LMFDB - Embedded newform 35.10.k.a.3.16

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			3.16
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.05635 - 1.62279i) q^{2} +(21.6603 + 80.8372i) q^{3} +(-409.359 - 236.344i) q^{4} +(1391.85 + 125.989i) q^{5} -524.728i q^{6} +(-6352.13 + 63.6305i) q^{7} +(4365.66 + 4365.66i) q^{8} +(10980.5 - 6339.59i) q^{9} +(-8225.08 - 3021.72i) q^{10} +(15736.1 - 27255.8i) q^{11} +(10238.5 - 38210.7i) q^{12} +(-51912.6 + 51912.6i) q^{13} +(38574.0 + 9922.83i) q^{14} +(19963.3 + 115242. i) q^{15} +(101653. + 176067. i) q^{16} +(-14537.4 + 3895.29i) q^{17} +(-76789.5 + 20575.7i) q^{18} +(391609. + 678286. i) q^{19} +(-539991. - 380530. i) q^{20} +(-142733. - 512110. i) q^{21} +(-139534. + 139534. i) q^{22} +(-158327. + 590883. i) q^{23} +(-258347. + 447470. i) q^{24} +(1.92138e6 + 350716. i) q^{25} +(398644. - 230157. i) q^{26} +(1.91509e6 + 1.91509e6i) q^{27} +(2.61534e6 + 1.47524e6i) q^{28} +7.28756e6i q^{29} +(66110.1 - 730344. i) q^{30} +(8.04245e6 + 4.64331e6i) q^{31} +(-1.14807e6 - 4.28465e6i) q^{32} +(2.54413e6 + 681698. i) q^{33} +94365.0 q^{34} +(-8.84924e6 - 711735. i) q^{35} -5.99328e6 q^{36} +(-3.86561e6 - 1.03579e6i) q^{37} +(-1.27100e6 - 4.74344e6i) q^{38} +(-5.32091e6 - 3.07203e6i) q^{39} +(5.52633e6 + 6.62638e6i) q^{40} +4.95585e6i q^{41} +(33388.7 + 3.33314e6i) q^{42} +(-9.30301e6 - 9.30301e6i) q^{43} +(-1.28835e7 + 7.43827e6i) q^{44} +(1.60819e7 - 7.44035e6i) q^{45} +(1.91776e6 - 3.32166e6i) q^{46} +(1.15867e7 - 4.32423e7i) q^{47} +(-1.20310e7 + 1.20310e7i) q^{48} +(4.03455e7 - 808378. i) q^{49} +(-1.10674e7 - 5.24206e6i) q^{50} +(-629769. - 1.09079e6i) q^{51} +(3.35201e7 - 8.98169e6i) q^{52} +(-7.99801e7 + 2.14306e7i) q^{53} +(-8.49068e6 - 1.47063e7i) q^{54} +(2.53363e7 - 3.59534e7i) q^{55} +(-2.80091e7 - 2.74535e7i) q^{56} +(-4.63484e7 + 4.63484e7i) q^{57} +(1.18262e7 - 4.41360e7i) q^{58} +(5.95342e7 - 1.03116e8i) q^{59} +(1.90647e7 - 5.18937e7i) q^{60} +(-8.24305e7 + 4.75913e7i) q^{61} +(-4.11728e7 - 4.11728e7i) q^{62} +(-6.93461e7 + 4.09686e7i) q^{63} -7.62797e7i q^{64} +(-7.87951e7 + 6.57142e7i) q^{65} +(-1.43019e7 - 8.25720e6i) q^{66} +(3.52475e7 + 1.31546e8i) q^{67} +(6.87166e6 + 1.84126e6i) q^{68} -5.11947e7 q^{69} +(5.24391e7 + 1.86710e7i) q^{70} +2.95103e8 q^{71} +(7.56136e7 + 2.02606e7i) q^{72} +(4.67359e7 + 1.74421e8i) q^{73} +(2.17306e7 + 1.25462e7i) q^{74} +(1.32666e7 + 1.62915e8i) q^{75} -3.70217e8i q^{76} +(-9.82237e7 + 1.74134e8i) q^{77} +(2.72400e7 + 2.72400e7i) q^{78} +(-3.03492e7 + 1.75221e7i) q^{79} +(1.19303e8 + 2.57867e8i) q^{80} +(1.14526e7 - 1.98366e7i) q^{81} +(8.04232e6 - 3.00144e7i) q^{82} +(2.43875e8 - 2.43875e8i) q^{83} +(-6.26051e7 + 2.43371e8i) q^{84} +(-2.07247e7 + 3.59011e6i) q^{85} +(4.12454e7 + 7.14391e7i) q^{86} +(-5.89106e8 + 1.57851e8i) q^{87} +(1.87688e8 - 5.02909e7i) q^{88} +(-3.20271e7 - 5.54726e7i) q^{89} +(-1.09472e8 + 1.89637e7i) q^{90} +(3.26452e8 - 3.33059e8i) q^{91} +(2.04464e8 - 2.04464e8i) q^{92} +(-2.01151e8 + 7.50705e8i) q^{93} +(-1.40347e8 + 2.43087e8i) q^{94} +(4.59605e8 + 9.93412e8i) q^{95} +(3.21492e8 - 1.85613e8i) q^{96} +(9.43605e8 + 9.43605e8i) q^{97} +(-2.45658e8 - 6.05766e7i) q^{98} -3.99042e8i 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 $

$2$	−6.05635	−	1.62279i	−0.267655	−	0.0717180i	0.122495	−	0.992469i	$-0.460910\pi$
$2$	−6.05635	−	1.62279i	−0.267655	−	0.0717180i	−0.390151	+	0.920751i	$0.627577\pi$
$3$	21.6603	+	80.8372i	0.154390	+	0.576190i	0.999157	+	0.0410560i	$0.0130722\pi$
$3$	21.6603	+	80.8372i	0.154390	+	0.576190i	−0.844767	+	0.535134i	$0.820261\pi$
$4$	−409.359	−	236.344i	−0.799530	−	0.461609i
$5$	1391.85	+	125.989i	0.995928	+	0.0901505i
$5$	1391.85	+	125.989i	0.995928	+	0.0901505i
$6$		−	524.728i		−	0.165293i
$7$	−6352.13	+	63.6305i	−0.999950	+	0.0100167i
$7$	−6352.13	+	63.6305i	−0.999950	+	0.0100167i
$8$	4365.66	+	4365.66i	0.376830	+	0.376830i
$9$	10980.5	−	6339.59i	0.557867	−	0.322084i
$10$	−8225.08	−	3021.72i	−0.260100	−	0.0955552i
$11$	15736.1	−	27255.8i	0.324064	−	0.561295i	−0.657258	−	0.753665i	$-0.728284\pi$
$11$	15736.1	−	27255.8i	0.324064	−	0.561295i	0.981322	+	0.192370i	$0.0616173\pi$
$12$	10238.5	−	38210.7i	0.142535	−	0.531948i
$13$	−51912.6	+	51912.6i	−0.504113	+	0.504113i	−0.912713	−	0.408601i	$-0.866017\pi$
$13$	−51912.6	+	51912.6i	−0.504113	+	0.504113i	0.408601	+	0.912713i	$0.366017\pi$
$14$	38574.0	+	9922.83i	0.268360	+	0.0690334i
$15$	19963.3	+	115242.i	0.101817	+	0.587762i
$16$	101653.	+	176067.i	0.387774	+	0.671644i
$17$	−14537.4	+	3895.29i	−0.0422151	+	0.0113115i	−0.279865	−	0.960039i	$-0.590290\pi$
$17$	−14537.4	+	3895.29i	−0.0422151	+	0.0113115i	0.237650	+	0.971351i	$0.423623\pi$
$18$	−76789.5	+	20575.7i	−0.172415	+	0.0461985i
$19$	391609.	+	678286.i	0.689384	+	1.19405i	0.972038	+	0.234826i	$0.0754519\pi$
$19$	391609.	+	678286.i	0.689384	+	1.19405i	−0.282654	+	0.959222i	$0.591215\pi$
$20$	−539991.	−	380530.i	−0.754660	−	0.531807i
$21$	−142733.	−	512110.i	−0.160153	−	0.574615i
$22$	−139534.	+	139534.i	−0.126992	+	0.126992i
$23$	−158327.	+	590883.i	−0.117972	+	0.440277i	−0.999492	−	0.0318693i	$-0.989854\pi$
$23$	−158327.	+	590883.i	−0.117972	+	0.440277i	0.881520	+	0.472146i	$0.156521\pi$
$24$	−258347.	+	447470.i	−0.158947	+	0.275304i
$25$	1.92138e6	+	350716.i	0.983746	+	0.179567i
$26$	398644.	−	230157.i	0.171082	−	0.0987745i
$27$	1.91509e6	+	1.91509e6i	0.693511	+	0.693511i
$28$	2.61534e6	+	1.47524e6i	0.804113	+	0.453577i
$29$			7.28756e6i			1.91334i	0.291179	+	0.956668i	$0.405952\pi$
$29$			7.28756e6i			1.91334i	−0.291179	+	0.956668i	$0.594048\pi$
$30$	66110.1	−	730344.i	0.0149012	−	0.164620i
$31$	8.04245e6	+	4.64331e6i	1.56409	+	0.903026i	0.996836	+	0.0794811i	$0.0253263\pi$
$31$	8.04245e6	+	4.64331e6i	1.56409	+	0.903026i	0.567251	+	0.823545i	$0.308007\pi$
$32$	−1.14807e6	−	4.28465e6i	−0.193550	−	0.722339i
$33$	2.54413e6	+	681698.i	0.373445	+	0.100064i
$34$	94365.0			0.0121103
$35$	−8.84924e6	−	711735.i	−0.996781	−	0.0801700i
$36$	−5.99328e6			−0.594708
$37$	−3.86561e6	−	1.03579e6i	−0.339087	−	0.0908580i	0.0852576	−	0.996359i	$-0.472829\pi$
$37$	−3.86561e6	−	1.03579e6i	−0.339087	−	0.0908580i	−0.424344	+	0.905501i	$0.639495\pi$
$38$	−1.27100e6	−	4.74344e6i	−0.0988825	−	0.369034i
$39$	−5.32091e6	−	3.07203e6i	−0.368295	−	0.212635i
$40$	5.52633e6	+	6.62638e6i	0.341324	+	0.409267i
$41$			4.95585e6i			0.273899i	0.990578	+	0.136950i	$0.0437299\pi$
$41$			4.95585e6i			0.273899i	−0.990578	+	0.136950i	$0.956270\pi$
$42$	33388.7	+	3.33314e6i	0.00165569	+	0.165285i
$43$	−9.30301e6	−	9.30301e6i	−0.414969	−	0.414969i	0.468497	−	0.883465i	$-0.344796\pi$
$43$	−9.30301e6	−	9.30301e6i	−0.414969	−	0.414969i	−0.883465	+	0.468497i	$0.844796\pi$
$44$	−1.28835e7	+	7.43827e6i	−0.518198	+	0.299182i
$45$	1.60819e7	−	7.44035e6i	0.584631	−	0.270481i
$46$	1.91776e6	−	3.32166e6i	0.0631516	−	0.109382i
$47$	1.15867e7	−	4.32423e7i	0.346354	−	1.29261i	−0.544668	−	0.838652i	$-0.683344\pi$
$47$	1.15867e7	−	4.32423e7i	0.346354	−	1.29261i	0.891022	−	0.453960i	$-0.149989\pi$
$48$	−1.20310e7	+	1.20310e7i	−0.327126	+	0.327126i
$49$	4.03455e7	−	808378.i	0.999799	−	0.0200324i
$50$	−1.10674e7	−	5.24206e6i	−0.250427	−	0.118614i
$51$	−629769.	−	1.09079e6i	−0.0130351	−	0.0225775i
$52$	3.35201e7	−	8.98169e6i	0.635756	−	0.170350i
$53$	−7.99801e7	+	2.14306e7i	−1.39232	+	0.373072i	−0.875582	−	0.483069i	$-0.839522\pi$
$53$	−7.99801e7	+	2.14306e7i	−1.39232	+	0.373072i	−0.516742	+	0.856141i	$0.672855\pi$
$54$	−8.49068e6	−	1.47063e7i	−0.135885	−	0.235359i
$55$	2.53363e7	−	3.59534e7i	0.373346	−	0.529795i
$56$	−2.80091e7	−	2.74535e7i	−0.380586	−	0.373036i
$57$	−4.63484e7	+	4.63484e7i	−0.581565	+	0.581565i
$58$	1.18262e7	−	4.41360e7i	0.137221	−	0.512115i
$59$	5.95342e7	−	1.03116e8i	0.639636	−	1.10788i	−0.345877	−	0.938280i	$-0.612419\pi$
$59$	5.95342e7	−	1.03116e8i	0.639636	−	1.10788i	0.985513	−	0.169601i	$-0.0542480\pi$
$60$	1.90647e7	−	5.18937e7i	0.189910	−	0.516933i
$61$	−8.24305e7	+	4.75913e7i	−0.762261	+	0.440091i	−0.830107	−	0.557604i	$-0.811721\pi$
$61$	−8.24305e7	+	4.75913e7i	−0.762261	+	0.440091i	0.0678462	+	0.997696i	$0.478387\pi$
$62$	−4.11728e7	−	4.11728e7i	−0.353873	−	0.353873i
$63$	−6.93461e7	+	4.09686e7i	−0.554612	+	0.327656i
$64$		−	7.62797e7i		−	0.568328i
$65$	−7.87951e7	+	6.57142e7i	−0.547506	+	0.456614i
$66$	−1.43019e7	−	8.25720e6i	−0.0927781	−	0.0535655i
$67$	3.52475e7	+	1.31546e8i	0.213694	+	0.797516i	0.986622	+	0.163023i	$0.0521245\pi$
$67$	3.52475e7	+	1.31546e8i	0.213694	+	0.797516i	−0.772928	+	0.634493i	$0.781209\pi$
$68$	6.87166e6	+	1.84126e6i	0.0389737	+	0.0104430i
$69$	−5.11947e7			−0.271897
$70$	5.24391e7	+	1.86710e7i	0.261044	+	0.0929451i
$71$	2.95103e8			1.37820			0.689099	−	0.724668i	$-0.258007\pi$
$71$	2.95103e8			1.37820			0.689099	+	0.724668i	$0.258007\pi$
$72$	7.56136e7	+	2.02606e7i	0.331592	+	0.0888498i
$73$	4.67359e7	+	1.74421e8i	0.192619	+	0.718862i	0.992870	+	0.119198i	$0.0380324\pi$
$73$	4.67359e7	+	1.74421e8i	0.192619	+	0.718862i	−0.800252	+	0.599664i	$0.795301\pi$
$74$	2.17306e7	+	1.25462e7i	0.0842422	+	0.0486372i
$75$	1.32666e7	+	1.62915e8i	0.0484156	+	0.594548i
$76$		−	3.70217e8i		−	1.27290i
$77$	−9.82237e7	+	1.74134e8i	−0.318425	+	0.564513i
$78$	2.72400e7	+	2.72400e7i	0.0833262	+	0.0833262i
$79$	−3.03492e7	+	1.75221e7i	−0.0876649	+	0.0506133i	−0.543192	−	0.839609i	$-0.682784\pi$
$79$	−3.03492e7	+	1.75221e7i	−0.0876649	+	0.0506133i	0.455527	+	0.890222i	$0.349451\pi$
$80$	1.19303e8	+	2.57867e8i	0.325646	+	0.703867i
$81$	1.14526e7	−	1.98366e7i	0.0295613	−	0.0512016i
$82$	8.04232e6	−	3.00144e7i	0.0196435	−	0.0733106i
$83$	2.43875e8	−	2.43875e8i	0.564048	−	0.564048i	−0.366407	−	0.930455i	$-0.619412\pi$
$83$	2.43875e8	−	2.43875e8i	0.564048	−	0.564048i	0.930455	+	0.366407i	$0.119412\pi$
$84$	−6.26051e7	+	2.43371e8i	−0.137200	+	0.533350i
