LMFDB - Embedded newform 35.10.k.a.33.25

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			33.25
Character	$\chi$	$=$	35.33
Dual form			35.10.k.a.17.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.98917 + 22.3519i) q^{2} +(-37.4181 - 10.0261i) q^{3} +(-20.3322 + 11.7388i) q^{4} +(-1369.91 - 276.533i) q^{5} -896.413i q^{6} +(518.872 + 6331.22i) q^{7} +(7993.56 + 7993.56i) q^{8} +(-15746.4 - 9091.18i) q^{9} +(-2023.59 - 32276.3i) q^{10} +(-30456.2 - 52751.6i) q^{11} +(878.486 - 235.390i) q^{12} +(117199. - 117199. i) q^{13} +(-138407. + 49516.6i) q^{14} +(48486.8 + 24082.3i) q^{15} +(-136807. + 236956. i) q^{16} +(84522.3 - 315442. i) q^{17} +(108897. - 406410. 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} +(-536228. + 143682. i) q^{23} +(-218959. - 379248. i) q^{24} +(1.80018e6 + 757652. i) q^{25} +(3.32153e6 + 1.91769e6i) q^{26} +(1.03721e6 + 1.03721e6i) q^{27} +(-84870.7 - 122637. i) q^{28} -5.36320e6i q^{29} +(-247888. + 1.22801e6i) q^{30} +(-885940. + 511497. i) q^{31} +(-525043. - 140685. i) q^{32} +(610716. + 2.27922e6i) q^{33} +7.55694e6 q^{34} +(1.03999e6 - 8.81669e6i) q^{35} +426878. q^{36} +(-3.01894e6 - 1.12669e7i) q^{37} +(6.46641e6 + 1.73267e6i) q^{38} +(-5.56039e6 + 3.21029e6i) q^{39} +(-8.73997e6 - 1.31609e7i) q^{40} +2.35954e6i q^{41} +(5.67539e6 - 465124. i) q^{42} +(-9.45901e6 - 9.45901e6i) q^{43} +(1.23848e6 + 715037. i) q^{44} +(1.90571e7 + 1.68085e7i) q^{45} +(-6.42312e6 - 1.11252e7i) q^{46} +(-4.23397e7 + 1.13449e7i) 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} +(-1.00713e6 + 3.75867e6i) q^{52} +(-1.40178e6 + 5.23150e6i) 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} +(1.19878e8 - 3.21211e7i) q^{58} +(-4.55608e7 - 7.89137e7i) q^{59} +(-1.26854e6 + 79532.0i) q^{60} +(1.10097e8 + 6.35646e7i) q^{61} +(-1.67390e7 - 1.67390e7i) q^{62} +(4.93879e7 - 1.04411e8i) q^{63} +1.27512e8i q^{64} +(-1.92961e8 + 1.28142e8i) q^{65} +(-4.72872e7 + 2.73013e7i) q^{66} +(-2.19419e8 - 5.87933e7i) q^{67} +(1.98438e6 + 7.40581e6i) q^{68} +2.15052e7 q^{69} +(2.03298e8 - 2.95590e7i) q^{70} -3.71610e7 q^{71} +(-5.31988e7 - 1.98541e8i) q^{72} +(1.10030e8 + 2.94824e7i) q^{73} +(2.33755e8 - 1.34958e8i) q^{74} +(-5.97631e7 - 4.63988e7i) q^{75} +6.79207e6i q^{76} +(3.18179e8 - 2.20196e8i) q^{77} +(-1.05058e8 - 1.05058e8i) q^{78} +(-4.88106e8 - 2.81808e8i) q^{79} +(2.52939e8 - 2.86777e8i) q^{80} +(1.50531e8 + 2.60727e8i) q^{81} +(-5.27402e7 + 1.41317e7i) 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} +(-5.37722e7 + 2.00681e8i) q^{87} +(1.78220e8 - 6.65126e8i) 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} +(3.82785e7 - 1.02567e7i) q^{93} +(-5.07159e8 - 8.78425e8i) q^{94} +(-2.67441e8 + 3.03219e8i) q^{95} +(1.82356e7 + 1.05283e7i) q^{96} +(9.93544e8 + 9.93544e8i) q^{97} +(-3.85316e8 - 8.50594e8i) 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 $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	5.98917	+	22.3519i	0.264687	+	0.987824i	0.962442	+	0.271488i	$0.0875156\pi$
$2$	5.98917	+	22.3519i	0.264687	+	0.987824i	−0.697755	+	0.716336i	$0.745818\pi$
$3$	−37.4181	−	10.0261i	−0.266708	−	0.0714641i	0.122987	−	0.992408i	$-0.460753\pi$
$3$	−37.4181	−	10.0261i	−0.266708	−	0.0714641i	−0.389695	+	0.920944i	$0.627419\pi$
$4$	−20.3322	+	11.7388i	−0.0397113	+	0.0229273i
$5$	−1369.91	−	276.533i	−0.980228	−	0.197871i
$5$	−1369.91	−	276.533i	−0.980228	−	0.197871i
$6$		−	896.413i		−	0.282376i
$7$	518.872	+	6331.22i	0.0816806	+	0.996659i
$7$	518.872	+	6331.22i	0.0816806	+	0.996659i
$8$	7993.56	+	7993.56i	0.689978	+	0.689978i
$9$	−15746.4	−	9091.18i	−0.799999	−	0.461880i
$10$	−2023.59	−	32276.3i	−0.0639914	−	1.02067i
$11$	−30456.2	−	52751.6i	−0.627203	−	1.08635i	−0.988110	−	0.153746i	$-0.950866\pi$
$11$	−30456.2	−	52751.6i	−0.627203	−	1.08635i	0.360908	−	0.932602i	$-0.382467\pi$
$12$	878.486	−	235.390i	0.0122298	−	0.00327696i
$13$	117199.	−	117199.i	1.13809	−	1.13809i	0.149299	−	0.988792i	$-0.452298\pi$
$13$	117199.	−	117199.i	1.13809	−	1.13809i	0.988792	−	0.149299i	$-0.0477018\pi$
$14$	−138407.	+	49516.6i	−0.962903	+	0.344488i
$15$	48486.8	+	24082.3i	0.247294	+	0.122825i
$16$	−136807.	+	236956.i	−0.521876	+	0.903916i
$17$	84522.3	−	315442.i	0.245443	−	0.916007i	−0.727717	−	0.685878i	$-0.759418\pi$
$17$	84522.3	−	315442.i	0.245443	−	0.916007i	0.973160	−	0.230129i	$-0.0739149\pi$
$18$	108897.	−	406410.i	0.244507	−	0.912512i
$19$	144650.	−	250541.i	0.254641	−	0.441051i	−0.710157	−	0.704043i	$-0.751376\pi$
$19$	144650.	−	250541.i	0.254641	−	0.441051i	0.964798	+	0.262993i	$0.0847095\pi$
$20$	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
$23$	−536228.	+	143682.i	−0.399553	+	0.107060i	−0.452999	−	0.891511i	$-0.649646\pi$
$23$	−536228.	+	143682.i	−0.399553	+	0.107060i	0.0534467	+	0.998571i	$0.482979\pi$
$24$	−218959.	−	379248.i	−0.134714	−	0.233331i
$25$	1.80018e6	+	757652.i	0.921694	+	0.387918i
$26$	3.32153e6	+	1.91769e6i	1.42547	+	0.822996i
$27$	1.03721e6	+	1.03721e6i	0.375602	+	0.375602i
$28$	−84870.7	−	122637.i	−0.0260944	−	0.0377059i
$29$		−	5.36320e6i		−	1.40810i	−0.710151	−	0.704049i	$-0.751373\pi$
$29$		−	5.36320e6i		−	1.40810i	0.710151	−	0.704049i	$-0.248627\pi$
$30$	−247888.	+	1.22801e6i	−0.0558740	+	0.276793i
$31$	−885940.	+	511497.i	−0.172297	+	0.0994754i	−0.583668	−	0.811992i	$-0.698383\pi$
$31$	−885940.	+	511497.i	−0.172297	+	0.0994754i	0.411372	+	0.911468i	$0.365050\pi$
$32$	−525043.	−	140685.i	−0.0885156	−	0.0237177i
$33$	610716.	+	2.27922e6i	0.0896450	+	0.334560i
$34$	7.55694e6			0.969819
$35$	1.03999e6	−	8.81669e6i	0.117144	−	0.993115i
$36$	426878.			0.0423587
$37$	−3.01894e6	−	1.12669e7i	−0.264818	−	0.988314i	−0.962362	−	0.271772i	$-0.912390\pi$
$37$	−3.01894e6	−	1.12669e7i	−0.264818	−	0.988314i	0.697544	−	0.716542i	$-0.254276\pi$
$38$	6.46641e6	+	1.73267e6i	0.503080	+	0.134800i
$39$	−5.56039e6	+	3.21029e6i	−0.384871	+	0.222205i
$40$	−8.73997e6	−	1.31609e7i	−0.539809	−	0.812862i
$41$			2.35954e6i			0.130407i	0.997872	+	0.0652034i	$0.0207696\pi$
$41$			2.35954e6i			0.130407i	−0.997872	+	0.0652034i	$0.979230\pi$
$42$	5.67539e6	−	465124.i	0.281432	−	0.0230646i
$43$	−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
$45$	1.90571e7	+	1.68085e7i	0.692789	+	0.611044i
$46$	−6.42312e6	−	1.11252e7i	−0.211512	−	0.366350i
$47$	−4.23397e7	+	1.13449e7i	−1.26563	+	0.339125i	−0.828355	−	0.560203i	$-0.810723\pi$
$47$	−4.23397e7	+	1.13449e7i	−1.26563	+	0.339125i	−0.437275	+	0.899328i	$0.644056\pi$
$48$	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
$52$	−1.00713e6	+	3.75867e6i	−0.0191017	+	0.0712885i
$53$	−1.40178e6	+	5.23150e6i	−0.0244026	+	0.0910719i	−0.977053	−	0.212995i	$-0.931678\pi$
$53$	−1.40178e6	+	5.23150e6i	−0.0244026	+	0.0910719i	0.952651	+	0.304067i	$0.0983448\pi$
$54$	−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
$58$	1.19878e8	−	3.21211e7i	1.39095	−	0.372705i
$59$	−4.55608e7	−	7.89137e7i	−0.489506	−	0.847849i	0.510421	−	0.859924i	$-0.329489\pi$
$59$	−4.55608e7	−	7.89137e7i	−0.489506	−	0.847849i	−0.999927	+	0.0120758i	$0.996156\pi$
$60$	−1.26854e6	+	79532.0i	−0.0126364	+	0.000792249i
$61$	1.10097e8	+	6.35646e7i	1.01810	+	0.587802i	0.913554	−	0.406718i	$-0.133327\pi$
$61$	1.10097e8	+	6.35646e7i	1.01810	+	0.587802i	0.104549	+	0.994520i	$0.466660\pi$
$62$	−1.67390e7	−	1.67390e7i	−0.143869	−	0.143869i
$63$	4.93879e7	−	1.04411e8i	0.394992	−	0.835053i
$64$			1.27512e8i			0.950036i
$65$	−1.92961e8	+	1.28142e8i	−1.34078	+	0.890394i
$66$	−4.72872e7	+	2.73013e7i	−0.306758	+	0.177107i
$67$	−2.19419e8	−	5.87933e7i	−1.33027	−	0.356444i	−0.477452	−	0.878658i	$-0.658439\pi$
$67$	−2.19419e8	−	5.87933e7i	−1.33027	−	0.356444i	−0.852814	+	0.522214i	$0.825106\pi$
$68$	1.98438e6	+	7.40581e6i	0.0112547	+	0.0420032i
$69$	2.15052e7			0.114215
$70$	2.03298e8	−	2.95590e7i	1.01203	−	0.147146i
$71$	−3.71610e7			−0.173550			−0.0867750	−	0.996228i	$-0.527656\pi$
$71$	−3.71610e7			−0.173550			−0.0867750	+	0.996228i	$0.527656\pi$
$72$	−5.31988e7	−	1.98541e8i	−0.233295	−	0.870669i
$73$	1.10030e8	+	2.94824e7i	0.453480	+	0.121510i	0.478327	−	0.878182i	$-0.341243\pi$
$73$	1.10030e8	+	2.94824e7i	0.453480	+	0.121510i	−0.0248473	+	0.999691i	$0.507910\pi$
$74$	2.33755e8	−	1.34958e8i	0.906186	−	0.523187i
$75$	−5.97631e7	−	4.63988e7i	−0.218101	−	0.169329i
$76$			6.79207e6i			0.0233529i
$77$	3.18179e8	−	2.20196e8i	1.03149	−	0.713841i
$78$	−1.05058e8	−	1.05058e8i	−0.321370	−	0.321370i
$79$	−4.88106e8	−	2.81808e8i	−1.40991	−	0.814014i	−0.414534	−	0.910034i	$-0.636056\pi$
