LMFDB - Embedded newform 841.2.d.m.190.3

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			190.3
Character	$\chi$	$=$	841.190
Dual form			841.2.d.m.571.3

$q$-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	0.487563	−	0.873088i	$-0.337886\pi$
$2$	0.154074	+	0.0741982i	0.108947	+	0.0524661i	−0.378617	+	0.925554i	$0.623600\pi$
$3$	0.701005	−	0.879032i	0.404725	−	0.507509i	−0.537143	−	0.843491i	$-0.680497\pi$
$3$	0.701005	−	0.879032i	0.404725	−	0.507509i	0.941869	+	0.335982i	$0.109068\pi$
$4$	−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	$0.277025\pi$
$11$	−0.888454	+	3.89257i	−0.267879	+	1.17365i	−0.912475	+	0.409132i	$0.865832\pi$
$12$	−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	$-0.518641\pi$
$17$	−0.482650			−0.117060			−0.0585299	+	0.998286i	$0.518641\pi$
$18$	−0.0660563	+	0.289412i	−0.0155696	+	0.0682150i
$19$	1.90144	+	2.38432i	0.436219	+	0.547002i	0.950542	−	0.310595i	$-0.100528\pi$
$19$	1.90144	+	2.38432i	0.436219	+	0.547002i	−0.514323	+	0.857596i	$0.671957\pi$
$20$	−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	0.0952000	−	0.995458i	$-0.469651\pi$
$31$	−3.47275	−	1.67239i	−0.623724	−	0.300370i	−0.718924	+	0.695088i	$0.755365\pi$
$32$	−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	$-0.673655\pi$
$37$	−2.56868	−	11.2541i	−0.422288	−	1.85016i	0.0966033	−	0.995323i	$-0.469202\pi$
$38$	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	$-0.369415\pi$
$41$	5.10756			0.797667			0.398833	+	0.917023i	$0.369415\pi$
$42$	−0.125186	+	0.548475i	−0.0193166	+	0.0846315i
$43$	7.40439	−	3.56577i	1.12916	−	0.543775i	0.226449	−	0.974023i	$-0.427288\pi$
$43$	7.40439	−	3.56577i	1.12916	−	0.543775i	0.902711	+	0.430248i	$0.141574\pi$
$44$	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	−0.921287	−	0.388885i	$-0.872861\pi$
$47$	0.531276	−	2.32767i	0.0774946	−	0.339526i	0.998781	+	0.0493584i	$0.0157176\pi$
$48$	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	−0.310016	−	0.950731i	$-0.600334\pi$
$61$	5.35677	−	6.71717i	0.685864	−	0.860046i	0.995880	+	0.0906856i	$0.0289058\pi$
$62$	−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	−0.408227	−	0.912880i	$-0.633853\pi$
$73$	0.435458	−	0.209705i	0.0509665	−	0.0245442i	0.459193	+	0.888336i	$0.348138\pi$
$74$	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	0.992800	−	0.119781i	$-0.0382191\pi$
$79$	0.411944	+	1.80484i	0.0463473	+	0.203061i	−0.946453	+	0.322841i	$0.895362\pi$
$80$	−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	0.988378	−	0.152015i	$-0.0485761\pi$
$89$	14.0167	+	6.75011i	1.48577	+	0.715510i	0.497394	+	0.867525i	$0.334290\pi$
$90$	−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	0.699431	−	0.714700i	$-0.253437\pi$
$97$	−1.50675	−	1.88941i	−0.152988	−	0.191840i	−0.852419	+	0.522859i	$0.824865\pi$
$98$	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	−0.926453	−	0.376411i	$-0.877158\pi$
$101$	−12.1583	+	5.85513i	−1.20980	+	0.582607i	−0.283344	+	0.959018i	$0.591444\pi$
$102$	−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	−0.254069	−	0.967186i	$-0.581769\pi$
