LMFDB - Embedded newform 35.10.k.a.17.19

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			17.19
Character	$\chi$	$=$	35.17
Dual form			35.10.k.a.33.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.62279 - 6.05635i) q^{2} +(80.8372 - 21.6603i) q^{3} +(409.359 + 236.344i) q^{4} +(586.816 - 1268.37i) q^{5} -524.728i q^{6} +(-63.6305 - 6352.13i) q^{7} +(4365.66 - 4365.66i) q^{8} +(-10980.5 + 6339.59i) q^{9} +(-6729.43 - 5612.27i) q^{10} +(15736.1 - 27255.8i) q^{11} +(38210.7 + 10238.5i) 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} +(-3895.29 - 14537.4i) q^{17} +(20575.7 + 76789.5i) q^{18} +(-391609. - 678286. i) q^{19} +(539991. - 380530. i) q^{20} +(-142733. - 512110. i) q^{21} +(-139534. - 139534. i) q^{22} +(590883. + 158327. i) q^{23} +(258347. - 447470. i) q^{24} +(-1.26442e6 - 1.48860e6i) q^{25} +(398644. - 230157. i) q^{26} +(-1.91509e6 + 1.91509e6i) q^{27} +(1.47524e6 - 2.61534e6i) q^{28} -7.28756e6i q^{29} +(-665552. - 307919. i) q^{30} +(8.04245e6 + 4.64331e6i) q^{31} +(4.28465e6 - 1.14807e6i) q^{32} +(681698. - 2.54413e6i) q^{33} -94365.0 q^{34} +(-8.09421e6 - 3.64683e6i) q^{35} -5.99328e6 q^{36} +(1.03579e6 - 3.86561e6i) q^{37} +(-4.74344e6 + 1.27100e6i) q^{38} +(5.32091e6 + 3.07203e6i) q^{39} +(-2.97545e6 - 8.09914e6i) q^{40} +4.95585e6i q^{41} +(-3.33314e6 + 33388.7i) q^{42} +(-9.30301e6 + 9.30301e6i) q^{43} +(1.28835e7 - 7.43827e6i) q^{44} +(1.59744e6 + 1.76475e7i) q^{45} +(1.91776e6 - 3.32166e6i) q^{46} +(4.32423e7 + 1.15867e7i) 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} +(8.98169e6 + 3.35201e7i) q^{52} +(2.14306e7 + 7.99801e7i) 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} +(-4.41360e7 - 1.18262e7i) q^{58} +(-5.95342e7 + 1.03116e8i) q^{59} +(3.54090e7 - 4.24573e7i) q^{60} +(-8.24305e7 + 4.75913e7i) q^{61} +(4.11728e7 - 4.11728e7i) q^{62} +(4.09686e7 + 6.93461e7i) q^{63} +7.62797e7i q^{64} +(9.63077e7 - 3.53814e7i) q^{65} +(-1.43019e7 - 8.25720e6i) q^{66} +(-1.31546e8 + 3.52475e7i) q^{67} +(1.84126e6 - 6.87166e6i) q^{68} +5.11947e7 q^{69} +(-3.52217e7 + 4.31033e7i) q^{70} +2.95103e8 q^{71} +(-2.02606e7 + 7.56136e7i) q^{72} +(1.74421e8 - 4.67359e7i) q^{73} +(-2.17306e7 - 1.25462e7i) q^{74} +(-1.34456e8 - 9.29470e7i) q^{75} -3.70217e8i q^{76} +(-1.74134e8 - 9.82237e7i) q^{77} +(2.72400e7 - 2.72400e7i) q^{78} +(3.03492e7 - 1.75221e7i) q^{79} +(2.82970e8 - 2.56142e7i) q^{80} +(1.14526e7 - 1.98366e7i) q^{81} +(3.00144e7 + 8.04232e6i) 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} +(-1.57851e8 - 5.89106e8i) q^{87} +(-5.02909e7 - 1.87688e8i) 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} +(7.50705e8 + 2.01151e8i) q^{93} +(1.40347e8 - 2.43087e8i) q^{94} +(-1.09012e9 + 9.86768e7i) q^{95} +(3.21492e8 - 1.85613e8i) q^{96} +(-9.43605e8 + 9.43605e8i) q^{97} +(-6.05766e7 + 2.45658e8i) 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 $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.62279	−	6.05635i	0.0717180	−	0.267655i	−0.920751	−	0.390151i	$-0.872423\pi$
$2$	1.62279	−	6.05635i	0.0717180	−	0.267655i	0.992469	+	0.122495i	$0.0390896\pi$
$3$	80.8372	−	21.6603i	0.576190	−	0.154390i	0.0410560	−	0.999157i	$-0.486928\pi$
$3$	80.8372	−	21.6603i	0.576190	−	0.154390i	0.535134	+	0.844767i	$0.320261\pi$
$4$	409.359	+	236.344i	0.799530	+	0.461609i
$5$	586.816	−	1268.37i	0.419891	−	0.907574i
$5$	586.816	−	1268.37i	0.419891	−	0.907574i
$6$		−	524.728i		−	0.165293i
$7$	−63.6305	−	6352.13i	−0.0100167	−	0.999950i
$7$	−63.6305	−	6352.13i	−0.0100167	−	0.999950i
$8$	4365.66	−	4365.66i	0.376830	−	0.376830i
$9$	−10980.5	+	6339.59i	−0.557867	+	0.322084i
$10$	−6729.43	−	5612.27i	−0.212803	−	0.177476i
$11$	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	$0.0616173\pi$
$12$	38210.7	+	10238.5i	0.531948	+	0.142535i
$13$	51912.6	+	51912.6i	0.504113	+	0.504113i	0.912713	−	0.408601i	$-0.133983\pi$
$13$	51912.6	+	51912.6i	0.504113	+	0.504113i	−0.408601	+	0.912713i	$0.633983\pi$
$14$	−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
$17$	−3895.29	−	14537.4i	−0.0113115	−	0.0422151i	0.960039	−	0.279865i	$-0.0902896\pi$
$17$	−3895.29	−	14537.4i	−0.0113115	−	0.0422151i	−0.971351	+	0.237650i	$0.923623\pi$
$18$	20575.7	+	76789.5i	0.0461985	+	0.172415i
$19$	−391609.	−	678286.i	−0.689384	−	1.19405i	−0.972038	−	0.234826i	$-0.924548\pi$
$19$	−391609.	−	678286.i	−0.689384	−	1.19405i	0.282654	−	0.959222i	$-0.408785\pi$
$20$	539991.	−	380530.i	0.754660	−	0.531807i
$21$	−142733.	−	512110.i	−0.160153	−	0.574615i
$22$	−139534.	−	139534.i	−0.126992	−	0.126992i
$23$	590883.	+	158327.i	0.440277	+	0.117972i	0.472146	−	0.881520i	$-0.343479\pi$
$23$	590883.	+	158327.i	0.440277	+	0.117972i	−0.0318693	+	0.999492i	$0.510146\pi$
$24$	258347.	−	447470.i	0.158947	−	0.275304i
$25$	−1.26442e6	−	1.48860e6i	−0.647382	−	0.762165i
$26$	398644.	−	230157.i	0.171082	−	0.0987745i
$27$	−1.91509e6	+	1.91509e6i	−0.693511	+	0.693511i
$28$	1.47524e6	−	2.61534e6i	0.453577	−	0.804113i
$29$		−	7.28756e6i		−	1.91334i	−0.291179	−	0.956668i	$-0.594048\pi$
$29$		−	7.28756e6i		−	1.91334i	0.291179	−	0.956668i	$-0.405952\pi$
$30$	−665552.	−	307919.i	−0.150016	−	0.0694050i
$31$	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	$0.308007\pi$
$32$	4.28465e6	−	1.14807e6i	0.722339	−	0.193550i
$33$	681698.	−	2.54413e6i	0.100064	−	0.373445i
$34$	−94365.0			−0.0121103
$35$	−8.09421e6	−	3.64683e6i	−0.911735	−	0.410780i
$36$	−5.99328e6			−0.594708
$37$	1.03579e6	−	3.86561e6i	0.0908580	−	0.339087i	−0.905501	−	0.424344i	$-0.860505\pi$
$37$	1.03579e6	−	3.86561e6i	0.0908580	−	0.339087i	0.996359	+	0.0852576i	$0.0271713\pi$
$38$	−4.74344e6	+	1.27100e6i	−0.369034	+	0.0988825i
$39$	5.32091e6	+	3.07203e6i	0.368295	+	0.212635i
$40$	−2.97545e6	−	8.09914e6i	−0.183773	−	0.500229i
$41$			4.95585e6i			0.273899i	0.990578	+	0.136950i	$0.0437299\pi$
$41$			4.95585e6i			0.273899i	−0.990578	+	0.136950i	$0.956270\pi$
$42$	−3.33314e6	+	33388.7i	−0.165285	+	0.00165569i
$43$	−9.30301e6	+	9.30301e6i	−0.414969	+	0.414969i	−0.883465	−	0.468497i	$-0.844796\pi$
$43$	−9.30301e6	+	9.30301e6i	−0.414969	+	0.414969i	0.468497	+	0.883465i	$0.344796\pi$
$44$	1.28835e7	−	7.43827e6i	0.518198	−	0.299182i
$45$	1.59744e6	+	1.76475e7i	0.0580721	+	0.641546i
$46$	1.91776e6	−	3.32166e6i	0.0631516	−	0.109382i
$47$	4.32423e7	+	1.15867e7i	1.29261	+	0.346354i	0.838652	−	0.544668i	$-0.183344\pi$
$47$	4.32423e7	+	1.15867e7i	1.29261	+	0.346354i	0.453960	+	0.891022i	$0.350011\pi$
$48$	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
$52$	8.98169e6	+	3.35201e7i	0.170350	+	0.635756i
$53$	2.14306e7	+	7.99801e7i	0.373072	+	1.39232i	0.856141	+	0.516742i	$0.172855\pi$
$53$	2.14306e7	+	7.99801e7i	0.373072	+	1.39232i	−0.483069	+	0.875582i	$0.660478\pi$
$54$	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
$58$	−4.41360e7	−	1.18262e7i	−0.512115	−	0.137221i
$59$	−5.95342e7	+	1.03116e8i	−0.639636	+	1.10788i	0.345877	+	0.938280i	$0.387581\pi$
$59$	−5.95342e7	+	1.03116e8i	−0.639636	+	1.10788i	−0.985513	+	0.169601i	$0.945752\pi$
$60$	3.54090e7	−	4.24573e7i	0.352722	−	0.422933i
$61$	−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
$63$	4.09686e7	+	6.93461e7i	0.327656	+	0.554612i
$64$			7.62797e7i			0.568328i
$65$	9.63077e7	−	3.53814e7i	0.669192	−	0.245847i
$66$	−1.43019e7	−	8.25720e6i	−0.0927781	−	0.0535655i
$67$	−1.31546e8	+	3.52475e7i	−0.797516	+	0.213694i	−0.634493	−	0.772928i	$-0.718791\pi$
$67$	−1.31546e8	+	3.52475e7i	−0.797516	+	0.213694i	−0.163023	+	0.986622i	$0.552124\pi$
$68$	1.84126e6	−	6.87166e6i	0.0104430	−	0.0389737i
$69$	5.11947e7			0.271897
$70$	−3.52217e7	+	4.31033e7i	−0.175335	+	0.214570i
$71$	2.95103e8			1.37820			0.689099	−	0.724668i	$-0.258007\pi$
$71$	2.95103e8			1.37820			0.689099	+	0.724668i	$0.258007\pi$
$72$	−2.02606e7	+	7.56136e7i	−0.0888498	+	0.331592i
$73$	1.74421e8	−	4.67359e7i	0.718862	−	0.192619i	0.119198	−	0.992870i	$-0.461968\pi$
$73$	1.74421e8	−	4.67359e7i	0.718862	−	0.192619i	0.599664	+	0.800252i	$0.295301\pi$
$74$	−2.17306e7	−	1.25462e7i	−0.0842422	−	0.0486372i
$75$	−1.34456e8	−	9.29470e7i	−0.490686	−	0.339203i
$76$		−	3.70217e8i		−	1.27290i
$77$	−1.74134e8	−	9.82237e7i	−0.564513	−	0.318425i
$78$	2.72400e7	−	2.72400e7i	0.0833262	−	0.0833262i
$79$	3.03492e7	−	1.75221e7i	0.0876649	−	0.0506133i	−0.455527	−	0.890222i	$-0.650549\pi$
$79$	3.03492e7	−	1.75221e7i	0.0876649	−	0.0506133i	0.543192	+	0.839609i	$0.317216\pi$
