LMFDB - Embedded newform 19.10.c.a.7.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,10,Mod(7,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19.7"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	19.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.78568088711$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	19.7
Dual form			19.10.c.a.11.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.32582 + 5.76048i) q^{2} +(-131.258 - 227.345i) q^{3} +(233.878 - 405.088i) q^{4} +(-77.5423 - 134.307i) q^{5} +(873.077 - 1512.21i) q^{6} -3034.24 q^{7} +6516.98 q^{8} +(-24615.6 + 42635.4i) q^{9} +(515.783 - 893.362i) q^{10} -8232.96 q^{11} -122793. q^{12} +(30100.6 - 52135.8i) q^{13} +(-10091.3 - 17478.7i) q^{14} +(-20356.0 + 35257.7i) q^{15} +(-98071.2 - 169864. i) q^{16} +(3650.67 + 6323.15i) q^{17} -327467. q^{18} +(-319734. + 469529. i) q^{19} -72541.7 q^{20} +(398267. + 689818. i) q^{21} +(-27381.3 - 47425.8i) q^{22} +(-897370. + 1.55429e6i) q^{23} +(-855402. - 1.48160e6i) q^{24} +(964537. - 1.67063e6i) q^{25} +400436. q^{26} +7.75683e6 q^{27} +(-709642. + 1.22914e6i) q^{28} +(3.22780e6 - 5.59072e6i) q^{29} -270801. q^{30} -8.52731e6 q^{31} +(2.32068e6 - 4.01953e6i) q^{32} +(1.08064e6 + 1.87172e6i) q^{33} +(-24282.9 + 42059.3i) q^{34} +(235282. + 407520. i) q^{35} +(1.15141e7 + 1.99430e7i) q^{36} +3.89204e6 q^{37} +(-3.76809e6 - 280256. i) q^{38} -1.58037e7 q^{39} +(-505341. - 875277. i) q^{40} +(-7.18606e6 - 1.24466e7i) q^{41} +(-2.64912e6 + 4.58842e6i) q^{42} +(-1.07420e7 - 1.86058e7i) q^{43} +(-1.92551e6 + 3.33508e6i) q^{44} +7.63499e6 q^{45} -1.19380e7 q^{46} +(1.20907e7 - 2.09418e7i) q^{47} +(-2.57452e7 + 4.45919e7i) q^{48} -3.11470e7 q^{49} +1.28315e7 q^{50} +(958357. - 1.65992e6i) q^{51} +(-1.40797e7 - 2.43868e7i) q^{52} +(-3.12697e7 + 5.41607e7i) q^{53} +(2.57978e7 + 4.46831e7i) q^{54} +(638403. + 1.10575e6i) q^{55} -1.97741e7 q^{56} +(1.48712e8 + 1.10607e7i) q^{57} +4.29403e7 q^{58} +(-4.03909e7 - 6.99592e7i) q^{59} +(9.52164e6 + 1.64920e7i) q^{60} +(7.77978e7 - 1.34750e8i) q^{61} +(-2.83603e7 - 4.91214e7i) q^{62} +(7.46895e7 - 1.29366e8i) q^{63} -6.95523e7 q^{64} -9.33628e6 q^{65} +(-7.18801e6 + 1.24500e7i) q^{66} +(-9.84979e7 + 1.70603e8i) q^{67} +3.41525e6 q^{68} +4.71146e8 q^{69} +(-1.56501e6 + 2.71067e6i) q^{70} +(4.29274e7 + 7.43524e7i) q^{71} +(-1.60419e8 + 2.77854e8i) q^{72} +(-9.37194e7 - 1.62327e8i) q^{73} +(1.29442e7 + 2.24201e7i) q^{74} -5.06411e8 q^{75} +(1.15422e8 + 2.39333e8i) q^{76} +2.49808e7 q^{77} +(-5.25603e7 - 9.10370e7i) q^{78} +(2.10548e8 + 3.64679e8i) q^{79} +(-1.52093e7 + 2.63433e7i) q^{80} +(-5.33634e8 - 9.24281e8i) q^{81} +(4.77990e7 - 8.27903e7i) q^{82} +2.50490e7 q^{83} +3.72583e8 q^{84} +(566163. - 980623. i) q^{85} +(7.14521e7 - 1.23759e8i) q^{86} -1.69469e9 q^{87} -5.36540e7 q^{88} +(4.65160e8 - 8.05681e8i) q^{89} +(2.53926e7 + 4.39812e7i) q^{90} +(-9.13324e7 + 1.58192e8i) q^{91} +(4.19750e8 + 7.27029e8i) q^{92} +(1.11927e9 + 1.93864e9i) q^{93} +1.60846e8 q^{94} +(8.78541e7 + 6.53425e6i) q^{95} -1.21843e9 q^{96} +(4.18681e8 + 7.25176e8i) q^{97} +(-1.03589e8 - 1.79422e8i) q^{98} +(2.02659e8 - 3.51016e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9} + 41180 q^{10} - 114810 q^{11} + 235458 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} - 279203 q^{16}+ \cdots - 736622698 q^{99}+O(q^{100}) $ 28 * q + 15 * q^2 - 74 * q^3 - 2987 * q^4 - 285 * q^5 - 535 * q^6 - 2676 * q^7 - 24270 * q^8 - 57928 * q^9 + 41180 * q^10 - 114810 * q^11 + 235458 * q^12 + 98671 * q^13 - 148290 * q^14 + 428251 * q^15 - 279203 * q^16 + 466251 * q^17 + 734964 * q^18 + 387157 * q^19 - 3343620 * q^20 + 689090 * q^21 - 1689395 * q^22 - 3087747 * q^23 - 234183 * q^24 - 3260823 * q^25 + 9033144 * q^26 + 4216540 * q^27 - 703814 * q^28 + 7831383 * q^29 - 11859224 * q^30 - 9265632 * q^31 + 11470815 * q^32 + 22791973 * q^33 + 13457096 * q^34 - 13222428 * q^35 + 7355018 * q^36 + 27205020 * q^37 - 67677738 * q^38 - 20775702 * q^39 - 16500258 * q^40 + 20419440 * q^41 - 10220798 * q^42 + 27415427 * q^43 + 41775405 * q^44 - 85982588 * q^45 - 137234708 * q^46 - 90906681 * q^47 + 33057375 * q^48 + 229824892 * q^49 + 44406714 * q^50 + 134429123 * q^51 + 66195006 * q^52 + 47827863 * q^53 - 130507669 * q^54 - 157712310 * q^55 + 382459116 * q^56 - 162912873 * q^57 - 344026048 * q^58 + 255540 * q^59 + 287916794 * q^60 + 304035459 * q^61 + 693626280 * q^62 - 122148024 * q^63 - 908491514 * q^64 - 1424960190 * q^65 - 611099417 * q^66 + 165758480 * q^67 + 357518508 * q^68 + 271237278 * q^69 + 1167527028 * q^70 + 685508589 * q^71 + 142349670 * q^72 - 602867050 * q^73 - 82104492 * q^74 + 1900274774 * q^75 - 1298297525 * q^76 - 491994756 * q^77 - 911449840 * q^78 + 78162339 * q^79 + 227607150 * q^80 + 1230916118 * q^81 + 360208019 * q^82 + 413839926 * q^83 - 467304924 * q^84 - 1440537237 * q^85 + 936824310 * q^86 - 678876318 * q^87 - 1646777694 * q^88 + 1256827551 * q^89 + 1879090924 * q^90 + 537759588 * q^91 - 677003592 * q^92 - 492493440 * q^93 - 848375184 * q^94 - 2034458607 * q^95 - 6041588930 * q^96 + 2109813492 * q^97 + 2689941591 * q^98 - 736622698 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	3.32582	+	5.76048i	0.146982	+	0.254580i	0.930111	−	0.367280i	$-0.119711\pi$
$2$	3.32582	+	5.76048i	0.146982	+	0.254580i	−0.783129	+	0.621859i	$0.786377\pi$
$3$	−131.258	−	227.345i	−0.935575	−	1.62046i	−0.773606	−	0.633667i	$-0.781549\pi$
$3$	−131.258	−	227.345i	−0.935575	−	1.62046i	−0.161969	−	0.986796i	$-0.551784\pi$
$4$	233.878	−	405.088i	0.456793	−	0.791188i
$5$	−77.5423	−	134.307i	−0.0554848	−	0.0961024i	0.836949	−	0.547281i	$-0.184337\pi$
$5$	−77.5423	−	134.307i	−0.0554848	−	0.0961024i	−0.892434	+	0.451179i	$0.851004\pi$
$6$	873.077	−	1512.21i	0.275025	−	0.476357i
$7$	−3034.24			−0.477649			−0.238824	−	0.971063i	$-0.576762\pi$
$7$	−3034.24			−0.477649			−0.238824	+	0.971063i	$0.576762\pi$
$8$	6516.98			0.562524
$9$	−24615.6	+	42635.4i	−1.25060	+	2.16610i
$10$	515.783	−	893.362i	0.0163105	−	0.0282506i
$11$	−8232.96			−0.169547			−0.0847733	−	0.996400i	$-0.527017\pi$
$11$	−8232.96			−0.169547			−0.0847733	+	0.996400i	$0.527017\pi$
$12$	−122793.			−1.70946
$13$	30100.6	−	52135.8i	0.292301	−	0.506280i	−0.682053	−	0.731303i	$-0.738913\pi$
$13$	30100.6	−	52135.8i	0.292301	−	0.506280i	0.974353	+	0.225023i	$0.0722458\pi$
$14$	−10091.3	−	17478.7i	−0.0702056	−	0.121600i
$15$	−20356.0	+	35257.7i	−0.103820	+	0.179822i
$16$	−98071.2	−	169864.i	−0.374112	−	0.647981i
$17$	3650.67	+	6323.15i	0.0106011	+	0.0183617i	0.871277	−	0.490791i	$-0.163292\pi$
$17$	3650.67	+	6323.15i	0.0106011	+	0.0183617i	−0.860676	+	0.509153i	$0.829959\pi$
$18$	−327467.			−0.735261
$19$	−319734.	+	469529.i	−0.562857	+	0.826554i
$19$	−319734.	+	469529.i	−0.562857	+	0.826554i
$20$	−72541.7			−0.101380
$21$	398267.	+	689818.i	0.446876	+	0.774012i
$22$	−27381.3	−	47425.8i	−0.0249203	−	0.0431631i
$23$	−897370.	+	1.55429e6i	−0.668646	+	1.15813i	0.309637	+	0.950855i	$0.399793\pi$
$23$	−897370.	+	1.55429e6i	−0.668646	+	1.15813i	−0.978283	+	0.207274i	$0.933541\pi$
$24$	−855402.	−	1.48160e6i	−0.526283	−	0.911550i
$25$	964537.	−	1.67063e6i	0.493843	−	0.855361i
$26$	400436.			0.171851
$27$	7.75683e6			2.80897
$28$	−709642.	+	1.22914e6i	−0.218187	+	0.377910i
$29$	3.22780e6	−	5.59072e6i	0.847453	−	1.46783i	−0.0360200	−	0.999351i	$-0.511468\pi$
$29$	3.22780e6	−	5.59072e6i	0.847453	−	1.46783i	0.883473	−	0.468481i	$-0.155199\pi$
$30$	−270801.			−0.0610387
$31$	−8.52731e6			−1.65838			−0.829191	−	0.558965i	$-0.811198\pi$
$31$	−8.52731e6			−1.65838			−0.829191	+	0.558965i	$0.811198\pi$
$32$	2.32068e6	−	4.01953e6i	0.391237	−	0.677643i
$33$	1.08064e6	+	1.87172e6i	0.158624	+	0.274744i
$34$	−24282.9	+	42059.3i	−0.00311635	+	0.00539768i
$35$	235282.	+	407520.i	0.0265022	+	0.0459032i
$36$	1.15141e7	+	1.99430e7i	1.14253	+	1.97892i
$37$	3.89204e6			0.341405			0.170703	−	0.985323i	$-0.445396\pi$
$37$	3.89204e6			0.341405			0.170703	+	0.985323i	$0.445396\pi$
$38$	−3.76809e6	−	280256.i	−0.293154	−	0.0218036i
$39$	−1.58037e7			−1.09388
$40$	−505341.	−	875277.i	−0.0312115	−	0.0540599i
$41$	−7.18606e6	−	1.24466e7i	−0.397158	−	0.687898i	0.596216	−	0.802824i	$-0.296670\pi$
$41$	−7.18606e6	−	1.24466e7i	−0.397158	−	0.687898i	−0.993374	+	0.114926i	$0.963337\pi$
$42$	−2.64912e6	+	4.58842e6i	−0.131365	+	0.227531i
$43$	−1.07420e7	−	1.86058e7i	−0.479158	−	0.829926i	0.520557	−	0.853827i	$-0.325725\pi$
$43$	−1.07420e7	−	1.86058e7i	−0.479158	−	0.829926i	−0.999714	+	0.0239016i	$0.992391\pi$
$44$	−1.92551e6	+	3.33508e6i	−0.0774477	+	0.134143i
$45$	7.63499e6			0.277557
$46$	−1.19380e7			−0.393115
$47$	1.20907e7	−	2.09418e7i	0.361420	−	0.625998i	−0.626775	−	0.779201i	$-0.715625\pi$
$47$	1.20907e7	−	2.09418e7i	0.361420	−	0.625998i	0.988195	+	0.153202i	$0.0489587\pi$
$48$	−2.57452e7	+	4.45919e7i	−0.700020	+	1.21247i
$49$	−3.11470e7			−0.771852
$50$	1.28315e7			0.290343
$51$	958357.	−	1.65992e6i	0.0198363	−	0.0343575i
$52$	−1.40797e7	−	2.43868e7i	−0.267042	−	0.462530i
$53$	−3.12697e7	+	5.41607e7i	−0.544355	+	0.942851i	0.454292	+	0.890853i	$0.349892\pi$
$53$	−3.12697e7	+	5.41607e7i	−0.544355	+	0.942851i	−0.998647	+	0.0519981i	$0.983441\pi$
$54$	2.57978e7	+	4.46831e7i	0.412867	+	0.715107i
$55$	638403.	+	1.10575e6i	0.00940725	+	0.0162938i
$56$	−1.97741e7			−0.268689
$57$	1.48712e8	+	1.10607e7i	1.86600	+	0.138786i
$58$	4.29403e7			0.498241
$59$	−4.03909e7	−	6.99592e7i	−0.433960	−	0.751641i	0.563250	−	0.826287i	$-0.309551\pi$
$59$	−4.03909e7	−	6.99592e7i	−0.433960	−	0.751641i	−0.997210	+	0.0746455i	$0.976217\pi$