$85$	−2.07247e7	+	3.59011e6i	−0.0430629	+	0.00745973i
$86$	4.12454e7	+	7.14391e7i	0.0813079	+	0.140829i
$87$	−5.89106e8	+	1.57851e8i	−1.10245	+	0.295399i
$88$	1.87688e8	−	5.02909e7i	0.333630	−	0.0893959i
$89$	−3.20271e7	−	5.54726e7i	−0.0541082	−	0.0937181i	0.837703	−	0.546127i	$-0.183898\pi$
$89$	−3.20271e7	−	5.54726e7i	−0.0541082	−	0.0937181i	−0.891811	+	0.452409i	$0.850565\pi$
$90$	−1.09472e8	+	1.89637e7i	−0.175878	+	0.0304671i
$91$	3.26452e8	−	3.33059e8i	0.499038	−	0.509137i
$92$	2.04464e8	−	2.04464e8i	0.297558	−	0.297558i
$93$	−2.01151e8	+	7.50705e8i	−0.278836	+	1.04063i
$94$	−1.40347e8	+	2.43087e8i	−0.185407	+	0.321135i
$95$	4.59605e8	+	9.93412e8i	0.578933	+	1.25133i
$96$	3.21492e8	−	1.85613e8i	0.386322	−	0.223043i
$97$	9.43605e8	+	9.43605e8i	1.08222	+	1.08222i	0.996302	+	0.0859232i	$0.0273840\pi$
$97$	9.43605e8	+	9.43605e8i	1.08222	+	1.08222i	0.0859232	+	0.996302i	$0.472616\pi$
$98$	−2.45658e8	−	6.05766e7i	−0.269038	−	0.0663419i
$99$		−	3.99042e8i		−	0.417504i
$100$	−7.03644e8	−	5.97674e8i	−0.703644	−	0.597674i
$101$	3.03333e8	+	1.75129e8i	0.290050	+	0.167461i	0.637965	−	0.770066i	$-0.279777\pi$
$101$	3.03333e8	+	1.75129e8i	0.290050	+	0.167461i	−0.347914	+	0.937526i	$0.613110\pi$
$102$	2.04397e6	+	7.62821e6i	0.00186971	+	0.00697785i
$103$	−1.17644e9	−	3.15227e8i	−1.02992	−	0.275967i	−0.295990	−	0.955191i	$-0.595650\pi$
$103$	−1.17644e9	−	3.15227e8i	−1.02992	−	0.275967i	−0.733931	+	0.679224i	$0.762316\pi$
$104$	−4.53266e8			−0.379930
$105$	−1.34142e8	−	7.30764e8i	−0.107700	−	0.586713i
$106$	5.19165e8			0.399419
$107$	1.24471e9	+	3.33520e8i	0.918000	+	0.245977i	0.686730	−	0.726912i	$-0.259045\pi$
$107$	1.24471e9	+	3.33520e8i	0.918000	+	0.245977i	0.231269	+	0.972890i	$0.425712\pi$
$108$	−3.31341e8	−	1.23658e9i	−0.234352	−	0.874613i
$109$	−1.03842e9	−	5.99532e8i	−0.704618	−	0.406811i	0.104447	−	0.994530i	$-0.466693\pi$
$109$	−1.03842e9	−	5.99532e8i	−0.704618	−	0.406811i	−0.809065	+	0.587719i	$0.800026\pi$
$110$	−2.11790e8	+	1.76631e8i	−0.137924	+	0.115027i
$111$		−	3.34921e8i		−	0.209406i
$112$	−6.56913e8	−	1.11193e9i	−0.394482	−	0.667726i
$113$	−1.50124e9	−	1.50124e9i	−0.866160	−	0.866160i	0.125885	−	0.992045i	$-0.459823\pi$
$113$	−1.50124e9	−	1.50124e9i	−0.866160	−	0.866160i	−0.992045	+	0.125885i	$0.959823\pi$
$114$	3.55916e8	−	2.05488e8i	0.197367	−	0.113950i
$115$	−2.94812e8	+	8.02474e8i	−0.157183	+	0.427849i
$116$	1.72237e9	−	2.98323e9i	0.883213	−	1.52977i
$117$	−2.40921e8	+	8.99130e8i	−0.118861	+	0.443595i
$118$	−5.27896e8	+	5.27896e8i	−0.250657	+	0.250657i
$119$	9.20958e7	−	2.56684e7i	0.0420997	−	0.0117338i
$120$	−4.15957e8	+	5.90263e8i	−0.183119	+	0.259854i
$121$	6.83722e8	+	1.18424e9i	0.289965	+	0.502234i
$122$	5.76458e8	−	1.54462e8i	0.235586	−	0.0631250i
$123$	−4.00617e8	+	1.07345e8i	−0.157818	+	0.0422872i
$124$	−2.19483e9	−	3.80156e9i	−0.833689	−	1.44399i
$125$	2.63009e9	+	7.30218e8i	0.963552	+	0.267521i
$126$	4.86468e8	−	1.35586e8i	0.171944	−	0.0479232i
$127$	−2.36202e9	+	2.36202e9i	−0.805687	+	0.805687i	−0.983978	−	0.178291i	$-0.942943\pi$
$127$	−2.36202e9	+	2.36202e9i	−0.805687	+	0.805687i	0.178291	+	0.983978i	$0.442943\pi$
$128$	−7.11598e8	+	2.65572e9i	−0.234309	+	0.874455i
$129$	5.50524e8	−	9.53535e8i	0.175034	−	0.303168i
$130$	5.83851e8	−	2.70120e8i	0.179290	−	0.0829491i
$131$	−1.40365e9	+	8.10397e8i	−0.416426	+	0.240424i	−0.693547	−	0.720411i	$-0.743953\pi$
$131$	−1.40365e9	+	8.10397e8i	−0.416426	+	0.240424i	0.277121	+	0.960835i	$0.410620\pi$
$132$	−8.80348e8	−	8.80348e8i	−0.252390	−	0.252390i
$133$	−2.53071e9	−	4.28364e9i	−0.701310	−	1.18708i
$134$		−	8.53885e8i		−	0.228785i
$135$	2.42425e9	+	2.90681e9i	0.628167	+	0.753207i
$136$	−8.04711e7	−	4.64600e7i	−0.0201704	−	0.0116454i
$137$	−1.01864e9	−	3.80162e9i	−0.247047	−	0.921991i	−0.972344	−	0.233555i	$-0.924964\pi$
$137$	−1.01864e9	−	3.80162e9i	−0.247047	−	0.921991i	0.725297	−	0.688436i	$-0.241702\pi$
$138$	3.10053e8	+	8.30785e7i	0.0727746	+	0.0194999i
$139$	7.93977e7			0.0180402			0.00902010	−	0.999959i	$-0.497129\pi$
$139$	7.93977e7			0.0180402			0.00902010	+	0.999959i	$0.497129\pi$
$140$	3.45430e9	+	2.38282e9i	0.759949	+	0.524221i
$141$	3.74656e9			0.798263
$142$	−1.78725e9	−	4.78892e8i	−0.368882	−	0.0988416i
$143$	5.98015e8	+	2.23182e9i	0.119591	+	0.446321i
$144$	2.23239e9	+	1.28887e9i	0.432652	+	0.249792i
$145$	−9.18154e8	+	1.01432e10i	−0.172488	+	1.90555i
$146$		−	1.13220e9i		−	0.206222i
$147$	9.39242e8	+	3.24391e9i	0.165901	+	0.572982i
$148$	1.33762e9	+	1.33762e9i	0.229169	+	0.229169i
$149$	−5.19264e9	+	2.99797e9i	−0.863078	+	0.498298i	−0.865042	−	0.501700i	$-0.832708\pi$
$149$	−5.19264e9	+	2.99797e9i	−0.863078	+	0.498298i	0.00196393	+	0.999998i	$0.499375\pi$
$150$	1.84031e8	−	1.00820e9i	0.0296811	−	0.162606i
$151$	4.20657e9	−	7.28599e9i	0.658464	−	1.14049i	−0.322550	−	0.946553i	$-0.604540\pi$
$151$	4.20657e9	−	7.28599e9i	0.658464	−	1.14049i	0.981013	−	0.193940i	$-0.0621268\pi$
$152$	−1.25154e9	+	4.67080e9i	−0.190172	+	0.709733i
$153$	−1.34934e8	+	1.34934e8i	−0.0199071	+	0.0199071i
$154$	8.77459e8	−	8.95217e8i	0.125714	−	0.128258i
$155$	1.06089e10	+	7.47607e9i	1.47631	+	1.04035i
$156$	1.45211e9	+	2.51513e9i	0.196308	+	0.340016i
$157$	−3.24593e9	+	8.69745e8i	−0.426374	+	0.114247i	−0.465624	−	0.884983i	$-0.654170\pi$
$157$	−3.24593e9	+	8.69745e8i	−0.426374	+	0.114247i	0.0392494	+	0.999229i	$0.487503\pi$
$158$	2.12240e8	−	5.68696e7i	0.0270939	−	0.00725978i
$159$	−3.46478e9	−	6.00118e9i	−0.429921	−	0.744645i
$160$	−1.05812e9	−	6.10825e9i	−0.127643	−	0.736846i
$161$	9.68113e8	−	3.76344e9i	0.113556	−	0.441437i
$162$	−1.01552e8	+	1.01552e8i	−0.0115843	+	0.0115843i
$163$	−1.44709e9	+	5.40060e9i	−0.160565	+	0.599236i	0.838000	+	0.545671i	$0.183725\pi$
$163$	−1.44709e9	+	5.40060e9i	−0.160565	+	0.599236i	−0.998564	+	0.0535649i	$0.982942\pi$
$164$	1.17128e9	−	2.02872e9i	0.126434	−	0.218991i
$165$	3.45517e9	+	1.26935e9i	0.362903	+	0.133323i
$166$	−1.87275e9	+	1.08123e9i	−0.191423	+	0.110518i
$167$	7.57451e8	+	7.57451e8i	0.0753581	+	0.0753581i	0.743781	−	0.668423i	$-0.233030\pi$
$167$	7.57451e8	+	7.57451e8i	0.0753581	+	0.0753581i	−0.668423	+	0.743781i	$0.733030\pi$
$168$	1.61258e9	−	2.85882e9i	0.156181	−	0.276883i
$169$			5.21466e9i			0.491741i
$170$	1.31342e8	+	1.18890e7i	0.0120610	+	0.00109175i
$171$	8.60011e9	+	4.96527e9i	0.769168	+	0.444080i
$172$	1.60957e9	+	6.00698e9i	0.140227	+	0.523333i
$173$	−1.73436e10	−	4.64720e9i	−1.47208	−	0.394443i	−0.568437	−	0.822727i	$-0.692452\pi$
$173$	−1.73436e10	−	4.64720e9i	−1.47208	−	0.394443i	−0.903644	+	0.428284i	$0.859118\pi$
$174$	3.82399e9			0.316261
$175$	−1.22272e10	−	2.10554e9i	−0.985495	−	0.169704i
$176$	6.39847e9			0.502654
$177$	9.62516e9	+	2.57905e9i	0.737103	+	0.197506i
$178$	1.03947e8	+	3.87935e8i	0.00776106	+	0.0289647i
$179$	−1.43711e9	−	8.29718e8i	−0.104629	−	0.0604076i	0.446772	−	0.894648i	$-0.352573\pi$
$179$	−1.43711e9	−	8.29718e8i	−0.104629	−	0.0604076i	−0.551401	+	0.834240i	$0.685907\pi$
$180$	−8.34176e9	−	7.55089e8i	−0.592286	−	0.0536132i
$181$		−	2.30426e10i		−	1.59580i	−0.602793	−	0.797898i	$-0.705945\pi$
$181$		−	2.30426e10i		−	1.59580i	0.602793	−	0.797898i	$-0.294055\pi$
$182$	−2.51759e9	+	1.48736e9i	−0.170084	+	0.100483i
$183$	−5.63261e9	−	5.63261e9i	−0.371261	−	0.371261i
$184$	−3.27080e9	+	1.88840e9i	−0.210365	+	0.121454i
$185$	−5.24986e9	−	1.92869e9i	−0.329515	−	0.121057i
$186$	2.43648e9	−	4.22010e9i	0.149264	−	0.258532i
$187$	−1.22594e8	+	4.57526e8i	−0.00733130	+	0.0273608i
$188$	−1.49632e10	+	1.49632e10i	−0.873601	+	0.873601i
$189$	−1.22868e10	−	1.20431e10i	−0.700423	−	0.686530i
$190$	−1.17142e9	−	6.76229e9i	−0.0652112	−	0.376446i
$191$	6.88318e9	+	1.19220e10i	0.374230	+	0.648185i	0.990211	−	0.139575i	$-0.0445737\pi$
$191$	6.88318e9	+	1.19220e10i	0.374230	+	0.648185i	−0.615981	+	0.787761i	$0.711240\pi$
$192$	6.16624e9	−	1.65224e9i	0.327465	−	0.0877440i
$193$	2.60310e10	−	6.97499e9i	1.35046	−	0.361856i	0.490158	−	0.871633i	$-0.336939\pi$
$193$	2.60310e10	−	6.97499e9i	1.35046	−	0.361856i	0.860306	+	0.509778i	$0.170272\pi$
$194$	−4.18352e9	−	7.24608e9i	−0.212048	−	0.367278i
$195$	−7.01888e9	−	4.94619e9i	−0.347626	−	0.244971i
$196$	−1.67069e10	−	9.20449e9i	−0.808616	−	0.445499i
$197$	6.92580e9	−	6.92580e9i	0.327621	−	0.327621i	−0.524060	−	0.851681i	$-0.675583\pi$
$197$	6.92580e9	−	6.92580e9i	0.327621	−	0.327621i	0.851681	+	0.524060i	$0.175583\pi$
$198$	−6.47563e8	+	2.41674e9i	−0.0299426	+	0.111747i
$199$	1.26833e9	−	2.19681e9i	0.0573316	−	0.0993012i	−0.835935	−	0.548828i	$-0.815074\pi$
$199$	1.26833e9	−	2.19681e9i	0.0573316	−	0.0993012i	0.893267	+	0.449527i	$0.148407\pi$
$200$	6.85698e9	+	9.91920e9i	0.303039	+	0.438371i
$201$	−9.87030e9	+	5.69862e9i	−0.426529	+	0.246256i
$202$	−1.55289e9	−	1.55289e9i	−0.0656236	−	0.0656236i
$203$	−4.63711e8	−	4.62916e10i	−0.0191653	−	1.91324i
$204$			5.95368e8i			0.0240685i
$205$	−6.24383e8	+	6.89781e9i	−0.0246921	+	0.272784i
$206$	6.61341e9	+	3.81825e9i	0.255872	+	0.147728i
$207$	2.00745e9	+	7.49191e9i	0.0759938	+	0.283613i
$208$	−1.44172e10	−	3.86307e9i	−0.534066	−	0.143102i
$209$	2.46496e10			0.893618
$210$	−3.73468e8	+	4.64345e9i	−0.0132515	+	0.164761i
$211$	1.25279e10			0.435119			0.217559	−	0.976047i	$-0.430190\pi$
$211$	1.25279e10			0.435119			0.217559	+	0.976047i	$0.430190\pi$
$212$	3.78056e10	+	1.01300e10i	1.28542	+	0.344427i
$213$	6.39201e9	+	2.38553e10i	0.212779	+	0.794103i
$214$	−6.99719e9	−	4.03983e9i	−0.228066	−	0.131674i
$215$	−1.17763e10	−	1.41205e10i	−0.375869	−	0.450689i
$216$			1.67213e10i			0.522671i
$217$	−5.13822e10	−	2.89832e10i	−1.57305	−	0.887314i
$218$	5.31611e9	+	5.31611e9i	0.159419	+	0.159419i
$219$	−1.30874e10	+	7.55601e9i	−0.384463	+	0.221970i
$220$	−1.88690e10	+	8.72979e9i	−0.543059	+	0.251248i
$221$	5.52461e8	−	9.56891e8i	0.0155789	−	0.0269834i