$79$	−4.88106e8	−	2.81808e8i	−1.40991	−	0.814014i	−0.995379	+	0.0960196i	$0.969389\pi$
$80$	2.52939e8	−	2.86777e8i	0.690416	−	0.782779i
$81$	1.50531e8	+	2.60727e8i	0.388546	+	0.672981i
$82$	−5.27402e7	+	1.41317e7i	−0.128819	+	0.0345169i
$83$	1.58033e8	−	1.58033e8i	0.365507	−	0.365507i	−0.500329	−	0.865836i	$-0.666788\pi$
$83$	1.58033e8	−	1.58033e8i	0.365507	−	0.365507i	0.865836	+	0.500329i	$0.166788\pi$
$84$	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
$87$	−5.37722e7	+	2.00681e8i	−0.100629	+	0.375551i
$88$	1.78220e8	−	6.65126e8i	0.316800	−	1.18231i
$89$	2.79946e8	−	4.84880e8i	0.472954	−	0.819180i	−0.526567	−	0.850134i	$-0.676521\pi$
$89$	2.79946e8	−	4.84880e8i	0.472954	−	0.819180i	0.999521	+	0.0309536i	$0.00985441\pi$
$90$	−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
$93$	3.82785e7	−	1.02567e7i	0.0530618	−	0.0142179i
$94$	−5.07159e8	−	8.78425e8i	−0.669991	−	1.16046i
$95$	−2.67441e8	+	3.03219e8i	−0.336877	+	0.381944i
$96$	1.82356e7	+	1.05283e7i	0.0219128	+	0.0126514i
$97$	9.93544e8	+	9.93544e8i	1.13950	+	1.13950i	0.988540	+	0.150960i	$0.0482364\pi$
$97$	9.93544e8	+	9.93544e8i	1.13950	+	1.13950i	0.150960	+	0.988540i	$0.451764\pi$
$98$	−3.85316e8	−	8.50594e8i	−0.421988	−	0.931548i
$99$			1.10753e9i			1.15877i
$100$	−4.54956e7	+	5.72727e6i	−0.0454956	+	0.00572727i
$101$	−9.77608e7	+	5.64422e7i	−0.0934800	+	0.0539707i	−0.546011	−	0.837778i	$-0.683854\pi$
$101$	−9.77608e7	+	5.64422e7i	−0.0934800	+	0.0539707i	0.452531	+	0.891749i	$0.350521\pi$
$102$	−2.82766e8	−	7.57670e7i	−0.258658	−	0.0693073i
$103$	3.33685e8	+	1.24533e9i	0.292126	+	1.09023i	0.943473	+	0.331448i	$0.107537\pi$
$103$	3.33685e8	+	1.24533e9i	0.292126	+	1.09023i	−0.651348	+	0.758779i	$0.725796\pi$
$104$	1.87367e9			1.57052
$105$	−1.27312e8	+	3.19477e8i	−0.102215	+	0.256500i
$106$	−1.25329e8			−0.0964220
$107$	−4.73214e8	−	1.76606e9i	−0.349004	−	1.30250i	−0.887864	−	0.460106i	$-0.847811\pi$
$107$	−4.73214e8	−	1.76606e9i	−0.349004	−	1.30250i	0.538860	−	0.842396i	$-0.318855\pi$
$108$	−3.32642e7	−	8.91311e6i	−0.0235272	−	0.00630409i
$109$	−9.71246e8	+	5.60749e8i	−0.659038	+	0.380496i	−0.791910	−	0.610638i	$-0.790913\pi$
$109$	−9.71246e8	+	5.60749e8i	−0.659038	+	0.380496i	0.132873	+	0.991133i	$0.457580\pi$
$110$	−1.64100e9	+	1.08976e9i	−1.06866	+	0.709682i
$111$			4.51852e8i			0.282516i
$112$	−1.57121e9	−	7.43204e8i	−0.943523	−	0.446300i
$113$	−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
$115$	7.74317e8	−	4.85463e7i	0.412837	−	0.0258831i
$116$	6.29575e7	+	1.09046e8i	0.0322839	+	0.0559174i
$117$	−2.91093e9	+	7.79981e8i	−1.43613	+	0.384811i
$118$	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
$122$	−7.61399e8	+	2.84158e9i	−0.311167	+	1.16129i
$123$	2.36571e7	−	8.82895e7i	0.00931941	−	0.0347805i
$124$	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	$0.392080\pi$
$128$	−3.11895e9	+	8.35720e8i	−1.02698	+	0.275180i
$129$	2.59101e8	+	4.48775e8i	0.0823786	+	0.142684i
$130$	−4.01990e9	−	3.54557e9i	−1.23444	−	1.08878i
$131$	1.93710e9	+	1.11838e9i	0.574686	+	0.331795i	0.759019	−	0.651069i	$-0.225679\pi$
$131$	1.93710e9	+	1.11838e9i	0.574686	+	0.331795i	−0.184333	+	0.982864i	$0.559012\pi$
$132$	−3.91725e7	−	3.91725e7i	−0.0112305	−	0.0112305i
$133$	1.66129e9	+	7.85814e8i	0.460376	+	0.217765i
$134$		−	5.25656e9i		−	1.40841i
$135$	−1.13406e9	−	1.70770e9i	−0.293855	−	0.442496i
$136$	3.19714e9	−	1.84587e9i	0.801375	−	0.462674i
$137$	6.50457e9	+	1.74290e9i	1.57753	+	0.422697i	0.938159	−	0.346206i	$-0.112530\pi$
$137$	6.50457e9	+	1.74290e9i	1.57753	+	0.422697i	0.639366	+	0.768902i	$0.279197\pi$
$138$	1.28798e8	+	4.80682e8i	0.0302311	+	0.112824i
$139$	6.73839e9			1.53105			0.765525	−	0.643406i	$-0.222479\pi$
$139$	6.73839e9			1.53105			0.765525	+	0.643406i	$0.222479\pi$
$140$	8.23521e7	+	1.91471e8i	0.0181175	+	0.0421237i
$141$	1.69801e9			0.361789
$142$	−2.22563e8	−	8.30618e8i	−0.0459363	−	0.171437i
$143$	−9.75183e9	−	2.61299e9i	−1.95018	−	0.522548i
$144$	4.30842e9	−	2.48747e9i	0.835001	−	0.482088i
$145$	−1.48310e9	+	7.34710e9i	−0.278622	+	1.38026i
$146$			2.63595e9i			0.480120i
$147$	1.55568e9	+	1.53349e8i	0.274784	+	0.0270864i
$148$	1.93641e8	+	1.93641e8i	0.0331757	+	0.0331757i
$149$	−4.23370e9	−	2.44433e9i	−0.703691	−	0.406276i	0.105030	−	0.994469i	$-0.466506\pi$
$149$	−4.23370e9	−	2.44433e9i	−0.703691	−	0.406276i	−0.808721	+	0.588193i	$0.799840\pi$
$150$	6.79169e8	−	1.61371e9i	0.109539	−	0.260264i
$151$	4.36771e9	+	7.56509e9i	0.683687	+	1.18418i	0.973847	+	0.227203i	$0.0729580\pi$
$151$	4.36771e9	+	7.56509e9i	0.683687	+	1.18418i	−0.290160	+	0.956978i	$0.593709\pi$
$152$	3.15899e9	−	8.46448e8i	0.480012	−	0.128619i
$153$	−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
$157$	2.19839e9	−	8.20449e9i	0.288772	−	1.07771i	−0.657266	−	0.753658i	$-0.728287\pi$
$157$	2.19839e9	−	8.20449e9i	0.288772	−	1.07771i	0.946038	−	0.324054i	$-0.105046\pi$
$158$	3.37560e9	−	1.25979e10i	0.430917	−	1.60820i
$159$	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
$163$	3.81630e9	−	1.02258e9i	0.423447	−	0.113462i	−0.0408016	−	0.999167i	$-0.512991\pi$
$163$	3.81630e9	−	1.02258e9i	0.423447	−	0.113462i	0.464248	+	0.885705i	$0.346324\pi$
$164$	−2.76982e7	−	4.79746e7i	−0.00298988	−	0.00517862i
$165$	−2.06345e8	−	3.29121e9i	−0.0216729	−	0.345683i
$166$	4.47881e9	+	2.58584e9i	0.457801	+	0.264312i
$167$	−1.02529e10	−	1.02529e10i	−1.02005	−	1.02005i	−0.999795	−	0.0202573i	$-0.993551\pi$
$167$	−1.02529e10	−	1.02529e10i	−1.02005	−	1.02005i	−0.0202573	−	0.999795i	$-0.506449\pi$
$168$	2.28749e9	−	1.58306e9i	0.221548	−	0.153322i
$169$		−	1.68665e10i		−	1.59050i
$170$	−1.03523e10	−	2.08975e9i	−0.950644	−	0.191899i
$171$	−4.55544e9	+	2.63008e9i	−0.407425	+	0.235227i
$172$	3.03360e8	+	8.12850e7i	0.0264289	+	0.00708161i
$173$	−1.06214e9	−	3.96395e9i	−0.0901515	−	0.336450i	0.906088	−	0.423089i	$-0.139054\pi$
$173$	−1.06214e9	−	3.96395e9i	−0.0901515	−	0.336450i	−0.996240	+	0.0866387i	$0.972387\pi$
$174$	−4.80764e9			−0.397613
$175$	−3.86280e9	+	1.17905e10i	−0.311337	+	0.950300i
$176$	1.66664e10			1.30929
$177$	9.13599e8	+	3.40960e9i	0.0699642	+	0.261110i
$178$	1.25146e10	+	3.35329e9i	0.934390	+	0.250369i
$179$	5.18020e9	−	2.99079e9i	0.377145	−	0.217744i	−0.299431	−	0.954118i	$-0.596797\pi$
$179$	5.18020e9	−	2.99079e9i	0.377145	−	0.217744i	0.676575	+	0.736374i	$0.263463\pi$
$180$	−5.84785e8	−	1.18046e8i	−0.0415212	−	0.00838156i
$181$		−	1.10387e10i		−	0.764478i	−0.924064	−	0.382239i	$-0.875153\pi$
$181$		−	1.10387e10i		−	0.764478i	0.924064	−	0.382239i	$-0.124847\pi$
$182$	−1.04179e10	+	2.20244e10i	−0.703813	+	1.48793i
$183$	−3.48232e9	−	3.48232e9i	−0.229529	−	0.229529i
$184$	−5.43489e9	−	3.13784e9i	−0.349551	−	0.201814i
$185$	1.02002e9	+	1.62694e10i	0.0640232	+	1.02117i
$186$	4.58513e8	+	7.94168e8i	0.0280895	+	0.0486524i
$187$	−1.92143e10	+	5.14845e9i	−1.14904	+	0.307886i
$188$	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	0.266189	+	0.963921i	$0.414235\pi$
$191$	−1.29060e10	+	2.23539e10i	−0.701685	+	1.21535i	−0.967874	+	0.251434i	$0.919098\pi$
$192$	1.27845e9	−	4.77124e9i	0.0678935	−	0.253382i
$193$	6.07206e9	−	2.26612e10i	0.315013	−	1.17564i	−0.608965	−	0.793197i	$-0.708415\pi$
$193$	6.07206e9	−	2.26612e10i	0.315013	−	1.17564i	0.923978	−	0.382446i	$-0.124918\pi$
$194$	−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	$0.0423417\pi$
$198$	−2.47554e10	+	6.63319e9i	−1.14466	+	0.306711i
$199$	3.03084e9	+	5.24957e9i	0.137001	+	0.237293i	0.926360	−	0.376639i	$-0.122920\pi$
$199$	3.03084e9	+	5.24957e9i	0.137001	+	0.237293i	−0.789359	+	0.613932i	$0.789587\pi$
$200$	8.33354e9	+	2.04462e10i	0.368294	+	0.903603i
$201$	7.62078e9	+	4.39986e9i	0.329319	+	0.190133i
$202$	−1.84710e9	−	1.84710e9i	−0.0780564	−	0.0780564i
$203$	3.39556e10	−	2.78281e9i	1.40339	−	0.115014i
$204$		−	2.97007e8i		−	0.0120069i
$205$	6.52492e8	−	3.23236e9i	0.0258037	−	0.127828i
$206$	−2.58370e10	+	1.49170e10i	−0.999631	+	0.577137i
$207$	9.74989e9	+	2.61247e9i	0.369091	+	0.0988975i
$208$	1.17374e10	+	4.38044e10i	0.434796	+	1.62268i
$209$	−1.76220e10			−0.638845
$210$	−7.90340e9	−	9.32257e8i	−0.280432	−	0.0330787i
$211$	−8.88326e9			−0.308533			−0.154266	−	0.988029i	$-0.549301\pi$
$211$	−8.88326e9			−0.308533			−0.154266	+	0.988029i	$0.549301\pi$
$212$	−3.29103e7	−	1.22823e8i	−0.00111897	−	0.00417607i
$213$	1.39049e9	+	3.72581e8i	0.0462871	+	0.0124026i
$214$	3.66406e10	−	2.11545e10i	1.19427	−	0.689509i
$215$	1.03423e10	+	1.55737e10i	0.330098	+	0.497072i
