LMFDB - Embedded newform 35.10.k.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,10,Mod(3,35)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("35.3");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.0262542657$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$34$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			3.1
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-42.4707 - 11.3800i) q^{2} +(54.8950 + 204.871i) q^{3} +(1230.85 + 710.632i) q^{4} +(-1352.09 + 353.508i) q^{5} -9325.71i q^{6} +(-5765.26 + 2667.46i) q^{7} +(-28269.7 - 28269.7i) q^{8} +(-21912.6 + 12651.2i) q^{9} +(61447.3 + 373.073i) q^{10} +(-9135.71 + 15823.5i) q^{11} +(-78020.2 + 291175. i) q^{12} +(-5582.21 + 5582.21i) q^{13} +(275210. - 47680.2i) q^{14} +(-146647. - 257599. i) q^{15} +(515080. + 892145. i) q^{16} +(-588348. + 157647. i) q^{17} +(1.07461e6 - 287942. i) q^{18} +(76307.7 + 132169. i) q^{19} +(-1.91544e6 - 525725. i) q^{20} +(-862969. - 1.03470e6i) q^{21} +(568072. - 568072. i) q^{22} +(-12714.5 + 47451.2i) q^{23} +(4.23977e6 - 7.34349e6i) q^{24} +(1.70319e6 - 955952. i) q^{25} +(300606. - 173555. i) q^{26} +(-842789. - 842789. i) q^{27} +(-8.99176e6 - 813736. i) q^{28} +1.42296e6i q^{29} +(3.29671e6 + 1.26092e7i) q^{30} +(2.72474e6 + 1.57313e6i) q^{31} +(-6.42534e6 - 2.39797e7i) q^{32} +(-3.74328e6 - 1.00301e6i) q^{33} +2.67816e7 q^{34} +(6.85221e6 - 5.64472e6i) q^{35} -3.59615e7 q^{36} +(-7.10815e6 - 1.90462e6i) q^{37} +(-1.73676e6 - 6.48169e6i) q^{38} +(-1.45007e6 - 837196. i) q^{39} +(4.82168e7 + 2.82297e7i) q^{40} -1.89085e7i q^{41} +(2.48760e7 + 5.37652e7i) q^{42} +(1.92423e7 + 1.92423e7i) q^{43} +(-2.24894e7 + 1.29843e7i) q^{44} +(2.51556e7 - 2.48520e7i) q^{45} +(1.07999e6 - 1.87059e6i) q^{46} +(2.32464e6 - 8.67567e6i) q^{47} +(-1.54499e8 + 1.54499e8i) q^{48} +(2.61229e7 - 3.07572e7i) q^{49} +(-8.32143e7 + 2.12177e7i) q^{50} +(-6.45947e7 - 1.11881e8i) q^{51} +(-1.08378e7 + 2.90397e6i) q^{52} +(3.86579e7 - 1.03583e7i) q^{53} +(2.62029e7 + 4.53847e7i) q^{54} +(6.75860e6 - 2.46244e7i) q^{55} +(2.38390e8 + 8.75739e7i) q^{56} +(-2.28886e7 + 2.28886e7i) q^{57} +(1.61932e7 - 6.04340e7i) q^{58} +(4.10960e7 - 7.11804e7i) q^{59} +(2.55776e6 - 4.21277e8i) q^{60} +(-7.61586e7 + 4.39702e7i) q^{61} +(-9.78193e7 - 9.78193e7i) q^{62} +(9.25852e7 - 1.31389e8i) q^{63} +5.64112e8i q^{64} +(5.57431e6 - 9.52102e6i) q^{65} +(1.47566e8 + 8.51970e7i) q^{66} +(2.00687e7 + 7.48975e7i) q^{67} +(-8.36198e8 - 2.24059e8i) q^{68} -1.04193e7 q^{69} +(-3.55255e8 + 1.61757e8i) q^{70} +1.38499e8 q^{71} +(9.77108e8 + 2.61815e8i) q^{72} +(4.77827e7 + 1.78328e8i) q^{73} +(2.80214e8 + 1.61781e8i) q^{74} +(2.89343e8 + 2.96457e8i) q^{75} +2.16907e8i q^{76} +(1.04612e7 - 1.15596e8i) q^{77} +(5.20580e7 + 5.20580e7i) q^{78} +(2.85953e8 - 1.65095e8i) q^{79} +(-1.01182e9 - 1.02418e9i) q^{80} +(-1.22617e8 + 2.12378e8i) q^{81} +(-2.15178e8 + 8.03057e8i) q^{82} +(-5.47918e7 + 5.47918e7i) q^{83} +(-3.26892e8 - 1.88682e9i) q^{84} +(7.39772e8 - 4.21140e8i) q^{85} +(-5.98258e8 - 1.03621e9i) q^{86} +(-2.91522e8 + 7.81132e7i) q^{87} +(7.05589e8 - 1.89062e8i) q^{88} +(1.21663e8 + 2.10726e8i) q^{89} +(-1.35119e9 + 7.69210e8i) q^{90} +(1.72926e7 - 4.70732e7i) q^{91} +(-4.93700e7 + 4.93700e7i) q^{92} +(-1.72714e8 + 6.44576e8i) q^{93} +(-1.97458e8 + 3.42008e8i) q^{94} +(-1.49898e8 - 1.51729e8i) q^{95} +(4.56002e9 - 2.63273e9i) q^{96} +(-8.49197e8 - 8.49197e8i) q^{97} +(-1.45948e9 + 1.00900e9i) q^{98} -4.62313e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) $ 136 * q - 2 * q^2 - 6 * q^3 - 1710 * q^5 + 5940 * q^7 - 3484 * q^8 + 153786 * q^10 - 87752 * q^11 + 3066 * q^12 - 318872 * q^15 + 3132804 * q^16 - 1578678 * q^17 - 239036 * q^18 - 5745396 * q^21 + 2132088 * q^22 + 312550 * q^23 + 4308518 * q^25 + 2294580 * q^26 - 9559382 * q^28 + 21412708 * q^30 + 8900220 * q^31 + 17154282 * q^32 - 13729410 * q^33 + 6034552 * q^35 - 114903056 * q^36 + 26817310 * q^37 - 20958672 * q^38 + 143985558 * q^40 - 38052106 * q^42 + 46427728 * q^43 - 96332286 * q^45 + 2421124 * q^46 + 147698754 * q^47 - 11742092 * q^50 - 138178540 * q^51 - 126665976 * q^52 - 16288570 * q^53 + 501495076 * q^56 - 71567164 * q^57 - 681848346 * q^58 + 254653694 * q^60 - 575844240 * q^61 + 491512776 * q^63 + 833960586 * q^65 + 260439612 * q^66 + 22092746 * q^67 - 2824755312 * q^68 - 1044240840 * q^70 + 355056144 * q^71 + 98662792 * q^72 + 1852831146 * q^73 + 2937834474 * q^75 + 1226263510 * q^77 + 2595615712 * q^78 - 3778385244 * q^80 + 1504403888 * q^81 - 3707543946 * q^82 - 1726556112 * q^85 + 1771746456 * q^86 + 30331668 * q^87 - 1182712628 * q^88 - 4378590056 * q^91 + 2593806924 * q^92 - 4305536726 * q^93 + 861804818 * q^95 + 15624596040 * q^96 + 5117393178 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−42.4707	−	11.3800i	−1.87696	−	0.502929i	−0.999739	−	0.0228371i	$-0.992730\pi$
$2$	−42.4707	−	11.3800i	−1.87696	−	0.502929i	−0.877218	−	0.480092i	$-0.840603\pi$
$3$	54.8950	+	204.871i	0.391279	+	1.46027i	0.828026	+	0.560690i	$0.189464\pi$
$3$	54.8950	+	204.871i	0.391279	+	1.46027i	−0.436747	+	0.899584i	$0.643869\pi$
$4$	1230.85	+	710.632i	2.40401	+	1.38795i
$5$	−1352.09	+	353.508i	−0.967479	+	0.252950i
$5$	−1352.09	+	353.508i	−0.967479	+	0.252950i
$6$		−	9325.71i		−	2.93766i
$7$	−5765.26	+	2667.46i	−0.907566	+	0.419910i
$7$	−5765.26	+	2667.46i	−0.907566	+	0.419910i
$8$	−28269.7	−	28269.7i	−2.44015	−	2.44015i
$9$	−21912.6	+	12651.2i	−1.11328	+	0.642750i
$10$	61447.3	+	373.073i	1.94313	+	0.0117976i
$11$	−9135.71	+	15823.5i	−0.188138	+	0.325864i	−0.944629	−	0.328139i	$-0.893578\pi$
$11$	−9135.71	+	15823.5i	−0.188138	+	0.325864i	0.756492	+	0.654003i	$0.226912\pi$
$12$	−78020.2	+	291175.i	−1.08615	+	4.05358i
$13$	−5582.21	+	5582.21i	−0.0542077	+	0.0542077i	−0.733691	−	0.679483i	$-0.762204\pi$
$13$	−5582.21	+	5582.21i	−0.0542077	+	0.0542077i	0.679483	+	0.733691i	$0.262204\pi$
$14$	275210.	−	47680.2i	1.91465	−	0.331713i
$15$	−146647.	−	257599.i	−0.747931	−	1.31381i
$16$	515080.	+	892145.i	1.96488	+	3.40326i
$17$	−588348.	+	157647.i	−1.70850	+	0.457791i	−0.975056	−	0.221961i	$-0.928754\pi$
$17$	−588348.	+	157647.i	−1.70850	+	0.457791i	−0.733442	+	0.679752i	$0.762088\pi$
$18$	1.07461e6	−	287942.i	2.41283	−	0.646515i
$19$	76307.7	+	132169.i	0.134331	+	0.232669i	0.925342	−	0.379134i	$-0.123778\pi$
$19$	76307.7	+	132169.i	0.134331	+	0.232669i	−0.791010	+	0.611803i	$0.790445\pi$
$20$	−1.91544e6	−	525725.i	−2.67691	−	0.734723i
$21$	−862969.	−	1.03470e6i	−0.968296	−	1.16099i
$22$	568072.	−	568072.i	0.517012	−	0.517012i
$23$	−12714.5	+	47451.2i	−0.00947380	+	0.0353567i	−0.970501	−	0.241097i	$-0.922493\pi$
$23$	−12714.5	+	47451.2i	−0.00947380	+	0.0353567i	0.961027	+	0.276454i	$0.0891594\pi$
$24$	4.23977e6	−	7.34349e6i	2.60850	−	4.51806i
$25$	1.70319e6	−	955952.i	0.872033	−	0.489447i
$26$	300606.	−	173555.i	0.129008	−	0.0744829i
$27$	−842789.	−	842789.i	−0.305198	−	0.305198i
$28$	−8.99176e6	−	813736.i	−2.76461	−	0.250191i
$29$			1.42296e6i			0.373595i	0.982398	+	0.186797i	$0.0598108\pi$
$29$			1.42296e6i			0.373595i	−0.982398	+	0.186797i	$0.940189\pi$
$30$	3.29671e6	+	1.26092e7i	0.743080	+	2.84212i
$31$	2.72474e6	+	1.57313e6i	0.529904	+	0.305940i	0.740977	−	0.671530i	$-0.234363\pi$
$31$	2.72474e6	+	1.57313e6i	0.529904	+	0.305940i	−0.211073	+	0.977470i	$0.567696\pi$
$32$	−6.42534e6	−	2.39797e7i	−1.08323	−	4.04267i
$33$	−3.74328e6	−	1.00301e6i	−0.549465	−	0.147229i
$34$	2.67816e7			3.43701
$35$	6.85221e6	−	5.64472e6i	0.771835	−	0.635823i
$36$	−3.59615e7			−3.56843
$37$	−7.10815e6	−	1.90462e6i	−0.623518	−	0.167071i	−0.0667914	−	0.997767i	$-0.521276\pi$
$37$	−7.10815e6	−	1.90462e6i	−0.623518	−	0.167071i	−0.556727	+	0.830696i	$0.687943\pi$
$38$	−1.73676e6	−	6.48169e6i	−0.135118	−	0.504268i
$39$	−1.45007e6	−	837196.i	−0.100368	−	0.0579477i
$40$	4.82168e7	+	2.82297e7i	2.97802	+	1.74356i
$41$		−	1.89085e7i		−	1.04503i	−0.852629	−	0.522516i	$-0.824993\pi$
$41$		−	1.89085e7i		−	1.04503i	0.852629	−	0.522516i	$-0.175007\pi$
$42$	2.48760e7	+	5.37652e7i	1.23355	+	2.66612i
$43$	1.92423e7	+	1.92423e7i	0.858321	+	0.858321i	0.991140	−	0.132819i	$-0.0424030\pi$
$43$	1.92423e7	+	1.92423e7i	0.858321	+	0.858321i	−0.132819	+	0.991140i	$0.542403\pi$
$44$	−2.24894e7	+	1.29843e7i	−0.904567	+	0.522252i
$45$	2.51556e7	−	2.48520e7i	0.914488	−	0.903450i
$46$	1.07999e6	−	1.87059e6i	0.0355638	−	0.0615984i
$47$	2.32464e6	−	8.67567e6i	0.0694889	−	0.259336i	−0.922438	−	0.386144i	$-0.873807\pi$
$47$	2.32464e6	−	8.67567e6i	0.0694889	−	0.259336i	0.991927	+	0.126808i	$0.0404733\pi$
$48$	−1.54499e8	+	1.54499e8i	−4.20088	+	4.20088i
$49$	2.61229e7	−	3.07572e7i	0.647350	−	0.762193i
$50$	−8.32143e7	+	2.12177e7i	−1.88293	+	0.480101i
$51$	−6.45947e7	−	1.11881e8i	−1.33700	−	2.31575i
$52$	−1.08378e7	+	2.90397e6i	−0.205553	+	0.0550778i
$53$	3.86579e7	−	1.03583e7i	0.672972	−	0.180322i	0.0938785	−	0.995584i	$-0.470073\pi$
$53$	3.86579e7	−	1.03583e7i	0.672972	−	0.180322i	0.579093	+	0.815261i	$0.303407\pi$
$54$	2.62029e7	+	4.53847e7i	0.419351	+	0.726337i
$55$	6.75860e6	−	2.46244e7i	0.0995920	−	0.362856i
$56$	2.38390e8	+	8.75739e7i	3.23923	+	1.18995i
$57$	−2.28886e7	+	2.28886e7i	−0.287199	+	0.287199i
$58$	1.61932e7	−	6.04340e7i	0.187892	−	0.701221i
$59$	4.10960e7	−	7.11804e7i	0.441535	−	0.764762i	−0.556268	−	0.831003i	$-0.687767\pi$
$59$	4.10960e7	−	7.11804e7i	0.441535	−	0.764762i	0.997804	+	0.0662410i	$0.0211006\pi$
$60$	2.55776e6	−	4.21277e8i	0.0254788	−	4.19650i
$61$	−7.61586e7	+	4.39702e7i	−0.704262	+	0.406606i	−0.808933	−	0.587901i	$-0.799954\pi$
$61$	−7.61586e7	+	4.39702e7i	−0.704262	+	0.406606i	0.104671	+	0.994507i	$0.466621\pi$
$62$	−9.78193e7	−	9.78193e7i	−0.840741	−	0.840741i
$63$	9.25852e7	−	1.31389e8i	0.740473	−	1.05081i
$64$			5.64112e8i			4.20296i
$65$	5.57431e6	−	9.52102e6i	0.0387330	−	0.0661566i
$66$	1.47566e8	+	8.51970e7i	0.957276	+	0.552684i
$67$	2.00687e7	+	7.48975e7i	0.121670	+	0.454078i	0.999699	−	0.0245288i	$-0.00780855\pi$