$60$	9.52164e6	+	1.64920e7i	0.0948487	+	0.164283i
$61$	7.77978e7	−	1.34750e8i	0.719421	−	1.24607i	−0.241809	−	0.970324i	$-0.577741\pi$
$61$	7.77978e7	−	1.34750e8i	0.719421	−	1.24607i	0.961230	−	0.275749i	$-0.0889259\pi$
$62$	−2.83603e7	−	4.91214e7i	−0.243752	−	0.422191i
$63$	7.46895e7	−	1.29366e8i	0.597348	−	1.03464i
$64$	−6.95523e7			−0.518205
$65$	−9.33628e6			−0.0648729
$66$	−7.18801e6	+	1.24500e7i	−0.0466295	+	0.0807647i
$67$	−9.84979e7	+	1.70603e8i	−0.597159	+	1.03431i	0.396079	+	0.918217i	$0.370371\pi$
$67$	−9.84979e7	+	1.70603e8i	−0.597159	+	1.03431i	−0.993238	+	0.116094i	$0.962963\pi$
$68$	3.41525e6			0.0193701
$69$	4.71146e8			2.50227
$70$	−1.56501e6	+	2.71067e6i	−0.00779068	+	0.0134939i
$71$	4.29274e7	+	7.43524e7i	0.200480	+	0.347242i	0.948683	−	0.316228i	$-0.102416\pi$
$71$	4.29274e7	+	7.43524e7i	0.200480	+	0.347242i	−0.748203	+	0.663470i	$0.769083\pi$
$72$	−1.60419e8	+	2.77854e8i	−0.703493	+	1.21849i
$73$	−9.37194e7	−	1.62327e8i	−0.386257	−	0.669017i	0.605686	−	0.795704i	$-0.292899\pi$
$73$	−9.37194e7	−	1.62327e8i	−0.386257	−	0.669017i	−0.991943	+	0.126687i	$0.959566\pi$
$74$	1.29442e7	+	2.24201e7i	0.0501803	+	0.0869148i
$75$	−5.06411e8			−1.84811
$76$	1.15422e8	+	2.39333e8i	0.396851	+	0.822890i
$77$	2.49808e7			0.0809837
$78$	−5.25603e7	−	9.10370e7i	−0.160780	−	0.278479i
$79$	2.10548e8	+	3.64679e8i	0.608175	+	1.05339i	0.991541	+	0.129794i	$0.0414314\pi$
$79$	2.10548e8	+	3.64679e8i	0.608175	+	1.05339i	−0.383366	+	0.923596i	$0.625235\pi$
$80$	−1.52093e7	+	2.63433e7i	−0.0415150	+	0.0719061i
$81$	−5.33634e8	−	9.24281e8i	−1.37740	−	2.38573i
$82$	4.77990e7	−	8.27903e7i	0.116750	−	0.202217i
$83$	2.50490e7			0.0579348			0.0289674	−	0.999580i	$-0.490778\pi$
$83$	2.50490e7			0.0579348			0.0289674	+	0.999580i	$0.490778\pi$
$84$	3.72583e8			0.816519
$85$	566163.	−	980623.i	0.00117640	−	0.00203759i
$86$	7.14521e7	−	1.23759e8i	0.140855	−	0.243968i
$87$	−1.69469e9			−3.17142
$88$	−5.36540e7			−0.0953741
$89$	4.65160e8	−	8.05681e8i	0.785864	−	1.36116i	−0.142618	−	0.989778i	$-0.545552\pi$
$89$	4.65160e8	−	8.05681e8i	0.785864	−	1.36116i	0.928482	−	0.371378i	$-0.121115\pi$
$90$	2.53926e7	+	4.39812e7i	0.0407958	+	0.0706604i
$91$	−9.13324e7	+	1.58192e8i	−0.139617	+	0.241824i
$92$	4.19750e8	+	7.27029e8i	0.610866	+	1.05805i
$93$	1.11927e9	+	1.93864e9i	1.55154	+	2.68735i
$94$	1.60846e8			0.212489
$95$	8.78541e7	+	6.53425e6i	0.110664	+	0.00823075i
$96$	−1.21843e9			−1.46413
$97$	4.18681e8	+	7.25176e8i	0.480187	+	0.831708i	0.999742	−	0.0227294i	$-0.00723562\pi$
$97$	4.18681e8	+	7.25176e8i	0.480187	+	0.831708i	−0.519555	+	0.854437i	$0.673902\pi$
$98$	−1.03589e8	−	1.79422e8i	−0.113448	−	0.196498i
$99$	2.02659e8	−	3.51016e8i	0.212035	−	0.367255i
$100$	−4.51168e8	−	7.81445e8i	−0.451168	−	0.781445i
$101$	5.16312e8	−	8.94279e8i	0.493704	−	0.855120i	−0.506270	−	0.862375i	$-0.668976\pi$
$101$	5.16312e8	−	8.94279e8i	0.493704	−	0.855120i	0.999974	+	0.00725530i	$0.00230945\pi$
$102$	1.27493e7			0.0116623
$103$	−3.28210e8			−0.287333			−0.143666	−	0.989626i	$-0.545889\pi$
$103$	−3.28210e8			−0.287333			−0.143666	+	0.989626i	$0.545889\pi$
$104$	1.96165e8	−	3.39767e8i	0.164426	−	0.284795i
$105$	6.17650e7	−	1.06980e8i	0.0495896	−	0.0858917i
$106$	−4.15989e8			−0.320041
$107$	1.86323e9			1.37416			0.687082	−	0.726580i	$-0.258891\pi$
$107$	1.86323e9			1.37416			0.687082	+	0.726580i	$0.258891\pi$
$108$	1.81415e9	−	3.14220e9i	1.28312	−	2.22242i
$109$	8.36386e8	+	1.44866e9i	0.567528	+	0.982988i	0.996810	+	0.0798169i	$0.0254335\pi$
$109$	8.36386e8	+	1.44866e9i	0.567528	+	0.982988i	−0.429281	+	0.903171i	$0.641233\pi$
$110$	−4.24642e6	+	7.35502e6i	−0.00276539	+	0.00478979i
$111$	−5.10860e8	−	8.84835e8i	−0.319410	−	0.553234i
$112$	2.97572e8	+	5.15409e8i	0.178694	+	0.309507i
$113$	−1.00637e9			−0.580637			−0.290319	−	0.956930i	$-0.593761\pi$
$113$	−1.00637e9			−0.580637			−0.290319	+	0.956930i	$0.593761\pi$
$114$	4.30876e8	+	8.93441e8i	0.238935	+	0.495444i
$115$	2.78337e8			0.148399
$116$	−1.50982e9	−	2.61509e9i	−0.774221	−	1.34099i
$117$	1.48189e9	+	2.56670e9i	0.731103	+	1.26631i
$118$	2.68666e8	−	4.65343e8i	0.127568	−	0.220955i
$119$	−1.10770e7	−	1.91860e7i	−0.00506362	−	0.00877046i
$120$	−1.32660e8	+	2.29773e8i	−0.0584014	+	0.101154i
$121$	−2.29017e9			−0.971254
$122$	1.03496e9			0.422967
$123$	−1.88645e9	+	3.26742e9i	−0.743142	+	1.28716i
$124$	−1.99435e9	+	3.45432e9i	−0.757537	+	1.31209i
$125$	−6.02069e8			−0.220572
$126$	9.93614e8			0.351197
$127$	1.38995e7	−	2.40746e7i	0.00474113	−	0.00821188i	−0.863645	−	0.504100i	$-0.831824\pi$
$127$	1.38995e7	−	2.40746e7i	0.00474113	−	0.00821188i	0.868386	+	0.495888i	$0.165158\pi$
$128$	−1.41951e9	−	2.45866e9i	−0.467404	−	0.809567i
$129$	−2.81995e9	+	4.88429e9i	−0.896576	+	1.55291i
$130$	−3.10507e7	−	5.37815e7i	−0.00953514	−	0.0165153i
$131$	−2.24366e9	−	3.88613e9i	−0.665635	−	1.15291i	−0.979113	−	0.203318i	$-0.934828\pi$
$131$	−2.24366e9	−	3.88613e9i	−0.665635	−	1.15291i	0.313478	−	0.949595i	$-0.398506\pi$
$132$	1.01095e9			0.289832
$133$	9.70150e8	−	1.42466e9i	0.268848	−	0.394803i
$134$	−1.31034e9			−0.351086
$135$	−6.01482e8	−	1.04180e9i	−0.155855	−	0.269949i
$136$	2.37913e7	+	4.12078e7i	0.00596340	+	0.0103289i
$137$	2.92685e9	−	5.06945e9i	0.709836	−	1.22947i	−0.255082	−	0.966919i	$-0.582102\pi$
$137$	2.92685e9	−	5.06945e9i	0.709836	−	1.22947i	0.964918	−	0.262552i	$-0.0845642\pi$
$138$	1.56695e9	+	2.71403e9i	0.367789	+	0.637028i
$139$	6.19380e8	−	1.07280e9i	0.140731	−	0.243754i	−0.787041	−	0.616901i	$-0.788388\pi$
$139$	6.19380e8	−	1.07280e9i	0.140731	−	0.243754i	0.927772	+	0.373147i	$0.121721\pi$
$140$	2.20109e8			0.0484241
$141$	−6.34800e9			−1.35254
$142$	−2.85537e8	+	4.94565e8i	−0.0589339	+	0.102076i
$143$	−2.47817e8	+	4.29232e8i	−0.0495586	+	0.0858380i
$144$	9.65631e9			1.87146
$145$	−1.00116e9			−0.188083
$146$	6.23387e8	−	1.07974e9i	0.113545	−	0.196666i
$147$	4.08828e9	+	7.08110e9i	0.722125	+	1.25076i
$148$	9.10263e8	−	1.57662e9i	0.155951	−	0.270116i
$149$	−4.16535e9	−	7.21461e9i	−0.692331	−	1.19915i	−0.971072	−	0.238786i	$-0.923251\pi$
$149$	−4.16535e9	−	7.21461e9i	−0.692331	−	1.19915i	0.278741	−	0.960366i	$-0.410083\pi$
$150$	−1.68423e9	−	2.91717e9i	−0.271638	−	0.470491i
$151$	3.02884e7			0.00474111			0.00237056	−	0.999997i	$-0.499245\pi$
$151$	3.02884e7			0.00474111			0.00237056	+	0.999997i	$0.499245\pi$
$152$	−2.08370e9	+	3.05991e9i	−0.316621	+	0.464957i
$153$	−3.59454e8			−0.0530312
$154$	8.30815e7	+	1.43901e8i	0.0119031	+	0.0206168i
$155$	6.61227e8	+	1.14528e9i	0.0920149	+	0.159375i
$156$	−3.69614e9	+	6.40190e9i	−0.499675	+	0.865463i
$157$	4.29521e9	+	7.43952e9i	0.564204	+	0.977230i	0.997123	+	0.0757971i	$0.0241501\pi$
$157$	4.29521e9	+	7.43952e9i	0.564204	+	0.977230i	−0.432919	+	0.901433i	$0.642517\pi$
$158$	−1.40049e9	+	2.42571e9i	−0.178781	+	0.309658i
$159$	1.64175e10			2.03714
$160$	−7.19803e8			−0.0868308
$161$	2.72284e9	−	4.71609e9i	0.319378	−	0.553179i
$162$	3.54954e9	−	6.14798e9i	0.404906	−	0.701317i
$163$	−7.93769e6			−0.000880745			−0.000440372	−	1.00000i	$-0.500140\pi$
$163$	−7.93769e6			−0.000880745			−0.000440372		1.00000i	$0.500140\pi$
$164$	−6.72264e9			−0.725676
$165$	1.67590e8	−	2.90275e8i	0.0176024	−	0.0304882i
$166$	8.33085e7	+	1.44295e8i	0.00851536	+	0.0147490i
$167$	9.61418e9	−	1.66523e10i	0.956507	−	1.65672i	0.225627	−	0.974214i	$-0.427557\pi$
$167$	9.61418e9	−	1.66523e10i	0.956507	−	1.65672i	0.730881	−	0.682505i	$-0.239110\pi$
$168$	2.59549e9	+	4.49553e9i	0.251379	+	0.435401i
$169$	3.49016e9	+	6.04513e9i	0.329121	+	0.570053i
$170$	7.53182e6			0.000691639
$171$	−1.21481e10	−	2.51897e10i	−1.08649	−	2.25290i
$172$	−1.00493e10			−0.875503
$173$	9.33981e9	+	1.61770e10i	0.792739	+	1.37306i	0.924265	+	0.381752i	$0.124679\pi$
$173$	9.33981e9	+	1.61770e10i	0.792739	+	1.37306i	−0.131525	+	0.991313i	$0.541987\pi$
$174$	−5.63624e9	−	9.76225e9i	−0.466141	−	0.807380i
$175$	−2.92664e9	+	5.06908e9i	−0.235883	+	0.408562i
$176$	8.07417e8	+	1.39849e9i	0.0634294	+	0.109863i
$177$	−1.06032e10	+	1.83653e10i	−0.812004	+	1.40643i
$178$	6.18815e9			0.462030
$179$	1.99130e10			1.44977			0.724884	−	0.688871i	$-0.241894\pi$
$179$	1.99130e10			1.44977			0.724884	+	0.688871i	$0.241894\pi$
$180$	1.78566e9	−	3.09285e9i	0.126786	−	0.219600i
$181$	3.10006e9	−	5.36947e9i	0.214692	−	0.371858i	−0.738485	−	0.674270i	$-0.764458\pi$
$181$	3.10006e9	−	5.36947e9i	0.214692	−	0.371858i	0.953177	+	0.302412i	$0.0977917\pi$
$182$	−1.21502e9			−0.0820846
$183$	−4.08462e10			−2.69229
$184$	−5.84814e9	+	1.01293e10i	−0.376130	+	0.651476i
$185$	−3.01798e8	−	5.22730e8i	−0.0189428	−	0.0328099i
$186$	−7.44500e9	+	1.28951e10i	−0.456096	+	0.789982i
$187$	−3.00559e7	−	5.20583e7i	−0.00179739	−	0.00311317i
$188$	−5.65551e9	−	9.79563e9i	−0.330188	−	0.571903i
$189$	−2.35361e10			−1.34170
$190$	2.54546e8	+	5.27814e8i	0.0141702	+	0.0293825i
$191$	1.08813e10			0.591602			0.295801	−	0.955250i	$-0.404414\pi$
$191$	1.08813e10			0.591602			0.295801	+	0.955250i	$0.404414\pi$
$192$	9.12926e9	+	1.58123e10i	0.484820	+	0.839732i
$193$	−2.37868e9	−	4.12000e9i	−0.123404	−	0.213742i	0.797704	−	0.603049i	$-0.206048\pi$
$193$	−2.37868e9	−	4.12000e9i	−0.123404	−	0.213742i	−0.921108	+	0.389308i	$0.872714\pi$
$194$	−2.78491e9	+	4.82360e9i	−0.141157	+	0.244492i
$195$	1.22546e9	+	2.12255e9i	0.0606935	+	0.105124i
$196$	−7.28459e9	+	1.26173e10i	−0.352576	+	0.610680i
$197$	−8.90251e8			−0.0421128			−0.0210564	−	0.999778i	$-0.506703\pi$
$197$	−8.90251e8			−0.0421128			−0.0210564	+	0.999778i	$0.506703\pi$
$198$	2.69603e9			0.124661
