LMFDB - Embedded newform 1000.2.bd.a.109.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(29,1000)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1000.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([0, 25, 31])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.bd (of order $50$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$2960$
Relative dimension:	$148$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			109.25
Character	$\chi$	$=$	1000.109
Dual form			1000.2.bd.a.789.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21934 - 0.716384i) q^{2} +(-0.290927 - 0.351670i) q^{3} +(0.973587 + 1.74703i) q^{4} +(-1.00978 - 1.99508i) q^{5} +(0.102808 + 0.637222i) q^{6} +(3.27785 - 1.06504i) q^{7} +(0.0644140 - 2.82769i) q^{8} +(0.523110 - 2.74224i) q^{9} +(-0.197982 + 3.15607i) q^{10} +(0.505692 - 4.00297i) q^{11} +(0.331138 - 0.850641i) q^{12} +(0.348849 - 1.82873i) q^{13} +(-4.75980 - 1.04956i) q^{14} +(-0.407839 + 0.935532i) q^{15} +(-2.10426 + 3.40178i) q^{16} +(-0.351077 - 1.36735i) q^{17} +(-2.60235 + 2.96898i) q^{18} +(4.46290 + 3.69203i) q^{19} +(2.50237 - 3.70650i) q^{20} +(-1.32816 - 0.842875i) q^{21} +(-3.48428 + 4.51871i) q^{22} +(-2.55506 + 2.72086i) q^{23} +(-1.01316 + 0.800000i) q^{24} +(-2.96070 + 4.02918i) q^{25} +(-1.73544 + 1.97994i) q^{26} +(-2.31642 + 1.27346i) q^{27} +(5.05193 + 4.68962i) q^{28} +(8.15530 - 0.513088i) q^{29} +(1.16750 - 0.848563i) q^{30} +(5.40358 - 1.38740i) q^{31} +(5.00279 - 2.64047i) q^{32} +(-1.55484 + 0.986735i) q^{33} +(-0.551469 + 1.91878i) q^{34} +(-5.43474 - 5.46413i) q^{35} +(5.30008 - 1.75592i) q^{36} +(-4.18774 - 2.30223i) q^{37} +(-2.79688 - 7.69899i) q^{38} +(-0.744600 + 0.409347i) q^{39} +(-5.70652 + 2.72683i) q^{40} +(-2.71681 + 2.55125i) q^{41} +(1.01566 + 1.97923i) q^{42} +(0.804593 - 0.584571i) q^{43} +(7.48566 - 3.01377i) q^{44} +(-5.99922 + 1.72541i) q^{45} +(5.06467 - 1.48725i) q^{46} +(-2.83510 - 7.16065i) q^{47} +(1.80849 - 0.249664i) q^{48} +(3.94690 - 2.86759i) q^{49} +(6.49654 - 2.79194i) q^{50} +(-0.378720 + 0.521264i) q^{51} +(3.53449 - 1.17098i) q^{52} +(0.588932 - 0.928008i) q^{53} +(3.73679 + 0.106662i) q^{54} +(-8.49688 + 3.03321i) q^{55} +(-2.80046 - 9.33737i) q^{56} -2.64358i q^{57} +(-10.3117 - 5.21670i) q^{58} +(-6.95804 + 3.27421i) q^{59} +(-2.03147 + 0.198312i) q^{60} +(-4.68088 + 4.98463i) q^{61} +(-7.58272 - 2.17932i) q^{62} +(-1.20591 - 9.54580i) q^{63} +(-7.99170 - 0.364286i) q^{64} +(-4.00073 + 1.15063i) q^{65} +(2.60277 - 0.0892995i) q^{66} +(0.294826 - 4.68612i) q^{67} +(2.04701 - 1.94458i) q^{68} +(1.70018 + 0.106966i) q^{69} +(2.71239 + 10.5560i) q^{70} +(-0.689360 + 0.272937i) q^{71} +(-7.72052 - 1.65583i) q^{72} +(10.0179 + 4.71405i) q^{73} +(3.45700 + 5.80723i) q^{74} +(2.27829 - 0.131006i) q^{75} +(-2.10509 + 11.3913i) q^{76} +(-2.60573 - 13.6597i) q^{77} +(1.20117 + 0.0342858i) q^{78} +(1.98242 + 2.39634i) q^{79} +(8.91166 + 0.763128i) q^{80} +(-6.66519 - 2.63894i) q^{81} +(5.14039 - 1.16457i) q^{82} +(7.58982 - 9.17452i) q^{83} +(0.179454 - 3.14095i) q^{84} +(-2.37347 + 2.08115i) q^{85} +(-1.39985 + 0.136394i) q^{86} +(-2.55303 - 2.71871i) q^{87} +(-11.2866 - 1.68779i) q^{88} +(-5.18908 + 11.0274i) q^{89} +(8.55115 + 2.19389i) q^{90} +(-0.804194 - 6.36585i) q^{91} +(-7.24100 - 1.81478i) q^{92} +(-2.05996 - 1.49665i) q^{93} +(-1.67282 + 10.7623i) q^{94} +(2.85937 - 12.6320i) q^{95} +(-2.38402 - 0.991149i) q^{96} +(-15.5640 + 0.979204i) q^{97} +(-6.86691 + 0.669073i) q^{98} +(-10.7126 - 3.48072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2960 q - 20 q^{2} - 20 q^{4} - 20 q^{6} - 50 q^{7} - 35 q^{8} - 40 q^{9} - 20 q^{10} - 20 q^{12} - 30 q^{14} - 40 q^{15} - 40 q^{17} - 25 q^{18} - 20 q^{20} + 5 q^{22} - 40 q^{23} - 15 q^{24} - 40 q^{25}+ \cdots - 115 q^{98}+O(q^{100}) $ 2960 * q - 20 * q^2 - 20 * q^4 - 20 * q^6 - 50 * q^7 - 35 * q^8 - 40 * q^9 - 20 * q^10 - 20 * q^12 - 30 * q^14 - 40 * q^15 - 40 * q^17 - 25 * q^18 - 20 * q^20 + 5 * q^22 - 40 * q^23 - 15 * q^24 - 40 * q^25 - 15 * q^26 - 40 * q^28 + 20 * q^30 - 40 * q^31 - 25 * q^32 - 40 * q^33 - 20 * q^34 + 180 * q^36 - 70 * q^38 - 40 * q^39 + 5 * q^40 - 40 * q^41 - 100 * q^42 + 15 * q^44 - 20 * q^46 - 40 * q^47 + 45 * q^48 + 650 * q^49 - 30 * q^50 + 75 * q^52 - 70 * q^54 - 40 * q^55 - 55 * q^56 - 295 * q^58 - 5 * q^60 - 45 * q^62 - 110 * q^63 - 5 * q^64 - 90 * q^65 - 95 * q^66 - 55 * q^70 - 40 * q^71 + 40 * q^72 - 40 * q^73 - 15 * q^74 - 15 * q^76 + 30 * q^78 - 40 * q^79 - 400 * q^80 - 40 * q^81 - 25 * q^82 - 95 * q^84 + 40 * q^86 - 40 * q^87 - 135 * q^88 - 90 * q^89 - 70 * q^90 - 115 * q^92 - 100 * q^94 + 60 * q^95 - 55 * q^96 - 115 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{27}{50}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.21934	−	0.716384i	−0.862205	−	0.506560i
$2$	−1.21934	−	0.716384i	−0.862205	−	0.506560i
$3$	−0.290927	−	0.351670i	−0.167967	−	0.203037i	0.679813	−	0.733386i	$-0.262061\pi$
$3$	−0.290927	−	0.351670i	−0.167967	−	0.203037i	−0.847780	+	0.530349i	$0.822061\pi$
$4$	0.973587	+	1.74703i	0.486793	+	0.873517i
$5$	−1.00978	−	1.99508i	−0.451586	−	0.892227i
$5$	−1.00978	−	1.99508i	−0.451586	−	0.892227i
$6$	0.102808	+	0.637222i	0.0419713	+	0.260145i
$7$	3.27785	−	1.06504i	1.23891	−	0.402547i	0.384977	−	0.922926i	$-0.374209\pi$
$7$	3.27785	−	1.06504i	1.23891	−	0.402547i	0.853935	+	0.520379i	$0.174209\pi$
$8$	0.0644140	−	2.82769i	0.0227738	−	0.999741i
$9$	0.523110	−	2.74224i	0.174370	−	0.914080i
$10$	−0.197982	+	3.15607i	−0.0626074	+	0.998038i
$11$	0.505692	−	4.00297i	0.152472	−	1.20694i	−0.711238	−	0.702951i	$-0.751865\pi$
$11$	0.505692	−	4.00297i	0.152472	−	1.20694i	0.863710	−	0.503989i	$-0.168135\pi$
$12$	0.331138	−	0.850641i	0.0955912	−	0.245559i
$13$	0.348849	−	1.82873i	0.0967533	−	0.507199i	−0.900610	−	0.434628i	$-0.856880\pi$
$13$	0.348849	−	1.82873i	0.0967533	−	0.507199i	0.997363	−	0.0725705i	$-0.0231202\pi$
$14$	−4.75980	−	1.04956i	−1.27211	−	0.280506i
$15$	−0.407839	+	0.935532i	−0.105304	+	0.241553i
$16$	−2.10426	+	3.40178i	−0.526065	+	0.850445i
$17$	−0.351077	−	1.36735i	−0.0851487	−	0.331632i	0.911710	−	0.410835i	$-0.134763\pi$
$17$	−0.351077	−	1.36735i	−0.0851487	−	0.331632i	−0.996859	+	0.0792024i	$0.974763\pi$
$18$	−2.60235	+	2.96898i	−0.613380	+	0.699795i
$19$	4.46290	+	3.69203i	1.02386	+	0.847010i	0.988325	−	0.152359i	$-0.0486870\pi$
$19$	4.46290	+	3.69203i	1.02386	+	0.847010i	0.0355335	+	0.999368i	$0.488687\pi$
$20$	2.50237	−	3.70650i	0.559547	−	0.828799i
$21$	−1.32816	−	0.842875i	−0.289828	−	0.183930i
$22$	−3.48428	+	4.51871i	−0.742850	+	0.963393i
$23$	−2.55506	+	2.72086i	−0.532766	+	0.567338i	−0.937894	−	0.346922i	$-0.887227\pi$
$23$	−2.55506	+	2.72086i	−0.532766	+	0.567338i	0.405128	+	0.914260i	$0.367227\pi$
$24$	−1.01316	+	0.800000i	−0.206810	+	0.163299i
$25$	−2.96070	+	4.02918i	−0.592140	+	0.805835i
$26$	−1.73544	+	1.97994i	−0.340348	+	0.388298i
$27$	−2.31642	+	1.27346i	−0.445795	+	0.245078i
$28$	5.05193	+	4.68962i	0.954726	+	0.886254i
$29$	8.15530	−	0.513088i	1.51440	−	0.0952780i	0.716296	−	0.697797i	$-0.245836\pi$
$29$	8.15530	−	0.513088i	1.51440	−	0.0952780i	0.798105	+	0.602519i	$0.205836\pi$
$30$	1.16750	−	0.848563i	0.213155	−	0.154926i
$31$	5.40358	−	1.38740i	0.970511	−	0.249185i	0.270027	−	0.962853i	$-0.412967\pi$
$31$	5.40358	−	1.38740i	0.970511	−	0.249185i	0.700484	+	0.713668i	$0.252967\pi$
$32$	5.00279	−	2.64047i	0.884377	−	0.466774i
$33$	−1.55484	+	0.986735i	−0.270664	+	0.171768i
$34$	−0.551469	+	1.91878i	−0.0945761	+	0.329068i
$35$	−5.43474	−	5.46413i	−0.918639	−	0.923607i
$36$	5.30008	−	1.75592i	0.883347	−	0.292653i
$37$	−4.18774	−	2.30223i	−0.688460	−	0.378484i	0.0987985	−	0.995107i	$-0.468500\pi$
$37$	−4.18774	−	2.30223i	−0.688460	−	0.378484i	−0.787258	+	0.616624i	$0.788500\pi$
$38$	−2.79688	−	7.69899i	−0.453714	−	1.24894i
$39$	−0.744600	+	0.409347i	−0.119231	+	0.0655480i
$40$	−5.70652	+	2.72683i	−0.902280	+	0.431150i
$41$	−2.71681	+	2.55125i	−0.424294	+	0.398439i	−0.867064	−	0.498197i	$-0.833996\pi$
$41$	−2.71681	+	2.55125i	−0.424294	+	0.398439i	0.442770	+	0.896635i	$0.353996\pi$
$42$	1.01566	+	1.97923i	0.156719	+	0.305401i
$43$	0.804593	−	0.584571i	0.122699	−	0.0891463i	−0.524743	−	0.851261i	$-0.675839\pi$
$43$	0.804593	−	0.584571i	0.122699	−	0.0891463i	0.647442	+	0.762114i	$0.275839\pi$
$44$	7.48566	−	3.01377i	1.12851	−	0.454343i
$45$	−5.99922	+	1.72541i	−0.894311	+	0.257208i
$46$	5.06467	−	1.48725i	0.746745	−	0.219284i
$47$	−2.83510	−	7.16065i	−0.413542	−	1.04449i	−0.976021	−	0.217676i	$-0.930152\pi$
$47$	−2.83510	−	7.16065i	−0.413542	−	1.04449i	0.562479	−	0.826811i	$-0.309848\pi$
$48$	1.80849	−	0.249664i	0.261033	−	0.0360359i
$49$	3.94690	−	2.86759i	0.563842	−	0.409655i
$50$	6.49654	−	2.79194i	0.918750	−	0.394840i
$51$	−0.378720	+	0.521264i	−0.0530314	+	0.0729915i
$52$	3.53449	−	1.17098i	0.490146	−	0.162385i
$53$	0.588932	−	0.928008i	0.0808960	−	0.127472i	−0.801471	−	0.598034i	$-0.795949\pi$
$53$	0.588932	−	0.928008i	0.0808960	−	0.127472i	0.882367	+	0.470562i	$0.155949\pi$
$54$	3.73679	+	0.106662i	0.508513	+	0.0145148i
$55$	−8.49688	+	3.03321i	−1.14572	+	0.408998i
$56$	−2.80046	−	9.33737i	−0.374228	−	1.24776i
$57$		−	2.64358i		−	0.350151i
$58$	−10.3117	−	5.21670i	−1.35399	−	0.684986i
$59$	−6.95804	+	3.27421i	−0.905860	+	0.426265i	−0.821525	−	0.570172i	$-0.806876\pi$
$59$	−6.95804	+	3.27421i	−0.905860	+	0.426265i	−0.0843347	+	0.996437i	$0.526876\pi$
$60$	−2.03147	+	0.198312i	−0.262262	+	0.0256019i
$61$	−4.68088	+	4.98463i	−0.599325	+	0.638217i	−0.955075	−	0.296365i	$-0.904226\pi$
$61$	−4.68088	+	4.98463i	−0.599325	+	0.638217i	0.355750	+	0.934581i	$0.384226\pi$
$62$	−7.58272	−	2.17932i	−0.963007	−	0.276774i
