LMFDB - Embedded newform 13.14.c.a.3.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,14,Mod(3,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 14, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.3"); S:= CuspForms(chi, 14); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	13.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:	$13.9400207637$
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			3.9
Character	$\chi$	$=$	13.3
Dual form			13.14.c.a.9.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(11.2286 + 19.4486i) q^{2} +(-1142.04 - 1978.08i) q^{3} +(3843.84 - 6657.72i) q^{4} +17999.0 q^{5} +(25647.2 - 44422.2i) q^{6} +(281521. - 487609. i) q^{7} +356614. q^{8} +(-1.81136e6 + 3.13737e6i) q^{9} +(202104. + 350055. i) q^{10} +(-3.49471e6 - 6.05302e6i) q^{11} -1.75593e7 q^{12} +(9.43504e6 + 1.46238e7i) q^{13} +1.26444e7 q^{14} +(-2.05556e7 - 3.56034e7i) q^{15} +(-2.74844e7 - 4.76044e7i) q^{16} +(1.89678e7 - 3.28532e7i) q^{17} -8.13565e7 q^{18} +(-3.28052e7 + 5.68203e7i) q^{19} +(6.91852e7 - 1.19832e8i) q^{20} -1.28604e9 q^{21} +(7.84817e7 - 1.35934e8i) q^{22} +(4.98922e8 + 8.64159e8i) q^{23} +(-4.07269e8 - 7.05410e8i) q^{24} -8.96739e8 q^{25} +(-1.78469e8 + 3.47703e8i) q^{26} +4.63303e9 q^{27} +(-2.16424e9 - 3.74858e9i) q^{28} +(1.74170e9 + 3.01672e9i) q^{29} +(4.61624e8 - 7.99556e8i) q^{30} +2.61380e9 q^{31} +(2.07792e9 - 3.59906e9i) q^{32} +(-7.98222e9 + 1.38256e10i) q^{33} +8.51932e8 q^{34} +(5.06710e9 - 8.77648e9i) q^{35} +(1.39251e10 + 2.41190e10i) q^{36} +(-4.31490e8 - 7.47363e8i) q^{37} -1.47343e9 q^{38} +(1.81517e10 - 3.53642e10i) q^{39} +6.41870e9 q^{40} +(-8.87545e8 - 1.53727e9i) q^{41} +(-1.44404e10 - 2.50116e10i) q^{42} +(-3.49859e8 + 6.05974e8i) q^{43} -5.37324e10 q^{44} +(-3.26027e10 + 5.64695e10i) q^{45} +(-1.12044e10 + 1.94067e10i) q^{46} +4.91139e10 q^{47} +(-6.27767e10 + 1.08732e11i) q^{48} +(-1.10064e11 - 1.90636e11i) q^{49} +(-1.00692e10 - 1.74403e10i) q^{50} -8.66483e10 q^{51} +(1.33628e11 - 6.60443e9i) q^{52} +3.91615e10 q^{53} +(5.20227e10 + 9.01059e10i) q^{54} +(-6.29014e10 - 1.08948e11i) q^{55} +(1.00394e11 - 1.73888e11i) q^{56} +1.49860e11 q^{57} +(-3.91139e10 + 6.77473e10i) q^{58} +(1.16103e11 - 2.01097e11i) q^{59} -3.16050e11 q^{60} +(-1.52787e10 + 2.64635e10i) q^{61} +(2.93494e10 + 5.08347e10i) q^{62} +(1.01987e12 + 1.76647e12i) q^{63} -3.56976e11 q^{64} +(1.69821e11 + 2.63214e11i) q^{65} -3.58518e11 q^{66} +(-4.37449e11 - 7.57685e11i) q^{67} +(-1.45818e11 - 2.52565e11i) q^{68} +(1.13958e12 - 1.97381e12i) q^{69} +2.27587e11 q^{70} +(4.80131e11 - 8.31612e11i) q^{71} +(-6.45957e11 + 1.11883e12i) q^{72} +8.68862e11 q^{73} +(9.69010e9 - 1.67837e10i) q^{74} +(1.02411e12 + 1.77382e12i) q^{75} +(2.52196e11 + 4.36816e11i) q^{76} -3.93534e12 q^{77} +(8.91603e11 - 4.40667e10i) q^{78} -7.23289e11 q^{79} +(-4.94692e11 - 8.56832e11i) q^{80} +(-2.40323e12 - 4.16251e12i) q^{81} +(1.99318e10 - 3.45230e10i) q^{82} -2.62815e12 q^{83} +(-4.94331e12 + 8.56207e12i) q^{84} +(3.41402e11 - 5.91326e11i) q^{85} -1.57138e10 q^{86} +(3.97819e12 - 6.89043e12i) q^{87} +(-1.24626e12 - 2.15859e12i) q^{88} +(2.45111e12 + 4.24546e12i) q^{89} -1.46434e12 q^{90} +(9.78685e12 - 4.83706e11i) q^{91} +7.67110e12 q^{92} +(-2.98507e12 - 5.17029e12i) q^{93} +(5.51482e11 + 9.55195e11i) q^{94} +(-5.90462e11 + 1.02271e12i) q^{95} -9.49228e12 q^{96} +(-3.25335e12 + 5.63496e12i) q^{97} +(2.47174e12 - 4.28117e12i) q^{98} +2.53207e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 65 q^{2} + 728 q^{3} - 53249 q^{4} + 41860 q^{5} + 143910 q^{6} - 173992 q^{7} + 2616978 q^{8} - 5231838 q^{9} + 2769243 q^{10} + 10986144 q^{11} - 45205464 q^{12} + 25107706 q^{13} - 23731756 q^{14}+ \cdots + 33239809172544 q^{99}+O(q^{100}) $ 28 * q - 65 * q^2 + 728 * q^3 - 53249 * q^4 + 41860 * q^5 + 143910 * q^6 - 173992 * q^7 + 2616978 * q^8 - 5231838 * q^9 + 2769243 * q^10 + 10986144 * q^11 - 45205464 * q^12 + 25107706 * q^13 - 23731756 * q^14 - 75354448 * q^15 - 273433217 * q^16 + 255934950 * q^17 - 350685842 * q^18 - 266623552 * q^19 - 225433091 * q^20 - 2515875856 * q^21 + 77223114 * q^22 + 1914406544 * q^23 - 680727216 * q^24 + 5225878768 * q^25 - 9205789749 * q^26 + 3550452320 * q^27 - 3680076400 * q^28 + 6211296126 * q^29 + 5703660004 * q^30 + 6997674944 * q^31 + 2312486527 * q^32 + 5621901584 * q^33 - 23373723594 * q^34 + 23009265024 * q^35 + 23496114839 * q^36 + 19577630774 * q^37 + 51648723644 * q^38 + 31282255680 * q^39 - 111700587858 * q^40 - 6039692074 * q^41 + 143590583874 * q^42 + 16878499784 * q^43 - 489551846992 * q^44 - 148673926778 * q^45 + 177583142490 * q^46 + 369404914944 * q^47 + 92920518608 * q^48 - 195653684766 * q^49 - 753661423970 * q^50 + 617169279136 * q^51 - 727838751302 * q^52 - 287550769100 * q^53 + 365361720282 * q^54 + 855926433792 * q^55 + 192505368988 * q^56 - 1924513438848 * q^57 - 660641292207 * q^58 + 637655529992 * q^59 + 2555257062384 * q^60 + 1530666437030 * q^61 + 1907899186036 * q^62 - 832654573712 * q^63 + 632232280450 * q^64 - 2489693680994 * q^65 - 270853649100 * q^66 - 1120398677944 * q^67 + 4085795015901 * q^68 + 1473200404976 * q^69 - 9377684744688 * q^70 + 1506585643472 * q^71 + 3521118562923 * q^72 - 852513981436 * q^73 + 4665118313621 * q^74 + 2605103918408 * q^75 - 6106356745372 * q^76 + 2854115035024 * q^77 - 8622775525858 * q^78 - 7032676662784 * q^79 + 5983641421745 * q^80 + 2512348302642 * q^81 - 8600700659175 * q^82 + 2033940247872 * q^83 - 4374201207844 * q^84 + 2527554975426 * q^85 - 7547295057588 * q^86 - 1118899666832 * q^87 - 5943200108772 * q^88 + 5229645042596 * q^89 + 4220465391930 * q^90 + 18401936100704 * q^91 + 3830251788320 * q^92 - 1283055655752 * q^93 - 32271602536104 * q^94 + 8980600417472 * q^95 + 51692558969792 * q^96 + 3129146550452 * q^97 - 5503659823363 * q^98 + 33239809172544 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

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

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 $

$2$	11.2286	+	19.4486i	0.124060	+	0.214879i	0.921365	−	0.388698i	$-0.127075\pi$
$2$	11.2286	+	19.4486i	0.124060	+	0.214879i	−0.797305	+	0.603577i	$0.793742\pi$
$3$	−1142.04	−	1978.08i	−0.904470	−	1.56659i	−0.821627	−	0.570025i	$-0.806934\pi$
$3$	−1142.04	−	1978.08i	−0.904470	−	1.56659i	−0.0828425	−	0.996563i	$-0.526400\pi$
$4$	3843.84	−	6657.72i	0.469218	−	0.812710i
$5$	17999.0			0.515162			0.257581	−	0.966257i	$-0.417075\pi$
$5$	17999.0			0.515162			0.257581	+	0.966257i	$0.417075\pi$
$6$	25647.2	−	44422.2i	0.224417	−	0.388702i
$7$	281521.	−	487609.i	0.904428	−	1.56651i	0.0827441	−	0.996571i	$-0.473632\pi$
$7$	281521.	−	487609.i	0.904428	−	1.56651i	0.821684	−	0.569944i	$-0.193035\pi$
$8$	356614.			0.480965
$9$	−1.81136e6	+	3.13737e6i	−1.13613	+	1.96784i
$10$	202104.	+	350055.i	0.0639110	+	0.110697i
$11$	−3.49471e6	−	6.05302e6i	−0.594783	−	1.03020i	−0.993577	−	0.113155i	$-0.963904\pi$
$11$	−3.49471e6	−	6.05302e6i	−0.594783	−	1.03020i	0.398794	−	0.917041i	$-0.369429\pi$
$12$	−1.75593e7			−1.69757
$13$	9.43504e6	+	1.46238e7i	0.542141	+	0.840288i
$13$	9.43504e6	+	1.46238e7i	0.542141	+	0.840288i
$14$	1.26444e7			0.448814
$15$	−2.05556e7	−	3.56034e7i	−0.465948	−	0.807046i
$16$	−2.74844e7	−	4.76044e7i	−0.409550	−	0.709361i
$17$	1.89678e7	−	3.28532e7i	0.190590	−	0.330111i	−0.754856	−	0.655890i	$-0.772293\pi$
$17$	1.89678e7	−	3.28532e7i	0.190590	−	0.330111i	0.945446	+	0.325779i	$0.105627\pi$
$18$	−8.13565e7			−0.563794
$19$	−3.28052e7	+	5.68203e7i	−0.159972	+	0.277080i	−0.934858	−	0.355021i	$-0.884474\pi$
$19$	−3.28052e7	+	5.68203e7i	−0.159972	+	0.277080i	0.774886	+	0.632101i	$0.217807\pi$
$20$	6.91852e7	−	1.19832e8i	0.241723	−	0.418677i
$21$	−1.28604e9			−3.27211
$22$	7.84817e7	−	1.35934e8i	0.147578	−	0.255612i
$23$	4.98922e8	+	8.64159e8i	0.702752	+	1.21720i	0.967497	+	0.252884i	$0.0813790\pi$
$23$	4.98922e8	+	8.64159e8i	0.702752	+	1.21720i	−0.264745	+	0.964319i	$0.585288\pi$
$24$	−4.07269e8	−	7.05410e8i	−0.435019	−	0.753475i
$25$	−8.96739e8			−0.734608
$26$	−1.78469e8	+	3.47703e8i	−0.113302	+	0.220741i
$27$	4.63303e9			2.30145
$28$	−2.16424e9	−	3.74858e9i	−0.848748	−	1.47007i
$29$	1.74170e9	+	3.01672e9i	0.543734	+	0.941776i	0.998685	+	0.0512591i	$0.0163234\pi$
$29$	1.74170e9	+	3.01672e9i	0.543734	+	0.941776i	−0.454951	+	0.890516i	$0.650343\pi$
$30$	4.61624e8	−	7.99556e8i	0.115611	−	0.200245i
$31$	2.61380e9			0.528958			0.264479	−	0.964391i	$-0.414800\pi$
$31$	2.61380e9			0.528958			0.264479	+	0.964391i	$0.414800\pi$
$32$	2.07792e9	−	3.59906e9i	0.342100	−	0.592535i
$33$	−7.98222e9	+	1.38256e10i	−1.07593	+	1.86356i
$34$	8.51932e8			0.0945784
$35$	5.06710e9	−	8.77648e9i	0.465927	−	0.807008i
$36$	1.39251e10	+	2.41190e10i	1.06619	+	1.84669i
$37$	−4.31490e8	−	7.47363e8i	−0.0276477	−	0.0478873i	0.851870	−	0.523753i	$-0.175468\pi$
$37$	−4.31490e8	−	7.47363e8i	−0.0276477	−	0.0478873i	−0.879518	+	0.475865i	$0.842135\pi$
$38$	−1.47343e9			−0.0793847
$39$	1.81517e10	−	3.53642e10i	0.826034	−	1.60933i
$40$	6.41870e9			0.247775
$41$	−8.87545e8	−	1.53727e9i	−0.0291807	−	0.0505424i	0.851066	−	0.525058i	$-0.175956\pi$
$41$	−8.87545e8	−	1.53727e9i	−0.0291807	−	0.0505424i	−0.880247	+	0.474516i	$0.842623\pi$
$42$	−1.44404e10	−	2.50116e10i	−0.405939	−	0.703106i
$43$	−3.49859e8	+	6.05974e8i	−0.00844011	+	0.0146187i	−0.870215	−	0.492673i	$-0.836020\pi$
$43$	−3.49859e8	+	6.05974e8i	−0.00844011	+	0.0146187i	0.861775	+	0.507292i	$0.169353\pi$
$44$	−5.37324e10			−1.11633
$45$	−3.26027e10	+	5.64695e10i	−0.585291	+	1.01375i
$46$	−1.12044e10	+	1.94067e10i	−0.174367	+	0.302013i
$47$	4.91139e10			0.664612			0.332306	−	0.943172i	$-0.392173\pi$
$47$	4.91139e10			0.664612			0.332306	+	0.943172i	$0.392173\pi$
$48$	−6.27767e10	+	1.08732e11i	−0.740850	+	1.28319i
