LMFDB - Embedded newform 968.2.o.d.493.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [968,2,Mod(245,968)] 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("968.245"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(968, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,-5,0,-1,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			493.7
Character	$\chi$	$=$	968.493
Dual form			968.2.o.d.269.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.730005 + 1.21124i) q^{2} +(1.62101 + 2.23113i) q^{3} +(-0.934186 + 1.76842i) q^{4} +(2.76352 - 0.897923i) q^{5} +(-1.51908 + 3.59217i) q^{6} +(1.91213 + 1.38924i) q^{7} +(-2.82393 + 0.159432i) q^{8} +(-1.42322 + 4.38022i) q^{9} +(3.10498 + 2.69179i) q^{10} +(-5.45990 + 0.782332i) q^{12} +(-2.42023 - 0.786381i) q^{13} +(-0.286838 + 3.33019i) q^{14} +(6.48309 + 4.71024i) q^{15} +(-2.25459 - 3.30406i) q^{16} +(-1.82314 - 5.61105i) q^{17} +(-6.34444 + 1.47373i) q^{18} +(-0.156289 - 0.215114i) q^{19} +(-0.993743 + 5.72588i) q^{20} +6.51819i q^{21} +4.18146 q^{23} +(-4.93334 - 6.04212i) q^{24} +(2.78570 - 2.02393i) q^{25} +(-0.814288 - 3.50554i) q^{26} +(-4.21136 + 1.36835i) q^{27} +(-4.24304 + 2.08363i) q^{28} +(-1.90967 + 2.62843i) q^{29} +(-0.972528 + 11.2911i) q^{30} +(0.635838 - 1.95691i) q^{31} +(2.35613 - 5.14282i) q^{32} +(5.46541 - 6.30435i) q^{34} +(6.53164 + 2.12226i) q^{35} +(-6.41651 - 6.60879i) q^{36} +(-0.457360 + 0.629502i) q^{37} +(0.146462 - 0.346338i) q^{38} +(-2.16871 - 6.67460i) q^{39} +(-7.66084 + 2.97627i) q^{40} +(2.42756 - 1.76373i) q^{41} +(-7.89507 + 4.75831i) q^{42} -1.14207i q^{43} +13.3828i q^{45} +(3.05248 + 5.06473i) q^{46} +(-7.80663 + 5.67185i) q^{47} +(3.71707 - 10.3862i) q^{48} +(-0.436880 - 1.34458i) q^{49} +(4.48504 + 1.89667i) q^{50} +(9.56367 - 13.1633i) q^{51} +(3.65160 - 3.54535i) q^{52} +(9.34068 + 3.03497i) q^{53} +(-4.73171 - 4.10205i) q^{54} +(-5.62121 - 3.61827i) q^{56} +(0.226601 - 0.697405i) q^{57} +(-4.57772 - 0.394290i) q^{58} +(3.40294 - 4.68375i) q^{59} +(-14.3861 + 7.06456i) q^{60} +(-5.83684 + 1.89650i) q^{61} +(2.83444 - 0.658402i) q^{62} +(-8.80657 + 6.39835i) q^{63} +(7.94916 - 0.900451i) q^{64} -7.39448 q^{65} -0.241089i q^{67} +(11.6258 + 2.01769i) q^{68} +(6.77819 + 9.32938i) q^{69} +(2.19757 + 9.46062i) q^{70} +(-1.21893 - 3.75148i) q^{71} +(3.32073 - 12.5964i) q^{72} +(-5.14067 - 3.73492i) q^{73} +(-1.09635 - 0.0944315i) q^{74} +(9.03133 + 2.93446i) q^{75} +(0.526414 - 0.0754283i) q^{76} +(6.50135 - 7.49930i) q^{78} +(1.60276 - 4.93279i) q^{79} +(-9.19741 - 7.10639i) q^{80} +(1.29848 + 0.943398i) q^{81} +(3.90843 + 1.65282i) q^{82} +(14.4918 - 4.70867i) q^{83} +(-11.5269 - 6.08921i) q^{84} +(-10.0766 - 13.8692i) q^{85} +(1.38331 - 0.833714i) q^{86} -8.95997 q^{87} -16.2052 q^{89} +(-16.2097 + 9.76950i) q^{90} +(-3.53532 - 4.86595i) q^{91} +(-3.90626 + 7.39455i) q^{92} +(5.39682 - 1.75353i) q^{93} +(-12.5688 - 5.31519i) q^{94} +(-0.625065 - 0.454136i) q^{95} +(15.2936 - 3.07974i) q^{96} +(-2.25552 + 6.94179i) q^{97} +(1.30968 - 1.51071i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - q^{4} - 8 q^{6} - 5 q^{8} + 10 q^{9} + 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} - 4 q^{17} - 25 q^{18} + 8 q^{20} - 8 q^{23} + 40 q^{24} + 6 q^{25} - 20 q^{26} + 18 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) $ 40 * q - 5 * q^2 - q^4 - 8 * q^6 - 5 * q^8 + 10 * q^9 + 20 * q^10 - 6 * q^12 + 2 * q^14 + 22 * q^15 - 25 * q^16 - 4 * q^17 - 25 * q^18 + 8 * q^20 - 8 * q^23 + 40 * q^24 + 6 * q^25 - 20 * q^26 + 18 * q^28 - 12 * q^30 + 4 * q^31 - 20 * q^32 + 10 * q^34 - 27 * q^36 - 33 * q^38 - 6 * q^39 + 20 * q^40 - 16 * q^41 - 20 * q^42 + 42 * q^46 + 4 * q^47 + 23 * q^48 + 6 * q^49 + 39 * q^50 - 108 * q^54 - 32 * q^56 - 4 * q^57 - 16 * q^58 + 94 * q^60 + 52 * q^62 + 30 * q^63 + 11 * q^64 + 36 * q^65 - 63 * q^68 + 52 * q^70 + 12 * q^71 - 44 * q^72 - 4 * q^73 + 26 * q^74 + 134 * q^76 - 12 * q^78 + 16 * q^79 + 16 * q^80 + 16 * q^81 + 54 * q^82 - 72 * q^84 - 10 * q^86 - 68 * q^87 - 16 * q^89 - 126 * q^90 - 64 * q^92 - 40 * q^94 - 26 * q^95 + 5 * q^96 - 20 * q^97 + 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.730005	+	1.21124i	0.516191	+	0.856473i
$2$	0.730005	+	1.21124i	0.516191	+	0.856473i
$3$	1.62101	+	2.23113i	0.935892	+	1.28815i	0.957516	+	0.288379i	$0.0931164\pi$
$3$	1.62101	+	2.23113i	0.935892	+	1.28815i	−0.0216239	+	0.999766i	$0.506884\pi$
$4$	−0.934186	+	1.76842i	−0.467093	+	0.884208i
$5$	2.76352	−	0.897923i	1.23588	−	0.401563i	0.383042	−	0.923731i	$-0.374876\pi$
$5$	2.76352	−	0.897923i	1.23588	−	0.401563i	0.852843	+	0.522168i	$0.174876\pi$
$6$	−1.51908	+	3.59217i	−0.620163	+	1.46650i
$7$	1.91213	+	1.38924i	0.722716	+	0.525084i	0.887251	−	0.461287i	$-0.152612\pi$
$7$	1.91213	+	1.38924i	0.722716	+	0.525084i	−0.164534	+	0.986371i	$0.552612\pi$
$8$	−2.82393	+	0.159432i	−0.998410	+	0.0563678i
$9$	−1.42322	+	4.38022i	−0.474407	+	1.46007i
$10$	3.10498	+	2.69179i	0.981881	+	0.851219i
$11$		0			0
$11$		0			0
$12$	−5.45990	+	0.782332i	−1.57614	+	0.225840i
$13$	−2.42023	−	0.786381i	−0.671252	−	0.218103i	−0.0464905	−	0.998919i	$-0.514804\pi$
$13$	−2.42023	−	0.786381i	−0.671252	−	0.218103i	−0.624761	+	0.780816i	$0.714804\pi$
$14$	−0.286838	+	3.33019i	−0.0766607	+	0.890031i
$15$	6.48309	+	4.71024i	1.67393	+	1.21618i
$16$	−2.25459	−	3.30406i	−0.563648	−	0.826015i
$17$	−1.82314	−	5.61105i	−0.442177	−	1.36088i	−0.885551	−	0.464543i	$-0.846219\pi$
$17$	−1.82314	−	5.61105i	−0.442177	−	1.36088i	0.443374	−	0.896337i	$-0.353781\pi$
$18$	−6.34444	+	1.47373i	−1.49540	+	0.347361i
$19$	−0.156289	−	0.215114i	−0.0358552	−	0.0493505i	0.790713	−	0.612187i	$-0.209710\pi$
$19$	−0.156289	−	0.215114i	−0.0358552	−	0.0493505i	−0.826568	+	0.562837i	$0.809710\pi$
$20$	−0.993743	+	5.72588i	−0.222208	+	1.28035i
$21$			6.51819i			1.42239i
$22$		0			0
$23$	4.18146			0.871894			0.435947	−	0.899972i	$-0.356414\pi$
$23$	4.18146			0.871894			0.435947	+	0.899972i	$0.356414\pi$
$24$	−4.93334	−	6.04212i	−1.00701	−	1.23334i
$25$	2.78570	−	2.02393i	0.557141	−	0.404787i
$26$	−0.814288	−	3.50554i	−0.159695	−	0.687492i
$27$	−4.21136	+	1.36835i	−0.810476	+	0.263340i
$28$	−4.24304	+	2.08363i	−0.801860	+	0.393769i
$29$	−1.90967	+	2.62843i	−0.354616	+	0.488087i	−0.948639	−	0.316361i	$-0.897539\pi$
$29$	−1.90967	+	2.62843i	−0.354616	+	0.488087i	0.594023	+	0.804448i	$0.297539\pi$
$30$	−0.972528	+	11.2911i	−0.177558	+	2.06145i
$31$	0.635838	−	1.95691i	0.114200	−	0.351471i	−0.877579	−	0.479431i	$-0.840843\pi$
$31$	0.635838	−	1.95691i	0.114200	−	0.351471i	0.991779	+	0.127960i	$0.0408430\pi$
$32$	2.35613	−	5.14282i	0.416510	−	0.909131i
$33$		0			0
$34$	5.46541	−	6.30435i	0.937309	−	1.08119i
$35$	6.53164	+	2.12226i	1.10405	+	0.358727i
$36$	−6.41651	−	6.60879i	−1.06942	−	1.10147i
$37$	−0.457360	+	0.629502i	−0.0751895	+	0.103489i	−0.844955	−	0.534837i	$-0.820373\pi$
$37$	−0.457360	+	0.629502i	−0.0751895	+	0.103489i	0.769766	+	0.638326i	$0.220373\pi$
$38$	0.146462	−	0.346338i	0.0237592	−	0.0561834i
$39$	−2.16871	−	6.67460i	−0.347271	−	1.06879i
$40$	−7.66084	+	2.97627i	−1.21128	+	0.470589i
$41$	2.42756	−	1.76373i	0.379122	−	0.275448i	−0.381861	−	0.924220i	$-0.624717\pi$
$41$	2.42756	−	1.76373i	0.379122	−	0.275448i	0.760983	+	0.648771i	$0.224717\pi$
$42$	−7.89507	+	4.75831i	−1.21824	+	0.734223i
$43$		−	1.14207i		−	0.174164i	−0.996201	−	0.0870818i	$-0.972246\pi$
$43$		−	1.14207i		−	0.174164i	0.996201	−	0.0870818i	$-0.0277541\pi$
$44$		0			0
$45$			13.3828i			1.99499i
$46$	3.05248	+	5.06473i	0.450064	+	0.746754i
$47$	−7.80663	+	5.67185i	−1.13871	+	0.827324i	−0.986940	−	0.161091i	$-0.948499\pi$
$47$	−7.80663	+	5.67185i	−1.13871	+	0.827324i	−0.151774	+	0.988415i	$0.548499\pi$
$48$	3.71707	−	10.3862i	0.536513	−	1.49912i
$49$	−0.436880	−	1.34458i	−0.0624114	−	0.192082i
$50$	4.48504	+	1.89667i	0.634280	+	0.268229i
$51$	9.56367	−	13.1633i	1.33918	−	1.84322i
$52$	3.65160	−	3.54535i	0.506385	−	0.491652i
$53$	9.34068	+	3.03497i	1.28304	+	0.416885i	0.869650	−	0.493669i	$-0.164344\pi$
$53$	9.34068	+	3.03497i	1.28304	+	0.416885i	0.413390	+	0.910554i	$0.364344\pi$
$54$	−4.73171	−	4.10205i	−0.643904	−	0.558218i
$55$		0			0
$56$	−5.62121	−	3.61827i	−0.751165	−	0.483511i
$57$	0.226601	−	0.697405i	0.0300140	−	0.0923735i
$58$	−4.57772	−	0.394290i	−0.601083	−	0.0517729i
$59$	3.40294	−	4.68375i	0.443025	−	0.609772i	−0.527856	−	0.849334i	$-0.677004\pi$
$59$	3.40294	−	4.68375i	0.443025	−	0.609772i	0.970881	+	0.239562i	$0.0770039\pi$
$60$	−14.3861	+	7.06456i	−1.85724	+	0.912031i
$61$	−5.83684	+	1.89650i	−0.747331	+	0.242823i	−0.657832	−	0.753164i	$-0.728526\pi$
$61$	−5.83684	+	1.89650i	−0.747331	+	0.242823i	−0.0894986	+	0.995987i	$0.528526\pi$
$62$	2.83444	−	0.658402i	0.359975	−	0.0836172i
$63$	−8.80657	+	6.39835i	−1.10952	+	0.806116i
$64$	7.94916	−	0.900451i	0.993645	−	0.112556i
$65$	−7.39448			−0.917172
$66$		0			0
$67$		−	0.241089i		−	0.0294537i	−0.999892	−	0.0147268i	$-0.995312\pi$
$67$		−	0.241089i		−	0.0294537i	0.999892	−	0.0147268i	$-0.00468787\pi$
$68$	11.6258	+	2.01769i	1.40984	+	0.244681i
$69$	6.77819	+	9.32938i	0.815999	+	1.12313i
