LMFDB - Embedded newform 961.2.g.n.338.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] 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("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,-3,6,-3,-11,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			338.1
Root			$-0.333129i$ of defining polynomial
Character	$\chi$	$=$	961.338
Dual form			961.2.g.n.816.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67638 + 1.21796i) q^{2} +(-0.223627 + 2.12767i) q^{3} +(0.708788 - 2.18143i) q^{4} +(-1.17396 + 2.03335i) q^{5} +(-2.21654 - 3.83916i) q^{6} +(3.59424 - 0.763980i) q^{7} +(0.188054 + 0.578772i) q^{8} +(-1.54253 - 0.327876i) q^{9} +(-0.508547 - 4.83851i) q^{10} +(2.86431 + 3.18114i) q^{11} +(4.48286 + 1.99590i) q^{12} +(1.90675 - 0.848940i) q^{13} +(-5.09482 + 5.65838i) q^{14} +(-4.06377 - 2.95251i) q^{15} +(2.69109 + 1.95519i) q^{16} +(-1.42397 + 1.58148i) q^{17} +(2.98522 - 1.32910i) q^{18} +(-0.566412 - 0.252183i) q^{19} +(3.60352 + 4.00211i) q^{20} +(0.821728 + 7.81822i) q^{21} +(-8.67618 - 1.84418i) q^{22} +(1.03640 + 3.18973i) q^{23} +(-1.27349 + 0.270689i) q^{24} +(-0.256344 - 0.444001i) q^{25} +(-2.16247 + 3.74550i) q^{26} +(-0.940760 + 2.89536i) q^{27} +(0.880992 - 8.38208i) q^{28} +(-1.11435 + 0.809625i) q^{29} +10.4085 q^{30} -8.10976 q^{32} +(-7.40895 + 5.38292i) q^{33} +(0.460935 - 4.38551i) q^{34} +(-2.66604 + 8.20524i) q^{35} +(-1.80857 + 3.13253i) q^{36} +(0.137239 + 0.237704i) q^{37} +(1.25667 - 0.267114i) q^{38} +(1.37986 + 4.24679i) q^{39} +(-1.39761 - 0.297072i) q^{40} +(0.447164 + 4.25448i) q^{41} +(-10.8998 - 12.1055i) q^{42} +(-0.246376 - 0.109694i) q^{43} +(8.96960 - 3.99353i) q^{44} +(2.47755 - 2.75160i) q^{45} +(-5.62238 - 4.08489i) q^{46} +(-4.35183 - 3.16179i) q^{47} +(-4.76181 + 5.28853i) q^{48} +(5.94010 - 2.64470i) q^{49} +(0.970507 + 0.432098i) q^{50} +(-3.04643 - 3.38341i) q^{51} +(-0.500418 - 4.76116i) q^{52} +(9.30090 + 1.97697i) q^{53} +(-1.94937 - 5.99954i) q^{54} +(-9.83094 + 2.08963i) q^{55} +(1.11808 + 1.93658i) q^{56} +(0.663228 - 1.14874i) q^{57} +(0.881988 - 2.71448i) q^{58} +(0.609133 - 5.79551i) q^{59} +(-9.32103 + 6.77212i) q^{60} -2.22719 q^{61} -5.79474 q^{63} +(8.21287 - 5.96700i) q^{64} +(-0.512248 + 4.87371i) q^{65} +(5.86404 - 18.0477i) q^{66} +(6.80719 - 11.7904i) q^{67} +(2.44059 + 4.22722i) q^{68} +(-7.01846 + 1.49182i) q^{69} +(-5.52437 - 17.0022i) q^{70} +(1.30673 + 0.277754i) q^{71} +(-0.100315 - 0.954434i) q^{72} +(9.47892 + 10.5274i) q^{73} +(-0.519579 - 0.231331i) q^{74} +(1.00201 - 0.446125i) q^{75} +(-0.951585 + 1.05684i) q^{76} +(12.7253 + 9.24551i) q^{77} +(-7.48561 - 5.43861i) q^{78} +(-5.80579 + 6.44798i) q^{79} +(-7.13482 + 3.17662i) q^{80} +(-10.2720 - 4.57338i) q^{81} +(-5.93141 - 6.58750i) q^{82} +(-0.542030 - 5.15707i) q^{83} +(17.6373 + 3.74892i) q^{84} +(-1.54403 - 4.75202i) q^{85} +(0.546623 - 0.116188i) q^{86} +(-1.47342 - 2.55203i) q^{87} +(-1.30251 + 2.25601i) q^{88} +(-1.54897 + 4.76725i) q^{89} +(-0.801977 + 7.63030i) q^{90} +(6.20475 - 4.50802i) q^{91} +7.69274 q^{92} +11.1463 q^{94} +(1.17772 - 0.855663i) q^{95} +(1.81356 - 17.2549i) q^{96} +(2.07474 - 6.38538i) q^{97} +(-6.73673 + 11.6684i) q^{98} +(-3.37528 - 5.84615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} + 12 q^{7} - 8 q^{8} + 5 q^{9} - 12 q^{10} + 2 q^{11} - 25 q^{12} - 18 q^{13} + 24 q^{14} - 4 q^{15} - 2 q^{16} + q^{17} - 8 q^{18} + 11 q^{19} - 18 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 11 * q^6 + 12 * q^7 - 8 * q^8 + 5 * q^9 - 12 * q^10 + 2 * q^11 - 25 * q^12 - 18 * q^13 + 24 * q^14 - 4 * q^15 - 2 * q^16 + q^17 - 8 * q^18 + 11 * q^19 - 18 * q^20 + 31 * q^21 - 4 * q^22 - 21 * q^23 - 20 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 - 28 * q^34 + 21 * q^35 + q^36 + 8 * q^37 + 3 * q^38 + 2 * q^39 + 29 * q^40 - 3 * q^41 - 39 * q^42 - 8 * q^43 + 41 * q^44 - 20 * q^45 + 16 * q^46 + 4 * q^47 - 49 * q^48 + 12 * q^49 + 48 * q^50 - 2 * q^51 + 6 * q^52 + 69 * q^53 - 39 * q^54 - 23 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 54 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 + 27 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 27 * q^69 + 27 * q^70 + 6 * q^71 + 2 * q^72 + 18 * q^73 + 92 * q^74 - 13 * q^75 - 27 * q^76 + 42 * q^77 + 15 * q^78 + 22 * q^79 + 21 * q^80 - 22 * q^81 - 61 * q^82 + 71 * q^83 + 12 * q^84 + 63 * q^85 + 11 * q^86 + 15 * q^87 + 17 * q^88 - 26 * q^89 - 33 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 58 * q^96 - 37 * q^97 - 10 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−1.67638	+	1.21796i	−1.18538	+	0.861230i	−0.992768	−	0.120045i	$-0.961696\pi$
$2$	−1.67638	+	1.21796i	−1.18538	+	0.861230i	−0.192612	+	0.981275i	$0.561696\pi$
$3$	−0.223627	+	2.12767i	−0.129111	+	1.22841i	0.717637	+	0.696418i	$0.245224\pi$
$3$	−0.223627	+	2.12767i	−0.129111	+	1.22841i	−0.846748	+	0.531994i	$0.821443\pi$
$4$	0.708788	−	2.18143i	0.354394	−	1.09071i
$5$	−1.17396	+	2.03335i	−0.525009	+	0.909342i	0.474567	+	0.880219i	$0.342605\pi$
$5$	−1.17396	+	2.03335i	−0.525009	+	0.909342i	−0.999576	+	0.0291228i	$0.990729\pi$
$6$	−2.21654	−	3.83916i	−0.904898	−	1.56733i
$7$	3.59424	−	0.763980i	1.35850	−	0.288757i	0.529642	−	0.848221i	$-0.322326\pi$
$7$	3.59424	−	0.763980i	1.35850	−	0.288757i	0.828855	+	0.559464i	$0.188993\pi$
