LMFDB - Embedded newform 841.2.d.m.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(190,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("841.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.2
Character	$\chi$	$=$	841.190
Dual form			841.2.d.m.571.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.154074 - 0.0741982i) q^{2} +(-0.701005 + 0.879032i) q^{3} +(-1.22875 - 1.54080i) q^{4} +(2.54740 + 1.22676i) q^{5} +(0.173229 - 0.0834229i) q^{6} +(-1.82432 + 2.28763i) q^{7} +(0.151100 + 0.662012i) q^{8} +(0.386273 + 1.69237i) q^{9} +O(q^{10})$	\(q+(-0.154074 - 0.0741982i) q^{2} +(-0.701005 + 0.879032i) q^{3} +(-1.22875 - 1.54080i) q^{4} +(2.54740 + 1.22676i) q^{5} +(0.173229 - 0.0834229i) q^{6} +(-1.82432 + 2.28763i) q^{7} +(0.151100 + 0.662012i) q^{8} +(0.386273 + 1.69237i) q^{9} +(-0.301465 - 0.378025i) q^{10} +(0.888454 - 3.89257i) q^{11} +2.21577 q^{12} +(-0.625512 + 2.74055i) q^{13} +(0.450819 - 0.217103i) q^{14} +(-2.86411 + 1.37928i) q^{15} +(-0.851229 + 3.72948i) q^{16} +0.482650 q^{17} +(0.0660563 - 0.289412i) q^{18} +(-1.90144 - 2.38432i) q^{19} +(-1.23991 - 5.43242i) q^{20} +(-0.732040 - 3.20728i) q^{21} +(-0.425710 + 0.533823i) q^{22} +(-4.96829 + 2.39260i) q^{23} +(-0.687851 - 0.331252i) q^{24} +(1.86686 + 2.34097i) q^{25} +(0.299719 - 0.375836i) q^{26} +(-4.79737 - 2.31029i) q^{27} +5.76640 q^{28} +0.543625 q^{30} +(3.47275 + 1.67239i) q^{31} +(1.25462 - 1.57324i) q^{32} +(2.79888 + 3.50969i) q^{33} +(-0.0743639 - 0.0358118i) q^{34} +(-7.45366 + 3.58950i) q^{35} +(2.13297 - 2.67467i) q^{36} +(2.56868 + 11.2541i) q^{37} +(0.116049 + 0.508446i) q^{38} +(-1.97054 - 2.47098i) q^{39} +(-0.427220 + 1.87177i) q^{40} -5.10756 q^{41} +(-0.125186 + 0.548475i) q^{42} +(-7.40439 + 3.56577i) q^{43} +(-7.08936 + 3.41405i) q^{44} +(-1.09215 + 4.78502i) q^{45} +0.943011 q^{46} +(-0.531276 + 2.32767i) q^{47} +(-2.68162 - 3.36264i) q^{48} +(-0.347443 - 1.52225i) q^{49} +(-0.113939 - 0.499200i) q^{50} +(-0.338340 + 0.424265i) q^{51} +(4.99123 - 2.40365i) q^{52} +(0.401975 + 0.193581i) q^{53} +(0.567732 + 0.711913i) q^{54} +(7.03852 - 8.82602i) q^{55} +(-1.79009 - 0.862063i) q^{56} +3.42881 q^{57} +1.24537 q^{59} +(5.64445 + 2.71823i) q^{60} +(-5.35677 + 6.71717i) q^{61} +(-0.410973 - 0.515344i) q^{62} +(-4.57621 - 2.20378i) q^{63} +(6.58308 - 3.17024i) q^{64} +(-4.95544 + 6.21392i) q^{65} +(-0.170823 - 0.748425i) q^{66} +(0.210269 + 0.921249i) q^{67} +(-0.593055 - 0.743667i) q^{68} +(1.37962 - 6.04451i) q^{69} +1.41475 q^{70} +(-1.33021 + 5.82802i) q^{71} +(-1.06201 + 0.511435i) q^{72} +(-0.435458 + 0.209705i) q^{73} +(0.439268 - 1.92456i) q^{74} -3.36646 q^{75} +(-1.33738 + 5.85946i) q^{76} +(7.28393 + 9.13376i) q^{77} +(0.120267 + 0.526925i) q^{78} +(-0.411944 - 1.80484i) q^{79} +(-6.74361 + 8.45623i) q^{80} +(0.701839 - 0.337988i) q^{81} +(0.786943 + 0.378972i) q^{82} +(2.71744 + 3.40756i) q^{83} +(-4.04228 + 5.06885i) q^{84} +(1.22950 + 0.592098i) q^{85} +1.40540 q^{86} +2.71117 q^{88} +(-14.0167 - 6.75011i) q^{89} +(0.523312 - 0.656213i) q^{90} +(-5.12822 - 6.43058i) q^{91} +(9.79128 + 4.71523i) q^{92} +(-3.90450 + 1.88031i) q^{93} +(0.254565 - 0.319215i) q^{94} +(-1.91872 - 8.40645i) q^{95} +(0.503437 + 2.20570i) q^{96} +(1.50675 + 1.88941i) q^{97} +(-0.0594161 + 0.260319i) q^{98} +6.93087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{4} + 2 q^{5} + 6 q^{6} - 22 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q + 2 * q^4 + 2 * q^5 + 6 * q^6 - 22 * q^7 + 6 * q^9	$ 24 q + 2 q^{4} + 2 q^{5} + 6 q^{6} - 22 q^{7} + 6 q^{9} - 18 q^{13} + 18 q^{16} - 22 q^{20} + 8 q^{22} - 10 q^{23} - 50 q^{24} + 26 q^{25} - 24 q^{28} + 4 q^{30} + 34 q^{33} + 26 q^{34} - 38 q^{35} - 80 q^{36} - 56 q^{38} - 100 q^{42} + 32 q^{45} + 26 q^{49} - 40 q^{51} - 12 q^{52} - 20 q^{53} - 76 q^{54} + 28 q^{57} + 88 q^{59} - 74 q^{62} + 26 q^{63} + 52 q^{64} - 12 q^{65} + 74 q^{67} + 42 q^{71} + 34 q^{78} + 12 q^{80} + 2 q^{81} + 44 q^{82} + 10 q^{83} + 88 q^{86} - 132 q^{88} + 6 q^{91} + 12 q^{92} - 38 q^{93} + 132 q^{94} - 60 q^{96}+O(q^{100}) $ 24 * q + 2 * q^4 + 2 * q^5 + 6 * q^6 - 22 * q^7 + 6 * q^9 - 18 * q^13 + 18 * q^16 - 22 * q^20 + 8 * q^22 - 10 * q^23 - 50 * q^24 + 26 * q^25 - 24 * q^28 + 4 * q^30 + 34 * q^33 + 26 * q^34 - 38 * q^35 - 80 * q^36 - 56 * q^38 - 100 * q^42 + 32 * q^45 + 26 * q^49 - 40 * q^51 - 12 * q^52 - 20 * q^53 - 76 * q^54 + 28 * q^57 + 88 * q^59 - 74 * q^62 + 26 * q^63 + 52 * q^64 - 12 * q^65 + 74 * q^67 + 42 * q^71 + 34 * q^78 + 12 * q^80 + 2 * q^81 + 44 * q^82 + 10 * q^83 + 88 * q^86 - 132 * q^88 + 6 * q^91 + 12 * q^92 - 38 * q^93 + 132 * q^94 - 60 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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 $

$2$	−0.154074	−	0.0741982i	−0.108947	−	0.0524661i	0.378617	−	0.925554i	$-0.376400\pi$
$2$	−0.154074	−	0.0741982i	−0.108947	−	0.0524661i	−0.487563	+	0.873088i	$0.662114\pi$
$3$	−0.701005	+	0.879032i	−0.404725	+	0.507509i	−0.941869	−	0.335982i	$-0.890932\pi$
$3$	−0.701005	+	0.879032i	−0.404725	+	0.507509i	0.537143	+	0.843491i	$0.319503\pi$
$4$	−1.22875	−	1.54080i	−0.614373	−	0.770399i
$5$	2.54740	+	1.22676i	1.13923	+	0.548626i	0.905782	−	0.423743i	$-0.139284\pi$
$5$	2.54740	+	1.22676i	1.13923	+	0.548626i	0.233450	+	0.972369i	$0.424998\pi$
$6$	0.173229	−	0.0834229i	0.0707206	−	0.0340572i
$7$	−1.82432	+	2.28763i	−0.689529	+	0.864642i	−0.996193	−	0.0871757i	$-0.972216\pi$
$7$	−1.82432	+	2.28763i	−0.689529	+	0.864642i	0.306664	+	0.951818i	$0.400787\pi$
$8$	0.151100	+	0.662012i	0.0534219	+	0.234057i
$9$	0.386273	+	1.69237i	0.128758	+	0.564124i
$10$	−0.301465	−	0.378025i	−0.0953317	−	0.119542i
$11$	0.888454	−	3.89257i	0.267879	−	1.17365i	−0.644596	−	0.764523i	$-0.722975\pi$
$11$	0.888454	−	3.89257i	0.267879	−	1.17365i	0.912475	−	0.409132i	$-0.134168\pi$
$12$	2.21577			0.639637
$13$	−0.625512	+	2.74055i	−0.173486	+	0.760091i	0.811060	+	0.584963i	$0.198891\pi$
$13$	−0.625512	+	2.74055i	−0.173486	+	0.760091i	−0.984546	+	0.175128i	$0.943966\pi$
$14$	0.450819	−	0.217103i	0.120486	−	0.0580232i
$15$	−2.86411	+	1.37928i	−0.739509	+	0.356129i
$16$	−0.851229	+	3.72948i	−0.212807	+	0.932370i
$17$	0.482650			0.117060			0.0585299	−	0.998286i	$-0.481359\pi$
$17$	0.482650			0.117060			0.0585299	+	0.998286i	$0.481359\pi$
$18$	0.0660563	−	0.289412i	0.0155696	−	0.0682150i
$19$	−1.90144	−	2.38432i	−0.436219	−	0.547002i	0.514323	−	0.857596i	$-0.328043\pi$
$19$	−1.90144	−	2.38432i	−0.436219	−	0.547002i	−0.950542	+	0.310595i	$0.899472\pi$
$20$	−1.23991	−	5.43242i	−0.277253	−	1.21473i
$21$	−0.732040	−	3.20728i	−0.159744	−	0.699885i
$22$	−0.425710	+	0.533823i	−0.0907616	+	0.113811i
$23$	−4.96829	+	2.39260i	−1.03596	+	0.498892i	−0.872989	−	0.487739i	$-0.837822\pi$
$23$	−4.96829	+	2.39260i	−1.03596	+	0.498892i	−0.162970	+	0.986631i	$0.552107\pi$
$24$	−0.687851	−	0.331252i	−0.140407	−	0.0676165i
$25$	1.86686	+	2.34097i	0.373372	+	0.468193i
$26$	0.299719	−	0.375836i	0.0587797	−	0.0737075i
$27$	−4.79737	−	2.31029i	−0.923255	−	0.444616i
$28$	5.76640			1.08975
$29$		0			0
$29$		0			0
$30$	0.543625			0.0992519
$31$	3.47275	+	1.67239i	0.623724	+	0.300370i	0.718924	−	0.695088i	$-0.244635\pi$
$31$	3.47275	+	1.67239i	0.623724	+	0.300370i	−0.0952000	+	0.995458i	$0.530349\pi$
$32$	1.25462	−	1.57324i	0.221787	−	0.278112i
$33$	2.79888	+	3.50969i	0.487223	+	0.610959i
$34$	−0.0743639	−	0.0358118i	−0.0127533	−	0.00614167i
$35$	−7.45366	+	3.58950i	−1.25990	+	0.606735i
$36$	2.13297	−	2.67467i	0.355496	−	0.445778i
$37$	2.56868	+	11.2541i	0.422288	+	1.85016i	0.518891	+	0.854840i	$0.326345\pi$
$37$	2.56868	+	11.2541i	0.422288	+	1.85016i	−0.0966033	+	0.995323i	$0.530798\pi$
$38$	0.116049	+	0.508446i	0.0188257	+	0.0824808i
$39$	−1.97054	−	2.47098i	−0.315539	−	0.395674i
$40$	−0.427220	+	1.87177i	−0.0675495	+	0.295954i
$41$	−5.10756			−0.797667			−0.398833	−	0.917023i	$-0.630585\pi$
$41$	−5.10756			−0.797667			−0.398833	+	0.917023i	$0.630585\pi$
$42$	−0.125186	+	0.548475i	−0.0193166	+	0.0846315i
$43$	−7.40439	+	3.56577i	−1.12916	+	0.543775i	−0.902711	−	0.430248i	$-0.858426\pi$
$43$	−7.40439	+	3.56577i	−1.12916	+	0.543775i	−0.226449	+	0.974023i	$0.572712\pi$
$44$	−7.08936	+	3.41405i	−1.06876	+	0.514688i
$45$	−1.09215	+	4.78502i	−0.162808	+	0.713309i
$46$	0.943011			0.139039
$47$	−0.531276	+	2.32767i	−0.0774946	+	0.339526i	−0.998781	−	0.0493584i	$-0.984282\pi$
$47$	−0.531276	+	2.32767i	−0.0774946	+	0.339526i	0.921287	+	0.388885i	$0.127139\pi$
$48$	−2.68162	−	3.36264i	−0.387058	−	0.485355i
$49$	−0.347443	−	1.52225i	−0.0496347	−	0.217464i
$50$	−0.113939	−	0.499200i	−0.0161134	−	0.0705975i
$51$	−0.338340	+	0.424265i	−0.0473771	+	0.0594090i
$52$	4.99123	−	2.40365i	0.692159	−	0.333326i
$53$	0.401975	+	0.193581i	0.0552156	+	0.0265904i	0.461288	−	0.887251i	$-0.347388\pi$
$53$	0.401975	+	0.193581i	0.0552156	+	0.0265904i	−0.406072	+	0.913841i	$0.633102\pi$
$54$	0.567732	+	0.711913i	0.0772585	+	0.0968791i
$55$	7.03852	−	8.82602i	0.949074	−	1.19010i
$56$	−1.79009	−	0.862063i	−0.239211	−	0.115198i
$57$	3.42881			0.454157
$58$		0			0
$59$	1.24537			0.162133			0.0810664	−	0.996709i	$-0.474167\pi$
$59$	1.24537			0.162133			0.0810664	+	0.996709i	$0.474167\pi$
$60$	5.64445	+	2.71823i	0.728696	+	0.350921i
$61$	−5.35677	+	6.71717i	−0.685864	+	0.860046i	−0.995880	−	0.0906856i	$-0.971094\pi$
$61$	−5.35677	+	6.71717i	−0.685864	+	0.860046i	0.310016	+	0.950731i	$0.399666\pi$
$62$	−0.410973	−	0.515344i	−0.0521936	−	0.0654487i
$63$	−4.57621	−	2.20378i	−0.576548	−	0.277651i
$64$	6.58308	−	3.17024i	0.822885	−	0.396280i