$63$	−1.20591	−	9.54580i	−0.151931	−	1.20266i
$64$	−7.99170	−	0.364286i	−0.998963	−	0.0455358i
$65$	−4.00073	+	1.15063i	−0.496229	+	0.142718i
$66$	2.60277	−	0.0892995i	0.320379	−	0.0109920i
$67$	0.294826	−	4.68612i	0.0360187	−	0.572500i	−0.938086	−	0.346403i	$-0.887403\pi$
$67$	0.294826	−	4.68612i	0.0360187	−	0.572500i	0.974105	−	0.226098i	$-0.0725969\pi$
$68$	2.04701	−	1.94458i	0.248237	−	0.235815i
$69$	1.70018	+	0.106966i	0.204678	+	0.0128772i
$70$	2.71239	+	10.5560i	0.324192	+	1.26168i
$71$	−0.689360	+	0.272937i	−0.0818120	+	0.0323917i	−0.408674	−	0.912680i	$-0.634009\pi$
$71$	−0.689360	+	0.272937i	−0.0818120	+	0.0323917i	0.326862	+	0.945072i	$0.394009\pi$
$72$	−7.72052	−	1.65583i	−0.909872	−	0.195142i
$73$	10.0179	+	4.71405i	1.17250	+	0.551737i	0.910572	−	0.413350i	$-0.135641\pi$
$73$	10.0179	+	4.71405i	1.17250	+	0.551737i	0.261929	+	0.965087i	$0.415641\pi$
$74$	3.45700	+	5.80723i	0.401868	+	0.675077i
$75$	2.27829	−	0.131006i	0.263074	−	0.0151273i
$76$	−2.10509	+	11.3913i	−0.241470	+	1.30668i
$77$	−2.60573	−	13.6597i	−0.296951	−	1.55667i
$78$	1.20117	+	0.0342858i	0.136006	+	0.00388210i
$79$	1.98242	+	2.39634i	0.223040	+	0.269609i	0.870149	−	0.492788i	$-0.164022\pi$
$79$	1.98242	+	2.39634i	0.223040	+	0.269609i	−0.647109	+	0.762397i	$0.724022\pi$
$80$	8.91166	+	0.763128i	0.996354	+	0.0853203i
$81$	−6.66519	−	2.63894i	−0.740577	−	0.293215i
$82$	5.14039	−	1.16457i	0.567661	−	0.128605i
$83$	7.58982	−	9.17452i	0.833091	−	1.00703i	−0.166688	−	0.986010i	$-0.553307\pi$
$83$	7.58982	−	9.17452i	0.833091	−	1.00703i	0.999779	−	0.0210247i	$-0.00669288\pi$
$84$	0.179454	−	3.14095i	0.0195801	−	0.342706i
$85$	−2.37347	+	2.08115i	−0.257439	+	0.225733i
$86$	−1.39985	+	0.136394i	−0.150950	+	0.0147077i
$87$	−2.55303	−	2.71871i	−0.273714	−	0.291476i
$88$	−11.2866	−	1.68779i	−1.20315	−	0.179919i
$89$	−5.18908	+	11.0274i	−0.550041	+	1.16890i	0.415727	+	0.909490i	$0.363527\pi$
$89$	−5.18908	+	11.0274i	−0.550041	+	1.16890i	−0.965768	+	0.259407i	$0.916473\pi$
$90$	8.55115	+	2.19389i	0.901370	+	0.231256i
$91$	−0.804194	−	6.36585i	−0.0843024	−	0.667322i
$92$	−7.24100	−	1.81478i	−0.754927	−	0.189204i
$93$	−2.05996	−	1.49665i	−0.213607	−	0.155195i
$94$	−1.67282	+	10.7623i	−0.172538	+	1.11005i
$95$	2.85937	−	12.6320i	0.293365	−	1.29601i
$96$	−2.38402	−	0.991149i	−0.243318	−	0.101159i
$97$	−15.5640	+	0.979204i	−1.58029	+	0.0994231i	−0.828502	−	0.559987i	$-0.810806\pi$
$97$	−15.5640	+	0.979204i	−1.58029	+	0.0994231i	−0.751784	+	0.659410i	$0.770806\pi$
$98$	−6.86691	+	0.669073i	−0.693663	+	0.0675866i
$99$	−10.7126	−	3.48072i	−1.07665	−	0.349826i
$100$	−9.92161	−	1.24969i	−0.992161	−	0.124969i
$101$	15.1157	−	4.91140i	1.50407	−	0.488703i	0.562870	−	0.826545i	$-0.309697\pi$
$101$	15.1157	−	4.91140i	1.50407	−	0.488703i	0.941203	+	0.337842i	$0.109697\pi$
$102$	0.835215	−	0.364289i	0.0826986	−	0.0360700i
$103$	3.13738	−	12.2193i	0.309136	−	1.20400i	−0.604212	−	0.796823i	$-0.706512\pi$
$103$	3.13738	−	12.2193i	0.309136	−	1.20400i	0.913348	−	0.407180i	$-0.133488\pi$
$104$	−5.14862	−	1.10423i	−0.504864	−	0.108279i
$105$	−0.340460	+	3.50090i	−0.0332255	+	0.341653i
$106$	−1.38292	+	0.709657i	−0.134321	+	0.0689279i
$107$	−4.23113	+	13.0221i	−0.409038	+	1.25889i	0.508437	+	0.861099i	$0.330223\pi$
$107$	−4.23113	+	13.0221i	−0.409038	+	1.25889i	−0.917476	+	0.397792i	$0.869777\pi$
$108$	−4.48002	−	2.80704i	−0.431090	−	0.270107i
$109$	−5.29263	+	9.62727i	−0.506942	+	0.922125i	0.491737	+	0.870744i	$0.336362\pi$
$109$	−5.29263	+	9.62727i	−0.506942	+	0.922125i	−0.998679	+	0.0513809i	$0.983638\pi$
$110$	12.5335	+	2.38852i	1.19503	+	0.227736i
$111$	0.408701	+	2.14248i	0.0387921	+	0.203355i
$112$	−3.27442	+	13.3916i	−0.309404	+	1.26539i
$113$	−3.04577	+	1.43323i	−0.286522	+	0.134827i	−0.563670	−	0.826000i	$-0.690611\pi$
$113$	−3.04577	+	1.43323i	−0.286522	+	0.134827i	0.277147	+	0.960827i	$0.410611\pi$
$114$	−1.89382	+	3.22343i	−0.177372	+	0.301902i
$115$	8.00837	+	2.35008i	0.746785	+	0.219146i
$116$	8.83627	+	13.7480i	0.820427	+	1.27647i
$117$	−4.83233	−	1.91326i	−0.446749	−	0.176881i
$118$	10.8298	+	0.992259i	0.996966	+	0.0913448i
$119$	−2.60707	−	4.10808i	−0.238989	−	0.376587i
$120$	2.61913	+	1.21351i	0.239092	+	0.110777i
$121$	−5.11361	−	1.31295i	−0.464874	−	0.119359i
$122$	9.27850	−	2.72466i	0.840036	−	0.246679i
$123$	1.68759	+	0.213193i	0.152165	+	0.0192229i
$124$	7.68469	+	8.08948i	0.690106	+	0.726457i
$125$	11.0282	+	1.83826i	0.986391	+	0.164419i
$126$	−5.36804	+	12.5035i	−0.478223	+	1.11390i
$127$	2.03195	−	16.0845i	0.180306	−	1.42727i	−0.599061	−	0.800703i	$-0.704459\pi$
$127$	2.03195	−	16.0845i	0.180306	−	1.42727i	0.779367	−	0.626567i	$-0.215541\pi$
$128$	9.48364	+	6.16932i	0.838244	+	0.545296i
$129$	−0.439654	−	0.112884i	−0.0387094	−	0.00993889i
$130$	5.70254	+	1.46305i	0.500146	+	0.128318i
$131$	−4.80715	+	3.05071i	−0.420002	+	0.266542i	−0.728990	−	0.684524i	$-0.760010\pi$
$131$	−4.80715	+	3.05071i	−0.420002	+	0.266542i	0.308987	+	0.951066i	$0.400010\pi$
$132$	−3.23764	−	1.75570i	−0.281800	−	0.152814i
$133$	18.5609	+	7.34877i	1.60943	+	0.637219i
$134$	−3.71656	+	5.50277i	−0.321061	+	0.475367i
$135$	4.87973	+	3.33553i	0.419980	+	0.287077i
$136$	−3.88907	+	0.904661i	−0.333485	+	0.0775741i
$137$	−15.1610	+	7.13425i	−1.29530	+	0.609520i	−0.944985	−	0.327114i	$-0.893924\pi$
$137$	−15.1610	+	7.13425i	−1.29530	+	0.609520i	−0.350310	+	0.936634i	$0.613924\pi$
$138$	−1.99647	−	1.34841i	−0.169951	−	0.114784i
$139$	−2.43530	+	0.464559i	−0.206560	+	0.0394034i	−0.289623	−	0.957141i	$-0.593530\pi$
$139$	−2.43530	+	0.464559i	−0.206560	+	0.0394034i	0.0830628	+	0.996544i	$0.473530\pi$
$140$	4.25483	−	14.8145i	0.359599	−	1.25205i
$141$	−1.69338	+	3.08025i	−0.142608	+	0.259404i
$142$	1.03609	+	0.161044i	0.0869470	+	0.0135145i
$143$	−7.14394	−	2.32121i	−0.597406	−	0.194109i
$144$	8.22774	+	7.54989i	0.685645	+	0.629157i
$145$	−9.25869	−	15.7524i	−0.768892	−	1.30816i
$146$	−8.83812	−	12.9247i	−0.731448	−	1.06965i
$147$	−2.15670	−	0.553748i	−0.177882	−	0.0456723i
$148$	−0.0550530	−	9.55754i	−0.00452533	−	0.785625i
$149$	12.4597	−	4.04840i	1.02074	−	0.331658i	0.249616	−	0.968345i	$-0.419696\pi$
$149$	12.4597	−	4.04840i	1.02074	−	0.331658i	0.771123	+	0.636687i	$0.219696\pi$
$150$	−2.87186	−	1.47239i	−0.234487	−	0.120220i
$151$	−0.462123	+	1.42227i	−0.0376070	+	0.115743i	−0.968098	−	0.250573i	$-0.919381\pi$
$151$	−0.462123	+	1.42227i	−0.0376070	+	0.115743i	0.930491	+	0.366316i	$0.119381\pi$
$152$	10.7274	−	12.3819i	0.870107	−	1.00430i
$153$	−3.93327	+	0.247460i	−0.317986	+	0.0200060i
$154$	−6.60834	+	18.5226i	−0.532515	+	1.49259i
$155$	−8.22439	−	9.37961i	−0.660599	−	0.753389i
$156$	−1.44008	−	0.902307i	−0.115298	−	0.0722424i
$157$	−7.36669	−	5.35221i	−0.587926	−	0.427153i	0.253647	−	0.967297i	$-0.418370\pi$
$157$	−7.36669	−	5.35221i	−0.587926	−	0.427153i	−0.841573	+	0.540144i	$0.818370\pi$
$158$	−0.700550	−	4.34213i	−0.0557328	−	0.345441i
$159$	−0.497689	+	0.0628727i	−0.0394693	+	0.00498613i
$160$	−10.3197	−	7.31469i	−0.815841	−	0.578277i
$161$	−5.47728	+	11.6398i	−0.431670	+	0.917346i
$162$	6.23665	+	7.99261i	0.489998	+	0.627958i
$163$	−1.02521	+	0.962738i	−0.0803008	+	0.0754075i	−0.723658	−	0.690158i	$-0.757541\pi$
$163$	−1.02521	+	0.962738i	−0.0803008	+	0.0754075i	0.643358	+	0.765566i	$0.277541\pi$
$164$	−7.10217	−	2.26249i	−0.554587	−	0.176671i
$165$	3.53866	+	2.10566i	0.275485	+	0.163925i
$166$	−15.8271	+	5.74964i	−1.22842	+	0.446259i
$167$	−4.45358	−	3.68432i	−0.344628	−	0.285101i	0.448966	−	0.893549i	$-0.351793\pi$
$167$	−4.45358	−	3.68432i	−0.344628	−	0.285101i	−0.793594	+	0.608448i	$0.791793\pi$
$168$	−2.46895	+	3.70133i	−0.190483	+	0.285564i
$169$	8.86453	+	3.50972i	0.681887	+	0.269978i
$170$	4.38498	−	0.837313i	0.336313	−	0.0642190i
$171$	12.4590	−	10.3070i	0.952765	−	0.788196i
$172$	1.80461	+	0.836521i	0.137600	+	0.0637842i
$173$	0.813244	+	4.26318i	0.0618298	+	0.324123i	0.999741	−	0.0227519i	$-0.00724276\pi$
$173$	0.813244	+	4.26318i	0.0618298	+	0.324123i	−0.937911	+	0.346875i	$0.887243\pi$
$174$	1.16538	+	5.14398i	0.0883474	+	0.389964i
$175$	−5.41351	+	16.3603i	−0.409223	+	1.23672i
$176$	12.5531	+	10.1435i	0.946226	+	0.764598i
$177$	3.17572	+	1.49438i	0.238702	+	0.112325i
$178$	14.2271	−	9.72873i	1.06636	−	0.729199i
$179$	−8.75985	−	22.1249i	−0.654742	−	1.65369i	−0.752591	−	0.658489i	$-0.771196\pi$
$179$	−8.75985	−	22.1249i	−0.654742	−	1.65369i	0.0978483	−	0.995201i	$-0.468804\pi$
$180$	−8.85510	−	8.80101i	−0.660020	−	0.655989i
$181$	19.6857	+	1.23852i	1.46323	+	0.0920584i	0.774321	−	0.632793i	$-0.218091\pi$
$181$	19.6857	+	1.23852i	1.46323	+	0.0920584i	0.688906	+	0.724851i	$0.258091\pi$
$182$	−3.57981	+	8.33826i	−0.265353	+	0.618073i
$183$	3.11474	+	0.195963i	0.230248	+	0.0144860i
$184$	7.52918	+	7.40018i	0.555058	+	0.545548i
$185$	−0.364450	+	10.6796i	−0.0267949	+	0.785181i
$186$	1.43962	+	3.30064i	0.105558	+	0.242015i
$187$	−5.65101	+	0.713889i	−0.413243	+	0.0522047i
$188$	9.74968	−	11.9245i	0.711068	−	0.869685i
$189$	−6.23659	+	6.64130i	−0.453645	+	0.483083i
$190$	−12.5359	+	13.3543i	−0.909449	+	0.968821i
$191$	−5.18087	−	11.0099i	−0.374874	−	0.796648i	−0.999872	−	0.0160215i	$-0.994900\pi$
$191$	−5.18087	−	11.0099i	−0.374874	−	0.796648i	0.624997	−	0.780627i	$-0.285100\pi$
$192$	2.19689	+	2.91643i	0.158547	+	0.210475i
$193$			8.67952i			0.624765i	0.949956	+	0.312383i	$0.101127\pi$
$193$			8.67952i			0.624765i	−0.949956	+	0.312383i	$0.898873\pi$
$194$	19.6793	+	9.95583i	1.41289	+	0.714787i
$195$	1.56856	+	1.07219i	0.112327	+	0.0767810i
$196$	8.85242	+	4.10352i	0.632316	+	0.293108i
$197$	−8.06603	+	12.7100i	−0.574681	+	0.905552i	0.425319	+	0.905044i	$0.360162\pi$