$222$	−5.43507e8	+	2.02840e9i	−0.0150182	+	0.0560486i
$223$	−1.96985e7	+	1.96985e7i	−0.000533411	+	0.000533411i	−0.707373	−	0.706840i	$-0.750120\pi$
$223$	−1.96985e7	+	1.96985e7i	−0.000533411	+	0.000533411i	0.706840	+	0.707373i	$0.250120\pi$
$224$	7.56532e9	+	2.71436e10i	0.200776	+	0.720364i
$225$	2.33211e10	−	8.32971e9i	0.606635	−	0.216675i
$226$	6.65585e9	+	1.15283e10i	0.169713	+	0.293952i
$227$	2.66545e10	−	7.14206e9i	0.666277	−	0.178528i	0.0901997	−	0.995924i	$-0.471249\pi$
$227$	2.66545e10	−	7.14206e9i	0.666277	−	0.178528i	0.576077	+	0.817395i	$0.304583\pi$
$228$	2.99273e10	−	8.01899e9i	0.733433	−	0.196523i
$229$	2.91621e9	+	5.05102e9i	0.0700743	+	0.121372i	0.898934	−	0.438085i	$-0.144343\pi$
$229$	2.91621e9	+	5.05102e9i	0.0700743	+	0.121372i	−0.828859	+	0.559457i	$0.811010\pi$
$230$	3.08773e9	−	4.38164e9i	0.0727553	−	0.103243i
$231$	−1.62040e10	−	4.16835e9i	−0.374429	−	0.0963186i
$232$	−3.18151e10	+	3.18151e10i	−0.721003	+	0.721003i
$233$	−1.57210e10	+	5.86715e10i	−0.349444	+	1.30414i	0.537890	+	0.843015i	$0.319222\pi$
$233$	−1.57210e10	+	5.86715e10i	−0.349444	+	1.30414i	−0.887334	+	0.461128i	$0.847445\pi$
$234$	2.91821e9	−	5.05448e9i	0.0636274	−	0.110206i
$235$	2.15751e10	−	5.87270e10i	0.461473	−	1.25612i
$236$	−4.87417e10	+	2.81411e10i	−1.02281	+	0.590523i
$237$	−2.07381e9	−	2.07381e9i	−0.0426975	−	0.0426975i
$238$	−5.99419e8	+	6.00449e6i	−0.0121097	+	0.000121305i
$239$			3.32434e10i			0.659044i	0.944148	+	0.329522i	$0.106888\pi$
$239$			3.32434e10i			0.659044i	−0.944148	+	0.329522i	$0.893112\pi$
$240$	−1.82611e10	+	1.52296e10i	−0.355285	+	0.296303i
$241$	−4.49640e10	−	2.59600e10i	−0.858595	−	0.495710i	0.00494685	−	0.999988i	$-0.498425\pi$
$241$	−4.49640e10	−	2.59600e10i	−0.858595	−	0.495710i	−0.863541	+	0.504278i	$0.831759\pi$
$242$	−2.21908e9	−	8.28172e9i	−0.0415914	−	0.155221i
$243$	5.33437e10	+	1.42934e10i	0.981420	+	0.262971i
$244$	4.49916e10			0.812600
$245$	5.62568e10	+	3.95795e9i	0.997534	+	0.0701816i
$246$	2.60048e9			0.0452736
$247$	−5.55410e10	−	1.48822e10i	−0.949462	−	0.254408i
$248$	1.48395e10	+	5.53818e10i	0.249108	+	0.929682i
$249$	2.49966e10	+	1.44318e10i	0.412082	+	0.237916i
$250$	−1.47437e10	−	8.69054e9i	−0.238714	−	0.140707i
$251$		−	5.44822e10i		−	0.866408i	−0.901296	−	0.433204i	$-0.857383\pi$
$251$		−	5.44822e10i		−	0.866408i	0.901296	−	0.433204i	$-0.142617\pi$
$252$	3.80701e10	−	3.81356e8i	0.594678	−	0.00595700i
$253$	1.36135e10	+	1.36135e10i	0.208895	+	0.208895i
$254$	1.81383e10	−	1.04721e10i	0.273429	−	0.157864i
$255$	−7.39118e8	−	1.59757e9i	−0.0109467	−	0.0236607i
$256$	−1.09082e10	+	1.88936e10i	−0.158736	+	0.274939i
$257$	7.23834e9	−	2.70138e10i	0.103500	−	0.386267i	−0.894671	−	0.446726i	$-0.852590\pi$
$257$	7.23834e9	−	2.70138e10i	0.103500	−	0.386267i	0.998171	+	0.0604593i	$0.0192565\pi$
$258$	−4.88155e9	+	4.88155e9i	−0.0685914	+	0.0685914i
$259$	2.46208e10	+	6.33349e9i	0.339980	+	0.0874569i
$260$	4.77866e10	−	8.27801e9i	0.648524	−	0.112343i
$261$	4.62002e10	+	8.00210e10i	0.616256	+	1.06739i
$262$	9.81610e9	−	2.63021e9i	0.128701	−	0.0344854i
$263$	3.37220e10	−	9.03579e9i	0.434623	−	0.116457i	−0.0348724	−	0.999392i	$-0.511102\pi$
$263$	3.37220e10	−	9.03579e9i	0.434623	−	0.116457i	0.469496	+	0.882935i	$0.344436\pi$
$264$	8.13075e9	+	1.40829e10i	0.103018	+	0.178432i
$265$	−1.14020e11	+	1.97516e10i	−1.42029	+	0.246034i
$266$	8.37538e9	+	3.00500e10i	0.102574	+	0.368025i
$267$	3.79053e9	−	3.79053e9i	0.0456457	−	0.0456457i
$268$	1.66611e10	−	6.21799e10i	0.197286	−	0.736281i
$269$	−9.38488e9	+	1.62551e10i	−0.109281	+	0.189280i	−0.915479	−	0.402366i	$-0.868188\pi$
$269$	−9.38488e9	+	1.62551e10i	−0.109281	+	0.189280i	0.806198	+	0.591645i	$0.201521\pi$
$270$	−9.96493e9	−	2.15387e10i	−0.114114	−	0.246651i
$271$	−1.35677e11	+	7.83330e10i	−1.52807	+	0.882232i	−0.528627	+	0.848854i	$0.677293\pi$
$271$	−1.35677e11	+	7.83330e10i	−1.52807	+	0.882232i	−0.999443	+	0.0333779i	$0.989374\pi$
$272$	−2.16360e9	−	2.16360e9i	−0.0239672	−	0.0239672i
$273$	3.39946e10	+	1.91754e10i	0.370406	+	0.208935i
$274$			2.46770e10i			0.264493i
$275$	3.97941e10	−	4.68497e10i	0.419587	−	0.493981i
$276$	2.09570e10	+	1.20995e10i	0.217390	+	0.125510i
$277$	−2.70257e10	−	1.00861e11i	−0.275815	−	1.02935i	−0.955293	−	0.295659i	$-0.904461\pi$
$277$	−2.70257e10	−	1.00861e11i	−0.275815	−	1.02935i	0.679479	−	0.733695i	$-0.262206\pi$
$278$	−4.80860e8	−	1.28846e8i	−0.00482856	−	0.00129381i
$279$	1.17747e11			1.16340
$280$	−3.55256e10	−	4.17400e10i	−0.345407	−	0.405827i
$281$	−8.29793e10			−0.793947			−0.396973	−	0.917830i	$-0.629940\pi$
$281$	−8.29793e10			−0.793947			−0.396973	+	0.917830i	$0.629940\pi$
$282$	−2.26904e10	−	6.07989e9i	−0.213659	−	0.0572499i
$283$	−4.88082e10	−	1.82155e11i	−0.452328	−	1.68811i	−0.695826	−	0.718210i	$-0.744962\pi$
$283$	−4.88082e10	−	1.82155e11i	−0.452328	−	1.68811i	0.243498	−	0.969901i	$-0.421705\pi$
$284$	−1.20803e11	−	6.97457e10i	−1.10191	−	0.636188i
$285$	−7.03495e10	+	5.86707e10i	−0.631625	+	0.526768i
$286$		−	1.44871e10i		−	0.128037i
$287$	−3.15343e8	−	3.14802e10i	−0.00274356	−	0.273886i
$288$	−3.97693e10	−	3.97693e10i	−0.340629	−	0.340629i
$289$	−1.02504e11	+	5.91807e10i	−0.864371	+	0.499045i
$290$	2.20210e10	−	5.99408e10i	0.182829	−	0.497659i
$291$	−5.58397e10	+	9.67172e10i	−0.456483	+	0.790651i
$292$	2.20915e10	−	8.24465e10i	0.177829	−	0.663666i
$293$	−2.40273e10	+	2.40273e10i	−0.190459	+	0.190459i	−0.795894	−	0.605435i	$-0.792999\pi$
$293$	−2.40273e10	+	2.40273e10i	−0.190459	+	0.190459i	0.605435	+	0.795894i	$0.292999\pi$
$294$	−4.24179e8	−	2.11704e10i	−0.00331121	−	0.165260i
$295$	9.58543e10	−	1.36022e11i	0.736907	−	1.04571i
$296$	−1.23541e10	−	2.13979e10i	−0.0935400	−	0.162016i
$297$	8.23336e10	−	2.20612e10i	0.614007	−	0.164523i
$298$	3.63135e10	−	9.73018e9i	0.266744	−	0.0714739i
$299$	−2.24551e10	−	3.88934e10i	−0.162478	−	0.281420i
$300$	3.30732e10	−	6.98264e10i	0.235739	−	0.497708i
$301$	5.96859e10	+	5.85020e10i	0.419105	+	0.410791i
$302$	−3.73001e10	+	3.73001e10i	−0.258035	+	0.258035i
$303$	−7.58670e9	+	2.83139e10i	−0.0517084	+	0.192978i
$304$	−7.96160e10	+	1.37899e11i	−0.534650	+	0.926040i
$305$	−1.20727e11	+	5.58546e10i	−0.798831	+	0.369581i
$306$	1.03617e9	−	5.98235e8i	0.00675595	−	0.00390055i
$307$	8.86323e9	+	8.86323e9i	0.0569468	+	0.0569468i	0.735007	−	0.678060i	$-0.237179\pi$
$307$	8.86323e9	+	8.86323e9i	0.0569468	+	0.0569468i	−0.678060	+	0.735007i	$0.737179\pi$
$308$	8.13641e10	−	4.80686e10i	0.515175	−	0.304357i
$309$		−	1.01928e11i		−	0.636037i
$310$	−5.21191e10	−	6.24937e10i	−0.320530	−	0.384334i
$311$	1.89438e9	+	1.09372e9i	0.0114827	+	0.00662956i	0.505730	−	0.862692i	$-0.331223\pi$
$311$	1.89438e9	+	1.09372e9i	0.0114827	+	0.00662956i	−0.494248	+	0.869321i	$0.664556\pi$
$312$	−9.81786e9	−	3.66408e10i	−0.0586572	−	0.218912i
$313$	2.26100e11	+	6.05834e10i	1.33153	+	0.356783i	0.853286	−	0.521443i	$-0.174606\pi$
$313$	2.26100e11	+	6.05834e10i	1.33153	+	0.356783i	0.478246	+	0.878226i	$0.341273\pi$
$314$	2.10699e10			0.122315
$315$	−1.01681e11	+	4.82854e10i	−0.581893	+	0.276324i
$316$	1.65650e10			0.0934542
$317$	2.87425e11	+	7.70152e10i	1.59866	+	0.428361i	0.944639	−	0.328112i	$-0.106412\pi$
$317$	2.87425e11	+	7.70152e10i	1.59866	+	0.428361i	0.654025	+	0.756473i	$0.273079\pi$
$318$	1.12452e10	+	4.19678e10i	0.0616662	+	0.230141i
$319$	1.98628e11	+	1.14678e11i	1.07395	+	0.620044i
$320$	9.61042e9	−	1.06170e11i	0.0512351	−	0.566014i
$321$			1.07843e11i			0.566919i
$322$	−1.19705e10	+	2.12216e10i	−0.0620528	+	0.110009i
$323$	−8.33511e9	−	8.33511e9i	−0.0426089	−	0.0426089i
$324$	−9.37649e9	+	5.41352e9i	−0.0472702	+	0.0272915i
$325$	−1.17950e11	+	8.15372e10i	−0.586441	+	0.405397i
$326$	1.75281e10	−	3.03596e10i	0.0859520	−	0.148873i
$327$	2.59720e10	−	9.69290e10i	0.125615	−	0.468801i
$328$	−2.16356e10	+	2.16356e10i	−0.103213	+	0.103213i
$329$	−7.08489e10	+	2.75418e11i	−0.333389	+	1.29602i
$330$	−1.88658e10	−	1.32947e10i	−0.0875714	−	0.0617113i
$331$	−1.79417e11	−	3.10760e11i	−0.821558	−	1.42298i	−0.904522	−	0.426427i	$-0.859772\pi$
$331$	−1.79417e11	−	3.10760e11i	−0.821558	−	1.42298i	0.0829639	−	0.996553i	$-0.473561\pi$
$332$	−1.57471e11	+	4.21942e10i	−0.711343	+	0.190604i
$333$	−4.90128e10	+	1.31329e10i	−0.218429	+	0.0585279i
$334$	−3.35820e9	−	5.81657e9i	−0.0147655	−	0.0255745i
$335$	3.24860e10	+	1.87533e11i	0.140927	+	0.813533i
$336$	7.56568e10	−	7.71878e10i	0.323833	−	0.330386i
$337$	−2.19428e11	+	2.19428e11i	−0.926740	+	0.926740i	−0.997494	−	0.0707536i	$-0.977460\pi$
$337$	−2.19428e11	+	2.19428e11i	−0.926740	+	0.926740i	0.0707536	+	0.997494i	$0.477460\pi$
$338$	8.46232e9	−	3.15818e10i	0.0352667	−	0.131617i
$339$	8.88390e10	−	1.53874e11i	0.365347	−	0.632799i
$340$	9.33235e9	+	3.42851e9i	0.0378736	+	0.0139139i
$341$	2.53114e11	−	1.46136e11i	1.01373	−	0.585277i
$342$	−4.40276e10	−	4.40276e10i	−0.174023	−	0.174023i
$343$	−2.56228e11	+	7.70213e9i	−0.999549	+	0.0300460i
$344$		−	8.12276e10i		−	0.312745i
$345$	−7.12555e10	−	6.44998e9i	−0.270790	−	0.0245116i
$346$	9.74974e10	+	5.62902e10i	0.365722	+	0.211149i
$347$	1.17266e11	+	4.37644e11i	0.434201	+	1.62046i	0.742972	+	0.669323i	$0.233416\pi$
$347$	1.17266e11	+	4.37644e11i	0.434201	+	1.62046i	−0.308771	+	0.951136i	$0.599918\pi$
$348$	2.78463e11	+	7.46140e10i	1.01780	+	0.272718i
$349$	9.68004e10			0.349271			0.174635	−	0.984633i	$-0.444125\pi$
$349$	9.68004e10			0.349271			0.174635	+	0.984633i	$0.444125\pi$
$350$	7.06351e10	+	3.25940e10i	0.251602	+	0.116100i
$351$	−1.98835e11			−0.699216
$352$	−1.34848e11	−	3.61323e10i	−0.468168	−	0.125445i
$353$	9.02545e10	+	3.36834e11i	0.309373	+	1.15460i	0.929115	+	0.369791i	$0.120571\pi$
$353$	9.02545e10	+	3.36834e11i	0.309373	+	1.15460i	−0.619742	+	0.784806i	$0.712763\pi$
$354$	−5.41080e10	−	3.12393e10i	−0.183125	−	0.105727i
$355$	4.10740e11	+	3.71798e10i	1.37259	+	0.124245i