$80$	2.82970e8	−	2.56142e7i	0.772389	−	0.0699159i
$81$	1.14526e7	−	1.98366e7i	0.0295613	−	0.0512016i
$82$	3.00144e7	+	8.04232e6i	0.0733106	+	0.0196435i
$83$	−2.43875e8	−	2.43875e8i	−0.564048	−	0.564048i	0.366407	−	0.930455i	$-0.380588\pi$
$83$	−2.43875e8	−	2.43875e8i	−0.564048	−	0.564048i	−0.930455	+	0.366407i	$0.880588\pi$
$84$	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
$87$	−1.57851e8	−	5.89106e8i	−0.295399	−	1.10245i
$88$	−5.02909e7	−	1.87688e8i	−0.0893959	−	0.333630i
$89$	3.20271e7	+	5.54726e7i	0.0541082	+	0.0937181i	0.891811	−	0.452409i	$-0.149435\pi$
$89$	3.20271e7	+	5.54726e7i	0.0541082	+	0.0937181i	−0.837703	+	0.546127i	$0.816102\pi$
$90$	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
$93$	7.50705e8	+	2.01151e8i	1.04063	+	0.278836i
$94$	1.40347e8	−	2.43087e8i	0.185407	−	0.321135i
$95$	−1.09012e9	+	9.86768e7i	−1.37315	+	0.124297i
$96$	3.21492e8	−	1.85613e8i	0.386322	−	0.223043i
$97$	−9.43605e8	+	9.43605e8i	−1.08222	+	1.08222i	−0.0859232	+	0.996302i	$0.527384\pi$
$97$	−9.43605e8	+	9.43605e8i	−1.08222	+	1.08222i	−0.996302	+	0.0859232i	$0.972616\pi$
$98$	−6.05766e7	+	2.45658e8i	−0.0663419	+	0.269038i
$99$			3.99042e8i			0.417504i
$100$	−1.65779e8	−	9.08211e8i	−0.165779	−	0.908211i
$101$	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	$0.613110\pi$
$102$	−7.62821e6	+	2.04397e6i	−0.00697785	+	0.00186971i
$103$	−3.15227e8	+	1.17644e9i	−0.275967	+	1.02992i	0.679224	+	0.733931i	$0.262316\pi$
$103$	−3.15227e8	+	1.17644e9i	−0.275967	+	1.02992i	−0.955191	+	0.295990i	$0.904350\pi$
$104$	4.53266e8			0.379930
$105$	−7.33305e8	−	1.19476e8i	−0.588753	−	0.0959247i
$106$	5.19165e8			0.399419
$107$	−3.33520e8	+	1.24471e9i	−0.245977	+	0.918000i	0.726912	+	0.686730i	$0.240955\pi$
$107$	−3.33520e8	+	1.24471e9i	−0.245977	+	0.918000i	−0.972890	+	0.231269i	$0.925712\pi$
$108$	−1.23658e9	+	3.31341e8i	−0.874613	+	0.234352i
$109$	1.03842e9	+	5.99532e8i	0.704618	+	0.406811i	0.809065	−	0.587719i	$-0.199974\pi$
$109$	1.03842e9	+	5.99532e8i	0.704618	+	0.406811i	−0.104447	+	0.994530i	$0.533307\pi$
$110$	−2.58862e8	+	9.51004e7i	−0.168578	+	0.0619320i
$111$		−	3.34921e8i		−	0.209406i
$112$	1.11193e9	−	6.56913e8i	0.667726	−	0.394482i
$113$	−1.50124e9	+	1.50124e9i	−0.866160	+	0.866160i	−0.992045	−	0.125885i	$-0.959823\pi$
$113$	−1.50124e9	+	1.50124e9i	−0.866160	+	0.866160i	0.125885	+	0.992045i	$0.459823\pi$
$114$	−3.55916e8	+	2.05488e8i	−0.197367	+	0.113950i
$115$	5.47557e8	−	6.56552e8i	0.291937	−	0.350049i
$116$	1.72237e9	−	2.98323e9i	0.883213	−	1.52977i
$117$	−8.99130e8	−	2.40921e8i	−0.443595	−	0.118861i
$118$	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
$122$	1.54462e8	+	5.76458e8i	0.0631250	+	0.235586i
$123$	1.07345e8	+	4.00617e8i	0.0422872	+	0.157818i
$124$	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	0.178291	−	0.983978i	$-0.442943\pi$
$127$	−2.36202e9	−	2.36202e9i	−0.805687	−	0.805687i	−0.983978	+	0.178291i	$0.942943\pi$
$128$	2.65572e9	+	7.11598e8i	0.874455	+	0.234309i
$129$	−5.50524e8	+	9.53535e8i	−0.175034	+	0.303168i
$130$	−5.79946e7	−	6.40690e8i	−0.0178091	−	0.196745i
$131$	−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
$133$	−4.28364e9	+	2.53071e9i	−1.18708	+	0.701310i
$134$			8.53885e8i			0.228785i
$135$	1.30525e9	+	3.55286e9i	0.338213	+	0.920612i
$136$	−8.04711e7	−	4.64600e7i	−0.0201704	−	0.0116454i
$137$	3.80162e9	−	1.01864e9i	0.921991	−	0.247047i	0.233555	−	0.972344i	$-0.424964\pi$
$137$	3.80162e9	−	1.01864e9i	0.921991	−	0.247047i	0.688436	+	0.725297i	$0.258298\pi$
$138$	8.30785e7	−	3.10053e8i	0.0194999	−	0.0727746i
$139$	−7.93977e7			−0.0180402			−0.00902010	−	0.999959i	$-0.502871\pi$
$139$	−7.93977e7			−0.0180402			−0.00902010	+	0.999959i	$0.502871\pi$
$140$	−2.45154e9	−	3.40588e9i	−0.539339	−	0.749295i
$141$	3.74656e9			0.798263
$142$	4.78892e8	−	1.78725e9i	0.0988416	−	0.368882i
$143$	2.23182e9	−	5.98015e8i	0.446321	−	0.119591i
$144$	−2.23239e9	−	1.28887e9i	−0.432652	−	0.249792i
$145$	−9.24336e9	−	4.27646e9i	−1.73650	−	0.803394i
$146$		−	1.13220e9i		−	0.206222i
$147$	−3.24391e9	+	9.39242e8i	−0.572982	+	0.165901i
$148$	1.33762e9	−	1.33762e9i	0.229169	−	0.229169i
$149$	5.19264e9	−	2.99797e9i	0.863078	−	0.498298i	−0.00196393	−	0.999998i	$-0.500625\pi$
$149$	5.19264e9	−	2.99797e9i	0.863078	−	0.498298i	0.865042	+	0.501700i	$0.167292\pi$
$150$	−7.81113e8	+	6.63476e8i	−0.125980	+	0.107008i
$151$	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	$-0.0621268\pi$
$152$	−4.67080e9	−	1.25154e9i	−0.709733	−	0.190172i
$153$	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
$157$	−8.69745e8	−	3.24593e9i	−0.114247	−	0.426374i	0.884983	−	0.465624i	$-0.154170\pi$
$157$	−8.69745e8	−	3.24593e9i	−0.114247	−	0.426374i	−0.999229	+	0.0392494i	$0.987503\pi$
$158$	−5.68696e7	−	2.12240e8i	−0.00725978	−	0.0270939i
$159$	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
$163$	5.40060e9	+	1.44709e9i	0.599236	+	0.160565i	0.545671	−	0.838000i	$-0.316275\pi$
$163$	5.40060e9	+	1.44709e9i	0.599236	+	0.160565i	0.0535649	+	0.998564i	$0.482942\pi$
$164$	−1.17128e9	+	2.02872e9i	−0.126434	+	0.218991i
$165$	−2.82688e9	−	2.35758e9i	−0.296913	−	0.247622i
$166$	−1.87275e9	+	1.08123e9i	−0.191423	+	0.110518i
$167$	−7.57451e8	+	7.57451e8i	−0.0753581	+	0.0753581i	−0.743781	−	0.668423i	$-0.766970\pi$
$167$	−7.57451e8	+	7.57451e8i	−0.0753581	+	0.0753581i	0.668423	+	0.743781i	$0.266970\pi$
$168$	−2.85882e9	−	1.61258e9i	−0.276883	−	0.156181i
$169$		−	5.21466e9i		−	0.491741i
$170$	−5.53749e7	+	1.19690e8i	−0.00508502	+	0.0109910i
$171$	8.60011e9	+	4.96527e9i	0.769168	+	0.444080i
$172$	−6.00698e9	+	1.60957e9i	−0.523333	+	0.140227i
$173$	−4.64720e9	+	1.73436e10i	−0.394443	+	1.47208i	0.428284	+	0.903644i	$0.359118\pi$
$173$	−4.64720e9	+	1.73436e10i	−0.394443	+	1.47208i	−0.822727	+	0.568437i	$0.807548\pi$
$174$	−3.82399e9			−0.316261
$175$	−9.37535e9	+	8.12647e9i	−0.755643	+	0.654984i
$176$	6.39847e9			0.502654
$177$	−2.57905e9	+	9.62516e9i	−0.197506	+	0.737103i
$178$	3.87935e8	−	1.03947e8i	0.0289647	−	0.00776106i
$179$	1.43711e9	+	8.29718e8i	0.104629	+	0.0604076i	0.551401	−	0.834240i	$-0.314093\pi$
$179$	1.43711e9	+	8.29718e8i	0.104629	+	0.0604076i	−0.446772	+	0.894648i	$0.647427\pi$
$180$	−3.51696e9	+	7.60172e9i	−0.249713	+	0.539742i
$181$		−	2.30426e10i		−	1.59580i	−0.602793	−	0.797898i	$-0.705945\pi$
$181$		−	2.30426e10i		−	1.59580i	0.602793	−	0.797898i	$-0.294055\pi$
$182$	−1.48736e9	−	2.51759e9i	−0.100483	−	0.170084i
$183$	−5.63261e9	+	5.63261e9i	−0.371261	+	0.371261i
$184$	3.27080e9	−	1.88840e9i	0.210365	−	0.121454i
$185$	−4.29523e9	−	3.58217e9i	−0.269596	−	0.224840i
$186$	2.43648e9	−	4.22010e9i	0.149264	−	0.258532i
$187$	−4.57526e8	−	1.22594e8i	−0.0273608	−	0.00733130i
$188$	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	$0.711240\pi$
$192$	1.65224e9	+	6.16624e9i	0.0877440	+	0.327465i
$193$	−6.97499e9	−	2.60310e10i	−0.361856	−	1.35046i	−0.871633	−	0.490158i	$-0.836939\pi$
$193$	−6.97499e9	−	2.60310e10i	−0.361856	−	1.35046i	0.509778	−	0.860306i	$-0.329728\pi$
$194$	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	0.851681	−	0.524060i	$-0.175583\pi$
$197$	6.92580e9	+	6.92580e9i	0.327621	+	0.327621i	−0.524060	+	0.851681i	$0.675583\pi$
$198$	2.41674e9	+	6.47563e8i	0.111747	+	0.0299426i
$199$	−1.26833e9	+	2.19681e9i	−0.0573316	+	0.0993012i	−0.893267	−	0.449527i	$-0.851593\pi$
$199$	−1.26833e9	+	2.19681e9i	−0.0573316	+	0.0993012i	0.835935	+	0.548828i	$0.184926\pi$
$200$	−1.20188e10	−	9.78720e8i	−0.531160	−	0.0432537i
$201$	−9.87030e9	+	5.69862e9i	−0.426529	+	0.246256i
$202$	1.55289e9	−	1.55289e9i	0.0656236	−	0.0656236i
$203$	−4.62916e10	+	4.63711e8i	−1.91324	+	0.0191653i
$204$		−	5.95368e8i		−	0.0240685i
$205$	6.28587e9	+	2.90817e9i	0.248584	+	0.115008i
$206$	6.61341e9	+	3.81825e9i	0.255872	+	0.147728i
$207$	−7.49191e9	+	2.00745e9i	−0.283613	+	0.0759938i
$208$	−3.86307e9	+	1.44172e10i	−0.143102	+	0.534066i
$209$	−2.46496e10			−0.893618
$210$	−1.91359e9	+	4.24726e9i	−0.0678989	+	0.150703i
$211$	1.25279e10			0.435119			0.217559	−	0.976047i	$-0.430190\pi$
$211$	1.25279e10			0.435119			0.217559	+	0.976047i	$0.430190\pi$
$212$	−1.01300e10	+	3.78056e10i	−0.344427	+	1.28542i
$213$	2.38553e10	−	6.39201e9i	0.794103	−	0.212779i
$214$	6.99719e9	+	4.03983e9i	0.228066	+	0.131674i
$215$	6.34054e9	+	1.72589e10i	0.202373	+	0.550857i
$216$			1.67213e10i			0.522671i