$49$	−1.10064e11	−	1.90636e11i	−1.13598	−	1.96757i
$50$	−1.00692e10	−	1.74403e10i	−0.0911356	−	0.157852i
$51$	−8.66483e10			−0.689531
$52$	1.33628e11	−	6.60443e9i	0.937292	−	0.0463248i
$53$	3.91615e10			0.242698			0.121349	−	0.992610i	$-0.461278\pi$
$53$	3.91615e10			0.242698			0.121349	+	0.992610i	$0.461278\pi$
$54$	5.20227e10	+	9.01059e10i	0.285518	+	0.494531i
$55$	−6.29014e10	−	1.08948e11i	−0.306410	−	0.530717i
$56$	1.00394e11	−	1.73888e11i	0.434998	−	0.753439i
$57$	1.49860e11			0.578760
$58$	−3.91139e10	+	6.77473e10i	−0.134912	+	0.233674i
$59$	1.16103e11	−	2.01097e11i	0.358349	−	0.620678i	−0.629336	−	0.777133i	$-0.716673\pi$
$59$	1.16103e11	−	2.01097e11i	0.358349	−	0.620678i	0.987685	+	0.156455i	$0.0500066\pi$
$60$	−3.16050e11			−0.874525
$61$	−1.52787e10	+	2.64635e10i	−0.0379701	+	0.0657662i	−0.884386	−	0.466756i	$-0.845423\pi$
$61$	−1.52787e10	+	2.64635e10i	−0.0379701	+	0.0657662i	0.846416	+	0.532523i	$0.178756\pi$
$62$	2.93494e10	+	5.08347e10i	0.0656226	+	0.113662i
$63$	1.01987e12	+	1.76647e12i	2.05510	+	3.55953i
$64$	−3.56976e11			−0.649335
$65$	1.69821e11	+	2.63214e11i	0.279290	+	0.432884i
$66$	−3.58518e11			−0.533919
$67$	−4.37449e11	−	7.57685e11i	−0.590802	−	1.02330i	−0.994125	−	0.108241i	$-0.965478\pi$
$67$	−4.37449e11	−	7.57685e11i	−0.590802	−	1.02330i	0.403323	−	0.915058i	$-0.367855\pi$
$68$	−1.45818e11	−	2.52565e11i	−0.178856	−	0.309788i
$69$	1.13958e12	−	1.97381e12i	1.27124	−	2.20185i
$70$	2.27587e11			0.231212
$71$	4.80131e11	−	8.31612e11i	0.444816	−	0.770444i	−0.553223	−	0.833033i	$-0.686602\pi$
$71$	4.80131e11	−	8.31612e11i	0.444816	−	0.770444i	0.998039	+	0.0625888i	$0.0199357\pi$
$72$	−6.45957e11	+	1.11883e12i	−0.546440	+	0.946462i
$73$	8.68862e11			0.671974			0.335987	−	0.941867i	$-0.390930\pi$
$73$	8.68862e11			0.671974			0.335987	+	0.941867i	$0.390930\pi$
$74$	9.69010e9	−	1.67837e10i	0.00685997	−	0.0118818i
$75$	1.02411e12	+	1.77382e12i	0.664431	+	1.15083i
$76$	2.52196e11	+	4.36816e11i	0.150124	+	0.260022i
$77$	−3.93534e12			−2.15175
$78$	8.91603e11	−	4.40667e10i	0.448287	−	0.0221562i
$79$	−7.23289e11			−0.334762			−0.167381	−	0.985892i	$-0.553531\pi$
$79$	−7.23289e11			−0.334762			−0.167381	+	0.985892i	$0.553531\pi$
$80$	−4.94692e11	−	8.56832e11i	−0.210984	−	0.365435i
$81$	−2.40323e12	−	4.16251e12i	−0.945457	−	1.63758i
$82$	1.99318e10	−	3.45230e10i	0.00724031	−	0.0125406i
$83$	−2.62815e12			−0.882353			−0.441176	−	0.897420i	$-0.645439\pi$
$83$	−2.62815e12			−0.882353			−0.441176	+	0.897420i	$0.645439\pi$
$84$	−4.94331e12	+	8.56207e12i	−1.53533	+	2.65928i
$85$	3.41402e11	−	5.91326e11i	0.0981846	−	0.170061i
$86$	−1.57138e10			−0.00418833
$87$	3.97819e12	−	6.89043e12i	0.983583	−	1.70362i
$88$	−1.24626e12	−	2.15859e12i	−0.286070	−	0.495488i
$89$	2.45111e12	+	4.24546e12i	0.522792	+	0.905502i	0.999648	+	0.0265206i	$0.00844276\pi$
$89$	2.45111e12	+	4.24546e12i	0.522792	+	0.905502i	−0.476857	+	0.878981i	$0.658224\pi$
$90$	−1.46434e12			−0.290445
$91$	9.78685e12	−	4.83706e11i	1.80665	−	0.0892920i
$92$	7.67110e12			1.31898
$93$	−2.98507e12	−	5.17029e12i	−0.478426	−	0.828659i
$94$	5.51482e11	+	9.55195e11i	0.0824518	+	0.142811i
$95$	−5.90462e11	+	1.02271e12i	−0.0824116	+	0.142741i
$96$	−9.49228e12			−1.23768
$97$	−3.25335e12	+	5.63496e12i	−0.396565	+	0.686870i	−0.993300	−	0.115568i	$-0.963131\pi$
$97$	−3.25335e12	+	5.63496e12i	−0.396565	+	0.686870i	0.596735	+	0.802439i	$0.296464\pi$
$98$	2.47174e12	−	4.28117e12i	0.281859	−	0.488195i
$99$	2.53207e13			2.70301
$100$	−3.44692e12	+	5.97023e12i	−0.344692	+	0.597023i
$101$	3.66877e12	+	6.35449e12i	0.343899	+	0.595651i	0.985153	−	0.171678i	$-0.0549188\pi$
$101$	3.66877e12	+	6.35449e12i	0.343899	+	0.595651i	−0.641254	+	0.767329i	$0.721585\pi$
$102$	−9.72942e11	−	1.68519e12i	−0.0855433	−	0.148165i
$103$	−1.44084e13			−1.18898			−0.594489	−	0.804103i	$-0.702646\pi$
$103$	−1.44084e13			−1.18898			−0.594489	+	0.804103i	$0.702646\pi$
$104$	3.36467e12	+	5.21505e12i	0.260751	+	0.404149i
$105$	−2.31474e13			−1.68567
$106$	4.39731e11	+	7.61636e11i	0.0301092	+	0.0521506i
$107$	1.33135e13	+	2.30597e13i	0.857628	+	1.48545i	0.874186	+	0.485592i	$0.161396\pi$
$107$	1.33135e13	+	2.30597e13i	0.857628	+	1.48545i	−0.0165579	+	0.999863i	$0.505271\pi$
$108$	1.78086e13	−	3.08454e13i	1.07988	−	1.87041i
$109$	6.54899e12			0.374026			0.187013	−	0.982357i	$-0.440119\pi$
$109$	6.54899e12			0.374026			0.187013	+	0.982357i	$0.440119\pi$
$110$	1.41259e12	−	2.44668e12i	0.0760265	−	0.131682i
$111$	−9.85560e11	+	1.70704e12i	−0.0500131	+	0.0866252i
$112$	−3.09498e13			−1.48163
$113$	1.47218e13	−	2.54989e13i	0.665198	−	1.15216i	−0.314034	−	0.949412i	$-0.601681\pi$
$113$	1.47218e13	−	2.54989e13i	0.665198	−	1.15216i	0.979232	−	0.202744i	$-0.0649860\pi$
$114$	1.68272e12	+	2.91456e12i	0.0718011	+	0.124363i
$115$	8.98011e12	+	1.55540e13i	0.362031	+	0.627056i
$116$	2.67793e13			1.02052
$117$	−6.29705e13	+	3.11226e12i	−2.26949	+	0.112168i
$118$	5.21472e12			0.177827
$119$	−1.06797e13	−	1.84978e13i	−0.344749	−	0.597123i
$120$	−7.33043e12	−	1.26967e13i	−0.224105	−	0.388161i
$121$	−7.16466e12	+	1.24096e13i	−0.207535	+	0.359461i
$122$	−6.86236e11			−0.0188423
$123$	−2.02723e12	+	3.51126e12i	−0.0527860	+	0.0914281i
$124$	1.00470e13	−	1.74019e13i	0.248197	−	0.429889i
$125$	−3.81119e13			−0.893604
$126$	−2.29036e13	+	3.96702e13i	−0.509911	+	0.883192i
$127$	−1.50351e13	−	2.60416e13i	−0.317968	−	0.550736i	0.662096	−	0.749419i	$-0.269667\pi$
$127$	−1.50351e13	−	2.60416e13i	−0.317968	−	0.550736i	−0.980064	+	0.198683i	$0.936334\pi$
$128$	−2.10307e13	−	3.64262e13i	−0.422657	−	0.732063i
$129$	1.59822e12			0.0305353
$130$	−3.21227e12	+	6.25832e12i	−0.0583687	+	0.113717i
$131$	3.69868e12			0.0639416			0.0319708	−	0.999489i	$-0.489822\pi$
$131$	3.69868e12			0.0639416			0.0319708	+	0.999489i	$0.489822\pi$
$132$	6.13647e13	+	1.06287e14i	1.00969	+	1.74883i
$133$	1.84707e13	+	3.19922e13i	0.289367	+	0.501198i
$134$	9.82393e12	−	1.70155e13i	0.146590	−	0.253901i
$135$	8.33900e13			1.18562
$136$	6.76420e12	−	1.17159e13i	0.0916671	−	0.158772i
$137$	8.00730e12	−	1.38691e13i	0.103467	−	0.179210i	−0.809644	−	0.586922i	$-0.800340\pi$
$137$	8.00730e12	−	1.38691e13i	0.103467	−	0.179210i	0.913111	+	0.407711i	$0.133673\pi$
$138$	5.11838e13			0.630839
$139$	4.93991e11	−	8.55617e11i	0.00580928	−	0.0100620i	−0.863106	−	0.505023i	$-0.831484\pi$
$139$	4.93991e11	−	8.55617e11i	0.00580928	−	0.0100620i	0.868915	+	0.494961i	$0.164818\pi$
$140$	−3.89542e13	−	6.74707e13i	−0.437242	−	0.757326i
$141$	−5.60901e13	−	9.71509e13i	−0.601121	−	1.04117i
$142$	2.15649e13			0.220736
$143$	5.55453e13	−	1.08216e14i	0.543204	−	1.05830i
$144$	1.99137e14			1.86121
$145$	3.13489e13	+	5.42979e13i	0.280111	+	0.485167i
$146$	9.75614e12	+	1.68981e13i	0.0833652	+	0.144393i
$147$	−2.51395e14	+	4.35429e14i	−2.05492	+	3.55922i
$148$	−6.63431e12			−0.0518913
$149$	6.41701e13	−	1.11146e14i	0.480421	−	0.832114i	−0.519326	−	0.854576i	$-0.673817\pi$
$149$	6.41701e13	−	1.11146e14i	0.480421	−	0.832114i	0.999748	+	0.0224620i	$0.00715047\pi$
$150$	−2.29988e13	+	3.98351e13i	−0.164859	+	0.285544i
$151$	−3.79463e13			−0.260507			−0.130253	−	0.991481i	$-0.541579\pi$
$151$	−3.79463e13			−0.260507			−0.130253	+	0.991481i	$0.541579\pi$
$152$	−1.16988e13	+	2.02629e13i	−0.0769411	+	0.133266i
$153$	6.87151e13	+	1.19018e14i	0.433070	+	0.750099i
$154$	−4.41886e13	−	7.65368e13i	−0.266947	−	0.462366i
$155$	4.70458e13			0.272499
$156$	−1.65673e14	−	2.56783e14i	−0.920324	−	1.42645i
$157$	−2.24267e14			−1.19513			−0.597567	−	0.801819i	$-0.703866\pi$
$157$	−2.24267e14			−1.19513			−0.597567	+	0.801819i	$0.703866\pi$
$158$	−8.12155e12	−	1.40669e13i	−0.0415306	−	0.0719331i
$159$	−4.47241e13	−	7.74644e13i	−0.219513	−	0.380208i
$160$	3.74005e13	−	6.47795e13i	0.176237	−	0.305251i
$161$	5.61829e14			2.54235
$162$	5.39699e13	−	9.34786e13i	0.234587	−	0.406317i
$163$	−7.91441e11	+	1.37082e12i	−0.00330521	+	0.00572479i	−0.867673	−	0.497135i	$-0.834385\pi$
$163$	−7.91441e11	+	1.37082e12i	−0.00330521	+	0.00572479i	0.864368	+	0.502860i	$0.167719\pi$
$164$	−1.36463e13			−0.0547684
$165$	−1.43672e14	+	2.48847e14i	−0.554277	+	0.960035i
$166$	−2.95105e13	−	5.11137e13i	−0.109465	−	0.189599i
$167$	−1.91979e14	−	3.32518e14i	−0.684852	−	1.18620i	−0.973483	−	0.228758i	$-0.926533\pi$
$167$	−1.91979e14	−	3.32518e14i	−0.684852	−	1.18620i	0.288631	−	0.957440i	$-0.406800\pi$
$168$	−4.58619e14			−1.57377
$169$	−1.24835e14	+	2.75952e14i	−0.412167	+	0.911108i
$170$	1.53339e13			0.0487232
$171$	−1.18844e14	−	2.05844e14i	−0.363499	−	0.629599i
$172$	2.68960e12	+	4.65853e12i	0.00792051	+	0.0137187i
$173$	3.24283e14	−	5.61675e14i	0.919655	−	1.59289i	0.119715	−	0.992808i	$-0.461802\pi$
$173$	3.24283e14	−	5.61675e14i	0.919655	−	1.59289i	0.799939	−	0.600081i	$-0.204865\pi$
$174$	1.78679e14			0.488094
$175$	−2.52451e14	+	4.37258e14i	−0.664400	+	1.15077i
$176$	−1.92100e14	+	3.32727e14i	−0.487187	+	0.843832i
$177$	−5.30379e14			−1.29646
$178$	−5.50454e13	+	9.53414e13i	−0.129715	+	0.224673i
$179$	1.47496e14	+	2.55470e14i	0.335147	+	0.580491i	0.983513	−	0.180838i	$-0.0578808\pi$
$179$	1.47496e14	+	2.55470e14i	0.335147	+	0.580491i	−0.648366	+	0.761328i	$0.724548\pi$
$180$	2.50639e14	+	4.34119e14i	0.549259	+	0.951344i
$181$	3.58502e14			0.757846			0.378923	−	0.925428i	$-0.376294\pi$
$181$	3.58502e14			0.757846			0.378923	+	0.925428i	$0.376294\pi$
$182$	1.19301e14	+	1.84909e14i	0.243320	+	0.377133i
$183$	6.97956e13			0.137371
$184$	1.77923e14	+	3.08171e14i	0.337999	+	0.585432i
$185$	−7.76640e12	−	1.34518e13i	−0.0142431	−	0.0246697i
$186$	6.70365e13	−	1.16111e14i	0.118707	−	0.205607i
$187$	−2.65148e14			−0.453439
$188$	1.88786e14	−	3.26986e14i	0.311848	−	0.540136i
$189$	1.30430e15	−	2.25911e15i	2.08149	−	3.60525i
$190$	−2.65203e13			−0.0408960
$191$	2.85573e14	−	4.94626e14i	0.425598	−	0.737157i	−0.570878	−	0.821035i	$-0.693397\pi$