$65$	−4.95544	+	6.21392i	−0.614646	+	0.770742i
$66$	−0.170823	−	0.748425i	−0.0210269	−	0.0921248i
$67$	0.210269	+	0.921249i	0.0256885	+	0.112548i	0.986147	−	0.165876i	$-0.0530450\pi$
$67$	0.210269	+	0.921249i	0.0256885	+	0.112548i	−0.960458	+	0.278424i	$0.910188\pi$
$68$	−0.593055	−	0.743667i	−0.0719184	−	0.0901829i
$69$	1.37962	−	6.04451i	0.166087	−	0.727673i
$70$	1.41475			0.169095
$71$	−1.33021	+	5.82802i	−0.157867	+	0.691659i	0.832597	+	0.553880i	$0.186853\pi$
$71$	−1.33021	+	5.82802i	−0.157867	+	0.691659i	−0.990463	+	0.137779i	$0.956004\pi$
$72$	−1.06201	+	0.511435i	−0.125158	+	0.0602732i
$73$	−0.435458	+	0.209705i	−0.0509665	+	0.0245442i	−0.459193	−	0.888336i	$-0.651862\pi$
$73$	−0.435458	+	0.209705i	−0.0509665	+	0.0245442i	0.408227	+	0.912880i	$0.366147\pi$
$74$	0.439268	−	1.92456i	0.0510639	−	0.223725i
$75$	−3.36646			−0.388725
$76$	−1.33738	+	5.85946i	−0.153408	+	0.672126i
$77$	7.28393	+	9.13376i	0.830081	+	1.04089i
$78$	0.120267	+	0.526925i	0.0136176	+	0.0596625i
$79$	−0.411944	−	1.80484i	−0.0463473	−	0.203061i	0.946453	−	0.322841i	$-0.104638\pi$
$79$	−0.411944	−	1.80484i	−0.0463473	−	0.203061i	−0.992800	+	0.119781i	$0.961781\pi$
$80$	−6.74361	+	8.45623i	−0.753959	+	0.945435i
$81$	0.701839	−	0.337988i	0.0779821	−	0.0375542i
$82$	0.786943	+	0.378972i	0.0869033	+	0.0418504i
$83$	2.71744	+	3.40756i	0.298277	+	0.374028i	0.908274	−	0.418376i	$-0.137401\pi$
$83$	2.71744	+	3.40756i	0.298277	+	0.374028i	−0.609996	+	0.792404i	$0.708829\pi$
$84$	−4.04228	+	5.06885i	−0.441048	+	0.553057i
$85$	1.22950	+	0.592098i	0.133358	+	0.0642220i
$86$	1.40540			0.151548
$87$		0			0
$88$	2.71117			0.289012
$89$	−14.0167	−	6.75011i	−1.48577	−	0.715510i	−0.497394	−	0.867525i	$-0.665710\pi$
$89$	−14.0167	−	6.75011i	−1.48577	−	0.715510i	−0.988378	+	0.152015i	$0.951424\pi$
$90$	0.523312	−	0.656213i	0.0551619	−	0.0691709i
$91$	−5.12822	−	6.43058i	−0.537583	−	0.674108i
$92$	9.79128	+	4.71523i	1.02081	+	0.491597i
$93$	−3.90450	+	1.88031i	−0.404878	+	0.194979i
$94$	0.254565	−	0.319215i	0.0262564	−	0.0329245i
$95$	−1.91872	−	8.40645i	−0.196856	−	0.862483i
$96$	0.503437	+	2.20570i	0.0513818	+	0.225118i
$97$	1.50675	+	1.88941i	0.152988	+	0.191840i	0.852419	−	0.522859i	$-0.175135\pi$
$97$	1.50675	+	1.88941i	0.152988	+	0.191840i	−0.699431	+	0.714700i	$0.746563\pi$
$98$	−0.0594161	+	0.260319i	−0.00600193	+	0.0262962i
$99$	6.93087			0.696578
$100$	1.31306	−	5.75291i	0.131306	−	0.575291i
$101$	12.1583	−	5.85513i	1.20980	−	0.582607i	0.283344	−	0.959018i	$-0.408556\pi$
$101$	12.1583	−	5.85513i	1.20980	−	0.582607i	0.926453	+	0.376411i	$0.122842\pi$
$102$	0.0836092	−	0.0402641i	0.00827854	−	0.00398674i
$103$	−0.389459	+	1.70633i	−0.0383745	+	0.168130i	−0.990484	−	0.137627i	$-0.956052\pi$
$103$	−0.389459	+	1.70633i	−0.0383745	+	0.168130i	0.952110	+	0.305757i	$0.0989095\pi$
$104$	−1.90879			−0.187172
$105$	2.06977	−	9.06826i	0.201989	−	0.884972i
$106$	−0.0475707	−	0.0596517i	−0.00462047	−	0.00579389i
$107$	0.580401	+	2.54290i	0.0561095	+	0.245832i	0.995203	−	0.0978294i	$-0.0311900\pi$
$107$	0.580401	+	2.54290i	0.0561095	+	0.245832i	−0.939094	+	0.343661i	$0.888333\pi$
$108$	2.33506	+	10.2305i	0.224691	+	0.984435i
$109$	5.70347	−	7.15192i	0.546293	−	0.685030i	−0.429665	−	0.902988i	$-0.641368\pi$
$109$	5.70347	−	7.15192i	0.546293	−	0.685030i	0.975958	+	0.217959i	$0.0699398\pi$
$110$	−1.73933	+	0.837617i	−0.165839	+	0.0798636i
$111$	−11.6934	−	5.63123i	−1.10989	−	0.534493i
$112$	−6.97874	−	8.75107i	−0.659429	−	0.826898i
$113$	−7.92375	+	9.93607i	−0.745404	+	0.934706i	−0.999472	−	0.0324796i	$-0.989660\pi$
$113$	−7.92375	+	9.93607i	−0.745404	+	0.934706i	0.254069	+	0.967186i	$0.418231\pi$
$114$	−0.528292	−	0.254412i	−0.0494790	−	0.0238278i
$115$	−15.5914			−1.45390
$116$		0			0
$117$	−4.87965			−0.451123
$118$	−0.191879	−	0.0924039i	−0.0176639	−	0.00850647i
$119$	−0.880510	+	1.10412i	−0.0807162	+	0.101215i
$120$	−1.34587	−	1.68766i	−0.122860	−	0.154062i
$121$	−4.45211	−	2.14402i	−0.404737	−	0.194911i
$122$	1.32374	−	0.637480i	0.119846	−	0.0577148i
$123$	3.58042	−	4.48971i	0.322836	−	0.404823i
$124$	−1.69031	−	7.40575i	−0.151795	−	0.665056i
$125$	−1.26196	−	5.52899i	−0.112873	−	0.494528i
$126$	0.541558	+	0.679093i	0.0482459	+	0.0604984i
$127$	−0.254762	+	1.11618i	−0.0226064	+	0.0990453i	−0.984973	−	0.172711i	$-0.944747\pi$
$127$	−0.254762	+	1.11618i	−0.0226064	+	0.0990453i	0.962366	+	0.271756i	$0.0876045\pi$
$128$	−5.27401			−0.466161
$129$	2.05609	−	9.00832i	0.181029	−	0.793138i
$130$	1.22457	−	0.589720i	0.107402	−	0.0517219i
$131$	15.7567	−	7.58804i	1.37667	−	0.662970i	0.408385	−	0.912810i	$-0.366092\pi$
$131$	15.7567	−	7.58804i	1.37667	−	0.662970i	0.968287	+	0.249840i	$0.0803780\pi$
$132$	1.96861	−	8.62504i	0.171345	−	0.750713i
$133$	8.92328			0.773746
$134$	0.0359580	−	0.157542i	0.00310630	−	0.0136096i
$135$	−9.38665	−	11.7705i	−0.807874	−	1.01304i
$136$	0.0729284	+	0.319520i	0.00625356	+	0.0273986i
$137$	−0.211198	−	0.925317i	−0.0180438	−	0.0790552i	0.965104	−	0.261866i	$-0.0843377\pi$
$137$	−0.211198	−	0.925317i	−0.0180438	−	0.0790552i	−0.983148	+	0.182810i	$0.941481\pi$
$138$	−0.661055	+	0.828937i	−0.0562728	+	0.0705638i
$139$	−6.53941	+	3.14921i	−0.554665	+	0.267113i	−0.690150	−	0.723667i	$-0.742455\pi$
$139$	−6.53941	+	3.14921i	−0.554665	+	0.267113i	0.135484	+	0.990779i	$0.456741\pi$
$140$	14.6893	+	7.07402i	1.24148	+	0.597864i
$141$	−1.67367	−	2.09872i	−0.140949	−	0.176744i
$142$	0.637379	−	0.799248i	0.0534877	−	0.0670714i
$143$	10.1120	+	4.86970i	0.845611	+	0.407225i
$144$	−6.64048			−0.553373
$145$		0			0
$146$	0.0826526			0.00684038
$147$	1.58166	+	0.761689i	0.130453	+	0.0628231i
$148$	14.1841	−	17.7863i	1.16592	−	1.46202i
$149$	10.6334	+	13.3339i	0.871126	+	1.09236i	0.994982	+	0.100057i	$0.0319026\pi$
$149$	10.6334	+	13.3339i	0.871126	+	1.09236i	−0.123856	+	0.992300i	$0.539526\pi$
$150$	0.518685	+	0.249785i	0.0423504	+	0.0203949i
$151$	8.86929	−	4.27122i	0.721772	−	0.347587i	−0.0366700	−	0.999327i	$-0.511675\pi$
$151$	8.86929	−	4.27122i	0.721772	−	0.347587i	0.758442	+	0.651740i	$0.225961\pi$
$152$	1.29114	−	1.61904i	0.104726	−	0.131322i
$153$	0.186435	+	0.816824i	0.0150724	+	0.0660363i
$154$	−0.444557	−	1.94773i	−0.0358234	−	0.156953i
$155$	6.79487	+	8.52049i	0.545777	+	0.684382i
$156$	−1.38599	+	6.07242i	−0.110968	+	0.486183i
$157$	2.64062			0.210744			0.105372	−	0.994433i	$-0.466397\pi$
$157$	2.64062			0.210744			0.105372	+	0.994433i	$0.466397\pi$
$158$	−0.0704463	+	0.308645i	−0.00560440	+	0.0245545i
$159$	−0.451951	+	0.217648i	−0.0358420	+	0.0172606i
$160$	5.12601	−	2.46856i	0.405247	−	0.195157i
$161$	3.59038	−	15.7305i	0.282961	−	1.23973i
$162$	−0.133213			−0.0104662
$163$	2.17559	−	9.53190i	0.170406	−	0.746596i	−0.815426	−	0.578861i	$-0.803498\pi$
$163$	2.17559	−	9.53190i	0.170406	−	0.746596i	0.985832	−	0.167735i	$-0.0536453\pi$
$164$	6.27589	+	7.86972i	0.490065	+	0.614522i
$165$	2.82432	+	12.3742i	0.219873	+	0.963327i
$166$	−0.165852	−	0.726646i	−0.0128726	−	0.0563987i
$167$	14.7231	−	18.4622i	1.13931	−	1.42865i	0.251847	−	0.967767i	$-0.418962\pi$
$167$	14.7231	−	18.4622i	1.13931	−	1.42865i	0.887462	−	0.460881i	$-0.152467\pi$
$168$	2.01264	−	0.969238i	0.155279	−	0.0747784i
$169$	4.59326	+	2.21200i	0.353328	+	0.170154i
$170$	−0.145502	−	0.182454i	−0.0111595	−	0.0139936i
$171$	3.30069	−	4.13894i	0.252410	−	0.316512i
$172$	14.5923	+	7.02726i	1.11265	+	0.535823i
$173$	5.22521			0.397265			0.198633	−	0.980074i	$-0.436350\pi$
$173$	5.22521			0.397265			0.198633	+	0.980074i	$0.436350\pi$
$174$		0			0
$175$	−8.76101			−0.662270
$176$	13.7610	+	6.62694i	1.03727	+	0.499525i
$177$	−0.873007	+	1.09472i	−0.0656192	+	0.0822839i
$178$	1.65877	+	2.08004i	0.124330	+	0.155905i
$179$	−10.2128	−	4.91824i	−0.763343	−	0.367607i	0.0113570	−	0.999936i	$-0.496385\pi$
$179$	−10.2128	−	4.91824i	−0.763343	−	0.367607i	−0.774700	+	0.632329i	$0.782099\pi$
$180$	8.71473	−	4.19679i	0.649557	−	0.312810i
$181$	6.44743	−	8.08482i	0.479233	−	0.600940i	−0.482172	−	0.876077i	$-0.660152\pi$
$181$	6.44743	−	8.08482i	0.479233	−	0.600940i	0.961405	+	0.275137i	$0.0887232\pi$
$182$	0.312988	+	1.37129i	0.0232002	+	0.101647i
$183$	−2.14949	−	9.41754i	−0.158895	−	0.696164i
$184$	−2.33464	−	2.92754i	−0.172112	−	0.215821i
$185$	−7.26268	+	31.8199i	−0.533963	+	2.33944i
$186$	0.741098			0.0543399
$187$	0.428813	−	1.87875i	0.0313579	−	0.137388i
$188$	4.23928	−	2.04153i	0.309181	−	0.148894i
$189$	14.0370	−	6.75988i	1.02104	−	0.491709i
$190$	−0.328119	+	1.43758i	−0.0238042	+	0.104293i
$191$	6.30617			0.456299			0.228149	−	0.973626i	$-0.426733\pi$
$191$	6.30617			0.456299			0.228149	+	0.973626i	$0.426733\pi$
$192$	−1.82802	+	8.00909i	−0.131926	+	0.578006i
$193$	2.55769	+	3.20725i	0.184107	+	0.230863i	0.865317	−	0.501226i	$-0.167117\pi$
$193$	2.55769	+	3.20725i	0.184107	+	0.230863i	−0.681210	+	0.732088i	$0.738546\pi$
$194$	−0.0919610	−	0.402908i	−0.00660242	−	0.0289271i
$195$	−1.98845	−	8.71198i	−0.142396	−	0.623878i
$196$	−1.91856	+	2.40580i	−0.137040	+	0.171843i
$197$	18.3245	−	8.82462i	1.30557	−	0.628728i	0.353735	−	0.935346i	$-0.384912\pi$
$197$	18.3245	−	8.82462i	1.30557	−	0.628728i	0.951833	+	0.306618i	$0.0991974\pi$
$198$	−1.06787	−	0.514258i	−0.0758901	−	0.0365467i
$199$	−1.22899	−	1.54111i	−0.0871211	−	0.109246i	0.736360	−	0.676589i	$-0.236543\pi$
$199$	−1.22899	−	1.54111i	−0.0871211	−	0.109246i	−0.823482	+	0.567343i	$0.807971\pi$
$200$	−1.26767	+	1.58960i	−0.0896375	+	0.112402i
$201$	−0.957207	−	0.460967i	−0.0675162	−	0.0325141i
$202$	−2.30772			−0.162371
$203$		0			0
$204$	1.06944			0.0748758
