LMFDB - Embedded newform 35.10.k.a.17.20

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			17.20
Character	$\chi$	$=$	35.17
Dual form			35.10.k.a.33.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.68066 - 6.27232i) q^{2} +(56.4624 - 15.1291i) q^{3} +(406.888 + 234.917i) q^{4} +(507.562 + 1302.12i) q^{5} -379.577i q^{6} +(6347.14 + 259.777i) q^{7} +(4508.24 - 4508.24i) q^{8} +(-14086.9 + 8133.05i) q^{9} +(9020.33 - 995.174i) q^{10} +(-44961.3 + 77875.2i) q^{11} +(26527.9 + 7108.13i) q^{12} +(-60467.0 - 60467.0i) q^{13} +(12296.8 - 39374.7i) q^{14} +(48358.0 + 65841.7i) q^{15} +(99577.0 + 172472. i) q^{16} +(-121333. - 452819. i) q^{17} +(27337.8 + 102026. i) q^{18} +(291502. + 504896. i) q^{19} +(-99368.0 + 649050. i) q^{20} +(362305. - 81358.5i) q^{21} +(412894. + 412894. i) q^{22} +(1.51451e6 + 405811. i) q^{23} +(186341. - 322752. i) q^{24} +(-1.43789e6 + 1.32181e6i) q^{25} +(-480893. + 277644. i) q^{26} +(-1.48590e6 + 1.48590e6i) q^{27} +(2.52154e6 + 1.59675e6i) q^{28} -3.27059e6i q^{29} +(494253. - 192659. i) q^{30} +(6.78743e6 + 3.91873e6i) q^{31} +(4.40225e6 - 1.17958e6i) q^{32} +(-1.36044e6 + 5.07724e6i) q^{33} -3.04415e6 q^{34} +(2.88331e6 + 8.39656e6i) q^{35} -7.64236e6 q^{36} +(436363. - 1.62853e6i) q^{37} +(3.65679e6 - 979833. i) q^{38} +(-4.32892e6 - 2.49930e6i) q^{39} +(8.15847e6 + 3.58204e6i) q^{40} -7.67652e6i q^{41} +(98605.4 - 2.40923e6i) q^{42} +(9.94440e6 - 9.94440e6i) q^{43} +(-3.65884e7 + 2.11243e7i) q^{44} +(-1.77401e7 - 1.42147e7i) q^{45} +(5.09075e6 - 8.81743e6i) q^{46} +(-6.86081e6 - 1.83835e6i) q^{47} +(8.23170e6 + 8.23170e6i) q^{48} +(4.02186e7 + 3.29768e6i) q^{49} +(5.87421e6 + 1.12404e7i) q^{50} +(-1.37015e7 - 2.37316e7i) q^{51} +(-1.03986e7 - 3.88080e7i) q^{52} +(-1.59142e7 - 5.93925e7i) q^{53} +(6.82273e6 + 1.18173e7i) q^{54} +(-1.24223e8 - 1.90183e7i) q^{55} +(2.97856e7 - 2.74433e7i) q^{56} +(2.40975e7 + 2.40975e7i) q^{57} +(-2.05142e7 - 5.49676e6i) q^{58} +(3.15723e7 - 5.46849e7i) q^{59} +(4.20895e6 + 3.81502e7i) q^{60} +(-2.44912e7 + 1.41400e7i) q^{61} +(3.59869e7 - 3.59869e7i) q^{62} +(-9.15240e7 + 4.79622e7i) q^{63} +7.23721e7i q^{64} +(4.80443e7 - 1.09426e8i) q^{65} +(2.95597e7 + 1.70663e7i) q^{66} +(4.36465e7 - 1.16951e7i) q^{67} +(5.70061e7 - 2.12750e8i) q^{68} +9.16521e7 q^{69} +(5.75118e7 - 3.97323e6i) q^{70} -2.78044e8 q^{71} +(-2.68412e7 + 1.00173e8i) q^{72} +(1.86852e8 - 5.00668e7i) q^{73} +(-9.48128e6 - 5.47402e6i) q^{74} +(-6.11888e7 + 9.63864e7i) q^{75} +2.73915e8i q^{76} +(-3.05606e8 + 4.82605e8i) q^{77} +(-2.29519e7 + 2.29519e7i) q^{78} +(1.28788e8 - 7.43557e7i) q^{79} +(-1.74038e8 + 2.17201e8i) q^{80} +(9.86658e7 - 1.70894e8i) q^{81} +(-4.81496e7 - 1.29016e7i) q^{82} +(4.43112e8 + 4.43112e8i) q^{83} +(1.66530e8 + 5.20076e7i) q^{84} +(5.28039e8 - 3.87823e8i) q^{85} +(-4.56613e7 - 7.90876e7i) q^{86} +(-4.94809e7 - 1.84665e8i) q^{87} +(1.48384e8 + 5.53777e8i) q^{88} +(1.22183e8 + 2.11627e8i) q^{89} +(-1.18974e8 + 8.73817e7i) q^{90} +(-3.68084e8 - 3.99500e8i) q^{91} +(5.20902e8 + 5.20902e8i) q^{92} +(4.42521e8 + 1.18573e8i) q^{93} +(-2.30614e7 + 3.99436e7i) q^{94} +(-5.09478e8 + 6.35836e8i) q^{95} +(2.30715e8 - 1.33204e8i) q^{96} +(2.41447e8 - 2.41447e8i) q^{97} +(8.82781e7 - 2.46722e8i) q^{98} -1.46269e9i 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 $

$2$	1.68066	−	6.27232i	0.0742755	−	0.277200i	−0.918793	−	0.394741i	$-0.870834\pi$
$2$	1.68066	−	6.27232i	0.0742755	−	0.277200i	0.993068	+	0.117541i	$0.0375011\pi$
$3$	56.4624	−	15.1291i	0.402452	−	0.107837i	−0.0519147	−	0.998652i	$-0.516532\pi$
$3$	56.4624	−	15.1291i	0.402452	−	0.107837i	0.454366	+	0.890815i	$0.349866\pi$
$4$	406.888	+	234.917i	0.794702	+	0.458822i
$5$	507.562	+	1302.12i	0.363182	+	0.931718i
$5$	507.562	+	1302.12i	0.363182	+	0.931718i
$6$		−	379.577i		−	0.119569i
$7$	6347.14	+	259.777i	0.999163	+	0.0408940i
$7$	6347.14	+	259.777i	0.999163	+	0.0408940i
$8$	4508.24	−	4508.24i	0.389137	−	0.389137i
$9$	−14086.9	+	8133.05i	−0.715687	+	0.413202i
$10$	9020.33	−	995.174i	0.285248	−	0.0314702i
$11$	−44961.3	+	77875.2i	−0.925916	+	1.60373i	−0.135835	+	0.990731i	$0.543372\pi$
$11$	−44961.3	+	77875.2i	−0.925916	+	1.60373i	−0.790081	+	0.613002i	$0.789962\pi$
$12$	26527.9	+	7108.13i	0.369307	+	0.0989555i
$13$	−60467.0	−	60467.0i	−0.587183	−	0.587183i	0.349685	−	0.936867i	$-0.386289\pi$
$13$	−60467.0	−	60467.0i	−0.587183	−	0.587183i	−0.936867	+	0.349685i	$0.886289\pi$
$14$	12296.8	−	39374.7i	0.0855492	−	0.273931i
$15$	48358.0	+	65841.7i	0.246636	+	0.335807i
$16$	99577.0	+	172472.i	0.379856	+	0.657930i
$17$	−121333.	−	452819.i	−0.352336	−	1.31494i	−0.883804	−	0.467858i	$-0.845026\pi$
$17$	−121333.	−	452819.i	−0.352336	−	1.31494i	0.531468	−	0.847079i	$-0.321641\pi$
$18$	27337.8	+	102026.i	0.0613816	+	0.229079i
$19$	291502.	+	504896.i	0.513157	+	0.888814i	0.999884	+	0.0152598i	$0.00485755\pi$
$19$	291502.	+	504896.i	0.513157	+	0.888814i	−0.486726	+	0.873554i	$0.661809\pi$
$20$	−99368.0	+	649050.i	−0.138871	+	0.907074i
$21$	362305.	−	81358.5i	0.406525	−	0.0912885i
$22$	412894.	+	412894.i	0.375782	+	0.375782i
$23$	1.51451e6	+	405811.i	1.12848	+	0.302376i	0.774312	−	0.632804i	$-0.218096\pi$
$23$	1.51451e6	+	405811.i	1.12848	+	0.302376i	0.354172	+	0.935180i	$0.384763\pi$
$24$	186341.	−	322752.i	0.114646	−	0.198572i
$25$	−1.43789e6	+	1.32181e6i	−0.736198	+	0.676766i
$26$	−480893.	+	277644.i	−0.206380	+	0.119154i
$27$	−1.48590e6	+	1.48590e6i	−0.538086	+	0.538086i
$28$	2.52154e6	+	1.59675e6i	0.775275	+	0.490936i
$29$		−	3.27059e6i		−	0.858687i	−0.903141	−	0.429344i	$-0.858745\pi$
$29$		−	3.27059e6i		−	0.858687i	0.903141	−	0.429344i	$-0.141255\pi$
$30$	494253.	−	192659.i	0.111405	−	0.0434254i
$31$	6.78743e6	+	3.91873e6i	1.32001	+	0.762109i	0.983730	−	0.179652i	$-0.0574971\pi$
$31$	6.78743e6	+	3.91873e6i	1.32001	+	0.762109i	0.336282	+	0.941761i	$0.390830\pi$
$32$	4.40225e6	−	1.17958e6i	0.742163	−	0.198862i
$33$	−1.36044e6	+	5.07724e6i	−0.199695	+	0.745273i
$34$	−3.04415e6			−0.390670
$35$	2.88331e6	+	8.39656e6i	0.324776	+	0.945791i
$36$	−7.64236e6			−0.758344
$37$	436363.	−	1.62853e6i	0.0382772	−	0.142853i	−0.944143	−	0.329537i	$-0.893107\pi$
$37$	436363.	−	1.62853e6i	0.0382772	−	0.142853i	0.982420	+	0.186684i	$0.0597741\pi$
$38$	3.65679e6	−	979833.i	0.284494	−	0.0762300i
$39$	−4.32892e6	−	2.49930e6i	−0.299632	−	0.172993i
$40$	8.15847e6	+	3.58204e6i	0.503893	+	0.221238i
$41$		−	7.67652e6i		−	0.424265i	−0.977241	−	0.212132i	$-0.931959\pi$
$41$		−	7.67652e6i		−	0.424265i	0.977241	−	0.212132i	$-0.0680408\pi$
$42$	98605.4	−	2.40923e6i	0.00488966	−	0.119469i
$43$	9.94440e6	−	9.94440e6i	0.443578	−	0.443578i	−0.449634	−	0.893213i	$-0.648446\pi$
$43$	9.94440e6	−	9.94440e6i	0.443578	−	0.443578i	0.893213	+	0.449634i	$0.148446\pi$
$44$	−3.65884e7	+	2.11243e7i	−1.47166	+	0.849661i
$45$	−1.77401e7	−	1.42147e7i	−0.644912	−	0.516751i
$46$	5.09075e6	−	8.81743e6i	0.167638	−	0.290357i
$47$	−6.86081e6	−	1.83835e6i	−0.205086	−	0.0549525i	0.154814	−	0.987944i	$-0.450522\pi$
$47$	−6.86081e6	−	1.83835e6i	−0.205086	−	0.0549525i	−0.359899	+	0.932991i	$0.617189\pi$
$48$	8.23170e6	+	8.23170e6i	0.223823	+	0.223823i
$49$	4.02186e7	+	3.29768e6i	0.996655	+	0.0817196i
$50$	5.87421e6	+	1.12404e7i	0.132918	+	0.254341i
$51$	−1.37015e7	−	2.37316e7i	−0.283597	−	0.491204i
$52$	−1.03986e7	−	3.88080e7i	−0.197223	−	0.736047i
$53$	−1.59142e7	−	5.93925e7i	−0.277040	−	1.03393i	−0.954462	−	0.298333i	$-0.903569\pi$
$53$	−1.59142e7	−	5.93925e7i	−0.277040	−	1.03393i	0.677422	−	0.735595i	$-0.263097\pi$
$54$	6.82273e6	+	1.18173e7i	0.109191	+	0.189124i
$55$	−1.24223e8	−	1.90183e7i	−1.83050	−	0.280246i
$56$	2.97856e7	−	2.74433e7i	0.404725	−	0.372898i
$57$	2.40975e7	+	2.40975e7i	0.302368	+	0.302368i
$58$	−2.05142e7	−	5.49676e6i	−0.238028	−	0.0637794i
$59$	3.15723e7	−	5.46849e7i	0.339213	−	0.587534i	−0.645072	−	0.764122i	$-0.723173\pi$
$59$	3.15723e7	−	5.46849e7i	0.339213	−	0.587534i	0.984285	+	0.176588i	$0.0565059\pi$
$60$	4.20895e6	+	3.81502e7i	0.0419269	+	0.380029i
$61$	−2.44912e7	+	1.41400e7i	−0.226477	+	0.130757i	−0.608946	−	0.793212i	$-0.708407\pi$
$61$	−2.44912e7	+	1.41400e7i	−0.226477	+	0.130757i	0.382468	+	0.923969i	$0.375074\pi$
$62$	3.59869e7	−	3.59869e7i	0.309301	−	0.309301i
$63$	−9.15240e7	+	4.79622e7i	−0.731986	+	0.383589i
$64$			7.23721e7i			0.539214i
$65$	4.80443e7	−	1.09426e8i	0.333835	−	0.760343i
$66$	2.95597e7	+	1.70663e7i	0.191757	+	0.110711i
$67$	4.36465e7	−	1.16951e7i	0.264614	−	0.0709032i	−0.124072	−	0.992273i	$-0.539596\pi$
$67$	4.36465e7	−	1.16951e7i	0.264614	−	0.0709032i	0.388687	+	0.921370i	$0.372929\pi$
$68$	5.70061e7	−	2.12750e8i	0.323319	−	1.20664i
$69$	9.16521e7			0.486768
$70$	5.75118e7	−	3.97323e6i	0.286296	−	0.0197789i
$71$	−2.78044e8			−1.29853			−0.649263	−	0.760564i	$-0.724923\pi$
$71$	−2.78044e8			−1.29853			−0.649263	+	0.760564i	$0.724923\pi$
$72$	−2.68412e7	+	1.00173e8i	−0.117708	+	0.439292i
$73$	1.86852e8	−	5.00668e7i	0.770096	−	0.206347i	0.147682	−	0.989035i	$-0.452819\pi$
$73$	1.86852e8	−	5.00668e7i	0.770096	−	0.206347i	0.622414	+	0.782688i	$0.286152\pi$
$74$	−9.48128e6	−	5.47402e6i	−0.0367557	−	0.0212209i
$75$	−6.11888e7	+	9.63864e7i	−0.223304	+	0.351755i
$76$			2.73915e8i			0.941791i
$77$	−3.05606e8	+	4.82605e8i	−0.990725	+	1.56453i
$78$	−2.29519e7	+	2.29519e7i	−0.0702090	+	0.0702090i
$79$	1.28788e8	−	7.43557e7i	0.372009	−	0.214779i	−0.302327	−	0.953204i	$-0.597763\pi$
$79$	1.28788e8	−	7.43557e7i	0.372009	−	0.214779i	0.674336	+	0.738425i	$0.264430\pi$
$80$	−1.74038e8	+	2.17201e8i	−0.475049	+	0.592867i
$81$	9.86658e7	−	1.70894e8i	0.254674	−	0.441108i
$82$	−4.81496e7	−	1.29016e7i	−0.117606	−	0.0315125i
$83$	4.43112e8	+	4.43112e8i	1.02485	+	1.02485i	0.999683	+	0.0251706i	$0.00801290\pi$
$83$	4.43112e8	+	4.43112e8i	1.02485	+	1.02485i	0.0251706	+	0.999683i	$0.491987\pi$