$67$	2.00687e7	+	7.48975e7i	0.121670	+	0.454078i	−0.878029	+	0.478607i	$0.841142\pi$
$68$	−8.36198e8	−	2.24059e8i	−4.74263	−	1.27078i
$69$	−1.04193e7			−0.0553374
$70$	−3.55255e8	+	1.61757e8i	−1.76847	+	0.805235i
$71$	1.38499e8			0.646820			0.323410	−	0.946259i	$-0.395171\pi$
$71$	1.38499e8			0.646820			0.323410	+	0.946259i	$0.395171\pi$
$72$	9.77108e8	+	2.61815e8i	4.28496	+	1.14815i
$73$	4.77827e7	+	1.78328e8i	0.196933	+	0.734963i	0.991758	+	0.128125i	$0.0408958\pi$
$73$	4.77827e7	+	1.78328e8i	0.196933	+	0.734963i	−0.794825	+	0.606838i	$0.792438\pi$
$74$	2.80214e8	+	1.61781e8i	1.08629	+	0.627171i
$75$	2.89343e8	+	2.96457e8i	1.05594	+	1.08190i
$76$			2.16907e8i			0.745783i
$77$	1.04612e7	−	1.15596e8i	0.0339135	−	0.374744i
$78$	5.20580e7	+	5.20580e7i	0.159244	+	0.159244i
$79$	2.85953e8	−	1.65095e8i	0.825987	−	0.476884i	−0.0264900	−	0.999649i	$-0.508433\pi$
$79$	2.85953e8	−	1.65095e8i	0.825987	−	0.476884i	0.852477	+	0.522766i	$0.175100\pi$
$80$	−1.01182e9	−	1.02418e9i	−2.76183	−	2.79557i
$81$	−1.22617e8	+	2.12378e8i	−0.316495	+	0.548185i
$82$	−2.15178e8	+	8.03057e8i	−0.525577	+	1.96148i
$83$	−5.47918e7	+	5.47918e7i	−0.126726	+	0.126726i	−0.767625	−	0.640899i	$-0.778562\pi$
$83$	−5.47918e7	+	5.47918e7i	−0.126726	+	0.126726i	0.640899	+	0.767625i	$0.278562\pi$
$84$	−3.26892e8	−	1.88682e9i	−0.716386	−	4.13498i
$85$	7.39772e8	−	4.21140e8i	1.53714	−	0.875067i
$86$	−5.98258e8	−	1.03621e9i	−1.17936	−	2.04271i
$87$	−2.91522e8	+	7.81132e7i	−0.545551	+	0.146180i
$88$	7.05589e8	−	1.89062e8i	1.25424	−	0.336072i
$89$	1.21663e8	+	2.10726e8i	0.205543	+	0.356010i	0.950305	−	0.311319i	$-0.100771\pi$
$89$	1.21663e8	+	2.10726e8i	0.205543	+	0.356010i	−0.744763	+	0.667329i	$0.767437\pi$
$90$	−1.35119e9	+	7.69210e8i	−2.17083	+	1.23581i
$91$	1.72926e7	−	4.70732e7i	0.0264347	−	0.0719594i
$92$	−4.93700e7	+	4.93700e7i	−0.0718485	+	0.0718485i
$93$	−1.72714e8	+	6.44576e8i	−0.239416	+	0.893513i
$94$	−1.97458e8	+	3.42008e8i	−0.260855	+	0.451815i
$95$	−1.49898e8	−	1.51729e8i	−0.188816	−	0.191123i
$96$	4.56002e9	−	2.63273e9i	5.47956	−	3.16363i
$97$	−8.49197e8	−	8.49197e8i	−0.973947	−	0.973947i	0.0257217	−	0.999669i	$-0.491812\pi$
$97$	−8.49197e8	−	8.49197e8i	−0.973947	−	0.973947i	−0.999669	+	0.0257217i	$0.991812\pi$
$98$	−1.45948e9	+	1.00900e9i	−1.59838	+	1.10503i
$99$		−	4.62313e8i		−	0.483702i
$100$	2.77570e9	+	3.37062e7i	2.77570	+	0.0337062i
$101$	−4.56595e8	−	2.63615e8i	−0.436601	−	0.252072i	0.265554	−	0.964096i	$-0.414445\pi$
$101$	−4.56595e8	−	2.63615e8i	−0.436601	−	0.252072i	−0.702155	+	0.712024i	$0.747779\pi$
$102$	1.47017e9	+	5.48677e9i	1.34483	+	5.01898i
$103$	−2.40336e8	−	6.43979e7i	−0.210403	−	0.0563773i	0.152078	−	0.988369i	$-0.451404\pi$
$103$	−2.40336e8	−	6.43979e7i	−0.210403	−	0.0563773i	−0.362481	+	0.931991i	$0.618070\pi$
$104$	3.15614e8			0.264549
$105$	1.53259e9	+	1.09395e9i	1.23048	+	0.878306i
$106$	−1.75971e9			−1.35383
$107$	−1.86518e9	−	4.99773e8i	−1.37560	−	0.368592i	−0.506082	−	0.862485i	$-0.668907\pi$
$107$	−1.86518e9	−	4.99773e8i	−1.37560	−	0.368592i	−0.869522	+	0.493893i	$0.835573\pi$
$108$	−4.38434e8	−	1.63626e9i	−0.310097	−	1.15730i
$109$	−2.09436e9	−	1.20918e9i	−1.42113	−	0.820488i	−0.424731	−	0.905319i	$-0.639631\pi$
$109$	−2.09436e9	−	1.20918e9i	−1.42113	−	0.820488i	−0.996395	+	0.0848315i	$0.972965\pi$
$110$	−5.67268e8	+	9.68904e8i	−0.369421	+	0.630977i
$111$		−	1.56081e9i		−	0.975879i
$112$	−5.34933e9	−	3.76950e9i	−3.21232	−	2.26361i
$113$	1.27210e9	+	1.27210e9i	0.733956	+	0.733956i	0.971401	−	0.237445i	$-0.0763100\pi$
$113$	1.27210e9	+	1.27210e9i	0.733956	+	0.733956i	−0.237445	+	0.971401i	$0.576310\pi$
$114$	1.23257e9	−	7.11624e8i	0.683501	−	0.394620i
$115$	416823.	−	6.86531e7i	0.000222234	−	0.0366033i
$116$	−1.01120e9	+	1.75145e9i	−0.518532	+	0.898124i
$117$	5.16988e7	−	1.92943e8i	0.0255061	−	0.0951901i
$118$	−2.55541e9	+	2.55541e9i	−1.21336	+	1.21336i
$119$	2.97147e9	−	2.47827e9i	1.35834	−	1.13289i
$120$	−3.13658e9	+	1.14279e10i	−1.38083	+	5.03095i
$121$	1.01205e9	+	1.75292e9i	0.429209	+	0.743411i
$122$	3.73489e9	−	1.00076e9i	1.52636	−	0.408988i
$123$	3.87380e9	−	1.03798e9i	1.52603	−	0.408899i
$124$	2.23583e9	+	3.87257e9i	0.849261	+	1.47096i
$125$	−1.96493e9	+	1.89463e9i	−0.719868	+	0.694111i
$126$	−5.42736e9	+	4.52655e9i	−1.91832	+	1.59993i
$127$	3.35676e9	−	3.35676e9i	1.14500	−	1.14500i	0.157473	−	0.987523i	$-0.449665\pi$
$127$	3.35676e9	−	3.35676e9i	1.14500	−	1.14500i	0.987523	−	0.157473i	$-0.0503348\pi$
$128$	3.12982e9	−	1.16806e10i	1.03056	−	3.84611i
$129$	−2.88589e9	+	4.99850e9i	−0.917541	+	1.58923i
$130$	−3.45094e8	+	3.40929e8i	−0.105972	+	0.104693i
$131$	−3.95651e9	+	2.28429e9i	−1.17379	+	0.677689i	−0.954570	−	0.297986i	$-0.903685\pi$
$131$	−3.95651e9	+	2.28429e9i	−1.17379	+	0.677689i	−0.219222	+	0.975675i	$0.570352\pi$
$132$	−3.89465e9	−	3.89465e9i	−1.11657	−	1.11657i
$133$	−7.92489e8	−	5.58441e8i	−0.219615	−	0.154755i
$134$		−	3.40933e9i		−	0.913477i
$135$	1.43746e9	+	8.41596e8i	0.372473	+	0.218073i
$136$	2.10891e10	+	1.21758e10i	5.28606	+	3.05191i
$137$	4.08728e8	+	1.52539e9i	0.0991269	+	0.369947i	0.997613	−	0.0690557i	$-0.0219986\pi$
$137$	4.08728e8	+	1.52539e9i	0.0991269	+	0.369947i	−0.898486	+	0.439002i	$0.855332\pi$
$138$	4.42516e8	+	1.18572e8i	0.103866	+	0.0278308i
$139$	−5.60315e9			−1.27311			−0.636555	−	0.771231i	$-0.719641\pi$
$139$	−5.60315e9			−1.27311			−0.636555	+	0.771231i	$0.719641\pi$
$140$	1.24454e10	−	2.07841e9i	2.73799	−	0.457252i
$141$	1.90500e9			0.405891
$142$	−5.88214e9	−	1.57611e9i	−1.21405	−	0.325305i
$143$	−3.73327e7	−	1.39328e8i	−0.00746582	−	0.0278628i
$144$	−2.25735e10	−	1.30328e10i	−4.37490	−	2.52585i
$145$	−5.03027e8	−	1.92397e9i	−0.0945007	−	0.361445i
$146$		−	8.11746e9i		−	1.47854i
$147$	7.73527e9	+	3.66341e9i	1.36630	+	0.647079i
$148$	−7.39559e9	−	7.39559e9i	−1.26705	−	1.26705i
$149$	−8.85702e7	+	5.11361e7i	−0.0147214	+	0.00849941i	−0.507343	−	0.861744i	$-0.669372\pi$
$149$	−8.85702e7	+	5.11361e7i	−0.0147214	+	0.00849941i	0.492621	+	0.870244i	$0.336039\pi$
$150$	−8.91493e9	−	1.58834e10i	−1.43783	−	2.56173i
$151$	4.72080e9	−	8.17666e9i	0.738957	−	1.27991i	−0.214009	−	0.976832i	$-0.568652\pi$
$151$	4.72080e9	−	8.17666e9i	0.738957	−	1.27991i	0.952966	−	0.303079i	$-0.0980145\pi$
$152$	1.57918e9	−	5.89356e9i	0.239957	−	0.895534i
$153$	1.08978e10	−	1.08978e10i	1.60778	−	1.60778i
$154$	−1.75977e9	+	4.79039e9i	−0.252124	+	0.686322i
$155$	−4.24021e9	−	1.16380e9i	−0.590059	−	0.161952i
$156$	−1.18988e9	−	2.06093e9i	−0.160857	−	0.278613i
$157$	−5.61549e9	+	1.50466e9i	−0.737631	+	0.197648i	−0.608025	−	0.793918i	$-0.708038\pi$
$157$	−5.61549e9	+	1.50466e9i	−0.737631	+	0.197648i	−0.129606	+	0.991566i	$0.541371\pi$
$158$	−1.40234e10	+	3.75756e9i	−1.79018	+	0.479677i
$159$	4.24425e9	+	7.35125e9i	0.526640	+	0.912167i
$160$	1.71647e10	+	3.01514e10i	2.07060	+	3.63720i
$161$	−5.32717e7	−	3.07484e8i	−0.00624856	−	0.0360667i
$162$	7.62447e9	−	7.62447e9i	0.869746	−	0.869746i
$163$	4.00347e9	−	1.49412e10i	0.444214	−	1.65783i	−0.273789	−	0.961790i	$-0.588277\pi$
$163$	4.00347e9	−	1.49412e10i	0.444214	−	1.65783i	0.718003	−	0.696040i	$-0.245056\pi$
$164$	1.34370e10	−	2.32735e10i	1.45046	−	2.51226i
$165$	5.41584e9	+	3.28819e7i	0.568837	+	0.00345366i
$166$	2.95058e9	−	1.70352e9i	0.301593	−	0.174125i
$167$	−6.04785e9	−	6.04785e9i	−0.601696	−	0.601696i	0.339067	−	0.940762i	$-0.389889\pi$
$167$	−6.04785e9	−	6.04785e9i	−0.601696	−	0.601696i	−0.940762	+	0.339067i	$0.889889\pi$
$168$	−4.85490e9	+	5.36466e10i	−0.470207	+	5.19577i
$169$			1.05422e10i			0.994123i
$170$	−3.62112e10	+	9.46751e9i	−3.32524	+	0.869392i
$171$	−3.34420e9	−	1.93078e9i	−0.299096	−	0.172683i
$172$	1.00102e10	+	3.73587e10i	0.872099	+	3.25472i
$173$	−3.37815e9	−	9.05172e8i	−0.286729	−	0.0768287i	0.112588	−	0.993642i	$-0.464086\pi$
$173$	−3.37815e9	−	9.05172e8i	−0.286729	−	0.0768287i	−0.399317	+	0.916813i	$0.630753\pi$
$174$	1.32701e10			1.09749
$175$	−7.26937e9	+	1.00545e10i	−0.585903	+	0.810381i
$176$	−1.88225e10			−1.47867
$177$	1.68387e10	+	4.51193e9i	1.28953	+	0.345527i
$178$	−2.76904e9	−	1.03342e10i	−0.206747	−	0.771589i
$179$	−8.33686e9	−	4.81329e9i	−0.606966	−	0.350432i	0.164811	−	0.986325i	$-0.447298\pi$
$179$	−8.33686e9	−	4.81329e9i	−0.606966	−	0.350432i	−0.771777	+	0.635893i	$0.780632\pi$
$180$	4.86234e10	−	1.27127e10i	3.45238	−	0.902633i
$181$			9.42022e9i			0.652390i	0.945302	+	0.326195i	$0.105767\pi$
$181$			9.42022e9i			0.652390i	−0.945302	+	0.326195i	$0.894233\pi$
$182$	−1.27012e9	+	1.80244e9i	−0.0858072	+	0.121770i
$183$	−1.31889e10	−	1.31889e10i	−0.869319	−	0.869319i
$184$	1.70086e9	−	9.81994e8i	0.109393	−	0.0631581i
$185$	1.02842e10	+	6.24398e7i	0.645501	+	0.00391912i
$186$	1.46705e10	−	2.54101e10i	0.898747	−	1.55668i
$187$	2.88044e9	−	1.07500e10i	0.172255	−	0.642865i
$188$	9.02650e9	−	9.02650e9i	0.526998	−	0.526998i
$189$	7.10700e9	+	2.61079e9i	0.405143	+	0.148831i
$190$	4.63959e9	+	8.14989e9i	0.258279	+	0.453691i
$191$	−3.35522e9	−	5.81142e9i	−0.182419	−	0.315960i	0.760284	−	0.649590i	$-0.225060\pi$
$191$	−3.35522e9	−	5.81142e9i	−0.182419	−	0.315960i	−0.942704	+	0.333631i	$0.891726\pi$
$192$	−1.15570e11	+	3.09669e10i	−6.13748	+	1.64453i
$193$	−5.17735e9	+	1.38727e9i	−0.268596	+	0.0719701i	−0.390603	−	0.920559i	$-0.627734\pi$
$193$	−5.17735e9	+	1.38727e9i	−0.268596	+	0.0719701i	0.122007	+	0.992529i	$0.461067\pi$
$194$	2.64021e10	+	4.57298e10i	1.33823	+	2.31788i
$195$	2.25658e9	+	6.19357e8i	0.111762	+	0.0306751i
$196$	5.40105e10	−	1.92938e10i	2.61412	−	0.933823i
$197$	1.76798e10	−	1.76798e10i	0.836333	−	0.836333i	−0.152041	−	0.988374i	$-0.548585\pi$
$197$	1.76798e10	−	1.76798e10i	0.836333	−	0.836333i	0.988374	+	0.152041i	$0.0485847\pi$
$198$	−5.26111e9	+	1.96347e10i	−0.243268	+	0.907887i
$199$	−1.84850e10	+	3.20170e10i	−0.835566	+	1.44724i	0.0580025	+	0.998316i	$0.481527\pi$
$199$	−1.84850e10	+	3.20170e10i	−0.835566	+	1.44724i	−0.893569	+	0.448927i	$0.851806\pi$