$199$	8.86513e9	−	1.53549e10i	0.400725	−	0.694076i	−0.593089	−	0.805137i	$-0.702092\pi$
$199$	8.86513e9	−	1.53549e10i	0.400725	−	0.694076i	0.993814	+	0.111061i	$0.0354250\pi$
$200$	6.28586e9	−	1.08874e10i	0.277799	−	0.481161i
$201$	5.17143e10			2.23475
$202$	6.86864e9			0.290262
$203$	−9.79392e9	+	1.69636e10i	−0.404785	+	0.701108i
$204$	−4.48277e8	−	7.76438e8i	−0.0181222	−	0.0313885i
$205$	−1.11445e9	+	1.93028e9i	−0.0440724	+	0.0763357i
$206$	−1.09157e9	−	1.89065e9i	−0.0422326	−	0.0731491i
$207$	−4.41786e10	−	7.65195e10i	−1.67242	−	2.89671i
$208$	−1.18080e10			−0.437413
$209$	2.63236e9	−	3.86562e9i	0.0954305	−	0.140139i
$210$	8.21677e8			0.0291551
$211$	−5.17502e9	−	8.96339e9i	−0.179738	−	0.311316i	0.762053	−	0.647515i	$-0.224192\pi$
$211$	−5.17502e9	−	8.96339e9i	−0.179738	−	0.311316i	−0.941791	+	0.336199i	$0.890858\pi$
$212$	1.46266e10	+	2.53340e10i	0.497315	+	0.861375i
$213$	1.12691e10	−	1.95186e10i	0.375129	−	0.649742i
$214$	6.19675e9	+	1.07331e10i	0.201977	+	0.349834i
$215$	−1.66592e9	+	2.88547e9i	−0.0531719	+	0.0920964i
$216$	5.05511e10			1.58011
$217$	2.58739e10			0.792124
$218$	−5.56333e9	+	9.63597e9i	−0.166833	+	0.288962i
$219$	−2.46027e10	+	4.26132e10i	−0.722745	+	1.25183i
$220$	5.97233e8			0.0171887
$221$	4.39550e8			0.0123949
$222$	3.39805e9	−	5.88560e9i	0.0938948	−	0.162631i
$223$	−2.44083e9	−	4.22764e9i	−0.0660945	−	0.114479i	0.831084	−	0.556146i	$-0.187721\pi$
$223$	−2.44083e9	−	4.22764e9i	−0.0660945	−	0.114479i	−0.897179	+	0.441667i	$0.854387\pi$
$224$	−7.04150e9	+	1.21962e10i	−0.186874	+	0.323675i
$225$	4.74852e10	+	8.22469e10i	1.23520	+	2.13943i
$226$	−3.34700e9	−	5.79718e9i	−0.0853430	−	0.147818i
$227$	−2.19389e10			−0.548402			−0.274201	−	0.961672i	$-0.588413\pi$
$227$	−2.19389e10			−0.548402			−0.274201	+	0.961672i	$0.588413\pi$
$228$	3.92611e10	−	5.76549e10i	0.962179	−	1.41296i
$229$	−3.29643e10			−0.792107			−0.396053	−	0.918227i	$-0.629621\pi$
$229$	−3.29643e10			−0.792107			−0.396053	+	0.918227i	$0.629621\pi$
$230$	9.25696e8	+	1.60335e9i	0.0218119	+	0.0377793i
$231$	−3.27892e9	−	5.67925e9i	−0.0757663	−	0.131231i
$232$	2.10355e10	−	3.64346e10i	0.476713	−	0.825691i
$233$	1.34212e10	+	2.32462e10i	0.298325	+	0.516715i	0.975753	−	0.218875i	$-0.0702386\pi$
$233$	1.34212e10	+	2.32462e10i	0.298325	+	0.516715i	−0.677428	+	0.735589i	$0.736905\pi$
$234$	−9.85696e9	+	1.70728e10i	−0.214917	+	0.372248i
$235$	−3.75017e9			−0.0802132
$236$	−3.77862e10			−0.792919
$237$	5.52719e10	−	9.57338e10i	1.13799	−	1.97105i
$238$	7.36803e7	−	1.27618e8i	0.00148852	−	0.00257819i
$239$	−1.46906e10			−0.291239			−0.145619	−	0.989341i	$-0.546517\pi$
$239$	−1.46906e10			−0.291239			−0.145619	+	0.989341i	$0.546517\pi$
$240$	7.98536e9			0.155362
$241$	2.65114e10	−	4.59190e10i	0.506239	−	0.876831i	−0.493735	−	0.869612i	$-0.664369\pi$
$241$	2.65114e10	−	4.59190e10i	0.506239	−	0.876831i	0.999974	−	0.00721909i	$-0.00229793\pi$
$242$	−7.61667e9	−	1.31925e10i	−0.142757	−	0.247262i
$243$	−6.37480e10	+	1.10415e11i	−1.17284	+	2.03142i
$244$	−3.63904e10	−	6.30299e10i	−0.657252	−	1.13839i
$245$	2.41521e9	+	4.18327e9i	0.0428260	+	0.0741768i
$246$	−2.50959e10			−0.436913
$247$	1.48551e10	+	3.08027e10i	0.253944	+	0.526566i
$248$	−5.55723e10			−0.932880
$249$	−3.28787e9	−	5.69477e9i	−0.0542024	−	0.0938812i
$250$	−2.00237e9	−	3.46821e9i	−0.0324201	−	0.0561533i
$251$	−1.94011e10	+	3.36036e10i	−0.308527	+	0.534385i	−0.978040	−	0.208415i	$-0.933170\pi$
$251$	−1.94011e10	+	3.36036e10i	−0.308527	+	0.534385i	0.669513	+	0.742800i	$0.266503\pi$
$252$	−3.49365e10	−	6.05117e10i	−0.545728	−	0.945229i
$253$	7.38802e9	−	1.27964e10i	0.113367	−	0.196357i
$254$	1.84909e8			0.00278744
$255$	−2.97253e8			−0.00440246
$256$	−8.36336e9	+	1.44858e10i	−0.121703	+	0.210796i
$257$	−2.35229e10	+	4.07428e10i	−0.336350	+	0.582575i	−0.983743	−	0.179581i	$-0.942526\pi$
$257$	−2.35229e10	+	4.07428e10i	−0.336350	+	0.582575i	0.647393	+	0.762156i	$0.275859\pi$
$258$	−3.75145e10			−0.527121
$259$	−1.18094e10			−0.163072
$260$	−2.18355e9	+	3.78202e9i	−0.0296335	+	0.0513267i
$261$	1.58908e11	+	2.75237e11i	2.11965	+	3.67134i
$262$	1.49240e10	−	2.58491e10i	0.195672	−	0.338914i
$263$	−8.42294e9	−	1.45890e10i	−0.108558	−	0.188028i	0.806628	−	0.591059i	$-0.201290\pi$
$263$	−8.42294e9	−	1.45890e10i	−0.108558	−	0.188028i	−0.915186	+	0.403031i	$0.867957\pi$
$264$	7.04249e9	+	1.21980e10i	0.0892296	+	0.154550i
$265$	9.69890e9			0.120814
$266$	1.14333e10	+	8.50364e8i	0.140025	+	0.0104145i
$267$	−2.44223e11			−2.94094
$268$	4.60730e10	+	7.98007e10i	0.545556	+	0.944931i
$269$	4.56595e9	+	7.90847e9i	0.0531675	+	0.0920888i	0.891384	−	0.453248i	$-0.149735\pi$
$269$	4.56595e9	+	7.90847e9i	0.0531675	+	0.0920888i	−0.838217	+	0.545337i	$0.816402\pi$
$270$	4.00084e9	−	6.92966e9i	0.0458157	−	0.0793551i
$271$	−4.56645e10	−	7.90933e10i	−0.514301	−	0.890795i	−0.999862	−	0.0165928i	$-0.994718\pi$
$271$	−4.56645e10	−	7.90933e10i	−0.514301	−	0.890795i	0.485561	−	0.874203i	$-0.338615\pi$
$272$	7.16052e8	−	1.24024e9i	0.00793203	−	0.0137387i
$273$	4.79523e10			0.522489
$274$	3.89367e10			0.417332
$275$	−7.94100e9	+	1.37542e10i	−0.0837294	+	0.145024i
$276$	1.10191e11	−	1.90856e11i	1.14302	−	1.97977i
$277$	−1.22484e11			−1.25003			−0.625016	−	0.780612i	$-0.714908\pi$
$277$	−1.22484e11			−1.25003			−0.625016	+	0.780612i	$0.714908\pi$
$278$	8.23978e9			0.0827397
$279$	2.09905e11	−	3.63565e11i	2.07397	−	3.59223i
$280$	1.53333e9	+	2.65580e9i	0.0149081	+	0.0258217i
$281$	−6.12417e10	+	1.06074e11i	−0.585961	+	1.01491i	0.408794	+	0.912627i	$0.365950\pi$
$281$	−6.12417e10	+	1.06074e11i	−0.585961	+	1.01491i	−0.994755	+	0.102288i	$0.967384\pi$
$282$	−2.11123e10	−	3.65675e10i	−0.198799	−	0.344330i
$283$	1.97567e10	+	3.42196e10i	0.183094	+	0.317129i	0.942933	−	0.332983i	$-0.108055\pi$
$283$	1.97567e10	+	3.42196e10i	0.183094	+	0.317129i	−0.759838	+	0.650112i	$0.774722\pi$
$284$	4.01590e10			0.366312
$285$	−1.00460e10	−	2.08308e10i	−0.0901967	−	0.187027i
$286$	−3.29678e9			−0.0291368
$287$	2.18042e10	+	3.77660e10i	0.189702	+	0.328574i
$288$	1.14250e11	+	1.97886e11i	0.978563	+	1.69492i
$289$	5.92673e10	−	1.02654e11i	0.499775	−	0.865636i
$290$	−3.32969e9	−	5.76719e9i	−0.0276448	−	0.0478821i
$291$	1.09910e11	−	1.90370e11i	0.898501	−	1.55625i
$292$	−8.76755e10			−0.705758
$293$	1.26562e11			1.00323			0.501615	−	0.865091i	$-0.332739\pi$
$293$	1.26562e11			1.00323			0.501615	+	0.865091i	$0.332739\pi$
$294$	−2.71937e10	+	4.71009e10i	−0.212278	+	0.367677i
$295$	−6.26401e9	+	1.08496e10i	−0.0481563	+	0.0834092i
$296$	2.53644e10			0.192049
$297$	−6.38617e10			−0.476252
$298$	2.77064e10	−	4.79889e10i	0.203520	−	0.352507i
$299$	5.40228e10	+	9.35702e10i	0.390892	+	0.677044i
$300$	−1.18438e11	+	2.05141e11i	−0.844202	+	1.46220i
$301$	3.25939e10	+	5.64543e10i	0.228869	+	0.396413i
$302$	1.00734e8	+	1.74476e8i	0.000696857	+	0.00120699i
$303$	−2.71079e11			−1.84759
$304$	1.11113e11	+	8.26416e9i	0.746163	+	0.0554967i
$305$	−2.41305e10			−0.159667
$306$	−1.19548e9	−	2.07063e9i	−0.00779461	−	0.0135007i
$307$	5.91046e10	+	1.02372e11i	0.379751	+	0.657748i	0.991026	−	0.133670i	$-0.0426763\pi$
$307$	5.91046e10	+	1.02372e11i	0.379751	+	0.657748i	−0.611275	+	0.791418i	$0.709343\pi$
$308$	5.84245e9	−	1.01194e10i	0.0369928	−	0.0640734i
$309$	4.30801e10	+	7.46169e10i	0.268821	+	0.465612i
$310$	−4.39824e9	+	7.61798e9i	−0.0270490	+	0.0468503i
$311$	2.71676e10			0.164675			0.0823377	−	0.996604i	$-0.473761\pi$
$311$	2.71676e10			0.164675			0.0823377	+	0.996604i	$0.473761\pi$
$312$	−1.02992e11			−0.615332
$313$	−1.19822e10	+	2.07538e10i	−0.0705647	+	0.122222i	−0.899149	−	0.437643i	$-0.855813\pi$
$313$	−1.19822e10	+	2.07538e10i	−0.0705647	+	0.122222i	0.828584	+	0.559864i	$0.189147\pi$
$314$	−2.85702e10	+	4.94850e10i	−0.165855	+	0.287270i
$315$	−2.31664e10			−0.132575
$316$	1.96970e11			1.11124
$317$	1.52539e10	−	2.64205e10i	0.0848427	−	0.146952i	−0.820481	−	0.571673i	$-0.806295\pi$
$317$	1.52539e10	−	2.64205e10i	0.0848427	−	0.146952i	0.905324	+	0.424721i	$0.139628\pi$
$318$	5.46017e10	+	9.45729e10i	0.299422	+	0.518615i
$319$	−2.65744e10	+	4.60282e10i	−0.143683	+	0.248866i
$320$	5.39325e9	+	9.34138e9i	0.0287525	+	0.0498008i
$321$	−2.44562e11	−	4.23595e11i	−1.28563	−	2.22678i
$322$	3.62226e10			0.187771
$323$	−4.13615e9	−	3.07631e8i	−0.0211439	−	0.00157260i
$324$	−4.99221e11			−2.51675
$325$	−5.80663e10	−	1.00574e11i	−0.288701	−	0.500045i
$326$	−2.63993e7	−	4.57249e7i	−0.000129453	−	0.000224220i
$327$	2.19564e11	−	3.80296e11i	1.06193	−	1.83932i
$328$	−4.68314e10	−	8.11143e10i	−0.223411	−	0.386959i
$329$	−3.66862e10	+	6.35423e10i	−0.172632	+	0.299007i
$330$	2.22950e9			0.0103489
$331$	−3.47960e11			−1.59332			−0.796662	−	0.604426i	$-0.793403\pi$
$331$	−3.47960e11			−1.59332			−0.796662	+	0.604426i	$0.793403\pi$
$332$	5.85842e9	−	1.01471e10i	0.0264642	−	0.0458374i
$333$	−9.58049e10	+	1.65939e11i	−0.426961	+	0.739519i
$334$	1.27900e11			0.562356
$335$	3.05510e10			0.132533
$336$	7.81170e10	−	1.35303e11i	0.334363	−	0.579135i
$337$	1.60397e11	+	2.77816e11i	0.677427	+	1.17334i	0.975753	+	0.218873i	$0.0702382\pi$
$337$	1.60397e11	+	2.77816e11i	0.677427	+	1.17334i	−0.298327	+	0.954464i	$0.596428\pi$
$338$	−2.32153e10	+	4.02100e10i	−0.0967494	+	0.167575i
$339$	1.32094e11	+	2.28793e11i	0.543229	+	0.940901i
$340$	−2.64826e8	−	4.58692e8i	−0.00107475	−	0.00186151i
$341$	7.02051e10			0.281173
$342$	1.04703e11	−	1.53756e11i	0.413847	−	0.607734i
$343$	2.16950e11			0.846323
$344$	−7.00056e10	−	1.21253e11i	−0.269538	−	0.466853i
$345$	−3.65338e10	−	6.32783e10i	−0.138838	−	0.240475i