$217$	2.89832e10	−	5.13822e10i	0.887314	−	1.57305i
$218$	5.31611e9	−	5.31611e9i	0.159419	−	0.159419i
$219$	1.30874e10	−	7.55601e9i	0.384463	−	0.221970i
$220$	−1.87428e9	−	2.07059e10i	−0.0539427	−	0.595927i
$221$	5.52461e8	−	9.56891e8i	0.0155789	−	0.0269834i
$222$	−2.02840e9	−	5.43507e8i	−0.0560486	−	0.0150182i
$223$	1.96985e7	+	1.96985e7i	0.000533411	+	0.000533411i	0.707373	−	0.706840i	$-0.249880\pi$
$223$	1.96985e7	+	1.96985e7i	0.000533411	+	0.000533411i	−0.706840	+	0.707373i	$0.749880\pi$
$224$	−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
$227$	7.14206e9	+	2.66545e10i	0.178528	+	0.666277i	0.995924	+	0.0901997i	$0.0287505\pi$
$227$	7.14206e9	+	2.66545e10i	0.178528	+	0.666277i	−0.817395	+	0.576077i	$0.804583\pi$
$228$	−8.01899e9	−	2.99273e10i	−0.196523	−	0.733433i
$229$	−2.91621e9	−	5.05102e9i	−0.0700743	−	0.121372i	0.828859	−	0.559457i	$-0.188990\pi$
$229$	−2.91621e9	−	5.05102e9i	−0.0700743	−	0.121372i	−0.898934	+	0.438085i	$0.855657\pi$
$230$	−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
$233$	5.86715e10	+	1.57210e10i	1.30414	+	0.349444i	0.843015	−	0.537890i	$-0.180778\pi$
$233$	5.86715e10	+	1.57210e10i	1.30414	+	0.349444i	0.461128	+	0.887334i	$0.347445\pi$
$234$	−2.91821e9	+	5.05448e9i	−0.0636274	+	0.110206i
$235$	4.00716e10	−	4.80481e10i	0.857099	−	1.02771i
$236$	−4.87417e10	+	2.81411e10i	−1.02281	+	0.590523i
$237$	2.07381e9	−	2.07381e9i	0.0426975	−	0.0426975i
$238$	6.00449e6	+	5.99419e8i	0.000121305	+	0.0121097i
$239$		−	3.32434e10i		−	0.659044i	−0.944148	−	0.329522i	$-0.893112\pi$
$239$		−	3.32434e10i		−	0.659044i	0.944148	−	0.329522i	$-0.106888\pi$
$240$	2.23197e10	−	8.19980e9i	0.434249	−	0.159534i
$241$	−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	$0.831759\pi$
$242$	8.28172e9	−	2.21908e9i	0.155221	−	0.0415914i
$243$	1.42934e10	−	5.33437e10i	0.262971	−	0.981420i
$244$	−4.49916e10			−0.812600
$245$	−2.26501e10	+	5.16476e10i	−0.401626	+	0.915804i
$246$	2.60048e9			0.0452736
$247$	1.48822e10	−	5.55410e10i	0.254408	−	0.949462i
$248$	5.53818e10	−	1.48395e10i	0.929682	−	0.249108i
$249$	−2.49966e10	−	1.44318e10i	−0.412082	−	0.237916i
$250$	1.54364e8	+	1.71137e10i	0.00249929	+	0.277086i
$251$		−	5.44822e10i		−	0.866408i	−0.901296	−	0.433204i	$-0.857383\pi$
$251$		−	5.44822e10i		−	0.866408i	0.901296	−	0.433204i	$-0.142617\pi$
$252$	3.81356e8	+	3.80701e10i	0.00595700	+	0.594678i
$253$	1.36135e10	−	1.36135e10i	0.208895	−	0.208895i
$254$	−1.81383e10	+	1.04721e10i	−0.273429	+	0.157864i
$255$	−1.75309e9	+	1.58688e8i	−0.0259641	+	0.00235025i
$256$	−1.09082e10	+	1.88936e10i	−0.158736	+	0.274939i
$257$	2.70138e10	+	7.23834e9i	0.386267	+	0.103500i	0.446726	−	0.894671i	$-0.352590\pi$
$257$	2.70138e10	+	7.23834e9i	0.386267	+	0.103500i	−0.0604593	+	0.998171i	$0.519257\pi$
$258$	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
$262$	2.63021e9	+	9.81610e9i	0.0344854	+	0.128701i
$263$	−9.03579e9	−	3.37220e10i	−0.116457	−	0.434623i	0.882935	−	0.469496i	$-0.155564\pi$
$263$	−9.03579e9	−	3.37220e10i	−0.116457	−	0.434623i	−0.999392	+	0.0348724i	$0.988898\pi$
$264$	−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
$268$	−6.21799e10	−	1.66611e10i	−0.736281	−	0.197286i
$269$	9.38488e9	−	1.62551e10i	0.109281	−	0.189280i	−0.806198	−	0.591645i	$-0.798479\pi$
$269$	9.38488e9	−	1.62551e10i	0.109281	−	0.189280i	0.915479	+	0.402366i	$0.131812\pi$
$270$	2.36355e10	−	2.13947e9i	0.270663	−	0.0245001i
$271$	−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
$273$	1.91754e10	−	3.39946e10i	0.208935	−	0.370406i
$274$		−	2.46770e10i		−	0.264493i
$275$	−6.04701e10	+	1.10378e10i	−0.637593	+	0.116382i
$276$	2.09570e10	+	1.20995e10i	0.217390	+	0.125510i
$277$	1.00861e11	−	2.70257e10i	1.02935	−	0.275815i	0.295659	−	0.955293i	$-0.404461\pi$
$277$	1.00861e11	−	2.70257e10i	1.02935	−	0.275815i	0.733695	+	0.679479i	$0.237794\pi$
$278$	−1.28846e8	+	4.80860e8i	−0.00129381	+	0.00482856i
$279$	−1.17747e11			−1.16340
$280$	−5.12574e10	+	1.94158e10i	−0.498363	+	0.188775i
$281$	−8.29793e10			−0.793947			−0.396973	−	0.917830i	$-0.629940\pi$
$281$	−8.29793e10			−0.793947			−0.396973	+	0.917830i	$0.629940\pi$
$282$	6.07989e9	−	2.26904e10i	0.0572499	−	0.213659i
$283$	−1.82155e11	+	4.88082e10i	−1.68811	+	0.452328i	−0.969901	−	0.243498i	$-0.921705\pi$
$283$	−1.82155e11	+	4.88082e10i	−1.68811	+	0.452328i	−0.718210	+	0.695826i	$0.755038\pi$
$284$	1.20803e11	+	6.97457e10i	1.10191	+	0.636188i
$285$	−8.59851e10	+	3.15891e10i	−0.772007	+	0.283619i
$286$		−	1.44871e10i		−	0.128037i
$287$	3.14802e10	−	3.15343e8i	0.273886	−	0.00274356i
$288$	−3.97693e10	+	3.97693e10i	−0.340629	+	0.340629i
$289$	1.02504e11	−	5.91807e10i	0.864371	−	0.499045i
$290$	−4.08998e10	+	4.90412e10i	−0.339571	+	0.407164i
$291$	−5.58397e10	+	9.67172e10i	−0.456483	+	0.790651i
$292$	8.24465e10	+	2.20915e10i	0.663666	+	0.177829i
$293$	2.40273e10	+	2.40273e10i	0.190459	+	0.190459i	0.795894	−	0.605435i	$-0.207001\pi$
$293$	2.40273e10	+	2.40273e10i	0.190459	+	0.190459i	−0.605435	+	0.795894i	$0.707001\pi$
$294$	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
$297$	2.20612e10	+	8.23336e10i	0.164523	+	0.614007i
$298$	−9.73018e9	−	3.63135e10i	−0.0714739	−	0.266744i
$299$	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
$303$	2.83139e10	+	7.58670e9i	0.192978	+	0.0517084i
$304$	7.96160e10	−	1.37899e11i	0.534650	−	0.926040i
$305$	1.19920e10	+	1.32480e11i	0.0793489	+	0.876599i
$306$	1.03617e9	−	5.98235e8i	0.00675595	−	0.00390055i
$307$	−8.86323e9	+	8.86323e9i	−0.0569468	+	0.0569468i	−0.735007	−	0.678060i	$-0.762821\pi$
$307$	−8.86323e9	+	8.86323e9i	−0.0569468	+	0.0569468i	0.678060	+	0.735007i	$0.262821\pi$
$308$	−4.80686e10	−	8.13641e10i	−0.304357	−	0.515175i
$309$			1.01928e11i			0.636037i
$310$	−2.80616e10	−	7.63833e10i	−0.172578	−	0.469754i
$311$	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	$0.664556\pi$
$312$	3.66408e10	−	9.81786e9i	0.218912	−	0.0586572i
$313$	6.05834e10	−	2.26100e11i	0.356783	−	1.33153i	−0.521443	−	0.853286i	$-0.674606\pi$
$313$	6.05834e10	−	2.26100e11i	0.356783	−	1.33153i	0.878226	−	0.478246i	$-0.158727\pi$
$314$	−2.10699e10			−0.122315
$315$	1.11998e11	−	1.12701e10i	0.640932	−	0.0644954i
$316$	1.65650e10			0.0934542
$317$	−7.70152e10	+	2.87425e11i	−0.428361	+	1.59866i	0.328112	+	0.944639i	$0.393588\pi$
$317$	−7.70152e10	+	2.87425e11i	−0.428361	+	1.59866i	−0.756473	+	0.654025i	$0.773079\pi$
$318$	4.19678e10	−	1.12452e10i	0.230141	−	0.0616662i
$319$	−1.98628e11	−	1.14678e11i	−1.07395	−	0.620044i
$320$	9.67512e10	+	4.47622e10i	0.515800	+	0.238636i
$321$			1.07843e11i			0.566919i
$322$	−2.12216e10	−	1.19705e10i	−0.110009	−	0.0620528i
$323$	−8.33511e9	+	8.33511e9i	−0.0426089	+	0.0426089i
$324$	9.37649e9	−	5.41352e9i	0.0472702	−	0.0272915i
$325$	1.16381e10	−	1.42917e11i	0.0578637	−	0.710571i
$326$	1.75281e10	−	3.03596e10i	0.0859520	−	0.148873i
$327$	9.69290e10	+	2.59720e10i	0.468801	+	0.125615i
$328$	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	$-0.473561\pi$
$332$	−4.21942e10	−	1.57471e11i	−0.190604	−	0.711343i
$333$	1.31329e10	+	4.90128e10i	0.0585279	+	0.218429i
$334$	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	0.0707536	−	0.997494i	$-0.477460\pi$
$337$	−2.19428e11	−	2.19428e11i	−0.926740	−	0.926740i	−0.997494	+	0.0707536i	$0.977460\pi$
$338$	−3.15818e10	−	8.46232e9i	−0.131617	−	0.0352667i
$339$	−8.88390e10	+	1.53874e11i	−0.365347	+	0.632799i
$340$	−7.63535e9	−	6.36780e9i	−0.0309866	−	0.0258425i
$341$	2.53114e11	−	1.46136e11i	1.01373	−	0.585277i
$342$	4.40276e10	−	4.40276e10i	0.174023	−	0.174023i
$343$	7.70213e9	+	2.56228e11i	0.0300460	+	0.999549i
$344$			8.12276e10i			0.312745i
$345$	3.00419e10	−	6.49340e10i	0.114167	−	0.246767i
$346$	9.74974e10	+	5.62902e10i	0.365722	+	0.211149i
$347$	−4.37644e11	+	1.17266e11i	−1.62046	+	0.434201i	−0.951136	−	0.308771i	$-0.900082\pi$
$347$	−4.37644e11	+	1.17266e11i	−1.62046	+	0.434201i	−0.669323	+	0.742972i	$0.733416\pi$
$348$	7.46140e10	−	2.78463e11i	0.272718	−	1.01780i
$349$	−9.68004e10			−0.349271			−0.174635	−	0.984633i	$-0.555875\pi$
$349$	−9.68004e10			−0.349271			−0.174635	+	0.984633i	$0.555875\pi$
$350$	3.40025e10	+	6.99680e10i	0.121117	+	0.249226i
$351$	−1.98835e11			−0.699216
$352$	3.61323e10	−	1.34848e11i	0.125445	−	0.468168i
$353$	3.36834e11	−	9.02545e10i	1.15460	−	0.309373i	0.369791	−	0.929115i	$-0.379429\pi$