$216$			1.65819e10i			0.518314i
$217$	−3.69809e9	−	5.34368e9i	−0.113216	−	0.163596i
$218$	−1.83508e10	−	1.83508e10i	−0.550301	−	0.550301i
$219$	−3.82151e9	−	2.20635e9i	−0.112263	−	0.0648151i
$220$	−1.49888e9	−	1.32202e9i	−0.0431383	−	0.0380483i
$221$	−2.70634e10	−	4.68752e10i	−0.763163	−	1.32184i
$222$	−1.00998e10	+	2.70622e9i	−0.279076	+	0.0747782i
$223$	3.62273e10	−	3.62273e10i	0.980988	−	0.980988i	−0.0188344	−	0.999823i	$-0.505996\pi$
$223$	3.62273e10	−	3.62273e10i	0.980988	−	0.980988i	0.999823	+	0.0188344i	$0.00599554\pi$
$224$	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
$227$	−3.89988e8	+	1.45545e9i	−0.00974843	+	0.0363816i	−0.970629	−	0.240582i	$-0.922662\pi$
$227$	−3.89988e8	+	1.45545e9i	−0.00974843	+	0.0363816i	0.960880	+	0.276964i	$0.0893283\pi$
$228$	6.80983e7	−	2.54146e8i	0.00166890	−	0.00622841i
$229$	−2.65942e10	+	4.60625e10i	−0.639038	+	1.10685i	0.346606	+	0.938011i	$0.387334\pi$
$229$	−2.65942e10	+	4.60625e10i	−0.639038	+	1.10685i	−0.985644	+	0.168836i	$0.945999\pi$
$230$	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
$233$	−1.47162e10	+	3.94319e9i	−0.327110	+	0.0876488i	−0.418637	−	0.908154i	$-0.637492\pi$
$233$	−1.47162e10	+	3.94319e9i	−0.327110	+	0.0876488i	0.0915269	+	0.995803i	$0.470825\pi$
$234$	−3.48681e10	−	6.03933e10i	−0.760251	−	1.31679i
$235$	6.11388e10	−	3.83314e9i	1.30771	−	0.0819878i
$236$	1.85270e9	+	1.06966e9i	0.0388778	+	0.0224461i
$237$	1.54385e10	+	1.54385e10i	0.317862	+	0.317862i
$238$	3.92108e9	+	4.78447e10i	0.0792154	+	0.966579i
$239$			7.73103e9i			0.153266i	0.997059	+	0.0766331i	$0.0244170\pi$
$239$			7.73103e9i			0.153266i	−0.997059	+	0.0766331i	$0.975583\pi$
$240$	−1.23398e10	+	8.19464e9i	−0.240080	+	0.159433i
$241$	6.29437e10	−	3.63405e10i	1.20192	−	0.693928i	0.240938	−	0.970541i	$-0.422545\pi$
$241$	6.29437e10	−	3.63405e10i	1.20192	−	0.693928i	0.960982	+	0.276612i	$0.0892118\pi$
$242$	−3.02279e10	−	8.09954e9i	−0.566551	−	0.151807i
$243$	−1.04910e10	−	3.91530e10i	−0.193014	−	0.720338i
$244$	−2.98469e9			−0.0539069
$245$	5.63601e10	+	2.00965e9i	0.999365	+	0.0356347i
$246$	2.11512e9			0.0368238
$247$	−1.24103e10	−	4.63159e10i	−0.212151	−	0.791760i
$248$	−1.11705e10	−	2.99313e9i	−0.187517	−	0.0502449i
$249$	−7.49773e9	+	4.32882e9i	−0.123604	+	0.0713629i
$250$	2.08114e10	−	5.96364e10i	0.336954	−	0.965565i
$251$		−	1.45028e9i		−	0.0230632i	−0.999934	−	0.0115316i	$-0.996329\pi$
$251$		−	1.45028e9i		−	0.0230632i	0.999934	−	0.0115316i	$-0.00367071\pi$
$252$	2.21495e8	+	2.70266e9i	0.00345988	+	0.0422171i
$253$	2.39109e10	+	2.39109e10i	0.366905	+	0.366905i
$254$	−5.07239e10	−	2.92855e10i	−0.764647	−	0.441469i
$255$	1.16948e10	−	1.32593e10i	0.173205	−	0.196376i
$256$	−4.71687e9	−	8.16987e9i	−0.0686396	−	0.118887i
$257$	5.94443e10	−	1.59280e10i	0.849984	−	0.227753i	0.192571	−	0.981283i	$-0.438317\pi$
$257$	5.94443e10	−	1.59280e10i	0.849984	−	0.227753i	0.657413	+	0.753530i	$0.271651\pi$
$258$	−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
$262$	−1.33964e10	+	4.99960e10i	−0.175643	+	0.655510i
$263$	−3.92481e10	+	1.46476e11i	−0.505846	+	1.88784i	−0.0479214	+	0.998851i	$0.515260\pi$
$263$	−3.92481e10	+	1.46476e11i	−0.505846	+	1.88784i	−0.457924	+	0.888991i	$0.651407\pi$
$264$	−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
$268$	5.15144e9	−	1.38032e9i	0.0609989	−	0.0163446i
$269$	2.63703e10	+	4.56746e10i	0.307064	+	0.531851i	0.977719	−	0.209919i	$-0.0673200\pi$
$269$	2.63703e10	+	4.56746e10i	0.307064	+	0.531851i	−0.670655	+	0.741770i	$0.733987\pi$
$270$	3.13783e10	−	3.55760e10i	0.359329	−	0.407400i
$271$	−1.01529e11	−	5.86178e10i	−1.14348	−	0.660188i	−0.196189	−	0.980566i	$-0.562857\pi$
$271$	−1.01529e11	−	5.86178e10i	−1.14348	−	0.660188i	−0.947290	+	0.320378i	$0.896190\pi$
$272$	6.31826e10	+	6.31826e10i	0.699902	+	0.699902i
$273$	−2.32102e10	−	3.35383e10i	−0.252899	−	0.365435i
$274$			1.55828e11i			1.67020i
$275$	−1.48593e10	−	1.18038e11i	−0.156676	−	1.24458i
$276$	−4.37247e8	+	2.52445e8i	−0.00453561	+	0.00261864i
$277$	5.77036e10	+	1.54616e10i	0.588903	+	0.157796i	0.540952	−	0.841054i	$-0.318064\pi$
$277$	5.77036e10	+	1.54616e10i	0.588903	+	0.157796i	0.0479513	+	0.998850i	$0.484731\pi$
$278$	4.03574e10	+	1.50616e11i	0.405248	+	1.51241i
$279$	1.86005e10			0.183783
$280$	7.87899e10	−	6.21636e10i	0.766054	−	0.604400i
$281$	−1.49997e11			−1.43517			−0.717587	−	0.696469i	$-0.754753\pi$
$281$	−1.49997e11			−1.43517			−0.717587	+	0.696469i	$0.754753\pi$
$282$	1.01697e10	+	3.79538e10i	0.0957606	+	0.357384i
$283$	−5.76663e10	−	1.54516e10i	−0.534420	−	0.143197i	−0.0184916	−	0.999829i	$-0.505886\pi$
$283$	−5.76663e10	−	1.54516e10i	−0.534420	−	0.143197i	−0.515929	+	0.856632i	$0.672553\pi$
$284$	7.55563e8	−	4.36225e8i	0.00689189	−	0.00397904i
$285$	1.30472e10	−	8.66446e9i	0.117143	−	0.0777928i
$286$		−	2.33622e11i		−	2.06474i
$287$	−1.49388e10	+	1.22430e9i	−0.129971	+	0.0106517i
$288$	6.98854e9	+	6.98854e9i	0.0598577	+	0.0598577i
$289$	1.03407e10	+	5.97020e9i	0.0871985	+	0.0503441i
$290$	−1.73104e11	+	1.08529e10i	−1.43720	+	0.0901062i
$291$	−2.72151e10	−	4.71379e10i	−0.222480	−	0.385347i
$292$	−2.58324e9	+	6.92176e8i	−0.0207942	+	0.00557178i
$293$	−1.48691e11	+	1.48691e11i	−1.17864	+	1.17864i	−0.198550	+	0.980091i	$0.563623\pi$
$293$	−1.48691e11	+	1.48691e11i	−1.17864	+	1.17864i	−0.980091	+	0.198550i	$0.936377\pi$
$294$	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
$297$	2.31250e10	−	8.63036e10i	0.172456	−	0.643613i
$298$	2.92790e10	−	1.09271e11i	0.215072	−	0.802659i
$299$	−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
$303$	4.22392e9	−	1.13180e9i	0.0287888	−	0.00771394i
$304$	3.95782e10	+	6.85515e10i	0.265782	+	0.460347i
$305$	−1.33245e11	−	1.17523e11i	−0.881664	−	0.777633i
$306$	−1.18995e11	−	6.87015e10i	−0.775855	−	0.447940i
$307$	1.20986e11	+	1.20986e11i	0.777346	+	0.777346i	0.979379	−	0.202033i	$-0.0647548\pi$
$307$	1.20986e11	+	1.20986e11i	0.777346	+	0.777346i	−0.202033	+	0.979379i	$0.564755\pi$
$308$	−3.88445e9	+	8.21211e9i	−0.0245952	+	0.0519968i
$309$		−	4.99435e10i		−	0.311649i
$310$	1.83020e10	+	2.75598e10i	0.112557	+	0.169492i
$311$	3.49223e10	−	2.01624e10i	0.211681	−	0.122214i	−0.390412	−	0.920640i	$-0.627667\pi$
$311$	3.49223e10	−	2.01624e10i	0.211681	−	0.122214i	0.602092	+	0.798427i	$0.294334\pi$
$312$	−7.01090e10	−	1.87856e10i	−0.418869	−	0.112236i
$313$	1.39969e10	+	5.22373e10i	0.0824297	+	0.307632i	0.994815	−	0.101700i	$-0.0324283\pi$
$313$	1.39969e10	+	5.22373e10i	0.0824297	+	0.307632i	−0.912385	+	0.409332i	$0.865762\pi$
$314$	1.96552e11			1.14102
$315$	−9.65302e10	+	1.29376e11i	−0.552415	+	0.740385i
$316$	1.32324e10			0.0746527
$317$	−2.07666e10	−	7.75021e10i	−0.115505	−	0.431069i	0.883820	−	0.467828i	$-0.154963\pi$
$317$	−2.07666e10	−	7.75021e10i	−0.115505	−	0.431069i	−0.999324	+	0.0367590i	$0.988297\pi$
$318$	4.68958e9	+	1.25657e9i	0.0257165	+	0.00689072i
$319$	−2.82917e11	+	1.63342e11i	−1.52968	+	0.883163i
$320$	3.52612e10	−	1.74680e11i	0.187985	−	0.931252i
$321$			7.08270e10i			0.372329i
$322$	6.71032e10	−	4.64387e10i	0.347850	−	0.240729i
$323$	−6.68050e10	−	6.68050e10i	−0.341506	−	0.341506i
$324$	−6.12123e9	−	3.53410e9i	−0.0308593	−	0.0178166i
$325$	2.99775e11	−	1.22183e11i	1.49046	−	0.607486i
$326$	4.57130e10	+	7.91773e10i	0.224161	+	0.388259i
$327$	4.19643e10	−	1.12443e10i	0.202962	−	0.0543836i
$328$	−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	0.174370	+	0.984680i	$0.444211\pi$
$331$	−1.67191e11	+	2.89583e11i	−0.765573	+	1.32601i	−0.939943	+	0.341331i	$0.889122\pi$
$332$	−1.35804e9	+	5.06826e9i	−0.00613465	+	0.0228948i
$333$	−5.48916e10	+	2.04858e11i	−0.244628	+	0.912965i
$334$	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	$0.100946\pi$
$338$	3.76998e11	−	1.01016e11i	1.57114	−	0.420985i
$339$	3.19077e10	+	5.52657e10i	0.131219	+	0.227278i
$340$	−6.70471e8	−	1.06940e10i	−0.00272098	−	0.0433997i
$341$	5.39646e10	+	3.11565e10i	0.216130	+	0.124783i
$342$	−8.60706e10	−	8.60706e10i	−0.340202	−	0.340202i
$343$	−6.22563e10	−	2.48669e11i	−0.242862	−	0.970061i
$344$		−	1.51222e11i		−	0.582241i
$345$	−2.94602e10	−	5.94690e9i	−0.111956	−	0.0225998i
$346$	8.22404e10	−	4.74815e10i	0.308491	−	0.178108i
$347$	2.64064e11	+	7.07556e10i	0.977746	+	0.261986i	0.712095	−	0.702083i	$-0.247747\pi$
$347$	2.64064e11	+	7.07556e10i	0.977746	+	0.261986i	0.265651	+	0.964069i	$0.414413\pi$
$348$	−1.26244e9	−	4.71149e9i	−0.00461429	−	0.0172208i