$356$			3.02776e10i			0.0999072i
$357$	4.06979e9	+	6.88878e9i	0.0132606	+	0.0224458i
$358$	7.35720e9	+	7.35720e9i	0.0236722	+	0.0236722i
$359$	1.92984e11	−	1.11419e11i	0.613192	−	0.354027i	−0.161022	−	0.986951i	$-0.551479\pi$
$359$	1.92984e11	−	1.11419e11i	0.613192	−	0.354027i	0.774214	+	0.632924i	$0.218146\pi$
$360$	1.02690e11	+	3.77263e10i	0.322232	+	0.118381i
$361$	−1.45371e11	+	2.51790e11i	−0.450500	+	0.780289i
$362$	−3.73933e10	+	1.39554e11i	−0.114447	+	0.427123i
$363$	−8.09212e10	+	8.09212e10i	−0.244615	+	0.244615i
$364$	−2.12353e11	+	5.91857e10i	−0.634018	+	0.176710i
$365$	4.30744e10	+	2.48656e11i	0.127028	+	0.733300i
$366$	2.49725e10	+	4.32536e10i	0.0727439	+	0.125996i
$367$	8.89106e10	−	2.38235e10i	0.255833	−	0.0685502i	−0.128623	−	0.991694i	$-0.541056\pi$
$367$	8.89106e10	−	2.38235e10i	0.255833	−	0.0685502i	0.384456	+	0.923143i	$0.374389\pi$
$368$	−1.20129e11	+	3.21886e10i	−0.341456	+	0.0914928i
$369$	3.14181e10	+	5.44177e10i	0.0882187	+	0.152799i
$370$	2.86651e10	+	2.02003e10i	0.0795145	+	0.0560337i
$371$	5.06680e11	−	1.41219e11i	1.38852	−	0.387000i
$372$	2.59767e11	−	2.59767e11i	0.703301	−	0.703301i
$373$	5.44454e10	−	2.03193e11i	0.145637	−	0.543525i	−0.854089	−	0.520127i	$-0.825885\pi$
$373$	5.44454e10	−	2.03193e11i	0.145637	−	0.543525i	0.999726	−	0.0233982i	$-0.00744855\pi$
$374$	1.48494e9	−	2.57199e9i	0.00392452	−	0.00679747i
$375$	−2.06038e9	+	2.28426e11i	−0.00538030	+	0.596492i
$376$	2.39365e11	−	1.38197e11i	0.617611	−	0.356578i
$377$	−3.78316e11	−	3.78316e11i	−0.964538	−	0.964538i
$378$	5.48697e10	+	9.28760e10i	0.138235	+	0.233986i
$379$		−	3.22937e11i		−	0.803973i	−0.915646	−	0.401986i	$-0.868320\pi$
$379$		−	3.22937e11i		−	0.803973i	0.915646	−	0.401986i	$-0.131680\pi$
$380$	4.66433e10	−	5.15287e11i	0.114753	−	1.26772i
$381$	−2.42101e11	−	1.39777e11i	−0.588618	−	0.339839i
$382$	−2.23399e10	−	8.33738e10i	−0.0536781	−	0.200329i
$383$	−3.36410e11	−	9.01407e10i	−0.798866	−	0.214056i	−0.163780	−	0.986497i	$-0.552369\pi$
$383$	−3.36410e11	−	9.01407e10i	−0.798866	−	0.214056i	−0.635086	+	0.772441i	$0.719035\pi$
$384$	−2.30094e11			−0.540027
$385$	−1.58652e11	+	2.29993e11i	−0.368020	+	0.533508i
$386$	−1.68972e11			−0.387411
$387$	−1.61129e11	−	4.31744e10i	−0.365152	−	0.0978423i
$388$	−1.63258e11	−	6.09288e11i	−0.365706	−	1.36484i
$389$	−3.54460e11	−	2.04648e11i	−0.784864	−	0.453142i	0.0532871	−	0.998579i	$-0.483030\pi$
$389$	−3.54460e11	−	2.04648e11i	−0.784864	−	0.453142i	−0.838151	+	0.545438i	$0.816363\pi$
$390$	3.44821e10	+	4.13460e10i	0.0754750	+	0.0904988i
$391$		−	9.20665e9i		−	0.0199208i
$392$	1.79664e11	+	1.72606e11i	0.384303	+	0.369205i
$393$	−9.59137e10	−	9.59137e10i	−0.202822	−	0.202822i
$394$	−5.31842e10	+	3.07059e10i	−0.111186	+	0.0641932i
$395$	−4.44492e10	+	2.05645e10i	−0.0918708	+	0.0425042i
$396$	−9.43111e10	+	1.63352e11i	−0.192723	+	0.333807i
$397$	1.51381e10	−	5.64962e10i	0.0305854	−	0.114146i	−0.948946	−	0.315440i	$-0.897848\pi$
$397$	1.51381e10	−	5.64962e10i	0.0305854	−	0.114146i	0.979531	+	0.201294i	$0.0645145\pi$
$398$	−1.12464e10	+	1.12464e10i	−0.0224668	+	0.0224668i
$399$	2.91462e11	−	2.97360e11i	0.575710	−	0.587361i
$400$	1.33563e11	+	3.73943e11i	0.260866	+	0.730358i
$401$	−2.55372e11	−	4.42317e11i	−0.493200	−	0.854247i	0.506769	−	0.862082i	$-0.330840\pi$
$401$	−2.55372e11	−	4.42317e11i	−0.493200	−	0.854247i	−0.999969	+	0.00783443i	$0.997506\pi$
$402$	6.90257e10	−	1.84954e10i	0.131824	−	0.0353220i
$403$	−6.58551e11	+	1.76458e11i	−1.24370	+	0.333249i
$404$	−8.27814e10	−	1.43382e11i	−0.154603	−	0.267780i
$405$	1.84396e10	−	2.61667e10i	0.0340568	−	0.0483282i
$406$	−7.23132e10	+	2.81110e11i	−0.132084	+	0.513464i
$407$	−8.90610e10	+	8.90610e10i	−0.160884	+	0.160884i
$408$	2.01267e9	−	7.51140e9i	0.00359586	−	0.0134199i
$409$	2.33222e11	−	4.03952e11i	0.412111	−	0.713797i	−0.583010	−	0.812465i	$-0.698125\pi$
$409$	2.33222e11	−	4.03952e11i	0.412111	−	0.713797i	0.995120	+	0.0986685i	$0.0314583\pi$
$410$	1.49752e10	−	4.07623e10i	0.0261725	−	0.0712412i
$411$	2.85249e11	−	1.64688e11i	0.493100	−	0.284692i
$412$	4.07086e11	+	4.07086e11i	0.696064	+	0.696064i
$413$	−3.71608e11	+	6.58796e11i	−0.628506	+	1.11423i
$414$		−	4.86313e10i		−	0.0813606i
$415$	3.70164e11	−	3.08712e11i	0.612601	−	0.510902i
$416$	2.82027e11	+	1.62828e11i	0.461711	+	0.266569i
$417$	1.71978e9	+	6.41829e9i	0.00278522	+	0.0103946i
$418$	−1.49287e11	−	4.00012e10i	−0.239182	−	0.0640885i
$419$	−2.82987e9			−0.00448542			−0.00224271	−	0.999997i	$-0.500714\pi$
$419$	−2.82987e9			−0.00448542			−0.00224271	+	0.999997i	$0.500714\pi$
$420$	−1.17799e11	+	3.30849e11i	−0.184723	+	0.518809i
$421$	6.93519e11			1.07594			0.537971	−	0.842963i	$-0.319191\pi$
$421$	6.93519e11			1.07594			0.537971	+	0.842963i	$0.319191\pi$
$422$	−7.58734e10	−	2.03302e10i	−0.116462	−	0.0312058i
$423$	−1.46910e11	−	5.48276e11i	−0.223111	−	0.832660i
$424$	−4.42725e11	−	2.55607e11i	−0.665254	−	0.384085i
$425$	−2.92981e10	+	2.38582e9i	−0.0435601	+	0.00354721i
$426$		−	1.54849e11i		−	0.227806i
$427$	5.20581e11	−	3.07551e11i	0.757814	−	0.447705i
$428$	−4.30710e11	−	4.30710e11i	−0.620423	−	0.620423i
$429$	−1.67461e11	+	9.66837e10i	−0.238702	+	0.137815i
$430$	4.84069e10	+	1.04629e11i	0.0682810	+	0.147586i
$431$	5.65826e11	−	9.80039e11i	0.789833	−	1.36803i	−0.136236	−	0.990676i	$-0.543501\pi$
$431$	5.65826e11	−	9.80039e11i	0.789833	−	1.36803i	0.926069	−	0.377354i	$-0.123166\pi$
$432$	−1.42511e11	+	5.31860e11i	−0.196867	+	0.734717i
$433$	−5.88944e11	+	5.88944e11i	−0.805154	+	0.805154i	−0.983896	−	0.178742i	$-0.942797\pi$
$433$	−5.88944e11	+	5.88944e11i	−0.805154	+	0.805154i	0.178742	+	0.983896i	$0.442797\pi$
$434$	2.64155e11	+	2.58915e11i	0.357400	+	0.350311i
$435$	−8.39836e11	+	1.45484e11i	−1.12459	+	0.194811i
$436$	2.83391e11	+	4.90848e11i	0.375575	+	0.650515i
$437$	−4.62790e11	+	1.24004e11i	−0.607040	+	0.162656i
$438$	9.15236e10	−	2.45237e10i	0.118823	−	0.0318385i
$439$	5.16062e11	+	8.93846e11i	0.663150	+	1.14861i	0.979783	+	0.200061i	$0.0641141\pi$
$439$	5.16062e11	+	8.93846e11i	0.663150	+	1.14861i	−0.316634	+	0.948548i	$0.602553\pi$
$440$	2.67570e11	−	4.63508e10i	0.340331	−	0.0589550i
$441$	4.37889e11	−	2.64650e11i	0.551303	−	0.333195i
$442$	−4.89873e9	+	4.89873e9i	−0.00610497	+	0.00610497i
$443$	2.62266e11	−	9.78790e11i	0.323538	−	1.20746i	−0.592236	−	0.805765i	$-0.701755\pi$
$443$	2.62266e11	−	9.78790e11i	0.323538	−	1.20746i	0.915774	−	0.401695i	$-0.131579\pi$
$444$	−7.91564e10	+	1.37103e11i	−0.0966635	+	0.167426i
$445$	−3.75881e10	−	8.12447e10i	−0.0454391	−	0.0982143i
$446$	1.51268e8	−	8.73344e7i	0.000181025	−	0.000104515i
$447$	−3.54822e11	−	3.54822e11i	−0.420365	−	0.420365i
$448$	4.85372e9	+	4.84539e11i	0.00569277	+	0.568300i
$449$		−	5.75341e10i		−	0.0668062i	−0.999442	−	0.0334031i	$-0.989365\pi$
$449$		−	5.75341e10i		−	0.0668062i	0.999442	−	0.0334031i	$-0.0106345\pi$
$450$	−1.54758e11	+	1.26023e10i	−0.177908	+	0.0144876i
$451$	1.35076e11	+	7.79859e10i	0.153738	+	0.0887609i
$452$	2.59738e11	+	9.69357e11i	0.292694	+	1.09235i
$453$	6.80095e11	+	1.82231e11i	0.758801	+	0.203320i
$454$	−1.73019e11			−0.191136
$455$	4.96335e11	−	4.22439e11i	0.542905	−	0.462075i
$456$	−4.04683e11			−0.438302
$457$	−9.21358e10	−	2.46877e10i	−0.0988111	−	0.0264764i	0.209075	−	0.977900i	$-0.432955\pi$
$457$	−9.21358e10	−	2.46877e10i	−0.0988111	−	0.0264764i	−0.307886	+	0.951423i	$0.599621\pi$
$458$	−9.46480e9	−	3.53231e10i	−0.0100512	−	0.0375115i
$459$	−3.53004e10	−	2.03807e10i	−0.0371213	−	0.0214320i
$460$	3.10344e11	−	2.58823e11i	0.323171	−	0.269521i
$461$		−	5.60003e10i		−	0.0577479i	−0.999583	−	0.0288740i	$-0.990808\pi$
$461$		−	5.60003e10i		−	0.0577479i	0.999583	−	0.0288740i	$-0.00919214\pi$
$462$	9.13728e10	+	5.15407e10i	0.0933100	+	0.0526334i
$463$	1.14526e12	+	1.14526e12i	1.15821	+	1.15821i	0.984860	+	0.173352i	$0.0554598\pi$
$463$	1.14526e12	+	1.14526e12i	1.15821	+	1.15821i	0.173352	+	0.984860i	$0.444540\pi$
$464$	−1.28310e12	+	7.40799e11i	−1.28508	+	0.741941i
$465$	−3.74553e11	+	1.01953e12i	−0.371514	+	1.01125i
$466$	1.90423e11	−	3.29823e11i	0.187061	−	0.323999i
$467$	2.25493e11	−	8.41550e11i	0.219385	−	0.818755i	−0.765192	−	0.643802i	$-0.777356\pi$
$467$	2.25493e11	−	8.41550e11i	0.219385	−	0.818755i	0.984577	−	0.174953i	$-0.0559774\pi$
$468$	3.11127e11	−	3.11127e11i	0.299800	−	0.299800i
$469$	−2.32267e11	−	8.33352e11i	−0.221672	−	0.795336i
$470$	−2.25968e11	+	3.20659e11i	−0.213603	+	0.303112i
$471$	−1.40616e11	−	2.43553e11i	−0.131656	−	0.228034i
$472$	7.10077e11	−	1.90265e11i	0.658517	−	0.176449i
$473$	−3.99954e11	+	1.07167e11i	−0.367397	+	0.0984436i
$474$	9.19436e9	+	1.59251e10i	0.00836602	+	0.0144904i
$475$	5.14542e11	+	1.44059e12i	0.463767	+	1.29843i
$476$	−4.37668e10	−	1.12586e10i	−0.0390763	−	0.0100521i
$477$	−7.42359e11	+	7.42359e11i	−0.656571	+	0.656571i
$478$	5.39471e10	−	2.01333e11i	0.0472653	−	0.176397i
$479$	−3.88617e11	+	6.73104e11i	−0.337296	+	0.584214i	−0.983923	−	0.178592i	$-0.942846\pi$
$479$	−3.88617e11	+	6.73104e11i	−0.337296	+	0.584214i	0.646627	+	0.762806i	$0.276179\pi$
$480$	4.70854e11	−	2.17842e11i	0.404857	−	0.187308i
$481$	2.54444e11	−	1.46904e11i	0.216741	−	0.125135i
$482$	2.30190e11	+	2.30190e11i	0.194256	+	0.194256i
$483$	3.25196e11	−	3.25754e9i	0.271883	−	0.00272351i
$484$		−	6.46373e11i		−	0.535401i
$485$	1.19447e12	+	1.43224e12i	0.980255	+	1.17538i
$486$	−2.99873e11	−	1.73132e11i	−0.243822	−	0.140771i
$487$	1.29318e11	+	4.82621e11i	0.104178	+	0.388799i	0.998251	−	0.0591235i	$-0.0188306\pi$
$487$	1.29318e11	+	4.82621e11i	0.104178	+	0.388799i	−0.894072	+	0.447923i	$0.852164\pi$
$488$	−5.67631e11	−	1.52096e11i	−0.453082	−	0.121403i
$489$	−4.67914e11			−0.370063
$490$	−3.34288e11	−	1.15264e11i	−0.261962	−	0.0903256i
$491$	−3.22411e11			−0.250347			−0.125174	−	0.992135i	$-0.539949\pi$
