LMFDB - Embedded newform 729.2.i.a.10.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(10,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(162))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("729.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			10.11
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.506689 - 0.0792447i) q^{2} +(-1.65404 - 0.530347i) q^{4} +(-2.15085 - 0.977679i) q^{5} +(0.325167 + 2.38064i) q^{7} +(1.71265 + 0.860127i) q^{8} +O(q^{10})$	\(q+(-0.506689 - 0.0792447i) q^{2} +(-1.65404 - 0.530347i) q^{4} +(-2.15085 - 0.977679i) q^{5} +(0.325167 + 2.38064i) q^{7} +(1.71265 + 0.860127i) q^{8} +(1.01233 + 0.665822i) q^{10} +(-4.00167 + 0.311035i) q^{11} +(1.40610 + 4.10947i) q^{13} +(0.0238949 - 1.23201i) q^{14} +(2.02664 + 1.44855i) q^{16} +(2.67793 - 6.20814i) q^{17} +(2.92979 - 3.93539i) q^{19} +(3.03908 + 2.75782i) q^{20} +(2.05225 + 0.159514i) q^{22} +(1.79471 + 1.39101i) q^{23} +(0.382672 + 0.438493i) q^{25} +(-0.386799 - 2.19365i) q^{26} +(0.724728 - 4.11013i) q^{28} +(-0.410704 + 0.247861i) q^{29} +(3.75797 - 0.145826i) q^{31} +(-3.64859 - 3.57851i) q^{32} +(-1.84884 + 2.93339i) q^{34} +(1.62812 - 5.43830i) q^{35} +(-0.469010 + 0.497121i) q^{37} +(-1.79635 + 1.76185i) q^{38} +(-2.84273 - 3.52443i) q^{40} +(2.01042 - 5.20712i) q^{41} +(-2.80371 - 10.8847i) q^{43} +(6.78389 + 1.60781i) q^{44} +(-0.799130 - 0.847029i) q^{46} +(9.70816 + 0.376721i) q^{47} +(1.18187 - 0.328995i) q^{49} +(-0.159147 - 0.252504i) q^{50} +(-0.146295 - 7.54295i) q^{52} +(1.71274 - 0.623385i) q^{53} +(8.91107 + 3.24337i) q^{55} +(-1.49076 + 4.35690i) q^{56} +(0.227741 - 0.0930423i) q^{58} +(-1.16596 - 2.43840i) q^{59} +(-4.58755 + 1.47094i) q^{61} +(-1.91568 - 0.223911i) q^{62} +(-1.41004 - 1.89401i) q^{64} +(0.993448 - 10.2135i) q^{65} +(13.7924 + 8.32375i) q^{67} +(-7.72188 + 8.84829i) q^{68} +(-1.25591 + 2.62651i) q^{70} +(-0.658236 + 11.3015i) q^{71} +(11.2020 - 7.36770i) q^{73} +(0.277036 - 0.214719i) q^{74} +(-6.93312 + 4.95549i) q^{76} +(-2.04167 - 9.42542i) q^{77} +(-0.666324 + 0.826113i) q^{79} +(-2.94276 - 5.09701i) q^{80} +(-1.43129 + 2.47907i) q^{82} +(3.05886 + 7.92264i) q^{83} +(-11.8294 + 10.7346i) q^{85} +(0.558056 + 5.73732i) q^{86} +(-7.12101 - 2.90925i) q^{88} +(0.434386 + 7.45812i) q^{89} +(-9.32596 + 4.68367i) q^{91} +(-2.23081 - 3.25260i) q^{92} +(-4.88916 - 0.960201i) q^{94} +(-10.1491 + 5.60002i) q^{95} +(12.7406 - 5.79132i) q^{97} +(-0.624910 + 0.0730416i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{81}\right)$

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 $

$2$	−0.506689	−	0.0792447i	−0.358283	−	0.0560345i	−0.0271841	−	0.999630i	$-0.508654\pi$
$2$	−0.506689	−	0.0792447i	−0.358283	−	0.0560345i	−0.331099	+	0.943596i	$0.607419\pi$
$3$		0			0
$3$		0			0
$4$	−1.65404	−	0.530347i	−0.827021	−	0.265174i
$5$	−2.15085	−	0.977679i	−0.961887	−	0.437231i	−0.129594	−	0.991567i	$-0.541367\pi$
$5$	−2.15085	−	0.977679i	−0.961887	−	0.437231i	−0.832293	+	0.554336i	$0.812972\pi$
$6$		0			0
$7$	0.325167	+	2.38064i	0.122902	+	0.899799i	0.944217	+	0.329324i	$0.106821\pi$
$7$	0.325167	+	2.38064i	0.122902	+	0.899799i	−0.821315	+	0.570474i	$0.806759\pi$
$8$	1.71265	+	0.860127i	0.605515	+	0.304101i
$9$		0			0
$10$	1.01233	+	0.665822i	0.320128	+	0.210552i
$11$	−4.00167	+	0.311035i	−1.20655	+	0.0937805i	−0.664971	−	0.746869i	$-0.731556\pi$
$11$	−4.00167	+	0.311035i	−1.20655	+	0.0937805i	−0.541579	+	0.840650i	$0.682173\pi$
$12$		0			0
$13$	1.40610	+	4.10947i	0.389981	+	1.13976i	0.950260	+	0.311458i	$0.100817\pi$
$13$	1.40610	+	4.10947i	0.389981	+	1.13976i	−0.560279	+	0.828304i	$0.689306\pi$
$14$	0.0238949	−	1.23201i	0.00638618	−	0.329270i
$15$		0			0
$16$	2.02664	+	1.44855i	0.506659	+	0.362138i
$17$	2.67793	−	6.20814i	0.649494	−	1.50570i	−0.200935	−	0.979605i	$-0.564398\pi$
$17$	2.67793	−	6.20814i	0.649494	−	1.50570i	0.850428	−	0.526091i	$-0.176343\pi$
$18$		0			0
$19$	2.92979	−	3.93539i	0.672140	−	0.902840i	−0.326970	−	0.945035i	$-0.606027\pi$
$19$	2.92979	−	3.93539i	0.672140	−	0.902840i	0.999109	+	0.0421945i	$0.0134349\pi$
$20$	3.03908	+	2.75782i	0.679559	+	0.616667i
$21$		0			0
$22$	2.05225	+	0.159514i	0.437542	+	0.0340084i
$23$	1.79471	+	1.39101i	0.374223	+	0.290045i	0.782299	−	0.622903i	$-0.214047\pi$
$23$	1.79471	+	1.39101i	0.374223	+	0.290045i	−0.408076	+	0.912948i	$0.633800\pi$
$24$		0			0
$25$	0.382672	+	0.438493i	0.0765344	+	0.0876987i
$26$	−0.386799	−	2.19365i	−0.0758576	−	0.430210i
$27$		0			0
$28$	0.724728	−	4.11013i	0.136961	−	0.776742i
$29$	−0.410704	+	0.247861i	−0.0762657	+	0.0460266i	−0.554319	−	0.832304i	$-0.687021\pi$
$29$	−0.410704	+	0.247861i	−0.0762657	+	0.0460266i	0.478054	+	0.878331i	$0.341342\pi$
$30$		0			0
$31$	3.75797	−	0.145826i	0.674951	−	0.0261912i	0.300979	−	0.953631i	$-0.402687\pi$
$31$	3.75797	−	0.145826i	0.674951	−	0.0261912i	0.373973	+	0.927440i	$0.377995\pi$
$32$	−3.64859	−	3.57851i	−0.644985	−	0.632597i
$33$		0			0
$34$	−1.84884	+	2.93339i	−0.317074	+	0.503071i
$35$	1.62812	−	5.43830i	0.275203	−	0.919241i
$36$		0			0
$37$	−0.469010	+	0.497121i	−0.0771047	+	0.0817262i	−0.764777	−	0.644295i	$-0.777151\pi$
$37$	−0.469010	+	0.497121i	−0.0771047	+	0.0817262i	0.687673	+	0.726021i	$0.258632\pi$
$38$	−1.79635	+	1.76185i	−0.291407	+	0.285810i
$39$		0			0
$40$	−2.84273	−	3.52443i	−0.449474	−	0.557261i
$41$	2.01042	−	5.20712i	0.313975	−	0.813215i	−0.682621	−	0.730773i	$-0.739160\pi$
$41$	2.01042	−	5.20712i	0.313975	−	0.813215i	0.996596	−	0.0824426i	$-0.0262721\pi$
$42$		0			0
$43$	−2.80371	−	10.8847i	−0.427561	−	1.65990i	−0.712746	−	0.701422i	$-0.752549\pi$
$43$	−2.80371	−	10.8847i	−0.427561	−	1.65990i	0.285184	−	0.958473i	$-0.407945\pi$
$44$	6.78389	+	1.60781i	1.02271	+	0.242387i
$45$		0			0
$46$	−0.799130	−	0.847029i	−0.117825	−	0.124888i
$47$	9.70816	+	0.376721i	1.41608	+	0.0549504i	0.735402	−	0.677632i	$-0.236994\pi$
$47$	9.70816	+	0.376721i	1.41608	+	0.0549504i	0.680679	+	0.732582i	$0.261685\pi$
$48$		0			0
$49$	1.18187	−	0.328995i	0.168838	−	0.0469993i
$50$	−0.159147	−	0.252504i	−0.0225068	−	0.0357095i
$51$		0			0
$52$	−0.146295	−	7.54295i	−0.0202875	−	1.04602i
$53$	1.71274	−	0.623385i	0.235262	−	0.0856285i	−0.221699	−	0.975115i	$-0.571160\pi$
$53$	1.71274	−	0.623385i	0.235262	−	0.0856285i	0.456961	+	0.889487i	$0.348938\pi$
$54$		0			0
$55$	8.91107	+	3.24337i	1.20157	+	0.437335i
$56$	−1.49076	+	4.35690i	−0.199211	+	0.582216i
$57$		0			0
$58$	0.227741	−	0.0930423i	0.0299038	−	0.0122171i
$59$	−1.16596	−	2.43840i	−0.151795	−	0.317453i	0.812197	−	0.583383i	$-0.198271\pi$
$59$	−1.16596	−	2.43840i	−0.151795	−	0.317453i	−0.963992	+	0.265931i	$0.914321\pi$
$60$		0			0
$61$	−4.58755	+	1.47094i	−0.587375	+	0.188334i	−0.584130	−	0.811660i	$-0.698564\pi$
$61$	−4.58755	+	1.47094i	−0.587375	+	0.188334i	−0.00324579	+	0.999995i	$0.501033\pi$
$62$	−1.91568	−	0.223911i	−0.243291	−	0.0284367i
$63$		0			0
$64$	−1.41004	−	1.89401i	−0.176254	−	0.236751i
$65$	0.993448	−	10.2135i	0.123222	−	1.26683i
$66$		0			0
$67$	13.7924	+	8.32375i	1.68501	+	1.01691i	0.934444	+	0.356109i	$0.115897\pi$
$67$	13.7924	+	8.32375i	1.68501	+	1.01691i	0.750563	+	0.660799i	$0.229782\pi$
$68$	−7.72188	+	8.84829i	−0.936415	+	1.07301i
$69$		0			0
$70$	−1.25591	+	2.62651i	−0.150110	+	0.313928i
$71$	−0.658236	+	11.3015i	−0.0781182	+	1.34124i	0.700460	+	0.713691i	$0.252978\pi$
$71$	−0.658236	+	11.3015i	−0.0781182	+	1.34124i	−0.778579	+	0.627547i	$0.784059\pi$
$72$		0			0
$73$	11.2020	−	7.36770i	1.31110	−	0.862324i	0.314875	−	0.949133i	$-0.398037\pi$
$73$	11.2020	−	7.36770i	1.31110	−	0.862324i	0.996225	+	0.0868086i	$0.0276669\pi$
$74$	0.277036	−	0.214719i	0.0322048	−	0.0249606i
$75$		0			0
$76$	−6.93312	+	4.95549i	−0.795283	+	0.568434i
$77$	−2.04167	−	9.42542i	−0.232670	−	1.07413i