$200$	−7.51730e10	−	2.11241e10i	−3.32221	−	0.933564i
$201$	−1.42426e10	+	8.22299e9i	−0.615472	+	0.355343i
$202$	1.63920e10	+	1.63920e10i	0.692708	+	0.692708i
$203$	−3.79568e9	−	8.20372e9i	−0.156876	−	0.339062i
$204$		−	1.83612e11i		−	7.42277i
$205$	6.68431e9	+	2.55661e10i	0.264341	+	1.01105i
$206$	9.47440e9	+	5.47005e9i	0.366564	+	0.211636i
$207$	−3.21709e8	−	1.20063e9i	−0.0121786	−	0.0454511i
$208$	−7.85542e9	−	2.10485e9i	−0.290994	−	0.0779717i
$209$	−2.78850e9			−0.101091
$210$	−5.26410e10	−	6.39017e10i	−1.86783	−	2.26739i
$211$	−2.61464e10			−0.908116			−0.454058	−	0.890972i	$-0.650024\pi$
$211$	−2.61464e10			−0.908116			−0.454058	+	0.890972i	$0.650024\pi$
$212$	5.49431e10	+	1.47219e10i	1.86811	+	0.500557i
$213$	7.60289e9	+	2.83744e10i	0.253087	+	0.944535i
$214$	7.35280e10	+	4.24514e10i	2.39657	+	1.38366i
$215$	−3.28198e10	−	1.92151e10i	−1.04752	−	0.613296i
$216$			4.76507e10i			1.48946i
$217$	−1.99051e10	−	1.80137e9i	−0.609390	−	0.0551485i
$218$	7.51886e10	+	7.51886e10i	2.25475	+	2.25475i
$219$	−3.39111e10	+	1.95786e10i	−0.996192	+	0.575152i
$220$	2.58177e10	−	2.55061e10i	0.743047	−	0.734078i
$221$	2.40426e9	−	4.16430e9i	0.0677979	−	0.117429i
$222$	−1.77620e10	+	6.62886e10i	−0.490798	+	1.83168i
$223$	9.62626e9	−	9.62626e9i	0.260667	−	0.260667i	−0.564658	−	0.825325i	$-0.690992\pi$
$223$	9.62626e9	−	9.62626e9i	0.260667	−	0.260667i	0.825325	+	0.564658i	$0.190992\pi$
$224$	1.01009e11	+	1.21110e11i	2.68066	+	3.21413i
$225$	−2.52273e10	+	4.24949e10i	−0.656220	+	1.10539i
$226$	−3.95506e10	−	6.85037e10i	−1.00848	−	1.74673i
$227$	2.95391e10	−	7.91499e9i	0.738383	−	0.197849i	0.130024	−	0.991511i	$-0.458495\pi$
$227$	2.95391e10	−	7.91499e9i	0.738383	−	0.197849i	0.608359	+	0.793662i	$0.291828\pi$
$228$	−4.44379e10	+	1.19071e10i	−1.08905	+	0.291809i
$229$	−3.87271e10	−	6.70773e10i	−0.930584	−	1.61182i	−0.782325	−	0.622870i	$-0.785966\pi$
$229$	−3.87271e10	−	6.70773e10i	−0.930584	−	1.61182i	−0.148259	−	0.988949i	$-0.547367\pi$
$230$	−7.98975e8	+	2.91100e9i	−0.0188260	+	0.0685910i
$231$	2.42565e10	−	4.20244e9i	0.560498	−	0.0971064i
$232$	4.02265e10	−	4.02265e10i	0.911626	−	0.911626i
$233$	1.28807e10	−	4.80715e10i	0.286311	−	1.06853i	−0.661565	−	0.749888i	$-0.730107\pi$
$233$	1.28807e10	−	4.80715e10i	0.286311	−	1.06853i	0.947876	−	0.318639i	$-0.103226\pi$
$234$	−4.39137e9	+	7.60607e9i	−0.0957477	+	0.165840i
$235$	−7.62093e7	+	1.25521e10i	−0.00163006	+	0.268479i
$236$	1.01166e11	−	5.84083e10i	2.12291	−	1.22566i
$237$	4.95206e10	+	4.95206e10i	1.01957	+	1.01957i
$238$	−1.54403e11	+	7.14388e10i	−3.11932	+	1.44324i
$239$			8.83538e10i			1.75160i	0.482674	+	0.875800i	$0.339665\pi$
$239$			8.83538e10i			1.75160i	−0.482674	+	0.875800i	$0.660335\pi$
$240$	1.54281e11	−	2.63514e11i	3.00165	−	5.12688i
$241$	−3.00872e10	−	1.73709e10i	−0.574520	−	0.331699i	0.184432	−	0.982845i	$-0.440955\pi$
$241$	−3.00872e10	−	1.73709e10i	−0.574520	−	0.331699i	−0.758953	+	0.651146i	$0.774289\pi$
$242$	−2.30343e10	−	8.59650e10i	−0.431723	−	1.61121i
$243$	−7.29016e10	−	1.95339e10i	−1.34125	−	0.359386i
$244$	−1.24986e11			−2.25740
$245$	−2.44477e10	+	5.08213e10i	−0.433502	+	0.901153i
$246$	−1.76335e11			−3.06995
$247$	−1.16376e9	−	3.11828e8i	−0.0198942	−	0.00533064i
$248$	−3.25556e10	−	1.21499e11i	−0.546504	−	2.03958i
$249$	−1.42330e10	−	8.21745e9i	−0.234639	−	0.135469i
$250$	1.05013e11	−	5.81052e10i	1.70025	−	0.940774i
$251$			1.18259e11i			1.88063i	0.340304	+	0.940315i	$0.389470\pi$
$251$			1.18259e11i			1.88063i	−0.340304	+	0.940315i	$0.610530\pi$
$252$	2.07328e11	−	9.59259e10i	3.23858	−	1.49842i
$253$	−6.34689e8	−	6.34689e8i	−0.00973909	−	0.00973909i
$254$	−1.80764e11	+	1.04364e11i	−2.72496	+	1.57326i
$255$	1.26889e11	+	1.28439e11i	1.87929	+	1.90225i
$256$	−1.21438e11	+	2.10337e11i	−1.76716	+	3.06081i
$257$	−1.37284e10	+	5.12349e10i	−0.196300	+	0.732600i	0.795627	+	0.605787i	$0.207142\pi$
$257$	−1.37284e10	+	5.12349e10i	−0.196300	+	0.732600i	−0.991927	+	0.126813i	$0.959525\pi$
$258$	1.79448e11	−	1.79448e11i	2.52145	−	2.52145i
$259$	4.60609e10	−	7.98005e9i	0.636038	−	0.110194i
$260$	1.36271e10	−	7.75767e9i	0.184937	−	0.105281i
$261$	−1.80022e10	−	3.11807e10i	−0.240128	−	0.415914i
$262$	1.94031e11	−	5.19904e10i	2.54399	−	0.681659i
$263$	−1.26060e10	+	3.37777e9i	−0.162472	+	0.0435341i	−0.339138	−	0.940737i	$-0.610135\pi$
$263$	−1.26060e10	+	3.37777e9i	−0.162472	+	0.0435341i	0.176666	+	0.984271i	$0.443469\pi$
$264$	7.74666e10	+	1.34176e11i	0.981515	+	1.70003i
$265$	−4.86073e10	+	2.76713e10i	−0.605474	+	0.344686i
$266$	2.73025e10	+	3.27359e10i	0.334376	+	0.400919i
$267$	−3.64929e10	+	3.64929e10i	−0.439448	+	0.439448i
$268$	−2.85230e10	+	1.06449e11i	−0.337744	+	1.26048i
$269$	6.43765e10	−	1.11503e11i	0.749622	−	1.29838i	−0.198383	−	0.980125i	$-0.563569\pi$
$269$	6.43765e10	−	1.11503e11i	0.749622	−	1.29838i	0.948004	−	0.318258i	$-0.103098\pi$
$270$	−5.14726e10	−	5.21015e10i	−0.589440	−	0.596641i
$271$	6.45908e10	−	3.72915e10i	0.727459	−	0.419999i	−0.0900328	−	0.995939i	$-0.528697\pi$
$271$	6.45908e10	−	3.72915e10i	0.727459	−	0.419999i	0.817492	+	0.575940i	$0.195364\pi$
$272$	−4.43691e11	−	4.43691e11i	−4.91497	−	4.91497i
$273$	1.05932e10	+	9.58663e8i	0.115424	+	0.0104456i
$274$		−	6.94358e10i		−	0.744228i
$275$	−4.33319e8	+	3.56838e10i	−0.00456889	+	0.376247i
$276$	−1.28246e10	−	7.40431e9i	−0.133031	−	0.0768057i
$277$	−1.89927e10	−	7.08817e10i	−0.193833	−	0.723395i	−0.992566	−	0.121709i	$-0.961163\pi$
$277$	−1.89927e10	−	7.08817e10i	−0.193833	−	0.723395i	0.798733	−	0.601686i	$-0.205504\pi$
$278$	2.37970e11	+	6.37638e10i	2.38957	+	0.640284i
$279$	−7.96081e10			−0.786572
$280$	−3.53284e11	−	3.41352e10i	−3.43489	−	0.331888i
$281$	−1.47678e11			−1.41298			−0.706492	−	0.707721i	$-0.749723\pi$
$281$	−1.47678e11			−1.41298			−0.706492	+	0.707721i	$0.749723\pi$
$282$	−8.09068e10	−	2.16789e10i	−0.761841	−	0.204135i
$283$	−6.19464e9	−	2.31187e10i	−0.0574086	−	0.214252i	0.931263	−	0.364348i	$-0.118708\pi$
$283$	−6.19464e9	−	2.31187e10i	−0.0574086	−	0.214252i	−0.988671	+	0.150096i	$0.952042\pi$
$284$	1.70471e11	+	9.84217e10i	1.55496	+	0.897756i
$285$	2.28563e10	−	3.90389e10i	0.205212	−	0.350506i
$286$			6.34219e9i			0.0560521i
$287$	5.04377e10	+	1.09012e11i	0.438820	+	0.948435i
$288$	4.44169e11	+	4.44169e11i	3.80436	+	3.80436i
$289$	2.18601e11	−	1.26209e11i	1.84337	−	1.06427i
$290$	−5.30867e8	+	8.74368e10i	−0.00440752	+	0.725944i
$291$	1.27359e11	−	2.20592e11i	1.04114	−	1.80332i
$292$	−6.79119e10	+	2.53451e11i	−0.546667	+	2.04019i
$293$	8.61304e10	−	8.61304e10i	0.682735	−	0.682735i	−0.277880	−	0.960616i	$-0.589632\pi$
$293$	8.61304e10	−	8.61304e10i	0.682735	−	0.682735i	0.960616	+	0.277880i	$0.0896319\pi$
$294$	−2.86833e11	−	2.43615e11i	−2.23906	−	1.90169i
$295$	−3.04028e10	+	1.10770e11i	−0.233730	+	0.851578i
$296$	1.47102e11	+	2.54788e11i	1.11380	+	1.92915i
$297$	2.10354e10	−	5.63641e9i	0.156872	−	0.0420338i
$298$	4.34357e9	−	1.16386e9i	0.0319061	−	0.00854921i
$299$	−1.93907e8	−	3.35857e8i	−0.00140305	−	0.00243016i
$300$	1.45467e11	+	5.70511e11i	1.03685	+	4.06647i
$301$	−1.62265e11	−	5.96090e10i	−1.13940	−	0.418565i
$302$	−2.93546e11	+	2.93546e11i	−2.03069	+	2.03069i
$303$	2.89423e10	−	1.08014e11i	0.197261	−	0.736188i
$304$	−7.86092e10	+	1.36155e11i	−0.527889	+	0.914330i
$305$	8.74297e10	−	8.63744e10i	0.578508	−	0.571526i
$306$	−5.86854e11	+	3.38821e11i	−3.82634	+	2.20914i
$307$	−8.27257e10	−	8.27257e10i	−0.531518	−	0.531518i	0.389506	−	0.921024i	$-0.372646\pi$
$307$	−8.27257e10	−	8.27257e10i	−0.531518	−	0.531518i	−0.921024	+	0.389506i	$0.872646\pi$
$308$	9.50223e10	−	1.34847e11i	0.601655	−	0.853815i
$309$		−	5.27730e10i		−	0.329305i
$310$	1.66841e11	+	9.76810e10i	1.02606	+	0.600734i
$311$	2.60109e10	+	1.50174e10i	0.157665	+	0.0910277i	0.576756	−	0.816916i	$-0.304318\pi$
$311$	2.60109e10	+	1.50174e10i	0.157665	+	0.0910277i	−0.419092	+	0.907944i	$0.637651\pi$
$312$	1.73256e10	+	6.46601e10i	0.103513	+	0.386314i
$313$	4.38888e10	+	1.17600e10i	0.258466	+	0.0692559i	0.385725	−	0.922614i	$-0.373951\pi$
$313$	4.38888e10	+	1.17600e10i	0.258466	+	0.0692559i	−0.127259	+	0.991870i	$0.540618\pi$
$314$	2.55617e11			1.48390
$315$	−7.87369e10	+	2.10380e11i	−0.450589	+	1.20394i
$316$	4.69288e11			2.64757
$317$	1.36211e11	+	3.64975e10i	0.757608	+	0.203000i	0.616890	−	0.787049i	$-0.288392\pi$
$317$	1.36211e11	+	3.64975e10i	0.757608	+	0.203000i	0.140718	+	0.990050i	$0.455059\pi$
$318$	−9.65989e10	−	3.60512e11i	−0.529725	−	1.97696i
$319$	−2.25162e10	−	1.29997e10i	−0.121741	−	0.0702872i
$320$	−1.99418e11	−	7.62732e11i	−1.06314	−	4.06628i
$321$		−	4.09556e11i		−	2.15298i
$322$	−1.23668e9	+	1.36653e10i	−0.00641071	+	0.0708382i
$323$	−6.57316e10	−	6.57316e10i	−0.336018	−	0.336018i
$324$	−3.01846e11	+	1.74271e11i	−1.52171	+	0.878560i
$325$	−4.17123e9	+	1.48439e10i	−0.0207391	+	0.0738027i
$326$	−3.40060e11	+	5.89002e11i	−1.66754	+	2.88827i
$327$	1.32756e11	−	4.95452e11i	0.642080	−	2.39627i
$328$	−5.34537e11	+	5.34537e11i	−2.55003	+	2.55003i
$329$	9.73985e9	+	5.62184e10i	0.0458322	+	0.264544i
$330$	−2.29640e11	−	6.30287e10i	−1.06595	−	0.292567i
$331$	−1.45032e11	−	2.51202e11i	−0.664106	−	1.15026i	−0.979527	−	0.201313i	$-0.935479\pi$
$331$	−1.45032e11	−	2.51202e11i	−0.664106	−	1.15026i	0.315421	−	0.948952i	$-0.397854\pi$
$332$	−1.06377e11	+	2.85037e10i	−0.480538	+	0.128760i
$333$	1.79854e11	−	4.81917e10i	0.801532	−	0.214770i
$334$	1.88032e11	+	3.25681e11i	0.826747	+	1.43197i
$335$	−5.36117e10	−	9.41739e10i	−0.232572	−	0.408535i
$336$	4.78608e11	−	1.30285e12i	2.04858	−	5.57657i
$337$	2.19810e11	−	2.19810e11i	0.928352	−	0.928352i	−0.0692478	−	0.997599i	$-0.522060\pi$
$337$	2.19810e11	−	2.19810e11i	0.928352	−	0.928352i	0.997599	+	0.0692478i	$0.0220599\pi$
$338$	1.19970e11	−	4.47734e11i	0.499974	−	1.86593i
$339$	−1.90785e11	+	3.30449e11i	−0.784595	+	1.35896i
$340$	1.20983e12	+	7.34537e9i	4.90984	+	0.0298098i
