LMFDB - Embedded newform 177.9.c.a.58.80

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,9,Mod(58,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	177.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$72.1060139808$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.80
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+31.6572i q^{2} +46.7654 q^{3} -746.176 q^{4} +733.576 q^{5} +1480.46i q^{6} -1197.79 q^{7} -15517.6i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q+31.6572i q^{2} +46.7654 q^{3} -746.176 q^{4} +733.576 q^{5} +1480.46i q^{6} -1197.79 q^{7} -15517.6i q^{8} +2187.00 q^{9} +23222.9i q^{10} +8187.51i q^{11} -34895.2 q^{12} +19649.3i q^{13} -37918.7i q^{14} +34305.9 q^{15} +300222. q^{16} +39112.0 q^{17} +69234.2i q^{18} +148050. q^{19} -547377. q^{20} -56015.2 q^{21} -259193. q^{22} +347255. i q^{23} -725686. i q^{24} +147508. q^{25} -622042. q^{26} +102276. q^{27} +893763. q^{28} +718866. q^{29} +1.08603e6i q^{30} +540311. i q^{31} +5.53166e6i q^{32} +382892. i q^{33} +1.23818e6i q^{34} -878671. q^{35} -1.63189e6 q^{36} +504723. i q^{37} +4.68684e6i q^{38} +918909. i q^{39} -1.13833e7i q^{40} -2.24431e6 q^{41} -1.77328e6i q^{42} -5.44442e6i q^{43} -6.10932e6i q^{44} +1.60433e6 q^{45} -1.09931e7 q^{46} +6.80833e6i q^{47} +1.40400e7 q^{48} -4.33010e6 q^{49} +4.66969e6i q^{50} +1.82909e6 q^{51} -1.46619e7i q^{52} -1.10727e7 q^{53} +3.23776e6i q^{54} +6.00616e6i q^{55} +1.85868e7i q^{56} +6.92361e6 q^{57} +2.27573e7i q^{58} +(8.67636e6 - 8.45880e6i) q^{59} -2.55983e7 q^{60} +5.93306e6i q^{61} -1.71047e7 q^{62} -2.61957e6 q^{63} -9.82600e7 q^{64} +1.44143e7i q^{65} -1.21213e7 q^{66} +850839. i q^{67} -2.91844e7 q^{68} +1.62395e7i q^{69} -2.78162e7i q^{70} -3.91294e7 q^{71} -3.39370e7i q^{72} +2.01737e7i q^{73} -1.59781e7 q^{74} +6.89827e6 q^{75} -1.10471e8 q^{76} -9.80693e6i q^{77} -2.90900e7 q^{78} -6.48702e6 q^{79} +2.20235e8 q^{80} +4.78297e6 q^{81} -7.10484e7i q^{82} +5.10830e7i q^{83} +4.17972e7 q^{84} +2.86916e7 q^{85} +1.72355e8 q^{86} +3.36180e7 q^{87} +1.27050e8 q^{88} +3.40734e7i q^{89} +5.07885e7i q^{90} -2.35358e7i q^{91} -2.59113e8i q^{92} +2.52678e7i q^{93} -2.15533e8 q^{94} +1.08606e8 q^{95} +2.58690e8i q^{96} -1.35148e8i q^{97} -1.37079e8i q^{98} +1.79061e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$			31.6572i			1.97857i	0.145988	+	0.989286i	$0.453364\pi$
$2$			31.6572i			1.97857i	−0.145988	+	0.989286i	$0.546636\pi$
$3$	46.7654			0.577350
$3$	46.7654			0.577350
$4$	−746.176			−2.91475
$5$	733.576			1.17372			0.586860	−	0.809688i	$-0.300364\pi$
$5$	733.576			1.17372			0.586860	+	0.809688i	$0.300364\pi$
$6$			1480.46i			1.14233i
$7$	−1197.79			−0.498872			−0.249436	−	0.968391i	$-0.580245\pi$
$7$	−1197.79			−0.498872			−0.249436	+	0.968391i	$0.580245\pi$
$8$		−	15517.6i		−	3.78847i
$9$	2187.00			0.333333
$10$			23222.9i			2.32229i
$11$			8187.51i			0.559218i	0.960114	+	0.279609i	$0.0902048\pi$
$11$			8187.51i			0.559218i	−0.960114	+	0.279609i	$0.909795\pi$
$12$	−34895.2			−1.68283
$13$			19649.3i			0.687978i	0.938974	+	0.343989i	$0.111778\pi$
$13$			19649.3i			0.687978i	−0.938974	+	0.343989i	$0.888222\pi$
$14$		−	37918.7i		−	0.987054i
$15$	34305.9			0.677648
$16$	300222.			4.58102
$17$	39112.0			0.468289			0.234145	−	0.972202i	$-0.424771\pi$
$17$	39112.0			0.468289			0.234145	+	0.972202i	$0.424771\pi$
$18$			69234.2i			0.659524i
$19$	148050.			1.13604			0.568021	−	0.823014i	$-0.307709\pi$
$19$	148050.			1.13604			0.568021	+	0.823014i	$0.307709\pi$
$20$	−547377.			−3.42110
$21$	−56015.2			−0.288024
$22$	−259193.			−1.10645
$23$			347255.i			1.24090i	0.784246	+	0.620450i	$0.213050\pi$
$23$			347255.i			1.24090i	−0.784246	+	0.620450i	$0.786950\pi$
$24$		−	725686.i		−	2.18728i
$25$	147508.			0.377621
$26$	−622042.			−1.36121
$27$	102276.			0.192450
$28$	893763.			1.45409
$29$	718866.			1.01638			0.508190	−	0.861245i	$-0.330315\pi$
$29$	718866.			1.01638			0.508190	+	0.861245i	$0.330315\pi$
$30$			1.08603e6i			1.34078i
$31$			540311.i			0.585055i	0.956257	+	0.292527i	$0.0944963\pi$
$31$			540311.i			0.585055i	−0.956257	+	0.292527i	$0.905504\pi$
$32$			5.53166e6i			5.27540i
$33$			382892.i			0.322865i
$34$			1.23818e6i			0.926545i
$35$	−878671.			−0.585536
$36$	−1.63189e6			−0.971583
$37$			504723.i			0.269306i	0.990893	+	0.134653i	$0.0429920\pi$
$37$			504723.i			0.269306i	−0.990893	+	0.134653i	$0.957008\pi$
$38$			4.68684e6i			2.24774i
$39$			918909.i			0.397204i
$40$		−	1.13833e7i		−	4.44661i
$41$	−2.24431e6			−0.794231			−0.397115	−	0.917769i	$-0.629989\pi$
$41$	−2.24431e6			−0.794231			−0.397115	+	0.917769i	$0.629989\pi$
$42$		−	1.77328e6i		−	0.569876i
$43$		−	5.44442e6i		−	1.59249i	−0.604972	−	0.796246i	$-0.706816\pi$
$43$		−	5.44442e6i		−	1.59249i	0.604972	−	0.796246i	$-0.293184\pi$
$44$		−	6.10932e6i		−	1.62998i
$45$	1.60433e6			0.391240
$46$	−1.09931e7			−2.45521
$47$			6.80833e6i			1.39524i	0.716467	+	0.697621i	$0.245758\pi$
$47$			6.80833e6i			1.39524i	−0.716467	+	0.697621i	$0.754242\pi$
$48$	1.40400e7			2.64485
$49$	−4.33010e6			−0.751127
$50$			4.66969e6i			0.747150i
$51$	1.82909e6			0.270367
$52$		−	1.46619e7i		−	2.00528i
$53$	−1.10727e7			−1.40330			−0.701648	−	0.712524i	$-0.747552\pi$
$53$	−1.10727e7			−1.40330			−0.701648	+	0.712524i	$0.747552\pi$
$54$			3.23776e6i			0.380776i
$55$			6.00616e6i			0.656366i
$56$			1.85868e7i			1.88996i
$57$	6.92361e6			0.655894
$58$			2.27573e7i			2.01098i
$59$	8.67636e6	−	8.45880e6i	0.716027	−	0.698073i
$59$	8.67636e6	−	8.45880e6i	0.716027	−	0.698073i
$60$	−2.55983e7			−1.97517
$61$			5.93306e6i			0.428508i	0.976778	+	0.214254i	$0.0687321\pi$
$61$			5.93306e6i			0.428508i	−0.976778	+	0.214254i	$0.931268\pi$
$62$	−1.71047e7			−1.15757
$63$	−2.61957e6			−0.166291
$64$	−9.82600e7			−5.85675
$65$			1.44143e7i			0.807494i
$66$	−1.21213e7			−0.638811
$67$			850839.i			0.0422229i	0.999777	+	0.0211115i	$0.00672049\pi$
$67$			850839.i			0.0422229i	−0.999777	+	0.0211115i	$0.993280\pi$
$68$	−2.91844e7			−1.36495
$69$			1.62395e7i			0.716434i
$70$		−	2.78162e7i		−	1.15853i
$71$	−3.91294e7			−1.53982			−0.769910	−	0.638152i	$-0.779699\pi$
$71$	−3.91294e7			−1.53982			−0.769910	+	0.638152i	$0.779699\pi$
$72$		−	3.39370e7i		−	1.26282i
$73$			2.01737e7i			0.710384i	0.934793	+	0.355192i	$0.115585\pi$
$73$			2.01737e7i			0.710384i	−0.934793	+	0.355192i	$0.884415\pi$
$74$	−1.59781e7			−0.532842
$75$	6.89827e6			0.218020
$76$	−1.10471e8			−3.31128
$77$		−	9.80693e6i		−	0.278978i
$78$	−2.90900e7			−0.785898
$79$	−6.48702e6			−0.166547			−0.0832736	−	0.996527i	$-0.526538\pi$
$79$	−6.48702e6			−0.166547			−0.0832736	+	0.996527i	$0.526538\pi$