$70$	2.19757	+	9.46062i	0.262660	+	1.13076i
$71$	−1.21893	−	3.75148i	−0.144660	−	0.445219i	0.852307	−	0.523042i	$-0.175203\pi$
$71$	−1.21893	−	3.75148i	−0.144660	−	0.445219i	−0.996967	+	0.0778233i	$0.975203\pi$
$72$	3.32073	−	12.5964i	0.391351	−	1.48449i
$73$	−5.14067	−	3.73492i	−0.601670	−	0.437139i	0.244801	−	0.969573i	$-0.421277\pi$
$73$	−5.14067	−	3.73492i	−0.601670	−	0.437139i	−0.846471	+	0.532434i	$0.821277\pi$
$74$	−1.09635	−	0.0944315i	−0.127448	−	0.0109774i
$75$	9.03133	+	2.93446i	1.04285	+	0.338842i
$76$	0.526414	−	0.0754283i	0.0603839	−	0.00865222i
$77$		0			0
$78$	6.50135	−	7.49930i	0.736132	−	0.849129i
$79$	1.60276	−	4.93279i	0.180325	−	0.554982i	−0.819512	−	0.573062i	$-0.805755\pi$
$79$	1.60276	−	4.93279i	0.180325	−	0.554982i	0.999837	+	0.0180798i	$0.00575530\pi$
$80$	−9.19741	−	7.10639i	−1.02830	−	0.794519i
$81$	1.29848	+	0.943398i	0.144275	+	0.104822i
$82$	3.90843	+	1.65282i	0.431613	+	0.182524i
$83$	14.4918	−	4.70867i	1.59068	−	0.516843i	0.625900	−	0.779903i	$-0.284732\pi$
$83$	14.4918	−	4.70867i	1.59068	−	0.516843i	0.964780	+	0.263060i	$0.0847317\pi$
$84$	−11.5269	−	6.08921i	−1.25769	−	0.664387i
$85$	−10.0766	−	13.8692i	−1.09296	−	1.50433i
$86$	1.38331	−	0.833714i	0.149166	−	0.0899017i
$87$	−8.95997			−0.960610
$88$		0			0
$89$	−16.2052			−1.71774			−0.858872	−	0.512190i	$-0.828834\pi$
$89$	−16.2052			−1.71774			−0.858872	+	0.512190i	$0.828834\pi$
$90$	−16.2097	+	9.76950i	−1.70865	+	1.02980i
$91$	−3.53532	−	4.86595i	−0.370602	−	0.510090i
$92$	−3.90626	+	7.39455i	−0.407255	+	0.770935i
$93$	5.39682	−	1.75353i	0.559625	−	0.181833i
$94$	−12.5688	−	5.31519i	−1.29637	−	0.548220i
$95$	−0.625065	−	0.454136i	−0.0641303	−	0.0465934i
$96$	15.2936	−	3.07974i	1.56090	−	0.314324i
$97$	−2.25552	+	6.94179i	−0.229014	+	0.704832i	0.768845	+	0.639435i	$0.220832\pi$
$97$	−2.25552	+	6.94179i	−0.229014	+	0.704832i	−0.997859	+	0.0653975i	$0.979168\pi$
$98$	1.30968	−	1.51071i	0.132297	−	0.152605i
$99$		0			0
$100$	0.976789	+	6.81702i	0.0976789	+	0.681702i
$101$	−8.63500	−	2.80568i	−0.859214	−	0.279176i	−0.153914	−	0.988084i	$-0.549188\pi$
$101$	−8.63500	−	2.80568i	−0.859214	−	0.279176i	−0.705300	+	0.708909i	$0.749188\pi$
$102$	22.9253	+	1.97462i	2.26995	+	0.195516i
$103$	−15.3149	−	11.1269i	−1.50902	−	1.09637i	−0.966610	−	0.256252i	$-0.917512\pi$
$103$	−15.3149	−	11.1269i	−1.50902	−	1.09637i	−0.542409	−	0.840114i	$-0.682488\pi$
$104$	6.95994	+	1.83482i	0.682479	+	0.179919i
$105$	5.85283	+	18.0132i	0.571178	+	1.75791i
$106$	3.14267	+	13.5293i	0.305243	+	1.31408i
$107$	2.47726	+	3.40966i	0.239486	+	0.329624i	0.911794	−	0.410647i	$-0.134697\pi$
$107$	2.47726	+	3.40966i	0.239486	+	0.329624i	−0.672308	+	0.740271i	$0.734697\pi$
$108$	1.51437	−	8.72573i	0.145721	−	0.839634i
$109$			4.60753i			0.441321i	0.975351	+	0.220661i	$0.0708213\pi$
$109$			4.60753i			0.441321i	−0.975351	+	0.220661i	$0.929179\pi$
$110$		0			0
$111$	−2.14589			−0.203679
$112$	0.279070	−	9.44996i	0.0263697	−	0.892937i
$113$	12.5337	−	9.10627i	1.17907	−	0.856646i	0.187005	−	0.982359i	$-0.440122\pi$
$113$	12.5337	−	9.10627i	1.17907	−	0.856646i	0.992067	+	0.125713i	$0.0401219\pi$
$114$	1.01014	−	0.234642i	0.0946084	−	0.0219762i
$115$	11.5555	−	3.75462i	1.07756	−	0.350120i
$116$	−2.86418	−	5.83253i	−0.265932	−	0.541537i
$117$	6.88905	−	9.48197i	0.636893	−	0.876608i
$118$	8.15728	+	0.702608i	0.750939	+	0.0646803i
$119$	4.30903	−	13.2618i	0.395008	−	1.21571i
$120$	−19.0588	−	12.2678i	−1.73982	−	1.11989i
$121$		0			0
$122$	−6.55804	−	5.68534i	−0.593737	−	0.514726i
$123$	7.87023	+	2.55719i	0.709635	+	0.230574i
$124$	2.86664	+	2.95254i	0.257432	+	0.265146i
$125$	−2.65873	+	3.65943i	−0.237804	+	0.327309i
$126$	−14.1788	−	5.99601i	−1.26314	−	0.534167i
$127$	2.84750	+	8.76371i	0.252675	+	0.777653i	0.994279	+	0.106815i	$0.0340654\pi$
$127$	2.84750	+	8.76371i	0.252675	+	0.777653i	−0.741604	+	0.670838i	$0.765935\pi$
$128$	6.89359	+	8.97098i	0.609313	+	0.792930i
$129$	2.54810	−	1.85131i	0.224348	−	0.162998i
$130$	−5.39800	−	8.95646i	−0.473436	−	0.785533i
$131$			9.14472i			0.798978i	0.916738	+	0.399489i	$0.130812\pi$
$131$			9.14472i			0.798978i	−0.916738	+	0.399489i	$0.869188\pi$
$132$		0			0
$133$		−	0.628449i		−	0.0544935i
$134$	0.292015	−	0.175996i	0.0252263	−	0.0152037i
$135$	−10.4095	+	7.56295i	−0.895908	+	0.650915i
$136$	6.04300	+	15.5545i	0.518183	+	1.33379i
$137$	−4.35355	−	13.3989i	−0.371949	−	1.14474i	−0.945514	−	0.325581i	$-0.894440\pi$
$137$	−4.35355	−	13.3989i	−0.371949	−	1.14474i	0.573565	−	0.819160i	$-0.305560\pi$
$138$	−6.35197	+	15.0205i	−0.540716	+	1.27863i
$139$	−2.88127	+	3.96573i	−0.244386	+	0.336369i	−0.913535	−	0.406759i	$-0.866659\pi$
$139$	−2.88127	+	3.96573i	−0.244386	+	0.336369i	0.669149	+	0.743128i	$0.266659\pi$
$140$	−9.85480	+	9.56808i	−0.832883	+	0.808650i
$141$	−25.3093	−	8.22349i	−2.13143	−	0.692543i
$142$	3.65410	−	4.21501i	0.306646	−	0.353716i
$143$		0			0
$144$	17.6813	−	5.17321i	1.47344	−	0.431101i
$145$	−2.91728	+	8.97846i	−0.242267	+	0.745620i
$146$	0.771152	−	8.95308i	0.0638210	−	0.740962i
$147$	2.29174	−	3.15431i	0.189020	−	0.260163i
$148$	−0.685962	−	1.39687i	−0.0563858	−	0.114822i
$149$	−9.59749	+	3.11841i	−0.786257	+	0.255470i	−0.674509	−	0.738266i	$-0.735645\pi$
$149$	−9.59749	+	3.11841i	−0.786257	+	0.255470i	−0.111748	+	0.993737i	$0.535645\pi$
$150$	3.03859	+	13.0812i	0.248100	+	1.06808i
$151$	12.2118	−	8.87236i	0.993778	−	0.722022i	0.0330330	−	0.999454i	$-0.489483\pi$
$151$	12.2118	−	8.87236i	0.993778	−	0.722022i	0.960745	+	0.277432i	$0.0894834\pi$
$152$	0.475646	+	0.582549i	0.0385800	+	0.0472510i
$153$	27.1724			2.19676
$154$		0			0
$155$		−	5.97889i		−	0.480236i
$156$	13.8294	+	2.40014i	1.10724	+	0.192165i
$157$	11.0810	+	15.2517i	0.884361	+	1.21722i	0.975194	+	0.221352i	$0.0710470\pi$
$157$	11.0810	+	15.2517i	0.884361	+	1.21722i	−0.0908333	+	0.995866i	$0.528953\pi$
$158$	7.14480	−	1.65964i	0.568410	−	0.132034i
$159$	8.36994	+	25.7600i	0.663779	+	2.04290i
$160$	1.89337	−	16.3279i	0.149684	−	1.29084i
$161$	7.99548	+	5.80905i	0.630132	+	0.457818i
$162$	−0.194784	+	2.26145i	−0.0153037	+	0.177676i
$163$	5.78743	+	1.88045i	0.453306	+	0.147288i	0.526767	−	0.850010i	$-0.323404\pi$
$163$	5.78743	+	1.88045i	0.453306	+	0.147288i	−0.0734603	+	0.997298i	$0.523404\pi$
$164$	0.851210	+	5.94060i	0.0664683	+	0.463883i
$165$		0			0
$166$	16.2824	+	14.1156i	1.26376	+	1.09558i
$167$	−5.36575	+	16.5141i	−0.415215	+	1.27790i	0.496844	+	0.867840i	$0.334492\pi$
$167$	−5.36575	+	16.5141i	−0.415215	+	1.27790i	−0.912059	+	0.410059i	$0.865508\pi$
$168$	−1.03921	−	18.4069i	−0.0801768	−	1.42012i
$169$	−5.27809	−	3.83476i	−0.406007	−	0.294981i
$170$	9.44295	−	22.3297i	0.724241	−	1.71261i
$171$	1.16468	−	0.378428i	0.0890654	−	0.0289391i
$172$	2.01965	+	1.06690i	0.153997	+	0.0813506i
$173$	14.3218	+	19.7123i	1.08887	+	1.49870i	0.849365	+	0.527805i	$0.176985\pi$
$173$	14.3218	+	19.7123i	1.08887	+	1.49870i	0.239504	+	0.970895i	$0.423015\pi$
$174$	−6.54082	−	10.8526i	−0.495858	−	0.822737i
$175$	8.13836			0.615202
$176$		0			0
$177$	15.9663			1.20010
$178$	−11.8299	−	19.6283i	−0.886685	−	1.47120i
$179$	1.75832	+	2.42012i	0.131423	+	0.180889i	0.869657	−	0.493656i	$-0.164340\pi$
$179$	1.75832	+	2.42012i	0.131423	+	0.180889i	−0.738234	+	0.674545i	$0.764340\pi$
$180$	−23.6663	−	12.5020i	−1.76398	−	0.931845i
$181$	7.39886	−	2.40404i	0.549953	−	0.178691i	−0.0208426	−	0.999783i	$-0.506635\pi$
$181$	7.39886	−	2.40404i	0.549953	−	0.178691i	0.570796	+	0.821092i	$0.306635\pi$
$182$	3.31302	−	7.83428i	0.245577	−	0.580715i
$183$	−13.6929	−	9.94851i	−1.01221	−	0.735415i
$184$	−11.8081	+	0.666659i	−0.870507	+	0.0491467i
$185$	−0.698680	+	2.15032i	−0.0513680	+	0.158094i
$186$	6.06365	+	5.25674i	0.444608	+	0.385443i
$187$		0			0
$188$	−2.73734	−	19.1039i	−0.199641	−	1.39330i
$189$	−9.95363	−	3.23413i	−0.724020	−	0.235248i
$190$	0.0937659	−	1.08862i	0.00680249	−	0.0789770i
$191$	1.56476	+	1.13687i	0.113222	+	0.0822609i	0.642956	−	0.765903i	$-0.277708\pi$
$191$	1.56476	+	1.13687i	0.113222	+	0.0822609i	−0.529733	+	0.848164i	$0.677708\pi$
$192$	14.8947	+	16.2760i	1.07493	+	1.17462i
$193$	4.02316	+	12.3820i	0.289594	+	0.891278i	0.984984	+	0.172645i	$0.0552315\pi$
$193$	4.02316	+	12.3820i	0.289594	+	0.891278i	−0.695390	+	0.718632i	$0.744769\pi$
$194$	−10.0547	+	2.33557i	−0.721885	+	0.167684i
$195$	−11.9865	−	16.4981i	−0.858374	−	1.18145i
$196$	2.78590	+	0.483500i	0.198993	+	0.0345357i
$197$			6.20231i			0.441896i	0.975286	+	0.220948i	$0.0709152\pi$
$197$			6.20231i			0.441896i	−0.975286	+	0.220948i	$0.929085\pi$
$198$		0			0
$199$	−18.9189			−1.34112			−0.670562	−	0.741854i	$-0.733947\pi$
$199$	−18.9189			−1.34112			−0.670562	+	0.741854i	$0.733947\pi$
$200$	−7.54396	+	6.15958i	−0.533438	+	0.435548i
$201$	0.537901	−	0.390808i	0.0379406	−	0.0275655i
$202$	−2.90525	−	12.5072i	−0.204413	−	0.880002i
$203$	−7.30305	+	2.37291i	−0.512574	+	0.166545i
$204$	14.3439	+	29.2095i	1.00427	+	2.04507i
$205$	5.12494	−	7.05387i	0.357941	−	0.492664i
$206$	2.29738	−	26.6726i	0.160066	−	1.85837i
$207$	−5.95113	+	18.3157i	−0.413632	+	1.27303i