$353$	3.36834e11	−	9.02545e10i	1.15460	−	0.309373i	0.784806	+	0.619742i	$0.212763\pi$
$354$	5.41080e10	+	3.12393e10i	0.183125	+	0.105727i
$355$	1.73171e11	−	3.74301e11i	0.578693	−	1.25082i
$356$			3.02776e10i			0.0999072i
$357$	−6.88878e9	+	4.06979e9i	−0.0224458	+	0.0132606i
$358$	7.35720e9	−	7.35720e9i	0.0236722	−	0.0236722i
$359$	−1.92984e11	+	1.11419e11i	−0.613192	+	0.354027i	−0.774214	−	0.632924i	$-0.781854\pi$
$359$	−1.92984e11	+	1.11419e11i	−0.613192	+	0.354027i	0.161022	+	0.986951i	$0.448521\pi$
$360$	8.40171e10	+	7.00693e10i	0.263637	+	0.219870i
$361$	−1.45371e11	+	2.51790e11i	−0.450500	+	0.780289i
$362$	−1.39554e11	−	3.73933e10i	−0.427123	−	0.114447i
$363$	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
$367$	2.38235e10	+	8.89106e10i	0.0685502	+	0.255833i	0.991694	−	0.128623i	$-0.0410558\pi$
$367$	2.38235e10	+	8.89106e10i	0.0685502	+	0.255833i	−0.923143	+	0.384456i	$0.874389\pi$
$368$	3.21886e10	+	1.20129e11i	0.0914928	+	0.341456i
$369$	−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
$373$	−2.03193e11	−	5.44454e10i	−0.543525	−	0.145637i	−0.0233982	−	0.999726i	$-0.507449\pi$
$373$	−2.03193e11	−	5.44454e10i	−0.543525	−	0.145637i	−0.520127	+	0.854089i	$0.674115\pi$
$374$	−1.48494e9	+	2.57199e9i	−0.00392452	+	0.00679747i
$375$	−1.96792e11	+	1.15997e11i	−0.513887	+	0.302905i
$376$	2.39365e11	−	1.38197e11i	0.617611	−	0.356578i
$377$	3.78316e11	−	3.78316e11i	0.964538	−	0.964538i
$378$	9.28760e10	−	5.48697e10i	0.233986	−	0.138235i
$379$			3.22937e11i			0.803973i	0.915646	+	0.401986i	$0.131680\pi$
$379$			3.22937e11i			0.803973i	−0.915646	+	0.401986i	$0.868320\pi$
$380$	−4.69573e11	−	2.17249e11i	−1.15525	−	0.534481i
$381$	−2.42101e11	−	1.39777e11i	−0.588618	−	0.339839i
$382$	8.33738e10	−	2.23399e10i	0.200329	−	0.0536781i
$383$	−9.01407e10	+	3.36410e11i	−0.214056	+	0.798866i	0.772441	+	0.635086i	$0.219035\pi$
$383$	−9.01407e10	+	3.36410e11i	−0.214056	+	0.798866i	−0.986497	+	0.163780i	$0.947631\pi$
$384$	2.30094e11			0.540027
$385$	−2.26769e11	+	1.63227e11i	−0.526029	+	0.378634i
$386$	−1.68972e11			−0.387411
$387$	4.31744e10	−	1.61129e11i	0.0978423	−	0.365152i
$388$	−6.09288e11	+	1.63258e11i	−1.36484	+	0.365706i
$389$	3.54460e11	+	2.04648e11i	0.784864	+	0.453142i	0.838151	−	0.545438i	$-0.183637\pi$
$389$	3.54460e11	+	2.04648e11i	0.784864	+	0.453142i	−0.0532871	+	0.998579i	$0.516970\pi$
$390$	−1.85656e10	−	5.05354e10i	−0.0406368	−	0.110613i
$391$		−	9.20665e9i		−	0.0199208i
$392$	−1.72606e11	+	1.79664e11i	−0.369205	+	0.384303i
$393$	−9.59137e10	+	9.59137e10i	−0.202822	+	0.202822i
$394$	5.31842e10	−	3.07059e10i	0.111186	−	0.0641932i
$395$	−4.41520e9	−	4.87764e10i	−0.00912563	−	0.100815i
$396$	−9.43111e10	+	1.63352e11i	−0.192723	+	0.333807i
$397$	5.64962e10	+	1.51381e10i	0.114146	+	0.0305854i	0.315440	−	0.948946i	$-0.397848\pi$
$397$	5.64962e10	+	1.51381e10i	0.114146	+	0.0305854i	−0.201294	+	0.979531i	$0.564515\pi$
$398$	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	$0.997506\pi$
$402$	1.84954e10	+	6.90257e10i	0.0353220	+	0.131824i
$403$	1.76458e11	+	6.58551e11i	0.333249	+	1.24370i
$404$	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
$408$	−7.51140e9	−	2.01267e9i	−0.0134199	−	0.00359586i
$409$	−2.33222e11	+	4.03952e11i	−0.412111	+	0.713797i	−0.995120	−	0.0986685i	$-0.968542\pi$
$409$	−2.33222e11	+	4.03952e11i	−0.412111	+	0.713797i	0.583010	+	0.812465i	$0.301875\pi$
$410$	2.78136e10	−	3.33501e10i	0.0486104	−	0.0582867i
$411$	2.85249e11	−	1.64688e11i	0.493100	−	0.284692i
$412$	−4.07086e11	+	4.07086e11i	−0.696064	+	0.696064i
$413$	6.58796e11	+	3.71608e11i	1.11423	+	0.628506i
$414$			4.86313e10i			0.0813606i
$415$	−4.52435e11	+	1.66215e11i	−0.748755	+	0.275077i
$416$	2.82027e11	+	1.62828e11i	0.461711	+	0.266569i
$417$	−6.41829e9	+	1.71978e9i	−0.0103946	+	0.00278522i
$418$	−4.00012e10	+	1.49287e11i	−0.0640885	+	0.239182i
$419$	2.82987e9			0.00448542			0.00224271	−	0.999997i	$-0.499286\pi$
$419$	2.82987e9			0.00448542			0.00224271	+	0.999997i	$0.499286\pi$
$420$	−2.71948e11	−	2.22221e11i	−0.426445	−	0.348468i
$421$	6.93519e11			1.07594			0.537971	−	0.842963i	$-0.319191\pi$
$421$	6.93519e11			1.07594			0.537971	+	0.842963i	$0.319191\pi$
$422$	2.03302e10	−	7.58734e10i	0.0312058	−	0.116462i
$423$	−5.48276e11	+	1.46910e11i	−0.832660	+	0.223111i
$424$	4.42725e11	+	2.55607e11i	0.665254	+	0.384085i
$425$	−1.67152e10	+	2.41800e10i	−0.0248520	+	0.0359505i
$426$		−	1.54849e11i		−	0.227806i
$427$	3.07551e11	+	5.20581e11i	0.447705	+	0.757814i
$428$	−4.30710e11	+	4.30710e11i	−0.620423	+	0.620423i
$429$	1.67461e11	−	9.66837e10i	0.238702	−	0.137815i
$430$	1.14815e11	−	1.03929e10i	0.161954	−	0.0146599i
$431$	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	$-0.123166\pi$
$432$	−5.31860e11	−	1.42511e11i	−0.734717	−	0.196867i
$433$	5.88944e11	+	5.88944e11i	0.805154	+	0.805154i	0.983896	−	0.178742i	$-0.0572028\pi$
$433$	5.88944e11	+	5.88944e11i	0.805154	+	0.805154i	−0.178742	+	0.983896i	$0.557203\pi$
$434$	−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
$437$	−1.24004e11	−	4.62790e11i	−0.162656	−	0.607040i
$438$	−2.45237e10	−	9.15236e10i	−0.0318385	−	0.118823i
$439$	−5.16062e11	−	8.93846e11i	−0.663150	−	1.14861i	−0.979783	−	0.200061i	$-0.935886\pi$
$439$	−5.16062e11	−	8.93846e11i	−0.663150	−	1.14861i	0.316634	−	0.948548i	$-0.397447\pi$
$440$	−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
$443$	−9.78790e11	−	2.62266e11i	−1.20746	−	0.323538i	−0.401695	−	0.915774i	$-0.631579\pi$
$443$	−9.78790e11	−	2.62266e11i	−1.20746	−	0.323538i	−0.805765	+	0.592236i	$0.798245\pi$
$444$	7.91564e10	−	1.37103e11i	0.0966635	−	0.167426i
$445$	8.91540e10	−	8.07013e9i	0.107776	−	0.00975575i
$446$	1.51268e8	−	8.73344e7i	0.000181025	−	0.000104515i
$447$	3.54822e11	−	3.54822e11i	0.420365	−	0.420365i
$448$	4.84539e11	−	4.85372e9i	0.568300	−	0.00569277i
$449$			5.75341e10i			0.0668062i	0.999442	+	0.0334031i	$0.0106345\pi$
$449$			5.75341e10i			0.0668062i	−0.999442	+	0.0334031i	$0.989365\pi$
$450$	8.82929e10	−	1.27723e11i	0.101501	−	0.146829i
$451$	1.35076e11	+	7.79859e10i	0.153738	+	0.0887609i
$452$	−9.69357e11	+	2.59738e11i	−1.09235	+	0.292694i
$453$	1.82231e11	−	6.80095e11i	0.203320	−	0.758801i
$454$	1.73019e11			0.191136
$455$	−2.30875e11	−	6.09508e11i	−0.252538	−	0.666696i
$456$	−4.04683e11			−0.438302
$457$	2.46877e10	−	9.21358e10i	0.0264764	−	0.0988111i	−0.951423	−	0.307886i	$-0.900379\pi$
$457$	2.46877e10	−	9.21358e10i	0.0264764	−	0.0988111i	0.977900	+	0.209075i	$0.0670452\pi$
$458$	−3.53231e10	+	9.46480e9i	−0.0375115	+	0.0100512i
$459$	3.53004e10	+	2.03807e10i	0.0371213	+	0.0214320i
$460$	3.79319e11	−	1.39354e11i	0.394998	−	0.145114i
$461$		−	5.60003e10i		−	0.0577479i	−0.999583	−	0.0288740i	$-0.990808\pi$
$461$		−	5.60003e10i		−	0.0577479i	0.999583	−	0.0288740i	$-0.00919214\pi$
$462$	−5.15407e10	+	9.13728e10i	−0.0526334	+	0.0933100i
$463$	1.14526e12	−	1.14526e12i	1.15821	−	1.15821i	0.173352	−	0.984860i	$-0.444540\pi$
$463$	1.14526e12	−	1.14526e12i	1.15821	−	1.15821i	0.984860	−	0.173352i	$-0.0554598\pi$
$464$	1.28310e12	−	7.40799e11i	1.28508	−	0.741941i
$465$	6.95660e11	−	8.34136e11i	0.690016	−	0.827368i
$466$	1.90423e11	−	3.29823e11i	0.187061	−	0.323999i
$467$	8.41550e11	+	2.25493e11i	0.818755	+	0.219385i	0.643802	−	0.765192i	$-0.277356\pi$
$467$	8.41550e11	+	2.25493e11i	0.818755	+	0.219385i	0.174953	+	0.984577i	$0.444023\pi$
$468$	−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
$472$	1.90265e11	+	7.10077e11i	0.176449	+	0.658517i
$473$	1.07167e11	+	3.99954e11i	0.0984436	+	0.367397i
$474$	−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
$478$	−2.01333e11	−	5.39471e10i	−0.176397	−	0.0472653i
$479$	3.88617e11	−	6.73104e11i	0.337296	−	0.584214i	−0.646627	−	0.762806i	$-0.723821\pi$
$479$	3.88617e11	−	6.73104e11i	0.337296	−	0.584214i	0.983923	+	0.178592i	$0.0571542\pi$
$480$	−4.67705e10	−	5.16693e11i	−0.0402149	−	0.444270i
$481$	2.54444e11	−	1.46904e11i	0.216741	−	0.125135i
$482$	−2.30190e11	+	2.30190e11i	−0.194256	+	0.194256i
$483$	−3.25754e9	−	3.25196e11i	−0.00272351	−	0.271883i
$484$			6.46373e11i			0.535401i
$485$	6.43121e11	+	1.75057e12i	0.527783	+	1.43662i
$486$	−2.99873e11	−	1.73132e11i	−0.243822	−	0.140771i
$487$	−4.82621e11	+	1.29318e11i	−0.388799	+	0.104178i	−0.447923	−	0.894072i	$-0.647836\pi$
$487$	−4.82621e11	+	1.29318e11i	−0.388799	+	0.104178i	0.0591235	+	0.998251i	$0.481169\pi$