$80$	2.20235e8			5.37684
$81$	4.78297e6			0.111111
$82$		−	7.10484e7i		−	1.57144i
$83$			5.10830e7i			1.07638i	0.842825	+	0.538188i	$0.180891\pi$
$83$			5.10830e7i			1.07638i	−0.842825	+	0.538188i	$0.819109\pi$
$84$	4.17972e7			0.839517
$85$	2.86916e7			0.549641
$86$	1.72355e8			3.15086
$87$	3.36180e7			0.586807
$88$	1.27050e8			2.11858
$89$			3.40734e7i			0.543070i	0.962429	+	0.271535i	$0.0875312\pi$
$89$			3.40734e7i			0.543070i	−0.962429	+	0.271535i	$0.912469\pi$
$90$			5.07885e7i			0.774097i
$91$		−	2.35358e7i		−	0.343213i
$92$		−	2.59113e8i		−	3.61691i
$93$			2.52678e7i			0.337782i
$94$	−2.15533e8			−2.76059
$95$	1.08606e8			1.33340
$96$			2.58690e8i			3.04576i
$97$		−	1.35148e8i		−	1.52659i	−0.646052	−	0.763294i	$-0.723581\pi$
$97$		−	1.35148e8i		−	1.52659i	0.646052	−	0.763294i	$-0.276419\pi$
$98$		−	1.37079e8i		−	1.48616i
$99$			1.79061e7i			0.186406i
$100$	−1.10067e8			−1.10067
$101$			1.75070e8i			1.68239i	0.540731	+	0.841195i	$0.318148\pi$
$101$			1.75070e8i			1.68239i	−0.540731	+	0.841195i	$0.681852\pi$
$102$			5.79037e7i			0.534941i
$103$			1.84171e7i			0.163634i	0.996647	+	0.0818170i	$0.0260723\pi$
$103$			1.84171e7i			0.163634i	−0.996647	+	0.0818170i	$0.973928\pi$
$104$	3.04910e8			2.60639
$105$	−4.10914e7			−0.338060
$106$		−	3.50530e8i		−	2.77652i
$107$	1.46786e8			1.11982			0.559912	−	0.828552i	$-0.310835\pi$
$107$	1.46786e8			1.11982			0.559912	+	0.828552i	$0.310835\pi$
$108$	−7.63158e7			−0.560944
$109$		−	2.24376e7i		−	0.158953i	−0.996837	−	0.0794767i	$-0.974675\pi$
$109$		−	2.24376e7i		−	0.158953i	0.996837	−	0.0794767i	$-0.0253249\pi$
$110$	−1.90138e8			−1.29867
$111$			2.36036e7i			0.155484i
$112$	−3.59603e8			−2.28534
$113$		−	1.10893e8i		−	0.680126i	−0.940403	−	0.340063i	$-0.889552\pi$
$113$		−	1.10893e8i		−	0.680126i	0.940403	−	0.340063i	$-0.110448\pi$
$114$			2.19182e8i			1.29773i
$115$			2.54738e8i			1.45647i
$116$	−5.36400e8			−2.96249
$117$			4.29731e7i			0.229326i
$118$	2.67782e8	+	2.74669e8i	1.38119	+	1.41671i
$119$	−4.68480e7			−0.233616
$120$		−	5.32345e8i		−	2.56725i
$121$	1.47324e8			0.687275
$122$	−1.87824e8			−0.847835
$123$	−1.04956e8			−0.458549
$124$		−	4.03167e8i		−	1.70529i
$125$	−1.78345e8			−0.730499
$126$		−	8.29281e7i		−	0.329018i
$127$	4.05456e8			1.55858			0.779289	−	0.626664i	$-0.215580\pi$
$127$	4.05456e8			1.55858			0.779289	+	0.626664i	$0.215580\pi$
$128$		−	1.69453e9i		−	6.31261i
$129$		−	2.54610e8i		−	0.919426i
$130$	−4.56315e8			−1.59769
$131$			8.31505e7i			0.282345i	0.989985	+	0.141172i	$0.0450872\pi$
$131$			8.31505e7i			0.282345i	−0.989985	+	0.141172i	$0.954913\pi$
$132$		−	2.85705e8i		−	0.941070i
$133$	−1.77333e8			−0.566739
$134$	−2.69352e7			−0.0835411
$135$	7.50271e7			0.225883
$136$		−	6.06924e8i		−	1.77410i
$137$	−1.03226e8			−0.293027			−0.146514	−	0.989209i	$-0.546805\pi$
$137$	−1.03226e8			−0.293027			−0.146514	+	0.989209i	$0.546805\pi$
$138$	−5.14096e8			−1.41752
$139$	7.82094e7			0.209508			0.104754	−	0.994498i	$-0.466595\pi$
$139$	7.82094e7			0.209508			0.104754	+	0.994498i	$0.466595\pi$
$140$	6.55643e8			1.70669
$141$			3.18394e8i			0.805543i
$142$		−	1.23873e9i		−	3.04665i
$143$	−1.60879e8			−0.384730
$144$	6.56585e8			1.52701
$145$	5.27342e8			1.19295
$146$	−6.38641e8			−1.40555
$147$	−2.02499e8			−0.433663
$148$		−	3.76612e8i		−	0.784960i
$149$			8.16267e8i			1.65610i	0.560653	+	0.828051i	$0.310550\pi$
$149$			8.16267e8i			1.65610i	−0.560653	+	0.828051i	$0.689450\pi$
$150$			2.18380e8i			0.431368i
$151$			4.79472e8i			0.922264i	0.887332	+	0.461132i	$0.152557\pi$
$151$			4.79472e8i			0.922264i	−0.887332	+	0.461132i	$0.847443\pi$
$152$		−	2.29738e9i		−	4.30386i
$153$	8.55379e7			0.156096
$154$	3.10459e8			0.551978
$155$			3.96359e8i			0.686691i
$156$		−	6.85668e8i		−	1.15775i
$157$			4.02372e8i			0.662261i	0.943585	+	0.331130i	$0.107430\pi$
$157$			4.02372e8i			0.662261i	−0.943585	+	0.331130i	$0.892570\pi$
$158$		−	2.05361e8i		−	0.329526i
$159$	−5.17818e8			−0.810194
$160$			4.05789e9i			6.19185i
$161$		−	4.15939e8i		−	0.619050i
$162$			1.51415e8i			0.219841i
$163$	−8.79422e8			−1.24580			−0.622898	−	0.782303i	$-0.714045\pi$
$163$	−8.79422e8			−1.24580			−0.622898	+	0.782303i	$0.714045\pi$
$164$	1.67465e9			2.31498
$165$			2.80880e8i			0.378953i
$166$	−1.61714e9			−2.12969
$167$	−1.26373e9			−1.62476			−0.812380	−	0.583128i	$-0.801829\pi$
$167$	−1.26373e9			−1.62476			−0.812380	+	0.583128i	$0.801829\pi$
$168$			8.69220e8i			1.09117i
$169$	4.29634e8			0.526686
$170$			9.08295e8i			1.08750i
$171$	3.23785e8			0.378680
$172$			4.06249e9i			4.64172i
$173$			3.66882e8i			0.409583i	0.978806	+	0.204792i	$0.0656517\pi$
$173$			3.66882e8i			0.409583i	−0.978806	+	0.204792i	$0.934348\pi$
$174$			1.06425e9i			1.16104i
$175$	−1.76684e8			−0.188384
$176$			2.45807e9i			2.56179i
$177$	4.05753e8	−	3.95579e8i	0.413398	−	0.403032i
$178$	−1.07867e9			−1.07450
$179$		−	6.49482e8i		−	0.632638i	−0.948653	−	0.316319i	$-0.897553\pi$
$179$		−	6.49482e8i		−	0.632638i	0.948653	−	0.316319i	$-0.102447\pi$
$180$	−1.19711e9			−1.14037
$181$	−4.52457e8			−0.421564			−0.210782	−	0.977533i	$-0.567601\pi$
$181$	−4.52457e8			−0.421564			−0.210782	+	0.977533i	$0.567601\pi$
$182$	7.45077e8			0.679072
$183$			2.77462e8i			0.247399i
$184$	5.38855e9			4.70112
$185$			3.70252e8i			0.316090i
$186$	−7.99908e8			−0.668326
$187$			3.20230e8i			0.261876i
$188$		−	5.08021e9i		−	4.06678i
$189$	−1.22505e8			−0.0960079
$190$			3.43815e9i			2.63822i
$191$		−	5.25421e8i		−	0.394797i	−0.980323	−	0.197399i	$-0.936751\pi$
$191$		−	5.25421e8i		−	0.394797i	0.980323	−	0.197399i	$-0.0632494\pi$
$192$	−4.59517e9			−3.38140
$193$	1.33758e9			0.964028			0.482014	−	0.876164i	$-0.339905\pi$
$193$	1.33758e9			0.964028			0.482014	+	0.876164i	$0.339905\pi$
$194$	4.27839e9			3.02046
$195$			6.74089e8i			0.466207i
$196$	3.23101e9			2.18935
$197$	2.94549e8			0.195565			0.0977827	−	0.995208i	$-0.468825\pi$
$197$	2.94549e8			0.195565			0.0977827	+	0.995208i	$0.468825\pi$
$198$	−5.66856e8			−0.368818
$199$	7.82763e8			0.499135			0.249568	−	0.968357i	$-0.419712\pi$
$199$	7.82763e8			0.499135			0.249568	+	0.968357i	$0.419712\pi$
$200$		−	2.28897e9i		−	1.43061i
$201$			3.97898e7i			0.0243774i
$202$	−5.54223e9			−3.32873
$203$	−8.61051e8			−0.507043
$204$	−1.36482e9			−0.788052
$205$	−1.64637e9			−0.932205
$206$	−5.83035e8			−0.323762
$207$			7.59446e8i			0.413633i
$208$			5.89916e9i			3.15164i
$209$			1.21216e9i			0.635295i
$210$		−	1.30084e9i		−	0.668875i
$211$		−	3.91593e9i		−	1.97563i	−0.155640	−	0.987814i	$-0.549744\pi$
$211$		−	3.91593e9i		−	1.97563i	0.155640	−	0.987814i	$-0.450256\pi$
$212$	8.26217e9			4.09026