$78$		0			0
$79$	−0.666324	+	0.826113i	−0.0749673	+	0.0929449i	−0.814460	−	0.580220i	$-0.802967\pi$
$79$	−0.666324	+	0.826113i	−0.0749673	+	0.0929449i	0.739493	+	0.673165i	$0.235065\pi$
$80$	−2.94276	−	5.09701i	−0.329011	−	0.569863i
$81$		0			0
$82$	−1.43129	+	2.47907i	−0.158060	+	0.273768i
$83$	3.05886	+	7.92264i	0.335753	+	0.869623i	0.993232	+	0.116149i	$0.0370551\pi$
$83$	3.05886	+	7.92264i	0.335753	+	0.869623i	−0.657479	+	0.753473i	$0.728377\pi$
$84$		0			0
$85$	−11.8294	+	10.7346i	−1.28308	+	1.16433i
$86$	0.558056	+	5.73732i	0.0601767	+	0.618671i
$87$		0			0
$88$	−7.12101	−	2.90925i	−0.759102	−	0.310127i
$89$	0.434386	+	7.45812i	0.0460448	+	0.790559i	0.939741	+	0.341887i	$0.111066\pi$
$89$	0.434386	+	7.45812i	0.0460448	+	0.790559i	−0.893696	+	0.448672i	$0.851897\pi$
$90$		0			0
$91$	−9.32596	+	4.68367i	−0.977626	+	0.490982i
$92$	−2.23081	−	3.25260i	−0.232578	−	0.339107i
$93$		0			0
$94$	−4.88916	−	0.960201i	−0.504279	−	0.0990371i
$95$	−10.1491	+	5.60002i	−1.04127	+	0.574550i
$96$		0			0
$97$	12.7406	−	5.79132i	1.29361	−	0.588020i	0.355607	−	0.934636i	$-0.384274\pi$
$97$	12.7406	−	5.79132i	1.29361	−	0.588020i	0.938007	+	0.346616i	$0.112669\pi$
$98$	−0.624910	+	0.0730416i	−0.0631255	+	0.00737831i
$99$		0			0
$100$	−0.400402	−	0.928235i	−0.0400402	−	0.0928235i
$101$	0.962516	−	4.44347i	0.0957739	−	0.442142i	−0.904116	−	0.427288i	$-0.859469\pi$
$101$	0.962516	−	4.44347i	0.0957739	−	0.442142i	0.999890	−	0.0148540i	$-0.00472836\pi$
$102$		0			0
$103$	−4.33985	+	6.32765i	−0.427618	+	0.623482i	−0.977292	−	0.211897i	$-0.932036\pi$
$103$	−4.33985	+	6.32765i	−0.427618	+	0.623482i	0.549674	+	0.835379i	$0.314752\pi$
$104$	−1.12651	+	8.24752i	−0.110463	+	0.808736i
$105$		0			0
$106$	−0.917225	+	0.180137i	−0.0890888	+	0.0174965i
$107$	8.71243	−	7.31060i	0.842262	−	0.706742i	−0.115809	−	0.993271i	$-0.536946\pi$
$107$	8.71243	−	7.31060i	0.842262	−	0.706742i	0.958071	+	0.286530i	$0.0925017\pi$
$108$		0			0
$109$	−2.48665	−	2.08655i	−0.238178	−	0.199855i	0.515884	−	0.856659i	$-0.327464\pi$
$109$	−2.48665	−	2.08655i	−0.238178	−	0.199855i	−0.754062	+	0.656803i	$0.771908\pi$
$110$	−4.25812	−	2.34953i	−0.405996	−	0.224019i
$111$		0			0
$112$	−2.78949	+	5.29572i	−0.263582	+	0.500398i
$113$	−0.644167	+	2.50081i	−0.0605981	+	0.235256i	−0.991518	−	0.129966i	$-0.958513\pi$
$113$	−0.644167	+	2.50081i	−0.0605981	+	0.235256i	0.930920	+	0.365222i	$0.119007\pi$
$114$		0			0
$115$	−2.50019	−	4.74649i	−0.233144	−	0.442612i
$116$	0.810773	−	0.192157i	0.0752784	−	0.0178413i
$117$		0			0
$118$	0.397549	+	1.32791i	0.0365974	+	0.122244i
$119$	15.6501	+	4.35652i	1.43465	+	0.399361i
$120$		0			0
$121$	5.04876	−	0.789612i	0.458979	−	0.0717829i
$122$	2.44102	−	0.381769i	0.221000	−	0.0345638i
$123$		0			0
$124$	−6.29318	−	1.75183i	−0.565144	−	0.157319i
$125$	2.99368	+	9.99958i	0.267763	+	0.894390i
$126$		0			0
$127$	−5.83192	+	1.38219i	−0.517500	+	0.122650i	−0.481063	−	0.876686i	$-0.659749\pi$
$127$	−5.83192	+	1.38219i	−0.517500	+	0.122650i	−0.0364371	+	0.999336i	$0.511601\pi$
$128$	5.32786	+	10.1147i	0.470920	+	0.894020i
$129$		0			0
$130$	−1.31274	+	5.09636i	−0.115135	+	0.446981i
$131$	5.59855	−	10.6286i	0.489147	−	0.928623i	−0.508565	−	0.861023i	$-0.669824\pi$
$131$	5.59855	−	10.6286i	0.489147	−	0.928623i	0.997713	−	0.0675997i	$-0.0215341\pi$
$132$		0			0
$133$	10.3214	+	5.69512i	0.894982	+	0.493830i
$134$	−6.32884	−	5.31052i	−0.546728	−	0.458759i
$135$		0			0
$136$	9.92616	−	8.32904i	0.851161	−	0.714209i
$137$	−5.62656	+	1.10502i	−0.480709	+	0.0944083i	−0.427196	−	0.904159i	$-0.640499\pi$
$137$	−5.62656	+	1.10502i	−0.480709	+	0.0944083i	−0.0535131	+	0.998567i	$0.517042\pi$
$138$		0			0
$139$	−0.358745	+	2.62648i	−0.0304284	+	0.222775i	−0.999733	−	0.0230858i	$-0.992651\pi$
$139$	−0.358745	+	2.62648i	−0.0304284	+	0.222775i	0.969305	+	0.245861i	$0.0790706\pi$
$140$	−5.57717	+	8.13171i	−0.471357	+	0.687255i
$141$		0			0
$142$	1.22910	−	5.67417i	0.103144	−	0.476166i
$143$	−6.90492	−	16.0074i	−0.577419	−	1.33861i
$144$		0			0
$145$	1.12569	−	0.131574i	0.0934833	−	0.0109266i
$146$	−6.25981	+	2.84543i	−0.518065	+	0.235490i
$147$		0			0
$148$	1.03941	−	0.573521i	0.0854388	−	0.0471432i
$149$	−13.1435	−	2.58130i	−1.07676	−	0.211468i	−0.377263	−	0.926106i	$-0.623135\pi$
$149$	−13.1435	−	2.58130i	−1.07676	−	0.211468i	−0.699495	+	0.714638i	$0.746592\pi$
$150$		0			0
$151$	−12.6705	−	18.4740i	−1.03111	−	1.50339i	−0.854733	−	0.519068i	$-0.826279\pi$
$151$	−12.6705	−	18.4740i	−1.03111	−	1.50339i	−0.176374	−	0.984323i	$-0.556437\pi$
$152$	8.40265	−	4.21997i	0.681545	−	0.342285i
$153$		0			0
$154$	0.287580	+	4.93755i	0.0231738	+	0.397879i
$155$	−8.22538	−	3.36044i	−0.660679	−	0.269917i
$156$		0			0
$157$	−1.86951	−	19.2202i	−0.149203	−	1.53394i	−0.708938	−	0.705271i	$-0.750825\pi$
$157$	−1.86951	−	19.2202i	−0.149203	−	1.53394i	0.559735	−	0.828672i	$-0.310903\pi$
$158$	0.403084	−	0.365780i	0.0320677	−	0.0290999i
$159$		0			0
$160$	4.34891	+	11.2640i	0.343812	+	0.890495i
$161$	−2.72791	+	4.72487i	−0.214989	+	0.372372i
$162$		0			0
$163$	−3.77309	−	6.53518i	−0.295531	−	0.511875i	0.679577	−	0.733604i	$-0.262163\pi$
$163$	−3.77309	−	6.53518i	−0.295531	−	0.511875i	−0.975108	+	0.221729i	$0.928830\pi$
$164$	−6.08690	+	7.54657i	−0.475307	+	0.589288i
$165$		0			0
$166$	−0.922062	−	4.25671i	−0.0715659	−	0.330385i
$167$	4.55659	−	3.25686i	0.352600	−	0.252023i	−0.391374	−	0.920232i	$-0.628000\pi$
$167$	4.55659	−	3.25686i	0.352600	−	0.252023i	0.743974	+	0.668208i	$0.232939\pi$
$168$		0			0
$169$	−4.63552	+	3.59280i	−0.356578	+	0.276369i
$170$	6.84448	−	4.50169i	0.524948	−	0.345264i
$171$		0			0
$172$	−1.13520	+	19.4906i	−0.0865581	+	1.48615i
$173$	−1.04389	+	2.18312i	−0.0793659	+	0.165980i	−0.938025	−	0.346567i	$-0.887347\pi$
$173$	−1.04389	+	2.18312i	−0.0793659	+	0.165980i	0.858659	+	0.512547i	$0.171298\pi$
$174$		0			0
$175$	−0.919464	+	1.05359i	−0.0695049	+	0.0796438i
$176$	−8.56048	−	5.16628i	−0.645271	−	0.389423i
$177$		0			0
$178$	0.370918	−	3.81337i	0.0278015	−	0.285824i
$179$	−2.95454	−	3.96864i	−0.220833	−	0.296630i	0.677876	−	0.735177i	$-0.262901\pi$
$179$	−2.95454	−	3.96864i	−0.220833	−	0.296630i	−0.898708	+	0.438547i	$0.855493\pi$
$180$		0			0
$181$	−6.31020	−	0.737557i	−0.469034	−	0.0548222i	−0.121706	−	0.992566i	$-0.538837\pi$
$181$	−6.31020	−	0.737557i	−0.469034	−	0.0548222i	−0.347327	+	0.937744i	$0.612911\pi$
$182$	5.09652	−	1.63413i	0.377779	−	0.121130i
$183$		0			0
$184$	1.87728	+	3.92599i	0.138395	+	0.289428i
$185$	1.49479	−	0.610690i	0.109899	−	0.0448988i
$186$		0			0
$187$	−8.78526	+	25.6759i	−0.642442	+	1.87761i
$188$	−15.8579	−	5.77181i	−1.15656	−	0.420952i
$189$		0			0
$190$	5.58620	−	2.03321i	0.405265	−	0.147504i
$191$	0.434180	+	22.3862i	0.0314161	+	1.61981i	0.601950	+	0.798534i	$0.294391\pi$
$191$	0.434180	+	22.3862i	0.0314161	+	1.61981i	−0.570534	+	0.821274i	$0.693264\pi$
$192$		0			0
$193$	−12.3939	−	19.6643i	−0.892133	−	1.41547i	−0.909540	−	0.415617i	$-0.863566\pi$
$193$	−12.3939	−	19.6643i	−0.892133	−	1.41547i	0.0174063	−	0.999848i	$-0.494459\pi$
$194$	−6.91447	+	1.92477i	−0.496430	+	0.138191i
$195$		0			0
$196$	−2.12934	−	0.0826281i	−0.152096	−	0.00590200i
$197$	13.3869	+	14.1893i	0.953780	+	1.01095i	0.999928	+	0.0120135i	$0.00382412\pi$
$197$	13.3869	+	14.1893i	0.953780	+	1.01095i	−0.0461474	+	0.998935i	$0.514694\pi$
$198$		0			0
$199$	20.9993	+	4.97692i	1.48860	+	0.352804i	0.892845	−	0.450363i	$-0.148705\pi$
$199$	20.9993	+	4.97692i	1.48860	+	0.352804i	0.595753	+	0.803168i	$0.296854\pi$
$200$	0.278224	+	1.08013i	0.0196734	+	0.0763770i
$201$		0			0
$202$	−0.839818	+	2.17518i	−0.0590894	+	0.153045i
$203$	−0.723616	−	0.897143i	−0.0507879	−	0.0629671i
$204$		0			0
$205$	−9.41499	+	9.23416i	−0.657572	+	0.644942i