$491$	−3.22411e11			−0.250347			−0.125174	+	0.992135i	$0.539949\pi$
$492$	1.89367e11	+	5.07406e10i	0.145700	+	0.0390403i
$493$	−2.83872e10	−	1.05943e11i	−0.0216427	−	0.0807717i
$494$	3.12225e11	+	1.80263e11i	0.235883	+	0.136187i
$495$	5.02750e10	−	5.55408e11i	0.0376382	−	0.415804i
$496$			1.88802e12i			1.40068i
$497$	−1.87453e12	+	1.87776e10i	−1.37813	+	0.0138050i
$498$	−1.27968e11	−	1.27968e11i	−0.0932331	−	0.0932331i
$499$	1.59337e12	−	9.19933e11i	1.15044	−	0.664208i	0.201447	−	0.979499i	$-0.435436\pi$
$499$	1.59337e12	−	9.19933e11i	1.15044	−	0.664208i	0.948995	+	0.315292i	$0.102102\pi$
$500$	−9.04068e11	−	9.20526e11i	−0.646898	−	0.658675i
$501$	−4.48236e10	+	7.76368e10i	−0.0317861	+	0.0550551i
$502$	−8.84133e10	+	3.29963e11i	−0.0621371	+	0.231899i
$503$	1.81776e12	−	1.81776e12i	1.26613	−	1.26613i	0.318065	−	0.948069i	$-0.396967\pi$
$503$	1.81776e12	−	1.81776e12i	1.26613	−	1.26613i	0.948069	−	0.318065i	$-0.103033\pi$
$504$	−4.81597e11	−	1.23887e11i	−0.332465	−	0.0855239i
$505$	4.00130e11	+	2.81971e11i	0.273773	+	0.192927i
$506$	−6.03563e10	−	1.04540e11i	−0.0409303	−	0.0708934i
$507$	−4.21539e11	+	1.12951e11i	−0.283336	+	0.0759197i
$508$	1.52516e12	−	4.08666e11i	1.01608	−	0.272258i
$509$	−1.99720e10	−	3.45925e10i	−0.0131884	−	0.0228430i	0.859356	−	0.511378i	$-0.170865\pi$
$509$	−1.99720e10	−	3.45925e10i	−0.0131884	−	0.0228430i	−0.872544	+	0.488535i	$0.837531\pi$
$510$	1.88383e9	+	1.08749e10i	0.00123304	+	0.00711799i
$511$	−3.07971e11	−	1.10497e12i	−0.199810	−	0.716897i
$512$	1.09211e12	−	1.09211e12i	0.702350	−	0.702350i
$513$	−5.49014e11	+	2.04895e12i	−0.349990	+	1.30618i
$514$	−8.76758e10	+	1.51859e11i	−0.0554046	+	0.0959635i
$515$	−1.59772e12	−	5.86969e11i	−1.00085	−	0.367691i
$516$	−4.50724e11	+	2.60226e11i	−0.279890	+	0.161594i
$517$	−9.96271e11	−	9.96271e11i	−0.613296	−	0.613296i
$518$	−1.38834e11	−	7.83123e10i	−0.0847251	−	0.0477910i
$519$		−	1.50267e12i		−	0.909096i
$520$	−6.30879e11	−	5.71066e10i	−0.378383	−	0.0342508i
$521$	3.98317e11	+	2.29968e11i	0.236842	+	0.136741i	0.613725	−	0.789520i	$-0.289671\pi$
$521$	3.98317e11	+	2.29968e11i	0.236842	+	0.136741i	−0.376882	+	0.926261i	$0.623004\pi$
$522$	−1.49947e11	−	5.59609e11i	−0.0883933	−	0.329888i
$523$	−2.99113e12	−	8.01470e11i	−1.74814	−	0.468414i	−0.763915	−	0.645317i	$-0.776725\pi$
$523$	−2.99113e12	−	8.01470e11i	−1.74814	−	0.468414i	−0.984228	+	0.176903i	$0.943392\pi$
$524$	7.66129e11			0.443926
$525$	−9.46378e10	−	1.03402e12i	−0.0543686	−	0.594033i
$526$	−2.18896e11			−0.124681
$527$	−1.35004e11	−	3.61741e10i	−0.0762426	−	0.0204292i
$528$	1.38593e11	+	5.17234e11i	0.0776046	+	0.289624i
$529$	1.23577e12	+	7.13471e11i	0.686099	+	0.396119i
$530$	7.22600e11	+	6.54091e10i	0.397793	+	0.0360078i
$531$		−	1.50969e12i		−	0.824067i
$532$	2.35571e10	+	2.35166e12i	0.0127503	+	1.27284i
$533$	−2.57271e11	−	2.57271e11i	−0.138076	−	0.138076i
$534$	−2.91080e10	+	1.68055e10i	−0.0154909	+	0.00894369i
$535$	1.69044e12	+	6.21031e11i	0.892087	+	0.327734i
$536$	−4.20405e11	+	7.28162e11i	−0.220002	+	0.381054i
$537$	3.59438e10	−	1.34144e11i	0.0186526	−	0.0696125i
$538$	8.32167e10	−	8.32167e10i	0.0428243	−	0.0428243i
$539$	6.12849e11	−	1.11237e12i	0.312755	−	0.567675i
$540$	−3.05382e11	−	1.76288e12i	−0.154551	−	0.892179i
$541$	3.47779e11	+	6.02371e11i	0.174548	+	0.302327i	0.940005	−	0.341161i	$-0.110820\pi$
$541$	3.47779e11	+	6.02371e11i	0.174548	+	0.302327i	−0.765457	+	0.643488i	$0.777487\pi$
$542$	9.48823e11	−	2.54236e11i	0.472268	−	0.126544i
$543$	1.86270e12	−	4.99108e11i	0.919481	−	0.246374i
$544$	3.33800e10	+	5.78158e10i	0.0163415	+	0.0283042i
$545$	−1.36979e12	−	9.65289e11i	−0.665074	−	0.468676i
$546$	−1.74765e11	−	1.71299e11i	−0.0841567	−	0.0824874i
$547$	2.15129e12	−	2.15129e12i	1.02744	−	1.02744i	0.0278237	−	0.999613i	$-0.491142\pi$
$547$	2.15129e12	−	2.15129e12i	1.02744	−	1.02744i	0.999613	−	0.0278237i	$-0.00885771\pi$
$548$	−4.81499e11	+	1.79698e12i	−0.228078	+	0.851197i
$549$	−6.03418e11	+	1.04515e12i	−0.283493	+	0.491025i
$550$	−3.17034e11	+	2.19161e11i	−0.147732	+	0.102125i
$551$	−4.94305e12	+	2.85387e12i	−2.28462	+	1.31902i
$552$	−2.23499e11	−	2.23499e11i	−0.102459	−	0.102459i
$553$	1.91667e11	−	1.13234e11i	0.0871535	−	0.0514889i
$554$			6.54707e11i			0.295293i
$555$	4.21964e10	−	4.66160e11i	0.0188780	−	0.208553i
$556$	−3.25022e10	−	1.87651e10i	−0.0144237	−	0.00832751i
$557$	−1.27804e11	−	4.76973e11i	−0.0562597	−	0.209964i	0.932074	−	0.362268i	$-0.117997\pi$
$557$	−1.27804e11	−	4.76973e11i	−0.0562597	−	0.209964i	−0.988334	+	0.152304i	$0.951331\pi$
$558$	−7.13115e11	−	1.91079e11i	−0.311391	−	0.0834369i
$559$	9.65887e11			0.418382
$560$	−7.74234e11	−	1.63041e12i	−0.332680	−	0.700569i
$561$	−3.96405e10			−0.0168969
$562$	5.02552e11	+	1.34658e11i	0.212504	+	0.0569403i
$563$	−5.34457e11	−	1.99462e12i	−0.224195	−	0.836706i	−0.982726	−	0.185069i	$-0.940749\pi$
$563$	−5.34457e11	−	1.99462e12i	−0.224195	−	0.836706i	0.758531	−	0.651637i	$-0.225917\pi$
$564$	−1.53369e12	−	8.85475e11i	−0.638235	−	0.368485i
$565$	−1.90037e12	−	2.27865e12i	−0.784549	−	0.940718i
$566$			1.18240e12i			0.484272i
$567$	−7.14865e10	+	1.26733e11i	−0.0290469	+	0.0514952i
$568$	1.28832e12	+	1.28832e12i	0.519346	+	0.519346i
$569$	1.05636e10	−	6.09889e9i	0.00422480	−	0.00243919i	−0.497886	−	0.867242i	$-0.665890\pi$
$569$	1.05636e10	−	6.09889e9i	0.00422480	−	0.00243919i	0.502111	+	0.864803i	$0.332557\pi$
$570$	5.21272e11	−	2.41168e11i	0.206836	−	0.0956934i
$571$	1.66349e11	−	2.88125e11i	0.0654873	−	0.113427i	−0.831423	−	0.555640i	$-0.812473\pi$
$571$	1.66349e11	−	2.88125e11i	0.0654873	−	0.113427i	0.896910	+	0.442213i	$0.145806\pi$
$572$	2.82674e11	−	1.05495e12i	0.110409	−	0.412051i
$573$	−8.14651e11	+	8.14651e11i	−0.315701	+	0.315701i
$574$	−4.91761e10	+	1.91167e11i	−0.0189082	+	0.0735037i
$575$	−5.11438e11	+	1.07978e12i	−0.195114	+	0.411937i
$576$	−4.83582e11	−	8.37589e11i	−0.183050	−	0.317051i
$577$	1.37266e12	−	3.67804e11i	0.515553	−	0.138142i	0.00834410	−	0.999965i	$-0.497344\pi$
$577$	1.37266e12	−	3.67804e11i	0.515553	−	0.138142i	0.507209	+	0.861823i	$0.330677\pi$
$578$	7.16838e11	−	1.92076e11i	0.267144	−	0.0715810i
$579$	1.12768e12	+	1.95319e12i	0.416995	+	0.722257i
$580$	2.77314e12	−	3.93522e12i	1.01753	−	1.44392i
$581$	−1.53361e12	+	1.56464e12i	−0.558370	+	0.569670i
$582$	4.95136e11	−	4.95136e11i	0.178884	−	0.178884i
$583$	−6.74469e11	+	2.51715e12i	−0.241799	+	0.902405i
$584$	−5.57430e11	+	9.65497e11i	−0.198304	+	0.343473i
$585$	−4.48607e11	+	1.22110e12i	−0.158367	+	0.431073i
$586$	1.84509e11	−	1.06526e11i	0.0646367	−	0.0373180i
$587$	−2.56314e12	−	2.56314e12i	−0.891047	−	0.891047i	0.103575	−	0.994622i	$-0.466972\pi$
$587$	−2.56314e12	−	2.56314e12i	−0.891047	−	0.891047i	−0.994622	+	0.103575i	$0.966972\pi$
$588$	3.82190e11	−	1.54991e12i	0.131850	−	0.534697i
$589$			7.27345e12i			2.49013i
$590$	−8.01263e11	+	6.68244e11i	−0.272233	+	0.227039i
$591$	7.09877e11	+	4.09848e11i	0.239353	+	0.138191i
$592$	−2.10581e11	−	7.85899e11i	−0.0704647	−	0.262978i
$593$	2.52518e12	+	6.76620e11i	0.838584	+	0.224698i	0.652455	−	0.757827i	$-0.273739\pi$
$593$	2.52518e12	+	6.76620e11i	0.838584	+	0.224698i	0.186129	+	0.982525i	$0.440406\pi$
$594$	−5.34442e11			−0.176141
$595$	1.31418e11	−	2.41236e10i	0.0429860	−	0.00789070i
$596$	2.83421e12			0.920075
$597$	2.05057e11	+	5.49448e10i	0.0660678	+	0.0177028i
$598$	7.28800e10	+	2.71992e11i	0.0233052	+	0.0869763i
$599$	3.70542e12	+	2.13932e12i	1.17603	+	0.678979i	0.955092	−	0.296310i	$-0.0957562\pi$
$599$	3.70542e12	+	2.13932e12i	1.17603	+	0.678979i	0.220934	+	0.975289i	$0.429090\pi$
$600$	−6.53317e11	+	7.69152e11i	−0.205799	+	0.242288i
$601$			1.96323e12i			0.613812i	0.951740	+	0.306906i	$0.0992937\pi$
$601$			1.96323e12i			0.613812i	−0.951740	+	0.306906i	$0.900706\pi$
$602$	−2.66542e11	−	4.51166e11i	−0.0827144	−	0.140008i
$603$	1.22098e12	+	1.22098e12i	0.376080	+	0.376080i
$604$	−3.44400e12	+	1.98839e12i	−1.05292	+	0.607905i
$605$	8.02439e11	+	1.73443e12i	0.243508	+	0.526330i
$606$	9.18954e10	−	1.59167e11i	0.0276800	−	0.0479432i
$607$	−4.48162e10	+	1.67256e11i	−0.0133994	+	0.0500073i	−0.972302	−	0.233729i	$-0.924907\pi$
$607$	−4.48162e10	+	1.67256e11i	−0.0133994	+	0.0500073i	0.958902	+	0.283736i	$0.0915739\pi$
$608$	2.45663e12	−	2.45663e12i	0.729076	−	0.729076i
$609$	3.73204e12	−	1.04017e12i	1.09943	−	0.306427i
$610$	8.21805e11	−	1.42360e11i	0.240317	−	0.0416298i
$611$	1.64332e12	+	2.84632e12i	0.477020	+	0.826224i
$612$	8.71270e10	−	2.33456e10i	0.0251056	−	0.00672704i
$613$	2.89776e12	−	7.76452e11i	0.828876	−	0.222097i	0.180653	−	0.983547i	$-0.442179\pi$
$613$	2.89776e12	−	7.76452e11i	0.828876	−	0.222097i	0.648223	+	0.761450i	$0.275512\pi$
$614$	−3.92956e10	−	6.80620e10i	−0.0111580	−	0.0193262i
$615$	−5.71124e11	+	9.89350e10i	−0.160988	+	0.0278877i
$616$	−1.18902e12	+	3.31397e11i	−0.332718	+	0.0927333i
$617$	−1.83960e12	+	1.83960e12i	−0.511024	+	0.511024i	−0.914840	−	0.403816i	$-0.867683\pi$
$617$	−1.83960e12	+	1.83960e12i	−0.511024	+	0.511024i	0.403816	+	0.914840i	$0.367683\pi$
$618$	−1.65409e11	+	6.17314e11i	−0.0456153	+	0.170239i
$619$	1.51261e12	−	2.61992e12i	0.414114	−	0.717266i	−0.581221	−	0.813745i	$-0.697425\pi$
$619$	1.51261e12	−	2.61992e12i	0.414114	−	0.717266i	0.995335	+	0.0964797i	$0.0307583\pi$
$620$	−2.57593e12	−	5.56774e12i	−0.700118	−	1.51327i
$621$	−1.43481e12	+	8.28386e11i	−0.387152	+	0.223522i
$622$	−9.69814e9	−	9.69814e9i	−0.00259795	−	0.00259795i
$623$	2.06970e11	+	3.50331e11i	0.0550442	+	0.0931714i
$624$		−	1.24912e12i		−	0.329817i
$625$	3.56869e12	+	1.34772e12i	0.935512	+	0.353296i
$626$	−1.27103e12	−	7.33828e11i	−0.330804	−	0.190990i
$627$	5.33917e11	+	1.99261e12i	0.137965	+	0.514894i
$628$	1.53431e12	+	4.11117e11i	0.393636	+	0.105474i
$629$	6.02308e10			0.0153423
$630$	6.94173e11	−	1.27425e11i	0.175564	−	0.0322273i