$113$	7.92375	−	9.93607i	0.745404	−	0.934706i	0.999472	+	0.0324796i	$0.0103404\pi$
$114$	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	−0.962366	−	0.271756i	$-0.912396\pi$
$127$	0.254762	−	1.11618i	0.0226064	−	0.0990453i	0.984973	+	0.172711i	$0.0552527\pi$
$128$	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	−0.968287	−	0.249840i	$-0.919622\pi$
$131$	−15.7567	+	7.58804i	−1.37667	+	0.662970i	−0.408385	+	0.912810i	$0.633908\pi$
$132$	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	0.983148	−	0.182810i	$-0.0585194\pi$
$137$	0.211198	+	0.925317i	0.0180438	+	0.0790552i	−0.965104	+	0.261866i	$0.915662\pi$
$138$	−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	$-0.533603\pi$
$157$	−2.64062			−0.210744			−0.105372	+	0.994433i	$0.533603\pi$
$158$	−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	$0.196502\pi$
$163$	−2.17559	+	9.53190i	−0.170406	+	0.746596i	−0.985832	+	0.167735i	$0.946355\pi$
$164$	−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	$-0.573267\pi$
$191$	−6.30617			−0.456299			−0.228149	+	0.973626i	$0.573267\pi$
$192$	1.82802	−	8.00909i	0.131926	−	0.578006i
$193$	−2.55769	−	3.20725i	−0.184107	−	0.230863i	0.681210	−	0.732088i	$-0.261454\pi$
$193$	−2.55769	−	3.20725i	−0.184107	−	0.230863i	−0.865317	+	0.501226i	$0.832883\pi$
$194$	−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	$0.138484\pi$
$211$	3.96080	+	17.3534i	0.272673	+	1.19466i	−0.634172	+	0.773192i	$0.718659\pi$
$212$	−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	−0.431602	−	0.902064i	$-0.642051\pi$
$229$	8.23049	−	10.3207i	0.543886	−	0.682012i	0.975488	+	0.220053i	$0.0706229\pi$
$230$	−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	$-0.989833\pi$
$251$	−12.8046	−	16.0564i	−0.808216	−	1.01347i	0.191274	−	0.981537i	$-0.438738\pi$
$252$	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	0.798625	−	0.601829i	$-0.205561\pi$
$263$	13.3960	+	6.45116i	0.826031	+	0.397796i	0.0274060	+	0.999624i	$0.491275\pi$
$264$	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	0.984391	−	0.175998i	$-0.0563153\pi$
$269$	0.346436	+	1.51784i	0.0211226	+	0.0925441i	−0.963268	+	0.268542i	$0.913458\pi$
$270$	0.572892	+	2.51000i	0.0348651	+	0.152754i
$271$	−7.57624	−	9.50030i	−0.460224	−	0.577102i	0.496523	−	0.868023i	$-0.334610\pi$
$271$	−7.57624	−	9.50030i	−0.460224	−	0.577102i	−0.956747	+	0.290921i	$0.906038\pi$
$272$	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	−0.666527	−	0.745481i	$-0.732220\pi$
$293$	3.57030	−	4.47701i	0.208579	−	0.261550i	0.875106	+	0.483931i	$0.160791\pi$
$294$	−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	$-0.618631\pi$
$307$	−12.7599			−0.728244			−0.364122	+	0.931351i	$0.618631\pi$
$308$	−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	$0.0440372\pi$
$311$	2.78495	+	12.2017i	0.157920	+	0.691893i	−0.832525	+	0.553987i	$0.813106\pi$
$312$	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	−0.404489	−	0.914543i	$-0.632551\pi$
$317$	−24.4225	−	11.7612i	−1.37170	−	0.660577i	−0.967213	+	0.253966i	$0.918265\pi$