$206$	2.70039	−	2.86224i	0.188145	−	0.199422i
$207$		0			0
$208$	−3.10314	+	10.3652i	−0.215164	+	0.718697i
$209$	−10.5000	+	16.6594i	−0.726301	+	1.15236i
$210$		0			0
$211$	13.8003	+	13.5353i	0.950053	+	0.931806i	0.997749	−	0.0670563i	$-0.0213607\pi$
$211$	13.8003	+	13.5353i	0.950053	+	0.931806i	−0.0476960	+	0.998862i	$0.515188\pi$
$212$	−3.16355	+	0.122760i	−0.217273	+	0.00843120i
$213$		0			0
$214$	−4.99382	+	3.01378i	−0.341370	+	0.206018i
$215$	−4.61136	+	26.1523i	−0.314492	+	1.78358i
$216$		0			0
$217$	1.56913	+	8.89897i	0.106519	+	0.604101i
$218$	1.09461	+	1.25429i	0.0741365	+	0.0849510i
$219$		0			0
$220$	−13.0192	−	10.0906i	−0.877753	−	0.680310i
$221$	29.2776	+	2.27563i	1.96942	+	0.153076i
$222$		0			0
$223$	−9.91964	−	9.00160i	−0.664268	−	0.602792i	0.268495	−	0.963281i	$-0.413474\pi$
$223$	−9.91964	−	9.00160i	−0.664268	−	0.602792i	−0.932763	+	0.360490i	$0.882610\pi$
$224$	7.33275	−	9.84960i	0.489940	−	0.658104i
$225$		0			0
$226$	0.524568	−	1.21609i	0.0348938	−	0.0808928i
$227$	−12.0672	−	8.62515i	−0.800931	−	0.572471i	0.105699	−	0.994398i	$-0.466292\pi$
$227$	−12.0672	−	8.62515i	−0.800931	−	0.572471i	−0.906630	+	0.421927i	$0.861354\pi$
$228$		0			0
$229$	−0.0768204	+	3.96084i	−0.00507643	+	0.261740i	0.988672	+	0.150094i	$0.0479577\pi$
$229$	−0.0768204	+	3.96084i	−0.00507643	+	0.261740i	−0.993748	+	0.111645i	$0.964388\pi$
$230$	0.890683	+	2.60312i	0.0587299	+	0.171645i
$231$		0			0
$232$	−0.916585	+	0.0712426i	−0.0601767	+	0.00467731i
$233$	−12.8975	−	8.48280i	−0.844941	−	0.555727i	0.0516097	−	0.998667i	$-0.483565\pi$
$233$	−12.8975	−	8.48280i	−0.844941	−	0.555727i	−0.896551	+	0.442941i	$0.853935\pi$
$234$		0			0
$235$	−20.5124	−	10.3017i	−1.33808	−	0.672011i
$236$	0.635349	+	4.65158i	0.0413577	+	0.302792i
$237$		0			0
$238$	−7.58453	−	3.44759i	−0.491632	−	0.223474i
$239$	18.7539	+	6.01320i	1.21309	+	0.388962i	0.841919	−	0.539603i	$-0.181426\pi$
$239$	18.7539	+	6.01320i	1.21309	+	0.388962i	0.371170	+	0.928565i	$0.378957\pi$
$240$		0			0
$241$	19.1863	+	3.00069i	1.23590	+	0.193291i	0.738514	−	0.674238i	$-0.235528\pi$
$241$	19.1863	+	3.00069i	1.23590	+	0.193291i	0.497387	+	0.867529i	$0.334293\pi$
$242$	−2.62073			−0.168467
$243$		0			0
$244$	8.36810			0.535713
$245$	−2.86367	−	0.447869i	−0.182953	−	0.0286133i
$246$		0			0
$247$	20.2919	+	6.50634i	1.29114	+	0.413989i
$248$	6.56153	+	2.98258i	0.416658	+	0.189394i
$249$		0			0
$250$	−0.724450	−	5.30391i	−0.0458182	−	0.335449i
$251$	−4.66957	−	2.34515i	−0.294741	−	0.148024i	0.295284	−	0.955410i	$-0.404586\pi$
$251$	−4.66957	−	2.34515i	−0.294741	−	0.148024i	−0.590025	+	0.807385i	$0.700882\pi$
$252$		0			0
$253$	−7.61450	−	5.00813i	−0.478719	−	0.314859i
$254$	3.06450	−	0.238192i	0.192284	−	0.0149455i
$255$		0			0
$256$	−0.369203	−	1.07904i	−0.0230752	−	0.0674397i
$257$	−0.269649	+	13.9030i	−0.0168202	+	0.867247i	0.892475	+	0.451096i	$0.148967\pi$
$257$	−0.269649	+	13.9030i	−0.0168202	+	0.867247i	−0.909295	+	0.416151i	$0.863379\pi$
$258$		0			0
$259$	−1.33597	−	0.954897i	−0.0830134	−	0.0593344i
$260$	−7.05993	+	16.3667i	−0.437838	+	1.01502i
$261$		0			0
$262$	−3.67898	+	4.94173i	−0.227288	+	0.305301i
$263$	−0.0878633	−	0.0797317i	−0.00541788	−	0.00491647i	0.669294	−	0.742997i	$-0.266596\pi$
$263$	−0.0878633	−	0.0797317i	−0.00541788	−	0.00491647i	−0.674712	+	0.738081i	$0.735732\pi$
$264$		0			0
$265$	−4.29330	−	0.333702i	−0.263735	−	0.0204991i
$266$	−4.77845	−	3.70358i	−0.292985	−	0.227081i
$267$		0			0
$268$	−18.3987	−	21.0826i	−1.12388	−	1.28782i
$269$	−0.425161	−	2.41121i	−0.0259225	−	0.147014i	0.969099	−	0.246671i	$-0.0793366\pi$
$269$	−0.425161	−	2.41121i	−0.0259225	−	0.147014i	−0.995022	+	0.0996569i	$0.968225\pi$
$270$		0			0
$271$	4.19162	−	23.7719i	0.254623	−	1.44404i	−0.542416	−	0.840110i	$-0.682490\pi$
$271$	4.19162	−	23.7719i	0.254623	−	1.44404i	0.797039	−	0.603928i	$-0.206399\pi$
$272$	14.4200	−	8.70252i	0.874341	−	0.527668i
$273$		0			0
$274$	2.93848	−	0.114027i	0.177520	−	0.00688859i
$275$	−1.66771	−	1.63568i	−0.100567	−	0.0986354i
$276$		0			0
$277$	−3.84814	+	6.10548i	−0.231212	+	0.366843i	−0.941469	−	0.337100i	$-0.890554\pi$
$277$	−3.84814	+	6.10548i	−0.231212	+	0.366843i	0.710257	+	0.703943i	$0.248579\pi$
$278$	0.389907	−	1.30238i	0.0233851	−	0.0781115i
$279$		0			0
$280$	7.46604	−	7.91354i	0.446181	−	0.472925i
$281$	21.0259	−	20.6221i	1.25430	−	1.23021i	0.292561	−	0.956247i	$-0.405493\pi$
$281$	21.0259	−	20.6221i	1.25430	−	1.23021i	0.961740	−	0.273963i	$-0.0883345\pi$
$282$		0			0
$283$	5.22894	+	6.48286i	0.310828	+	0.385366i	0.909553	−	0.415589i	$-0.136424\pi$
$283$	5.22894	+	6.48286i	0.310828	+	0.385366i	−0.598725	+	0.800955i	$0.704326\pi$
$284$	7.08246	−	18.3440i	0.420266	−	1.08852i
$285$		0			0
$286$	2.23015	+	8.65796i	0.131871	+	0.511956i
$287$	13.0500	+	3.09291i	0.770318	+	0.182569i
$288$		0			0
$289$	−19.7036	−	20.8846i	−1.15904	−	1.22851i
$290$	−0.580800	−	0.0225377i	−0.0341058	−	0.00132346i
$291$		0			0
$292$	−22.4361	+	6.24551i	−1.31297	+	0.365491i
$293$	−14.8583	−	23.5742i	−0.868028	−	1.37722i	−0.925450	−	0.378871i	$-0.876313\pi$
$293$	−14.8583	−	23.5742i	−0.868028	−	1.37722i	0.0574214	−	0.998350i	$-0.481712\pi$
$294$		0			0
$295$	0.123828	+	6.38456i	0.00720957	+	0.371723i
$296$	−1.23084	+	0.447989i	−0.0715410	+	0.0260388i
$297$		0			0
$298$	6.45512	+	2.34947i	0.373935	+	0.136101i
$299$	−3.19276	+	9.33119i	−0.184642	+	0.539637i
$300$		0			0
$301$	25.0008	−	10.2140i	1.44102	−	0.588723i
$302$	4.95602	+	10.3646i	0.285187	+	0.596417i
$303$		0			0
$304$	11.6382	−	3.73165i	0.667498	−	0.214025i
$305$	11.3052	+	1.32139i	0.647335	+	0.0756626i
$306$		0			0
$307$	7.80569	+	10.4849i	0.445494	+	0.598403i	0.966978	−	0.254858i	$-0.0820288\pi$
$307$	7.80569	+	10.4849i	0.445494	+	0.598403i	−0.521484	+	0.853261i	$0.674621\pi$
$308$	−1.62173	+	16.6728i	−0.0924066	+	0.950023i
$309$		0			0
$310$	3.90142	+	2.35452i	0.221585	+	0.133728i
$311$	2.56871	−	2.94342i	0.145658	−	0.166906i	−0.675971	−	0.736929i	$-0.736275\pi$
$311$	2.56871	−	2.94342i	0.145658	−	0.166906i	0.821629	+	0.570023i	$0.193066\pi$
$312$		0			0
$313$	−2.45502	+	5.13423i	−0.138766	+	0.290204i	−0.959805	−	0.280668i	$-0.909444\pi$
$313$	−2.45502	+	5.13423i	−0.138766	+	0.290204i	0.821039	+	0.570872i	$0.193395\pi$
$314$	−0.575843	+	9.88684i	−0.0324967	+	0.557946i
$315$		0			0
$316$	1.54025	−	1.01304i	0.0866461	−	0.0569880i
$317$	8.34355	−	6.46674i	0.468620	−	0.363208i	−0.350753	−	0.936468i	$-0.614074\pi$
$317$	8.34355	−	6.46674i	0.468620	−	0.363208i	0.819374	+	0.573260i	$0.194321\pi$
$318$		0			0
$319$	1.56641	−	1.11960i	0.0877020	−	0.0626856i
$320$	1.18104	+	5.45228i	0.0660220	+	0.304792i
$321$		0			0
$322$	1.75662	−	2.17787i	0.0978927	−	0.121368i
$323$	−16.5857	−	28.7272i	−0.922852	−	1.59843i
$324$		0			0
$325$	−1.26390	+	2.18914i	−0.0701086	+	0.121432i
$326$	1.39390	+	3.61030i	0.0772012	+	0.199956i
$327$		0			0
$328$	7.92194	−	7.18877i	0.437416	−	0.396934i
$329$	2.25993	+	23.2342i	0.124594	+	1.28094i
$330$		0			0
$331$	−1.48771	−	0.607797i	−0.0817720	−	0.0334075i	0.336945	−	0.941524i	$-0.390606\pi$
$331$	−1.48771	−	0.607797i	−0.0817720	−	0.0334075i	−0.418717	+	0.908117i	$0.637520\pi$
$332$	−0.857729	−	14.7266i	−0.0470740	−	0.808229i
$333$		0			0
$334$	−2.56686	+	1.28913i	−0.140453	+	0.0705379i
$335$	−21.5273	−	31.3876i	−1.17616	−	1.71489i
$336$		0			0
$337$	0.965825	+	0.189682i	0.0526118	+	0.0103326i	0.218949	−	0.975736i	$-0.429737\pi$
$337$	0.965825	+	0.189682i	0.0526118	+	0.0103326i	−0.166337	+	0.986069i	$0.553194\pi$
$338$	2.63348	−	1.45309i	0.143242	−	0.0790377i
$339$		0			0
$340$	25.2594	−	11.4818i	1.36988	−	0.622687i
$341$	−14.9928	+	1.75241i	−0.811906	+	0.0948983i
$342$		0			0
$343$	7.82928	+	18.1503i	0.422742	+	0.980025i