$8$	0.188054	+	0.578772i	0.0664872	+	0.204627i
$9$	−1.54253	−	0.327876i	−0.514178	−	0.109292i
$10$	−0.508547	−	4.83851i	−0.160817	−	1.53007i
$11$	2.86431	+	3.18114i	0.863621	+	0.959149i	0.999501	−	0.0315765i	$-0.0100528\pi$
$11$	2.86431	+	3.18114i	0.863621	+	0.959149i	−0.135880	+	0.990725i	$0.543386\pi$
$12$	4.48286	+	1.99590i	1.29409	+	0.576165i
$13$	1.90675	−	0.848940i	0.528838	−	0.235454i	−0.124908	−	0.992168i	$-0.539863\pi$
$13$	1.90675	−	0.848940i	0.528838	−	0.235454i	0.653745	+	0.756715i	$0.273197\pi$
$14$	−5.09482	+	5.65838i	−1.36165	+	1.51226i
$15$	−4.06377	−	2.95251i	−1.04926	−	0.762334i
$16$	2.69109	+	1.95519i	0.672773	+	0.488798i
$17$	−1.42397	+	1.58148i	−0.345364	+	0.383565i	−0.890654	−	0.454682i	$-0.849753\pi$
$17$	−1.42397	+	1.58148i	−0.345364	+	0.383565i	0.545290	+	0.838247i	$0.316420\pi$
$18$	2.98522	−	1.32910i	0.703622	−	0.313273i
$19$	−0.566412	−	0.252183i	−0.129944	−	0.0578547i	0.340735	−	0.940159i	$-0.389324\pi$
$19$	−0.566412	−	0.252183i	−0.129944	−	0.0578547i	−0.470679	+	0.882305i	$0.655991\pi$
$20$	3.60352	+	4.00211i	0.805771	+	0.894900i
$21$	0.821728	+	7.81822i	0.179316	+	1.70607i
$22$	−8.67618	−	1.84418i	−1.84977	−	0.393180i
$23$	1.03640	+	3.18973i	0.216105	+	0.665104i	0.999073	+	0.0430417i	$0.0137048\pi$
$23$	1.03640	+	3.18973i	0.216105	+	0.665104i	−0.782968	+	0.622062i	$0.786295\pi$
$24$	−1.27349	+	0.270689i	−0.259950	+	0.0552541i
$25$	−0.256344	−	0.444001i	−0.0512688	−	0.0888002i
$26$	−2.16247	+	3.74550i	−0.424094	+	0.734553i
$27$	−0.940760	+	2.89536i	−0.181049	+	0.557213i
$28$	0.880992	−	8.38208i	0.166492	−	1.58406i
$29$	−1.11435	+	0.809625i	−0.206930	+	0.150344i	−0.686424	−	0.727202i	$-0.740820\pi$
$29$	−1.11435	+	0.809625i	−0.206930	+	0.150344i	0.479493	+	0.877545i	$0.340820\pi$
$30$	10.4085			1.90032
$31$		0			0
$31$		0			0
$32$	−8.10976			−1.43362
$33$	−7.40895	+	5.38292i	−1.28973	+	0.937046i
$34$	0.460935	−	4.38551i	0.0790498	−	0.752108i
$35$	−2.66604	+	8.20524i	−0.450644	+	1.38694i
$36$	−1.80857	+	3.13253i	−0.301428	+	0.522089i
$37$	0.137239	+	0.237704i	0.0225619	+	0.0390783i	0.877086	−	0.480334i	$-0.159484\pi$
$37$	0.137239	+	0.237704i	0.0225619	+	0.0390783i	−0.854524	+	0.519412i	$0.826151\pi$
$38$	1.25667	−	0.267114i	0.203859	−	0.0433316i
$39$	1.37986	+	4.24679i	0.220955	+	0.680030i
$40$	−1.39761	−	0.297072i	−0.220982	−	0.0469712i
$41$	0.447164	+	4.25448i	0.0698353	+	0.664438i	0.972310	+	0.233695i	$0.0750818\pi$
$41$	0.447164	+	4.25448i	0.0698353	+	0.664438i	−0.902475	+	0.430743i	$0.858252\pi$
$42$	−10.8998	−	12.1055i	−1.68188	−	1.86792i
$43$	−0.246376	−	0.109694i	−0.0375720	−	0.0167281i	0.387865	−	0.921716i	$-0.373213\pi$
$43$	−0.246376	−	0.109694i	−0.0375720	−	0.0167281i	−0.425437	+	0.904988i	$0.639879\pi$
$44$	8.96960	−	3.99353i	1.35222	−	0.602047i
$45$	2.47755	−	2.75160i	0.369332	−	0.410185i
$46$	−5.62238	−	4.08489i	−0.828974	−	0.602285i
$47$	−4.35183	−	3.16179i	−0.634780	−	0.461195i	0.223273	−	0.974756i	$-0.428326\pi$
$47$	−4.35183	−	3.16179i	−0.634780	−	0.461195i	−0.858053	+	0.513561i	$0.828326\pi$
$48$	−4.76181	+	5.28853i	−0.687308	+	0.763333i
$49$	5.94010	−	2.64470i	0.848586	−	0.377815i
$50$	0.970507	+	0.432098i	0.137250	+	0.0611078i
$51$	−3.04643	−	3.38341i	−0.426586	−	0.473772i
$52$	−0.500418	−	4.76116i	−0.0693955	−	0.660254i
$53$	9.30090	+	1.97697i	1.27758	+	0.271557i	0.796241	−	0.604979i	$-0.206819\pi$
$53$	9.30090	+	1.97697i	1.27758	+	0.271557i	0.481335	+	0.876537i	$0.340152\pi$
$54$	−1.94937	−	5.99954i	−0.265276	−	0.816434i
$55$	−9.83094	+	2.08963i	−1.32560	+	0.281766i
$56$	1.11808	+	1.93658i	0.149410	+	0.258786i
$57$	0.663228	−	1.14874i	0.0878467	−	0.152155i
$58$	0.881988	−	2.71448i	0.115811	−	0.356429i
$59$	0.609133	−	5.79551i	0.0793024	−	0.754512i	−0.880540	−	0.473972i	$-0.842820\pi$
$59$	0.609133	−	5.79551i	0.0793024	−	0.754512i	0.959842	−	0.280540i	$-0.0905135\pi$
$60$	−9.32103	+	6.77212i	−1.20334	+	0.874278i
$61$	−2.22719			−0.285162			−0.142581	−	0.989783i	$-0.545540\pi$
$61$	−2.22719			−0.285162			−0.142581	+	0.989783i	$0.545540\pi$
$62$		0			0
$63$	−5.79474			−0.730068
$64$	8.21287	−	5.96700i	1.02661	−	0.745875i
$65$	−0.512248	+	4.87371i	−0.0635365	+	0.604510i
$66$	5.86404	−	18.0477i	0.721813	−	2.22151i
$67$	6.80719	−	11.7904i	0.831631	−	1.44043i	−0.0651129	−	0.997878i	$-0.520741\pi$
$67$	6.80719	−	11.7904i	0.831631	−	1.44043i	0.896744	−	0.442550i	$-0.145926\pi$
$68$	2.44059	+	4.22722i	0.295965	+	0.512626i
$69$	−7.01846	+	1.49182i	−0.844923	+	0.179594i
$70$	−5.52437	−	17.0022i	−0.660288	−	2.03216i
$71$	1.30673	+	0.277754i	0.155080	+	0.0329634i	0.284798	−	0.958588i	$-0.408074\pi$
$71$	1.30673	+	0.277754i	0.155080	+	0.0329634i	−0.129717	+	0.991551i	$0.541407\pi$
$72$	−0.100315	−	0.954434i	−0.0118222	−	0.112481i
$73$	9.47892	+	10.5274i	1.10942	+	1.23214i	0.970310	+	0.241863i	$0.0777584\pi$
$73$	9.47892	+	10.5274i	1.10942	+	1.23214i	0.139113	+	0.990277i	$0.455575\pi$
$74$	−0.519579	−	0.231331i	−0.0603998	−	0.0268917i
$75$	1.00201	−	0.446125i	0.115703	−	0.0515141i
$76$	−0.951585	+	1.05684i	−0.109154	+	0.121228i
$77$	12.7253	+	9.24551i	1.45019	+	1.05362i
$78$	−7.48561	−	5.43861i	−0.847578	−	0.615801i
$79$	−5.80579	+	6.44798i	−0.653202	+	0.725455i	−0.975210	−	0.221282i	$-0.928976\pi$
$79$	−5.80579	+	6.44798i	−0.653202	+	0.725455i	0.322007	+	0.946737i	$0.395642\pi$
$80$	−7.13482	+	3.17662i	−0.797697	+	0.355157i