$488$	−1.52096e11	+	5.67631e11i	−0.121403	+	0.453082i
$489$	4.67914e11			0.370063
$490$	2.76039e11	+	2.20990e11i	0.216316	+	0.173177i
$491$	−3.22411e11			−0.250347			−0.125174	−	0.992135i	$-0.539949\pi$
$491$	−3.22411e11			−0.250347			−0.125174	+	0.992135i	$0.539949\pi$
$492$	−5.07406e10	+	1.89367e11i	−0.0390403	+	0.145700i
$493$	−1.05943e11	+	2.83872e10i	−0.0807717	+	0.0216427i
$494$	−3.12225e11	−	1.80263e11i	−0.235883	−	0.136187i
$495$	5.06135e11	+	2.34165e11i	0.378916	+	0.175306i
$496$			1.88802e12i			1.40068i
$497$	−1.87776e10	−	1.87453e12i	−0.0138050	−	1.37813i
$498$	−1.27968e11	+	1.27968e11i	−0.0932331	+	0.0932331i
$499$	−1.59337e12	+	9.19933e11i	−1.15044	+	0.664208i	−0.948995	−	0.315292i	$-0.897898\pi$
$499$	−1.59337e12	+	9.19933e11i	−1.15044	+	0.664208i	−0.201447	+	0.979499i	$0.564564\pi$
$500$	−1.24923e12	−	3.22683e11i	−0.893878	−	0.230893i
$501$	−4.48236e10	+	7.76368e10i	−0.0317861	+	0.0550551i
$502$	−3.29963e11	−	8.84133e10i	−0.231899	−	0.0621371i
$503$	−1.81776e12	−	1.81776e12i	−1.26613	−	1.26613i	−0.948069	−	0.318065i	$-0.896967\pi$
$503$	−1.81776e12	−	1.81776e12i	−1.26613	−	1.26613i	−0.318065	−	0.948069i	$-0.603033\pi$
$504$	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
$507$	−1.12951e11	−	4.21539e11i	−0.0759197	−	0.283336i
$508$	−4.08666e11	−	1.52516e12i	−0.272258	−	1.01608i
$509$	1.99720e10	+	3.45925e10i	0.0131884	+	0.0228430i	0.872544	−	0.488535i	$-0.162469\pi$
$509$	1.99720e10	+	3.45925e10i	0.0131884	+	0.0228430i	−0.859356	+	0.511378i	$0.829135\pi$
$510$	−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
$513$	2.04895e12	+	5.49014e11i	1.30618	+	0.349990i
$514$	8.76758e10	−	1.51859e11i	0.0554046	−	0.0959635i
$515$	1.30719e12	+	1.09018e12i	0.818854	+	0.682915i
$516$	−4.50724e11	+	2.60226e11i	−0.279890	+	0.161594i
$517$	9.96271e11	−	9.96271e11i	0.613296	−	0.613296i
$518$	−7.83123e10	+	1.38834e11i	−0.0477910	+	0.0847251i
$519$			1.50267e12i			0.909096i
$520$	2.65984e11	−	5.74911e11i	0.159529	−	0.344814i
$521$	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	$0.623004\pi$
$522$	5.59609e11	−	1.49947e11i	0.329888	−	0.0883933i
$523$	−8.01470e11	+	2.99113e12i	−0.468414	+	1.74814i	0.176903	+	0.984228i	$0.443392\pi$
$523$	−8.01470e11	+	2.99113e12i	−0.468414	+	1.74814i	−0.645317	+	0.763915i	$0.723275\pi$
$524$	−7.66129e11			−0.443926
$525$	−5.81856e11	+	8.59994e11i	−0.334271	+	0.494059i
$526$	−2.18896e11			−0.124681
$527$	3.61741e10	−	1.35004e11i	0.0204292	−	0.0762426i
$528$	5.17234e11	−	1.38593e11i	0.289624	−	0.0776046i
$529$	−1.23577e12	−	7.13471e11i	−0.686099	−	0.396119i
$530$	3.04654e11	−	6.58495e11i	0.167713	−	0.362502i
$531$		−	1.50969e12i		−	0.824067i
$532$	−2.35166e12	+	2.35571e10i	−1.27284	+	0.0127503i
$533$	−2.57271e11	+	2.57271e11i	−0.138076	+	0.138076i
$534$	2.91080e10	−	1.68055e10i	0.0154909	−	0.00894369i
$535$	1.38305e12	+	1.15345e12i	0.729869	+	0.608703i
$536$	−4.20405e11	+	7.28162e11i	−0.220002	+	0.381054i
$537$	1.34144e11	+	3.59438e10i	0.0696125	+	0.0186526i
$538$	−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	$0.777487\pi$
$542$	2.54236e11	+	9.48823e11i	0.126544	+	0.472268i
$543$	−4.99108e11	−	1.86270e12i	−0.246374	−	0.919481i
$544$	−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	0.999613	+	0.0278237i	$0.00885771\pi$
$547$	2.15129e12	+	2.15129e12i	1.02744	+	1.02744i	0.0278237	+	0.999613i	$0.491142\pi$
$548$	1.79698e12	+	4.81499e11i	0.851197	+	0.228078i
$549$	6.03418e11	−	1.04515e12i	0.283493	−	0.491025i
$550$	−3.12816e10	+	3.84140e11i	−0.0145766	+	0.179002i
$551$	−4.94305e12	+	2.85387e12i	−2.28462	+	1.31902i
$552$	2.23499e11	−	2.23499e11i	0.102459	−	0.102459i
$553$	−1.13234e11	−	1.91667e11i	−0.0514889	−	0.0871535i
$554$		−	6.54707e11i		−	0.295293i
$555$	−4.24805e11	−	1.96537e11i	−0.190051	−	0.0879277i
$556$	−3.25022e10	−	1.87651e10i	−0.0144237	−	0.00832751i
$557$	4.76973e11	−	1.27804e11i	0.209964	−	0.0562597i	−0.152304	−	0.988334i	$-0.548669\pi$
$557$	4.76973e11	−	1.27804e11i	0.209964	−	0.0562597i	0.362268	+	0.932074i	$0.382003\pi$
$558$	−1.91079e11	+	7.13115e11i	−0.0834369	+	0.311391i
$559$	−9.65887e11			−0.418382
$560$	−1.80710e11	−	1.79584e12i	−0.0776492	−	0.771650i
$561$	−3.96405e10			−0.0168969
$562$	−1.34658e11	+	5.02552e11i	−0.0569403	+	0.212504i
$563$	−1.99462e12	+	5.34457e11i	−0.836706	+	0.224195i	−0.651637	−	0.758531i	$-0.725917\pi$
$563$	−1.99462e12	+	5.34457e11i	−0.836706	+	0.224195i	−0.185069	+	0.982726i	$0.559251\pi$
$564$	1.53369e12	+	8.85475e11i	0.638235	+	0.368485i
$565$	1.02318e12	+	2.78509e12i	0.422411	+	1.14980i
$566$			1.18240e12i			0.484272i
$567$	−1.26733e11	−	7.14865e10i	−0.0514952	−	0.0290469i
$568$	1.28832e12	−	1.28832e12i	0.519346	−	0.519346i
$569$	−1.05636e10	+	6.09889e9i	−0.00422480	+	0.00243919i	−0.502111	−	0.864803i	$-0.667443\pi$
$569$	−1.05636e10	+	6.09889e9i	−0.00422480	+	0.00243919i	0.497886	+	0.867242i	$0.334110\pi$
$570$	5.17785e10	+	5.72018e11i	0.0205453	+	0.226972i
$571$	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	$0.145806\pi$
$572$	1.05495e12	+	2.82674e11i	0.412051	+	0.110409i
$573$	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
$577$	3.67804e11	+	1.37266e12i	0.138142	+	0.515553i	0.999965	+	0.00834410i	$0.00265604\pi$
$577$	3.67804e11	+	1.37266e12i	0.138142	+	0.515553i	−0.861823	+	0.507209i	$0.830677\pi$
$578$	−1.92076e11	−	7.16838e11i	−0.0715810	−	0.267144i
$579$	−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
$583$	2.51715e12	+	6.74469e11i	0.902405	+	0.241799i
$584$	5.57430e11	−	9.65497e11i	0.198304	−	0.343473i
$585$	−8.33202e11	+	9.99057e11i	−0.294137	+	0.352686i
$586$	1.84509e11	−	1.06526e11i	0.0646367	−	0.0373180i
$587$	2.56314e12	−	2.56314e12i	0.891047	−	0.891047i	−0.103575	−	0.994622i	$-0.533028\pi$
$587$	2.56314e12	−	2.56314e12i	0.891047	−	0.891047i	0.994622	+	0.103575i	$0.0330281\pi$
$588$	−1.54991e12	−	3.82190e11i	−0.534697	−	0.131850i
$589$		−	7.27345e12i		−	2.49013i
$590$	9.79348e11	−	3.59792e11i	0.332738	−	0.122241i
$591$	7.09877e11	+	4.09848e11i	0.239353	+	0.138191i
$592$	7.85899e11	−	2.10581e11i	0.262978	−	0.0704647i
$593$	6.76620e11	−	2.52518e12i	0.224698	−	0.838584i	−0.757827	−	0.652455i	$-0.773739\pi$
$593$	6.76620e11	−	2.52518e12i	0.224698	−	0.838584i	0.982525	−	0.186129i	$-0.0595942\pi$
$594$	5.34442e11			0.176141
$595$	−2.14861e10	+	1.31875e11i	−0.00702801	+	0.0431355i
$596$	2.83421e12			0.920075
$597$	−5.49448e10	+	2.05057e11i	−0.0177028	+	0.0660678i
$598$	2.71992e11	−	7.28800e10i	0.0869763	−	0.0233052i
$599$	−3.70542e12	−	2.13932e12i	−1.17603	−	0.678979i	−0.220934	−	0.975289i	$-0.570910\pi$
$599$	−3.70542e12	−	2.13932e12i	−1.17603	−	0.678979i	−0.955092	+	0.296310i	$0.904244\pi$
$600$	−9.92764e11	+	1.81213e11i	−0.312727	+	0.0570832i
$601$			1.96323e12i			0.613812i	0.951740	+	0.306906i	$0.0992937\pi$
$601$			1.96323e12i			0.613812i	−0.951740	+	0.306906i	$0.900706\pi$
$602$	4.51166e11	−	2.66542e11i	0.140008	−	0.0827144i
$603$	1.22098e12	−	1.22098e12i	0.376080	−	0.376080i
$604$	3.44400e12	−	1.98839e12i	1.05292	−	0.607905i
$605$	1.90328e12	−	1.72283e11i	0.577569	−	0.0522810i
$606$	9.18954e10	−	1.59167e11i	0.0276800	−	0.0479432i
$607$	−1.67256e11	−	4.48162e10i	−0.0500073	−	0.0133994i	0.233729	−	0.972302i	$-0.424907\pi$
$607$	−1.67256e11	−	4.48162e10i	−0.0500073	−	0.0133994i	−0.283736	+	0.958902i	$0.591574\pi$
$608$	−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
$612$	2.33456e10	+	8.71270e10i	0.00672704	+	0.0251056i
$613$	−7.76452e11	−	2.89776e12i	−0.222097	−	0.828876i	−0.983547	−	0.180653i	$-0.942179\pi$
$613$	−7.76452e11	−	2.89776e12i	−0.222097	−	0.828876i	0.761450	−	0.648223i	$-0.224488\pi$
$614$	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	0.403816	−	0.914840i	$-0.367683\pi$
$617$	−1.83960e12	−	1.83960e12i	−0.511024	−	0.511024i	−0.914840	+	0.403816i	$0.867683\pi$
$618$	6.17314e11	+	1.65409e11i	0.170239	+	0.0456153i
$619$	−1.51261e12	+	2.61992e12i	−0.414114	+	0.717266i	−0.995335	−	0.0964797i	$-0.969242\pi$
$619$	−1.51261e12	+	2.61992e12i	−0.414114	+	0.717266i	0.581221	+	0.813745i	$0.302575\pi$
$620$	6.10977e12	−	5.53050e11i	1.66059	−	0.150315i
$621$	−1.43481e12	+	8.28386e11i	−0.387152	+	0.223522i
$622$	9.69814e9	−	9.69814e9i	0.00259795	−	0.00259795i
$623$	3.50331e11	−	2.06970e11i	0.0931714	−	0.0550442i
$624$			1.24912e12i			0.329817i
$625$	−6.17189e11	+	3.76444e12i	−0.161792	+	0.986825i