$213$	−1.82990e9			−0.889016
$214$			4.64683e9i			2.21565i
$215$		−	3.99389e9i		−	1.86914i
$216$		−	1.58707e9i		−	0.729092i
$217$		−	6.47179e8i		−	0.291867i
$218$	7.10310e8			0.314501
$219$			9.43429e8i			0.410140i
$220$		−	4.48165e9i		−	1.91314i
$221$			7.68525e8i			0.322173i
$222$	−7.47222e8			−0.307636
$223$	−3.32777e9			−1.34565			−0.672827	−	0.739800i	$-0.734920\pi$
$223$	−3.32777e9			−1.34565			−0.672827	+	0.739800i	$0.734920\pi$
$224$		−	6.62578e9i		−	2.63175i
$225$	3.22600e8			0.125874
$226$	3.51055e9			1.34568
$227$		−	2.28317e9i		−	0.859872i	−0.902859	−	0.429936i	$-0.858536\pi$
$227$		−	2.28317e9i		−	0.859872i	0.902859	−	0.429936i	$-0.141464\pi$
$228$	−5.16624e9			−1.91177
$229$			4.40320e9i			1.60113i	0.599247	+	0.800564i	$0.295467\pi$
$229$			4.40320e9i			1.60113i	−0.599247	+	0.800564i	$0.704533\pi$
$230$	−8.06427e9			−2.88173
$231$		−	4.58625e8i		−	0.161068i
$232$		−	1.11551e10i		−	3.85052i
$233$			4.30991e9i			1.46233i	0.682203	+	0.731163i	$0.261022\pi$
$233$			4.30991e9i			1.46233i	−0.682203	+	0.731163i	$0.738978\pi$
$234$	−1.36041e9			−0.453738
$235$			4.99443e9i			1.63762i
$236$	−6.47409e9	+	6.31175e9i	−2.08704	+	2.03471i
$237$	−3.03368e8			−0.0961560
$238$		−	1.48308e9i		−	0.462227i
$239$	−2.83177e9			−0.867893			−0.433947	−	0.900939i	$-0.642879\pi$
$239$	−2.83177e9			−0.867893			−0.433947	+	0.900939i	$0.642879\pi$
$240$	1.02994e10			3.10432
$241$	−1.47889e9			−0.438396			−0.219198	−	0.975680i	$-0.570344\pi$
$241$	−1.47889e9			−0.438396			−0.219198	+	0.975680i	$0.570344\pi$
$242$			4.66385e9i			1.35982i
$243$	2.23677e8			0.0641500
$244$		−	4.42711e9i		−	1.24899i
$245$	−3.17645e9			−0.881613
$246$		−	3.32260e9i		−	0.907273i
$247$			2.90909e9i			0.781572i
$248$	8.38431e9			2.21646
$249$			2.38891e9i			0.621446i
$250$		−	5.64588e9i		−	1.44535i
$251$	9.81508e7			0.0247286			0.0123643	−	0.999924i	$-0.496064\pi$
$251$	9.81508e7			0.0247286			0.0123643	+	0.999924i	$0.496064\pi$
$252$	1.95466e9			0.484696
$253$	−2.84315e9			−0.693934
$254$			1.28356e10i			3.08376i
$255$	1.34177e9			0.317335
$256$	2.84894e10			6.63320
$257$	8.52646e9			1.95450			0.977251	−	0.212086i	$-0.0680256\pi$
$257$	8.52646e9			1.95450			0.977251	+	0.212086i	$0.0680256\pi$
$258$	8.06023e9			1.81915
$259$		−	6.04553e8i		−	0.134349i
$260$		−	1.07556e10i		−	2.35364i
$261$	1.57216e9			0.338793
$262$	−2.63231e9			−0.558640
$263$	−4.65933e9			−0.973868			−0.486934	−	0.873439i	$-0.661885\pi$
$263$	−4.65933e9			−0.973868			−0.486934	+	0.873439i	$0.661885\pi$
$264$	5.94156e9			1.22316
$265$	−8.12265e9			−1.64708
$266$		−	5.61386e9i		−	1.12133i
$267$			1.59346e9i			0.313541i
$268$		−	6.34876e8i		−	0.123069i
$269$			4.27626e9i			0.816687i	0.912828	+	0.408343i	$0.133893\pi$
$269$			4.27626e9i			0.816687i	−0.912828	+	0.408343i	$0.866107\pi$
$270$			2.37514e9i			0.446925i
$271$	−8.14416e9			−1.50997			−0.754987	−	0.655740i	$-0.772357\pi$
$271$	−8.14416e9			−1.50997			−0.754987	+	0.655740i	$0.772357\pi$
$272$	1.17423e10			2.14524
$273$		−	1.10066e9i		−	0.198154i
$274$		−	3.26785e9i		−	0.579775i
$275$			1.20772e9i			0.211172i
$276$		−	1.21175e10i		−	2.08823i
$277$	1.03683e10			1.76112			0.880559	−	0.473936i	$-0.157167\pi$
$277$	1.03683e10			1.76112			0.880559	+	0.473936i	$0.157167\pi$
$278$			2.47589e9i			0.414526i
$279$			1.18166e9i			0.195018i
$280$			1.36348e10i			2.21829i
$281$	−2.14005e8			−0.0343241			−0.0171620	−	0.999853i	$-0.505463\pi$
$281$	−2.14005e8			−0.0343241			−0.0171620	+	0.999853i	$0.505463\pi$
$282$	−1.00795e10			−1.59383
$283$			9.06708e9i			1.41358i	0.707421	+	0.706792i	$0.249858\pi$
$283$			9.06708e9i			1.41358i	−0.707421	+	0.706792i	$0.750142\pi$
$284$	2.91974e10			4.48819
$285$	5.07899e9			0.769836
$286$		−	5.09298e9i		−	0.761216i
$287$	2.68821e9			0.396219
$288$			1.20977e10i			1.75847i
$289$	−5.44601e9			−0.780705
$290$			1.66942e10i			2.36033i
$291$		−	6.32023e9i		−	0.881376i
$292$		−	1.50531e10i		−	2.07059i
$293$	−1.32943e10			−1.80382			−0.901910	−	0.431923i	$-0.857835\pi$
$293$	−1.32943e10			−1.80382			−0.901910	+	0.431923i	$0.857835\pi$
$294$		−	6.41053e9i		−	0.858034i
$295$	6.36476e9	−	6.20517e9i	0.840416	−	0.819343i
$296$	7.83208e9			1.02026
$297$			8.37385e8i			0.107622i
$298$	−2.58407e10			−3.27672
$299$	−6.82333e9			−0.853712
$300$	−5.14733e9			−0.635472
$301$			6.52127e9i			0.794450i
$302$	−1.51787e10			−1.82477
$303$			8.18723e9i			0.971329i
$304$	4.44478e10			5.20423
$305$			4.35235e9i			0.502949i
$306$			2.70789e9i			0.308848i
$307$	9.29689e8			0.104661			0.0523304	−	0.998630i	$-0.483335\pi$
$307$	9.29689e8			0.104661			0.0523304	+	0.998630i	$0.483335\pi$
$308$			7.31769e9i			0.813151i
$309$			8.61285e8i			0.0944741i
$310$	−1.25476e10			−1.35867
$311$	2.49791e9			0.267015			0.133508	−	0.991048i	$-0.457376\pi$
$311$	2.49791e9			0.267015			0.133508	+	0.991048i	$0.457376\pi$
$312$	1.42592e10			1.50480
$313$			1.13268e10i			1.18013i	0.807354	+	0.590067i	$0.200899\pi$
$313$			1.13268e10i			1.18013i	−0.807354	+	0.590067i	$0.799101\pi$
$314$	−1.27379e10			−1.31033
$315$	−1.92165e9			−0.195179
$316$	4.84046e9			0.485443
$317$	1.91351e10			1.89494			0.947468	−	0.319850i	$-0.103633\pi$
$317$	1.91351e10			1.89494			0.947468	+	0.319850i	$0.103633\pi$
$318$		−	1.63927e10i		−	1.60303i
$319$			5.88572e9i			0.568377i
$320$	−7.20812e10			−6.87419
$321$	6.86450e9			0.646530
$322$	1.31674e10			1.22484
$323$	5.79053e9			0.531996
$324$	−3.56894e9			−0.323861
$325$			2.89844e9i			0.259795i
$326$		−	2.78400e10i		−	2.46490i
$327$		−	1.04930e9i		−	0.0917718i
$328$			3.48262e10i			3.00892i
$329$		−	8.15496e9i		−	0.696047i
$330$	−8.89187e9			−0.749786
$331$	7.74326e8			0.0645078			0.0322539	−	0.999480i	$-0.489731\pi$
$331$	7.74326e8			0.0645078			0.0322539	+	0.999480i	$0.489731\pi$
$332$		−	3.81169e10i		−	3.13737i
$333$			1.10383e9i			0.0897687i
$334$		−	4.00062e10i		−	3.21471i
$335$			6.24155e8i			0.0495579i
$336$	−1.68170e10			−1.31944
$337$		−	6.97385e8i		−	0.0540696i	−0.999634	−	0.0270348i	$-0.991394\pi$
$337$		−	6.97385e8i		−	0.0540696i	0.999634	−	0.0270348i	$-0.00860649\pi$
$338$			1.36010e10i			1.04209i
$339$		−	5.18594e9i		−	0.392671i
$340$	−2.14090e10			−1.60207
$341$	−4.42380e9			−0.327173
$342$			1.02501e10i			0.749247i
$343$	1.20916e10			0.873588
$344$	−8.44842e10			−6.03311
$345$			1.19129e10i			0.840894i
$346$	−1.16144e10			−0.810390
$347$		−	5.54324e9i		−	0.382336i	−0.981557	−	0.191168i	$-0.938772\pi$
$347$		−	5.54324e9i		−	0.382336i	0.981557	−	0.191168i	$-0.0612276\pi$
$348$	−2.50850e10			−1.71040
$349$		−	1.82467e10i		−	1.22994i	−0.788552	−	0.614968i	$-0.789169\pi$
$349$		−	1.82467e10i		−	1.22994i	0.788552	−	0.614968i	$-0.210831\pi$