$81$	−10.2720	−	4.57338i	−1.14133	−	0.508153i
$82$	−5.93141	−	6.58750i	−0.655015	−	0.727468i
$83$	−0.542030	−	5.15707i	−0.0594955	−	0.566062i	−0.983145	−	0.182825i	$-0.941476\pi$
$83$	−0.542030	−	5.15707i	−0.0594955	−	0.566062i	0.923650	−	0.383237i	$-0.125191\pi$
$84$	17.6373	+	3.74892i	1.92439	+	0.409041i
$85$	−1.54403	−	4.75202i	−0.167473	−	0.515429i
$86$	0.546623	−	0.116188i	0.0589439	−	0.0125289i
$87$	−1.47342	−	2.55203i	−0.157967	−	0.273607i
$88$	−1.30251	+	2.25601i	−0.138848	+	0.240491i
$89$	−1.54897	+	4.76725i	−0.164191	+	0.505327i	−0.998976	−	0.0452489i	$-0.985592\pi$
$89$	−1.54897	+	4.76725i	−0.164191	+	0.505327i	0.834785	+	0.550576i	$0.185592\pi$
$90$	−0.801977	+	7.63030i	−0.0845358	+	0.804305i
$91$	6.20475	−	4.50802i	0.650435	−	0.472569i
$92$	7.69274			0.802024
$93$		0			0
$94$	11.1463			1.14965
$95$	1.17772	−	0.855663i	0.120831	−	0.0877892i
$96$	1.81356	−	17.2549i	0.185096	−	1.76107i
$97$	2.07474	−	6.38538i	0.210657	−	0.648337i	−0.788776	−	0.614681i	$-0.789285\pi$
$97$	2.07474	−	6.38538i	0.210657	−	0.648337i	0.999433	−	0.0336562i	$-0.0107151\pi$
$98$	−6.73673	+	11.6684i	−0.680512	+	1.17868i
$99$	−3.37528	−	5.84615i	−0.339228	−	0.587560i
$100$	−1.15025	+	0.244493i	−0.115025	+	0.0244493i
$101$	−5.58165	−	17.1786i	−0.555395	−	1.70933i	−0.694898	−	0.719108i	$-0.744550\pi$
$101$	−5.58165	−	17.1786i	−0.555395	−	1.70933i	0.139503	−	0.990222i	$-0.455450\pi$
$102$	9.22784	+	1.96144i	0.913693	+	0.194211i
$103$	−0.409262	−	3.89387i	−0.0403258	−	0.383675i	−0.996007	−	0.0892719i	$-0.971546\pi$
$103$	−0.409262	−	3.89387i	−0.0403258	−	0.383675i	0.955681	−	0.294403i	$-0.0951207\pi$
$104$	0.849915	+	0.943927i	0.0833411	+	0.0925596i
$105$	−16.8619	−	7.50738i	−1.64555	−	0.732645i
$106$	−17.9997	+	8.01399i	−1.74829	+	0.778388i
$107$	7.43780	−	8.26052i	0.719040	−	0.798574i	−0.267245	−	0.963629i	$-0.586113\pi$
$107$	7.43780	−	8.26052i	0.719040	−	0.798574i	0.986284	+	0.165054i	$0.0527799\pi$
$108$	5.64922	+	4.10440i	0.543596	+	0.394946i
$109$	−14.6379	−	10.6350i	−1.40205	−	1.01865i	−0.994419	−	0.105505i	$-0.966354\pi$
$109$	−14.6379	−	10.6350i	−1.40205	−	1.01865i	−0.407633	−	0.913146i	$-0.633646\pi$
$110$	13.9353	−	15.4767i	1.32868	−	1.47565i
$111$	−0.536447	+	0.238841i	−0.0509173	+	0.0226698i
$112$	11.1662	+	4.97150i	1.05510	+	0.469762i
$113$	11.7357	+	13.0338i	1.10400	+	1.22612i	0.972028	+	0.234867i	$0.0754655\pi$
$113$	11.7357	+	13.0338i	1.10400	+	1.22612i	0.131976	+	0.991253i	$0.457868\pi$
$114$	0.287305	+	2.73352i	0.0269085	+	0.256018i
$115$	−7.70252	−	1.63722i	−0.718264	−	0.152672i
$116$	0.976297	+	3.00473i	0.0906469	+	0.278982i
$117$	−3.21958	+	0.684342i	−0.297650	+	0.0632675i
$118$	6.03758	+	10.4574i	0.555804	+	0.962681i
$119$	−3.90988	+	6.77211i	−0.358418	+	0.620798i
$120$	0.944616	−	2.90723i	0.0862312	−	0.265392i
$121$	−0.765555	+	7.28377i	−0.0695959	+	0.662161i
$122$	3.73362	−	2.71263i	0.338026	−	0.245590i
$123$	−9.15213			−0.825220
$124$		0			0
$125$	−10.5358			−0.942352
$126$	9.71419	−	7.05777i	0.865409	−	0.628756i
$127$	−1.48412	+	14.1205i	−0.131695	+	1.25299i	0.706536	+	0.707677i	$0.250257\pi$
$127$	−1.48412	+	14.1205i	−0.131695	+	1.25299i	−0.838231	+	0.545315i	$0.816410\pi$
$128$	−1.48821	+	4.58025i	−0.131541	+	0.404841i
$129$	0.288489	−	0.499677i	0.0254000	−	0.0439941i
$130$	−5.07728	−	8.79410i	−0.445307	−	0.771294i
$131$	−7.03143	+	1.49458i	−0.614339	+	0.130582i	−0.504563	−	0.863375i	$-0.668346\pi$
$131$	−7.03143	+	1.49458i	−0.614339	+	0.130582i	−0.109775	+	0.993956i	$0.535013\pi$
$132$	6.49106	+	19.9774i	0.564974	+	1.73881i
$133$	−2.22849	−	0.473679i	−0.193234	−	0.0410732i
$134$	2.94882	+	28.0561i	0.254739	+	2.42368i
$135$	−4.78288	−	5.31192i	−0.411644	−	0.457177i
$136$	−1.18310	−	0.526750i	−0.101450	−	0.0451684i
$137$	−6.92253	+	3.08211i	−0.591432	+	0.263322i	−0.680553	−	0.732698i	$-0.738261\pi$
$137$	−6.92253	+	3.08211i	−0.591432	+	0.263322i	0.0891219	+	0.996021i	$0.471594\pi$
$138$	9.94863	−	11.0491i	0.846884	−	0.940560i
$139$	−16.2598	−	11.8134i	−1.37914	−	1.00200i	−0.996960	−	0.0779138i	$-0.975174\pi$
$139$	−16.2598	−	11.8134i	−1.37914	−	1.00200i	−0.382178	−	0.924089i	$-0.624826\pi$
$140$	16.0095	+	11.6316i	1.35305	+	0.983046i
$141$	7.70044	−	8.55221i	0.648494	−	0.720226i
$142$	−2.52887	+	1.12593i	−0.212218	+	0.0944857i
$143$	8.16212	+	3.63401i	0.682551	+	0.303891i
$144$	−3.51004	−	3.89830i	−0.292503	−	0.324858i
$145$	−0.338050	−	3.21634i	−0.0280736	−	0.267102i
$146$	−28.7123	−	6.10298i	−2.37624	−	0.505086i
$147$	4.29869	+	13.2300i	0.354550	+	1.09119i
$148$	0.615807	−	0.130894i	0.0506190	−	0.0107594i
$149$	−6.15749	−	10.6651i	−0.504441	−	0.873717i	−0.999987	−	0.00513554i	$-0.998365\pi$
$149$	−6.15749	−	10.6651i	−0.504441	−	0.873717i	0.495546	−	0.868582i	$-0.334968\pi$
$150$	−1.13639	+	1.96829i	−0.0927862	+	0.160710i
$151$	6.14232	−	18.9041i	0.499855	−	1.53840i	−0.309397	−	0.950933i	$-0.600127\pi$
$151$	6.14232	−	18.9041i	0.499855	−	1.53840i	0.809252	−	0.587462i	$-0.199873\pi$
$152$	0.0394401	−	0.375247i	0.00319901	−	0.0304366i
$153$	2.71505	−	1.97260i	0.219499	−	0.159475i
$154$	−32.5932			−2.62644
$155$		0			0
$156$	10.2421			0.820023
$157$	4.69603	−	3.41187i	0.374784	−	0.272297i	−0.384408	−	0.923163i	$-0.625594\pi$
$157$	4.69603	−	3.41187i	0.374784	−	0.272297i	0.759192	+	0.650867i	$0.225594\pi$
$158$	1.87932	−	17.8805i	0.149510	−	1.42250i
