75825e10i	−0.364689	−	0.0977182i
$454$	3.48679e10			0.0385189
$455$	−2.81881e10	+	1.47117e12i	−0.0308329	+	1.60921i
$456$	−1.26690e11			−0.137214
$457$	−1.54783e11	−	4.14739e10i	−0.165997	−	0.0444786i	0.174864	−	0.984593i	$-0.444052\pi$
$457$	−1.54783e11	−	4.14739e10i	−0.165997	−	0.0444786i	−0.340860	+	0.940114i	$0.610718\pi$
$458$	−3.18554e11	−	1.18886e12i	−0.338290	−	1.26251i
$459$	−4.14845e11	−	2.39511e11i	−0.436243	−	0.251865i
$460$	1.13975e9	+	1.81791e10i	0.00118686	+	0.0189305i
$461$			1.81186e12i			1.86840i	0.356750	+	0.934200i	$0.383885\pi$
$461$			1.81186e12i			1.86840i	−0.356750	+	0.934200i	$0.616115\pi$
$462$	2.85220e11	+	1.97387e11i	0.291267	+	0.201571i
$463$	−7.15780e11	−	7.15780e11i	−0.723878	−	0.723878i	0.245515	−	0.969393i	$-0.421043\pi$
$463$	−7.15780e11	−	7.15780e11i	−0.723878	−	0.723878i	−0.969393	+	0.245515i	$0.921043\pi$
$464$	−1.27084e12	+	7.33721e11i	−1.27280	+	0.734853i
$465$	−3.06384e10	−	4.61363e10i	−0.0303898	−	0.0457620i
$466$	−1.76276e11	+	3.05318e11i	−0.173163	+	0.299927i
$467$	3.67380e10	−	1.37108e11i	0.0357428	−	0.133394i	−0.945749	−	0.324898i	$-0.894670\pi$
$467$	3.67380e10	−	1.37108e11i	0.0357428	−	0.133394i	0.981492	+	0.191504i	$0.0613366\pi$
$468$	−5.00295e10	+	5.00295e10i	−0.0482080	+	0.0482080i
$469$	−2.58383e11	−	1.41970e12i	−0.246596	−	1.35494i
$470$	4.51849e11	+	1.34361e12i	0.427123	+	1.27009i
$471$	−1.64519e11	−	2.84955e11i	−0.154036	−	0.266798i
$472$	9.94994e11	−	2.66608e11i	0.922745	−	0.247249i
$473$	7.87063e11	−	2.10893e11i	0.722994	−	0.193726i
$474$	2.52617e11	+	4.37545e11i	0.229858	+	0.398126i
$475$	−4.50220e11	+	3.41426e11i	−0.405792	+	0.307734i
$476$	−4.58582e10	−	1.64062e10i	−0.0409436	−	0.0146480i
$477$	6.96334e10	−	6.96334e10i	0.0615864	−	0.0615864i
$478$	4.63025e10	−	1.72803e11i	0.0405675	−	0.151400i
$479$	−4.29437e11	+	7.43807e11i	−0.372726	+	0.645581i	−0.989984	−	0.141180i	$-0.954910\pi$
$479$	−4.29437e11	+	7.43807e11i	−0.372726	+	0.645581i	0.617258	+	0.786761i	$0.288244\pi$
$480$	−5.82285e9	+	2.88457e10i	−0.00500669	+	0.0248025i
$481$	−1.67427e12	+	9.66643e11i	−1.42618	+	0.823405i
$482$	−1.18926e12	−	1.18926e12i	−1.00361	−	1.00361i
$483$	1.36154e11	+	1.11584e10i	0.113833	+	0.00932913i
$484$		−	3.17502e10i		−	0.0262992i
$485$	1.95982e12	−	1.22872e11i	1.60834	−	0.100836i
$486$	8.12311e11	+	4.68988e11i	0.660479	+	0.381328i
$487$	−2.71878e11	−	1.01466e12i	−0.219025	−	0.817412i	−0.984711	−	0.174197i	$-0.944267\pi$
$487$	−2.71878e11	−	1.01466e12i	−0.219025	−	0.817412i	0.765686	−	0.643215i	$-0.222400\pi$
$488$	1.38818e12	+	3.71961e11i	1.10804	+	0.296898i
$489$	1.53051e11			0.121045
$490$	1.19018e12	−	5.35315e11i	0.932673	−	0.419495i
$491$	1.01910e12			0.791317			0.395658	−	0.918398i	$-0.370516\pi$
$491$	1.01910e12			0.791317			0.395658	+	0.918398i	$0.370516\pi$
$492$	−2.07282e9	−	5.55412e8i	−0.00159485	−	0.000427338i
$493$	−4.53310e11	−	1.69178e12i	−0.345608	−	1.28983i
$494$	−9.60920e11	−	5.54788e11i	−0.725966	−	0.419137i
$495$	−1.16081e12	−	1.02385e12i	−0.869039	−	0.766498i
$496$			2.79905e11i			0.207655i
$497$	2.35274e11	+	1.92818e10i	0.172970	+	0.0141757i
$498$	−1.41663e11	−	1.41663e11i	−0.103210	−	0.103210i
$499$	1.28296e12	−	7.40719e11i	0.926322	−	0.534812i	0.0406755	−	0.999172i	$-0.487049\pi$
$499$	1.28296e12	−	7.40719e11i	0.926322	−	0.534812i	0.885646	+	0.464360i	$0.153716\pi$
$500$	2.78535e10	+	5.77141e10i	0.0199304	+	0.0412969i
$501$	2.80847e11	−	4.86440e11i	0.199159	−	0.344953i
$502$	8.68598e9	−	3.24165e10i	0.00610453	−	0.0227824i
$503$	−6.61569e11	+	6.61569e11i	−0.460807	+	0.460807i	−0.898920	−	0.438113i	$-0.855647\pi$
$503$	−6.61569e11	+	6.61569e11i	−0.460807	+	0.460807i	0.438113	+	0.898920i	$0.355647\pi$
$504$	−1.22940e12	−	4.39830e11i	−0.848704	−	0.303632i
$505$	1.49532e11	−	5.02867e10i	0.102311	−	0.0344066i
$506$	−3.91247e11	−	6.77660e11i	−0.265322	−	0.459552i
$507$	−6.31112e11	+	1.69106e11i	−0.424200	+	0.113664i
$508$	−5.73996e10	+	1.53802e10i	−0.0382404	+	0.0102465i
$509$	1.38306e12	+	2.39552e12i	0.913292	+	1.58187i	0.809383	+	0.587281i	$0.199802\pi$
$509$	1.38306e12	+	2.39552e12i	0.913292	+	1.58187i	0.103909	+	0.994587i	$0.466865\pi$
$510$	−3.66412e11	−	1.81988e11i	−0.239830	−	0.119118i
$511$	−1.29568e11	−	7.11922e11i	−0.0840630	−	0.461890i
$512$	−1.01465e12	+	1.01465e12i	−0.652533	+	0.652533i
$513$	−1.09831e11	+	4.09895e11i	−0.0700159	+	0.261303i
$514$	−7.12044e11	+	1.23330e12i	−0.449959	+	0.779352i
$515$	−1.50097e12	+	9.96772e11i	−0.940243	+	0.624401i
$516$	−1.05362e10	+	6.08305e9i	−0.00654272	+	0.00377744i
$517$	−1.88796e12	−	1.88796e12i	−1.16221	−	1.16221i
$518$	1.40993e12	+	9.75740e11i	0.860424	+	0.595457i
$519$			1.58972e11i			0.0961764i
$520$	1.73209e12	−	1.96381e12i	1.03886	−	1.17783i
$521$	1.27095e12	+	7.33781e11i	0.755714	+	0.436312i	0.827755	−	0.561090i	$-0.189618\pi$
$521$	1.27095e12	+	7.33781e11i	0.755714	+	0.436312i	−0.0720408	+	0.997402i	$0.522951\pi$
$522$	5.84038e11	+	2.17966e12i	0.344290	+	1.28491i
$523$	2.76686e12	+	7.41378e11i	1.61707	+	0.433294i	0.950140	−	0.311823i	$-0.100940\pi$
$523$	2.76686e12	+	7.41378e11i	1.61707	+	0.433294i	0.666934	+	0.745117i	$0.267606\pi$
$524$	5.25139e10			0.0304287
$525$	4.58408e11	−	1.44446e11i	0.263351	−	0.0829831i
$526$	−3.50908e12			−1.99875