$84$	1.66530e8	+	5.20076e7i	0.364951	+	0.113975i
$85$	5.28039e8	−	3.87823e8i	1.09719	−	0.805839i
$86$	−4.56613e7	−	7.90876e7i	−0.0900129	−	0.155907i
$87$	−4.94809e7	−	1.84665e8i	−0.0925979	−	0.345580i
$88$	1.48384e8	+	5.53777e8i	0.263764	+	0.984380i
$89$	1.22183e8	+	2.11627e8i	0.206422	+	0.357533i	0.950585	−	0.310465i	$-0.100485\pi$
$89$	1.22183e8	+	2.11627e8i	0.206422	+	0.357533i	−0.744163	+	0.667998i	$0.767151\pi$
$90$	−1.18974e8	+	8.73817e7i	−0.191145	+	0.140388i
$91$	−3.68084e8	−	3.99500e8i	−0.562679	−	0.610704i
$92$	5.20902e8	+	5.20902e8i	0.758072	+	0.758072i
$93$	4.42521e8	+	1.18573e8i	0.613424	+	0.164367i
$94$	−2.30614e7	+	3.99436e7i	−0.0304657	+	0.0527681i
$95$	−5.09478e8	+	6.35836e8i	−0.641755	+	0.800919i
$96$	2.30715e8	−	1.33204e8i	0.277240	−	0.160065i
$97$	2.41447e8	−	2.41447e8i	0.276916	−	0.276916i	−0.554960	−	0.831877i	$-0.687267\pi$
$97$	2.41447e8	−	2.41447e8i	0.276916	−	0.276916i	0.831877	+	0.554960i	$0.187267\pi$
$98$	8.82781e7	−	2.46722e8i	0.0966798	−	0.270203i
$99$		−	1.46269e9i		−	1.53036i
$100$	−8.95573e8	+	2.00044e8i	−0.895573	+	0.200044i
$101$	−8.23980e8	−	4.75725e8i	−0.787898	−	0.454893i	0.0513237	−	0.998682i	$-0.483656\pi$
$101$	−8.23980e8	−	4.75725e8i	−0.787898	−	0.454893i	−0.839222	+	0.543789i	$0.816989\pi$
$102$	−1.71880e8	+	4.60551e7i	−0.157226	+	0.0421286i
$103$	4.35190e8	−	1.62415e9i	0.380988	−	1.42187i	−0.463407	−	0.886146i	$-0.653373\pi$
$103$	4.35190e8	−	1.62415e9i	0.380988	−	1.42187i	0.844395	−	0.535721i	$-0.179960\pi$
$104$	−5.45199e8			−0.456989
$105$	2.89830e8	+	4.30468e8i	0.232698	+	0.345612i
$106$	−3.99275e8			−0.307182
$107$	1.94275e8	−	7.25044e8i	0.143281	−	0.534734i	−0.856544	−	0.516073i	$-0.827393\pi$
$107$	1.94275e8	−	7.25044e8i	0.143281	−	0.534734i	0.999826	−	0.0186604i	$-0.00594014\pi$
$108$	−9.53655e8	+	2.55531e8i	−0.674504	+	0.180733i
$109$	1.54734e8	+	8.93357e7i	0.104995	+	0.0606186i	0.551578	−	0.834123i	$-0.314026\pi$
$109$	1.54734e8	+	8.93357e7i	0.104995	+	0.0606186i	−0.446583	+	0.894742i	$0.647359\pi$
$110$	−3.28066e8	+	7.47204e8i	−0.213646	+	0.486600i
$111$		−	9.85525e7i		−	0.0616189i
$112$	5.87225e8	+	1.12057e9i	0.352633	+	0.672914i
$113$	−6.04469e8	+	6.04469e8i	−0.348756	+	0.348756i	−0.859646	−	0.510890i	$-0.829316\pi$
$113$	−6.04469e8	+	6.04469e8i	−0.348756	+	0.348756i	0.510890	+	0.859646i	$0.329316\pi$
$114$	1.91647e8	−	1.10648e8i	0.106275	−	0.0613578i
$115$	2.40293e8	+	2.17804e9i	0.128115	+	1.16125i
$116$	7.68316e8	−	1.33076e9i	0.393984	−	0.682401i
$117$	1.34357e9	+	3.60009e8i	0.662864	+	0.177614i
$118$	−2.89939e8	−	2.89939e8i	−0.137669	−	0.137669i
$119$	−6.52482e8	−	2.90562e9i	−0.298268	−	1.32824i
$120$	5.14839e8	+	7.88207e7i	0.226650	+	0.0346996i
$121$	−2.86406e9	−	4.96070e9i	−1.21464	−	2.10382i
$122$	4.75291e7	+	1.77381e8i	0.0194241	+	0.0724916i
$123$	−1.16139e8	−	4.33435e8i	−0.0457513	−	0.170746i
$124$	1.84115e9	+	3.18896e9i	0.699345	+	1.21130i
$125$	−2.45097e9	−	1.20139e9i	−0.897929	−	0.440140i
$126$	1.47013e8	+	6.54676e8i	0.0519623	+	0.231398i
$127$	−1.67878e9	−	1.67878e9i	−0.572635	−	0.572635i	0.360229	−	0.932864i	$-0.382699\pi$
$127$	−1.67878e9	−	1.67878e9i	−0.572635	−	0.572635i	−0.932864	+	0.360229i	$0.882699\pi$
$128$	2.70789e9	+	7.25577e8i	0.891633	+	0.238912i
$129$	4.11035e8	−	7.11934e8i	0.130685	−	0.226353i
$130$	−6.05607e8	−	4.85257e8i	−0.185971	−	0.149014i
$131$	1.07942e9	−	6.23201e8i	0.320234	−	0.184887i	−0.331263	−	0.943539i	$-0.607475\pi$
$131$	1.07942e9	−	6.23201e8i	0.320234	−	0.184887i	0.651497	+	0.758651i	$0.274141\pi$
$132$	−1.74628e9	+	1.74628e9i	−0.500646	+	0.500646i
$133$	1.71904e9	+	3.28037e9i	0.476381	+	0.909056i
$134$		−	2.93420e8i		−	0.0786174i
$135$	−2.68900e9	−	1.18063e9i	−0.696768	−	0.305922i
$136$	−2.58842e9	−	1.49442e9i	−0.648797	−	0.374583i
$137$	−5.78750e9	+	1.55076e9i	−1.40362	+	0.376098i	−0.879642	−	0.475636i	$-0.842218\pi$
$137$	−5.78750e9	+	1.55076e9i	−1.40362	+	0.376098i	−0.523975	+	0.851734i	$0.675551\pi$
$138$	1.54036e8	−	5.74872e8i	0.0361549	−	0.134932i
$139$	5.13206e9			1.16607			0.583036	−	0.812446i	$-0.301865\pi$
$139$	5.13206e9			1.16607			0.583036	+	0.812446i	$0.301865\pi$
$140$	−7.99310e8	+	4.09379e9i	−0.175849	+	0.900637i
$141$	−4.15191e8			−0.0884629
$142$	−4.67298e8	+	1.74398e9i	−0.0964487	+	0.359952i
$143$	7.42755e9	−	1.99021e9i	1.48537	−	0.398003i
$144$	−2.80546e9	−	1.61973e9i	−0.543716	−	0.313915i
$145$	4.25869e9	−	1.66003e9i	0.800054	−	0.311860i
$146$		−	1.25614e9i		−	0.228797i
$147$	2.32073e9	−	4.22275e8i	0.409918	−	0.0745877i
$148$	5.60120e8	−	5.60120e8i	0.0959628	−	0.0959628i
$149$	5.87833e9	−	3.39385e9i	0.977047	−	0.564099i	0.0756699	−	0.997133i	$-0.475890\pi$
$149$	5.87833e9	−	3.39385e9i	0.977047	−	0.564099i	0.901377	+	0.433034i	$0.142557\pi$
$150$	5.01729e8	+	5.45789e8i	0.0809204	+	0.0880266i
$151$	−5.45111e9	+	9.44160e9i	−0.853274	+	1.47791i	0.0249632	+	0.999688i	$0.492053\pi$
$151$	−5.45111e9	+	9.44160e9i	−0.853274	+	1.47791i	−0.878237	+	0.478225i	$0.841280\pi$
$152$	3.59036e9	+	9.62033e8i	0.545559	+	0.146182i
$153$	5.39200e9	+	5.39200e9i	0.795497	+	0.795497i
$154$	2.51343e9	+	2.72795e9i	0.360101	+	0.390835i
$155$	−1.65759e9	+	1.08270e10i	−0.230667	+	1.50666i
$156$	−1.17426e9	−	2.03387e9i	−0.158746	−	0.274956i
$157$	−2.16337e8	−	8.07380e8i	−0.0284172	−	0.106055i	0.950261	−	0.311456i	$-0.100817\pi$
$157$	−2.16337e8	−	8.07380e8i	−0.0284172	−	0.106055i	−0.978678	+	0.205401i	$0.934150\pi$
$158$	−2.49934e8	−	9.32766e8i	−0.0319057	−	0.119074i
$159$	−1.79711e9	−	3.11268e9i	−0.222991	−	0.386231i
$160$	3.77036e9	+	5.13352e9i	0.454823	+	0.619264i
$161$	9.50735e9	+	2.96917e9i	1.11518	+	0.348272i
$162$	−9.06079e8	−	9.06079e8i	−0.103359	−	0.103359i
$163$	−3.04941e9	−	8.17087e8i	−0.338354	−	0.0906617i	0.0856413	−	0.996326i	$-0.472706\pi$
$163$	−3.04941e9	−	8.17087e8i	−0.338354	−	0.0906617i	−0.423996	+	0.905664i	$0.639373\pi$
$164$	1.80334e9	−	3.12348e9i	0.194662	−	0.337164i
$165$	−7.30167e9	+	8.05562e8i	−0.766910	+	0.0846099i
$166$	3.52406e9	−	2.03462e9i	0.360211	−	0.207968i
$167$	−1.08077e10	+	1.08077e10i	−1.07525	+	1.07525i	−0.0783248	+	0.996928i	$0.524957\pi$
$167$	−1.08077e10	+	1.08077e10i	−1.07525	+	1.07525i	−0.996928	+	0.0783248i	$0.975043\pi$
$168$	1.26657e9	−	2.00014e9i	0.122670	−	0.193717i
$169$		−	3.29199e9i		−	0.310433i
$170$	−1.54509e9	−	3.96383e9i	−0.141884	−	0.363995i
$171$	−8.21270e9	−	4.74160e9i	−0.734520	−	0.424075i
$172$	6.38236e9	−	1.71015e9i	0.556036	−	0.148989i
$173$	7.65592e7	−	2.85723e8i	0.00649815	−	0.0242514i	−0.962601	−	0.270924i	$-0.912671\pi$
$173$	7.65592e7	−	2.85723e8i	0.00649815	−	0.0242514i	0.969099	+	0.246673i	$0.0793373\pi$
$174$	−1.24144e9			−0.102673
$175$	−9.46984e9	+	8.01617e9i	−0.763258	+	0.646094i
$176$	−1.79084e10			−1.40686
$177$	9.55319e8	−	3.56530e9i	0.0731592	−	0.273034i
$178$	1.53274e9	−	4.10697e8i	0.114440	−	0.0306642i
$179$	4.63733e9	+	2.67737e9i	0.337621	+	0.194926i	0.659220	−	0.751950i	$-0.270887\pi$
$179$	4.63733e9	+	2.67737e9i	0.337621	+	0.194926i	−0.321598	+	0.946876i	$0.604220\pi$
$180$	−3.87897e9	−	9.95124e9i	−0.275417	−	0.706563i
$181$		−	2.38648e10i		−	1.65274i	−0.563128	−	0.826370i	$-0.690402\pi$
$181$		−	2.38648e10i		−	1.65274i	0.563128	−	0.826370i	$-0.309598\pi$
$182$	−3.12442e9	+	1.63732e9i	−0.211080	+	0.110614i
$183$	−1.16890e9	+	1.16890e9i	−0.0770459	+	0.0770459i
$184$	8.65725e9	−	4.99827e9i	0.556801	−	0.321469i
$185$	2.34202e9	−	2.58384e8i	0.147000	−	0.0162179i
$186$	1.48746e9	−	2.57635e9i	0.0911248	−	0.157833i
$187$	4.07187e10	+	1.09105e10i	2.43504	+	0.652467i
$188$	−2.35972e9	−	2.35972e9i	−0.137769	−	0.137769i
$189$	−9.81719e9	+	9.04519e9i	−0.559640	+	0.515631i
$190$	3.13190e9	+	4.26424e9i	0.174348	+	0.237383i
$191$	−1.39276e10	−	2.41233e10i	−0.757227	−	1.31156i	−0.944259	−	0.329202i	$-0.893220\pi$
$191$	−1.39276e10	−	2.41233e10i	−0.757227	−	1.31156i	0.187032	−	0.982354i	$-0.440113\pi$
$192$	1.09492e9	+	4.08630e9i	0.0581470	+	0.217008i
$193$	3.69162e9	+	1.37773e10i	0.191518	+	0.714755i	0.993141	+	0.116925i	$0.0373036\pi$
$193$	3.69162e9	+	1.37773e10i	0.191518	+	0.714755i	−0.801623	+	0.597830i	$0.796030\pi$
$194$	−1.10864e9	−	1.92022e9i	−0.0561931	−	0.0973293i
$195$	1.05719e9	−	6.90530e9i	0.0523595	−	0.342001i
$196$	1.55898e10	+	1.07898e10i	0.754550	+	0.522230i
$197$	−2.40693e10	−	2.40693e10i	−1.13858	−	1.13858i	−0.988704	−	0.149878i	$-0.952112\pi$
$197$	−2.40693e10	−	2.40693e10i	−1.13858	−	1.13858i	−0.149878	−	0.988704i	$-0.547888\pi$
$198$	−9.17446e9	−	2.45829e9i	−0.424216	−	0.113668i
$199$	−4.43889e9	+	7.68839e9i	−0.200649	+	0.347533i	−0.948738	−	0.316065i	$-0.897638\pi$
$199$	−4.43889e9	+	7.68839e9i	−0.200649	+	0.347533i	0.748089	+	0.663598i	$0.230972\pi$
$200$	−5.23304e8	+	1.24414e10i	−0.0231270	+	0.549836i
$201$	2.28745e9	−	1.32066e9i	0.0988485	−	0.0570702i
$202$	−4.36873e9	+	4.36873e9i	−0.184618	+	0.184618i
$203$	8.49624e8	−	2.07589e10i	0.0351152	−	0.857969i
$204$		−	1.28748e10i		−	0.520481i
$205$	9.99572e9	−	3.89631e9i	0.395295	−	0.154085i
$206$	−9.45579e9	−	5.45930e9i	−0.365843	−	0.211220i
$207$	−2.46351e10	+	6.60096e9i	−0.932584	+	0.249885i
$208$	4.40777e9	−	1.64500e10i	0.163280	−	0.609370i
$209$	−5.24252e10			−1.90056
$210$	3.18714e9	−	1.09444e9i	0.113087	−	0.0388333i
$211$	2.30423e10			0.800302			0.400151	−	0.916449i	$-0.368958\pi$
$211$	2.30423e10			0.800302			0.400151	+	0.916449i	$0.368958\pi$
$212$	7.47701e9	−	2.79046e10i	0.254224	−	0.948777i
$213$	−1.56990e10	+	4.20654e9i	−0.522594	+	0.140029i
$214$	−4.22120e9	−	2.43711e9i	−0.137586	−	0.0794353i
$215$	1.79962e10	+	7.90136e9i	0.574390	+	0.252191i
$216$			1.33976e10i			0.418778i
$217$	4.20628e10	+	2.66359e10i	1.28774	+	0.815452i
$218$	8.20398e8	−	8.20398e8i	0.0246020	−	0.0246020i
$219$	9.79265e9	−	5.65379e9i	0.287675	−	0.166089i
$220$	−4.60772e10	−	3.69204e10i	−1.32612	−	1.06259i