$159$	−6.28627	+	19.3472i	−0.498534	+	1.53433i
$160$	9.52050	−	16.4900i	0.752662	−	1.30365i
$161$	6.16198	+	10.6729i	0.485632	+	0.841139i
$162$	22.7899	−	4.84415i	1.79055	−	0.380593i
$163$	5.49535	+	16.9129i	0.430429	+	1.32472i	0.897699	+	0.440610i	$0.145238\pi$
$163$	5.49535	+	16.9129i	0.430429	+	1.32472i	−0.467270	+	0.884115i	$0.654762\pi$
$164$	9.59778	+	2.04007i	0.749461	+	0.159303i
$165$	−2.24758	−	21.3843i	−0.174974	−	1.66477i
$166$	7.18977	+	7.98505i	0.558034	+	0.619760i
$167$	−1.99338	−	0.887512i	−0.154253	−	0.0686777i	0.328158	−	0.944623i	$-0.393572\pi$
$167$	−1.99338	−	0.887512i	−0.154253	−	0.0686777i	−0.482411	+	0.875945i	$0.660239\pi$
$168$	−4.37043	+	1.94584i	−0.337186	+	0.150125i
$169$	−5.78370	+	6.42345i	−0.444900	+	0.494111i
$170$	8.37616	+	6.08564i	0.642422	+	0.466747i
$171$	0.791026	+	0.574714i	0.0604912	+	0.0439495i
$172$	−0.413918	+	0.459702i	−0.0315609	+	0.0350520i
$173$	−5.03174	+	2.24028i	−0.382556	+	0.170325i	−0.588999	−	0.808134i	$-0.700478\pi$
$173$	−5.03174	+	2.24028i	−0.382556	+	0.170325i	0.206443	+	0.978459i	$0.433811\pi$
$174$	5.57829	+	2.48361i	0.422889	+	0.188282i
$175$	−1.26057	−	1.40001i	−0.0952902	−	0.105831i
$176$	1.48838	+	14.1610i	0.112191	+	1.06743i
$177$	12.1947	+	2.59207i	0.916612	+	0.194832i
$178$	−3.20966	−	9.87832i	−0.240574	−	0.740411i
$179$	11.8687	−	2.52278i	0.887111	−	0.188561i	0.258249	−	0.966078i	$-0.416854\pi$
$179$	11.8687	−	2.52278i	0.887111	−	0.188561i	0.628862	+	0.777517i	$0.283521\pi$
$180$	−4.24636	−	7.35491i	−0.316505	−	0.548202i
$181$	4.82344	−	8.35444i	0.358523	−	0.620980i	−0.629191	−	0.777251i	$-0.716614\pi$
$181$	4.82344	−	8.35444i	0.358523	−	0.620980i	0.987714	+	0.156270i	$0.0499471\pi$
$182$	−4.91094	+	15.1143i	−0.364023	+	1.12035i
$183$	0.498060	−	4.73873i	0.0368177	−	0.350297i
$184$	−1.65122	+	1.19968i	−0.121730	+	0.0884418i
$185$	−0.644448			−0.0473808
$186$		0			0
$187$	−9.10960			−0.666160
$188$	−9.98175	+	7.25216i	−0.727994	+	0.528918i
$189$	−1.16932	+	11.1254i	−0.0850557	+	0.809251i
$190$	−0.932141	+	2.86884i	−0.0676246	+	0.208127i
$191$	−5.23270	+	9.06331i	−0.378625	+	0.655798i	−0.990862	−	0.134876i	$-0.956936\pi$
$191$	−5.23270	+	9.06331i	−0.378625	+	0.655798i	0.612237	+	0.790674i	$0.290270\pi$
$192$	10.8592	+	18.8087i	0.783695	+	1.35740i
$193$	1.75152	−	0.372297i	0.126077	−	0.0267985i	−0.144441	−	0.989513i	$-0.546138\pi$
$193$	1.75152	−	0.372297i	0.126077	−	0.0267985i	0.270518	+	0.962715i	$0.412805\pi$
$194$	4.29910	+	13.2313i	0.308658	+	0.949951i
$195$	−10.2551	−	2.17979i	−0.734384	−	0.156098i
$196$	−1.55895	−	14.8324i	−0.111354	−	1.05946i
$197$	−4.28040	−	4.75387i	−0.304966	−	0.338699i	0.571109	−	0.820874i	$-0.306513\pi$
$197$	−4.28040	−	4.75387i	−0.304966	−	0.338699i	−0.876075	+	0.482175i	$0.839847\pi$
$198$	12.7786	+	5.68942i	0.908139	+	0.404329i
$199$	−0.847000	+	0.377108i	−0.0600422	+	0.0267325i	−0.436538	−	0.899686i	$-0.643796\pi$
$199$	−0.847000	+	0.377108i	−0.0600422	+	0.0267325i	0.376496	+	0.926418i	$0.377129\pi$
$200$	0.208769	−	0.231861i	0.0147622	−	0.0163950i
$201$	23.5638	+	17.1201i	1.66207	+	1.20756i
$202$	30.2798	+	21.9996i	2.13048	+	1.54788i
$203$	−3.38672	+	3.76133i	−0.237701	+	0.263994i
$204$	−9.53993	+	4.24745i	−0.667928	+	0.297381i
$205$	−9.17580	−	4.08533i	−0.640866	−	0.285332i
$206$	5.42867	+	6.02915i	0.378233	+	0.420071i
$207$	−0.552856	−	5.26007i	−0.0384262	−	0.365600i
$208$	6.79108	+	1.44349i	0.470877	+	0.100088i
$209$	−0.820151	−	2.52416i	−0.0567310	−	0.174600i
$210$	37.4106	−	7.95187i	2.58158	−	0.548731i
$211$	3.09072	+	5.35328i	0.212774	+	0.368535i	0.952582	−	0.304283i	$-0.0984169\pi$
$211$	3.09072	+	5.35328i	0.212774	+	0.368535i	−0.739808	+	0.672818i	$0.765084\pi$
$212$	10.9050	−	18.8880i	0.748957	−	1.29723i
$213$	−0.883191	+	2.71818i	−0.0605152	+	0.186247i
$214$	−2.40760	+	22.9067i	−0.164580	+	1.56587i
$215$	0.512281	−	0.372194i	0.0349373	−	0.0253834i
$216$	−1.85267			−0.126058
$217$		0			0
$218$	37.4917			2.53926
$219$	−24.5186	+	17.8138i	−1.65681	+	1.20375i
$220$	−2.40968	+	22.9266i	−0.162461	+	1.54571i
$221$	−1.37258	+	4.22436i	−0.0923295	+	0.284161i
$222$	0.608389	−	1.05376i	0.0408324	−	0.0707238i
$223$	7.94891	+	13.7679i	0.532298	+	0.921968i	0.999289	+	0.0377054i	$0.0120048\pi$
$223$	7.94891	+	13.7679i	0.532298	+	0.921968i	−0.466991	+	0.884262i	$0.654662\pi$
$224$	−29.1485	+	6.19570i	−1.94756	+	0.413967i
$225$	0.249842	+	0.768936i	0.0166562	+	0.0512624i
$226$	−35.5483	−	7.55602i	−2.36463	−	0.502619i
$227$	0.485530	+	4.61951i	0.0322258	+	0.306608i	0.998748	+	0.0500248i	$0.0159300\pi$
$227$	0.485530	+	4.61951i	0.0322258	+	0.306608i	−0.966522	+	0.256583i	$0.917403\pi$
$228$	−2.03581	−	2.26100i	−0.134825	−	0.149738i
$229$	17.7396	+	7.89816i	1.17226	+	0.521925i	0.898114	−	0.439762i	$-0.144937\pi$
$229$	17.7396	+	7.89816i	1.17226	+	0.521925i	0.274149	+	0.961687i	$0.411604\pi$
$230$	14.9064	−	6.63678i	0.982902	−	0.437616i
$231$	−22.5171	+	25.0078i	−1.48152	+	1.64539i
$232$	−0.678147	−	0.492703i	−0.0445225	−	0.0323475i
$233$	11.5273	+	8.37505i	0.755176	+	0.548667i	0.897427	−	0.441163i	$-0.145434\pi$
$233$	11.5273	+	8.37505i	0.755176	+	0.548667i	−0.142251	+	0.989831i	$0.545434\pi$
$234$	4.56374	−	5.06854i	0.298341	−	0.331341i
$235$	11.5379	−	5.13700i	0.752649	−	0.335101i
$236$	−12.2107	−	5.43657i	−0.794852	−	0.353891i