$197$	−8.06603	+	12.7100i	−0.574681	+	0.905552i	−1.00000		0.000508842i	$0.999838\pi$
$198$	10.5687	+	11.9185i	0.751088	+	0.847012i
$199$	7.17147	+	5.21038i	0.508372	+	0.369354i	0.812206	−	0.583371i	$-0.198267\pi$
$199$	7.17147	+	5.21038i	0.508372	+	0.369354i	−0.303834	+	0.952725i	$0.598267\pi$
$200$	11.2026	+	8.63149i	0.792141	+	0.610338i
$201$	−1.73374	+	1.25964i	−0.122289	+	0.0888479i
$202$	−21.9497	−	4.84001i	−1.54438	−	0.340542i
$203$	26.1854	−	10.3675i	1.83786	−	0.727659i
$204$	−1.27938	−	0.154142i	−0.0895747	−	0.0107921i
$205$	7.83333	+	2.84406i	0.547103	+	0.198637i
$206$	−12.5793	+	12.6519i	−0.876438	+	0.881501i
$207$	6.12467	+	8.42989i	0.425694	+	0.585918i
$208$	5.48687	+	5.03483i	0.380446	+	0.349103i
$209$	17.0359	−	15.9978i	1.17840	−	1.10659i
$210$	2.92313	−	4.02489i	0.201715	−	0.277744i
$211$	−10.9440	−	19.9071i	−0.753419	−	1.37046i	−0.922943	−	0.384937i	$-0.874223\pi$
$211$	−10.9440	−	19.9071i	−0.753419	−	1.37046i	0.169524	−	0.985526i	$-0.445777\pi$
$212$	2.19464	+	0.125388i	0.150728	+	0.00861168i
$213$	0.296537	+	0.163023i	0.0203184	+	0.0111701i
$214$	14.4880	−	12.8472i	0.990379	−	0.878219i
$215$	−1.97873	−	1.01494i	−0.134948	−	0.0692185i
$216$	3.45175	+	6.63215i	0.234862	+	0.451261i
$217$	16.2345	−	10.3027i	1.10207	−	0.699395i
$218$	13.3504	−	7.94736i	0.904200	−	0.538263i
$219$	−1.25668	−	4.89443i	−0.0849182	−	0.330735i
$220$	−13.5716	−	11.8913i	−0.914995	−	0.801708i
$221$	−2.62300	+	0.165025i	−0.176442	+	0.0111008i
$222$	1.03650	−	2.90520i	0.0695651	−	0.194985i
$223$	−2.48709	−	4.52399i	−0.166548	−	0.302949i	0.779842	−	0.625976i	$-0.215299\pi$
$223$	−2.48709	−	4.52399i	−0.166548	−	0.302949i	−0.946390	+	0.323027i	$0.895299\pi$
$224$	13.5862	−	13.9832i	0.907767	−	0.934295i
$225$	9.50020	+	10.2267i	0.633347	+	0.681777i
$226$	4.74058	+	0.434346i	0.315339	+	0.0288922i
$227$	5.59237	+	5.25159i	0.371179	+	0.348560i	0.847580	−	0.530668i	$-0.178059\pi$
$227$	5.59237	+	5.25159i	0.371179	+	0.348560i	−0.476401	+	0.879228i	$0.658059\pi$
$228$	4.61842	−	2.57375i	0.305863	−	0.170451i
$229$	16.6214	+	10.5483i	1.09837	+	0.697048i	0.956177	−	0.292790i	$-0.0945837\pi$
$229$	16.6214	+	10.5483i	1.09837	+	0.697048i	0.142196	+	0.989839i	$0.454584\pi$
$230$	−8.08138	−	8.60263i	−0.532870	−	0.567241i
$231$	−4.04564	+	4.89034i	−0.266184	+	0.321761i
$232$	−0.925540	−	23.0937i	−0.0607647	−	1.51618i
$233$	1.96687	+	7.66047i	0.128854	+	0.501854i	0.999942	+	0.0107275i	$0.00341473\pi$
$233$	1.96687	+	7.66047i	0.128854	+	0.501854i	−0.871088	+	0.491127i	$0.836585\pi$
$234$	4.52164	+	5.79472i	0.295589	+	0.378813i
$235$	−11.4232	+	12.8869i	−0.745171	+	0.840650i
$236$	−12.4944	−	8.96822i	−0.813317	−	0.583781i
$237$	0.265980	−	1.39432i	0.0172773	−	0.0905707i
$238$	0.235939	+	6.87681i	0.0152937	+	0.445757i
$239$	28.2885	+	3.57367i	1.82983	+	0.231161i	0.963387	−	0.268113i	$-0.0864001\pi$
$239$	28.2885	+	3.57367i	1.82983	+	0.231161i	0.866444	+	0.499275i	$0.166400\pi$
$240$	−2.32427	−	3.35598i	−0.150031	−	0.216628i
$241$	−4.13502	+	21.6765i	−0.266360	+	1.39631i	0.557812	+	0.829967i	$0.311641\pi$
$241$	−4.13502	+	21.6765i	−0.266360	+	1.39631i	−0.824172	+	0.566340i	$0.808359\pi$
$242$	5.29466	+	5.26425i	0.340354	+	0.338399i
$243$	3.46160	+	10.6537i	0.222062	+	0.683437i
$244$	−13.2656	−	3.32469i	−0.849241	−	0.212841i
$245$	−9.70656	−	4.97875i	−0.620129	−	0.318081i
$246$	−1.90502	−	1.46892i	−0.121460	−	0.0936549i
$247$	8.30861	−	6.87348i	0.528664	−	0.437349i
$248$	−3.57509	−	15.3690i	−0.227018	−	0.975935i
$249$	−5.43449			−0.344397
$250$	−12.1302	−	10.1419i	−0.767182	−	0.641429i
$251$			13.5579i			0.855766i	0.903834	+	0.427883i	$0.140740\pi$
$251$			13.5579i			0.855766i	−0.903834	+	0.427883i	$0.859260\pi$
$252$	15.5028	−	11.4004i	0.976583	−	0.718160i
$253$	9.59944	+	11.6037i	0.603512	+	0.729520i
$254$	−14.0003	+	18.1569i	−0.878459	+	1.13926i
$255$	1.42239	+	0.229217i	0.0890733	+	0.0143542i
$256$	−7.14419	−	14.3164i	−0.446512	−	0.894778i
$257$	−23.3093	+	7.57364i	−1.45399	+	0.472431i	−0.926229	−	0.376961i	$-0.876969\pi$
$257$	−23.3093	+	7.57364i	−1.45399	+	0.472431i	−0.527763	+	0.849392i	$0.676969\pi$
$258$	0.455220	+	0.452606i	0.0283408	+	0.0281780i
$259$	−16.1787	−	3.08626i	−1.00530	−	0.191771i
$260$	−5.90524	−	5.86917i	−0.366228	−	0.363991i
$261$	2.85911	−	22.6322i	0.176975	−	1.40090i
$262$	8.04703	−	0.276089i	0.497147	−	0.0170568i
$263$	29.3478	+	5.59840i	1.80967	+	0.345212i	0.977763	−	0.209711i	$-0.0672523\pi$
$263$	29.3478	+	5.59840i	1.80967	+	0.345212i	0.831902	+	0.554923i	$0.187252\pi$
$264$	2.69003	+	4.46018i	0.165560	+	0.274505i
$265$	−2.44614	−	0.237885i	−0.150265	−	0.0146132i
$266$	−17.3675	−	22.2574i	−1.06487	−	1.36469i
$267$	5.38764	−	1.38331i	0.329718	−	0.0846572i
$268$	8.47385	−	4.04727i	0.517623	−	0.247226i
$269$	−6.50943	−	5.38507i	−0.396887	−	0.328334i	0.417477	−	0.908687i	$-0.362914\pi$
$269$	−6.50943	−	5.38507i	−0.396887	−	0.328334i	−0.814365	+	0.580354i	$0.802914\pi$
$270$	−3.56053	−	7.56291i	−0.216687	−	0.460264i
$271$	−8.47168	+	13.3492i	−0.514618	+	0.810908i	−0.997915	−	0.0645484i	$-0.979439\pi$
$271$	−8.47168	+	13.3492i	−0.514618	+	0.810908i	0.483297	+	0.875457i	$0.339439\pi$
$272$	5.39019	+	1.68298i	0.326829	+	0.102046i
$273$	−2.00472	+	2.13481i	−0.121331	+	0.129205i
$274$	23.5973	+	2.16206i	1.42557	+	0.130615i
$275$	14.6315	+	13.8891i	0.882310	+	0.837545i
$276$	1.46840	+	3.07442i	0.0883873	+	0.185058i
$277$	16.3136	−	8.96848i	0.980189	−	0.538864i	0.0907287	−	0.995876i	$-0.471080\pi$
$277$	16.3136	−	8.96848i	0.980189	−	0.538864i	0.889460	+	0.457012i	$0.151080\pi$
$278$	3.30227	+	1.17816i	0.198057	+	0.0706612i
$279$	−0.977926	−	15.5437i	−0.0585469	−	0.930576i
$280$	−15.8010	+	15.0158i	−0.944288	+	0.897367i
$281$	21.3707	−	5.48706i	1.27487	−	0.327330i	0.450189	−	0.892933i	$-0.351356\pi$
$281$	21.3707	−	5.48706i	1.27487	−	0.327330i	0.824678	+	0.565603i	$0.191356\pi$
$282$	4.27145	−	2.54276i	0.254361	−	0.151419i
$283$	8.67231	+	13.6654i	0.515515	+	0.812322i	0.997976	−	0.0635955i	$-0.0202568\pi$
$283$	8.67231	+	13.6654i	0.515515	+	0.812322i	−0.482460	+	0.875918i	$0.660257\pi$
$284$	−1.14798	−	0.938608i	−0.0681202	−	0.0556961i
$285$	−5.27416	+	2.66943i	−0.312414	+	0.158123i
$286$	7.04803	+	7.94815i	0.416759	+	0.469984i
$287$	−6.18811	+	11.2561i	−0.365273	+	0.664429i
$288$	−4.62380	−	15.1001i	−0.272460	−	0.889783i
$289$	13.1508	−	7.22972i	0.773577	−	0.425278i
$290$	0.00474137	+	25.8403i	0.000278423	+	1.51739i
$291$	4.87235	+	5.18852i	0.285622	+	0.304157i
$292$	1.51765	+	22.0911i	0.0888138	+	1.29278i
$293$	0.572309	−	0.415807i	0.0334346	−	0.0242917i	−0.570942	−	0.820990i	$-0.693422\pi$
$293$	0.572309	−	0.415807i	0.0334346	−	0.0242917i	0.604377	+	0.796698i	$0.293422\pi$
$294$	2.23306	+	2.22024i	0.130235	+	0.129487i
$295$	13.5584	+	10.5756i	0.789399	+	0.615738i
$296$	−6.77974	+	11.6933i	−0.394065	+	0.679662i
$297$	3.92623	+	9.91653i	0.227823	+	0.575415i
$298$	−18.0928	−	3.98955i	−1.04809	−	0.231109i
$299$	4.08439	+	5.62168i	0.236206	+	0.325110i
$300$	2.44698	+	3.85270i	0.141277	+	0.222436i
$301$	2.01475	−	2.77306i	0.116128	−	0.159837i
$302$	1.58238	−	1.40317i	0.0910555	−	0.0807435i
$303$	−6.12478	−	3.88690i	−0.351859	−	0.223297i
$304$	−21.9506	+	7.41280i	−1.25895	+	0.425153i
$305$	14.6714	+	4.30537i	0.840081	+	0.246525i
$306$	4.97327	+	2.51599i	0.284303	+	0.143830i
$307$	14.0393			0.801268			0.400634	−	0.916238i	$-0.368790\pi$
$307$	14.0393			0.801268			0.400634	+	0.916238i	$0.368790\pi$
$308$	21.3271	−	17.8512i	1.21522	−	1.01717i
$309$	−5.20992	+	2.45160i	−0.296382	+	0.139467i
$310$	3.30894	+	17.3288i	0.187935	+	0.984208i
$311$	1.71296	+	1.60858i	0.0971331	+	0.0912140i	0.731593	−	0.681742i	$-0.238777\pi$
$311$	1.71296	+	1.60858i	0.0971331	+	0.0912140i	−0.634460	+	0.772956i	$0.718777\pi$
$312$	1.10955	+	2.13187i	0.0628157	+	0.120693i
$313$	−0.237345	−	1.87878i	−0.0134155	−	0.106195i	0.983985	−	0.178251i	$-0.0570439\pi$
$313$	−0.237345	−	1.87878i	−0.0134155	−	0.106195i	−0.997401	+	0.0720563i	$0.977044\pi$
$314$	5.14827	+	11.8036i	0.290533	+	0.666113i
$315$	−17.8269	+	12.0450i	−1.00443	+	0.678660i
$316$	−2.25642	+	5.79640i	−0.126934	+	0.326073i
$317$	−1.14059	+	18.1292i	−0.0640622	+	1.01824i	0.826371	+	0.563126i	$0.190401\pi$
$317$	−1.14059	+	18.1292i	−0.0640622	+	1.01824i	−0.890433	+	0.455114i	$0.849599\pi$
$318$	0.651894	+	0.279873i	0.0365564	+	0.0156945i
$319$	2.07020	−	32.9049i	0.115909	−	1.84232i
$320$	7.34306	+	16.3119i	0.410489	+	0.911865i
$321$	5.81042	−	2.30051i	0.324306	−	0.128402i
$322$	15.0173	−	10.2691i	0.836879	−	0.572273i
$323$	3.48149	−	7.39855i	0.193715	−	0.411666i
$324$	−1.87883	−	14.2136i	−0.104379	−	0.789642i
$325$	6.33544	+	6.81990i	0.351427	+	0.378300i
$326$	1.93977	−	0.439461i	0.107434	−	0.0243395i
$327$	4.92539	−	0.939569i	0.272375	−	0.0519583i
$328$	7.03916	+	7.84664i	0.388673	+	0.433258i
$329$	−16.9194	−	20.4521i	−0.932797	−	1.12756i
$330$	−2.80638	−	5.10256i	−0.154486	−	0.280887i
$331$	−11.6864	+	29.5166i	−0.642345	+	1.62238i	0.133202	+	0.991089i	$0.457474\pi$
$331$	−11.6864	+	29.5166i	−0.642345	+	1.62238i	−0.775547	+	0.631290i	$0.782526\pi$
$332$	23.4176	+	4.32749i	1.28521	+	0.237502i
$333$	−8.50391	+	10.2795i	−0.466011	+	0.563311i
$334$	2.79104	+	7.68292i	0.152719	+	0.420391i
$335$	−9.64689	+	4.14374i	−0.527066	+	0.226396i
$336$	5.66206	−	2.74447i	0.308891	−	0.149723i
$337$	−9.77590	−	10.4103i	−0.532527	−	0.567084i	0.405301	−	0.914183i	$-0.367167\pi$
$337$	−9.77590	−	10.4103i	−0.532527	−	0.567084i	−0.937828	+	0.347099i	$0.887167\pi$
$338$	−8.29458	−	10.6300i	−0.451166	−	0.578193i
$339$	1.39012	+	0.654142i	0.0755011	+	0.0355281i
$340$	−5.94662	−	2.12036i	−0.322501	−	0.114993i
$341$	−2.82118	−	22.3320i	−0.152776	−	1.20934i