$191$	2.85573e14	−	4.94626e14i	0.425598	−	0.737157i	0.996476	+	0.0838775i	$0.0267304\pi$
$192$	4.07681e14	+	7.06125e14i	0.587304	+	1.01724i
$193$	4.82871e14	+	8.36357e14i	0.672525	+	1.16485i	0.977186	+	0.212387i	$0.0681237\pi$
$193$	4.82871e14	+	8.36357e14i	0.672525	+	1.16485i	−0.304660	+	0.952461i	$0.598543\pi$
$194$	−1.46123e14			−0.196792
$195$	3.26713e14	−	6.36521e14i	0.425541	−	0.829063i
$196$	−1.69227e15			−2.13209
$197$	4.40338e14	+	7.62688e14i	0.536730	+	0.929643i	0.999077	+	0.0429444i	$0.0136738\pi$
$197$	4.40338e14	+	7.62688e14i	0.536730	+	0.929643i	−0.462348	+	0.886699i	$0.652993\pi$
$198$	2.84317e14	+	4.92452e14i	0.335336	+	0.580818i
$199$	3.34865e14	−	5.80003e14i	0.382230	−	0.662041i	−0.609151	−	0.793054i	$-0.708490\pi$
$199$	3.34865e14	−	5.80003e14i	0.382230	−	0.662041i	0.991381	+	0.131013i	$0.0418229\pi$
$200$	−3.19790e14			−0.353321
$201$	−9.99172e14	+	1.73062e15i	−1.06872	+	1.85109i
$202$	−8.23905e13	+	1.42705e14i	−0.0853284	+	0.147793i
$203$	1.96130e15			1.96707
$204$	−3.33062e14	+	5.76880e14i	−0.323540	+	0.560388i
$205$	−1.59749e13	−	2.76694e13i	−0.0150328	−	0.0260375i
$206$	−1.61787e14	−	2.80223e14i	−0.147505	−	0.255486i
$207$	−3.61491e15			−3.19367
$208$	4.36840e14	−	8.51075e14i	0.374033	−	0.728713i
$209$	4.58579e14			0.380595
$210$	−2.59914e14	−	4.50184e14i	−0.209124	−	0.362213i
$211$	1.97253e14	+	3.41652e14i	0.153882	+	0.266531i	0.932651	−	0.360779i	$-0.117489\pi$
$211$	1.97253e14	+	3.41652e14i	0.153882	+	0.266531i	−0.778769	+	0.627310i	$0.784156\pi$
$212$	1.50530e14	−	2.60726e14i	0.113878	−	0.197243i
$213$	−2.19332e15			−1.60929
$214$	−2.98986e14	+	5.17859e14i	−0.212795	+	0.368572i
$215$	−6.29712e12	+	1.09069e13i	−0.00434802	+	0.00753099i
$216$	1.65221e15			1.10692
$217$	7.35840e14	−	1.27451e15i	0.478404	−	0.828620i
$218$	7.35363e13	+	1.27369e14i	0.0464018	+	0.0803702i
$219$	−9.92278e14	−	1.71868e15i	−0.607780	−	1.05271i
$220$	−9.67130e14			−0.575092
$221$	6.59401e14	−	3.25903e13i	0.380715	−	0.0188165i
$222$	−4.42660e13			−0.0248185
$223$	6.25902e14	+	1.08409e15i	0.340820	+	0.590317i	0.984585	−	0.174906i	$-0.0559622\pi$
$223$	6.25902e14	+	1.08409e15i	0.340820	+	0.590317i	−0.643766	+	0.765223i	$0.722629\pi$
$224$	−1.16996e15	−	2.02642e15i	−0.618810	−	1.07181i
$225$	1.62432e15	−	2.81340e15i	0.834612	−	1.44559i
$226$	6.61223e14			0.330098
$227$	−4.96678e14	+	8.60272e14i	−0.240939	+	0.417318i	−0.960982	−	0.276611i	$-0.910789\pi$
$227$	−4.96678e14	+	8.60272e14i	−0.240939	+	0.417318i	0.720043	+	0.693929i	$0.244122\pi$
$228$	5.76037e14	−	9.97724e14i	0.271565	−	0.470364i
$229$	−3.21076e15			−1.47122			−0.735610	−	0.677406i	$-0.763104\pi$
$229$	−3.21076e15			−1.47122			−0.735610	+	0.677406i	$0.763104\pi$
$230$	−2.01669e14	+	3.49301e14i	−0.0898272	+	0.155585i
$231$	4.49433e15	+	7.78440e15i	1.94620	+	3.37091i
$232$	6.21116e14	+	1.07580e15i	0.261517	+	0.452962i
$233$	−2.86663e15			−1.17370			−0.586852	−	0.809694i	$-0.699633\pi$
$233$	−2.86663e15			−1.17370			−0.586852	+	0.809694i	$0.699633\pi$
$234$	−7.67602e14	−	1.18974e15i	−0.305656	−	0.473750i
$235$	8.84001e14			0.342382
$236$	−8.92563e14	−	1.54596e15i	−0.336287	−	0.582467i
$237$	8.26027e14	+	1.43072e15i	0.302782	+	0.524434i
$238$	2.39837e14	−	4.15410e14i	0.0855393	−	0.148158i
$239$	1.30135e15			0.451656			0.225828	−	0.974167i	$-0.427491\pi$
$239$	1.30135e15			0.451656			0.225828	+	0.974167i	$0.427491\pi$
$240$	−1.12992e15	+	1.95708e15i	−0.381658	+	0.661051i
$241$	1.85191e15	−	3.20760e15i	0.608847	−	1.05455i	−0.382583	−	0.923921i	$-0.624966\pi$
$241$	1.85191e15	−	3.20760e15i	0.608847	−	1.05455i	0.991431	−	0.130633i	$-0.0417011\pi$
$242$	−3.21798e14			−0.102987
$243$	−1.79590e15	+	3.11058e15i	−0.559552	+	0.969172i
$244$	1.17458e14	+	2.03442e14i	0.0356325	+	0.0617174i
$245$	−1.98104e15	−	3.43126e15i	−0.585213	−	1.01362i
$246$	−9.10520e13			−0.0261946
$247$	−1.14045e15	+	5.63655e13i	−0.319554	+	0.0157937i
$248$	9.32118e14			0.254410
$249$	3.00146e15	+	5.19867e15i	0.798061	+	1.38228i
$250$	−4.27944e14	−	7.41222e14i	−0.110861	−	0.192016i
$251$	−3.51967e14	+	6.09625e14i	−0.0888429	+	0.153880i	−0.907022	−	0.421083i	$-0.861650\pi$
$251$	−3.51967e14	+	6.09625e14i	−0.0888429	+	0.153880i	0.818179	+	0.574963i	$0.194984\pi$
$252$	1.56809e16			3.85716
$253$	3.48718e15	−	6.03997e15i	0.835971	−	1.44794i
$254$	3.37648e14	−	5.84824e14i	0.0788942	−	0.136649i
$255$	−1.55958e15			−0.355220
$256$	−9.89881e14	+	1.71452e15i	−0.219798	+	0.380701i
$257$	−3.36722e15	−	5.83220e15i	−0.728965	−	1.26260i	−0.957321	−	0.289026i	$-0.906669\pi$
$257$	−3.36722e15	−	5.83220e15i	−0.728965	−	1.26260i	0.228357	−	0.973578i	$-0.426665\pi$
$258$	1.79458e13	+	3.10830e13i	0.00378821	+	0.00656138i
$259$	−4.85895e14			−0.100022
$260$	2.40517e15	−	1.18873e14i	0.482857	−	0.0238648i
$261$	−1.26194e16			−2.47101
$262$	4.15311e13	+	7.19341e13i	0.00793260	+	0.0137397i
$263$	5.29280e15	+	9.16740e15i	0.986218	+	1.70818i	0.636392	+	0.771366i	$0.280426\pi$
$263$	5.29280e15	+	9.16740e15i	0.986218	+	1.70818i	0.349826	+	0.936815i	$0.386241\pi$
$264$	−2.84657e15	+	4.93041e15i	−0.517484	+	0.896308i
$265$	7.04869e14			0.125029
$266$	−4.14803e14	+	7.18459e14i	−0.0717977	+	0.124357i
$267$	5.59855e15	−	9.69698e15i	0.945698	−	1.63800i
$268$	−6.72593e15			−1.10886
$269$	−4.63182e15	+	8.02256e15i	−0.745354	+	1.29099i	0.204676	+	0.978830i	$0.434386\pi$
$269$	−4.63182e15	+	8.02256e15i	−0.745354	+	1.29099i	−0.950029	+	0.312160i	$0.898947\pi$
$270$	9.36356e14	+	1.62182e15i	0.147088	+	0.254764i
$271$	1.03346e15	+	1.79001e15i	0.158487	+	0.274508i	0.934323	−	0.356426i	$-0.116005\pi$
$271$	1.03346e15	+	1.79001e15i	0.158487	+	0.274508i	−0.775836	+	0.630935i	$0.782672\pi$
$272$	−2.08528e15			−0.312224
$273$	−1.21338e16	−	1.88067e16i	−1.77394	−	2.74951i
$274$	3.59645e14			0.0513446
$275$	3.13384e15	+	5.42798e15i	0.436933	+	0.756790i
$276$	−8.76072e15	−	1.51740e16i	−1.19297	−	2.06629i
$277$	−5.07358e15	+	8.78771e15i	−0.674833	+	1.16885i	0.301685	+	0.953408i	$0.402451\pi$
$277$	−5.07358e15	+	8.78771e15i	−0.674833	+	1.16885i	−0.976518	+	0.215437i	$0.930882\pi$
$278$	2.21874e13			0.00288280
$279$	−4.73453e15	+	8.20045e15i	−0.600965	+	1.04090i
$280$	1.80700e15	−	3.12982e15i	0.224095	−	0.388143i
$281$	9.99465e15			1.21109			0.605545	−	0.795811i	$-0.292955\pi$
$281$	9.99465e15			1.21109			0.605545	+	0.795811i	$0.292955\pi$
$282$	1.25963e15	−	2.18175e15i	0.149150	−	0.258336i
$283$	1.07476e14	+	1.86154e14i	0.0124365	+	0.0215407i	0.872177	−	0.489191i	$-0.162708\pi$
$283$	1.07476e14	+	1.86154e14i	0.0124365	+	0.0215407i	−0.859740	+	0.510732i	$0.829375\pi$
$284$	−3.69109e15	−	6.39316e15i	−0.417432	−	0.723013i
$285$	2.69733e15			0.298155
$286$	2.72835e15	−	1.34846e14i	0.294796	−	0.0145700i
$287$	−9.99450e14			−0.105567
$288$	7.52771e15	+	1.30384e16i	0.777342	+	1.34640i
$289$	4.23273e15	+	7.33131e15i	0.427351	+	0.740194i
$290$	−7.04011e14	+	1.21938e15i	−0.0695013	+	0.120380i
$291$	1.48618e16			1.43472
$292$	3.33976e15	−	5.78464e15i	0.315302	−	0.546120i
$293$	−2.69453e15	+	4.66707e15i	−0.248796	+	0.430928i	−0.963192	−	0.268814i	$-0.913368\pi$
$293$	−2.69453e15	+	4.66707e15i	−0.248796	+	0.430928i	0.714396	+	0.699742i	$0.246702\pi$
$294$	−1.12913e16			−1.01973
$295$	2.08974e15	−	3.61954e15i	0.184608	−	0.319750i
$296$	−1.53876e14	−	2.66520e14i	−0.0132976	−	0.0230321i
$297$	−1.61911e16	−	2.80438e16i	−1.36886	−	2.37094i
$298$	2.88217e15			0.238405
$299$	−7.92992e15	+	1.54495e16i	−0.641810	+	1.25041i
$300$	1.57461e16			1.24705
$301$	1.96985e14	+	3.41189e14i	0.0152669	+	0.0264431i
$302$	−4.26086e14	−	7.38002e14i	−0.0323185	−	0.0559773i
$303$	8.37977e15	−	1.45142e16i	0.622093	−	1.07750i
$304$	3.60653e15			0.262066
$305$	−2.75001e14	+	4.76316e14i	−0.0195608	+	0.0338802i
$306$	−1.54316e15	+	2.67282e15i	−0.107453	+	0.186115i
$307$	8.55076e15			0.582915			0.291458	−	0.956584i	$-0.405860\pi$
$307$	8.55076e15			0.582915			0.291458	+	0.956584i	$0.405860\pi$
$308$	−1.51268e16	+	2.62004e16i	−1.00964	+	1.74875i
$309$	1.64550e16	+	2.85009e16i	1.07540	+	1.86264i
$310$	5.28260e14	+	9.14974e14i	0.0338062	+	0.0585541i
$311$	−2.68661e16			−1.68369			−0.841846	−	0.539719i	$-0.818531\pi$
$311$	−2.68661e16			−1.68369			−0.841846	+	0.539719i	$0.818531\pi$
$312$	6.47317e15	−	1.26114e16i	0.397294	−	0.774030i
$313$	1.98404e16			1.19265			0.596325	−	0.802743i	$-0.296627\pi$
$313$	1.98404e16			1.19265			0.596325	+	0.802743i	$0.296627\pi$
$314$	−2.51821e15	−	4.36167e15i	−0.148269	−	0.256809i
$315$	1.83567e16	+	3.17947e16i	1.05871	+	1.83374i
$316$	−2.78020e15	+	4.81545e15i	−0.157076	+	0.272064i
$317$	−5.96403e15			−0.330107			−0.165053	−	0.986285i	$-0.552780\pi$
$317$	−5.96403e15			−0.330107			−0.165053	+	0.986285i	$0.552780\pi$
$318$	1.00438e15	−	1.73964e15i	0.0544657	−	0.0943373i
$319$	1.21735e16	−	2.10851e16i	0.646808	−	1.12031i
$320$	−6.42521e15			−0.334513
$321$	3.04092e16	−	5.26704e16i	1.55140	−	2.68710i
$322$	6.30858e15	+	1.09268e16i	0.315405	+	0.546297i
$323$	1.24449e15	+	2.15552e15i	0.0609782	+	0.105617i
$324$	−3.69504e16			−1.77450
$325$	−8.46077e15	−	1.31137e16i	−0.398261	−	0.617282i
$326$	−3.55472e13			−0.00164018
$327$	−7.47922e15	−	1.29544e16i	−0.338295	−	0.585945i
$328$	−3.16511e14	−	5.48213e14i	−0.0140349	−	0.0243091i
$329$	1.38266e16	−	2.39484e16i	0.601093	−	1.04112i
$330$	−6.45297e15			−0.275055
$331$	−1.82200e16	+	3.15580e16i	−0.761495	+	1.31895i	0.180585	+	0.983559i	$0.442201\pi$
$331$	−1.82200e16	+	3.15580e16i	−0.761495	+	1.31895i	−0.942080	+	0.335388i	$0.891133\pi$
$332$	−1.01022e16	+	1.74975e16i	−0.414016	+	0.717096i
$333$	3.12634e15			0.125646
$334$	4.31133e15	−	7.46744e15i	0.169926	−	0.294320i
$335$	−7.87366e15	−	1.36376e16i	−0.304358	−	0.527164i
$336$	3.53459e16	+	6.12210e16i	1.34009	+	2.32111i
$337$	2.45702e16			0.913723			0.456861	−	0.889538i	$-0.348974\pi$