$631$	−4.44649e12			−1.11657			−0.558284	−	0.829650i	$-0.688540\pi$
$631$	−4.44649e12			−1.11657			−0.558284	+	0.829650i	$0.688540\pi$
$632$	−2.08990e11	−	5.59988e10i	−0.0521074	−	0.0139621i
$633$	2.71358e11	+	1.01272e12i	0.0671778	+	0.250711i
$634$	−1.61576e12	−	9.32862e11i	−0.397170	−	0.229306i
$635$	−3.58517e12	+	2.98999e12i	−0.875039	+	0.729773i
$636$			3.27551e12i			0.793821i
$637$	−2.05248e12	+	2.13641e12i	−0.493913	+	0.514110i
$638$	−1.01686e12	−	1.01686e12i	−0.242979	−	0.242979i
$639$	3.24038e12	−	1.87083e12i	0.768850	−	0.443896i
$640$	−1.32503e12	+	3.60671e12i	−0.312188	+	0.849771i
$641$	3.63629e12	−	6.29823e12i	0.850740	−	1.47353i	−0.0298010	−	0.999556i	$-0.509487\pi$
$641$	3.63629e12	−	6.29823e12i	0.850740	−	1.47353i	0.880541	−	0.473970i	$-0.157179\pi$
$642$	1.75007e11	−	6.53137e11i	0.0406583	−	0.151739i
$643$	−3.24579e12	+	3.24579e12i	−0.748809	+	0.748809i	−0.974256	−	0.225446i	$-0.927616\pi$
$643$	−3.24579e12	+	3.24579e12i	−0.748809	+	0.748809i	0.225446	+	0.974256i	$0.427616\pi$
$644$	−1.28577e12	+	1.31179e12i	−0.294562	+	0.300523i
$645$	8.86383e11	−	1.25782e12i	0.201652	−	0.286154i
$646$	3.69542e10	+	6.40065e10i	0.00834866	+	0.0144603i
$647$	3.97352e12	−	1.06470e12i	0.891468	−	0.238868i	0.216120	−	0.976367i	$-0.430660\pi$
$647$	3.97352e12	−	1.06470e12i	0.891468	−	0.238868i	0.675349	+	0.737499i	$0.263993\pi$
$648$	1.36598e11	−	3.66014e10i	0.0304339	−	0.00815474i
$649$	−1.87368e12	−	3.24530e12i	−0.414566	−	0.718049i
$650$	8.46666e11	−	3.02408e11i	0.186038	−	0.0664483i
$651$	1.22997e12	−	4.78138e12i	0.268398	−	1.04337i
$652$	1.86877e12	−	1.86877e12i	0.404988	−	0.404988i
$653$	−8.31481e11	+	3.10313e12i	−0.178955	+	0.667868i	0.816890	+	0.576794i	$0.195697\pi$
$653$	−8.31481e11	+	3.10313e12i	−0.178955	+	0.667868i	−0.995844	+	0.0910737i	$0.970970\pi$
$654$	−3.14591e11	+	5.44888e11i	−0.0672430	+	0.116468i
$655$	−2.05577e12	+	9.51108e11i	−0.436405	+	0.201904i
$656$	−8.72563e11	+	5.03775e11i	−0.183963	+	0.106211i
$657$	1.61894e12	+	1.61894e12i	0.338990	+	0.338990i
$658$	8.76032e11	−	1.55305e12i	0.182181	−	0.322976i
$659$			3.51029e12i			0.725035i	0.931977	+	0.362517i	$0.118083\pi$
$659$			3.51029e12i			0.725035i	−0.931977	+	0.362517i	$0.881917\pi$
$660$	−1.11440e12	−	1.33623e12i	−0.228609	−	0.274115i
$661$	−6.14805e12	−	3.54958e12i	−1.25265	−	0.723220i	−0.281017	−	0.959703i	$-0.590672\pi$
$661$	−6.14805e12	−	3.54958e12i	−1.25265	−	0.723220i	−0.971636	+	0.236483i	$0.924005\pi$
$662$	5.82314e11	+	2.17323e12i	0.117841	+	0.439789i
$663$	8.93189e10	+	2.39329e10i	0.0179528	+	0.00481044i
$664$	2.12935e12			0.425100
$665$	−2.98268e12	−	6.28104e12i	−0.591438	−	1.24547i
$666$	3.18151e11			0.0626612
$667$	−4.30610e12	−	1.15382e12i	−0.842398	−	0.225720i
$668$	−1.31051e11	−	4.89088e11i	−0.0254651	−	0.0950370i
$669$	−2.01905e9	−	1.16570e9i	−0.000389699	−	0.000224993i
$670$	1.07580e11	−	1.18848e12i	0.0206251	−	0.227854i
$671$			2.99561e12i			0.570471i
$672$	−2.03035e12	+	1.19950e12i	−0.384069	+	0.226902i
$673$	−5.31516e12	−	5.31516e12i	−0.998730	−	0.998730i	0.00126883	−	0.999999i	$-0.499596\pi$
$673$	−5.31516e12	−	5.31516e12i	−0.998730	−	0.998730i	−0.999999	+	0.00126883i	$0.999596\pi$
$674$	1.68502e12	−	9.72847e11i	0.314511	−	0.181583i
$675$	3.00797e12	+	4.35128e12i	0.557707	+	0.806770i
$676$	1.23245e12	−	2.13467e12i	0.226992	−	0.393161i
$677$	5.45308e11	−	2.03512e12i	0.0997683	−	0.372340i	−0.897931	−	0.440136i	$-0.854930\pi$
$677$	5.45308e11	−	2.03512e12i	0.0997683	−	0.372340i	0.997699	+	0.0677961i	$0.0215967\pi$
$678$	−7.87745e11	+	7.87745e11i	−0.143170	+	0.143170i
$679$	−6.05395e12	−	5.93386e12i	−1.09301	−	1.07133i
$680$	−1.06150e11	−	7.48039e10i	−0.0190384	−	0.0134163i
$681$	1.15469e12	+	1.99998e12i	0.205732	+	0.356339i
$682$	−1.77010e12	+	4.74296e11i	−0.313305	+	0.0839498i
$683$	2.51579e12	−	6.74105e11i	0.442366	−	0.118532i	−0.0307592	−	0.999527i	$-0.509793\pi$
$683$	2.51579e12	−	6.74105e11i	0.442366	−	0.118532i	0.473125	+	0.880995i	$0.343126\pi$
$684$	−2.34702e12	−	4.06516e12i	−0.409982	−	0.710109i
$685$	−9.38835e11	−	5.41963e12i	−0.162923	−	0.940508i
$686$	1.56431e12	+	3.69159e11i	0.269689	+	0.0636437i
$687$	−3.45144e11	+	3.45144e11i	−0.0591147	+	0.0591147i
$688$	6.92282e11	−	2.58363e12i	0.117797	−	0.439625i
$689$	3.03946e12	−	5.26449e12i	0.513818	−	0.889959i
$690$	4.21081e11	+	1.54696e11i	0.0707204	+	0.0259812i
$691$	−2.94124e12	+	1.69812e12i	−0.490771	+	0.283347i	−0.724894	−	0.688860i	$-0.758111\pi$
$691$	−2.94124e12	+	1.69812e12i	−0.490771	+	0.283347i	0.234123	+	0.972207i	$0.424778\pi$
$692$	6.00142e12	+	6.00142e12i	0.994894	+	0.994894i
$693$	2.53913e10	+	2.53477e12i	0.00418201	+	0.417483i
$694$		−	2.84082e12i		−	0.464864i
$695$	1.10510e11	+	1.00032e10i	0.0179668	+	0.00162633i
$696$	−3.26096e12	−	1.88272e12i	−0.526750	−	0.304119i
$697$	−1.93045e10	−	7.20454e10i	−0.00309821	−	0.0115627i
$698$	−5.86257e11	−	1.57087e11i	−0.0934842	−	0.0250490i
$699$	−5.08336e12			−0.805385
$700$	4.50767e12	+	3.75173e12i	0.709596	+	0.590596i
$701$	8.69134e12			1.35943			0.679713	−	0.733478i	$-0.262104\pi$
$701$	8.69134e12			1.35943			0.679713	+	0.733478i	$0.262104\pi$
$702$	1.20421e12	+	3.22668e11i	0.187149	+	0.0501463i
$703$	−8.11247e11	−	3.02762e12i	−0.125272	−	0.467522i
$704$	−2.07906e12	−	1.20035e12i	−0.319000	−	0.184175i
$705$	5.21465e12	+	4.72025e11i	0.795013	+	0.0719638i
$706$		−	2.18645e12i		−	0.331221i
$707$	−1.93795e12	−	1.09314e12i	−0.291713	−	0.164547i
$708$	−3.33060e12	−	3.33060e12i	−0.498165	−	0.498165i
$709$	7.10831e12	−	4.10398e12i	1.05647	−	0.609955i	0.132018	−	0.991247i	$-0.457854\pi$
$709$	7.10831e12	−	4.10398e12i	1.05647	−	0.609955i	0.924454	+	0.381292i	$0.124521\pi$
$710$	−2.42725e12	−	8.91720e11i	−0.358469	−	0.131694i
$711$	−2.22166e11	+	3.84803e11i	−0.0326035	+	0.0564710i
$712$	1.02355e11	−	3.81994e11i	0.0149262	−	0.0557053i
$713$	−4.01699e12	+	4.01699e12i	−0.582100	+	0.582100i
$714$	−1.34690e10	−	4.83253e10i	−0.00193951	−	0.00695877i
$715$	5.51163e11	+	3.18171e12i	0.0788684	+	0.455285i
$716$	3.92197e11	+	6.79305e11i	0.0557693	+	0.0965953i
$717$	−2.68730e12	+	7.20060e11i	−0.379734	+	0.101750i
$718$	−1.34959e12	+	3.61621e11i	−0.189514	+	0.0507802i
$719$	3.76974e12	+	6.52938e12i	0.526055	+	0.911154i	0.999539	+	0.0303520i	$0.00966284\pi$
$719$	3.76974e12	+	6.52938e12i	0.526055	+	0.911154i	−0.473484	+	0.880802i	$0.657004\pi$
$720$	2.94477e12	+	2.07517e12i	0.408371	+	0.287778i
$721$	7.49299e12	+	1.92751e12i	1.03263	+	0.265636i
$722$	1.28902e12	−	1.28902e12i	0.176539	−	0.176539i
$723$	1.12460e12	−	4.19706e12i	0.153065	−	0.571246i
$724$	−5.44596e12	+	9.43269e12i	−0.736633	+	1.27589i
$725$	−2.55587e12	+	1.40022e13i	−0.343572	+	1.88224i
$726$	6.21405e11	−	3.58768e11i	0.0830157	−	0.0479291i
$727$	−6.95723e12	−	6.95723e12i	−0.923701	−	0.923701i	0.0735879	−	0.997289i	$-0.476555\pi$
$727$	−6.95723e12	−	6.95723e12i	−0.923701	−	0.923701i	−0.997289	+	0.0735879i	$0.976555\pi$
$728$	2.87920e12	−	2.88415e10i	0.379910	−	0.00380563i
$729$			4.17091e12i			0.546961i
$730$	1.42644e11	−	1.57585e12i	0.0185910	−	0.205382i
$731$	1.71480e11	+	9.90040e10i	0.0222119	+	0.0128240i
$732$	9.74529e11	+	3.63699e12i	0.125457	+	0.468212i
$733$	−4.58336e12	−	1.22811e12i	−0.586430	−	0.157133i	−0.0466090	−	0.998913i	$-0.514841\pi$
$733$	−4.58336e12	−	1.22811e12i	−0.586430	−	0.157133i	−0.539821	+	0.841780i	$0.681508\pi$
$734$	−5.77134e11			−0.0733913
$735$	8.98588e11	+	4.63338e12i	0.113571	+	0.585605i
$736$	2.71350e12			0.340863
$737$	4.14004e12	+	1.10932e12i	0.516893	+	0.138501i
$738$	−1.01970e11	−	3.80557e11i	−0.0126537	−	0.0472244i
$739$	−5.40813e12	−	3.12238e12i	−0.667032	−	0.385111i	0.127919	−	0.991785i	$-0.459170\pi$
$739$	−5.40813e12	−	3.12238e12i	−0.667032	−	0.385111i	−0.794951	+	0.606673i	$0.792504\pi$
$740$	1.69325e12	+	2.03030e12i	0.207576	+	0.248896i
$741$		−	4.81213e12i		−	0.586348i
$742$	−3.29780e12	+	3.30347e10i	−0.399399	+	0.00400085i
$743$	1.89917e12	+	1.89917e12i	0.228620	+	0.228620i	0.812116	−	0.583496i	$-0.198316\pi$
$743$	1.89917e12	+	1.89917e12i	0.228620	+	0.228620i	−0.583496	+	0.812116i	$0.698316\pi$
$744$	−4.15548e12	+	2.39917e12i	−0.497214	+	0.287067i
$745$	−7.60510e12	+	3.51852e12i	−0.904485	+	0.418462i
$746$	−6.59481e11	+	1.14225e12i	−0.0779610	+	0.135032i
$747$	1.13180e12	−	4.22394e12i	0.132992	−	0.496335i
$748$	1.58318e11	−	1.58318e11i	0.0184916	−	0.0184916i
$749$	−7.92781e12	−	2.03936e12i	−0.920417	−	0.236770i
$750$	3.83166e11	−	1.38008e12i	0.0442193	−	0.159268i
$751$	−6.43190e12	−	1.11404e13i	−0.737836	−	1.27797i	−0.953468	−	0.301495i	$-0.902515\pi$
$751$	−6.43190e12	−	1.11404e13i	−0.737836	−	1.27797i	0.215632	−	0.976475i	$-0.430819\pi$
$752$	8.79137e12	−	2.35564e12i	1.00248	−	0.268614i
$753$	4.40419e12	−	1.18010e12i	0.499216	−	0.133764i
$754$	1.67729e12	+	2.90515e12i	0.188989	+	0.327338i
$755$	6.77288e12	−	9.61104e12i	0.758599	−	1.07649i
$756$	2.18341e12	+	7.83385e12i	0.243101	+	0.872222i
$757$	−8.48245e12	+	8.48245e12i	−0.938837	+	0.938837i	−0.998234	−	0.0593979i	$-0.981082\pi$
$757$	−8.48245e12	+	8.48245e12i	−0.938837	+	0.938837i	0.0593979	+	0.998234i	$0.481082\pi$
$758$	−5.24060e11	+	1.95582e12i	−0.0576593	+	0.215188i
$759$	−8.05607e11	+	1.39535e12i	−0.0881120	+	0.152614i
$760$	−2.33042e12	+	6.34338e12i	−0.253381	+	0.689699i
$761$	1.32422e13	−	7.64538e12i	1.43129	−	0.826357i	0.434073	−	0.900878i	$-0.357076\pi$
$761$	1.32422e13	−	7.64538e12i	1.43129	−	0.826357i	0.997220	+	0.0745202i	$0.0237425\pi$
$762$	1.23942e12	+	1.23942e12i	0.133174	+	0.133174i
$763$	6.63432e12	+	3.74223e12i	0.708657	+	0.399733i
$764$		−	6.50718e12i		−	0.690991i
$765$	−2.04808e11	+	1.70807e11i	−0.0216207	+	0.0180314i
$766$	1.89114e12	+	1.09185e12i	0.198469	+	0.114586i
$767$	2.26246e12	+	8.44361e12i	0.236049	+	0.880945i
$768$	−1.76358e12	−	4.72551e11i	−0.182924	−	0.0490144i