$349$	−2.89272e11			−1.04374			−0.521870	−	0.853025i	$-0.674765\pi$
$349$	−2.89272e11			−1.04374			−0.521870	+	0.853025i	$0.674765\pi$
$350$	−2.86675e11	−	1.57256e10i	−1.02114	−	0.0560144i
$351$	2.43118e11			0.854939
$352$	8.56944e9	+	3.19816e10i	0.0297516	+	0.111034i
$353$	−1.83618e11	−	4.92003e10i	−0.629404	−	0.168648i	−0.0700045	−	0.997547i	$-0.522301\pi$
$353$	−1.83618e11	−	4.92003e10i	−0.629404	−	0.168648i	−0.559399	+	0.828899i	$0.688968\pi$
$354$	−7.07393e10	+	4.08413e10i	−0.239412	+	0.138225i
$355$	5.09072e10	+	1.02762e10i	0.170118	+	0.0343405i
$356$			1.31449e10i			0.0433743i
$357$	−7.26456e10	−	3.43624e10i	−0.236702	−	0.111964i
$358$	9.78749e10	+	9.78749e10i	0.314918	+	0.314918i
$359$	3.11120e11	+	1.79625e11i	0.988561	+	0.570746i	0.904844	−	0.425744i	$-0.139987\pi$
$359$	3.11120e11	+	1.79625e11i	0.988561	+	0.570746i	0.0837171	+	0.996490i	$0.473321\pi$
$360$	1.79745e10	+	2.86694e11i	0.0564021	+	0.899616i
$361$	1.19497e11	+	2.06974e11i	0.370316	+	0.641407i
$362$	2.46736e11	−	6.61128e10i	0.755169	−	0.202347i
$363$	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
$367$	−9.47449e10	+	3.53593e11i	−0.272621	+	1.01743i	0.684798	+	0.728732i	$0.259890\pi$
$367$	−9.47449e10	+	3.53593e11i	−0.272621	+	1.01743i	−0.957419	+	0.288702i	$0.906776\pi$
$368$	3.93132e10	−	1.46719e11i	0.111744	−	0.417034i
$369$	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
$373$	5.79951e11	−	1.55398e11i	1.55132	−	0.415675i	0.621418	−	0.783479i	$-0.286557\pi$
$373$	5.79951e11	−	1.55398e11i	1.55132	−	0.415675i	0.929904	+	0.367804i	$0.119890\pi$
$374$	−2.30155e11	−	3.98641e11i	−0.608274	−	1.05356i
$375$	6.90393e10	+	8.00886e10i	0.180283	+	0.209137i
$376$	−4.29130e11	−	2.47759e11i	−1.10725	−	0.639269i
$377$	−6.28559e11	−	6.28559e11i	−1.60254	−	1.60254i
$378$	−1.94916e11	−	9.21979e10i	−0.491059	−	0.232278i
$379$			2.29583e11i			0.571562i	0.958295	+	0.285781i	$0.0922530\pi$
$379$			2.29583e11i			0.571562i	−0.958295	+	0.285781i	$0.907747\pi$
$380$	1.87823e9	−	9.30453e9i	0.00462087	−	0.0228912i
$381$	8.49141e10	−	4.90252e10i	0.206451	−	0.119195i
$382$	−5.76948e11	−	1.54593e11i	−1.38628	−	0.371453i
$383$	−1.21843e11	−	4.54725e11i	−0.289339	−	1.07983i	−0.945610	−	0.325303i	$-0.894534\pi$
$383$	−1.21843e11	−	4.54725e11i	−0.289339	−	1.07983i	0.656271	−	0.754525i	$-0.272133\pi$
$384$	1.25084e11			0.293570
$385$	−4.96769e11	+	2.13662e11i	−1.15234	+	0.495625i
$386$	5.42888e11			1.24471
$387$	6.29517e10	+	2.34939e11i	0.142662	+	0.532421i
$388$	−3.18639e10	−	8.53791e9i	−0.0713767	−	0.0191253i
$389$	1.41271e10	−	8.15630e9i	0.0312810	−	0.0180601i	−0.484278	−	0.874914i	$-0.660918\pi$
$389$	1.41271e10	−	8.15630e9i	0.0312810	−	0.0180601i	0.515559	+	0.856854i	$0.327584\pi$
$390$	1.14868e11	+	1.72973e11i	0.251426	+	0.378605i
$391$			1.81293e11i			0.392270i
$392$	−3.70784e11	−	2.65746e11i	−0.793110	−	0.568432i
$393$	−6.12694e10	−	6.12694e10i	−0.129562	−	0.129562i
$394$	5.14367e11	+	2.96970e11i	1.07533	+	0.620840i
$395$	5.90733e11	+	5.21030e11i	1.22097	+	1.07690i
$396$	−1.30011e10	−	2.25185e10i	−0.0265675	−	0.0460162i
$397$	6.08423e11	−	1.63027e11i	1.22927	−	0.329383i	0.414977	−	0.909832i	$-0.363790\pi$
$397$	6.08423e11	−	1.63027e11i	1.22927	−	0.329383i	0.814297	+	0.580449i	$0.197123\pi$
$398$	−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	0.195175	+	0.980768i	$0.437473\pi$
$401$	−3.89262e11	+	6.74222e11i	−0.751783	+	1.30213i	−0.946958	+	0.321358i	$0.895861\pi$
$402$	−5.27031e10	+	1.96690e11i	−0.100651	+	0.375635i
$403$	−4.38841e10	+	1.63778e11i	−0.0828770	+	0.309301i
$404$	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
$408$	−1.38138e11	+	3.70139e10i	−0.246798	+	0.0661292i
$409$	−3.23504e11	−	5.60325e11i	−0.571643	−	0.990114i	−0.996398	−	0.0848056i	$-0.972973\pi$
$409$	−3.23504e11	−	5.60325e11i	−0.571643	−	0.990114i	0.424755	−	0.905308i	$-0.360360\pi$
$410$	7.61573e10	−	4.77474e9i	0.133102	−	0.00834492i
$411$	−2.25914e11	−	1.30432e11i	−0.390531	−	0.225473i
$412$	−2.14032e10	−	2.14032e10i	−0.0365967	−	0.0365967i
$413$	4.75980e11	−	3.29402e11i	0.805032	−	0.557123i
$414$			2.33575e11i			0.390773i
$415$	−2.60192e11	+	1.72789e11i	−0.430603	+	0.285957i
$416$	−7.80223e10	+	4.50462e10i	−0.127732	+	0.0737459i
$417$	−2.52137e11	−	6.75600e10i	−0.408343	−	0.109415i
$418$	−1.05541e11	−	3.93884e11i	−0.169094	−	0.631067i
$419$	−4.97851e11			−0.789107			−0.394554	−	0.918873i	$-0.629101\pi$
$419$	−4.97851e11			−0.789107			−0.394554	+	0.918873i	$0.629101\pi$
$420$	−1.16174e9	−	7.99014e9i	−0.00182175	−	0.0125295i
$421$	3.31117e11			0.513703			0.256851	−	0.966451i	$-0.417315\pi$
$421$	3.31117e11			0.513703			0.256851	+	0.966451i	$0.417315\pi$
$422$	−5.32034e10	−	1.98558e11i	−0.0816645	−	0.304776i
$423$	7.69835e11	+	2.06277e11i	1.16914	+	0.313270i
$424$	−5.30234e10	+	3.06131e10i	−0.0796749	+	0.0460003i
$425$	3.91151e11	−	5.03814e11i	0.581559	−	0.749067i
$426$			3.33116e10i			0.0490063i
$427$	−3.45315e11	+	7.30031e11i	−0.502679	+	1.06271i
$428$	3.03529e10	+	3.03529e10i	0.0437223	+	0.0437223i
$429$	3.38696e11	+	1.95546e11i	0.482784	+	0.278735i
$430$	−2.86161e11	+	3.24443e11i	−0.403647	+	0.457647i
$431$	3.23601e11	+	5.60493e11i	0.451713	+	0.782389i	0.998493	−	0.0548873i	$-0.0174799\pi$
$431$	3.23601e11	+	5.60493e11i	0.451713	+	0.782389i	−0.546780	+	0.837276i	$0.684147\pi$
$432$	−3.87669e11	+	1.03876e11i	−0.535530	+	0.143495i
$433$	4.79907e8	−	4.79907e8i	0.000656087	−	0.000656087i	−0.706779	−	0.707435i	$-0.749852\pi$
$433$	4.79907e8	−	4.79907e8i	0.000656087	−	0.000656087i	0.707435	+	0.706779i	$0.249852\pi$
$434$	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
$437$	−4.15672e10	+	1.55131e11i	−0.0545235	+	0.203485i
$438$	2.64284e10	−	9.86323e10i	0.0343114	−	0.128052i
$439$	1.35469e11	−	2.34639e11i	0.174080	−	0.301516i	−0.765762	−	0.643124i	$-0.777638\pi$
$439$	1.35469e11	−	2.34639e11i	0.174080	−	0.301516i	0.939843	+	0.341608i	$0.110971\pi$
$440$	−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
$443$	6.35120e11	−	1.70180e11i	0.783500	−	0.209938i	0.155173	−	0.987887i	$-0.450407\pi$
$443$	6.35120e11	−	1.70180e11i	0.783500	−	0.209938i	0.628327	+	0.777949i	$0.283740\pi$
$444$	−5.30420e9	−	9.18715e9i	−0.00647734	−	0.0112191i
$445$	−5.17586e11	+	5.86828e11i	−0.625695	+	0.709399i
$446$	1.02672e12	+	5.92777e11i	1.22870	+	0.709389i
$447$	1.33910e11	+	1.33910e11i	0.158646	+	0.158646i
$448$	−8.07305e11	+	6.61623e10i	−0.946862	+	0.0775996i
$449$		−	1.05911e12i		−	1.22980i	−0.788606	−	0.614898i	$-0.789197\pi$
$449$		−	1.05911e12i		−	1.22980i	0.788606	−	0.614898i	$-0.210803\pi$
$450$	5.03953e11	−	6.49107e11i	0.579340	−	0.746208i
$451$	1.24470e11	−	7.18626e10i	0.141667	−	0.0817916i
$452$	3.73581e10	+	1.00101e10i	0.0420980	+	0.0112801i
$453$	−8.75825e10	−	3.26862e11i	−0.0977182	−	0.364689i
$454$	−3.48679e10			−0.0385189
$455$	−9.11419e11	−	1.15519e12i	−0.996934	−	1.26358i
$456$	−1.26690e11			−0.137214
$457$	4.14739e10	+	1.54783e11i	0.0444786	+	0.165997i	0.984593	−	0.174864i	$-0.0559484\pi$
$457$	4.14739e10	+	1.54783e11i	0.0444786	+	0.165997i	−0.940114	+	0.340860i	$0.889282\pi$
$458$	−1.18886e12	−	3.18554e11i	−1.26251	−	0.338290i
$459$	4.14845e11	−	2.39511e11i	0.436243	−	0.251865i
$460$	−1.51737e10	+	1.00766e10i	−0.0158008	+	0.0104931i
$461$		−	1.81186e12i		−	1.86840i	−0.356750	−	0.934200i	$-0.616115\pi$
$461$		−	1.81186e12i		−	1.86840i	0.356750	−	0.934200i	$-0.383885\pi$
$462$	−1.97387e11	−	2.85220e11i	−0.201571	−	0.291267i
$463$	−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
$465$	−5.52744e10	+	3.46547e9i	−0.0548259	+	0.00343735i
$466$	−1.76276e11	−	3.05318e11i	−0.173163	−	0.299927i
$467$	1.37108e11	−	3.67380e10i	0.133394	−	0.0357428i	−0.191504	−	0.981492i	$-0.561337\pi$
$467$	1.37108e11	−	3.67380e10i	0.133394	−	0.0357428i	0.324898	+	0.945749i	$0.394670\pi$
$468$	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
$472$	2.66608e11	−	9.94994e11i	0.247249	−	0.922745i
$473$	−2.10893e11	+	7.87063e11i	−0.193726	+	0.722994i
$474$	−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
$478$	−1.72803e11	+	4.63025e10i	−0.151400	+	0.0405675i
$479$	4.29437e11	+	7.43807e11i	0.372726	+	0.645581i	0.989984	−	0.141180i	$-0.0450898\pi$
$479$	4.29437e11	+	7.43807e11i	0.372726	+	0.645581i	−0.617258	+	0.786761i	$0.711756\pi$
$480$	−2.20697e10	−	1.94656e10i	−0.0189762	−	0.0167372i
$481$	−1.67427e12	−	9.66643e11i	−1.42618	−	0.823405i
$482$	1.18926e12	+	1.18926e12i	1.00361	+	1.00361i
$483$	1.11584e10	+	1.36154e11i	0.00932913	+	0.113833i
$484$		−	3.17502e10i		−	0.0262992i