$337$	2.45702e16			0.913723			0.456861	+	0.889538i	$0.348974\pi$
$338$	−6.76860e15	+	6.70702e14i	−0.246911	+	0.0244665i
$339$	−6.72516e16			−2.40660
$340$	−2.62459e15	−	4.54592e15i	−0.0921400	−	0.159591i
$341$	−9.13447e15	−	1.58214e16i	−0.314615	−	0.544930i
$342$	2.66892e15	−	4.62270e15i	0.0901915	−	0.156216i
$343$	−6.93886e16			−2.30079
$344$	−1.24765e14	+	2.16099e14i	−0.00405940	+	0.00703109i
$345$	2.05113e16	−	3.55267e16i	0.654892	−	1.13431i
$346$	1.45650e16			0.456370
$347$	−1.37893e16	+	2.38837e16i	−0.424033	+	0.734446i	−0.996330	−	0.0856005i	$-0.972719\pi$
$347$	−1.37893e16	+	2.38837e16i	−0.424033	+	0.734446i	0.572297	+	0.820046i	$0.306052\pi$
$348$	−3.05830e16	−	5.29714e16i	−0.923030	−	1.59873i
$349$	−6.34974e15	−	1.09981e16i	−0.188101	−	0.325800i	0.756516	−	0.653975i	$-0.226900\pi$
$349$	−6.34974e15	−	1.09981e16i	−0.188101	−	0.325800i	−0.944617	+	0.328175i	$0.893567\pi$
$350$	−1.13387e16			−0.329702
$351$	4.37128e16	+	6.77525e16i	1.24771	+	1.93388i
$352$	−2.90469e16			−0.813902
$353$	9.80075e14	+	1.69754e15i	0.0269603	+	0.0466965i	0.879191	−	0.476470i	$-0.158084\pi$
$353$	9.80075e14	+	1.69754e15i	0.0269603	+	0.0466965i	−0.852230	+	0.523167i	$0.824751\pi$
$354$	−5.95543e15	−	1.03151e16i	−0.160839	−	0.278582i
$355$	8.64189e15	−	1.49682e16i	0.229152	−	0.396903i
$356$	3.76867e16			0.981213
$357$	−2.43933e16	+	4.22505e16i	−0.623631	+	1.08016i
$358$	−3.31235e15	+	5.73716e15i	−0.0831567	+	0.144032i
$359$	7.65438e16			1.88710			0.943552	−	0.331223i	$-0.107461\pi$
$359$	7.65438e16			1.88710			0.943552	+	0.331223i	$0.107461\pi$
$360$	−1.16266e16	+	2.01378e16i	−0.281505	+	0.487581i
$361$	1.88741e16	+	3.26909e16i	0.448818	+	0.777375i
$362$	4.02549e15	+	6.97236e15i	0.0940186	+	0.162845i
$363$	3.27294e16			0.750836
$364$	3.43987e16	−	6.70174e16i	0.775145	−	1.51018i
$365$	1.56387e16			0.346175
$366$	7.83710e14	+	1.35743e15i	0.0170423	+	0.0295181i
$367$	−3.66097e16	−	6.34099e16i	−0.782109	−	1.35465i	−0.930711	−	0.365755i	$-0.880811\pi$
$367$	−3.66097e16	−	6.34099e16i	−0.782109	−	1.35465i	0.148602	−	0.988897i	$-0.452523\pi$
$368$	2.74252e16	−	4.75018e16i	0.575623	−	0.997009i
$369$	6.43065e15			0.132612
$370$	1.74412e14	−	3.02091e14i	0.00353399	−	0.00612106i
$371$	1.10248e16	−	1.90955e16i	0.219503	−	0.380190i
$372$	−4.58964e16			−0.897945
$373$	2.02543e16	−	3.50815e16i	0.389413	−	0.674482i	−0.602958	−	0.797773i	$-0.706011\pi$
$373$	2.02543e16	−	3.50815e16i	0.389413	−	0.674482i	0.992371	+	0.123291i	$0.0393447\pi$
$374$	−2.97726e15	−	5.15676e15i	−0.0562537	−	0.0974342i
$375$	4.35254e16	+	7.53881e16i	0.808238	+	1.39991i
$376$	1.75147e16			0.319655
$377$	−2.76828e16	+	5.39331e16i	−0.496582	+	0.967468i
$378$	5.85819e16			1.03292
$379$	−7.32469e15	−	1.26867e16i	−0.126950	−	0.219885i	0.795543	−	0.605897i	$-0.207186\pi$
$379$	−7.32469e15	−	1.26867e16i	−0.126950	−	0.219885i	−0.922494	+	0.386012i	$0.873852\pi$
$380$	4.53927e15	+	7.86225e15i	0.0773380	+	0.133953i
$381$	−3.43415e16	+	5.94812e16i	−0.575184	+	0.996248i
$382$	1.28264e16			0.211199
$383$	−1.95998e16	+	3.39478e16i	−0.317292	+	0.549566i	−0.979922	−	0.199381i	$-0.936107\pi$
$383$	−1.95998e16	+	3.39478e16i	−0.317292	+	0.549566i	0.662630	+	0.748947i	$0.269440\pi$
$384$	−4.80358e16	+	8.32004e16i	−0.764561	+	1.32426i
$385$	−7.08323e16			−1.10850
$386$	−1.08440e16	+	1.87823e16i	−0.166867	+	0.289022i
$387$	−1.26744e15	−	2.19527e15i	−0.0191781	−	0.0332175i
$388$	2.50107e16	+	4.33197e16i	0.372151	+	0.644584i
$389$	1.62572e16			0.237888			0.118944	−	0.992901i	$-0.462049\pi$
$389$	1.62572e16			0.237888			0.118944	+	0.992901i	$0.462049\pi$
$390$	1.60480e16	−	7.93156e14i	0.230941	−	0.0114140i
$391$	3.78539e16			0.535749
$392$	−3.92504e16	−	6.79836e16i	−0.546367	−	0.946335i
$393$	−4.22405e15	−	7.31627e15i	−0.0578332	−	0.100170i
$394$	−9.88879e15	+	1.71279e16i	−0.133174	+	0.230663i
$395$	−1.30185e16			−0.172456
$396$	9.73287e16	−	1.68578e17i	1.26830	−	2.19676i
$397$	−6.92658e16	+	1.19972e17i	−0.887933	+	1.53795i	−0.0456188	+	0.998959i	$0.514526\pi$
$397$	−6.92658e16	+	1.19972e17i	−0.887933	+	1.53795i	−0.842314	+	0.538986i	$0.818807\pi$
$398$	1.50403e16			0.189678
$399$	4.21887e16	−	7.30730e16i	0.523447	−	0.906636i
$400$	2.46463e16	+	4.26887e16i	0.300858	+	0.521102i
$401$	−8.03729e16	−	1.39210e17i	−0.965320	−	1.67198i	−0.708752	−	0.705458i	$-0.750741\pi$
$401$	−8.03729e16	−	1.39210e17i	−0.965320	−	1.67198i	−0.256568	−	0.966526i	$-0.582592\pi$
$402$	−4.48774e16			−0.530345
$403$	2.46613e16	+	3.82236e16i	0.286770	+	0.444477i
$404$	5.64085e16			0.645455
$405$	−4.32557e16	−	7.49210e16i	−0.487063	−	0.843619i
$406$	2.20228e16	+	3.81446e16i	0.244035	+	0.422682i
$407$	−3.01587e15	+	5.22364e15i	−0.0328888	+	0.0569652i
$408$	−3.09000e16			−0.331641
$409$	8.90405e16	−	1.54223e17i	0.940560	−	1.62910i	0.176153	−	0.984363i	$-0.443635\pi$
$409$	8.90405e16	−	1.54223e17i	0.940560	−	1.62910i	0.764407	−	0.644734i	$-0.223032\pi$
$410$	3.58753e14	−	6.21379e14i	0.00372993	−	0.00646043i
$411$	−3.65787e16			−0.374332
$412$	−5.53836e16	+	9.59271e16i	−0.557890	+	0.966295i
$413$	−6.53710e16	−	1.13226e17i	−0.648201	−	1.12272i
$414$	−4.05906e16	−	7.03049e16i	−0.396208	−	0.686252i
$415$	−4.73041e16			−0.454554
$416$	7.22371e16	−	3.57025e15i	0.683366	−	0.0337748i
$417$	−2.25663e15			−0.0210173
$418$	5.14922e15	+	8.91872e15i	0.0472167	+	0.0817818i
$419$	5.80333e16	+	1.00517e17i	0.523945	+	0.907500i	0.999611	+	0.0278739i	$0.00887369\pi$
$419$	5.80333e16	+	1.00517e17i	0.523945	+	0.907500i	−0.475666	+	0.879626i	$0.657793\pi$
$420$	−8.89747e16	+	1.54109e17i	−0.790945	+	1.36996i
$421$	−8.56586e16			−0.749786			−0.374893	−	0.927068i	$-0.622321\pi$
$421$	−8.56586e16			−0.749786			−0.374893	+	0.927068i	$0.622321\pi$
$422$	−4.42977e15	+	7.67259e15i	−0.0381813	+	0.0661319i
$423$	−8.89629e16	+	1.54088e17i	−0.755086	+	1.30785i
$424$	1.39656e16			0.116729
$425$	−1.70092e16	+	2.94608e16i	−0.140009	+	0.242502i
$426$	−2.46280e16	−	4.26570e16i	−0.199649	−	0.345802i
$427$	8.60255e15	+	1.49001e16i	0.0686825	+	0.118962i
$428$	2.04700e17			1.60966
$429$	−2.77495e17	+	1.37149e16i	−2.14923	+	0.106224i
$430$	−2.82832e14			−0.00215767
$431$	9.84152e16	+	1.70460e17i	0.739537	+	1.28092i	0.952704	+	0.303900i	$0.0982890\pi$
$431$	9.84152e16	+	1.70460e17i	0.739537	+	1.28092i	−0.213166	+	0.977016i	$0.568378\pi$
$432$	−1.27336e17	−	2.20553e17i	−0.942556	−	1.63256i
$433$	−8.74168e16	+	1.51410e17i	−0.637417	+	1.10404i	0.348581	+	0.937279i	$0.386664\pi$
$433$	−8.74168e16	+	1.51410e17i	−0.637417	+	1.10404i	−0.985998	+	0.166760i	$0.946670\pi$
$434$	3.30499e16			0.237404
$435$	7.16036e16	−	1.24021e17i	0.506704	−	0.877637i
$436$	2.51732e16	−	4.36013e16i	0.175500	−	0.303975i
$437$	−6.54691e16			−0.449683
$438$	2.22839e16	−	3.85968e16i	0.150803	−	0.261198i
$439$	−5.99434e16	−	1.03825e17i	−0.399689	−	0.692281i	0.593999	−	0.804466i	$-0.297548\pi$
$439$	−5.99434e16	−	1.03825e17i	−0.399689	−	0.692281i	−0.993687	+	0.112185i	$0.964215\pi$
$440$	−2.24315e16	−	3.88525e16i	−0.147372	−	0.255257i
$441$	7.97461e17			5.16248
$442$	8.03801e15	+	1.24585e16i	0.0512748	+	0.0794731i
$443$	1.17204e17			0.736745			0.368372	−	0.929678i	$-0.379915\pi$
$443$	1.17204e17			0.736745			0.368372	+	0.929678i	$0.379915\pi$
$444$	7.57666e15	+	1.31232e16i	0.0469341	+	0.0812923i
$445$	4.41176e16	+	7.64140e16i	0.269322	+	0.466480i
$446$	−1.40561e16	+	2.43458e16i	−0.0845643	+	0.146470i
$447$	−2.93140e17			−1.73811
$448$	−1.00496e17	+	1.74065e17i	−0.587277	+	1.01719i
$449$	9.02223e16	−	1.56270e17i	0.519652	−	0.900063i	−0.480087	−	0.877221i	$-0.659395\pi$
$449$	9.02223e16	−	1.56270e17i	0.519652	−	0.900063i	0.999739	−	0.0228427i	$-0.00727168\pi$
$450$	7.29555e16			0.414168
$451$	−6.20342e15	+	1.07446e16i	−0.0347123	+	0.0601235i
$452$	−1.13176e17	−	1.96027e17i	−0.624246	−	1.08123i
$453$	4.33363e16	+	7.50606e16i	0.235621	+	0.408107i
$454$	−2.23081e16			−0.119564
$455$	1.76154e17	−	8.70623e15i	0.930717	−	0.0459998i
$456$	5.34422e16			0.278364
$457$	1.14155e17	+	1.97722e17i	0.586191	+	1.01531i	0.994726	+	0.102570i	$0.0327067\pi$
$457$	1.14155e17	+	1.97722e17i	0.586191	+	1.01531i	−0.408534	+	0.912743i	$0.633960\pi$
$458$	−3.60525e16	−	6.24448e16i	−0.182520	−	0.316133i
$459$	8.78786e16	−	1.52210e17i	0.438632	−	0.759733i
$460$	1.38072e17			0.679486
$461$	3.66369e16	−	6.34571e16i	0.177772	−	0.307910i	−0.763345	−	0.645991i	$-0.776444\pi$
$461$	3.66369e16	−	6.34571e16i	0.177772	−	0.307910i	0.941117	+	0.338081i	$0.109778\pi$
$462$	−1.00930e17	+	1.74817e17i	−0.482891	+	0.836392i
$463$	1.35914e17			0.641190			0.320595	−	0.947216i	$-0.396117\pi$
$463$	1.35914e17			0.641190			0.320595	+	0.947216i	$0.396117\pi$
$464$	9.57393e16	−	1.65825e17i	0.445372	−	0.771407i
$465$	−5.37283e16	−	9.30601e16i	−0.246467	−	0.426893i
$466$	−3.21884e16	−	5.57519e16i	−0.145610	−	0.252204i
$467$	−1.92016e17			−0.856600			−0.428300	−	0.903637i	$-0.640887\pi$
$467$	−1.92016e17			−0.856600			−0.428300	+	0.903637i	$0.640887\pi$
$468$	−2.21328e17	+	4.31203e17i	−0.973727	+	1.89707i
$469$	−4.92605e17			−2.13735
$470$	9.92613e15	+	1.71926e16i	0.0424760	+	0.0735706i
$471$	2.56122e17	+	4.43616e17i	1.08096	+	1.87228i
$472$	4.14040e16	−	7.17139e16i	0.172353	−	0.298525i
$473$	4.89063e15			0.0200802
$474$	−1.85503e16	+	3.21301e16i	−0.0751263	+	0.130123i
$475$	2.94177e16	−	5.09530e16i	0.117517	−	0.203545i
$476$	−1.64204e17			−0.647051
$477$	−7.09356e16	+	1.22864e17i	−0.275737	+	0.477590i
$478$	1.46124e16	+	2.53094e16i	0.0560325	+	0.0970511i
$479$	9.77204e16	+	1.69257e17i	0.369662	+	0.640273i	0.989513	−	0.144447i	$-0.0461403\pi$
$479$	9.77204e16	+	1.69257e17i	0.369662	+	0.640273i	−0.619851	+	0.784720i	$0.712807\pi$
$480$	−1.70852e17			−0.637604
$481$	6.85815e15	−	1.33614e16i	0.0252501	−	0.0491937i
$482$	8.31776e16			0.302135
$483$	−6.41633e17	−	1.11134e18i	−2.29948	−	3.98282i