$205$	−13.0110	−	6.26577i	−0.908728	−	0.437620i
$206$	0.186612	−	0.234004i	0.0130019	−	0.0163038i
$207$	−5.96829	−	7.48399i	−0.414825	−	0.520173i
$208$	−9.68836	−	4.66567i	−0.671767	−	0.323506i
$209$	−10.9705	+	5.28311i	−0.758845	+	0.365440i
$210$	−0.991747	+	1.24361i	−0.0684371	+	0.0858174i
$211$	−3.96080	−	17.3534i	−0.272673	−	1.19466i	−0.906844	−	0.421466i	$-0.861516\pi$
$211$	−3.96080	−	17.3534i	−0.272673	−	1.19466i	0.634172	−	0.773192i	$-0.281341\pi$
$212$	−0.195656	−	0.857226i	−0.0134377	−	0.0588745i
$213$	−4.19053	−	5.25476i	−0.287131	−	0.360050i
$214$	0.0992541	−	0.434861i	0.00678487	−	0.0297265i
$215$	−23.2363			−1.58470
$216$	0.804559	−	3.52500i	0.0547433	−	0.239846i
$217$	−10.1612	+	4.89339i	−0.689789	+	0.332185i
$218$	−1.40942	+	0.678739i	−0.0954577	+	0.0459700i
$219$	0.120920	−	0.529786i	0.00817103	−	0.0357996i
$220$	−22.2477			−1.49994
$221$	−0.301904	+	1.32273i	−0.0203082	+	0.0889762i
$222$	1.38382	+	1.73526i	0.0928759	+	0.116463i
$223$	4.22512	+	18.5115i	0.282935	+	1.23962i	0.894010	+	0.448047i	$0.147880\pi$
$223$	4.22512	+	18.5115i	0.282935	+	1.23962i	−0.611075	+	0.791572i	$0.709263\pi$
$224$	1.31016	+	5.74020i	0.0875390	+	0.383533i
$225$	−3.24067	+	4.06367i	−0.216045	+	0.270911i
$226$	1.95808	−	0.942963i	0.130250	−	0.0627250i
$227$	−0.0933811	−	0.0449699i	−0.00619792	−	0.00298476i	0.430782	−	0.902456i	$-0.358238\pi$
$227$	−0.0933811	−	0.0449699i	−0.00619792	−	0.00298476i	−0.436980	+	0.899471i	$0.643952\pi$
$228$	−4.21314	−	5.28311i	−0.279022	−	0.349883i
$229$	−8.23049	+	10.3207i	−0.543886	+	0.682012i	−0.975488	−	0.220053i	$-0.929377\pi$
$229$	−8.23049	+	10.3207i	−0.543886	+	0.682012i	0.431602	+	0.902064i	$0.357949\pi$
$230$	2.40223	+	1.15685i	0.158398	+	0.0762806i
$231$	−13.1349			−0.864215
$232$		0			0
$233$	−2.18750			−0.143308			−0.0716538	−	0.997430i	$-0.522828\pi$
$233$	−2.18750			−0.143308			−0.0716538	+	0.997430i	$0.522828\pi$
$234$	0.751828	+	0.362061i	0.0491485	+	0.0236687i
$235$	−4.20888	+	5.27777i	−0.274557	+	0.344284i
$236$	−1.53024	−	1.91886i	−0.0996100	−	0.124907i
$237$	1.87529	+	0.903092i	0.121813	+	0.0586621i
$238$	0.217588	−	0.104785i	0.0141041	−	0.00679219i
$239$	9.54386	−	11.9676i	0.617341	−	0.774121i	−0.370627	−	0.928782i	$-0.620857\pi$
$239$	9.54386	−	11.9676i	0.617341	−	0.774121i	0.987968	+	0.154661i	$0.0494285\pi$
$240$	−2.70599	−	11.8557i	−0.174671	−	0.765283i
$241$	3.02515	+	13.2541i	0.194867	+	0.853768i	0.973935	+	0.226829i	$0.0728357\pi$
$241$	3.02515	+	13.2541i	0.194867	+	0.853768i	−0.779068	+	0.626940i	$0.784307\pi$
$242$	0.526872	+	0.660677i	0.0338686	+	0.0424699i
$243$	3.35967	−	14.7197i	0.215523	−	0.944267i
$244$	16.9319			1.08395
$245$	0.982362	−	4.30401i	0.0627608	−	0.274973i
$246$	−0.884779	+	0.426087i	−0.0564115	+	0.0271663i
$247$	7.72373	−	3.71955i	0.491449	−	0.236669i
$248$	−0.582409	+	2.55170i	−0.0369830	+	0.162033i
$249$	−4.90029			−0.310543
$250$	−0.215807	+	0.945510i	−0.0136488	+	0.0597993i
$251$	12.8046	+	16.0564i	0.808216	+	1.01347i	0.999490	+	0.0319344i	$0.0101668\pi$
$251$	12.8046	+	16.0564i	0.808216	+	1.01347i	−0.191274	+	0.981537i	$0.561262\pi$
$252$	2.22741	+	9.75890i	0.140313	+	0.614753i
$253$	4.89927	+	21.4651i	0.308015	+	1.34950i
$254$	0.122071	−	0.153072i	0.00765942	−	0.00960461i
$255$	−1.38236	+	0.665710i	−0.0865668	+	0.0416884i
$256$	−12.3536	−	5.94916i	−0.772098	−	0.371823i
$257$	12.3518	+	15.4887i	0.770486	+	0.966159i	0.999974	−	0.00715224i	$-0.00227665\pi$
$257$	12.3518	+	15.4887i	0.770486	+	0.966159i	−0.229488	+	0.973311i	$0.573705\pi$
$258$	−0.985192	+	1.23539i	−0.0613354	+	0.0769121i
$259$	−30.4313	−	14.6549i	−1.89091	−	0.910614i
$260$	15.6634			0.971401
$261$		0			0
$262$	−2.99072			−0.184768
$263$	−13.3960	−	6.45116i	−0.826031	−	0.397796i	−0.0274060	−	0.999624i	$-0.508725\pi$
$263$	−13.3960	−	6.45116i	−0.826031	−	0.397796i	−0.798625	+	0.601829i	$0.794439\pi$
$264$	−1.90055	+	2.38321i	−0.116971	+	0.146676i
$265$	0.786515	+	0.986258i	0.0483152	+	0.0605854i
$266$	−1.37485	−	0.662091i	−0.0842973	−	0.0405954i
$267$	15.7594	−	7.58931i	0.964458	−	0.464458i
$268$	1.16109	−	1.45596i	0.0709250	−	0.0889371i
$269$	−0.346436	−	1.51784i	−0.0211226	−	0.0925441i	0.963268	−	0.268542i	$-0.0865419\pi$
$269$	−0.346436	−	1.51784i	−0.0211226	−	0.0925441i	−0.984391	+	0.175998i	$0.943685\pi$
$270$	0.572892	+	2.51000i	0.0348651	+	0.152754i
$271$	7.57624	+	9.50030i	0.460224	+	0.577102i	0.956747	−	0.290921i	$-0.0939618\pi$
$271$	7.57624	+	9.50030i	0.460224	+	0.577102i	−0.496523	+	0.868023i	$0.665390\pi$
$272$	−0.410846	+	1.80003i	−0.0249112	+	0.109143i
$273$	9.24759			0.559690
$274$	−0.0361168	+	0.158238i	−0.00218189	+	0.00955950i
$275$	10.7710	−	5.18704i	0.649516	−	0.312790i
$276$	−11.0086	+	5.30145i	−0.662638	+	0.319110i
$277$	2.67977	−	11.7409i	0.161012	−	0.705439i	−0.828380	−	0.560167i	$-0.810737\pi$
$277$	2.67977	−	11.7409i	0.161012	−	0.705439i	0.989392	−	0.145272i	$-0.0464059\pi$
$278$	1.24122			0.0744434
$279$	−1.48887	+	6.52319i	−0.0891366	+	0.390533i
$280$	−3.50254	−	4.39204i	−0.209317	−	0.262475i
$281$	−3.04306	−	13.3325i	−0.181534	−	0.795351i	−0.980901	−	0.194508i	$-0.937689\pi$
$281$	−3.04306	−	13.3325i	−0.181534	−	0.795351i	0.799367	−	0.600843i	$-0.205168\pi$
$282$	0.102149	+	0.447542i	0.00608286	+	0.0266507i
$283$	−16.2063	+	20.3221i	−0.963367	+	1.20802i	0.0147331	+	0.999891i	$0.495310\pi$
$283$	−16.2063	+	20.3221i	−0.963367	+	1.20802i	−0.978101	+	0.208133i	$0.933261\pi$
$284$	10.6143	−	5.11157i	0.629842	−	0.303316i
$285$	8.73456	+	4.20634i	0.517391	+	0.249162i
$286$	−1.19668	−	1.50059i	−0.0707613	−	0.0887318i
$287$	9.31784	−	11.6842i	0.550015	−	0.689696i
$288$	3.14714	+	1.51558i	0.185447	+	0.0893065i
$289$	−16.7670			−0.986297
$290$		0			0
$291$	−2.71709			−0.159279
$292$	0.858181	+	0.413278i	0.0502212	+	0.0241853i
$293$	−3.57030	+	4.47701i	−0.208579	+	0.261550i	−0.875106	−	0.483931i	$-0.839209\pi$
$293$	−3.57030	+	4.47701i	−0.208579	+	0.261550i	0.666527	+	0.745481i	$0.267780\pi$
$294$	−0.187178	−	0.234713i	−0.0109164	−	0.0136888i
$295$	3.17245	+	1.52777i	0.184707	+	0.0889502i
$296$	−7.06223	+	3.40099i	−0.410483	+	0.197678i
$297$	−13.2552	+	16.6215i	−0.769146	+	0.964479i
$298$	−0.648987	−	2.84340i	−0.0375948	−	0.164714i
$299$	−3.44931	−	15.1124i	−0.199479	−	0.873974i
$300$	4.13653	+	5.18704i	0.238822	+	0.299474i
$301$	5.35085	−	23.4436i	0.308418	−	1.35127i
$302$	−1.68345			−0.0968714
$303$	−3.37618	+	14.7920i	−0.193956	+	0.849779i
$304$	10.5108	−	5.06176i	0.602838	−	0.290312i
$305$	−21.8862	+	10.5398i	−1.25320	+	0.603510i
$306$	0.0318821	−	0.139685i	0.00182258	−	0.00798524i
$307$	12.7599			0.728244			0.364122	−	0.931351i	$-0.381369\pi$
$307$	12.7599			0.728244			0.364122	+	0.931351i	$0.381369\pi$
$308$	5.12319	−	22.4461i	0.291921	−	1.27899i
$309$	−1.22691	−	1.53849i	−0.0697963	−	0.0875217i
$310$	−0.414708	−	1.81695i	−0.0235538	−	0.103196i
$311$	−2.78495	−	12.2017i	−0.157920	−	0.691893i	−0.990445	−	0.137906i	$-0.955963\pi$
$311$	−2.78495	−	12.2017i	−0.157920	−	0.691893i	0.832525	−	0.553987i	$-0.186894\pi$
$312$	1.33807	−	1.67789i	0.0757533	−	0.0949917i
$313$	−23.2978	+	11.2196i	−1.31687	+	0.634171i	−0.954597	−	0.297900i	$-0.903714\pi$
$313$	−23.2978	+	11.2196i	−1.31687	+	0.634171i	−0.362274	+	0.932072i	$0.617999\pi$
$314$	−0.406851	−	0.195929i	−0.0229599	−	0.0110569i
$315$	−8.95391	−	11.2279i	−0.504496	−	0.632618i
$316$	−2.27473	+	2.85242i	−0.127963	+	0.160461i
$317$	24.4225	+	11.7612i	1.37170	+	0.660577i	0.967213	−	0.253966i	$-0.0817352\pi$
$317$	24.4225	+	11.7612i	1.37170	+	0.660577i	0.404489	+	0.914543i	$0.367449\pi$
$318$	0.0857831			0.00481047
$319$		0			0
$320$	20.6589			1.15487
$321$	−2.64216	−	1.27240i	−0.147471	−	0.0710182i
$322$	−1.72036	+	2.15726i	−0.0958717	+	0.120219i
$323$	−0.917728	−	1.15079i	−0.0510638	−	0.0640319i
$324$	−1.38315	−	0.666092i	−0.0768419	−	0.0370051i
$325$	−7.58327	+	3.65191i	−0.420644	+	0.202572i
$326$	−1.04245	+	1.30719i	−0.0577361	+	0.0723988i
$327$	2.28861	+	10.0271i	0.126560	+	0.554498i
$328$	−0.771752	−	3.38127i	−0.0426129	−	0.186699i
$329$	−4.35563	−	5.46179i	−0.240134	−	0.301118i
$330$	0.482986	−	2.11610i	0.0265875	−	0.116487i
$331$	−10.9792			−0.603470			−0.301735	−	0.953392i	$-0.597566\pi$
$331$	−10.9792			−0.603470			−0.301735	+	0.953392i	$0.597566\pi$
$332$	1.91132	−	8.37405i	0.104897	−	0.459586i
$333$	−18.0539	+	8.69431i	−0.989349	+	0.476445i
$334$	−3.63831	+	1.75212i	−0.199080	+	0.0958717i
$335$	−0.594515	+	2.60474i	−0.0324819	+	0.142312i
$336$	12.5846			0.686546
$337$	−3.82563	+	16.7612i	−0.208395	+	0.913040i	0.757240	+	0.653137i	$0.226548\pi$
$337$	−3.82563	+	16.7612i	−0.208395	+	0.913040i	−0.965635	+	0.259902i	$0.916310\pi$
$338$	−0.543576	−	0.681623i	−0.0295667	−	0.0370754i
$339$	−3.17954	−	13.9305i	−0.172689	−	0.756599i
$340$	−0.598444	−	2.62196i	−0.0324552	−	0.142196i
$341$	9.59527	−	12.0321i	0.519613	−	0.651574i
$342$	−0.815653	+	0.392798i	−0.0441055	+	0.0212401i
$343$	−14.3374	−	6.90451i	−0.774145	−	0.372809i
$344$	−3.47938	−	4.36301i	−0.187596	−	0.235238i
$345$	10.9296	−	13.7053i	0.588431	−	0.737870i
$346$	−0.805070	−	0.387701i	−0.0432808	−	0.0208429i
$347$	31.2968			1.68010			0.840049	−	0.542510i	$-0.182526\pi$
$347$	31.2968			1.68010			0.840049	+	0.542510i	$0.182526\pi$
$348$		0			0
$349$	−16.8395			−0.901398			−0.450699	−	0.892676i	$-0.648825\pi$
$349$	−16.8395			−0.901398			−0.450699	+	0.892676i	$0.648825\pi$
$350$	1.34985	+	0.650051i	0.0721523	+	0.0347467i
$351$	9.33228	−	11.7023i	0.498120	−	0.624623i
$352$	−5.00929	−	6.28145i	−0.266996	−	0.334802i
$353$	24.0306	+	11.5725i	1.27902	+	0.615944i	0.945138	−	0.326671i	$-0.105927\pi$