$221$	−2.00440e10	+	3.47172e10i	−0.565222	+	0.978993i
$222$	−6.18153e8	−	1.65633e8i	−0.0170808	−	0.00457678i
$223$	3.11011e10	+	3.11011e10i	0.842179	+	0.842179i	0.989142	−	0.146963i	$-0.0469499\pi$
$223$	3.11011e10	+	3.11011e10i	0.842179	+	0.842179i	−0.146963	+	0.989142i	$0.546950\pi$
$224$	2.82481e10	−	6.34334e9i	0.749674	−	0.168346i
$225$	9.50496e9	−	3.03146e10i	0.247246	−	0.788551i
$226$	2.77552e9	+	4.80733e9i	0.0707711	+	0.122579i
$227$	6.88539e9	+	2.56966e10i	0.172112	+	0.642332i	0.997025	+	0.0770725i	$0.0245573\pi$
$227$	6.88539e9	+	2.56966e10i	0.172112	+	0.642332i	−0.824913	+	0.565259i	$0.808776\pi$
$228$	4.14407e9	+	1.54659e10i	0.101559	+	0.379025i
$229$	3.09771e10	+	5.36539e10i	0.744356	+	1.28926i	0.950495	+	0.310740i	$0.100577\pi$
$229$	3.09771e10	+	5.36539e10i	0.744356	+	1.28926i	−0.206139	+	0.978523i	$0.566090\pi$
$230$	1.40652e10	+	2.15335e9i	0.331414	+	0.0507387i
$231$	−9.95387e9	+	3.18725e10i	−0.230005	+	0.736483i
$232$	−1.47446e10	−	1.47446e10i	−0.334147	−	0.334147i
$233$	−2.49380e10	−	6.68212e9i	−0.554319	−	0.148529i	−0.0292240	−	0.999573i	$-0.509304\pi$
$233$	−2.49380e10	−	6.68212e9i	−0.554319	−	0.148529i	−0.525095	+	0.851044i	$0.675970\pi$
$234$	4.51618e9	−	7.82225e9i	0.0984691	−	0.170553i
$235$	−1.08854e9	−	9.86665e9i	−0.0232831	−	0.211040i
$236$	2.56928e10	−	1.48337e10i	0.539147	−	0.311277i
$237$	6.14674e9	−	6.14674e9i	0.126554	−	0.126554i
$238$	−1.93216e10	−	7.90799e8i	−0.390344	−	0.0159761i
$239$			1.20764e10i			0.239412i	0.992809	+	0.119706i	$0.0381952\pi$
$239$			1.20764e10i			0.239412i	−0.992809	+	0.119706i	$0.961805\pi$
$240$	−6.54053e9	+	1.48967e10i	−0.127251	+	0.289828i
$241$	5.71490e10	+	3.29950e10i	1.09127	+	0.630044i	0.933914	−	0.357498i	$-0.116370\pi$
$241$	5.71490e10	+	3.29950e10i	1.09127	+	0.630044i	0.157355	+	0.987542i	$0.449703\pi$
$242$	−3.59286e10	+	9.62704e9i	−0.673397	+	0.180436i
$243$	1.36906e10	−	5.10938e10i	0.251879	−	0.940027i
$244$	−1.32869e10			−0.239976
$245$	1.61195e10	+	5.40431e10i	0.285828	+	0.958281i
$246$	−2.91383e9			−0.0507290
$247$	1.29033e10	−	4.81558e10i	0.220579	−	0.823213i
$248$	4.82660e10	−	1.29328e10i	0.810230	−	0.217101i
$249$	3.17230e10	+	1.83153e10i	0.522971	+	0.301937i
$250$	−1.16548e10	+	1.33541e10i	−0.188701	+	0.216214i
$251$			7.86729e10i			1.25110i	0.780183	+	0.625552i	$0.215126\pi$
$251$			7.86729e10i			1.25110i	−0.780183	+	0.625552i	$0.784874\pi$
$252$	−4.85071e10	−	1.98531e9i	−0.757710	−	0.0310117i
$253$	−9.96967e10	+	9.96967e10i	−1.52981	+	1.52981i
$254$	−1.33513e10	+	7.70840e9i	−0.201267	+	0.116202i
$255$	2.39470e10	−	2.98861e10i	0.354666	−	0.442628i
$256$	−9.42516e9	+	1.63249e10i	−0.137154	+	0.237558i
$257$	−4.62160e10	−	1.23835e10i	−0.660835	−	0.177070i	−0.0872124	−	0.996190i	$-0.527796\pi$
$257$	−4.62160e10	−	1.23835e10i	−0.660835	−	0.177070i	−0.573623	+	0.819119i	$0.694463\pi$
$258$	−3.77467e9	−	3.77467e9i	−0.0530383	−	0.0530383i
$259$	3.19271e9	−	1.02231e10i	0.0440870	−	0.141168i
$260$	4.52546e10	−	3.32376e10i	0.614161	−	0.451076i
$261$	2.65999e10	+	4.60723e10i	0.354811	+	0.614551i
$262$	−2.09478e9	−	7.81783e9i	−0.0274652	−	0.102502i
$263$	−3.06118e10	−	1.14245e11i	−0.394538	−	1.47243i	−0.822566	−	0.568670i	$-0.807458\pi$
$263$	−3.06118e10	−	1.14245e11i	−0.394538	−	1.47243i	0.428028	−	0.903765i	$-0.359208\pi$
$264$	1.67562e10	+	2.90227e10i	0.212304	+	0.367722i
$265$	6.92585e10	−	5.08675e10i	0.862714	−	0.633627i
$266$	2.34647e10	−	5.26919e9i	0.287374	−	0.0645321i
$267$	1.01005e10	+	1.01005e10i	0.121630	+	0.121630i
$268$	2.05066e10	+	5.49473e9i	0.242821	+	0.0650638i
$269$	−6.61492e9	+	1.14574e10i	−0.0770263	+	0.133414i	−0.901966	−	0.431808i	$-0.857876\pi$
$269$	−6.61492e9	+	1.14574e10i	−0.0770263	+	0.133414i	0.824939	+	0.565221i	$0.191209\pi$
$270$	−1.19246e10	+	1.48820e10i	−0.136554	+	0.170422i
$271$	3.16240e10	−	1.82581e10i	0.356168	−	0.205634i	−0.311230	−	0.950335i	$-0.600741\pi$
$271$	3.16240e10	−	1.82581e10i	0.356168	−	0.205634i	0.667399	+	0.744701i	$0.267408\pi$
$272$	6.60169e10	−	6.60169e10i	0.731299	−	0.731299i
$273$	−2.68270e10	−	1.69880e10i	−0.292307	−	0.185101i
$274$			3.89074e10i			0.417018i
$275$	−3.82870e10	−	1.71406e11i	−0.403696	−	1.80729i
$276$	3.72921e10	+	2.15306e10i	0.386835	+	0.223340i
$277$	1.12089e10	−	3.00342e9i	0.114394	−	0.0306519i	−0.201168	−	0.979557i	$-0.564474\pi$
$277$	1.12089e10	−	3.00342e9i	0.114394	−	0.0306519i	0.315562	+	0.948905i	$0.397807\pi$
$278$	8.62527e9	−	3.21900e10i	0.0866106	−	0.323235i
$279$	−1.27485e11			−1.25962
$280$	5.08524e10	+	2.48551e10i	0.494424	+	0.241660i
$281$	−6.83073e9			−0.0653565			−0.0326782	−	0.999466i	$-0.510404\pi$
$281$	−6.83073e9			−0.0653565			−0.0326782	+	0.999466i	$0.510404\pi$
$282$	−6.97795e8	+	2.60421e9i	−0.00657063	+	0.0245219i
$283$	−1.15259e11	+	3.08835e10i	−1.06816	+	0.286212i	−0.749735	−	0.661738i	$-0.769819\pi$
$283$	−1.15259e11	+	3.08835e10i	−1.06816	+	0.286212i	−0.318421	+	0.947949i	$0.603153\pi$
$284$	−1.13133e11	−	6.53172e10i	−1.03194	−	0.595792i
$285$	−1.91468e10	+	4.36087e10i	−0.171907	+	0.391536i
$286$		−	4.99329e10i		−	0.441305i
$287$	1.99418e9	−	4.87239e10i	0.0173499	−	0.423910i
$288$	−5.24203e10	+	5.24203e10i	−0.448986	+	0.448986i
$289$	−8.76236e10	+	5.05895e10i	−0.738891	+	0.426599i
$290$	−3.25480e9	−	2.95018e10i	−0.0270230	−	0.244939i
$291$	9.97980e9	−	1.72855e10i	0.0815837	−	0.141307i
$292$	8.77893e10	+	2.35231e10i	0.706674	+	0.189353i
$293$	1.00166e11	+	1.00166e11i	0.793991	+	0.793991i	0.982140	−	0.188149i	$-0.0602488\pi$
$293$	1.00166e11	+	1.00166e11i	0.793991	+	0.793991i	−0.188149	+	0.982140i	$0.560249\pi$
$294$	1.25172e9	−	1.52661e10i	0.00977115	−	0.119169i
$295$	8.72310e10	+	1.33549e10i	0.670613	+	0.102669i
$296$	−5.37457e9	−	9.30904e9i	−0.0406941	−	0.0704842i
$297$	−4.89067e10	−	1.82522e11i	−0.364724	−	1.36117i
$298$	−1.14079e10	−	4.25747e10i	−0.0837974	−	0.312736i
$299$	−6.70394e10	−	1.16116e11i	−0.485076	−	0.840177i
$300$	−4.75397e10	+	2.48442e10i	−0.338853	+	0.177084i
$301$	6.57018e10	−	6.05351e10i	0.461347	−	0.425068i
$302$	5.00592e10	+	5.00592e10i	0.346300	+	0.346300i
$303$	−5.37211e10	−	1.43945e10i	−0.366145	−	0.0981083i
$304$	−5.80538e10	+	1.00552e11i	−0.389852	+	0.675243i
$305$	−3.08427e10	−	2.47134e10i	−0.204081	−	0.163525i
$306$	4.28825e10	−	2.47582e10i	0.279598	−	0.161426i
$307$	8.10579e9	−	8.10579e9i	0.0520802	−	0.0520802i	−0.680587	−	0.732667i	$-0.738275\pi$
$307$	8.10579e9	−	8.10579e9i	0.0520802	−	0.0520802i	0.732667	+	0.680587i	$0.238275\pi$
$308$	−2.37719e11	+	1.24574e11i	−1.50517	+	0.788768i
$309$		−	9.82875e10i		−	0.613317i
$310$	6.51247e10	+	2.85935e10i	0.400514	+	0.175849i
$311$	−5.74237e9	−	3.31536e9i	−0.0348073	−	0.0200960i	0.482495	−	0.875899i	$-0.339731\pi$
$311$	−5.74237e9	−	3.31536e9i	−0.0348073	−	0.0200960i	−0.517303	+	0.855803i	$0.673064\pi$
$312$	−3.07833e10	+	8.24835e9i	−0.183916	+	0.0492801i
$313$	−1.31632e10	+	4.91256e10i	−0.0775195	+	0.289307i	−0.993793	−	0.111247i	$-0.964516\pi$
$313$	−1.31632e10	+	4.91256e10i	−0.0775195	+	0.289307i	0.916273	+	0.400554i	$0.131182\pi$
$314$	−5.42773e9			−0.0315090
$315$	−1.08906e11	−	9.48311e10i	−0.623241	−	0.542692i
$316$	6.98696e10			0.394182
$317$	−4.03608e10	+	1.50628e11i	−0.224488	+	0.837800i	0.758121	+	0.652114i	$0.226117\pi$
$317$	−4.03608e10	+	1.50628e11i	−0.224488	+	0.837800i	−0.982609	+	0.185686i	$0.940549\pi$
$318$	−2.25440e10	+	6.04066e9i	−0.123626	+	0.0331255i
$319$	2.54698e11	+	1.47050e11i	1.37711	+	0.795072i
$320$	−9.42369e10	+	3.67333e10i	−0.502396	+	0.195833i
$321$		−	4.38769e10i		−	0.230655i
$322$	3.46022e10	−	5.46430e10i	0.179371	−	0.283258i
$323$	1.93258e11	−	1.93258e11i	0.987930	−	0.987930i
$324$	8.02918e10	−	4.63565e10i	0.404780	−	0.233700i
$325$	1.66870e11	+	7.01884e9i	0.829668	+	0.0348972i
$326$	−1.02501e10	+	1.77536e10i	−0.0502629	+	0.0870578i
$327$	1.00882e10	+	2.70313e9i	0.0487921	+	0.0130738i
$328$	−3.46076e10	−	3.46076e10i	−0.165097	−	0.165097i
$329$	−4.30689e10	−	1.34505e10i	−0.202667	−	0.0632933i
$330$	−7.21891e9	+	4.71523e10i	−0.0335088	+	0.218872i
$331$	8.82408e10	+	1.52838e11i	0.404058	+	0.699848i	0.994211	−	0.107443i	$-0.0342662\pi$
$331$	8.82408e10	+	1.52838e11i	0.404058	+	0.699848i	−0.590154	+	0.807291i	$0.700933\pi$
$332$	7.62024e10	+	2.84391e11i	0.344229	+	1.28468i
$333$	7.09793e9	+	2.64898e10i	0.0316324	+	0.118054i
$334$	4.96254e10	+	8.59537e10i	0.218195	+	0.377925i
$335$	3.73816e10	+	5.08969e10i	0.162165	+	0.220795i
$336$	5.01093e10	+	5.43862e10i	0.214483	+	0.232789i
$337$	−2.86251e11	−	2.86251e11i	−1.20896	−	1.20896i	−0.971364	−	0.237595i	$-0.923641\pi$
$337$	−2.86251e11	−	2.86251e11i	−1.20896	−	1.20896i	−0.237595	−	0.971364i	$-0.576359\pi$
$338$	−2.06484e10	−	5.53273e9i	−0.0860521	−	0.0230576i
$339$	−2.49847e10	+	4.32748e10i	−0.102749	+	0.177966i
$340$	3.05959e11	−	3.37551e10i	1.24167	−	0.136989i
$341$	−6.10343e11	+	3.52382e11i	−2.44444	+	1.41130i
$342$	−4.35436e10	+	4.35436e10i	−0.172110	+	0.172110i
$343$	2.54416e11	+	3.13787e10i	0.992480	+	0.122408i
$344$		−	8.96635e10i		−	0.345225i
$345$	4.65192e10	+	1.19342e11i	0.176785	+	0.453530i
$346$	−1.66347e9	−	9.60407e8i	−0.00623984	−	0.00360257i
$347$	4.39629e11	−	1.17798e11i	1.62781	−	0.436170i	0.674527	−	0.738251i	$-0.264348\pi$
$347$	4.39629e11	−	1.17798e11i	1.62781	−	0.436170i	0.953282	+	0.302080i	$0.0976811\pi$
$348$	2.32478e10	−	8.67619e10i	0.0849718	−	0.317119i
$349$	8.78400e10			0.316941			0.158470	−	0.987364i	$-0.449344\pi$
$349$	8.78400e10			0.316941			0.158470	+	0.987364i	$0.449344\pi$
$350$	3.43644e10	+	7.28703e10i	0.122406	+	0.259564i
$351$	1.79695e11			0.631910
$352$	−1.06071e11	+	3.95861e11i	−0.368259	+	1.37436i
$353$	−5.57270e10	+	1.49320e10i	−0.191020	+	0.0511838i	−0.353061	−	0.935600i	$-0.614859\pi$
$353$	−5.57270e10	+	1.49320e10i	−0.191020	+	0.0511838i	0.162040	+	0.986784i	$0.448192\pi$
$354$	−2.07571e10	−	1.19841e10i	−0.0702510	−	0.0405594i