$208$	2.85839	+	9.76956i	0.198194	+	0.677397i
$209$		0			0
$210$	−17.5456	+	20.2389i	−1.21076	+	1.39661i
$211$	2.77628	+	0.902067i	0.191127	+	0.0621008i	0.403016	−	0.915193i	$-0.367962\pi$
$211$	2.77628	+	0.902067i	0.191127	+	0.0621008i	−0.211890	+	0.977294i	$0.567962\pi$
$212$	−14.0930	+	13.6830i	−0.967913	+	0.939751i
$213$	6.39415	−	8.80080i	0.438120	−	0.603021i
$214$	−2.32149	+	5.48962i	−0.158694	+	0.375263i
$215$	−1.02549	−	3.15613i	−0.0699377	−	0.215246i
$216$	11.6744	−	4.53556i	0.794344	−	0.308606i
$217$	3.93442	−	2.85853i	0.267086	−	0.194049i
$218$	−5.58081	+	3.36352i	−0.377980	+	0.227806i
$219$		−	17.5239i		−	1.18415i
$220$		0			0
$221$			15.0137i			1.00993i
$222$	−1.56651	−	2.59918i	−0.105137	−	0.174445i
$223$	2.25396	−	1.63760i	0.150936	−	0.109662i	−0.509754	−	0.860320i	$-0.670264\pi$
$223$	2.25396	−	1.63760i	0.150936	−	0.109662i	0.660690	+	0.750658i	$0.270264\pi$
$224$	11.6499	−	6.56050i	0.778389	−	0.438342i
$225$	4.90061	+	15.0825i	0.326707	+	1.00550i
$226$	20.1795	+	8.53366i	1.34232	+	0.567650i
$227$	7.08626	−	9.75340i	0.470331	−	0.647356i	−0.506280	−	0.862369i	$-0.668980\pi$
$227$	7.08626	−	9.75340i	0.470331	−	0.647356i	0.976611	+	0.215014i	$0.0689796\pi$
$228$	1.02162	+	1.05223i	0.0676581	+	0.0696857i
$229$	6.13769	+	1.99426i	0.405590	+	0.131784i	0.504705	−	0.863292i	$-0.331601\pi$
$229$	6.13769	+	1.99426i	0.405590	+	0.131784i	−0.0991151	+	0.995076i	$0.531601\pi$
$230$	12.9833	+	11.2556i	0.856096	+	0.742172i
$231$		0			0
$232$	4.97371	−	7.72697i	0.326540	−	0.507300i
$233$	−2.62352	+	8.07436i	−0.171872	+	0.528969i	−0.999477	−	0.0323428i	$-0.989703\pi$
$233$	−2.62352	+	8.07436i	−0.171872	+	0.528969i	0.827604	+	0.561312i	$0.189703\pi$
$234$	16.5139	+	1.42239i	1.07955	+	0.0929844i
$235$	−16.4809	+	22.6840i	−1.07510	+	1.47974i
$236$	5.10383	+	10.3933i	0.332231	+	0.676547i
$237$	13.6038	−	4.42015i	0.883663	−	0.287119i
$238$	19.2088	−	4.46195i	1.24512	−	0.289225i
$239$	2.65558	−	1.92939i	0.171775	−	0.124802i	−0.498576	−	0.866846i	$-0.666143\pi$
$239$	2.65558	−	1.92939i	0.171775	−	0.124802i	0.670351	+	0.742044i	$0.266143\pi$
$240$	0.946191	−	32.0402i	0.0610764	−	2.06819i
$241$	9.76241			0.628852			0.314426	−	0.949282i	$-0.398188\pi$
$241$	9.76241			0.628852			0.314426	+	0.949282i	$0.398188\pi$
$242$		0			0
$243$			17.7106i			1.13613i
$244$	2.09889	−	12.0937i	0.134367	−	0.774217i
$245$	−2.41465	−	3.32349i	−0.154267	−	0.212330i
$246$	2.64794	+	11.3995i	0.168827	+	0.726804i
$247$	0.209095	+	0.643529i	0.0133044	+	0.0409468i
$248$	−1.48357	+	5.62754i	−0.0942066	+	0.357349i
$249$	33.9970	+	24.7003i	2.15447	+	1.56532i
$250$	−6.37332	−	0.548951i	−0.403084	−	0.0347187i
$251$	−14.2419	−	4.62746i	−0.898938	−	0.292083i	−0.177140	−	0.984186i	$-0.556684\pi$
$251$	−14.2419	−	4.62746i	−0.898938	−	0.292083i	−0.721799	+	0.692103i	$0.756684\pi$
$252$	−3.08797	−	21.5509i	−0.194524	−	1.35758i
$253$		0			0
$254$	−8.53623	+	9.84655i	−0.535611	+	0.617827i
$255$	14.6098	−	44.9644i	0.914902	−	2.81578i
$256$	−5.83363	+	14.8986i	−0.364602	+	0.931164i
$257$	−0.225988	−	0.164190i	−0.0140967	−	0.0102419i	0.580715	−	0.814107i	$-0.302773\pi$
$257$	−0.225988	−	0.164190i	−0.0140967	−	0.0102419i	−0.594811	+	0.803865i	$0.702773\pi$
$258$	4.10250	+	1.73489i	0.255410	+	0.108010i
$259$	−1.74906	+	0.568305i	−0.108681	+	0.0353127i
$260$	6.90782	−	13.0765i	0.428405	−	0.810971i
$261$	−8.79523	−	12.1056i	−0.544411	−	0.749318i
$262$	−11.0764	+	6.67569i	−0.684303	+	0.412425i
$263$	−20.2340			−1.24768			−0.623842	−	0.781551i	$-0.714429\pi$
$263$	−20.2340			−1.24768			−0.623842	+	0.781551i	$0.714429\pi$
$264$		0			0
$265$	28.5383			1.75310
$266$	0.761200	−	0.458771i	0.0466722	−	0.0281290i
$267$	−26.2688	−	36.1559i	−1.60762	−	2.21270i
$268$	0.426345	+	0.225222i	0.0260432	+	0.0137576i
$269$	−11.7789	+	3.82719i	−0.718172	+	0.233348i	−0.645230	−	0.763988i	$-0.723239\pi$
$269$	−11.7789	+	3.82719i	−0.718172	+	0.233348i	−0.0729415	+	0.997336i	$0.523239\pi$
$270$	−16.7595	−	7.08738i	−1.01995	−	0.431324i
$271$	−1.50476	−	1.09327i	−0.0914078	−	0.0664117i	0.541143	−	0.840931i	$-0.317992\pi$
$271$	−1.50476	−	1.09327i	−0.0914078	−	0.0664117i	−0.632550	+	0.774519i	$0.717992\pi$
$272$	−14.4288	+	18.6744i	−0.874875	+	1.13230i
$273$	5.12578	−	15.7755i	0.310227	−	0.954779i
$274$	13.0511	−	15.0544i	0.788443	−	0.909470i
$275$		0			0
$276$	−22.8303	+	3.27129i	−1.37422	+	0.196908i
$277$	17.3875	+	5.64955i	1.04472	+	0.339449i	0.780593	−	0.625040i	$-0.214917\pi$
$277$	17.3875	+	5.64955i	1.04472	+	0.339449i	0.264123	+	0.964489i	$0.414917\pi$
$278$	−6.90678	−	0.594899i	−0.414241	−	0.0356797i
$279$	7.66676	+	5.57022i	0.458997	+	0.333481i
$280$	−18.7833	−	4.95176i	−1.12251	−	0.295924i
$281$	−4.29479	−	13.2180i	−0.256205	−	0.788519i	−0.993590	−	0.113046i	$-0.963939\pi$
$281$	−4.29479	−	13.2180i	−0.256205	−	0.788519i	0.737384	−	0.675474i	$-0.236061\pi$
$282$	−8.51532	−	36.6587i	−0.507080	−	2.18299i
$283$	−3.93414	−	5.41488i	−0.233860	−	0.321881i	0.675917	−	0.736978i	$-0.263748\pi$
$283$	−3.93414	−	5.41488i	−0.233860	−	0.321881i	−0.909777	+	0.415097i	$0.863748\pi$
$284$	7.77289	+	1.34901i	0.461236	+	0.0800488i
$285$		−	2.13076i		−	0.126216i
$286$		0			0
$287$	7.09206			0.418631
$288$	19.1734	+	17.6398i	1.12980	+	1.03943i
$289$	−14.4068	+	10.4671i	−0.847456	+	0.615713i
$290$	−13.0047	+	3.02080i	−0.763660	+	0.177388i
$291$	−19.1443	+	6.22036i	−1.12226	+	0.364644i
$292$	11.4072	−	5.60174i	0.667558	−	0.327817i
$293$	−13.7920	+	18.9831i	−0.805738	+	1.10900i	0.186228	+	0.982506i	$0.440374\pi$
$293$	−13.7920	+	18.9831i	−0.805738	+	1.10900i	−0.991967	+	0.126497i	$0.959626\pi$
$294$	5.49360	+	0.473178i	0.320393	+	0.0275963i
$295$	5.19846	−	15.9992i	0.302666	−	0.931510i
$296$	1.19119	−	1.85059i	0.0692365	−	0.107563i
$297$		0			0
$298$	−10.7833	−	9.34837i	−0.624663	−	0.541537i
$299$	−10.1201	−	3.28822i	−0.585260	−	0.190163i
$300$	−13.6263	+	13.2298i	−0.786714	+	0.763824i
$301$	1.58661	−	2.18378i	0.0914506	−	0.125871i
$302$	19.6612	+	8.31445i	1.13137	+	0.478443i
$303$	−7.73760	−	23.8139i	−0.444513	−	1.36807i
$304$	−0.358380	+	1.00138i	−0.0205545	+	0.0574333i
$305$	−14.4273	+	10.4821i	−0.826106	+	0.600201i
$306$	19.8360	+	32.9122i	1.13395	+	1.88146i
$307$		−	9.08397i		−	0.518450i	−0.965817	−	0.259225i	$-0.916533\pi$
$307$		−	9.08397i		−	0.518450i	0.965817	−	0.259225i	$-0.0834671\pi$
$308$		0			0
$309$		−	52.2064i		−	2.96992i
$310$	7.24185	−	4.36462i	0.411309	−	0.247894i
$311$	14.9523	−	10.8635i	0.847865	−	0.616010i	−0.0766915	−	0.997055i	$-0.524436\pi$
$311$	14.9523	−	10.8635i	0.847865	−	0.616010i	0.924557	+	0.381045i	$0.124436\pi$
$312$	7.18843	+	18.5028i	0.406964	+	1.04752i
$313$	−3.04418	−	9.36902i	−0.172067	−	0.529568i	0.827420	−	0.561583i	$-0.189808\pi$
$313$	−3.04418	−	9.36902i	−0.172067	−	0.529568i	−0.999487	+	0.0320151i	$0.989808\pi$
$314$	−10.3842	+	24.5555i	−0.586015	+	1.38575i
$315$	−18.5919	+	25.5896i	−1.04754	+	1.44181i
$316$	7.22595	+	7.44250i	0.406492	+	0.418673i
$317$	−28.3215	−	9.20221i	−1.59069	−	0.516848i	−0.625911	−	0.779895i	$-0.715273\pi$
$317$	−28.3215	−	9.20221i	−1.59069	−	0.516848i	−0.964783	+	0.263047i	$0.915273\pi$
$318$	−25.0914	+	28.9429i	−1.40705	+	1.62304i
$319$		0			0
$320$	21.1592	−	9.62615i	1.18283	−	0.538118i
$321$	−3.59173	+	11.0542i	−0.200471	+	0.616986i
$322$	−1.19940	+	13.9250i	−0.0668400	+	0.776013i
$323$	−0.922077	+	1.26913i	−0.0513058	+	0.0706163i
$324$	−2.88134	+	1.41494i	−0.160074	+	0.0786076i
$325$	−8.33364	+	2.70776i	−0.462267	+	0.150200i
$326$	1.94718	+	8.38268i	0.107844	+	0.464274i
$327$	−10.2800	+	7.46887i	−0.568486	+	0.413029i
$328$	−6.57408	+	5.36768i	−0.362993	+	0.296381i
$329$	−22.8068			−1.25738
$330$		0			0
$331$		−	19.1337i		−	1.05168i	−0.850583	−	0.525841i	$-0.823751\pi$
$331$		−	19.1337i		−	1.05168i	0.850583	−	0.525841i	$-0.176249\pi$
$332$	−5.21114	+	30.0263i	−0.285999	+	1.64791i
$333$	−2.10644	−	2.89926i	−0.115432	−	0.158878i
$334$	−23.9195	+	5.55617i	−1.30882	+	0.304020i
$335$	−0.216479	−	0.666254i	−0.0118275	−	0.0364014i
$336$	21.5365	−	14.6959i	1.17491	−	0.801725i
$337$	−23.5271	−	17.0935i	−1.28160	−	0.931140i	−0.282004	−	0.959413i	$-0.590999\pi$
$337$	−23.5271	−	17.0935i	−1.28160	−	0.931140i	−0.999600	+	0.0282737i	$0.990999\pi$
$338$	0.791765	−	9.19240i	0.0430664	−	0.500001i
$339$	40.6346	+	13.2030i	2.20697	+	0.717088i
$340$	33.9400	−	4.86315i	1.84065	−	0.263742i
$341$		0			0
$342$	1.30859	+	1.13445i	0.0707604	+	0.0613440i
$343$	6.14515	−	18.9128i	0.331807	−	1.02120i
$344$	0.182082	+	3.22512i	0.00981722	+	0.173887i
$345$	27.1088	+	19.6957i	1.45949	+	1.06038i
$346$	−13.4213	+	31.7372i	−0.721532	+	1.70620i
$347$	7.65429	−	2.48703i	0.410904	−	0.133511i	−0.0962686	−	0.995355i	$-0.530691\pi$
$347$	7.65429	−	2.48703i	0.410904	−	0.133511i	0.507172	+	0.861845i	$0.330691\pi$
$348$	8.37028	−	15.8450i	0.448694	−	0.849379i
$349$	18.1832	+	25.0270i	0.973322	+	1.33966i	0.940351	+	0.340207i	$0.110497\pi$
$349$	18.1832	+	25.0270i	0.973322	+	1.33966i	0.0329717	+	0.999456i	$0.489503\pi$
$350$	5.94104	+	9.85747i	0.317562	+	0.526904i
$351$	11.2685			0.601469
$352$		0			0