$626$	−1.27103e12	−	7.33828e11i	−0.330804	−	0.190990i
$627$	−1.99261e12	+	5.33917e11i	−0.514894	+	0.137965i
$628$	4.11117e11	−	1.53431e12i	0.105474	−	0.393636i
$629$	−6.02308e10			−0.0153423
$630$	1.13494e11	−	6.96587e11i	0.0287039	−	0.176174i
$631$	−4.44649e12			−1.11657			−0.558284	−	0.829650i	$-0.688540\pi$
$631$	−4.44649e12			−1.11657			−0.558284	+	0.829650i	$0.688540\pi$
$632$	5.59988e10	−	2.08990e11i	0.0139621	−	0.0521074i
$633$	1.01272e12	−	2.71358e11i	0.250711	−	0.0671778i
$634$	1.61576e12	+	9.32862e11i	0.397170	+	0.229306i
$635$	−4.38199e12	+	1.60985e12i	−1.06952	+	0.392920i
$636$			3.27551e12i			0.793821i
$637$	−2.13641e12	−	2.05248e12i	−0.514110	−	0.493913i
$638$	−1.01686e12	+	1.01686e12i	−0.242979	+	0.242979i
$639$	−3.24038e12	+	1.87083e12i	−0.768850	+	0.443896i
$640$	2.46099e12	−	2.95087e12i	0.579829	−	0.695248i
$641$	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	$-0.157179\pi$
$642$	6.53137e11	+	1.75007e11i	0.151739	+	0.0406583i
$643$	3.24579e12	+	3.24579e12i	0.748809	+	0.748809i	0.974256	−	0.225446i	$-0.0723840\pi$
$643$	3.24579e12	+	3.24579e12i	0.748809	+	0.748809i	−0.225446	+	0.974256i	$0.572384\pi$
$644$	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
$647$	1.06470e12	+	3.97352e12i	0.238868	+	0.891468i	0.976367	+	0.216120i	$0.0693401\pi$
$647$	1.06470e12	+	3.97352e12i	0.238868	+	0.891468i	−0.737499	+	0.675349i	$0.763993\pi$
$648$	−3.66014e10	−	1.36598e11i	−0.00815474	−	0.0304339i
$649$	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
$653$	3.10313e12	+	8.31481e11i	0.667868	+	0.178955i	0.576794	−	0.816890i	$-0.304303\pi$
$653$	3.10313e12	+	8.31481e11i	0.667868	+	0.178955i	0.0910737	+	0.995844i	$0.470970\pi$
$654$	3.14591e11	−	5.44888e11i	0.0672430	−	0.116468i
$655$	2.04202e11	+	2.25591e12i	0.0433486	+	0.478889i
$656$	−8.72563e11	+	5.03775e11i	−0.183963	+	0.106211i
$657$	−1.61894e12	+	1.61894e12i	−0.338990	+	0.338990i
$658$	−1.55305e12	−	8.76032e11i	−0.322976	−	0.182181i
$659$		−	3.51029e12i		−	0.725035i	−0.931977	−	0.362517i	$-0.881917\pi$
$659$		−	3.51029e12i		−	0.725035i	0.931977	−	0.362517i	$-0.118083\pi$
$660$	−6.00008e11	−	1.63321e12i	−0.123086	−	0.335039i
$661$	−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	$0.924005\pi$
$662$	−2.17323e12	+	5.82314e11i	−0.439789	+	0.117841i
$663$	2.39329e10	−	8.93189e10i	0.00481044	−	0.0179528i
$664$	−2.12935e12			−0.425100
$665$	6.96173e11	+	6.91832e12i	0.138045	+	1.37184i
$666$	3.18151e11			0.0626612
$667$	1.15382e12	−	4.30610e12i	0.225720	−	0.842398i
$668$	−4.89088e11	+	1.31051e11i	−0.0950370	+	0.0254651i
$669$	2.01905e9	+	1.16570e9i	0.000389699	+	0.000224993i
$670$	1.08305e12	+	5.01073e11i	0.207639	+	0.0960649i
$671$			2.99561e12i			0.570471i
$672$	−1.19950e12	−	2.03035e12i	−0.226902	−	0.384069i
$673$	−5.31516e12	+	5.31516e12i	−0.998730	+	0.998730i	−0.999999	−	0.00126883i	$-0.999596\pi$
$673$	−5.31516e12	+	5.31516e12i	−0.998730	+	0.998730i	0.00126883	+	0.999999i	$0.499596\pi$
$674$	−1.68502e12	+	9.72847e11i	−0.314511	+	0.181583i
$675$	5.27230e12	+	4.29337e11i	0.977537	+	0.0796034i
$676$	1.23245e12	−	2.13467e12i	0.226992	−	0.393161i
$677$	2.03512e12	+	5.45308e11i	0.372340	+	0.0997683i	0.440136	−	0.897931i	$-0.354930\pi$
$677$	2.03512e12	+	5.45308e11i	0.372340	+	0.0997683i	−0.0677961	+	0.997699i	$0.521597\pi$
$678$	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
$682$	−4.74296e11	−	1.77010e12i	−0.0839498	−	0.313305i
$683$	−6.74105e11	−	2.51579e12i	−0.118532	−	0.442366i	0.880995	−	0.473125i	$-0.156874\pi$
$683$	−6.74105e11	−	2.51579e12i	−0.118532	−	0.442366i	−0.999527	+	0.0307592i	$0.990207\pi$
$684$	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
$688$	−2.58363e12	−	6.92282e11i	−0.439625	−	0.117797i
$689$	−3.03946e12	+	5.26449e12i	−0.513818	+	0.889959i
$690$	−3.44511e11	−	2.87319e11i	−0.0578606	−	0.0482551i
$691$	−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
$693$	2.53477e12	−	2.53913e10i	0.417483	−	0.00418201i
$694$			2.84082e12i			0.464864i
$695$	−4.65919e10	+	1.00706e11i	−0.00757493	+	0.0163728i
$696$	−3.26096e12	−	1.88272e12i	−0.526750	−	0.304119i
$697$	7.20454e10	−	1.93045e10i	0.0115627	−	0.00309821i
$698$	−1.57087e11	+	5.86257e11i	−0.0250490	+	0.0934842i
$699$	5.08336e12			0.805385
$700$	−5.75853e12	+	1.11084e12i	−0.906505	+	0.174868i
$701$	8.69134e12			1.35943			0.679713	−	0.733478i	$-0.262104\pi$
$701$	8.69134e12			1.35943			0.679713	+	0.733478i	$0.262104\pi$
$702$	−3.22668e11	+	1.20421e12i	−0.0501463	+	0.187149i
$703$	−3.02762e12	+	8.11247e11i	−0.467522	+	0.125272i
$704$	2.07906e12	+	1.20035e12i	0.319000	+	0.184175i
$705$	2.19854e12	−	4.75203e12i	0.335184	−	0.724483i
$706$		−	2.18645e12i		−	0.331221i
$707$	1.09314e12	−	1.93795e12i	0.164547	−	0.291713i
$708$	−3.33060e12	+	3.33060e12i	−0.498165	+	0.498165i
$709$	−7.10831e12	+	4.10398e12i	−1.05647	+	0.609955i	−0.924454	−	0.381292i	$-0.875479\pi$
$709$	−7.10831e12	+	4.10398e12i	−1.05647	+	0.609955i	−0.132018	+	0.991247i	$0.542146\pi$
$710$	−1.98588e12	−	1.65620e12i	−0.293285	−	0.244596i
$711$	−2.22166e11	+	3.84803e11i	−0.0326035	+	0.0564710i
$712$	3.81994e11	+	1.02355e11i	0.0557053	+	0.0149262i
$713$	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
$717$	−7.20060e11	−	2.68730e12i	−0.101750	−	0.379734i
$718$	3.61621e11	+	1.34959e12i	0.0507802	+	0.189514i
$719$	−3.76974e12	−	6.52938e12i	−0.526055	−	0.911154i	−0.999539	−	0.0303520i	$-0.990337\pi$
$719$	−3.76974e12	−	6.52938e12i	−0.526055	−	0.911154i	0.473484	−	0.880802i	$-0.342996\pi$
$720$	−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
$723$	−4.19706e12	−	1.12460e12i	−0.571246	−	0.153065i
$724$	5.44596e12	−	9.43269e12i	0.736633	−	1.27589i
$725$	−1.08483e13	+	9.21453e12i	−1.45828	+	1.23866i
$726$	6.21405e11	−	3.58768e11i	0.0830157	−	0.0479291i
$727$	6.95723e12	−	6.95723e12i	0.923701	−	0.923701i	−0.0735879	−	0.997289i	$-0.523445\pi$
$727$	6.95723e12	−	6.95723e12i	0.923701	−	0.923701i	0.997289	+	0.0735879i	$0.0234450\pi$
$728$	−2.88415e10	−	2.87920e12i	−0.00380563	−	0.379910i
$729$		−	4.17091e12i		−	0.546961i
$730$	−1.43605e12	−	6.64391e11i	−0.187161	−	0.0865907i
$731$	1.71480e11	+	9.90040e10i	0.0222119	+	0.0128240i
$732$	−3.63699e12	+	9.74529e11i	−0.468212	+	0.125457i
$733$	−1.22811e12	+	4.58336e12i	−0.157133	+	0.586430i	0.841780	+	0.539821i	$0.181508\pi$
$733$	−1.22811e12	+	4.58336e12i	−0.157133	+	0.586430i	−0.998913	+	0.0466090i	$0.985159\pi$
$734$	5.77134e11			0.0733913
$735$	−7.12269e11	+	4.66565e12i	−0.0900225	+	0.589684i
$736$	2.71350e12			0.340863
$737$	−1.10932e12	+	4.14004e12i	−0.138501	+	0.516893i
$738$	−3.80557e11	+	1.01970e11i	−0.0472244	+	0.0126537i
$739$	5.40813e12	+	3.12238e12i	0.667032	+	0.385111i	0.794951	−	0.606673i	$-0.207496\pi$
$739$	5.40813e12	+	3.12238e12i	0.667032	+	0.385111i	−0.127919	+	0.991785i	$0.540830\pi$
$740$	−9.11666e11	−	2.48154e12i	−0.111762	−	0.304214i
$741$		−	4.81213e12i		−	0.586348i
$742$	−3.30347e10	−	3.29780e12i	−0.00400085	−	0.399399i
$743$	1.89917e12	−	1.89917e12i	0.228620	−	0.228620i	−0.583496	−	0.812116i	$-0.698316\pi$
$743$	1.89917e12	−	1.89917e12i	0.228620	−	0.228620i	0.812116	+	0.583496i	$0.198316\pi$
$744$	4.15548e12	−	2.39917e12i	0.497214	−	0.287067i
$745$	−7.55424e11	−	8.34547e12i	−0.0898436	−	0.992538i
$746$	−6.59481e11	+	1.14225e12i	−0.0779610	+	0.135032i
$747$	4.22394e12	+	1.13180e12i	0.496335	+	0.132992i
$748$	−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	$-0.430819\pi$
$752$	2.35564e12	+	8.79137e12i	0.268614	+	1.00248i
$753$	−1.18010e12	−	4.40419e12i	−0.133764	−	0.499216i
$754$	−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	0.0593979	−	0.998234i	$-0.481082\pi$
$757$	−8.48245e12	−	8.48245e12i	−0.938837	−	0.938837i	−0.998234	+	0.0593979i	$0.981082\pi$
$758$	1.95582e12	+	5.24060e11i	0.215188	+	0.0576593i
$759$	8.05607e11	−	1.39535e12i	0.0881120	−	0.152614i
$760$	−4.32832e12	+	5.18990e12i	−0.470607	+	0.564284i
$761$	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
$763$	3.74223e12	−	6.63432e12i	0.399733	−	0.708657i
$764$			6.50718e12i			0.690991i
$765$	2.50327e11	−	9.19650e10i	0.0264260	−	0.00970837i
$766$	1.89114e12	+	1.09185e12i	0.198469	+	0.114586i
$767$	−8.44361e12	+	2.26246e12i	−0.880945	+	0.236049i
$768$	−4.72551e11	+	1.76358e12i	−0.0490144	+	0.182924i
$769$	−7.14188e12			−0.736451			−0.368226	−	0.929736i	$-0.620035\pi$
$769$	−7.14188e12			−0.736451			−0.368226	+	0.929736i	$0.620035\pi$