$342$	−22.5756	+	3.64230i	−1.22075	+	0.196953i
$343$	−4.29752	+	5.91503i	−0.232044	+	0.319381i
$344$	−1.60116	−	2.31280i	−0.0863288	−	0.124698i
$345$	−1.50340	−	3.50001i	−0.0809402	−	0.188434i
$346$	2.06245	−	5.78086i	0.110878	−	0.310781i
$347$	0.359254	+	5.71018i	0.0192858	+	0.306538i	0.995830	+	0.0912235i	$0.0290778\pi$
$347$	0.359254	+	5.71018i	0.0192858	+	0.306538i	−0.976545	+	0.215315i	$0.930922\pi$
$348$	2.26407	−	7.10713i	0.121367	−	0.380982i
$349$	−14.4366	−	4.69073i	−0.772773	−	0.251089i	−0.104021	−	0.994575i	$-0.533171\pi$
$349$	−14.4366	−	4.69073i	−0.772773	−	0.251089i	−0.668752	+	0.743486i	$0.733171\pi$
$350$	18.3212	−	16.0706i	0.979309	−	0.859012i
$351$	1.52074	+	4.68035i	0.0811710	+	0.249819i
$352$	−8.03985	−	21.3613i	−0.428525	−	1.13856i
$353$	1.75991	−	6.85440i	0.0936706	−	0.364823i	−0.904416	−	0.426651i	$-0.859693\pi$
$353$	1.75991	−	6.85440i	0.0936706	−	0.364823i	0.998087	+	0.0618285i	$0.0196932\pi$
$354$	−2.80174	−	4.09720i	−0.148911	−	0.217764i
$355$	1.24063	+	1.09972i	0.0658459	+	0.0583673i
$356$	−24.3172	+	1.67058i	−1.28881	+	0.0885408i
$357$	−0.686223	+	2.11198i	−0.0363188	+	0.111778i
$358$	−5.16866	+	33.2532i	−0.273172	+	1.75749i
$359$	20.9422	+	11.5131i	1.10529	+	0.607638i	0.926517	−	0.376253i	$-0.122788\pi$
$359$	20.9422	+	11.5131i	1.10529	+	0.607638i	0.178772	+	0.983891i	$0.442788\pi$
$360$	4.49248	+	17.0751i	0.236775	+	0.899936i
$361$	2.72612	+	14.2908i	0.143480	+	0.752149i
$362$	−23.1163	−	15.6127i	−1.21497	−	0.820586i
$363$	1.02596	+	2.18028i	0.0538490	+	0.114435i
$364$	10.3384	−	7.60266i	0.541880	−	0.398488i
$365$	−0.710901	−	24.7466i	−0.0372103	−	1.29530i
$366$	−3.65755	−	2.47030i	−0.191183	−	0.129125i
$367$	10.1048	−	25.5218i	0.527466	−	1.33223i	−0.384940	−	0.922942i	$-0.625778\pi$
$367$	10.1048	−	25.5218i	0.527466	−	1.33223i	0.912406	−	0.409286i	$-0.134222\pi$
$368$	−3.87926	−	14.4171i	−0.202220	−	0.751545i
$369$	5.57496	+	8.78473i	0.290221	+	0.457315i
$370$	8.09510	−	12.7610i	0.420844	−	0.663413i
$371$	0.942067	−	3.66911i	0.0489097	−	0.190491i
$372$	0.609146	−	5.05593i	0.0315827	−	0.262138i
$373$	−24.1490	−	3.05073i	−1.25039	−	0.157961i	−0.527878	−	0.849320i	$-0.677012\pi$
$373$	−24.1490	−	3.05073i	−1.25039	−	0.157961i	−0.722511	+	0.691359i	$0.757012\pi$
$374$	7.40193	+	3.17782i	0.382745	+	0.164321i
$375$	−2.56193	−	4.41309i	−0.132298	−	0.227891i
$376$	−20.4307	+	7.55555i	−1.05363	+	0.389648i
$377$	1.90667	−	15.0928i	0.0981984	−	0.777321i
$378$	12.3623	−	3.63021i	0.635846	−	0.186718i
$379$	0.108505	−	0.422598i	0.00557351	−	0.0217074i	−0.965736	−	0.259528i	$-0.916433\pi$
$379$	0.108505	−	0.422598i	0.00557351	−	0.0217074i	0.971309	+	0.237821i	$0.0764330\pi$
$380$	24.8523	−	7.30290i	1.27490	−	0.374631i
$381$	−6.24760	+	3.96485i	−0.320074	+	0.203125i
$382$	−1.57008	+	17.1363i	−0.0803322	+	0.876770i
$383$	−4.83142	+	12.2028i	−0.246874	+	0.623533i	−0.999386	−	0.0350462i	$-0.988842\pi$
$383$	−4.83142	+	12.2028i	−0.246874	+	0.623533i	0.752512	+	0.658579i	$0.228842\pi$
$384$	−0.589481	−	5.12994i	−0.0300818	−	0.261786i
$385$	−24.6211	+	18.9919i	−1.25481	+	0.967918i
$386$	6.21787	−	10.5833i	0.316481	−	0.538675i
$387$	−1.18214	−	2.51218i	−0.0600918	−	0.127701i
$388$	−16.8636	−	26.2375i	−0.856120	−	1.33201i
$389$	−30.1636	+	5.75401i	−1.52935	+	0.291740i	−0.882294	−	0.470699i	$-0.844002\pi$
$389$	−30.1636	+	5.75401i	−1.52935	+	0.291740i	−0.647060	+	0.762439i	$0.724002\pi$
$390$	−1.14451	−	2.43106i	−0.0579547	−	0.123101i
$391$	4.61740	+	2.53844i	0.233512	+	0.128374i
$392$	−7.85443	−	11.3453i	−0.396708	−	0.573026i
$393$	2.47137	+	0.802998i	0.124664	+	0.0405059i
$394$	18.9405	−	9.71949i	0.954210	−	0.489661i
$395$	2.77908	−	6.37486i	0.139831	−	0.320754i
$396$	−4.34867	−	22.1040i	−0.218529	−	1.11077i
$397$	−3.67020	−	0.942348i	−0.184202	−	0.0472951i	0.155462	−	0.987842i	$-0.450313\pi$
$397$	−3.67020	−	0.942348i	−0.184202	−	0.0472951i	−0.339664	+	0.940547i	$0.610313\pi$
$398$	−5.01184	−	11.4908i	−0.251221	−	0.575980i
$399$	−2.81552	−	8.66527i	−0.140952	−	0.433806i
$400$	−7.47629	−	18.5501i	−0.373814	−	0.927504i
$401$	−9.74348	+	29.9873i	−0.486566	+	1.49750i	0.343134	+	0.939287i	$0.388512\pi$
$401$	−9.74348	+	29.9873i	−0.486566	+	1.49750i	−0.829700	+	0.558210i	$0.811488\pi$
$402$	3.01641	−	0.293902i	0.150445	−	0.0146585i
$403$	−0.652154	−	10.3657i	−0.0324861	−	0.516352i
$404$	23.2969	+	21.6261i	1.15906	+	1.07594i
$405$	1.46547	+	15.9623i	0.0728197	+	0.793175i
$406$	−39.3561	−	6.11726i	−1.95321	−	0.303594i
$407$	−11.3334	+	15.5992i	−0.561778	+	0.773221i
$408$	1.44958	+	1.10448i	0.0717649	+	0.0546800i
$409$	11.2914	−	1.42643i	0.558322	−	0.0705325i	0.158892	−	0.987296i	$-0.449208\pi$
$409$	11.2914	−	1.42643i	0.558322	−	0.0705325i	0.399430	+	0.916764i	$0.369208\pi$
$410$	−7.51406	−	9.07955i	−0.371093	−	0.448407i
$411$	6.91966	+	3.25614i	0.341322	+	0.160614i
$412$	24.4021	−	6.41543i	1.20220	−	0.316066i
$413$	−19.3203	+	18.1430i	−0.950689	+	0.892756i
$414$	−1.42903	−	14.6665i	−0.0702328	−	0.720821i
$415$	−25.9679	−	5.87809i	−1.27472	−	0.288544i
$416$	−3.08349	−	10.0699i	−0.151181	−	0.493717i
$417$	0.871867	+	0.721271i	0.0426955	+	0.0353208i
$418$	−32.2332	+	7.30251i	−1.57658	+	0.357177i
$419$	8.00527	−	20.2190i	0.391083	−	0.987763i	−0.592218	−	0.805778i	$-0.701748\pi$
$419$	8.00527	−	20.2190i	0.391083	−	0.987763i	0.983301	−	0.181986i	$-0.0582524\pi$
$420$	−6.44766	+	2.81364i	−0.314614	+	0.137291i
$421$	16.9653	−	14.0349i	0.826837	−	0.684019i	−0.124484	−	0.992222i	$-0.539727\pi$
$421$	16.9653	−	14.0349i	0.826837	−	0.684019i	0.951321	+	0.308203i	$0.0997275\pi$
$422$	−0.916642	+	32.1137i	−0.0446214	+	1.56327i
$423$	−21.1193	+	4.02872i	−1.02685	+	0.195883i
$424$	−2.58619	−	1.72509i	−0.125596	−	0.0837780i
$425$	6.54875	+	2.63377i	0.317661	+	0.127757i
$426$	−0.244793	−	0.411215i	−0.0118603	−	0.0199234i
$427$	−10.0344	+	21.3242i	−0.485599	+	1.03195i
$428$	−26.8694	+	5.28619i	−1.29878	+	0.255517i
$429$	1.26207	+	3.18761i	0.0609331	+	0.153899i
$430$	1.68565	+	2.65509i	0.0812895	+	0.128040i
$431$	1.68301	−	26.7506i	0.0810676	−	1.28853i	−0.721685	−	0.692221i	$-0.756632\pi$
$431$	1.68301	−	26.7506i	0.0810676	−	1.28853i	0.802753	−	0.596312i	$-0.203368\pi$
$432$	0.542308	−	10.5596i	0.0260918	−	0.508051i
$433$	20.0251	+	1.25988i	0.962347	+	0.0605457i	0.536184	−	0.844101i	$-0.319865\pi$
$433$	20.0251	+	1.25988i	0.962347	+	0.0605457i	0.426163	+	0.904647i	$0.359865\pi$
$434$	−27.1761	+	0.932397i	−1.30450	+	0.0447565i
$435$	−2.84604	+	7.83880i	−0.136457	+	0.375842i
$436$	−21.9720	+	0.126562i	−1.05227	+	0.00606124i
$437$	−21.4484	+	2.70957i	−1.02602	+	0.129616i
$438$	−1.97398	+	6.86824i	−0.0943202	+	0.328177i
$439$	3.88603	+	3.64923i	0.185470	+	0.174168i	0.771720	−	0.635962i	$-0.219396\pi$
$439$	3.88603	+	3.64923i	0.185470	+	0.174168i	−0.586250	+	0.810130i	$0.699396\pi$
$440$	8.02967	+	24.2220i	0.382799	+	1.15474i
$441$	−5.79895	−	12.3234i	−0.276141	−	0.586829i
$442$	3.31655	+	1.67785i	0.157752	+	0.0798073i
$443$	−20.8359			−0.989943			−0.494971	−	0.868909i	$-0.664821\pi$
$443$	−20.8359			−0.989943			−0.494971	+	0.868909i	$0.664821\pi$
$444$	−3.34509	+	2.79991i	−0.158751	+	0.132878i
$445$	27.2403	−	0.782538i	1.29131	−	0.0370959i
$446$	−0.208311	+	7.29800i	−0.00986383	+	0.345570i
$447$	−5.04857	−	3.20392i	−0.238789	−	0.151540i
$448$	−26.5836	+	7.31740i	−1.25596	+	0.345715i
$449$	18.8765	+	13.7146i	0.890836	+	0.647230i	0.936096	−	0.351745i	$-0.114412\pi$
$449$	18.8765	+	13.7146i	0.890836	+	0.647230i	−0.0452600	+	0.998975i	$0.514412\pi$
$450$	−4.25777	−	19.2756i	−0.200713	−	0.908659i
$451$	8.83871	+	12.1654i	0.416199	+	0.572848i
$452$	−5.46923	−	3.92570i	−0.257251	−	0.184649i
$453$	0.634614	−	0.251261i	0.0298168	−	0.0118053i
$454$	−3.05685	−	10.4098i	−0.143465	−	0.488554i
$455$	−11.8883	+	8.03252i	−0.557334	+	0.376571i
$456$	−7.47523	−	0.170284i	−0.350060	−	0.00797426i
$457$	−12.3766	−	17.0350i	−0.578955	−	0.796864i	0.414625	−	0.909992i	$-0.363913\pi$
$457$	−12.3766	−	17.0350i	−0.578955	−	0.796864i	−0.993580	+	0.113129i	$0.963913\pi$
$458$	−12.7105	−	24.7692i	−0.593925	−	1.15739i
$459$	2.55452	+	2.72028i	0.119235	+	0.126972i
$460$	3.69117	+	16.2789i	0.172102	+	0.759008i
$461$	−5.33721	−	9.70835i	−0.248579	−	0.452163i	0.722351	−	0.691526i	$-0.243061\pi$
$461$	−5.33721	−	9.70835i	−0.248579	−	0.452163i	−0.970930	+	0.239363i	$0.923061\pi$
$462$	8.43638	−	3.06476i	0.392496	−	0.142586i
$463$	−5.17085	+	9.40574i	−0.240310	+	0.437122i	−0.968768	−	0.247968i	$-0.920237\pi$
$463$	−5.17085	+	9.40574i	−0.240310	+	0.437122i	0.728458	+	0.685090i	$0.240237\pi$
$464$	−15.4154	+	28.8222i	−0.715644	+	1.33804i
$465$	−0.905833	+	5.62106i	−0.0420070	+	0.260670i
$466$	3.08955	−	10.7498i	0.143121	−	0.497973i
$467$	8.99203	+	14.1692i	0.416101	+	0.655671i	0.986134	−	0.165951i	$-0.0530694\pi$
$467$	8.99203	+	14.1692i	0.416101	+	0.655671i	−0.570032	+	0.821622i	$0.693069\pi$
$468$	−1.36217	−	10.3050i	−0.0629664	−	0.476348i
$469$	−4.02450	−	15.6744i	−0.185834	−	0.723777i
$470$	23.1608	−	7.53011i	1.06833	−	0.347338i
$471$	0.260954	+	4.14775i	0.0120241	+	0.191118i
$472$	8.81026	+	19.8861i	0.405525	+	0.915333i
$473$	−1.93314	−	3.51637i	−0.0888860	−	0.161683i
$474$	−1.32319	+	1.50960i	−0.0607761	+	0.0693385i
$475$	−28.0891	+	7.05081i	−1.28882	+	0.323513i
$476$	4.63875	−	8.55420i	0.212617	−	0.392081i
$477$	−2.23674	−	2.10044i	−0.102413	−	0.0961727i
$478$	−31.9332	−	24.6230i	−1.46059	−	1.12623i
$479$	17.5597	−	27.6697i	0.802324	−	1.26426i	−0.158572	−	0.987347i	$-0.550689\pi$
$479$	17.5597	−	27.6697i	0.802324	−	1.26426i	0.960895	−	0.276912i	$-0.0893111\pi$
$480$	0.429909	+	5.75716i	0.0196226	+	0.262777i
$481$	−5.67104	+	6.85511i	−0.258577	+	0.312566i
$482$	20.5707	−	23.4688i	0.936970	−	1.06897i