$346$	−6.21250e10	+	1.07604e11i	−0.233036	+	0.403631i
$347$	2.43259e11	+	4.21336e11i	0.900711	+	1.56008i	0.826573	+	0.562830i	$0.190287\pi$
$347$	2.43259e11	+	4.21336e11i	0.900711	+	1.56008i	0.0741389	+	0.997248i	$0.476379\pi$
$348$	−3.96351e11	+	6.86500e11i	−1.44868	+	2.50919i
$349$	−6.09543e10			−0.219933			−0.109966	−	0.993935i	$-0.535074\pi$
$349$	−6.09543e10			−0.219933			−0.109966	+	0.993935i	$0.535074\pi$
$350$	−3.89338e10			−0.138682
$351$	2.33485e11	−	4.04408e11i	0.821064	−	1.42213i
$352$	−1.91061e10	+	3.30927e10i	−0.0663330	+	0.114892i
$353$	−2.90432e11			−0.995540			−0.497770	−	0.867309i	$-0.665848\pi$
$353$	−2.90432e11			−0.995540			−0.497770	+	0.867309i	$0.665848\pi$
$354$	−1.41058e11			−0.477399
$355$	6.65737e9	−	1.15309e10i	0.0222472	−	0.0385333i
$356$	−2.17581e11	−	3.76862e11i	−0.717954	−	1.24353i
$357$	−2.90788e9	+	5.03660e9i	−0.00947480	+	0.0164108i
$358$	6.62270e10	+	1.14709e11i	0.213089	+	0.369081i
$359$	−8.83175e10	−	1.52970e11i	−0.280622	−	0.486051i	0.690916	−	0.722935i	$-0.257207\pi$
$359$	−8.83175e10	−	1.52970e11i	−0.280622	−	0.486051i	−0.971538	+	0.236883i	$0.923874\pi$
$360$	4.97570e10			0.156132
$361$	−1.18228e11	−	3.00249e11i	−0.366384	−	0.930464i
$362$	4.12409e10			0.126223
$363$	3.00601e11	+	5.20657e11i	0.908681	+	1.57388i
$364$	4.27213e10	+	7.39954e10i	0.127552	+	0.220927i
$365$	−1.45344e10	+	2.51744e10i	−0.0428628	+	0.0742405i
$366$	−1.35847e11	−	2.35294e11i	−0.395717	−	0.685402i
$367$	1.76643e11	−	3.05955e11i	0.508277	−	0.880361i	−0.491677	−	0.870778i	$-0.663616\pi$
$367$	1.76643e11	−	3.05955e11i	0.508277	−	0.880361i	0.999954	−	0.00958378i	$-0.00305066\pi$
$368$	3.52025e11			1.00059
$369$	7.07555e11			1.98674
$370$	2.00745e9	−	3.47700e9i	0.00556848	−	0.00964490i
$371$	9.48798e10	−	1.64337e11i	0.260011	−	0.450352i
$372$	1.04709e12			2.83493
$373$	−3.56405e11			−0.953355			−0.476677	−	0.879078i	$-0.658159\pi$
$373$	−3.56405e11			−0.953355			−0.476677	+	0.879078i	$0.658159\pi$
$374$	1.99921e8	−	3.46273e8i	0.000528366	−	0.000915158i
$375$	7.90261e10	+	1.36877e11i	0.206362	+	0.357430i
$376$	7.87950e10	−	1.36477e11i	0.203308	−	0.352139i
$377$	−1.94317e11	−	3.36568e11i	−0.495423	−	0.858097i
$378$	−7.82767e10	−	1.35579e11i	−0.197206	−	0.341570i
$379$	−7.31311e11			−1.82065			−0.910323	−	0.413898i	$-0.864167\pi$
$379$	−7.31311e11			−1.82065			−0.910323	+	0.413898i	$0.864167\pi$
$380$	2.31941e10	−	3.40605e10i	0.0570625	−	0.0837962i
$381$	−7.29765e9			−0.0177427
$382$	3.61891e10	+	6.26814e10i	0.0869546	+	0.150610i
$383$	−3.19488e11	−	5.53370e11i	−0.758684	−	1.31408i	−0.943522	−	0.331310i	$-0.892509\pi$
$383$	−3.19488e11	−	5.53370e11i	−0.758684	−	1.31408i	0.184838	−	0.982769i	$-0.440824\pi$
$384$	−3.72642e11	+	6.45434e11i	−0.874583	+	1.51482i
$385$	−1.93707e9	−	3.35510e9i	−0.00449336	−	0.00778273i
$386$	1.58221e10	−	2.74047e10i	0.0362762	−	0.0628322i
$387$	1.05769e12			2.39694
$388$	3.91681e11			0.877383
$389$	1.56175e11	−	2.70503e11i	0.345811	−	0.598962i	−0.639690	−	0.768633i	$-0.720937\pi$
$389$	1.56175e11	−	2.70503e11i	0.345811	−	0.598962i	0.985501	+	0.169671i	$0.0542706\pi$
$390$	−8.15128e9	+	1.41184e10i	−0.0178417	+	0.0309027i
$391$	−1.31040e10			−0.0283537
$392$	−2.02984e11			−0.434185
$393$	−5.88994e11	+	1.02017e12i	−1.24550	+	2.15727i
$394$	−2.96081e9	−	5.12828e9i	−0.00618982	−	0.0107211i
$395$	3.26527e10	−	5.65561e10i	0.0674889	−	0.116894i
$396$	−9.47950e10	−	1.64190e11i	−0.193712	−	0.335519i
$397$	4.41677e10	+	7.65007e10i	0.0892375	+	0.154564i	0.907189	−	0.420723i	$-0.138224\pi$
$397$	4.41677e10	+	7.65007e10i	0.0892375	+	0.154564i	−0.817952	+	0.575287i	$0.804890\pi$
$398$	1.17935e11			0.235597
$399$	−4.51229e11	−	3.35607e10i	−0.891290	−	0.0662907i
$400$	−3.78373e11			−0.739010
$401$	1.31269e11	+	2.27364e11i	0.253520	+	0.439109i	0.964492	−	0.264110i	$-0.0850784\pi$
$401$	1.31269e11	+	2.27364e11i	0.253520	+	0.439109i	−0.710973	+	0.703220i	$0.751745\pi$
$402$	1.71992e11	+	2.97900e11i	0.328467	+	0.568922i
$403$	−2.56677e11	+	4.44578e11i	−0.484746	+	0.839605i
$404$	−2.41508e11	−	4.18304e11i	−0.451040	−	0.781225i
$405$	−8.27584e10	+	1.43342e11i	−0.152850	+	0.264743i
$406$	−1.30291e11			−0.237984
$407$	−3.20431e10			−0.0578841
$408$	6.24559e9	−	1.08177e10i	0.0111584	−	0.0193269i
$409$	1.34741e11	−	2.33379e11i	0.238093	−	0.412388i	−0.722074	−	0.691815i	$-0.756811\pi$
$409$	1.34741e11	−	2.33379e11i	0.238093	−	0.412388i	0.960167	+	0.279427i	$0.0901445\pi$
$410$	−1.48258e10			−0.0259114
$411$	−1.53668e12			−2.65642
$412$	−7.67612e10	+	1.32954e11i	−0.131251	+	0.227334i
$413$	1.22556e11	+	2.12273e11i	0.207281	+	0.359020i
$414$	2.93860e11	−	5.08980e11i	0.491630	−	0.851528i
$415$	−1.94236e9	−	3.36427e9i	−0.00321450	−	0.00556768i
$416$	−1.39708e11	−	2.41981e11i	−0.228718	−	0.396151i
$417$	−3.25193e11			−0.526659
$418$	3.10226e10	+	2.30734e9i	0.0497032	+	0.00369673i
$419$	9.90155e11			1.56942			0.784712	−	0.619861i	$-0.212811\pi$
$419$	9.90155e11			1.56942			0.784712	+	0.619861i	$0.212811\pi$
$420$	−2.88910e10	−	5.00406e10i	−0.0453044	−	0.0784695i
$421$	−1.98224e11	−	3.43335e11i	−0.307530	−	0.532658i	0.670291	−	0.742098i	$-0.266169\pi$
$421$	−1.98224e11	−	3.43335e11i	−0.307530	−	0.532658i	−0.977821	+	0.209440i	$0.932836\pi$
$422$	3.44223e10	−	5.96212e10i	0.0528365	−	0.0915155i
$423$	5.95241e11	+	1.03099e12i	0.903984	+	1.56575i
$424$	−2.03784e11	+	3.52964e11i	−0.306213	+	0.530376i
$425$	1.40848e10			0.0209412
$426$	1.49916e11			0.220548
$427$	−2.36057e11	+	4.08863e11i	−0.343630	+	0.595185i
$428$	4.35768e11	−	7.54771e11i	0.627708	−	1.08722i
$429$	1.30111e11			0.185463
$430$	−2.21622e10			−0.0312612
$431$	−5.38564e10	+	9.32821e10i	−0.0751778	+	0.130212i	−0.901164	−	0.433479i	$-0.857286\pi$
$431$	−5.38564e10	+	9.32821e10i	−0.0751778	+	0.130212i	0.825986	+	0.563691i	$0.190619\pi$
$432$	−7.60722e11	−	1.31761e12i	−1.05087	−	1.82016i
$433$	−3.27184e11	+	5.66700e11i	−0.447298	+	0.774743i	−0.998209	−	0.0598210i	$-0.980947\pi$
$433$	−3.27184e11	+	5.66700e11i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$434$	8.60519e10	+	1.49046e11i	0.116428	+	0.201659i
$435$	1.31410e11	+	2.27609e11i	0.175966	+	0.304781i
$436$	7.82449e11			1.03697
$437$	−4.42865e11	−	9.18302e11i	−0.580905	−	1.20453i
$438$	−3.27297e11			−0.424921
$439$	1.10258e11	+	1.90972e11i	0.141684	+	0.245403i	0.928131	−	0.372254i	$-0.121415\pi$
$439$	1.10258e11	+	1.90972e11i	0.141684	+	0.245403i	−0.786447	+	0.617658i	$0.788082\pi$
$440$	4.16046e9	+	7.20612e9i	0.00529181	+	0.00916568i
$441$	7.66701e11	−	1.32797e12i	0.965278	−	1.67191i
$442$	1.46186e9	+	2.53202e9i	0.00182182	+	0.00315549i
$443$	−5.37184e10	+	9.30431e10i	−0.0662684	+	0.114780i	−0.897256	−	0.441511i	$-0.854443\pi$
$443$	−5.37184e10	+	9.30431e10i	−0.0662684	+	0.114780i	0.830988	+	0.556291i	$0.187776\pi$
$444$	−4.77915e11			−0.583617
$445$	−1.44278e11			−0.174414
$446$	1.62355e10	−	2.81207e10i	0.0194294	−	0.0336527i
$447$	−1.09347e12	+	1.89394e12i	−1.29545	+	2.24379i
$448$	2.11038e11			0.247520
$449$	1.41361e12			1.64142			0.820710	−	0.571345i	$-0.193578\pi$
$449$	1.41361e12			1.64142			0.820710	+	0.571345i	$0.193578\pi$
$450$	−3.15854e11	+	5.47076e11i	−0.363104	+	0.628914i
$451$	5.91625e10	+	1.02473e11i	0.0673368	+	0.116631i
$452$	−2.35368e11	+	4.07669e11i	−0.265231	+	0.459393i
$453$	−3.97558e9	−	6.88591e9i	−0.00443566	−	0.00768280i
$454$	−7.29648e10	−	1.26379e11i	−0.0806051	−	0.139612i
$455$	2.83285e10			0.0309865
$456$	9.69156e11	+	7.20821e10i	1.04967	+	0.0780702i
$457$	1.34799e12			1.44565			0.722825	−	0.691031i	$-0.242843\pi$
$457$	1.34799e12			1.44565			0.722825	+	0.691031i	$0.242843\pi$
$458$	−1.09633e11	−	1.89890e11i	−0.116425	−	0.201654i
$459$	2.83176e10	+	4.90476e10i	0.0297783	+	0.0515775i
$460$	6.50968e10	−	1.12751e11i	0.0677874	−	0.117411i
$461$	1.97080e11	+	3.41352e11i	0.203230	+	0.352005i	0.949567	−	0.313563i	$-0.101523\pi$
$461$	1.97080e11	+	3.41352e11i	0.203230	+	0.352005i	−0.746337	+	0.665568i	$0.768189\pi$
$462$	2.18101e10	−	3.77763e10i	0.0222725	−	0.0385772i
$463$	3.20938e11			0.324569			0.162284	−	0.986744i	$-0.448114\pi$
$463$	3.20938e11			0.324569			0.162284	+	0.986744i	$0.448114\pi$
$464$	−1.26622e12			−1.26817
$465$	1.73582e11	−	3.00653e11i	0.172174	−	0.298214i
$466$	−8.92730e10	+	1.54625e11i	−0.0876968	+	0.151895i
$467$	−9.48220e10			−0.0922535			−0.0461268	−	0.998936i	$-0.514688\pi$
$467$	−9.48220e10			−0.0922535			−0.0461268	+	0.998936i	$0.514688\pi$
$468$	1.38632e12			1.33585
$469$	2.98866e11	−	5.17651e11i	0.285232	−	0.494037i
$470$	−1.24724e10	−	2.16028e10i	−0.0117899	−	0.0204207i
$471$	1.12756e12	−	1.95299e12i	1.05571	−	1.82854i
$472$	−2.63227e11	−	4.55922e11i	−0.244113	−	0.422816i
$473$	8.84388e10	+	1.53180e11i	0.0812396	+	0.140711i
$474$	7.35297e11			0.669053
$475$	4.76013e11	+	9.87035e11i	0.429039	+	0.889634i
$476$	−1.03627e10			−0.00925211
$477$	−1.53944e12	−	2.66639e12i	−1.36154	−	2.35826i
$478$	−4.88583e10	−	8.46250e10i	−0.0428068	−	0.0741435i
$479$	−3.86292e11	+	6.69078e11i	−0.335279	+	0.580720i	−0.983538	−	0.180699i	$-0.942164\pi$
$479$	−3.86292e11	+	6.69078e11i	−0.335279	+	0.580720i	0.648259	+	0.761420i	$0.275497\pi$
$480$	9.44796e10	+	1.63643e11i	0.0812367	+	0.140706i
$481$	1.17153e11	−	2.02915e11i	0.0997930	−	0.172846i
$482$	3.52688e11			0.297631
$483$	−1.42957e12			−1.19521
$484$	−5.35619e11	+	9.27720e11i	−0.443662	+	0.768445i
$485$	6.49309e10	−	1.12464e11i	0.0532861	−	0.0922942i
$486$	−8.48057e11			−0.689544
$487$	4.39878e11			0.354366			0.177183	−	0.984178i	$-0.443302\pi$
$487$	4.39878e11			0.354366			0.177183	+	0.984178i	$0.443302\pi$