$355$	−1.41125e11	−	3.62045e11i	−0.471601	−	1.20986i
$356$			1.14811e11i			0.378843i
$357$	−8.08001e10	−	1.54187e11i	−0.263272	−	0.502390i
$358$	2.45871e10	−	2.45871e10i	0.0791104	−	0.0791104i
$359$	1.66527e11	−	9.61446e10i	0.529128	−	0.305492i	−0.211534	−	0.977371i	$-0.567846\pi$
$359$	1.66527e11	−	9.61446e10i	0.529128	−	0.305492i	0.740661	+	0.671879i	$0.234512\pi$
$360$	−1.44060e11	+	1.58935e10i	−0.452046	+	0.0498723i
$361$	−8.60305e9	+	1.49009e10i	−0.0266606	+	0.0461775i
$362$	−1.49688e11	−	4.01087e10i	−0.458139	−	0.122758i
$363$	−2.36762e11	−	2.36762e11i	−0.715703	−	0.715703i
$364$	−5.59197e10	−	2.49021e11i	−0.166958	−	0.743497i
$365$	1.60032e11	+	2.17891e11i	0.471942	+	0.642571i
$366$	5.36721e9	+	9.29628e9i	0.0156345	+	0.0270797i
$367$	8.43105e8	+	3.14651e9i	0.00242596	+	0.00905382i	0.967128	−	0.254289i	$-0.0818415\pi$
$367$	8.43105e8	+	3.14651e9i	0.00242596	+	0.00905382i	−0.964702	+	0.263343i	$0.915175\pi$
$368$	8.08188e10	+	3.01620e11i	0.229719	+	0.857324i
$369$	6.24336e10	+	1.08138e11i	0.175307	+	0.303641i
$370$	2.31547e9	−	1.51241e10i	0.00642290	−	0.0419530i
$371$	−8.55806e10	−	3.81106e11i	−0.234527	−	1.04439i
$372$	1.52202e11	+	1.52202e11i	0.412075	+	0.412075i
$373$	6.17782e11	+	1.65534e11i	1.65251	+	0.442790i	0.960315	−	0.278916i	$-0.0899751\pi$
$373$	6.17782e11	+	1.65534e11i	1.65251	+	0.442790i	0.692200	+	0.721706i	$0.256642\pi$
$374$	1.36869e11	−	2.37064e11i	0.361728	−	0.626531i
$375$	−1.56563e11	−	3.07528e10i	−0.408836	−	0.0803053i
$376$	−3.92179e10	+	2.26425e10i	−0.101190	+	0.0584223i
$377$	−1.97763e11	+	1.97763e11i	−0.504206	+	0.504206i
$378$	4.02349e10	+	7.67785e10i	0.101365	+	0.193431i
$379$			6.26332e11i			1.55929i	0.626219	+	0.779647i	$0.284601\pi$
$379$			6.26332e11i			1.55929i	−0.626219	+	0.779647i	$0.715399\pi$
$380$	−3.56669e11	+	1.39029e11i	−0.877483	+	0.342041i
$381$	−1.20187e11	−	6.93897e10i	−0.292209	−	0.168707i
$382$	−1.74717e11	+	4.68152e10i	−0.419807	+	0.112487i
$383$	−1.78024e10	+	6.64395e10i	−0.0422751	+	0.157773i	−0.983837	−	0.179068i	$-0.942692\pi$
$383$	−1.78024e10	+	6.64395e10i	−0.0422751	+	0.157773i	0.941562	+	0.336841i	$0.109358\pi$
$384$	1.63871e11			0.384603
$385$	−7.83521e11	−	1.52982e11i	−1.81751	−	0.354868i
$386$	9.26202e10			0.212355
$387$	−5.92071e10	+	2.20964e11i	−0.134176	+	0.500751i
$388$	1.54962e11	−	4.15218e10i	0.347121	−	0.0930109i
$389$	−1.56904e10	−	9.05888e9i	−0.0347426	−	0.0200586i	0.482528	−	0.875880i	$-0.339719\pi$
$389$	−1.56904e10	−	9.05888e9i	−0.0347426	−	0.0200586i	−0.517271	+	0.855822i	$0.673052\pi$
$390$	−4.15355e10	−	1.82365e10i	−0.0909136	−	0.0399163i
$391$		−	7.35035e11i		−	1.59042i
$392$	1.96182e11	−	1.66449e11i	0.419635	−	0.356035i
$393$	5.15180e10	−	5.15180e10i	0.108941	−	0.108941i
$394$	−1.91422e11	+	1.10518e11i	−0.400184	+	0.231046i
$395$	1.62188e11	+	1.29957e11i	0.335221	+	0.268603i
$396$	3.43610e11	−	5.95151e11i	0.702163	−	1.21618i
$397$	−2.58409e11	−	6.92405e10i	−0.522096	−	0.139895i	−0.0118601	−	0.999930i	$-0.503775\pi$
$397$	−2.58409e11	−	6.92405e10i	−0.522096	−	0.139895i	−0.510236	+	0.860034i	$0.670442\pi$
$398$	4.07638e10	+	4.07638e10i	0.0814330	+	0.0814330i
$399$	1.46690e11	+	1.59210e11i	0.289750	+	0.314480i
$400$	−3.71156e11	−	1.16374e11i	−0.724915	−	0.227293i
$401$	−9.05200e10	−	1.56785e11i	−0.174821	−	0.302800i	0.765278	−	0.643700i	$-0.222602\pi$
$401$	−9.05200e10	−	1.56785e11i	−0.174821	−	0.302800i	−0.940099	+	0.340900i	$0.889268\pi$
$402$	−4.43917e9	−	1.65672e10i	−0.00847784	−	0.0316397i
$403$	−1.73462e11	−	6.47369e11i	−0.327591	−	1.22259i
$404$	−2.23511e11	−	3.87133e11i	−0.417430	−	0.723010i
$405$	2.72603e11	+	4.17349e10i	0.503481	+	0.0770818i
$406$	−1.28778e11	−	4.02178e10i	−0.235221	−	0.0734600i
$407$	1.07203e11	+	1.07203e11i	0.193656	+	0.193656i
$408$	−1.68757e11	−	4.52184e10i	−0.301503	−	0.0807875i
$409$	1.96145e11	−	3.39733e11i	0.346595	−	0.600320i	−0.639047	−	0.769168i	$-0.720671\pi$
$409$	1.96145e11	−	3.39733e11i	0.346595	−	0.600320i	0.985642	+	0.168847i	$0.0540045\pi$
$410$	−7.63947e9	−	6.92447e10i	−0.0133517	−	0.121021i
$411$	−3.03315e11	+	1.75119e11i	−0.524331	+	0.302723i
$412$	5.58614e11	−	5.58614e11i	0.955156	−	0.955156i
$413$	2.14600e11	−	3.38891e11i	0.362956	−	0.573171i
$414$			1.65613e11i			0.277073i
$415$	−3.52076e11	+	8.01890e11i	−0.582667	+	1.32708i
$416$	−3.37516e11	−	1.94865e11i	−0.552553	−	0.319017i
$417$	2.89769e11	−	7.76433e10i	0.469288	−	0.125745i
$418$	−8.81092e10	+	3.28828e11i	−0.141165	+	0.526836i
$419$	−1.16519e11			−0.184687			−0.0923433	−	0.995727i	$-0.529436\pi$
$419$	−1.16519e11			−0.184687			−0.0923433	+	0.995727i	$0.529436\pi$
$420$	1.68042e10	+	2.43238e11i	0.0263510	+	0.381426i
$421$	−9.23539e11			−1.43280			−0.716401	−	0.697689i	$-0.754212\pi$
$421$	−9.23539e11			−1.43280			−0.716401	+	0.697689i	$0.754212\pi$
$422$	3.87263e10	−	1.44528e11i	0.0594428	−	0.221844i
$423$	1.11599e11	−	2.99028e10i	0.169484	−	0.0454130i
$424$	−3.39501e11	−	1.96011e11i	−0.510146	−	0.294533i
$425$	7.73003e11	+	4.90724e11i	1.14929	+	0.729604i
$426$			1.05539e11i			0.155264i
$427$	−1.59122e11	+	8.33861e10i	−0.231635	+	0.121386i
$428$	2.49373e11	−	2.49373e11i	0.359214	−	0.359214i
$429$	3.89268e11	−	2.24744e11i	0.554869	−	0.320354i
$430$	7.98053e10	−	9.95981e10i	0.112570	−	0.140489i
$431$	3.05580e11	−	5.29280e11i	0.426557	−	0.738819i	−0.570007	−	0.821640i	$-0.693060\pi$
$431$	3.05580e11	−	5.29280e11i	0.426557	−	0.738819i	0.996564	+	0.0828210i	$0.0263930\pi$
$432$	−4.04238e11	−	1.08315e11i	−0.558419	−	0.149628i
$433$	3.66141e9	+	3.66141e9i	0.00500556	+	0.00500556i	0.709605	−	0.704600i	$-0.248873\pi$
$433$	3.66141e9	+	3.66141e9i	0.00500556	+	0.00500556i	−0.704600	+	0.709605i	$0.748873\pi$
$434$	2.37762e11	−	2.19065e11i	0.321691	−	0.296394i
$435$	2.15341e11	−	1.58159e11i	0.288353	−	0.211784i
$436$	4.19729e10	+	7.26992e10i	0.0556263	+	0.0963475i
$437$	2.36589e11	+	8.82963e11i	0.310333	+	1.15818i
$438$	−1.90042e10	−	7.09248e10i	−0.0246727	−	0.0920798i
$439$	−5.74101e11	−	9.94372e11i	−0.737731	−	1.27779i	−0.953515	−	0.301346i	$-0.902564\pi$
$439$	−5.74101e11	−	9.94372e11i	−0.737731	−	1.27779i	0.215784	−	0.976441i	$-0.430769\pi$
$440$	−6.45767e11	+	4.74289e11i	−0.821370	+	0.603262i
$441$	−5.93375e11	+	2.80646e11i	−0.747060	+	0.353334i
$442$	1.84070e11	+	1.84070e11i	0.229395	+	0.229395i
$443$	4.73357e11	+	1.26836e11i	0.583945	+	0.156468i	0.538684	−	0.842508i	$-0.318922\pi$
$443$	4.73357e11	+	1.26836e11i	0.583945	+	0.156468i	0.0452605	+	0.998975i	$0.485588\pi$
$444$	2.31516e10	−	4.00998e10i	0.0282721	−	0.0489687i
$445$	−2.13548e11	+	2.66510e11i	−0.258152	+	0.322177i
$446$	2.47347e11	−	1.42806e11i	0.296005	−	0.170899i
$447$	2.80559e11	−	2.80559e11i	0.332384	−	0.332384i
$448$	−1.88006e10	+	4.59356e11i	−0.0220506	+	0.538763i
$449$			1.17618e12i			1.36573i	0.730545	+	0.682865i	$0.239266\pi$
$449$			1.17618e12i			1.36573i	−0.730545	+	0.682865i	$0.760734\pi$
$450$	−1.74168e11	−	1.10567e11i	−0.200222	−	0.127107i
$451$	5.97811e11	+	3.45146e11i	0.680408	+	0.392834i
$452$	−3.87951e11	+	1.03951e11i	−0.437174	+	0.117140i
$453$	−1.64940e11	+	6.15565e11i	−0.184028	+	0.686803i
$454$	1.72749e11			0.190838
$455$	3.33370e11	−	6.82059e11i	0.364649	−	0.746055i
$456$	2.17275e11			0.235325
$457$	−1.62847e11	+	6.07755e11i	−0.174646	+	0.651787i	0.821966	+	0.569537i	$0.192877\pi$
$457$	−1.62847e11	+	6.07755e11i	−0.174646	+	0.651787i	−0.996612	+	0.0822503i	$0.973789\pi$
$458$	3.88596e11	−	1.04124e11i	0.412671	−	0.110575i
$459$	8.53130e11	+	4.92555e11i	0.897136	+	0.517962i
$460$	−4.13885e11	+	9.42665e11i	−0.430992	+	0.981628i
$461$			6.73735e10i			0.0694761i	0.999396	+	0.0347380i	$0.0110597\pi$
$461$			6.73735e10i			0.0694761i	−0.999396	+	0.0347380i	$0.988940\pi$
$462$	1.83186e11	+	1.16001e11i	0.187069	+	0.118460i
$463$	2.82268e11	−	2.82268e11i	0.285461	−	0.285461i	−0.549821	−	0.835282i	$-0.685304\pi$
$463$	2.82268e11	−	2.82268e11i	0.285461	−	0.285461i	0.835282	+	0.549821i	$0.185304\pi$
$464$	5.64087e11	−	3.25676e11i	0.564956	−	0.326178i
$465$	7.02110e10	+	6.36397e11i	0.0696413	+	0.631234i
$466$	−8.38247e10	+	1.45189e11i	−0.0823447	+	0.142625i
$467$	−1.97134e11	−	5.28219e10i	−0.191794	−	0.0513911i	0.161643	−	0.986849i	$-0.448321\pi$
$467$	−1.97134e11	−	5.28219e10i	−0.191794	−	0.0513911i	−0.353438	+	0.935458i	$0.614987\pi$
$468$	4.62110e11	+	4.62110e11i	0.445286	+	0.445286i
$469$	2.80069e11	−	6.28917e10i	0.267292	−	0.0600227i
$470$	−6.37163e10	−	9.75481e9i	−0.0602296	−	0.00922101i
$471$	−2.44298e10	−	4.23136e10i	−0.0228731	−	0.0396174i
$472$	−1.04197e11	−	3.88868e11i	−0.0966309	−	0.360632i
$473$	3.27309e11	+	1.22154e12i	0.300665	+	1.12210i
$474$	−2.82237e10	−	4.88849e10i	−0.0256810	−	0.0444808i
$475$	−1.08652e12	−	3.40674e11i	−0.979305	−	0.307056i
$476$	4.17093e11	−	1.33554e12i	0.372393	−	1.19241i
$477$	7.07223e11	+	7.07223e11i	0.625495	+	0.625495i
$478$	7.57468e10	+	2.02963e10i	0.0663649	+	0.0177824i
$479$	−2.79003e11	+	4.83248e11i	−0.242159	+	0.419431i	−0.961329	−	0.275403i	$-0.911189\pi$
$479$	−2.79003e11	+	4.83248e11i	−0.242159	+	0.419431i	0.719170	+	0.694834i	$0.244522\pi$
$480$	2.90549e11	+	2.32809e11i	0.249824	+	0.200177i
$481$	−1.24858e11	+	7.20867e10i	−0.106356	+	0.0614048i
$482$	3.03003e11	−	3.03003e11i	0.255703	−	0.255703i
$483$	5.81729e11	+	2.38091e10i	0.486360	+	0.0199059i
$484$		−	2.69126e12i		−	2.22922i
$485$	4.36941e11	+	1.91842e11i	0.358579	+	0.157437i
$486$	−2.97468e11	−	1.71743e11i	−0.241867	−	0.139642i
$487$	−1.94376e12	+	5.20830e11i	−1.56590	+	0.419581i	−0.934525	−	0.355898i	$-0.884175\pi$
$487$	−1.94376e12	+	5.20830e11i	−1.56590	+	0.419581i	−0.631373	+	0.775479i	$0.717508\pi$
$488$	−4.66656e10	+	1.74158e11i	−0.0372484	+	0.139013i
$489$	−1.84539e11			−0.145948
$490$	3.66067e11	−	1.02784e10i	0.286866	−	0.00805456i
$491$	−8.65785e11			−0.672269			−0.336135	−	0.941814i	$-0.609120\pi$