$485$	−1.08632e12	−	1.63581e12i	−0.891496	−	1.34244i
$486$	8.12311e11	−	4.68988e11i	0.660479	−	0.381328i
$487$	1.01466e12	+	2.71878e11i	0.817412	+	0.219025i	0.643215	−	0.765686i	$-0.277600\pi$
$487$	1.01466e12	+	2.71878e11i	0.817412	+	0.219025i	0.174197	+	0.984711i	$0.444267\pi$
$488$	3.71961e11	+	1.38818e12i	0.296898	+	1.10804i
$489$	−1.53051e11			−0.121045
$490$	2.92631e11	+	1.27179e12i	0.229318	+	0.996628i
$491$	1.01910e12			0.791317			0.395658	−	0.918398i	$-0.370516\pi$
$491$	1.01910e12			0.791317			0.395658	+	0.918398i	$0.370516\pi$
$492$	5.55412e8	+	2.07282e9i	0.000427338	+	0.00159485i
$493$	−1.69178e12	−	4.53310e11i	−1.28983	−	0.345608i
$494$	9.60920e11	−	5.54788e11i	0.725966	−	0.419137i
$495$	3.06269e11	−	1.51722e12i	0.229287	−	1.13586i
$496$		−	2.79905e11i		−	0.207655i
$497$	−1.92818e10	−	2.35274e11i	−0.0141757	−	0.172970i
$498$	−1.41663e11	−	1.41663e11i	−0.103210	−	0.103210i
$499$	−1.28296e12	−	7.40719e11i	−0.926322	−	0.534812i	−0.0406755	−	0.999172i	$-0.512951\pi$
$499$	−1.28296e12	−	7.40719e11i	−0.926322	−	0.534812i	−0.885646	+	0.464360i	$0.846284\pi$
$500$	6.39086e10	+	4.73519e9i	0.0457293	+	0.00338823i
$501$	2.80847e11	+	4.86440e11i	0.199159	+	0.344953i
$502$	3.24165e10	−	8.68598e9i	0.0227824	−	0.00610453i
$503$	6.61569e11	−	6.61569e11i	0.460807	−	0.460807i	−0.438113	−	0.898920i	$-0.644353\pi$
$503$	6.61569e11	−	6.61569e11i	0.460807	−	0.460807i	0.898920	+	0.438113i	$0.144353\pi$
$504$	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
$507$	−1.69106e11	+	6.31112e11i	−0.113664	+	0.424200i
$508$	1.53802e10	−	5.73996e10i	0.0102465	−	0.0382404i
$509$	−1.38306e12	+	2.39552e12i	−0.913292	+	1.58187i	−0.103909	+	0.994587i	$0.533135\pi$
$509$	−1.38306e12	+	2.39552e12i	−0.913292	+	1.58187i	−0.809383	+	0.587281i	$0.800198\pi$
$510$	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
$513$	4.09895e11	−	1.09831e11i	0.261303	−	0.0700159i
$514$	7.12044e11	+	1.23330e12i	0.449959	+	0.779352i
$515$	−1.12744e11	−	1.79827e12i	−0.0706252	−	1.12648i
$516$	−1.05362e10	−	6.08305e9i	−0.00654272	−	0.00377744i
$517$	1.88796e12	+	1.88796e12i	1.16221	+	1.16221i
$518$	9.75740e11	+	1.40993e12i	0.595457	+	0.860424i
$519$			1.58972e11i			0.0961764i
$520$	−2.56676e12	−	5.18131e11i	−1.53946	−	0.310760i
$521$	1.27095e12	−	7.33781e11i	0.755714	−	0.436312i	−0.0720408	−	0.997402i	$-0.522951\pi$
$521$	1.27095e12	−	7.33781e11i	0.755714	−	0.436312i	0.827755	+	0.561090i	$0.189618\pi$
$522$	−2.17966e12	−	5.84038e11i	−1.28491	−	0.344290i
$523$	7.41378e11	+	2.76686e12i	0.433294	+	1.61707i	0.745117	+	0.666934i	$0.232394\pi$
$523$	7.41378e11	+	2.76686e12i	0.433294	+	1.61707i	−0.311823	+	0.950140i	$0.600940\pi$
$524$	−5.25139e10			−0.0304287
$525$	2.62751e11	−	4.02448e11i	0.150948	−	0.231203i
$526$	−3.50908e12			−1.99875
$527$	8.64659e10	+	3.22695e11i	0.0488312	+	0.182240i
$528$	−6.23625e11	−	1.67100e11i	−0.349198	−	0.0935672i
$529$	−1.29295e12	+	7.46484e11i	−0.717845	+	0.414448i
$530$	1.71690e11	+	3.46577e10i	0.0945156	+	0.0190791i
$531$			1.65681e12i			0.904371i
$532$	−4.30021e10	+	3.52422e9i	−0.0232749	+	0.00190748i
$533$	2.76535e11	+	2.76535e11i	0.148415	+	0.148415i
$534$	−4.34653e11	−	2.50947e11i	−0.231317	−	0.133551i
$535$	1.59887e11	+	2.55020e12i	0.0843763	+	1.34581i
$536$	−1.28397e12	−	2.22391e12i	−0.671916	−	1.16379i
$537$	−2.23819e11	+	5.99722e10i	−0.116148	+	0.0311218i
$538$	−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	−0.961208	−	0.275824i	$-0.911049\pi$
$541$	−4.81642e11	+	8.34228e11i	−0.241733	+	0.418694i	0.719475	+	0.694519i	$0.244383\pi$
$542$	7.02144e11	−	2.62044e12i	0.349486	−	1.30430i
$543$	−1.10676e11	+	4.13047e11i	−0.0546328	+	0.203892i
$544$	−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	$0.386410\pi$
$548$	−1.52712e11	+	4.09190e10i	−0.0723369	+	0.0193826i
$549$	−1.15576e12	−	2.00183e12i	−0.542988	−	0.940483i
$550$	2.54937e12	−	1.03908e12i	1.18796	−	0.484193i
$551$	−1.34370e12	−	7.75788e11i	−0.621043	−	0.358559i
$552$	1.71903e11	+	1.71903e11i	0.0788056	+	0.0788056i
$553$	1.53093e12	−	3.23653e12i	0.696132	−	1.47169i
$554$			1.38239e12i			0.623499i
$555$	1.24952e11	−	6.18997e11i	0.0559018	−	0.276930i
$556$	−1.37006e11	+	7.91005e10i	−0.0608000	+	0.0351029i
$557$	−7.17270e11	−	1.92192e11i	−0.315743	−	0.0846032i	0.0974671	−	0.995239i	$-0.468926\pi$
$557$	−7.17270e11	−	1.92192e11i	−0.315743	−	0.0846032i	−0.413210	+	0.910636i	$0.635593\pi$
$558$	1.11401e11	+	4.15756e11i	0.0486448	+	0.181545i
$559$	−2.21716e12			−0.960384
$560$	1.94689e12	+	1.45261e12i	0.836557	+	0.624171i
$561$	7.70581e11			0.328462
$562$	−8.98358e11	−	3.35272e12i	−0.379871	−	1.41770i
$563$	−3.30095e11	−	8.84487e10i	−0.138469	−	0.0371026i	0.188919	−	0.981993i	$-0.439502\pi$
$563$	−3.30095e11	−	8.84487e10i	−0.138469	−	0.0371026i	−0.327388	+	0.944890i	$0.606168\pi$
$564$	−3.45243e10	+	1.99326e10i	−0.0143671	+	0.00829485i
$565$	1.27363e12	+	1.91787e12i	0.525804	+	0.791774i
$566$		−	1.38149e12i		−	0.565815i
$567$	−1.57261e12	+	1.08833e12i	−0.638996	+	0.442217i
$568$	−2.97048e11	−	2.97048e11i	−0.119746	−	0.119746i
$569$	−3.14402e12	−	1.81520e12i	−1.25742	−	0.725970i	−0.284846	−	0.958573i	$-0.591942\pi$
$569$	−3.14402e12	−	1.81520e12i	−1.25742	−	0.725970i	−0.972572	+	0.232603i	$0.925276\pi$
$570$	2.71809e11	+	2.39737e11i	0.107852	+	0.0951260i
$571$	−2.90001e11	−	5.02296e11i	−0.114166	−	0.197741i	0.803280	−	0.595601i	$-0.203086\pi$
$571$	−2.90001e11	−	5.02296e11i	−0.114166	−	0.197741i	−0.917446	+	0.397860i	$0.869753\pi$
$572$	2.28949e11	−	6.13468e10i	0.0894247	−	0.0239613i
$573$	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
$577$	2.59485e11	−	9.68412e11i	0.0974589	−	0.363722i	−0.899922	−	0.436051i	$-0.856377\pi$
$577$	2.59485e11	−	9.68412e11i	0.0974589	−	0.363722i	0.997381	+	0.0723295i	$0.0230433\pi$
$578$	−7.15131e10	+	2.66890e11i	−0.0266508	+	0.0994621i
$579$	−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
$583$	3.18663e11	−	8.53854e10i	0.114241	−	0.0306108i
$584$	6.43861e11	+	1.11520e12i	0.229052	+	0.396730i
$585$	4.20340e12	−	2.63535e11i	1.48388	−	0.0930331i
$586$	−4.21407e12	−	2.43300e12i	−1.47626	−	0.852319i
$587$	2.84556e11	+	2.84556e11i	0.0989228	+	0.0989228i	0.754836	−	0.655913i	$-0.227716\pi$
$587$	2.84556e11	+	2.84556e11i	0.0989228	+	0.0989228i	−0.655913	+	0.754836i	$0.727716\pi$
$588$	−3.34305e10	+	1.51439e10i	−0.0115331	+	0.00522444i
$589$			2.95953e11i			0.101322i
$590$	−2.45485e12	+	1.63022e12i	−0.834046	+	0.553877i
$591$	−8.61074e11	+	4.97141e11i	−0.290333	+	0.167624i
$592$	3.08276e12	+	8.26024e11i	1.03155	+	0.276404i
$593$	9.78880e11	+	3.65323e12i	0.325075	+	1.21320i	0.914237	+	0.405181i	$0.132791\pi$
$593$	9.78880e11	+	3.65323e12i	0.325075	+	1.21320i	−0.589162	+	0.808015i	$0.700542\pi$
$594$	2.06755e12			0.681423
$595$	−2.69325e12	−	1.07326e12i	−0.880948	−	0.351059i
$596$	1.14774e11			0.0372593
$597$	−6.07753e10	−	2.26817e11i	−0.0195814	−	0.0730786i
$598$	−2.05663e12	−	5.51073e11i	−0.657660	−	0.176220i
$599$	2.48340e12	−	1.43379e12i	0.788180	−	0.455056i	−0.0511416	−	0.998691i	$-0.516286\pi$
$599$	2.48340e12	−	1.43379e12i	0.788180	−	0.455056i	0.839321	+	0.543636i	$0.182953\pi$
$600$	−1.06828e11	−	8.48611e11i	−0.0336517	−	0.267318i
$601$		−	1.52213e12i		−	0.475901i	−0.971277	−	0.237950i	$-0.923524\pi$
$601$		−	1.52213e12i		−	0.475901i	0.971277	−	0.237950i	$-0.0764756\pi$
$602$	1.77757e12	+	8.40818e11i	0.551624	+	0.260926i
$603$	2.92056e12	+	2.92056e12i	0.899578	+	0.899578i
$604$	−1.77610e11	−	1.02543e11i	−0.0543002	−	0.0313502i
$605$	1.25018e12	−	1.41743e12i	0.379379	−	0.430131i
$606$	5.05956e10	+	8.76341e10i	0.0152400	+	0.0263965i
$607$	5.24579e12	−	1.40560e12i	1.56842	−	0.420256i	0.633101	−	0.774069i	$-0.281782\pi$
$607$	5.24579e12	−	1.40560e12i	1.56842	−	0.420256i	0.935316	+	0.353813i	$0.115115\pi$
$608$	−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
$612$	3.60807e10	−	1.34655e11i	0.0103967	−	0.0388009i
$613$	2.78209e11	−	1.03829e12i	0.0795791	−	0.296993i	−0.914653	−	0.404239i	$-0.867536\pi$
$613$	2.78209e11	−	1.03829e12i	0.0795791	−	0.296993i	0.994233	+	0.107246i	$0.0342031\pi$
$614$	−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	$0.104722\pi$
$618$	1.11633e12	−	2.99120e11i	0.307854	−	0.0824892i
$619$	−1.53089e12	−	2.65157e12i	−0.419117	−	0.725931i	0.576734	−	0.816932i	$-0.304327\pi$
$619$	−1.53089e12	−	2.65157e12i	−0.419117	−	0.725931i	−0.995851	+	0.0910006i	$0.970993\pi$
$620$	−2.22027e10	+	2.51729e10i	−0.00603452	+	0.00684182i