$350$		−	5.59331e9i		−	0.372732i
$351$			2.00965e9i			0.132401i
$352$	−4.52905e10			−2.95010
$353$		−	2.27785e10i		−	1.46699i	−0.679695	−	0.733494i	$-0.737888\pi$
$353$		−	2.27785e10i		−	1.46699i	0.679695	−	0.733494i	$-0.262112\pi$
$354$	1.25229e10	+	1.28450e10i	0.797429	+	0.817939i
$355$	−2.87044e10			−1.80732
$356$		−	2.54248e10i		−	1.58291i
$357$	−2.19086e9			−0.134879
$358$	2.05608e10			1.25172
$359$	2.93931e10			1.76957			0.884786	−	0.465998i	$-0.154305\pi$
$359$	2.93931e10			1.76957			0.884786	+	0.465998i	$0.154305\pi$
$360$		−	2.48953e10i		−	1.48220i
$361$	4.93525e9			0.290590
$362$		−	1.43235e10i		−	0.834094i
$363$	6.88964e9			0.396799
$364$			1.75619e10i			1.00038i
$365$			1.47989e10i			0.833793i
$366$	−8.78365e9			−0.489498
$367$		−	1.53824e10i		−	0.847928i	−0.905679	−	0.423964i	$-0.860638\pi$
$367$		−	1.53824e10i		−	0.847928i	0.905679	−	0.423964i	$-0.139362\pi$
$368$			1.04253e11i			5.68459i
$369$	−4.90830e9			−0.264744
$370$	−1.17211e10			−0.625407
$371$	1.32628e10			0.700065
$372$		−	1.88542e10i		−	0.984549i
$373$	3.36236e10			1.73704			0.868518	−	0.495657i	$-0.165073\pi$
$373$	3.36236e10			1.73704			0.868518	+	0.495657i	$0.165073\pi$
$374$	−1.01376e10			−0.518140
$375$	−8.34035e9			−0.421754
$376$	1.05649e11			5.28583
$377$			1.41252e10i			0.699247i
$378$		−	3.87817e9i		−	0.189959i
$379$	−7.79257e9			−0.377680			−0.188840	−	0.982008i	$-0.560473\pi$
$379$	−7.79257e9			−0.377680			−0.188840	+	0.982008i	$0.560473\pi$
$380$	−8.10391e10			−3.88651
$381$	1.89613e10			0.899846
$382$	1.66334e10			0.781135
$383$	−4.04627e9			−0.188044			−0.0940220	−	0.995570i	$-0.529972\pi$
$383$	−4.04627e9			−0.188044			−0.0940220	+	0.995570i	$0.529972\pi$
$384$		−	7.92452e10i		−	3.64459i
$385$		−	7.19412e9i		−	0.327442i
$386$			4.23439e10i			1.90740i
$387$		−	1.19069e10i		−	0.530831i
$388$			1.00844e11i			4.44962i
$389$	2.62751e10			1.14748			0.573742	−	0.819036i	$-0.305491\pi$
$389$	2.62751e10			1.14748			0.573742	+	0.819036i	$0.305491\pi$
$390$	−2.13397e10			−0.922425
$391$			1.35818e10i			0.581101i
$392$			6.71926e10i			2.84562i
$393$			3.88856e9i			0.163012i
$394$			9.32457e9i			0.386940i
$395$	−4.75872e9			−0.195480
$396$		−	1.33611e10i		−	0.543327i
$397$			1.38325e10i			0.556852i	0.960458	+	0.278426i	$0.0898127\pi$
$397$			1.38325e10i			0.556852i	−0.960458	+	0.278426i	$0.910187\pi$
$398$			2.47801e10i			0.987575i
$399$	−8.29305e9			−0.327207
$400$	4.42851e10			1.72989
$401$			1.03051e10i			0.398544i	0.979944	+	0.199272i	$0.0638577\pi$
$401$			1.03051e10i			0.398544i	−0.979944	+	0.199272i	$0.936142\pi$
$402$	−1.25963e9			−0.0482325
$403$	−1.06167e10			−0.402505
$404$		−	1.30633e11i		−	4.90375i
$405$	3.50867e9			0.130413
$406$		−	2.72584e10i		−	1.00322i
$407$	−4.13242e9			−0.150601
$408$		−	2.83830e10i		−	1.02428i
$409$		−	4.00344e10i		−	1.43067i	−0.698781	−	0.715335i	$-0.746274\pi$
$409$		−	4.00344e10i		−	1.43067i	0.698781	−	0.715335i	$-0.253726\pi$
$410$		−	5.21193e10i		−	1.84444i
$411$	−4.82741e9			−0.169179
$412$		−	1.37424e10i		−	0.476952i
$413$	−1.03925e10	+	1.01319e10i	−0.357206	+	0.348249i
$414$	−2.40419e10			−0.818404
$415$			3.74732e10i			1.26336i
$416$	−1.08694e11			−3.62936
$417$	3.65749e9			0.120959
$418$	−3.83736e10			−1.25698
$419$		−	2.85527e10i		−	0.926383i	−0.886258	−	0.463192i	$-0.846704\pi$
$419$		−	2.85527e10i		−	0.926383i	0.886258	−	0.463192i	$-0.153296\pi$
$420$	3.06614e10			0.985359
$421$		−	3.69925e10i		−	1.17757i	−0.808291	−	0.588783i	$-0.799607\pi$
$421$		−	3.69925e10i		−	1.17757i	0.808291	−	0.588783i	$-0.200393\pi$
$422$	1.23967e11			3.90892
$423$			1.48898e10i			0.465080i
$424$			1.71821e11i			5.31635i
$425$	5.76934e9			0.176836
$426$		−	5.79295e10i		−	1.75898i
$427$		−	7.10657e9i		−	0.213771i
$428$	−1.09528e11			−3.26400
$429$	−7.52357e9			−0.222124
$430$	1.26435e11			3.69823
$431$			2.20682e9i			0.0639525i	0.999489	+	0.0319763i	$0.0101801\pi$
$431$			2.20682e9i			0.0639525i	−0.999489	+	0.0319763i	$0.989820\pi$
$432$	3.07054e10			0.881617
$433$	4.65743e10			1.32493			0.662467	−	0.749091i	$-0.269509\pi$
$433$	4.65743e10			1.32493			0.662467	+	0.749091i	$0.269509\pi$
$434$	2.04879e10			0.577481
$435$	2.46614e10			0.688748
$436$			1.67424e10i			0.463309i
$437$			5.14111e10i			1.40971i
$438$	−2.98663e10			−0.811493
$439$	1.99444e10			0.536985			0.268492	−	0.963282i	$-0.413475\pi$
$439$	1.99444e10			0.536985			0.268492	+	0.963282i	$0.413475\pi$
$440$	9.32010e10			2.48662
$441$	−9.46992e9			−0.250376
$442$	−2.43293e10			−0.637442
$443$		−	2.86671e10i		−	0.744335i	−0.928166	−	0.372167i	$-0.878615\pi$
$443$		−	2.86671e10i		−	0.744335i	0.928166	−	0.372167i	$-0.121385\pi$
$444$		−	1.76124e10i		−	0.453197i
$445$			2.49954e10i			0.637412i
$446$		−	1.05348e11i		−	2.66247i
$447$			3.81730e10i			0.956151i
$448$	1.17695e11			2.92177
$449$	−3.58071e10			−0.881015			−0.440507	−	0.897749i	$-0.645201\pi$
$449$	−3.58071e10			−0.881015			−0.440507	+	0.897749i	$0.645201\pi$
$450$			1.02126e10i			0.249050i
$451$		−	1.83753e10i		−	0.444148i
$452$			8.27456e10i			1.98240i
$453$			2.24227e10i			0.532469i
$454$	7.22785e10			1.70132
$455$		−	1.72653e10i		−	0.402836i
$456$		−	1.07438e11i		−	2.48484i
$457$		−	6.09304e10i		−	1.39691i	−0.715653	−	0.698456i	$-0.753871\pi$
$457$		−	6.09304e10i		−	1.39691i	0.715653	−	0.698456i	$-0.246129\pi$
$458$	−1.39393e11			−3.16795
$459$	4.00021e9			0.0901223
$460$		−	1.90079e11i		−	4.24525i
$461$	3.61230e10			0.799797			0.399898	−	0.916559i	$-0.369045\pi$
$461$	3.61230e10			0.799797			0.399898	+	0.916559i	$0.369045\pi$
$462$	1.45188e10			0.318685
$463$			1.00251e10i			0.218155i	0.994033	+	0.109077i	$0.0347896\pi$
$463$			1.00251e10i			0.218155i	−0.994033	+	0.109077i	$0.965210\pi$
$464$	2.15819e11			4.65605
$465$			1.85359e10i			0.396461i
$466$	−1.36439e11			−2.89332
$467$			3.09772e10i			0.651291i	0.945492	+	0.325646i	$0.105582\pi$
$467$			3.09772e10i			0.651291i	−0.945492	+	0.325646i	$0.894418\pi$
$468$		−	3.20655e10i		−	0.668428i
$469$		−	1.01913e9i		−	0.0210638i
$470$	−1.58109e11			−3.24016
$471$			1.88171e10i			0.382356i
$472$	−1.31260e11	−	1.34636e11i	−2.64463	−	2.71265i
$473$	4.45762e10			0.890550
$474$		−	9.60377e9i		−	0.190252i
$475$	2.18386e10			0.428993
$476$	3.49569e10			0.680933
$477$	−2.42160e10			−0.467765
$478$		−	8.96458e10i		−	1.71719i
$479$	5.23904e10			0.995199			0.497599	−	0.867407i	$-0.334215\pi$
$479$	5.23904e10			0.995199			0.497599	+	0.867407i	$0.334215\pi$
$480$			1.89769e11i			3.57487i
$481$	−9.91747e9			−0.185277
$482$		−	4.68173e10i		−	0.867398i
$483$		−	1.94515e10i		−	0.357409i
$484$	−1.09929e11			−2.00324
$485$		−	9.91410e10i		−	1.79179i