$344$	4.56041	−	21.0532i	0.245881	−	1.13511i
$345$		0			0
$346$	0.701931	−	1.02344i	0.0377360	−	0.0550205i
$347$	3.04965	−	22.3274i	0.163714	−	1.19860i	−0.707146	−	0.707067i	$-0.750018\pi$
$347$	3.04965	−	22.3274i	0.163714	−	1.19860i	0.870860	−	0.491531i	$-0.163562\pi$
$348$		0			0
$349$	−14.2459	+	2.79781i	−0.762568	+	0.149763i	−0.558853	−	0.829267i	$-0.688758\pi$
$349$	−14.2459	+	2.79781i	−0.762568	+	0.149763i	−0.203715	+	0.979030i	$0.565302\pi$
$350$	0.549374	−	0.460979i	0.0293653	−	0.0246404i
$351$		0			0
$352$	15.7135	+	13.1852i	0.837532	+	0.702773i
$353$	−22.5440	−	12.4393i	−1.19990	−	0.662075i	−0.248079	−	0.968740i	$-0.579799\pi$
$353$	−22.5440	−	12.4393i	−1.19990	−	0.662075i	−0.951817	+	0.306665i	$0.900787\pi$
$354$		0			0
$355$	12.4650	−	23.6642i	0.661572	−	1.25596i
$356$	3.23690	−	12.5664i	0.171555	−	0.666019i
$357$		0			0
$358$	1.18254	+	2.24500i	0.0624992	+	0.118652i
$359$	18.7908	−	4.45350i	0.991739	−	0.235047i	0.297446	−	0.954739i	$-0.403865\pi$
$359$	18.7908	−	4.45350i	0.991739	−	0.235047i	0.694293	+	0.719692i	$0.255717\pi$
$360$		0			0
$361$	−1.45437	−	4.85793i	−0.0765457	−	0.255680i
$362$	3.13886	+	0.873763i	0.164975	+	0.0459239i
$363$		0			0
$364$	17.9095	−	2.80099i	0.938713	−	0.146812i
$365$	−31.2971	+	4.89478i	−1.63817	+	0.256204i
$366$		0			0
$367$	33.6570	+	9.36906i	1.75688	+	0.489061i	0.988537	−	0.150978i	$-0.0482422\pi$
$367$	33.6570	+	9.36906i	1.75688	+	0.489061i	0.768343	+	0.640039i	$0.221082\pi$
$368$	1.62228	+	5.41879i	0.0845672	+	0.282474i
$369$		0			0
$370$	−0.805789	+	0.190975i	−0.0418910	+	0.00992834i
$371$	2.04098	+	3.87471i	0.105963	+	0.201165i
$372$		0			0
$373$	−7.18647	+	27.8996i	−0.372101	+	1.44459i	0.458986	+	0.888444i	$0.348213\pi$
$373$	−7.18647	+	27.8996i	−0.372101	+	1.44459i	−0.831087	+	0.556142i	$0.812281\pi$
$374$	6.48607	−	12.3135i	0.335387	−	0.636716i
$375$		0			0
$376$	16.3027	+	8.99544i	0.840747	+	0.463905i
$377$	−1.59606	−	1.33926i	−0.0822015	−	0.0689753i
$378$		0			0
$379$	14.0828	−	11.8169i	0.723386	−	0.606993i	−0.204934	−	0.978776i	$-0.565698\pi$
$379$	14.0828	−	11.8169i	0.723386	−	0.606993i	0.928320	+	0.371783i	$0.121253\pi$
$380$	19.7569	−	3.88014i	1.01351	−	0.199047i
$381$		0			0
$382$	1.55399	−	11.3772i	0.0795092	−	0.582111i
$383$	8.02514	−	11.7009i	0.410066	−	0.597890i	−0.563551	−	0.826081i	$-0.690565\pi$
$383$	8.02514	−	11.7009i	0.410066	−	0.597890i	0.973616	+	0.228191i	$0.0732811\pi$
$384$		0			0
$385$	−4.82371	+	22.2687i	−0.245839	+	1.13492i
$386$	4.72157	+	10.9458i	0.240322	+	0.557128i
$387$		0			0
$388$	−24.1449	+	2.82214i	−1.22577	+	0.143272i
$389$	−1.80488	+	0.820419i	−0.0915111	+	0.0415969i	−0.459043	−	0.888414i	$-0.651808\pi$
$389$	−1.80488	+	0.820419i	−0.0915111	+	0.0415969i	0.367532	+	0.930011i	$0.380203\pi$
$390$		0			0
$391$	13.4417	−	7.41680i	0.679774	−	0.375084i
$392$	2.30711	+	0.453101i	0.116527	+	0.0228851i
$393$		0			0
$394$	−5.65859	−	8.25043i	−0.285076	−	0.415650i
$395$	2.24083	−	1.12539i	0.112749	−	0.0566245i
$396$		0			0
$397$	0.0341134	+	0.585705i	0.00171210	+	0.0293957i	0.999056	−	0.0434407i	$-0.0138320\pi$
$397$	0.0341134	+	0.585705i	0.00171210	+	0.0293957i	−0.997344	+	0.0728364i	$0.976795\pi$
$398$	−10.2457	−	4.18583i	−0.513571	−	0.209817i
$399$		0			0
$400$	0.140356	+	1.44299i	0.00701780	+	0.0721493i
$401$	−2.97607	+	2.70064i	−0.148618	+	0.134863i	−0.742925	−	0.669375i	$-0.766562\pi$
$401$	−2.97607	+	2.70064i	−0.148618	+	0.134863i	0.594307	+	0.804238i	$0.297426\pi$
$402$		0			0
$403$	5.88333	+	15.2382i	0.293070	+	0.759069i
$404$	−3.94862	+	6.83921i	−0.196451	+	0.340264i
$405$		0			0
$406$	0.295554	+	0.511915i	0.0146681	+	0.0254059i
$407$	1.72220	−	2.13520i	0.0853664	−	0.105838i
$408$		0			0
$409$	0.378461	+	1.74717i	0.0187137	+	0.0863920i	0.985736	−	0.168301i	$-0.0538281\pi$
$409$	0.378461	+	1.74717i	0.0187137	+	0.0863920i	−0.967022	+	0.254693i	$0.918026\pi$
$410$	5.50223	−	3.93276i	0.271736	−	0.194225i
$411$		0			0
$412$	10.5341	−	8.16458i	0.518980	−	0.402240i
$413$	5.42583	−	3.56862i	0.266988	−	0.175601i
$414$		0			0
$415$	1.16667	−	20.0310i	0.0572696	−	0.983281i
$416$	9.57551	−	20.0255i	0.469478	−	0.981830i
$417$		0			0
$418$	6.64042	−	7.60907i	0.324793	−	0.372172i
$419$	11.0103	+	6.64477i	0.537890	+	0.324618i	0.759490	−	0.650519i	$-0.225449\pi$
$419$	11.0103	+	6.64477i	0.537890	+	0.324618i	−0.221600	+	0.975138i	$0.571128\pi$
$420$		0			0
$421$	−0.230929	+	2.37416i	−0.0112548	+	0.115709i	−0.999247	−	0.0387925i	$-0.987649\pi$
$421$	−0.230929	+	2.37416i	−0.0112548	+	0.115709i	0.987993	+	0.154502i	$0.0493772\pi$
$422$	−5.91987	−	7.95177i	−0.288175	−	0.387086i
$423$		0			0
$424$	3.46952	+	0.405528i	0.168495	+	0.0196942i
$425$	3.74700	−	1.20143i	0.181756	−	0.0582777i
$426$		0			0
$427$	−4.99350	−	10.4430i	−0.241652	−	0.505373i
$428$	−18.2879	+	7.47142i	−0.883978	+	0.361145i
$429$		0			0
$430$	4.40896	−	12.8857i	0.212619	−	0.621403i
$431$	27.5209	+	10.0168i	1.32564	+	0.482493i	0.905260	−	0.424857i	$-0.139676\pi$
$431$	27.5209	+	10.0168i	1.32564	+	0.482493i	0.420377	+	0.907350i	$0.361898\pi$
$432$		0			0
$433$	−37.0156	+	13.4726i	−1.77886	+	0.647451i	−0.779068	+	0.626939i	$0.784307\pi$
$433$	−37.0156	+	13.4726i	−1.77886	+	0.647451i	−0.999790	+	0.0205122i	$0.993470\pi$
$434$	−0.0898638	−	4.63336i	−0.00431360	−	0.222408i
$435$		0			0
$436$	3.00643	+	4.77003i	0.143982	+	0.228443i
$437$	10.7323	−	2.98753i	0.513394	−	0.142913i
$438$		0			0
$439$	8.54833	+	0.331714i	0.407990	+	0.0158319i	0.241954	−	0.970288i	$-0.422212\pi$
$439$	8.54833	+	0.331714i	0.407990	+	0.0158319i	0.166036	+	0.986120i	$0.446903\pi$
$440$	12.4719	+	13.2194i	0.594573	+	0.630211i
$441$		0			0
$442$	−14.6543	−	3.47313i	−0.697034	−	0.165200i
$443$	−1.86066	−	7.22354i	−0.0884028	−	0.343201i	0.908863	−	0.417094i	$-0.136951\pi$
$443$	−1.86066	−	7.22354i	−0.0884028	−	0.343201i	−0.997266	+	0.0738932i	$0.976458\pi$
$444$		0			0
$445$	6.35735	−	16.4660i	0.301367	−	0.780561i
$446$	4.31285	+	5.34709i	0.204219	+	0.253192i
$447$		0			0
$448$	4.05046	−	3.97266i	0.191366	−	0.187691i
$449$	−7.79423	+	8.26140i	−0.367833	+	0.389880i	−0.884681	−	0.466197i	$-0.845624\pi$
$449$	−7.79423	+	8.26140i	−0.367833	+	0.389880i	0.516848	+	0.856077i	$0.327105\pi$
$450$		0			0
$451$	−6.42545	+	21.4625i	−0.302563	+	1.01063i
$452$	2.39178	−	3.79481i	0.112500	−	0.178493i
$453$		0			0
$454$	5.43084	+	5.32653i	0.254882	+	0.249987i
$455$	24.6378	−	0.956060i	1.15504	−	0.0448208i
$456$		0			0
$457$	27.5231	−	16.6102i	1.28747	−	0.776995i	0.303079	−	0.952965i	$-0.401985\pi$
$457$	27.5231	−	16.6102i	1.28747	−	0.776995i	0.984395	+	0.175971i	$0.0563064\pi$
$458$	0.352800	−	2.00083i	0.0164852	−	0.0934925i
$459$		0			0
$460$	1.61813	+	9.17686i	0.0754456	+	0.427873i
$461$	−9.53763	−	10.9289i	−0.444212	−	0.509010i	0.487043	−	0.873378i	$-0.338075\pi$
$461$	−9.53763	−	10.9289i	−0.444212	−	0.509010i	−0.931255	+	0.364368i	$0.881285\pi$
$462$		0			0
$463$	−24.3382	−	18.8635i	−1.13109	−	0.876661i	−0.137590	−	0.990489i	$-0.543936\pi$
$463$	−24.3382	−	18.8635i	−1.13109	−	0.876661i	−0.993500	+	0.113828i	$0.963689\pi$
$464$	−1.19139	−	0.0926018i	−0.0553087	−	0.00429893i
$465$		0			0
$466$	5.86279	+	5.32020i	0.271588	+	0.246453i
$467$	−21.4712	+	28.8409i	−0.993569	+	1.33460i	−0.0516832	+	0.998664i	$0.516459\pi$
$467$	−21.4712	+	28.8409i	−0.993569	+	1.33460i	−0.941886	+	0.335932i	$0.890949\pi$
$468$		0			0
$469$	−15.3310	+	35.5414i	−0.707922	+	1.64115i
$470$	9.57707	+	6.84528i	0.441757	+	0.315749i
$471$		0			0
$472$	0.100447	−	5.17901i	0.00462344	−	0.238383i
$473$	14.6050	+	42.6848i	0.671540	+	1.96265i
$474$		0			0
$475$	2.84679	−	0.221270i	0.130620	−	0.0101526i
$476$	−23.5755	−	15.5059i	−1.08058	−	0.710710i
$477$		0			0
$478$	−9.02589	−	4.53297i	−0.412835	−	0.207333i