$341$	−4.97849e10	+	2.87433e10i	−0.199390	+	0.115118i
$342$	1.20058e11	+	1.20058e11i	0.474542	+	0.474542i
$343$	−6.85619e10	+	2.47005e11i	−0.267460	+	0.963569i
$344$		−	1.08795e12i		−	4.18886i
$345$	1.40879e10	−	3.68332e9i	0.0535378	−	0.0139976i
$346$	1.33171e11	+	7.68866e10i	0.499538	+	0.288409i
$347$	6.49638e10	+	2.42448e11i	0.240541	+	0.897711i	0.975572	+	0.219678i	$0.0705007\pi$
$347$	6.49638e10	+	2.42448e11i	0.240541	+	0.897711i	−0.735031	+	0.678033i	$0.762833\pi$
$348$	−4.14330e11	−	1.11019e11i	−1.51440	−	0.405782i
$349$	5.28967e10			0.190860			0.0954298	−	0.995436i	$-0.469577\pi$
$349$	5.28967e10			0.190860			0.0954298	+	0.995436i	$0.469577\pi$
$350$	4.23155e11	−	3.44296e11i	1.50728	−	1.22638i
$351$	9.40924e9			0.0330882
$352$	4.38143e11	+	1.17400e11i	1.52116	+	0.407593i
$353$	5.23914e10	+	1.95527e11i	0.179587	+	0.670226i	0.995725	+	0.0923696i	$0.0294441\pi$
$353$	5.23914e10	+	1.95527e11i	0.179587	+	0.670226i	−0.816138	+	0.577857i	$0.803889\pi$
$354$	−6.63807e11	−	3.83249e11i	−2.24661	−	1.29708i
$355$	−1.87263e11	+	4.89605e10i	−0.625785	+	0.163613i
$356$			3.45829e11i			1.14113i
$357$	6.70845e11	+	4.72722e11i	2.18582	+	1.54028i
$358$	2.99297e11	+	2.99297e11i	0.963006	+	0.963006i
$359$	−2.77132e11	+	1.60002e11i	−0.880565	+	0.508394i	−0.870845	−	0.491558i	$-0.836427\pi$
$359$	−2.77132e11	+	1.60002e11i	−0.880565	+	0.508394i	−0.00972034	+	0.999953i	$0.503094\pi$
$360$	−1.41370e12	−	8.58316e9i	−4.43603	−	0.0269331i
$361$	1.49698e11	−	2.59285e11i	0.463910	−	0.803516i
$362$	1.07202e11	−	4.00083e11i	0.328106	−	1.22451i
$363$	−3.03566e11	+	3.03566e11i	−0.917643	+	0.917643i
$364$	5.47363e10	−	4.56514e10i	0.163425	−	0.136301i
$365$	−1.27647e11	−	2.24224e11i	−0.376437	−	0.661248i
$366$	4.10053e11	+	7.10233e11i	1.19447	+	2.06888i
$367$	3.59016e11	−	9.61981e10i	1.03304	−	0.276802i	0.297813	−	0.954624i	$-0.403743\pi$
$367$	3.59016e11	−	9.61981e10i	1.03304	−	0.276802i	0.735226	+	0.677822i	$0.237076\pi$
$368$	−4.88823e10	+	1.30980e10i	−0.138943	+	0.0372297i
$369$	2.39216e11	+	4.14334e11i	0.671694	+	1.16341i
$370$	−4.36066e11	−	1.19686e11i	−1.20961	−	0.331997i
$371$	−1.95242e11	+	1.62837e11i	−0.535047	+	0.446242i
$372$	−6.70641e11	+	6.70641e11i	−1.81571	+	1.81571i
$373$	5.16808e9	−	1.92875e10i	0.0138242	−	0.0515926i	−0.958669	−	0.284523i	$-0.908165\pi$
$373$	5.16808e9	−	1.92875e10i	0.0138242	−	0.0515926i	0.972493	+	0.232930i	$0.0748315\pi$
$374$	−2.44669e11	+	4.23779e11i	−0.646631	+	1.12000i
$375$	−4.96019e11	−	2.98552e11i	−1.29526	−	0.779614i
$376$	−3.10975e11	+	1.79542e11i	−0.802381	+	0.463255i
$377$	−7.94324e9	−	7.94324e9i	−0.0202517	−	0.0202517i
$378$	−2.72129e11	−	1.91760e11i	−0.685585	−	0.483108i
$379$			2.24842e11i			0.559758i	0.960035	+	0.279879i	$0.0902943\pi$
$379$			2.24842e11i			0.559758i	−0.960035	+	0.279879i	$0.909706\pi$
$380$	−7.66784e10	−	2.93278e11i	−0.188646	−	0.721529i
$381$	8.71973e11	+	5.03434e11i	2.12002	+	1.22400i
$382$	7.63648e10	+	2.84997e11i	0.183488	+	0.684787i
$383$	−1.23348e11	−	3.30510e10i	−0.292913	−	0.0784857i	0.109370	−	0.994001i	$-0.465117\pi$
$383$	−1.23348e11	−	3.30510e10i	−0.292913	−	0.0784857i	−0.402283	+	0.915515i	$0.631783\pi$
$384$	2.56483e12			6.01961
$385$	2.67196e10	+	1.59995e11i	0.0619807	+	0.371135i
$386$	2.35673e11			0.540339
$387$	−6.65089e11	−	1.78210e11i	−1.50723	−	0.403862i
$388$	−4.41768e11	−	1.64870e12i	−0.989582	−	3.69317i
$389$	5.86375e11	+	3.38544e11i	1.29838	+	0.749621i	0.980125	−	0.198383i	$-0.0635690\pi$
$389$	5.86375e11	+	3.38544e11i	1.29838	+	0.749621i	0.318257	+	0.948004i	$0.396902\pi$
$390$	−8.87903e10	−	5.19844e10i	−0.194346	−	0.113784i
$391$		−	2.99222e10i		−	0.0647439i
$392$	−1.60798e12	+	1.31010e11i	−3.43949	+	0.280232i
$393$	−6.85177e11	−	6.85177e11i	−1.44889	−	1.44889i
$394$	−9.52069e11	+	5.49677e11i	−1.99038	+	1.14914i
$395$	−3.28273e11	+	3.24311e11i	−0.678497	+	0.670308i
$396$	3.28534e11	−	5.69038e11i	0.671355	−	1.16282i
$397$	−1.87286e11	+	6.98960e11i	−0.378397	+	1.41220i	0.469921	+	0.882708i	$0.344282\pi$
$397$	−1.87286e11	+	6.98960e11i	−0.378397	+	1.41220i	−0.848318	+	0.529487i	$0.822384\pi$
$398$	1.14942e12	−	1.14942e12i	2.29618	−	2.29618i
$399$	7.09045e10	−	1.93014e11i	0.140054	−	0.381250i
$400$	1.73013e12	+	1.02710e12i	3.37915	+	2.00605i
$401$	−1.62327e11	−	2.81158e11i	−0.313502	−	0.543001i	0.665616	−	0.746294i	$-0.268169\pi$
$401$	−1.62327e11	−	2.81158e11i	−0.313502	−	0.543001i	−0.979118	+	0.203293i	$0.934836\pi$
$402$	6.98472e11	−	1.87155e11i	1.33393	−	0.357424i
$403$	−2.39916e10	+	6.42852e9i	−0.0453092	+	0.0121406i
$404$	−3.74667e11	−	6.48942e11i	−0.699728	−	1.21196i
$405$	9.07117e10	−	3.30501e11i	0.167539	−	0.610415i
$406$	6.78469e10	+	3.91613e11i	0.123926	+	0.715302i
$407$	9.50759e10	−	9.50759e10i	0.171750	−	0.171750i
$408$	−1.33678e12	+	4.98892e12i	−2.38830	+	8.91324i
$409$	1.98900e11	−	3.44506e11i	0.351464	−	0.608754i	−0.635042	−	0.772478i	$-0.719017\pi$
$409$	1.98900e11	−	3.44506e11i	0.351464	−	0.608754i	0.986506	+	0.163724i	$0.0523506\pi$
$410$	7.05425e9	−	1.16188e12i	0.0123289	−	2.03064i
$411$	−2.90071e11	+	1.67473e11i	−0.501437	+	0.289505i
$412$	−2.50055e11	−	2.50055e11i	−0.427561	−	0.427561i
$413$	−4.70585e10	+	5.19996e11i	−0.0795909	+	0.879477i
$414$			5.46528e10i			0.0914346i
$415$	5.47143e10	−	9.34531e10i	0.0905492	−	0.154660i
$416$	1.69727e11	+	9.79920e10i	0.277863	+	0.160424i
$417$	−3.07585e11	−	1.14792e12i	−0.498141	−	1.85909i
$418$	1.18430e11	+	3.17331e10i	0.189744	+	0.0508417i
$419$	4.29192e11			0.680282			0.340141	−	0.940374i	$-0.389525\pi$
$419$	4.29192e11			0.680282			0.340141	+	0.940374i	$0.389525\pi$
$420$	1.10899e12	+	2.43560e12i	1.73903	+	3.81930i
$421$	2.54333e11			0.394578			0.197289	−	0.980345i	$-0.436786\pi$
$421$	2.54333e11			0.394578			0.197289	+	0.980345i	$0.436786\pi$
$422$	1.11046e12	+	2.97546e11i	1.70450	+	0.456718i
$423$	5.88192e10	+	2.19516e11i	0.0893280	+	0.333376i
$424$	−1.38567e12	−	8.00018e11i	−2.08216	−	1.20214i
$425$	−8.51365e11	+	8.30936e11i	−1.26580	+	1.23543i
$426$		−	1.29160e12i		−	1.90014i
$427$	3.21786e11	−	4.56649e11i	0.468426	−	0.664749i
$428$	−1.94060e12	−	1.94060e12i	−2.79537	−	2.79537i
$429$	2.64948e10	−	1.52968e10i	0.0377661	−	0.0218043i
$430$	1.17521e12	+	1.18957e12i	1.65771	+	1.67796i
$431$	−2.26938e10	+	3.93067e10i	−0.0316781	+	0.0548680i	−0.881430	−	0.472315i	$-0.843418\pi$
$431$	−2.26938e10	+	3.93067e10i	−0.0316781	+	0.0548680i	0.849752	+	0.527183i	$0.176752\pi$
$432$	3.17786e11	−	1.18599e12i	0.438993	−	1.63835i
$433$	−6.91571e11	+	6.91571e11i	−0.945455	+	0.945455i	−0.998587	−	0.0531323i	$-0.983080\pi$
$433$	−6.91571e11	+	6.91571e11i	−0.945455	+	0.945455i	0.0531323	+	0.998587i	$0.483080\pi$
$434$	8.24883e11	+	3.03025e11i	1.11606	+	0.409991i
$435$	3.66552e11	−	2.08672e11i	0.490833	−	0.279423i
$436$	−1.71857e12	−	2.97664e12i	−2.27760	−	3.94491i
$437$	−7.24179e9	+	1.94043e9i	−0.00949903	+	0.00254526i
$438$	1.66303e12	−	4.45608e11i	2.15907	−	0.578521i
$439$	−2.89651e11	−	5.01690e11i	−0.372207	−	0.644681i	0.617698	−	0.786416i	$-0.288065\pi$
$439$	−2.89651e11	−	5.01690e11i	−0.372207	−	0.644681i	−0.989905	+	0.141734i	$0.954732\pi$
$440$	−8.87188e11	+	5.05061e11i	−1.12844	+	0.642402i
$441$	−1.83304e11	+	1.00446e12i	−0.230780	+	1.26461i
$442$	−1.49500e11	+	1.49500e11i	−0.186313	+	0.186313i
$443$	3.75254e10	−	1.40047e11i	0.0462923	−	0.172765i	−0.938909	−	0.344165i	$-0.888162\pi$
$443$	3.75254e10	−	1.40047e11i	0.0462923	−	0.172765i	0.985202	+	0.171399i	$0.0548288\pi$
$444$	1.10916e12	−	1.92112e12i	1.35447	−	2.34602i
$445$	−2.38992e11	−	2.41912e11i	−0.288911	−	0.292441i
$446$	−5.18381e11	+	2.99287e11i	−0.620358	+	0.358164i
$447$	−1.53383e10	−	1.53383e10i	−0.0181717	−	0.0181717i
$448$	−1.50475e12	−	3.25225e12i	−1.76487	−	3.81446i
$449$			3.20969e11i			0.372696i	0.982484	+	0.186348i	$0.0596652\pi$
$449$			3.20969e11i			0.372696i	−0.982484	+	0.186348i	$0.940335\pi$
$450$	1.55501e12	−	1.51770e12i	1.78763	−	1.74474i
$451$	2.99199e11	+	1.72743e11i	0.340538	+	0.196610i
$452$	6.61773e11	+	2.46977e12i	0.745737	+	2.78313i
$453$	1.93431e12	+	5.18296e11i	2.15816	+	0.578277i
$454$	−1.34462e12			−1.48542
$455$	−6.74043e9	+	6.97604e10i	−0.00737286	+	0.0763059i
$456$	1.29411e12			1.40161
$457$	−9.34167e11	−	2.50309e11i	−1.00185	−	0.268444i	−0.279628	−	0.960108i	$-0.590211\pi$
$457$	−9.34167e11	−	2.50309e11i	−1.00185	−	0.268444i	−0.722219	+	0.691664i	$0.756878\pi$
$458$	8.81428e11	+	3.28954e12i	0.936036	+	3.49333i
$459$	6.28717e11	+	3.62990e11i	0.661147	+	0.381713i
$460$	4.93002e10	−	8.42056e10i	0.0513379	−	0.0876861i
$461$		−	4.52733e10i		−	0.0466862i	−0.999728	−	0.0233431i	$-0.992569\pi$
$461$		−	4.52733e10i		−	0.0466862i	0.999728	−	0.0233431i	$-0.00743101\pi$
$462$	−1.07801e12	−	9.75581e10i	−1.10087	−	0.0996264i
$463$	−5.07567e11	−	5.07567e11i	−0.513309	−	0.513309i	0.402229	−	0.915539i	$-0.368235\pi$
$463$	−5.07567e11	−	5.07567e11i	−0.513309	−	0.513309i	−0.915539	+	0.402229i	$0.868235\pi$
$464$	−1.26948e12	+	7.32937e11i	−1.27144	+	0.734067i
$465$	5.66211e9	−	9.32583e11i	0.00561617	−	0.925016i
$466$	−1.09411e12	+	1.89505e12i	−1.07479	+	1.86159i
$467$	−2.42996e11	+	9.06873e11i	−0.236414	+	0.882308i	0.741093	+	0.671403i	$0.234308\pi$
$467$	−2.42996e11	+	9.06873e11i	−0.236414	+	0.882308i	−0.977506	+	0.210906i	$0.932359\pi$
$468$	2.00745e11	−	2.00745e11i	0.193436	−	0.193436i
$469$	−3.15487e11	−	3.78271e11i	−0.301096	−	0.361015i
$470$	1.46079e11	−	5.32229e11i	0.138086	−	0.503105i
$471$	−6.16524e11	−	1.06785e12i	−0.577239	−	0.999807i
$472$	−3.17402e12	+	8.50475e11i	−2.94354	+	0.788719i
$473$	−4.80274e11	+	1.28689e11i	−0.441178	+	0.118213i
$474$	−1.53963e12	−	2.66672e12i	−1.40092	−	2.42647i
$475$	2.56314e11	+	1.52162e11i	0.231020	+	0.137147i
$476$	5.41857e12	−	9.38768e11i	4.83786	−	0.838160i
$477$	−7.16049e11	+	7.16049e11i	−0.633301	+	0.633301i
$478$	1.00547e12	−	3.75245e12i	0.880931	−	3.28768i
$479$	3.94115e11	−	6.82627e11i	0.342068	−	0.592480i	−0.642748	−	0.766077i	$-0.722206\pi$