$769$	7.14188e12			0.736451			0.368226	−	0.929736i	$-0.379965\pi$
$769$	7.14188e12			0.736451			0.368226	+	0.929736i	$0.379965\pi$
$770$	1.33408e12	−	1.13546e12i	0.136765	−	0.116403i
$771$	2.34051e12			0.238542
$772$	−1.23045e13	−	3.29699e12i	−1.24677	−	0.334072i
$773$	−1.88672e12	−	7.04134e12i	−0.190064	−	0.709329i	−0.993490	−	0.113923i	$-0.963658\pi$
$773$	−1.88672e12	−	7.04134e12i	−0.190064	−	0.709329i	0.803425	−	0.595405i	$-0.203009\pi$
$774$	9.05789e11	+	5.22958e11i	0.0907179	+	0.0523760i
$775$	1.38241e13	+	1.17422e13i	1.37651	+	1.16921i
$776$			8.23893e12i			0.815629i
$777$	2.13112e10	+	2.12746e12i	0.00209755	+	0.209395i
$778$	1.81463e12	+	1.81463e12i	0.177575	+	0.177575i
$779$	−3.36148e12	+	1.94075e12i	−0.327049	+	0.188822i
$780$	1.70424e12	+	3.68363e12i	0.164856	+	0.356329i
$781$	4.64378e12	−	8.04327e12i	0.446624	−	0.773576i
$782$	−1.49405e10	+	5.57587e10i	−0.00142868	+	0.00533190i
$783$	−1.39564e13	+	1.39564e13i	−1.32692	+	1.32692i
$784$	4.24355e12	+	7.02135e12i	0.401150	+	0.663741i
$785$	−4.62744e12	+	8.01604e11i	−0.434938	+	0.0753436i
$786$	4.25238e11	+	7.36535e11i	0.0397403	+	0.0688322i
$787$	1.81498e13	−	4.86323e12i	1.68650	−	0.451896i	0.717016	−	0.697057i	$-0.245507\pi$
$787$	1.81498e13	−	4.86323e12i	1.68650	−	0.451896i	0.969482	+	0.245161i	$0.0788408\pi$
$788$	−4.47201e12	+	1.19827e12i	−0.413175	+	0.110710i
$789$	1.46086e12	+	2.53028e12i	0.134203	+	0.232446i
$790$	3.02572e11	−	5.24141e10i	0.0276380	−	0.00478769i
$791$	9.63162e12	+	9.44057e12i	0.874793	+	0.857441i
$792$	1.74208e12	−	1.74208e12i	0.157328	−	0.157328i
$793$	1.80859e12	−	6.74977e12i	0.162410	−	0.606121i
$794$	−1.83363e11	+	3.17595e11i	−0.0163727	+	0.0283584i
$795$	−4.06638e12	−	8.78927e12i	−0.361040	−	0.780370i
$796$	−1.03841e12	+	5.99524e11i	−0.0916766	+	0.0529295i
$797$	−9.09936e12	−	9.09936e12i	−0.798819	−	0.798819i	0.184091	−	0.982909i	$-0.441066\pi$
$797$	−9.09936e12	−	9.09936e12i	−0.798819	−	0.798819i	−0.982909	+	0.184091i	$0.941066\pi$
$798$	−2.24775e12	+	1.32793e12i	−0.196216	+	0.115921i
$799$			6.73765e11i			0.0584855i
$800$	−7.03178e11	−	8.63509e12i	−0.0606960	−	0.745353i
$801$	−7.03347e11	−	4.06077e11i	−0.0603703	−	0.0348548i
$802$	8.28831e11	+	3.09324e12i	0.0707426	+	0.264015i
$803$	5.48942e12	+	1.47089e12i	0.465915	+	0.124842i
$804$	5.38733e12			0.454696
$805$	1.82162e12	−	5.11618e12i	0.152889	−	0.429402i
$806$	4.27477e12			0.356784
$807$	−1.51729e12	−	4.06558e11i	−0.125933	−	0.0337436i
$808$	5.59694e11	+	2.08881e12i	0.0461955	+	0.172404i
$809$	−1.37655e13	−	7.94749e12i	−1.12985	−	0.652321i	−0.185956	−	0.982558i	$-0.559538\pi$
$809$	−1.37655e13	−	7.94749e12i	−1.12985	−	0.652321i	−0.943898	+	0.330237i	$0.892871\pi$
$810$	−1.54140e11	+	1.28551e11i	−0.0125815	+	0.0104928i
$811$		−	8.23210e12i		−	0.668216i	−0.942535	−	0.334108i	$-0.891565\pi$
$811$		−	8.23210e12i		−	0.668216i	0.942535	−	0.334108i	$-0.108435\pi$
$812$	−1.07509e13	+	1.90595e13i	−0.867845	+	1.53854i
$813$	−9.27101e12	−	9.27101e12i	−0.744251	−	0.744251i
$814$	6.83912e11	−	3.94857e11i	0.0545997	−	0.0315232i
$815$	−2.69455e12	+	7.33451e12i	−0.213932	+	0.582321i
$816$	1.28035e11	−	2.21764e11i	0.0101094	−	0.0175099i
$817$	2.66696e12	−	9.95324e12i	0.209420	−	0.781565i
$818$	−2.06800e12	+	2.06800e12i	−0.161496	+	0.161496i
$819$	1.47315e12	−	5.72672e12i	0.114412	−	0.444763i
$820$	1.88585e12	−	2.67611e12i	0.145662	−	0.206701i
$821$	−2.01457e12	−	3.48933e12i	−0.154752	−	0.268039i	0.778216	−	0.627996i	$-0.216125\pi$
$821$	−2.01457e12	−	3.48933e12i	−0.154752	−	0.268039i	−0.932969	+	0.359957i	$0.882791\pi$
$822$	−1.99482e12	+	5.34510e11i	−0.152398	+	0.0408350i
$823$	−2.03729e13	+	5.45890e12i	−1.54794	+	0.414769i	−0.928821	−	0.370530i	$-0.879176\pi$
$823$	−2.03729e13	+	5.45890e12i	−1.54794	+	0.414769i	−0.619117	+	0.785299i	$0.712509\pi$
$824$	−3.75978e12	−	6.51214e12i	−0.284113	−	0.492097i
$825$	4.64915e12	+	2.20207e12i	0.349407	+	0.165496i
$826$	3.31968e12	−	3.38686e12i	0.248134	−	0.253155i
$827$	1.74099e12	−	1.74099e12i	0.129426	−	0.129426i	−0.639426	−	0.768852i	$-0.720828\pi$
$827$	1.74099e12	−	1.74099e12i	0.129426	−	0.129426i	0.768852	+	0.639426i	$0.220828\pi$
$828$	9.48896e11	−	3.54133e12i	0.0701588	−	0.261836i
$829$	6.02736e12	−	1.04397e13i	0.443233	−	0.767702i	−0.554694	−	0.832054i	$-0.687165\pi$
$829$	6.02736e12	−	1.04397e13i	0.443233	−	0.767702i	0.997927	+	0.0643522i	$0.0204981\pi$
$830$	−2.74282e12	+	1.26897e12i	−0.200607	+	0.0928112i
$831$	7.56795e12	−	4.36936e12i	0.550521	−	0.317843i
$832$	3.95988e12	+	3.95988e12i	0.286502	+	0.286502i
$833$	−5.83371e11	+	1.68909e11i	−0.0419800	+	0.0121549i
$834$		−	4.16622e10i		−	0.00298192i
$835$	9.58829e11	+	1.14969e12i	0.0682577	+	0.0818449i
$836$	−1.00905e13	−	5.82578e12i	−0.714474	−	0.412502i
$837$	6.50968e12	+	2.42944e13i	0.458453	+	1.71097i
$838$	1.71387e10	+	4.59229e9i	0.00120055	+	0.000321685i
$839$	3.46989e12			0.241761			0.120881	−	0.992667i	$-0.461428\pi$
$839$	3.46989e12			0.241761			0.120881	+	0.992667i	$0.461428\pi$
$840$	2.60465e12	−	3.77589e12i	0.180507	−	0.261675i
$841$	−3.86015e13			−2.66086
$842$	−4.20019e12	−	1.12544e12i	−0.287982	−	0.0771645i
$843$	−1.79735e12	−	6.70782e12i	−0.122577	−	0.457464i
$844$	−5.12842e12	−	2.96089e12i	−0.347890	−	0.200854i
$845$	−6.56991e11	+	7.25804e12i	−0.0443306	+	0.489738i
$846$			3.55896e12i			0.238867i
$847$	−4.41845e12	−	7.47895e12i	−0.294981	−	0.499304i
$848$	−1.19034e13	−	1.19034e13i	−0.790478	−	0.790478i
$849$	1.36677e13	−	7.89103e12i	0.902838	−	0.521254i
$850$	1.81311e11	+	3.30954e10i	0.0119135	+	0.00217461i
$851$	1.22406e12	−	2.12013e12i	0.0800054	−	0.138573i
$852$	3.02142e12	−	1.12761e13i	0.196442	−	0.733130i
$853$	1.17980e12	−	1.17980e12i	0.0763026	−	0.0763026i	−0.667926	−	0.744228i	$-0.732818\pi$
$853$	1.17980e12	−	1.17980e12i	0.0763026	−	0.0763026i	0.744228	+	0.667926i	$0.232818\pi$
$854$	−3.65191e12	+	1.01784e12i	−0.234941	+	0.0654816i
$855$	1.13445e13	+	7.99445e12i	0.726002	+	0.511612i
$856$	3.97797e12	+	6.89004e12i	0.253238	+	0.438621i
$857$	2.51740e13	−	6.74536e12i	1.59419	−	0.427161i	0.650906	−	0.759158i	$-0.274389\pi$
$857$	2.51740e13	−	6.74536e12i	1.59419	−	0.427161i	0.943281	+	0.331997i	$0.107722\pi$
$858$	1.17110e12	−	3.13795e11i	0.0737737	−	0.0197676i
$859$	−5.00271e12	−	8.66496e12i	−0.313499	−	0.542997i	0.665618	−	0.746293i	$-0.268168\pi$
$859$	−5.00271e12	−	8.66496e12i	−0.313499	−	0.542997i	−0.979117	+	0.203296i	$0.934835\pi$
$860$	1.48346e12	+	8.56361e12i	0.0924770	+	0.533844i
$861$	2.53794e12	−	7.07361e11i	0.157387	−	0.0438659i
$862$	−5.01724e12	+	5.01724e12i	−0.309515	+	0.309515i
$863$	−1.93480e11	+	7.22078e11i	−0.0118738	+	0.0443135i	−0.971609	−	0.236594i	$-0.923969\pi$
$863$	−1.93480e11	+	7.22078e11i	−0.0118738	+	0.0443135i	0.959735	+	0.280908i	$0.0906355\pi$
$864$	6.00686e12	−	1.04042e13i	0.366721	−	0.635179i
$865$	−2.35542e13	−	8.65332e12i	−1.43053	−	0.525546i
$866$	4.52259e12	−	2.61112e12i	0.273248	−	0.157760i
$867$	−7.00426e12	−	7.00426e12i	−0.420995	−	0.420995i
$868$	1.41838e13	+	2.40084e13i	0.848111	+	1.43557i
$869$			1.10292e12i			0.0656079i
$870$	5.32243e12	+	4.81781e11i	0.314973	+	0.0285111i
$871$	−8.65866e12	−	4.99908e12i	−0.509764	−	0.294312i
$872$	−1.91604e12	−	7.15074e12i	−0.112222	−	0.418820i
$873$	1.63433e13	+	4.37918e12i	0.952305	+	0.255169i
$874$	3.00405e12			0.174143
$875$	−1.67531e13	−	4.47109e12i	−0.966183	−	0.257856i
$876$	7.14326e12			0.409853
$877$	−1.05603e13	−	2.82963e12i	−0.602808	−	0.161522i	−0.0555076	−	0.998458i	$-0.517678\pi$
$877$	−1.05603e13	−	2.82963e12i	−0.602808	−	0.161522i	−0.547300	+	0.836936i	$0.684344\pi$
$878$	−1.67492e12	−	6.25090e12i	−0.0951196	−	0.354991i
$879$	−2.46274e12	−	1.42186e12i	−0.139145	−	0.0803356i
$880$	8.90572e12	+	8.06137e11i	0.500607	+	0.0453145i
$881$			1.64269e13i			0.918681i	0.888260	+	0.459341i	$0.151914\pi$
$881$			1.64269e13i			0.918681i	−0.888260	+	0.459341i	$0.848086\pi$
$882$	−3.08148e12	+	8.92211e11i	−0.171455	+	0.0496431i
$883$	5.67686e12	+	5.67686e12i	0.314257	+	0.314257i	0.846556	−	0.532299i	$-0.178672\pi$
$883$	5.67686e12	+	5.67686e12i	0.314257	+	0.314257i	−0.532299	+	0.846556i	$0.678672\pi$
$884$	−4.52310e11	+	2.61141e11i	−0.0249116	+	0.0143827i
$885$	1.30719e13	+	4.80233e12i	0.716297	+	0.263152i
$886$	−3.17675e12	+	5.50229e12i	−0.173193	+	0.299979i
$887$	−1.81783e12	+	6.78424e12i	−0.0986047	+	0.367998i	−0.997541	−	0.0700810i	$-0.977674\pi$
$887$	−1.81783e12	+	6.78424e12i	−0.0986047	+	0.367998i	0.898937	+	0.438079i	$0.144341\pi$
$888$	1.46215e12	−	1.46215e12i	0.0789104	−	0.0789104i
$889$	1.48535e13	−	1.51541e13i	0.797576	−	0.813717i
$890$	9.58030e10	+	5.53044e11i	0.00511828	+	0.0295464i
$891$	−3.60441e11	−	6.24302e11i	−0.0191595	−	0.0331852i
$892$	1.27194e10	−	3.40815e9i	0.000672704	−	0.000180251i
$893$	3.38681e13	−	9.07493e12i	1.78221	−	0.477542i
$894$	1.57312e12	+	2.72473e12i	0.0823651	+	0.142661i
$895$	−1.89571e12	−	1.33590e12i	−0.0987572	−	0.0695940i
$896$	4.35118e12	−	1.69148e13i	0.225539	−	0.876758i
$897$	2.65765e12	−	2.65765e12i	0.137067	−	0.137067i
$898$	−9.33660e10	+	3.48447e11i	−0.00479121	+	0.0178810i
$899$	−3.38384e13	+	5.86099e13i	−1.72779	+	2.99263i
$900$	−1.15154e13	−	2.10194e12i	−0.585041	−	0.106790i
$901$	1.07923e12	−	6.23092e11i	0.0545571	−	0.0314986i
$902$	−6.91510e11	−	6.91510e11i	−0.0347831	−	0.0347831i
$903$	−3.43632e12	+	6.09201e12i	−0.171988	+	0.304906i
$904$		−	1.31079e13i		−	0.652790i
$905$	2.90311e12	−	3.20718e13i	0.143862	−	1.58930i
$906$	−3.82317e12	−	2.20731e12i	−0.188515	−	0.108839i
$907$	1.03662e13	+	3.86873e13i	0.508614	+	1.89817i	0.433880	+	0.900971i	$0.357144\pi$
$907$	1.03662e13	+	3.86873e13i	0.508614	+	1.89817i	0.0747346	+	0.997203i	$0.476189\pi$
$908$	−1.25993e13	−	3.37596e12i	−0.615118	−	0.164820i
$909$	4.44099e12			0.215746
$910$	−3.69151e12	+	1.75299e12i	−0.178450	+	0.0847409i
$911$	−3.74604e12			−0.180194			−0.0900970	−	0.995933i	$-0.528718\pi$