$479$	−2.16236	−	15.8313i	−0.0988008	−	0.723350i	−0.971830	−	0.235682i	$-0.924268\pi$
$479$	−2.16236	−	15.8313i	−0.0988008	−	0.723350i	0.873029	−	0.487668i	$-0.162152\pi$
$480$		0			0
$481$	−2.70238	−	1.22838i	−0.123218	−	0.0560093i
$482$	−9.48372	−	3.04083i	−0.431972	−	0.138506i
$483$		0			0
$484$	−8.76963	−	1.37155i	−0.398620	−	0.0623430i
$485$	−33.0652			−1.50141
$486$		0			0
$487$	14.4787			0.656093			0.328047	−	0.944662i	$-0.393610\pi$
$487$	14.4787			0.656093			0.328047	+	0.944662i	$0.393610\pi$
$488$	−9.12208	−	1.42667i	−0.412937	−	0.0645822i
$489$		0			0
$490$	1.41550	+	0.453861i	0.0639456	+	0.0205033i
$491$	17.4294	+	7.92262i	0.786577	+	0.357543i	0.766491	−	0.642255i	$-0.222001\pi$
$491$	17.4294	+	7.92262i	0.786577	+	0.357543i	0.0200859	+	0.999798i	$0.493606\pi$
$492$		0			0
$493$	0.438920	+	3.21346i	0.0197679	+	0.144727i
$494$	−9.76610	−	4.90472i	−0.439398	−	0.220674i
$495$		0			0
$496$	7.82727	+	5.14808i	0.351455	+	0.231156i
$497$	−27.1188	+	2.10784i	−1.21645	+	0.0945496i
$498$		0			0
$499$	0.475572	+	1.38991i	0.0212895	+	0.0622210i	0.956281	−	0.292448i	$-0.0944700\pi$
$499$	0.475572	+	1.38991i	0.0212895	+	0.0622210i	−0.934992	+	0.354669i	$0.884593\pi$
$500$	0.351581	−	18.1274i	0.0157232	−	0.810683i
$501$		0			0
$502$	2.18018	+	1.55830i	0.0973063	+	0.0695503i
$503$	−7.29507	+	16.9119i	−0.325271	+	0.754063i	0.674603	+	0.738181i	$0.264315\pi$
$503$	−7.29507	+	16.9119i	−0.325271	+	0.754063i	−0.999874	+	0.0158820i	$0.994944\pi$
$504$		0			0
$505$	−6.41451	+	8.61618i	−0.285442	+	0.383415i
$506$	3.46131	+	3.14097i	0.153874	+	0.139633i
$507$		0			0
$508$	10.3793	+	0.806742i	0.460506	+	0.0357934i
$509$	−11.6236	−	9.00894i	−0.515205	−	0.399314i	0.321549	−	0.946893i	$-0.395797\pi$
$509$	−11.6236	−	9.00894i	−0.515205	−	0.399314i	−0.836754	+	0.547579i	$0.815550\pi$
$510$		0			0
$511$	21.1824	+	24.2723i	0.937055	+	1.07375i
$512$	−3.86876	−	21.9408i	−0.170977	−	0.969658i
$513$		0			0
$514$	1.23837	−	7.02315i	0.0546222	−	0.309778i
$515$	15.5208	−	9.36683i	0.683926	−	0.412752i
$516$		0			0
$517$	−38.9661	+	1.51206i	−1.71373	+	0.0665003i
$518$	0.601253	+	0.589705i	0.0264176	+	0.0259102i
$519$		0			0
$520$	10.4864	−	16.6378i	0.459858	−	0.729614i
$521$	−1.23210	+	4.11550i	−0.0539793	+	0.180303i	−0.980728	−	0.195379i	$-0.937406\pi$
$521$	−1.23210	+	4.11550i	−0.0539793	+	0.180303i	0.926749	+	0.375682i	$0.122592\pi$
$522$		0			0
$523$	−4.17807	+	4.42850i	−0.182694	+	0.193645i	−0.812248	−	0.583312i	$-0.801756\pi$
$523$	−4.17807	+	4.42850i	−0.182694	+	0.193645i	0.629554	+	0.776957i	$0.283238\pi$
$524$	−14.8971	+	14.6109i	−0.650781	+	0.638282i
$525$		0			0
$526$	0.0382010	+	0.0473619i	0.00166564	+	0.00206508i
$527$	9.15827	−	23.7205i	0.398941	−	1.03328i
$528$		0			0
$529$	−4.45106	−	17.2801i	−0.193524	−	0.751307i
$530$	2.14893	+	0.509305i	0.0933433	+	0.0221228i
$531$		0			0
$532$	−14.0517	−	14.8939i	−0.609218	−	0.645733i
$533$	24.2253	+	0.940053i	1.04932	+	0.0407182i
$534$		0			0
$535$	−25.8865	+	7.20600i	−1.11917	+	0.311543i
$536$	16.4621	+	26.1189i	0.711054	+	1.12816i
$537$		0			0
$538$	0.0243489	+	1.25542i	0.00104976	+	0.0541251i
$539$	−4.62712	+	1.68413i	−0.199304	+	0.0725408i
$540$		0			0
$541$	−28.8796	−	10.5113i	−1.24163	−	0.451917i	−0.364065	−	0.931373i	$-0.618611\pi$
$541$	−28.8796	−	10.5113i	−1.24163	−	0.451917i	−0.877565	+	0.479457i	$0.840834\pi$
$542$	−4.00765	+	11.7128i	−0.172143	+	0.503107i
$543$		0			0
$544$	−31.9866	+	13.0679i	−1.37141	+	0.560284i
$545$	3.30843	+	6.91899i	0.141718	+	0.296377i
$546$		0			0
$547$	−12.7238	+	4.07971i	−0.544029	+	0.174436i	−0.564618	−	0.825352i	$-0.690977\pi$
$547$	−12.7238	+	4.07971i	−0.544029	+	0.174436i	0.0205891	+	0.999788i	$0.493446\pi$
$548$	9.89261	+	1.15628i	0.422591	+	0.0493938i
$549$		0			0
$550$	0.715394	+	0.960940i	0.0305045	+	0.0409746i
$551$	−0.227846	+	2.34246i	−0.00970655	+	0.0997921i
$552$		0			0
$553$	−2.18335	−	1.31766i	−0.0928453	−	0.0560324i
$554$	2.43364	−	2.78864i	0.103395	−	0.118478i
$555$		0			0
$556$	1.98633	−	4.15405i	0.0842389	−	0.176171i
$557$	−2.39955	+	41.1986i	−0.101672	+	1.74564i	0.433730	+	0.901043i	$0.357197\pi$
$557$	−2.39955	+	41.1986i	−0.101672	+	1.74564i	−0.535402	+	0.844598i	$0.679840\pi$
$558$		0			0
$559$	40.7879	−	26.8266i	1.72514	−	1.13464i
$560$	11.1773	−	8.66304i	0.472326	−	0.366080i
$561$		0			0
$562$	−12.2878	+	8.78279i	−0.518329	+	0.370479i
$563$	5.28238	+	24.3862i	0.222626	+	1.02775i	0.942644	+	0.333799i	$0.108331\pi$
$563$	5.28238	+	24.3862i	0.222626	+	1.02775i	−0.720019	+	0.693955i	$0.755867\pi$
$564$		0			0
$565$	3.83049	−	4.74907i	0.161150	−	0.199795i
$566$	−2.13571	−	3.69916i	−0.0897707	−	0.155487i
$567$		0			0
$568$	−10.8480	+	18.7894i	−0.455174	+	0.788384i
$569$	−12.8961	−	33.4018i	−0.540634	−	1.40028i	−0.886821	−	0.462112i	$-0.847092\pi$
$569$	−12.8961	−	33.4018i	−0.540634	−	1.40028i	0.346187	−	0.938166i	$-0.387476\pi$
$570$		0			0
$571$	13.9601	−	12.6681i	0.584211	−	0.530143i	−0.325415	−	0.945571i	$-0.605504\pi$
$571$	13.9601	−	12.6681i	0.584211	−	0.530143i	0.909626	+	0.415428i	$0.136368\pi$
$572$	2.93155	+	30.1389i	0.122574	+	1.26017i
$573$		0			0
$574$	−6.36720	−	2.60129i	−0.265762	−	0.108576i
$575$	0.0768385	+	1.31927i	0.00320439	+	0.0550172i
$576$		0			0
$577$	19.2618	−	9.67366i	0.801881	−	0.402720i	−0.000151910	−	1.00000i	$-0.500048\pi$
$577$	19.2618	−	9.67366i	0.801881	−	0.402720i	0.802032	+	0.597280i	$0.203752\pi$
$578$	8.32860	+	12.1434i	0.346424	+	0.505099i
$579$		0			0
$580$	−1.93172	−	0.379376i	−0.0802101	−	0.0157528i
$581$	−17.8663	+	9.85823i	−0.741221	+	0.408988i
$582$		0			0
$583$	−6.65992	+	3.02730i	−0.275826	+	0.125378i
$584$	25.5224	−	2.98314i	1.05612	−	0.123443i
$585$		0			0
$586$	5.66038	+	13.1222i	0.233828	+	0.542075i
$587$	0.958070	−	4.42294i	0.0395438	−	0.182554i	−0.953290	−	0.302056i	$-0.902327\pi$
$587$	0.958070	−	4.42294i	0.0395438	−	0.182554i	0.992834	+	0.119501i	$0.0381296\pi$
$588$		0			0
$589$	10.4362	−	15.2163i	0.430015	−	0.626978i
$590$	0.443200	−	3.24480i	0.0182463	−	0.133586i
$591$		0			0
$592$	−1.67062	+	0.328099i	−0.0686620	+	0.0134848i
$593$	−4.23253	+	3.55151i	−0.173809	+	0.145843i	−0.725542	−	0.688177i	$-0.758411\pi$
$593$	−4.23253	+	3.55151i	−0.173809	+	0.145843i	0.551733	+	0.834021i	$0.313967\pi$
$594$		0			0
$595$	−29.4018	−	24.6710i	−1.20535	−	1.01141i
$596$	20.3709	+	11.2402i	0.834426	+	0.460417i
$597$		0			0
$598$	2.35718	−	4.47500i	0.0963924	−	0.182996i
$599$	11.0884	−	43.0477i	0.453058	−	1.75888i	−0.178890	−	0.983869i	$-0.557251\pi$
$599$	11.0884	−	43.0477i	0.453058	−	1.75888i	0.631948	−	0.775010i	$-0.282255\pi$
$600$		0			0
$601$	−1.97571	−	3.75078i	−0.0805907	−	0.152998i	0.841153	−	0.540797i	$-0.181877\pi$
$601$	−1.97571	−	3.75078i	−0.0805907	−	0.152998i	−0.921744	+	0.387799i	$0.873235\pi$
$602$	−13.4770	+	3.19412i	−0.549283	+	0.130183i
$603$		0			0
$604$	11.1598	+	37.2765i	0.454088	+	1.51676i
$605$	−11.6311	−	3.23774i	−0.472871	−	0.131633i
$606$		0			0
$607$	7.28993	−	1.14012i	0.295889	−	0.0462762i	−0.00483194	−	0.999988i	$-0.501538\pi$
$607$	7.28993	−	1.14012i	0.295889	−	0.0462762i	0.300721	+	0.953712i	$0.402773\pi$
$608$	−24.7724	+	3.87434i	−1.00465	+	0.157125i
$609$		0			0
$610$	−5.62351	−	1.56541i	−0.227689	−	0.0633817i
$611$	12.1025	+	40.4251i	0.489614	+	1.63542i
$612$		0			0
$613$	−23.8838	+	5.66057i	−0.964658	+	0.228628i	−0.682619	−	0.730775i	$-0.739159\pi$
$613$	−23.8838	+	5.66057i	−0.964658	+	0.228628i	−0.282039	+	0.959403i	$0.591011\pi$
$614$	−3.12419	−	5.93113i	−0.126082	−	0.239361i
$615$		0			0
$616$	4.61038	−	17.8986i	0.185757	−	0.721154i
$617$	−9.17737	+	17.4228i	−0.369467	+	0.701416i	−0.997019	−	0.0771590i	$-0.975415\pi$
$617$	−9.17737	+	17.4228i	−0.369467	+	0.701416i	0.627552	+	0.778575i	$0.284057\pi$
$618$		0			0