$527$	−3.22695e11	−	8.64659e10i	−0.182240	−	0.0488312i
$528$	−1.67100e11	−	6.23625e11i	−0.0935672	−	0.349198i
$529$	1.29295e12	+	7.46484e11i	0.717845	+	0.414448i
$530$	1.15859e11	−	1.31359e11i	0.0637808	−	0.0723133i
$531$		−	1.65681e12i		−	0.904371i
$532$	−3.52422e9	+	4.30021e10i	−0.00190748	+	0.0232749i
$533$	2.76535e11	+	2.76535e11i	0.148415	+	0.148415i
$534$	4.34653e11	−	2.50947e11i	0.231317	−	0.133551i
$535$	−2.12860e12	+	1.41357e12i	−1.12331	+	0.745975i
$536$	−1.28397e12	+	2.22391e12i	−0.671916	+	1.16379i
$537$	−5.99722e10	+	2.23819e11i	−0.0311218	+	0.116148i
$538$	8.62979e11	−	8.62979e11i	0.444099	−	0.444099i
$539$	−1.55920e12	+	1.90021e12i	−0.795708	+	0.969733i
$540$	4.31042e10	+	2.14088e10i	0.0218146	+	0.0108348i
$541$	−4.81642e11	−	8.34228e11i	−0.241733	−	0.418694i	0.719475	−	0.694519i	$-0.244383\pi$
$541$	−4.81642e11	−	8.34228e11i	−0.241733	−	0.418694i	−0.961208	+	0.275824i	$0.911049\pi$
$542$	2.62044e12	−	7.02144e11i	1.30430	−	0.349486i
$543$	4.13047e11	−	1.10676e11i	0.203892	−	0.0546328i
$544$	8.87557e10	+	1.53729e11i	0.0434511	+	0.0752596i
$545$	−1.48559e12	+	4.99594e11i	−0.721296	+	0.242568i
$546$	6.10636e11	+	7.19659e11i	0.294046	+	0.346545i
$547$	−1.23049e12	+	1.23049e12i	−0.587672	+	0.587672i	−0.937000	−	0.349329i	$-0.886410\pi$
$547$	−1.23049e12	+	1.23049e12i	−0.587672	+	0.587672i	0.349329	+	0.937000i	$0.386410\pi$
$548$	4.09190e10	−	1.52712e11i	0.0193826	−	0.0723369i
$549$	1.15576e12	−	2.00183e12i	0.542988	−	0.940483i
$550$	−2.17456e12	−	1.68828e12i	−1.01330	−	0.786706i
$551$	−1.34370e12	+	7.75788e11i	−0.621043	+	0.358559i
$552$	−1.71903e11	−	1.71903e11i	−0.0788056	−	0.0788056i
$553$	−3.23653e12	+	1.53093e12i	−1.47169	+	0.696132i
$554$			1.38239e12i			0.623499i
$555$	4.73591e11	+	4.17710e11i	0.211878	+	0.186877i
$556$	−1.37006e11	−	7.91005e10i	−0.0608000	−	0.0351029i
$557$	1.92192e11	+	7.17270e11i	0.0846032	+	0.315743i	0.995239	−	0.0974671i	$-0.0310741\pi$
$557$	1.92192e11	+	7.17270e11i	0.0846032	+	0.315743i	−0.910636	+	0.413210i	$0.864407\pi$
$558$	4.15756e11	+	1.11401e11i	0.181545	+	0.0486448i
$559$	2.21716e12			0.960384
$560$	−2.33385e12	−	6.73527e11i	−1.00283	−	0.289407i
$561$	7.70581e11			0.328462
$562$	3.35272e12	+	8.98358e11i	1.41770	+	0.379871i
$563$	−8.84487e10	−	3.30095e11i	−0.0371026	−	0.138469i	0.944890	−	0.327388i	$-0.106168\pi$
$563$	−8.84487e10	−	3.30095e11i	−0.0371026	−	0.138469i	−0.981993	+	0.188919i	$0.939502\pi$
$564$	3.45243e10	+	1.99326e10i	0.0143671	+	0.00829485i
$565$	2.29774e12	−	1.44058e11i	0.948599	−	0.0594731i
$566$			1.38149e12i			0.565815i
$567$	−1.08833e12	+	1.57261e12i	−0.442217	+	0.638996i
$568$	−2.97048e11	−	2.97048e11i	−0.119746	−	0.119746i
$569$	3.14402e12	−	1.81520e12i	1.25742	−	0.725970i	0.284846	−	0.958573i	$-0.408058\pi$
$569$	3.14402e12	−	1.81520e12i	1.25742	−	0.725970i	0.972572	+	0.232603i	$0.0747242\pi$
$570$	−7.17141e10	+	3.55262e11i	−0.0284556	+	0.140965i
$571$	−2.90001e11	+	5.02296e11i	−0.114166	+	0.197741i	−0.917446	−	0.397860i	$-0.869753\pi$
$571$	−2.90001e11	+	5.02296e11i	−0.114166	+	0.197741i	0.803280	+	0.595601i	$0.203086\pi$
$572$	6.13468e10	−	2.28949e11i	0.0239613	−	0.0894247i
$573$	−7.07042e11	+	7.07042e11i	−0.273999	+	0.273999i
$574$	1.16836e11	−	3.26578e11i	0.0449236	−	0.125569i
$575$	−1.07417e12	−	1.47620e11i	−0.409796	−	0.0563171i
$576$	1.15923e12	+	2.00785e12i	0.438803	+	0.760029i
$577$	9.68412e11	−	2.59485e11i	0.363722	−	0.0974589i	−0.0723295	−	0.997381i	$-0.523043\pi$
$577$	9.68412e11	−	2.59485e11i	0.363722	−	0.0974589i	0.436051	+	0.899922i	$0.356377\pi$
$578$	2.66890e11	−	7.15131e10i	0.0994621	−	0.0266508i
$579$	4.54409e11	+	7.87060e11i	0.168033	+	0.291041i
$580$	5.60914e10	+	1.66792e11i	0.0205812	+	0.0611999i
$581$	1.08254e12	−	9.18541e11i	0.394140	−	0.334431i
$582$	8.90626e11	−	8.90626e11i	0.321767	−	0.321767i
$583$	−8.53854e10	+	3.18663e11i	−0.0306108	+	0.114241i
$584$	−6.43861e11	+	1.11520e12i	−0.229052	+	0.396730i
$585$	−2.32993e12	−	3.50848e12i	−0.822510	−	1.23856i
$586$	−4.21407e12	+	2.43300e12i	−1.47626	+	0.852319i
$587$	−2.84556e11	−	2.84556e11i	−0.0989228	−	0.0989228i	0.655913	−	0.754836i	$-0.272284\pi$
$587$	−2.84556e11	−	2.84556e11i	−0.0989228	−	0.0989228i	−0.754836	+	0.655913i	$0.772284\pi$
$588$	1.51439e10	−	3.34305e10i	0.00522444	−	0.0115331i
$589$			2.95953e11i			0.101322i
$590$	−1.84393e11	−	2.94107e12i	−0.0626483	−	0.999244i
$591$	−8.61074e11	−	4.97141e11i	−0.290333	−	0.167624i
$592$	−8.26024e11	−	3.08276e12i	−0.276404	−	1.03155i
$593$	3.65323e12	+	9.78880e11i	1.21320	+	0.325075i	0.808015	−	0.589162i	$-0.200542\pi$
$593$	3.65323e12	+	9.78880e11i	1.21320	+	0.325075i	0.405181	+	0.914237i	$0.367209\pi$
$594$	−2.06755e12			−0.681423
$595$	1.49744e12	−	2.48257e12i	0.489806	−	0.812036i
$596$	1.14774e11			0.0372593
$597$	2.26817e11	+	6.07753e10i	0.0730786	+	0.0195814i
$598$	−5.51073e11	−	2.05663e12i	−0.176220	−	0.657660i
$599$	−2.48340e12	−	1.43379e12i	−0.788180	−	0.455056i	0.0511416	−	0.998691i	$-0.483714\pi$
$599$	−2.48340e12	−	1.43379e12i	−0.788180	−	0.455056i	−0.839321	+	0.543636i	$0.817047\pi$
$600$	−7.88333e11	−	3.31789e11i	−0.248330	−	0.104516i
$601$			1.52213e12i			0.475901i	0.971277	+	0.237950i	$0.0764756\pi$
$601$			1.52213e12i			0.475901i	−0.971277	+	0.237950i	$0.923524\pi$