$486$			7.08099e9i			0.126925i
$487$	−6.48399e10			−1.15273			−0.576364	−	0.817193i	$-0.695529\pi$
$487$	−6.48399e10			−1.15273			−0.576364	+	0.817193i	$0.695529\pi$
$488$	9.20667e10			1.62339
$489$	−4.11265e10			−0.719261
$490$		−	1.00558e11i		−	1.74434i
$491$	8.45331e10			1.45446			0.727229	−	0.686395i	$-0.240808\pi$
$491$	8.45331e10			1.45446			0.727229	+	0.686395i	$0.240808\pi$
$492$	7.83155e10			1.33656
$493$	2.81163e10			0.475960
$494$	−9.20934e10			−1.54640
$495$			1.31355e10i			0.218789i
$496$			1.62213e11i			2.68015i
$497$	4.68689e10			0.768173
$498$	−7.56262e10			−1.22958
$499$	3.58704e10			0.578540			0.289270	−	0.957248i	$-0.406587\pi$
$499$	3.58704e10			0.578540			0.289270	+	0.957248i	$0.406587\pi$
$500$	1.33076e11			2.12922
$501$	−5.90989e10			−0.938056
$502$			3.10717e9i			0.0489272i
$503$		−	3.60231e10i		−	0.562742i	−0.959599	−	0.281371i	$-0.909211\pi$
$503$		−	3.60231e10i		−	0.562742i	0.959599	−	0.281371i	$-0.0907891\pi$
$504$			4.06494e10i			0.629987i
$505$			1.28427e11i			1.97466i
$506$		−	9.00061e10i		−	1.37300i
$507$	2.00920e10			0.304082
$508$	−3.02541e11			−4.54287
$509$			7.97449e9i			0.118804i	0.998234	+	0.0594021i	$0.0189194\pi$
$509$			7.97449e9i			0.118804i	−0.998234	+	0.0594021i	$0.981081\pi$
$510$			4.24768e10i			0.627871i
$511$		−	2.41638e10i		−	0.354391i
$512$			4.68094e11i			6.81166i
$513$	1.51419e10			0.218631
$514$			2.69923e11i			3.86712i
$515$			1.35104e10i			0.192061i
$516$			1.89984e11i			2.67990i
$517$	−5.57433e10			−0.780244
$518$	1.91384e10			0.265820
$519$			1.71574e10i			0.236473i
$520$	2.23675e11			3.05917
$521$	1.27604e11			1.73186			0.865931	−	0.500164i	$-0.166727\pi$
$521$	1.27604e11			1.73186			0.865931	+	0.500164i	$0.166727\pi$
$522$			4.97701e10i			0.670327i
$523$	−6.01563e10			−0.804034			−0.402017	−	0.915632i	$-0.631691\pi$
$523$	−6.01563e10			−0.804034			−0.402017	+	0.915632i	$0.631691\pi$
$524$		−	6.20449e10i		−	0.822964i
$525$	−8.26269e9			−0.108764
$526$		−	1.47501e11i		−	1.92687i
$527$			2.11326e10i			0.273975i
$528$			1.14952e11i			1.47905i
$529$	−4.22749e10			−0.539834
$530$		−	2.57140e11i		−	3.25886i
$531$	1.89752e10	−	1.84994e10i	0.238676	−	0.232691i
$532$	1.32322e11			1.65190
$533$		−	4.40991e10i		−	0.546413i
$534$	−5.04443e10			−0.620364
$535$	1.07679e11			1.31436
$536$	1.32030e10			0.159960
$537$		−	3.03733e10i		−	0.365254i
$538$	−1.35374e11			−1.61587
$539$		−	3.54527e10i		−	0.420044i
$540$	−5.59834e10			−0.658392
$541$			3.14461e10i			0.367095i	0.983011	+	0.183547i	$0.0587580\pi$
$541$			3.14461e10i			0.367095i	−0.983011	+	0.183547i	$0.941242\pi$
$542$		−	2.57821e11i		−	2.98759i
$543$	−2.11593e10			−0.243390
$544$			2.16354e11i			2.47042i
$545$		−	1.64596e10i		−	0.186567i
$546$	3.48438e10			0.392062
$547$	9.18262e10			1.02569			0.512846	−	0.858480i	$-0.328591\pi$
$547$	9.18262e10			1.02569			0.512846	+	0.858480i	$0.328591\pi$
$548$	7.70249e10			0.854101
$549$			1.29756e10i			0.142836i
$550$	−3.82331e10			−0.417820
$551$	1.06428e11			1.15465
$552$	2.51998e11			2.71419
$553$	7.77010e9			0.0830857
$554$			3.28231e11i			3.48450i
$555$			1.73150e10i			0.182495i
$556$	−5.83580e10			−0.610662
$557$	1.00723e11			1.04643			0.523215	−	0.852201i	$-0.324733\pi$
$557$	1.00723e11			1.04643			0.523215	+	0.852201i	$0.324733\pi$
$558$	−3.74080e10			−0.385858
$559$	1.06979e11			1.09560
$560$	−2.63796e11			−2.68235
$561$			1.49757e10i			0.151194i
$562$		−	6.77479e9i		−	0.0679126i
$563$		−	1.45204e10i		−	0.144525i	−0.997386	−	0.0722626i	$-0.976978\pi$
$563$		−	1.45204e10i		−	0.144525i	0.997386	−	0.0722626i	$-0.0230220\pi$
$564$		−	2.37578e11i		−	2.34796i
$565$		−	8.13483e10i		−	0.798279i
$566$	−2.87038e11			−2.79688
$567$	−5.72900e9			−0.0554302
$568$			6.07194e11i			5.83357i
$569$		−	2.82153e10i		−	0.269176i	−0.990902	−	0.134588i	$-0.957029\pi$
$569$		−	2.82153e10i		−	0.269176i	0.990902	−	0.134588i	$-0.0429711\pi$
$570$			1.60787e11i			1.52318i
$571$			3.31259e10i			0.311619i	0.987787	+	0.155809i	$0.0497985\pi$
$571$			3.31259e10i			0.311619i	−0.987787	+	0.155809i	$0.950201\pi$
$572$	1.20044e11			1.12139
$573$		−	2.45715e10i		−	0.227936i
$574$			8.51011e10i			0.783949i
$575$			5.12229e10i			0.468590i
$576$	−2.14895e11			−1.95225
$577$	2.26829e10			0.204643			0.102321	−	0.994751i	$-0.467373\pi$
$577$	2.26829e10			0.204643			0.102321	+	0.994751i	$0.467373\pi$
$578$		−	1.72405e11i		−	1.54468i
$579$	6.25523e10			0.556582
$580$	−3.93490e11			−3.47714
$581$		−	6.11867e10i		−	0.536973i
$582$	2.00081e11			1.74387
$583$		−	9.06577e10i		−	0.784748i
$584$	3.13046e11			2.69127
$585$			3.15240e10i			0.269165i
$586$		−	4.20858e11i		−	3.56899i
$587$			2.15182e11i			1.81239i	0.422855	+	0.906197i	$0.361028\pi$
$587$			2.15182e11i			1.81239i	−0.422855	+	0.906197i	$0.638972\pi$
$588$	1.51100e11			1.26402
$589$			7.99930e10i			0.664647i
$590$	1.96438e11	+	2.01490e11i	1.62113	+	1.66282i
$591$	1.37747e10			0.112910
$592$			1.51529e11i			1.23370i
$593$	−1.24514e11			−1.00693			−0.503464	−	0.864016i	$-0.667941\pi$
$593$	−1.24514e11			−1.00693			−0.503464	+	0.864016i	$0.667941\pi$
$594$	−2.65092e10			−0.212937
$595$	−3.43666e10			−0.274200
$596$		−	6.09079e11i		−	4.82712i
$597$	3.66062e10			0.288176
$598$		−	2.16007e11i		−	1.68913i
$599$	1.38265e11			1.07400			0.536999	−	0.843583i	$-0.319558\pi$
$599$	1.38265e11			1.07400			0.536999	+	0.843583i	$0.319558\pi$
$600$		−	1.07045e11i		−	0.825961i
$601$			1.22659e11i			0.940160i	0.882624	+	0.470080i	$0.155775\pi$
$601$			1.22659e11i			0.940160i	−0.882624	+	0.470080i	$0.844225\pi$
$602$	−2.06445e11			−1.57188
$603$			1.86079e9i			0.0140743i
$604$		−	3.57770e11i		−	2.68817i
$605$	1.08073e11			0.806670
$606$	−2.59184e11			−1.92184
$607$	−1.20353e11			−0.886546			−0.443273	−	0.896387i	$-0.646183\pi$
$607$	−1.20353e11			−0.886546			−0.443273	+	0.896387i	$0.646183\pi$
$608$			8.18963e11i			5.99308i
$609$	−4.02674e10			−0.292741
$610$	−1.37783e11			−0.995122
$611$	−1.33779e11			−0.959896
$612$	−6.38264e10			−0.454982
$613$		−	6.28488e9i		−	0.0445097i	−0.999752	−	0.0222549i	$-0.992915\pi$
$613$		−	6.28488e9i		−	0.0445097i	0.999752	−	0.0222549i	$-0.00708453\pi$
$614$			2.94313e10i			0.207079i
$615$	−7.69930e10			−0.538209
$616$	−1.52180e11			−1.05690
$617$	1.45402e11			1.00330			0.501649	−	0.865071i	$-0.332727\pi$
$617$	1.45402e11			1.00330			0.501649	+	0.865071i	$0.332727\pi$
$618$	−2.72658e10			−0.186924
$619$	−7.31126e10			−0.498000			−0.249000	−	0.968503i	$-0.580102\pi$
$619$	−7.31126e10			−0.498000			−0.249000	+	0.968503i	$0.580102\pi$
$620$		−	2.95753e11i		−	2.00153i
$621$			3.55158e10i			0.238811i
$622$			7.90768e10i			0.528309i
$623$		−	4.08128e10i		−	0.270922i