$619$	−11.9534	−	6.59558i	−0.480446	−	0.265099i	0.224350	−	0.974509i	$-0.427974\pi$
$619$	−11.9534	−	6.59558i	−0.480446	−	0.265099i	−0.704796	+	0.709410i	$0.748962\pi$
$620$	11.8229	+	9.92062i	0.474820	+	0.398421i
$621$		0			0
$622$	−1.53479	+	1.28784i	−0.0615395	+	0.0516377i
$623$	−17.6139	+	3.45925i	−0.705685	+	0.138592i
$624$		0			0
$625$	3.73125	−	27.3176i	0.149250	−	1.09270i
$626$	1.65079	−	2.40691i	0.0659789	−	0.0961995i
$627$		0			0
$628$	−7.10115	+	32.7826i	−0.283367	+	1.30817i
$629$	1.83022	+	4.24293i	0.0729758	+	0.169177i
$630$		0			0
$631$	−8.04715	+	0.940577i	−0.320352	+	0.0374438i	−0.274749	−	0.961516i	$-0.588595\pi$
$631$	−8.04715	+	0.940577i	−0.320352	+	0.0374438i	−0.0456026	+	0.998960i	$0.514521\pi$
$632$	−1.85174	+	0.841721i	−0.0736585	+	0.0334819i
$633$		0			0
$634$	−4.74004	+	2.61544i	−0.188251	+	0.103872i
$635$	13.8949	+	2.72887i	0.551403	+	0.108292i
$636$		0			0
$637$	3.01381	+	4.39425i	0.119412	+	0.174106i
$638$	−0.882405	+	0.443160i	−0.0349347	+	0.0175449i
$639$		0			0
$640$	−1.57048	−	26.9641i	−0.0620786	−	1.06585i
$641$	9.97685	+	4.07599i	0.394062	+	0.160992i	0.566565	−	0.824017i	$-0.308272\pi$
$641$	9.97685	+	4.07599i	0.394062	+	0.160992i	−0.172503	+	0.985009i	$0.555186\pi$
$642$		0			0
$643$	−2.26138	−	23.2490i	−0.0891800	−	0.916850i	−0.928034	−	0.372495i	$-0.878503\pi$
$643$	−2.26138	−	23.2490i	−0.0891800	−	0.916850i	0.838854	−	0.544356i	$-0.183226\pi$
$644$	7.01789	−	6.36840i	0.276544	−	0.250950i
$645$		0			0
$646$	6.12730	+	15.8701i	0.241075	+	0.624401i
$647$	11.2986	−	19.5697i	0.444193	−	0.769364i	−0.553803	−	0.832648i	$-0.686824\pi$
$647$	11.2986	−	19.5697i	0.444193	−	0.769364i	0.997996	+	0.0632836i	$0.0201573\pi$
$648$		0			0
$649$	5.42422	+	9.39503i	0.212919	+	0.368787i
$650$	0.813883	−	1.00906i	0.0319231	−	0.0395784i
$651$		0			0
$652$	2.77493	+	12.8105i	0.108675	+	0.501698i
$653$	−38.3480	+	27.4095i	−1.50067	+	1.07262i	−0.525603	+	0.850730i	$0.676160\pi$
$653$	−38.3480	+	27.4095i	−1.50067	+	1.07262i	−0.975072	+	0.221888i	$0.928778\pi$
$654$		0			0
$655$	−22.4329	+	17.3868i	−0.876528	+	0.679360i
$656$	11.6172	−	7.64073i	0.453574	−	0.298320i
$657$		0			0
$658$	0.696100	−	11.9516i	0.0271368	−	0.465921i
$659$	1.16075	−	2.42751i	0.0452165	−	0.0945623i	−0.878319	−	0.478074i	$-0.841335\pi$
$659$	1.16075	−	2.42751i	0.0452165	−	0.0945623i	0.923536	+	0.383512i	$0.125286\pi$
$660$		0			0
$661$	−27.4641	+	31.4704i	−1.06823	+	1.22406i	−0.0946991	+	0.995506i	$0.530189\pi$
$661$	−27.4641	+	31.4704i	−1.06823	+	1.22406i	−0.973532	+	0.228551i	$0.926601\pi$
$662$	0.705642	+	0.425857i	0.0274256	+	0.0165514i
$663$		0			0
$664$	−1.57571	+	16.1997i	−0.0611495	+	0.628672i
$665$	−16.6318	−	22.3404i	−0.644953	−	0.866323i
$666$		0			0
$667$	−1.08187	−	0.126452i	−0.0418902	−	0.00489626i
$668$	−9.26406	+	2.97040i	−0.358437	+	0.114928i
$669$		0			0
$670$	8.42036	+	17.6097i	0.325307	+	0.680322i
$671$	17.9004	−	7.31310i	0.691036	−	0.282319i
$672$		0			0
$673$	−1.31947	+	3.85629i	−0.0508618	+	0.148649i	−0.968655	−	0.248409i	$-0.920092\pi$
$673$	−1.31947	+	3.85629i	−0.0508618	+	0.148649i	0.917793	+	0.397058i	$0.129969\pi$
$674$	−0.474342	−	0.172646i	−0.0182710	−	0.00665009i
$675$		0			0
$676$	9.57277	−	3.48420i	0.368184	−	0.134008i
$677$	0.0293906	+	1.51537i	0.00112957	+	0.0582405i	0.999953	+	0.00973714i	$0.00309948\pi$
$677$	0.0293906	+	1.51537i	0.00112957	+	0.0582405i	−0.998823	+	0.0485033i	$0.984555\pi$
$678$		0			0
$679$	17.9299	+	28.4477i	0.688087	+	1.09172i
$680$	−29.4928	+	8.20987i	−1.13100	+	0.314834i
$681$		0			0
$682$	7.73557	+	0.300175i	0.296210	+	0.0114943i
$683$	−10.5711	−	11.2048i	−0.404493	−	0.428738i	0.492820	−	0.870131i	$-0.335966\pi$
$683$	−10.5711	−	11.2048i	−0.404493	−	0.428738i	−0.897314	+	0.441393i	$0.854484\pi$
$684$		0			0
$685$	13.1822	+	3.12424i	0.503666	+	0.119371i
$686$	−2.52870	−	9.81700i	−0.0965460	−	0.374815i
$687$		0			0
$688$	10.0849	−	26.1206i	0.384483	−	0.995837i
$689$	4.97005	+	6.16190i	0.189344	+	0.234750i
$690$		0			0
$691$	−17.8792	+	17.5358i	−0.680158	+	0.667095i	−0.955750	−	0.294180i	$-0.904953\pi$
$691$	−17.8792	+	17.5358i	−0.680158	+	0.667095i	0.275592	+	0.961275i	$0.411126\pi$
$692$	2.88446	−	3.05735i	0.109651	−	0.116223i
$693$		0			0
$694$	−3.31455	+	11.0714i	−0.125819	+	0.420264i
$695$	3.33946	−	5.29841i	0.126673	−	0.200980i
$696$		0			0
$697$	−26.9428	−	26.4253i	−1.02053	−	1.00093i
$698$	7.43997	−	0.288705i	0.281607	−	0.0109276i
$699$		0			0
$700$	2.07960	−	1.25504i	0.0786015	−	0.0474362i
$701$	1.47905	−	8.38808i	0.0558628	−	0.316813i	−0.944053	−	0.329794i	$-0.893021\pi$
$701$	1.47905	−	8.38808i	0.0558628	−	0.316813i	0.999916	+	0.0129803i	$0.00413188\pi$
$702$		0			0
$703$	0.582266	+	3.30220i	0.0219606	+	0.124545i
$704$	6.23161	+	7.14063i	0.234862	+	0.269123i
$705$		0			0
$706$	10.4371	+	8.08933i	0.392804	+	0.304446i
$707$	10.8913	+	0.846538i	0.409609	+	0.0318373i
$708$		0			0
$709$	13.4132	+	12.1718i	0.503742	+	0.457121i	0.883816	−	0.467835i	$-0.154966\pi$
$709$	13.4132	+	12.1718i	0.503742	+	0.457121i	−0.380074	+	0.924956i	$0.624102\pi$
$710$	−8.19113	+	11.0026i	−0.307408	+	0.412920i
$711$		0			0
$712$	−5.67098	+	13.1468i	−0.212529	+	0.492697i
$713$	6.94731	+	4.96564i	0.260179	+	0.185965i
$714$		0			0
$715$	−0.798690	+	41.1803i	−0.0298693	+	1.54005i
$716$	2.78218	+	8.13122i	0.103975	+	0.303878i
$717$		0			0
$718$	−9.87400	+	0.767468i	−0.368494	+	0.0286416i
$719$	−8.51960	−	5.60343i	−0.317728	−	0.208973i	0.380620	−	0.924732i	$-0.375711\pi$
$719$	−8.51960	−	5.60343i	−0.317728	−	0.208973i	−0.698348	+	0.715759i	$0.746081\pi$
$720$		0			0
$721$	−16.4751	−	8.27409i	−0.613563	−	0.308143i
$722$	0.351947	+	2.57671i	0.0130981	+	0.0958952i
$723$		0			0
$724$	10.0462	+	4.56655i	0.373363	+	0.169714i
$725$	−0.265850	−	0.0852414i	−0.00987342	−	0.00316579i
$726$		0			0
$727$	−24.1164	−	3.77173i	−0.894427	−	0.139886i	−0.309431	−	0.950922i	$-0.600139\pi$
$727$	−24.1164	−	3.77173i	−0.894427	−	0.139886i	−0.584996	+	0.811036i	$0.698904\pi$
$728$	−20.0007			−0.741275
$729$		0			0
$730$	16.2458			0.601284
$731$	−75.0816	−	11.7426i	−2.77699	−	0.434314i
$732$		0			0
$733$	12.9907	+	4.16529i	0.479822	+	0.153849i	0.535388	−	0.844606i	$-0.320165\pi$
$733$	12.9907	+	4.16529i	0.479822	+	0.153849i	−0.0555660	+	0.998455i	$0.517696\pi$
$734$	−16.3112	−	7.41434i	−0.602056	−	0.273668i
$735$		0			0
$736$	−1.57043	−	11.4976i	−0.0578869	−	0.423807i
$737$	−57.7816	−	29.0190i	−2.12841	−	1.06893i
$738$		0			0
$739$	−11.5370	−	7.58803i	−0.424397	−	0.279130i	0.319292	−	0.947656i	$-0.396555\pi$
$739$	−11.5370	−	7.58803i	−0.424397	−	0.279130i	−0.743688	+	0.668526i	$0.766925\pi$
$740$	−2.79633	+	0.217348i	−0.102795	+	0.00798986i
$741$		0			0
$742$	−0.727093	−	2.12501i	−0.0266924	−	0.0780116i
$743$	−0.159906	+	8.24471i	−0.00586638	+	0.302469i	0.985374	+	0.170403i	$0.0545069\pi$
$743$	−0.159906	+	8.24471i	−0.00586638	+	0.302469i	−0.991241	+	0.132066i	$0.957839\pi$
$744$		0			0
$745$	25.7460	+	18.4021i	0.943259	+	0.674201i
$746$	5.85220	−	13.5669i	0.214264	−	0.496720i
$747$		0			0
$748$	28.1483	−	37.8098i	1.02920	−	1.38246i
$749$	20.2369	+	18.3640i	0.739441	+	0.671007i
$750$		0			0
$751$	46.0397	+	3.57849i	1.68001	+	0.130581i	0.881746	−	0.471725i	$-0.156368\pi$
$751$	46.0397	+	3.57849i	1.68001	+	0.130581i	0.798266	+	0.602305i	$0.205751\pi$
$752$	19.1292	+	14.8262i	0.697570	+	0.540658i
$753$		0			0
$754$	0.702579	+	0.805067i	0.0255864	+	0.0293188i
$755$	9.19057	+	52.1223i	0.334479	+	1.89693i
$756$		0			0
$757$	2.17465	−	12.3331i	0.0790390	−	0.448252i	−0.919445	−	0.393218i	$-0.871362\pi$
$757$	2.17465	−	12.3331i	0.0790390	−	0.448252i	0.998484	−	0.0550348i	$-0.0175270\pi$
$758$	−8.07204	+	4.87150i	−0.293190	+	0.176941i
$759$		0			0
$760$	−22.1986	+	0.861406i	−0.805227	+	0.0312465i