$353$	24.0306	+	11.5725i	1.27902	+	0.615944i	0.333883	+	0.942615i	$0.391641\pi$
$354$	0.215734	−	0.103892i	0.0114661	−	0.00552179i
$355$	−10.5382	+	13.2145i	−0.559308	+	0.701350i
$356$	6.82246	+	29.8912i	0.361590	+	1.58423i
$357$	−0.353319	−	1.54799i	−0.0186996	−	0.0819284i
$358$	1.20861	+	1.51555i	0.0638770	+	0.0800992i
$359$	−2.69123	+	11.7911i	−0.142038	+	0.622308i	0.852923	+	0.522038i	$0.174828\pi$
$359$	−2.69123	+	11.7911i	−0.142038	+	0.622308i	−0.994960	+	0.100270i	$0.968029\pi$
$360$	−3.33276			−0.175652
$361$	2.15835	−	9.45635i	0.113597	−	0.497703i
$362$	−1.59326	+	0.767274i	−0.0837400	+	0.0403270i
$363$	5.00561	−	2.41058i	0.262727	−	0.126522i
$364$	−3.60696	+	15.8031i	−0.189056	+	0.828308i
$365$	−1.36655			−0.0715282
$366$	−0.367583	+	1.61049i	−0.0192139	+	0.0841816i
$367$	−21.1776	−	26.5559i	−1.10546	−	1.38621i	−0.914488	−	0.404612i	$-0.867406\pi$
$367$	−21.1776	−	26.5559i	−1.10546	−	1.38621i	−0.190975	−	0.981595i	$-0.561165\pi$
$368$	−4.69400	−	20.5658i	−0.244692	−	1.07206i
$369$	−1.97291	−	8.64389i	−0.102706	−	0.449983i
$370$	3.47997	−	4.36375i	0.180915	−	0.226860i
$371$	−1.17617	+	0.566416i	−0.0610639	+	0.0294068i
$372$	7.69481	+	3.70563i	0.398957	+	0.192128i
$373$	3.86240	+	4.84329i	0.199987	+	0.250776i	0.871705	−	0.490031i	$-0.163015\pi$
$373$	3.86240	+	4.84329i	0.199987	+	0.250776i	−0.671718	+	0.740807i	$0.734443\pi$
$374$	−0.205469	+	0.257650i	−0.0106245	+	0.0133228i
$375$	5.74480	+	2.76655i	0.296660	+	0.142864i
$376$	−1.62122			−0.0836082
$377$		0			0
$378$	−2.66432			−0.137038
$379$	23.5109	+	11.3223i	1.20767	+	0.581585i	0.925854	−	0.377882i	$-0.123348\pi$
$379$	23.5109	+	11.3223i	1.20767	+	0.581585i	0.281820	+	0.959467i	$0.409062\pi$
$380$	−10.5950	+	13.2857i	−0.543513	+	0.681544i
$381$	−0.802572	−	1.00639i	−0.0411170	−	0.0515591i
$382$	−0.971619	−	0.467907i	−0.0497123	−	0.0239402i
$383$	−18.8120	+	9.05940i	−0.961250	+	0.462914i	−0.847617	−	0.530609i	$-0.821963\pi$
$383$	−18.8120	+	9.05940i	−0.961250	+	0.462914i	−0.113633	+	0.993523i	$0.536249\pi$
$384$	3.69711	−	4.63603i	0.188667	−	0.236581i
$385$	7.35013	+	32.2030i	0.374597	+	1.64122i
$386$	−0.156103	−	0.683930i	−0.00794541	−	0.0348111i
$387$	−8.89473	−	11.1536i	−0.452144	−	0.566971i
$388$	1.05978	−	4.64321i	0.0538023	−	0.235723i
$389$	15.7075			0.796400			0.398200	−	0.917299i	$-0.369635\pi$
$389$	15.7075			0.796400			0.398200	+	0.917299i	$0.369635\pi$
$390$	−0.340044	+	1.48983i	−0.0172188	+	0.0754405i
$391$	−2.39794	+	1.15479i	−0.121269	+	0.0584002i
$392$	0.955248	−	0.460023i	0.0482473	−	0.0232347i
$393$	−4.37541	+	19.1699i	−0.220710	+	0.966995i
$394$	−3.47811			−0.175224
$395$	1.16473	−	5.10302i	0.0586040	−	0.256761i
$396$	−8.51628	−	10.6791i	−0.427959	−	0.536644i
$397$	−2.57280	−	11.2722i	−0.129125	−	0.565734i	−0.997553	−	0.0699182i	$-0.977726\pi$
$397$	−2.57280	−	11.2722i	−0.129125	−	0.565734i	0.868428	−	0.495816i	$-0.165131\pi$
$398$	0.0750087	+	0.328634i	0.00375984	+	0.0164730i
$399$	−6.25526	+	7.84385i	−0.313155	+	0.392684i
$400$	−10.3197	+	4.96971i	−0.515985	+	0.248485i
$401$	4.33830	+	2.08921i	0.216644	+	0.104330i	0.539059	−	0.842268i	$-0.318780\pi$
$401$	4.33830	+	2.08921i	0.216644	+	0.104330i	−0.322414	+	0.946599i	$0.604494\pi$
$402$	0.113278	+	0.142046i	0.00564979	+	0.00708462i
$403$	−6.75551	+	8.47114i	−0.336516	+	0.421978i
$404$	−23.9610	−	11.5390i	−1.19211	−	0.574088i
$405$	2.20250			0.109443
$406$		0			0
$407$	46.0896			2.28457
$408$	−0.331992	−	0.159879i	−0.0164360	−	0.00791518i
$409$	14.8889	−	18.6701i	0.736209	−	0.923177i	−0.262924	−	0.964817i	$-0.584687\pi$
$409$	14.8889	−	18.6701i	0.736209	−	0.923177i	0.999133	+	0.0416399i	$0.0132582\pi$
$410$	1.53975	+	1.93079i	0.0760429	+	0.0953548i
$411$	0.961434	+	0.463002i	0.0474240	+	0.0228382i
$412$	3.10766	−	1.49657i	0.153103	−	0.0737306i
$413$	−2.27195	+	2.84893i	−0.111795	+	0.140187i
$414$	0.364260	+	1.59593i	0.0179024	+	0.0784355i
$415$	2.74213	+	12.0141i	0.134606	+	0.589748i
$416$	3.52676	+	4.42242i	0.172914	+	0.216827i
$417$	1.81590	−	7.95596i	0.0889248	−	0.389605i
$418$	2.08227			0.101847
$419$	−6.86486	+	30.0769i	−0.335370	+	1.46935i	0.473200	+	0.880955i	$0.343099\pi$
$419$	−6.86486	+	30.0769i	−0.335370	+	1.46935i	−0.808571	+	0.588399i	$0.799758\pi$
$420$	−16.5156	+	7.95349i	−0.805878	+	0.388091i
$421$	−9.39489	+	4.52434i	−0.457879	+	0.220503i	−0.648582	−	0.761145i	$-0.724638\pi$
$421$	−9.39489	+	4.52434i	−0.457879	+	0.220503i	0.190703	+	0.981648i	$0.438923\pi$
$422$	−0.677335	+	2.96760i	−0.0329721	+	0.144460i
$423$	−4.14451			−0.201513
$424$	−0.0674146	+	0.295363i	−0.00327394	+	0.0143441i
$425$	0.901039	+	1.12987i	0.0437068	+	0.0548066i
$426$	0.255759	+	1.12055i	0.0123916	+	0.0542910i
$427$	−5.59392	−	24.5086i	−0.270709	−	1.18605i
$428$	3.20494	−	4.01886i	0.154916	−	0.194259i
$429$	−11.3692	+	5.47512i	−0.548911	+	0.264341i
$430$	3.58012	+	1.72409i	0.172649	+	0.0831432i
$431$	6.65691	+	8.34750i	0.320652	+	0.402085i	0.915867	−	0.401482i	$-0.131505\pi$
$431$	6.65691	+	8.34750i	0.320652	+	0.402085i	−0.595215	+	0.803566i	$0.702933\pi$
$432$	12.6999	−	15.9251i	0.611022	−	0.766197i
$433$	−24.8145	−	11.9500i	−1.19251	−	0.574282i	−0.270978	−	0.962586i	$-0.587347\pi$
$433$	−24.8145	−	11.9500i	−1.19251	−	0.574282i	−0.921532	+	0.388303i	$0.873061\pi$
$434$	1.92866			0.0925788
$435$		0			0
$436$	−18.0278			−0.863374
$437$	15.1516	+	7.29663i	0.724800	+	0.349045i
$438$	−0.0579398	+	0.0726543i	−0.00276847	+	0.00347155i
$439$	16.1160	+	20.2088i	0.769173	+	0.964512i	0.999964	−	0.00849123i	$-0.00270287\pi$
$439$	16.1160	+	20.2088i	0.769173	+	0.964512i	−0.230791	+	0.973003i	$0.574131\pi$
$440$	6.90645	+	3.32597i	0.329252	+	0.158559i
$441$	2.44200	−	1.17601i	0.116286	−	0.0560003i
$442$	0.144659	−	0.181397i	0.00688075	−	0.00862819i
$443$	−3.14077	−	13.7606i	−0.149222	−	0.653786i	−0.993102	−	0.117254i	$-0.962591\pi$
$443$	−3.14077	−	13.7606i	−0.149222	−	0.653786i	0.843880	−	0.536533i	$-0.180266\pi$
$444$	5.69159	+	24.9365i	0.270111	+	1.18343i
$445$	−27.4255	−	34.3905i	−1.30009	−	1.63027i
$446$	0.722535	−	3.16563i	0.0342130	−	0.149897i
$447$	−19.1750			−0.906948
$448$	−4.75732	+	20.8432i	−0.224762	+	0.984748i
$449$	19.9286	−	9.59709i	0.940487	−	0.452915i	0.100146	−	0.994973i	$-0.468069\pi$
$449$	19.9286	−	9.59709i	0.940487	−	0.452915i	0.840341	+	0.542058i	$0.182355\pi$
$450$	0.800821	−	0.385655i	0.0377511	−	0.0181800i
$451$	−4.53783	+	19.8815i	−0.213678	+	0.936185i
$452$	25.0458			1.17805
$453$	−2.46287	+	10.7905i	−0.115716	+	0.506983i
$454$	0.0110509	+	0.0138574i	0.000518645	+	0.000650361i
$455$	−5.17483	−	22.6724i	−0.242600	−	1.06290i
$456$	0.518093	+	2.26991i	0.0242619	+	0.106299i
$457$	−6.08500	+	7.63035i	−0.284644	+	0.356933i	−0.903512	−	0.428562i	$-0.859020\pi$
$457$	−6.08500	+	7.63035i	−0.284644	+	0.356933i	0.618868	+	0.785495i	$0.287592\pi$
$458$	2.03388	−	0.979467i	0.0950372	−	0.0457675i
$459$	−2.31545	−	1.11506i	−0.108076	−	0.0520467i
$460$	19.1578	+	24.0232i	0.893239	+	1.12009i
$461$	−12.5614	+	15.7515i	−0.585043	+	0.733621i	−0.982964	−	0.183799i	$-0.941160\pi$
$461$	−12.5614	+	15.7515i	−0.585043	+	0.733621i	0.397921	+	0.917420i	$0.369732\pi$
$462$	2.02375	+	0.974589i	0.0941536	+	0.0453420i
$463$	15.7776			0.733249			0.366624	−	0.930369i	$-0.380513\pi$
$463$	15.7776			0.733249			0.366624	+	0.930369i	$0.380513\pi$
$464$		0			0
$465$	−12.2530			−0.568220
$466$	0.337037	+	0.162308i	0.0156129	+	0.00751879i
$467$	−24.4451	+	30.6532i	−1.13119	+	1.41846i	−0.236577	+	0.971613i	$0.576025\pi$
$467$	−24.4451	+	30.6532i	−1.13119	+	1.41846i	−0.894609	+	0.446849i	$0.852546\pi$
$468$	5.99585	+	7.51855i	0.277158	+	0.347545i
$469$	−2.49107	−	1.19964i	−0.115027	−	0.0553941i
$470$	1.04008	−	0.500877i	0.0479754	−	0.0231037i
$471$	−1.85109	+	2.32119i	−0.0852935	+	0.106955i
$472$	0.188175	+	0.824447i	0.00866144	+	0.0379482i
$473$	7.30155	+	31.9902i	0.335725	+	1.47091i
$474$	−0.221926	−	0.278286i	−0.0101934	−	0.0127821i
$475$	2.03191	−	8.90239i	0.0932305	−	0.408470i
$476$	2.78316			0.127566
$477$	−0.172339	+	0.755067i	−0.00789087	+	0.0345722i
$478$	−2.35844	+	1.13576i	−0.107872	+	0.0519487i
$479$	−38.0820	+	18.3393i	−1.74001	+	0.837945i	−0.757236	+	0.653141i	$0.773451\pi$
$479$	−38.0820	+	18.3393i	−1.74001	+	0.837945i	−0.982775	+	0.184805i	$0.940835\pi$
$480$	−1.42342	+	6.23640i	−0.0649698	+	0.284651i
$481$	−32.4492			−1.47955
$482$	0.517329	−	2.26657i	0.0235637	−	0.103239i
$483$	11.3107	+	14.1832i	0.514655	+	0.645357i
$484$	2.16700	+	9.49426i	0.0985002	+	0.431557i
$485$	1.52045	+	6.66151i	0.0690399	+	0.302484i
$486$	−1.60981	+	2.01864i	−0.0730225	+	0.0915674i
$487$	12.2269	−	5.88815i	0.554052	−	0.266817i	−0.135839	−	0.990731i	$-0.543373\pi$
$487$	12.2269	−	5.88815i	0.554052	−	0.266817i	0.689891	+	0.723914i	$0.257659\pi$
$488$	−5.25625	−	2.53128i	−0.237939	−	0.114586i
$489$	6.85374	+	8.59432i	0.309937	+	0.388649i
$490$	−0.470706	+	0.590247i	−0.0212643	+	0.0266646i
$491$	−3.68233	−	1.77332i	−0.166181	−	0.0800287i	0.348944	−	0.937144i	$-0.386540\pi$
$491$	−3.68233	−	1.77332i	−0.166181	−	0.0800287i	−0.515125	+	0.857115i	$0.672255\pi$
$492$	−11.3172			−0.510217
$493$		0			0
$494$	−1.46601			−0.0659590
$495$	17.6557	+	8.50254i	0.793565	+	0.382161i
$496$	−9.19325	+	11.5280i	−0.412789	+	0.517621i
$497$	−10.9056	−	13.6752i	−0.489184	−	0.613417i
$498$	0.755008	+	0.363593i	0.0338327	+	0.0162930i
$499$	−11.2754	+	5.42993i	−0.504755	+	0.243077i	−0.668891	−	0.743361i	$-0.733231\pi$
$499$	−11.2754	+	5.42993i	−0.504755	+	0.243077i	0.164136	+	0.986438i	$0.447516\pi$
$500$	−6.96844	+	8.73815i	−0.311638	+	0.390782i