$353$	−3.26850			−0.173965			−0.0869824	−	0.996210i	$-0.527722\pi$
$353$	−3.26850			−0.173965			−0.0869824	+	0.996210i	$0.527722\pi$
$354$	11.6555	+	19.3389i	0.619480	+	1.02785i
$355$	−6.73708	−	9.27280i	−0.357567	−	0.492149i
$356$	15.1386	−	28.6575i	0.802347	−	1.51884i
$357$	36.5739	−	11.8836i	1.93570	−	0.628946i
$358$	−1.64776	+	3.89645i	−0.0870867	+	0.205934i
$359$	23.8156	+	17.3030i	1.25694	+	0.913219i	0.998603	−	0.0528370i	$-0.0168264\pi$
$359$	23.8156	+	17.3030i	1.25694	+	0.913219i	0.258334	+	0.966056i	$0.416826\pi$
$360$	−2.13365	−	37.7921i	−0.112453	−	1.99182i
$361$	5.84948	−	18.0028i	0.307867	−	0.947518i
$362$	8.31306	+	7.20681i	0.436925	+	0.378782i
$363$		0			0
$364$	11.9077	−	1.70621i	0.624132	−	0.0894299i
$365$	−17.5600	−	5.70560i	−0.919134	−	0.298645i
$366$	2.05408	−	23.8479i	0.107368	−	1.24655i
$367$	3.71820	+	2.70143i	0.194089	+	0.141014i	0.680585	−	0.732669i	$-0.261726\pi$
$367$	3.71820	+	2.70143i	0.194089	+	0.141014i	−0.486497	+	0.873682i	$0.661726\pi$
$368$	−9.42748	−	13.8158i	−0.491441	−	0.720197i
$369$	4.27057	+	13.1435i	0.222317	+	0.684221i
$370$	−3.11458	+	0.723475i	−0.161919	+	0.0376117i
$371$	13.6443	+	18.7797i	0.708375	+	0.974994i
$372$	−1.94066	+	11.1820i	−0.100618	+	0.579758i
$373$		−	29.1898i		−	1.51139i	−0.654923	−	0.755696i	$-0.727299\pi$
$373$		−	29.1898i		−	1.51139i	0.654923	−	0.755696i	$-0.272701\pi$
$374$		0			0
$375$	−12.4745			−0.644181
$376$	21.1411	−	17.2615i	1.09027	−	0.890195i
$377$	6.68879	−	4.85969i	0.344490	−	0.250287i
$378$	−3.34890	−	14.4171i	−0.172249	−	0.741537i
$379$	−7.64148	+	2.48287i	−0.392517	+	0.127536i	−0.498624	−	0.866818i	$-0.666161\pi$
$379$	−7.64148	+	2.48287i	−0.392517	+	0.127536i	0.106108	+	0.994355i	$0.466161\pi$
$380$	1.38703	−	0.681127i	0.0711531	−	0.0349411i
$381$	−14.9372	+	20.5592i	−0.765254	+	1.05328i
$382$	−0.234730	+	2.72522i	−0.0120098	+	0.139434i
$383$	9.39669	−	28.9200i	0.480149	−	1.47775i	−0.358738	−	0.933438i	$-0.616793\pi$
$383$	9.39669	−	28.9200i	0.480149	−	1.47775i	0.838886	−	0.544307i	$-0.183207\pi$
$384$	−8.84086	+	29.9226i	−0.451158	+	1.52698i
$385$		0			0
$386$	−12.0606	+	13.9119i	−0.613870	+	0.708099i
$387$	5.00251	+	1.62541i	0.254292	+	0.0826244i
$388$	−10.1689	−	10.4736i	−0.516248	−	0.531718i
$389$	−3.75735	+	5.17155i	−0.190505	+	0.262208i	−0.893576	−	0.448912i	$-0.851812\pi$
$389$	−3.75735	+	5.17155i	−0.190505	+	0.262208i	0.703071	+	0.711120i	$0.251812\pi$
$390$	11.2328	−	26.5622i	0.568796	−	1.34503i
$391$	−7.62338	−	23.4624i	−0.385531	−	1.18654i
$392$	1.44809	+	3.72734i	0.0731394	+	0.188259i
$393$	−20.4031	+	14.8237i	−1.02920	+	0.747757i
$394$	−7.51246	+	4.52772i	−0.378472	+	0.228103i
$395$		−	15.0710i		−	0.758306i
$396$		0			0
$397$		−	17.8629i		−	0.896512i	−0.893905	−	0.448256i	$-0.852045\pi$
$397$		−	17.8629i		−	0.896512i	0.893905	−	0.448256i	$-0.147955\pi$
$398$	−13.8109	−	22.9152i	−0.692276	−	1.14864i
$399$	1.40215	−	1.01872i	0.0701955	−	0.0510000i
$400$	−12.9678	−	4.64099i	−0.648391	−	0.232050i
$401$	−3.32477	−	10.2326i	−0.166031	−	0.510991i	0.833080	−	0.553153i	$-0.186575\pi$
$401$	−3.32477	−	10.2326i	−0.166031	−	0.510991i	−0.999111	+	0.0421619i	$0.986575\pi$
$402$	0.866031	+	0.366234i	0.0431937	+	0.0182661i
$403$	−3.07775	+	4.23616i	−0.153314	+	0.211018i
$404$	13.0283	−	12.6492i	0.648183	−	0.629323i
$405$	4.43547	+	1.44117i	0.220400	+	0.0716123i
$406$	−8.20541	−	7.11349i	−0.407228	−	0.353037i
$407$		0			0
$408$	−24.9085	+	38.6969i	−1.23315	+	1.91578i
$409$	−2.35488	+	7.24756i	−0.116441	+	0.358369i	−0.992245	−	0.124298i	$-0.960332\pi$
$409$	−2.35488	+	7.24756i	−0.116441	+	0.358369i	0.875804	+	0.482667i	$0.160332\pi$
$410$	12.2851	+	1.05815i	0.606719	+	0.0522583i
$411$	22.8375	−	31.4331i	1.12649	−	1.55048i
$412$	33.9839	−	16.6885i	1.67427	−	0.822182i
$413$	13.0137	−	4.22841i	0.640363	−	0.208067i
$414$	−26.5290	+	6.16232i	−1.30383	+	0.302862i
$415$	35.8203	−	26.0250i	1.75835	−	1.27752i
$416$	−9.74661	+	10.5940i	−0.477867	+	0.519414i
$417$	−13.5187			−0.662011
$418$		0			0
$419$			21.1065i			1.03112i	0.856853	+	0.515561i	$0.172416\pi$
$419$			21.1065i			1.03112i	−0.856853	+	0.515561i	$0.827584\pi$
$420$	−37.3224	−	6.47741i	−1.82115	−	0.316065i
$421$	4.73622	+	6.51884i	0.230829	+	0.317709i	0.908682	−	0.417488i	$-0.137090\pi$
$421$	4.73622	+	6.51884i	0.230829	+	0.317709i	−0.677853	+	0.735197i	$0.737090\pi$
$422$	0.934079	+	4.02124i	0.0454702	+	0.195751i
$423$	−13.7334	−	42.2671i	−0.667741	−	2.05509i
$424$	−26.8613	−	7.08134i	−1.30450	−	0.343900i
$425$	−16.4351	−	11.9408i	−0.797221	−	0.579215i
$426$	15.3276	+	1.32021i	0.742625	+	0.0639642i
$427$	−13.7955	−	4.48243i	−0.667611	−	0.216920i
$428$	−8.34393	+	1.19558i	−0.403319	+	0.0577903i
$429$		0			0
$430$	3.07420	−	3.54610i	0.148251	−	0.171008i
$431$	−1.94084	+	5.97328i	−0.0934868	+	0.287723i	−0.986856	−	0.161600i	$-0.948335\pi$
$431$	−1.94084	+	5.97328i	−0.0934868	+	0.287723i	0.893370	+	0.449323i	$0.148335\pi$
$432$	14.0160	+	10.8295i	0.674346	+	0.521035i
$433$	−18.0393	−	13.1064i	−0.866916	−	0.629851i	0.0628420	−	0.998023i	$-0.479984\pi$
$433$	−18.0393	−	13.1064i	−0.866916	−	0.629851i	−0.929758	+	0.368172i	$0.879984\pi$
$434$	6.33450	+	2.67878i	0.304066	+	0.128585i
$435$	−24.7611	+	8.04536i	−1.18720	+	0.385746i
$436$	−8.14803	−	4.30429i	−0.390220	−	0.206138i
$437$	−0.653517	−	0.899489i	−0.0312620	−	0.0430284i
$438$	21.2256	−	12.7925i	1.01420	−	0.611250i
$439$	7.42386			0.354321			0.177161	−	0.984182i	$-0.443309\pi$
$439$	7.42386			0.354321			0.177161	+	0.984182i	$0.443309\pi$
$440$		0			0
$441$	6.51133			0.310063
$442$	−18.1852	+	10.9601i	−0.864981	+	0.521319i
$443$	8.17884	+	11.2572i	0.388588	+	0.534846i	0.957834	−	0.287321i	$-0.0927648\pi$
$443$	8.17884	+	11.2572i	0.388588	+	0.534846i	−0.569246	+	0.822167i	$0.692765\pi$
$444$	2.00466	−	3.79483i	0.0951370	−	0.180094i
$445$	−44.7833	+	14.5510i	−2.12293	+	0.689783i
$446$	3.62892	+	1.53463i	0.171834	+	0.0726666i
$447$	−22.5153	−	16.3583i	−1.06494	−	0.773721i
$448$	16.4508	+	9.32154i	0.777225	+	0.440401i
$449$	−9.74967	+	30.0064i	−0.460115	+	1.41609i	0.404908	+	0.914358i	$0.367304\pi$
$449$	−9.74967	+	30.0064i	−0.460115	+	1.41609i	−0.865023	+	0.501732i	$0.832696\pi$
$450$	−14.6910	+	16.9461i	−0.692541	+	0.798847i
$451$		0			0
$452$	4.39486	+	30.6718i	0.206717	+	1.44268i
$453$	39.5908	+	12.8638i	1.86014	+	0.604396i
$454$	16.9867	+	1.46311i	0.797224	+	0.0686670i
$455$	−14.1392	−	10.2727i	−0.662855	−	0.481593i
$456$	−0.528715	+	2.00555i	−0.0247594	+	0.0939185i
$457$	−10.7034	−	32.9416i	−0.500683	−	1.54094i	−0.807909	−	0.589307i	$-0.799401\pi$
$457$	−10.7034	−	32.9416i	−0.500683	−	1.54094i	0.307227	−	0.951636i	$-0.400599\pi$
$458$	2.06503	+	8.89001i	0.0964924	+	0.415403i
$459$	15.3558	+	21.1354i	0.716747	+	0.986518i
$460$	−4.15529	+	23.9425i	−0.193741	+	1.11633i
$461$			25.6385i			1.19410i	0.802203	+	0.597051i	$0.203661\pi$
$461$			25.6385i			1.19410i	−0.802203	+	0.597051i	$0.796339\pi$
$462$		0			0
$463$	9.30958			0.432653			0.216326	−	0.976321i	$-0.430592\pi$
$463$	9.30958			0.432653			0.216326	+	0.976321i	$0.430592\pi$
$464$	12.9900	+	0.383613i	0.603046	+	0.0178088i
$465$	13.3397	−	9.69186i	0.618614	−	0.449449i
$466$	−11.6951	+	2.71662i	−0.541767	+	0.125845i
$467$	−3.91728	+	1.27280i	−0.181270	+	0.0588983i	−0.398246	−	0.917279i	$-0.630381\pi$
$467$	−3.91728	+	1.27280i	−0.181270	+	0.0588983i	0.216975	+	0.976177i	$0.430381\pi$
$468$	10.3324	+	21.0406i	0.477616	+	0.972604i
$469$	0.334931	−	0.460993i	0.0154657	−	0.0212867i
$470$	−39.5068	−	3.40283i	−1.82232	−	0.156961i
$471$	−16.0661	+	49.4464i	−0.740287	+	2.27837i
$472$	−8.86293	+	13.7691i	−0.407949	+	0.633775i
$473$		0			0
$474$	15.2847	+	13.2507i	0.702049	+	0.608625i
$475$	−0.870752	−	0.282925i	−0.0399529	−	0.0129815i
$476$	19.4270	+	20.0092i	0.890435	+	0.917119i
$477$	−26.5877	+	36.5948i	−1.21737	+	1.67556i
$478$	4.27554	+	1.80807i	0.195559	+	0.0826992i
$479$	10.9500	+	33.7005i	0.500316	+	1.53981i	0.808505	+	0.588489i	$0.200277\pi$
$479$	10.9500	+	33.7005i	0.500316	+	1.53981i	−0.308189	+	0.951325i	$0.599723\pi$
$480$	39.4990	−	22.2434i	1.80287	−	1.01527i
$481$	1.60195	−	1.16388i	0.0730425	−	0.0530685i
$482$	7.12660	+	11.8246i	0.324608	+	0.538595i
$483$			27.2555i			1.24017i
$484$		0			0
$485$			21.2091i			0.963055i
$486$	−21.4517	+	12.9288i	−0.973069	+	0.586463i
$487$	−10.9545	+	7.95894i	−0.496398	+	0.360654i	−0.807639	−	0.589677i	$-0.799255\pi$
$487$	−10.9545	+	7.95894i	−0.496398	+	0.360654i	0.311242	+	0.950331i	$0.399255\pi$
$488$	16.1805	−	6.28618i	0.732455	−	0.284562i
$489$	5.18596	+	15.9608i	0.234517	+	0.721770i
$490$	2.26282	−	5.35088i	0.102224	−	0.241728i
$491$	3.55430	−	4.89207i	0.160403	−	0.220776i	−0.721249	−	0.692676i	$-0.756432\pi$
$491$	3.55430	−	4.89207i	0.160403	−	0.220776i	0.881652	+	0.471900i	$0.156432\pi$
$492$	−11.8744	+	11.5289i	−0.535341	+	0.519765i
$493$	18.2298	+	5.92324i	0.821031	+	0.266769i
$494$	−0.626825	+	0.723043i	−0.0282022	+	0.0325312i
$495$		0			0
$496$	−7.89930	+	2.31118i	−0.354689	+	0.103775i
$497$	2.88097	−	8.86670i	0.129229	−	0.397726i
$498$	−5.09989	+	59.2098i	−0.228532	+	2.65325i
$499$	4.37583	−	6.02281i	0.195889	−	0.269618i	−0.699762	−	0.714376i	$-0.746710\pi$