$237$	−12.4209	−	13.7948i	−0.806821	−	0.896066i
$238$	−1.69373	−	16.1147i	−0.109788	−	1.04456i
$239$	−6.65289	−	1.41412i	−0.430340	−	0.0914715i	−0.0123509	−	0.999924i	$-0.503932\pi$
$239$	−6.65289	−	1.41412i	−0.430340	−	0.0914715i	−0.417989	+	0.908452i	$0.637265\pi$
$240$	−5.16327	−	15.8909i	−0.333288	−	1.02575i
$241$	−11.2537	+	2.39205i	−0.724915	+	0.154085i	−0.555568	−	0.831471i	$-0.687499\pi$
$241$	−11.2537	+	2.39205i	−0.724915	+	0.154085i	−0.169347	+	0.985557i	$0.554166\pi$
$242$	−7.58800	−	13.1428i	−0.487775	−	0.844851i
$243$	7.46119	−	12.9232i	0.478636	−	0.829021i
$244$	−1.57861	+	4.85845i	−0.101060	+	0.311030i
$245$	−1.59581	+	15.1831i	−0.101952	+	0.970011i
$246$	15.3425	−	11.1470i	0.978200	−	0.710704i
$247$	−1.29410			−0.0823413
$248$		0			0
$249$	11.0938			0.703039
$250$	17.6620	−	12.8322i	1.11705	−	0.811581i
$251$	−0.762473	+	7.25445i	−0.0481269	+	0.457897i	0.943747	+	0.330669i	$0.107274\pi$
$251$	−0.762473	+	7.25445i	−0.0481269	+	0.457897i	−0.991874	+	0.127227i	$0.959392\pi$
$252$	−4.10724	+	12.6408i	−0.258732	+	0.796295i
$253$	−7.17837	+	12.4333i	−0.451300	+	0.781675i
$254$	−14.7103	−	25.4790i	−0.923005	−	1.59869i
$255$	10.4560	−	2.22250i	0.654782	−	0.139178i
$256$	3.19031	+	9.81877i	0.199395	+	0.613673i
$257$	24.1169	+	5.12621i	1.50437	+	0.319764i	0.885096	−	0.465409i	$-0.154093\pi$
$257$	24.1169	+	5.12621i	1.50437	+	0.319764i	0.619276	+	0.785173i	$0.287426\pi$
$258$	0.124971	+	1.18902i	0.00778035	+	0.0740250i
$259$	0.674870	+	0.749519i	0.0419344	+	0.0465728i
$260$	10.2686	+	4.57186i	0.636830	+	0.283535i
$261$	1.98439	−	0.883505i	0.122830	−	0.0546876i
$262$	9.96702	−	11.0695i	0.615764	−	0.683876i
$263$	−21.2666	−	15.4511i	−1.31136	−	0.952757i	−0.999997	−	0.00246465i	$-0.999215\pi$
$263$	−21.2666	−	15.4511i	−1.31136	−	0.952757i	−0.311360	−	0.950292i	$-0.600785\pi$
$264$	−4.50877	−	3.27581i	−0.277495	−	0.201612i
$265$	−14.9387	+	16.5911i	−0.917678	+	1.01918i
$266$	4.31272	−	1.92015i	0.264430	−	0.117732i
$267$	−9.79675	−	4.36179i	−0.599551	−	0.266937i
$268$	−20.8950	−	23.2063i	−1.27637	−	1.41755i
$269$	−2.18253	−	20.7654i	−0.133071	−	1.26609i	−0.833561	−	0.552427i	$-0.813702\pi$
$269$	−2.18253	−	20.7654i	−0.133071	−	1.26609i	0.700490	−	0.713662i	$-0.252965\pi$
$270$	14.4876	+	3.07944i	0.881690	+	0.187409i
$271$	6.49271	+	19.9825i	0.394404	+	1.21385i	0.929425	+	0.369012i	$0.120304\pi$
$271$	6.49271	+	19.9825i	0.394404	+	1.21385i	−0.535021	+	0.844839i	$0.679696\pi$
$272$	−6.92414	+	1.47177i	−0.419837	+	0.0892392i
$273$	8.20403	+	14.2098i	0.496530	+	0.860016i
$274$	7.85091	−	13.5982i	0.474291	−	0.821496i
$275$	0.678179	−	2.08722i	0.0408958	−	0.125864i
$276$	−1.72031	+	16.3676i	−0.103550	+	0.985216i
$277$	−3.85034	+	2.79744i	−0.231345	+	0.168082i	−0.697418	−	0.716664i	$-0.745668\pi$
$277$	−3.85034	+	2.79744i	−0.231345	+	0.168082i	0.466074	+	0.884746i	$0.345668\pi$
$278$	41.6459			2.49776
$279$		0			0
$280$	−5.25032			−0.313767
$281$	5.38386	−	3.91160i	0.321174	−	0.233347i	−0.415502	−	0.909592i	$-0.636394\pi$
$281$	5.38386	−	3.91160i	0.321174	−	0.233347i	0.736676	+	0.676246i	$0.236394\pi$
$282$	−2.49261	+	23.7156i	−0.148433	+	1.41224i
$283$	−2.23921	+	6.89159i	−0.133107	+	0.409662i	−0.995291	−	0.0969338i	$-0.969096\pi$
$283$	−2.23921	+	6.89159i	−0.133107	+	0.409662i	0.862183	+	0.506596i	$0.169096\pi$
$284$	1.53210	−	2.65367i	0.0909132	−	0.157466i
$285$	1.55720	+	2.69715i	0.0922406	+	0.159765i
$286$	−18.1089	+	3.84917i	−1.07080	+	0.227606i
$287$	4.85755	+	14.9500i	0.286732	+	0.882471i
$288$	12.5096	+	2.65899i	0.737134	+	0.156683i
$289$	1.30360	+	12.4029i	0.0766822	+	0.729583i
$290$	4.48408	+	4.98007i	0.263314	+	0.292440i
$291$	13.1220	+	5.84230i	0.769227	+	0.342482i
$292$	29.6833	−	13.2159i	1.73708	−	0.773400i
$293$	9.04097	−	10.0410i	0.528179	−	0.586602i	−0.418727	−	0.908112i	$-0.637524\pi$
$293$	9.04097	−	10.0410i	0.528179	−	0.586602i	0.946906	+	0.321510i	$0.104190\pi$
$294$	−23.3199	−	16.9429i	−1.36004	−	0.988131i
$295$	11.0692	+	8.04226i	0.644475	+	0.468238i
$296$	−0.111768	+	0.124131i	−0.00649639	+	0.00721497i
$297$	−11.9052	+	5.30052i	−0.690808	+	0.307567i
$298$	23.3120	+	10.3792i	1.35043	+	0.601248i
$299$	4.68405	+	5.20217i	0.270886	+	0.300849i
$300$	−0.262974	−	2.50203i	−0.0151828	−	0.144455i
$301$	−0.969340	−	0.206040i	−0.0558718	−	0.0118759i
$302$	12.7276	+	39.1716i	0.732393	+	2.25407i
$303$	37.7985	−	8.03433i	2.17147	−	0.461560i
$304$	−1.03120	−	1.78609i	−0.0591434	−	0.102439i
$305$	2.61462	−	4.52866i	0.149713	−	0.259310i
$306$	−2.14891	+	6.61367i	−0.122845	+	0.378078i
$307$	2.37550	−	22.6013i	0.135577	−	1.28993i	−0.689243	−	0.724530i	$-0.742057\pi$
$307$	2.37550	−	22.6013i	0.135577	−	1.28993i	0.824820	−	0.565396i	$-0.191277\pi$
$308$	29.1880	−	21.2063i	1.66314	−	1.20834i
$309$	8.37640			0.476517
$310$		0			0
$311$	9.49330			0.538315			0.269158	−	0.963096i	$-0.413255\pi$
$311$	9.49330			0.538315			0.269158	+	0.963096i	$0.413255\pi$
$312$	−2.19843	+	1.59725i	−0.124462	+	0.0904266i
$313$	2.93694	−	27.9431i	0.166006	−	1.57944i	−0.521494	−	0.853255i	$-0.674625\pi$
$313$	2.93694	−	27.9431i	0.166006	−	1.57944i	0.687500	−	0.726184i	$-0.258708\pi$
$314$	−3.71682	+	11.4392i	−0.209752	+	0.645551i
$315$	6.80276	−	11.7827i	0.383292	−	0.663882i
$316$	9.95072	+	17.2352i	0.559772	+	0.969553i
$317$	15.4712	−	3.28850i	0.868949	−	0.184701i	0.248198	−	0.968709i	$-0.420161\pi$