$501$	5.90790	+	25.8842i	0.263945	+	1.15642i
$502$	−0.781495	−	3.42395i	−0.0348798	−	0.152818i
$503$	16.0447	+	20.1194i	0.715398	+	0.897080i	0.998068	−	0.0621370i	$-0.0197916\pi$
$503$	16.0447	+	20.1194i	0.715398	+	0.897080i	−0.282670	+	0.959217i	$0.591220\pi$
$504$	0.767467	−	3.36249i	0.0341857	−	0.149777i
$505$	38.1549			1.69787
$506$	0.837822	−	3.67074i	0.0372457	−	0.163184i
$507$	−5.16431	+	2.48700i	−0.229355	+	0.110452i
$508$	2.03285	−	0.978970i	0.0901932	−	0.0434348i
$509$	−3.53552	+	15.4901i	−0.156709	+	0.686588i	0.834133	+	0.551563i	$0.185968\pi$
$509$	−3.53552	+	15.4901i	−0.156709	+	0.686588i	−0.990842	+	0.135024i	$0.956889\pi$
$510$	0.262381			0.0116184
$511$	0.314687	−	1.37874i	0.0139210	−	0.0609917i
$512$	8.03853	+	10.0800i	0.355256	+	0.445477i
$513$	3.61341	+	15.8314i	0.159536	+	0.698972i
$514$	−0.753864	−	3.30290i	−0.0332515	−	0.145684i
$515$	−3.08537	+	3.86893i	−0.135958	+	0.170486i
$516$	−16.4064	+	7.90092i	−0.722253	+	0.347818i
$517$	8.58862	+	4.13606i	0.377727	+	0.181904i
$518$	3.60131	+	4.51590i	0.158232	+	0.198417i
$519$	−3.66289	+	4.59313i	−0.160783	+	0.201616i
$520$	−4.86246	−	2.34164i	−0.213233	−	0.102688i
$521$	22.1399			0.969965			0.484982	−	0.874524i	$-0.338826\pi$
$521$	22.1399			0.969965			0.484982	+	0.874524i	$0.338826\pi$
$522$		0			0
$523$	31.1728			1.36309			0.681546	−	0.731775i	$-0.261308\pi$
$523$	31.1728			1.36309			0.681546	+	0.731775i	$0.261308\pi$
$524$	−31.0527	−	14.9542i	−1.35654	−	0.653276i
$525$	6.14151	−	7.70121i	0.268037	−	0.336108i
$526$	1.58531	+	1.98792i	0.0691228	+	0.0866772i
$527$	1.67612	+	0.807179i	0.0730131	+	0.0351613i
$528$	−15.4718	+	7.45083i	−0.673324	+	0.324256i
$529$	4.61906	−	5.79212i	0.200829	−	0.251831i
$530$	−0.0480030	−	0.210315i	−0.00208512	−	0.00913550i
$531$	0.481051	+	2.10762i	0.0208758	+	0.0914630i
$532$	−10.9644	−	13.7490i	−0.475369	−	0.596094i
$533$	3.19484	−	13.9975i	0.138384	−	0.606300i
$534$	−2.99123			−0.129443
$535$	−1.64103	+	7.18981i	−0.0709478	+	0.310843i
$536$	−0.578106	+	0.278401i	−0.0249704	+	0.0120251i
$537$	11.4825	−	5.52970i	0.495508	−	0.238624i
$538$	−0.0592439	+	0.259564i	−0.00255419	+	0.0111906i
$539$	−6.23415			−0.268524
$540$	−6.60214	+	28.9259i	−0.284111	+	1.24477i
$541$	0.446058	+	0.559338i	0.0191775	+	0.0240478i	0.791328	−	0.611392i	$-0.209390\pi$
$541$	0.446058	+	0.559338i	0.0191775	+	0.0240478i	−0.772150	+	0.635440i	$0.780819\pi$
$542$	−0.462397	−	2.02589i	−0.0198617	−	0.0870196i
$543$	2.58714	+	11.3350i	0.111025	+	0.486431i
$544$	0.605542	−	0.759325i	0.0259624	−	0.0325558i
$545$	23.3027	−	11.2220i	0.998180	−	0.480698i
$546$	−1.42482	−	0.686155i	−0.0609765	−	0.0293647i
$547$	−25.7613	−	32.3036i	−1.10147	−	1.38120i	−0.917247	−	0.398318i	$-0.869594\pi$
$547$	−25.7613	−	32.3036i	−1.10147	−	1.38120i	−0.184225	−	0.982884i	$-0.558977\pi$
$548$	−1.16622	+	1.46239i	−0.0498184	+	0.0624703i
$549$	−13.4371	−	6.47098i	−0.573483	−	0.276175i
$550$	−2.04440			−0.0871736
$551$		0			0
$552$	4.21000			0.179189
$553$	4.88033	+	2.35024i	0.207533	+	0.0999425i
$554$	−1.28403	+	1.61013i	−0.0545534	+	0.0684078i
$555$	−22.8795	−	28.6900i	−0.971182	−	1.21782i
$556$	12.8876	+	6.20633i	0.546555	+	0.263207i
$557$	19.1398	−	9.21726i	0.810981	−	0.390548i	0.0180332	−	0.999837i	$-0.494260\pi$
$557$	19.1398	−	9.21726i	0.810981	−	0.390548i	0.792948	+	0.609290i	$0.208545\pi$
$558$	0.713406	−	0.894583i	0.0302009	−	0.0378707i
$559$	−5.14062	−	22.5225i	−0.217425	−	0.952601i
$560$	−7.04217	−	30.8538i	−0.297586	−	1.30381i
$561$	1.35088	+	1.69395i	0.0570343	+	0.0715187i
$562$	−0.520392	+	2.27998i	−0.0219514	+	0.0961753i
$563$	−14.3265			−0.603790			−0.301895	−	0.953341i	$-0.597619\pi$
$563$	−14.3265			−0.603790			−0.301895	+	0.953341i	$0.597619\pi$
$564$	−1.17719	+	5.15759i	−0.0495684	+	0.217174i
$565$	−32.3742	+	15.5906i	−1.36199	+	0.655901i
$566$	4.00485	−	1.92863i	0.168336	−	0.0810664i
$567$	−0.507190	+	2.22215i	−0.0213000	+	0.0933214i
$568$	−4.05921			−0.170321
$569$	3.82222	−	16.7463i	0.160236	−	0.702039i	−0.829426	−	0.558617i	$-0.811332\pi$
$569$	3.82222	−	16.7463i	0.160236	−	0.702039i	0.989662	−	0.143422i	$-0.0458107\pi$
$570$	−1.03367	−	1.29618i	−0.0432956	−	0.0542909i
$571$	−0.918962	−	4.02624i	−0.0384574	−	0.168493i	0.952052	−	0.305935i	$-0.0989690\pi$
$571$	−0.918962	−	4.02624i	−0.0384574	−	0.168493i	−0.990510	+	0.137442i	$0.956112\pi$
$572$	−4.92190	−	21.5642i	−0.205795	−	0.901647i
$573$	−4.42066	+	5.54333i	−0.184676	+	0.231576i
$574$	−2.30259	+	1.10887i	−0.0961080	+	0.0462832i
$575$	−14.8761	−	7.16394i	−0.620375	−	0.298757i
$576$	7.90810	+	9.91644i	0.329504	+	0.413185i
$577$	28.4272	−	35.6466i	1.18344	−	1.48399i	0.345338	−	0.938479i	$-0.387764\pi$
$577$	28.4272	−	35.6466i	1.18344	−	1.48399i	0.838104	−	0.545510i	$-0.183664\pi$
$578$	2.58337	+	1.24409i	0.107454	+	0.0517471i
$579$	−4.61223			−0.191678
$580$		0			0
$581$	−12.7527			−0.529071
$582$	0.418634	+	0.201603i	0.0173529	+	0.00835673i
$583$	1.11067	−	1.39273i	0.0459991	−	0.0576810i
$584$	−0.204625	−	0.256592i	−0.00846745	−	0.0106178i
$585$	−12.4304	−	5.98618i	−0.513935	−	0.247498i
$586$	0.882277	−	0.424882i	0.0364465	−	0.0175517i
$587$	−12.0226	+	15.0759i	−0.496227	+	0.622249i	−0.965374	−	0.260871i	$-0.915990\pi$
$587$	−12.0226	+	15.0759i	−0.496227	+	0.622249i	0.469147	+	0.883120i	$0.344562\pi$
$588$	−0.769853	−	3.37295i	−0.0317482	−	0.139098i
$589$	−2.61569	−	11.4601i	−0.107778	−	0.472205i
$590$	−0.375434	−	0.470780i	−0.0154564	−	0.0193817i
$591$	−5.08844	+	22.2939i	−0.209311	+	0.917050i
$592$	−44.1585			−1.81490
$593$	7.52102	−	32.9517i	0.308851	−	1.35317i	−0.547514	−	0.836796i	$-0.684426\pi$
$593$	7.52102	−	32.9517i	0.308851	−	1.35317i	0.856366	−	0.516370i	$-0.172717\pi$
$594$	3.27558	−	1.57743i	0.134399	−	0.0647229i
$595$	−3.59751	+	1.73247i	−0.147484	+	0.0710244i
$596$	7.47909	−	32.7680i	0.306355	−	1.34223i
$597$	2.21622			0.0907036
$598$	−0.589865	+	2.58437i	−0.0241214	+	0.105683i
$599$	−12.0784	−	15.1458i	−0.493509	−	0.618841i	0.471242	−	0.882004i	$-0.343806\pi$
$599$	−12.0784	−	15.1458i	−0.493509	−	0.618841i	−0.964751	+	0.263163i	$0.915234\pi$
$600$	−0.508672	−	2.22864i	−0.0207664	−	0.0909837i
$601$	3.79958	+	16.6470i	0.154988	+	0.679047i	0.991391	+	0.130932i	$0.0417970\pi$
$601$	3.79958	+	16.6470i	0.154988	+	0.679047i	−0.836403	+	0.548114i	$0.815346\pi$
$602$	−2.56390	+	3.21503i	−0.104497	+	0.131035i
$603$	−1.47788	+	0.711707i	−0.0601837	+	0.0289830i
$604$	−17.4792	−	8.41754i	−0.711218	−	0.342505i
$605$	−8.71110	−	10.9234i	−0.354157	−	0.444098i
$606$	1.61772	−	2.02856i	0.0657155	−	0.0824046i
$607$	37.2517	+	17.9395i	1.51200	+	0.728140i	0.992025	−	0.126042i	$-0.0402276\pi$
$607$	37.2517	+	17.9395i	1.51200	+	0.728140i	0.519973	+	0.854182i	$0.325942\pi$
$608$	−6.13669			−0.248876
$609$		0			0
$610$	4.15414			0.168196
$611$	−6.04678	−	2.91198i	−0.244627	−	0.117806i
$612$	1.02948	−	1.29093i	0.0416143	−	0.0521827i
$613$	−6.00843	−	7.53434i	−0.242678	−	0.304309i	0.645544	−	0.763723i	$-0.276631\pi$
$613$	−6.00843	−	7.53434i	−0.242678	−	0.304309i	−0.888222	+	0.459414i	$0.848059\pi$
$614$	−1.96597	−	0.946759i	−0.0793399	−	0.0382081i
$615$	14.6286	−	7.04476i	0.589882	−	0.284072i
$616$	−4.94606	+	6.20216i	−0.199282	+	0.249892i
$617$	2.77673	+	12.1657i	0.111787	+	0.489771i	0.999565	+	0.0294988i	$0.00939113\pi$
$617$	2.77673	+	12.1657i	0.111787	+	0.489771i	−0.887778	+	0.460272i	$0.847752\pi$
$618$	0.0748812	+	0.328076i	0.00301217	+	0.0131972i
$619$	19.6007	+	24.5785i	0.787818	+	0.987892i	0.999943	+	0.0106499i	$0.00339003\pi$
$619$	19.6007	+	24.5785i	0.787818	+	0.987892i	−0.212125	+	0.977242i	$0.568039\pi$
$620$	4.77920	−	20.9390i	0.191937	−	0.840932i
$621$	29.3623			1.17827
$622$	−0.476253	+	2.08660i	−0.0190960	+	0.0836651i
$623$	41.0128	−	19.7507i	1.64314	−	0.791296i
$624$	10.8929	−	5.24572i	0.436063	−	0.209997i
$625$	6.89943	−	30.2284i	0.275977	−	1.20914i
$626$	4.42207			0.176741
$627$	3.04634	−	13.3469i	0.121659	−	0.533024i
$628$	−3.24465	−	4.06866i	−0.129476	−	0.162357i
$629$	1.23977	+	5.43180i	0.0494329	+	0.216580i
$630$	0.546480	+	2.39429i	0.0217723	+	0.0953907i
$631$	−2.93725	+	3.68320i	−0.116930	+	0.146626i	−0.836852	−	0.547430i	$-0.815606\pi$
$631$	−2.93725	+	3.68320i	−0.116930	+	0.146626i	0.719922	+	0.694055i	$0.244178\pi$
$632$	1.13258	−	0.545423i	0.0450517	−	0.0216958i
$633$	18.0307	+	8.68315i	0.716658	+	0.345124i
$634$	−2.89021	−	3.62421i	−0.114785	−	0.143936i
$635$	−2.01827	+	2.53084i	−0.0800928	+	0.100433i
$636$	0.890685	+	0.428931i	0.0353179	+	0.0170082i
$637$	4.38912			0.173903
$638$		0			0
$639$	−10.3770			−0.410508
$640$	−13.4350	−	6.46997i	−0.531066	−	0.255748i
$641$	18.1970	−	22.8183i	0.718738	−	0.901268i	−0.279528	−	0.960137i	$-0.590178\pi$
$641$	18.1970	−	22.8183i	0.718738	−	0.901268i	0.998266	+	0.0588691i	$0.0187495\pi$
$642$	0.312679	+	0.392087i	0.0123404	+	0.0154744i
$643$	−11.9567	−	5.75803i	−0.471526	−	0.227075i	0.183003	−	0.983112i	$-0.441418\pi$
$643$	−11.9567	−	5.75803i	−0.471526	−	0.227075i	−0.654528	+	0.756038i	$0.727133\pi$
$644$	−28.6491	+	13.7967i	−1.12893	+	0.543666i
$645$	16.2888	−	20.4255i	0.641370	−	0.804252i
$646$	0.0560113	+	0.245402i	0.00220374	+	0.00965519i
$647$	−7.64780	−	33.5072i	−0.300666	−	1.31730i	−0.869125	−	0.494592i	$-0.835317\pi$
$647$	−7.64780	−	33.5072i	−0.300666	−	1.31730i	0.568459	−	0.822712i	$-0.307540\pi$
$648$	0.329800	+	0.413556i	0.0129558	+	0.0162460i
$649$	1.10645	−	4.84767i	0.0434320	−	0.190288i
$650$	1.43935			0.0564560
$651$	2.82162	−	12.3623i	0.110588	−	0.484518i
$652$	−17.3600	+	8.36013i	−0.679870	+	0.327408i