$602$	−8.40818e11	−	1.77757e12i	−0.260926	−	0.551624i
$603$	2.92056e12	+	2.92056e12i	0.899578	+	0.899578i
$604$	1.77610e11	−	1.02543e11i	0.0543002	−	0.0313502i
$605$	1.85262e12	+	3.73973e11i	0.562194	+	0.113486i
$606$	5.05956e10	−	8.76341e10i	0.0152400	−	0.0263965i
$607$	1.40560e12	−	5.24579e12i	0.420256	−	1.56842i	−0.353813	−	0.935316i	$-0.615115\pi$
$607$	1.40560e12	−	5.24579e12i	0.420256	−	1.56842i	0.774069	−	0.633101i	$-0.218218\pi$
$608$	1.11195e11	−	1.11195e11i	0.0330004	−	0.0330004i
$609$	1.29845e12	−	2.36316e11i	0.382515	−	0.0696171i
$610$	1.82884e12	−	3.68216e12i	0.534800	−	1.07676i
$611$	−3.63254e12	−	6.29175e12i	−1.05445	−	1.82636i
$612$	1.34655e11	−	3.60807e10i	0.0388009	−	0.0103967i
$613$	−1.03829e12	+	2.78209e11i	−0.296993	+	0.0795791i	−0.404239	−	0.914653i	$-0.632464\pi$
$613$	−1.03829e12	+	2.78209e11i	−0.296993	+	0.0795791i	0.107246	+	0.994233i	$0.465797\pi$
$614$	1.97967e12	+	3.42889e12i	0.562127	+	0.973633i
$615$	5.68231e10	−	1.14407e11i	0.0160172	−	0.0322488i
$616$	4.30354e12	−	7.83235e11i	1.20424	−	0.219169i
$617$	2.24369e12	−	2.24369e12i	0.623275	−	0.623275i	−0.323092	−	0.946367i	$-0.604722\pi$
$617$	2.24369e12	−	2.24369e12i	0.623275	−	0.623275i	0.946367	+	0.323092i	$0.104722\pi$
$618$	−2.99120e11	+	1.11633e12i	−0.0824892	+	0.307854i
$619$	1.53089e12	−	2.65157e12i	0.419117	−	0.725931i	−0.576734	−	0.816932i	$-0.695673\pi$
$619$	1.53089e12	−	2.65157e12i	0.419117	−	0.725931i	0.995851	+	0.0910006i	$0.0290065\pi$
$620$	3.29018e10	+	6.64162e9i	0.00894245	+	0.00180514i
$621$	−7.05206e11	+	4.07151e11i	−0.190285	+	0.109861i
$622$	−6.59823e11	−	6.59823e11i	−0.176755	−	0.176755i
$623$	1.52081e12	+	3.21514e12i	0.404462	+	0.855074i
$624$		−	1.75676e12i		−	0.463854i
$625$	−3.69568e12	+	9.45453e11i	−0.968800	+	0.247845i
$626$	−1.08377e12	−	6.25717e11i	−0.282068	−	0.162852i
$627$	−1.76680e11	−	6.59380e11i	−0.0456545	−	0.170385i
$628$	1.92622e11	+	5.16128e10i	0.0494181	+	0.0132416i
$629$	3.80920e12			0.970301
$630$	−1.92928e12	+	3.19851e12i	−0.487937	+	0.808937i
$631$	1.59709e12			0.401048			0.200524	−	0.979689i	$-0.435735\pi$
$631$	1.59709e12			0.401048			0.200524	+	0.979689i	$0.435735\pi$
$632$	6.15436e12	+	1.64906e12i	1.53446	+	0.411158i
$633$	8.90648e10	+	3.32394e11i	0.0220490	+	0.0822881i
$634$	−1.60794e12	−	9.28347e11i	−0.395247	−	0.228196i
$635$	−2.21341e11	−	3.53041e12i	−0.0540233	−	0.861674i
$636$		−	4.92576e9i		−	0.00119376i
$637$	−5.43629e12	+	3.89626e12i	−1.30820	+	0.937607i
$638$	−5.34546e12	−	5.34546e12i	−1.27730	−	1.27730i
$639$	−5.85151e11	+	3.37837e11i	−0.138840	+	0.0801592i
$640$	2.49643e12	+	3.75921e12i	0.588180	+	0.885700i
$641$	2.46658e11	−	4.27224e11i	0.0577077	−	0.0999527i	−0.835728	−	0.549143i	$-0.814954\pi$
$641$	2.46658e11	−	4.27224e11i	0.0577077	−	0.0999527i	0.893436	+	0.449190i	$0.148288\pi$
$642$	−4.24195e11	+	1.58312e12i	−0.0985504	+	0.367795i
$643$	−9.60573e11	+	9.60573e11i	−0.221606	+	0.221606i	−0.809174	−	0.587569i	$-0.800085\pi$
$643$	−9.60573e11	+	9.60573e11i	−0.221606	+	0.221606i	0.587569	+	0.809174i	$0.300085\pi$
$644$	−6.31307e10	+	5.35668e10i	−0.0144629	+	0.0122718i
$645$	−2.30843e11	−	6.86432e11i	−0.0525168	−	0.156163i
$646$	1.09311e12	+	1.89333e12i	0.246955	+	0.427739i
$647$	−2.37037e12	+	6.35139e11i	−0.531798	+	0.142495i	−0.514719	−	0.857359i	$-0.672104\pi$
$647$	−2.37037e12	+	6.35139e11i	−0.531798	+	0.142495i	−0.0170798	+	0.999854i	$0.505437\pi$
$648$	3.28741e12	−	8.80859e11i	0.732431	−	0.196254i
$649$	2.77522e12	+	4.80682e12i	0.614039	+	1.06355i
$650$	−4.52643e12	−	5.96875e12i	−0.994593	−	1.31152i
$651$	8.47990e10	−	2.37028e11i	0.0185045	−	0.0517231i
$652$	−6.55900e10	+	6.55900e10i	−0.0142142	+	0.0142142i
$653$	7.20578e11	−	2.68924e12i	0.155086	−	0.578788i	−0.844012	−	0.536324i	$-0.819813\pi$
$653$	7.20578e11	−	2.68924e12i	0.155086	−	0.578788i	0.999098	−	0.0424640i	$-0.0135208\pi$
$654$	−5.02663e11	+	8.70638e11i	−0.107443	+	0.186096i
$655$	−6.18541e11	+	3.06417e12i	−0.131305	+	0.650470i
$656$	−5.59108e11	+	3.22801e11i	−0.117877	+	0.0680562i
$657$	1.46454e12	+	1.46454e12i	0.306661	+	0.306661i
$658$	−3.66673e12	+	5.29836e12i	−0.762539	+	1.10186i
$659$		−	8.40596e12i		−	1.73621i	−0.496378	−	0.868106i	$-0.665337\pi$
$659$		−	8.40596e12i		−	1.73621i	0.496378	−	0.868106i	$-0.334663\pi$
$660$	−7.72697e10	+	4.84448e9i	−0.0158512	+	0.000993801i
$661$	−2.66008e12	−	1.53580e12i	−0.541985	−	0.312915i	0.203898	−	0.978992i	$-0.434639\pi$
$661$	−2.66008e12	−	1.53580e12i	−0.541985	−	0.312915i	−0.745883	+	0.666077i	$0.767972\pi$
$662$	2.00267e12	+	7.47407e12i	0.405274	+	1.51250i
$663$	2.02532e12	+	5.42683e11i	0.407083	+	0.109078i
$664$	−2.52649e12			−0.504383
$665$	−2.46765e12	−	7.12142e11i	−0.489313	−	0.141211i
$666$	−4.90772e12			−0.966598
$667$	−2.87590e12	−	7.70594e11i	−0.562609	−	0.150751i
$668$	8.81071e10	+	3.28820e11i	0.0171205	+	0.0638947i
$669$	1.71877e12	+	9.92335e11i	0.331743	+	0.191532i
$670$	5.50946e12	+	4.85938e12i	1.05626	+	0.931631i
$671$			7.74374e12i			1.47468i
$672$	−1.20916e11	+	5.71951e10i	−0.0228730	+	0.0108193i
$673$	1.91522e12	+	1.91522e12i	0.359874	+	0.359874i	0.863766	−	0.503893i	$-0.168099\pi$
$673$	1.91522e12	+	1.91522e12i	0.359874	+	0.359874i	−0.503893	+	0.863766i	$0.668099\pi$