$479$	3.94115e11	−	6.82627e11i	0.342068	−	0.592480i	0.984817	+	0.173598i	$0.0555393\pi$
$480$	−5.23488e12	+	5.17170e12i	−4.50113	+	4.44680i
$481$	5.03112e10	−	2.90472e10i	0.0428560	−	0.0247429i
$482$	1.08014e12	+	1.08014e12i	0.911529	+	0.911529i
$483$	6.00702e10	−	2.77931e10i	0.0502223	−	0.0232368i
$484$			2.87678e12i			2.38289i
$485$	1.44839e12	+	8.47996e11i	1.18863	+	0.695914i
$486$	2.87389e12	+	1.65924e12i	2.33672	+	1.34910i
$487$	−4.88444e11	−	1.82290e12i	−0.393490	−	1.46853i	−0.824336	−	0.566100i	$-0.808451\pi$
$487$	−4.88444e11	−	1.82290e12i	−0.393490	−	1.46853i	0.430846	−	0.902425i	$-0.358215\pi$
$488$	3.39600e12	+	9.09955e11i	2.71068	+	0.726325i
$489$	3.28078e12			2.59470
$490$	1.61666e12	−	1.88020e12i	1.26688	−	1.47340i
$491$	−1.98728e12			−1.54310			−0.771549	−	0.636170i	$-0.780518\pi$
$491$	−1.98728e12			−1.54310			−0.771549	+	0.636170i	$0.780518\pi$
$492$	5.50569e12	+	1.47525e12i	4.23613	+	1.13507i
$493$	−2.24326e11	−	8.37194e11i	−0.171028	−	0.638286i
$494$	4.58771e10	+	2.64871e10i	0.0346597	+	0.0200108i
$495$	1.63431e11	+	6.25090e11i	0.122352	+	0.467971i
$496$			3.24115e12i			2.40454i
$497$	−7.98482e11	+	3.69440e11i	−0.587032	+	0.271606i
$498$	5.10973e11	+	5.10973e11i	0.372277	+	0.372277i
$499$	−1.26020e12	+	7.27576e11i	−0.909885	+	0.525322i	−0.880394	−	0.474243i	$-0.842722\pi$
$499$	−1.26020e12	+	7.27576e11i	−0.909885	+	0.525322i	−0.0294910	+	0.999565i	$0.509389\pi$
$500$	−3.76492e12	+	9.35659e11i	−2.69396	+	0.669503i
$501$	9.07031e11	−	1.57102e12i	0.643210	−	1.11407i
$502$	1.34579e12	−	5.02255e12i	0.945824	−	3.52986i
$503$	−1.89576e11	+	1.89576e11i	−0.132047	+	0.132047i	−0.770041	−	0.637994i	$-0.779764\pi$
$503$	−1.89576e11	+	1.89576e11i	−0.132047	+	0.132047i	0.637994	+	0.770041i	$0.279764\pi$
$504$	−6.33167e12	+	1.09696e12i	−4.37100	+	0.757276i
$505$	7.10550e11	+	1.95023e11i	0.486164	+	0.133436i
$506$	1.97329e10	+	3.41784e10i	0.0133818	+	0.0231779i
$507$	−2.15978e12	+	5.78712e11i	−1.45169	+	0.388980i
$508$	6.51710e12	−	1.74625e12i	4.34178	−	1.16338i
$509$	−6.95258e11	−	1.20422e12i	−0.459109	−	0.795200i	0.539805	−	0.841790i	$-0.318498\pi$
$509$	−6.95258e11	−	1.20422e12i	−0.459109	−	0.795200i	−0.998914	+	0.0465900i	$0.985165\pi$
$510$	−3.92743e12	−	6.89890e12i	−2.57065	−	4.51559i
$511$	−7.51162e11	−	9.00647e11i	−0.487348	−	0.584333i
$512$	3.17318e12	−	3.17318e12i	2.04071	−	2.04071i
$513$	4.70791e10	−	1.75702e11i	0.0300124	−	0.112008i
$514$	1.16611e12	−	2.01975e12i	0.736892	−	1.27633i
$515$	3.47722e11	+	2.11117e9i	0.217821	+	0.00132249i
$516$	−7.10419e12	+	4.10161e12i	−4.41155	+	2.54701i
$517$	1.16042e11	+	1.16042e11i	0.0714348	+	0.0714348i
$518$	−2.04705e12	−	1.85254e11i	−1.24924	−	0.113053i
$519$		−	7.41773e11i		−	0.448764i
$520$	−4.26740e11	+	1.11572e11i	−0.255946	+	0.0669177i
$521$	4.62460e11	+	2.67002e11i	0.274982	+	0.158761i	0.631150	−	0.775661i	$-0.282583\pi$
$521$	4.62460e11	+	2.67002e11i	0.274982	+	0.158761i	−0.356167	+	0.934422i	$0.615917\pi$
$522$	4.09729e11	+	1.52913e12i	0.241535	+	0.901420i
$523$	8.40149e11	+	2.25117e11i	0.491019	+	0.131568i	0.495829	−	0.868420i	$-0.334864\pi$
$523$	8.40149e11	+	2.25117e11i	0.491019	+	0.131568i	−0.00480957	+	0.999988i	$0.501531\pi$
$524$	−6.49316e12			−3.76240
$525$	−2.45893e12	−	9.37340e11i	−1.41263	−	0.538493i
$526$	5.73826e11			0.326847
$527$	−1.85109e12	−	4.95999e11i	−1.04540	−	0.280113i
$528$	−1.03326e12	−	3.85618e12i	−0.578572	−	2.15926i
$529$	1.55775e12	+	8.99370e11i	0.864865	+	0.499330i
$530$	2.37929e12	−	6.22070e11i	1.30980	−	0.342451i
$531$			2.07966e12i			1.13519i
$532$	−5.78590e11	−	1.25053e12i	−0.313162	−	0.676847i
$533$	1.05551e11	+	1.05551e11i	0.0566488	+	0.0566488i
$534$	1.96517e12	−	1.13459e12i	1.04584	−	0.603814i
$535$	2.69857e12	+	1.63842e10i	1.42410	+	0.00864635i
$536$	1.54999e12	−	2.68466e12i	0.811124	−	1.40491i
$537$	5.28451e11	−	1.97221e12i	0.274233	−	1.02345i
$538$	−4.00302e12	+	4.00302e12i	−2.06000	+	2.06000i
$539$	2.48036e11	+	6.94346e11i	0.126580	+	0.354345i
$540$	1.17124e12	+	2.05739e12i	0.592751	+	1.04122i
$541$	1.63256e12	+	2.82767e12i	0.819371	+	1.41919i	0.906146	+	0.422965i	$0.139011\pi$
$541$	1.63256e12	+	2.82767e12i	0.819371	+	1.41919i	−0.0867748	+	0.996228i	$0.527656\pi$
$542$	−3.16759e12	+	8.48754e11i	−1.57664	+	0.422459i
$543$	−1.92993e12	+	5.17123e11i	−0.952669	+	0.255267i
$544$	7.56067e12	+	1.30955e13i	3.70140	+	6.41100i
$545$	3.25923e12	+	8.94552e11i	1.58245	+	0.434331i
$546$	−4.38991e11	−	1.61266e11i	−0.211392	−	0.0776560i
$547$	−8.79604e11	+	8.79604e11i	−0.420092	+	0.420092i	−0.885235	−	0.465143i	$-0.846003\pi$
$547$	−8.79604e11	+	8.79604e11i	−0.420092	+	0.420092i	0.465143	+	0.885235i	$0.346003\pi$
$548$	−5.80910e11	+	2.16799e12i	−0.275167	+	1.02694i
$549$	1.11255e12	−	1.92700e12i	0.522692	−	0.905329i
$550$	4.24484e11	−	1.51058e12i	0.197801	−	0.703902i
$551$	−1.88071e11	+	1.08583e11i	−0.0869238	+	0.0501855i
$552$	2.94551e11	+	2.94551e11i	0.135031	+	0.135031i
$553$	−1.20821e12	+	1.71459e12i	−0.549389	+	0.779643i
$554$			3.22653e12i			1.45527i
$555$	5.51758e11	+	2.11036e12i	0.246848	+	0.944142i
$556$	−6.89664e12	−	3.98178e12i	−3.06056	−	1.76702i
$557$	5.60749e11	+	2.09275e12i	0.246843	+	0.921230i	0.972448	+	0.233119i	$0.0748931\pi$
$557$	5.60749e11	+	2.09275e12i	0.246843	+	0.921230i	−0.725605	+	0.688111i	$0.758440\pi$
$558$	3.38101e12	+	9.05940e11i	1.47636	+	0.395590i
$559$	−2.14829e11			−0.0930552
$560$	8.56535e12	+	3.20568e12i	3.68043	+	1.37744i
$561$	2.36048e12			1.00616
$562$	6.27198e12	+	1.68057e12i	2.65211	+	0.710630i
$563$	7.46512e11	+	2.78602e12i	0.313148	+	1.16868i	0.925702	+	0.378254i	$0.123476\pi$
$563$	7.46512e11	+	2.78602e12i	0.313148	+	1.16868i	−0.612554	+	0.790429i	$0.709858\pi$
$564$	2.34477e12	+	1.35376e12i	0.975765	+	0.563358i
$565$	−2.16970e12	−	1.27031e12i	−0.895741	−	0.524433i
$566$			1.05236e12i			0.431014i
$567$	1.40407e11	−	1.55149e12i	0.0570511	−	0.630414i
$568$	−3.91531e12	−	3.91531e12i	−1.57833	−	1.57833i
$569$	−7.40747e11	+	4.27670e11i	−0.296254	+	0.171042i	−0.640759	−	0.767742i	$-0.721380\pi$
$569$	−7.40747e11	+	4.27670e11i	−0.296254	+	0.171042i	0.344505	+	0.938785i	$0.388047\pi$
$570$	−1.41498e12	+	1.39790e12i	−0.561454	+	0.554678i
$571$	1.61568e12	−	2.79843e12i	0.636051	−	1.10167i	−0.350241	−	0.936660i	$-0.613900\pi$
$571$	1.61568e12	−	2.79843e12i	0.636051	−	1.10167i	0.986291	−	0.165012i	$-0.0527664\pi$
$572$	5.30597e10	−	1.98021e11i	0.0207244	−	0.0773446i
$573$	1.00640e12	−	1.00640e12i	0.390011	−	0.390011i
$574$	−9.01562e11	−	5.20382e12i	−0.346651	−	2.00087i
$575$	2.37059e10	+	9.29728e10i	0.00904379	+	0.0354691i
$576$	−7.13672e12	−	1.23612e13i	−2.70145	−	4.67906i
$577$	−1.71627e12	+	4.59874e11i	−0.644607	+	0.172722i	−0.566289	−	0.824206i	$-0.691622\pi$
$577$	−1.71627e12	+	4.59874e11i	−0.644607	+	0.172722i	−0.0783178	+	0.996928i	$0.524955\pi$
$578$	−1.07204e13	+	2.87252e12i	−3.99517	+	1.07050i
$579$	−5.68421e11	−	9.84534e11i	−0.210192	−	0.364064i
$580$	7.48084e11	−	2.72559e12i	0.274489	−	1.00008i
$581$	1.69734e11	−	4.62044e11i	0.0617984	−	0.168225i
$582$	−7.91936e12	+	7.91936e12i	−2.86112	+	2.86112i
$583$	−1.89262e11	+	7.06335e11i	−0.0678507	+	0.253222i
$584$	3.69046e12	−	6.39206e12i	1.31287	−	2.27396i
$585$	−1.69486e9	+	2.79152e11i	−0.000598317	+	0.0985462i
$586$	−4.63818e12	+	2.67786e12i	−1.62483	+	0.938097i
$587$	5.27503e11	+	5.27503e11i	0.183380	+	0.183380i	0.792827	−	0.609447i	$-0.208608\pi$
$587$	5.27503e11	+	5.27503e11i	0.183380	+	0.183380i	−0.609447	+	0.792827i	$0.708608\pi$
$588$	6.91763e12	+	1.00060e13i	2.38649	+	3.45195i
$589$			4.80167e11i			0.164389i
$590$	2.55179e12	−	4.35851e12i	0.866985	−	1.48083i
$591$	4.59260e12	+	2.65154e12i	1.54851	+	0.894035i
$592$	−1.96207e12	−	7.32254e12i	−0.656548	−	2.45027i
$593$	4.62403e12	+	1.23901e12i	1.53559	+	0.411460i	0.924837	−	0.380363i	$-0.124201\pi$
$593$	4.62403e12	+	1.23901e12i	1.53559	+	0.411460i	0.610751	+	0.791823i	$0.290868\pi$
$594$	−9.57529e11			−0.315582
$595$	−3.14161e12	+	4.40130e12i	−1.02760	+	1.43964i
$596$	−1.45356e11			−0.0471872
$597$	−7.57408e12	−	2.02947e12i	−2.44031	−	0.653879i
$598$	4.41333e9	+	1.64708e10i	0.00141127	+	0.00526694i
$599$	−1.85959e12	−	1.07364e12i	−0.590197	−	0.340751i	0.174978	−	0.984572i	$-0.444014\pi$
$599$	−1.85959e12	−	1.07364e12i	−0.590197	−	0.340751i	−0.765176	+	0.643822i	$0.777348\pi$
$600$	2.01098e11	−	1.65604e13i	0.0633471	−	5.21662i
$601$		−	1.45862e12i		−	0.456043i	−0.973656	−	0.228022i	$-0.926774\pi$
$601$		−	1.45862e12i		−	0.456043i	0.973656	−	0.228022i	$-0.0732257\pi$
$602$	6.21317e12	+	4.37821e12i	1.92810	+	1.35867i
$603$	−1.38730e12	−	1.38730e12i	−0.427311	−	0.427311i
$604$	1.16212e13	−	6.70950e12i	3.55291	−	2.05127i
$605$	−1.98806e12	−	2.01235e12i	−0.603296	−	0.610667i
$606$	−2.45840e12	+	4.25807e12i	−0.740501	+	1.28259i
$607$	1.39901e12	−	5.22117e12i	0.418284	−	1.56106i	−0.359881	−	0.932998i	$-0.617183\pi$
$607$	1.39901e12	−	5.22117e12i	0.418284	−	1.56106i	0.778165	−	0.628059i	$-0.216151\pi$
$608$	2.67907e12	−	2.67907e12i	0.795092	−	0.795092i
$609$	1.47234e12	−	1.22797e12i	0.433741	−	0.361750i
$610$	−4.69614e12	+	2.67343e12i	−1.37327	+	0.781781i
$611$	3.54528e10	+	6.14060e10i	0.0102912	+	0.0178248i
$612$	2.11579e13	−	5.66924e12i	6.09665	−	1.63359i
$613$	−1.18146e12	+	3.16572e11i	−0.337946	+	0.0905524i	−0.423801	−	0.905755i	$-0.639304\pi$
$613$	−1.18146e12	+	3.16572e11i	−0.337946	+	0.0905524i	0.0858550	+	0.996308i	$0.472638\pi$
$614$	2.57200e12	+	4.45484e12i	0.730321	+	1.26495i
$615$	−4.87080e12	+	2.77287e12i	−1.37297	+	0.781612i
$616$	−3.56359e12	+	2.97212e12i	−0.997183	+	0.831675i
$617$	−3.54505e11	+	3.54505e11i	−0.0984780	+	0.0984780i	−0.754629	−	0.656151i	$-0.772183\pi$
$617$	−3.54505e11	+	3.54505e11i	−0.0984780	+	0.0984780i	0.656151	+	0.754629i	$0.272183\pi$
$618$	−6.00556e11	+	2.24131e12i	−0.165617	+	0.618092i
$619$	−1.82830e12	+	3.16670e12i	−0.500540	+	0.866961i	0.499460	+	0.866337i	$0.333532\pi$
$619$	−1.82830e12	+	3.16670e12i	−0.500540	+	0.866961i	−1.00000		0.000623703i	$0.999801\pi$