$491$	−8.65785e11			−0.672269			−0.336135	+	0.941814i	$0.609120\pi$
$492$	5.45657e10	−	2.03642e11i	0.0419834	−	0.156684i
$493$	−1.48099e12	+	3.96829e11i	−1.12912	+	0.302546i
$494$	−2.80362e11	−	1.61867e11i	−0.211811	−	0.122289i
$495$	1.90459e12	−	7.42406e11i	1.42587	−	0.555800i
$496$			1.56086e12i			1.15797i
$497$	−1.76478e12	−	7.22294e10i	−1.29744	−	0.0531019i
$498$	1.68195e11	−	1.68195e11i	0.122541	−	0.122541i
$499$	−5.39904e11	+	3.11714e11i	−0.389820	+	0.225063i	−0.682082	−	0.731276i	$-0.738925\pi$
$499$	−5.39904e11	+	3.11714e11i	−0.389820	+	0.225063i	0.292262	+	0.956338i	$0.405592\pi$
$500$	−7.15040e11	−	1.06461e12i	−0.511641	−	0.761770i
$501$	−4.46720e11	+	7.73741e11i	−0.316786	+	0.548689i
$502$	4.93461e11	+	1.32223e11i	0.346806	+	0.0929264i
$503$	−4.23651e11	−	4.23651e11i	−0.295088	−	0.295088i	0.543998	−	0.839086i	$-0.316910\pi$
$503$	−4.23651e11	−	4.23651e11i	−0.295088	−	0.295088i	−0.839086	+	0.543998i	$0.816910\pi$
$504$	−1.96387e11	+	6.28837e11i	−0.135574	+	0.434111i
$505$	2.01228e11	−	1.31438e12i	0.137682	−	0.899308i
$506$	4.57773e11	+	7.92886e11i	0.310437	+	0.537692i
$507$	−4.98047e10	−	1.85874e11i	−0.0334761	−	0.124934i
$508$	−2.88702e11	−	1.07745e12i	−0.192337	−	0.717812i
$509$	7.92976e11	+	1.37347e12i	0.523636	+	0.906965i	0.999621	+	0.0275114i	$0.00875827\pi$
$509$	7.92976e11	+	1.37347e12i	0.523636	+	0.906965i	−0.475985	+	0.879453i	$0.657908\pi$
$510$	−1.47209e11	−	2.00432e11i	−0.0963535	−	0.131190i
$511$	1.19898e12	−	2.69241e11i	0.777890	−	0.174682i
$512$	1.10150e12	+	1.10150e12i	0.708385	+	0.708385i
$513$	−1.18337e12	−	3.17082e11i	−0.754381	−	0.202136i
$514$	−1.55347e11	+	2.69069e11i	−0.0981678	+	0.170032i
$515$	2.33572e12	−	2.57690e11i	1.46315	−	0.161423i
$516$	3.34490e11	−	1.93118e11i	0.207711	−	0.119922i
$517$	4.51633e11	−	4.51633e11i	0.278021	−	0.278021i
$518$	−5.87569e10	−	3.72074e10i	−0.0358571	−	0.0227062i
$519$		−	1.72909e10i		−	0.0104608i
$520$	−2.76723e11	−	7.09913e11i	−0.165970	−	0.425785i
$521$	−1.47798e11	−	8.53312e10i	−0.0878817	−	0.0507385i	0.455415	−	0.890279i	$-0.349491\pi$
$521$	−1.47798e11	−	8.53312e10i	−0.0878817	−	0.0507385i	−0.543297	+	0.839541i	$0.682824\pi$
$522$	3.33686e11	−	8.94109e10i	0.196707	−	0.0527076i
$523$	3.92018e11	−	1.46303e12i	0.229112	−	0.855058i	−0.751603	−	0.659616i	$-0.770719\pi$
$523$	3.92018e11	−	1.46303e12i	0.229112	−	0.855058i	0.980715	−	0.195442i	$-0.0626142\pi$
$524$	5.85601e11			0.339321
$525$	−4.13413e11	+	5.95882e11i	−0.237502	+	0.342329i
$526$	−7.68029e11			−0.437463
$527$	9.50938e11	−	3.54895e12i	0.537037	−	2.00425i
$528$	−1.01115e12	+	2.70938e11i	−0.566193	+	0.151711i
$529$	5.69201e11	+	3.28628e11i	0.316020	+	0.182454i
$530$	−2.02657e11	−	5.19903e11i	−0.111563	−	0.286207i
$531$			1.02712e12i			0.560654i
$532$	−7.11568e10	+	1.73857e12i	−0.0385136	+	0.941003i
$533$	−4.64176e11	+	4.64176e11i	−0.249121	+	0.249121i
$534$	8.03288e10	−	4.63779e10i	0.0427500	−	0.0246817i
$535$	1.04270e12	−	1.15036e11i	0.550258	−	0.0607076i
$536$	1.44045e11	−	2.49493e11i	0.0753801	−	0.130562i
$537$	3.02341e11	+	8.10120e10i	0.156896	+	0.0420402i
$538$	6.07469e10	+	6.07469e10i	0.0312611	+	0.0312611i
$539$	−2.06509e12	+	2.98377e12i	−1.05388	+	1.52270i
$540$	−8.16770e11	−	1.11207e12i	−0.413360	−	0.562809i
$541$	−1.46186e12	−	2.53201e12i	−0.733697	−	1.27080i	−0.955293	−	0.295662i	$-0.904460\pi$
$541$	−1.46186e12	−	2.53201e12i	−0.733697	−	1.27080i	0.221596	−	0.975139i	$-0.428873\pi$
$542$	−6.13716e10	−	2.29042e11i	−0.0305471	−	0.114003i
$543$	−3.61052e11	−	1.34746e12i	−0.178226	−	0.665148i
$544$	−1.06827e12	−	1.85030e12i	−0.522982	−	0.905831i
$545$	−3.77884e10	+	2.46825e11i	−0.0183474	+	0.119841i
$546$	−1.51641e11	+	1.39716e11i	−0.0730214	+	0.0672791i
$547$	−1.38972e12	−	1.38972e12i	−0.663719	−	0.663719i	0.292536	−	0.956255i	$-0.405501\pi$
$547$	−1.38972e12	−	1.38972e12i	−0.663719	−	0.663719i	−0.956255	+	0.292536i	$0.905501\pi$
$548$	−2.71916e12	−	7.28597e11i	−1.28802	−	0.345124i
$549$	2.30002e11	−	3.98376e11i	0.108058	−	0.187162i
$550$	−1.13946e12	−	4.79275e10i	−0.530967	−	0.0223333i
$551$	1.65131e12	−	9.53383e11i	0.763213	−	0.440641i
$552$	4.13190e11	−	4.13190e11i	0.189419	−	0.189419i
$553$	8.36750e11	−	4.38490e11i	0.380481	−	0.199387i
$554$		−	7.53536e10i		−	0.0339868i
$555$	1.28327e11	−	5.00215e10i	0.0574115	−	0.0223789i
$556$	2.08817e12	+	1.20561e12i	0.926681	+	0.535019i
$557$	−1.76435e12	+	4.72757e11i	−0.776672	+	0.208109i	−0.625317	−	0.780371i	$-0.715030\pi$
$557$	−1.76435e12	+	4.72757e11i	−0.776672	+	0.208109i	−0.151355	+	0.988480i	$0.548364\pi$
$558$	−2.14259e11	+	7.99626e11i	−0.0935590	+	0.349167i
$559$	−1.20262e12			−0.520923
$560$	−1.16106e12	+	1.33340e12i	−0.498896	+	0.572945i
$561$	2.46414e12			1.05035
$562$	−1.14802e10	+	4.28445e10i	−0.00485439	+	0.0181168i
$563$	−1.31603e12	+	3.52630e11i	−0.552050	+	0.147921i	−0.524052	−	0.851686i	$-0.675580\pi$
$563$	−1.31603e12	+	3.52630e11i	−0.552050	+	0.147921i	−0.0279988	+	0.999608i	$0.508913\pi$
$564$	−1.68936e11	−	9.75352e10i	−0.0703017	−	0.0405887i
$565$	−1.09389e12	−	4.80283e11i	−0.451604	−	0.198280i
$566$			7.74844e11i			0.317351i
$567$	6.70640e11	−	1.05906e12i	0.272499	−	0.430324i
$568$	−1.25349e12	+	1.25349e12i	−0.505304	+	0.505304i
$569$	7.70812e11	−	4.45028e11i	0.308278	−	0.177985i	−0.337877	−	0.941190i	$-0.609709\pi$
$569$	7.70812e11	−	4.45028e11i	0.308278	−	0.177985i	0.646156	+	0.763205i	$0.276376\pi$
$570$	2.41349e11	+	1.93386e11i	0.0957653	+	0.0767342i
$571$	−9.51420e11	+	1.64791e12i	−0.374550	+	0.648739i	−0.990260	−	0.139234i	$-0.955536\pi$
$571$	−9.51420e11	+	1.64791e12i	−0.374550	+	0.648739i	0.615710	+	0.787973i	$0.288869\pi$
$572$	3.48971e12	+	9.35066e11i	1.36304	+	0.365225i
$573$	−1.15135e12	−	1.15135e12i	−0.446181	−	0.446181i
$574$	−3.02260e11	−	9.43966e10i	−0.116219	−	0.0362955i
$575$	−2.71409e12	+	1.41838e12i	−1.03543	+	0.541111i
$576$	−5.88606e11	−	1.01950e12i	−0.222804	−	0.385909i
$577$	−9.18808e11	−	3.42904e12i	−0.345091	−	1.28790i	−0.892506	−	0.451036i	$-0.851055\pi$
$577$	−9.18808e11	−	3.42904e12i	−0.345091	−	1.28790i	0.547415	−	0.836862i	$-0.315612\pi$
$578$	1.70048e11	+	6.34627e11i	0.0633717	+	0.236507i
$579$	4.16876e11	+	7.22050e11i	0.154153	+	0.267002i
$580$	2.12277e12	+	3.24992e11i	0.778893	+	0.119247i
$581$	2.69738e12	+	2.92760e12i	0.982086	+	1.06591i
$582$	−9.16477e10	−	9.16477e10i	−0.0331107	−	0.0331107i
$583$	5.34073e12	+	1.43104e12i	1.91466	+	0.513032i
$584$	6.16661e11	−	1.06809e12i	0.219376	−	0.379970i
$585$	2.13173e11	+	1.93221e12i	0.0752541	+	0.682108i
$586$	7.96618e11	−	4.59928e11i	0.279069	−	0.161120i
$587$	−3.16164e11	+	3.16164e11i	−0.109911	+	0.109911i	−0.759923	−	0.650013i	$-0.774764\pi$
$587$	−3.16164e11	+	3.16164e11i	−0.109911	+	0.109911i	0.650013	+	0.759923i	$0.274764\pi$
$588$	1.04348e12	+	3.73360e11i	0.359985	+	0.128804i
$589$			4.56927e12i			1.56433i
$590$	2.30372e11	−	5.24696e11i	0.0782700	−	0.178268i
$591$	−1.72315e12	−	9.94863e11i	−0.581005	−	0.335444i
$592$	3.24328e11	−	8.69035e10i	0.108527	−	0.0290797i
$593$	3.38426e11	−	1.26302e12i	0.112388	−	0.419436i	−0.886691	−	0.462363i	$-0.847002\pi$
$593$	3.38426e11	−	1.26302e12i	0.112388	−	0.419436i	0.999078	+	0.0429271i	$0.0136683\pi$
$594$	−1.22703e12			−0.404406
$595$	3.45228e12	−	2.32439e12i	1.12922	−	0.760297i
$596$	3.18909e12			1.03528
$597$	−1.34313e11	+	5.01261e11i	−0.0432745	+	0.161503i
$598$	−8.40985e11	+	2.25341e11i	−0.268926	+	0.0720586i
$599$	−2.94190e12	−	1.69851e12i	−0.933701	−	0.539072i	−0.0457205	−	0.998954i	$-0.514558\pi$
$599$	−2.94190e12	−	1.69851e12i	−0.933701	−	0.539072i	−0.887980	+	0.459882i	$0.847892\pi$
$600$	1.58679e11	+	7.10387e11i	0.0499850	+	0.223776i
$601$			5.86013e12i			1.83220i	0.400954	+	0.916098i	$0.368679\pi$
$601$			5.86013e12i			1.83220i	−0.400954	+	0.916098i	$0.631321\pi$
$602$	−2.69273e11	−	5.13842e11i	−0.0835620	−	0.159458i
$603$	−5.19726e11	+	5.19726e11i	−0.160084	+	0.160084i
$604$	−4.43598e12	+	2.56111e12i	−1.35620	+	0.783001i
$605$	5.00572e12	−	6.24720e12i	1.51903	−	1.89577i
$606$	−1.80574e11	+	3.12764e11i	−0.0543912	+	0.0942084i
$607$	3.73146e12	+	9.99843e11i	1.11566	+	0.298939i	0.769124	−	0.639099i	$-0.220693\pi$
$607$	3.73146e12	+	9.99843e11i	1.11566	+	0.298939i	0.346532	+	0.938038i	$0.387359\pi$
$608$	1.87883e12	+	1.87883e12i	0.557598	+	0.557598i
$609$	−2.66090e11	−	1.18495e12i	−0.0783883	−	0.349078i
$610$	−2.06847e11	+	1.51920e11i	−0.0604873	+	0.0444254i
$611$	3.03693e11	+	5.26012e11i	0.0881555	+	0.152690i
$612$	9.27267e11	+	3.46061e12i	0.267192	+	0.997174i
$613$	2.00332e10	+	7.47647e10i	0.00573030	+	0.0213858i	0.968732	−	0.248110i	$-0.0798095\pi$
$613$	2.00332e10	+	7.47647e10i	0.00573030	+	0.0213858i	−0.963001	+	0.269496i	$0.913143\pi$
$614$	−3.72190e10	−	6.44652e10i	−0.0105684	−	0.0183049i
$615$	5.05435e11	−	3.71221e11i	0.142471	−	0.104639i
$616$	7.97955e11	+	3.55344e12i	0.223288	+	0.994343i
$617$	−3.09216e12	−	3.09216e12i	−0.858971	−	0.858971i	0.132246	−	0.991217i	$-0.457781\pi$
$617$	−3.09216e12	−	3.09216e12i	−0.858971	−	0.858971i	−0.991217	+	0.132246i	$0.957781\pi$
$618$	−6.16491e11	−	1.65188e11i	−0.170012	−	0.0455545i
$619$	−4.24866e9	+	7.35889e9i	−0.00116317	+	0.00201467i	−0.866606	−	0.498992i	$-0.833704\pi$
$619$	−4.24866e9	+	7.35889e9i	−0.00116317	+	0.00201467i	0.865443	+	0.501007i	$0.167037\pi$
$620$	−3.21790e12	+	4.01599e12i	−0.874601	+	1.09151i
$621$	−2.85339e12	+	1.64741e12i	−0.769926	+	0.444517i
$622$	−3.04460e10	+	3.04460e10i	−0.00815593	+	0.00815593i
$623$	7.20536e11	+	1.37497e12i	0.191628	+	0.365676i
$624$		−	9.95493e11i		−	0.262850i
$625$	3.20338e11	−	3.80122e12i	0.0839746	−	0.996468i
$626$	2.86009e11	+	1.65127e11i	0.0744380	+	0.0429768i
$627$	−2.96005e12	+	7.93144e11i	−0.764884	+	0.204950i
$628$	1.01642e11	−	3.79334e11i	0.0260769	−	0.0973203i
$629$	−7.90375e11			−0.201328