$621$	−7.05206e11	−	4.07151e11i	−0.190285	−	0.109861i
$622$	6.59823e11	+	6.59823e11i	0.176755	+	0.176755i
$623$	3.21514e12	+	1.52081e12i	0.855074	+	0.404462i
$624$		−	1.75676e12i		−	0.463854i
$625$	2.66663e12	+	2.72782e12i	0.699040	+	0.715083i
$626$	−1.08377e12	+	6.25717e11i	−0.282068	+	0.162852i
$627$	6.59380e11	+	1.76680e11i	0.170385	+	0.0456545i
$628$	5.16128e10	+	1.92622e11i	0.0132416	+	0.0494181i
$629$	−3.80920e12			−0.970301
$630$	−3.46994e12	−	1.38278e12i	−0.877587	−	0.349719i
$631$	1.59709e12			0.401048			0.200524	−	0.979689i	$-0.435735\pi$
$631$	1.59709e12			0.401048			0.200524	+	0.979689i	$0.435735\pi$
$632$	−1.64906e12	−	6.15436e12i	−0.411158	−	1.53446i
$633$	3.32394e11	+	8.90648e10i	0.0822881	+	0.0220490i
$634$	1.60794e12	−	9.28347e11i	0.395247	−	0.228196i
$635$	2.94675e12	−	1.95689e12i	0.719220	−	0.477622i
$636$			4.92576e9i			0.00119376i
$637$	−3.89626e12	+	5.43629e12i	−0.937607	+	1.30820i
$638$	−5.34546e12	−	5.34546e12i	−1.27730	−	1.27730i
$639$	5.85151e11	+	3.37837e11i	0.138840	+	0.0801592i
$640$	4.50379e12	−	2.82368e11i	1.06113	−	0.0665282i
$641$	2.46658e11	+	4.27224e11i	0.0577077	+	0.0999527i	0.893436	−	0.449190i	$-0.148288\pi$
$641$	2.46658e11	+	4.27224e11i	0.0577077	+	0.0999527i	−0.835728	+	0.549143i	$0.814954\pi$
$642$	−1.58312e12	+	4.24195e11i	−0.367795	+	0.0985504i
$643$	9.60573e11	−	9.60573e11i	0.221606	−	0.221606i	−0.587569	−	0.809174i	$-0.699915\pi$
$643$	9.60573e11	−	9.60573e11i	0.221606	−	0.221606i	0.809174	+	0.587569i	$0.199915\pi$
$644$	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
$647$	−6.35139e11	+	2.37037e12i	−0.142495	+	0.531798i	0.857359	+	0.514719i	$0.172104\pi$
$647$	−6.35139e11	+	2.37037e12i	−0.142495	+	0.531798i	−0.999854	+	0.0170798i	$0.994563\pi$
$648$	−8.80859e11	+	3.28741e12i	−0.196254	+	0.732431i
$649$	−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
$653$	−2.68924e12	+	7.20578e11i	−0.578788	+	0.155086i	−0.536324	−	0.844012i	$-0.680187\pi$
$653$	−2.68924e12	+	7.20578e11i	−0.578788	+	0.155086i	−0.0424640	+	0.999098i	$0.513521\pi$
$654$	5.02663e11	+	8.70638e11i	0.107443	+	0.186096i
$655$	−2.34438e12	−	2.06776e12i	−0.497671	−	0.438949i
$656$	−5.59108e11	−	3.22801e11i	−0.117877	−	0.0680562i
$657$	−1.46454e12	−	1.46454e12i	−0.306661	−	0.306661i
$658$	5.29836e12	−	3.66673e12i	1.10186	−	0.762539i
$659$		−	8.40596e12i		−	1.73621i	−0.496378	−	0.868106i	$-0.665337\pi$
$659$		−	8.40596e12i		−	1.73621i	0.496378	−	0.868106i	$-0.334663\pi$
$660$	4.28303e10	+	6.44953e10i	0.00878625	+	0.0132306i
$661$	−2.66008e12	+	1.53580e12i	−0.541985	+	0.312915i	−0.745883	−	0.666077i	$-0.767972\pi$
$661$	−2.66008e12	+	1.53580e12i	−0.541985	+	0.312915i	0.203898	+	0.978992i	$0.434639\pi$
$662$	−7.47407e12	−	2.00267e12i	−1.51250	−	0.405274i
$663$	5.42683e11	+	2.02532e12i	0.109078	+	0.407083i
$664$	2.52649e12			0.504383
$665$	−2.05851e12	−	1.53590e12i	−0.408184	−	0.304554i
$666$	−4.90772e12			−0.966598
$667$	7.70594e11	+	2.87590e12i	0.150751	+	0.562609i
$668$	3.28820e11	+	8.81071e10i	0.0638947	+	0.0171205i
$669$	−1.71877e12	+	9.92335e11i	−0.331743	+	0.191532i
$670$	−1.45361e12	+	7.20102e12i	−0.278684	+	1.38057i
$671$		−	7.74374e12i		−	1.47468i
$672$	−5.71951e10	+	1.20916e11i	−0.0108193	+	0.0228730i
$673$	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
$675$	1.08132e12	+	2.65300e12i	0.200487	+	0.491893i
$676$	1.97992e11	+	3.42933e11i	0.0364660	+	0.0631610i
$677$	−8.49337e11	+	2.27579e11i	−0.155393	+	0.0416374i	−0.335677	−	0.941977i	$-0.608965\pi$
$677$	−8.49337e11	+	2.27579e11i	−0.155393	+	0.0416374i	0.180284	+	0.983615i	$0.442298\pi$
$678$	−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
$682$	−3.73203e11	+	1.39281e12i	−0.0660565	+	0.246526i
$683$	6.27705e11	−	2.34263e12i	0.110373	−	0.411917i	−0.888526	−	0.458826i	$-0.848270\pi$
$683$	6.27705e11	−	2.34263e12i	0.110373	−	0.411917i	0.998899	+	0.0469085i	$0.0149369\pi$
$684$	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
$688$	3.53543e12	−	9.47314e11i	0.601581	−	0.161193i
$689$	4.48838e11	+	7.77410e11i	0.0758757	+	0.131421i
$690$	−4.35176e10	−	6.94108e11i	−0.00730876	−	0.116575i
$691$	−1.15072e12	−	6.64371e11i	−0.192008	−	0.110856i	0.400914	−	0.916116i	$-0.368693\pi$
$691$	−1.15072e12	−	6.64371e11i	−0.192008	−	0.110856i	−0.592922	+	0.805260i	$0.702026\pi$
$692$	6.81275e10	+	6.81275e10i	0.0112939	+	0.0112939i
$693$	−7.01202e12	+	5.74666e11i	−1.15490	+	0.0946490i
$694$			6.32609e12i			1.03518i
$695$	−9.23098e12	−	1.86339e12i	−1.50078	−	0.302950i
$696$	−2.03398e12	+	1.17432e12i	−0.328553	+	0.189690i
$697$	7.44298e11	+	1.99434e11i	0.119454	+	0.0320075i
$698$	−1.73250e12	−	6.46578e12i	−0.276264	−	1.03103i
$699$	5.90186e11			0.0935065
$700$	−5.98670e10	−	2.85071e11i	−0.00942424	−	0.0448757i
$701$	7.31544e12			1.14422			0.572109	−	0.820177i	$-0.306125\pi$
$701$	7.31544e12			1.14422			0.572109	+	0.820177i	$0.306125\pi$
$702$	1.45608e12	+	5.43415e12i	0.226291	+	0.844529i
$703$	−3.25951e12	−	8.73382e11i	−0.503330	−	0.134867i
$704$	6.72645e12	−	3.88352e12i	1.03207	−	0.595866i
$705$	−2.32613e12	−	4.69557e11i	−0.354636	−	0.0715876i
$706$		−	4.39888e12i		−	0.666379i
$707$	−4.08074e11	−	5.89659e11i	−0.0614258	−	0.0887592i
$708$	−5.86000e10	−	5.86000e10i	−0.00876492	−	0.00876492i
$709$	7.01192e12	+	4.04833e12i	1.04215	+	0.601684i	0.920441	−	0.390883i	$-0.127830\pi$
$709$	7.01192e12	+	4.04833e12i	1.04215	+	0.601684i	0.121706	+	0.992566i	$0.461163\pi$
$710$	7.51984e10	+	1.19942e12i	0.0111057	+	0.177137i
$711$	5.12394e12	+	8.87493e12i	0.751954	+	1.30242i
$712$	6.11368e12	−	1.63816e12i	0.891544	−	0.238888i
$713$	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
$717$	7.75124e10	−	2.89280e11i	0.0109530	−	0.0408773i
$718$	−2.15162e12	+	8.02994e12i	−0.302138	+	1.12759i
$719$	3.08140e12	−	5.33714e12i	0.429999	−	0.744781i	−0.566873	−	0.823805i	$-0.691847\pi$
$719$	3.08140e12	−	5.33714e12i	0.429999	−	0.744781i	0.996873	+	0.0790243i	$0.0251805\pi$
$720$	−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
$723$	−2.71959e12	+	7.28711e11i	−0.370152	+	0.0991820i
$724$	1.29581e11	+	2.24441e11i	0.0175274	+	0.0303584i
$725$	4.06344e12	−	9.65474e12i	0.546226	−	1.29784i
$726$	1.04986e12	+	6.06138e11i	0.140255	+	0.0809761i
$727$	3.27755e12	+	3.27755e12i	0.435155	+	0.435155i	0.890378	−	0.455223i	$-0.150440\pi$
$727$	3.27755e12	+	3.27755e12i	0.435155	+	0.435155i	−0.455223	+	0.890378i	$0.650440\pi$
$728$	9.72193e11	+	1.18626e13i	0.128281	+	1.56527i
$729$		−	4.35558e12i		−	0.571179i
$730$	7.28929e11	−	3.61102e12i	0.0950019	−	0.470627i
$731$	−3.78326e12	+	2.18427e12i	−0.490048	+	0.282929i
$732$	1.11681e11	+	2.99249e10i	0.0143774	+	0.00385241i
$733$	−2.85478e12	−	1.06542e13i	−0.365262	−	1.36318i	−0.867066	−	0.498194i	$-0.833997\pi$
$733$	−2.85478e12	−	1.06542e13i	−0.365262	−	1.36318i	0.501804	−	0.864981i	$-0.332670\pi$
$734$	−8.47092e12			−1.07720
$735$	−2.08874e12	−	6.40271e11i	−0.263992	−	0.0809228i
$736$	3.01756e11			0.0379058
$737$	3.58123e12	+	1.33653e13i	0.447125	+	1.66869i
$738$	9.58942e11	+	2.56948e11i	0.118998	+	0.0318854i
$739$	−4.69583e11	+	2.71114e11i	−0.0579178	+	0.0334389i	−0.528679	−	0.848822i	$-0.677313\pi$
$739$	−4.69583e11	+	2.71114e11i	−0.0579178	+	0.0334389i	0.470761	+	0.882261i	$0.343979\pi$
$740$	−2.11723e11	−	3.18819e11i	−0.0259552	−	0.0390842i
$741$			1.85748e12i			0.226330i
$742$	−6.50299e10	−	7.93488e11i	−0.00787581	−	0.0960999i
$743$	−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
$745$	5.12385e12	+	4.51927e12i	0.609387	+	0.537484i
$746$	6.94686e12	+	1.20323e13i	0.821228	+	1.42241i
$747$	−3.92515e12	+	1.05174e12i	−0.461225	+	0.123585i
$748$	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	0.00529815	−	0.999986i	$-0.498314\pi$
$751$	7.57235e12	−	1.31157e13i	0.868662	−	1.50457i	0.863364	−	0.504581i	$-0.168353\pi$
$752$	3.10411e12	−	1.15847e13i	0.353962	−	1.32100i
$753$	−1.45407e10	+	5.42667e10i	−0.00164819	+	0.00615114i
$754$	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	$0.00326612\pi$
$758$	−5.13162e12	+	1.37501e12i	−0.564602	+	0.151285i
$759$	−6.54965e11	−	1.13443e12i	−0.0716358	−	0.124077i
$760$	−4.56160e12	+	2.85993e11i	−0.495971	+	0.0310953i
$761$	1.30630e13	+	7.54194e12i	1.41193	+	0.815178i	0.995570	−	0.0940228i	$-0.0299727\pi$
$761$	1.30630e13	+	7.54194e12i	1.41193	+	0.815178i	0.416359	+	0.909200i	$0.363306\pi$
$762$	1.60437e12	+	1.60437e12i	0.172388	+	0.172388i
$763$	−4.05418e12	−	5.85822e12i	−0.433055	−	0.625756i
$764$		−	6.06005e11i		−	0.0643511i