$653$	−26.0069	+	12.5243i	−1.01773	+	0.490112i	−0.866918	−	0.498451i	$-0.833902\pi$
$653$	−26.0069	+	12.5243i	−1.01773	+	0.490112i	−0.150810	+	0.988563i	$0.548188\pi$
$654$	0.391374	−	1.71472i	0.0153039	−	0.0670509i
$655$	49.4475			1.93207
$656$	4.34770	−	19.0485i	0.169749	−	0.743721i
$657$	−0.523105	−	0.655953i	−0.0204083	−	0.0255912i
$658$	0.265835	+	1.16470i	0.0103633	+	0.0454048i
$659$	7.48039	+	32.7737i	0.291395	+	1.27668i	0.882585	+	0.470152i	$0.155801\pi$
$659$	7.48039	+	32.7737i	0.291395	+	1.27668i	−0.591191	+	0.806532i	$0.701342\pi$
$660$	15.5957	−	19.5564i	0.607063	−	0.761233i
$661$	16.8358	−	8.10769i	0.654836	−	0.315353i	−0.0768012	−	0.997046i	$-0.524471\pi$
$661$	16.8358	−	8.10769i	0.654836	−	0.315353i	0.731638	+	0.681694i	$0.238756\pi$
$662$	1.69161	+	0.814636i	0.0657462	+	0.0316617i
$663$	−0.951083	−	1.19262i	−0.0369370	−	0.0463175i
$664$	−1.84524	+	2.31386i	−0.0716092	+	0.0897951i
$665$	22.7312	+	10.9468i	0.881477	+	0.424497i
$666$	3.42675			0.132784
$667$		0			0
$668$	−46.5375			−1.80059
$669$	−19.2340	−	9.26260i	−0.743629	−	0.358113i
$670$	0.284867	−	0.357212i	0.0110054	−	0.0138003i
$671$	21.3878	+	26.8195i	0.825668	+	1.03536i
$672$	−5.96425	−	2.87223i	−0.230076	−	0.110799i
$673$	28.7262	−	13.8338i	1.10731	−	0.533254i	0.211363	−	0.977408i	$-0.432210\pi$
$673$	28.7262	−	13.8338i	1.10731	−	0.533254i	0.895951	+	0.444153i	$0.146495\pi$
$674$	1.83308	−	2.29861i	0.0706076	−	0.0885392i
$675$	−3.54770	−	15.5435i	−0.136551	−	0.598269i
$676$	−2.23571	−	9.79527i	−0.0859887	−	0.376741i
$677$	23.5474	+	29.5275i	0.905000	+	1.13483i	0.990365	+	0.138484i	$0.0442231\pi$
$677$	23.5474	+	29.5275i	0.905000	+	1.13483i	−0.0853646	+	0.996350i	$0.527206\pi$
$678$	−0.543731	+	2.38224i	−0.0208819	+	0.0914894i
$679$	−7.07107			−0.271363
$680$	−0.206198	+	0.903412i	−0.00790733	+	0.0346443i
$681$	0.104991	−	0.0505608i	0.00402325	−	0.00193749i
$682$	−2.37114	+	1.14188i	−0.0907958	+	0.0437249i
$683$	3.52930	−	15.4629i	0.135045	−	0.591671i	−0.861437	−	0.507864i	$-0.830435\pi$
$683$	3.52930	−	15.4629i	0.135045	−	0.591671i	0.996482	−	0.0838066i	$-0.0267078\pi$
$684$	−10.4330			−0.398915
$685$	0.597141	−	2.61624i	0.0228156	−	0.0999615i
$686$	1.69672	+	2.12762i	0.0647809	+	0.0812327i
$687$	−3.30262	−	14.4697i	−0.126003	−	0.552055i
$688$	−6.99562	−	30.6498i	−0.266706	−	1.16851i
$689$	−0.781959	+	0.980546i	−0.0297903	+	0.0373558i
$690$	−2.70088	+	1.30068i	−0.102821	+	0.0495159i
$691$	26.4855	+	12.7548i	1.00756	+	0.485214i	0.863496	−	0.504355i	$-0.168270\pi$
$691$	26.4855	+	12.7548i	1.00756	+	0.485214i	0.144061	+	0.989569i	$0.453984\pi$
$692$	−6.42045	−	8.05099i	−0.244069	−	0.306053i
$693$	−12.6441	+	15.8552i	−0.480311	+	0.602291i
$694$	−4.82202	−	2.32216i	−0.183042	−	0.0881482i
$695$	−20.5218			−0.778438
$696$		0			0
$697$	−2.46516			−0.0933748
$698$	2.59453	+	1.24946i	0.0982045	+	0.0472928i
$699$	1.53344	−	1.92288i	0.0580002	−	0.0727299i
$700$	10.7651	+	13.4990i	0.406881	+	0.510213i
$701$	9.93285	+	4.78341i	0.375159	+	0.180667i	0.611955	−	0.790892i	$-0.290383\pi$
$701$	9.93285	+	4.78341i	0.375159	+	0.180667i	−0.236797	+	0.971559i	$0.576098\pi$
$702$	−2.30615	+	1.11059i	−0.0870402	+	0.0419164i
$703$	21.9493	−	27.5235i	0.827832	−	1.03807i
$704$	−6.49164	−	28.4417i	−0.244663	−	1.07194i
$705$	−1.68888	−	7.39948i	−0.0636070	−	0.278681i
$706$	−2.84384	−	3.56606i	−0.107029	−	0.134210i
$707$	−8.78630	+	38.4953i	−0.330443	+	1.44777i
$708$	2.75944			0.103706
$709$	7.44065	−	32.5996i	0.279439	−	1.22430i	−0.619065	−	0.785340i	$-0.712488\pi$
$709$	7.44065	−	32.5996i	0.279439	−	1.22430i	0.898505	−	0.438964i	$-0.144654\pi$
$710$	2.60415	−	1.25409i	0.0977320	−	0.0470653i
$711$	2.89534	−	1.39432i	0.108584	−	0.0522912i
$712$	2.35072	−	10.2992i	0.0880971	−	0.385979i
$713$	−21.2550			−0.796005
$714$	−0.0604209	+	0.264721i	−0.00226120	+	0.00990695i
$715$	19.7855	+	24.8102i	0.739934	+	0.927848i
$716$	4.97096	+	21.7792i	0.185773	+	0.813927i
$717$	3.82963	+	16.7787i	0.143020	+	0.626613i
$718$	1.28952	−	1.61701i	0.0481246	−	0.0603464i
$719$	−44.2582	+	21.3136i	−1.65055	+	0.794864i	−0.651199	+	0.758907i	$0.725734\pi$
$719$	−44.2582	+	21.3136i	−1.65055	+	0.794864i	−0.999353	+	0.0359569i	$0.988552\pi$
$720$	−16.9160	−	8.14630i	−0.630421	−	0.303595i
$721$	−3.19295	−	4.00383i	−0.118912	−	0.149111i
$722$	−1.03419	+	1.29683i	−0.0384886	+	0.0482632i
$723$	−13.7714	−	6.63195i	−0.512163	−	0.246645i
$724$	−20.3793			−0.757392
$725$		0			0
$726$	−0.950096			−0.0352614
$727$	31.8392	+	15.3329i	1.18085	+	0.568667i	0.918159	−	0.396213i	$-0.129676\pi$
$727$	31.8392	+	15.3329i	1.18085	+	0.568667i	0.262691	+	0.964880i	$0.415390\pi$
$728$	3.48225	−	4.36660i	0.129061	−	0.161837i
$729$	12.0410	+	15.0989i	0.445962	+	0.559219i
$730$	0.210549	+	0.101395i	0.00779278	+	0.00375281i
$731$	−3.57373	+	1.72102i	−0.132179	+	0.0636542i
$732$	−11.8694	+	14.8837i	−0.438704	+	0.550117i
$733$	−3.76896	−	16.5129i	−0.139210	−	0.609918i	−0.995609	−	0.0936046i	$-0.970161\pi$
$733$	−3.76896	−	16.5129i	−0.139210	−	0.609918i	0.856400	−	0.516314i	$-0.172696\pi$
$734$	1.29253	+	5.66292i	0.0477080	+	0.209022i
$735$	3.09472	+	3.88066i	0.114150	+	0.143140i
$736$	−2.46916	+	10.8181i	−0.0910146	+	0.398761i
$737$	3.77284			0.138974
$738$	−0.337387	+	1.47819i	−0.0124194	+	0.0544128i
$739$	30.7656	−	14.8159i	1.13173	−	0.545012i	0.228233	−	0.973607i	$-0.426705\pi$
$739$	30.7656	−	14.8159i	1.13173	−	0.545012i	0.903497	+	0.428594i	$0.140991\pi$
$740$	57.9520	−	27.9082i	2.13036	−	1.02593i
$741$	−2.14476	+	9.39682i	−0.0787899	+	0.345201i
$742$	0.223245			0.00819559
$743$	−6.13024	+	26.8583i	−0.224897	+	0.985337i	0.728838	+	0.684686i	$0.240061\pi$
$743$	−6.13024	+	26.8583i	−0.224897	+	0.985337i	−0.953734	+	0.300650i	$0.902796\pi$
$744$	−1.83475	−	2.30071i	−0.0672654	−	0.0843481i
$745$	10.7301	+	47.0116i	0.393120	+	1.72237i
$746$	−0.235732	−	1.03281i	−0.00863076	−	0.0378138i
$747$	−4.71719	+	5.91516i	−0.172593	+	0.216424i
$748$	−3.42168	+	1.64779i	−0.125109	+	0.0602493i
$749$	−6.87606	−	3.31133i	−0.251246	−	0.120994i
$750$	−0.679853	−	0.852508i	−0.0248247	−	0.0311292i
$751$	−3.59519	+	4.50823i	−0.131190	+	0.164508i	−0.843088	−	0.537776i	$-0.819265\pi$
$751$	−3.59519	+	4.50823i	−0.131190	+	0.164508i	0.711897	+	0.702284i	$0.247836\pi$
$752$	−8.22877	−	3.96277i	−0.300072	−	0.144507i
$753$	−23.0901			−0.841452
$754$		0			0
$755$	27.8334			1.01296
$756$	−27.6636	−	13.3221i	−1.00611	−	0.484519i
$757$	2.83380	−	3.55347i	0.102996	−	0.129153i	−0.727662	−	0.685936i	$-0.759393\pi$
$757$	2.83380	−	3.55347i	0.102996	−	0.129153i	0.830658	+	0.556783i	$0.187964\pi$
$758$	−2.78233	−	3.48893i	−0.101059	−	0.126724i
$759$	−22.3029	−	10.7405i	−0.809546	−	0.389857i
$760$	5.27525	−	2.54043i	0.191353	−	0.0921509i
$761$	22.6200	−	28.3646i	0.819974	−	1.02822i	−0.179041	−	0.983842i	$-0.557299\pi$
$761$	22.6200	−	28.3646i	0.819974	−	1.02822i	0.999015	−	0.0443736i	$-0.0141292\pi$
$762$	0.0489830	+	0.214609i	0.00177447	+	0.00777445i
$763$	5.95597	+	26.0948i	0.215621	+	0.944696i
$764$	−7.74869	−	9.71655i	−0.280338	−	0.351532i
$765$	−0.527126	+	2.30949i	−0.0190583	+	0.0834998i
$766$	3.57064			0.129012
$767$	−0.778991	+	3.41298i	−0.0281277	+	0.123236i
$768$	13.8894	−	6.68879i	0.501191	−	0.241361i
$769$	30.6375	−	14.7542i	1.10482	−	0.532052i	0.209647	−	0.977777i	$-0.432768\pi$
$769$	30.6375	−	14.7542i	1.10482	−	0.532052i	0.895170	+	0.445725i	$0.147054\pi$
$770$	1.25694	−	5.50702i	0.0452970	−	0.198459i
$771$	−22.2738			−0.802170
$772$	1.79897	−	7.88178i	0.0647462	−	0.283672i
$773$	−4.39238	−	5.50787i	−0.157983	−	0.198104i	0.696540	−	0.717518i	$-0.254722\pi$
$773$	−4.39238	−	5.50787i	−0.157983	−	0.198104i	−0.854523	+	0.519414i	$0.826150\pi$
$774$	0.542868	+	2.37846i	0.0195130	+	0.0854920i
$775$	2.56813	+	11.2517i	0.0922499	+	0.404173i
$776$	−1.02314	+	1.28298i	−0.0367286	+	0.0460562i
$777$	34.2146	−	16.4769i	1.22744	−	0.591106i
$778$	−2.42011	−	1.16547i	−0.0867653	−	0.0417840i
$779$	9.71169	+	12.1781i	0.347958	+	0.436325i
$780$	−10.9801	+	13.7686i	−0.393151	+	0.492995i
$781$	21.5042	+	10.3559i	0.769479	+	0.370562i
$782$	0.455145			0.0162759
$783$		0			0
$784$	5.97294			0.213319
$785$	6.72672	+	3.23942i	0.240087	+	0.115620i
$786$	2.09651	−	2.62894i	0.0747801	−	0.0937713i
$787$	−30.6610	−	38.4477i	−1.09295	−	1.37051i	−0.922884	−	0.385077i	$-0.874175\pi$
$787$	−30.6610	−	38.4477i	−1.09295	−	1.37051i	−0.170062	−	0.985433i	$-0.554397\pi$
$788$	−36.1131	−	17.3912i	−1.28648	−	0.619535i
$789$	15.0614	−	7.25320i	0.536201	−	0.258221i
$790$	−0.558090	+	0.699823i	−0.0198559	+	0.0248986i
$791$	−8.27455	−	36.2532i	−0.294209	−	1.28901i
$792$	1.04725	+	4.58832i	0.0372125	+	0.163039i
$793$	−15.0580	−	18.8821i	−0.534726	−	0.670525i
$794$	−0.439973	+	1.92765i	−0.0156141	+	0.0684097i
$795$	−1.41830			−0.0503020
$796$	−0.864418	+	3.78726i	−0.0306385	+	0.134236i
$797$	−31.3518	+	15.0982i	−1.11054	+	0.534806i	−0.896956	−	0.442119i	$-0.854227\pi$
$797$	−31.3518	+	15.0982i	−1.11054	+	0.534806i	−0.213581	+	0.976925i	$0.568513\pi$
$798$	1.54577	−	0.744405i	0.0547198	−	0.0263517i
$799$	−0.256421	+	1.12345i	−0.00907151	+	0.0397449i
$800$	6.02510			0.213019
$801$	6.00941	−	26.3289i	0.212332	−	0.930287i
$802$	−0.513404	−	0.643788i	−0.0181289	−	0.0227329i
$803$	0.429409	+	1.88136i	0.0151535	+	0.0663919i
$804$	0.465908	+	2.04127i	0.0164313	+	0.0719902i
$805$	28.4437	−	35.6673i	1.00251	−	1.25711i
$806$	1.66939	−	0.803937i	0.0588019	−	0.0283175i
$807$	1.57708	+	0.759482i	0.0555159	+	0.0267350i
$808$	5.71328	+	7.16423i	0.200993	+	0.252037i
$809$	−31.3880	+	39.3593i	−1.10354	+	1.38380i	−0.187717	+	0.982223i	$0.560109\pi$