$488$	5.07006e11	−	8.78160e11i	0.404691	−	0.700946i
$489$	1.04188e9	+	1.80459e9i	0.000824002	+	0.00142721i
$490$	−1.60651e10	+	2.78255e10i	−0.0125893	+	0.0218053i
$491$	4.07793e11	+	7.06319e11i	0.316646	+	0.548446i	0.979786	−	0.200049i	$-0.0641101\pi$
$491$	4.07793e11	+	7.06319e11i	0.316646	+	0.548446i	−0.663140	+	0.748495i	$0.730777\pi$
$492$	8.82397e11	+	1.52836e12i	0.678924	+	1.17593i
$493$	4.71346e10			0.0359359
$494$	−1.28033e11	+	1.88016e11i	−0.0967278	+	0.142045i
$495$	−6.28586e10			−0.0470588
$496$	8.36284e11	+	1.44849e12i	0.620421	+	1.07460i
$497$	−1.30252e11	−	2.25603e11i	−0.0957592	−	0.165860i
$498$	2.18697e10	−	3.78795e10i	0.0159335	−	0.0275977i
$499$	−5.69772e11	−	9.86874e11i	−0.411385	−	0.712540i	0.583656	−	0.812001i	$-0.301622\pi$
$499$	−5.69772e11	−	9.86874e11i	−0.411385	−	0.712540i	−0.995041	+	0.0994609i	$0.968288\pi$
$500$	−1.40811e11	+	2.43891e11i	−0.100756	+	0.174514i
$501$	−5.04773e12			−3.57954
$502$	−2.58097e11			−0.181392
$503$	−9.83882e11	+	1.70413e12i	−0.685310	+	1.18699i	0.288029	+	0.957622i	$0.407000\pi$
$503$	−9.83882e11	+	1.70413e12i	−0.685310	+	1.18699i	−0.973339	+	0.229370i	$0.926333\pi$
$504$	4.86750e11	−	8.43075e11i	0.336022	−	0.582008i
$505$	−1.60144e11			−0.109572
$506$	9.82848e10			0.0666513
$507$	9.16219e11	−	1.58694e12i	0.615834	−	1.06666i
$508$	−6.50156e9	−	1.12610e10i	−0.00433143	−	0.00750226i
$509$	−4.84147e11	+	8.38568e11i	−0.319704	+	0.553743i	−0.980426	−	0.196887i	$-0.936917\pi$
$509$	−4.84147e11	+	8.38568e11i	−0.319704	+	0.553743i	0.660723	+	0.750630i	$0.270250\pi$
$510$	−9.88608e8	−	1.71232e9i	−0.000647080	−	0.00112078i
$511$	2.84367e11	+	4.92538e11i	0.184495	+	0.319555i
$512$	−1.56483e12			−1.00636
$513$	−2.48012e12	+	3.64206e12i	−1.58105	+	2.32177i
$514$	−3.12931e11			−0.197749
$515$	2.54502e10	+	4.40810e10i	0.0159426	+	0.0276134i
$516$	1.31905e12	+	2.28465e12i	0.819099	+	1.41872i
$517$	−9.95426e10	+	1.72413e11i	−0.0612776	+	0.106136i
$518$	−3.92759e10	−	6.80278e10i	−0.0239686	−	0.0415148i
$519$	2.45184e12	−	4.24671e12i	1.48333	−	2.56921i
$520$	−6.08443e10			−0.0364926
$521$	3.08992e12			1.83729			0.918644	−	0.395087i	$-0.129286\pi$
$521$	3.08992e12			1.83729			0.918644	+	0.395087i	$0.129286\pi$
$522$	−1.05700e12	+	1.83078e12i	−0.623100	+	1.07924i
$523$	1.99493e11	−	3.45532e11i	0.116592	−	0.201944i	−0.801823	−	0.597562i	$-0.796136\pi$
$523$	1.99493e11	−	3.45532e11i	0.116592	−	0.201944i	0.918415	+	0.395618i	$0.129470\pi$
$524$	−2.09897e12			−1.21623
$525$	1.53657e12			0.882746
$526$	5.60263e10	−	9.70404e10i	0.0319122	−	0.0552735i
$527$	−3.11304e10	−	5.39195e10i	−0.0175808	−	0.0304508i
$528$	2.11959e11	−	3.67124e11i	0.118686	−	0.205570i
$529$	−7.09971e11	−	1.22971e12i	−0.394176	−	0.682732i
$530$	3.22568e10	+	5.58703e10i	0.0177574	+	0.0307567i
$531$	3.97698e12			2.17084
$532$	−3.50218e11	−	7.26194e11i	−0.189555	−	0.393052i
$533$	−8.65218e11			−0.464358
$534$	−8.12241e11	−	1.40684e12i	−0.432264	−	0.748703i
$535$	−1.44479e11	−	2.50245e11i	−0.0762452	−	0.132061i
$536$	−6.41908e11	+	1.11182e12i	−0.335917	+	0.581825i
$537$	−2.61373e12	−	4.52712e12i	−1.35637	−	2.34929i
$538$	−3.03711e10	+	5.26042e10i	−0.0156293	+	0.0270707i
$539$	2.56432e11			0.130865
$540$	−5.62694e11			−0.284774
$541$	1.29958e12	−	2.25094e12i	0.652253	−	1.12974i	−0.330322	−	0.943868i	$-0.607157\pi$
$541$	1.29958e12	−	2.25094e12i	0.652253	−	1.12974i	0.982575	−	0.185867i	$-0.0595093\pi$
$542$	3.03744e11	−	5.26100e11i	0.151186	−	0.261861i
$543$	−1.62763e12			−0.803443
$544$	3.38882e10			0.0165903
$545$	1.29711e11	−	2.24665e11i	0.0629783	−	0.109082i
$546$	1.59480e11	+	2.76228e11i	0.0767963	+	0.133015i
$547$	1.05789e12	−	1.83233e12i	0.505242	−	0.875104i	−0.494740	−	0.869041i	$-0.664737\pi$
$547$	1.05789e12	−	1.83233e12i	0.505242	−	0.875104i	0.999982	−	0.00606302i	$-0.00192993\pi$
$548$	−1.36905e12	−	2.37127e12i	−0.648496	−	1.12323i
$549$	3.83007e12	+	6.63388e12i	1.79942	+	3.11668i
$550$	−1.05641e11			−0.0492268
$551$	1.59297e12	+	3.30309e12i	0.736248	+	1.52665i
$552$	3.07045e12			1.40759
$553$	−6.38852e11	−	1.10652e12i	−0.290494	−	0.503150i
$554$	−4.07360e11	−	7.05568e11i	−0.183732	−	0.318233i
$555$	−7.92265e10	+	1.37224e11i	−0.0354448	+	0.0613921i
$556$	−2.89719e11	−	5.01807e11i	−0.128570	−	0.222690i
$557$	−9.03633e11	+	1.56514e12i	−0.397780	+	0.688976i	−0.993452	−	0.114252i	$-0.963553\pi$
$557$	−9.03633e11	+	1.56514e12i	−0.397780	+	0.688976i	0.595671	+	0.803228i	$0.296886\pi$
$558$	2.79242e12			1.21934
$559$	−1.29337e12			−0.560233
$560$	4.61488e10	−	7.99320e10i	0.0198296	−	0.0343459i
$561$	−7.89012e9	+	1.36661e10i	−0.00336318	+	0.00582520i
$562$	−8.14715e11			−0.344502
$563$	2.07814e12			0.871742			0.435871	−	0.900009i	$-0.356440\pi$
$563$	2.07814e12			0.871742			0.435871	+	0.900009i	$0.356440\pi$
$564$	−1.48466e12	+	2.57150e12i	−0.617832	+	1.07012i
$565$	7.80362e10	+	1.35163e11i	0.0322165	+	0.0558006i
$566$	−1.31414e11	+	2.27616e11i	−0.0538230	+	0.0932242i
$567$	1.61917e12	+	2.80449e12i	0.657914	+	1.13954i
$568$	2.79757e11	+	4.84553e11i	0.112775	+	0.195332i
$569$	−2.40792e11			−0.0963024			−0.0481512	−	0.998840i	$-0.515333\pi$
$569$	−2.40792e11			−0.0963024			−0.0481512	+	0.998840i	$0.515333\pi$
$570$	8.65845e10	−	1.27149e11i	0.0343561	−	0.0504518i
$571$	2.34064e10			0.00921451			0.00460726	−	0.999989i	$-0.498533\pi$
$571$	2.34064e10			0.00921451			0.00460726	+	0.999989i	$0.498533\pi$
$572$	1.15918e11	+	2.00776e11i	0.0452760	+	0.0784204i
$573$	−1.42825e12	−	2.47380e12i	−0.553488	−	0.958669i
$574$	−1.45034e11	+	2.51206e11i	−0.0557655	+	0.0965886i
$575$	1.73109e12	+	2.99834e12i	0.660412	+	1.14387i
$576$	1.71207e12	−	2.96539e12i	0.648067	−	1.12249i
$577$	−4.50905e12			−1.69354			−0.846768	−	0.531963i	$-0.821455\pi$
$577$	−4.50905e12			−1.69354			−0.846768	+	0.531963i	$0.821455\pi$
$578$	7.88448e11			0.293831
$579$	−6.24439e11	+	1.08156e12i	−0.230907	+	0.399942i
$580$	−2.34150e11	+	4.05560e11i	−0.0859149	+	0.148809i
$581$	−7.60048e10			−0.0276725
$582$	1.46216e12			0.528253
$583$	2.57442e11	−	4.45903e11i	0.0922936	−	0.159857i
$584$	−6.10767e11	−	1.05788e12i	−0.217279	−	0.376338i
$585$	2.29818e11	−	3.98056e11i	0.0811301	−	0.140521i
$586$	4.20923e11	+	7.29061e11i	0.147456	+	0.255402i
$587$	−3.64067e11	−	6.30582e11i	−0.126564	−	0.219215i	0.795779	−	0.605587i	$-0.207062\pi$
$587$	−3.64067e11	−	6.30582e11i	−0.126564	−	0.219215i	−0.922343	+	0.386372i	$0.873728\pi$
$588$	3.82463e12			1.31945
$589$	2.72647e12	−	4.00382e12i	0.933432	−	1.37074i
$590$	−8.33318e10			−0.0283124
$591$	1.16852e11	+	2.02394e11i	0.0393997	+	0.0682423i
$592$	−3.81698e11	−	6.61119e11i	−0.127724	−	0.221224i
$593$	1.29700e12	−	2.24648e12i	0.430720	−	0.746029i	−0.566215	−	0.824257i	$-0.691593\pi$
$593$	1.29700e12	−	2.24648e12i	0.430720	−	0.746029i	0.996935	+	0.0782283i	$0.0249263\pi$
$594$	−2.12392e11	−	3.67874e11i	−0.0700003	−	0.121244i
$595$	−1.71787e9	+	2.97545e9i	−0.000561908	+	0.000973253i
$596$	−3.89674e12			−1.26501
$597$	−4.65446e12			−1.49963
$598$	−3.59340e11	+	6.22394e11i	−0.114908	+	0.199026i
$599$	−7.12775e11	+	1.23456e12i	−0.226221	+	0.391825i	−0.956685	−	0.291125i	$-0.905970\pi$
$599$	−7.12775e11	+	1.23456e12i	−0.226221	+	0.391825i	0.730464	+	0.682951i	$0.239304\pi$
$600$	−3.30027e12			−1.03961
$601$	−1.26960e12			−0.396948			−0.198474	−	0.980106i	$-0.563599\pi$
$601$	−1.26960e12			−0.396948			−0.198474	+	0.980106i	$0.563599\pi$
$602$	−2.16803e11	+	3.75513e11i	−0.0672792	+	0.116531i
$603$	−4.84916e12	−	8.39900e12i	−1.49362	−	2.58702i
$604$	7.08379e9	−	1.22695e10i	0.00216571	−	0.00375111i
$605$	1.77585e11	+	3.07586e11i	0.0538898	+	0.0933398i
$606$	−9.01560e11	−	1.56155e12i	−0.271561	−	0.470358i
$607$	−8.15991e11			−0.243970			−0.121985	−	0.992532i	$-0.538926\pi$
$607$	−8.15991e11			−0.243970			−0.121985	+	0.992532i	$0.538926\pi$
$608$	1.14529e12	+	2.37481e12i	0.339898	+	0.704795i
$609$	5.14210e12			1.51483
$610$	−8.02535e10	−	1.39003e11i	−0.0234682	−	0.0406481i
$611$	−7.27877e11	−	1.26072e12i	−0.211287	−	0.365959i
$612$	−8.40682e10	+	1.45610e11i	−0.0242243	+	0.0419577i
$613$	1.60715e12	+	2.78366e12i	0.459710	+	0.796241i	0.998945	−	0.0459140i	$-0.0146200\pi$
$613$	1.60715e12	+	2.78366e12i	0.459710	+	0.796241i	−0.539235	+	0.842155i	$0.681287\pi$
$614$	−3.93142e11	+	6.80943e11i	−0.111633	+	0.193354i
$615$	5.85118e11			0.164932
$616$	1.62799e11			0.0455553
$617$	−1.21812e12	+	2.10985e12i	−0.338382	+	0.586095i	−0.984129	−	0.177457i	$-0.943213\pi$
$617$	−1.21812e12	+	2.10985e12i	−0.338382	+	0.586095i	0.645747	+	0.763552i	$0.276546\pi$
$618$	−2.86553e11	+	4.96324e11i	−0.0790236	+	0.136873i
$619$	3.56770e12			0.976743			0.488372	−	0.872636i	$-0.337591\pi$
$619$	3.56770e12			0.976743			0.488372	+	0.872636i	$0.337591\pi$
$620$	6.18586e11			0.168127
$621$	−6.96075e12	+	1.20564e13i	−1.87821	+	3.25315i
$622$	9.03543e10	+	1.56498e11i	0.0242043	+	0.0419230i
$623$	−1.41141e12	+	2.44463e12i	−0.375367	+	0.650155i
$624$	1.54989e12	+	2.68449e12i	0.409232	+	0.708811i
$625$	−1.83718e12	−	3.18208e12i	−0.481604	−	0.834163i
$626$	−1.59403e11			−0.0414869
$627$	−1.22434e12	−	9.10620e10i	−0.316373	−	0.0235306i
$628$	4.01822e12			1.03090
$629$	1.42086e10	+	2.46100e10i	0.00361929	+	0.00626879i
$630$	−7.70471e10	−	1.33450e11i	−0.0194861	−	0.0337509i
$631$	−2.58086e12	+	4.47018e12i	−0.648086	+	1.12252i	0.335493	+	0.942043i	$0.391097\pi$
$631$	−2.58086e12	+	4.47018e12i	−0.648086	+	1.12252i	−0.983579	+	0.180475i	$0.942236\pi$
$632$	1.37213e12	+	2.37661e12i	0.342113	+	0.592557i
$633$	−1.35852e12	+	2.35302e12i	−0.336317	+	0.582518i
$634$	2.02927e11			0.0498813