$765$	6.91286e12	−	4.59072e12i	0.729762	−	0.484623i
$766$	9.43423e12	−	5.44686e12i	0.990095	−	0.571632i
$767$	−1.45882e13	−	3.90890e12i	−1.52203	−	0.407827i
$768$	9.45841e10	+	3.52993e11i	0.00981054	+	0.0366134i
$769$	1.03458e11			0.0106683			0.00533415	−	0.999986i	$-0.498302\pi$
$769$	1.03458e11			0.0106683			0.00533415	+	0.999986i	$0.498302\pi$
$770$	−7.75098e12	−	9.82407e12i	−0.794599	−	1.00712i
$771$	−2.38399e12			−0.242974
$772$	1.42557e11	+	5.32031e11i	0.0144448	+	0.0539087i
$773$	−8.45906e12	−	2.26660e12i	−0.852147	−	0.228332i	−0.193795	−	0.981042i	$-0.562080\pi$
$773$	−8.45906e12	−	2.26660e12i	−0.852147	−	0.228332i	−0.658352	+	0.752710i	$0.728746\pi$
$774$	−4.87430e12	+	2.81418e12i	−0.488178	+	0.281850i
$775$	−1.98239e12	+	2.49556e11i	−0.197393	+	0.0248491i
$776$			1.58839e13i			1.57246i
$777$	−2.86078e12	+	2.34453e11i	−0.281572	+	0.0230761i
$778$	2.66919e11	+	2.66919e11i	0.0261199	+	0.0261199i
$779$	5.91163e11	+	3.41308e11i	0.0575160	+	0.0332069i
$780$	−1.39350e11	+	1.57992e11i	−0.0134797	+	0.0152830i
$781$	1.13178e12	+	1.96030e12i	0.108851	+	0.188535i
$782$	−4.05224e12	+	1.08579e12i	−0.387494	+	0.103829i
$783$	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
$787$	3.35110e12	−	1.25065e13i	0.311387	−	1.16211i	−0.615919	−	0.787809i	$-0.711215\pi$
$787$	3.35110e12	−	1.25065e13i	0.311387	−	1.16211i	0.927306	−	0.374303i	$-0.122118\pi$
$788$	−1.55963e11	+	5.82062e11i	−0.0144097	+	0.0537776i
$789$	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
$793$	2.03529e13	−	5.45354e12i	1.82767	−	0.489722i
$794$	7.28791e12	+	1.26230e13i	0.650744	+	1.12712i
$795$	−1.93954e11	+	2.19901e11i	−0.0172205	+	0.0195243i
$796$	−1.23247e11	−	7.11568e10i	−0.0108810	−	0.00628214i
$797$	3.83196e12	+	3.83196e12i	0.336402	+	0.336402i	0.855011	−	0.518609i	$-0.173550\pi$
$797$	3.83196e12	+	3.83196e12i	0.336402	+	0.336402i	−0.518609	+	0.855011i	$0.673550\pi$
$798$	7.04414e11	−	1.48920e12i	0.0614915	−	0.129999i
$799$			1.43146e13i			1.24256i
$800$	−8.38583e11	−	6.51058e11i	−0.0723838	−	0.0561972i
$801$	−8.81627e12	+	5.09007e12i	−0.756726	+	0.436896i
$802$	−1.74015e13	−	4.66272e12i	−1.48526	−	0.397974i
$803$	−1.79584e12	−	6.70218e12i	−0.152422	−	0.568848i
$804$	−2.06596e11			−0.0174369
$805$	7.09129e11	+	4.87718e12i	0.0595174	+	0.409343i
$806$	−3.92357e12			−0.327472
$807$	−5.28784e11	−	1.97345e12i	−0.0438882	−	0.163793i
$808$	−1.23263e12	−	3.30282e11i	−0.101738	−	0.0272605i
$809$	4.10941e11	−	2.37257e11i	0.0337296	−	0.0194738i	−0.483040	−	0.875598i	$-0.660468\pi$
$809$	4.10941e11	−	2.37257e11i	0.0337296	−	0.0194738i	0.516770	+	0.856124i	$0.327134\pi$
$810$	8.11069e12	−	5.38618e12i	0.662026	−	0.439641i
$811$		−	9.13605e12i		−	0.741591i	−0.928714	−	0.370796i	$-0.879085\pi$
$811$		−	9.13605e12i		−	0.741591i	0.928714	−	0.370796i	$-0.120915\pi$
$812$	−6.57725e11	+	4.55178e11i	−0.0530936	+	0.0367434i
$813$	3.21131e12	+	3.21131e12i	0.257795	+	0.257795i
$814$	−1.42385e13	−	8.22062e12i	−1.13673	−	0.656289i
$815$	−5.51077e12	+	3.45502e11i	−0.437525	+	0.0274310i
$816$	−1.73069e12	−	2.99765e12i	−0.136652	−	0.236687i
$817$	−3.73812e12	+	1.00163e12i	−0.293531	+	0.0786514i
$818$	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	0.457995	+	0.888955i	$0.348568\pi$
$821$	−7.04092e12	+	1.21952e13i	−0.540860	+	0.936798i	−0.998855	+	0.0478426i	$0.984765\pi$
$822$	1.56235e12	−	5.83079e12i	0.119359	−	0.445455i
$823$	−1.40478e12	+	5.24273e12i	−0.106736	+	0.398344i	−0.998536	−	0.0540852i	$-0.982776\pi$
$823$	−1.40478e12	+	5.24273e12i	−0.106736	+	0.398344i	0.891800	+	0.452429i	$0.149442\pi$
$824$	−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	$0.162959\pi$
$828$	−2.28904e11	+	6.13346e10i	−0.0169245	+	0.00453491i
$829$	8.10264e12	+	1.40342e13i	0.595842	+	1.03203i	0.993427	+	0.114463i	$0.0365148\pi$
$829$	8.10264e12	+	1.40342e13i	0.595842	+	1.03203i	−0.397586	+	0.917565i	$0.630152\pi$
$830$	−5.42050e12	−	4.78092e12i	−0.396450	−	0.349671i
$831$	−2.00414e12	−	1.15709e12i	−0.145788	−	0.0841709i
$832$	1.49442e13	+	1.49442e13i	1.08123	+	1.08123i
$833$	−1.29276e12	+	1.31147e13i	−0.0930283	+	0.943747i
$834$		−	6.04038e12i		−	0.432332i
$835$	1.12103e13	+	1.68808e13i	0.798045	+	1.20172i
$836$	3.58293e11	−	2.06860e11i	0.0253694	−	0.0146470i
$837$	−1.44943e12	−	3.88373e11i	−0.102078	−	0.0273517i
$838$	−2.98171e12	−	1.11279e13i	−0.208866	−	0.779499i
$839$	−2.39905e12			−0.167151			−0.0835757	−	0.996501i	$-0.526634\pi$
$839$	−2.39905e12			−0.167151			−0.0835757	+	0.996501i	$0.526634\pi$
$840$	−3.57143e12	+	1.53608e12i	−0.247506	+	0.106453i
$841$	−1.42568e13			−0.982741
$842$	1.98312e12	+	7.40109e12i	0.135970	+	0.507448i
$843$	5.61260e12	+	1.50389e12i	0.382772	+	0.102563i
$844$	1.80616e11	−	1.04279e11i	0.0122522	−	0.00707383i
$845$	−4.66415e12	+	2.31056e13i	−0.314715	+	1.55906i
$846$			1.84427e13i			1.23782i
$847$	−7.76586e12	−	3.67336e12i	−0.518459	−	0.245238i
$848$	−1.04786e12	−	1.04786e12i	−0.0695862	−	0.0695862i
$849$	2.00284e12	+	1.15634e12i	0.132301	+	0.0763838i
$850$	1.36039e13	+	5.72553e12i	0.893877	+	0.376210i
$851$	3.23768e12	+	5.60783e12i	0.211617	+	0.366532i
$852$	−3.26454e10	+	8.74730e9i	−0.00212248	+	0.000568717i
$853$	1.11316e13	−	1.11316e13i	0.719928	−	0.719928i	−0.248663	−	0.968590i	$-0.579991\pi$
$853$	1.11316e13	−	1.11316e13i	0.719928	−	0.719928i	0.968590	+	0.248663i	$0.0799910\pi$
$854$	−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
$857$	4.06061e12	−	1.51544e13i	0.257145	−	0.959677i	−0.709740	−	0.704463i	$-0.751188\pi$
$857$	4.06061e12	−	1.51544e13i	0.257145	−	0.959677i	0.966885	−	0.255213i	$-0.0821456\pi$
$858$	−2.34232e12	+	8.74167e12i	−0.147555	+	0.550683i
$859$	2.33636e12	−	4.04669e12i	0.146410	−	0.253589i	−0.783488	−	0.621407i	$-0.786562\pi$
$859$	2.33636e12	−	4.04669e12i	0.146410	−	0.253589i	0.929898	+	0.367817i	$0.119895\pi$
$860$	−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
$863$	−1.56399e13	+	4.19071e12i	−0.959813	+	0.257181i	−0.704521	−	0.709683i	$-0.748838\pi$
$863$	−1.56399e13	+	4.19071e12i	−0.959813	+	0.257181i	−0.255292	+	0.966864i	$0.582172\pi$
$864$	−3.98658e11	−	6.90496e11i	−0.0243382	−	0.0421550i
$865$	3.58868e11	+	5.72397e12i	0.0217953	+	0.347636i
$866$	1.36011e10	+	7.85259e9i	0.000821756	+	0.000474441i
$867$	−3.27070e11	−	3.27070e11i	−0.0196587	−	0.0196587i
$868$	1.37919e11	+	6.52375e10i	0.00824678	+	0.00390084i
$869$			3.43312e13i			2.04221i
$870$	6.58604e12	+	1.32947e12i	0.389751	+	0.0786761i
$871$	−3.26061e13	+	1.88252e13i	−1.91963	+	1.10830i
$872$	−1.22461e13	−	3.28133e12i	−0.717255	−	0.192188i
$873$	−6.61224e12	−	2.46772e13i	−0.385287	−	1.43791i
$874$	−3.71642e12			−0.215439
$875$	8.55215e12	−	1.50837e13i	0.493218	−	0.869906i
$876$	1.03600e11			0.00594415
$877$	−2.24262e10	−	8.36958e10i	−0.00128014	−	0.00477755i	0.965283	−	0.261207i	$-0.0841205\pi$
$877$	−2.24262e10	−	8.36958e10i	−0.00128014	−	0.00477755i	−0.966563	+	0.256429i	$0.917454\pi$
$878$	6.05598e12	+	1.62269e12i	0.343921	+	0.0921534i
$879$	7.05454e12	−	4.07294e12i	0.398583	−	0.230122i
$880$	−2.28315e13	−	4.60882e12i	−1.28340	−	0.259070i
$881$		−	2.39476e13i		−	1.33928i	−0.742687	−	0.669639i	$-0.766449\pi$
$881$		−	2.39476e13i		−	1.33928i	0.742687	−	0.669639i	$-0.233551\pi$
$882$	−1.66557e12	+	1.68968e13i	−0.0926733	+	0.940145i
$883$	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
$885$	−3.08681e11	−	4.92348e12i	−0.0169148	−	0.269791i
$886$	7.60769e12	+	1.31769e13i	0.414764	+	0.718392i
$887$	1.98234e13	−	5.31167e12i	1.07528	−	0.288121i	0.322620	−	0.946529i	$-0.395436\pi$
$887$	1.98234e13	−	5.31167e12i	1.07528	−	0.288121i	0.752661	+	0.658408i	$0.228770\pi$
$888$	−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
$892$	−3.11315e11	+	1.16184e12i	−0.0164649	+	0.0614477i
$893$	−3.28208e12	+	1.22489e13i	−0.172710	+	0.644562i
$894$	−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
$898$	2.36732e13	−	6.34320e12i	1.21482	−	0.325511i
$899$	2.74326e12	+	4.75147e12i	0.140071	+	0.242610i
$900$	7.68459e11	+	3.23425e11i	0.0390417	+	0.0164317i
$901$	1.53175e12	+	8.84357e11i	0.0774331	+	0.0447060i
$902$	2.35174e12	+	2.35174e12i	0.118293	+	0.118293i
$903$	−2.70686e12	+	1.87328e12i	−0.135478	+	0.0937579i
$904$		−	1.86227e13i		−	0.927437i
$905$	−3.05257e12	+	1.51221e13i	−0.151268	+	0.749363i
$906$	6.78145e12	−	3.91527e12i	0.334384	−	0.193057i
$907$	−2.55282e13	−	6.84027e12i	−1.25253	−	0.335614i	−0.429217	−	0.903202i	$-0.641210\pi$
$907$	−2.55282e13	−	6.84027e12i	−1.25253	−	0.335614i	−0.823313	+	0.567587i	$0.807877\pi$