$630$	−7.77846e11	+	5.23717e11i	−0.196726	+	0.132454i
$631$	−2.06194e12			−0.517778			−0.258889	−	0.965907i	$-0.583356\pi$
$631$	−2.06194e12			−0.517778			−0.258889	+	0.965907i	$0.583356\pi$
$632$	2.45393e11	−	9.15821e11i	0.0611837	−	0.228341i
$633$	1.30102e12	−	3.48608e11i	0.322083	−	0.0863018i
$634$	8.76957e11	+	5.06311e11i	0.215564	+	0.124456i
$635$	1.33388e12	−	3.03806e12i	0.325564	−	0.741505i
$636$		−	1.68868e12i		−	0.409252i
$637$	−2.23250e12	−	2.63130e12i	−0.537234	−	0.633203i
$638$	1.35041e12	−	1.35041e12i	0.322679	−	0.322679i
$639$	3.91677e12	−	2.26135e12i	0.929338	−	0.536554i
$640$	4.29637e11	+	3.89426e12i	0.101226	+	0.917520i
$641$	1.86433e12	−	3.22912e12i	0.436176	−	0.755479i	−0.561215	−	0.827670i	$-0.689666\pi$
$641$	1.86433e12	−	3.22912e12i	0.436176	−	0.755479i	0.997391	+	0.0721909i	$0.0229991\pi$
$642$	−2.75210e11	−	7.37424e10i	−0.0639377	−	0.0171321i
$643$	−5.07481e12	−	5.07481e12i	−1.17077	−	1.17077i	−0.982027	−	0.188741i	$-0.939559\pi$
$643$	−5.07481e12	−	5.07481e12i	−1.17077	−	1.17077i	−0.188741	−	0.982027i	$-0.560441\pi$
$644$	3.17092e12	+	3.44155e12i	0.726438	+	0.788439i
$645$	1.13565e12	+	1.73865e11i	0.258360	+	0.0395542i
$646$	−8.87375e11	−	1.53698e12i	−0.200475	−	0.347233i
$647$	1.45296e12	+	5.42252e12i	0.325975	+	1.21655i	0.913328	+	0.407224i	$0.133503\pi$
$647$	1.45296e12	+	5.42252e12i	0.325975	+	1.21655i	−0.587353	+	0.809331i	$0.699830\pi$
$648$	−3.25623e11	−	1.21524e12i	−0.0725484	−	0.270754i
$649$	2.83907e12	+	4.91741e12i	0.628166	+	1.08802i
$650$	3.24477e11	−	1.03487e12i	0.0712975	−	0.227392i
$651$	2.77794e12	+	8.67557e11i	0.606190	+	0.189314i
$652$	−1.04882e12	−	1.04882e12i	−0.227293	−	0.227293i
$653$	−2.80001e12	−	7.50260e11i	−0.602629	−	0.161474i	−0.0554104	−	0.998464i	$-0.517647\pi$
$653$	−2.80001e12	−	7.50260e11i	−0.602629	−	0.161474i	−0.547219	+	0.836990i	$0.684313\pi$
$654$	3.39098e10	−	5.87335e10i	0.00724812	−	0.0125541i
$655$	1.35935e12	+	1.08921e12i	0.288566	+	0.231220i
$656$	1.32399e12	−	7.64405e11i	0.279137	−	0.161160i
$657$	−2.22496e12	+	2.22496e12i	−0.465885	+	0.465885i
$658$	−1.56750e11	+	2.47536e11i	−0.0325981	+	0.0514781i
$659$		−	5.11092e12i		−	1.05564i	−0.849357	−	0.527819i	$-0.823010\pi$
$659$		−	5.11092e12i		−	1.05564i	0.849357	−	0.527819i	$-0.176990\pi$
$660$	−3.16020e12	−	1.38751e12i	−0.648286	−	0.284635i
$661$	−4.61705e12	−	2.66566e12i	−0.940715	−	0.543122i	−0.0505308	−	0.998723i	$-0.516091\pi$
$661$	−4.61705e12	−	2.66566e12i	−0.940715	−	0.543122i	−0.890184	+	0.455600i	$0.849425\pi$
$662$	1.10695e12	−	2.96606e11i	0.224010	−	0.0600232i
$663$	−6.06493e11	+	2.26346e12i	−0.121903	+	0.454949i
$664$	3.99531e12			0.797617
$665$	−3.39890e12	+	3.90338e12i	−0.673971	+	0.774005i
$666$	1.78082e11			0.0350741
$667$	1.32724e12	−	4.95332e12i	0.259647	−	0.969015i
$668$	−6.93645e12	+	1.85862e12i	−1.34786	+	0.361157i
$669$	2.22657e12	+	1.28551e12i	0.429754	+	0.248118i
$670$	3.82067e11	−	1.48929e11i	0.0732493	−	0.0285524i
$671$		−	2.54301e12i		−	0.484279i
$672$	1.49899e12	−	7.85527e11i	0.283554	−	0.148593i
$673$	−2.87257e12	+	2.87257e12i	−0.539763	+	0.539763i	−0.923459	−	0.383696i	$-0.874651\pi$
$673$	−2.87257e12	+	2.87257e12i	−0.539763	+	0.539763i	0.383696	+	0.923459i	$0.374651\pi$
$674$	−2.27655e12	+	1.31436e12i	−0.424920	+	0.245327i
$675$	1.72479e11	−	4.10062e12i	0.0319793	−	0.760296i
$676$	7.73343e11	−	1.33947e12i	0.142434	−	0.246702i
$677$	3.47673e12	+	9.31586e11i	0.636094	+	0.170441i	0.562434	−	0.826842i	$-0.309865\pi$
$677$	3.47673e12	+	9.31586e11i	0.636094	+	0.170441i	0.0736605	+	0.997283i	$0.476532\pi$
$678$	2.29443e11	+	2.29443e11i	0.0417004	+	0.0417004i
$679$	1.59522e12	−	1.46977e12i	0.288009	−	0.265361i
$680$	6.32130e11	−	4.12893e12i	0.113375	−	0.740538i
$681$	7.77531e11	+	1.34672e12i	0.138534	+	0.239948i
$682$	1.18447e12	+	4.42051e12i	0.209650	+	0.782424i
$683$	−4.00316e11	−	1.49400e12i	−0.0703897	−	0.262698i	0.921759	−	0.387764i	$-0.126752\pi$
$683$	−4.00316e11	−	1.49400e12i	−0.0703897	−	0.262698i	−0.992148	+	0.125066i	$0.960086\pi$
$684$	−2.22776e12	−	3.85860e12i	−0.389150	−	0.674027i
$685$	−4.95678e12	−	6.74889e12i	−0.860186	−	1.17118i
$686$	6.24406e11	−	1.54304e12i	0.107649	−	0.266023i
$687$	2.56077e12	+	2.56077e12i	0.438597	+	0.438597i
$688$	2.70537e12	+	7.24901e11i	0.460340	+	0.123348i
$689$	−2.62900e12	+	4.55357e12i	−0.444431	+	0.769778i
$690$	8.26732e11	−	9.12098e10i	0.138849	−	0.0153187i
$691$	−3.23684e12	+	1.86879e12i	−0.540095	+	0.311824i	−0.745117	−	0.666933i	$-0.767607\pi$
$691$	−3.23684e12	+	1.86879e12i	−0.540095	+	0.311824i	0.205023	+	0.978757i	$0.434273\pi$
$692$	9.82720e10	−	9.82720e10i	0.0162912	−	0.0162912i
$693$	3.79973e11	−	9.28389e12i	0.0625826	−	1.52908i
$694$		−	2.95547e12i		−	0.483625i
$695$	2.60484e12	+	6.68254e12i	0.423496	+	1.08645i
$696$	−1.05559e12	−	6.09444e11i	−0.170511	−	0.0984446i
$697$	−3.47608e12	+	9.31412e11i	−0.557881	+	0.149484i
$698$	1.47629e11	−	5.50960e11i	0.0235409	−	0.0878559i
$699$	−1.50915e12			−0.239104
$700$	−5.73629e12	+	1.03706e12i	−0.903005	+	0.163253i
$701$	−6.73685e12			−1.05372			−0.526860	−	0.849952i	$-0.676631\pi$
$701$	−6.73685e12			−1.05372			−0.526860	+	0.849952i	$0.676631\pi$
$702$	3.02007e11	−	1.12711e12i	0.0469354	−	0.175165i
$703$	9.49439e11	−	2.54402e11i	0.146612	−	0.0392845i
$704$	−5.63600e12	−	3.25394e12i	−0.864756	−	0.499267i
$705$	−2.10735e11	−	5.40626e11i	−0.0321281	−	0.0824225i
$706$			3.74633e11i			0.0567526i
$707$	−5.10633e12	−	3.23354e12i	−0.768637	−	0.486733i
$708$	1.22626e12	−	1.22626e12i	0.183414	−	0.183414i
$709$	−2.63583e12	+	1.52180e12i	−0.391750	+	0.226177i	−0.682918	−	0.730495i	$-0.739289\pi$
$709$	−2.63583e12	+	1.52180e12i	−0.391750	+	0.226177i	0.291168	+	0.956672i	$0.405956\pi$
$710$	−2.50805e12	+	2.76702e11i	−0.370402	+	0.0408648i
$711$	−1.20948e12	+	2.09488e12i	−0.177495	+	0.307430i
$712$	1.50490e12	+	4.03236e11i	0.219456	+	0.0588030i
$713$	8.68934e12	+	8.68934e12i	1.25917	+	1.25917i
$714$	−1.10291e12	+	2.47667e11i	−0.158817	+	0.0356637i
$715$	6.36142e12	+	8.66138e12i	0.910284	+	1.23940i
$716$	1.25792e12	+	2.17877e12i	0.178872	+	0.309816i
$717$	1.82704e11	+	6.81860e11i	0.0258173	+	0.0963516i
$718$	−3.23173e11	−	1.20610e12i	−0.0453811	−	0.169365i
$719$	−1.18211e12	−	2.04747e12i	−0.164959	−	0.285718i	0.771681	−	0.636009i	$-0.219416\pi$
$719$	−1.18211e12	−	2.04747e12i	−0.164959	−	0.285718i	−0.936641	+	0.350291i	$0.886083\pi$
$720$	6.85134e11	−	4.47514e12i	0.0950122	−	0.620598i
$721$	3.18413e12	−	1.01957e13i	0.438815	−	1.40510i
$722$	7.90045e10	+	7.90045e10i	0.0108202	+	0.0108202i
$723$	3.72595e12	+	9.98366e11i	0.507125	+	0.135884i
$724$	5.60624e12	−	9.71030e12i	0.758313	−	1.31344i
$725$	4.32309e12	+	4.70273e12i	0.581130	+	0.632164i
$726$	−1.88297e12	+	1.08713e12i	−0.251552	+	0.145234i
$727$	4.39801e12	−	4.39801e12i	0.583917	−	0.583917i	−0.352060	−	0.935977i	$-0.614519\pi$
$727$	4.39801e12	−	4.39801e12i	0.583917	−	0.583917i	0.935977	+	0.352060i	$0.114519\pi$
$728$	−3.46045e12	−	1.41630e11i	−0.456606	−	0.0186881i
$729$			7.92072e11i			0.103870i
$730$	1.63564e12	−	6.37570e11i	0.213174	−	0.0830950i
$731$	−5.70959e12	−	3.29644e12i	−0.739566	−	0.426989i
$732$	−7.50208e11	+	2.01018e11i	−0.0965788	+	0.0258782i
$733$	2.03163e12	−	7.58215e12i	0.259942	−	0.970118i	−0.705331	−	0.708878i	$-0.749202\pi$
$733$	2.03163e12	−	7.58215e12i	0.259942	−	0.970118i	0.965274	−	0.261240i	$-0.0841315\pi$
$734$	2.11529e10			0.00268991
$735$	1.72777e12	+	2.80753e12i	0.218370	+	0.354839i
$736$	7.14591e12			0.897651
$737$	−1.05165e12	+	3.92481e12i	−0.131301	+	0.490021i
$738$	7.83207e11	−	2.09860e11i	0.0971902	−	0.0260420i
$739$	1.17477e13	+	6.78251e12i	1.44894	+	0.836548i	0.998419	−	0.0562162i	$-0.0179036\pi$
$739$	1.17477e13	+	6.78251e12i	1.44894	+	0.836548i	0.450525	+	0.892764i	$0.351237\pi$
$740$	1.01364e12	+	4.45045e11i	0.124262	+	0.0545584i
$741$		−	2.91421e12i		−	0.355090i
$742$	−2.53425e12	−	1.03723e11i	−0.306925	−	0.0125619i
$743$	−7.53425e12	+	7.53425e12i	−0.906965	+	0.906965i	−0.996026	−	0.0890612i	$-0.971613\pi$
$743$	−7.53425e12	+	7.53425e12i	−0.906965	+	0.906965i	0.0890612	+	0.996026i	$0.471613\pi$
$744$	2.52955e12	−	1.46044e12i	0.302667	−	0.174745i
$745$	7.40281e12	+	5.93167e12i	0.880427	+	0.705462i
$746$	2.07657e12	−	3.59672e12i	0.245483	−	0.425189i
$747$	−9.84591e12	−	2.63820e12i	−1.15695	−	0.310003i
$748$	1.40049e13	+	1.40049e13i	1.63577	+	1.63577i
$749$	1.42144e12	−	4.55149e12i	0.165029	−	0.528427i
$750$	−4.56022e11	+	9.30330e11i	−0.0526272	+	0.107365i
$751$	1.29672e12	+	2.24599e12i	0.148754	+	0.257649i	0.930767	−	0.365613i	$-0.119141\pi$
$751$	1.29672e12	+	2.24599e12i	0.148754	+	0.257649i	−0.782013	+	0.623262i	$0.785807\pi$
$752$	−3.66115e11	−	1.36636e12i	−0.0417481	−	0.155806i
$753$	1.19025e12	+	4.44206e12i	0.134915	+	0.503509i
$754$	9.08058e11	+	1.57280e12i	0.102316	+	0.177216i
$755$	−1.50608e13	−	2.30578e12i	−1.68689	−	0.258259i
$756$	−6.11936e12	+	1.37415e12i	−0.681331	+	0.152998i
$757$	1.03813e13	+	1.03813e13i	1.14900	+	1.14900i	0.986750	+	0.162248i	$0.0518746\pi$
$757$	1.03813e13	+	1.03813e13i	1.14900	+	1.14900i	0.162248	+	0.986750i	$0.448125\pi$
$758$	3.92855e12	+	1.05265e12i	0.432236	+	0.115817i
$759$	−4.12080e12	+	7.13743e12i	−0.450706	+	0.780646i
$760$	5.69650e11	+	5.16335e12i	0.0619366	+	0.561398i
$761$	−5.08472e12	+	2.93567e12i	−0.549587	+	0.317304i	−0.748955	−	0.662621i	$-0.769444\pi$
$761$	−5.08472e12	+	2.93567e12i	−0.549587	+	0.317304i	0.199369	+	0.979925i	$0.436111\pi$
$762$	−6.37228e11	+	6.37228e11i	−0.0684695	+	0.0684695i
$763$	9.58910e11	+	6.07222e11i	0.102428	+	0.0648616i
$764$		−	1.30873e13i		−	1.38973i
$765$	−4.28423e12	+	9.75778e12i	−0.452269	+	1.03009i
$766$	3.86810e11	+	2.23325e11i	0.0405946	+	0.0234373i
$767$	−5.21571e12	+	1.39755e12i	−0.544170	+	0.145810i
$768$	−2.85188e11	+	1.06433e12i	−0.0295805	+	0.110396i