$624$			2.75876e11i			1.81960i
$625$	−1.88450e11			−1.23502
$626$	−3.58576e11			−2.33498
$627$			5.66872e10i			0.366787i
$628$		−	3.00240e11i		−	1.93032i
$629$			1.97407e10i			0.126113i
$630$		−	6.08341e10i		−	0.386175i
$631$	−2.88787e11			−1.82163			−0.910815	−	0.412815i	$-0.864545\pi$
$631$	−2.88787e11			−1.82163			−0.910815	+	0.412815i	$0.864545\pi$
$632$			1.00663e11i			0.630959i
$633$		−	1.83130e11i		−	1.14063i
$634$			6.05764e11i			3.74927i
$635$	2.97433e11			1.82934
$636$	3.86383e11			2.36151
$637$		−	8.50836e10i		−	0.516759i
$638$	−1.86325e11			−1.12458
$639$	−8.55761e10			−0.513274
$640$		−	1.24306e12i		−	7.40924i
$641$	−3.01745e11			−1.78734			−0.893671	−	0.448723i	$-0.851879\pi$
$641$	−3.01745e11			−1.78734			−0.893671	+	0.448723i	$0.851879\pi$
$642$			2.17311e11i			1.27921i
$643$	1.54047e11			0.901175			0.450588	−	0.892732i	$-0.351215\pi$
$643$	1.54047e11			0.901175			0.450588	+	0.892732i	$0.351215\pi$
$644$			3.10364e11i			1.80438i
$645$		−	1.86776e11i		−	1.07915i
$646$			1.83312e11i			1.05259i
$647$	4.93100e10			0.281396			0.140698	−	0.990053i	$-0.455065\pi$
$647$	4.93100e10			0.281396			0.140698	+	0.990053i	$0.455065\pi$
$648$		−	7.42201e10i		−	0.420941i
$649$	6.92565e10	+	7.10377e10i	0.390375	+	0.400415i
$650$	−9.17563e10			−0.514023
$651$		−	3.02656e10i		−	0.168510i
$652$	6.56204e11			3.63119
$653$	7.30997e10			0.402034			0.201017	−	0.979588i	$-0.435575\pi$
$653$	7.30997e10			0.402034			0.201017	+	0.979588i	$0.435575\pi$
$654$	3.32179e10			0.181577
$655$			6.09972e10i			0.331394i
$656$	−6.73789e11			−3.63838
$657$			4.41198e10i			0.236795i
$658$	2.58163e11			1.37718
$659$		−	2.17792e11i		−	1.15479i	−0.816467	−	0.577393i	$-0.804070\pi$
$659$		−	2.17792e11i		−	1.15479i	0.816467	−	0.577393i	$-0.195930\pi$
$660$		−	2.09586e11i		−	1.10455i
$661$	−3.45668e10			−0.181073			−0.0905363	−	0.995893i	$-0.528858\pi$
$661$	−3.45668e10			−0.181073			−0.0905363	+	0.995893i	$0.528858\pi$
$662$			2.45130e10i			0.127633i
$663$			3.59404e10i			0.186007i
$664$	7.92684e11			4.07782
$665$	−1.30087e11			−0.665193
$666$	−3.49441e10			−0.177614
$667$			2.49630e11i			1.26123i
$668$	9.42967e11			4.73577
$669$	−1.55624e11			−0.776914
$670$	−1.97590e10			−0.0980540
$671$	−4.85770e10			−0.239630
$672$		−	3.09857e11i		−	1.51944i
$673$			2.40096e11i			1.17038i	0.810898	+	0.585188i	$0.198979\pi$
$673$			2.40096e11i			1.17038i	−0.810898	+	0.585188i	$0.801021\pi$
$674$	2.20772e10			0.106981
$675$	1.50865e10			0.0726732
$676$	−3.20583e11			−1.53516
$677$	5.36933e10			0.255602			0.127801	−	0.991800i	$-0.459208\pi$
$677$	5.36933e10			0.255602			0.127801	+	0.991800i	$0.459208\pi$
$678$	1.64172e11			0.776929
$679$			1.61879e11i			0.761572i
$680$		−	4.45224e11i		−	2.08230i
$681$		−	1.06773e11i		−	0.496447i
$682$		−	1.40045e11i		−	0.647336i
$683$		−	2.99414e11i		−	1.37591i	−0.725754	−	0.687954i	$-0.758509\pi$
$683$		−	2.99414e11i		−	1.37591i	0.725754	−	0.687954i	$-0.241491\pi$
$684$	−2.41601e11			−1.10376
$685$	−7.57242e10			−0.343932
$686$			3.82785e11i			1.72846i
$687$			2.05917e11i			0.924412i
$688$		−	1.63453e12i		−	7.29524i
$689$		−	2.17571e11i		−	0.965437i
$690$	−3.77129e11			−1.66377
$691$			4.19619e11i			1.84053i	0.391296	+	0.920265i	$0.372027\pi$
$691$			4.19619e11i			1.84053i	−0.391296	+	0.920265i	$0.627973\pi$
$692$		−	2.73759e11i		−	1.19383i
$693$		−	2.14477e10i		−	0.0929927i
$694$	1.75483e11			0.756480
$695$	5.73725e10			0.245903
$696$		−	5.21670e11i		−	2.22310i
$697$	−8.77793e10			−0.371930
$698$	5.77639e11			2.43352
$699$			2.01554e11i			0.844274i
$700$	1.31837e11			0.549094
$701$			1.02598e11i			0.424879i	0.977174	+	0.212439i	$0.0681408\pi$
$701$			1.02598e11i			0.424879i	−0.977174	+	0.212439i	$0.931859\pi$
$702$	−6.36199e10			−0.261966
$703$			7.47243e10i			0.305943i
$704$		−	8.04505e11i		−	3.27520i
$705$			2.33566e11i			0.945483i
$706$	7.21104e11			2.90254
$707$		−	2.09698e11i		−	0.839297i
$708$	−3.02763e11	+	2.95171e11i	−1.20495	+	1.17474i
$709$	−1.17044e11			−0.463195			−0.231597	−	0.972812i	$-0.574395\pi$
$709$	−1.17044e11			−0.463195			−0.231597	+	0.972812i	$0.574395\pi$
$710$		−	9.08700e11i		−	3.57591i
$711$	−1.41871e10			−0.0555157
$712$	5.28737e11			2.05740
$713$	−1.87625e11			−0.725995
$714$		−	6.93566e10i		−	0.266867i
$715$	−1.18017e11			−0.451565
$716$			4.84628e11i			1.84398i
$717$	−1.32429e11			−0.501078
$718$			9.30503e11i			3.50123i
$719$		−	1.38582e10i		−	0.0518552i	−0.999664	−	0.0259276i	$-0.991746\pi$
$719$		−	1.38582e10i		−	0.0518552i	0.999664	−	0.0259276i	$-0.00825394\pi$
$720$	4.81654e11			1.79228
$721$		−	2.20599e10i		−	0.0816324i
$722$			1.56236e11i			0.574953i
$723$	−6.91606e10			−0.253108
$724$	3.37613e11			1.22875
$725$	1.06039e11			0.383806
$726$			2.18107e11i			0.785095i
$727$	−3.58114e11			−1.28199			−0.640993	−	0.767547i	$-0.721477\pi$
$727$	−3.58114e11			−1.28199			−0.640993	+	0.767547i	$0.721477\pi$
$728$	−3.65219e11			−1.30025
$729$	1.04604e10			0.0370370
$730$	−4.68491e11			−1.64972
$731$		−	2.12942e11i		−	0.745748i
$732$		−	2.07035e11i		−	0.721108i
$733$	2.02524e11			0.701552			0.350776	−	0.936459i	$-0.385918\pi$
$733$	2.02524e11			0.701552			0.350776	+	0.936459i	$0.385918\pi$
$734$	4.86962e11			1.67769
$735$	−1.48548e11			−0.509000
$736$	−1.92090e12			−6.54625
$737$	−6.96625e9			−0.0236118
$738$		−	1.55383e11i		−	0.523814i
$739$		−	1.94915e11i		−	0.653532i	−0.945105	−	0.326766i	$-0.894041\pi$
$739$		−	1.94915e11i		−	0.653532i	0.945105	−	0.326766i	$-0.105959\pi$
$740$		−	2.76274e11i		−	0.921324i
$741$			1.36044e11i			0.451241i
$742$			4.19862e11i			1.38513i
$743$	3.03802e11			0.996862			0.498431	−	0.866929i	$-0.333910\pi$
$743$	3.03802e11			0.996862			0.498431	+	0.866929i	$0.333910\pi$
$744$	3.92096e11			1.27968
$745$			5.98794e11i			1.94380i
$746$			1.06443e12i			3.43685i
$747$			1.11718e11i			0.358792i
$748$		−	2.38948e11i		−	0.763302i
$749$	−1.75819e11			−0.558648
$750$		−	2.64032e11i		−	0.834471i
$751$		−	2.65517e11i		−	0.834703i	−0.908745	−	0.417351i	$-0.862958\pi$
$751$		−	2.65517e11i		−	0.834703i	0.908745	−	0.417351i	$-0.137042\pi$
$752$			2.04401e12i			6.39163i
$753$	4.59006e9			0.0142770
$754$	−4.47165e11			−1.38351
$755$			3.51729e11i			1.08248i
$756$	9.14104e10			0.279839
$757$	−3.43882e11			−1.04719			−0.523595	−	0.851967i	$-0.675409\pi$
$757$	−3.43882e11			−1.04719			−0.523595	+	0.851967i	$0.675409\pi$
$758$		−	2.46691e11i		−	0.747268i
$759$	−1.32961e11			−0.400643
$760$		−	1.68530e12i		−	5.05153i
$761$	1.02985e11			0.307069			0.153534	−	0.988143i	$-0.450934\pi$
$761$	1.02985e11			0.307069			0.153534	+	0.988143i	$0.450934\pi$
$762$			6.00261e11i			1.78041i
$763$			2.68755e10i			0.0792974i