$483$	5.68687	−	1.46014i	0.258761	−	0.0664386i
$484$	−2.68477	−	10.2119i	−0.122035	−	0.464179i
$485$	17.6698	+	30.0627i	0.802343	+	1.36508i
$486$	3.41128	−	15.4704i	0.154739	−	0.701750i
$487$	−29.7235	−	5.67005i	−1.34690	−	0.256935i	−0.537039	−	0.843558i	$-0.680457\pi$
$487$	−29.7235	−	5.67005i	−1.34690	−	0.256935i	−0.809860	+	0.586623i	$0.800457\pi$
$488$	13.7935	+	13.5572i	0.624402	+	0.613704i
$489$	0.636829	+	0.0804502i	0.0287984	+	0.00363808i
$490$	8.26891	+	13.0244i	0.373551	+	0.588384i
$491$	−35.2092	−	6.71651i	−1.58897	−	0.303112i	−0.684291	−	0.729209i	$-0.739888\pi$
$491$	−35.2092	−	6.71651i	−1.58897	−	0.303112i	−0.904678	+	0.426097i	$0.859888\pi$
$492$	1.27056	+	3.15584i	0.0572814	+	0.142276i
$493$	−3.56471	−	10.9710i	−0.160546	−	0.494111i
$494$	−15.0551	+	2.42896i	−0.677360	+	0.109284i
$495$	3.87298	+	24.8872i	0.174078	+	1.11860i
$496$	−6.65089	+	21.3012i	−0.298634	+	0.956454i
$497$	−1.96893	+	1.62884i	−0.0883187	+	0.0730636i
$498$	6.62650	+	3.89319i	0.296941	+	0.174458i
$499$		−	27.7624i		−	1.24281i	−0.783488	−	0.621407i	$-0.786561\pi$
$499$		−	27.7624i		−	1.24281i	0.783488	−	0.621407i	$-0.213439\pi$
$500$	7.52538	+	21.0563i	0.336545	+	0.941667i
$501$			2.63806i			0.117860i
$502$	9.71266	−	16.5317i	0.433497	−	0.737845i
$503$	17.0091	−	14.0711i	0.758397	−	0.627400i	−0.175691	−	0.984445i	$-0.556216\pi$
$503$	17.0091	−	14.0711i	0.758397	−	0.627400i	0.934087	+	0.357045i	$0.116216\pi$
$504$	−27.0703	+	2.79507i	−1.20581	+	0.124502i
$505$	−25.0622	−	25.1977i	−1.11525	−	1.12128i
$506$	−3.39226	−	21.0258i	−0.150804	−	0.934711i
$507$	−1.34467	−	4.13847i	−0.0597188	−	0.183796i
$508$	30.0785	−	12.1098i	1.33452	−	0.537285i
$509$	−11.8893	−	2.26801i	−0.526984	−	0.100528i	−0.0829782	−	0.996551i	$-0.526443\pi$
$509$	−11.8893	−	2.26801i	−0.526984	−	0.100528i	−0.444006	+	0.896024i	$0.646443\pi$
$510$	−1.57017	−	1.29847i	−0.0695282	−	0.0574972i
$511$	37.8577	+	4.78254i	1.67473	+	0.211567i
$512$	−1.54487	+	22.5746i	−0.0682741	+	0.997667i
$513$	−15.0396	−	2.86896i	−0.664014	−	0.126668i
$514$	33.8476	+	7.46354i	1.49295	+	0.329203i
$515$	−27.5466	+	6.07944i	−1.21385	+	0.267892i
$516$	−0.230829	−	0.877994i	−0.0101617	−	0.0386515i
$517$	−30.0975	+	7.72773i	−1.32369	+	0.339865i
$518$	17.5165	+	15.3534i	0.769629	+	0.674590i
$519$	1.26264	−	1.52627i	0.0554237	−	0.0669957i
$520$	2.99592	+	11.3869i	0.131380	+	0.499351i
$521$	15.8951	−	25.0467i	0.696379	−	1.09732i	−0.293577	−	0.955936i	$-0.594846\pi$
$521$	15.8951	−	25.0467i	0.696379	−	1.09732i	0.989955	−	0.141381i	$-0.0451544\pi$
$522$	−19.6996	+	25.5481i	−0.862227	+	1.11821i
$523$	10.5062	+	9.86600i	0.459405	+	0.431410i	0.879376	−	0.476127i	$-0.157960\pi$
$523$	10.5062	+	9.86600i	0.459405	+	0.431410i	−0.419971	+	0.907537i	$0.637960\pi$
$524$	−10.0099	−	5.42812i	−0.437283	−	0.237129i
$525$	7.32837	−	2.85589i	0.319836	−	0.124641i
$526$	−31.7744	−	27.8507i	−1.38543	−	1.21435i
$527$	−3.79414	−	6.90152i	−0.165276	−	0.300635i
$528$	−0.0848568	−	7.36558i	−0.00369292	−	0.320546i
$529$	0.569423	+	9.05071i	0.0247575	+	0.393509i
$530$	2.81226	+	2.04244i	0.122157	+	0.0887179i
$531$	5.33884	+	20.7934i	0.231686	+	0.902357i
$532$	5.23206	+	39.5812i	0.226839	+	1.71606i
$533$	3.71780	+	5.85831i	0.161036	+	0.253752i
$534$	−7.56035	−	2.17289i	−0.327168	−	0.0940302i
$535$	30.2526	−	4.70795i	1.30793	−	0.203542i
$536$	−13.2319	−	1.13553i	−0.571532	−	0.0490473i
$537$	−5.23218	+	9.51730i	−0.225785	+	0.410702i
$538$	4.07944	+	11.2295i	0.175877	+	0.484138i
$539$	−9.48295	−	17.2494i	−0.408459	−	0.742985i
$540$	−1.07645	+	11.7725i	−0.0463230	+	0.506607i
$541$	−7.68393	−	8.18256i	−0.330358	−	0.351796i	0.542250	−	0.840217i	$-0.317573\pi$
$541$	−7.68393	−	8.18256i	−0.330358	−	0.351796i	−0.872608	+	0.488422i	$0.837573\pi$
$542$	19.8931	−	10.2083i	0.854480	−	0.438484i
$543$	−5.29155	−	7.28320i	−0.227082	−	0.312552i
$544$	−5.36682	−	5.91358i	−0.230101	−	0.253543i
$545$	24.5516	+	0.837840i	1.05167	+	0.0358891i
$546$	3.97378	−	1.16691i	0.170062	−	0.0499392i
$547$	−0.411269	+	0.162833i	−0.0175846	+	0.00696223i	−0.376900	−	0.926254i	$-0.623010\pi$
$547$	−0.411269	+	0.162833i	−0.0175846	+	0.00696223i	0.359316	+	0.933216i	$0.383010\pi$
$548$	−27.2244	−	19.5411i	−1.16297	−	0.834753i
$549$	11.2204	+	15.4436i	0.478877	+	0.659117i
$550$	−7.89080	−	27.4173i	−0.336465	−	1.16908i
$551$	38.2906	+	27.8197i	1.63123	+	1.18516i
$552$	0.411983	−	4.80070i	0.0175352	−	0.204331i
$553$	9.05028	+	5.74348i	0.384857	+	0.244238i
$554$	−26.3167	−	0.751175i	−1.11809	−	0.0319143i
$555$	3.86173	−	2.97882i	0.163921	−	0.126444i
$556$	−3.18258	−	3.80227i	−0.134971	−	0.161252i
$557$	8.36975			0.354638			0.177319	−	0.984153i	$-0.443258\pi$
$557$	8.36975			0.354638			0.177319	+	0.984153i	$0.443258\pi$
$558$	−9.94283	+	19.6536i	−0.420913	+	0.832004i
$559$	−0.788342	−	1.67531i	−0.0333433	−	0.0708581i
$560$	30.0239	−	6.98984i	1.26874	−	0.295375i
$561$	1.89509	+	1.77960i	0.0800106	+	0.0751350i
$562$	−29.9890	−	8.61902i	−1.26501	−	0.363572i
$563$	37.0900	−	4.68555i	1.56316	−	0.197473i	0.704380	−	0.709823i	$-0.251225\pi$
$563$	37.0900	−	4.68555i	1.56316	−	0.197473i	0.858776	+	0.512351i	$0.171225\pi$
$564$	−7.02995	+	0.0404937i	−0.296014	+	0.00170509i
$565$	5.93497	+	4.62932i	0.249686	+	0.194757i
$566$	−0.784844	−	22.8755i	−0.0329895	−	0.961528i
$567$	−24.6581	−	1.55136i	−1.03554	−	0.0651508i
$568$	0.727378	+	1.96688i	0.0305201	+	0.0825285i
$569$	−0.914989	+	14.5433i	−0.0383583	+	0.609688i	0.931151	+	0.364634i	$0.118806\pi$
$569$	−0.914989	+	14.5433i	−0.0383583	+	0.609688i	−0.969509	+	0.245055i	$0.921194\pi$
$570$	8.34333	+	0.523381i	0.349464	+	0.0219220i
$571$	−1.00155	−	2.52963i	−0.0419137	−	0.105862i	0.907312	−	0.420458i	$-0.138131\pi$
$571$	−1.00155	−	2.52963i	−0.0419137	−	0.105862i	−0.949225	+	0.314597i	$0.898131\pi$
$572$	−2.90002	−	14.7406i	−0.121256	−	0.616336i
$573$	−2.36460	+	5.02503i	−0.0987826	+	0.209924i
$574$	15.6091	−	9.29200i	0.651513	−	0.387841i
$575$	−3.39807	−	18.3504i	−0.141709	−	0.765265i
$576$	−5.17950	+	21.7246i	−0.215813	+	0.905192i
$577$	21.9439	−	4.18602i	0.913536	−	0.174266i	0.290878	−	0.956760i	$-0.406053\pi$
$577$	21.9439	−	4.18602i	0.913536	−	0.174266i	0.622658	+	0.782494i	$0.286053\pi$
$578$	−21.2146	−	0.605541i	−0.882410	−	0.0251872i
$579$	3.05233	−	2.52511i	0.126850	−	0.104940i
$580$	18.5058	−	31.5115i	0.768412	−	1.30845i
$581$	15.1071	−	38.1562i	0.626748	−	1.58299i
$582$	−2.22408	−	9.81705i	−0.0921910	−	0.406930i
$583$	−3.41697	−	2.82676i	−0.141516	−	0.117072i
$584$	13.9752	−	28.0238i	0.578297	−	1.15963i
$585$	1.06248	+	11.5729i	0.0439281	+	0.478479i
$586$	−0.995717	+	0.0970171i	−0.0411327	+	0.00400774i
$587$	17.0953	−	16.0535i	0.705597	−	0.662600i	−0.246238	−	0.969209i	$-0.579195\pi$
$587$	17.0953	−	16.0535i	0.705597	−	0.662600i	0.951835	+	0.306609i	$0.0991945\pi$
$588$	−1.13232	−	4.30696i	−0.0466962	−	0.177616i
$589$	29.2379	+	13.7583i	1.20473	+	0.566902i
$590$	−8.95607	−	22.6083i	−0.368716	−	0.930770i
$591$	6.81637	−	0.861108i	0.280388	−	0.0354212i
$592$	16.6437	−	9.40127i	0.684054	−	0.386390i
$593$	−12.9743	+	17.8575i	−0.532789	+	0.733322i	−0.987552	−	0.157291i	$-0.949724\pi$
$593$	−12.9743	+	17.8575i	−0.532789	+	0.733322i	0.454763	+	0.890613i	$0.349724\pi$
$594$	2.31663	−	14.9043i	0.0950525	−	0.611532i
$595$	−5.56339	+	9.34955i	−0.228077	+	0.383294i
$596$	19.2033	+	17.8261i	0.786598	+	0.730184i
$597$	−0.254039	−	4.03783i	−0.0103971	−	0.165258i
$598$	−0.952981	−	9.78074i	−0.0389703	−	0.399964i
$599$	−10.7841	+	33.1901i	−0.440627	+	1.35611i	0.446582	+	0.894743i	$0.352641\pi$
$599$	−10.7841	+	33.1901i	−0.440627	+	1.35611i	−0.887209	+	0.461367i	$0.847359\pi$
$600$	−0.223691	−	6.45074i	−0.00913216	−	0.263350i
$601$	−6.03805	−	18.5832i	−0.246297	−	0.758025i	−0.995420	−	0.0955940i	$-0.969525\pi$
$601$	−6.03805	−	18.5832i	−0.246297	−	0.758025i	0.749123	−	0.662431i	$-0.230475\pi$
$602$	−4.44324	+	1.93798i	−0.181093	+	0.0789860i
$603$	−12.6962	−	3.25984i	−0.517031	−	0.132751i
$604$	−2.93467	+	0.577357i	−0.119410	+	0.0234923i
$605$	2.54416	+	11.5279i	0.103435	+	0.468674i
$606$	4.68368	+	9.12715i	0.190261	+	0.370765i
$607$	42.1219	+	13.6862i	1.70967	+	0.555507i	0.990279	−	0.139093i	$-0.0444188\pi$
$607$	42.1219	+	13.6862i	1.70967	+	0.555507i	0.719396	+	0.694600i	$0.244419\pi$
$608$	32.0756	+	6.68630i	1.30084	+	0.271165i
$609$	−11.2640	−	6.19244i	−0.456440	−	0.250930i
$610$	−14.8051	−	15.7601i	−0.599442	−	0.638107i
$611$	−14.0839	+	2.68665i	−0.569774	+	0.108690i
$612$	−4.26170	−	6.63063i	−0.172269	−	0.268027i
$613$	16.3682	+	34.7841i	0.661104	+	1.40492i	0.900871	+	0.434087i	$0.142929\pi$
$613$	16.3682	+	34.7841i	0.661104	+	1.40492i	−0.239767	+	0.970830i	$0.577071\pi$
$614$	−17.1188	−	10.0576i	−0.690857	−	0.405890i
$615$	−1.27876	−	3.58216i	−0.0515644	−	0.144447i
$616$	−38.7934	+	6.48833i	−1.56303	+	0.261422i
$617$	12.7395	−	32.1762i	0.512872	−	1.29537i	−0.410640	−	0.911797i	$-0.634695\pi$
$617$	12.7395	−	32.1762i	0.512872	−	1.29537i	0.923512	−	0.383569i	$-0.125305\pi$
$618$	8.10895	+	0.742965i	0.326190	+	0.0298864i
$619$	19.6786	−	12.4884i	0.790948	−	0.501951i	−0.0779411	−	0.996958i	$-0.524835\pi$
$619$	19.6786	−	12.4884i	0.790948	−	0.501951i	0.868889	+	0.495007i	$0.164835\pi$
$620$	8.37934	−	23.5002i	0.336523	−	0.943789i
$621$	2.45367	−	9.55642i	0.0984624	−	0.383486i
$622$	−0.936324	−	3.18854i	−0.0375432	−	0.127849i
$623$	−5.26448	+	41.6726i	−0.210917	+	1.66958i
$624$	0.174322	−	3.39434i	0.00697847	−	0.135882i
$625$	−7.46852	−	23.8584i	−0.298741	−	0.954334i
$626$	−1.05652	+	2.46090i	−0.0422271	+	0.0983573i
$627$	−10.5822	−	1.33684i	−0.422611	−	0.0533882i
$628$	2.17839	−	18.0807i	0.0869273	−	0.721499i
$629$	−1.67774	+	6.53438i	−0.0668960	+	0.260543i