$770$	6.20562e11	+	1.63827e12i	0.0636175	+	0.167949i
$771$	2.34051e12			0.238542
$772$	3.29699e12	−	1.23045e13i	0.334072	−	1.24677i
$773$	−7.04134e12	+	1.88672e12i	−0.709329	+	0.190064i	−0.595405	−	0.803425i	$-0.703009\pi$
$773$	−7.04134e12	+	1.88672e12i	−0.709329	+	0.190064i	−0.113923	+	0.993490i	$0.536342\pi$
$774$	−9.05789e11	−	5.22958e11i	−0.0907179	−	0.0523760i
$775$	−3.25697e12	−	1.78431e13i	−0.324307	−	1.77670i
$776$			8.23893e12i			0.815629i
$777$	−2.12746e12	+	2.13112e10i	−0.209395	+	0.00209755i
$778$	1.81463e12	−	1.81463e12i	0.177575	−	0.177575i
$779$	3.36148e12	−	1.94075e12i	0.327049	−	0.188822i
$780$	4.04224e12	−	3.65900e11i	0.391018	−	0.0353946i
$781$	4.64378e12	−	8.04327e12i	0.446624	−	0.773576i
$782$	−5.57587e10	−	1.49405e10i	−0.00533190	−	0.00142868i
$783$	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
$787$	4.86323e12	+	1.81498e13i	0.451896	+	1.68650i	0.697057	+	0.717016i	$0.254493\pi$
$787$	4.86323e12	+	1.81498e13i	0.451896	+	1.68650i	−0.245161	+	0.969482i	$0.578841\pi$
$788$	1.19827e12	+	4.47201e12i	0.110710	+	0.413175i
$789$	−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
$793$	−6.74977e12	−	1.80859e12i	−0.606121	−	0.162410i
$794$	1.83363e11	−	3.17595e11i	0.0163727	−	0.0283584i
$795$	9.64492e12	−	8.73049e11i	0.856341	−	0.0775151i
$796$	−1.03841e12	+	5.99524e11i	−0.0916766	+	0.0529295i
$797$	9.09936e12	−	9.09936e12i	0.798819	−	0.798819i	−0.184091	−	0.982909i	$-0.558934\pi$
$797$	9.09936e12	−	9.09936e12i	0.798819	−	0.798819i	0.982909	+	0.184091i	$0.0589340\pi$
$798$	1.32793e12	+	2.24775e12i	0.115921	+	0.196216i
$799$		−	6.73765e11i		−	0.0584855i
$800$	−7.12662e12	−	4.92651e12i	−0.615146	−	0.425241i
$801$	−7.03347e11	−	4.06077e11i	−0.0603703	−	0.0348548i
$802$	−3.09324e12	+	8.28831e11i	−0.264015	+	0.0707426i
$803$	1.47089e12	−	5.48942e12i	0.124842	−	0.465915i
$804$	−5.38733e12			−0.454696
$805$	−4.20534e12	−	3.43638e12i	−0.352955	−	0.288416i
$806$	4.27477e12			0.356784
$807$	4.06558e11	−	1.51729e12i	0.0337436	−	0.125933i
$808$	2.08881e12	−	5.59694e11i	0.172404	−	0.0461955i
$809$	1.37655e13	+	7.94749e12i	1.12985	+	0.652321i	0.943898	−	0.330237i	$-0.107129\pi$
$809$	1.37655e13	+	7.94749e12i	1.12985	+	0.652321i	0.185956	+	0.982558i	$0.440462\pi$
$810$	−1.88398e11	+	6.92134e10i	−0.0153778	+	0.00564947i
$811$		−	8.23210e12i		−	0.668216i	−0.942535	−	0.334108i	$-0.891565\pi$
$811$		−	8.23210e12i		−	0.668216i	0.942535	−	0.334108i	$-0.108435\pi$
$812$	−1.90595e13	−	1.07509e13i	−1.53854	−	0.867845i
$813$	−9.27101e12	+	9.27101e12i	−0.744251	+	0.744251i
$814$	−6.83912e11	+	3.94857e11i	−0.0545997	+	0.0315232i
$815$	5.00460e12	−	6.00080e12i	0.397338	−	0.476431i
$816$	1.28035e11	−	2.21764e11i	0.0101094	−	0.0175099i
$817$	9.95324e12	+	2.66696e12i	0.781565	+	0.209420i
$818$	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	$0.882791\pi$
$822$	−5.34510e11	−	1.99482e12i	−0.0408350	−	0.152398i
$823$	5.45890e12	+	2.03729e13i	0.414769	+	1.54794i	0.785299	+	0.619117i	$0.212509\pi$
$823$	5.45890e12	+	2.03729e13i	0.414769	+	1.54794i	−0.370530	+	0.928821i	$0.620824\pi$
$824$	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	0.768852	−	0.639426i	$-0.220828\pi$
$827$	1.74099e12	+	1.74099e12i	0.129426	+	0.129426i	−0.639426	+	0.768852i	$0.720828\pi$
$828$	−3.54133e12	−	9.48896e11i	−0.261836	−	0.0701588i
$829$	−6.02736e12	+	1.04397e13i	−0.443233	+	0.767702i	−0.997927	−	0.0643522i	$-0.979502\pi$
$829$	−6.02736e12	+	1.04397e13i	−0.443233	+	0.767702i	0.554694	+	0.832054i	$0.312835\pi$
$830$	2.72447e11	+	3.00983e12i	0.0199265	+	0.220136i
$831$	7.56795e12	−	4.36936e12i	0.550521	−	0.317843i
$832$	−3.95988e12	+	3.95988e12i	−0.286502	+	0.286502i
$833$	1.68909e11	+	5.83371e11i	0.0121549	+	0.0419800i
$834$			4.16622e10i			0.00298192i
$835$	5.16246e11	+	1.40521e12i	0.0367509	+	0.100035i
$836$	−1.00905e13	−	5.82578e12i	−0.714474	−	0.412502i
$837$	−2.42944e13	+	6.50968e12i	−1.71097	+	0.458453i
$838$	4.59229e9	−	1.71387e10i	0.000321685	−	0.00120055i
$839$	−3.46989e12			−0.241761			−0.120881	−	0.992667i	$-0.538572\pi$
$839$	−3.46989e12			−0.241761			−0.120881	+	0.992667i	$0.538572\pi$
$840$	−3.72296e12	+	2.67977e12i	−0.258007	+	0.185712i
$841$	−3.86015e13			−2.66086
$842$	1.12544e12	−	4.20019e12i	0.0771645	−	0.287982i
$843$	−6.70782e12	+	1.79735e12i	−0.457464	+	0.122577i
$844$	5.12842e12	+	2.96089e12i	0.347890	+	0.200854i
$845$	−6.61414e12	−	3.06005e12i	−0.446291	−	0.206478i
$846$			3.55896e12i			0.238867i
$847$	7.47895e12	−	4.41845e12i	0.499304	−	0.294981i
$848$	−1.19034e13	+	1.19034e13i	−0.790478	+	0.790478i
$849$	−1.36677e13	+	7.89103e12i	−0.902838	+	0.521254i
$850$	1.19317e11	+	1.40472e11i	0.00784001	+	0.00923007i
$851$	1.22406e12	−	2.12013e12i	0.0800054	−	0.138573i
$852$	1.12761e13	+	3.02142e12i	0.733130	+	0.196442i
$853$	−1.17980e12	−	1.17980e12i	−0.0763026	−	0.0763026i	0.667926	−	0.744228i	$-0.267182\pi$
$853$	−1.17980e12	−	1.17980e12i	−0.0763026	−	0.0763026i	−0.744228	+	0.667926i	$0.767182\pi$
$854$	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
$857$	6.74536e12	+	2.51740e13i	0.427161	+	1.59419i	0.759158	+	0.650906i	$0.225611\pi$
$857$	6.74536e12	+	2.51740e13i	0.427161	+	1.59419i	−0.331997	+	0.943281i	$0.607722\pi$
$858$	−3.13795e11	−	1.17110e12i	−0.0197676	−	0.0737737i
$859$	5.00271e12	+	8.66496e12i	0.313499	+	0.542997i	0.979117	−	0.203296i	$-0.0651653\pi$
$859$	5.00271e12	+	8.66496e12i	0.313499	+	0.542997i	−0.665618	+	0.746293i	$0.731832\pi$
$860$	−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
$863$	7.22078e11	+	1.93480e11i	0.0443135	+	0.0118738i	0.280908	−	0.959735i	$-0.409365\pi$
$863$	7.22078e11	+	1.93480e11i	0.0443135	+	0.0118738i	−0.236594	+	0.971609i	$0.576031\pi$
$864$	−6.00686e12	+	1.04042e13i	−0.366721	+	0.635179i
$865$	1.92711e13	+	1.60719e13i	1.17040	+	0.976101i
$866$	4.52259e12	−	2.61112e12i	0.273248	−	0.157760i
$867$	7.00426e12	−	7.00426e12i	0.420995	−	0.420995i
$868$	2.40084e13	−	1.41838e13i	1.43557	−	0.848111i
$869$		−	1.10292e12i		−	0.0656079i
$870$	−2.24398e12	+	4.85025e12i	−0.132795	+	0.287030i
$871$	−8.65866e12	−	4.99908e12i	−0.509764	−	0.294312i
$872$	7.15074e12	−	1.91604e12i	0.418820	−	0.112222i
$873$	4.37918e12	−	1.63433e13i	0.255169	−	0.952305i
$874$	−3.00405e12			−0.174143
$875$	4.80579e12	+	1.66602e13i	0.277159	+	0.960824i
$876$	7.14326e12			0.409853
$877$	2.82963e12	−	1.05603e13i	0.161522	−	0.602808i	−0.836936	−	0.547300i	$-0.815656\pi$
$877$	2.82963e12	−	1.05603e13i	0.161522	−	0.602808i	0.998458	−	0.0555076i	$-0.0176777\pi$
$878$	−6.25090e12	+	1.67492e12i	−0.354991	+	0.0951196i
$879$	2.46274e12	+	1.42186e12i	0.139145	+	0.0803356i
$880$	3.75473e12	−	8.11565e12i	0.211060	−	0.456196i
$881$			1.64269e13i			0.918681i	0.888260	+	0.459341i	$0.151914\pi$
$881$			1.64269e13i			0.918681i	−0.888260	+	0.459341i	$0.848086\pi$
$882$	−8.92211e11	−	3.08148e12i	−0.0496431	−	0.171455i
$883$	5.67686e12	−	5.67686e12i	0.314257	−	0.314257i	−0.532299	−	0.846556i	$-0.678672\pi$
$883$	5.67686e12	−	5.67686e12i	0.314257	−	0.314257i	0.846556	+	0.532299i	$0.178672\pi$
$884$	4.52310e11	−	2.61141e11i	0.0249116	−	0.0143827i
$885$	1.06949e13	+	8.91940e12i	0.586045	+	0.488755i
$886$	−3.17675e12	+	5.50229e12i	−0.173193	+	0.299979i
$887$	−6.78424e12	−	1.81783e12i	−0.367998	−	0.0986047i	0.0700810	−	0.997541i	$-0.477674\pi$
$887$	−6.78424e12	−	1.81783e12i	−0.367998	−	0.0986047i	−0.438079	+	0.898937i	$0.644341\pi$
$888$	−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
$892$	3.40815e9	+	1.27194e10i	0.000180251	+	0.000672704i
$893$	−9.07493e12	−	3.38681e13i	−0.477542	−	1.78221i
$894$	−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
$898$	3.48447e11	+	9.33660e10i	0.0178810	+	0.00479121i
$899$	3.38384e13	−	5.86099e13i	1.72779	−	2.99263i
$900$	7.57802e12	+	8.92163e12i	0.385003	+	0.453266i
$901$	1.07923e12	−	6.23092e11i	0.0545571	−	0.0314986i
$902$	6.91510e11	−	6.91510e11i	0.0347831	−	0.0347831i
$903$	6.09201e12	+	3.43632e12i	0.304906	+	0.171988i
$904$			1.31079e13i			0.652790i
$905$	−2.92266e13	−	1.35218e13i	−1.44830	−	0.670061i
$906$	−3.82317e12	−	2.20731e12i	−0.188515	−	0.108839i
$907$	−3.86873e13	+	1.03662e13i	−1.89817	+	0.508614i	−0.900971	+	0.433880i	$0.857144\pi$
$907$	−3.86873e13	+	1.03662e13i	−1.89817	+	0.508614i	−0.997203	+	0.0747346i	$0.976189\pi$
$908$	−3.37596e12	+	1.25993e13i	−0.164820	+	0.615118i
$909$	−4.44099e12			−0.215746