$499$	4.37583	−	6.02281i	0.195889	−	0.269618i	0.895651	+	0.444758i	$0.146710\pi$
$500$	−3.98765	−	8.12033i	−0.178333	−	0.363152i
$501$	−45.5431	+	14.7979i	−2.03472	+	0.661119i
$502$	−4.79168	−	20.6283i	−0.213863	−	0.920687i
$503$	−30.0126	+	21.8054i	−1.33819	+	0.972256i	−0.338687	+	0.940899i	$0.609983\pi$
$503$	−30.0126	+	21.8054i	−1.33819	+	0.972256i	−0.999508	+	0.0313563i	$0.990017\pi$
$504$	23.8490	−	19.4725i	1.06232	−	0.867376i
$505$	−26.3823			−1.17400
$506$		0			0
$507$		−	17.9923i		−	0.799067i
$508$	−18.1580	−	3.15137i	−0.805630	−	0.139819i
$509$	−4.60549	−	6.33891i	−0.204135	−	0.280967i	0.694659	−	0.719339i	$-0.255555\pi$
$509$	−4.60549	−	6.33891i	−0.204135	−	0.280967i	−0.898794	+	0.438372i	$0.855555\pi$
$510$	65.1277	−	15.1283i	2.88390	−	0.669891i
$511$	−4.64092	−	14.2833i	−0.205302	−	0.631855i
$512$	−22.3043	+	3.81016i	−0.985721	+	0.168387i
$513$	0.952543	+	0.692063i	0.0420558	+	0.0305553i
$514$	0.0339004	−	0.393584i	0.00149528	−	0.0173603i
$515$	−52.3141	−	16.9979i	−2.30523	−	0.749016i
$516$	0.893476	+	6.23557i	0.0393331	+	0.274506i
$517$		0			0
$518$	−1.96517	−	1.70366i	−0.0863448	−	0.0748546i
$519$	−20.7649	+	63.9079i	−0.911479	+	2.80525i
$520$	20.8815	−	1.17892i	0.915714	−	0.0516990i
$521$	−1.62246	−	1.17879i	−0.0710812	−	0.0516435i	0.551677	−	0.834058i	$-0.313988\pi$
$521$	−1.62246	−	1.17879i	−0.0710812	−	0.0516435i	−0.622758	+	0.782414i	$0.713988\pi$
$522$	8.24218	−	19.4903i	0.360750	−	0.853065i
$523$	−13.5473	+	4.40178i	−0.592382	+	0.192477i	−0.589840	−	0.807520i	$-0.700809\pi$
$523$	−13.5473	+	4.40178i	−0.592382	+	0.192477i	−0.00254195	+	0.999997i	$0.500809\pi$
$524$	−16.1717	−	8.54287i	−0.706463	−	0.373197i
$525$	13.1924	+	18.1578i	0.575763	+	0.792470i
$526$	−14.7709	−	24.5082i	−0.644043	−	1.06861i
$527$	−12.1395			−0.528806
$528$		0			0
$529$	−5.51543			−0.239801
$530$	20.8331	+	34.5667i	0.904933	+	1.50148i
$531$	15.6727	+	21.5716i	0.680138	+	0.936130i
$532$	1.11136	+	0.587089i	0.0481836	+	0.0254535i
$533$	−7.26224	+	2.35964i	−0.314562	+	0.102208i
$534$	24.6170	−	58.2117i	1.06528	−	2.51907i
$535$	9.90759	+	7.19828i	0.428342	+	0.311209i
$536$	0.0384373	+	0.680818i	0.00166024	+	0.0294069i
$537$	−2.54936	+	7.84611i	−0.110013	+	0.338585i
$538$	−13.2343	−	11.4732i	−0.570571	−	0.494643i
$539$		0			0
$540$	−3.65003	−	25.4735i	−0.157072	−	1.09621i
$541$	−37.5869	−	12.2127i	−1.61599	−	0.525067i	−0.644998	−	0.764184i	$-0.723142\pi$
$541$	−37.5869	−	12.2127i	−1.61599	−	0.525067i	−0.970991	+	0.239118i	$0.923142\pi$
$542$	0.225729	−	2.62072i	0.00969590	−	0.112570i
$543$	17.3574	+	12.6109i	0.744876	+	0.541184i
$544$	−33.1522	−	3.84429i	−1.42139	−	0.164823i
$545$	4.13721	+	12.7330i	0.177218	+	0.545422i
$546$	22.8498	−	5.30769i	0.977879	−	0.227148i
$547$	−20.2482	−	27.8692i	−0.865749	−	1.19160i	−0.980168	−	0.198169i	$-0.936500\pi$
$547$	−20.2482	−	27.8692i	−0.865749	−	1.19160i	0.114418	−	0.993433i	$-0.463500\pi$
$548$	27.7618	+	4.81813i	1.18592	+	0.205820i
$549$		−	28.2658i		−	1.20636i
$550$		0			0
$551$	0.863873			0.0368022
$552$	−20.6286	−	25.2649i	−0.878009	−	1.07534i
$553$	9.91753	−	7.20551i	0.421736	−	0.306409i
$554$	5.85004	+	25.1846i	0.248545	+	1.06999i
$555$	−5.93021	+	1.92684i	−0.251724	+	0.0817899i
$556$	−4.32142	−	8.80002i	−0.183269	−	0.373204i
$557$	−10.9948	+	15.1330i	−0.465863	+	0.641206i	−0.975712	−	0.219058i	$-0.929701\pi$
$557$	−10.9948	+	15.1330i	−0.465863	+	0.641206i	0.509848	+	0.860264i	$0.329701\pi$
$558$	−1.15009	+	13.3525i	−0.0486871	+	0.565258i
$559$	−0.898100	+	2.76407i	−0.0379856	+	0.116908i
$560$	−7.71412	−	26.3658i	−0.325981	−	1.11416i
$561$		0			0
$562$	12.8749	−	14.8512i	0.543095	−	0.626460i
$563$	−39.8420	−	12.9455i	−1.67914	−	0.545586i	−0.694397	−	0.719592i	$-0.744329\pi$
$563$	−39.8420	−	12.9455i	−1.67914	−	0.545586i	−0.984745	+	0.174006i	$0.944329\pi$
$564$	38.1861	−	37.0751i	1.60793	−	1.56114i
$565$	26.4604	−	36.4197i	1.11320	−	1.53219i
$566$	3.68676	−	8.71806i	0.154966	−	0.366447i
$567$	1.17224	+	3.60779i	0.0492296	+	0.151513i
$568$	4.04028	+	10.3996i	0.169526	+	0.436357i
$569$	34.1439	−	24.8070i	1.43139	−	1.03996i	0.441629	−	0.897198i	$-0.354401\pi$
$569$	34.1439	−	24.8070i	1.43139	−	1.03996i	0.989757	−	0.142765i	$-0.0455994\pi$
$570$	2.58086	−	1.55547i	0.108100	−	0.0651514i
$571$		−	19.8693i		−	0.831503i	−0.909478	−	0.415751i	$-0.863519\pi$
$571$		−	19.8693i		−	0.831503i	0.909478	−	0.415751i	$-0.136481\pi$
$572$		0			0
$573$			5.33408i			0.222834i
$574$	5.17724	+	8.59016i	0.216094	+	0.358546i
$575$	11.6483	−	8.46298i	0.485768	−	0.352931i
$576$	−7.36924	+	36.1006i	−0.307052	+	1.50419i
$577$	5.03386	+	15.4926i	0.209562	+	0.644966i	0.999495	+	0.0317730i	$0.0101154\pi$
$577$	5.03386	+	15.4926i	0.209562	+	0.644966i	−0.789933	+	0.613193i	$0.789885\pi$
$578$	−23.1952	−	9.80894i	−0.964791	−	0.407998i
$579$	−21.1043	+	29.0476i	−0.877067	+	1.20718i
$580$	−13.1524	−	13.5465i	−0.546122	−	0.562488i
$581$	34.2516	+	11.1290i	1.42100	+	0.461710i
$582$	−21.5098	−	18.6474i	−0.891608	−	0.772958i
$583$		0			0
$584$	15.1124	+	9.72756i	0.625354	+	0.402529i
$585$	10.5240	−	32.3895i	0.435113	−	1.33914i
$586$	−33.0612	−	2.84765i	−1.36575	−	0.117635i
$587$	−10.9205	+	15.0308i	−0.450739	+	0.620388i	−0.972556	−	0.232669i	$-0.925254\pi$
$587$	−10.9205	+	15.0308i	−0.450739	+	0.620388i	0.521817	+	0.853057i	$0.325254\pi$
$588$	3.43723	+	6.99947i	0.141749	+	0.288653i
$589$	−0.520333	+	0.169066i	−0.0214399	+	0.00696626i
$590$	23.1737	−	5.38294i	0.954047	−	0.221612i
$591$	−13.8382	+	10.0540i	−0.569227	+	0.413567i
$592$	3.11107	+	0.0918743i	0.127864	+	0.00377601i
$593$	41.6124			1.70882			0.854409	−	0.519602i	$-0.173920\pi$
$593$	41.6124			1.70882			0.854409	+	0.519602i	$0.173920\pi$
$594$		0			0
$595$		−	40.5185i		−	1.66110i
$596$	3.45119	−	19.8855i	0.141366	−	0.814543i
$597$	−30.6677	−	42.2105i	−1.25515	−	1.72756i
$598$	−3.40491	−	14.6582i	−0.139237	−	0.599420i
$599$	9.01286	+	27.7387i	0.368256	+	1.13337i	0.947917	+	0.318517i	$0.103185\pi$
$599$	9.01286	+	27.7387i	0.368256	+	1.13337i	−0.579662	+	0.814857i	$0.696815\pi$
$600$	−25.9717	−	6.84681i	−1.06029	−	0.279520i
$601$	−17.7659	−	12.9077i	−0.724688	−	0.526517i	0.163191	−	0.986595i	$-0.447821\pi$
$601$	−17.7659	−	12.9077i	−0.724688	−	0.526517i	−0.887879	+	0.460078i	$0.847821\pi$
$602$	3.80330	+	0.327588i	0.155011	+	0.0133515i
$603$	1.05602	+	0.343123i	0.0430046	+	0.0139730i
$604$	4.28197	+	29.8839i	0.174231	+	1.21596i
$605$		0			0
$606$	23.1957	−	26.7563i	0.942263	−	1.08690i
$607$	−4.71823	+	14.5212i	−0.191507	+	0.589398i	0.808492	+	0.588507i	$0.200284\pi$
$607$	−4.71823	+	14.5212i	−0.191507	+	0.589398i	−1.00000		0.000891883i	$0.999716\pi$
$608$	−1.47453	+	0.296932i	−0.0598002	+	0.0120422i
$609$	−17.1326	−	12.4476i	−0.694249	−	0.504401i
$610$	−23.2283	−	9.82294i	−0.940485	−	0.397719i
$611$	23.3541	−	7.58820i	0.944805	−	0.306986i
$612$	−25.3841	+	48.0521i	−1.02609	+	1.94239i
$613$	−23.1619	−	31.8796i	−0.935501	−	1.28761i	−0.957675	−	0.287853i	$-0.907059\pi$
$613$	−23.1619	−	31.8796i	−0.935501	−	1.28761i	0.0221738	−	0.999754i	$-0.492941\pi$
$614$	11.0028	−	6.63134i	0.444038	−	0.267619i
$615$	24.0457			0.969617
$616$		0			0
$617$	−34.3034			−1.38100			−0.690501	−	0.723331i	$-0.742610\pi$
$617$	−34.3034			−1.38100			−0.690501	+	0.723331i	$0.742610\pi$
$618$	63.2343	−	38.1109i	2.54366	−	1.53305i
$619$	8.42417	+	11.5949i	0.338596	+	0.466037i	0.944031	−	0.329858i	$-0.107001\pi$
$619$	8.42417	+	11.5949i	0.338596	+	0.466037i	−0.605435	+	0.795895i	$0.707001\pi$
$620$	10.5732	+	5.58540i	0.424629	+	0.224315i
$621$	−17.6096	+	5.72171i	−0.706649	+	0.229604i
$622$	24.0734	+	10.1803i	0.965257	+	0.408195i
$623$	−30.9864	−	22.5129i	−1.24144	−	0.901961i
$624$	−17.1637	+	22.2140i	−0.687099	+	0.889273i
$625$	−9.38180	+	28.8742i	−0.375272	+	1.15497i
$626$	9.12583	−	10.5266i	0.364741	−	0.420729i
$627$		0			0
$628$	−37.3231	+	5.34791i	−1.48935	+	0.213405i
$629$	4.36600	+	1.41860i	0.174084	+	0.0565633i
$630$	−44.5673	−	3.83869i	−1.77560	−	0.152937i
$631$	6.53161	+	4.74549i	0.260019	+	0.188915i	0.710156	−	0.704045i	$-0.248625\pi$
$631$	6.53161	+	4.74549i	0.260019	+	0.188915i	−0.450136	+	0.892960i	$0.648625\pi$
$632$	−3.73964	+	14.1854i	−0.148755	+	0.564265i
$633$	2.48775	+	7.65650i	0.0988791	+	0.304319i
$634$	−9.52878	−	41.0217i	−0.378436	−	1.62918i
$635$	15.7383	+	21.6619i	0.624554	+	0.859625i
$636$	−53.3735	−	9.26312i	−2.11640	−	0.367307i
$637$			3.59774i			0.142548i
$638$		0			0
$639$	18.1671			0.718681
$640$	27.1058	+	18.6016i	1.07145	+	0.735293i
$641$	−33.6141	+	24.4221i	−1.32768	+	0.964615i	−0.327876	+	0.944721i	$0.606333\pi$
$641$	−33.6141	+	24.4221i	−1.32768	+	0.964615i	−0.999802	+	0.0198941i	$0.993667\pi$
$642$	−16.0112	+	3.71919i	−0.631913	+	0.146785i
$643$	41.4305	−	13.4616i	1.63386	−	0.530874i	0.658707	−	0.752400i	$-0.271104\pi$
$643$	41.4305	−	13.4616i	1.63386	−	0.530874i	0.975154	+	0.221526i	$0.0711039\pi$
$644$	−17.7421	+	8.71259i	−0.699136	+	0.343324i
$645$	5.37941	−	7.40412i	0.211814	−	0.291537i
$646$	−2.21034	−	0.190382i	−0.0869646	−	0.00749048i