$674$	−4.28323e12	+	2.47292e12i	−0.799469	+	0.461573i
$675$	−1.75691e12	+	2.26295e12i	−0.325748	+	0.419574i
$676$	1.97992e11	−	3.42933e11i	0.0364660	−	0.0631610i
$677$	−2.27579e11	+	8.49337e11i	−0.0416374	+	0.155393i	−0.983615	−	0.180284i	$-0.942298\pi$
$677$	−2.27579e11	+	8.49337e11i	−0.0416374	+	0.155393i	0.941977	+	0.335677i	$0.108965\pi$
$678$	1.04419e12	−	1.04419e12i	0.189778	−	0.189778i
$679$	5.77483e12	+	6.80587e12i	1.04262	+	1.22877i
$680$	−4.89023e12	+	1.64456e12i	−0.877080	+	0.294957i
$681$	2.91852e10	+	5.05502e10i	0.00519996	+	0.00900660i
$682$	−1.39281e12	+	3.73203e11i	−0.246526	+	0.0660565i
$683$	−2.34263e12	+	6.27705e11i	−0.411917	+	0.110373i	−0.458826	−	0.888526i	$-0.651730\pi$
$683$	−2.34263e12	+	6.27705e11i	−0.411917	+	0.110373i	0.0469085	+	0.998899i	$0.485063\pi$
$684$	−6.17480e10	−	1.06951e11i	−0.0107862	−	0.0186823i
$685$	8.42871e12	+	4.18634e12i	1.46269	+	0.726486i
$686$	5.18537e12	+	2.88087e12i	0.893967	+	0.496667i
$687$	1.45693e12	−	1.45693e12i	0.249536	−	0.249536i
$688$	−9.47314e11	+	3.53543e12i	−0.161193	+	0.601581i
$689$	−4.48838e11	+	7.77410e11i	−0.0758757	+	0.131421i
$690$	−5.79356e11	+	3.84741e11i	−0.0973026	+	0.0646171i
$691$	−1.15072e12	+	6.64371e11i	−0.192008	+	0.110856i	−0.592922	−	0.805260i	$-0.702026\pi$
$691$	−1.15072e12	+	6.64371e11i	−0.192008	+	0.110856i	0.400914	+	0.916116i	$0.368693\pi$
$692$	−6.81275e10	−	6.81275e10i	−0.0112939	−	0.0112939i
$693$	5.74666e11	−	7.01202e12i	0.0946490	−	1.15490i
$694$			6.32609e12i			1.03518i
$695$	6.22923e12	−	7.06257e12i	1.01275	−	1.14824i
$696$	−2.03398e12	−	1.17432e12i	−0.328553	−	0.189690i
$697$	−1.99434e11	−	7.44298e11i	−0.0320075	−	0.119454i
$698$	−6.46578e12	−	1.73250e12i	−1.03103	−	0.276264i
$699$	−5.90186e11			−0.0935065
$700$	−1.34548e11	+	2.58353e11i	−0.0211805	+	0.0406698i
$701$	7.31544e12			1.14422			0.572109	−	0.820177i	$-0.306125\pi$
$701$	7.31544e12			1.14422			0.572109	+	0.820177i	$0.306125\pi$
$702$	−5.43415e12	−	1.45608e12i	−0.844529	−	0.226291i
$703$	−8.73382e11	−	3.25951e12i	−0.134867	−	0.503330i
$704$	−6.72645e12	−	3.88352e12i	−1.03207	−	0.595866i
$705$	−1.56971e12	+	1.77971e12i	−0.239314	+	0.271330i
$706$			4.39888e12i			0.666379i
$707$	5.89659e11	+	4.08074e11i	0.0887592	+	0.0614258i
$708$	−5.86000e10	−	5.86000e10i	−0.00876492	−	0.00876492i
$709$	−7.01192e12	+	4.04833e12i	−1.04215	+	0.601684i	−0.920441	−	0.390883i	$-0.872170\pi$
$709$	−7.01192e12	+	4.04833e12i	−1.04215	+	0.601684i	−0.121706	+	0.992566i	$0.538837\pi$
$710$	−1.00113e12	+	6.64833e11i	−0.147852	+	0.0981861i
$711$	5.12394e12	−	8.87493e12i	0.751954	−	1.30242i
$712$	1.63816e12	−	6.11368e12i	0.238888	−	0.891544i
$713$	−4.01572e11	+	4.01572e11i	−0.0581917	+	0.0581917i
$714$	−3.32978e11	−	1.82957e12i	−0.0479483	−	0.263455i
$715$	1.26366e13	+	6.27627e12i	1.80822	+	0.898100i
$716$	−7.02165e10	−	1.21619e11i	−0.00998460	−	0.0172938i
$717$	2.89280e11	−	7.75124e10i	0.0408773	−	0.0109530i
$718$	8.02994e12	−	2.15162e12i	1.12759	−	0.302138i
$719$	−3.08140e12	−	5.33714e12i	−0.429999	−	0.744781i	0.566873	−	0.823805i	$-0.308153\pi$
$719$	−3.08140e12	−	5.33714e12i	−0.429999	−	0.744781i	−0.996873	+	0.0790243i	$0.974820\pi$
$720$	6.59002e12	−	2.21619e12i	0.913883	−	0.307334i
$721$	−7.71133e12	−	2.75880e12i	−1.06272	−	0.380200i
$722$	−3.91058e12	+	3.91058e12i	−0.535579	+	0.535579i
$723$	7.28711e11	−	2.71959e12i	0.0991820	−	0.370152i
$724$	−1.29581e11	+	2.24441e11i	−0.0175274	+	0.0303584i
$725$	−1.03930e13	+	1.30833e12i	−1.39707	+	0.175872i
$726$	1.04986e12	−	6.06138e11i	0.140255	−	0.0809761i
$727$	−3.27755e12	−	3.27755e12i	−0.435155	−	0.435155i	0.455223	−	0.890378i	$-0.349560\pi$
$727$	−3.27755e12	−	3.27755e12i	−0.435155	−	0.435155i	−0.890378	+	0.455223i	$0.849560\pi$
$728$	1.18626e13	+	9.72193e11i	1.56527	+	0.128281i
$729$		−	4.35558e12i		−	0.571179i
$730$	2.76277e12	+	2.43678e12i	0.360074	+	0.317588i
$731$	−3.78326e12	−	2.18427e12i	−0.490048	−	0.282929i
$732$	−2.99249e10	−	1.11681e11i	−0.00385241	−	0.0143774i
$733$	−1.06542e13	−	2.85478e12i	−1.36318	−	0.365262i	−0.498194	−	0.867066i	$-0.666003\pi$
$733$	−1.06542e13	−	2.85478e12i	−1.36318	−	0.365262i	−0.864981	+	0.501804i	$0.832670\pi$
$734$	8.47092e12			1.07720
$735$	1.77229e12	+	1.27741e12i	0.223996	+	0.161449i
$736$	3.01756e11			0.0379058
$737$	−1.33653e13	−	3.58123e12i	−1.66869	−	0.447125i
$738$	2.56948e11	+	9.58942e11i	0.0318854	+	0.118998i
$739$	4.69583e11	+	2.71114e11i	0.0579178	+	0.0334389i	0.528679	−	0.848822i	$-0.322687\pi$
$739$	4.69583e11	+	2.71114e11i	0.0579178	+	0.0334389i	−0.470761	+	0.882261i	$0.656021\pi$
$740$	−3.81967e11	+	2.39477e10i	−0.0468255	+	0.00293576i
$741$		−	1.85748e12i		−	0.226330i
$742$	7.93488e11	+	6.50299e10i	0.0960999	+	0.00787581i
$743$	−3.53551e12	−	3.53551e12i	−0.425601	−	0.425601i	0.461526	−	0.887127i	$-0.347302\pi$
$743$	−3.53551e12	−	3.53551e12i	−0.425601	−	0.425601i	−0.887127	+	0.461526i	$0.847302\pi$
$744$	−3.87969e11	+	2.23994e11i	−0.0464214	+	0.0268014i
$745$	−1.35188e12	+	6.69702e12i	−0.160781	+	0.796487i
$746$	6.94686e12	−	1.20323e13i	0.821228	−	1.42241i
$747$	−1.05174e12	+	3.92515e12i	−0.123585	+	0.461225i
$748$	−3.30232e11	+	3.30232e11i	−0.0385711	+	0.0385711i
$749$	−1.09358e13	−	3.91238e12i	−1.26964	−	0.454227i
$750$	−1.37664e12	+	2.02282e12i	−0.158872	+	0.233444i