$910$	−4.06605e12	+	4.09157e11i	−0.196556	+	0.0197790i
$911$	−3.74604e12			−0.180194			−0.0900970	−	0.995933i	$-0.528718\pi$
$911$	−3.74604e12			−0.180194			−0.0900970	+	0.995933i	$0.528718\pi$
$912$	3.44901e12	−	1.28719e13i	0.165089	−	0.616119i
$913$	−1.04847e13	+	2.80936e12i	−0.499385	+	0.133810i
$914$	−5.17944e11	−	2.99035e11i	−0.0245485	−	0.0141731i
$915$	3.83895e12	+	1.04496e13i	0.181058	+	0.492837i
$916$		−	2.75691e12i		−	0.129388i
$917$	5.23706e12	+	8.86460e12i	0.244583	+	0.413997i
$918$	1.80718e11	−	1.80718e11i	0.00839865	−	0.00839865i
$919$	9.77955e12	−	5.64623e12i	0.452271	−	0.261119i	−0.256518	−	0.966540i	$-0.582575\pi$
$919$	9.77955e12	−	5.64623e12i	0.452271	−	0.261119i	0.708789	+	0.705421i	$0.249242\pi$
$920$	−4.75834e11	−	5.25673e12i	−0.0218983	−	0.241919i
$921$	−5.24499e11	+	9.08459e11i	−0.0240202	+	0.0416042i
$922$	−3.39157e11	−	9.08770e10i	−0.0154565	−	0.00414157i
$923$	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
$927$	−3.99682e12	−	1.49163e13i	−0.177769	−	0.663443i
$928$	−8.36663e12	−	3.12247e13i	−0.370326	−	1.38208i
$929$	−1.06673e13	−	1.84763e13i	−0.469876	−	0.813849i	0.529531	−	0.848291i	$-0.322368\pi$
$929$	−1.06673e13	−	1.84763e13i	−0.469876	−	0.813849i	−0.999407	+	0.0344417i	$0.989035\pi$
$930$	−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
$933$	1.76827e11	+	4.73805e10i	0.00763977	+	0.00204707i
$934$	2.73132e12	−	4.73079e12i	0.117439	−	0.203410i
$935$	−4.23978e11	+	5.08374e11i	−0.0181423	+	0.0217536i
$936$	−4.97708e12	+	2.87352e12i	−0.211950	+	0.122369i
$937$	2.03074e13	−	2.03074e13i	0.860650	−	0.860650i	−0.130764	−	0.991414i	$-0.541743\pi$
$937$	2.03074e13	−	2.03074e13i	0.860650	−	0.860650i	0.991414	+	0.130764i	$0.0417429\pi$
$938$	5.42399e12	−	5.43331e10i	0.228774	−	0.00229167i
$939$		−	1.95896e13i		−	0.822299i
$940$	2.77595e13	−	1.01983e13i	1.15968	−	0.426040i
$941$	−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	$0.766197\pi$
$942$	−1.70323e12	+	4.56380e11i	−0.0704766	+	0.0188842i
$943$	−7.84643e11	+	2.92833e12i	−0.0323124	+	0.120592i
$944$	−2.42072e13			−0.992135
$945$	2.24852e13	−	8.51717e12i	0.917178	−	0.347418i
$946$	2.59617e12			0.105396
$947$	−1.17694e13	+	4.39239e13i	−0.475530	+	1.77470i	0.143836	+	0.989602i	$0.454056\pi$
$947$	−1.17694e13	+	4.39239e13i	−0.475530	+	1.77470i	−0.619366	+	0.785102i	$0.712610\pi$
$948$	1.33907e12	−	3.58802e11i	0.0538474	−	0.0144284i
$949$	1.14808e13	+	6.62846e12i	0.459489	+	0.265286i
$950$	7.88970e12	+	5.45402e12i	0.314271	+	0.217251i
$951$			2.49028e13i			0.987269i
$952$	−2.90000e11	+	5.14119e11i	−0.0114428	+	0.0202861i
$953$	2.09083e13	−	2.09083e13i	0.821109	−	0.821109i	−0.165158	−	0.986267i	$-0.552813\pi$
$953$	2.09083e13	−	2.09083e13i	0.821109	−	0.821109i	0.986267	+	0.165158i	$0.0528134\pi$
$954$	−5.70068e12	+	3.29129e12i	−0.222823	+	0.128647i
$955$	1.91607e13	−	1.73441e12i	0.745413	−	0.0674740i
$956$	7.85686e12	−	1.36085e13i	0.304220	−	0.526925i
$957$	−1.85405e13	−	4.96792e12i	−0.714526	−	0.191457i
$958$	−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
$962$	−4.76788e11	−	1.77940e12i	−0.0179489	−	0.0669862i
$963$	−4.22876e12	−	1.57819e13i	−0.158451	−	0.591347i
$964$	−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	0.883501	−	0.468429i	$-0.155180\pi$
$967$	1.12861e13	+	1.12861e13i	0.415072	+	0.415072i	−0.468429	+	0.883501i	$0.655180\pi$
$968$	8.15490e12	+	2.18510e12i	0.298524	+	0.0799893i
$969$	−4.93246e11	+	8.54328e11i	−0.0179724	+	0.0311292i
$970$	1.16457e13	−	1.05416e12i	0.422370	−	0.0382325i
$971$	−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
$973$	5.05212e9	+	5.04345e11i	0.000180703	+	0.0180393i
$974$			3.13277e12i			0.111536i
$975$	−2.15482e12	−	1.18051e13i	−0.0763643	−	0.418357i
$976$	−1.67585e13	−	9.67554e12i	−0.591169	−	0.341312i
$977$	−1.16745e13	+	3.12817e12i	−0.409933	+	0.109841i	−0.457891	−	0.889008i	$-0.651395\pi$
$977$	−1.16745e13	+	3.12817e12i	−0.409933	+	0.109841i	0.0479586	+	0.998849i	$0.484728\pi$
$978$	7.59327e11	−	2.83385e12i	0.0265402	−	0.0990493i
$979$	2.01593e12			0.0701380
$980$	−2.14786e13	+	1.57892e13i	−0.743855	+	0.546818i
$981$	−1.52031e13			−0.524110
$982$	−5.23206e11	+	1.95263e12i	−0.0179544	+	0.0670068i
$983$	−2.52369e13	+	6.76220e12i	−0.862074	+	0.230992i	−0.662657	−	0.748923i	$-0.730571\pi$
$983$	−2.52369e13	+	6.76220e12i	−0.862074	+	0.230992i	−0.199417	+	0.979915i	$0.563905\pi$
$984$	2.21759e12	+	1.28033e12i	0.0754056	+	0.0435355i
$985$	1.28487e13	−	4.72033e12i	0.434906	−	0.159775i
$986$			6.87691e11i			0.0231711i
$987$	−2.38395e11	−	2.37986e13i	−0.00799595	−	0.798223i
$988$	1.92189e13	−	1.92189e13i	0.641686	−	0.641686i
$989$	−6.96990e12	+	4.02408e12i	−0.231656	+	0.133747i
$990$	2.23953e12	−	2.68533e12i	0.0740968	−	0.0888462i
$991$	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	$0.0462629\pi$
$992$	3.97900e13	+	1.06617e13i	1.30458	+	0.349561i
$993$	−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
$997$	1.28656e13	+	4.80151e13i	0.412385	+	1.53904i	0.790017	+	0.613085i	$0.210072\pi$
$997$	1.28656e13	+	4.80151e13i	0.412385	+	1.53904i	−0.377632	+	0.925956i	$0.623262\pi$
$998$	2.98572e12	+	1.11429e13i	0.0952713	+	0.355557i
$999$	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.17.19	yes	136
5.3	odd	4	inner	35.10.k.a.3.16	✓	136
7.5	odd	6	inner	35.10.k.a.12.16	yes	136
35.33	even	12	inner	35.10.k.a.33.19	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.16	✓	136	5.3	odd	4	inner
35.10.k.a.12.16	yes	136	7.5	odd	6	inner
35.10.k.a.17.19	yes	136	1.1	even	1	trivial
35.10.k.a.33.19	yes	136	35.33	even	12	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+(1.62279 - 6.05635i) q^{2} +(80.8372 - 21.6603i) q^{3} +(409.359 + 236.344i) q^{4} +(586.816 - 1268.37i) q^{5} -524.728i q^{6} +(-63.6305 - 6352.13i) q^{7} +(4365.66 - 4365.66i) q^{8} +(-10980.5 + 6339.59i) q^{9} +(-6729.43 - 5612.27i) q^{10} +(15736.1 - 27255.8i) q^{11} +(38210.7 + 10238.5i) 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} +(-3895.29 - 14537.4i) q^{17} +(20575.7 + 76789.5i) q^{18} +(-391609. - 678286. i) q^{19} +(539991. - 380530. i) q^{20} +(-142733. - 512110. i) q^{21} +(-139534. - 139534. i) q^{22} +(590883. + 158327. i) q^{23} +(258347. - 447470. i) q^{24} +(-1.26442e6 - 1.48860e6i) q^{25} +(398644. - 230157. i) q^{26} +(-1.91509e6 + 1.91509e6i) q^{27} +(1.47524e6 - 2.61534e6i) q^{28} -7.28756e6i q^{29} +(-665552. - 307919. i) q^{30} +(8.04245e6 + 4.64331e6i) q^{31} +(4.28465e6 - 1.14807e6i) q^{32} +(681698. - 2.54413e6i) q^{33} -94365.0 q^{34} +(-8.09421e6 - 3.64683e6i) q^{35} -5.99328e6 q^{36} +(1.03579e6 - 3.86561e6i) q^{37} +(-4.74344e6 + 1.27100e6i) q^{38} +(5.32091e6 + 3.07203e6i) q^{39} +(-2.97545e6 - 8.09914e6i) q^{40} +4.95585e6i q^{41} +(-3.33314e6 + 33388.7i) q^{42} +(-9.30301e6 + 9.30301e6i) q^{43} +(1.28835e7 - 7.43827e6i) q^{44} +(1.59744e6 + 1.76475e7i) q^{45} +(1.91776e6 - 3.32166e6i) q^{46} +(4.32423e7 + 1.15867e7i) 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} +(8.98169e6 + 3.35201e7i) q^{52} +(2.14306e7 + 7.99801e7i) 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} +(-4.41360e7 - 1.18262e7i) q^{58} +(-5.95342e7 + 1.03116e8i) q^{59} +(3.54090e7 - 4.24573e7i) q^{60} +(-8.24305e7 + 4.75913e7i) q^{61} +(4.11728e7 - 4.11728e7i) q^{62} +(4.09686e7 + 6.93461e7i) q^{63} +7.62797e7i q^{64} +(9.63077e7 - 3.53814e7i) q^{65} +(-1.43019e7 - 8.25720e6i) q^{66} +(-1.31546e8 + 3.52475e7i) q^{67} +(1.84126e6 - 6.87166e6i) q^{68} +5.11947e7 q^{69} +(-3.52217e7 + 4.31033e7i) q^{70} +2.95103e8 q^{71} +(-2.02606e7 + 7.56136e7i) q^{72} +(1.74421e8 - 4.67359e7i) q^{73} +(-2.17306e7 - 1.25462e7i) q^{74} +(-1.34456e8 - 9.29470e7i) q^{75} -3.70217e8i q^{76} +(-1.74134e8 - 9.82237e7i) q^{77} +(2.72400e7 - 2.72400e7i) q^{78} +(3.03492e7 - 1.75221e7i) q^{79} +(2.82970e8 - 2.56142e7i) q^{80} +(1.14526e7 - 1.98366e7i) q^{81} +(3.00144e7 + 8.04232e6i) 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} +(-1.57851e8 - 5.89106e8i) q^{87} +(-5.02909e7 - 1.87688e8i) 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} +(7.50705e8 + 2.01151e8i) q^{93} +(1.40347e8 - 2.43087e8i) q^{94} +(-1.09012e9 + 9.86768e7i) q^{95} +(3.21492e8 - 1.85613e8i) q^{96} +(-9.43605e8 + 9.43605e8i) q^{97} +(-6.05766e7 + 2.45658e8i) 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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