$809$	−31.3880	+	39.3593i	−1.10354	+	1.38380i	−0.915826	+	0.401576i	$0.868463\pi$
$810$	−0.339348	−	0.163421i	−0.0119235	−	0.00574205i
$811$	−8.56424			−0.300731			−0.150366	−	0.988630i	$-0.548045\pi$
$811$	−8.56424			−0.300731			−0.150366	+	0.988630i	$0.548045\pi$
$812$		0			0
$813$	−13.6620			−0.479149
$814$	−7.10121	−	3.41976i	−0.248897	−	0.119863i
$815$	17.2355	−	21.6126i	0.603733	−	0.757058i
$816$	−1.29428	−	1.62298i	−0.0453089	−	0.0568156i
$817$	22.5809	+	10.8744i	0.790007	+	0.380447i
$818$	−3.67928	+	1.77185i	−0.128643	+	0.0619513i
$819$	8.90205	−	11.1628i	0.311063	−	0.390060i
$820$	6.33293	+	27.7464i	0.221156	+	0.968946i
$821$	7.23124	+	31.6821i	0.252372	+	1.10571i	0.929201	+	0.369574i	$0.120496\pi$
$821$	7.23124	+	31.6821i	0.252372	+	1.10571i	−0.676829	+	0.736140i	$0.736646\pi$
$822$	−0.113778	−	0.142673i	−0.00396847	−	0.00497630i
$823$	−7.76814	+	34.0344i	−0.270780	+	1.18637i	0.638314	+	0.769776i	$0.279632\pi$
$823$	−7.76814	+	34.0344i	−0.270780	+	1.18637i	−0.909094	+	0.416590i	$0.863225\pi$
$824$	−1.18846			−0.0414019
$825$	−2.99095	+	13.1042i	−0.104131	+	0.456229i
$826$	0.561434	−	0.270372i	0.0195348	−	0.00940746i
$827$	38.1600	−	18.3769i	1.32695	−	0.639027i	0.369936	−	0.929057i	$-0.379380\pi$
$827$	38.1600	−	18.3769i	1.32695	−	0.639027i	0.957018	+	0.290030i	$0.0936653\pi$
$828$	−4.19782	+	18.3919i	−0.145884	+	0.639161i
$829$	−23.0078			−0.799094			−0.399547	−	0.916713i	$-0.630833\pi$
$829$	−23.0078			−0.799094			−0.399547	+	0.916713i	$0.630833\pi$
$830$	0.468931	−	2.05452i	0.0162768	−	0.0713134i
$831$	8.44205	+	10.5860i	0.292852	+	0.367224i
$832$	4.57041	+	20.0243i	0.158450	+	0.694217i
$833$	−0.167693	−	0.734713i	−0.00581023	−	0.0254563i
$834$	−0.870101	+	1.09107i	−0.0301291	+	0.0377807i
$835$	60.1545	−	28.9689i	2.08173	−	1.00251i
$836$	21.6202	+	10.4117i	0.747749	+	0.360097i
$837$	−12.7964	−	16.0461i	−0.442307	−	0.554636i
$838$	3.28935	−	4.12472i	0.113629	−	0.142486i
$839$	3.47970	+	1.67573i	0.120132	+	0.0578528i	0.492985	−	0.870038i	$-0.335906\pi$
$839$	3.47970	+	1.67573i	0.120132	+	0.0578528i	−0.372852	+	0.927891i	$0.621620\pi$
$840$	6.31604			0.217924
$841$		0			0
$842$	1.78321			0.0614534
$843$	13.8529	+	6.67120i	0.477119	+	0.229768i
$844$	−21.8713	+	27.4257i	−0.752841	+	0.944033i
$845$	8.98728	+	11.2697i	0.309172	+	0.387689i
$846$	0.638562	+	0.307515i	0.0219542	+	0.0105726i
$847$	13.0268	−	6.27338i	0.447606	−	0.215556i
$848$	−1.06413	+	1.33438i	−0.0365424	+	0.0458227i
$849$	−6.50307	−	28.4918i	−0.223185	−	0.977836i
$850$	−0.0549927	−	0.240939i	−0.00188624	−	0.00826414i
$851$	−39.6885	−	49.7678i	−1.36050	−	1.70602i
$852$	−2.94743	+	12.9135i	−0.100977	+	0.442411i
$853$	3.55963			0.121879			0.0609397	−	0.998141i	$-0.480590\pi$
$853$	3.55963			0.121879			0.0609397	+	0.998141i	$0.480590\pi$
$854$	−0.956614	+	4.19120i	−0.0327346	+	0.143420i
$855$	13.4857	−	6.49437i	0.461201	−	0.222103i
$856$	−1.59573	+	0.768465i	−0.0545411	+	0.0262656i
$857$	4.27323	−	18.7222i	0.145971	−	0.639540i	−0.848010	−	0.529981i	$-0.822199\pi$
$857$	4.27323	−	18.7222i	0.145971	−	0.639540i	0.993980	−	0.109559i	$-0.0349438\pi$
$858$	2.15795			0.0736711
$859$	−3.11986	+	13.6690i	−0.106448	+	0.466380i	0.893405	+	0.449252i	$0.148309\pi$
$859$	−3.11986	+	13.6690i	−0.106448	+	0.466380i	−0.999853	+	0.0171282i	$0.994548\pi$
$860$	28.5515	+	35.8025i	0.973600	+	1.22086i
$861$	3.73894	+	16.3814i	0.127423	+	0.558275i
$862$	−0.406288	−	1.78006i	−0.0138382	−	0.0606292i
$863$	−0.523014	+	0.655839i	−0.0178036	+	0.0223250i	−0.790654	−	0.612264i	$-0.790259\pi$
$863$	−0.523014	+	0.655839i	−0.0178036	+	0.0223250i	0.772850	+	0.634589i	$0.218831\pi$
$864$	−9.65352	+	4.64889i	−0.328419	+	0.158158i
$865$	13.3107	+	6.41010i	0.452578	+	0.217950i
$866$	2.93661	+	3.68239i	0.0997899	+	0.125133i
$867$	11.7538	−	14.7388i	0.399179	−	0.500555i
$868$	20.0253	+	9.64367i	0.679702	+	0.327327i
$869$	−7.39147			−0.250739
$870$		0			0
$871$	−2.65625			−0.0900037
$872$	5.59645	+	2.69511i	0.189520	+	0.0912679i
$873$	−2.61557	+	3.27982i	−0.0885235	+	0.111005i
$874$	−1.79307	−	2.24844i	−0.0606517	−	0.0760548i
$875$	14.9505	+	7.19978i	0.505419	+	0.243397i
$876$	−0.964873	+	0.464659i	−0.0326001	+	0.0156994i
$877$	−32.4944	+	40.7467i	−1.09726	+	1.37592i	−0.177182	+	0.984178i	$0.556698\pi$
$877$	−32.4944	+	40.7467i	−1.09726	+	1.37592i	−0.920076	+	0.391739i	$0.871873\pi$
$878$	−0.983598	−	4.30943i	−0.0331948	−	0.145436i
$879$	−1.43264	−	6.27681i	−0.0483218	−	0.211712i
$880$	26.9251	+	33.7630i	0.907644	+	1.13815i
$881$	−1.49513	+	6.55060i	−0.0503722	+	0.220695i	−0.993849	−	0.110743i	$-0.964677\pi$
$881$	−1.49513	+	6.55060i	−0.0503722	+	0.220695i	0.943477	+	0.331439i	$0.107534\pi$
$882$	−0.463507			−0.0156071
$883$	3.79146	−	16.6115i	0.127593	−	0.559020i	−0.870205	−	0.492690i	$-0.836014\pi$
$883$	3.79146	−	16.6115i	0.127593	−	0.559020i	0.997798	−	0.0663303i	$-0.0211291\pi$
$884$	2.40902	−	1.16012i	0.0810240	−	0.0390191i
$885$	−3.56686	+	1.71771i	−0.119899	+	0.0577401i
$886$	−0.537101	+	2.35320i	−0.0180443	+	0.0790571i
$887$	−15.9991			−0.537197			−0.268598	−	0.963252i	$-0.586560\pi$
$887$	−15.9991			−0.537197			−0.268598	+	0.963252i	$0.586560\pi$
$888$	1.96107	−	8.59203i	0.0658094	−	0.288330i
$889$	−2.08865	−	2.61908i	−0.0700509	−	0.0878411i
$890$	1.67385	+	7.33361i	0.0561075	+	0.245823i
$891$	−0.692091	−	3.03225i	−0.0231859	−	0.101584i
$892$	23.3308	−	29.2559i	0.781174	−	0.979561i
$893$	6.56012	−	3.15919i	0.219526	−	0.105718i
$894$	2.95438	+	1.42275i	0.0988092	+	0.0475840i
$895$	−19.9827	−	25.0575i	−0.667947	−	0.837579i
$896$	9.62150	−	12.0650i	0.321432	−	0.403063i
$897$	15.7023	+	7.56182i	0.524284	+	0.252482i
$898$	−3.78256			−0.126226
$899$		0			0
$900$	10.2433			0.341442
$901$	0.194014	+	0.0934320i	0.00646353	+	0.00311267i
$902$	2.17434	−	2.72653i	0.0723975	−	0.0907837i
$903$	16.8567	+	21.1377i	0.560956	+	0.703417i
$904$	−7.77507	−	3.74428i	−0.258595	−	0.124533i
$905$	26.3424	−	12.6858i	0.875649	−	0.421691i
$906$	1.18010	−	1.47980i	0.0392063	−	0.0491631i
$907$	−0.344600	−	1.50979i	−0.0114422	−	0.0501318i	0.968885	−	0.247513i	$-0.0796134\pi$
$907$	−0.344600	−	1.50979i	−0.0114422	−	0.0501318i	−0.980327	+	0.197381i	$0.936756\pi$
$908$	0.0454520	+	0.199138i	0.00150838	+	0.00660863i
$909$	14.6055	+	18.3147i	0.484433	+	0.607460i
$910$	−0.884944	+	3.87719i	−0.0293356	+	0.128528i
$911$	−19.4756			−0.645256			−0.322628	−	0.946526i	$-0.604566\pi$
$911$	−19.4756			−0.645256			−0.322628	+	0.946526i	$0.604566\pi$
$912$	−2.91871	+	12.7877i	−0.0966480	+	0.423443i
$913$	15.6785	−	7.55036i	0.518882	−	0.249880i
$914$	1.50370	−	0.724144i	0.0497380	−	0.0239525i
$915$	6.07748	−	26.6272i	0.200915	−	0.880267i
$916$	26.0153			0.859570
$917$	−11.3867	+	49.8886i	−0.376023	+	1.64747i
$918$	0.274016	+	0.343605i	0.00904387	+	0.0113407i
$919$	−9.23637	−	40.4672i	−0.304680	−	1.33489i	−0.862975	−	0.505247i	$-0.831401\pi$
$919$	−9.23637	−	40.4672i	−0.304680	−	1.33489i	0.558295	−	0.829642i	$-0.311456\pi$
$920$	−2.35586	−	10.3217i	−0.0776703	−	0.340296i
$921$	−8.94473	+	11.2163i	−0.294739	+	0.369591i
$922$	3.10412	−	1.49487i	0.102229	−	0.0492308i
$923$	−15.1399	−	7.29099i	−0.498336	−	0.239986i
$924$	16.1395	+	20.2383i	0.530951	+	0.665791i
$925$	−21.5501	+	27.0230i	−0.708564	+	0.888511i
$926$	−2.43093	−	1.17067i	−0.0798852	−	0.0384707i
$927$	−3.03818			−0.0997870
$928$		0			0
$929$	−12.1373			−0.398211			−0.199105	−	0.979978i	$-0.563804\pi$
$929$	−12.1373			−0.398211			−0.199105	+	0.979978i	$0.563804\pi$
$930$	1.88787	+	0.909152i	0.0619058	+	0.0298123i
$931$	−2.96889	+	3.72287i	−0.0973015	+	0.122012i
$932$	2.68788	+	3.37049i	0.0880443	+	0.110404i
$933$	12.6779	+	6.10536i	0.415056	+	0.199881i
$934$	6.04078	−	2.90909i	0.197660	−	0.0951882i
$935$	3.39714	−	4.25988i	0.111098	−	0.139313i
$936$	−0.737314	−	3.23038i	−0.0240999	−	0.105588i
$937$	−11.9126	−	52.1927i	−0.389169	−	1.70506i	−0.667530	−	0.744583i	$-0.732648\pi$
$937$	−11.9126	−	52.1927i	−0.389169	−	1.70506i	0.278361	−	0.960477i	$-0.410209\pi$
$938$	0.294799	+	0.369667i	0.00962554	+	0.0120700i
$939$	6.46946	−	28.3445i	0.211123	−	0.924989i
$940$	13.3036			0.433917
$941$	−3.25236	+	14.2495i	−0.106024	+	0.464521i	0.893846	+	0.448375i	$0.147997\pi$
$941$	−3.25236	+	14.2495i	−0.106024	+	0.464521i	−0.999870	+	0.0161466i	$0.994860\pi$
$942$	0.457433	−	0.220288i	0.0149040	−	0.00717737i
$943$	25.3758	−	12.2203i	0.826350	−	0.397949i
$944$	−1.06009	+	4.64456i	−0.0345030	+	0.151168i
$945$	44.0508			1.43297
$946$	1.24863	−	5.47062i	0.0405966	−	0.177865i
$947$	−8.97899	−	11.2593i	−0.291778	−	0.365878i	0.614239	−	0.789120i	$-0.289463\pi$
$947$	−8.97899	−	11.2593i	−0.291778	−	0.365878i	−0.906016	+	0.423242i	$0.860892\pi$
$948$	−0.912772	−	3.99911i	−0.0296454	−	0.129885i
$949$	−0.302324	−	1.32457i	−0.00981384	−	0.0429972i
$950$	−0.973607	+	1.22086i	−0.0315880	+	0.0396101i
$951$	−27.4588	+	13.2234i	−0.890411	+	0.428799i
$952$	−0.863988	−	0.416075i	−0.0280020	−	0.0134851i
$953$	4.15499	+	5.21020i	0.134593	+	0.168775i	0.844561	−	0.535460i	$-0.179862\pi$
$953$	4.15499	+	5.21020i	0.134593	+	0.168775i	−0.709967	+	0.704235i	$0.751290\pi$
$954$	0.0825777	−	0.103549i	0.00267355	−	0.00335253i
$955$	16.0644	+	7.73619i	0.519831	+	0.250337i
$956$	−30.1667			−0.975660
$957$		0			0
$958$	7.22820			0.233533
$959$	2.50207	+	1.20494i	0.0807962	+	0.0389094i
$960$	−14.4820	+	18.1598i	−0.467404	+	0.586106i
$961$	−10.0651	−	12.6212i	−0.324680	−	0.407135i
$962$	4.99958	+	2.40767i	0.161193	+	0.0776264i
$963$	−4.07935	+	1.96451i	−0.131455	+	0.0633055i
$964$	16.7047	−	20.9470i	0.538022	−	0.674658i