$630$	30.3660	−	1.91606i	1.20981	−	0.0763377i
$631$	−1.61671	−	2.54753i	−0.0643604	−	0.101416i	0.810624	−	0.585567i	$-0.199128\pi$
$631$	−1.61671	−	2.54753i	−0.0643604	−	0.101416i	−0.874984	+	0.484152i	$0.839128\pi$
$632$	6.90380	−	5.45132i	0.274618	−	0.216842i
$633$	−3.81683	+	9.64022i	−0.151705	+	0.383164i
$634$	14.3783	−	21.2886i	0.571034	−	0.845479i
$635$	−34.1417	+	12.1879i	−1.35487	+	0.483661i
$636$	−0.594384	−	0.808268i	−0.0235689	−	0.0320499i
$637$	−3.86718	−	8.21817i	−0.153223	−	0.325616i
$638$	−26.0968	+	38.6392i	−1.03318	+	1.52974i
$639$	0.387847	+	2.03317i	0.0153430	+	0.0804309i
$640$	2.73193	−	25.1503i	0.107989	−	0.994152i
$641$	19.2982	+	10.6093i	0.762231	+	0.419040i	0.814922	−	0.579571i	$-0.196780\pi$
$641$	19.2982	+	10.6093i	0.762231	+	0.419040i	−0.0526906	+	0.998611i	$0.516780\pi$
$642$	−8.73294	−	1.35739i	−0.344662	−	0.0535719i
$643$	−4.94794	+	15.2282i	−0.195128	+	0.600541i	0.804848	+	0.593482i	$0.202247\pi$
$643$	−4.94794	+	15.2282i	−0.195128	+	0.600541i	−0.999975	+	0.00705922i	$0.997753\pi$
$644$	−25.6678	+	1.76337i	−1.01145	+	0.0694865i
$645$	0.218740	+	0.991134i	0.00861288	+	0.0390259i
$646$	−9.54533	+	6.52727i	−0.375556	+	0.256812i
$647$	4.87451	−	18.9849i	0.191637	−	0.746375i	−0.797985	−	0.602677i	$-0.794101\pi$
$647$	4.87451	−	18.9849i	0.191637	−	0.746375i	0.989622	−	0.143698i	$-0.0458994\pi$
$648$	−7.89144	+	18.6771i	−0.310005	+	0.733707i
$649$	9.58791	+	29.5086i	0.376358	+	1.15831i
$650$	−2.83940	−	12.8544i	−0.111370	−	0.504191i
$651$	−8.34622	−	2.71185i	−0.327114	−	0.106286i
$652$	−2.68007	−	0.853772i	−0.104960	−	0.0334363i
$653$	−1.51791	−	24.1264i	−0.0594002	−	0.944139i	−0.909022	−	0.416747i	$-0.863170\pi$
$653$	−1.51791	−	24.1264i	−0.0594002	−	0.944139i	0.849622	−	0.527392i	$-0.176830\pi$
$654$	−6.67883	−	2.38282i	−0.261163	−	0.0931757i
$655$	10.9406	+	6.51011i	0.427483	+	0.254371i
$656$	−2.96193	−	14.6105i	−0.115644	−	0.570443i
$657$	18.1675	−	25.0054i	0.708781	−	0.975554i
$658$	5.97900	+	37.0588i	0.233086	+	1.44470i
$659$	1.66967	+	13.2168i	0.0650411	+	0.514854i	0.990656	+	0.136386i	$0.0435488\pi$
$659$	1.66967	+	13.2168i	0.0650411	+	0.514854i	−0.925615	+	0.378467i	$0.876451\pi$
$660$	−0.233465	+	8.23221i	−0.00908762	+	0.320438i
$661$	−33.7815	−	15.8964i	−1.31395	−	0.618297i	−0.364203	−	0.931320i	$-0.618659\pi$
$661$	−33.7815	−	15.8964i	−1.31395	−	0.618297i	−0.949746	+	0.313022i	$0.898659\pi$
$662$	35.3950	−	27.6188i	1.37567	−	1.07344i
$663$	0.821135	+	0.874420i	0.0318902	+	0.0339597i
$664$	−25.4538	−	22.0527i	−0.987801	−	0.855809i
$665$	−4.08096	−	44.4511i	−0.158253	−	1.72374i
$666$	17.7332	−	6.44210i	0.687148	−	0.249626i
$667$	−19.4412	+	23.5004i	−0.752767	+	0.909939i
$668$	2.10069	−	11.3676i	0.0812782	−	0.439824i
$669$	−0.867394	+	2.19079i	−0.0335354	+	0.0847007i
$670$	14.7314	+	1.85826i	0.569122	+	0.0717908i
$671$	17.5862	+	21.2581i	0.678909	+	0.820660i
$672$	−8.87009	−	0.709764i	−0.342171	−	0.0273797i
$673$	49.5724	−	9.45644i	1.91088	−	0.364519i	0.911926	−	0.410354i	$-0.134595\pi$
$673$	49.5724	−	9.45644i	1.91088	−	0.364519i	0.998949	+	0.0458354i	$0.0145950\pi$
$674$	4.46240	+	19.6970i	0.171885	+	0.758699i
$675$	1.72722	−	13.1036i	0.0664806	−	0.504358i
$676$	2.49879	+	18.9037i	0.0961075	+	0.727064i
$677$	−14.8852	+	31.6326i	−0.572084	+	1.21574i	0.384187	+	0.923255i	$0.374482\pi$
$677$	−14.8852	+	31.6326i	−0.572084	+	1.21574i	−0.956270	+	0.292484i	$0.905518\pi$
$678$	−1.22642	−	1.79349i	−0.0471003	−	0.0688784i
$679$	−49.9736	+	19.7860i	−1.91781	+	0.759316i
$680$	5.73197	+	6.84551i	0.219811	+	0.262513i
$681$	0.219855	−	3.49450i	0.00842487	−	0.133910i
$682$	−12.5583	+	29.2513i	−0.480881	+	1.12009i
$683$	1.28532	−	20.4296i	0.0491816	−	0.781719i	−0.893715	−	0.448634i	$-0.851911\pi$
$683$	1.28532	−	20.4296i	0.0491816	−	0.781719i	0.942897	−	0.333084i	$-0.108089\pi$
$684$	30.1366	+	11.7316i	1.15230	+	0.448568i
$685$	29.5427	+	23.0435i	1.12877	+	0.880447i
$686$	9.47758	−	4.13376i	0.361856	−	0.157828i
$687$	−1.12610	−	8.91402i	−0.0429635	−	0.340091i
$688$	0.295510	+	3.96714i	0.0112662	+	0.151246i
$689$	−1.49163	−	1.40073i	−0.0568265	−	0.0533636i
$690$	−0.674199	+	5.34472i	−0.0256663	+	0.203470i
$691$	21.4329	−	10.0855i	0.815345	−	0.383672i	0.0275580	−	0.999620i	$-0.491227\pi$
$691$	21.4329	−	10.0855i	0.815345	−	0.383672i	0.787787	+	0.615948i	$0.211227\pi$
$692$	−6.65615	+	5.57134i	−0.253029	+	0.211790i
$693$	−38.8213			−1.47470
$694$	3.65263	−	7.22002i	0.138652	−	0.274068i
$695$	3.38595	+	4.38953i	0.128436	+	0.166504i
$696$	−7.85212	+	7.04408i	−0.297634	+	0.267005i
$697$	4.44227	+	2.81915i	0.168263	+	0.106783i
$698$	14.2428	+	16.0618i	0.539097	+	0.607946i
$699$	2.12174	−	2.92033i	0.0802517	−	0.110457i
$700$	−33.8525	+	6.47059i	−1.27951	+	0.244565i
$701$	−4.78297	−	6.58319i	−0.180650	−	0.248644i	0.709083	−	0.705125i	$-0.249109\pi$
$701$	−4.78297	−	6.58319i	−0.180650	−	0.248644i	−0.889733	+	0.456482i	$0.849109\pi$
$702$	1.49863	−	6.79638i	0.0565622	−	0.256513i
$703$	−10.1895	−	25.7358i	−0.384306	−	0.970646i
$704$	−5.49957	+	31.8063i	−0.207273	+	1.19875i
$705$	7.85528	+	0.268067i	0.295847	+	0.0100960i
$706$	−7.05632	+	7.09708i	−0.265568	+	0.267102i
$707$	44.3164	−	32.1977i	1.66669	−	1.21092i
$708$	0.481105	+	7.00301i	0.0180810	+	0.263189i
$709$	−15.8972	−	16.9288i	−0.597033	−	0.635775i	0.357489	−	0.933917i	$-0.383633\pi$
$709$	−15.8972	−	16.9288i	−0.597033	−	0.635775i	−0.954521	+	0.298142i	$0.903633\pi$
$710$	−0.724928	−	2.22971i	−0.0272061	−	0.0836795i
$711$	7.60835	−	4.18273i	0.285336	−	0.156865i
$712$	30.8477	+	15.3834i	1.15607	+	0.576519i
$713$	−10.0315	+	18.2473i	−0.375684	+	0.683366i
$714$	2.34973	−	2.08362i	0.0879364	−	0.0779776i
$715$	2.58279	+	16.5966i	0.0965910	+	0.620679i
$716$	30.1244	−	36.8442i	1.12580	−	1.37693i
$717$	−6.97314	−	10.9879i	−0.260417	−	0.410351i
$718$	−17.2879	−	29.0411i	−0.645180	−	1.08380i
$719$	−29.3292	+	7.53047i	−1.09380	+	0.280839i	−0.752151	−	0.658990i	$-0.770984\pi$
$719$	−29.3292	+	7.53047i	−1.09380	+	0.280839i	−0.341644	+	0.939829i	$0.610984\pi$
$720$	6.75446	−	24.0387i	0.251724	−	0.895870i
$721$	−2.73015	−	43.3945i	−0.101676	−	1.61610i
$722$	6.91366	−	19.3784i	0.257300	−	0.721188i
$723$	8.82598	−	4.85212i	0.328242	−	0.180452i
$724$	17.0020	+	35.5974i	0.631874	+	1.32297i
$725$	−22.0781	+	34.3782i	−0.819959	+	1.27678i
$726$	0.310921	−	3.39349i	0.0115394	−	0.125944i
$727$	−11.9431	+	12.7181i	−0.442943	+	0.471687i	−0.911235	−	0.411887i	$-0.864870\pi$
$727$	−11.9431	+	12.7181i	−0.442943	+	0.471687i	0.468291	+	0.883574i	$0.344870\pi$
$728$	−18.0525	+	1.86396i	−0.669069	+	0.0690831i
$729$	−8.78386	+	13.8411i	−0.325328	+	0.512635i
$730$	−16.8612	+	30.6838i	−0.624062	+	1.13566i
$731$	−1.08179	−	0.894935i	−0.0400115	−	0.0331004i
$732$	2.69012	+	5.63235i	0.0994296	+	0.208178i
$733$	8.74750	−	2.24598i	0.323096	−	0.0829570i	−0.0836583	−	0.996494i	$-0.526660\pi$
$733$	8.74750	−	2.24598i	0.323096	−	0.0829570i	0.406755	+	0.913537i	$0.366660\pi$
$734$	−30.6046	+	23.8809i	−1.12964	+	0.881459i
$735$	1.07302	+	4.86196i	0.0395789	+	0.179336i
$736$	−5.59807	+	20.3584i	−0.206347	+	0.750422i
$737$	−18.6093	−	3.54991i	−0.685482	−	0.130763i
$738$	−0.504534	−	14.7054i	−0.0185721	−	0.541313i
$739$	2.37565	−	18.8052i	0.0873896	−	0.691760i	−0.886175	−	0.463350i	$-0.846647\pi$
$739$	2.37565	−	18.8052i	0.0873896	−	0.691760i	0.973565	−	0.228410i	$-0.0733527\pi$
$740$	−19.0125	+	9.76082i	−0.698912	+	0.358815i
$741$	−4.83440	−	0.922210i	−0.177596	−	0.0338782i
$742$	−3.77719	+	3.79901i	−0.138665	+	0.139466i
$743$	7.56779	−	2.45893i	0.277635	−	0.0902092i	−0.166890	−	0.985976i	$-0.553372\pi$
$743$	7.56779	−	2.45893i	0.277635	−	0.0902092i	0.444525	+	0.895766i	$0.353372\pi$
$744$	−4.36475	+	5.72852i	−0.160019	+	0.210018i
$745$	−20.6584	−	20.7701i	−0.756866	−	0.760959i
$746$	27.2604	+	21.0199i	0.998074	+	0.769592i
$747$	−21.1884	−	25.6124i	−0.775244	−	0.937109i
$748$	−6.74894	−	9.17748i	−0.246766	−	0.335562i
$749$			47.1907i			1.72431i
$750$	−0.0375952	+	7.21639i	−0.00137278	+	0.263505i
$751$	−9.07299			−0.331078			−0.165539	−	0.986203i	$-0.552936\pi$
$751$	−9.07299			−0.331078			−0.165539	+	0.986203i	$0.552936\pi$
$752$	30.3247	+	5.42347i	1.10583	+	0.197773i
$753$	4.76791	−	3.94436i	0.173752	−	0.143740i
$754$	−13.1372	+	17.0374i	−0.478427	+	0.620466i
$755$	3.30418	−	0.514202i	0.120252	−	0.0187137i
$756$	−17.6744	−	4.42967i	−0.642813	−	0.161105i
$757$	−10.3924	−	31.9846i	−0.377719	−	1.16250i	−0.941626	−	0.336662i	$-0.890702\pi$
$757$	−10.3924	−	31.9846i	−0.377719	−	1.16250i	0.563906	−	0.825839i	$-0.309298\pi$
$758$	−0.435046	+	0.437560i	−0.0158016	+	0.0158929i
$759$	1.28795	−	6.75168i	0.0467497	−	0.245070i
$760$	−35.5352	−	8.89909i	−1.28900	−	0.322804i
$761$	−30.8607	−	3.89861i	−1.11870	−	0.141324i	−0.455835	−	0.890064i	$-0.650659\pi$
$761$	−30.8607	−	3.89861i	−1.11870	−	0.141324i	−0.662864	+	0.748740i	$0.730659\pi$
$762$	10.4583	−	0.358819i	0.378865	−	0.0129986i
$763$	−7.09506	+	37.1936i	−0.256859	+	1.34650i
$764$	14.1907	−	19.7702i	0.513400	−	0.715262i
$765$	4.46543	+	7.59731i	0.161448	+	0.274681i
$766$	14.6330	−	11.4182i	0.528713	−	0.412556i
$767$	3.56034	+	13.8666i	0.128556	+	0.500694i
$768$	−2.95623	+	6.67744i	−0.106674	+	0.240951i
$769$	8.87838	−	10.7321i	0.320163	−	0.387010i	−0.585738	−	0.810500i	$-0.699195\pi$
$769$	8.87838	−	10.7321i	0.320163	−	0.387010i	0.905901	+	0.423490i	$0.139195\pi$
$770$	43.6270	−	5.51950i	1.57221	−	0.198909i
$771$	9.44472	+	5.99380i	0.340143	+	0.215861i
$772$	−15.1634	+	8.45026i	−0.545743	+	0.304132i
$773$	−7.97336	−	7.48748i	−0.286782	−	0.269306i	0.527782	−	0.849380i	$-0.323024\pi$
$773$	−7.97336	−	7.48748i	−0.286782	−	0.269306i	−0.814564	+	0.580074i	$0.803024\pi$