$635$	−4.31119e9			−0.00105224
$636$	3.83970e12	−	6.65055e12i	0.930551	−	1.61176i
$637$	−9.37543e11	+	1.62387e12i	−0.225613	+	0.390773i
$638$	−3.53526e11			−0.0844750
$639$	−4.22673e12			−1.00288
$640$	−2.20144e11	+	3.81300e11i	−0.0518676	+	0.0898373i
$641$	3.10166e11	+	5.37223e11i	0.0725660	+	0.125688i	0.900025	−	0.435838i	$-0.143548\pi$
$641$	3.10166e11	+	5.37223e11i	0.0725660	+	0.125688i	−0.827459	+	0.561526i	$0.810215\pi$
$642$	1.62674e12	−	2.81760e12i	0.377929	−	0.654593i
$643$	−2.04544e12	−	3.54281e12i	−0.471887	−	0.817332i	0.527596	−	0.849495i	$-0.323094\pi$
$643$	−2.04544e12	−	3.54281e12i	−0.471887	−	0.817332i	−0.999483	+	0.0321638i	$0.989760\pi$
$644$	−1.27362e12	−	2.20598e12i	−0.291779	−	0.505376i
$645$	8.74660e11			0.198985
$646$	−1.19840e10	−	2.48493e10i	−0.00270741	−	0.00561395i
$647$	3.27086e12			0.733826			0.366913	−	0.930255i	$-0.380415\pi$
$647$	3.27086e12			0.733826			0.366913	+	0.930255i	$0.380415\pi$
$648$	−3.47768e12	−	6.02351e12i	−0.774822	−	1.34203i
$649$	3.32537e11	+	5.75971e11i	0.0735765	+	0.127438i
$650$	3.86235e11	−	6.68979e11i	0.0848676	−	0.146995i
$651$	−3.39614e12	−	5.88230e12i	−0.741091	−	1.28361i
$652$	−1.85645e9	+	3.21547e9i	−0.000402318	+	0.000696835i
$653$	6.71890e12			1.44607			0.723034	−	0.690812i	$-0.242747\pi$
$653$	6.71890e12			1.44607			0.723034	+	0.690812i	$0.242747\pi$
$654$	2.92092e12			0.624337
$655$	−3.47957e11	+	6.02679e11i	−0.0738652	+	0.127938i
$656$	−1.40949e12	+	2.44131e12i	−0.297163	+	0.514702i
$657$	9.22782e12			1.93221
$658$	−4.88046e11			−0.101495
$659$	−1.70052e12	+	2.94539e12i	−0.351235	+	0.608357i	−0.986466	−	0.163965i	$-0.947572\pi$
$659$	−1.70052e12	+	2.94539e12i	−0.351235	+	0.608357i	0.635231	+	0.772322i	$0.280905\pi$
$660$	−7.83914e10	−	1.35778e11i	−0.0160813	−	0.0278536i
$661$	4.15217e12	−	7.19177e12i	0.845997	−	1.46531i	−0.0387561	−	0.999249i	$-0.512340\pi$
$661$	4.15217e12	−	7.19177e12i	0.845997	−	1.46531i	0.884753	−	0.466061i	$-0.154327\pi$
$662$	−1.15725e12	−	2.00442e12i	−0.234189	−	0.405628i
$663$	−5.76942e10	−	9.99293e10i	−0.0115963	−	0.0200855i
$664$	1.63244e11			0.0325897
$665$	−2.66570e11	−	1.98265e10i	−0.0528584	−	0.00393141i
$666$	−1.27452e12			−0.251022
$667$	5.79307e12	+	1.00339e13i	1.13329	+	1.96292i
$668$	−4.49709e12	−	7.78919e12i	−0.873851	−	1.51355i
$669$	−6.40755e11	+	1.10982e12i	−0.123673	+	0.214208i
$670$	1.01607e11	+	1.75989e11i	0.0194799	+	0.0337402i
$671$	−6.40506e11	+	1.10939e12i	−0.121975	+	0.211267i
$672$	3.69700e12			0.699338
$673$	8.74240e12			1.64272			0.821359	−	0.570412i	$-0.193217\pi$
$673$	8.74240e12			1.64272			0.821359	+	0.570412i	$0.193217\pi$
$674$	−1.06690e12	+	1.84793e12i	−0.199139	+	0.344918i
$675$	7.48175e12	−	1.29588e13i	1.38719	−	2.40268i
$676$	3.26508e12			0.601359
$677$	−1.09978e12			−0.201213			−0.100607	−	0.994926i	$-0.532078\pi$
$677$	−1.09978e12			−0.201213			−0.100607	+	0.994926i	$0.532078\pi$
$678$	−8.78638e11	+	1.52185e12i	−0.159690	+	0.276590i
$679$	−1.27038e12	−	2.20036e12i	−0.229361	−	0.397264i
$680$	3.68967e9	−	6.39070e9i	0.000661756	−	0.00114619i
$681$	2.87965e12	+	4.98770e12i	0.513071	+	0.888665i
$682$	2.33489e11	+	4.04415e11i	0.0413273	+	0.0715810i
$683$	−2.77349e12			−0.487678			−0.243839	−	0.969816i	$-0.578407\pi$
$683$	−2.77349e12			−0.487678			−0.243839	+	0.969816i	$0.578407\pi$
$684$	−1.30452e13	−	9.70255e11i	−2.27877	−	0.169486i
$685$	−9.07819e11			−0.157540
$686$	7.21536e11	+	1.24974e12i	0.124394	+	0.215457i
$687$	4.32681e12	+	7.49425e12i	0.741075	+	1.28358i
$688$	−2.10697e12	+	3.64938e12i	−0.358517	+	0.620970i
$689$	1.88247e12	+	3.26054e12i	0.318231	+	0.551192i
$690$	2.43009e11	−	4.20904e11i	0.0408133	−	0.0706907i
$691$	−8.19774e12			−1.36786			−0.683932	−	0.729546i	$-0.739732\pi$
$691$	−8.19774e12			−1.36786			−0.683932	+	0.729546i	$0.739732\pi$
$692$	8.73750e12			1.44847
$693$	−6.14916e11	+	1.06507e12i	−0.101278	+	0.175419i
$694$	−1.61807e12	+	2.80257e12i	−0.264776	+	0.458606i
$695$	−1.92113e11			−0.0312338
$696$	−1.10443e13			−1.78400
$697$	5.24679e10	−	9.08771e10i	0.00842066	−	0.0145850i
$698$	−2.02723e11	−	3.51126e11i	−0.0323261	−	0.0559905i
$699$	3.52327e12	−	6.10248e12i	0.558211	−	0.966851i
$700$	1.36895e12	+	2.37109e12i	0.215500	+	0.373256i
$701$	1.53167e12	+	2.65292e12i	0.239570	+	0.414948i	0.960591	−	0.277966i	$-0.0896602\pi$
$701$	1.53167e12	+	2.65292e12i	0.239570	+	0.414948i	−0.721021	+	0.692913i	$0.756327\pi$
$702$	3.10611e12			0.482726
$703$	−1.24442e12	+	1.82743e12i	−0.192162	+	0.282190i
$704$	5.72622e11			0.0878599
$705$	4.92238e11	+	8.52582e11i	0.0750455	+	0.129983i
$706$	−9.65924e11	−	1.67303e12i	−0.146326	−	0.253444i
$707$	−1.56662e12	+	2.71346e12i	−0.235817	+	0.408447i
$708$	4.95972e12	+	8.59049e12i	0.741835	+	1.28490i
$709$	−4.69568e12	+	8.13316e12i	−0.697896	+	1.20879i	0.271299	+	0.962495i	$0.412547\pi$
$709$	−4.69568e12	+	8.13316e12i	−0.697896	+	1.20879i	−0.969195	+	0.246296i	$0.920786\pi$
$710$	8.85648e10			0.0130797
$711$	−2.07310e13			−3.04234
$712$	3.03144e12	−	5.25060e12i	0.442067	−	0.765683i
$713$	7.65216e12	−	1.32539e13i	1.10887	−	1.92062i
$714$	−3.86843e10			−0.00557049
$715$	7.68652e10			0.0109990
$716$	4.65721e12	−	8.06653e12i	0.662243	−	1.14704i
$717$	1.92825e12	+	3.33983e12i	0.272476	+	0.471942i
$718$	5.87455e11	−	1.01750e12i	0.0824926	−	0.142881i
$719$	−4.56914e12	−	7.91397e12i	−0.637608	−	1.10437i	−0.985956	−	0.167005i	$-0.946590\pi$
$719$	−4.56914e12	−	7.91397e12i	−0.637608	−	1.10437i	0.348348	−	0.937365i	$-0.386743\pi$
$720$	−7.48773e11	−	1.29691e12i	−0.103837	−	0.179852i
$721$	9.95869e11			0.137244
$722$	1.33638e12	−	1.67962e12i	0.183025	−	0.230035i
$723$	−1.39193e13			−1.89450
$724$	−1.45007e12	−	2.51160e12i	−0.196140	−	0.339724i
$725$	−6.22667e12	−	1.07849e13i	−0.837018	−	1.44976i
$726$	−1.99949e12	+	3.46322e12i	−0.267119	+	0.462663i
$727$	−3.24375e11	−	5.61834e11i	−0.0430668	−	0.0745939i	0.843688	−	0.536833i	$-0.180379\pi$
$727$	−3.24375e11	−	5.61834e11i	−0.0430668	−	0.0745939i	−0.886755	+	0.462239i	$0.847046\pi$
$728$	−5.95211e11	+	1.03094e12i	−0.0785380	+	0.136032i
$729$	1.24626e13			1.63431
$730$	−1.93355e11			−0.0252002
$731$	7.84313e10	−	1.35847e11i	0.0101592	−	0.0175963i
$732$	−9.55301e12	+	1.65463e13i	−1.22982	+	2.13011i
$733$	−4.56621e12			−0.584235			−0.292117	−	0.956382i	$-0.594360\pi$
$733$	−4.56621e12			−0.584235			−0.292117	+	0.956382i	$0.594360\pi$
$734$	2.34993e12			0.298830
$735$	6.34029e11	−	1.09817e12i	0.0801338	−	0.138796i
$736$	4.16502e12	+	7.21402e12i	0.523199	+	0.906207i
$737$	8.10930e11	−	1.40457e12i	0.101246	−	0.175364i
$738$	2.35320e12	+	4.07586e12i	0.292015	+	0.505785i
$739$	−1.87342e12	−	3.24487e12i	−0.231066	−	0.400218i	0.727056	−	0.686578i	$-0.240888\pi$
$739$	−1.87342e12	−	3.24487e12i	−0.231066	−	0.400218i	−0.958122	+	0.286360i	$0.907555\pi$
$740$	−2.82336e11			−0.0346117
$741$	5.05299e12	−	7.42031e12i	0.615696	−	0.904149i
$742$	1.26221e12			0.152867
$743$	5.13412e11	+	8.89256e11i	0.0618040	+	0.107048i	0.895272	−	0.445520i	$-0.146981\pi$
$743$	5.13412e11	+	8.89256e11i	0.0618040	+	0.107048i	−0.833468	+	0.552568i	$0.813648\pi$
$744$	7.29428e12	+	1.26341e13i	0.872779	+	1.51170i
$745$	−6.45982e11	+	1.11887e12i	−0.0768276	+	0.133069i
$746$	−1.18534e12	−	2.05307e12i	−0.140126	−	0.242705i
$747$	−6.16596e11	+	1.06798e12i	−0.0724533	+	0.125493i
$748$	−2.81176e10			−0.00328414
$749$	−5.65348e12			−0.656368
$750$	−5.25653e11	+	9.10457e11i	−0.0606629	+	0.105071i
$751$	−2.43518e12	+	4.21785e12i	−0.279352	+	0.483851i	−0.971224	−	0.238169i	$-0.923453\pi$
$751$	−2.43518e12	+	4.21785e12i	−0.279352	+	0.483851i	0.691872	+	0.722020i	$0.256786\pi$
$752$	−4.74301e12			−0.540847
$753$	1.01861e13			1.15460
$754$	1.29253e12	−	2.23872e12i	0.145636	−	0.252249i
$755$	−2.34863e9	−	4.06795e9i	−0.000263059	−	0.000455632i
$756$	−5.50457e12	+	9.53419e12i	−0.612880	+	1.06154i
$757$	−4.64145e12	−	8.03923e12i	−0.513715	−	0.889781i	−0.999873	−	0.0159099i	$-0.994936\pi$
$757$	−4.64145e12	−	8.03923e12i	−0.513715	−	0.889781i	0.486158	−	0.873871i	$-0.338398\pi$
$758$	−2.43221e12	−	4.21271e12i	−0.267602	−	0.463500i
$759$	−3.87893e12			−0.424252
$760$	5.72543e11	+	4.25835e10i	0.0622511	+	0.00462999i
$761$	2.42871e12			0.262509			0.131255	−	0.991349i	$-0.458099\pi$
$761$	2.42871e12			0.262509			0.131255	+	0.991349i	$0.458099\pi$
$762$	−2.42706e10	−	4.20380e10i	−0.00260786	−	0.00451694i
$763$	−2.53780e12	−	4.39559e12i	−0.271079	−	0.469523i
$764$	2.54489e12	−	4.40788e12i	0.270239	−	0.468068i
$765$	2.78729e10	+	4.82772e10i	0.00294242	+	0.00509642i
$766$	2.12512e12	−	3.68082e12i	0.223025	−	0.386291i
$767$	−4.86316e12			−0.507388
$768$	4.39101e12			0.455449
$769$	−7.51050e12	+	1.30086e13i	−0.774463	+	1.34141i	0.160633	+	0.987014i	$0.448646\pi$
$769$	−7.51050e12	+	1.30086e13i	−0.774463	+	1.34141i	−0.935096	+	0.354395i	$0.884687\pi$
$770$	1.28847e10	−	2.23169e10i	0.00132088	−	0.00228784i
$771$	1.23502e13			1.25872
$772$	−2.22528e12			−0.225480
$773$	7.53007e12	−	1.30425e13i	0.758563	−	1.31387i	−0.185021	−	0.982735i	$-0.559235\pi$
$773$	7.53007e12	−	1.30425e13i	0.758563	−	1.31387i	0.943584	−	0.331134i	$-0.107431\pi$
$774$	3.51767e12	+	6.09278e12i	0.352306	+	0.610212i
$775$	−8.22491e12	+	1.42460e13i	−0.818980	+	1.41852i
$776$	2.72853e12	+	4.72595e12i	0.270117	+	0.467856i
$777$	1.55007e12	+	2.68480e12i	0.152566	+	0.264252i
$778$	2.07764e12			0.203311
$779$	8.14168e12	+	6.05547e11i	0.792128	+	0.0589154i
$780$	1.14643e12			0.110897
$781$	−3.53419e11	−	6.12140e11i	−0.0339908	−	0.0588737i
$782$	−4.35816e10	−	7.54855e10i	−0.00416747	−	0.00721827i