$647$	−6.01362	+	18.5080i	−0.236420	+	0.727625i	0.760510	+	0.649326i	$0.224949\pi$
$647$	−6.01362	+	18.5080i	−0.236420	+	0.727625i	−0.996930	+	0.0782990i	$0.975051\pi$
$648$	−3.81721	−	2.45707i	−0.149954	−	0.0965229i
$649$		0			0
$650$	−9.36334	−	8.11732i	−0.367260	−	0.318388i
$651$	12.7555	+	4.14451i	0.499928	+	0.162436i
$652$	−8.73195	+	8.47789i	−0.341970	+	0.332020i
$653$	10.4852	−	14.4316i	0.410316	−	0.564752i	−0.552979	−	0.833195i	$-0.686509\pi$
$653$	10.4852	−	14.4316i	0.410316	−	0.564752i	0.963296	+	0.268443i	$0.0865091\pi$
$654$	−16.5510	−	6.99922i	−0.647196	−	0.273691i
$655$	8.21125	+	25.2716i	0.320840	+	0.987444i
$656$	−11.3006	−	4.04433i	−0.441216	−	0.157905i
$657$	23.6761	−	17.2017i	0.923692	−	0.671102i
$658$	−16.6491	−	27.6245i	−0.649050	−	1.07691i
$659$		−	27.1210i		−	1.05648i	−0.849094	−	0.528242i	$-0.822851\pi$
$659$		−	27.1210i		−	1.05648i	0.849094	−	0.528242i	$-0.177149\pi$
$660$		0			0
$661$			25.9185i			1.00811i	0.863671	+	0.504056i	$0.168160\pi$
$661$			25.9185i			1.00811i	−0.863671	+	0.504056i	$0.831840\pi$
$662$	23.1754	−	13.9677i	0.900738	−	0.542869i
$663$	−33.4976	+	24.3375i	−1.30094	+	0.945189i
$664$	−40.1731	+	15.6074i	−1.55902	+	0.605685i
$665$	−0.564299	−	1.73673i	−0.0218826	−	0.0673476i
$666$	1.97398	−	4.66786i	0.0764902	−	0.180876i
$667$	−7.98518	+	10.9907i	−0.309188	+	0.425560i
$668$	−24.1912	−	24.9161i	−0.935985	−	0.964034i
$669$	7.30740	+	2.37432i	0.282521	+	0.0917965i
$670$	0.648960	−	0.748576i	0.0250715	−	0.0289200i
$671$		0			0
$672$	33.5219	+	15.3577i	1.29314	+	0.592437i
$673$	5.25869	−	16.1846i	0.202708	−	0.623870i	−0.797092	−	0.603858i	$-0.793629\pi$
$673$	5.25869	−	16.1846i	0.202708	−	0.623870i	0.999800	−	0.0200123i	$-0.00637054\pi$
$674$	3.52930	−	40.9752i	0.135944	−	1.57831i
$675$	−8.96215	+	12.3353i	−0.344953	+	0.474787i
$676$	11.7122	−	5.75148i	0.450468	−	0.221211i
$677$	25.8893	−	8.41193i	0.995005	−	0.323297i	0.234137	−	0.972204i	$-0.424774\pi$
$677$	25.8893	−	8.41193i	0.995005	−	0.323297i	0.760868	+	0.648907i	$0.224774\pi$
$678$	13.6715	+	58.8563i	0.525052	+	2.26036i
$679$	−13.9567	+	10.1401i	−0.535608	+	0.389142i
$680$	30.6668	+	37.5592i	1.17602	+	1.44033i
$681$	33.2480			1.27407
$682$		0			0
$683$		−	8.02880i		−	0.307214i	−0.988132	−	0.153607i	$-0.950911\pi$
$683$		−	8.02880i		−	0.307214i	0.988132	−	0.153607i	$-0.0490889\pi$
$684$	−0.418811	+	2.41316i	−0.0160136	+	0.0922696i
$685$	−24.0623	−	33.1189i	−0.919372	−	1.26541i
$686$	27.3939	−	6.36322i	1.04590	−	0.242949i
$687$	5.49983	+	16.9267i	0.209831	+	0.645795i
$688$	−3.77346	+	2.57490i	−0.143862	+	0.0981670i
$689$	−20.2200	−	14.6907i	−0.770319	−	0.559670i
$690$	−4.06658	+	47.2130i	−0.154812	+	1.79737i
$691$	20.0512	+	6.51504i	0.762784	+	0.247844i	0.664473	−	0.747312i	$-0.268656\pi$
$691$	20.0512	+	6.51504i	0.762784	+	0.247844i	0.0983111	+	0.995156i	$0.468656\pi$
$692$	−48.2389	+	6.91200i	−1.83377	+	0.262755i
$693$		0			0
$694$	8.60004	+	7.45561i	0.326453	+	0.283011i
$695$	−4.40154	+	13.5465i	−0.166960	+	0.513850i
$696$	25.3023	−	1.42851i	0.959083	−	0.0541475i
$697$	−14.3222	−	10.4057i	−0.542491	−	0.394143i
$698$	−17.0398	+	40.2939i	−0.644965	+	1.52515i
$699$	−22.2677	+	7.23523i	−0.842243	+	0.273661i
$700$	−7.60274	+	14.3920i	−0.287357	+	0.543967i
$701$	5.28521	+	7.27447i	0.199620	+	0.274753i	0.897078	−	0.441873i	$-0.145686\pi$
$701$	5.28521	+	7.27447i	0.199620	+	0.274753i	−0.697458	+	0.716626i	$0.745686\pi$
$702$	8.22607	+	13.6488i	0.310473	+	0.515142i
$703$	0.206895			0.00780320
$704$		0			0
$705$	−77.3268			−2.91230
$706$	−2.38602	−	3.95893i	−0.0897991	−	0.148996i
$707$	−12.6135	−	17.3609i	−0.474378	−	0.652925i
$708$	−14.9155	+	28.2350i	−0.560558	+	1.06114i
$709$	4.43373	−	1.44061i	0.166512	−	0.0541031i	−0.224575	−	0.974457i	$-0.572099\pi$
$709$	4.43373	−	1.44061i	0.166512	−	0.0541031i	0.391087	+	0.920354i	$0.372099\pi$
$710$	6.31345	−	14.9294i	0.236939	−	0.560290i
$711$	19.3256	+	14.0409i	0.724768	+	0.526575i
$712$	45.7623	−	2.58363i	1.71501	−	0.0968255i
$713$	2.65873	−	8.18272i	0.0995701	−	0.306445i
$714$	41.0930	+	35.6246i	1.53787	+	1.33322i
$715$		0			0
$716$	−5.92239	+	0.848601i	−0.221330	+	0.0317137i
$717$	8.60947	+	2.79739i	0.321526	+	0.104470i
$718$	−3.57257	+	41.4776i	−0.133327	+	1.54793i
$719$	−4.10845	−	2.98497i	−0.153220	−	0.111320i	0.508534	−	0.861042i	$-0.330188\pi$
$719$	−4.10845	−	2.98497i	−0.153220	−	0.111320i	−0.661754	+	0.749721i	$0.730188\pi$
$720$	44.2175	−	30.1727i	1.64789	−	1.12447i
$721$	−13.8260	−	42.5521i	−0.514908	−	1.58472i
$722$	26.0758	−	6.05706i	0.970442	−	0.225420i
$723$	15.8250	+	21.7812i	0.588538	+	0.810053i
$724$	−2.66058	+	15.3301i	−0.0988796	+	0.569738i
$725$			11.1871i			0.415477i
$726$		0			0
$727$	27.7902			1.03068			0.515341	−	0.856985i	$-0.327665\pi$
$727$	27.7902			1.03068			0.515341	+	0.856985i	$0.327665\pi$
$728$	10.7593	+	13.1775i	0.398766	+	0.488389i
$729$	−35.6192	+	25.8789i	−1.31923	+	0.958478i
$730$	−5.90808	−	25.4345i	−0.218668	−	0.941372i
$731$	−6.40820	+	2.08215i	−0.237016	+	0.0770111i
$732$	30.3849	−	14.9211i	1.12306	−	0.551499i
$733$	19.1820	−	26.4017i	0.708503	−	0.975171i	−0.291325	−	0.956624i	$-0.594096\pi$
$733$	19.1820	−	26.4017i	0.708503	−	0.975171i	0.999828	−	0.0185465i	$-0.00590389\pi$
$734$	−0.557767	+	6.47568i	−0.0205875	+	0.239022i
$735$	3.50095	−	10.7748i	0.129135	−	0.397435i
$736$	9.85207	−	21.5045i	0.363152	−	0.792666i
$737$		0			0
$738$	−12.8023	+	14.7674i	−0.471259	+	0.543597i
$739$	45.5471	+	14.7992i	1.67548	+	0.544396i	0.984026	−	0.178026i	$-0.0569712\pi$
$739$	45.5471	+	14.7992i	1.67548	+	0.544396i	0.691452	+	0.722422i	$0.256971\pi$
$740$	−3.14996	−	3.24435i	−0.115795	−	0.119265i
$741$	−1.09685	+	1.50969i	−0.0402939	+	0.0554598i
$742$	−12.7863	+	30.2357i	−0.469400	+	1.10999i
$743$	4.97496	+	15.3113i	0.182513	+	0.561719i	0.999897	−	0.0143757i	$-0.00457609\pi$
$743$	4.97496	+	15.3113i	0.182513	+	0.561719i	−0.817383	+	0.576094i	$0.804576\pi$
$744$	−14.9607	+	5.81229i	−0.548485	+	0.213089i
$745$	−23.7228	+	17.2356i	−0.869136	+	0.631464i
$746$	35.3558	−	21.3087i	1.29447	−	0.780167i
$747$			70.1787i			2.56771i
$748$		0			0
$749$			9.96123i			0.363975i
$750$	−9.10646	−	15.1096i	−0.332521	−	0.551724i
$751$	40.0588	−	29.1044i	1.46177	−	1.06204i	0.478870	−	0.877886i	$-0.341047\pi$
$751$	40.0588	−	29.1044i	1.46177	−	1.06204i	0.982898	−	0.184150i	$-0.0589533\pi$
$752$	36.3409	+	13.0059i	1.32522	+	0.474275i
$753$	−12.7618	−	39.2767i	−0.465065	−	1.43132i
$754$	10.7691	+	4.55410i	0.392187	+	0.165851i
$755$	25.7808	−	35.4842i	0.938258	−	1.29140i
$756$	15.0178	−	14.5809i	0.546193	−	0.530302i
$757$	−11.7749	−	3.82589i	−0.427965	−	0.139054i	0.0871113	−	0.996199i	$-0.472236\pi$
$757$	−11.7749	−	3.82589i	−0.427965	−	0.139054i	−0.515076	+	0.857144i	$0.672236\pi$
$758$	−8.58566	−	7.44314i	−0.311845	−	0.270347i
$759$		0			0
$760$	1.83754	+	1.18279i	0.0666547	+	0.0429044i
$761$	9.06311	−	27.8934i	0.328537	−	1.01113i	−0.641281	−	0.767306i	$-0.721597\pi$
$761$	9.06311	−	27.8934i	0.328537	−	1.01113i	0.969818	−	0.243828i	$-0.0784033\pi$
$762$	−35.8063	−	3.08409i	−1.29713	−	0.111725i
$763$	−6.40098	+	8.81019i	−0.231731	+	0.318950i
$764$	−3.47224	+	1.70511i	−0.125621	+	0.0616887i
$765$	75.0915	−	24.3987i	2.71494	−	0.882137i
$766$	41.8886	−	9.73016i	1.51350	−	0.351565i
$767$	−11.9191	+	8.65975i	−0.430374	+	0.312685i
$768$	−42.6972	+	11.1353i	−1.54070	+	0.401809i
$769$	−23.6034			−0.851162			−0.425581	−	0.904920i	$-0.639930\pi$
$769$	−23.6034			−0.851162			−0.425581	+	0.904920i	$0.639930\pi$
$770$		0			0
$771$		−	0.770364i		−	0.0277440i
$772$	−25.6550	−	4.45249i	−0.923342	−	0.160249i
$773$	−3.96398	−	5.45596i	−0.142575	−	0.196237i	0.731758	−	0.681565i	$-0.238700\pi$
$773$	−3.96398	−	5.45596i	−0.142575	−	0.196237i	−0.874332	+	0.485328i	$0.838700\pi$
$774$	1.68310	+	7.24578i	0.0604976	+	0.260444i
$775$	−2.18939	−	6.73826i	−0.0786453	−	0.242045i
$776$	5.26270	−	19.9627i	0.188920	−	0.716621i
$777$	−4.10322	−	2.98116i	−0.147202	−	0.106949i
$778$	−9.00684	−	0.775783i	−0.322911	−	0.0278132i
$779$	−0.758805	−	0.246551i	−0.0271870	−	0.00883360i
$780$	40.3731	−	5.78494i	1.44559	−	0.207134i
$781$		0			0
$782$	22.8533	−	26.3613i	0.817234	−	0.942680i
$783$	4.44567	−	13.6824i	0.158875	−	0.488968i
$784$	−3.45758	+	4.47495i	−0.123485	+	0.159820i
$785$	44.3175	+	32.1985i	1.58176	+	1.14921i
$786$	−32.8494	−	13.8916i	−1.17170	−	0.495496i
$787$	−0.0148213	+	0.00481574i	−0.000528323	+	0.000171663i	−0.309281	−	0.950971i	$-0.600088\pi$
$787$	−0.0148213	+	0.00481574i	−0.000528323	+	0.000171663i	0.308753	+	0.951142i	$0.400088\pi$
$788$	−10.9683	−	5.79411i	−0.390728	−	0.206407i
$789$	−32.7996	−	45.1448i	−1.16770	−	1.60720i
$790$	18.2546	−	11.0019i	0.649469	−	0.391431i
$791$	36.6169			1.30195
$792$		0			0
$793$	15.6179			0.554608
$794$	21.6362	−	13.0400i	0.767839	−	0.462772i
$795$	46.2610	+	63.6728i	1.64071	+	2.25824i
$796$	17.6737	−	33.4564i	0.626429	−	1.18583i
$797$	−26.1854	+	8.50814i	−0.927533	+	0.301374i	−0.733554	−	0.679632i	$-0.762140\pi$
$797$	−26.1854	+	8.50814i	−0.927533	+	0.301374i	−0.193980	+	0.981006i	$0.562140\pi$
$798$	2.25749	+	0.954666i	0.0799145	+	0.0337948i