$751$	7.57235e12	+	1.31157e13i	0.868662	+	1.50457i	0.863364	+	0.504581i	$0.168353\pi$
$751$	7.57235e12	+	1.31157e13i	0.868662	+	1.50457i	0.00529815	+	0.999986i	$0.498314\pi$
$752$	1.15847e13	−	3.10411e12i	1.32100	−	0.353962i
$753$	5.42667e10	−	1.45407e10i	0.00615114	−	0.00164819i
$754$	−1.02849e13	−	1.78140e13i	−1.15886	−	2.00720i
$755$	3.89137e12	+	1.15713e13i	0.435854	+	1.29605i
$756$	3.91710e10	+	2.15228e11i	0.00436131	+	0.0239635i
$757$	8.94189e12	−	8.94189e12i	0.989687	−	0.989687i	−0.0102606	−	0.999947i	$-0.503266\pi$
$757$	8.94189e12	−	8.94189e12i	0.989687	−	0.989687i	0.999947	+	0.0102606i	$0.00326612\pi$
$758$	1.37501e12	−	5.13162e12i	0.151285	−	0.564602i
$759$	6.54965e11	−	1.13443e12i	0.0716358	−	0.124077i
$760$	2.52848e12	+	3.80747e12i	0.274915	+	0.413976i
$761$	1.30630e13	−	7.54194e12i	1.41193	−	0.815178i	0.416359	−	0.909200i	$-0.363306\pi$
$761$	1.30630e13	−	7.54194e12i	1.41193	−	0.815178i	0.995570	+	0.0940228i	$0.0299727\pi$
$762$	−1.60437e12	−	1.60437e12i	−0.172388	−	0.172388i
$763$	−5.85822e12	−	4.05418e12i	−0.625756	−	0.433055i
$764$		−	6.06005e11i		−	0.0643511i
$765$	5.19250e11	+	8.28207e12i	0.0548151	+	0.874304i
$766$	9.43423e12	+	5.44686e12i	0.990095	+	0.571632i
$767$	3.90890e12	+	1.45882e13i	0.407827	+	1.52203i
$768$	3.52993e11	+	9.45841e10i	0.0366134	+	0.00981054i
$769$	−1.03458e11			−0.0106683			−0.00533415	−	0.999986i	$-0.501698\pi$
$769$	−1.03458e11			−0.0106683			−0.00533415	+	0.999986i	$0.501698\pi$
$770$	2.39720e11	−	1.25113e13i	0.0245751	−	1.28261i
$771$	−2.38399e12			−0.242974
$772$	−5.32031e11	−	1.42557e11i	−0.0539087	−	0.0144448i
$773$	−2.26660e12	−	8.45906e12i	−0.228332	−	0.852147i	−0.981042	−	0.193795i	$-0.937920\pi$
$773$	−2.26660e12	−	8.45906e12i	−0.228332	−	0.852147i	0.752710	−	0.658352i	$-0.228746\pi$
$774$	4.87430e12	+	2.81418e12i	0.488178	+	0.281850i
$775$	−7.75074e11	+	1.84158e12i	−0.0771766	+	0.183372i
$776$		−	1.58839e13i		−	1.57246i
$777$	−2.34453e11	+	2.86078e12i	−0.0230761	+	0.281572i
$778$	2.66919e11	+	2.66919e11i	0.0261199	+	0.0261199i
$779$	−5.91163e11	+	3.41308e11i	−0.0575160	+	0.0332069i
$780$	−2.06500e11	−	4.16846e10i	−0.0199754	−	0.00403227i
$781$	1.13178e12	−	1.96030e12i	0.108851	−	0.188535i
$782$	−1.08579e12	+	4.05224e12i	−0.103829	+	0.387494i
$783$	−5.56274e12	+	5.56274e12i	−0.528884	+	0.528884i
$784$	−3.89013e12	−	1.03333e13i	−0.367741	−	0.976824i
$785$	−5.28041e12	+	1.06315e13i	−0.496311	+	0.999265i
$786$	1.00253e12	+	1.73644e12i	0.0936909	+	0.162277i
$787$	1.25065e13	−	3.35110e12i	1.16211	−	0.311387i	0.374303	−	0.927306i	$-0.377882\pi$
$787$	1.25065e13	−	3.35110e12i	1.16211	−	0.311387i	0.787809	+	0.615919i	$0.211215\pi$
$788$	5.82062e11	−	1.55963e11i	0.0537776	−	0.0144097i
$789$	−2.93718e12	−	5.08734e12i	−0.269826	−	0.467352i
$790$	8.10801e12	−	1.63245e13i	0.740614	−	1.49114i
$791$	6.77055e12	+	7.97938e12i	0.614936	+	0.724727i
$792$	−8.85311e12	+	8.85311e12i	−0.799526	+	0.799526i
$793$	−5.45354e12	+	2.03529e13i	−0.489722	+	1.82767i
$794$	−7.28791e12	+	1.26230e13i	−0.650744	+	1.12712i
$795$	2.87417e11	+	5.80186e10i	0.0255188	+	0.00515128i
$796$	−1.23247e11	+	7.11568e10i	−0.0108810	+	0.00628214i
$797$	−3.83196e12	−	3.83196e12i	−0.336402	−	0.336402i	0.518609	−	0.855011i	$-0.326450\pi$
$797$	−3.83196e12	−	3.83196e12i	−0.336402	−	0.336402i	−0.855011	+	0.518609i	$0.826450\pi$
$798$	−1.48920e12	+	7.04414e11i	−0.129999	+	0.0614915i
$799$			1.43146e13i			1.24256i
$800$	9.83124e11	−	4.00705e11i	0.0848601	−	0.0345876i
$801$	−8.81627e12	−	5.09007e12i	−0.756726	−	0.436896i
$802$	4.66272e12	+	1.74015e13i	0.397974	+	1.48526i
$803$	−6.70218e12	−	1.79584e12i	−0.568848	−	0.152422i
$804$	2.06596e11			0.0174369
$805$	−2.38202e12	−	4.31460e12i	−0.199923	−	0.362125i
$806$	−3.92357e12			−0.327472
$807$	1.97345e12	+	5.28784e11i	0.163793	+	0.0438882i
$808$	−3.30282e11	−	1.23263e12i	−0.0272605	−	0.101738i
$809$	−4.10941e11	−	2.37257e11i	−0.0337296	−	0.0194738i	0.483040	−	0.875598i	$-0.339532\pi$
$809$	−4.10941e11	−	2.37257e11i	−0.0337296	−	0.0194738i	−0.516770	+	0.856124i	$0.672866\pi$
$810$	−6.09224e11	−	9.71715e12i	−0.0497272	−	0.793152i
$811$			9.13605e12i			0.741591i	0.928714	+	0.370796i	$0.120915\pi$
$811$			9.13605e12i			0.741591i	−0.928714	+	0.370796i	$0.879085\pi$
$812$	−4.55178e11	+	6.57725e11i	−0.0367434	+	0.0530936i
$813$	3.21131e12	+	3.21131e12i	0.257795	+	0.257795i
$814$	1.42385e13	−	8.22062e12i	1.13673	−	0.656289i
$815$	−3.05460e12	−	4.59972e12i	−0.242519	−	0.365193i
$816$	−1.73069e12	+	2.99765e12i	−0.136652	+	0.236687i
$817$	−1.00163e12	+	3.73812e12i	−0.0786514	+	0.293531i
$818$	−1.05868e13	+	1.05868e13i	−0.826752	+	0.826752i
$819$	6.44863e12	−	1.80250e13i	0.500829	−	1.39990i
$820$	2.46774e10	+	7.33804e10i	0.00190606	+	0.00566784i
$821$	−7.04092e12	−	1.21952e13i	−0.540860	−	0.936798i	−0.998855	−	0.0478426i	$-0.984765\pi$
$821$	−7.04092e12	−	1.21952e13i	−0.540860	−	0.936798i	0.457995	−	0.888955i	$-0.348568\pi$
$822$	5.83079e12	−	1.56235e12i	0.445455	−	0.119359i
$823$	5.24273e12	−	1.40478e12i	0.398344	−	0.106736i	−0.0540852	−	0.998536i	$-0.517224\pi$
$823$	5.24273e12	−	1.40478e12i	0.398344	−	0.106736i	0.452429	+	0.891800i	$0.350558\pi$
$824$	7.28729e12	+	1.26220e13i	0.550673	+	0.953793i