$783$	2.50375e13	−	4.33662e13i	2.38047	−	4.12310i
$784$	3.05462e12	+	5.29076e12i	0.288759	+	0.500145i
$785$	6.66121e11	−	1.15376e12i	0.0626094	−	0.108443i
$786$	−7.83555e12			−0.732264
$787$	3.74025e12			0.347548			0.173774	−	0.984786i	$-0.444404\pi$
$787$	3.74025e12			0.347548			0.173774	+	0.984786i	$0.444404\pi$
$788$	−2.08210e11	+	3.60630e11i	−0.0192368	+	0.0333192i
$789$	−2.21115e12	+	3.82982e12i	−0.203129	+	0.351829i
$790$	4.34388e11			0.0396785
$791$	3.05357e12			0.277341
$792$	1.32072e12	−	2.28756e12i	0.119275	−	0.206590i
$793$	−4.68352e12	−	8.11209e12i	−0.420574	−	0.728456i
$794$	−2.93787e11	+	5.08855e11i	−0.0262326	+	0.0454361i
$795$	−1.27305e12	−	2.20499e12i	−0.113030	−	0.195774i
$796$	−4.14672e12	−	7.18232e12i	−0.366096	−	0.634098i
$797$	−1.32235e13			−1.16087			−0.580434	−	0.814308i	$-0.697117\pi$
$797$	−1.32235e13			−1.16087			−0.580434	+	0.814308i	$0.697117\pi$
$798$	−1.30738e12	−	2.71092e12i	−0.114127	−	0.236648i
$799$	1.76557e11			0.0153259
$800$	−4.47676e12	−	7.75398e12i	−0.386420	−	0.669298i
$801$	2.29004e13	+	3.96646e13i	1.96560	+	3.40452i
$802$	−8.73152e11	+	1.51234e12i	−0.0745256	+	0.129082i
$803$	7.71588e11	+	1.33643e12i	0.0654886	+	0.113430i
$804$	1.20948e13	−	2.09489e13i	1.02082	−	1.76811i
$805$	−8.44540e11			−0.0708825
$806$	−3.41464e12			−0.284995
$807$	1.19863e12	−	2.07609e12i	0.0994844	−	0.172312i
$808$	3.36479e12	−	5.82799e12i	0.277720	−	0.481025i
$809$	6.05423e12			0.496924			0.248462	−	0.968642i	$-0.420075\pi$
$809$	6.05423e12			0.496924			0.248462	+	0.968642i	$0.420075\pi$
$810$	−1.10096e12			−0.0898644
$811$	8.72224e12	−	1.51074e13i	0.708002	−	1.22630i	−0.257595	−	0.966253i	$-0.582930\pi$
$811$	8.72224e12	−	1.51074e13i	0.708002	−	1.22630i	0.965597	−	0.260042i	$-0.0837365\pi$
$812$	4.58116e12	+	7.93481e12i	0.369806	+	0.640522i
$813$	−1.19876e13	+	2.07632e13i	−0.962334	+	1.66681i
$814$	−1.06569e11	−	1.84583e11i	−0.00850790	−	0.0147361i
$815$	6.15507e8	+	1.06609e9i	4.88679e−5	+	8.46417e-5i
$816$	−3.75949e11			−0.0296840
$817$	1.21705e13	+	9.05198e11i	0.955676	+	0.0710795i
$818$	1.79250e12			0.139981
$819$	−4.49640e12	−	7.78799e12i	−0.349210	−	0.604850i
$820$	5.21289e11	+	9.02899e11i	0.0402639	+	0.0697392i
$821$	−8.88305e12	+	1.53859e13i	−0.682367	+	1.18189i	0.291890	+	0.956452i	$0.405716\pi$
$821$	−8.88305e12	+	1.53859e13i	−0.682367	+	1.18189i	−0.974257	+	0.225442i	$0.927617\pi$
$822$	−5.11073e12	−	8.85204e12i	−0.390445	−	0.676270i
$823$	−6.39893e12	+	1.10833e13i	−0.486192	+	0.842110i	−0.999874	−	0.0158709i	$-0.994948\pi$
$823$	−6.39893e12	+	1.10833e13i	−0.486192	+	0.842110i	0.513682	+	0.857981i	$0.328281\pi$
$824$	−2.13894e12			−0.161632
$825$	4.16926e12			0.313340
$826$	−8.15196e11	+	1.41196e12i	−0.0609329	+	0.105539i
$827$	−4.25145e12	+	7.36373e12i	−0.316055	+	0.547423i	−0.979661	−	0.200659i	$-0.935692\pi$
$827$	−4.25145e12	+	7.36373e12i	−0.316055	+	0.547423i	0.663606	+	0.748082i	$0.269025\pi$
$828$	−4.13295e13			−3.05579
$829$	1.27711e13			0.939145			0.469573	−	0.882894i	$-0.344408\pi$
$829$	1.27711e13			0.939145			0.469573	+	0.882894i	$0.344408\pi$
$830$	1.29199e10	−	2.23779e10i	0.000944945	−	0.00163669i
$831$	1.60770e13	+	2.78461e13i	1.16950	+	2.02563i
$832$	−2.09357e12	+	3.62616e12i	−0.151472	+	0.262357i
$833$	−1.13708e11	−	1.96947e11i	−0.00818251	−	0.0141725i
$834$	−1.08153e12	−	1.87327e12i	−0.0774092	−	0.134077i
$835$	−2.98202e12			−0.212286
$836$	−9.50266e11	−	1.97042e12i	−0.0672848	−	0.139518i
$837$	−6.61449e13			−4.65835
$838$	3.29307e12	+	5.70377e12i	0.230677	+	0.399543i
$839$	−7.97998e12	−	1.38217e13i	−0.555998	−	0.963016i	−0.997825	−	0.0659162i	$-0.979003\pi$
$839$	−7.97998e12	−	1.38217e13i	−0.555998	−	0.963016i	0.441828	−	0.897100i	$-0.354330\pi$
$840$	4.02521e11	−	6.97187e11i	0.0278954	−	0.0483162i
$841$	−1.35838e13	−	2.35279e13i	−0.936354	−	1.62181i
$842$	1.31852e12	−	2.28374e12i	0.0904026	−	0.156582i
$843$	3.21537e13			2.19284
$844$	−4.84129e12			−0.328413
$845$	5.41270e11	−	9.37507e11i	0.0365223	−	0.0632586i
$846$	−3.95932e12	+	6.85775e12i	−0.265738	+	0.460272i
$847$	6.94891e12			0.463918
$848$	1.22666e13			0.814599
$849$	5.18642e12	−	8.98315e12i	0.342597	−	0.593395i
$850$	4.68436e10	+	8.11355e10i	0.00307797	+	0.00533121i
$851$	−3.49260e12	+	6.04937e12i	−0.228279	+	0.395391i
$852$	−5.27118e12	−	9.12994e12i	−0.342712	−	0.593595i
$853$	8.61672e12	+	1.49246e13i	0.557277	+	0.965233i	0.997722	+	0.0674531i	$0.0214873\pi$
$853$	8.61672e12	+	1.49246e13i	0.557277	+	0.965233i	−0.440445	+	0.897780i	$0.645179\pi$
$854$	−3.14033e12			−0.202029
$855$	−2.44117e12	+	3.58485e12i	−0.156225	+	0.229416i
$856$	1.21426e13			0.773001
$857$	6.15761e12	+	1.06653e13i	0.389940	+	0.675396i	0.992441	−	0.122722i	$-0.0391623\pi$
$857$	6.15761e12	+	1.06653e13i	0.389940	+	0.675396i	−0.602501	+	0.798118i	$0.705829\pi$
$858$	4.32727e11	+	7.49505e11i	0.0272597	+	0.0472152i
$859$	−9.28115e12	+	1.60754e13i	−0.581611	+	1.00738i	0.413677	+	0.910424i	$0.364244\pi$
$859$	−9.28115e12	+	1.60754e13i	−0.581611	+	1.00738i	−0.995289	+	0.0969566i	$0.969089\pi$
$860$	7.79246e11	+	1.34969e12i	0.0485771	+	0.0841380i
$861$	5.72393e12	−	9.91415e12i	0.354961	−	0.614810i
$862$	−7.16466e11			−0.0441991
$863$	2.15372e13			1.32173			0.660863	−	0.750507i	$-0.270191\pi$
$863$	2.15372e13			1.32173			0.660863	+	0.750507i	$0.270191\pi$
$864$	1.80011e13	−	3.11788e13i	1.09897	−	1.90348i
$865$	1.44846e12	−	2.50881e12i	0.0879699	−	0.152368i
$866$	−4.35262e12			−0.262979
$867$	−3.11171e13			−1.87031
$868$	6.05134e12	−	1.04812e13i	0.361837	−	0.626719i
$869$	−1.73343e12	−	3.00239e12i	−0.103114	−	0.178599i
$870$	−8.74093e11	+	1.51397e12i	−0.0517275	+	0.0895946i
$871$	5.92969e12	+	1.02705e13i	0.349100	+	0.604659i
$872$	5.45071e12	+	9.44090e12i	0.319248	+	0.552954i
$873$	−4.12242e13			−2.40209
$874$	3.81697e12	−	5.60522e12i	0.221268	−	0.324931i
$875$	1.82682e12			0.105356
$876$	1.15081e13	+	1.99326e13i	0.660289	+	1.14365i
$877$	−7.73785e12	−	1.34023e13i	−0.441695	−	0.765038i	0.556121	−	0.831101i	$-0.312289\pi$
$877$	−7.73785e12	−	1.34023e13i	−0.441695	−	0.765038i	−0.997815	+	0.0660640i	$0.978956\pi$
$878$	−7.33395e11	+	1.27028e12i	−0.0416498	+	0.0721396i
$879$	−1.66123e13	−	2.87733e13i	−0.938597	−	1.62570i
$880$	1.25218e11	−	2.16884e11i	0.00703873	−	0.0121914i
$881$	−1.17320e13			−0.656118			−0.328059	−	0.944657i	$-0.606394\pi$
$881$	−1.17320e13			−0.656118			−0.328059	+	0.944657i	$0.606394\pi$
$882$	1.01996e13			0.567513
$883$	−6.09976e11	+	1.05651e12i	−0.0337668	+	0.0584857i	−0.882415	−	0.470472i	$-0.844084\pi$
$883$	−6.09976e11	+	1.05651e12i	−0.0337668	+	0.0584857i	0.848648	+	0.528958i	$0.177417\pi$
$884$	1.02801e11	−	1.78056e11i	0.00566190	−	0.00980669i
$885$	3.28879e12			0.180215
$886$	−7.14631e11			−0.0389610
$887$	1.16999e13	−	2.02649e13i	0.634640	−	1.09923i	−0.351951	−	0.936018i	$-0.614482\pi$
$887$	1.16999e13	−	2.02649e13i	0.634640	−	1.09923i	0.986591	−	0.163210i	$-0.0521849\pi$
$888$	−3.32926e12	−	5.76645e12i	−0.179676	−	0.311208i
$889$	−4.21744e10	+	7.30481e10i	−0.00226460	+	0.00392239i
$890$	−4.79843e11	−	8.31113e11i	−0.0256356	−	0.0444022i
$891$	4.39339e12	+	7.60957e12i	0.233534	+	0.404492i
$892$	−2.28342e12			−0.120766
$893$	5.96695e12	+	1.23728e13i	0.313994	+	0.651081i
$894$	−1.45467e13			−0.761633
$895$	−1.54410e12	−	2.67446e12i	−0.0804400	−	0.139326i
$896$	4.30712e12	+	7.46015e12i	0.223255	+	0.386689i
$897$	1.41818e13	−	2.45636e13i	0.731417	−	1.26685i
$898$	4.70139e12	+	8.14305e12i	0.241259	+	0.417872i
$899$	−2.75245e13	+	4.76738e13i	−1.40540	+	2.43423i
$900$	4.44230e13			2.25692
$901$	−4.56622e11			−0.0230832
$902$	−3.93528e11	+	6.81610e11i	−0.0197946	+	0.0342852i
$903$	8.55639e12	−	1.48201e13i	0.428248	−	0.741748i
$904$	−6.55849e12			−0.326622
$905$	−9.61544e11			−0.0476486
$906$	2.64441e10	−	4.58025e10i	0.00130392	−	0.00225846i
$907$	1.37524e13	+	2.38199e13i	0.674755	+	1.16871i	0.976540	+	0.215334i	$0.0690840\pi$
$907$	1.37524e13	+	2.38199e13i	0.674755	+	1.16871i	−0.301786	+	0.953376i	$0.597583\pi$
$908$	−5.13103e12	+	8.88720e12i	−0.250506	+	0.433889i
$909$	2.54186e13	+	4.40264e13i	1.23485	+	2.13883i
$910$	9.42154e10	+	1.63186e11i	0.00455445	+	0.00788853i
$911$	2.11484e13			1.01729			0.508644	−	0.860977i	$-0.330147\pi$
$911$	2.11484e13			1.01729			0.508644	+	0.860977i	$0.330147\pi$
$912$	−1.27056e13	−	2.63457e13i	−0.608161	−	1.26105i
$913$	−2.06228e11			−0.00982265
$914$	4.48316e12	+	7.76507e12i	0.212484	+	0.368033i
$915$	3.16730e12	+	5.48593e12i	0.149381	+	0.258735i
$916$	−7.70961e12	+	1.33534e13i	−0.361829	+	0.626706i
$917$	6.80780e12	+	1.17915e13i	0.317940	+	0.550688i
$918$	−1.88359e11	+	3.26247e11i	−0.00875373	+	0.0151619i
$919$	−2.36100e13			−1.09188			−0.545942	−	0.837823i	$-0.683828\pi$
$919$	−2.36100e13			−1.09188			−0.545942	+	0.837823i	$0.683828\pi$
$920$	1.81391e12			0.0834778
$921$	1.55159e13	−	2.68743e13i	0.710571	−	1.23074i
$922$	−1.31090e12	+	2.27055e12i	−0.0597422	+	0.103477i
$923$	5.16856e12			0.234402
$924$	−3.06746e12			−0.138438
$925$	3.75402e12	−	6.50215e12i	0.168600	−	0.292025i
$926$	1.06738e12	+	1.84876e12i	0.0477057	+	0.0826287i
$927$	8.07909e12	−	1.39934e13i	0.359338	−	0.622392i
$928$	−1.49814e13	−	2.59485e13i	−0.663111	−	1.14854i
$929$	−2.16611e13	−	3.75181e13i	−0.954134	−	1.65261i	−0.736339	−	0.676613i	$-0.763447\pi$
$929$	−2.16611e13	−	3.75181e13i	−0.954134	−	1.65261i	−0.217795	−	0.975995i	$-0.569886\pi$
$930$	2.30921e12			0.101226
$931$	9.95876e12	−	1.46244e13i	0.434442	−	0.637977i
$932$	1.25557e13			0.545092
$933$	−3.56595e12	−	6.17640e12i	−0.154066	−	0.266850i
$934$	−3.15360e11	−	5.46220e11i	−0.0135596	−	0.0234859i