$318$	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	$-0.402434\pi$
$331$	10.9792			0.603470			0.301735	+	0.953392i	$0.402434\pi$
$332$	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	$-0.773452\pi$
$337$	3.82563	−	16.7612i	0.208395	−	0.913040i	0.965635	−	0.259902i	$-0.0836904\pi$
$338$	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	$-0.825172\pi$
$359$	2.69123	−	11.7911i	0.142038	−	0.622308i	0.994960	−	0.100270i	$-0.0319708\pi$
$360$	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	$0.132594\pi$
$367$	21.1776	+	26.5559i	1.10546	+	1.38621i	0.190975	+	0.981595i	$0.438835\pi$
$368$	−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	−0.281820	−	0.959467i	$-0.590938\pi$
$379$	−23.5109	−	11.3223i	−1.20767	−	0.581585i	−0.925854	+	0.377882i	$0.876652\pi$
$380$	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	$-0.630365\pi$
$389$	−15.7075			−0.796400			−0.398200	+	0.917299i	$0.630365\pi$
$390$	−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	−0.999133	−	0.0416399i	$-0.986742\pi$
$409$	−14.8889	+	18.6701i	−0.736209	+	0.923177i	0.262924	+	0.964817i	$0.415313\pi$
$410$	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	−0.190703	−	0.981648i	$-0.561077\pi$
$421$	9.39489	−	4.52434i	0.457879	−	0.220503i	0.648582	+	0.761145i	$0.275362\pi$
$422$	−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	0.921532	−	0.388303i	$-0.126939\pi$
$433$	24.8145	+	11.9500i	1.19251	+	0.574282i	0.270978	+	0.962586i	$0.412653\pi$
$434$	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	$0.0374091\pi$
$443$	3.14077	+	13.7606i	0.149222	+	0.653786i	−0.843880	+	0.536533i	$0.819734\pi$
$444$	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	−0.840341	−	0.542058i	$-0.817645\pi$
$449$	−19.9286	+	9.59709i	−0.940487	+	0.452915i	−0.100146	+	0.994973i	$0.531931\pi$
$450$	−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	−0.397921	−	0.917420i	$-0.630268\pi$
$461$	12.5614	−	15.7515i	0.585043	−	0.733621i	0.982964	+	0.183799i	$0.0588395\pi$
$462$	−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	$-0.423975\pi$
$467$	24.4451	−	30.6532i	1.13119	−	1.41846i	0.894609	−	0.446849i	$-0.147454\pi$
$468$	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	$-0.226549\pi$
$479$	38.0820	−	18.3393i	1.74001	−	0.837945i	0.982775	−	0.184805i	$-0.0591652\pi$
$480$	−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	0.515125	−	0.857115i	$-0.327745\pi$
$491$	3.68233	+	1.77332i	0.166181	+	0.0800287i	−0.348944	+	0.937144i	$0.613460\pi$
$492$	−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	0.282670	−	0.959217i	$-0.408780\pi$
$503$	−16.0447	−	20.1194i	−0.715398	−	0.897080i	−0.998068	+	0.0621370i	$0.980208\pi$
$504$	−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	0.772150	−	0.635440i	$-0.219181\pi$
$541$	−0.446058	−	0.559338i	−0.0191775	−	0.0240478i	−0.791328	+	0.611392i	$0.790610\pi$
$542$	−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	$-0.402381\pi$
$563$	14.3265			0.603790			0.301895	+	0.953341i	$0.402381\pi$