$799$	46.0576	+	33.4628i	1.62940	+	1.18383i
$800$	−3.84524	−	19.0950i	−0.135950	−	0.675112i
$801$	23.0635	−	70.9823i	0.814910	−	2.50803i
$802$	9.96698	−	11.4969i	0.351946	−	0.405970i
$803$		0			0
$804$	0.188612	+	1.31632i	0.00665182	+	0.0464231i
$805$	27.3118	+	8.87413i	0.962613	+	0.312772i
$806$	−7.37777	−	0.635466i	−0.259871	−	0.0223833i
$807$	−27.6327	−	20.0764i	−0.972718	−	0.706721i
$808$	24.8319	+	6.54635i	0.873585	+	0.230300i
$809$	2.78976	+	8.58600i	0.0980828	+	0.301868i	0.988045	−	0.154167i	$-0.0492693\pi$
$809$	2.78976	+	8.58600i	0.0980828	+	0.301868i	−0.889962	+	0.456035i	$0.849269\pi$
$810$	1.49231	+	6.42446i	0.0524345	+	0.225732i
$811$	−3.87229	−	5.32975i	−0.135975	−	0.187153i	0.735600	−	0.677417i	$-0.236901\pi$
$811$	−3.87229	−	5.32975i	−0.135975	−	0.187153i	−0.871574	+	0.490264i	$0.836901\pi$
$812$	2.62613	−	15.1316i	0.0921589	−	0.531014i
$813$		−	5.12954i		−	0.179901i
$814$		0			0
$815$	17.6822			0.619380
$816$	−65.0544	−	1.92115i	−2.27736	−	0.0672535i
$817$	−0.245675	+	0.178493i	−0.00859506	+	0.00624468i
$818$	−10.4976	+	2.43844i	−0.367039	+	0.0852582i
$819$	26.3455	−	8.56017i	0.920586	−	0.299117i
$820$	7.68653	+	15.6526i	0.268425	+	0.546614i
$821$	11.4245	−	15.7245i	0.398717	−	0.548787i	−0.561704	−	0.827338i	$-0.689854\pi$
$821$	11.4245	−	15.7245i	0.398717	−	0.548787i	0.960421	+	0.278551i	$0.0898541\pi$
$822$	54.7443	+	4.71527i	1.90943	+	0.164464i
$823$	6.78715	−	20.8887i	0.236585	−	0.728134i	−0.760322	−	0.649546i	$-0.774959\pi$
$823$	6.78715	−	20.8887i	0.236585	−	0.728134i	0.996907	−	0.0785880i	$-0.0250412\pi$
$824$	45.0221	+	28.9799i	1.56842	+	1.00956i
$825$		0			0
$826$	14.6217	+	12.6759i	0.508753	+	0.441052i
$827$	5.59050	+	1.81646i	0.194401	+	0.0631647i	0.404599	−	0.914494i	$-0.367411\pi$
$827$	5.59050	+	1.81646i	0.194401	+	0.0631647i	−0.210198	+	0.977659i	$0.567411\pi$
$828$	−26.8303	−	27.6344i	−0.932418	−	0.960360i
$829$	−3.28621	+	4.52308i	−0.114135	+	0.157093i	−0.862262	−	0.506462i	$-0.830953\pi$
$829$	−3.28621	+	4.52308i	−0.114135	+	0.157093i	0.748128	+	0.663555i	$0.230953\pi$
$830$	57.6715	+	24.3885i	2.00181	+	0.846538i
$831$	15.5805	+	47.9519i	0.540482	+	1.66343i
$832$	−19.9469	−	4.07177i	−0.691535	−	0.141163i
$833$	−6.74800	+	4.90271i	−0.233804	+	0.169869i
$834$	−9.86868	−	16.3743i	−0.341725	−	0.566995i
$835$			50.4551i			1.74607i
$836$		0			0
$837$			9.11129i			0.314932i
$838$	−25.5650	+	15.4079i	−0.883129	+	0.532256i
$839$	−20.3734	+	14.8021i	−0.703368	+	0.511027i	−0.881027	−	0.473065i	$-0.843148\pi$
$839$	−20.3734	+	14.8021i	−0.703368	+	0.511027i	0.177659	+	0.984092i	$0.443148\pi$
$840$	−19.3999	−	49.9348i	−0.669359	−	1.72291i
$841$	5.69967	+	17.5418i	0.196540	+	0.604889i
$842$	−4.43840	+	10.4955i	−0.152957	+	0.361698i
$843$	22.5292	−	31.0088i	0.775947	−	1.06800i
$844$	−4.18879	+	4.06691i	−0.144184	+	0.139989i
$845$	−18.0294	−	5.85812i	−0.620231	−	0.201525i
$846$	41.1699	−	47.4895i	1.41545	−	1.63272i
$847$		0			0
$848$	−11.0317	−	37.7048i	−0.378830	−	1.29479i
$849$	5.70403	−	17.5552i	0.195762	−	0.602492i
$850$	2.46543	−	28.6237i	0.0845636	−	0.981784i
$851$	−1.91243	+	2.63223i	−0.0655573	+	0.0902318i
$852$	9.59014	+	19.5291i	0.328553	+	0.669056i
$853$	−33.7492	+	10.9658i	−1.15555	+	0.375462i	−0.823232	−	0.567705i	$-0.807831\pi$
$853$	−33.7492	+	10.9658i	−1.15555	+	0.375462i	−0.332320	+	0.943167i	$0.607831\pi$
$854$	−4.64150	−	19.9818i	−0.158829	−	0.683763i
$855$	2.87882	−	2.09159i	0.0984537	−	0.0715308i
$856$	−7.53923	−	9.23369i	−0.257686	−	0.315601i
$857$	−27.0737			−0.924822			−0.462411	−	0.886666i	$-0.653015\pi$
$857$	−27.0737			−0.924822			−0.462411	+	0.886666i	$0.653015\pi$
$858$		0			0
$859$			32.8716i			1.12157i	0.827963	+	0.560783i	$0.189500\pi$
$859$			32.8716i			1.12157i	−0.827963	+	0.560783i	$0.810500\pi$
$860$	6.53934	+	1.13492i	0.222990	+	0.0387005i
$861$	11.4963	+	15.8233i	0.391794	+	0.539258i
$862$	−8.65187	+	2.00971i	−0.294684	+	0.0684510i
$863$	16.8222	+	51.7733i	0.572634	+	1.76238i	0.644099	+	0.764942i	$0.277232\pi$
$863$	16.8222	+	51.7733i	0.572634	+	1.76238i	−0.0714659	+	0.997443i	$0.522768\pi$
$864$	−2.88532	+	24.8823i	−0.0981607	+	0.846513i
$865$	57.2789	+	41.6155i	1.94754	+	1.41497i
$866$	2.70608	−	31.4176i	0.0919563	−	1.06761i
$867$	−46.7071	−	15.1761i	−1.58626	−	0.515406i
$868$	1.37958	+	9.62809i	0.0468260	+	0.326799i
$869$		0			0
$870$	−27.8205	−	24.1184i	−0.943205	−	0.817689i
$871$	−0.189588	+	0.583491i	−0.00642394	+	0.0197708i
$872$	−0.734589	−	13.0113i	−0.0248763	−	0.440620i
$873$	−27.1965	−	19.7594i	−0.920462	−	0.668755i
$874$	0.612423	−	1.44819i	0.0207155	−	0.0489859i
$875$	−10.1677	+	3.30368i	−0.343730	+	0.111685i
$876$	30.9895	+	16.3706i	1.04704	+	0.553110i
$877$	−18.4434	−	25.3852i	−0.622791	−	0.857198i	0.374762	−	0.927121i	$-0.377725\pi$
$877$	−18.4434	−	25.3852i	−0.622791	−	0.857198i	−0.997552	+	0.0699233i	$0.977725\pi$
$878$	5.41945	+	8.99205i	0.182898	+	0.303467i
$879$	−64.7108			−2.18264
$880$		0			0
$881$	34.3514			1.15733			0.578664	−	0.815566i	$-0.303574\pi$
$881$	34.3514			1.15733			0.578664	+	0.815566i	$0.303574\pi$
$882$	4.75330	+	7.88675i	0.160052	+	0.265561i
$883$	31.6783	+	43.6015i	1.06606	+	1.46731i	0.874001	+	0.485924i	$0.161517\pi$
$883$	31.6783	+	43.6015i	1.06606	+	1.46731i	0.192060	+	0.981383i	$0.438483\pi$
$884$	−26.5505	−	14.0256i	−0.892991	−	0.471733i
$885$	44.1231	−	14.3365i	1.48318	−	0.481915i
$886$	−7.66454	+	18.1243i	−0.257495	+	0.608898i
$887$	14.2499	+	10.3532i	0.478466	+	0.347626i	0.800732	−	0.599023i	$-0.204444\pi$
$887$	14.2499	+	10.3532i	0.478466	+	0.347626i	−0.322265	+	0.946649i	$0.604444\pi$
$888$	6.05984	−	0.342124i	0.203355	−	0.0114809i
$889$	−6.73013	+	20.7132i	−0.225721	+	0.694699i
$890$	−50.3167	−	43.6209i	−1.68662	−	1.46218i
$891$		0			0
$892$	0.790337	+	5.51577i	0.0264624	+	0.184682i
$893$	2.44019	+	0.792865i	0.0816577	+	0.0265322i
$894$	3.37751	−	39.2129i	0.112961	−	1.31148i
$895$	7.03225	+	5.10923i	0.235062	+	0.170783i
$896$	0.718553	+	26.7305i	0.0240052	+	0.893004i
$897$	−9.06835	−	27.9095i	−0.302784	−	0.931872i
$898$	−43.4621	+	10.0957i	−1.45035	+	0.336897i
$899$	3.92936	+	5.40830i	0.131051	+	0.180377i
$900$	−31.2502	−	5.42356i	−1.04167	−	0.180785i
$901$		−	57.9442i		−	1.93040i
$902$		0			0
$903$	7.44421			0.247728
$904$	−33.9425	+	27.7137i	−1.12891	+	0.921745i
$905$	18.2883	−	13.2872i	0.607923	−	0.441682i
$906$	13.3203	+	57.3445i	0.442539	+	1.90514i
$907$	53.9320	−	17.5236i	1.79078	−	0.581861i	0.791224	−	0.611526i	$-0.209444\pi$
$907$	53.9320	−	17.5236i	1.79078	−	0.581861i	0.999560	+	0.0296650i	$0.00944405\pi$
$908$	10.6282	+	21.6429i	0.352709	+	0.718246i
$909$	24.5790	−	33.8301i	0.815235	−	1.12207i
$910$	2.12102	−	24.6250i	0.0703110	−	0.816312i
$911$	0.0648141	−	0.199477i	0.00214739	−	0.00660898i	−0.949977	−	0.312320i	$-0.898894\pi$
$911$	0.0648141	−	0.199477i	0.00214739	−	0.00660898i	0.952124	+	0.305711i	$0.0988940\pi$
$912$	−2.81516	+	0.823662i	−0.0932193	+	0.0272742i
$913$		0			0
$914$	32.0865	−	37.0118i	1.06133	−	1.22424i
$915$	−46.7738	−	15.1977i	−1.54629	−	0.502421i
$916$	−9.26042	+	8.99099i	−0.305973	+	0.297071i
$917$	−12.7042	+	17.4859i	−0.419531	+	0.577434i
$918$	−14.3902	+	34.0285i	−0.474948	+	1.12311i
$919$	−8.39323	−	25.8317i	−0.276867	−	0.852109i	−0.988719	−	0.149780i	$-0.952144\pi$
$919$	−8.39323	−	25.8317i	−0.276867	−	0.852109i	0.711852	−	0.702329i	$-0.247856\pi$
$920$	−32.0334	+	12.4451i	−1.05611	+	0.410304i
$921$	20.2676	−	14.7252i	0.667839	−	0.485213i
$922$	−31.0542	+	18.7162i	−1.02272	+	0.616385i
$923$			10.0380i			0.330405i
$924$		0			0
$925$			2.67927i			0.0880939i
$926$	6.79604	+	11.2761i	0.223332	+	0.370556i
$927$	70.5348	−	51.2465i	2.31667	−	1.68316i
$928$	9.01812	+	16.0140i	0.296034	+	0.525686i
$929$	−1.94540	−	5.98732i	−0.0638265	−	0.196438i	0.914058	−	0.405584i	$-0.132932\pi$
$929$	−1.94540	−	5.98732i	−0.0638265	−	0.196438i	−0.977884	+	0.209146i	$0.932932\pi$
$930$	21.4772	+	9.08243i	0.704264	+	0.297824i
$931$	−0.220958	+	0.304122i	−0.00724159	+	0.00996720i
$932$	−11.8280	−	12.1824i	−0.387438	−	0.399049i
$933$	48.4756	+	15.7507i	1.58702	+	0.515654i
$934$	−4.40130	−	3.81560i	−0.144015	−	0.124850i
$935$		0			0
$936$	−17.9425	+	27.8747i	−0.586468	+	0.911115i
$937$	−6.50489	+	20.0200i	−0.212506	+	0.654025i	0.786816	+	0.617188i	$0.211728\pi$
$937$	−6.50489	+	20.0200i	−0.212506	+	0.654025i	−0.999321	+	0.0368369i	$0.988272\pi$
$938$	0.802872	+	0.0691534i	0.0262147	+	0.00225794i
$939$	15.9689	−	21.9793i	0.521124	−	0.717266i
$940$	−24.7186	−	50.3362i	−0.806231	−	1.64179i
$941$	−10.9813	+	3.56805i	−0.357981	+	0.116315i	−0.482486	−	0.875904i	$-0.660266\pi$
$941$	−10.9813	+	3.56805i	−0.357981	+	0.116315i	0.124504	+	0.992219i	$0.460266\pi$
$942$	−71.6196	+	16.6363i	−2.33349	+	0.542039i
$943$	10.1508	−	7.37495i	0.330554	−	0.240162i
$944$	−23.1476	−	0.683581i	−0.753391	−	0.0222487i
$945$	−30.4111			−0.989272
$946$		0			0
$947$			38.6713i			1.25665i	0.777951	+	0.628324i	$0.216259\pi$
$947$			38.6713i			1.25665i	−0.777951	+	0.628324i	$0.783741\pi$
$948$	−4.89183	+	28.1864i	−0.158879	+	0.915453i
$949$	9.50456	+	13.0819i	0.308531	+	0.424657i