$761$	19.6457	+	19.2684i	0.712156	+	0.698477i	0.962985	−	0.269554i	$-0.0868763\pi$
$761$	19.6457	+	19.2684i	0.712156	+	0.698477i	−0.250830	+	0.968031i	$0.580703\pi$
$762$		0			0
$763$	4.15875	−	6.59831i	0.150557	−	0.238875i
$764$	11.1543	−	37.2580i	0.403549	−	1.34795i
$765$		0			0
$766$	−4.99349	+	5.29279i	−0.180422	+	0.191236i
$767$	8.38108	−	8.22010i	0.302623	−	0.296811i
$768$		0			0
$769$	−1.41881	−	1.75905i	−0.0511636	−	0.0634329i	0.752137	−	0.659007i	$-0.229023\pi$
$769$	−1.41881	−	1.75905i	−0.0511636	−	0.0634329i	−0.803300	+	0.595574i	$0.796925\pi$
$770$	4.20880	−	10.9011i	0.151675	−	0.392847i
$771$		0			0
$772$	10.0712	+	39.0986i	0.362469	+	1.40719i
$773$	−17.0638	−	4.04419i	−0.613742	−	0.145459i	−0.0880238	−	0.996118i	$-0.528055\pi$
$773$	−17.0638	−	4.04419i	−0.613742	−	0.145459i	−0.525718	+	0.850659i	$0.676203\pi$
$774$		0			0
$775$	1.50201	+	1.59204i	0.0539539	+	0.0571878i
$776$	26.8016	+	1.04002i	0.962120	+	0.0373346i
$777$		0			0
$778$	0.979527	−	0.272670i	0.0351178	−	0.00977570i
$779$	−14.6019	−	23.1675i	−0.523168	−	0.830063i
$780$		0			0
$781$	−0.881105	−	45.4296i	−0.0315284	−	1.62560i
$782$	−7.39849	+	2.69283i	−0.264569	+	0.0962954i
$783$		0			0
$784$	2.87178	+	1.04524i	0.102564	+	0.0373301i
$785$	−14.7702	+	43.1676i	−0.527171	+	1.54072i
$786$		0			0
$787$	0.863726	−	0.352871i	0.0307885	−	0.0125785i	−0.362753	−	0.931885i	$-0.618163\pi$
$787$	0.863726	−	0.352871i	0.0307885	−	0.0125785i	0.393542	+	0.919307i	$0.371250\pi$
$788$	−14.6173	−	30.5695i	−0.520720	−	1.08899i
$789$		0			0
$790$	−1.22459	+	0.392648i	−0.0435689	+	0.0139698i
$791$	−6.16300	−	0.720351i	−0.219131	−	0.0256127i
$792$		0			0
$793$	−12.4953	−	16.7841i	−0.443721	−	0.596021i
$794$	0.0291291	−	0.299474i	0.00103375	−	0.0106279i
$795$		0			0
$796$	−32.0942	−	19.3689i	−1.13755	−	0.686514i
$797$	35.1786	−	40.3102i	1.24609	−	1.42786i	0.382275	−	0.924049i	$-0.375141\pi$
$797$	35.1786	−	40.3102i	1.24609	−	1.42786i	0.863814	−	0.503811i	$-0.168069\pi$
$798$		0			0
$799$	28.3365	−	59.2608i	1.00247	−	2.09650i
$800$	0.172941	−	2.96928i	0.00611437	−	0.104980i
$801$		0			0
$802$	1.72195	−	1.13255i	0.0608043	−	0.0399916i
$803$	−42.5353	+	32.9674i	−1.50104	+	1.16339i
$804$		0			0
$805$	10.4867	−	7.49545i	0.369608	−	0.264180i
$806$	−1.77347	−	8.18726i	−0.0624679	−	0.288384i
$807$		0			0
$808$	5.47040	−	6.78224i	0.192448	−	0.238598i
$809$	15.3188	+	26.5330i	0.538582	+	0.932851i	0.998981	+	0.0451389i	$0.0143731\pi$
$809$	15.3188	+	26.5330i	0.538582	+	0.932851i	−0.460399	+	0.887712i	$0.652294\pi$
$810$		0			0
$811$	−19.8600	+	34.3985i	−0.697379	+	1.20790i	0.271994	+	0.962299i	$0.412317\pi$
$811$	−19.8600	+	34.3985i	−0.697379	+	1.20790i	−0.969372	+	0.245596i	$0.921016\pi$
$812$	0.721093	+	1.86768i	0.0253054	+	0.0655427i
$813$		0			0
$814$	−1.04182	+	0.945405i	−0.0365159	+	0.0331364i
$815$	1.72602	+	17.7450i	0.0604599	+	0.621582i
$816$		0			0
$817$	−51.0497	−	20.8561i	−1.78600	−	0.729662i
$818$	−0.0533080	−	0.915263i	−0.00186387	−	0.0320014i
$819$		0			0
$820$	20.4701	−	10.2805i	0.714847	−	0.359010i
$821$	−0.852230	−	1.24258i	−0.0297430	−	0.0433664i	0.809518	−	0.587095i	$-0.199728\pi$
$821$	−0.852230	−	1.24258i	−0.0297430	−	0.0433664i	−0.839261	+	0.543728i	$0.817012\pi$
$822$		0			0
$823$	−13.2445	−	2.60113i	−0.461674	−	0.0906698i	−0.0435331	−	0.999052i	$-0.513861\pi$
$823$	−13.2445	−	2.60113i	−0.461674	−	0.0906698i	−0.418141	+	0.908382i	$0.637318\pi$
$824$	−12.8752	+	7.10426i	−0.448530	+	0.247489i
$825$		0			0
$826$	−3.03200	+	1.37821i	−0.105497	+	0.0479542i
$827$	45.5036	−	5.31861i	1.58232	−	0.184946i	0.720971	−	0.692966i	$-0.243696\pi$
$827$	45.5036	−	5.31861i	1.58232	−	0.184946i	0.861346	+	0.508019i	$0.169622\pi$
$828$		0			0
$829$	−2.32484	−	5.38959i	−0.0807451	−	0.187188i	0.873061	−	0.487611i	$-0.162132\pi$
$829$	−2.32484	−	5.38959i	−0.0807451	−	0.187188i	−0.953806	+	0.300423i	$0.902872\pi$
$830$	−2.17849	+	10.0570i	−0.0756164	+	0.349084i
$831$		0			0
$832$	5.80072	−	8.45765i	0.201104	−	0.293216i
$833$	1.12251	−	8.21823i	0.0388927	−	0.284745i
$834$		0			0
$835$	−12.9847	+	2.55011i	−0.449354	+	0.0882502i
$836$	26.2027	−	21.9867i	0.906241	−	0.760426i
$837$		0			0
$838$	−5.05225	−	4.23934i	−0.174527	−	0.146446i
$839$	34.8513	+	19.2302i	1.20320	+	0.663899i	0.952610	−	0.304194i	$-0.0983871\pi$
$839$	34.8513	+	19.2302i	1.20320	+	0.663899i	0.250592	+	0.968093i	$0.419375\pi$
$840$		0			0
$841$	−13.4080	+	25.4545i	−0.462346	+	0.877741i
$842$	0.305148	−	1.18466i	0.0105161	−	0.0408260i
$843$		0			0
$844$	−15.6479	−	29.7068i	−0.538624	−	1.02255i
$845$	13.4829	−	3.19550i	0.463825	−	0.109929i
$846$		0			0
$847$	3.52148	+	11.7626i	0.120999	+	0.404166i
$848$	4.37410	+	1.21761i	0.150207	+	0.0418130i
$849$		0			0
$850$	−1.99377	+	0.311820i	−0.0683857	+	0.0106953i
$851$	−1.53323	+	0.239794i	−0.0525586	+	0.00822002i
$852$		0			0
$853$	−24.7525	−	6.89033i	−0.847509	−	0.235920i	−0.182919	−	0.983128i	$-0.558555\pi$
$853$	−24.7525	−	6.89033i	−0.847509	−	0.235920i	−0.664591	+	0.747208i	$0.731394\pi$
$854$	1.70260	+	5.68707i	0.0582617	+	0.194608i
$855$		0			0
$856$	21.2094	−	5.02672i	0.724923	−	0.171810i
$857$	7.69871	+	14.6156i	0.262983	+	0.499261i	0.980307	−	0.197479i	$-0.0632753\pi$
$857$	7.69871	+	14.6156i	0.262983	+	0.499261i	−0.717324	+	0.696740i	$0.754633\pi$
$858$		0			0
$859$	−7.00441	+	27.1928i	−0.238987	+	0.927806i	0.730549	+	0.682860i	$0.239264\pi$
$859$	−7.00441	+	27.1928i	−0.238987	+	0.927806i	−0.969537	+	0.244946i	$0.921230\pi$
$860$	21.4972	−	40.8114i	0.733049	−	1.39166i
$861$		0			0
$862$	−13.1508	−	7.25630i	−0.447918	−	0.247150i
$863$	28.9991	+	24.3332i	0.987142	+	0.828310i	0.985151	−	0.171688i	$-0.0549221\pi$
$863$	28.9991	+	24.3332i	0.987142	+	0.828310i	0.00199021	+	0.999998i	$0.499366\pi$
$864$		0			0
$865$	4.37965	−	3.67496i	0.148913	−	0.124952i
$866$	19.8230	−	3.89312i	0.673615	−	0.132294i
$867$		0			0
$868$	2.12414	−	15.5514i	0.0720980	−	0.527851i
$869$	2.40946	−	3.51308i	0.0817354	−	0.119173i
$870$		0			0
$871$	−14.8128	+	68.3833i	−0.501911	+	2.31708i
$872$	−2.46408	−	5.71238i	−0.0834442	−	0.193445i
$873$		0			0
$874$	−5.67467	+	0.663274i	−0.191949	+	0.0224356i
$875$	−22.8320	+	10.3784i	−0.771862	+	0.350854i
$876$		0			0
$877$	−8.54528	+	4.71508i	−0.288553	+	0.159217i	−0.620785	−	0.783981i	$-0.713186\pi$
$877$	−8.54528	+	4.71508i	−0.288553	+	0.159217i	0.332232	+	0.943198i	$0.392198\pi$
$878$	−4.30506	−	0.845486i	−0.145289	−	0.0285338i
$879$		0			0
$880$	13.3613	+	19.4813i	0.450410	+	0.656714i
$881$	−7.34959	+	3.69110i	−0.247614	+	0.124356i	−0.568278	−	0.822837i	$-0.692390\pi$
$881$	−7.34959	+	3.69110i	−0.247614	+	0.124356i	0.320664	+	0.947193i	$0.396094\pi$
$882$		0			0
$883$	1.72105	+	29.5492i	0.0579178	+	0.994410i	0.894641	+	0.446785i	$0.147431\pi$
$883$	1.72105	+	29.5492i	0.0579178	+	0.994410i	−0.836724	+	0.547625i	$0.815532\pi$
$884$	−47.2195	−	19.2913i	−1.58816	−	0.648836i
$885$		0			0
$886$	0.370351	+	3.80754i	0.0124422	+	0.127917i
$887$	−21.1381	+	19.1818i	−0.709748	+	0.644062i	−0.944697	−	0.327946i	$-0.893644\pi$
$887$	−21.1381	+	19.1818i	−0.709748	+	0.644062i	0.234949	+	0.972008i	$0.424508\pi$
$888$		0			0
$889$	−5.18685	−	13.4343i	−0.173962	−	0.450572i
$890$	−4.52604	+	7.83933i	−0.151713	+	0.262775i
$891$		0			0
$892$	11.6335	+	20.1499i	0.389520	+	0.674668i
$893$	29.9254	−	37.1017i	1.00142	−	1.24156i
$894$		0			0
$895$	2.47471	+	11.4245i	0.0827203	+	0.381880i
$896$	−22.3470	+	15.9727i	−0.746561	+	0.533610i
$897$		0			0
$898$	4.60393	−	3.56831i	0.153635	−	0.119076i
$899$	−1.50727	+	0.991345i	−0.0502702	+	0.0330632i
$900$		0			0
$901$	0.716527	−	12.3023i	0.0238710	−	0.409849i
$902$	4.95649	−	10.3656i	0.165033	−	0.345138i
$903$		0			0
$904$	−3.25425	+	3.72896i	−0.108235	+	0.124023i
$905$	12.8512	+	7.75573i	0.427188	+	0.257809i