$825$	6.27456e11	−	4.56573e12i	0.0471564	−	0.343137i
$826$	1.02135e13	−	8.66621e12i	0.763420	−	0.647767i
$827$	5.13734e12	−	5.13734e12i	0.381912	−	0.381912i	−0.489878	−	0.871791i	$-0.662959\pi$
$827$	5.13734e12	−	5.13734e12i	0.381912	−	0.381912i	0.871791	+	0.489878i	$0.162959\pi$
$828$	6.13346e10	−	2.28904e11i	0.00453491	−	0.0169245i
$829$	−8.10264e12	+	1.40342e13i	−0.595842	+	1.03203i	0.397586	+	0.917565i	$0.369848\pi$
$829$	−8.10264e12	+	1.40342e13i	−0.595842	+	1.03203i	−0.993427	+	0.114463i	$0.963485\pi$
$830$	−1.43014e12	+	7.08475e12i	−0.104599	+	0.518171i
$831$	−2.00414e12	+	1.15709e12i	−0.145788	+	0.0841709i
$832$	−1.49442e13	−	1.49442e13i	−1.08123	−	1.08123i
$833$	1.31147e13	−	1.29276e12i	0.943747	−	0.0930283i
$834$		−	6.04038e12i		−	0.432332i
$835$	−2.02244e13	+	1.26798e12i	−1.43974	+	0.0902658i
$836$	3.58293e11	+	2.06860e11i	0.0253694	+	0.0146470i
$837$	3.88373e11	+	1.44943e12i	0.0273517	+	0.102078i
$838$	−1.11279e13	−	2.98171e12i	−0.779499	−	0.208866i
$839$	2.39905e12			0.167151			0.0835757	−	0.996501i	$-0.473366\pi$
$839$	2.39905e12			0.167151			0.0835757	+	0.996501i	$0.473366\pi$
$840$	−9.34102e11	−	3.77387e12i	−0.0647347	−	0.261535i
$841$	−1.42568e13			−0.982741
$842$	−7.40109e12	−	1.98312e12i	−0.507448	−	0.135970i
$843$	1.50389e12	+	5.61260e12i	0.102563	+	0.382772i
$844$	−1.80616e11	−	1.04279e11i	−0.0122522	−	0.00707383i
$845$	1.76779e13	+	1.55921e13i	1.19282	+	1.05208i
$846$		−	1.84427e13i		−	1.23782i
$847$	3.67336e12	+	7.76586e12i	0.245238	+	0.518459i
$848$	−1.04786e12	−	1.04786e12i	−0.0695862	−	0.0695862i
$849$	−2.00284e12	+	1.15634e12i	−0.132301	+	0.0763838i
$850$	1.84349e12	+	1.46441e13i	0.121131	+	0.962225i
$851$	3.23768e12	−	5.60783e12i	0.211617	−	0.366532i
$852$	−8.74730e9	+	3.26454e10i	−0.000568717	+	0.00212248i
$853$	−1.11316e13	+	1.11316e13i	−0.719928	+	0.719928i	−0.968590	−	0.248663i	$-0.920009\pi$
$853$	−1.11316e13	+	1.11316e13i	−0.719928	+	0.719928i	0.248663	+	0.968590i	$0.420009\pi$
$854$	1.83857e13	−	3.34617e12i	1.18283	−	0.215272i
$855$	6.96784e12	−	2.34325e12i	0.445914	−	0.149958i
$856$	1.03344e13	+	1.78998e13i	0.657892	+	1.13950i
$857$	1.51544e13	−	4.06061e12i	0.959677	−	0.257145i	0.255213	−	0.966885i	$-0.417854\pi$
$857$	1.51544e13	−	4.06061e12i	0.959677	−	0.257145i	0.704463	+	0.709740i	$0.251188\pi$
$858$	8.74167e12	−	2.34232e12i	0.550683	−	0.147555i
$859$	−2.33636e12	−	4.04669e12i	−0.146410	−	0.253589i	0.783488	−	0.621407i	$-0.213438\pi$
$859$	−2.33636e12	−	4.04669e12i	−0.146410	−	0.253589i	−0.929898	+	0.367817i	$0.880105\pi$
$860$	3.93098e11	+	1.95242e11i	0.0245051	+	0.0121711i
$861$	5.71256e11	−	1.03967e11i	0.0354255	−	0.00644738i
$862$	−1.05900e13	+	1.05900e13i	−0.653300	+	0.653300i
$863$	4.19071e12	−	1.56399e13i	0.257181	−	0.959813i	−0.709683	−	0.704521i	$-0.751162\pi$
$863$	4.19071e12	−	1.56399e13i	0.257181	−	0.959813i	0.966864	−	0.255292i	$-0.0821716\pi$
$864$	3.98658e11	−	6.90496e11i	0.0243382	−	0.0421550i
$865$	4.77767e12	−	3.17277e12i	0.290164	−	0.192693i
$866$	1.36011e10	−	7.85259e9i	0.000821756	−	0.000474441i
$867$	3.27070e11	+	3.27070e11i	0.0196587	+	0.0196587i
$868$	6.52375e10	+	1.37919e11i	0.00390084	+	0.00824678i
$869$			3.43312e13i			2.04221i
$870$	−4.44438e12	+	5.03894e12i	−0.263011	+	0.298197i
$871$	−3.26061e13	−	1.88252e13i	−1.91963	−	1.10830i
$872$	3.28133e12	+	1.22461e13i	0.192188	+	0.717255i
$873$	−2.46772e13	−	6.61224e12i	−1.43791	−	0.385287i
$874$	3.71642e12			0.215439
$875$	−1.34900e13	−	1.08939e13i	−0.777995	−	0.628271i
$876$	1.03600e11			0.00594415
$877$	8.36958e10	+	2.24262e10i	0.00477755	+	0.00128014i	0.261207	−	0.965283i	$-0.415879\pi$
$877$	8.36958e10	+	2.24262e10i	0.00477755	+	0.00128014i	−0.256429	+	0.966563i	$0.582546\pi$
$878$	1.62269e12	+	6.05598e12i	0.0921534	+	0.343921i
$879$	−7.05454e12	−	4.07294e12i	−0.398583	−	0.230122i
$880$	−1.54071e13	+	1.74683e13i	−0.866062	+	0.981923i
$881$			2.39476e13i			1.33928i	0.742687	+	0.669639i	$0.233551\pi$
$881$			2.39476e13i			1.33928i	−0.742687	+	0.669639i	$0.766449\pi$
$882$	−1.68968e13	+	1.66557e12i	−0.940145	+	0.0926733i
$883$	1.42084e13	+	1.42084e13i	0.786545	+	0.786545i	0.980926	−	0.194381i	$-0.0622699\pi$
$883$	1.42084e13	+	1.42084e13i	0.786545	+	0.786545i	−0.194381	+	0.980926i	$0.562270\pi$
$884$	−1.10052e12	+	6.35383e11i	−0.0606124	+	0.0349946i
$885$	4.10952e12	−	2.72907e12i	0.225189	−	0.149544i
$886$	7.60769e12	−	1.31769e13i	0.414764	−	0.718392i
$887$	5.31167e12	−	1.98234e13i	0.288121	−	1.07528i	−0.658408	−	0.752661i	$-0.728770\pi$
$887$	5.31167e12	−	1.98234e13i	0.288121	−	1.07528i	0.946529	−	0.322620i	$-0.104564\pi$
$888$	3.61191e12	−	3.61191e12i	0.194930	−	0.194930i
$889$	1.22601e13	−	1.04028e13i	0.658317	−	0.558586i
$890$	−1.62166e13	−	8.05441e12i	−0.866374	−	0.430308i
$891$	9.16917e12	+	1.58815e13i	0.487394	+	0.844192i
$892$	−1.16184e12	+	3.11315e11i	−0.0614477	+	0.0164649i
$893$	1.22489e13	−	3.28208e12i	0.644562	−	0.172710i
$894$	2.19113e12	+	3.79515e12i	0.114723	+	0.198705i
$895$	7.92346e12	−	2.66462e12i	0.412773	−	0.138813i
$896$	−6.90947e12	+	1.93131e13i	−0.358145	+	1.00108i
$897$	2.52038e12	−	2.52038e12i	0.129987	−	0.129987i
$898$	−6.34320e12	+	2.36732e13i	−0.325511	+	1.21482i
$899$	−2.74326e12	+	4.75147e12i	−0.140071	+	0.242610i
$900$	−1.04135e11	−	8.27217e11i	−0.00529062	−	0.0420270i