$620$	−4.39204e12	−	4.44570e12i	−1.19372	−	1.20831i
$621$	5.07070e10	−	2.92757e10i	0.0136822	−	0.00789941i
$622$	−9.33804e11	−	9.33804e11i	−0.250149	−	0.250149i
$623$	−1.26352e12	−	8.90359e11i	−0.336036	−	0.236793i
$624$		−	1.72489e12i		−	0.455440i
$625$	1.98701e12	−	3.25633e12i	0.520882	−	0.853629i
$626$	−1.73016e12	−	9.98908e11i	−0.450300	−	0.259981i
$627$	−1.53075e11	−	5.71283e11i	−0.0395548	−	0.147621i
$628$	−7.98109e12	−	2.13853e12i	−2.04759	−	0.548651i
$629$	4.48233e12			1.14176
$630$	5.73813e12	−	8.03894e12i	1.45124	−	2.03314i
$631$	4.74638e12			1.19187			0.595937	−	0.803031i	$-0.296781\pi$
$631$	4.74638e12			1.19187			0.595937	+	0.803031i	$0.296781\pi$
$632$	−1.27510e13	−	3.41662e12i	−3.17919	−	0.851862i
$633$	−1.43531e12	−	5.35664e12i	−0.355327	−	1.32610i
$634$	−5.36962e12	−	3.10015e12i	−1.31990	−	0.762046i
$635$	−3.35202e12	+	5.72530e12i	−0.818134	+	1.39739i
$636$			1.20644e13i			2.92380i
$637$	2.58696e10	+	3.17517e11i	0.00622533	+	0.0764081i
$638$	8.08341e11	+	8.08341e11i	0.193153	+	0.193153i
$639$	−3.03487e12	+	1.75218e12i	−0.720089	+	0.415744i
$640$	−1.02606e11	+	1.68997e13i	−0.0241747	+	3.98171i
$641$	9.75612e11	−	1.68981e12i	0.228253	−	0.395345i	−0.729038	−	0.684474i	$-0.760032\pi$
$641$	9.75612e11	−	1.68981e12i	0.228253	−	0.395345i	0.957290	+	0.289128i	$0.0933654\pi$
$642$	−4.66074e12	+	1.73941e13i	−1.08280	+	4.04105i
$643$	−2.75452e12	+	2.75452e12i	−0.635472	+	0.635472i	−0.949435	−	0.313963i	$-0.898343\pi$
$643$	−2.75452e12	+	2.75452e12i	−0.635472	+	0.635472i	0.313963	+	0.949435i	$0.398343\pi$
$644$	1.52939e11	−	4.16324e11i	0.0350373	−	0.0953772i
$645$	2.13498e12	−	7.77862e12i	0.485707	−	1.76964i
$646$	2.04364e12	+	3.53969e12i	0.461699	+	0.799686i
$647$	3.62029e12	−	9.70054e11i	0.812221	−	0.217634i	0.171279	−	0.985223i	$-0.445210\pi$
$647$	3.62029e12	−	9.70054e11i	0.812221	−	0.217634i	0.640943	+	0.767589i	$0.278544\pi$
$648$	9.47019e12	−	2.53753e12i	2.10995	−	0.565358i
$649$	7.50883e11	+	1.30057e12i	0.166139	+	0.287761i
$650$	3.46078e11	−	5.82961e11i	0.0760439	−	0.128094i
$651$	−7.23641e11	−	4.17686e12i	−0.157910	−	0.911455i
$652$	1.55453e13	−	1.55453e13i	3.36888	−	3.36888i
$653$	1.38743e12	−	5.17798e12i	0.298609	−	1.11442i	−0.639699	−	0.768625i	$-0.720941\pi$
$653$	1.38743e12	−	5.17798e12i	0.298609	−	1.11442i	0.938308	−	0.345799i	$-0.112392\pi$
$654$	−1.12765e13	+	1.95314e13i	−2.41031	+	4.17478i
$655$	4.54205e12	−	4.48723e12i	0.964198	−	0.952561i
$656$	1.68691e13	−	9.73939e12i	3.55652	−	2.05336i
$657$	−3.30311e12	−	3.30311e12i	−0.691638	−	0.691638i
$658$	2.26107e11	−	2.49848e12i	0.0470216	−	0.519587i
$659$			4.06342e12i			0.839282i	0.907690	+	0.419641i	$0.137844\pi$
$659$			4.06342e12i			0.839282i	−0.907690	+	0.419641i	$0.862156\pi$
$660$	6.64272e12	+	3.88914e12i	1.36269	+	0.797822i
$661$	−4.20958e12	−	2.43040e12i	−0.857694	−	0.495190i	0.00554563	−	0.999985i	$-0.498235\pi$
$661$	−4.20958e12	−	2.43040e12i	−0.857694	−	0.495190i	−0.863239	+	0.504795i	$0.831568\pi$
$662$	3.30092e12	+	1.23192e13i	0.667996	+	2.49300i
$663$	9.85126e11	+	2.63964e11i	0.198007	+	0.0530559i
$664$	3.09789e12			0.618458
$665$	1.26893e12	+	4.74913e11i	0.251618	+	0.0941708i
$666$	−8.18694e12			−1.61246
$667$	−6.75210e10	−	1.80922e10i	−0.0132091	−	0.00353936i
$668$	−3.14621e12	−	1.17418e13i	−0.611354	−	2.28161i
$669$	2.50057e12	+	1.44371e12i	0.482639	+	0.278652i
$670$	1.20523e12	+	4.60973e12i	0.231064	+	0.883770i
$671$		−	1.60680e12i		−	0.305991i
$672$	−1.92670e13	+	2.73420e13i	−3.64462	+	5.17213i
$673$	2.43082e12	+	2.43082e12i	0.456756	+	0.456756i	0.897589	−	0.440833i	$-0.145317\pi$
$673$	2.43082e12	+	2.43082e12i	0.456756	+	0.456756i	−0.440833	+	0.897589i	$0.645317\pi$
$674$	−1.18369e13	+	6.83404e12i	−2.20937	+	1.27558i
$675$	−2.24109e12	−	6.29763e11i	−0.415521	−	0.116764i
$676$	−7.49161e12	+	1.29758e13i	−1.37980	+	2.38988i
$677$	1.11982e12	−	4.17922e12i	0.204880	−	0.764621i	−0.784607	−	0.619994i	$-0.787135\pi$
$677$	1.11982e12	−	4.17922e12i	0.204880	−	0.764621i	0.989486	−	0.144627i	$-0.0461983\pi$
$678$	1.18633e13	−	1.18633e13i	2.15611	−	2.15611i
$679$	7.16104e12	+	2.63065e12i	1.29289	+	0.474950i
$680$	−3.28186e13	−	9.00763e12i	−5.88613	−	1.61555i
$681$	3.24310e12	+	5.61722e12i	0.577828	+	1.00083i
$682$	2.44150e12	−	6.54197e11i	0.432142	−	0.115792i
$683$	−5.23474e12	+	1.40264e12i	−0.920453	+	0.246635i	−0.687779	−	0.725920i	$-0.741414\pi$
$683$	−5.23474e12	+	1.40264e12i	−0.920453	+	0.246635i	−0.232674	+	0.972555i	$0.574747\pi$
$684$	−2.74414e12	−	4.75300e12i	−0.479352	−	0.830262i
$685$	−1.09188e12	−	1.91799e12i	−0.189481	−	0.332842i
$686$	5.72279e12	−	9.71025e12i	0.986618	−	1.67406i
$687$	1.16163e13	−	1.16163e13i	1.98958	−	1.98958i
$688$	−7.25561e12	+	2.70783e13i	−1.23460	+	4.60759i
$689$	−1.57974e11	+	2.73619e11i	−0.0267054	+	0.0462551i
$690$	−6.40239e11	−	3.88717e9i	−0.107528	−	0.000652849i
$691$	−3.55267e12	+	2.05113e12i	−0.592794	+	0.342250i	−0.766201	−	0.642601i	$-0.777855\pi$
$691$	−3.55267e12	+	2.05113e12i	−0.592794	+	0.342250i	0.173408	+	0.984850i	$0.444522\pi$
$692$	−3.51475e12	−	3.51475e12i	−0.582663	−	0.582663i
$693$	1.23320e12	+	2.66535e12i	0.203111	+	0.438991i
$694$		−	1.10362e13i		−	1.80594i
$695$	7.57599e12	−	1.98076e12i	1.23171	−	0.322033i
$696$	1.04495e13	+	6.03301e12i	1.68792	+	0.974523i
$697$	2.98088e12	+	1.11248e13i	0.478406	+	1.78544i
$698$	−2.24656e12	−	6.01964e11i	−0.358235	−	0.0959889i
$699$	1.05555e13			1.67237
$700$	−1.60926e13	+	7.20975e12i	−2.53328	+	1.13496i
$701$	1.18014e13			1.84587			0.922936	−	0.384954i	$-0.125783\pi$
$701$	1.18014e13			1.84587			0.922936	+	0.384954i	$0.125783\pi$
$702$	−3.99617e11	−	1.07077e11i	−0.0621050	−	0.0166410i
$703$	−2.90675e11	−	1.08481e12i	−0.0448858	−	0.167516i
$704$	−8.92624e12	−	5.15357e12i	−1.36959	−	0.790735i
$705$	−2.57574e12	+	6.73434e11i	−0.392691	+	0.102670i
$706$		−	8.90040e12i		−	1.34831i
$707$	3.33557e12	+	3.01863e11i	0.502092	+	0.0454383i
$708$	1.75197e13	+	1.75197e13i	2.62045	+	2.62045i
$709$	−8.21791e12	+	4.74461e12i	−1.22139	+	0.705168i	−0.965213	−	0.261463i	$-0.915795\pi$
$709$	−8.21791e12	+	4.74461e12i	−1.22139	+	0.705168i	−0.256173	+	0.966631i	$0.582462\pi$
$710$	8.51037e12	+	5.16702e10i	1.25686	+	0.00763093i
$711$	−4.17732e12	+	7.23533e12i	−0.613034	+	1.06181i
$712$	2.51779e12	−	9.39650e12i	0.367163	−	1.37027i
$713$	−1.09291e11	+	1.09291e11i	−0.0158372	+	0.0158372i
$714$	−2.31117e13	−	2.77110e13i	−3.32805	−	3.99035i
$715$	9.97308e10	+	1.75187e11i	0.0142709	+	0.0250682i
$716$	−6.84096e12	−	1.18489e13i	−0.972766	−	1.68488i
$717$	−1.81011e13	+	4.85018e12i	−2.55782	+	0.685365i
$718$	1.35908e13	−	3.64165e12i	1.90847	−	0.511373i
$719$	−1.27999e12	−	2.21700e12i	−0.178618	−	0.309375i	0.762789	−	0.646647i	$-0.223829\pi$
$719$	−1.27999e12	−	2.21700e12i	−0.178618	−	0.309375i	−0.941407	+	0.337272i	$0.890496\pi$
$720$	3.51287e13	+	9.64167e12i	4.87153	+	1.33708i
$721$	1.55738e12	−	2.69817e11i	0.214628	−	0.0371843i
$722$	−9.30844e12	+	9.30844e12i	−1.27485	+	1.27485i
$723$	1.90715e12	−	7.11757e12i	0.259574	−	0.968744i
$724$	−6.69431e12	+	1.15949e13i	−0.905487	+	1.56835i
$725$	1.36028e12	+	2.42356e12i	0.182855	+	0.325787i
$726$	1.63473e13	−	9.43810e12i	2.18389	−	1.26087i
$727$	5.34157e12	+	5.34157e12i	0.709193	+	0.709193i	0.966365	−	0.257173i	$-0.0827909\pi$
$727$	5.34157e12	+	5.34157e12i	0.709193	+	0.709193i	−0.257173	+	0.966365i	$0.582791\pi$
$728$	−1.81960e12	+	8.41888e11i	−0.240096	+	0.111087i
$729$		−	1.11808e13i		−	1.46622i
$730$	2.86959e12	+	1.09756e13i	0.373996	+	1.43045i
$731$	−1.43547e13	−	8.28769e12i	−1.85937	−	1.07351i
$732$	−6.86113e12	−	2.56061e13i	−0.883274	−	3.29642i
$733$	3.62618e11	+	9.71631e10i	0.0463961	+	0.0124318i	0.281942	−	0.959431i	$-0.409021\pi$
$733$	3.62618e11	+	9.71631e10i	0.0463961	+	0.0124318i	−0.235546	+	0.971863i	$0.575688\pi$
$734$	−1.63424e13			−2.07818
$735$	−1.17539e13	−	2.21879e12i	−1.48555	−	0.280429i
$736$	1.21956e12			0.153198
$737$	−1.36848e12	−	3.66684e11i	−0.170858	−	0.0457813i
$738$	−5.44455e12	−	2.03193e13i	−0.675629	−	2.52148i
$739$	7.91307e12	+	4.56861e12i	0.975989	+	0.563488i	0.901057	−	0.433701i	$-0.142793\pi$
$739$	7.91307e12	+	4.56861e12i	0.975989	+	0.563488i	0.0749322	+	0.997189i	$0.476126\pi$
$740$	1.26139e13	+	7.38513e12i	1.54635	+	0.905347i
$741$		−	2.55538e11i		−	0.0311368i
$742$	1.01452e13	−	4.69394e12i	1.22869	−	0.568487i
$743$	1.40792e12	+	1.40792e12i	0.169484	+	0.169484i	0.786752	−	0.617269i	$-0.211761\pi$
$743$	1.40792e12	+	1.40792e12i	0.169484	+	0.169484i	−0.617269	+	0.786752i	$0.711761\pi$
$744$	2.31045e13	−	1.33394e13i	2.76451	−	1.59609i
$745$	1.01678e11	−	1.00451e11i	0.0120927	−	0.0119468i
$746$	−4.38984e11	+	7.60343e11i	−0.0518948	+	0.0898845i
$747$	5.07447e11	−	1.89382e12i	0.0596277	−	0.222533i
$748$	1.11847e13	−	1.11847e13i	1.30637	−	1.30637i
$749$	1.20864e13	−	2.09397e12i	1.40323	−	0.243109i
$750$	1.76687e13	+	1.83244e13i	2.03906	+	2.11473i
$751$	−7.53759e12	−	1.30555e13i	−0.864675	−	1.49766i	−0.867370	−	0.497664i	$-0.834191\pi$
$751$	−7.53759e12	−	1.30555e13i	−0.864675	−	1.49766i	0.00269541	−	0.999996i	$-0.499142\pi$
$752$	8.93734e12	−	2.39475e12i	1.01913	−	0.273074i
$753$	−2.42279e13	+	6.49184e12i	−2.74624	+	0.735852i
$754$	2.46961e11	+	4.27749e11i	0.0278264	+	0.0481968i
$755$	−3.49244e12	+	1.27244e13i	−0.391172	+	1.42521i
$756$	6.89235e12	+	8.26396e12i	0.767395	+	0.920111i
$757$	1.52572e12	−	1.52572e12i	0.168867	−	0.168867i	−0.617614	−	0.786481i	$-0.711901\pi$
$757$	1.52572e12	−	1.52572e12i	0.168867	−	0.168867i	0.786481	+	0.617614i	$0.211901\pi$
$758$	2.55869e12	−	9.54918e12i	0.281519	−	1.05064i
$759$	9.51880e10	−	1.64870e11i	0.0104110	−	0.0180325i
$760$	−5.17705e10	+	8.52690e12i	−0.00562887	+	0.927107i
$761$	−2.75628e12	+	1.59134e12i	−0.297915	+	0.172001i	−0.641506	−	0.767118i	$-0.721690\pi$
$761$	−2.75628e12	+	1.59134e12i	−0.297915	+	0.172001i	0.343591	+	0.939119i	$0.388357\pi$
$762$	−3.13042e13	−	3.13042e13i	−3.36361	−	3.36361i