$908$	−9.15597e9	−	3.41705e10i	−0.000447011	−	0.00166827i
$909$	2.05251e12			0.0997119
$910$	2.03620e13	−	2.72906e13i	0.984315	−	1.31925i
$911$	2.21543e13			1.06568			0.532839	−	0.846217i	$-0.321125\pi$
$911$	2.21543e13			1.06568			0.532839	+	0.846217i	$0.321125\pi$
$912$	−7.93634e11	−	2.96188e12i	−0.0379877	−	0.141772i
$913$	−1.31495e13	−	3.52341e12i	−0.626314	−	0.167820i
$914$	−3.21129e12	+	1.85404e12i	−0.152202	+	0.0878741i
$915$	3.80748e12	+	5.73344e12i	0.179574	+	0.270408i
$916$		−	1.24873e12i		−	0.0586057i
$917$	−6.07563e12	+	1.28445e13i	−0.283746	+	0.599867i
$918$	7.83810e12	+	7.83810e12i	0.364266	+	0.364266i
$919$	−2.59112e13	−	1.49598e13i	−1.19830	−	0.691842i	−0.238128	−	0.971234i	$-0.576534\pi$
$919$	−2.59112e13	−	1.49598e13i	−1.19830	−	0.691842i	−0.960177	+	0.279392i	$0.909867\pi$
$920$	6.57760e12	+	5.80149e12i	0.302707	+	0.266989i
$921$	−3.31405e12	−	5.74011e12i	−0.151772	−	0.262877i
$922$	4.04985e13	−	1.08515e13i	1.84565	−	0.494540i
$923$	−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
$927$	6.06719e12	−	2.26431e13i	0.269854	−	1.00711i
$928$	−7.54520e11	+	2.81591e12i	−0.0333968	+	0.124639i
$929$	2.69415e12	−	4.66641e12i	0.118673	−	0.205547i	−0.800569	−	0.599240i	$-0.795469\pi$
$929$	2.69415e12	−	4.66641e12i	0.118673	−	0.205547i	0.919242	+	0.393693i	$0.128803\pi$
$930$	−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
$933$	−1.50888e12	+	4.04302e11i	−0.0651908	+	0.0174678i
$934$	1.64233e12	+	2.84459e12i	0.0706153	+	0.122309i
$935$	2.77456e13	−	1.73953e12i	1.18725	−	0.0744354i
$936$	−2.95035e13	−	1.70338e13i	−1.25641	−	0.725390i
$937$	−4.64335e12	−	4.64335e12i	−0.196790	−	0.196790i	0.601832	−	0.798622i	$-0.294438\pi$
$937$	−4.64335e12	−	4.64335e12i	−0.196790	−	0.196790i	−0.798622	+	0.601832i	$0.794438\pi$
$938$	3.32805e13	−	2.72748e12i	1.40371	−	0.115040i
$939$		−	2.09495e12i		−	0.0879386i
$940$	−1.19809e12	+	7.95631e11i	−0.0500511	+	0.0332381i
$941$	−2.44520e13	+	1.41174e13i	−1.01663	+	0.586949i	−0.913125	−	0.407680i	$-0.866338\pi$
$941$	−2.44520e13	+	1.41174e13i	−1.01663	+	0.586949i	−0.103501	+	0.994629i	$0.533005\pi$
$942$	−7.35461e12	−	1.97066e12i	−0.304320	−	0.0815423i
$943$	−3.39023e11	−	1.26525e12i	−0.0139613	−	0.0521044i
$944$	2.49321e13			1.02184
$945$	1.02234e13	−	8.06604e12i	0.417016	−	0.329016i
$946$	−1.88554e13			−0.765467
$947$	1.94844e12	+	7.27166e12i	0.0787247	+	0.293805i	0.994052	−	0.108906i	$-0.0347348\pi$
$947$	1.94844e12	+	7.27166e12i	0.0787247	+	0.293805i	−0.915327	+	0.402711i	$0.868068\pi$
$948$	−4.95129e11	−	1.32669e11i	−0.0199105	−	0.00533499i
$949$	1.63506e13	−	9.44005e12i	0.654390	−	0.377813i
$950$	1.03280e13	+	8.01841e12i	0.411395	+	0.319398i
$951$			3.10819e12i			0.123224i
$952$	1.33455e13	+	1.92840e13i	0.526585	+	0.760906i
$953$	−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
$955$	2.38617e13	−	2.70539e13i	0.928295	−	1.05248i
$956$	−9.07529e10	−	1.57189e11i	−0.00351399	−	0.00608640i
$957$	1.22239e13	−	3.27539e12i	0.471093	−	0.126229i
$958$	−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
$962$	1.15788e13	−	4.32126e13i	0.435888	−	1.62676i
$963$	−8.60415e12	+	3.21111e13i	−0.322396	+	1.20320i
$964$	−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	$0.0491432\pi$
$968$	−1.47670e13	+	3.95681e12i	−0.540572	+	0.144846i
$969$	1.82992e12	+	3.16951e12i	0.0666768	+	0.115488i
$970$	3.00574e13	−	3.40784e13i	1.09013	−	1.23597i
$971$	1.92722e13	+	1.11268e13i	0.695735	+	0.401683i	0.805757	−	0.592247i	$-0.201759\pi$
$971$	1.92722e13	+	1.11268e13i	0.695735	+	0.401683i	−0.110022	+	0.993929i	$0.535092\pi$
$972$	6.72914e11	+	6.72914e11i	0.0241803	+	0.0241803i
$973$	3.49636e12	+	4.26622e13i	0.125057	+	1.52593i
$974$			2.43079e13i			0.865432i
$975$	−1.24420e13	+	1.56628e12i	−0.440930	+	0.0555071i
$976$	−3.01240e13	+	1.73921e13i	−1.06265	+	0.613520i
$977$	2.70769e13	+	7.25525e12i	0.950767	+	0.254757i	0.700688	−	0.713468i	$-0.252877\pi$
$977$	2.70769e13	+	7.25525e12i	0.950767	+	0.254757i	0.250079	+	0.968225i	$0.419543\pi$
$978$	−9.16651e11	−	3.42099e12i	−0.0320390	−	0.119571i
$979$	−3.41043e13			−1.18655
$980$	−1.16951e12	+	6.20738e11i	−0.0405031	+	0.0214977i
$981$	2.03915e13			0.702973
$982$	6.10357e12	+	2.27788e13i	0.209451	+	0.781681i
$983$	−8.54142e12	−	2.28867e12i	−0.291769	−	0.0781793i	0.109966	−	0.993935i	$-0.464926\pi$
$983$	−8.54142e12	−	2.28867e12i	−0.291769	−	0.0781793i	−0.401735	+	0.915756i	$0.631593\pi$
$984$	8.94852e11	−	5.16643e11i	0.0304280	−	0.0175676i
$985$	−2.98816e13	+	1.98439e13i	−1.01144	+	0.671683i
$986$		−	4.05294e13i		−	1.36560i
$987$	8.81051e11	+	1.07505e13i	0.0295511	+	0.360580i
$988$	7.96021e11	+	7.96021e11i	0.0265778	+	0.0265778i
$989$	6.43127e12	+	3.71310e12i	0.213754	+	0.123411i
$990$	3.57470e13	−	2.24118e12i	1.18272	−	0.0741513i
$991$	−3.83070e12	−	6.63496e12i	−0.126167	−	0.218528i	0.796021	−	0.605268i	$-0.206934\pi$
$991$	−3.83070e12	−	6.63496e12i	−0.126167	−	0.218528i	−0.922189	+	0.386741i	$0.873601\pi$
$992$	5.37116e11	−	1.43920e11i	0.0176103	−	0.00471865i
$993$	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
$997$	−1.18100e13	+	4.40756e13i	−0.378550	+	1.41277i	0.469539	+	0.882912i	$0.344420\pi$
$997$	−1.18100e13	+	4.40756e13i	−0.378550	+	1.41277i	−0.848088	+	0.529855i	$0.822246\pi$
$998$	8.87259e12	−	3.31130e13i	0.283115	−	1.05660i
$999$	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.33.25	yes	136
5.2	odd	4	inner	35.10.k.a.12.10	yes	136
7.3	odd	6	inner	35.10.k.a.3.10	✓	136
35.17	even	12	inner	35.10.k.a.17.25	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.10	✓	136	7.3	odd	6	inner
35.10.k.a.12.10	yes	136	5.2	odd	4	inner
35.10.k.a.17.25	yes	136	35.17	even	12	inner
35.10.k.a.33.25	yes	136	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(5.98917 + 22.3519i) q^{2} +(-37.4181 - 10.0261i) q^{3} +(-20.3322 + 11.7388i) q^{4} +(-1369.91 - 276.533i) q^{5} -896.413i q^{6} +(518.872 + 6331.22i) q^{7} +(7993.56 + 7993.56i) q^{8} +(-15746.4 - 9091.18i) q^{9} +(-2023.59 - 32276.3i) q^{10} +(-30456.2 - 52751.6i) q^{11} +(878.486 - 235.390i) q^{12} +(117199. - 117199. i) q^{13} +(-138407. + 49516.6i) q^{14} +(48486.8 + 24082.3i) q^{15} +(-136807. + 236956. i) q^{16} +(84522.3 - 315442. i) q^{17} +(108897. - 406410. 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} +(-536228. + 143682. i) q^{23} +(-218959. - 379248. i) q^{24} +(1.80018e6 + 757652. i) q^{25} +(3.32153e6 + 1.91769e6i) q^{26} +(1.03721e6 + 1.03721e6i) q^{27} +(-84870.7 - 122637. i) q^{28} -5.36320e6i q^{29} +(-247888. + 1.22801e6i) q^{30} +(-885940. + 511497. i) q^{31} +(-525043. - 140685. i) q^{32} +(610716. + 2.27922e6i) q^{33} +7.55694e6 q^{34} +(1.03999e6 - 8.81669e6i) q^{35} +426878. q^{36} +(-3.01894e6 - 1.12669e7i) q^{37} +(6.46641e6 + 1.73267e6i) q^{38} +(-5.56039e6 + 3.21029e6i) q^{39} +(-8.73997e6 - 1.31609e7i) q^{40} +2.35954e6i q^{41} +(5.67539e6 - 465124. i) q^{42} +(-9.45901e6 - 9.45901e6i) q^{43} +(1.23848e6 + 715037. i) q^{44} +(1.90571e7 + 1.68085e7i) q^{45} +(-6.42312e6 - 1.11252e7i) q^{46} +(-4.23397e7 + 1.13449e7i) 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} +(-1.00713e6 + 3.75867e6i) q^{52} +(-1.40178e6 + 5.23150e6i) 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} +(1.19878e8 - 3.21211e7i) q^{58} +(-4.55608e7 - 7.89137e7i) q^{59} +(-1.26854e6 + 79532.0i) q^{60} +(1.10097e8 + 6.35646e7i) q^{61} +(-1.67390e7 - 1.67390e7i) q^{62} +(4.93879e7 - 1.04411e8i) q^{63} +1.27512e8i q^{64} +(-1.92961e8 + 1.28142e8i) q^{65} +(-4.72872e7 + 2.73013e7i) q^{66} +(-2.19419e8 - 5.87933e7i) q^{67} +(1.98438e6 + 7.40581e6i) q^{68} +2.15052e7 q^{69} +(2.03298e8 - 2.95590e7i) q^{70} -3.71610e7 q^{71} +(-5.31988e7 - 1.98541e8i) q^{72} +(1.10030e8 + 2.94824e7i) q^{73} +(2.33755e8 - 1.34958e8i) q^{74} +(-5.97631e7 - 4.63988e7i) q^{75} +6.79207e6i q^{76} +(3.18179e8 - 2.20196e8i) q^{77} +(-1.05058e8 - 1.05058e8i) q^{78} +(-4.88106e8 - 2.81808e8i) q^{79} +(2.52939e8 - 2.86777e8i) q^{80} +(1.50531e8 + 2.60727e8i) q^{81} +(-5.27402e7 + 1.41317e7i) 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} +(-5.37722e7 + 2.00681e8i) q^{87} +(1.78220e8 - 6.65126e8i) 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} +(3.82785e7 - 1.02567e7i) q^{93} +(-5.07159e8 - 8.78425e8i) q^{94} +(-2.67441e8 + 3.03219e8i) q^{95} +(1.82356e7 + 1.05283e7i) q^{96} +(9.93544e8 + 9.93544e8i) q^{97} +(-3.85316e8 - 8.50594e8i) 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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