$564$	−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	$0.188668\pi$
$569$	−3.82222	+	16.7463i	−0.160236	+	0.702039i	−0.989662	+	0.143422i	$0.954189\pi$
$570$	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	$0.612236\pi$
$577$	−28.4272	+	35.6466i	−1.18344	+	1.48399i	−0.838104	+	0.545510i	$0.816336\pi$
$578$	−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	0.964751	−	0.263163i	$-0.0847657\pi$
$599$	12.0784	+	15.1458i	0.493509	+	0.618841i	−0.471242	+	0.882004i	$0.656194\pi$
$600$	−0.508672	−	2.22864i	−0.0207664	−	0.0909837i
$601$	−3.79958	−	16.6470i	−0.154988	−	0.679047i	−0.991391	−	0.130932i	$-0.958203\pi$
$601$	−3.79958	−	16.6470i	−0.154988	−	0.679047i	0.836403	−	0.548114i	$-0.184654\pi$
$602$	−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	−0.519973	−	0.854182i	$-0.674058\pi$
$607$	−37.2517	−	17.9395i	−1.51200	−	0.728140i	−0.992025	+	0.126042i	$0.959772\pi$
$608$	−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	$-0.990609\pi$
$617$	−2.77673	−	12.1657i	−0.111787	−	0.489771i	0.887778	−	0.460272i	$-0.152248\pi$
$618$	0.0748812	+	0.328076i	0.00301217	+	0.0131972i
$619$	−19.6007	−	24.5785i	−0.787818	−	0.987892i	−0.999943	−	0.0106499i	$-0.996610\pi$
$619$	−19.6007	−	24.5785i	−0.787818	−	0.987892i	0.212125	−	0.977242i	$-0.431961\pi$
$620$	−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	−0.998266	−	0.0588691i	$-0.981251\pi$
$641$	−18.1970	+	22.8183i	−0.718738	+	0.901268i	0.279528	+	0.960137i	$0.409822\pi$
$642$	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	0.150810	−	0.988563i	$-0.451812\pi$
$653$	26.0069	−	12.5243i	1.01773	−	0.490112i	0.866918	+	0.498451i	$0.166098\pi$
$654$	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	$-0.844199\pi$
$659$	−7.48039	−	32.7737i	−0.291395	−	1.27668i	0.591191	−	0.806532i	$-0.298658\pi$
$660$	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	$-0.955777\pi$
$677$	−23.5474	−	29.5275i	−0.905000	−	1.13483i	0.0853646	−	0.996350i	$-0.472794\pi$
$678$	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	−0.262691	−	0.964880i	$-0.584610\pi$
$727$	−31.8392	−	15.3329i	−1.18085	−	0.568667i	−0.918159	+	0.396213i	$0.870324\pi$
$728$	−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	$0.0298389\pi$
$733$	3.76896	+	16.5129i	0.139210	+	0.609918i	−0.856400	+	0.516314i	$0.827304\pi$
$734$	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	−0.903497	−	0.428594i	$-0.859009\pi$
$739$	−30.7656	+	14.8159i	−1.13173	+	0.545012i	−0.228233	+	0.973607i	$0.573295\pi$
$740$	−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	$-0.759939\pi$
$743$	6.13024	−	26.8583i	0.224897	−	0.985337i	0.953734	−	0.300650i	$-0.0972037\pi$
$744$	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	−0.711897	−	0.702284i	$-0.752164\pi$
$751$	3.59519	−	4.50823i	0.131190	−	0.164508i	0.843088	+	0.537776i	$0.180735\pi$
$752$	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	−0.830658	−	0.556783i	$-0.812036\pi$
$757$	−2.83380	+	3.55347i	−0.102996	+	0.129153i	0.727662	+	0.685936i	$0.240607\pi$
$758$	−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	−0.895170	−	0.445725i	$-0.852946\pi$