$763$	1.53000e13	+	1.38462e12i	1.63430	+	0.147901i
$764$		−	9.53732e12i		−	1.01276i
$765$	−1.08824e13	+	1.85873e13i	−1.14881	+	1.96219i
$766$	4.86256e12	+	2.80740e12i	0.510312	+	0.294629i
$767$	1.67937e11	+	6.26750e11i	0.0175214	+	0.0653906i
$768$	−4.97583e13	−	1.33327e13i	−5.16107	−	1.38291i
$769$	−1.65970e13			−1.71143			−0.855717	−	0.517444i	$-0.826884\pi$
$769$	−1.65970e13			−1.71143			−0.855717	+	0.517444i	$0.826884\pi$
$770$	6.85938e11	−	7.09915e12i	0.0703196	−	0.727777i
$771$	−1.12502e13			−1.14660
$772$	−7.35838e12	−	1.97167e12i	−0.745598	−	0.199782i
$773$	2.88367e12	+	1.07620e13i	0.290495	+	1.08414i	0.944730	+	0.327850i	$0.106324\pi$
$773$	2.88367e12	+	1.07620e13i	0.290495	+	1.08414i	−0.654235	+	0.756291i	$0.727009\pi$
$774$	2.62188e13	+	1.51374e13i	2.62590	+	1.51606i
$775$	6.14458e12	+	7.46156e10i	0.611835	+	0.00742971i
$776$			4.80130e13i			4.75315i
$777$	4.16339e12	+	8.99846e12i	0.409782	+	0.885674i
$778$	−2.10511e13	−	2.10511e13i	−2.06000	−	2.06000i
$779$	2.49911e12	−	1.44286e12i	0.243146	−	0.140381i
$780$	2.33738e12	+	2.36593e12i	0.226102	+	0.228864i
$781$	−1.26529e12	+	2.19154e12i	−0.121691	+	0.210775i
$782$	−3.40515e11	+	1.27082e12i	−0.0325616	+	0.121521i
$783$	1.19925e12	−	1.19925e12i	0.114020	−	0.114020i
$784$	4.08953e13	+	7.46300e12i	3.86590	+	0.705491i
$785$	7.06075e12	−	4.01957e12i	0.663647	−	0.377803i
$786$	2.13026e13	+	3.68972e13i	1.99082	+	3.44820i
$787$	2.00775e12	−	5.37974e11i	0.186562	−	0.0499891i	−0.164328	−	0.986406i	$-0.552546\pi$
$787$	2.00775e12	−	5.37974e11i	0.186562	−	0.0499891i	0.350890	+	0.936417i	$0.385879\pi$
$788$	3.43250e13	−	9.19736e12i	3.17134	−	0.849758i
$789$	−1.38401e12	−	2.39718e12i	−0.127143	−	0.220219i
$790$	1.76326e13	−	1.00380e13i	1.61063	−	0.916904i
$791$	−1.07273e13	−	3.94073e12i	−0.974308	−	0.357917i
$792$	−1.30694e13	+	1.30694e13i	−1.18030	+	1.18030i
$793$	1.79682e11	−	6.70583e11i	0.0161353	−	0.0602176i
$794$	1.59083e13	−	2.75540e13i	1.42047	−	2.46032i
$795$	−8.33734e12	−	8.43920e12i	−0.740245	−	0.749289i
$796$	−4.55046e13	+	2.62721e13i	−4.01741	+	2.31945i
$797$	3.03107e12	+	3.03107e12i	0.266093	+	0.266093i	0.827524	−	0.561431i	$-0.189749\pi$
$797$	3.03107e12	+	3.03107e12i	0.266093	+	0.266093i	−0.561431	+	0.827524i	$0.689749\pi$
$798$	−5.20785e12	+	7.39053e12i	−0.454617	+	0.645152i
$799$			5.47079e12i			0.474886i
$800$	−3.38670e13	−	3.46996e13i	−2.92329	−	2.99516i
$801$	−5.33189e12	−	3.07837e12i	−0.457651	−	0.264225i
$802$	3.69455e12	+	1.37883e13i	0.315339	+	1.17686i
$803$	−3.25830e12	−	8.73059e11i	−0.276548	−	0.0741009i
$804$	−2.33741e13			−1.97280
$805$	1.80726e11	+	3.96915e11i	0.0151684	+	0.0333132i
$806$	1.09210e12			0.0911492
$807$	2.63777e13	+	7.06789e12i	2.18931	+	0.586623i
$808$	5.45547e12	+	2.03601e13i	0.450279	+	1.68046i
$809$	−1.85770e13	−	1.07254e13i	−1.52478	−	0.880331i	−0.999569	−	0.0293579i	$-0.990654\pi$
$809$	−1.85770e13	−	1.07254e13i	−1.52478	−	0.880331i	−0.525209	−	0.850973i	$-0.676013\pi$
$810$	−7.61369e12	+	1.30043e13i	−0.621459	+	1.06146i
$811$			1.83992e11i			0.0149350i	0.999972	+	0.00746749i	$0.00237700\pi$
$811$			1.83992e11i			0.0149350i	−0.999972	+	0.00746749i	$0.997623\pi$
$812$	1.15791e12	−	1.27949e13i	0.0934702	−	1.03284i
$813$	1.11856e13	+	1.11856e13i	0.897953	+	0.897953i
$814$	−5.11990e12	+	2.95598e12i	−0.408744	+	0.235989i
$815$	−1.31247e11	+	2.16171e13i	−0.0104203	+	1.71628i
$816$	6.65429e13	−	1.15256e14i	5.25407	−	9.10032i
$817$	−1.07490e12	+	4.01158e12i	−0.0844050	+	0.315004i
$818$	−1.23679e13	+	1.23679e13i	−0.965843	+	0.965843i
$819$	2.16609e11	+	1.25027e12i	0.0168228	+	0.0971015i
$820$	−9.94067e12	+	3.62181e13i	−0.767810	+	2.79746i
$821$	−7.81536e11	−	1.35366e12i	−0.0600350	−	0.103984i	0.834446	−	0.551090i	$-0.185788\pi$
$821$	−7.81536e11	−	1.35366e12i	−0.0600350	−	0.103984i	−0.894481	+	0.447106i	$0.852455\pi$
$822$	1.42254e13	−	3.81168e12i	1.08678	−	0.291201i
$823$	−1.48004e13	+	3.96575e12i	−1.12454	+	0.301319i	−0.772718	−	0.634749i	$-0.781103\pi$
$823$	−1.48004e13	+	3.96575e12i	−1.12454	+	0.301319i	−0.351819	+	0.936068i	$0.614437\pi$
$824$	4.97372e12	+	8.61474e12i	0.375845	+	0.650983i
$825$	−7.33435e12	+	1.87008e12i	−0.551212	+	0.140546i
$826$	7.91615e12	−	2.15490e13i	0.591703	−	1.61071i
$827$	3.14506e12	−	3.14506e12i	0.233805	−	0.233805i	−0.580474	−	0.814279i	$-0.697133\pi$
$827$	3.14506e12	−	3.14506e12i	0.233805	−	0.233805i	0.814279	+	0.580474i	$0.197133\pi$
$828$	4.57233e11	−	1.70642e12i	0.0338066	−	0.126168i
$829$	7.58416e11	−	1.31362e12i	0.0557715	−	0.0965991i	−0.836792	−	0.547521i	$-0.815571\pi$
$829$	7.58416e11	−	1.31362e12i	0.0557715	−	0.0965991i	0.892563	+	0.450922i	$0.148905\pi$
$830$	−3.38725e12	+	3.34637e12i	−0.247740	+	0.244750i
$831$	1.34790e13	−	7.78210e12i	0.980512	−	0.566099i
$832$	−3.14899e12	−	3.14899e12i	−0.227833	−	0.227833i
$833$	−1.05206e13	+	2.22142e13i	−0.757072	+	1.59856i
$834$			5.22534e13i			3.73996i
$835$	1.03152e13	+	6.03930e12i	0.734327	+	0.429929i
$836$	−3.43223e12	−	1.98160e12i	−0.243023	−	0.140310i
$837$	−9.70563e11	−	3.62219e12i	−0.0683533	−	0.255098i
$838$	−1.82281e13	−	4.88421e12i	−1.27686	−	0.342134i
$839$	3.14649e12			0.219229			0.109614	−	0.993974i	$-0.465038\pi$
$839$	3.14649e12			0.219229			0.109614	+	0.993974i	$0.465038\pi$
$840$	−1.24002e13	−	7.42514e13i	−0.859354	−	5.14574i
$841$	1.24823e13			0.860427
$842$	−1.08017e13	−	2.89431e12i	−0.740606	−	0.198445i
$843$	−8.10677e12	−	3.02549e13i	−0.552871	−	2.06334i
$844$	−3.21824e13	−	1.85805e13i	−2.18312	−	1.26042i
$845$	−3.72675e12	−	1.42540e13i	−0.251463	−	0.961794i
$846$		−	9.99237e12i		−	0.670659i
$847$	−1.05106e13	−	7.40646e12i	−0.701701	−	0.494465i
$848$	2.91531e13	+	2.91531e13i	1.93599	+	1.93599i
$849$	4.39629e12	−	2.53820e12i	0.290404	−	0.167665i
$850$	4.56141e13	−	2.56019e13i	2.99719	−	1.68224i
$851$	1.80753e11	−	3.13074e11i	0.0118142	−	0.0204627i
$852$	−1.08057e13	+	4.03275e13i	−0.702547	+	2.62194i
$853$	−5.41236e12	+	5.41236e12i	−0.350039	+	0.350039i	−0.860124	−	0.510085i	$-0.829614\pi$
$853$	−5.41236e12	+	5.41236e12i	−0.350039	+	0.350039i	0.510085	+	0.860124i	$0.329614\pi$
$854$	−1.88631e13	+	1.57323e13i	−1.21354	+	1.01212i
$855$	5.20422e12	+	1.42839e12i	0.333049	+	0.0914110i
$856$	3.85996e13	+	6.68564e13i	2.45726	+	4.25609i
$857$	−1.72074e13	+	4.61071e12i	−1.08969	+	0.291981i	−0.758559	−	0.651605i	$-0.774096\pi$
$857$	−1.72074e13	+	4.61071e12i	−1.08969	+	0.291981i	−0.331129	+	0.943586i	$0.607429\pi$
$858$	−1.29933e12	+	3.48154e11i	−0.0818514	+	0.0219320i
$859$	−8.90940e12	−	1.54315e13i	−0.558315	−	0.967030i	−0.997637	−	0.0687006i	$-0.978115\pi$
$859$	−8.90940e12	−	1.54315e13i	−0.558315	−	0.967030i	0.439322	−	0.898330i	$-0.355219\pi$
$860$	−2.67414e13	−	4.69737e13i	−1.66702	−	2.92828i
$861$	−1.95647e13	+	1.63174e13i	−1.21327	+	1.01190i
$862$	1.41113e12	−	1.41113e12i	0.0870531	−	0.0870531i
$863$	5.91328e12	−	2.20687e13i	0.362894	−	1.35434i	−0.507359	−	0.861735i	$-0.669378\pi$
$863$	5.91328e12	−	2.20687e13i	0.362894	−	1.35434i	0.870253	−	0.492605i	$-0.163955\pi$
$864$	−1.47946e13	+	2.56250e13i	−0.903216	+	1.56442i
$865$	4.88756e12	+	2.96745e10i	0.296838	+	0.00180223i
$866$	3.72415e13	−	2.15014e13i	2.25008	−	1.29908i
$867$	3.78567e13	+	3.78567e13i	2.27539	+	2.27539i
$868$	−2.32201e13	−	1.63624e13i	−1.38843	−	0.978382i
$869$			6.03305e12i			0.358879i
$870$	−1.79424e13	+	4.69108e12i	−1.06180	+	0.277611i
$871$	−5.30121e11	−	3.06065e11i	−0.0312100	−	0.0180191i
$872$	2.50238e13	+	9.33901e13i	1.46565	+	5.46987i
$873$	2.93515e13	+	7.86471e12i	1.71028	+	0.458267i
$874$	3.29646e11			0.0191094
$875$	6.27452e12	−	1.61644e13i	0.361863	−	0.932231i
$876$	−5.56526e13			−3.19314
$877$	−4.30816e12	−	1.15437e12i	−0.245920	−	0.0658940i	0.133754	−	0.991015i	$-0.457297\pi$
$877$	−4.30816e12	−	1.15437e12i	−0.245920	−	0.0658940i	−0.379673	+	0.925121i	$0.623964\pi$
$878$	6.59245e12	+	2.46033e13i	0.374387	+	1.39723i
$879$	2.23737e13	+	1.29175e13i	1.26412	+	0.729840i
$880$	2.54498e13	−	6.65391e12i	1.43058	−	0.374029i
$881$		−	1.85902e13i		−	1.03966i	−0.854269	−	0.519831i	$-0.825995\pi$
$881$		−	1.85902e13i		−	1.03966i	0.854269	−	0.519831i	$-0.174005\pi$
$882$	1.92158e13	−	4.05740e13i	1.06918	−	2.25756i
$883$	−1.37340e13	−	1.37340e13i	−0.760281	−	0.760281i	0.216092	−	0.976373i	$-0.430669\pi$
$883$	−1.37340e13	−	1.37340e13i	−0.760281	−	0.760281i	−0.976373	+	0.216092i	$0.930669\pi$
$884$	5.91857e12	−	3.41709e12i	0.325973	−	0.188201i
$885$	−2.43626e13	−	1.47916e11i	−1.33499	−	0.00810531i
$886$	−3.18746e12	+	5.52084e12i	−0.173777	+	0.300991i
$887$	5.47834e12	−	2.04454e13i	0.297162	−	1.10902i	−0.642324	−	0.766433i	$-0.722030\pi$
$887$	5.47834e12	−	2.04454e13i	0.297162	−	1.10902i	0.939485	−	0.342589i	$-0.111304\pi$
$888$	−4.41235e13	+	4.41235e13i	−2.38129	+	2.38129i
$889$	−1.03986e13	+	2.83067e13i	−0.558363	+	1.51996i
$890$	7.39721e12	+	1.29939e13i	0.395197	+	0.694200i
$891$	−2.24038e12	−	3.88045e12i	−0.119089	−	0.206268i
$892$	1.86892e13	−	5.00776e12i	0.988438	−	0.264851i
$893$	1.32404e12	−	3.54776e11i	0.0696739	−	0.0186691i
$894$	4.76880e11	+	8.25980e11i	0.0249684	+	0.0432465i
$895$	1.29738e13	+	3.56087e12i	0.675868	+	0.185504i
$896$	1.31134e13	+	7.56906e13i	0.679719	+	3.92334i
$897$	5.81628e10	−	5.81628e10i	0.00299971	−	0.00299971i
$898$	3.65263e12	−	1.36318e13i	0.187440	−	0.699535i
$899$	−2.23849e12	+	3.87718e12i	−0.114298	+	0.197969i
$900$	−6.12493e13	+	3.43775e13i	−3.11179	+	1.74656i
$901$	−2.11113e13	+	1.21886e13i	−1.06722	+	0.616160i
$902$	−1.07414e13	−	1.07414e13i	−0.540295	−	0.540295i
$903$	3.30459e12	−	3.65157e13i	0.165395	−	1.82761i
$904$		−	7.19239e13i		−	3.58192i
$905$	−3.33012e12	−	1.27370e13i	−0.165022	−	0.631174i
$906$	−7.62531e13	−	4.40248e13i	−3.75994	−	2.17080i
$907$	−2.65395e12	−	9.90468e12i	−0.130215	−	0.485968i	0.869757	−	0.493480i	$-0.164275\pi$
$907$	−2.65395e12	−	9.90468e12i	−0.130215	−	0.485968i	−0.999972	+	0.00751220i	$0.997609\pi$
$908$	4.19829e13	+	1.12493e13i	2.04968	+	0.549211i