$484$	5.50796e16	+	9.54006e16i	0.194758	+	0.337331i
$485$	−5.85570e16	+	1.01424e17i	−0.204295	+	0.353849i
$486$	−8.06619e16			−0.277672
$487$	2.43497e17	−	4.21748e17i	0.827094	−	1.43257i	−0.0732151	−	0.997316i	$-0.523326\pi$
$487$	2.43497e17	−	4.21748e17i	0.827094	−	1.43257i	0.900309	−	0.435252i	$-0.143341\pi$
$488$	−5.44860e15	+	9.43725e15i	−0.0182623	+	0.0316313i
$489$	3.61544e15			0.0119578
$490$	4.44888e16	−	7.70569e16i	0.145203	−	0.251499i
$491$	2.95124e16	+	5.11169e16i	0.0950549	+	0.164640i	0.909632	−	0.415416i	$-0.136364\pi$
$491$	2.95124e16	+	5.11169e16i	0.0950549	+	0.164640i	−0.814577	+	0.580056i	$0.803031\pi$
$492$	1.55847e16	+	2.69934e16i	0.0495363	+	0.0857995i
$493$	1.32145e17			0.414521
$494$	−1.39019e16	−	2.15472e16i	−0.0430377	−	0.0667060i
$495$	4.55748e17			1.39249
$496$	−7.18387e16	−	1.24428e17i	−0.216634	−	0.375222i
$497$	−2.70334e17	−	4.68233e17i	−0.804608	−	1.39362i
$498$	−6.74046e16	+	1.16748e17i	−0.198015	+	0.342972i
$499$	−4.34707e17			−1.26050			−0.630250	−	0.776392i	$-0.717048\pi$
$499$	−4.34707e17			−1.26050			−0.630250	+	0.776392i	$0.717048\pi$
$500$	−1.46496e17	+	2.53738e17i	−0.419295	+	0.726241i
$501$	−4.38497e17	+	7.59498e17i	−1.23886	+	2.14576i
$502$	−1.58084e16			−0.0440875
$503$	3.30610e17	−	5.72633e17i	0.910173	−	1.57647i	0.0963532	−	0.995347i	$-0.469282\pi$
$503$	3.30610e17	−	5.72633e17i	0.910173	−	1.57647i	0.813819	−	0.581118i	$-0.197384\pi$
$504$	3.63701e17	+	6.29949e17i	0.988431	+	1.71201i
$505$	6.60342e16	+	1.14375e17i	0.177164	+	0.306857i
$506$	1.56625e17			0.414843
$507$	6.88421e17	−	6.82158e16i	1.80012	−	0.178375i
$508$	−2.31170e17			−0.596785
$509$	2.94079e17	+	5.09360e17i	0.749547	+	1.29825i	0.948040	+	0.318151i	$0.103062\pi$
$509$	2.94079e17	+	5.09360e17i	0.749547	+	1.29825i	−0.198493	+	0.980102i	$0.563605\pi$
$510$	−1.75120e16	−	3.03317e16i	−0.0440686	−	0.0763291i
$511$	2.44603e17	−	4.23665e17i	0.607752	−	1.05266i
$512$	−3.89026e17			−0.954386
$513$	−1.51988e17	+	2.63250e17i	−0.368167	+	0.637685i
$514$	7.56187e16	−	1.30975e17i	0.180871	−	0.313278i
$515$	−2.59337e17			−0.612516
$516$	6.14328e15	−	1.06405e16i	0.0143277	−	0.0248163i
$517$	−1.71639e17	−	2.97287e17i	−0.395300	−	0.684680i
$518$	−5.45594e15	−	9.44996e15i	−0.0124087	−	0.0214925i
$519$	−1.48138e18			−3.32720
$520$	6.05608e16	+	9.38658e16i	0.134329	+	0.208202i
$521$	5.46350e17			1.19681			0.598405	−	0.801193i	$-0.295801\pi$
$521$	5.46350e17			1.19681			0.598405	+	0.801193i	$0.295801\pi$
$522$	−1.41699e17	−	2.45429e17i	−0.306554	−	0.530968i
$523$	−2.27549e17	−	3.94126e17i	−0.486198	−	0.842120i	0.513676	−	0.857984i	$-0.328283\pi$
$523$	−2.27549e17	−	3.94126e17i	−0.486198	−	0.842120i	−0.999874	+	0.0158642i	$0.994950\pi$
$524$	1.42171e16	−	2.46248e16i	0.0300025	−	0.0519659i
$525$	1.15324e18			2.40372
$526$	−1.18862e17	+	2.05875e17i	−0.244701	+	0.423834i
$527$	4.95781e16	−	8.58717e16i	0.100814	−	0.174615i
$528$	8.77546e17			1.76258
$529$	−2.45829e17	+	4.25788e17i	−0.487721	+	0.844757i
$530$	7.91472e15	+	1.37087e16i	0.0155111	+	0.0268660i
$531$	4.20609e17	+	7.28516e17i	0.814262	+	1.41034i
$532$	2.83994e17			0.543104
$533$	1.41067e16	−	2.74835e16i	0.0266501	−	0.0519212i
$534$	2.51457e17			0.469294
$535$	2.39630e17	+	4.15052e17i	0.441817	+	0.765249i
$536$	−1.56001e17	−	2.70201e17i	−0.284155	−	0.492171i
$537$	3.36893e17	−	5.83515e17i	0.606260	−	1.05007i
$538$	−2.08036e17			−0.369875
$539$	−7.69283e17	+	1.33244e18i	−1.35132	+	2.34056i
$540$	3.20537e17	−	5.55187e17i	0.556313	−	0.963562i
$541$	1.13354e18			1.94381			0.971904	−	0.235377i	$-0.0756326\pi$
$541$	1.13354e18			1.94381			0.971904	+	0.235377i	$0.0756326\pi$
$542$	−2.32088e16	+	4.01988e16i	−0.0393240	+	0.0681111i
$543$	−4.09425e17	−	7.09145e17i	−0.685449	−	1.18723i
$544$	−7.88272e16	−	1.36533e17i	−0.130402	−	0.225862i
$545$	1.17875e17			0.192684
$546$	2.29518e17	−	4.47159e17i	0.370736	−	0.722288i
$547$	−2.31128e17			−0.368922			−0.184461	−	0.982840i	$-0.559054\pi$
$547$	−2.31128e17			−0.368922			−0.184461	+	0.982840i	$0.559054\pi$
$548$	−6.15575e16	−	1.06621e17i	−0.0970974	−	0.168178i
$549$	−5.53504e16	−	9.58697e16i	−0.0862781	−	0.149438i
$550$	−7.03776e16	+	1.21898e17i	−0.108412	+	0.187775i
$551$	−2.28548e17			−0.347930
$552$	4.06391e17	−	7.03890e17i	0.611421	−	1.05901i
$553$	−2.03621e17	+	3.52682e17i	−0.302768	+	0.524409i
$554$	−2.27878e17			−0.334880
$555$	−1.77391e16	+	3.07250e16i	−0.0257648	+	0.0446260i
$556$	−3.79764e15	−	6.57770e15i	−0.00545164	−	0.00944252i
$557$	3.64871e17	+	6.31975e17i	0.517703	+	0.896688i	0.999789	+	0.0205637i	$0.00654609\pi$
$557$	3.64871e17	+	6.31975e17i	0.517703	+	0.896688i	−0.482086	+	0.876124i	$0.660121\pi$
$558$	−2.12649e17			−0.298223
$559$	−1.21626e16	+	6.01123e14i	−0.0168596	+	0.000833272i
$560$	−5.57065e17			−0.763280
$561$	3.02811e17	+	5.24483e17i	0.410122	+	0.710351i
$562$	1.12226e17	+	1.94382e17i	0.150248	+	0.260237i
$563$	−5.08867e17	+	8.81383e17i	−0.673441	+	1.16643i	0.303481	+	0.952837i	$0.401851\pi$
$563$	−5.08867e17	+	8.81383e17i	−0.673441	+	1.16643i	−0.976922	+	0.213596i	$0.931482\pi$
$564$	−8.62404e17			−1.12823
$565$	2.64978e17	−	4.58955e17i	0.342684	−	0.593547i
$566$	−2.41362e15	+	4.18051e15i	−0.00308576	+	0.00534469i
$567$	−2.70624e18			−3.42039
$568$	1.71222e17	−	2.96565e17i	0.213941	−	0.370557i
$569$	3.30230e17	+	5.71975e17i	0.407931	+	0.706557i	0.994658	−	0.103228i	$-0.0329172\pi$
$569$	3.30230e17	+	5.71975e17i	0.407931	+	0.706557i	−0.586727	+	0.809785i	$0.699584\pi$
$570$	3.02873e16	+	5.24592e16i	0.0369892	+	0.0640671i
$571$	−3.91758e16			−0.0473024			−0.0236512	−	0.999720i	$-0.507529\pi$
$571$	−3.91758e16			−0.0473024			−0.0236512	+	0.999720i	$0.507529\pi$
$572$	−5.06967e17	−	7.85771e17i	−0.605210	−	0.938041i
$573$	−1.30454e18			−1.53976
$574$	−1.12225e16	−	1.94379e16i	−0.0130967	−	0.0226841i
$575$	−4.47403e17	−	7.74925e17i	−0.516248	−	0.894167i
$576$	6.46612e17	−	1.11996e18i	0.737730	−	1.27779i
$577$	1.66029e18			1.87302			0.936508	−	0.350645i	$-0.114038\pi$
$577$	1.66029e18			1.87302			0.936508	+	0.350645i	$0.114038\pi$
$578$	−9.50557e16	+	1.64641e17i	−0.106034	+	0.183657i
$579$	1.10292e18	−	1.91031e18i	1.21656	−	2.10714i
$580$	4.82000e17			0.525733
$581$	−7.39879e17	+	1.28151e18i	−0.798024	+	1.38222i
$582$	1.66878e17	+	2.89042e17i	0.177992	+	0.308291i
$583$	−1.36858e17	−	2.37045e17i	−0.144353	−	0.250026i
$584$	3.09849e17			0.323196
$585$	−1.13341e18	+	5.60175e16i	−1.16916	+	0.0577844i
$586$	−1.21024e17			−0.123463
$587$	6.29362e16	+	1.09009e17i	0.0634969	+	0.109980i	0.896026	−	0.444001i	$-0.146441\pi$
$587$	6.29362e16	+	1.09009e17i	0.0634969	+	0.109980i	−0.832529	+	0.553981i	$0.813108\pi$
$588$	1.93264e18	+	3.34744e18i	1.92841	+	3.34010i
$589$	−8.57462e16	+	1.48517e17i	−0.0846186	+	0.146564i
$590$	9.38599e16			0.0916098
$591$	1.00577e18	−	1.74204e18i	0.970912	−	1.68167i
$592$	−2.37185e16	+	4.10817e16i	−0.0226462	+	0.0392244i
$593$	−8.66609e17			−0.818404			−0.409202	−	0.912444i	$-0.634193\pi$
$593$	−8.66609e17			−0.818404			−0.409202	+	0.912444i	$0.634193\pi$
$594$	3.63608e17	−	6.29788e17i	0.339642	−	0.588278i
$595$	−1.92224e17	−	3.32942e17i	−0.177602	−	0.307615i
$596$	−4.93319e17	−	8.54453e17i	−0.450845	−	0.780886i
$597$	−1.52972e18			−1.38286
$598$	−3.89513e17	+	1.92513e16i	−0.348309	+	0.0172149i
$599$	5.85295e17			0.517727			0.258863	−	0.965914i	$-0.416652\pi$
$599$	5.85295e17			0.517727			0.258863	+	0.965914i	$0.416652\pi$
$600$	3.65214e17	+	6.32569e17i	0.319568	+	0.553509i
$601$	−4.42701e16	−	7.66781e16i	−0.0383201	−	0.0663724i	0.846229	−	0.532819i	$-0.178867\pi$
$601$	−4.42701e16	−	7.66781e16i	−0.0383201	−	0.0663724i	−0.884549	+	0.466447i	$0.845534\pi$
$602$	−4.42376e15	+	7.66218e15i	−0.00378804	+	0.00656107i
$603$	3.16951e18			2.68491
$604$	−1.45859e17	+	2.52636e17i	−0.122235	+	0.211717i
$605$	−1.28957e17	+	2.23360e17i	−0.106914	+	0.185180i
$606$	3.76374e17			0.308708
$607$	−8.38765e17	+	1.45278e18i	−0.680634	+	1.17889i	0.294154	+	0.955758i	$0.404962\pi$
$607$	−8.38765e17	+	1.45278e18i	−0.680634	+	1.17889i	−0.974788	+	0.223135i	$0.928371\pi$
$608$	1.36333e17	+	2.36136e17i	0.109453	+	0.189578i
$609$	−2.23989e18	−	3.87961e18i	−1.77916	−	3.08159i
$610$	−1.23516e16			−0.00970684
$611$	4.63391e17	+	7.18230e17i	0.360313	+	0.558465i
$612$	1.05652e18			0.812817
$613$	−1.15297e17	−	1.99699e17i	−0.0877654	−	0.152014i	0.818801	−	0.574078i	$-0.194639\pi$
$613$	−1.15297e17	−	1.99699e17i	−0.0877654	−	0.152014i	−0.906566	+	0.422064i	$0.861306\pi$
$614$	9.60135e16	+	1.66300e17i	0.0723166	+	0.125256i
$615$	−3.64881e16	+	6.31992e16i	−0.0271934	+	0.0471003i
$616$	−1.40340e18			−1.03492
$617$	−1.00708e18	+	1.74431e18i	−0.734870	+	1.27283i	0.219911	+	0.975520i	$0.429423\pi$
$617$	−1.00708e18	+	1.74431e18i	−0.734870	+	1.27283i	−0.954780	+	0.297312i	$0.903910\pi$
$618$	−3.69535e17	+	6.40053e17i	−0.266827	+	0.462159i
$619$	1.59377e18			1.13877			0.569387	−	0.822070i	$-0.307181\pi$
$619$	1.59377e18			1.13877			0.569387	+	0.822070i	$0.307181\pi$
$620$	1.80836e17	−	3.13217e17i	0.127861	−	0.221462i
$621$	2.31152e18	+	4.00368e18i	1.61735	+	2.80133i
$622$	−3.01670e17	−	5.22508e17i	−0.208879	−	0.361789i
$623$	2.76016e18			1.89131
$624$	−2.18238e18	+	1.07862e17i	−1.47989	+	0.0731424i
$625$	4.08676e17			0.274258
$626$	2.22781e17	+	3.85868e17i	0.147960	+	0.256275i
$627$	−5.23717e17	−	9.07104e17i	−0.344237	−	0.596236i
$628$	−8.62044e17	+	1.49310e18i	−0.560779	+	0.971297i
$629$	−3.27377e16			−0.0210775
$630$	−4.12242e17	+	7.14023e17i	−0.262687	+	0.454987i
$631$	9.86604e17	−	1.70885e18i	0.622232	−	1.07774i	−0.366838	−	0.930285i	$-0.619560\pi$
$631$	9.86604e17	−	1.70885e18i	0.622232	−	1.07774i	0.989069	−	0.147452i	$-0.0471072\pi$
$632$	−2.57935e17			−0.161009
$633$	4.50543e17	−	7.80363e17i	0.278363	−	0.482139i
$634$	−6.69680e16	−	1.15992e17i	−0.0409531	−	0.0709329i