$769$	−30.6375	+	14.7542i	−1.10482	+	0.532052i	−0.209647	+	0.977777i	$0.567232\pi$
$770$	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	0.854523	−	0.519414i	$-0.173850\pi$
$773$	4.39238	+	5.50787i	0.157983	+	0.198104i	−0.696540	+	0.717518i	$0.745278\pi$
$774$	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	0.213581	−	0.976925i	$-0.431487\pi$
$797$	31.3518	−	15.0982i	1.11054	−	0.534806i	0.896956	+	0.442119i	$0.145773\pi$
$798$	−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	$-0.439891\pi$
$809$	31.3880	−	39.3593i	1.10354	−	1.38380i	0.915826	−	0.401576i	$-0.131537\pi$
$810$	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	$-0.720368\pi$
$823$	7.76814	−	34.0344i	0.270780	−	1.18637i	0.909094	−	0.416590i	$-0.136775\pi$
$824$	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	−0.957018	−	0.290030i	$-0.906335\pi$
$827$	−38.1600	+	18.3769i	−1.32695	+	0.639027i	−0.369936	+	0.929057i	$0.620620\pi$
$828$	−4.19782	+	18.3919i	−0.145884	+	0.639161i
$829$	23.0078			0.799094			0.399547	−	0.916713i	$-0.369167\pi$
$829$	23.0078			0.799094			0.399547	+	0.916713i	$0.369167\pi$
$830$	−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	0.372852	−	0.927891i	$-0.378380\pi$
$839$	−3.47970	−	1.67573i	−0.120132	−	0.0578528i	−0.492985	+	0.870038i	$0.664094\pi$
$840$	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	$-0.519410\pi$
$853$	−3.55963			−0.121879			−0.0609397	+	0.998141i	$0.519410\pi$
$854$	−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	$-0.851691\pi$
$859$	3.11986	−	13.6690i	0.106448	−	0.466380i	0.999853	−	0.0171282i	$-0.00545234\pi$
$860$	−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	−0.943477	−	0.331439i	$-0.892466\pi$
$881$	1.49513	−	6.55060i	0.0503722	−	0.220695i	0.993849	+	0.110743i	$0.0353232\pi$
$882$	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	$-0.413440\pi$
$887$	15.9991			0.537197			0.268598	+	0.963252i	$0.413440\pi$
$888$	−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	0.980327	−	0.197381i	$-0.0632438\pi$
$907$	0.344600	+	1.50979i	0.0114422	+	0.0501318i	−0.968885	+	0.247513i	$0.920387\pi$
$908$	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	$-0.395434\pi$
$911$	19.4756			0.645256			0.322628	+	0.946526i	$0.395434\pi$
$912$	−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	0.906016	−	0.423242i	$-0.139108\pi$
$947$	8.97899	+	11.2593i	0.291778	+	0.365878i	−0.614239	+	0.789120i	$0.710537\pi$
$948$	−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	0.569502	−	0.821990i	$-0.307136\pi$
$967$	−11.1514	−	13.9834i	−0.358605	−	0.449677i	−0.928107	+	0.372313i	$0.878565\pi$
$968$	−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	0.0649502	−	0.997889i	$-0.479311\pi$
$971$	27.5969	−	13.2900i	0.885627	−	0.426495i	0.820676	+	0.571393i	$0.193597\pi$
$972$	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	−0.990134	−	0.140127i	$-0.955249\pi$
$983$	−19.8524	+	24.8942i	−0.633195	+	0.794001i	0.356939	+	0.934128i	$0.383820\pi$