$774$	−0.358252	+	3.91008i	−0.0128771	+	0.140545i
$775$	−10.4083	+	25.8797i	−0.373876	+	0.929625i
$776$	1.76635	+	44.0733i	0.0634082	+	1.58214i
$777$	3.62149	+	6.58746i	0.129920	+	0.236324i
$778$	40.9018	+	14.5926i	1.46640	+	0.523171i
$779$	−21.5441	+	1.35544i	−0.771899	+	0.0485637i
$780$	−0.346019	+	3.78420i	−0.0123895	+	0.135496i
$781$	0.743954	+	2.89751i	0.0266208	+	0.103681i
$782$	−3.81169	−	6.40306i	−0.136306	−	0.228973i
$783$	−18.2377	+	11.5740i	−0.651762	+	0.413621i
$784$	1.44961	+	19.4606i	0.0517718	+	0.695022i
$785$	−3.23938	+	20.1017i	−0.115619	+	0.717460i
$786$	−2.43819	−	2.74958i	−0.0869674	−	0.0980743i
$787$	34.7687	+	19.1143i	1.23937	+	0.681350i	0.960313	−	0.278925i	$-0.0899779\pi$
$787$	34.7687	+	19.1143i	1.23937	+	0.681350i	0.279058	+	0.960274i	$0.409978\pi$
$788$	−30.0578	−	1.71732i	−1.07077	−	0.0611769i
$789$	−6.56929	−	11.9495i	−0.233873	−	0.425413i
$790$	−7.95550	+	5.78224i	−0.283044	+	0.205723i
$791$	−8.45715	+	7.94179i	−0.300702	+	0.282378i
$792$	−10.5325	+	30.0677i	−0.374255	+	1.06841i
$793$	7.48263	+	10.2990i	0.265716	+	0.365727i
$794$	3.80015	+	3.77832i	0.134862	+	0.134088i
$795$	0.627991	+	0.929442i	0.0222726	+	0.0329639i
$796$	−2.12066	+	17.6016i	−0.0751649	+	0.623871i
$797$	29.6457	−	11.7376i	1.05011	−	0.415766i	0.221243	−	0.975219i	$-0.428989\pi$
$797$	29.6457	−	11.7376i	1.05011	−	0.415766i	0.828862	+	0.559453i	$0.188989\pi$
$798$	−2.77459	+	12.5829i	−0.0982194	+	0.445430i
$799$	−8.79580	+	6.39052i	−0.311173	+	0.226081i
$800$	−4.17284	+	27.9748i	−0.147532	+	0.989057i
$801$	27.5252	+	19.9982i	0.972555	+	0.706602i
$802$	33.3631	−	29.5847i	1.17809	−	1.04467i
$803$	23.9361	−	37.7173i	0.844688	−	1.33101i
$804$	−3.88858	−	1.80254i	−0.137140	−	0.0635707i
$805$	28.7532	−	0.826001i	1.01342	−	0.0291127i
$806$	−6.63062	+	13.1065i	−0.233554	+	0.461657i
$807$			3.85584i			0.135732i
$808$	−12.9143	−	43.0591i	−0.454323	−	1.51481i
$809$	−6.96534	−	14.8021i	−0.244888	−	0.520414i	0.744161	−	0.668000i	$-0.232850\pi$
$809$	−6.96534	−	14.8021i	−0.244888	−	0.520414i	−0.989049	+	0.147586i	$0.952850\pi$
$810$	9.64827	−	20.5134i	0.339006	−	0.720767i
$811$	−11.7743	+	12.5383i	−0.413451	+	0.440281i	−0.901660	−	0.432446i	$-0.857651\pi$
$811$	−11.7743	+	12.5383i	−0.413451	+	0.440281i	0.488209	+	0.872727i	$0.337651\pi$
$812$	43.6062	+	35.6531i	1.53028	+	1.25118i
$813$	7.15917	−	0.904414i	0.251083	−	0.0317192i
$814$	24.9943	−	10.9016i	0.876051	−	0.382100i
$815$	2.95598	+	1.07323i	0.103543	+	0.0375936i
$816$	−0.976298	−	2.38520i	−0.0341773	−	0.0834986i
$817$	5.74907	+	0.361701i	0.201135	+	0.0126543i
$818$	−14.7899	−	6.34965i	−0.517117	−	0.222010i
$819$	−17.8774	−	1.12475i	−0.624686	−	0.0393019i
$820$	2.65776	+	16.4540i	0.0928130	+	0.574599i
$821$	−2.44435	−	6.17372i	−0.0853084	−	0.215464i	0.880860	−	0.473377i	$-0.156965\pi$
$821$	−2.44435	−	6.17372i	−0.0853084	−	0.215464i	−0.966168	+	0.257913i	$0.916965\pi$
$822$	−6.10478	−	8.92749i	−0.212929	−	0.311382i
$823$	12.2307	+	5.75531i	0.426334	+	0.200617i	0.626962	−	0.779050i	$-0.284298\pi$
$823$	12.2307	+	5.75531i	0.426334	+	0.200617i	−0.200628	+	0.979668i	$0.564298\pi$
$824$	−34.3503	−	9.65865i	−1.19665	−	0.336475i
$825$	0.627700	−	9.18617i	0.0218537	−	0.319821i
$826$	36.5554	−	8.28170i	1.27192	−	0.288157i
$827$	−2.59916	−	13.6253i	−0.0903816	−	0.473797i	−0.998484	−	0.0550481i	$-0.982469\pi$
$827$	−2.59916	−	13.6253i	−0.0903816	−	0.473797i	0.908102	−	0.418749i	$-0.137531\pi$
$828$	−8.76441	+	18.9072i	−0.304584	+	0.657072i
$829$	−28.6861	+	23.7312i	−0.996308	+	0.824218i	−0.984442	−	0.175712i	$-0.943777\pi$
$829$	−28.6861	+	23.7312i	−0.996308	+	0.824218i	−0.0118663	+	0.999930i	$0.503777\pi$
$830$	27.4528	+	25.7704i	0.952901	+	0.894505i
$831$	−7.90001	−	3.12784i	−0.274048	−	0.108503i
$832$	−3.45408	+	14.4876i	−0.119749	+	0.502267i
$833$	−5.30667	−	4.39006i	−0.183865	−	0.152107i
$834$	−0.546396	−	1.50407i	−0.0189202	−	0.0520816i
$835$	−2.85340	+	12.6056i	−0.0987458	+	0.436235i
$836$	44.5347	+	14.1871i	1.54026	+	0.490671i
$837$	−10.7501	+	10.0951i	−0.371579	+	0.348936i
$838$	−24.2457	+	18.9190i	−0.837555	+	0.653547i
$839$	−16.0575	+	34.1239i	−0.554366	+	1.17809i	0.409651	+	0.912243i	$0.365651\pi$
$839$	−16.0575	+	34.1239i	−0.554366	+	1.17809i	−0.964016	+	0.265844i	$0.914349\pi$
$840$	9.87755	+	1.18822i	0.340808	+	0.0409976i
$841$	37.4743	−	4.73410i	1.29222	−	0.163245i
$842$	−30.7408	+	4.95967i	−1.05940	+	0.170922i
$843$	−8.14694	−	5.91910i	−0.280596	−	0.203865i
$844$	24.1235	−	38.5009i	0.830364	−	1.32526i
$845$	−1.94903	−	21.2295i	−0.0670488	−	0.730317i
$846$	28.6377	+	10.2171i	0.984585	+	0.351273i
$847$	−18.1600	+	1.14253i	−0.623986	+	0.0392578i
$848$	1.91761	+	3.95618i	0.0658511	+	0.135856i
$849$	2.28270	−	7.02542i	0.0783420	−	0.241112i
$850$	−6.09836	−	7.90289i	−0.209172	−	0.271067i
$851$	16.9639	−	5.51192i	0.581516	−	0.188946i
$852$	0.00389836	+	0.676778i	0.000133555	+	0.0231860i
$853$	31.4248	+	8.06851i	1.07596	+	0.276260i	0.744783	−	0.667307i	$-0.232553\pi$
$853$	31.4248	+	8.06851i	1.07596	+	0.276260i	0.331180	+	0.943567i	$0.392553\pi$
$854$	27.5117	−	18.8130i	0.941431	−	0.643767i
$855$	−33.1441	−	14.4490i	−1.13351	−	0.494145i
$856$	36.5499	+	12.8031i	1.24925	+	0.437602i
$857$	36.6359	+	11.9037i	1.25146	+	0.406624i	0.858444	−	0.512908i	$-0.171432\pi$
$857$	36.6359	+	11.9037i	1.25146	+	0.406624i	0.393016	+	0.919532i	$0.371432\pi$
$858$	0.744669	−	4.79091i	0.0254226	−	0.163559i
$859$	17.4464	−	31.7349i	0.595265	−	1.08278i	−0.391432	−	0.920207i	$-0.628020\pi$
$859$	17.4464	−	31.7349i	0.595265	−	1.08278i	0.986696	−	0.162575i	$-0.0519800\pi$
$860$	−0.153323	−	4.44504i	−0.00522828	−	0.151575i
$861$	5.75874	−	1.09854i	0.196257	−	0.0374381i
$862$	−21.2159	+	31.4125i	−0.722616	+	1.06991i
$863$	−26.1886	+	12.3234i	−0.891469	+	0.419493i	−0.816267	−	0.577675i	$-0.803960\pi$
$863$	−26.1886	+	12.3234i	−0.891469	+	0.419493i	−0.0752019	+	0.997168i	$0.523960\pi$
$864$	−8.22602	+	12.4873i	−0.279855	+	0.424827i
$865$	7.68419	−	5.92735i	0.261270	−	0.201536i
$866$	−23.5149	−	15.8819i	−0.799070	−	0.539690i
$867$	−6.36840	−	2.52143i	−0.216282	−	0.0856322i
$868$	33.8049	+	18.3316i	1.14741	+	0.622216i
$869$	10.5949	−	6.72376i	0.359409	−	0.228088i
$870$	9.08589	−	7.51931i	0.308041	−	0.254929i
$871$	−8.46680	−	2.17390i	−0.286887	−	0.0736600i
$872$	26.8820	+	15.5861i	0.910341	+	0.527811i
$873$	−5.45648	+	43.1925i	−0.184674	+	1.46184i
$874$	28.0941	+	12.0614i	0.950296	+	0.407985i
$875$	38.1066	−	5.71988i	1.28824	−	0.193367i
$876$	7.32725	−	6.96060i	0.247565	−	0.235177i
$877$	−13.5006	−	1.70552i	−0.455883	−	0.0575914i	−0.105961	−	0.994370i	$-0.533792\pi$
$877$	−13.5006	−	1.70552i	−0.455883	−	0.0575914i	−0.349922	+	0.936779i	$0.613792\pi$
$878$	−2.12415	−	7.23355i	−0.0716866	−	0.244120i
$879$	−0.312727	−	0.0802946i	−0.0105480	−	0.00270827i
$880$	7.56133	−	35.2872i	0.254893	−	1.18953i
$881$	−27.8149	−	43.8293i	−0.937108	−	1.47665i	−0.878150	−	0.478385i	$-0.841222\pi$
$881$	−27.8149	−	43.8293i	−0.937108	−	1.47665i	−0.0589579	−	0.998260i	$-0.518778\pi$
$882$	−1.75739	+	19.1807i	−0.0591745	+	0.645848i
$883$	−32.9443	−	13.0436i	−1.10866	−	0.438951i	−0.258787	−	0.965934i	$-0.583323\pi$
$883$	−32.9443	−	13.0436i	−1.10866	−	0.438951i	−0.849875	+	0.526984i	$0.823323\pi$
$884$	−2.84202	−	4.42180i	−0.0955874	−	0.148721i
$885$	−0.225360	−	7.84482i	−0.00757540	−	0.263701i
$886$	25.4061	+	14.9265i	0.853533	+	0.501466i
$887$	50.0517	−	23.5525i	1.68057	−	0.790817i	0.682361	−	0.731015i	$-0.260953\pi$
$887$	50.0517	−	23.5525i	1.68057	−	0.790817i	0.998210	−	0.0598021i	$-0.0190470\pi$
$888$	6.08461	−	1.01767i	0.204186	−	0.0341509i
$889$	−10.4702	−	54.8868i	−0.351160	−	1.84084i
$890$	−33.7758	−	18.5603i	−1.13217	−	0.622144i
$891$	−13.9341	+	25.3461i	−0.466811	+	0.849125i
$892$	5.48218	−	8.74952i	0.183557	−	0.292956i
$893$	13.7846	−	42.4245i	0.461282	−	1.41968i
$894$	3.86069	+	7.52339i	0.129121	+	0.251620i
$895$	−35.2954	+	39.8178i	−1.17980	+	1.33096i
$896$	37.6566	+	10.1217i	1.25802	+	0.338141i
$897$	0.788719	−	3.07186i	0.0263346	−	0.102566i
$898$	−13.1920	−	30.2455i	−0.440222	−	1.00931i
$899$	43.3559	−	14.0872i	1.44600	−	0.469834i
$900$	−8.61705	+	26.5537i	−0.287235	+	0.885124i
$901$	−1.47568	−	0.479476i	−0.0491619	−	0.0159737i
$902$	−2.06227	−	21.1657i	−0.0686661	−	0.704742i
$903$	−1.56135	+	0.0982317i	−0.0519584	+	0.00326895i
$904$	3.85655	+	8.70483i	0.128267	+	0.289518i
$905$	−17.4072	−	40.5252i	−0.578636	−	1.34710i
$906$	−0.953811	−	0.148254i	−0.0316882	−	0.00492541i
$907$	32.9899	+	23.9686i	1.09541	+	0.795864i	0.980305	−	0.197489i	$-0.0632786\pi$
$907$	32.9899	+	23.9686i	1.09541	+	0.795864i	0.115108	+	0.993353i	$0.463279\pi$
$908$	−3.73004	+	14.8829i	−0.123786	+	0.493908i
$909$	−5.56105	−	44.0202i	−0.184448	−	1.46006i
$910$	20.2503	−	1.27777i	0.671291	−	0.0423577i
$911$	4.81907	−	10.2410i	0.159663	−	0.339301i	−0.808949	−	0.587879i	$-0.799963\pi$
$911$	4.81907	−	10.2410i	0.159663	−	0.339301i	0.968612	+	0.248578i	$0.0799632\pi$
$912$	8.99287	+	5.56278i	0.297784	+	0.184202i
$913$	−32.8872	−	35.0213i	−1.08841	−	1.15904i
$914$	2.88775	+	29.6379i	0.0955184	+	0.980335i
$915$	−2.75423	−	6.41204i	−0.0910522	−	0.211976i
$916$	−2.24580	+	39.3078i	−0.0742034	+	1.29877i
$917$	−12.5080	+	15.1196i	−0.413051	+	0.499292i
$918$	−1.16606	−	5.14697i	−0.0384856	−	0.169875i
$919$	−46.9941	−	18.6063i	−1.55019	−	0.613765i	−0.571777	−	0.820409i	$-0.693746\pi$
$919$	−46.9941	−	18.6063i	−1.55019	−	0.613765i	−0.978416	+	0.206644i	$0.933746\pi$
$920$	7.16117	−	22.4939i	0.236097	−	0.741600i
$921$	−4.08442	−	4.93722i	−0.134586	−	0.162687i
$922$	−0.447030	+	15.6613i	−0.0147221	+	0.515777i
$923$	0.258646	+	1.35587i	0.00851343	+	0.0446289i
$924$	−12.4824	−	2.30671i	−0.410640	−	0.0758851i