$635$	−2.70617e17	−	4.68723e17i	−0.163805	−	0.283718i
$636$	−6.87648e17			−0.411998
$637$	1.74937e18	−	3.40821e18i	1.03747	−	2.02125i
$638$	5.46767e17			0.320973
$639$	1.73938e18	+	3.01270e18i	1.01074	+	1.75065i
$640$	−3.78531e17	−	6.55635e17i	−0.217737	−	0.377131i
$641$	−9.23780e17	+	1.60003e18i	−0.526007	+	0.911070i	0.473534	+	0.880775i	$0.342978\pi$
$641$	−9.23780e17	+	1.60003e18i	−0.526007	+	0.911070i	−0.999541	+	0.0302948i	$0.990355\pi$
$642$	1.36582e18			0.769866
$643$	−9.35770e16	+	1.62080e17i	−0.0522153	+	0.0904396i	−0.890952	−	0.454098i	$-0.849962\pi$
$643$	−9.35770e16	+	1.62080e17i	−0.0522153	+	0.0904396i	0.838736	+	0.544538i	$0.183295\pi$
$644$	2.15958e18	−	3.74050e18i	1.19292	−	2.06620i
$645$	2.87663e16			0.0157306
$646$	−2.79478e16	+	4.84070e16i	−0.0151299	+	0.0262058i
$647$	−9.98339e17	−	1.72917e18i	−0.535057	−	0.926747i	−0.999161	−	0.0409654i	$-0.986957\pi$
$647$	−9.98339e17	−	1.72917e18i	−0.535057	−	0.926747i	0.464103	−	0.885781i	$-0.346377\pi$
$648$	−8.57025e17	−	1.48441e18i	−0.454732	−	0.787619i
$649$	−1.62299e18			−0.852560
$650$	1.60040e17	−	3.11799e17i	0.0832324	−	0.162158i
$651$	−3.36144e18			−1.73081
$652$	6.08433e15	+	1.05384e16i	0.00310173	+	0.00537235i
$653$	−4.88686e16	−	8.46430e16i	−0.0246658	−	0.0427224i	0.853429	−	0.521209i	$-0.174519\pi$
$653$	−4.88686e16	−	8.46430e16i	−0.0246658	−	0.0427224i	−0.878095	+	0.478487i	$0.841185\pi$
$654$	1.67963e17	−	2.90921e17i	0.0839380	−	0.145385i
$655$	6.65726e16			0.0329402
$656$	−4.87873e16	+	8.45020e16i	−0.0239018	+	0.0413992i
$657$	−1.57382e18	+	2.72594e18i	−0.763450	+	1.32233i
$658$	6.21016e17			0.298287
$659$	8.83544e17	−	1.53034e18i	0.420216	−	0.727836i	−0.575744	−	0.817630i	$-0.695288\pi$
$659$	8.83544e17	−	1.53034e18i	0.420216	−	0.727836i	0.995960	+	0.0897941i	$0.0286209\pi$
$660$	1.10450e18	+	1.91306e18i	0.520153	+	0.900932i
$661$	−1.05466e17	−	1.82673e17i	−0.0491818	−	0.0851854i	0.840386	−	0.541988i	$-0.182328\pi$
$661$	−1.05466e17	−	1.82673e17i	−0.0491818	−	0.0851854i	−0.889568	+	0.456802i	$0.848995\pi$
$662$	−8.18345e17			−0.377885
$663$	−8.17530e17	−	1.26713e18i	−0.373823	−	0.579404i
$664$	−9.37235e17			−0.424381
$665$	3.32455e17	+	5.75829e17i	0.149071	+	0.258198i
$666$	3.51045e16	+	6.08028e16i	0.0155876	+	0.0269986i
$667$	−1.73795e18	+	3.01021e18i	−0.764221	+	1.32367i
$668$	−2.95174e18			−1.28538
$669$	1.42961e18	−	2.47616e18i	0.616522	−	1.06785i
$670$	1.76821e17	−	3.06263e17i	0.0755175	−	0.130800i
$671$	2.13578e17			0.0903360
$672$	−2.67228e18	+	4.62852e18i	−1.11939	+	1.93884i
$673$	−1.28745e18	−	2.22992e18i	−0.534111	−	0.925107i	−0.999206	−	0.0398460i	$-0.987313\pi$
$673$	−1.28745e18	−	2.22992e18i	−0.534111	−	0.925107i	0.465095	−	0.885261i	$-0.346020\pi$
$674$	2.75890e17	+	4.77856e17i	0.113357	+	0.196339i
$675$	−4.15462e18			−1.69066
$676$	1.35737e18	+	1.89183e18i	0.547070	+	0.762481i
$677$	−1.54014e18			−0.614801			−0.307401	−	0.951580i	$-0.599459\pi$
$677$	−1.54014e18			−0.614801			−0.307401	+	0.951580i	$0.599459\pi$
$678$	−7.55144e17	−	1.30795e18i	−0.298564	−	0.517128i
$679$	1.83177e18	+	3.17272e18i	0.717328	+	1.24245i
$680$	1.21749e17	−	2.10875e17i	0.0472234	−	0.0817933i
$681$	2.26891e18			0.871688
$682$	2.05135e17	−	3.55305e17i	0.0780625	−	0.135208i
$683$	8.50125e17	−	1.47246e18i	0.320441	−	0.555020i	−0.660138	−	0.751144i	$-0.729502\pi$
$683$	8.50125e17	−	1.47246e18i	0.320441	−	0.555020i	0.980579	+	0.196124i	$0.0628355\pi$
$684$	−1.82727e18			−0.682241
$685$	1.44124e17	−	2.49629e17i	0.0533023	−	0.0923223i
$686$	−7.79140e17	−	1.34951e18i	−0.285436	−	0.494390i
$687$	3.66683e18	+	6.35113e18i	1.33067	+	2.30479i
$688$	3.84627e16			0.0138266
$689$	3.69491e17	+	5.72690e17i	0.131577	+	0.203936i
$690$	9.21258e17			0.324984
$691$	−1.26886e18	−	2.19773e18i	−0.443411	−	0.768010i	0.554529	−	0.832164i	$-0.312898\pi$
$691$	−1.26886e18	−	2.19773e18i	−0.443411	−	0.768010i	−0.997940	+	0.0641546i	$0.979565\pi$
$692$	−2.49298e18	−	4.31797e18i	−0.863038	−	1.49482i
$693$	7.12832e18	−	1.23466e19i	2.44468	−	4.23430i
$694$	−6.19339e17			−0.210422
$695$	8.89134e15	−	1.54003e16i	0.00299272	−	0.00518354i
$696$	1.41868e18	−	2.45723e18i	0.473069	−	0.819380i
$697$	−6.73392e16			−0.0222461
$698$	1.42598e17	−	2.46987e17i	0.0466717	−	0.0808377i
$699$	3.27381e18	+	5.67041e18i	1.06158	+	1.83871i
$700$	1.94076e18	+	3.36149e18i	0.623497	+	1.07993i
$701$	−6.08102e17			−0.193557			−0.0967786	−	0.995306i	$-0.530854\pi$
$701$	−6.08102e17			−0.193557			−0.0967786	+	0.995306i	$0.530854\pi$
$702$	−8.26853e17	+	1.61092e18i	−0.260758	+	0.508023i
$703$	5.66205e16			0.0176915
$704$	1.24753e18	+	2.16078e18i	0.386214	+	0.668942i
$705$	−1.00957e18	−	1.74862e18i	−0.309675	−	0.536372i
$706$	−2.20098e16	+	3.81222e16i	−0.00668939	+	0.0115864i
$707$	4.13134e18			1.24413
$708$	−2.03869e18	+	3.53111e18i	−0.608324	+	1.05365i
$709$	−6.55600e16	+	1.13553e17i	−0.0193838	+	0.0335737i	−0.875555	−	0.483119i	$-0.839504\pi$
$709$	−6.55600e16	+	1.13553e17i	−0.0193838	+	0.0335737i	0.856171	+	0.516693i	$0.172837\pi$
$710$	3.88147e17			0.113715
$711$	1.31014e18	−	2.26922e18i	0.380333	−	0.658756i
$712$	8.74103e17	+	1.51399e18i	0.251445	+	0.435515i
$713$	1.30408e18	+	2.25874e18i	0.371726	+	0.643849i
$714$	−1.09562e18			−0.309471
$715$	9.99760e17	−	1.94779e18i	0.279838	−	0.545196i
$716$	2.26780e18			0.629027
$717$	−1.48620e18	−	2.57417e18i	−0.408509	−	0.707558i
$718$	8.59483e17	+	1.48867e18i	0.234115	+	0.405498i
$719$	8.29934e17	−	1.43749e18i	0.224030	−	0.388031i	−0.731998	−	0.681307i	$-0.761412\pi$
$719$	8.29934e17	−	1.43749e18i	0.224030	−	0.388031i	0.956028	+	0.293276i	$0.0947454\pi$
$720$	3.58426e18			0.958823
$721$	−4.05627e18	+	7.02567e18i	−1.07535	+	1.86255i
$722$	−4.23862e17	+	7.34150e17i	−0.111361	+	0.192883i
$723$	−8.45982e18			−2.20274
$724$	1.37802e18	−	2.38681e18i	0.355595	−	0.615909i
$725$	−1.56185e18	−	2.70521e18i	−0.399432	−	0.691836i
$726$	3.67507e17	+	6.36540e17i	0.0931488	+	0.161338i
$727$	−4.82210e17			−0.121133			−0.0605666	−	0.998164i	$-0.519291\pi$
$727$	−4.82210e17			−0.121133			−0.0605666	+	0.998164i	$0.519291\pi$
$728$	3.49013e18	−	1.72497e17i	0.868936	−	0.0429464i
$729$	5.40923e17			0.133477
$730$	1.75601e17	+	3.04150e17i	0.0429465	+	0.0743856i
$731$	1.32721e16	+	2.29880e16i	0.00321720	+	0.00557235i
$732$	2.68283e17	−	4.64680e17i	0.0644571	−	0.111643i
$733$	−8.09696e18			−1.92817			−0.964086	−	0.265589i	$-0.914434\pi$
$733$	−8.09696e18			−1.92817			−0.964086	+	0.265589i	$0.914434\pi$
$734$	8.22155e17	−	1.42401e18i	0.194057	−	0.336117i
$735$	−4.52487e18	+	7.83730e18i	−1.05861	+	1.83357i
$736$	4.14688e18			0.961647
$737$	−3.05752e18	+	5.29578e18i	−0.702798	+	1.21728i
$738$	7.22075e16	+	1.25067e17i	0.0164519	+	0.0284955i
$739$	−1.66392e18	−	2.88199e18i	−0.375787	−	0.650883i	0.614657	−	0.788794i	$-0.289294\pi$
$739$	−1.66392e18	−	2.88199e18i	−0.375787	−	0.650883i	−0.990445	+	0.137911i	$0.955961\pi$
$740$	−1.19411e17			−0.0267324
$741$	1.41393e18	+	2.19152e18i	0.313770	+	0.486325i
$742$	4.95174e17			0.108926
$743$	2.96376e18	+	5.13339e18i	0.646273	+	1.11938i	0.984006	+	0.178136i	$0.0570068\pi$
$743$	2.96376e18	+	5.13339e18i	0.646273	+	1.11938i	−0.337732	+	0.941242i	$0.609660\pi$
$744$	−1.06452e18	−	1.84380e18i	−0.230107	−	0.398556i
$745$	1.15500e18	−	2.00052e18i	0.247495	−	0.428673i
$746$	9.09714e17			0.193242
$747$	4.76052e18	−	8.24547e18i	1.00247	−	1.73633i
$748$	−1.01919e18	+	1.76528e18i	−0.212762	+	0.368514i
$749$	1.49922e19			3.10265
$750$	−9.77461e17	+	1.69301e18i	−0.200540	+	0.347346i
$751$	−2.29822e18	−	3.98063e18i	−0.467447	−	0.809641i	0.531862	−	0.846831i	$-0.321493\pi$
$751$	−2.29822e18	−	3.98063e18i	−0.467447	−	0.809641i	−0.999308	+	0.0371900i	$0.988159\pi$
$752$	−1.34986e18	−	2.33803e18i	−0.272191	−	0.471449i
$753$	1.60784e18			0.321423
$754$	−1.35976e18	+	6.72050e16i	−0.269494	+	0.0133195i
$755$	−6.82996e17			−0.134203
$756$	−1.00270e19	−	1.73673e19i	−1.95335	−	3.38330i
$757$	−1.74187e18	−	3.01700e18i	−0.336428	−	0.582710i	0.647330	−	0.762210i	$-0.275885\pi$
$757$	−1.74187e18	−	3.01700e18i	−0.336428	−	0.582710i	−0.983758	+	0.179500i	$0.942552\pi$
$758$	1.64493e17	−	2.84910e17i	0.0314990	−	0.0545579i
$759$	−1.59300e19			−3.02444
$760$	−2.10567e17	+	3.64713e17i	−0.0396371	+	0.0686535i
$761$	1.27662e18	−	2.21117e18i	0.238265	−	0.412687i	−0.721951	−	0.691944i	$-0.756755\pi$
$761$	1.27662e18	−	2.21117e18i	0.238265	−	0.412687i	0.960217	+	0.279256i	$0.0900880\pi$
$762$	−1.54243e18			−0.285430
$763$	1.84368e18	−	3.19335e18i	0.338280	−	0.585918i
$764$	−2.19539e18	−	3.80252e18i	−0.399397	−	0.691775i
$765$	1.23680e18	+	2.14221e18i	0.223101	+	0.386422i
$766$	−8.80317e17			−0.157453
$767$	4.03623e18	−	1.99487e17i	0.715824	−	0.0353789i
$768$	4.52194e18			0.795202
$769$	4.30905e18	+	7.46349e18i	0.751381	+	1.30143i	0.947153	+	0.320781i	$0.103945\pi$
$769$	4.30905e18	+	7.46349e18i	0.751381	+	1.30143i	−0.195772	+	0.980649i	$0.562721\pi$
$770$	−7.95350e17	−	1.37759e18i	−0.137521	−	0.238193i
$771$	−7.69102e18	+	1.33212e19i	−1.31865	+	2.28397i
$772$	7.42431e18			1.26224
$773$	−5.10220e18	+	8.83727e18i	−0.860183	+	1.48988i	0.0115698	+	0.999933i	$0.496317\pi$
$773$	−5.10220e18	+	8.83727e18i	−0.860183	+	1.48988i	−0.871752	+	0.489947i	$0.837016\pi$
$774$	2.84633e16	−	4.92999e16i	0.00475849	−	0.00824194i
$775$	−2.34389e18			−0.388577
$776$	−1.16019e18	+	2.00951e18i	−0.190734	+	0.330361i
$777$	5.54912e17	+	9.61136e17i	0.0904665	+	0.156693i
$778$	1.82546e17	+	3.16179e17i	0.0295125	+	0.0511171i
$779$	1.16464e17			0.0186724
$780$	−2.98194e18	−	4.62185e18i	−0.474116	−	0.734853i
$781$	−6.71168e18			−1.05828
$782$	4.25048e17	+	7.36205e17i	0.0664652	+	0.115121i
$783$	8.06936e18	+	1.39765e19i	1.25138	+	2.16745i
$784$	−6.05008e18	+	1.04790e19i	−0.930479	+	1.61164i
$785$	−4.03658e18			−0.615687