$984$	−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	$-0.797742\pi$
$997$	5.61446	−	24.5985i	0.177812	−	0.779044i	0.982638	−	0.185533i	$-0.0594013\pi$
$998$	−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.190.3		24
29.2	odd	28		841.2.e.a.267.2		12
29.3	odd	28		841.2.b.e.840.7		12
29.4	even	14		841.2.d.l.778.3		24
29.5	even	14		841.2.d.l.574.3		24
29.6	even	14		841.2.d.k.605.2		24
29.7	even	7		841.2.a.k.1.6		12
29.8	odd	28		29.2.e.a.9.2	✓	12
29.9	even	14	inner	841.2.d.m.571.2		24
29.10	odd	28		841.2.e.a.63.2		12
29.11	odd	28		841.2.e.e.196.2		12
29.12	odd	4		841.2.e.i.651.1		12
29.13	even	14		841.2.d.k.645.2		24
29.14	odd	28		841.2.e.f.236.1		12
29.15	odd	28		841.2.e.e.236.2		12
29.16	even	7		841.2.d.k.645.3		24
29.17	odd	4		29.2.e.a.13.2	yes	12
29.18	odd	28		841.2.e.f.196.1		12
29.19	odd	28		841.2.e.h.63.1		12
29.20	even	7	inner	841.2.d.m.571.3		24
29.21	odd	28		841.2.e.i.270.1		12
29.22	even	14		841.2.a.k.1.7		12
29.23	even	7		841.2.d.k.605.3		24
29.24	even	7		841.2.d.l.574.2		24
29.25	even	7		841.2.d.l.778.2		24
29.26	odd	28		841.2.b.e.840.6		12
29.27	odd	28		841.2.e.h.267.1		12
29.28	even	2	inner	841.2.d.m.190.2		24
87.8	even	28		261.2.o.a.154.1		12
87.17	even	4		261.2.o.a.100.1		12
87.65	odd	14		7569.2.a.bp.1.7		12
87.80	odd	14		7569.2.a.bp.1.6		12
116.75	even	4		464.2.y.d.129.2		12
116.95	even	28		464.2.y.d.241.2		12
145.8	even	28		725.2.p.a.299.3		24
145.17	even	4		725.2.p.a.274.3		24
145.37	even	28		725.2.p.a.299.2		24
145.104	odd	4		725.2.q.a.651.1		12
145.124	odd	28		725.2.q.a.676.1		12
145.133	even	4		725.2.p.a.274.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.9.2	✓	12	29.8	odd	28
29.2.e.a.13.2	yes	12	29.17	odd	4
261.2.o.a.100.1		12	87.17	even	4
261.2.o.a.154.1		12	87.8	even	28
464.2.y.d.129.2		12	116.75	even	4
464.2.y.d.241.2		12	116.95	even	28
725.2.p.a.274.2		24	145.133	even	4
725.2.p.a.274.3		24	145.17	even	4
725.2.p.a.299.2		24	145.37	even	28
725.2.p.a.299.3		24	145.8	even	28
725.2.q.a.651.1		12	145.104	odd	4
725.2.q.a.676.1		12	145.124	odd	28
841.2.a.k.1.6		12	29.7	even	7
841.2.a.k.1.7		12	29.22	even	14
841.2.b.e.840.6		12	29.26	odd	28
841.2.b.e.840.7		12	29.3	odd	28
841.2.d.k.605.2		24	29.6	even	14
841.2.d.k.605.3		24	29.23	even	7
841.2.d.k.645.2		24	29.13	even	14
841.2.d.k.645.3		24	29.16	even	7
841.2.d.l.574.2		24	29.24	even	7
841.2.d.l.574.3		24	29.5	even	14
841.2.d.l.778.2		24	29.25	even	7
841.2.d.l.778.3		24	29.4	even	14
841.2.d.m.190.2		24	29.28	even	2	inner
841.2.d.m.190.3		24	1.1	even	1	trivial
841.2.d.m.571.2		24	29.9	even	14	inner
841.2.d.m.571.3		24	29.20	even	7	inner
841.2.e.a.63.2		12	29.10	odd	28
841.2.e.a.267.2		12	29.2	odd	28
841.2.e.e.196.2		12	29.11	odd	28
841.2.e.e.236.2		12	29.15	odd	28
841.2.e.f.196.1		12	29.18	odd	28
841.2.e.f.236.1		12	29.14	odd	28
841.2.e.h.63.1		12	29.19	odd	28
841.2.e.h.267.1		12	29.27	odd	28
841.2.e.i.270.1		12	29.21	odd	28
841.2.e.i.651.1		12	29.12	odd	4
7569.2.a.bp.1.6		12	87.80	odd	14
7569.2.a.bp.1.7		12	87.65	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

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