$769$	−7.42780e12			−0.765934			−0.382967	−	0.923762i	$-0.625098\pi$
$769$	−7.42780e12			−0.765934			−0.382967	+	0.923762i	$0.625098\pi$
$770$	−2.27639e12	+	4.65738e12i	−0.233366	+	0.477456i
$771$	−2.79682e12			−0.285049
$772$	−1.73445e12	+	6.47305e12i	−0.175745	+	0.655890i
$773$	1.80016e13	−	4.82352e12i	1.81344	−	0.485911i	0.817503	−	0.575925i	$-0.195358\pi$
$773$	1.80016e13	−	4.82352e12i	1.81344	−	0.485911i	0.995941	+	0.0900138i	$0.0286911\pi$
$774$	1.28645e12	+	7.42731e11i	0.128842	+	0.0743870i
$775$	−1.49394e13	+	3.33701e12i	−1.48756	+	0.332277i
$776$		−	2.17700e12i		−	0.215517i
$777$	2.56017e10	−	6.25526e11i	0.00251984	−	0.0615674i
$778$	−8.31905e10	+	8.31905e10i	−0.00814077	+	0.00814077i
$779$	3.87585e12	−	2.23772e12i	0.377093	−	0.217715i
$780$	2.05233e12	−	2.56133e12i	0.198528	−	0.247765i
$781$	1.25012e13	−	2.16527e13i	1.20233	−	2.08249i
$782$	−4.61038e12	−	1.23535e12i	−0.440865	−	0.118130i
$783$	4.85976e12	+	4.85976e12i	0.462048	+	0.462048i
$784$	3.43609e12	+	7.26498e12i	0.324820	+	0.686772i
$785$	9.41498e11	−	6.91491e11i	0.0884924	−	0.0649940i
$786$	−2.36553e11	−	4.09722e11i	−0.0221068	−	0.0382902i
$787$	3.27604e12	+	1.22263e13i	0.304412	+	1.13608i	0.933450	+	0.358708i	$0.116783\pi$
$787$	3.27604e12	+	1.22263e13i	0.304412	+	1.13608i	−0.629038	+	0.777375i	$0.716551\pi$
$788$	−4.13921e12	−	1.54478e13i	−0.382428	−	1.42724i
$789$	−3.45684e12	−	5.98742e12i	−0.317565	−	0.550038i
$790$	1.08771e12	−	7.98879e11i	0.0993556	−	0.0729725i
$791$	−3.99368e12	+	3.67962e12i	−0.362726	+	0.334202i
$792$	−6.59416e12	−	6.59416e12i	−0.595520	−	0.595520i
$793$	2.33591e12	+	6.25905e11i	0.209762	+	0.0562055i
$794$	−8.68597e11	+	1.50445e12i	−0.0775579	+	0.134334i
$795$	3.14092e12	−	3.91992e12i	0.278872	−	0.348036i
$796$	−3.61226e12	+	2.08554e12i	−0.318912	+	0.184124i
$797$	1.26672e13	−	1.26672e13i	1.11204	−	1.11204i	0.119162	−	0.992875i	$-0.461979\pi$
$797$	1.26672e13	−	1.26672e13i	1.11204	−	1.11204i	0.992875	−	0.119162i	$-0.0380207\pi$
$798$	1.24515e12	−	6.52509e11i	0.108695	−	0.0569605i
$799$			3.32976e12i			0.289036i
$800$	−4.77075e12	+	7.51503e12i	−0.411796	+	0.648673i
$801$	−3.44235e12	−	1.98744e12i	−0.295467	−	0.170588i
$802$	−1.13554e12	+	3.04267e11i	−0.0969210	+	0.0259699i
$803$	−4.50214e12	+	1.68022e13i	−0.382119	+	1.42609i
$804$	1.24098e12			0.104740
$805$	9.59370e11	+	1.38867e13i	0.0805201	+	1.16551i
$806$	−4.35204e12			−0.363233
$807$	−2.00155e11	+	7.46988e11i	−0.0166125	+	0.0619987i
$808$	−5.85938e12	+	1.57002e12i	−0.483616	+	0.129585i
$809$	7.69845e12	+	4.44470e12i	0.631880	+	0.364816i	0.781480	−	0.623930i	$-0.214465\pi$
$809$	7.69845e12	+	4.44470e12i	0.631880	+	0.364816i	−0.149600	+	0.988747i	$0.547798\pi$
$810$	7.19929e11	−	1.63971e12i	0.0587634	−	0.133840i
$811$			1.87779e13i			1.52424i	0.647435	+	0.762121i	$0.275842\pi$
$811$			1.87779e13i			1.52424i	−0.647435	+	0.762121i	$0.724158\pi$
$812$	5.22231e12	−	8.24694e12i	0.421561	−	0.665718i
$813$	1.50934e12	−	1.50934e12i	0.121166	−	0.121166i
$814$	8.52581e11	−	4.92238e11i	0.0680653	−	0.0392975i
$815$	−4.83823e11	−	4.38541e12i	−0.0384129	−	0.348178i
$816$	2.72870e12	−	4.72625e12i	0.215452	−	0.373174i
$817$	7.91970e12	+	2.12208e12i	0.621884	+	0.166633i
$818$	−1.80126e12	−	1.80126e12i	−0.140665	−	0.140665i
$819$	8.43431e12	+	2.63405e12i	0.655046	+	0.204572i
$820$	4.98244e12	+	7.62801e11i	0.384840	+	0.0589181i
$821$	4.66957e12	+	8.08794e12i	0.358701	+	0.621289i	0.987744	−	0.156082i	$-0.0498863\pi$
$821$	4.66957e12	+	8.08794e12i	0.358701	+	0.621289i	−0.629043	+	0.777371i	$0.716553\pi$
$822$	5.88632e11	+	2.19680e12i	0.0449698	+	0.167829i
$823$	−3.49600e12	−	1.30472e13i	−0.265627	−	0.991332i	−0.961866	−	0.273522i	$-0.911811\pi$
$823$	−3.49600e12	−	1.30472e13i	−0.265627	−	0.991332i	0.696239	−	0.717810i	$-0.254855\pi$
$824$	−5.36013e12	−	9.28401e12i	−0.405044	−	0.701557i
$825$	−4.75499e12	−	9.09875e12i	−0.357360	−	0.683815i
$826$	−1.76496e12	−	1.91560e12i	−0.131924	−	0.143184i
$827$	1.44832e13	+	1.44832e13i	1.07668	+	1.07668i	0.996804	+	0.0798805i	$0.0254539\pi$
$827$	1.44832e13	+	1.44832e13i	1.07668	+	1.07668i	0.0798805	+	0.996804i	$0.474546\pi$
$828$	−1.15744e13	−	3.10135e12i	−0.855779	−	0.229305i
$829$	1.25767e13	−	2.17835e13i	0.924851	−	1.60189i	0.133050	−	0.991109i	$-0.457523\pi$
$829$	1.25767e13	−	2.17835e13i	0.924851	−	1.60189i	0.791801	−	0.610779i	$-0.209144\pi$
$830$	4.43799e12	+	3.55604e12i	0.324590	+	0.260085i
$831$	5.87443e11	−	3.39161e11i	0.0427328	−	0.0246718i
$832$	4.37612e12	−	4.37612e12i	0.316617	−	0.316617i
$833$	−3.38658e12	−	1.86119e13i	−0.243702	−	1.33933i
$834$		−	1.94801e12i		−	0.139426i
$835$	−1.95585e13	−	8.58733e12i	−1.39234	−	0.611320i
$836$	−2.13312e13	−	1.23156e13i	−1.51038	−	0.872019i
$837$	−1.59083e13	+	4.26260e12i	−1.12036	+	0.300200i
$838$	−1.95830e11	+	7.30847e11i	−0.0137177	+	0.0511951i
$839$	−2.35415e13			−1.64024			−0.820118	−	0.572195i	$-0.806092\pi$
$839$	−2.35415e13			−1.64024			−0.820118	+	0.572195i	$0.806092\pi$
$840$	3.24728e12	+	6.34029e11i	0.225042	+	0.0439392i
$841$	3.81040e12			0.262657
$842$	−1.55216e12	+	5.79273e12i	−0.106422	+	0.397173i
$843$	−3.85679e11	+	1.03342e11i	−0.0263028	+	0.00704782i
$844$	9.37561e12	+	5.41301e12i	0.636002	+	0.367196i
$845$	4.28655e12	−	1.67089e12i	0.289236	−	0.112744i
$846$		−	7.50240e11i		−	0.0503539i
$847$	−1.68899e13	−	3.22302e13i	−1.12759	−	2.15173i
$848$	8.65889e12	−	8.65889e12i	0.575017	−	0.575017i
$849$	−6.04055e12	+	3.48751e12i	−0.399017	+	0.230373i
$850$	4.37714e12	−	4.02378e12i	0.287611	−	0.264393i
$851$	1.32175e12	−	2.28934e12i	0.0863905	−	0.149633i
$852$	−7.37593e12	−	1.97637e12i	−0.479555	−	0.128496i
$853$	−1.53128e13	−	1.53128e13i	−0.990342	−	0.990342i	0.00961185	−	0.999954i	$-0.496940\pi$
$853$	−1.53128e13	−	1.53128e13i	−0.990342	−	0.990342i	−0.999954	+	0.00961185i	$0.996940\pi$
$854$	2.55594e11	+	1.13821e12i	0.0164433	+	0.0732253i
$855$	2.00566e12	−	1.31005e13i	0.128354	−	0.838382i
$856$	−2.39284e12	−	4.14451e12i	−0.152328	−	0.263841i
$857$	4.18419e12	+	1.56156e13i	0.264971	+	0.988884i	0.962268	+	0.272103i	$0.0877190\pi$
$857$	4.18419e12	+	1.56156e13i	0.264971	+	0.988884i	−0.697297	+	0.716782i	$0.745614\pi$
$858$	−7.55437e11	−	2.81933e12i	−0.0475889	−	0.177604i
$859$	1.13702e13	+	1.96938e13i	0.712525	+	1.23413i	0.963906	+	0.266241i	$0.0857818\pi$
$859$	1.13702e13	+	1.96938e13i	0.712525	+	1.23413i	−0.251381	+	0.967888i	$0.580885\pi$
$860$	5.46625e12	+	7.44256e12i	0.340759	+	0.463959i
$861$	−6.24550e11	−	2.78124e12i	−0.0387305	−	0.172474i
$862$	−2.80624e12	−	2.80624e12i	−0.173118	−	0.173118i
$863$	2.17499e13	+	5.82787e12i	1.33478	+	0.357652i	0.854494	−	0.519461i	$-0.173867\pi$
$863$	2.17499e13	+	5.82787e12i	1.33478	+	0.357652i	0.480283	+	0.877114i	$0.340534\pi$
$864$	−4.78855e12	+	8.29401e12i	−0.292343	+	0.506352i
$865$	4.10903e11	−	4.53331e10i	0.0249555	−	0.00275323i
$866$	2.91191e10	−	1.68119e10i	0.00175933	−	0.00101575i
$867$	−4.18207e12	+	4.18207e12i	−0.251365	+	0.251365i
$868$	1.08576e13	+	2.07191e13i	0.649225	+	1.23889i
$869$			1.33725e13i			0.795471i
$870$	−6.30108e11	−	1.61650e12i	−0.0372888	−	0.0956619i
$871$	−3.34634e12	−	1.93201e12i	−0.197010	−	0.113744i
$872$	1.10033e12	−	2.94831e11i	0.0644462	−	0.0172683i
$873$	−1.43753e12	+	5.36493e12i	−0.0837630	+	0.312608i
$874$	5.93585e12			0.344098
$875$	−1.52445e13	−	8.26212e12i	−0.879179	−	0.476492i
$876$	5.31268e12			0.304821
$877$	−1.43508e11	+	5.35580e11i	−0.00819179	+	0.0305722i	−0.969901	−	0.243501i	$-0.921704\pi$
$877$	−1.43508e11	+	5.35580e11i	−0.00819179	+	0.0305722i	0.961709	+	0.274073i	$0.0883709\pi$
$878$	−7.20189e12	+	1.92974e12i	−0.408998	+	0.109591i
$879$	7.17103e12	+	4.14019e12i	0.405164	+	0.233922i
$880$	−9.08965e12	−	2.33189e13i	−0.510946	−	1.31080i
$881$		−	2.76382e13i		−	1.54568i	−0.634603	−	0.772839i	$-0.718836\pi$
$881$		−	2.76382e13i		−	1.54568i	0.634603	−	0.772839i	$-0.281164\pi$
$882$	7.63041e11	+	4.19351e12i	0.0424560	+	0.233329i
$883$	−4.14609e12	+	4.14609e12i	−0.229518	+	0.229518i	−0.812491	−	0.582974i	$-0.801889\pi$
$883$	−4.14609e12	+	4.14609e12i	−0.229518	+	0.229518i	0.582974	+	0.812491i	$0.301889\pi$
$884$	−1.63113e13	+	9.41734e12i	−0.898367	+	0.518672i
$885$	5.12732e12	−	5.65675e11i	0.280961	−	0.0309972i
$886$	1.59111e12	−	2.75588e12i	0.0867456	−	0.150248i
$887$	6.61057e12	+	1.77130e12i	0.358577	+	0.0960804i	0.433610	−	0.901101i	$-0.357240\pi$
$887$	6.61057e12	+	1.77130e12i	0.358577	+	0.0960804i	−0.0750330	+	0.997181i	$0.523906\pi$
$888$	−4.44298e11	−	4.44298e11i	−0.0239782	−	0.0239782i
$889$	−1.02194e13	−	1.10916e13i	−0.548739	−	0.595573i
$890$	1.31274e12	+	1.78735e12i	0.0701330	+	0.0954895i
$891$	8.87228e12	+	1.53672e13i	0.471613	+	0.816858i
$892$	5.34849e12	+	1.99608e13i	0.282872	+	1.05569i
$893$	−1.07177e12	−	3.99988e12i	−0.0563986	−	0.210482i
$894$	−1.28823e12	−	2.23128e12i	−0.0674488	−	0.116825i
$895$	−1.13251e12	+	7.39727e12i	−0.0589979	+	0.385361i
$896$	1.69989e13	+	5.30878e12i	0.881117	+	0.275175i
$897$	−5.54193e12	−	5.54193e12i	−0.285821	−	0.285821i
$898$	7.37737e12	+	1.97676e12i	0.378580	+	0.101440i
$899$	1.28165e13	−	2.21989e13i	0.654413	−	1.13348i
$900$	1.09888e13	−	1.01017e13i	0.558291	−	0.513222i
$901$	−2.49632e13	+	1.44125e13i	−1.26194	+	0.728580i
$902$	3.16959e12	−	3.16959e12i	0.159431	−	0.159431i
$903$	2.79384e12	−	4.41196e12i	0.139832	−	0.220819i
$904$			5.45019e12i			0.271427i
$905$	3.10747e13	−	1.21129e13i	1.53989	−	0.600245i
$906$	3.58381e12	+	2.06912e12i	0.176713	+	0.102025i
$907$	2.36471e12	−	6.33622e11i	0.116023	−	0.0310883i	−0.200340	−	0.979726i	$-0.564205\pi$
$907$	2.36471e12	−	6.33622e11i	0.116023	−	0.0310883i	0.316363	+	0.948638i	$0.397538\pi$
$908$	−3.23498e12	+	1.20731e13i	−0.157938	+	0.589432i
$909$	1.54764e13			0.751851
$910$	−3.71781e12	−	3.23731e12i	−0.179722	−	0.156494i