$317$	15.4712	−	3.28850i	0.868949	−	0.184701i	0.620750	+	0.784008i	$0.286828\pi$
$318$	−13.0259	−	40.0896i	−0.730457	−	2.24812i
$319$	−5.76738	−	1.22589i	−0.322911	−	0.0686369i
$320$	2.49146	+	23.7046i	0.139277	+	1.32513i
$321$	15.9124	+	17.6725i	0.888142	+	0.986382i
$322$	−23.3290	−	10.3867i	−1.30007	−	0.578829i
$323$	1.20538	−	0.536668i	0.0670690	−	0.0298610i
$324$	−17.2571	+	19.1660i	−0.958730	+	1.06478i
$325$	−0.865715	−	0.628979i	−0.0480212	−	0.0348895i
$326$	−29.8116	−	21.6594i	−1.65111	−	1.19960i
$327$	25.9013	−	28.7663i	1.43234	−	1.59078i
$328$	−2.37828	+	1.05888i	−0.131319	+	0.0584668i
$329$	−18.0571	−	8.03954i	−0.995520	−	0.443234i
$330$	29.8131	+	33.1108i	1.64116	+	1.82269i
$331$	1.35303	+	12.8732i	0.0743692	+	0.707576i	0.966651	+	0.256097i	$0.0824367\pi$
$331$	1.35303	+	12.8732i	0.0743692	+	0.707576i	−0.892282	+	0.451479i	$0.850897\pi$
$332$	−11.6340	−	2.47287i	−0.638496	−	0.135717i
$333$	−0.133758	−	0.411664i	−0.00732988	−	0.0225591i
$334$	4.42263	−	0.940059i	0.241995	−	0.0514377i
$335$	15.9827	+	27.6828i	0.873228	+	1.51247i
$336$	−13.0748	+	22.6462i	−0.713287	+	1.23545i
$337$	8.61116	−	26.5024i	0.469080	−	1.44368i	−0.384698	−	0.923042i	$-0.625694\pi$
$337$	8.61116	−	26.5024i	0.469080	−	1.44368i	0.853778	−	0.520637i	$-0.174306\pi$
$338$	1.87217	−	17.8125i	0.101832	−	0.968871i
$339$	−30.3561	+	22.0550i	−1.64872	+	1.19786i
$340$	−11.4606			−0.621537
$341$		0			0
$342$	−2.02604			−0.109556
$343$	−1.47969	+	1.07506i	−0.0798956	+	0.0580476i
$344$	0.0171555	−	0.163224i	0.000924964	−	0.00880045i
$345$	5.20597	−	16.0223i	0.280280	−	0.862612i
$346$	5.70655	−	9.88403i	0.306786	−	0.531369i
$347$	2.66175	+	4.61029i	0.142890	+	0.247493i	0.928584	−	0.371123i	$-0.121027\pi$
$347$	2.66175	+	4.61029i	0.142890	+	0.247493i	−0.785693	+	0.618616i	$0.787694\pi$
$348$	−6.61141	+	1.40530i	−0.354409	+	0.0753319i
$349$	−1.26632	−	3.89734i	−0.0677847	−	0.208620i	0.911427	−	0.411463i	$-0.134982\pi$
$349$	−1.26632	−	3.89734i	−0.0677847	−	0.208620i	−0.979211	+	0.202843i	$0.934982\pi$
$350$	3.81835	+	0.811616i	0.204100	+	0.0433827i
$351$	0.664194	+	6.31938i	0.0354520	+	0.337304i
$352$	−23.2289	−	25.7983i	−1.23810	−	1.37505i
$353$	−19.9056	−	8.86253i	−1.05947	−	0.471705i	−0.198360	−	0.980129i	$-0.563562\pi$
$353$	−19.9056	−	8.86253i	−1.05947	−	0.471705i	−0.861107	+	0.508424i	$0.830228\pi$
$354$	−23.6001	+	10.5074i	−1.25433	+	0.558464i
$355$	−2.09882	+	2.33097i	−0.111394	+	0.123715i
$356$	9.30151	+	6.75794i	0.492979	+	0.358170i
$357$	−13.5345	−	9.83337i	−0.716320	−	0.520437i
$358$	−16.8239	+	18.6848i	−0.889170	+	0.987523i
$359$	−6.46921	+	2.88028i	−0.341432	+	0.152015i	−0.570288	−	0.821445i	$-0.693168\pi$
$359$	−6.46921	+	2.88028i	−0.341432	+	0.152015i	0.228856	+	0.973460i	$0.426502\pi$
$360$	2.05846	+	0.916487i	0.108491	+	0.0483031i
$361$	−12.4563	−	13.8341i	−0.655592	−	0.728109i
$362$	2.08947	+	19.8800i	0.109820	+	1.04487i
$363$	−15.3263	−	3.25770i	−0.804421	−	0.170985i
$364$	−5.43605	−	16.7304i	−0.284927	−	0.876914i
$365$	−32.5337	+	6.91526i	−1.70289	+	0.361961i
$366$	4.93665	+	8.55053i	0.258043	+	0.446943i
$367$	−8.05884	+	13.9583i	−0.420668	+	0.728619i	−0.996005	−	0.0892980i	$-0.971538\pi$
$367$	−8.05884	+	13.9583i	−0.420668	+	0.728619i	0.575337	+	0.817917i	$0.304871\pi$
$368$	−3.44747	+	10.6102i	−0.179712	+	0.553096i
$369$	0.705175	−	6.70930i	0.0367100	−	0.349272i
$370$	1.08034	−	0.784913i	0.0561642	−	0.0408057i
$371$	34.9401			1.81400
$372$		0			0
$373$	−9.81895			−0.508406			−0.254203	−	0.967151i	$-0.581813\pi$
$373$	−9.81895			−0.508406			−0.254203	+	0.967151i	$0.581813\pi$
$374$	15.2712	−	11.0951i	0.789653	−	0.573716i
$375$	2.35609	−	22.4167i	0.121668	−	1.15760i
$376$	1.01157	−	3.11331i	0.0521680	−	0.160557i
$377$	−1.43747	+	2.48977i	−0.0740335	+	0.128230i
$378$	−11.5900	−	20.0745i	−0.596127	−	1.03252i
$379$	13.5137	−	2.87243i	0.694153	−	0.147547i	0.152694	−	0.988274i	$-0.451205\pi$
$379$	13.5137	−	2.87243i	0.694153	−	0.147547i	0.541460	+	0.840727i	$0.317872\pi$
$380$	−1.03181	−	3.17559i	−0.0529309	−	0.162904i
$381$	−29.7119	−	6.31546i	−1.52219	−	0.323551i
$382$	−2.26676	−	21.5668i	−0.115978	−	1.10345i
$383$	−6.89608	−	7.65887i	−0.352373	−	0.391350i	0.540734	−	0.841193i	$-0.318146\pi$
$383$	−6.89608	−	7.65887i	−0.352373	−	0.391350i	−0.893107	+	0.449844i	$0.851480\pi$
$384$	−9.41247	−	4.19070i	−0.480328	−	0.213856i
$385$	−33.7384	+	15.0213i	−1.71947	+	0.765555i
$386$	−2.48277	+	2.75740i	−0.126370	+	0.140348i
$387$	0.344078	+	0.249987i	0.0174905	+	0.0127076i
$388$	−12.4587	−	9.05177i	−0.632494	−	0.459534i
$389$	16.9728	−	18.8502i	0.860554	−	0.955742i	−0.138849	−	0.990314i	$-0.544340\pi$
$389$	16.9728	−	18.8502i	0.860554	−	0.955742i	0.999402	+	0.0345719i	$0.0110068\pi$
$390$	19.8464	−	8.83618i	1.00496	−	0.447437i
$391$	−6.52030	−	2.90302i	−0.329746	−	0.146812i
$392$	2.64774	+	2.94062i	0.133731	+	0.148523i
$393$	−1.60755	−	15.2948i	−0.0810900	−	0.771520i
$394$	12.9656	+	2.75593i	0.653198	+	0.138842i
$395$	−6.29527	−	19.3749i	−0.316749	−	0.974855i
$396$	−15.1453	+	3.21923i	−0.761080	+	0.161773i
$397$	−8.37941	−	14.5136i	−0.420550	−	0.728415i	0.575443	−	0.817842i	$-0.304830\pi$
$397$	−8.37941	−	14.5136i	−0.420550	−	0.728415i	−0.995993	+	0.0894272i	$0.971496\pi$
$398$	0.960590	−	1.66379i	0.0481500	−	0.0833983i