$935$	−4.66120e9	+	8.07344e9i	−0.000199455	+	0.000345467i
$936$	9.65742e12	+	1.67271e13i	0.411263	+	0.712328i
$937$	1.30954e13	−	2.26819e13i	0.554998	−	0.961285i	−0.442906	−	0.896568i	$-0.646052\pi$
$937$	1.30954e13	−	2.26819e13i	0.554998	−	0.961285i	0.997904	−	0.0647165i	$-0.0206143\pi$
$938$	3.97590e12			0.167696
$939$	6.29102e12			0.264074
$940$	−8.77083e11	+	1.51915e12i	−0.0366408	+	0.0634638i
$941$	−5.28526e12	+	9.15434e12i	−0.219742	+	0.380604i	−0.954729	−	0.297477i	$-0.903855\pi$
$941$	−5.28526e12	+	9.15434e12i	−0.219742	+	0.380604i	0.734987	+	0.678081i	$0.237188\pi$
$942$	1.50002e13			0.620680
$943$	2.57942e13			1.06223
$944$	−7.92238e12	+	1.37220e13i	−0.324699	+	0.562396i
$945$	1.82504e12	+	3.16106e12i	0.0744440	+	0.128941i
$946$	−5.88262e11	+	1.01890e12i	−0.0238815	+	0.0413639i
$947$	5.17466e12	+	8.96277e12i	0.209077	+	0.362132i	0.951424	−	0.307883i	$-0.0996207\pi$
$947$	5.17466e12	+	8.96277e12i	0.209077	+	0.362132i	−0.742347	+	0.670016i	$0.766287\pi$
$948$	−2.58538e13	−	4.47800e13i	−1.03965	−	1.80072i
$949$	−1.12840e13			−0.451613
$950$	−4.10267e12	+	6.02476e12i	−0.163422	+	0.239985i
$951$	−8.00876e12			−0.317507
$952$	−7.21887e10	−	1.25034e11i	−0.00284841	−	0.00493359i
$953$	−1.64757e13	−	2.85367e13i	−0.647031	−	1.12069i	−0.983829	−	0.179113i	$-0.942677\pi$
$953$	−1.64757e13	−	2.85367e13i	−0.647031	−	1.12069i	0.336798	−	0.941577i	$-0.390656\pi$
$954$	1.02398e13	−	1.77359e13i	0.400243	−	0.693242i
$955$	−8.43759e11	−	1.46143e12i	−0.0328249	−	0.0568543i
$956$	−3.43581e12	+	5.95100e12i	−0.133036	+	0.230425i
$957$	1.39523e13			0.537704
$958$	−5.13895e12			−0.197120
$959$	−8.88076e12	+	1.53819e13i	−0.339052	+	0.587256i
$960$	1.41581e12	−	2.45225e12i	0.0538002	−	0.0931847i
$961$	4.62754e13			1.75023
$962$	1.55852e12			0.0586710
$963$	−4.58644e13	+	7.94394e13i	−1.71853	+	2.97658i
$964$	−1.24008e13	−	2.14789e13i	−0.462493	−	0.801061i
$965$	−3.68897e11	+	6.38948e11i	−0.0136941	+	0.0237188i
$966$	−4.75449e12	−	8.23502e12i	−0.175674	−	0.304276i
$967$	−2.24991e13	−	3.89695e13i	−0.827457	−	1.43320i	−0.900027	−	0.435834i	$-0.856453\pi$
$967$	−2.24991e13	−	3.89695e13i	−0.827457	−	1.43320i	0.0725697	−	0.997363i	$-0.476880\pi$
$968$	−1.49250e13			−0.546354
$969$	4.72962e11	+	9.80711e11i	0.0172334	+	0.0357342i
$970$	8.63793e11			0.0313283
$971$	−4.43165e12	−	7.67585e12i	−0.159985	−	0.277102i	0.774878	−	0.632111i	$-0.217811\pi$
$971$	−4.43165e12	−	7.67585e12i	−0.159985	−	0.277102i	−0.934863	+	0.355009i	$0.884478\pi$
$972$	2.98185e13	+	5.16472e13i	1.07149	+	1.85587i
$973$	−1.87935e12	+	3.25513e12i	−0.0672201	+	0.116429i
$974$	1.46295e12	+	2.53391e12i	0.0520853	+	0.0902143i
$975$	−1.52433e13	+	2.64021e13i	−0.540203	+	0.935660i
$976$	−3.05189e13			−1.07658
$977$	−2.22925e13			−0.782770			−0.391385	−	0.920227i	$-0.628004\pi$
$977$	−2.22925e13			−0.782770			−0.391385	+	0.920227i	$0.628004\pi$
$978$	−6.93021e9	+	1.20035e10i	−0.000242227	+	0.000419549i
$979$	−3.82965e12	+	6.63314e12i	−0.133241	+	0.230779i
$980$	2.25946e12			0.0782504
$981$	−8.23524e13			−2.83900
$982$	−2.71249e12	+	4.69817e12i	−0.0930822	+	0.161223i
$983$	1.17602e12	+	2.03692e12i	0.0401720	+	0.0695799i	0.885412	−	0.464806i	$-0.153876\pi$
$983$	1.17602e12	+	2.03692e12i	0.0401720	+	0.0695799i	−0.845240	+	0.534386i	$0.820543\pi$
$984$	−1.22939e13	+	2.12937e13i	−0.418035	+	0.724058i
$985$	6.90321e10	+	1.19567e11i	0.00233662	+	0.00404715i
$986$	1.56761e11	+	2.71518e11i	0.00528192	+	0.00914856i
$987$	1.92614e13			0.646040
$988$	1.59521e13	+	1.18645e12i	0.532612	+	0.0396137i
$989$	3.85583e13			1.28155
$990$	−2.09056e11	−	3.62096e11i	−0.00691679	−	0.0119802i
$991$	−3.33915e12	−	5.78357e12i	−0.109978	−	0.190487i	0.805783	−	0.592210i	$-0.201745\pi$
$991$	−3.33915e12	−	5.78357e12i	−0.109978	−	0.190487i	−0.915761	+	0.401724i	$0.868411\pi$
$992$	−1.97892e13	+	3.42758e13i	−0.648821	+	1.12379i
$993$	4.56724e13	+	7.91069e13i	1.49067	+	2.58192i
$994$	8.66388e11	−	1.50063e12i	0.0281497	−	0.0487567i
$995$	−2.74969e12			−0.0889365
$996$	−3.07585e12			−0.0990370
$997$	−6.68365e12	+	1.15764e13i	−0.214233	+	0.371062i	−0.953035	−	0.302861i	$-0.902058\pi$
$997$	−6.68365e12	+	1.15764e13i	−0.214233	+	0.371062i	0.738802	+	0.673922i	$0.235392\pi$
$998$	3.78991e12	−	6.56432e12i	0.120932	−	0.209461i
$999$	3.01899e13			0.958997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.10.c.a.7.8	✓	28
19.7	even	3		361.10.a.e.1.7		14
19.11	even	3	inner	19.10.c.a.11.8	yes	28
19.12	odd	6		361.10.a.f.1.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.c.a.7.8	✓	28	1.1	even	1	trivial
19.10.c.a.11.8	yes	28	19.11	even	3	inner
361.10.a.e.1.7		14	19.7	even	3
361.10.a.f.1.8		14	19.12	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.32582 + 5.76048i) q^{2} +(-131.258 - 227.345i) q^{3} +(233.878 - 405.088i) q^{4} +(-77.5423 - 134.307i) q^{5} +(873.077 - 1512.21i) q^{6} -3034.24 q^{7} +6516.98 q^{8} +(-24615.6 + 42635.4i) q^{9} +(515.783 - 893.362i) q^{10} -8232.96 q^{11} -122793. q^{12} +(30100.6 - 52135.8i) q^{13} +(-10091.3 - 17478.7i) q^{14} +(-20356.0 + 35257.7i) q^{15} +(-98071.2 - 169864. i) q^{16} +(3650.67 + 6323.15i) q^{17} -327467. q^{18} +(-319734. + 469529. i) q^{19} -72541.7 q^{20} +(398267. + 689818. i) q^{21} +(-27381.3 - 47425.8i) q^{22} +(-897370. + 1.55429e6i) q^{23} +(-855402. - 1.48160e6i) q^{24} +(964537. - 1.67063e6i) q^{25} +400436. q^{26} +7.75683e6 q^{27} +(-709642. + 1.22914e6i) q^{28} +(3.22780e6 - 5.59072e6i) q^{29} -270801. q^{30} -8.52731e6 q^{31} +(2.32068e6 - 4.01953e6i) q^{32} +(1.08064e6 + 1.87172e6i) q^{33} +(-24282.9 + 42059.3i) q^{34} +(235282. + 407520. i) q^{35} +(1.15141e7 + 1.99430e7i) q^{36} +3.89204e6 q^{37} +(-3.76809e6 - 280256. i) q^{38} -1.58037e7 q^{39} +(-505341. - 875277. i) q^{40} +(-7.18606e6 - 1.24466e7i) q^{41} +(-2.64912e6 + 4.58842e6i) q^{42} +(-1.07420e7 - 1.86058e7i) q^{43} +(-1.92551e6 + 3.33508e6i) q^{44} +7.63499e6 q^{45} -1.19380e7 q^{46} +(1.20907e7 - 2.09418e7i) q^{47} +(-2.57452e7 + 4.45919e7i) q^{48} -3.11470e7 q^{49} +1.28315e7 q^{50} +(958357. - 1.65992e6i) q^{51} +(-1.40797e7 - 2.43868e7i) q^{52} +(-3.12697e7 + 5.41607e7i) q^{53} +(2.57978e7 + 4.46831e7i) q^{54} +(638403. + 1.10575e6i) q^{55} -1.97741e7 q^{56} +(1.48712e8 + 1.10607e7i) q^{57} +4.29403e7 q^{58} +(-4.03909e7 - 6.99592e7i) q^{59} +(9.52164e6 + 1.64920e7i) q^{60} +(7.77978e7 - 1.34750e8i) q^{61} +(-2.83603e7 - 4.91214e7i) q^{62} +(7.46895e7 - 1.29366e8i) q^{63} -6.95523e7 q^{64} -9.33628e6 q^{65} +(-7.18801e6 + 1.24500e7i) q^{66} +(-9.84979e7 + 1.70603e8i) q^{67} +3.41525e6 q^{68} +4.71146e8 q^{69} +(-1.56501e6 + 2.71067e6i) q^{70} +(4.29274e7 + 7.43524e7i) q^{71} +(-1.60419e8 + 2.77854e8i) q^{72} +(-9.37194e7 - 1.62327e8i) q^{73} +(1.29442e7 + 2.24201e7i) q^{74} -5.06411e8 q^{75} +(1.15422e8 + 2.39333e8i) q^{76} +2.49808e7 q^{77} +(-5.25603e7 - 9.10370e7i) q^{78} +(2.10548e8 + 3.64679e8i) q^{79} +(-1.52093e7 + 2.63433e7i) q^{80} +(-5.33634e8 - 9.24281e8i) q^{81} +(4.77990e7 - 8.27903e7i) q^{82} +2.50490e7 q^{83} +3.72583e8 q^{84} +(566163. - 980623. i) q^{85} +(7.14521e7 - 1.23759e8i) q^{86} -1.69469e9 q^{87} -5.36540e7 q^{88} +(4.65160e8 - 8.05681e8i) q^{89} +(2.53926e7 + 4.39812e7i) q^{90} +(-9.13324e7 + 1.58192e8i) q^{91} +(4.19750e8 + 7.27029e8i) q^{92} +(1.11927e9 + 1.93864e9i) q^{93} +1.60846e8 q^{94} +(8.78541e7 + 6.53425e6i) q^{95} -1.21843e9 q^{96} +(4.18681e8 + 7.25176e8i) q^{97} +(-1.03589e8 - 1.79422e8i) q^{98} +(2.02659e8 - 3.51016e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9} + 41180 q^{10} - 114810 q^{11} + 235458 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} - 279203 q^{16}+ \cdots - 736622698 q^{99}+O(q^{100}) \) 28 * q + 15 * q^2 - 74 * q^3 - 2987 * q^4 - 285 * q^5 - 535 * q^6 - 2676 * q^7 - 24270 * q^8 - 57928 * q^9 + 41180 * q^10 - 114810 * q^11 + 235458 * q^12 + 98671 * q^13 - 148290 * q^14 + 428251 * q^15 - 279203 * q^16 + 466251 * q^17 + 734964 * q^18 + 387157 * q^19 - 3343620 * q^20 + 689090 * q^21 - 1689395 * q^22 - 3087747 * q^23 - 234183 * q^24 - 3260823 * q^25 + 9033144 * q^26 + 4216540 * q^27 - 703814 * q^28 + 7831383 * q^29 - 11859224 * q^30 - 9265632 * q^31 + 11470815 * q^32 + 22791973 * q^33 + 13457096 * q^34 - 13222428 * q^35 + 7355018 * q^36 + 27205020 * q^37 - 67677738 * q^38 - 20775702 * q^39 - 16500258 * q^40 + 20419440 * q^41 - 10220798 * q^42 + 27415427 * q^43 + 41775405 * q^44 - 85982588 * q^45 - 137234708 * q^46 - 90906681 * q^47 + 33057375 * q^48 + 229824892 * q^49 + 44406714 * q^50 + 134429123 * q^51 + 66195006 * q^52 + 47827863 * q^53 - 130507669 * q^54 - 157712310 * q^55 + 382459116 * q^56 - 162912873 * q^57 - 344026048 * q^58 + 255540 * q^59 + 287916794 * q^60 + 304035459 * q^61 + 693626280 * q^62 - 122148024 * q^63 - 908491514 * q^64 - 1424960190 * q^65 - 611099417 * q^66 + 165758480 * q^67 + 357518508 * q^68 + 271237278 * q^69 + 1167527028 * q^70 + 685508589 * q^71 + 142349670 * q^72 - 602867050 * q^73 - 82104492 * q^74 + 1900274774 * q^75 - 1298297525 * q^76 - 491994756 * q^77 - 911449840 * q^78 + 78162339 * q^79 + 227607150 * q^80 + 1230916118 * q^81 + 360208019 * q^82 + 413839926 * q^83 - 467304924 * q^84 - 1440537237 * q^85 + 936824310 * q^86 - 678876318 * q^87 - 1646777694 * q^88 + 1256827551 * q^89 + 1879090924 * q^90 + 537759588 * q^91 - 677003592 * q^92 - 492493440 * q^93 - 848375184 * q^94 - 2034458607 * q^95 - 6041588930 * q^96 + 2109813492 * q^97 + 2689941591 * q^98 - 736622698 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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