$909$	1.33403e13			0.648077
$910$	1.08014e12	−	2.88607e12i	0.0522150	−	0.139515i
$911$	−1.80852e13			−0.869945			−0.434972	−	0.900444i	$-0.643242\pi$
$911$	−1.80852e13			−0.869945			−0.434972	+	0.900444i	$0.643242\pi$
$912$	−3.22095e13	−	8.63050e12i	−1.54172	−	0.413104i
$913$	−3.66437e11	−	1.36756e12i	−0.0174534	−	0.0651371i
$914$	3.68262e13	+	2.12616e13i	1.74542	+	1.00772i
$915$	2.24950e13	+	1.31703e13i	1.06094	+	0.621154i
$916$		−	1.10083e14i		−	5.16643i
$917$	1.67171e13	−	2.37234e13i	0.780724	−	1.10793i
$918$	−2.25712e13	−	2.25712e13i	−1.04897	−	1.04897i
$919$	−1.74750e13	+	1.00892e13i	−0.808161	+	0.466592i	−0.846317	−	0.532680i	$-0.821185\pi$
$919$	−1.74750e13	+	1.00892e13i	−0.808161	+	0.466592i	0.0381560	+	0.999272i	$0.487852\pi$
$920$	−1.95258e12	+	1.92902e12i	−0.0898596	+	0.0887751i
$921$	1.24069e13	−	2.14893e13i	0.568190	−	0.984134i
$922$	−5.15210e11	+	1.92279e12i	−0.0234798	+	0.0876279i
$923$	−7.73129e11	+	7.73129e11i	−0.0350626	+	0.0350626i
$924$	3.28425e13	+	1.20649e13i	1.48222	+	0.544501i
$925$	−1.39273e13	+	3.55112e12i	−0.625501	+	0.159488i
$926$	1.57806e13	+	2.73329e13i	0.705302	+	1.22162i
$927$	6.08111e12	−	1.62943e12i	0.270473	−	0.0724730i
$928$	3.41221e13	−	9.14298e12i	1.51032	−	0.404689i
$929$	−1.36461e13	−	2.36357e13i	−0.601088	−	1.04111i	−0.992657	−	0.120965i	$-0.961401\pi$
$929$	−1.36461e13	−	2.36357e13i	−0.601088	−	1.04111i	0.391569	−	0.920149i	$-0.371932\pi$
$930$	−1.08533e13	+	3.95430e13i	−0.475759	+	1.73339i
$931$	6.05853e12	+	1.10562e12i	0.264298	+	0.0482318i
$932$	5.00153e13	−	5.00153e13i	2.17136	−	2.17136i
$933$	−1.64876e12	+	6.15326e12i	−0.0712345	+	0.265851i
$934$	2.06404e13	−	3.57502e13i	0.887477	−	1.53716i
$935$	−9.44304e10	+	1.55532e13i	−0.00404073	+	0.665531i
$936$	−6.91593e12	+	3.99291e12i	−0.294516	+	0.170039i
$937$	1.84739e13	+	1.84739e13i	0.782943	+	0.782943i	0.980326	−	0.197383i	$-0.0632443\pi$
$937$	1.84739e13	+	1.84739e13i	0.782943	+	0.782943i	−0.197383	+	0.980326i	$0.563244\pi$
$938$	9.09425e12	+	1.96557e13i	0.383578	+	0.829040i
$939$			9.63710e12i			0.404530i
$940$	−9.01373e12	+	1.53956e13i	−0.376556	+	0.643164i
$941$	3.74793e13	+	2.16387e13i	1.55825	+	0.899657i	0.997424	+	0.0717245i	$0.0228502\pi$
$941$	3.74793e13	+	2.16387e13i	1.55825	+	0.899657i	0.560828	+	0.827933i	$0.310483\pi$
$942$	1.40321e13	+	5.23684e13i	0.580621	+	2.16691i
$943$	8.97231e11	+	2.40412e11i	0.0369489	+	0.00990043i
$944$	8.46710e13			3.47025
$945$	−1.05323e13	−	1.01765e12i	−0.429614	−	0.0415104i
$946$	2.18620e13			0.887525
$947$	−1.26207e13	−	3.38171e12i	−0.509928	−	0.136635i	−0.00532397	−	0.999986i	$-0.501695\pi$
$947$	−1.26207e13	−	3.38171e12i	−0.509928	−	0.136635i	−0.504604	+	0.863351i	$0.668361\pi$
$948$	2.57615e13	+	9.61433e13i	1.03594	+	3.86618i
$949$	−1.26219e12	−	7.28728e11i	−0.0505159	−	0.0291654i
$950$	−9.15422e12	−	9.37927e12i	−0.364641	−	0.373605i
$951$			2.99091e13i			1.18575i
$952$	−1.54062e14	−	1.39423e13i	−6.07897	−	0.550135i
$953$	4.65754e11	+	4.65754e11i	0.0182910	+	0.0182910i	0.716193	−	0.697902i	$-0.245883\pi$
$953$	4.65754e11	+	4.65754e11i	0.0182910	+	0.0182910i	−0.697902	+	0.716193i	$0.745883\pi$
$954$	3.85597e13	−	2.22625e13i	1.50718	−	0.870173i
$955$	6.59096e12	+	6.67148e12i	0.256409	+	0.259542i
$956$	−6.27871e13	+	1.08750e14i	−2.43114	+	4.21086i
$957$	1.42724e12	−	5.32653e12i	0.0550038	−	0.205277i
$958$	−2.45066e13	+	2.45066e13i	−0.940023	+	0.940023i
$959$	−6.42535e12	−	7.70403e12i	−0.245309	−	0.294126i
$960$	1.45315e14	−	8.27251e13i	5.52190	−	3.14352i
$961$	−8.27035e12	−	1.43247e13i	−0.312801	−	0.541788i
$962$	−2.46731e12	+	6.61113e11i	−0.0928828	+	0.0248879i
$963$	4.71937e13	−	1.26455e13i	1.76834	−	0.473825i
$964$	−2.46886e13	−	4.27619e13i	−0.920767	−	1.59481i
$965$	6.50985e12	−	3.70595e12i	0.241656	−	0.137571i
$966$	−2.86751e12	+	4.96796e11i	−0.105952	+	0.0183561i
$967$	−9.79810e12	+	9.79810e12i	−0.360349	+	0.360349i	−0.863941	−	0.503593i	$-0.832011\pi$
$967$	−9.79810e12	+	9.79810e12i	−0.360349	+	0.360349i	0.503593	+	0.863941i	$0.332011\pi$
$968$	2.09442e13	−	7.81649e13i	0.766700	−	2.86136i
$969$	9.85815e12	−	1.70748e13i	0.359202	−	0.622156i
$970$	−5.18640e13	−	5.24976e13i	−1.88102	−	1.90400i
$971$	2.57410e13	−	1.48616e13i	0.929264	−	0.536511i	0.0426850	−	0.999089i	$-0.486409\pi$
$971$	2.57410e13	−	1.48616e13i	0.929264	−	0.536511i	0.886579	+	0.462578i	$0.153075\pi$
$972$	−7.58495e13	−	7.58495e13i	−2.72555	−	2.72555i
$973$	3.23037e13	−	1.49462e13i	1.15543	−	0.534592i
$974$			8.29782e13i			2.95426i
$975$	−3.27006e12	−	3.97093e10i	−0.115887	−	0.00140725i
$976$	−7.84555e13	−	4.52963e13i	−2.76757	−	1.59786i
$977$	−6.98145e12	−	2.60551e13i	−0.245143	−	0.914887i	−0.973311	−	0.229488i	$-0.926295\pi$
$977$	−6.98145e12	−	2.60551e13i	−0.245143	−	0.914887i	0.728168	−	0.685398i	$-0.240372\pi$
$978$	−1.39337e14	−	3.73352e13i	−4.87014	−	1.30495i
$979$	−4.44590e12			−0.154681
$980$	−6.62067e13	+	4.51801e13i	−2.29290	+	1.56470i
$981$	6.11906e13			2.10947
$982$	8.44014e13	+	2.26153e13i	2.89633	+	0.776069i
$983$	−5.10305e12	−	1.90449e13i	−0.174317	−	0.650559i	−0.996667	−	0.0815776i	$-0.974004\pi$
$983$	−5.10305e12	−	1.90449e13i	−0.174317	−	0.650559i	0.822350	−	0.568982i	$-0.192663\pi$
$984$	−1.38854e14	−	8.01676e13i	−4.72152	−	2.72597i
$985$	−1.76548e13	+	3.01547e13i	−0.597584	+	1.02068i
$986$			3.81091e13i			1.28405i
$987$	−1.09828e13	+	5.08152e12i	−0.368373	+	0.170438i
$988$	−1.21082e12	−	1.21082e12i	−0.0404271	−	0.0404271i
$989$	−1.15773e12	+	6.68415e11i	−0.0384790	+	0.0222158i
$990$	1.72476e11	−	2.84079e13i	0.00570652	−	0.939897i
$991$	4.54461e12	−	7.87150e12i	0.149681	−	0.259254i	−0.781429	−	0.623994i	$-0.785509\pi$
$991$	4.54461e12	−	7.87150e12i	0.149681	−	0.259254i	0.931109	+	0.364740i	$0.118842\pi$
$992$	2.02158e13	−	7.54462e13i	0.662808	−	2.47363i
$993$	4.35025e13	−	4.35025e13i	1.41985	−	1.41985i
$994$	3.81163e13	−	6.60366e12i	1.23843	−	0.214558i
$995$	1.36752e13	−	4.98245e13i	0.442313	−	1.61153i
$996$	−1.16792e13	−	2.02289e13i	−0.376049	−	0.651337i
$997$	2.63832e12	−	7.06935e11i	0.0845666	−	0.0226595i	−0.216288	−	0.976330i	$-0.569395\pi$
$997$	2.63832e12	−	7.06935e11i	0.0845666	−	0.0226595i	0.300854	+	0.953670i	$0.402728\pi$
$998$	6.18013e13	−	1.65596e13i	1.97202	−	0.528400i
$999$	4.38547e12	+	7.59586e12i	0.139307	+	0.241286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.1	✓	136
5.2	odd	4	inner	35.10.k.a.17.34	yes	136
7.5	odd	6	inner	35.10.k.a.33.34	yes	136
35.12	even	12	inner	35.10.k.a.12.1	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.1	✓	136	1.1	even	1	trivial
35.10.k.a.12.1	yes	136	35.12	even	12	inner
35.10.k.a.17.34	yes	136	5.2	odd	4	inner
35.10.k.a.33.34	yes	136	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-42.4707 - 11.3800i) q^{2} +(54.8950 + 204.871i) q^{3} +(1230.85 + 710.632i) q^{4} +(-1352.09 + 353.508i) q^{5} -9325.71i q^{6} +(-5765.26 + 2667.46i) q^{7} +(-28269.7 - 28269.7i) q^{8} +(-21912.6 + 12651.2i) q^{9} +(61447.3 + 373.073i) q^{10} +(-9135.71 + 15823.5i) q^{11} +(-78020.2 + 291175. i) q^{12} +(-5582.21 + 5582.21i) q^{13} +(275210. - 47680.2i) q^{14} +(-146647. - 257599. i) q^{15} +(515080. + 892145. i) q^{16} +(-588348. + 157647. i) q^{17} +(1.07461e6 - 287942. i) q^{18} +(76307.7 + 132169. i) q^{19} +(-1.91544e6 - 525725. i) q^{20} +(-862969. - 1.03470e6i) q^{21} +(568072. - 568072. i) q^{22} +(-12714.5 + 47451.2i) q^{23} +(4.23977e6 - 7.34349e6i) q^{24} +(1.70319e6 - 955952. i) q^{25} +(300606. - 173555. i) q^{26} +(-842789. - 842789. i) q^{27} +(-8.99176e6 - 813736. i) q^{28} +1.42296e6i q^{29} +(3.29671e6 + 1.26092e7i) q^{30} +(2.72474e6 + 1.57313e6i) q^{31} +(-6.42534e6 - 2.39797e7i) q^{32} +(-3.74328e6 - 1.00301e6i) q^{33} +2.67816e7 q^{34} +(6.85221e6 - 5.64472e6i) q^{35} -3.59615e7 q^{36} +(-7.10815e6 - 1.90462e6i) q^{37} +(-1.73676e6 - 6.48169e6i) q^{38} +(-1.45007e6 - 837196. i) q^{39} +(4.82168e7 + 2.82297e7i) q^{40} -1.89085e7i q^{41} +(2.48760e7 + 5.37652e7i) q^{42} +(1.92423e7 + 1.92423e7i) q^{43} +(-2.24894e7 + 1.29843e7i) q^{44} +(2.51556e7 - 2.48520e7i) q^{45} +(1.07999e6 - 1.87059e6i) q^{46} +(2.32464e6 - 8.67567e6i) q^{47} +(-1.54499e8 + 1.54499e8i) q^{48} +(2.61229e7 - 3.07572e7i) q^{49} +(-8.32143e7 + 2.12177e7i) q^{50} +(-6.45947e7 - 1.11881e8i) q^{51} +(-1.08378e7 + 2.90397e6i) q^{52} +(3.86579e7 - 1.03583e7i) q^{53} +(2.62029e7 + 4.53847e7i) q^{54} +(6.75860e6 - 2.46244e7i) q^{55} +(2.38390e8 + 8.75739e7i) q^{56} +(-2.28886e7 + 2.28886e7i) q^{57} +(1.61932e7 - 6.04340e7i) q^{58} +(4.10960e7 - 7.11804e7i) q^{59} +(2.55776e6 - 4.21277e8i) q^{60} +(-7.61586e7 + 4.39702e7i) q^{61} +(-9.78193e7 - 9.78193e7i) q^{62} +(9.25852e7 - 1.31389e8i) q^{63} +5.64112e8i q^{64} +(5.57431e6 - 9.52102e6i) q^{65} +(1.47566e8 + 8.51970e7i) q^{66} +(2.00687e7 + 7.48975e7i) q^{67} +(-8.36198e8 - 2.24059e8i) q^{68} -1.04193e7 q^{69} +(-3.55255e8 + 1.61757e8i) q^{70} +1.38499e8 q^{71} +(9.77108e8 + 2.61815e8i) q^{72} +(4.77827e7 + 1.78328e8i) q^{73} +(2.80214e8 + 1.61781e8i) q^{74} +(2.89343e8 + 2.96457e8i) q^{75} +2.16907e8i q^{76} +(1.04612e7 - 1.15596e8i) q^{77} +(5.20580e7 + 5.20580e7i) q^{78} +(2.85953e8 - 1.65095e8i) q^{79} +(-1.01182e9 - 1.02418e9i) q^{80} +(-1.22617e8 + 2.12378e8i) q^{81} +(-2.15178e8 + 8.03057e8i) q^{82} +(-5.47918e7 + 5.47918e7i) q^{83} +(-3.26892e8 - 1.88682e9i) q^{84} +(7.39772e8 - 4.21140e8i) q^{85} +(-5.98258e8 - 1.03621e9i) q^{86} +(-2.91522e8 + 7.81132e7i) q^{87} +(7.05589e8 - 1.89062e8i) q^{88} +(1.21663e8 + 2.10726e8i) q^{89} +(-1.35119e9 + 7.69210e8i) q^{90} +(1.72926e7 - 4.70732e7i) q^{91} +(-4.93700e7 + 4.93700e7i) q^{92} +(-1.72714e8 + 6.44576e8i) q^{93} +(-1.97458e8 + 3.42008e8i) q^{94} +(-1.49898e8 - 1.51729e8i) q^{95} +(4.56002e9 - 2.63273e9i) q^{96} +(-8.49197e8 - 8.49197e8i) q^{97} +(-1.45948e9 + 1.00900e9i) q^{98} -4.62313e8i 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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