$906$		0			0
$907$	1.29929	−	13.3579i	0.0431422	−	0.443541i	−0.948710	−	0.316147i	$-0.897611\pi$
$907$	1.29929	−	13.3579i	0.0431422	−	0.443541i	0.991852	−	0.127393i	$-0.0406610\pi$
$908$	15.3854	+	20.6662i	0.510583	+	0.685831i
$909$		0			0
$910$	−12.5595	−	1.46799i	−0.416343	−	0.0486635i
$911$	22.4750	−	7.20633i	0.744631	−	0.238756i	0.0912944	−	0.995824i	$-0.470900\pi$
$911$	22.4750	−	7.20633i	0.744631	−	0.238756i	0.653337	+	0.757068i	$0.273369\pi$
$912$		0			0
$913$	−14.7048	−	30.7524i	−0.486657	−	1.01776i
$914$	−15.2619	+	6.23518i	−0.504819	+	0.206241i
$915$		0			0
$916$	2.22768	−	6.51065i	0.0736047	−	0.215118i
$917$	27.1233	+	9.87208i	0.895691	+	0.326005i
$918$		0			0
$919$	8.14478	−	2.96446i	0.268671	−	0.0977884i	−0.204172	−	0.978935i	$-0.565450\pi$
$919$	8.14478	−	2.96446i	0.268671	−	0.0977884i	0.472843	+	0.881147i	$0.343228\pi$
$920$	−0.199372	−	10.2796i	−0.00657310	−	0.338907i
$921$		0			0
$922$	3.96655	+	6.29337i	0.130632	+	0.207261i
$923$	−47.3686	+	13.1859i	−1.55916	+	0.434021i
$924$		0			0
$925$	−0.397461	−	0.0154233i	−0.0130684	−	0.000507115i
$926$	10.8370	+	11.4866i	0.356127	+	0.377473i
$927$		0			0
$928$	2.38546	+	0.565365i	0.0783066	+	0.0185590i
$929$	12.4503	+	48.3351i	0.408482	+	1.58582i	0.760181	+	0.649711i	$0.225110\pi$
$929$	12.4503	+	48.3351i	0.408482	+	1.58582i	−0.351699	+	0.936113i	$0.614396\pi$
$930$		0			0
$931$	2.16790	−	5.61500i	0.0710500	−	0.184024i
$932$	16.8341	+	20.8710i	0.551420	+	0.683653i
$933$		0			0
$934$	13.1647	−	12.9119i	0.430763	−	0.422489i
$935$	43.9985	−	46.6357i	1.43891	−	1.52515i
$936$		0			0
$937$	0.0653221	−	0.218191i	0.00213398	−	0.00712799i	−0.956916	−	0.290365i	$-0.906223\pi$
$937$	0.0653221	−	0.218191i	0.00213398	−	0.00712799i	0.959050	+	0.283237i	$0.0914084\pi$
$938$	10.5845	−	16.7935i	0.345597	−	0.548328i
$939$		0			0
$940$	28.4649	+	27.9182i	0.928423	+	0.910591i
$941$	−6.64911	+	0.258016i	−0.216755	+	0.00841107i	−0.146924	−	0.989148i	$-0.546937\pi$
$941$	−6.64911	+	0.258016i	−0.216755	+	0.00841107i	−0.0698308	+	0.997559i	$0.522246\pi$
$942$		0			0
$943$	10.8512	−	6.54876i	0.353365	−	0.213257i
$944$	1.16917	−	6.63070i	0.0380533	−	0.215811i
$945$		0			0
$946$	−4.01766	−	22.7853i	−0.130625	−	0.740814i
$947$	16.7085	+	19.1458i	0.542952	+	0.622154i	0.957695	−	0.287785i	$-0.0929187\pi$
$947$	16.7085	+	19.1458i	0.542952	+	0.622154i	−0.414743	+	0.909939i	$0.636129\pi$
$948$		0			0
$949$	46.0285	+	35.6748i	1.49415	+	1.15805i
$950$	−1.45997	−	0.113478i	−0.0473677	−	0.00368171i
$951$		0			0
$952$	23.0561	+	20.9223i	0.747253	+	0.678096i
$953$	−22.2455	+	29.8809i	−0.720602	+	0.967936i	0.279368	+	0.960184i	$0.409875\pi$
$953$	−22.2455	+	29.8809i	−0.720602	+	0.967936i	−0.999970	+	0.00775236i	$0.997532\pi$
$954$		0			0
$955$	20.9527	−	48.5737i	0.678012	−	1.57181i
$956$	−27.8307	−	19.8922i	−0.900108	−	0.643359i
$957$		0			0
$958$	−0.158901	+	8.19289i	−0.00513386	+	0.264700i
$959$	−4.46023	−	13.0355i	−0.144028	−	0.420939i
$960$		0			0
$961$	−16.8057	+	1.30624i	−0.542120	+	0.0421369i
$962$	1.27192	+	0.836556i	0.0410084	+	0.0269717i
$963$		0			0
$964$	−30.1436	−	15.1387i	−0.970860	−	0.487584i
$965$	7.43203	+	54.4121i	0.239246	+	1.75159i
$966$		0			0
$967$	−8.41733	−	3.82615i	−0.270683	−	0.123041i	0.273871	−	0.961767i	$-0.411696\pi$
$967$	−8.41733	−	3.82615i	−0.270683	−	0.123041i	−0.544554	+	0.838726i	$0.683301\pi$
$968$	9.32595	+	2.99025i	0.299747	+	0.0961102i
$969$		0			0
$970$	16.7538	+	2.62024i	0.537931	+	0.0841308i
$971$	3.52198			0.113026			0.0565129	−	0.998402i	$-0.482002\pi$
$971$	3.52198			0.113026			0.0565129	+	0.998402i	$0.482002\pi$
$972$		0			0
$973$	−6.36936			−0.204192
$974$	−7.33621	−	1.14736i	−0.235067	−	0.0367638i
$975$		0			0
$976$	−11.4280	−	3.66425i	−0.365802	−	0.117290i
$977$	−48.7265	−	22.1489i	−1.55890	−	0.708606i	−0.565654	−	0.824643i	$-0.691376\pi$
$977$	−48.7265	−	22.1489i	−1.55890	−	0.708606i	−0.993245	+	0.116036i	$0.962981\pi$
$978$		0			0
$979$	−4.05801	−	29.7099i	−0.129694	−	0.949531i
$980$	4.49910	+	2.25953i	0.143718	+	0.0721781i
$981$		0			0
$982$	−8.20345	−	5.39549i	−0.261783	−	0.172177i
$983$	36.6097	−	2.84553i	1.16767	−	0.0907583i	0.521018	−	0.853546i	$-0.325552\pi$
$983$	36.6097	−	2.84553i	1.16767	−	0.0907583i	0.646650	+	0.762787i	$0.276170\pi$
$984$		0			0
$985$	−14.9206	−	43.6072i	−0.475411	−	1.38944i
$986$	0.0322540	−	1.66301i	0.00102718	−	0.0529609i
$987$		0			0
$988$	−30.1131	−	21.5235i	−0.958024	−	0.684755i
$989$	10.1088	−	23.4348i	0.321440	−	0.745183i
$990$		0			0
$991$	−24.4255	+	32.8092i	−0.775902	+	1.04222i	0.221842	+	0.975083i	$0.428793\pi$
$991$	−24.4255	+	32.8092i	−0.775902	+	1.04222i	−0.997744	+	0.0671345i	$0.978614\pi$
$992$	−14.2331	−	12.9159i	−0.451902	−	0.410079i
$993$		0			0
$994$	13.9078	+	1.08100i	0.441130	+	0.0342873i
$995$	−40.3003	−	31.2351i	−1.27761	−	0.990220i
$996$		0			0
$997$	10.1685	+	11.6519i	0.322041	+	0.369018i	0.891515	−	0.452991i	$-0.149643\pi$
$997$	10.1685	+	11.6519i	0.322041	+	0.369018i	−0.569474	+	0.822009i	$0.692853\pi$
$998$	−0.130824	−	0.741940i	−0.00414116	−	0.0234857i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.11		1404
3.2	odd	2		243.2.i.a.13.16	✓	1404
243.56	odd	162		243.2.i.a.187.16	yes	1404
243.187	even	81	inner	729.2.i.a.73.11		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.16	✓	1404	3.2	odd	2
243.2.i.a.187.16	yes	1404	243.56	odd	162
729.2.i.a.10.11		1404	1.1	even	1	trivial
729.2.i.a.73.11		1404	243.187	even	81	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.506689 - 0.0792447i) q^{2} +(-1.65404 - 0.530347i) q^{4} +(-2.15085 - 0.977679i) q^{5} +(0.325167 + 2.38064i) q^{7} +(1.71265 + 0.860127i) q^{8} +O(q^{10})\)	\(q+(-0.506689 - 0.0792447i) q^{2} +(-1.65404 - 0.530347i) q^{4} +(-2.15085 - 0.977679i) q^{5} +(0.325167 + 2.38064i) q^{7} +(1.71265 + 0.860127i) q^{8} +(1.01233 + 0.665822i) q^{10} +(-4.00167 + 0.311035i) q^{11} +(1.40610 + 4.10947i) q^{13} +(0.0238949 - 1.23201i) q^{14} +(2.02664 + 1.44855i) q^{16} +(2.67793 - 6.20814i) q^{17} +(2.92979 - 3.93539i) q^{19} +(3.03908 + 2.75782i) q^{20} +(2.05225 + 0.159514i) q^{22} +(1.79471 + 1.39101i) q^{23} +(0.382672 + 0.438493i) q^{25} +(-0.386799 - 2.19365i) q^{26} +(0.724728 - 4.11013i) q^{28} +(-0.410704 + 0.247861i) q^{29} +(3.75797 - 0.145826i) q^{31} +(-3.64859 - 3.57851i) q^{32} +(-1.84884 + 2.93339i) q^{34} +(1.62812 - 5.43830i) q^{35} +(-0.469010 + 0.497121i) q^{37} +(-1.79635 + 1.76185i) q^{38} +(-2.84273 - 3.52443i) q^{40} +(2.01042 - 5.20712i) q^{41} +(-2.80371 - 10.8847i) q^{43} +(6.78389 + 1.60781i) q^{44} +(-0.799130 - 0.847029i) q^{46} +(9.70816 + 0.376721i) q^{47} +(1.18187 - 0.328995i) q^{49} +(-0.159147 - 0.252504i) q^{50} +(-0.146295 - 7.54295i) q^{52} +(1.71274 - 0.623385i) q^{53} +(8.91107 + 3.24337i) q^{55} +(-1.49076 + 4.35690i) q^{56} +(0.227741 - 0.0930423i) q^{58} +(-1.16596 - 2.43840i) q^{59} +(-4.58755 + 1.47094i) q^{61} +(-1.91568 - 0.223911i) q^{62} +(-1.41004 - 1.89401i) q^{64} +(0.993448 - 10.2135i) q^{65} +(13.7924 + 8.32375i) q^{67} +(-7.72188 + 8.84829i) q^{68} +(-1.25591 + 2.62651i) q^{70} +(-0.658236 + 11.3015i) q^{71} +(11.2020 - 7.36770i) q^{73} +(0.277036 - 0.214719i) q^{74} +(-6.93312 + 4.95549i) q^{76} +(-2.04167 - 9.42542i) q^{77} +(-0.666324 + 0.826113i) q^{79} +(-2.94276 - 5.09701i) q^{80} +(-1.43129 + 2.47907i) q^{82} +(3.05886 + 7.92264i) q^{83} +(-11.8294 + 10.7346i) q^{85} +(0.558056 + 5.73732i) q^{86} +(-7.12101 - 2.90925i) q^{88} +(0.434386 + 7.45812i) q^{89} +(-9.32596 + 4.68367i) q^{91} +(-2.23081 - 3.25260i) q^{92} +(-4.88916 - 0.960201i) q^{94} +(-10.1491 + 5.60002i) q^{95} +(12.7406 - 5.79132i) q^{97} +(-0.624910 + 0.0730416i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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