$764$			3.92057e11i			1.15074i
$765$	6.27486e10			0.183214
$766$		−	1.28093e11i		−	0.372059i
$767$	1.66210e11	+	1.70485e11i	0.480259	+	0.492611i
$768$	1.33232e12			3.82968
$769$		−	2.68135e11i		−	0.766741i	−0.923595	−	0.383370i	$-0.874763\pi$
$769$		−	2.68135e11i		−	0.766741i	0.923595	−	0.383370i	$-0.125237\pi$
$770$	2.27746e11			0.647869
$771$	3.98743e11			1.12843
$772$	−9.98068e11			−2.80990
$773$		−	1.90043e11i		−	0.532271i	−0.963936	−	0.266136i	$-0.914253\pi$
$773$		−	1.90043e11i		−	0.532271i	0.963936	−	0.266136i	$-0.0857469\pi$
$774$	3.76940e11			1.05029
$775$			7.97002e10i			0.220929i
$776$	−2.09717e12			−5.78343
$777$		−	2.82721e10i		−	0.0775666i
$778$			8.31796e11i			2.27038i
$779$	−3.32270e11			−0.902279
$780$		−	5.02989e11i		−	1.35888i
$781$		−	3.20373e11i		−	0.861095i
$782$	−4.29962e11			−1.14975
$783$	7.35226e10			0.195602
$784$	−1.29999e12			−3.44093
$785$			2.95170e11i			0.777309i
$786$	−1.23101e11			−0.322531
$787$	4.86524e11			1.26825			0.634126	−	0.773230i	$-0.281360\pi$
$787$	4.86524e11			1.26825			0.634126	+	0.773230i	$0.281360\pi$
$788$	−2.19785e11			−0.570024
$789$	−2.17895e11			−0.562263
$790$		−	1.50648e11i		−	0.386771i
$791$			1.32826e11i			0.339296i
$792$	2.77859e11			0.706194
$793$	−1.16581e11			−0.294804
$794$	−4.37899e11			−1.10177
$795$	−3.79859e11			−0.950941
$796$	−5.84079e11			−1.45485
$797$		−	1.98516e11i		−	0.491996i	−0.969270	−	0.245998i	$-0.920884\pi$
$797$		−	1.98516e11i		−	0.491996i	0.969270	−	0.245998i	$-0.0791156\pi$
$798$		−	2.62534e11i		−	0.647403i
$799$			2.66288e11i			0.653377i
$800$			8.15965e11i			1.99210i
$801$			7.45185e10i			0.181023i
$802$	−3.26231e11			−0.788548
$803$	−1.65172e11			−0.397259
$804$		−	2.96902e10i		−	0.0710541i
$805$		−	3.05123e11i		−	0.726592i
$806$		−	3.36096e11i		−	0.796385i
$807$			1.99981e11i			0.471514i
$808$	2.71667e12			6.37369
$809$			5.45812e11i			1.27423i	0.770767	+	0.637117i	$0.219873\pi$
$809$			5.45812e11i			1.27423i	−0.770767	+	0.637117i	$0.780127\pi$
$810$			1.11075e11i			0.258032i
$811$		−	2.01404e11i		−	0.465570i	−0.972528	−	0.232785i	$-0.925216\pi$
$811$		−	2.01404e11i		−	0.465570i	0.972528	−	0.232785i	$-0.0747838\pi$
$812$	6.42496e11			1.47790
$813$	−3.80865e11			−0.871784
$814$		−	1.30821e11i		−	0.297975i
$815$	−6.45123e11			−1.46222
$816$	5.49131e11			1.23856
$817$		−	8.06046e11i		−	1.80914i
$818$	1.26737e12			2.83069
$819$		−	5.14728e10i		−	0.114404i
$820$	1.22848e12			2.71714
$821$		−	2.59269e11i		−	0.570660i	−0.958429	−	0.285330i	$-0.907897\pi$
$821$		−	2.59269e11i		−	0.570660i	0.958429	−	0.285330i	$-0.0921033\pi$
$822$		−	1.52822e11i		−	0.334733i
$823$		−	2.26246e11i		−	0.493152i	−0.969123	−	0.246576i	$-0.920694\pi$
$823$		−	2.26246e11i		−	0.493152i	0.969123	−	0.246576i	$-0.0793055\pi$
$824$	2.85790e11			0.619923
$825$			5.64797e10i			0.121920i
$826$	−3.20746e11	−	3.28996e11i	−0.689036	−	0.706757i
$827$	1.91308e11			0.408987			0.204494	−	0.978868i	$-0.434445\pi$
$827$	1.91308e11			0.408987			0.204494	+	0.978868i	$0.434445\pi$
$828$		−	5.66681e11i		−	1.20564i
$829$	4.51294e11			0.955524			0.477762	−	0.878489i	$-0.341448\pi$
$829$	4.51294e11			0.955524			0.477762	+	0.878489i	$0.341448\pi$
$830$	−1.18630e12			−2.49966
$831$	4.84877e11			1.01678
$832$		−	1.93074e12i		−	4.02932i
$833$	−1.69359e11			−0.351745
$834$			1.15786e11i			0.239327i
$835$	−9.27043e11			−1.90702
$836$		−	9.04485e11i		−	1.85172i
$837$			5.52607e10i			0.112594i
$838$	9.03897e11			1.83292
$839$		−	7.94455e11i		−	1.60333i	−0.597777	−	0.801663i	$-0.703949\pi$
$839$		−	7.94455e11i		−	1.60333i	0.597777	−	0.801663i	$-0.296051\pi$
$840$			6.37638e11i			1.28073i
$841$	1.65216e10			0.0330269
$842$	1.17108e12			2.32990
$843$	−1.00080e10			−0.0198170
$844$			2.92197e12i			5.75846i
$845$	3.15169e11			0.618183
$846$	−4.71370e11			−0.920196
$847$	−1.76463e11			−0.342862
$848$	−3.32426e12			−6.42853
$849$			4.24025e11i			0.816133i
$850$			1.82641e11i			0.349883i
$851$	−1.75267e11			−0.334182
$852$	1.36543e12			2.59126
$853$	6.09676e10			0.115160			0.0575801	−	0.998341i	$-0.481662\pi$
$853$	6.09676e10			0.115160			0.0575801	+	0.998341i	$0.481662\pi$
$854$	2.24974e11			0.422961
$855$	2.37521e11			0.444465
$856$		−	2.27776e12i		−	4.24242i
$857$		−	5.99034e11i		−	1.11053i	−0.831675	−	0.555263i	$-0.812618\pi$
$857$		−	5.99034e11i		−	1.11053i	0.831675	−	0.555263i	$-0.187382\pi$
$858$		−	2.38175e11i		−	0.439488i
$859$			8.28663e11i			1.52197i	0.648771	+	0.760984i	$0.275283\pi$
$859$			8.28663e11i			1.52197i	−0.648771	+	0.760984i	$0.724717\pi$
$860$			2.98015e12i			5.44808i
$861$	1.25715e11			0.228757
$862$	−6.98617e10			−0.126535
$863$			5.59845e11i			1.00931i	0.863321	+	0.504655i	$0.168380\pi$
$863$			5.59845e11i			1.00931i	−0.863321	+	0.504655i	$0.831620\pi$
$864$			5.65756e11i			1.01525i
$865$			2.69136e11i			0.480736i
$866$			1.47441e12i			2.62148i
$867$	−2.54685e11			−0.450740
$868$			4.82910e11i			0.850721i
$869$		−	5.31126e10i		−	0.0931361i
$870$			7.80709e11i			1.36274i
$871$	−1.67184e10			−0.0290484
$872$	−3.48177e11			−0.602190
$873$		−	2.95568e11i		−	0.508862i
$874$	−1.62753e12			−2.78922
$875$	2.13620e11			0.364426
$876$		−	7.03964e11i		−	1.19546i
$877$	−2.97827e11			−0.503460			−0.251730	−	0.967797i	$-0.581000\pi$
$877$	−2.97827e11			−0.503460			−0.251730	+	0.967797i	$0.581000\pi$
$878$			6.31382e11i			1.06246i
$879$	−6.21711e11			−1.04144
$880$			1.80318e12i			3.00682i
$881$		−	5.60038e11i		−	0.929639i	−0.885406	−	0.464819i	$-0.846119\pi$
$881$		−	5.60038e11i		−	0.929639i	0.885406	−	0.464819i	$-0.153881\pi$
$882$		−	2.99791e11i		−	0.495386i
$883$	5.82725e11			0.958564			0.479282	−	0.877661i	$-0.340897\pi$
$883$	5.82725e11			0.958564			0.479282	+	0.877661i	$0.340897\pi$
$884$		−	5.73455e11i		−	0.939053i
$885$	2.97651e11	−	2.90187e11i	0.485214	−	0.473048i
$886$	9.07518e11			1.47272
$887$		−	1.77653e11i		−	0.286998i	−0.989650	−	0.143499i	$-0.954165\pi$
$887$		−	1.77653e11i		−	0.286998i	0.989650	−	0.143499i	$-0.0458354\pi$
$888$	3.66270e11			0.589047
$889$	−4.85652e11			−0.777531
$890$	−7.91284e11			−1.26117
$891$			3.91606e10i			0.0621353i
$892$	2.48310e12			3.92224
$893$			1.00797e12i			1.58505i
$894$	−1.20845e12			−1.89181
$895$		−	4.76444e11i		−	0.742540i
$896$			2.02969e12i			3.14918i
$897$	−3.19095e11			−0.492891
$898$		−	1.13355e12i		−	1.74315i
$899$			3.88411e11i			0.594638i
$900$	−2.40717e11			−0.366890
$901$	−4.33075e11			−0.657149
$902$	5.81709e11			0.878779
$903$			3.04970e11i			0.458676i
$904$	−1.72079e12			−2.57664
$905$	−3.31911e11			−0.494798
$906$	−7.09838e11			−1.05353
$907$	7.10401e11			1.04972			0.524861	−	0.851188i	$-0.324117\pi$