$911$	−3.74604e12			−0.180194			−0.0900970	+	0.995933i	$0.528718\pi$
$912$	−1.28719e13	−	3.44901e12i	−0.616119	−	0.165089i
$913$	−2.80936e12	−	1.04847e13i	−0.133810	−	0.499385i
$914$	5.17944e11	+	2.99035e11i	0.0245485	+	0.0141731i
$915$	−7.13011e12	−	8.54941e12i	−0.336280	−	0.403219i
$916$		−	2.75691e12i		−	0.129388i
$917$	8.86460e12	−	5.23706e12i	0.413997	−	0.244583i
$918$	1.80718e11	+	1.80718e11i	0.00839865	+	0.00839865i
$919$	−9.77955e12	+	5.64623e12i	−0.452271	+	0.261119i	−0.708789	−	0.705421i	$-0.750758\pi$
$919$	−9.77955e12	+	5.64623e12i	−0.452271	+	0.261119i	0.256518	+	0.966540i	$0.417425\pi$
$920$	−4.79038e12	+	2.21628e12i	−0.220458	+	0.101995i
$921$	−5.24499e11	+	9.08459e11i	−0.0240202	+	0.0416042i
$922$	−9.08770e10	+	3.39157e11i	−0.00414157	+	0.0154565i
$923$	−1.53196e13	+	1.53196e13i	−0.694767	+	0.694767i
$924$	5.64810e12	+	5.53607e12i	0.254905	+	0.249849i
$925$	−7.06404e12	−	3.34587e12i	−0.317260	−	0.150270i
$926$	−5.07755e12	−	8.79458e12i	−0.226937	−	0.393066i
$927$	−1.49163e13	+	3.99682e12i	−0.663443	+	0.177769i
$928$	3.12247e13	−	8.36663e12i	1.38208	−	0.370326i
$929$	1.06673e13	+	1.84763e13i	0.469876	+	0.813849i	0.999407	−	0.0344417i	$-0.0109653\pi$
$929$	1.06673e13	+	1.84763e13i	0.469876	+	0.813849i	−0.529531	+	0.848291i	$0.677632\pi$
$930$	3.92290e12	−	5.56679e12i	0.171963	−	0.244023i
$931$	1.63480e13	+	2.70492e13i	0.713165	+	1.18000i
$932$	2.03021e13	−	2.03021e13i	0.881394	−	0.881394i
$933$	−4.73805e10	+	1.76827e11i	−0.00204707	+	0.00763977i
$934$	−2.73132e12	+	4.73079e12i	−0.117439	+	0.203410i
$935$	−2.28276e11	+	6.21363e11i	−0.00976804	+	0.0265885i
$936$	−4.97708e12	+	2.87352e12i	−0.211950	+	0.122369i
$937$	−2.03074e13	−	2.03074e13i	−0.860650	−	0.860650i	0.130764	−	0.991414i	$-0.458257\pi$
$937$	−2.03074e13	−	2.03074e13i	−0.860650	−	0.860650i	−0.991414	+	0.130764i	$0.958257\pi$
$938$	5.43331e10	+	5.42399e12i	0.00229167	+	0.228774i
$939$			1.95896e13i			0.822299i
$940$	−2.27117e13	+	1.89413e13i	−0.948799	+	0.791288i
$941$	−1.28151e13	−	7.39878e12i	−0.532804	−	0.307614i	0.209354	−	0.977840i	$-0.432864\pi$
$941$	−1.28151e13	−	7.39878e12i	−0.532804	−	0.307614i	−0.742157	+	0.670226i	$0.766197\pi$
$942$	4.56380e11	+	1.70323e12i	0.0188842	+	0.0704766i
$943$	−2.92833e12	−	7.84643e11i	−0.120592	−	0.0323124i
$944$	2.42072e13			0.992135
$945$	−1.55841e13	−	1.83102e13i	−0.635680	−	0.746878i
$946$	2.59617e12			0.105396
$947$	4.39239e13	+	1.17694e13i	1.77470	+	0.475530i	0.989602	−	0.143836i	$-0.0459438\pi$
$947$	4.39239e13	+	1.17694e13i	1.77470	+	0.475530i	0.785102	+	0.619366i	$0.212610\pi$
$948$	3.58802e11	+	1.33907e12i	0.0144284	+	0.0538474i
$949$	−1.14808e13	−	6.62846e12i	−0.459489	−	0.265286i
$950$	−7.78471e11	−	9.55970e12i	−0.0310089	−	0.380792i
$951$			2.49028e13i			0.987269i
$952$	5.14119e11	+	2.90000e11i	0.0202861	+	0.0114428i
$953$	2.09083e13	+	2.09083e13i	0.821109	+	0.821109i	0.986267	−	0.165158i	$-0.0528134\pi$
$953$	2.09083e13	+	2.09083e13i	0.821109	+	0.821109i	−0.165158	+	0.986267i	$0.552813\pi$
$954$	5.70068e12	−	3.29129e12i	0.222823	−	0.128647i
$955$	8.07832e12	+	1.74609e13i	0.314272	+	0.679283i
$956$	7.85686e12	−	1.36085e13i	0.304220	−	0.526925i
$957$	−4.96792e12	+	1.85405e13i	−0.191457	+	0.714526i
$958$	3.44591e12	−	3.44591e12i	0.132178	−	0.132178i
$959$	6.71244e12	+	2.40836e13i	0.256270	+	0.919470i
$960$	8.79066e12	−	1.52279e12i	0.334042	−	0.0578656i
$961$	2.99009e13	+	5.17899e13i	1.13091	+	1.95880i
$962$	−1.77940e12	+	4.76788e11i	−0.0669862	+	0.0179489i
$963$	1.57819e13	−	4.22876e12i	0.591347	−	0.158451i
$964$	1.22709e13	+	2.12539e13i	0.457648	+	0.792669i
$965$	3.71101e13	−	6.42853e12i	1.37759	−	0.238637i
$966$	−1.97478e12	−	5.07996e11i	−0.0729663	−	0.0187700i
$967$	1.12861e13	−	1.12861e13i	0.415072	−	0.415072i	−0.468429	−	0.883501i	$-0.655180\pi$
$967$	1.12861e13	−	1.12861e13i	0.415072	−	0.415072i	0.883501	+	0.468429i	$0.155180\pi$
$968$	−2.18510e12	+	8.15490e12i	−0.0799893	+	0.298524i
$969$	4.93246e11	−	8.54328e11i	0.0179724	−	0.0311292i
$970$	−4.90992e12	−	1.06125e13i	−0.178074	−	0.384899i
$971$	−4.32293e13	+	2.49585e13i	−1.56060	+	0.901014i	−0.563406	+	0.826180i	$0.690509\pi$
$971$	−4.32293e13	+	2.49585e13i	−1.56060	+	0.901014i	−0.997196	+	0.0748338i	$0.976157\pi$
$972$	−1.84586e13	−	1.84586e13i	−0.663284	−	0.663284i
$973$	−5.04345e11	+	5.05212e9i	−0.0180393	+	0.000180703i
$974$		−	3.13277e12i		−	0.111536i
$975$	−9.14607e12	−	7.76866e12i	−0.324126	−	0.275312i
$976$	−1.67585e13	−	9.67554e12i	−0.591169	−	0.341312i
$977$	3.12817e12	+	1.16745e13i	0.109841	+	0.409933i	0.998849	−	0.0479586i	$-0.0152716\pi$
$977$	3.12817e12	+	1.16745e13i	0.109841	+	0.409933i	−0.889008	+	0.457891i	$0.848605\pi$
$978$	2.83385e12	+	7.59327e11i	0.0990493	+	0.0265402i
$979$	−2.01593e12			−0.0701380
$980$	−2.20938e13	−	1.49162e13i	−0.765162	−	0.516583i
$981$	−1.52031e13			−0.524110
$982$	1.95263e12	+	5.23206e11i	0.0670068	+	0.0179544i
$983$	−6.76220e12	−	2.52369e13i	−0.230992	−	0.862074i	−0.979915	−	0.199417i	$-0.936095\pi$
$983$	−6.76220e12	−	2.52369e13i	−0.230992	−	0.862074i	0.748923	−	0.662657i	$-0.230571\pi$
$984$	−2.21759e12	−	1.28033e12i	−0.0754056	−	0.0435355i
$985$	1.05123e13	−	8.76711e12i	0.355822	−	0.296752i
$986$			6.87691e11i			0.0231711i
$987$	−2.37986e13	+	2.38395e11i	−0.798223	+	0.00799595i
$988$	1.92189e13	+	1.92189e13i	0.641686	+	0.641686i
$989$	6.96990e12	−	4.02408e12i	0.231656	−	0.133747i
$990$	−1.20580e12	+	3.28216e12i	−0.0398947	+	0.108593i
$991$	1.12128e13	−	1.94212e13i	0.369304	−	0.639653i	−0.620153	−	0.784481i	$-0.712930\pi$
$991$	1.12128e13	−	1.94212e13i	0.369304	−	0.639653i	0.989457	+	0.144828i	$0.0462629\pi$
$992$	1.06617e13	−	3.97900e13i	0.349561	−	1.30458i
$993$	2.12347e13	−	2.12347e13i	0.693067	−	0.693067i
$994$	1.13833e13	+	2.92826e12i	0.369853	+	0.0951416i
$995$	2.04210e12	−	2.89784e12i	0.0660502	−	0.0937284i
$996$	−6.82172e12	−	1.18156e13i	−0.219648	−	0.380441i
$997$	4.80151e13	−	1.28656e13i	1.53904	−	0.412385i	0.613085	−	0.790017i	$-0.289928\pi$
$997$	4.80151e13	−	1.28656e13i	1.53904	−	0.412385i	0.925956	+	0.377632i	$0.123262\pi$
$998$	−1.11429e13	+	2.98572e12i	−0.355557	+	0.0952713i
$999$	−5.41938e12	−	9.38665e12i	−0.172149	−	0.298171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.16	✓	136
5.2	odd	4	inner	35.10.k.a.17.19	yes	136
7.5	odd	6	inner	35.10.k.a.33.19	yes	136
35.12	even	12	inner	35.10.k.a.12.16	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.16	✓	136	1.1	even	1	trivial
35.10.k.a.12.16	yes	136	35.12	even	12	inner
35.10.k.a.17.19	yes	136	5.2	odd	4	inner
35.10.k.a.33.19	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+(-6.05635 - 1.62279i) q^{2} +(21.6603 + 80.8372i) q^{3} +(-409.359 - 236.344i) q^{4} +(1391.85 + 125.989i) q^{5} -524.728i q^{6} +(-6352.13 + 63.6305i) q^{7} +(4365.66 + 4365.66i) q^{8} +(10980.5 - 6339.59i) q^{9} +(-8225.08 - 3021.72i) q^{10} +(15736.1 - 27255.8i) q^{11} +(10238.5 - 38210.7i) q^{12} +(-51912.6 + 51912.6i) q^{13} +(38574.0 + 9922.83i) q^{14} +(19963.3 + 115242. i) q^{15} +(101653. + 176067. i) q^{16} +(-14537.4 + 3895.29i) q^{17} +(-76789.5 + 20575.7i) q^{18} +(391609. + 678286. i) q^{19} +(-539991. - 380530. i) q^{20} +(-142733. - 512110. i) q^{21} +(-139534. + 139534. i) q^{22} +(-158327. + 590883. i) q^{23} +(-258347. + 447470. i) q^{24} +(1.92138e6 + 350716. i) q^{25} +(398644. - 230157. i) q^{26} +(1.91509e6 + 1.91509e6i) q^{27} +(2.61534e6 + 1.47524e6i) q^{28} +7.28756e6i q^{29} +(66110.1 - 730344. i) q^{30} +(8.04245e6 + 4.64331e6i) q^{31} +(-1.14807e6 - 4.28465e6i) q^{32} +(2.54413e6 + 681698. i) q^{33} +94365.0 q^{34} +(-8.84924e6 - 711735. i) q^{35} -5.99328e6 q^{36} +(-3.86561e6 - 1.03579e6i) q^{37} +(-1.27100e6 - 4.74344e6i) q^{38} +(-5.32091e6 - 3.07203e6i) q^{39} +(5.52633e6 + 6.62638e6i) q^{40} +4.95585e6i q^{41} +(33388.7 + 3.33314e6i) q^{42} +(-9.30301e6 - 9.30301e6i) q^{43} +(-1.28835e7 + 7.43827e6i) q^{44} +(1.60819e7 - 7.44035e6i) q^{45} +(1.91776e6 - 3.32166e6i) q^{46} +(1.15867e7 - 4.32423e7i) q^{47} +(-1.20310e7 + 1.20310e7i) q^{48} +(4.03455e7 - 808378. i) q^{49} +(-1.10674e7 - 5.24206e6i) q^{50} +(-629769. - 1.09079e6i) q^{51} +(3.35201e7 - 8.98169e6i) q^{52} +(-7.99801e7 + 2.14306e7i) q^{53} +(-8.49068e6 - 1.47063e7i) q^{54} +(2.53363e7 - 3.59534e7i) q^{55} +(-2.80091e7 - 2.74535e7i) q^{56} +(-4.63484e7 + 4.63484e7i) q^{57} +(1.18262e7 - 4.41360e7i) q^{58} +(5.95342e7 - 1.03116e8i) q^{59} +(1.90647e7 - 5.18937e7i) q^{60} +(-8.24305e7 + 4.75913e7i) q^{61} +(-4.11728e7 - 4.11728e7i) q^{62} +(-6.93461e7 + 4.09686e7i) q^{63} -7.62797e7i q^{64} +(-7.87951e7 + 6.57142e7i) q^{65} +(-1.43019e7 - 8.25720e6i) q^{66} +(3.52475e7 + 1.31546e8i) q^{67} +(6.87166e6 + 1.84126e6i) q^{68} -5.11947e7 q^{69} +(5.24391e7 + 1.86710e7i) q^{70} +2.95103e8 q^{71} +(7.56136e7 + 2.02606e7i) q^{72} +(4.67359e7 + 1.74421e8i) q^{73} +(2.17306e7 + 1.25462e7i) q^{74} +(1.32666e7 + 1.62915e8i) q^{75} -3.70217e8i q^{76} +(-9.82237e7 + 1.74134e8i) q^{77} +(2.72400e7 + 2.72400e7i) q^{78} +(-3.03492e7 + 1.75221e7i) q^{79} +(1.19303e8 + 2.57867e8i) q^{80} +(1.14526e7 - 1.98366e7i) q^{81} +(8.04232e6 - 3.00144e7i) q^{82} +(2.43875e8 - 2.43875e8i) q^{83} +(-6.26051e7 + 2.43371e8i) q^{84} +(-2.07247e7 + 3.59011e6i) q^{85} +(4.12454e7 + 7.14391e7i) q^{86} +(-5.89106e8 + 1.57851e8i) q^{87} +(1.87688e8 - 5.02909e7i) q^{88} +(-3.20271e7 - 5.54726e7i) q^{89} +(-1.09472e8 + 1.89637e7i) q^{90} +(3.26452e8 - 3.33059e8i) q^{91} +(2.04464e8 - 2.04464e8i) q^{92} +(-2.01151e8 + 7.50705e8i) q^{93} +(-1.40347e8 + 2.43087e8i) q^{94} +(4.59605e8 + 9.93412e8i) q^{95} +(3.21492e8 - 1.85613e8i) q^{96} +(9.43605e8 + 9.43605e8i) q^{97} +(-2.45658e8 - 6.05766e7i) q^{98} -3.99042e8i 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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