$925$	21.6747	−	10.0569i	0.712660	−	0.330670i
$926$	13.0432	−	7.76449i	0.428625	−	0.255157i
$927$	−31.8671	−	14.9955i	−1.04665	−	0.492517i
$928$	39.4445	−	24.1007i	1.29483	−	0.791144i
$929$	49.5313	−	19.6108i	1.62507	−	0.643410i	0.633588	−	0.773671i	$-0.281582\pi$
$929$	49.5313	−	19.6108i	1.62507	−	0.643410i	0.991480	+	0.130261i	$0.0415815\pi$
$930$	5.13136	−	6.20506i	0.168264	−	0.203472i
$931$	28.2018	+	1.77431i	0.924277	+	0.0581506i
$932$	−11.4682	+	10.8943i	−0.375653	+	0.356856i
$933$	0.0673423	−	1.07038i	0.00220469	−	0.0350425i
$934$	−0.813779	−	23.7188i	−0.0266277	−	0.776103i
$935$	7.13053	+	10.5534i	0.233193	+	0.345132i
$936$	−5.72137	+	13.5411i	−0.187009	+	0.442605i
$937$	5.68513	+	45.0024i	0.185725	+	1.47016i	0.759155	+	0.650910i	$0.225612\pi$
$937$	5.68513	+	45.0024i	0.185725	+	1.47016i	−0.573430	+	0.819255i	$0.694388\pi$
$938$	−6.32166	+	21.9955i	−0.206409	+	0.718180i
$939$	−0.591660	+	0.630054i	−0.0193081	+	0.0205610i
$940$	−33.6354	−	7.41029i	−1.09707	−	0.241697i
$941$	38.3397	−	18.0413i	1.24984	−	0.588130i	0.317001	−	0.948425i	$-0.397324\pi$
$941$	38.3397	−	18.0413i	1.24984	−	0.588130i	0.932838	+	0.360295i	$0.117324\pi$
$942$	2.65319	−	5.24447i	0.0864457	−	0.170874i
$943$		−	13.9106i		−	0.452993i
$944$	3.50340	−	30.5595i	0.114026	−	0.994627i
$945$	19.5475	+	5.73628i	0.635880	+	0.186601i
$946$	−0.161915	+	5.67253i	−0.00526430	+	0.184430i
$947$	−2.40672	+	3.79238i	−0.0782079	+	0.123236i	−0.881180	−	0.472780i	$-0.843251\pi$
$947$	−2.40672	+	3.79238i	−0.0782079	+	0.123236i	0.802973	+	0.596016i	$0.203251\pi$
$948$	2.69488	−	0.892812i	0.0875255	−	0.0289972i
$949$	12.1154	−	16.6755i	0.393284	−	0.541309i
$950$	39.3013	+	11.5253i	1.27510	+	0.373929i
$951$	6.70735	−	4.87317i	0.217501	−	0.158023i
$952$	−11.7843	+	7.10736i	−0.381932	+	0.230351i
$953$	0.442646	+	1.11800i	0.0143387	+	0.0362155i	0.936770	−	0.349947i	$-0.113800\pi$
$953$	0.442646	+	1.11800i	0.0143387	+	0.0362155i	−0.922431	+	0.386162i	$0.873800\pi$
$954$	1.22263	+	4.16353i	0.0395841	+	0.134799i
$955$	−16.7341	+	21.4538i	−0.541504	+	0.694228i
$956$	21.2980	+	52.9003i	0.688826	+	1.71092i
$957$	−12.1739	+	8.84489i	−0.393528	+	0.285915i
$958$	−41.2334	+	21.1593i	−1.33219	+	0.683625i
$959$	−42.0974	+	39.5321i	−1.35940	+	1.27656i
$960$	3.60013	−	7.32792i	0.116194	−	0.236508i
$961$	0.108272	−	0.0595232i	0.00349265	−	0.00192010i
$962$	11.8258	−	4.29608i	0.381280	−	0.138511i
$963$	33.4963	+	18.4147i	1.07940	+	0.593407i
$964$	−41.8954	+	13.8799i	−1.34936	+	0.447043i
$965$	17.3163	−	8.76438i	0.557433	−	0.282135i
$966$	−7.98025	−	2.29358i	−0.256760	−	0.0737946i
$967$	34.9725	−	22.1942i	1.12464	−	0.713718i	0.162618	−	0.986689i	$-0.448006\pi$
$967$	34.9725	−	22.1942i	1.12464	−	0.713718i	0.962022	+	0.272971i	$0.0880062\pi$
$968$	−4.04202	+	14.3752i	−0.129915	+	0.462035i
$969$	−3.61471	+	0.928100i	−0.116121	+	0.0298149i
$970$	−0.00904869	−	49.3150i	−0.000290536	−	1.58341i
$971$	19.8616	−	1.24959i	0.637389	−	0.0401011i	0.259191	−	0.965826i	$-0.416544\pi$
$971$	19.8616	−	1.24959i	0.637389	−	0.0401011i	0.378198	+	0.925725i	$0.376544\pi$
$972$	−15.2423	+	16.4199i	−0.488895	+	0.526667i
$973$	−7.48779	+	4.11645i	−0.240048	+	0.131967i
$974$	32.1811	+	28.2072i	1.03115	+	0.903816i
$975$	0.555204	−	4.21208i	0.0177808	−	0.134895i
$976$	−7.10683	−	26.4123i	−0.227484	−	0.845436i
$977$	−35.3700	+	37.6652i	−1.13159	+	1.20502i	−0.155452	+	0.987843i	$0.549683\pi$
$977$	−35.3700	+	37.6652i	−1.13159	+	1.20502i	−0.976133	+	0.217172i	$0.930317\pi$
$978$	−0.718878	−	0.554310i	−0.0229872	−	0.0177249i
$979$	41.5181	+	26.3482i	1.32692	+	0.842091i
$980$	−0.752121	−	21.8049i	−0.0240256	−	0.696533i
$981$	23.6317	+	19.5498i	0.754501	+	0.624177i
$982$	38.1204	+	33.4130i	1.21647	+	1.06625i
$983$	12.6011	+	49.0780i	0.401912	+	1.56535i	0.771549	+	0.636169i	$0.219482\pi$
$983$	12.6011	+	49.0780i	0.401912	+	1.56535i	−0.369637	+	0.929176i	$0.620518\pi$
$984$	0.711548	−	4.75826i	0.0226833	−	0.151688i
$985$	33.5024	+	3.25809i	1.06748	+	0.103811i
$986$	−3.51289	+	15.9312i	−0.111873	+	0.507351i
$987$	−2.27007	+	11.9001i	−0.0722570	+	0.378785i
$988$	20.0973	+	7.82350i	0.639382	+	0.248899i
$989$	−0.465246	+	3.68280i	−0.0147939	+	0.117106i
$990$	13.1063	−	33.1205i	0.416546	−	1.05264i
$991$	−1.88635	+	9.88859i	−0.0599218	+	0.314121i	−0.999610	−	0.0279099i	$-0.991115\pi$
$991$	−1.88635	+	9.88859i	−0.0599218	+	0.314121i	0.939689	+	0.342031i	$0.111115\pi$
$992$	23.3696	−	21.2089i	0.741985	−	0.673383i
$993$	13.7800	−	4.47740i	0.437296	−	0.142086i
$994$	3.56768	−	0.575603i	0.113160	−	0.0182570i
$995$	3.15354	−	19.5690i	0.0999739	−	0.620379i
$996$	−5.29095	−	9.49425i	−0.167650	−	0.300837i
$997$	−32.5543	−	39.3514i	−1.03101	−	1.24627i	−0.968705	−	0.248215i	$-0.920156\pi$
$997$	−32.5543	−	39.3514i	−1.03101	−	1.24627i	−0.0623016	−	0.998057i	$-0.519844\pi$
$998$	−19.8885	+	33.8518i	−0.629560	+	1.07156i
$999$	12.6324			0.399670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.bd.a.109.25	✓	2960
8.5	even	2	inner	1000.2.bd.a.109.138	yes	2960
125.39	even	50	inner	1000.2.bd.a.789.138	yes	2960
1000.789	even	50	inner	1000.2.bd.a.789.25	yes	2960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.bd.a.109.25	✓	2960	1.1	even	1	trivial
1000.2.bd.a.109.138	yes	2960	8.5	even	2	inner
1000.2.bd.a.789.25	yes	2960	1000.789	even	50	inner
1000.2.bd.a.789.138	yes	2960	125.39	even	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.bd (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21934 - 0.716384i) q^{2} +(-0.290927 - 0.351670i) q^{3} +(0.973587 + 1.74703i) q^{4} +(-1.00978 - 1.99508i) q^{5} +(0.102808 + 0.637222i) q^{6} +(3.27785 - 1.06504i) q^{7} +(0.0644140 - 2.82769i) q^{8} +(0.523110 - 2.74224i) q^{9} +(-0.197982 + 3.15607i) q^{10} +(0.505692 - 4.00297i) q^{11} +(0.331138 - 0.850641i) q^{12} +(0.348849 - 1.82873i) q^{13} +(-4.75980 - 1.04956i) q^{14} +(-0.407839 + 0.935532i) q^{15} +(-2.10426 + 3.40178i) q^{16} +(-0.351077 - 1.36735i) q^{17} +(-2.60235 + 2.96898i) q^{18} +(4.46290 + 3.69203i) q^{19} +(2.50237 - 3.70650i) q^{20} +(-1.32816 - 0.842875i) q^{21} +(-3.48428 + 4.51871i) q^{22} +(-2.55506 + 2.72086i) q^{23} +(-1.01316 + 0.800000i) q^{24} +(-2.96070 + 4.02918i) q^{25} +(-1.73544 + 1.97994i) q^{26} +(-2.31642 + 1.27346i) q^{27} +(5.05193 + 4.68962i) q^{28} +(8.15530 - 0.513088i) q^{29} +(1.16750 - 0.848563i) q^{30} +(5.40358 - 1.38740i) q^{31} +(5.00279 - 2.64047i) q^{32} +(-1.55484 + 0.986735i) q^{33} +(-0.551469 + 1.91878i) q^{34} +(-5.43474 - 5.46413i) q^{35} +(5.30008 - 1.75592i) q^{36} +(-4.18774 - 2.30223i) q^{37} +(-2.79688 - 7.69899i) q^{38} +(-0.744600 + 0.409347i) q^{39} +(-5.70652 + 2.72683i) q^{40} +(-2.71681 + 2.55125i) q^{41} +(1.01566 + 1.97923i) q^{42} +(0.804593 - 0.584571i) q^{43} +(7.48566 - 3.01377i) q^{44} +(-5.99922 + 1.72541i) q^{45} +(5.06467 - 1.48725i) q^{46} +(-2.83510 - 7.16065i) q^{47} +(1.80849 - 0.249664i) q^{48} +(3.94690 - 2.86759i) q^{49} +(6.49654 - 2.79194i) q^{50} +(-0.378720 + 0.521264i) q^{51} +(3.53449 - 1.17098i) q^{52} +(0.588932 - 0.928008i) q^{53} +(3.73679 + 0.106662i) q^{54} +(-8.49688 + 3.03321i) q^{55} +(-2.80046 - 9.33737i) q^{56} -2.64358i q^{57} +(-10.3117 - 5.21670i) q^{58} +(-6.95804 + 3.27421i) q^{59} +(-2.03147 + 0.198312i) q^{60} +(-4.68088 + 4.98463i) q^{61} +(-7.58272 - 2.17932i) q^{62} +(-1.20591 - 9.54580i) q^{63} +(-7.99170 - 0.364286i) q^{64} +(-4.00073 + 1.15063i) q^{65} +(2.60277 - 0.0892995i) q^{66} +(0.294826 - 4.68612i) q^{67} +(2.04701 - 1.94458i) q^{68} +(1.70018 + 0.106966i) q^{69} +(2.71239 + 10.5560i) q^{70} +(-0.689360 + 0.272937i) q^{71} +(-7.72052 - 1.65583i) q^{72} +(10.0179 + 4.71405i) q^{73} +(3.45700 + 5.80723i) q^{74} +(2.27829 - 0.131006i) q^{75} +(-2.10509 + 11.3913i) q^{76} +(-2.60573 - 13.6597i) q^{77} +(1.20117 + 0.0342858i) q^{78} +(1.98242 + 2.39634i) q^{79} +(8.91166 + 0.763128i) q^{80} +(-6.66519 - 2.63894i) q^{81} +(5.14039 - 1.16457i) q^{82} +(7.58982 - 9.17452i) q^{83} +(0.179454 - 3.14095i) q^{84} +(-2.37347 + 2.08115i) q^{85} +(-1.39985 + 0.136394i) q^{86} +(-2.55303 - 2.71871i) q^{87} +(-11.2866 - 1.68779i) q^{88} +(-5.18908 + 11.0274i) q^{89} +(8.55115 + 2.19389i) q^{90} +(-0.804194 - 6.36585i) q^{91} +(-7.24100 - 1.81478i) q^{92} +(-2.05996 - 1.49665i) q^{93} +(-1.67282 + 10.7623i) q^{94} +(2.85937 - 12.6320i) q^{95} +(-2.38402 - 0.991149i) q^{96} +(-15.5640 + 0.979204i) q^{97} +(-6.86691 + 0.669073i) q^{98} +(-10.7126 - 3.48072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2960 q - 20 q^{2} - 20 q^{4} - 20 q^{6} - 50 q^{7} - 35 q^{8} - 40 q^{9} - 20 q^{10} - 20 q^{12} - 30 q^{14} - 40 q^{15} - 40 q^{17} - 25 q^{18} - 20 q^{20} + 5 q^{22} - 40 q^{23} - 15 q^{24} - 40 q^{25}+ \cdots - 115 q^{98}+O(q^{100}) \) 2960 * q - 20 * q^2 - 20 * q^4 - 20 * q^6 - 50 * q^7 - 35 * q^8 - 40 * q^9 - 20 * q^10 - 20 * q^12 - 30 * q^14 - 40 * q^15 - 40 * q^17 - 25 * q^18 - 20 * q^20 + 5 * q^22 - 40 * q^23 - 15 * q^24 - 40 * q^25 - 15 * q^26 - 40 * q^28 + 20 * q^30 - 40 * q^31 - 25 * q^32 - 40 * q^33 - 20 * q^34 + 180 * q^36 - 70 * q^38 - 40 * q^39 + 5 * q^40 - 40 * q^41 - 100 * q^42 + 15 * q^44 - 20 * q^46 - 40 * q^47 + 45 * q^48 + 650 * q^49 - 30 * q^50 + 75 * q^52 - 70 * q^54 - 40 * q^55 - 55 * q^56 - 295 * q^58 - 5 * q^60 - 45 * q^62 - 110 * q^63 - 5 * q^64 - 90 * q^65 - 95 * q^66 - 55 * q^70 - 40 * q^71 + 40 * q^72 - 40 * q^73 - 15 * q^74 - 15 * q^76 + 30 * q^78 - 40 * q^79 - 400 * q^80 - 40 * q^81 - 25 * q^82 - 95 * q^84 + 40 * q^86 - 40 * q^87 - 135 * q^88 - 90 * q^89 - 70 * q^90 - 115 * q^92 - 100 * q^94 + 60 * q^95 - 55 * q^96 - 115 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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