$399$	1.50618	−	4.63556i	0.0754035	−	0.232068i
$400$	0.178262	−	1.69605i	0.00891310	−	0.0848025i
$401$	−22.3479	+	16.2367i	−1.11600	+	0.810823i	−0.983598	−	0.180372i	$-0.942270\pi$
$401$	−22.3479	+	16.2367i	−1.11600	+	0.810823i	−0.132404	+	0.991196i	$0.542270\pi$
$402$	−60.3537			−3.01017
$403$		0			0
$404$	−41.4300			−2.06122
$405$	21.3581	−	15.5176i	1.06129	−	0.771075i
$406$	1.09627	−	10.4303i	0.0544070	−	0.517648i
$407$	−0.363076	+	1.11743i	−0.0179970	+	0.0553891i
$408$	1.38532	−	2.39945i	0.0685838	−	0.118791i
$409$	−11.3053	−	19.5814i	−0.559013	−	0.968239i	−0.997579	−	0.0695399i	$-0.977847\pi$
$409$	−11.3053	−	19.5814i	−0.559013	−	0.968239i	0.438566	−	0.898699i	$-0.355486\pi$
$410$	20.3579	−	4.32721i	1.00541	−	0.213706i
$411$	−5.00965	−	15.4181i	−0.247108	−	0.760519i
$412$	−8.78427	−	1.86716i	−0.432770	−	0.0919881i
$413$	−2.23828	−	21.2959i	−0.110139	−	1.04790i
$414$	7.33337	+	8.14453i	0.360415	+	0.400282i
$415$	11.1225	+	4.95204i	0.545980	+	0.243086i
$416$	−15.4633	+	6.88470i	−0.758150	+	0.337550i
$417$	28.7712	−	31.9537i	1.40893	−	1.56478i
$418$	4.44922	+	3.23255i	0.217619	+	0.158109i
$419$	5.00860	+	3.63896i	0.244686	+	0.177775i	0.703368	−	0.710825i	$-0.251678\pi$
$419$	5.00860	+	3.63896i	0.244686	+	0.177775i	−0.458682	+	0.888600i	$0.651678\pi$
$420$	−28.3283	+	31.4617i	−1.38228	+	1.53518i
$421$	5.99225	−	2.66792i	0.292045	−	0.130027i	−0.255485	−	0.966813i	$-0.582235\pi$
$421$	5.99225	−	2.66792i	0.292045	−	0.130027i	0.547529	+	0.836786i	$0.315568\pi$
$422$	−11.7013	−	5.20976i	−0.569611	−	0.253607i
$423$	5.67618	+	6.30404i	0.275985	+	0.306513i
$424$	0.604861	+	5.75487i	0.0293747	+	0.279481i
$425$	1.06721	+	0.226842i	0.0517671	+	0.0110034i
$426$	−1.83008	−	5.63240i	−0.0886676	−	0.272891i
$427$	−8.00506	+	1.70153i	−0.387392	+	0.0823427i
$428$	−12.7479	−	22.0800i	−0.616192	−	1.06728i
$429$	−9.55725	+	16.5536i	−0.461428	+	0.799217i
$430$	−0.405460	+	1.24788i	−0.0195530	+	0.0601780i
$431$	−2.45304	+	23.3391i	−0.118159	+	1.12421i	0.761355	+	0.648335i	$0.224534\pi$
$431$	−2.45304	+	23.3391i	−0.118159	+	1.12421i	−0.879514	+	0.475872i	$0.842132\pi$
$432$	−8.19266	+	5.95232i	−0.394170	+	0.286381i
$433$	−24.3130			−1.16841			−0.584203	−	0.811607i	$-0.698593\pi$
$433$	−24.3130			−1.16841			−0.584203	+	0.811607i	$0.698593\pi$
$434$		0			0
$435$	6.91890			0.331736
$436$	−33.5747	+	24.3934i	−1.60793	+	1.16823i
$437$	0.217362	−	2.06806i	0.0103978	−	0.0989289i
$438$	19.4060	−	59.7255i	0.927254	−	2.85379i
$439$	−7.25318	+	12.5629i	−0.346175	+	0.599593i	−0.985567	−	0.169288i	$-0.945853\pi$
$439$	−7.25318	+	12.5629i	−0.346175	+	0.599593i	0.639391	+	0.768881i	$0.279186\pi$
$440$	−3.05817	−	5.29690i	−0.145792	−	0.252520i
$441$	−10.0299	+	2.13193i	−0.477617	+	0.101521i
$442$	−2.84415	−	8.75338i	−0.135282	−	0.416356i
$443$	16.2040	+	3.44426i	0.769874	+	0.163642i	0.576072	−	0.817399i	$-0.304585\pi$
$443$	16.2040	+	3.44426i	0.769874	+	0.163642i	0.193802	+	0.981041i	$0.437918\pi$
$444$	0.140788	+	1.33951i	0.00668150	+	0.0635702i
$445$	−7.87506	−	8.74614i	−0.373314	−	0.414607i
$446$	−30.0942	−	13.3988i	−1.42500	−	0.634452i
$447$	24.0688	−	10.7161i	1.13841	−	0.506854i
$448$	24.9604	−	27.7213i	1.17927	−	1.30971i
$449$	5.51532	+	4.00712i	0.260284	+	0.189107i	0.710272	−	0.703927i	$-0.248572\pi$
$449$	5.51532	+	4.00712i	0.260284	+	0.189107i	−0.449988	+	0.893035i	$0.648572\pi$
$450$	−1.35537	−	0.984731i	−0.0638926	−	0.0464207i
$451$	−12.2533	+	13.6086i	−0.576984	+	0.640805i
$452$	36.7505	−	16.3624i	1.72860	−	0.769621i
$453$	38.8482	+	17.2963i	1.82525	+	0.812652i
$454$	−6.44033	−	7.15271i	−0.302260	−	0.335693i
$455$	1.88228	+	17.9087i	0.0882425	+	0.839571i
$456$	0.789583	+	0.167831i	0.0369756	+	0.00785941i
$457$	−6.62154	−	20.3790i	−0.309742	−	0.953289i	−0.977865	−	0.209238i	$-0.932902\pi$
$457$	−6.62154	−	20.3790i	−0.309742	−	0.953289i	0.668122	−	0.744051i	$-0.267098\pi$
$458$	−39.3579	+	8.36579i	−1.83908	+	0.390908i
$459$	−3.23934	−	5.61070i	−0.151200	−	0.261885i
$460$	−9.03094	+	15.6420i	−0.421070	+	0.729314i
$461$	2.68057	−	8.24994i	0.124847	−	0.384238i	−0.869027	−	0.494766i	$-0.835254\pi$
$461$	2.68057	−	8.24994i	0.124847	−	0.384238i	0.993873	+	0.110527i	$0.0352540\pi$
$462$	7.28873	−	69.3477i	0.339103	−	3.22635i
$463$	2.95281	−	2.14534i	0.137229	−	0.0997025i	−0.517053	−	0.855953i	$-0.672971\pi$
$463$	2.95281	−	2.14534i	0.137229	−	0.0997025i	0.654282	+	0.756251i	$0.272971\pi$
$464$	−4.58180			−0.212705
$465$		0			0
$466$	−29.5246			−1.36770
$467$	2.49267	−	1.81103i	0.115347	−	0.0838045i	−0.528616	−	0.848861i	$-0.677289\pi$
$467$	2.49267	−	1.81103i	0.115347	−	0.0838045i	0.643963	+	0.765056i	$0.277289\pi$
$468$	−0.789157	+	7.50832i	−0.0364788	+	0.347072i
$469$	15.4591	−	47.5782i	0.713834	−	2.19696i
$470$	−13.0852	+	22.6643i	−0.603577	+	1.04543i
$471$	6.20917	+	10.7546i	0.286104	+	0.495546i
$472$	3.46883	−	0.737322i	0.159666	−	0.0339380i
$473$	−0.356747	−	1.09795i	−0.0164032	−	0.0504839i
$474$	37.6236	+	7.99714i	1.72811	+	0.367321i
$475$	0.0332269	+	0.316133i	0.00152456	+	0.0145052i
$476$	12.0016	+	13.3291i	0.550092	+	0.610939i
$477$	−13.6988	−	6.09908i	−0.627223	−	0.279258i
$478$	12.8751	−	5.73237i	0.588894	−	0.262193i
$479$	−11.6497	+	12.9383i	−0.532289	+	0.591167i	−0.947976	−	0.318341i	$-0.896874\pi$
$479$	−11.6497	+	12.9383i	−0.532289	+	0.591167i	0.415687	+	0.909508i	$0.363541\pi$