$950$	−0.292965	−	1.26122i	−0.00950503	−	0.0409195i
$951$	−25.3782	−	78.1060i	−0.822943	−	2.53276i
$952$	−10.0540	+	38.1375i	−0.325853	+	1.23604i
$953$	0.858479	+	0.623721i	0.0278089	+	0.0202043i	0.601603	−	0.798795i	$-0.294529\pi$
$953$	0.858479	+	0.623721i	0.0278089	+	0.0202043i	−0.573794	+	0.819000i	$0.694529\pi$
$954$	−63.7341	−	5.48958i	−2.06347	−	0.177732i
$955$	5.34508	+	1.73672i	0.172963	+	0.0561990i
$956$	0.931163	+	6.49859i	0.0301159	+	0.210179i
$957$		0			0
$958$	−32.8257	+	37.8645i	−1.06055	+	1.22335i
$959$	10.2897	−	31.6685i	0.332272	−	1.02263i
$960$	55.7765	+	31.6048i	1.80018	+	1.02004i
$961$	21.6543	+	15.7328i	0.698527	+	0.507509i
$962$	2.57916	+	1.09070i	0.0831556	+	0.0351654i
$963$	−18.4608	+	5.99827i	−0.594890	+	0.193292i
$964$	−9.11991	+	17.2640i	−0.293732	+	0.556036i
$965$	22.2362	+	30.6055i	0.715809	+	0.985226i
$966$	−33.0129	+	19.8967i	−1.06217	+	0.640165i
$967$	44.1328			1.41921			0.709607	−	0.704598i	$-0.248873\pi$
$967$	44.1328			1.41921			0.709607	+	0.704598i	$0.248873\pi$
$968$		0			0
$969$	−4.32630			−0.138981
$970$	−25.6892	+	15.4827i	−0.824831	+	0.497121i
$971$	−10.3123	−	14.1937i	−0.330939	−	0.455498i	0.610829	−	0.791763i	$-0.290836\pi$
$971$	−10.3123	−	14.1937i	−0.330939	−	0.455498i	−0.941768	+	0.336264i	$0.890836\pi$
$972$	−31.3197	−	16.5450i	−1.00458	−	0.530681i
$973$	−11.0187	+	3.58020i	−0.353244	+	0.114776i
$974$	−17.6370	−	7.45847i	−0.565127	−	0.238985i
$975$	−19.5503	−	14.2041i	−0.626111	−	0.454896i
$976$	19.4259	+	15.0094i	0.621807	+	0.480440i
$977$	16.3415	−	50.2939i	0.522810	−	1.60904i	−0.245797	−	0.969321i	$-0.579050\pi$
$977$	16.3415	−	50.2939i	0.522810	−	1.60904i	0.768607	−	0.639722i	$-0.220950\pi$
$978$	−15.5465	+	17.9328i	−0.497121	+	0.573429i
$979$		0			0
$980$	8.13304	−	1.16536i	0.259800	−	0.0372260i
$981$	−20.1820	−	6.55753i	−0.644362	−	0.209366i
$982$	8.52011	+	0.733859i	0.271888	+	0.0234184i
$983$	−5.38910	−	3.91541i	−0.171886	−	0.124882i	0.498516	−	0.866880i	$-0.333878\pi$
$983$	−5.38910	−	3.91541i	−0.171886	−	0.124882i	−0.670402	+	0.741998i	$0.733878\pi$
$984$	−22.6327	−	5.96656i	−0.721503	−	0.190207i
$985$	5.56920	+	17.1402i	0.177449	+	0.546133i
$986$	6.13344	+	26.4046i	0.195328	+	0.840895i
$987$	−36.9702	−	50.8851i	−1.17677	−	1.61969i
$988$	−1.33336	−	0.231408i	−0.0424199	−	0.00736208i
$989$		−	4.77550i		−	0.151852i
$990$		0			0
$991$	3.15937			0.100361			0.0501803	−	0.998740i	$-0.484020\pi$
$991$	3.15937			0.100361			0.0501803	+	0.998740i	$0.484020\pi$
$992$	−8.56591	−	7.88074i	−0.271968	−	0.250214i
$993$	42.6898	−	31.0159i	1.35472	−	0.984261i
$994$	12.8428	−	2.98320i	0.407349	−	0.0946215i
$995$	−52.2827	+	16.9877i	−1.65747	+	0.538546i
$996$	−75.4400	+	37.0462i	−2.39041	+	1.17386i
$997$	−14.3591	+	19.7636i	−0.454756	+	0.625918i	−0.973411	−	0.229065i	$-0.926433\pi$
$997$	−14.3591	+	19.7636i	−0.454756	+	0.625918i	0.518655	+	0.854984i	$0.326433\pi$
$998$	10.4894	+	0.903480i	0.332037	+	0.0285992i
$999$	1.06473	−	3.27689i	0.0336864	−	0.103676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.d.493.7		40
8.5	even	2	inner	968.2.o.d.493.2		40
11.2	odd	10		88.2.o.a.69.6	yes	40
11.3	even	5		968.2.o.i.565.10		40
11.4	even	5		968.2.c.i.485.6		20
11.5	even	5	inner	968.2.o.d.269.2		40
11.6	odd	10		968.2.o.j.269.9		40
11.7	odd	10		968.2.c.h.485.15		20
11.8	odd	10		88.2.o.a.37.1	✓	40
11.9	even	5		968.2.o.i.245.5		40
11.10	odd	2		968.2.o.j.493.4		40
33.2	even	10		792.2.br.b.685.5		40
33.8	even	10		792.2.br.b.37.10		40
44.7	even	10		3872.2.c.h.1937.19		20
44.15	odd	10		3872.2.c.i.1937.19		20
44.19	even	10		352.2.w.a.81.10		40
44.35	even	10		352.2.w.a.113.1		40
88.5	even	10	inner	968.2.o.d.269.7		40
88.13	odd	10		88.2.o.a.69.1	yes	40
88.19	even	10		352.2.w.a.81.1		40
88.21	odd	2		968.2.o.j.493.9		40
88.29	odd	10		968.2.c.h.485.16		20
88.35	even	10		352.2.w.a.113.10		40
88.37	even	10		968.2.c.i.485.5		20
88.51	even	10		3872.2.c.h.1937.2		20
88.53	even	10		968.2.o.i.245.10		40
88.59	odd	10		3872.2.c.i.1937.2		20
88.61	odd	10		968.2.o.j.269.4		40
88.69	even	10		968.2.o.i.565.5		40
88.85	odd	10		88.2.o.a.37.6	yes	40
264.101	even	10		792.2.br.b.685.10		40
264.173	even	10		792.2.br.b.37.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.1	✓	40	11.8	odd	10
88.2.o.a.37.6	yes	40	88.85	odd	10
88.2.o.a.69.1	yes	40	88.13	odd	10
88.2.o.a.69.6	yes	40	11.2	odd	10
352.2.w.a.81.1		40	88.19	even	10
352.2.w.a.81.10		40	44.19	even	10
352.2.w.a.113.1		40	44.35	even	10
352.2.w.a.113.10		40	88.35	even	10
792.2.br.b.37.5		40	264.173	even	10
792.2.br.b.37.10		40	33.8	even	10
792.2.br.b.685.5		40	33.2	even	10
792.2.br.b.685.10		40	264.101	even	10
968.2.c.h.485.15		20	11.7	odd	10
968.2.c.h.485.16		20	88.29	odd	10
968.2.c.i.485.5		20	88.37	even	10
968.2.c.i.485.6		20	11.4	even	5
968.2.o.d.269.2		40	11.5	even	5	inner
968.2.o.d.269.7		40	88.5	even	10	inner
968.2.o.d.493.2		40	8.5	even	2	inner
968.2.o.d.493.7		40	1.1	even	1	trivial
968.2.o.i.245.5		40	11.9	even	5
968.2.o.i.245.10		40	88.53	even	10
968.2.o.i.565.5		40	88.69	even	10
968.2.o.i.565.10		40	11.3	even	5
968.2.o.j.269.4		40	88.61	odd	10
968.2.o.j.269.9		40	11.6	odd	10
968.2.o.j.493.4		40	11.10	odd	2
968.2.o.j.493.9		40	88.21	odd	2
3872.2.c.h.1937.2		20	88.51	even	10
3872.2.c.h.1937.19		20	44.7	even	10
3872.2.c.i.1937.2		20	88.59	odd	10
3872.2.c.i.1937.19		20	44.15	odd	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.730005 + 1.21124i) q^{2} +(1.62101 + 2.23113i) q^{3} +(-0.934186 + 1.76842i) q^{4} +(2.76352 - 0.897923i) q^{5} +(-1.51908 + 3.59217i) q^{6} +(1.91213 + 1.38924i) q^{7} +(-2.82393 + 0.159432i) q^{8} +(-1.42322 + 4.38022i) q^{9} +(3.10498 + 2.69179i) q^{10} +(-5.45990 + 0.782332i) q^{12} +(-2.42023 - 0.786381i) q^{13} +(-0.286838 + 3.33019i) q^{14} +(6.48309 + 4.71024i) q^{15} +(-2.25459 - 3.30406i) q^{16} +(-1.82314 - 5.61105i) q^{17} +(-6.34444 + 1.47373i) q^{18} +(-0.156289 - 0.215114i) q^{19} +(-0.993743 + 5.72588i) q^{20} +6.51819i q^{21} +4.18146 q^{23} +(-4.93334 - 6.04212i) q^{24} +(2.78570 - 2.02393i) q^{25} +(-0.814288 - 3.50554i) q^{26} +(-4.21136 + 1.36835i) q^{27} +(-4.24304 + 2.08363i) q^{28} +(-1.90967 + 2.62843i) q^{29} +(-0.972528 + 11.2911i) q^{30} +(0.635838 - 1.95691i) q^{31} +(2.35613 - 5.14282i) q^{32} +(5.46541 - 6.30435i) q^{34} +(6.53164 + 2.12226i) q^{35} +(-6.41651 - 6.60879i) q^{36} +(-0.457360 + 0.629502i) q^{37} +(0.146462 - 0.346338i) q^{38} +(-2.16871 - 6.67460i) q^{39} +(-7.66084 + 2.97627i) q^{40} +(2.42756 - 1.76373i) q^{41} +(-7.89507 + 4.75831i) q^{42} -1.14207i q^{43} +13.3828i q^{45} +(3.05248 + 5.06473i) q^{46} +(-7.80663 + 5.67185i) q^{47} +(3.71707 - 10.3862i) q^{48} +(-0.436880 - 1.34458i) q^{49} +(4.48504 + 1.89667i) q^{50} +(9.56367 - 13.1633i) q^{51} +(3.65160 - 3.54535i) q^{52} +(9.34068 + 3.03497i) q^{53} +(-4.73171 - 4.10205i) q^{54} +(-5.62121 - 3.61827i) q^{56} +(0.226601 - 0.697405i) q^{57} +(-4.57772 - 0.394290i) q^{58} +(3.40294 - 4.68375i) q^{59} +(-14.3861 + 7.06456i) q^{60} +(-5.83684 + 1.89650i) q^{61} +(2.83444 - 0.658402i) q^{62} +(-8.80657 + 6.39835i) q^{63} +(7.94916 - 0.900451i) q^{64} -7.39448 q^{65} -0.241089i q^{67} +(11.6258 + 2.01769i) q^{68} +(6.77819 + 9.32938i) q^{69} +(2.19757 + 9.46062i) q^{70} +(-1.21893 - 3.75148i) q^{71} +(3.32073 - 12.5964i) q^{72} +(-5.14067 - 3.73492i) q^{73} +(-1.09635 - 0.0944315i) q^{74} +(9.03133 + 2.93446i) q^{75} +(0.526414 - 0.0754283i) q^{76} +(6.50135 - 7.49930i) q^{78} +(1.60276 - 4.93279i) q^{79} +(-9.19741 - 7.10639i) q^{80} +(1.29848 + 0.943398i) q^{81} +(3.90843 + 1.65282i) q^{82} +(14.4918 - 4.70867i) q^{83} +(-11.5269 - 6.08921i) q^{84} +(-10.0766 - 13.8692i) q^{85} +(1.38331 - 0.833714i) q^{86} -8.95997 q^{87} -16.2052 q^{89} +(-16.2097 + 9.76950i) q^{90} +(-3.53532 - 4.86595i) q^{91} +(-3.90626 + 7.39455i) q^{92} +(5.39682 - 1.75353i) q^{93} +(-12.5688 - 5.31519i) q^{94} +(-0.625065 - 0.454136i) q^{95} +(15.2936 - 3.07974i) q^{96} +(-2.25552 + 6.94179i) q^{97} +(1.30968 - 1.51071i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - q^{4} - 8 q^{6} - 5 q^{8} + 10 q^{9} + 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} - 4 q^{17} - 25 q^{18} + 8 q^{20} - 8 q^{23} + 40 q^{24} + 6 q^{25} - 20 q^{26} + 18 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) \) 40 * q - 5 * q^2 - q^4 - 8 * q^6 - 5 * q^8 + 10 * q^9 + 20 * q^10 - 6 * q^12 + 2 * q^14 + 22 * q^15 - 25 * q^16 - 4 * q^17 - 25 * q^18 + 8 * q^20 - 8 * q^23 + 40 * q^24 + 6 * q^25 - 20 * q^26 + 18 * q^28 - 12 * q^30 + 4 * q^31 - 20 * q^32 + 10 * q^34 - 27 * q^36 - 33 * q^38 - 6 * q^39 + 20 * q^40 - 16 * q^41 - 20 * q^42 + 42 * q^46 + 4 * q^47 + 23 * q^48 + 6 * q^49 + 39 * q^50 - 108 * q^54 - 32 * q^56 - 4 * q^57 - 16 * q^58 + 94 * q^60 + 52 * q^62 + 30 * q^63 + 11 * q^64 + 36 * q^65 - 63 * q^68 + 52 * q^70 + 12 * q^71 - 44 * q^72 - 4 * q^73 + 26 * q^74 + 134 * q^76 - 12 * q^78 + 16 * q^79 + 16 * q^80 + 16 * q^81 + 54 * q^82 - 72 * q^84 - 10 * q^86 - 68 * q^87 - 16 * q^89 - 126 * q^90 - 64 * q^92 - 40 * q^94 - 26 * q^95 + 5 * q^96 - 20 * q^97 + 144 * q^98

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