$901$	1.53175e12	−	8.84357e11i	0.0774331	−	0.0447060i
$902$	−2.35174e12	−	2.35174e12i	−0.118293	−	0.118293i
$903$	1.87328e12	−	2.70686e12i	0.0937579	−	0.135478i
$904$		−	1.86227e13i		−	0.927437i
$905$	−1.15698e13	−	1.02046e13i	−0.573333	−	0.505683i
$906$	6.78145e12	+	3.91527e12i	0.334384	+	0.193057i
$907$	6.84027e12	+	2.55282e13i	0.335614	+	1.25253i	0.903202	+	0.429217i	$0.141210\pi$
$907$	6.84027e12	+	2.55282e13i	0.335614	+	1.25253i	−0.567587	+	0.823313i	$0.692123\pi$
$908$	−3.41705e10	−	9.15597e9i	−0.00166827	−	0.000447011i
$909$	−2.05251e12			−0.0997119
$910$	9.44117e12	−	3.27147e13i	0.456393	−	1.58145i
$911$	2.21543e13			1.06568			0.532839	−	0.846217i	$-0.321125\pi$
$911$	2.21543e13			1.06568			0.532839	+	0.846217i	$0.321125\pi$
$912$	2.96188e12	+	7.93634e11i	0.141772	+	0.0379877i
$913$	−3.52341e12	−	1.31495e13i	−0.167820	−	0.626314i
$914$	3.21129e12	+	1.85404e12i	0.152202	+	0.0878741i
$915$	6.86904e12	−	4.30660e11i	0.323967	−	0.0203114i
$916$			1.24873e12i			0.0586057i
$917$	−1.28445e13	+	6.07563e12i	−0.599867	+	0.283746i
$918$	7.83810e12	+	7.83810e12i	0.364266	+	0.364266i
$919$	2.59112e13	−	1.49598e13i	1.19830	−	0.691842i	0.238128	−	0.971234i	$-0.423466\pi$
$919$	2.59112e13	−	1.49598e13i	1.19830	−	0.691842i	0.960177	+	0.279392i	$0.0901330\pi$
$920$	−1.73543e12	+	8.59711e12i	−0.0798661	+	0.395647i
$921$	−3.31405e12	+	5.74011e12i	−0.151772	+	0.262877i
$922$	1.08515e13	−	4.04985e13i	0.494540	−	1.84565i
$923$	4.35521e12	−	4.35521e12i	0.197516	−	0.197516i
$924$	−2.27684e11	−	2.68335e11i	−0.0102756	−	0.0121103i
$925$	3.10170e12	−	2.25697e13i	0.139303	−	1.01365i
$926$	1.17121e13	+	2.02860e13i	0.523463	+	0.906664i
$927$	2.26431e13	−	6.06719e12i	1.00711	−	0.269854i
$928$	2.81591e12	−	7.54520e11i	0.124639	−	0.0333968i
$929$	−2.69415e12	−	4.66641e12i	−0.118673	−	0.205547i	0.800569	−	0.599240i	$-0.204531\pi$
$929$	−2.69415e12	−	4.66641e12i	−0.118673	−	0.205547i	−0.919242	+	0.393693i	$0.871197\pi$
$930$	4.08508e11	+	1.21473e12i	0.0179072	+	0.0532485i
$931$	−4.11316e12	−	1.09257e13i	−0.179433	−	0.476625i
$932$	2.52924e11	−	2.52924e11i	0.0109804	−	0.0109804i
$933$	4.04302e11	−	1.50888e12i	0.0174678	−	0.0651908i
$934$	−1.64233e12	+	2.84459e12i	−0.0706153	+	0.122309i
$935$	−1.53793e13	−	2.31586e13i	−0.658087	−	0.990969i
$936$	−2.95035e13	+	1.70338e13i	−1.25641	+	0.725390i
$937$	4.64335e12	+	4.64335e12i	0.196790	+	0.196790i	0.798622	−	0.601832i	$-0.205562\pi$
$937$	4.64335e12	+	4.64335e12i	0.196790	+	0.196790i	−0.601832	+	0.798622i	$0.705562\pi$
$938$	−2.72748e12	+	3.32805e13i	−0.115040	+	1.40371i
$939$		−	2.09495e12i		−	0.0879386i
$940$	−8.99929e10	−	1.43539e12i	−0.00375952	−	0.0599646i
$941$	−2.44520e13	−	1.41174e13i	−1.01663	−	0.586949i	−0.103501	−	0.994629i	$-0.533005\pi$
$941$	−2.44520e13	−	1.41174e13i	−1.01663	−	0.586949i	−0.913125	+	0.407680i	$0.866338\pi$
$942$	1.97066e12	+	7.35461e12i	0.0815423	+	0.304320i
$943$	−1.26525e12	−	3.39023e11i	−0.0521044	−	0.0139613i
$944$	−2.49321e13			−1.02184
$945$	−1.30199e13	−	2.49464e11i	−0.531084	−	0.0101757i
$946$	−1.88554e13			−0.765467
$947$	−7.27166e12	−	1.94844e12i	−0.293805	−	0.0787247i	0.108906	−	0.994052i	$-0.465265\pi$
$947$	−7.27166e12	−	1.94844e12i	−0.293805	−	0.0787247i	−0.402711	+	0.915327i	$0.631932\pi$
$948$	−1.32669e11	−	4.95129e11i	−0.00533499	−	0.0199105i
$949$	−1.63506e13	−	9.44005e12i	−0.654390	−	0.377813i
$950$	1.21081e13	−	4.93508e12i	0.482304	−	0.196579i
$951$		−	3.10819e12i		−	0.123224i
$952$	−1.92840e13	−	1.33455e13i	−0.760906	−	0.526585i
$953$	−2.08350e13	−	2.08350e13i	−0.818231	−	0.818231i	0.167621	−	0.985852i	$-0.446392\pi$
$953$	−2.08350e13	−	2.08350e13i	−0.818231	−	0.818231i	−0.985852	+	0.167621i	$0.946392\pi$
$954$	−1.97348e12	+	1.13939e12i	−0.0771376	+	0.0445354i
$955$	3.53602e13	+	7.13789e12i	1.37562	+	0.277687i
$956$	−9.07529e10	+	1.57189e11i	−0.00351399	+	0.00608640i
$957$	3.27539e12	−	1.22239e13i	0.126229	−	0.471093i
$958$	1.40535e13	−	1.40535e13i	0.539064	−	0.539064i
$959$	7.65962e12	+	4.20862e13i	0.292431	+	1.60678i
$960$	−3.07077e12	+	6.18264e12i	−0.116688	+	0.234938i
$961$	−1.26966e13	−	2.19911e13i	−0.480209	−	0.831747i
$962$	4.32126e13	−	1.15788e13i	1.62676	−	0.435888i
$963$	3.21111e13	−	8.60415e12i	1.20320	−	0.322396i
$964$	8.53188e11	+	1.47776e12i	0.0318198	+	0.0551136i
$965$	1.45848e13	−	2.93647e13i	0.541410	−	1.09007i
$966$	−2.97647e12	−	1.06486e12i	−0.109978	−	0.0393456i
$967$	2.26860e13	−	2.26860e13i	0.834330	−	0.834330i	−0.153775	−	0.988106i	$-0.549143\pi$
$967$	2.26860e13	−	2.26860e13i	0.834330	−	0.834330i	0.988106	+	0.153775i	$0.0491432\pi$
$968$	3.95681e12	−	1.47670e13i	0.144846	−	0.540572i
$969$	−1.82992e12	+	3.16951e12i	−0.0666768	+	0.115488i
$970$	−4.45415e13	−	8.99125e12i	−1.61544	−	0.326097i
$971$	1.92722e13	−	1.11268e13i	0.695735	−	0.401683i	−0.110022	−	0.993929i	$-0.535092\pi$
$971$	1.92722e13	−	1.11268e13i	0.695735	−	0.401683i	0.805757	+	0.592247i	$0.201759\pi$
$972$	−6.72914e11	−	6.72914e11i	−0.0241803	−	0.0241803i
$973$	4.26622e13	+	3.49636e12i	1.52593	+	0.125057i
$974$			2.43079e13i			0.865432i
$975$	4.86457e12	−	1.15582e13i	0.172395	−	0.409610i
$976$	−3.01240e13	−	1.73921e13i	−1.06265	−	0.613520i
$977$	−7.25525e12	−	2.70769e13i	−0.254757	−	0.950767i	−0.968225	−	0.250079i	$-0.919543\pi$