$786$	9.48607e16	−	1.64303e17i	0.0143496	−	0.0248542i
$787$	−1.94979e18	+	3.37714e18i	−0.292518	+	0.506656i	−0.974404	−	0.224802i	$-0.927826\pi$
$787$	−1.94979e18	+	3.37714e18i	−0.292518	+	0.506656i	0.681886	+	0.731458i	$0.261160\pi$
$788$	6.77035e18			1.00737
$789$	1.20892e19	−	2.09391e19i	1.78401	−	3.09000i
$790$	−1.46180e17	−	2.53191e17i	−0.0213950	−	0.0370572i
$791$	−8.28899e18	−	1.43570e19i	−1.20325	−	2.08408i
$792$	9.02973e18			1.30005
$793$	−5.31151e17	+	2.62517e16i	−0.0758477	+	0.00374870i
$794$	−3.11104e18			−0.440629
$795$	−8.04990e17	−	1.39428e18i	−0.113085	−	0.195869i
$796$	−2.57433e18	−	4.45887e18i	−0.358698	−	0.621284i
$797$	5.23931e16	−	9.07474e16i	0.00724093	−	0.0125417i	−0.862382	−	0.506258i	$-0.831028\pi$
$797$	5.23931e16	−	9.07474e16i	0.00724093	−	0.0125417i	0.869623	+	0.493716i	$0.164362\pi$
$798$	1.89489e18			0.259756
$799$	9.31583e17	−	1.61355e18i	0.126668	−	0.219396i
$800$	−1.86335e18	+	3.22742e18i	−0.251310	+	0.435281i
$801$	−1.77594e19			−2.37584
$802$	1.80496e18	−	3.12628e18i	0.239516	−	0.414853i
$803$	−3.03642e18	−	5.25924e18i	−0.399679	−	0.692264i
$804$	7.68130e18	+	1.33044e19i	1.00293	+	1.73713i
$805$	1.01124e19			1.30972
$806$	−4.66482e17	+	9.08827e17i	−0.0599318	+	0.116762i
$807$	2.11590e19			2.69660
$808$	1.30833e18	+	2.26610e18i	0.165404	+	0.286487i
$809$	3.34961e18	+	5.80170e18i	0.420077	+	0.727595i	0.995947	−	0.0899468i	$-0.0286697\pi$
$809$	3.34961e18	+	5.80170e18i	0.420077	+	0.727595i	−0.575869	+	0.817542i	$0.695336\pi$
$810$	9.71405e17	−	1.68252e18i	0.120850	−	0.209319i
$811$	6.00687e18			0.741332			0.370666	−	0.928766i	$-0.379129\pi$
$811$	6.00687e18			0.741332			0.370666	+	0.928766i	$0.379129\pi$
$812$	7.53893e18	−	1.30578e19i	0.922987	−	1.59866i
$813$	2.36052e18	−	4.08854e18i	0.286694	−	0.496569i
$814$	−1.35456e17			−0.0163208
$815$	−1.42451e16	+	2.46733e16i	−0.00170272	+	0.00294919i
$816$	2.38148e18	+	4.12484e18i	0.282397	+	0.489126i
$817$	−2.29544e16	−	3.97582e16i	−0.00270037	−	0.00467717i
$818$	3.99922e18			0.466744
$819$	−1.62100e19	+	3.15811e19i	−1.87688	+	3.65664i
$820$	−2.45620e17			−0.0282146
$821$	−1.83701e18	−	3.18180e18i	−0.209354	−	0.362612i	0.742157	−	0.670226i	$-0.233803\pi$
$821$	−1.83701e18	−	3.18180e18i	−0.209354	−	0.362612i	−0.951511	+	0.307614i	$0.900470\pi$
$822$	−4.10729e17	−	7.11404e17i	−0.0464397	−	0.0804358i
$823$	1.47245e18	−	2.55035e18i	0.165173	−	0.286089i	−0.771543	−	0.636177i	$-0.780515\pi$
$823$	1.47245e18	−	2.55035e18i	0.165173	−	0.286089i	0.936717	+	0.350088i	$0.113848\pi$
$824$	−5.13825e18			−0.571858
$825$	7.15796e18	−	1.23980e19i	0.790385	−	1.36899i
$826$	1.46806e18	−	2.54275e18i	0.160832	−	0.278569i
$827$	6.74405e18			0.733053			0.366526	−	0.930408i	$-0.380547\pi$
$827$	6.74405e18			0.733053			0.366526	+	0.930408i	$0.380547\pi$
$828$	−1.38951e19	+	2.40671e19i	−1.49853	+	2.59553i
$829$	−6.04530e18	−	1.04708e19i	−0.646864	−	1.12040i	−0.983868	−	0.178898i	$-0.942747\pi$
$829$	−6.04530e18	−	1.04708e19i	−0.646864	−	1.12040i	0.337003	−	0.941503i	$-0.390587\pi$
$830$	−5.31160e17	−	9.19997e17i	−0.0563921	−	0.0976739i
$831$	2.31770e19			2.44146
$832$	−3.36808e18	−	5.22034e18i	−0.352031	−	0.545628i
$833$	−8.35069e18			−0.866024
$834$	−2.53389e16	−	4.38883e16i	−0.00260741	−	0.00451616i
$835$	−3.45543e18	−	5.98499e18i	−0.352810	−	0.611084i
$836$	1.76270e18	−	3.05309e18i	0.178582	−	0.309314i
$837$	1.21098e19			1.21737
$838$	−1.30327e18	+	2.25733e18i	−0.130001	+	0.225169i
$839$	−7.75782e18	+	1.34369e19i	−0.767868	+	1.32999i	0.170848	+	0.985297i	$0.445349\pi$
$839$	−7.75782e18	+	1.34369e19i	−0.767868	+	1.32999i	−0.938717	+	0.344690i	$0.887984\pi$
$840$	−8.25469e18			−0.810747
$841$	−9.36736e17	+	1.62247e18i	−0.0912942	+	0.158126i
$842$	−9.61830e17	−	1.66594e18i	−0.0930186	−	0.161113i
$843$	−1.14143e19	−	1.97702e19i	−1.09539	−	1.89728i
$844$	3.03283e18			0.288817
$845$	−2.24691e18	+	4.96686e18i	−0.212333	+	0.469368i
$846$	−3.99573e18			−0.374704
$847$	4.03401e18	+	6.98711e18i	0.375400	+	0.650213i
$848$	−1.07633e18	−	1.86426e18i	−0.0993969	−	0.172160i
$849$	2.45484e17	−	4.25191e17i	0.0224969	−	0.0389658i
$850$	−7.63960e17			−0.0694781
$851$	4.30560e17	−	7.45752e17i	0.0388590	−	0.0673058i
$852$	−8.43076e18	+	1.46025e19i	−0.755109	+	1.30789i
$853$	−8.08095e18			−0.718280			−0.359140	−	0.933284i	$-0.616930\pi$
$853$	−8.08095e18			−0.718280			−0.359140	+	0.933284i	$0.616930\pi$
$854$	−1.93190e17	+	3.34615e17i	−0.0170415	+	0.0295168i
$855$	−2.13908e18	−	3.70499e18i	−0.187261	−	0.324345i
$856$	4.74780e18	+	8.22343e18i	0.412489	+	0.714452i
$857$	−9.56317e18			−0.824568			−0.412284	−	0.911055i	$-0.635269\pi$
$857$	−9.56317e18			−0.824568			−0.412284	+	0.911055i	$0.635269\pi$
$858$	−3.38263e18	−	5.24289e18i	−0.289459	−	0.448645i
$859$	5.20067e18			0.441676			0.220838	−	0.975311i	$-0.429121\pi$
$859$	5.20067e18			0.441676			0.220838	+	0.975311i	$0.429121\pi$
$860$	4.84102e16	+	8.38488e16i	0.00408034	+	0.00706736i
$861$	1.14141e18	+	1.97699e18i	0.0954823	+	0.165380i
$862$	−2.21014e18	+	3.82807e18i	−0.183494	+	0.317821i
$863$	−4.34228e18			−0.357806			−0.178903	−	0.983867i	$-0.557255\pi$
$863$	−4.34228e18			−0.357806			−0.178903	+	0.983867i	$0.557255\pi$
$864$	9.62706e18	−	1.66746e19i	0.787325	−	1.36369i
$865$	5.83678e18	−	1.01096e19i	0.473771	−	0.820595i
$866$	−3.92629e18			−0.316312
$867$	9.66792e18	−	1.67453e19i	0.773052	−	1.33897i
$868$	−5.65689e18	−	9.79802e18i	−0.448952	−	0.777607i
$869$	2.52769e18	+	4.37808e18i	0.199111	+	0.344870i
$870$	3.21604e18			0.251447
$871$	6.95286e18	−	1.35460e19i	0.539567	−	1.05122i
$872$	2.33546e18			0.179894
$873$	−1.17860e19	−	2.04139e19i	−0.901099	−	1.56075i
$874$	−7.35129e17	−	1.27328e18i	−0.0557878	−	0.0966273i
$875$	−1.07293e19	+	1.85837e19i	−0.808200	+	1.39984i
$876$	−1.52566e19			−1.14073
$877$	−5.56838e18	+	9.64472e18i	−0.413268	+	0.715801i	−0.995245	−	0.0974043i	$-0.968946\pi$
$877$	−5.56838e18	+	9.64472e18i	−0.413268	+	0.715801i	0.581977	+	0.813205i	$0.302279\pi$
$878$	1.34617e18	−	2.33163e18i	0.0991709	−	0.171769i
$879$	1.23091e19			0.900115
$880$	−3.45761e18	+	5.98876e18i	−0.250980	+	0.434710i
$881$	−6.81995e17	−	1.18125e18i	−0.0491403	−	0.0851135i	0.840409	−	0.541953i	$-0.182315\pi$
$881$	−6.81995e17	−	1.18125e18i	−0.0491403	−	0.0851135i	−0.889549	+	0.456839i	$0.848981\pi$
$882$	8.95441e18	+	1.55095e19i	0.640459	+	1.10931i
$883$	2.56255e19			1.81940			0.909700	−	0.415265i	$-0.136311\pi$
$883$	2.56255e19			1.81940			0.909700	+	0.415265i	$0.136311\pi$
$884$	2.31765e18	−	4.51538e18i	0.163346	−	0.318240i
$885$	−9.54629e18			−0.667888
$886$	1.31604e18	+	2.27945e18i	0.0914007	+	0.158311i
$887$	3.25894e18	+	5.64465e18i	0.224685	+	0.389165i	0.956225	−	0.292633i	$-0.0945315\pi$
$887$	3.25894e18	+	5.64465e18i	0.224685	+	0.389165i	−0.731540	+	0.681798i	$0.761198\pi$
$888$	−3.51465e17	+	6.08755e17i	−0.0240546	+	0.0416637i
$889$	−1.69308e19			−1.15031
$890$	−9.90763e17	+	1.71605e18i	−0.0668243	+	0.115743i
$891$	−1.67972e19	+	2.90935e19i	−1.12468	+	1.94801i
$892$	9.62345e18			0.639675
$893$	−1.61119e18	+	2.79066e18i	−0.106319	+	0.184151i
$894$	−3.29157e18	−	5.70116e18i	−0.215630	−	0.373482i
$895$	2.65478e18	+	4.59821e18i	0.172655	+	0.299047i
$896$	−2.36823e19			−1.52905
$897$	3.96166e19	−	1.95801e18i	2.53937	−	0.125506i
$898$	4.05229e18			0.257872
$899$	4.55246e18	+	7.88509e18i	0.287613	+	0.498160i
$900$	−1.24872e19	−	2.16285e19i	−0.783230	−	1.35659i
$901$	7.42809e17	−	1.28658e18i	0.0462558	−	0.0801174i
$902$	−2.78624e17			−0.0172257
$903$	4.49932e17	−	7.79304e17i	0.0276170	−	0.0478340i
$904$	5.25000e18	−	9.09327e18i	0.319937	−	0.554147i
$905$	6.45269e18			0.390413
$906$	−9.73215e17	+	1.68566e18i	−0.0584623	+	0.101260i
$907$	−5.61185e18	−	9.72001e18i	−0.334702	−	0.579721i	0.648725	−	0.761023i	$-0.275302\pi$
$907$	−5.61185e18	−	9.72001e18i	−0.334702	−	0.579721i	−0.983428	+	0.181301i	$0.941969\pi$
$908$	3.81830e18	+	6.61348e18i	0.226106	+	0.391627i
$909$	−2.65818e19			−1.56286
$910$	2.14729e18	+	3.32818e18i	0.125349	+	0.194284i
$911$	−7.22046e18			−0.418500			−0.209250	−	0.977862i	$-0.567102\pi$
$911$	−7.22046e18			−0.418500			−0.209250	+	0.977862i	$0.567102\pi$
$912$	−4.11881e18	−	7.13398e18i	−0.237031	−	0.410550i
$913$	9.18462e18	+	1.59082e19i	0.524809	+	0.908995i
$914$	−2.56361e18	+	4.44030e18i	−0.145446	+	0.251920i
$915$	1.25625e18			0.0707685
$916$	−1.23416e19	+	2.13763e19i	−0.690323	+	1.19567i
$917$	1.04126e18	−	1.80351e18i	0.0578305	−	0.100165i
$918$	3.94703e18			0.217667
$919$	−1.03163e18	+	1.78684e18i	−0.0564902	+	0.0978439i	−0.892888	−	0.450280i	$-0.851324\pi$
$919$	−1.03163e18	+	1.78684e18i	−0.0564902	+	0.0978439i	0.836397	+	0.548124i	$0.184658\pi$
$920$	3.20244e18	+	5.54678e18i	0.174124	+	0.301592i
$921$	−9.76533e18	−	1.69141e19i	−0.527229	−	0.913188i
$922$	1.64553e18			0.0882177
$923$	1.66914e19	−	8.24955e17i	0.888548	−	0.0439157i
$924$	6.91018e19			3.65276
$925$	3.86934e17	+	6.70189e17i	0.0203103	+	0.0351784i
$926$	1.52613e18	+	2.64333e18i	0.0795461	+	0.137778i
$927$	2.60988e19	−	4.52045e19i	1.35084	−	2.33972i
$928$	1.44764e19			0.744047
$929$	1.50956e18	−	2.61464e18i	0.0770457	−	0.133447i	−0.824928	−	0.565237i	$-0.808785\pi$
$929$	1.50956e18	−	2.61464e18i	0.0770457	−	0.133447i	0.901974	+	0.431790i	$0.142118\pi$
$930$	1.20659e18	−	2.08988e18i	0.0611535	−	0.105921i
$931$	1.44427e19			0.726900
$932$	−1.10189e19	+	1.90852e19i	−0.550723	+	0.953880i
$933$	3.06822e19	+	5.31432e19i	1.52285	+	2.63765i
$934$	−2.15608e18	−	3.73444e18i	−0.106270	−	0.184065i
$935$	−4.77241e18			−0.233594
$936$	−2.24562e19	+	1.10988e18i	−1.09155	+	0.0539487i
$937$	−1.50446e19			−0.726229			−0.363114	−	0.931745i	$-0.618287\pi$
$937$	−1.50446e19			−0.726229			−0.363114	+	0.931745i	$0.618287\pi$
$938$	−5.53129e18	−	9.58047e18i	−0.265160	−	0.459270i
$939$	−2.26586e19	−	3.92459e19i	−1.07872	−	1.86839i