$911$	−6.50713e12			−0.313009			−0.156505	−	0.987677i	$-0.550023\pi$
$911$	−6.50713e12			−0.313009			−0.156505	+	0.987677i	$0.550023\pi$
$912$	−1.75660e12	+	6.55572e12i	−0.0840806	+	0.313793i
$913$	−5.44303e13	+	1.45846e13i	−2.59252	+	0.694664i
$914$	3.53834e12	+	2.04286e12i	0.167703	+	0.0968236i
$915$	−2.11534e12	−	9.28758e11i	−0.0997667	−	0.0438034i
$916$			2.91081e13i			1.36611i
$917$	7.01309e12	−	3.67513e12i	0.327527	−	0.171637i
$918$	4.52329e12	−	4.52329e12i	0.210214	−	0.210214i
$919$	−1.31374e13	+	7.58490e12i	−0.607562	+	0.350776i	−0.772011	−	0.635609i	$-0.780749\pi$
$919$	−1.31374e13	+	7.58490e12i	−0.607562	+	0.350776i	0.164449	+	0.986386i	$0.447416\pi$
$920$	1.09024e13	+	8.73581e12i	0.501738	+	0.402030i
$921$	3.35040e11	−	5.80306e11i	0.0153436	−	0.0265759i
$922$	4.22588e11	+	1.13232e11i	0.0192588	+	0.00516037i
$923$	1.68125e13	+	1.68125e13i	0.762472	+	0.762472i
$924$	−1.15375e13	+	1.06302e13i	−0.520700	+	0.479753i
$925$	1.52516e12	+	2.91843e12i	0.0684982	+	0.131072i
$926$	−1.29608e12	−	2.24487e12i	−0.0579270	−	0.100333i
$927$	7.07885e12	+	2.64186e13i	0.314850	+	1.17504i
$928$	−3.85791e12	−	1.43979e13i	−0.170760	−	0.637286i
$929$	−1.98471e13	−	3.43762e13i	−0.874233	−	1.51422i	−0.857578	−	0.514354i	$-0.828032\pi$
$929$	−1.98471e13	−	3.43762e13i	−0.874233	−	1.51422i	−0.0166544	−	0.999861i	$-0.505302\pi$
$930$	4.10969e12	+	6.29184e11i	0.180151	+	0.0275806i
$931$	1.00588e13	+	2.12675e13i	0.438807	+	0.927777i
$932$	−8.57722e12	−	8.57722e12i	−0.372370	−	0.372370i
$933$	−3.74387e11	−	1.00317e11i	−0.0161753	−	0.00433416i
$934$	−6.62632e11	+	1.14771e12i	−0.0284912	+	0.0493483i
$935$	6.46047e12	+	5.85582e13i	0.276447	+	2.50574i
$936$	7.68015e12	−	4.43414e12i	0.327061	−	0.188829i
$937$	1.34462e13	−	1.34462e13i	0.569863	−	0.569863i	−0.362227	−	0.932090i	$-0.617984\pi$
$937$	1.34462e13	−	1.34462e13i	0.569863	−	0.569863i	0.932090	+	0.362227i	$0.117984\pi$
$938$	7.62239e10	−	1.86238e12i	0.00321498	−	0.0785517i
$939$			2.97290e12i			0.124791i
$940$	1.87493e12	−	4.27034e12i	0.0783265	−	0.178397i
$941$	2.17510e13	+	1.25579e13i	0.904326	+	0.522113i	0.878601	−	0.477556i	$-0.158477\pi$
$941$	2.17510e13	+	1.25579e13i	0.904326	+	0.522113i	0.0257249	+	0.999669i	$0.491811\pi$
$942$	−3.06463e11	+	8.21165e10i	−0.0126809	+	0.00339783i
$943$	3.11521e12	−	1.16261e13i	0.128288	−	0.478776i
$944$	1.25755e13			0.515409
$945$	−1.67607e13	−	8.19213e12i	−0.683675	−	0.334159i
$946$	8.21196e12			0.333378
$947$	1.20363e13	−	4.49201e13i	0.486315	−	1.81495i	−0.0877476	−	0.996143i	$-0.527967\pi$
$947$	1.20363e13	−	4.49201e13i	0.486315	−	1.81495i	0.574063	−	0.818811i	$-0.305366\pi$
$948$	3.94501e12	−	1.05706e12i	0.158639	−	0.0425072i
$949$	−1.43258e13	−	8.27099e12i	−0.573350	−	0.331024i
$950$	−3.96289e12	+	6.24247e12i	−0.157854	+	0.248657i
$951$			9.11546e12i			0.361382i
$952$	−1.60408e13	−	1.01577e13i	−0.632936	−	0.400802i
$953$	4.90434e12	−	4.90434e12i	0.192603	−	0.192603i	−0.604217	−	0.796820i	$-0.706514\pi$
$953$	4.90434e12	−	4.90434e12i	0.192603	−	0.192603i	0.796820	+	0.604217i	$0.206514\pi$
$954$	5.62454e12	−	3.24733e12i	0.219846	−	0.126928i
$955$	2.43422e13	−	3.03794e13i	0.946989	−	1.18186i
$956$	−2.83694e12	+	4.91372e12i	−0.109847	+	0.190261i
$957$	1.66056e13	+	4.44945e12i	0.639956	+	0.171476i
$958$	2.56218e12	+	2.56218e12i	0.0982798	+	0.0982798i
$959$	−3.71369e13	+	8.33940e12i	−1.41782	+	0.318384i
$960$	−4.76510e12	+	3.49977e12i	−0.181072	+	0.132990i
$961$	1.74930e13	+	3.02988e13i	0.661622	+	1.14596i
$962$	2.42307e11	+	9.04302e11i	0.00912175	+	0.0340428i
$963$	3.16010e12	+	1.17937e13i	0.118408	+	0.441906i
$964$	1.55021e13	+	2.68505e13i	0.578156	+	1.00140i
$965$	−1.60659e13	+	1.17998e13i	−0.596394	+	0.438027i
$966$	1.12703e12	−	3.60877e12i	0.0416426	−	0.133341i
$967$	−8.16941e12	−	8.16941e12i	−0.300450	−	0.300450i	0.540740	−	0.841190i	$-0.318144\pi$
$967$	−8.16941e12	−	8.16941e12i	−0.300450	−	0.300450i	−0.841190	+	0.540740i	$0.818144\pi$
$968$	−3.52759e13	−	9.45215e12i	−1.29134	−	0.346012i
$969$	7.98800e12	−	1.38356e13i	0.291059	−	0.504129i
$970$	1.93765e12	−	2.41821e12i	0.0702752	−	0.0877044i
$971$	1.42976e13	−	8.25474e12i	0.516152	−	0.298000i	−0.219207	−	0.975678i	$-0.570347\pi$
$971$	1.42976e13	−	8.25474e12i	0.516152	−	0.298000i	0.735359	+	0.677678i	$0.237014\pi$
$972$	1.75733e13	−	1.75733e13i	0.631474	−	0.631474i
$973$	3.25739e13	+	1.33319e12i	1.16510	+	0.0476854i
$974$			1.30673e13i			0.465231i
$975$	9.52809e12	−	2.12829e12i	0.337664	−	0.0754241i
$976$	−4.87751e12	−	2.81603e12i	−0.172058	−	0.0993376i
$977$	−4.31580e13	+	1.15642e13i	−1.51543	+	0.406058i	−0.918234	−	0.396038i	$-0.870385\pi$
$977$	−4.31580e13	+	1.15642e13i	−1.51543	+	0.406058i	−0.597195	+	0.802096i	$0.703718\pi$
$978$	−3.10148e11	+	1.15749e12i	−0.0108404	+	0.0404568i
$979$	−2.19740e13			−0.764518
$980$	−6.13680e12	+	2.57762e13i	−0.212532	+	0.892692i
$981$	−2.90629e12			−0.100191
$982$	−1.45509e12	+	5.43048e12i	−0.0499332	+	0.186353i
$983$	−3.48659e13	+	9.34229e12i	−1.19099	+	0.319126i	−0.799279	−	0.600960i	$-0.794785\pi$
$983$	−3.48659e13	+	9.34229e12i	−1.19099	+	0.319126i	−0.391716	+	0.920086i	$0.628118\pi$
$984$	−2.47761e12	−	1.43045e12i	−0.0842471	−	0.0486401i
$985$	1.91243e13	−	4.35576e13i	0.647326	−	1.47435i
$986$			9.95615e12i			0.335464i
$987$	−2.63527e12	−	1.07857e11i	−0.0883889	−	0.00361760i
$988$	1.65628e13	−	1.65628e13i	0.553003	−	0.553003i
$989$	1.90964e13	−	1.10253e13i	0.634699	−	0.366444i
$990$	−1.45563e12	−	1.31939e13i	−0.0481607	−	0.436532i
$991$	1.04843e13	−	1.81594e13i	0.345311	−	0.598096i	−0.640099	−	0.768292i	$-0.721107\pi$
$991$	1.04843e13	−	1.81594e13i	0.345311	−	0.598096i	0.985410	+	0.170196i	$0.0544402\pi$
$992$	3.45024e13	+	9.24489e12i	1.13122	+	0.303109i
$993$	7.29457e12	+	7.29457e12i	0.238083	+	0.238083i
$994$	−3.41905e12	+	1.09479e13i	−0.111088	+	0.355706i
$995$	−1.22642e13	−	1.87762e12i	−0.396675	−	0.0607301i
$996$	8.60514e12	+	1.49045e13i	0.277071	+	0.479901i
$997$	−7.18889e12	−	2.68293e13i	−0.230427	−	0.859966i	−0.980157	−	0.198222i	$-0.936483\pi$
$997$	−7.18889e12	−	2.68293e13i	−0.230427	−	0.859966i	0.749730	−	0.661744i	$-0.230183\pi$
$998$	1.04777e12	+	3.91033e12i	0.0334333	+	0.124775i
$999$	1.77144e12	+	3.06822e12i	0.0562705	+	0.0974634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.17.20	yes	136
5.3	odd	4	inner	35.10.k.a.3.15	✓	136
7.5	odd	6	inner	35.10.k.a.12.15	yes	136
35.33	even	12	inner	35.10.k.a.33.20	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.15	✓	136	5.3	odd	4	inner
35.10.k.a.12.15	yes	136	7.5	odd	6	inner
35.10.k.a.17.20	yes	136	1.1	even	1	trivial
35.10.k.a.33.20	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+(1.68066 - 6.27232i) q^{2} +(56.4624 - 15.1291i) q^{3} +(406.888 + 234.917i) q^{4} +(507.562 + 1302.12i) q^{5} -379.577i q^{6} +(6347.14 + 259.777i) q^{7} +(4508.24 - 4508.24i) q^{8} +(-14086.9 + 8133.05i) q^{9} +(9020.33 - 995.174i) q^{10} +(-44961.3 + 77875.2i) q^{11} +(26527.9 + 7108.13i) q^{12} +(-60467.0 - 60467.0i) q^{13} +(12296.8 - 39374.7i) q^{14} +(48358.0 + 65841.7i) q^{15} +(99577.0 + 172472. i) q^{16} +(-121333. - 452819. i) q^{17} +(27337.8 + 102026. i) q^{18} +(291502. + 504896. i) q^{19} +(-99368.0 + 649050. i) q^{20} +(362305. - 81358.5i) q^{21} +(412894. + 412894. i) q^{22} +(1.51451e6 + 405811. i) q^{23} +(186341. - 322752. i) q^{24} +(-1.43789e6 + 1.32181e6i) q^{25} +(-480893. + 277644. i) q^{26} +(-1.48590e6 + 1.48590e6i) q^{27} +(2.52154e6 + 1.59675e6i) q^{28} -3.27059e6i q^{29} +(494253. - 192659. i) q^{30} +(6.78743e6 + 3.91873e6i) q^{31} +(4.40225e6 - 1.17958e6i) q^{32} +(-1.36044e6 + 5.07724e6i) q^{33} -3.04415e6 q^{34} +(2.88331e6 + 8.39656e6i) q^{35} -7.64236e6 q^{36} +(436363. - 1.62853e6i) q^{37} +(3.65679e6 - 979833. i) q^{38} +(-4.32892e6 - 2.49930e6i) q^{39} +(8.15847e6 + 3.58204e6i) q^{40} -7.67652e6i q^{41} +(98605.4 - 2.40923e6i) q^{42} +(9.94440e6 - 9.94440e6i) q^{43} +(-3.65884e7 + 2.11243e7i) q^{44} +(-1.77401e7 - 1.42147e7i) q^{45} +(5.09075e6 - 8.81743e6i) q^{46} +(-6.86081e6 - 1.83835e6i) q^{47} +(8.23170e6 + 8.23170e6i) q^{48} +(4.02186e7 + 3.29768e6i) q^{49} +(5.87421e6 + 1.12404e7i) q^{50} +(-1.37015e7 - 2.37316e7i) q^{51} +(-1.03986e7 - 3.88080e7i) q^{52} +(-1.59142e7 - 5.93925e7i) q^{53} +(6.82273e6 + 1.18173e7i) q^{54} +(-1.24223e8 - 1.90183e7i) q^{55} +(2.97856e7 - 2.74433e7i) q^{56} +(2.40975e7 + 2.40975e7i) q^{57} +(-2.05142e7 - 5.49676e6i) q^{58} +(3.15723e7 - 5.46849e7i) q^{59} +(4.20895e6 + 3.81502e7i) q^{60} +(-2.44912e7 + 1.41400e7i) q^{61} +(3.59869e7 - 3.59869e7i) q^{62} +(-9.15240e7 + 4.79622e7i) q^{63} +7.23721e7i q^{64} +(4.80443e7 - 1.09426e8i) q^{65} +(2.95597e7 + 1.70663e7i) q^{66} +(4.36465e7 - 1.16951e7i) q^{67} +(5.70061e7 - 2.12750e8i) q^{68} +9.16521e7 q^{69} +(5.75118e7 - 3.97323e6i) q^{70} -2.78044e8 q^{71} +(-2.68412e7 + 1.00173e8i) q^{72} +(1.86852e8 - 5.00668e7i) q^{73} +(-9.48128e6 - 5.47402e6i) q^{74} +(-6.11888e7 + 9.63864e7i) q^{75} +2.73915e8i q^{76} +(-3.05606e8 + 4.82605e8i) q^{77} +(-2.29519e7 + 2.29519e7i) q^{78} +(1.28788e8 - 7.43557e7i) q^{79} +(-1.74038e8 + 2.17201e8i) q^{80} +(9.86658e7 - 1.70894e8i) q^{81} +(-4.81496e7 - 1.29016e7i) q^{82} +(4.43112e8 + 4.43112e8i) q^{83} +(1.66530e8 + 5.20076e7i) q^{84} +(5.28039e8 - 3.87823e8i) q^{85} +(-4.56613e7 - 7.90876e7i) q^{86} +(-4.94809e7 - 1.84665e8i) q^{87} +(1.48384e8 + 5.53777e8i) q^{88} +(1.22183e8 + 2.11627e8i) q^{89} +(-1.18974e8 + 8.73817e7i) q^{90} +(-3.68084e8 - 3.99500e8i) q^{91} +(5.20902e8 + 5.20902e8i) q^{92} +(4.42521e8 + 1.18573e8i) q^{93} +(-2.30614e7 + 3.99436e7i) q^{94} +(-5.09478e8 + 6.35836e8i) q^{95} +(2.30715e8 - 1.33204e8i) q^{96} +(2.41447e8 - 2.41447e8i) q^{97} +(8.82781e7 - 2.46722e8i) q^{98} -1.46269e9i 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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