$907$	7.10401e11			1.04972			0.524861	+	0.851188i	$0.324117\pi$
$908$			1.70364e12i			2.50631i
$909$			3.82879e11i			0.560797i
$910$	5.46570e11			0.797041
$911$	1.26615e11			0.183829			0.0919143	−	0.995767i	$-0.470701\pi$
$911$	1.26615e11			0.183829			0.0919143	+	0.995767i	$0.470701\pi$
$912$	2.07862e12			3.00466
$913$	−4.18242e11			−0.601928
$914$	1.92888e12			2.76389
$915$			2.03539e11i			0.290378i
$916$		−	3.28556e12i		−	4.66689i
$917$		−	9.95969e10i		−	0.140854i
$918$			1.26635e11i			0.178314i
$919$		−	6.84616e11i		−	0.959809i	−0.877321	−	0.479905i	$-0.840671\pi$
$919$		−	6.84616e11i		−	0.959809i	0.877321	−	0.479905i	$-0.159329\pi$
$920$	3.95291e12			5.51780
$921$	4.34772e10			0.0604260
$922$			1.14355e12i			1.58246i
$923$		−	7.68868e11i		−	1.05936i
$924$			3.42215e11i			0.469473i
$925$			7.44508e10i			0.101696i
$926$	−3.17366e11			−0.431635
$927$			4.02783e10i			0.0545447i
$928$			3.97652e12i			5.36181i
$929$		−	8.44447e11i		−	1.13373i	−0.823811	−	0.566865i	$-0.808156\pi$
$929$		−	8.44447e11i		−	1.13373i	0.823811	−	0.566865i	$-0.191844\pi$
$930$	−5.86793e11			−0.784428
$931$	−6.41071e11			−0.853311
$932$		−	3.21595e12i		−	4.26232i
$933$	1.16816e11			0.154161
$934$	−9.80651e11			−1.28863
$935$			2.34913e11i			0.307369i
$936$	6.66839e11			0.868795
$937$			1.68307e10i			0.0218345i	0.999940	+	0.0109172i	$0.00347514\pi$
$937$			1.68307e10i			0.0218345i	−0.999940	+	0.0109172i	$0.996525\pi$
$938$	3.22627e10			0.0416763
$939$			5.29704e11i			0.681351i
$940$		−	3.72672e12i		−	4.77327i
$941$		−	3.61123e11i		−	0.460571i	−0.973123	−	0.230286i	$-0.926034\pi$
$941$		−	3.61123e11i		−	0.460571i	0.973123	−	0.230286i	$-0.0739661\pi$
$942$	−5.95695e11			−0.756520
$943$		−	7.79346e11i		−	0.985561i
$944$	2.60483e12	−	2.53951e12i	3.28013	−	3.19788i
$945$	−8.98668e10			−0.112687
$946$			1.41116e12i			1.76202i
$947$	8.93503e11			1.11095			0.555477	−	0.831532i	$-0.312536\pi$
$947$	8.93503e11			1.11095			0.555477	+	0.831532i	$0.312536\pi$
$948$	2.26366e11			0.280271
$949$	−3.96399e11			−0.488729
$950$			6.91348e11i			0.848794i
$951$	8.94862e11			1.09404
$952$			7.26968e11i			0.885049i
$953$	7.16761e11			0.868966			0.434483	−	0.900680i	$-0.356931\pi$
$953$	7.16761e11			0.868966			0.434483	+	0.900680i	$0.356931\pi$
$954$		−	7.66609e11i		−	0.925508i
$955$		−	3.85436e11i		−	0.463382i
$956$	2.11300e12			2.52969
$957$			2.75248e11i			0.328153i
$958$			1.65853e12i			1.96907i
$959$	1.23643e11			0.146183
$960$	−3.37090e12			−3.96882
$961$	5.60956e11			0.657711
$962$		−	3.13959e11i		−	0.366583i
$963$	3.21021e11			0.373274
$964$	1.10351e12			1.27781
$965$	9.81214e11			1.13150
$966$	6.15780e11			0.707159
$967$			7.65079e11i			0.874984i	0.899222	+	0.437492i	$0.144133\pi$
$967$			7.65079e11i			0.874984i	−0.899222	+	0.437492i	$0.855867\pi$
$968$		−	2.28611e12i		−	2.60372i
$969$	2.70796e11			0.307148
$970$	3.13852e12			3.54518
$971$	−1.41140e12			−1.58771			−0.793856	−	0.608106i	$-0.791930\pi$
$971$	−1.41140e12			−1.58771			−0.793856	+	0.608106i	$0.791930\pi$
$972$	−1.66903e11			−0.186981
$973$	−9.36786e10			−0.104517
$974$		−	2.05265e12i		−	2.28075i
$975$			1.35547e11i			0.149993i
$976$			1.78123e12i			1.96300i
$977$		−	1.59096e12i		−	1.74615i	−0.487589	−	0.873073i	$-0.662123\pi$
$977$		−	1.59096e12i		−	1.74615i	0.487589	−	0.873073i	$-0.337877\pi$
$978$		−	1.30195e12i		−	1.42311i
$979$	−2.78976e11			−0.303694
$980$	2.37019e12			2.56968
$981$		−	4.90710e10i		−	0.0529845i
$982$			2.67608e12i			2.87775i
$983$		−	1.36144e12i		−	1.45809i	−0.684466	−	0.729044i	$-0.739965\pi$
$983$		−	1.36144e12i		−	1.45809i	0.684466	−	0.729044i	$-0.260035\pi$
$984$			1.62866e12i			1.73720i
$985$	2.16074e11			0.229539
$986$			8.90082e11i			0.941721i
$987$		−	3.81370e11i		−	0.401863i
$988$		−	2.17069e12i		−	2.27809i
$989$	1.89060e12			1.97612
$990$	−4.15832e11			−0.432889
$991$		−	1.24574e12i		−	1.29162i	−0.763500	−	0.645808i	$-0.776521\pi$
$991$		−	1.24574e12i		−	1.29162i	0.763500	−	0.645808i	$-0.223479\pi$
$992$	−2.98882e12			−3.08640
$993$	3.62117e10			0.0372436
$994$			1.48374e12i			1.51989i
$995$	5.74216e11			0.585845
$996$		−	1.78255e12i		−	1.81136i
$997$	7.12689e10			0.0721306			0.0360653	−	0.999349i	$-0.488518\pi$
$997$	7.12689e10			0.0721306			0.0360653	+	0.999349i	$0.488518\pi$
$998$			1.13555e12i			1.14468i
$999$			5.16210e10i			0.0518280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.80	yes	80
59.58	odd	2	inner	177.9.c.a.58.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.1	✓	80	59.58	odd	2	inner
177.9.c.a.58.80	yes	80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+31.6572i q^{2} +46.7654 q^{3} -746.176 q^{4} +733.576 q^{5} +1480.46i q^{6} -1197.79 q^{7} -15517.6i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q+31.6572i q^{2} +46.7654 q^{3} -746.176 q^{4} +733.576 q^{5} +1480.46i q^{6} -1197.79 q^{7} -15517.6i q^{8} +2187.00 q^{9} +23222.9i q^{10} +8187.51i q^{11} -34895.2 q^{12} +19649.3i q^{13} -37918.7i q^{14} +34305.9 q^{15} +300222. q^{16} +39112.0 q^{17} +69234.2i q^{18} +148050. q^{19} -547377. q^{20} -56015.2 q^{21} -259193. q^{22} +347255. i q^{23} -725686. i q^{24} +147508. q^{25} -622042. q^{26} +102276. q^{27} +893763. q^{28} +718866. q^{29} +1.08603e6i q^{30} +540311. i q^{31} +5.53166e6i q^{32} +382892. i q^{33} +1.23818e6i q^{34} -878671. q^{35} -1.63189e6 q^{36} +504723. i q^{37} +4.68684e6i q^{38} +918909. i q^{39} -1.13833e7i q^{40} -2.24431e6 q^{41} -1.77328e6i q^{42} -5.44442e6i q^{43} -6.10932e6i q^{44} +1.60433e6 q^{45} -1.09931e7 q^{46} +6.80833e6i q^{47} +1.40400e7 q^{48} -4.33010e6 q^{49} +4.66969e6i q^{50} +1.82909e6 q^{51} -1.46619e7i q^{52} -1.10727e7 q^{53} +3.23776e6i q^{54} +6.00616e6i q^{55} +1.85868e7i q^{56} +6.92361e6 q^{57} +2.27573e7i q^{58} +(8.67636e6 - 8.45880e6i) q^{59} -2.55983e7 q^{60} +5.93306e6i q^{61} -1.71047e7 q^{62} -2.61957e6 q^{63} -9.82600e7 q^{64} +1.44143e7i q^{65} -1.21213e7 q^{66} +850839. i q^{67} -2.91844e7 q^{68} +1.62395e7i q^{69} -2.78162e7i q^{70} -3.91294e7 q^{71} -3.39370e7i q^{72} +2.01737e7i q^{73} -1.59781e7 q^{74} +6.89827e6 q^{75} -1.10471e8 q^{76} -9.80693e6i q^{77} -2.90900e7 q^{78} -6.48702e6 q^{79} +2.20235e8 q^{80} +4.78297e6 q^{81} -7.10484e7i q^{82} +5.10830e7i q^{83} +4.17972e7 q^{84} +2.86916e7 q^{85} +1.72355e8 q^{86} +3.36180e7 q^{87} +1.27050e8 q^{88} +3.40734e7i q^{89} +5.07885e7i q^{90} -2.35358e7i q^{91} -2.59113e8i q^{92} +2.52678e7i q^{93} -2.15533e8 q^{94} +1.08606e8 q^{95} +2.58690e8i q^{96} -1.35148e8i q^{97} -1.37079e8i q^{98} +1.79061e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Introduction

L-functions

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