$940$	3.39795e18	−	5.88543e18i	0.160652	−	0.278258i
$941$	−4.24474e18			−0.199305			−0.0996526	−	0.995022i	$-0.531773\pi$
$941$	−4.24474e18			−0.199305			−0.0996526	+	0.995022i	$0.531773\pi$
$942$	−5.75180e18	+	9.96241e18i	−0.268209	+	0.464551i
$943$	8.85632e17	−	1.53396e18i	0.0410135	−	0.0710375i
$944$	−1.27641e19			−0.587046
$945$	2.34760e19	−	4.06617e19i	1.07230	−	1.85729i
$946$	5.49151e16	+	9.51157e16i	0.00249115	+	0.00431479i
$947$	1.99965e19	+	3.46350e19i	0.900906	+	1.56041i	0.826321	+	0.563200i	$0.190430\pi$
$947$	1.99965e19	+	3.46350e19i	0.900906	+	1.56041i	0.0745848	+	0.997215i	$0.476237\pi$
$948$	1.27004e19			0.568283
$949$	8.19775e18	+	1.27061e19i	0.364304	+	0.564651i
$950$	1.32128e18			0.0583167
$951$	6.81118e18	+	1.17973e19i	0.298572	+	0.517142i
$952$	−3.80853e18	−	6.59657e18i	−0.165813	−	0.287196i
$953$	−8.30724e18	+	1.43886e19i	−0.359214	+	0.622176i	−0.987830	−	0.155540i	$-0.950288\pi$
$953$	−8.30724e18	+	1.43886e19i	−0.359214	+	0.622176i	0.628616	+	0.777716i	$0.283622\pi$
$954$	−3.18604e18			−0.136832
$955$	5.14002e18	−	8.90278e18i	0.219252	−	0.379755i
$956$	5.00217e18	−	8.66401e18i	0.211925	−	0.367065i
$957$	−5.56106e19			−2.34007
$958$	−2.19453e18	+	3.80105e18i	−0.0917206	+	0.158865i
$959$	−4.50845e18	−	7.80887e18i	−0.187157	−	0.324166i
$960$	7.33786e18	+	1.27095e19i	0.302556	+	0.524043i
$961$	−1.75856e19			−0.720204
$962$	3.36868e17	−	1.66494e16i	0.0137032	−	0.000677269i
$963$	−9.64624e19			−3.89751
$964$	−1.42368e19	−	2.46589e19i	−0.571364	−	0.989632i
$965$	8.69120e18	+	1.50536e19i	0.346459	+	0.600085i
$966$	1.44093e19	−	2.49577e19i	0.570548	−	0.988219i
$967$	−3.07638e19			−1.20995			−0.604976	−	0.796244i	$-0.706817\pi$
$967$	−3.07638e19			−1.20995			−0.604976	+	0.796244i	$0.706817\pi$
$968$	−2.55502e18	+	4.42543e18i	−0.0998170	+	0.172888i
$969$	2.84252e18	−	4.92338e18i	0.110306	−	0.191055i
$970$	−2.63006e18			−0.101380
$971$	1.27119e19	−	2.20177e19i	0.486727	−	0.843036i	−0.513156	−	0.858295i	$-0.671524\pi$
$971$	1.27119e19	−	2.20177e19i	0.486727	−	0.843036i	0.999884	+	0.0152590i	$0.00485727\pi$
$972$	1.38063e19	+	2.39131e19i	0.525104	+	0.909507i
$973$	−2.78138e17	−	4.81749e17i	−0.0105082	−	0.0182007i
$974$	1.09365e19			0.410437
$975$	−1.62774e19	+	3.17125e19i	−0.606812	+	1.18222i
$976$	1.67970e18			0.0622026
$977$	1.39512e18	+	2.41643e18i	0.0513214	+	0.0888912i	0.890545	−	0.454895i	$-0.150323\pi$
$977$	1.39512e18	+	2.41643e18i	0.0513214	+	0.0888912i	−0.839223	+	0.543787i	$0.816990\pi$
$978$	4.05964e16	+	7.03151e16i	0.00148349	+	0.00256948i
$979$	1.71319e19	−	2.96733e19i	0.621896	−	1.07715i
$980$	−3.04592e19			−1.09837
$981$	−1.18626e19	+	2.05466e19i	−0.424943	+	0.736023i
$982$	−6.62768e17	+	1.14795e18i	−0.0235850	+	0.0408505i
$983$	3.74867e19			1.32519			0.662596	−	0.748977i	$-0.269455\pi$
$983$	3.74867e19			1.32519			0.662596	+	0.748977i	$0.269455\pi$
$984$	−7.22938e17	+	1.25217e18i	−0.0253883	+	0.0439738i
$985$	7.92565e18	+	1.37276e19i	0.276503	+	0.478917i
$986$	1.48381e18	+	2.57004e18i	0.0514255	+	0.0890716i
$987$	−6.31622e19			−2.17468
$988$	−4.00842e18	+	7.80943e18i	−0.137105	+	0.267116i
$989$	−6.98210e17			−0.0237252
$990$	5.11743e18	+	8.86365e18i	0.172752	+	0.299215i
$991$	2.50738e18	+	4.34291e18i	0.0840895	+	0.145647i	0.905003	−	0.425405i	$-0.139869\pi$
$991$	2.50738e18	+	4.34291e18i	0.0840895	+	0.145647i	−0.820913	+	0.571053i	$0.806535\pi$
$992$	5.43126e18	−	9.40721e18i	0.180957	−	0.313426i
$993$	8.32321e19			2.75500
$994$	6.07097e18	−	1.05152e19i	0.199640	−	0.345786i
$995$	6.02724e18	−	1.04395e19i	0.196910	−	0.341058i
$996$	4.61484e19			1.49786
$997$	−1.62713e19	+	2.81827e19i	−0.524691	+	0.908791i	0.474896	+	0.880042i	$0.342486\pi$
$997$	−1.62713e19	+	2.81827e19i	−0.524691	+	0.908791i	−0.999587	+	0.0287491i	$0.990848\pi$
$998$	−4.88117e18	−	8.45443e18i	−0.156378	−	0.270854i
$999$	−1.99911e18	−	3.46256e18i	−0.0636298	−	0.110210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.14.c.a.3.9	✓	28
13.3	even	3		169.14.a.e.1.6		14
13.9	even	3	inner	13.14.c.a.9.9	yes	28
13.10	even	6		169.14.a.c.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.c.a.3.9	✓	28	1.1	even	1	trivial
13.14.c.a.9.9	yes	28	13.9	even	3	inner
169.14.a.c.1.9		14	13.10	even	6
169.14.a.e.1.6		14	13.3	even	3

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	13.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.2286 + 19.4486i) q^{2} +(-1142.04 - 1978.08i) q^{3} +(3843.84 - 6657.72i) q^{4} +17999.0 q^{5} +(25647.2 - 44422.2i) q^{6} +(281521. - 487609. i) q^{7} +356614. q^{8} +(-1.81136e6 + 3.13737e6i) q^{9} +(202104. + 350055. i) q^{10} +(-3.49471e6 - 6.05302e6i) q^{11} -1.75593e7 q^{12} +(9.43504e6 + 1.46238e7i) q^{13} +1.26444e7 q^{14} +(-2.05556e7 - 3.56034e7i) q^{15} +(-2.74844e7 - 4.76044e7i) q^{16} +(1.89678e7 - 3.28532e7i) q^{17} -8.13565e7 q^{18} +(-3.28052e7 + 5.68203e7i) q^{19} +(6.91852e7 - 1.19832e8i) q^{20} -1.28604e9 q^{21} +(7.84817e7 - 1.35934e8i) q^{22} +(4.98922e8 + 8.64159e8i) q^{23} +(-4.07269e8 - 7.05410e8i) q^{24} -8.96739e8 q^{25} +(-1.78469e8 + 3.47703e8i) q^{26} +4.63303e9 q^{27} +(-2.16424e9 - 3.74858e9i) q^{28} +(1.74170e9 + 3.01672e9i) q^{29} +(4.61624e8 - 7.99556e8i) q^{30} +2.61380e9 q^{31} +(2.07792e9 - 3.59906e9i) q^{32} +(-7.98222e9 + 1.38256e10i) q^{33} +8.51932e8 q^{34} +(5.06710e9 - 8.77648e9i) q^{35} +(1.39251e10 + 2.41190e10i) q^{36} +(-4.31490e8 - 7.47363e8i) q^{37} -1.47343e9 q^{38} +(1.81517e10 - 3.53642e10i) q^{39} +6.41870e9 q^{40} +(-8.87545e8 - 1.53727e9i) q^{41} +(-1.44404e10 - 2.50116e10i) q^{42} +(-3.49859e8 + 6.05974e8i) q^{43} -5.37324e10 q^{44} +(-3.26027e10 + 5.64695e10i) q^{45} +(-1.12044e10 + 1.94067e10i) q^{46} +4.91139e10 q^{47} +(-6.27767e10 + 1.08732e11i) q^{48} +(-1.10064e11 - 1.90636e11i) q^{49} +(-1.00692e10 - 1.74403e10i) q^{50} -8.66483e10 q^{51} +(1.33628e11 - 6.60443e9i) q^{52} +3.91615e10 q^{53} +(5.20227e10 + 9.01059e10i) q^{54} +(-6.29014e10 - 1.08948e11i) q^{55} +(1.00394e11 - 1.73888e11i) q^{56} +1.49860e11 q^{57} +(-3.91139e10 + 6.77473e10i) q^{58} +(1.16103e11 - 2.01097e11i) q^{59} -3.16050e11 q^{60} +(-1.52787e10 + 2.64635e10i) q^{61} +(2.93494e10 + 5.08347e10i) q^{62} +(1.01987e12 + 1.76647e12i) q^{63} -3.56976e11 q^{64} +(1.69821e11 + 2.63214e11i) q^{65} -3.58518e11 q^{66} +(-4.37449e11 - 7.57685e11i) q^{67} +(-1.45818e11 - 2.52565e11i) q^{68} +(1.13958e12 - 1.97381e12i) q^{69} +2.27587e11 q^{70} +(4.80131e11 - 8.31612e11i) q^{71} +(-6.45957e11 + 1.11883e12i) q^{72} +8.68862e11 q^{73} +(9.69010e9 - 1.67837e10i) q^{74} +(1.02411e12 + 1.77382e12i) q^{75} +(2.52196e11 + 4.36816e11i) q^{76} -3.93534e12 q^{77} +(8.91603e11 - 4.40667e10i) q^{78} -7.23289e11 q^{79} +(-4.94692e11 - 8.56832e11i) q^{80} +(-2.40323e12 - 4.16251e12i) q^{81} +(1.99318e10 - 3.45230e10i) q^{82} -2.62815e12 q^{83} +(-4.94331e12 + 8.56207e12i) q^{84} +(3.41402e11 - 5.91326e11i) q^{85} -1.57138e10 q^{86} +(3.97819e12 - 6.89043e12i) q^{87} +(-1.24626e12 - 2.15859e12i) q^{88} +(2.45111e12 + 4.24546e12i) q^{89} -1.46434e12 q^{90} +(9.78685e12 - 4.83706e11i) q^{91} +7.67110e12 q^{92} +(-2.98507e12 - 5.17029e12i) q^{93} +(5.51482e11 + 9.55195e11i) q^{94} +(-5.90462e11 + 1.02271e12i) q^{95} -9.49228e12 q^{96} +(-3.25335e12 + 5.63496e12i) q^{97} +(2.47174e12 - 4.28117e12i) q^{98} +2.53207e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 65 q^{2} + 728 q^{3} - 53249 q^{4} + 41860 q^{5} + 143910 q^{6} - 173992 q^{7} + 2616978 q^{8} - 5231838 q^{9} + 2769243 q^{10} + 10986144 q^{11} - 45205464 q^{12} + 25107706 q^{13} - 23731756 q^{14}+ \cdots + 33239809172544 q^{99}+O(q^{100}) \) 28 * q - 65 * q^2 + 728 * q^3 - 53249 * q^4 + 41860 * q^5 + 143910 * q^6 - 173992 * q^7 + 2616978 * q^8 - 5231838 * q^9 + 2769243 * q^10 + 10986144 * q^11 - 45205464 * q^12 + 25107706 * q^13 - 23731756 * q^14 - 75354448 * q^15 - 273433217 * q^16 + 255934950 * q^17 - 350685842 * q^18 - 266623552 * q^19 - 225433091 * q^20 - 2515875856 * q^21 + 77223114 * q^22 + 1914406544 * q^23 - 680727216 * q^24 + 5225878768 * q^25 - 9205789749 * q^26 + 3550452320 * q^27 - 3680076400 * q^28 + 6211296126 * q^29 + 5703660004 * q^30 + 6997674944 * q^31 + 2312486527 * q^32 + 5621901584 * q^33 - 23373723594 * q^34 + 23009265024 * q^35 + 23496114839 * q^36 + 19577630774 * q^37 + 51648723644 * q^38 + 31282255680 * q^39 - 111700587858 * q^40 - 6039692074 * q^41 + 143590583874 * q^42 + 16878499784 * q^43 - 489551846992 * q^44 - 148673926778 * q^45 + 177583142490 * q^46 + 369404914944 * q^47 + 92920518608 * q^48 - 195653684766 * q^49 - 753661423970 * q^50 + 617169279136 * q^51 - 727838751302 * q^52 - 287550769100 * q^53 + 365361720282 * q^54 + 855926433792 * q^55 + 192505368988 * q^56 - 1924513438848 * q^57 - 660641292207 * q^58 + 637655529992 * q^59 + 2555257062384 * q^60 + 1530666437030 * q^61 + 1907899186036 * q^62 - 832654573712 * q^63 + 632232280450 * q^64 - 2489693680994 * q^65 - 270853649100 * q^66 - 1120398677944 * q^67 + 4085795015901 * q^68 + 1473200404976 * q^69 - 9377684744688 * q^70 + 1506585643472 * q^71 + 3521118562923 * q^72 - 852513981436 * q^73 + 4665118313621 * q^74 + 2605103918408 * q^75 - 6106356745372 * q^76 + 2854115035024 * q^77 - 8622775525858 * q^78 - 7032676662784 * q^79 + 5983641421745 * q^80 + 2512348302642 * q^81 - 8600700659175 * q^82 + 2033940247872 * q^83 - 4374201207844 * q^84 + 2527554975426 * q^85 - 7547295057588 * q^86 - 1118899666832 * q^87 - 5943200108772 * q^88 + 5229645042596 * q^89 + 4220465391930 * q^90 + 18401936100704 * q^91 + 3830251788320 * q^92 - 1283055655752 * q^93 - 32271602536104 * q^94 + 8980600417472 * q^95 + 51692558969792 * q^96 + 3129146550452 * q^97 - 5503659823363 * q^98 + 33239809172544 * q^99

Introduction

L-functions

Modular forms

Varieties

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