$977$	−7.25525e12	−	2.70769e13i	−0.254757	−	0.950767i	0.713468	−	0.700688i	$-0.247123\pi$
$978$	−3.42099e12	−	9.16651e11i	−0.119571	−	0.0320390i
$979$	3.41043e13			1.18655
$980$	−1.30694e12	+	2.12080e11i	−0.0452626	+	0.00734485i
$981$	2.03915e13			0.702973
$982$	−2.27788e13	−	6.10357e12i	−0.781681	−	0.209451i
$983$	−2.28867e12	−	8.54142e12i	−0.0781793	−	0.291769i	0.915756	−	0.401735i	$-0.131593\pi$
$983$	−2.28867e12	−	8.54142e12i	−0.0781793	−	0.291769i	−0.993935	+	0.109966i	$0.964926\pi$
$984$	−8.94852e11	−	5.16643e11i	−0.0304280	−	0.0175676i
$985$	2.24452e12	+	3.58002e13i	0.0759732	+	1.21178i
$986$			4.05294e13i			1.36560i
$987$	−1.07505e13	−	8.81051e11i	−0.360580	−	0.0295511i
$988$	7.96021e11	+	7.96021e11i	0.0265778	+	0.0265778i
$989$	−6.43127e12	+	3.71310e12i	−0.213754	+	0.123411i
$990$	1.98144e13	+	2.98372e13i	0.655576	+	0.987187i
$991$	−3.83070e12	+	6.63496e12i	−0.126167	+	0.218528i	−0.922189	−	0.386741i	$-0.873601\pi$
$991$	−3.83070e12	+	6.63496e12i	−0.126167	+	0.218528i	0.796021	+	0.605268i	$0.206934\pi$
$992$	1.43920e11	−	5.37116e11i	0.00471865	−	0.0176103i
$993$	−9.15936e12	+	9.15936e12i	−0.298947	+	0.298947i
$994$	−5.14335e12	−	1.84008e12i	−0.167112	−	0.0597859i
$995$	−2.70030e12	−	8.02957e12i	−0.0873390	−	0.259710i
$996$	1.01630e11	+	1.76029e11i	0.00327232	+	0.00566782i
$997$	−4.40756e13	+	1.18100e13i	−1.41277	+	0.378550i	−0.882912	−	0.469539i	$-0.844420\pi$
$997$	−4.40756e13	+	1.18100e13i	−1.41277	+	0.378550i	−0.529855	+	0.848088i	$0.677754\pi$
$998$	−3.31130e13	+	8.87259e12i	−1.05660	+	0.283115i
$999$	−8.55478e12	−	1.48173e13i	−0.271747	−	0.470679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.10	✓	136
5.2	odd	4	inner	35.10.k.a.17.25	yes	136
7.5	odd	6	inner	35.10.k.a.33.25	yes	136
35.12	even	12	inner	35.10.k.a.12.10	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.10	✓	136	1.1	even	1	trivial
35.10.k.a.12.10	yes	136	35.12	even	12	inner
35.10.k.a.17.25	yes	136	5.2	odd	4	inner
35.10.k.a.33.25	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+(-22.3519 - 5.98917i) q^{2} +(-10.0261 - 37.4181i) q^{3} +(20.3322 + 11.7388i) q^{4} +(-924.440 + 1048.11i) q^{5} +896.413i q^{6} +(-6331.22 - 518.872i) q^{7} +(7993.56 + 7993.56i) q^{8} +(15746.4 - 9091.18i) q^{9} +(26940.3 - 17890.6i) q^{10} +(-30456.2 + 52751.6i) q^{11} +(235.390 - 878.486i) q^{12} +(-117199. + 117199. i) q^{13} +(138407. + 49516.6i) q^{14} +(48486.8 + 24082.3i) q^{15} +(-136807. - 236956. i) q^{16} +(315442. - 84522.3i) q^{17} +(-406410. + 108897. i) q^{18} +(-144650. - 250541. i) q^{19} +(-31099.4 + 10458.6i) q^{20} +(44062.6 + 242104. i) q^{21} +(996692. - 996692. i) q^{22} +(143682. - 536228. i) q^{23} +(218959. - 379248. i) q^{24} +(-243946. - 1.93783e6i) q^{25} +(3.32153e6 - 1.91769e6i) q^{26} +(-1.03721e6 - 1.03721e6i) q^{27} +(-122637. - 84870.7i) q^{28} -5.36320e6i q^{29} +(-939540. - 828680. i) q^{30} +(-885940. - 511497. i) q^{31} +(140685. + 525043. i) q^{32} +(2.27922e6 + 610716. i) q^{33} -7.55694e6 q^{34} +(6.39667e6 - 6.15616e6i) q^{35} +426878. q^{36} +(1.12669e7 + 3.01894e6i) q^{37} +(1.73267e6 + 6.46641e6i) q^{38} +(5.56039e6 + 3.21029e6i) q^{39} +(-1.57677e7 + 988567. i) q^{40} -2.35954e6i q^{41} +(465124. - 5.67539e6i) q^{42} +(-9.45901e6 - 9.45901e6i) q^{43} +(-1.23848e6 + 715037. i) q^{44} +(-5.02803e6 + 2.49082e7i) q^{45} +(-6.42312e6 + 1.11252e7i) q^{46} +(-1.13449e7 + 4.23397e7i) q^{47} +(-7.49480e6 + 7.49480e6i) q^{48} +(3.98152e7 + 6.57019e6i) q^{49} +(-6.15334e6 + 4.47752e7i) q^{50} +(-6.32533e6 - 1.09558e7i) q^{51} +(-3.75867e6 + 1.00713e6i) q^{52} +(5.23150e6 - 1.40178e6i) q^{53} +(1.69715e7 + 2.93955e7i) q^{54} +(-2.71346e7 - 8.06871e7i) q^{55} +(-4.64614e7 - 5.47566e7i) q^{56} +(-7.92449e6 + 7.92449e6i) q^{57} +(-3.21211e7 + 1.19878e8i) q^{58} +(4.55608e7 - 7.89137e7i) q^{59} +(703147. + 1.05882e6i) q^{60} +(1.10097e8 - 6.35646e7i) q^{61} +(1.67390e7 + 1.67390e7i) q^{62} +(-1.04411e8 + 4.93879e7i) q^{63} +1.27512e8i q^{64} +(-1.44940e7 - 2.31180e8i) q^{65} +(-4.72872e7 - 2.73013e7i) q^{66} +(5.87933e7 + 2.19419e8i) q^{67} +(7.40581e6 + 1.98438e6i) q^{68} -2.15052e7 q^{69} +(-1.79848e8 + 9.92910e7i) q^{70} -3.71610e7 q^{71} +(1.98541e8 + 5.31988e7i) q^{72} +(2.94824e7 + 1.10030e8i) q^{73} +(-2.33755e8 - 1.34958e8i) q^{74} +(-7.00640e7 + 2.85570e7i) q^{75} -6.79207e6i q^{76} +(2.20196e8 - 3.18179e8i) q^{77} +(-1.05058e8 - 1.05058e8i) q^{78} +(4.88106e8 - 2.81808e8i) q^{79} +(3.74826e8 + 7.56632e7i) q^{80} +(1.50531e8 - 2.60727e8i) q^{81} +(-1.41317e7 + 5.27402e7i) q^{82} +(-1.58033e8 + 1.58033e8i) q^{83} +(-1.94613e6 + 5.43975e6i) q^{84} +(-2.03018e8 + 4.08754e8i) q^{85} +(1.54775e8 + 2.68078e8i) q^{86} +(-2.00681e8 + 5.37722e7i) q^{87} +(-6.65126e8 + 1.78220e8i) q^{88} +(-2.79946e8 - 4.84880e8i) q^{89} +(2.61566e8 - 5.26632e8i) q^{90} +(8.02821e8 - 6.81199e8i) q^{91} +(9.21603e6 - 9.21603e6i) q^{92} +(-1.02567e7 + 3.82785e7i) q^{93} +(5.07159e8 - 8.78425e8i) q^{94} +(3.96316e8 + 8.00012e7i) q^{95} +(1.82356e7 - 1.05283e7i) q^{96} +(-9.93544e8 - 9.93544e8i) q^{97} +(-8.50594e8 - 3.85316e8i) q^{98} +1.10753e9i 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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