$965$	2.58094	+	11.3078i	0.0830834	+	0.364012i
$966$	−0.690322	−	3.02450i	−0.0222107	−	0.0973116i
$967$	11.1514	+	13.9834i	0.358605	+	0.449677i	0.928107	−	0.372313i	$-0.121435\pi$
$967$	11.1514	+	13.9834i	0.358605	+	0.449677i	−0.569502	+	0.821990i	$0.692864\pi$
$968$	0.746655	−	3.27131i	0.0239984	−	0.105144i
$969$	1.65492			0.0531636
$970$	0.260011	−	1.13918i	0.00834845	−	0.0365769i
$971$	−27.5969	+	13.2900i	−0.885627	+	0.426495i	−0.820676	−	0.571393i	$-0.806403\pi$
$971$	−27.5969	+	13.2900i	−0.885627	+	0.426495i	−0.0649502	+	0.997889i	$0.520689\pi$
$972$	−26.8082	+	12.9102i	−0.859874	+	0.414094i
$973$	4.72576	−	20.7049i	0.151501	−	0.663769i
$974$	−2.32073			−0.0743611
$975$	2.10576	−	9.22595i	0.0674384	−	0.295467i
$976$	−20.4917	−	25.6958i	−0.655924	−	0.822503i
$977$	6.02069	+	26.3784i	0.192619	+	0.843919i	0.975192	+	0.221360i	$0.0710497\pi$
$977$	6.02069	+	26.3784i	0.192619	+	0.843919i	−0.782573	+	0.622559i	$0.786093\pi$
$978$	−0.418302	−	1.83270i	−0.0133758	−	0.0586032i
$979$	−38.7285	+	48.5640i	−1.23777	+	1.55211i
$980$	−7.83868	+	3.77491i	−0.250398	+	0.120585i
$981$	14.3068	+	6.88979i	0.456781	+	0.219974i
$982$	0.435775	+	0.546445i	0.0139062	+	0.0174378i
$983$	19.8524	−	24.8942i	0.633195	−	0.794001i	−0.356939	−	0.934128i	$-0.616180\pi$
$983$	19.8524	−	24.8942i	0.633195	−	0.794001i	0.990134	+	0.140127i	$0.0447510\pi$
$984$	3.51324	+	1.69189i	0.111998	+	0.0539354i
$985$	57.5056			1.83228
$986$		0			0
$987$	7.85441			0.250009
$988$	−15.2216	−	7.33033i	−0.484263	−	0.233209i
$989$	28.2557	−	35.4315i	0.898479	−	1.12666i
$990$	−2.08942	−	2.62004i	−0.0664060	−	0.0832705i
$991$	−21.9543	−	10.5726i	−0.697401	−	0.335851i	0.0513697	−	0.998680i	$-0.483641\pi$
$991$	−21.9543	−	10.5726i	−0.697401	−	0.335851i	−0.748771	+	0.662829i	$0.769356\pi$
$992$	6.98805	−	3.36527i	0.221871	−	0.106847i
$993$	7.69646	−	9.65105i	0.244240	−	0.306267i
$994$	0.665598	+	2.91617i	0.0211115	+	0.0924954i
$995$	−1.24016	−	5.43351i	−0.0393158	−	0.172254i
$996$	6.02121	+	7.55036i	0.190789	+	0.239242i
$997$	−5.61446	+	24.5985i	−0.177812	+	0.779044i	0.804826	+	0.593510i	$0.202258\pi$
$997$	−5.61446	+	24.5985i	−0.177812	+	0.779044i	−0.982638	+	0.185533i	$0.940599\pi$
$998$	2.14013			0.0677448
$999$	13.6774	−	59.9245i	0.432733	−	1.89593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.m.190.2		24
29.2	odd	28		841.2.e.h.267.1		12
29.3	odd	28		841.2.b.e.840.6		12
29.4	even	14		841.2.d.l.778.2		24
29.5	even	14		841.2.d.l.574.2		24
29.6	even	14		841.2.d.k.605.3		24
29.7	even	7		841.2.a.k.1.7		12
29.8	odd	28		841.2.e.i.270.1		12
29.9	even	14	inner	841.2.d.m.571.3		24
29.10	odd	28		841.2.e.h.63.1		12
29.11	odd	28		841.2.e.f.196.1		12
29.12	odd	4		29.2.e.a.13.2	yes	12
29.13	even	14		841.2.d.k.645.3		24
29.14	odd	28		841.2.e.e.236.2		12
29.15	odd	28		841.2.e.f.236.1		12
29.16	even	7		841.2.d.k.645.2		24
29.17	odd	4		841.2.e.i.651.1		12
29.18	odd	28		841.2.e.e.196.2		12
29.19	odd	28		841.2.e.a.63.2		12
29.20	even	7	inner	841.2.d.m.571.2		24
29.21	odd	28		29.2.e.a.9.2	✓	12
29.22	even	14		841.2.a.k.1.6		12
29.23	even	7		841.2.d.k.605.2		24
29.24	even	7		841.2.d.l.574.3		24
29.25	even	7		841.2.d.l.778.3		24
29.26	odd	28		841.2.b.e.840.7		12
29.27	odd	28		841.2.e.a.267.2		12
29.28	even	2	inner	841.2.d.m.190.3		24
87.41	even	4		261.2.o.a.100.1		12
87.50	even	28		261.2.o.a.154.1		12
87.65	odd	14		7569.2.a.bp.1.6		12
87.80	odd	14		7569.2.a.bp.1.7		12
116.79	even	28		464.2.y.d.241.2		12
116.99	even	4		464.2.y.d.129.2		12
145.12	even	4		725.2.p.a.274.3		24
145.79	odd	28		725.2.q.a.676.1		12
145.99	odd	4		725.2.q.a.651.1		12
145.108	even	28		725.2.p.a.299.3		24
145.128	even	4		725.2.p.a.274.2		24
145.137	even	28		725.2.p.a.299.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.9.2	✓	12	29.21	odd	28
29.2.e.a.13.2	yes	12	29.12	odd	4
261.2.o.a.100.1		12	87.41	even	4
261.2.o.a.154.1		12	87.50	even	28
464.2.y.d.129.2		12	116.99	even	4
464.2.y.d.241.2		12	116.79	even	28
725.2.p.a.274.2		24	145.128	even	4
725.2.p.a.274.3		24	145.12	even	4
725.2.p.a.299.2		24	145.137	even	28
725.2.p.a.299.3		24	145.108	even	28
725.2.q.a.651.1		12	145.99	odd	4
725.2.q.a.676.1		12	145.79	odd	28
841.2.a.k.1.6		12	29.22	even	14
841.2.a.k.1.7		12	29.7	even	7
841.2.b.e.840.6		12	29.3	odd	28
841.2.b.e.840.7		12	29.26	odd	28
841.2.d.k.605.2		24	29.23	even	7
841.2.d.k.605.3		24	29.6	even	14
841.2.d.k.645.2		24	29.16	even	7
841.2.d.k.645.3		24	29.13	even	14
841.2.d.l.574.2		24	29.5	even	14
841.2.d.l.574.3		24	29.24	even	7
841.2.d.l.778.2		24	29.4	even	14
841.2.d.l.778.3		24	29.25	even	7
841.2.d.m.190.2		24	1.1	even	1	trivial
841.2.d.m.190.3		24	29.28	even	2	inner
841.2.d.m.571.2		24	29.20	even	7	inner
841.2.d.m.571.3		24	29.9	even	14	inner
841.2.e.a.63.2		12	29.19	odd	28
841.2.e.a.267.2		12	29.27	odd	28
841.2.e.e.196.2		12	29.18	odd	28
841.2.e.e.236.2		12	29.14	odd	28
841.2.e.f.196.1		12	29.11	odd	28
841.2.e.f.236.1		12	29.15	odd	28
841.2.e.h.63.1		12	29.10	odd	28
841.2.e.h.267.1		12	29.2	odd	28
841.2.e.i.270.1		12	29.8	odd	28
841.2.e.i.651.1		12	29.17	odd	4
7569.2.a.bp.1.6		12	87.65	odd	14
7569.2.a.bp.1.7		12	87.80	odd	14

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.154074 - 0.0741982i) q^{2} +(-0.701005 + 0.879032i) q^{3} +(-1.22875 - 1.54080i) q^{4} +(2.54740 + 1.22676i) q^{5} +(0.173229 - 0.0834229i) q^{6} +(-1.82432 + 2.28763i) q^{7} +(0.151100 + 0.662012i) q^{8} +(0.386273 + 1.69237i) q^{9} +O(q^{10})\)	\(q+(-0.154074 - 0.0741982i) q^{2} +(-0.701005 + 0.879032i) q^{3} +(-1.22875 - 1.54080i) q^{4} +(2.54740 + 1.22676i) q^{5} +(0.173229 - 0.0834229i) q^{6} +(-1.82432 + 2.28763i) q^{7} +(0.151100 + 0.662012i) q^{8} +(0.386273 + 1.69237i) q^{9} +(-0.301465 - 0.378025i) q^{10} +(0.888454 - 3.89257i) q^{11} +2.21577 q^{12} +(-0.625512 + 2.74055i) q^{13} +(0.450819 - 0.217103i) q^{14} +(-2.86411 + 1.37928i) q^{15} +(-0.851229 + 3.72948i) q^{16} +0.482650 q^{17} +(0.0660563 - 0.289412i) q^{18} +(-1.90144 - 2.38432i) q^{19} +(-1.23991 - 5.43242i) q^{20} +(-0.732040 - 3.20728i) q^{21} +(-0.425710 + 0.533823i) q^{22} +(-4.96829 + 2.39260i) q^{23} +(-0.687851 - 0.331252i) q^{24} +(1.86686 + 2.34097i) q^{25} +(0.299719 - 0.375836i) q^{26} +(-4.79737 - 2.31029i) q^{27} +5.76640 q^{28} +0.543625 q^{30} +(3.47275 + 1.67239i) q^{31} +(1.25462 - 1.57324i) q^{32} +(2.79888 + 3.50969i) q^{33} +(-0.0743639 - 0.0358118i) q^{34} +(-7.45366 + 3.58950i) q^{35} +(2.13297 - 2.67467i) q^{36} +(2.56868 + 11.2541i) q^{37} +(0.116049 + 0.508446i) q^{38} +(-1.97054 - 2.47098i) q^{39} +(-0.427220 + 1.87177i) q^{40} -5.10756 q^{41} +(-0.125186 + 0.548475i) q^{42} +(-7.40439 + 3.56577i) q^{43} +(-7.08936 + 3.41405i) q^{44} +(-1.09215 + 4.78502i) q^{45} +0.943011 q^{46} +(-0.531276 + 2.32767i) q^{47} +(-2.68162 - 3.36264i) q^{48} +(-0.347443 - 1.52225i) q^{49} +(-0.113939 - 0.499200i) q^{50} +(-0.338340 + 0.424265i) q^{51} +(4.99123 - 2.40365i) q^{52} +(0.401975 + 0.193581i) q^{53} +(0.567732 + 0.711913i) q^{54} +(7.03852 - 8.82602i) q^{55} +(-1.79009 - 0.862063i) q^{56} +3.42881 q^{57} +1.24537 q^{59} +(5.64445 + 2.71823i) q^{60} +(-5.35677 + 6.71717i) q^{61} +(-0.410973 - 0.515344i) q^{62} +(-4.57621 - 2.20378i) q^{63} +(6.58308 - 3.17024i) q^{64} +(-4.95544 + 6.21392i) q^{65} +(-0.170823 - 0.748425i) q^{66} +(0.210269 + 0.921249i) q^{67} +(-0.593055 - 0.743667i) q^{68} +(1.37962 - 6.04451i) q^{69} +1.41475 q^{70} +(-1.33021 + 5.82802i) q^{71} +(-1.06201 + 0.511435i) q^{72} +(-0.435458 + 0.209705i) q^{73} +(0.439268 - 1.92456i) q^{74} -3.36646 q^{75} +(-1.33738 + 5.85946i) q^{76} +(7.28393 + 9.13376i) q^{77} +(0.120267 + 0.526925i) q^{78} +(-0.411944 - 1.80484i) q^{79} +(-6.74361 + 8.45623i) q^{80} +(0.701839 - 0.337988i) q^{81} +(0.786943 + 0.378972i) q^{82} +(2.71744 + 3.40756i) q^{83} +(-4.04228 + 5.06885i) q^{84} +(1.22950 + 0.592098i) q^{85} +1.40540 q^{86} +2.71117 q^{88} +(-14.0167 - 6.75011i) q^{89} +(0.523312 - 0.656213i) q^{90} +(-5.12822 - 6.43058i) q^{91} +(9.79128 + 4.71523i) q^{92} +(-3.90450 + 1.88031i) q^{93} +(0.254565 - 0.319215i) q^{94} +(-1.91872 - 8.40645i) q^{95} +(0.503437 + 2.20570i) q^{96} +(1.50675 + 1.88941i) q^{97} +(-0.0594161 + 0.260319i) q^{98} +6.93087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{4} + 2 q^{5} + 6 q^{6} - 22 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q + 2 * q^4 + 2 * q^5 + 6 * q^6 - 22 * q^7 + 6 * q^9	\( 24 q + 2 q^{4} + 2 q^{5} + 6 q^{6} - 22 q^{7} + 6 q^{9} - 18 q^{13} + 18 q^{16} - 22 q^{20} + 8 q^{22} - 10 q^{23} - 50 q^{24} + 26 q^{25} - 24 q^{28} + 4 q^{30} + 34 q^{33} + 26 q^{34} - 38 q^{35} - 80 q^{36} - 56 q^{38} - 100 q^{42} + 32 q^{45} + 26 q^{49} - 40 q^{51} - 12 q^{52} - 20 q^{53} - 76 q^{54} + 28 q^{57} + 88 q^{59} - 74 q^{62} + 26 q^{63} + 52 q^{64} - 12 q^{65} + 74 q^{67} + 42 q^{71} + 34 q^{78} + 12 q^{80} + 2 q^{81} + 44 q^{82} + 10 q^{83} + 88 q^{86} - 132 q^{88} + 6 q^{91} + 12 q^{92} - 38 q^{93} + 132 q^{94} - 60 q^{96}+O(q^{100}) \) 24 * q + 2 * q^4 + 2 * q^5 + 6 * q^6 - 22 * q^7 + 6 * q^9 - 18 * q^13 + 18 * q^16 - 22 * q^20 + 8 * q^22 - 10 * q^23 - 50 * q^24 + 26 * q^25 - 24 * q^28 + 4 * q^30 + 34 * q^33 + 26 * q^34 - 38 * q^35 - 80 * q^36 - 56 * q^38 - 100 * q^42 + 32 * q^45 + 26 * q^49 - 40 * q^51 - 12 * q^52 - 20 * q^53 - 76 * q^54 + 28 * q^57 + 88 * q^59 - 74 * q^62 + 26 * q^63 + 52 * q^64 - 12 * q^65 + 74 * q^67 + 42 * q^71 + 34 * q^78 + 12 * q^80 + 2 * q^81 + 44 * q^82 + 10 * q^83 + 88 * q^86 - 132 * q^88 + 6 * q^91 + 12 * q^92 - 38 * q^93 + 132 * q^94 - 60 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more