$480$	32.9562	+	23.9441i	1.50424	+	1.09289i
$481$	0.463476	+	0.336735i	0.0211327	+	0.0153538i
$482$	15.9521	−	17.7166i	0.726597	−	0.806968i
$483$	−24.0863	+	10.7239i	−1.09597	+	0.487955i
$484$	15.3464	+	6.83266i	0.697563	+	0.310575i
$485$	10.5481	+	11.7148i	0.478963	+	0.531942i
$486$	3.23212	+	30.7516i	0.146612	+	1.39492i
$487$	28.1448	+	5.98237i	1.27536	+	0.271087i	0.795338	−	0.606167i	$-0.207294\pi$
$487$	28.1448	+	5.98237i	1.27536	+	0.271087i	0.480027	+	0.877254i	$0.340627\pi$
$488$	−0.418832	−	1.28903i	−0.0189596	−	0.0583518i
$489$	−37.2141	+	7.91010i	−1.68288	+	0.357707i
$490$	−15.8172	−	27.3963i	−0.714550	−	1.23764i
$491$	−4.91284	+	8.50929i	−0.221713	+	0.384019i	−0.955328	−	0.295546i	$-0.904498\pi$
$491$	−4.91284	+	8.50929i	−0.221713	+	0.384019i	0.733615	+	0.679565i	$0.237832\pi$
$492$	−6.48693	+	19.9647i	−0.292453	+	0.900078i
$493$	0.306401	−	2.91521i	0.0137996	−	0.131294i
$494$	2.16940	−	1.57616i	0.0976058	−	0.0709148i
$495$	15.8497			0.712391
$496$		0			0
$497$	4.90891			0.220195
$498$	−18.5974	+	13.5118i	−0.833369	+	0.605478i
$499$	−1.13393	+	10.7886i	−0.0507615	+	0.482963i	0.939379	+	0.342882i	$0.111403\pi$
$499$	−1.13393	+	10.7886i	−0.0507615	+	0.482963i	−0.990140	+	0.140081i	$0.955264\pi$
$500$	−7.46766	+	22.9831i	−0.333964	+	1.02784i
$501$	2.33411	−	4.04280i	0.104280	−	0.180619i
$502$	−7.55745	−	13.0899i	−0.337305	−	0.584230i
$503$	−8.37387	+	1.77992i	−0.373372	+	0.0793628i	−0.390776	−	0.920486i	$-0.627793\pi$
$503$	−8.37387	+	1.77992i	−0.373372	+	0.0793628i	0.0174036	+	0.999849i	$0.494460\pi$
$504$	−1.08973	−	3.35383i	−0.0485402	−	0.149391i
$505$	41.4826	+	8.81741i	1.84595	+	0.392369i
$506$	−3.10961	−	29.5859i	−0.138239	−	1.31526i
$507$	−12.3736	−	13.7423i	−0.549531	−	0.610316i
$508$	29.7509	+	13.2460i	1.31998	+	0.587694i
$509$	36.1603	−	16.0996i	1.60278	−	0.713601i	0.606124	−	0.795370i	$-0.292724\pi$
$509$	36.1603	−	16.0996i	1.60278	−	0.713601i	0.996651	+	0.0817689i	$0.0260569\pi$
$510$	−14.8214	+	16.4608i	−0.656301	+	0.728897i
$511$	42.1123	+	30.5963i	1.86294	+	1.35350i
$512$	−25.0995	−	18.2358i	−1.10925	−	0.805918i
$513$	1.26302	−	1.40272i	0.0557636	−	0.0619318i
$514$	−46.6727	+	20.7800i	−2.05864	+	0.916567i
$515$	8.39806	+	3.73906i	0.370063	+	0.164763i
$516$	−0.885532	−	0.983483i	−0.0389834	−	0.0432954i
$517$	−2.40690	−	22.9001i	−0.105855	−	1.00715i
$518$	−2.04423	−	0.434514i	−0.0898181	−	0.0190914i
$519$	−3.64134	−	11.2069i	−0.159837	−	0.491927i
$520$	−2.91710	+	0.620048i	−0.127923	+	0.0271909i
$521$	0.674660	+	1.16855i	0.0295574	+	0.0511949i	0.880426	−	0.474184i	$-0.157257\pi$
$521$	0.674660	+	1.16855i	0.0295574	+	0.0511949i	−0.850868	+	0.525379i	$0.823924\pi$
$522$	−2.25051	+	3.89800i	−0.0985022	+	0.170611i
$523$	−8.79861	+	27.0793i	−0.384736	+	1.18410i	0.551935	+	0.833887i	$0.313890\pi$
$523$	−8.79861	+	27.0793i	−0.384736	+	1.18410i	−0.936671	+	0.350210i	$0.886110\pi$
$524$	−1.72349	+	16.3979i	−0.0752909	+	0.716345i
$525$	3.26065	−	2.36900i	0.142306	−	0.103392i
$526$	54.4699			2.37500
$527$		0			0
$528$	−30.4628			−1.32572
$529$	9.50718	−	6.90737i	0.413356	−	0.300320i
$530$	4.83562	−	46.0078i	0.210046	−	1.99845i
$531$	−2.83982	+	8.74006i	−0.123238	+	0.379286i
$532$	−2.61282	+	4.52554i	−0.113280	+	0.196207i
$533$	4.46443	+	7.73262i	0.193376	+	0.334937i
$534$	21.7356	−	4.62004i	0.940591	−	0.199929i
$535$	8.06488	+	24.8211i	0.348675	+	1.07311i
$536$	8.10408	+	1.72257i	0.350043	+	0.0744039i
$537$	2.71347	+	25.8169i	0.117095	+	1.11408i
$538$	28.9503	+	32.1525i	1.24813	+	1.38619i
$539$	25.4275	+	11.3210i	1.09524	+	0.487631i
$540$	−14.9776	+	6.66846i	−0.644534	+	0.286965i
$541$	−9.57499	+	10.6341i	−0.411661	+	0.457196i	−0.912942	−	0.408088i	$-0.866196\pi$
$541$	−9.57499	+	10.6341i	−0.411661	+	0.457196i	0.501281	+	0.865284i	$0.332862\pi$
$542$	−35.2222	−	25.5904i	−1.51292	−	1.09920i
$543$	16.6968	+	12.1310i	0.716530	+	0.520590i
$544$	11.5481	−	12.8254i	0.495119	−	0.549886i
$545$	38.8089	−	17.2788i	1.66239	−	0.740145i
$546$	−31.0601	−	13.8288i	−1.32925	−	0.591820i
$547$	28.3490	+	31.4848i	1.21212	+	1.34619i	0.921029	+	0.389494i	$0.127350\pi$
$547$	28.3490	+	31.4848i	1.21212	+	1.34619i	0.291087	+	0.956697i	$0.405983\pi$
$548$	1.81678	+	17.2856i	0.0776092	+	0.738402i
$549$	3.43551	+	0.730241i	0.146624	+	0.0311659i
$550$	1.40527	+	4.32498i	0.0599209	+	0.184418i
$551$	0.835357	−	0.177561i	0.0355874	−	0.00756434i
$552$	−2.18327	−	3.78154i	−0.0929263	−	0.160953i
$553$	−15.9413	+	27.6111i	−0.677893	+	1.17414i
$554$	3.04747	−	9.37914i	0.129474	−	0.398481i
$555$	0.144116	−	1.37117i	0.00611739	−	0.0582031i
$556$	−37.2949	+	27.0963i	−1.58166	+	1.14914i
$557$	−27.3019			−1.15682			−0.578409	−	0.815747i	$-0.696326\pi$
$557$	−27.3019			−1.15682			−0.578409	+	0.815747i	$0.696326\pi$
$558$		0			0
$559$	−0.562902			−0.0238082
$560$	−23.2174	+	16.8684i	−0.981114	+	0.712821i
$561$	2.03715	−	19.3822i	0.0860087	−	0.818319i
$562$	−4.26122	+	13.1147i	−0.179749	+	0.553209i
$563$	−2.59399	+	4.49293i	−0.109324	+	0.189354i	−0.915497	−	0.402326i	$-0.868202\pi$
$563$	−2.59399	+	4.49293i	−0.109324	+	0.189354i	0.806173	+	0.591680i	$0.201535\pi$
$564$	−13.1980	−	22.8597i	−0.555737	−	0.962565i
$565$	−40.2796	+	8.56169i	−1.69457	+	0.360193i
$566$	−4.63992	−	14.2802i	−0.195030	−	0.600242i
$567$	−40.4139	−	8.59025i	−1.69723	−	0.360756i
$568$	0.0849801	+	0.808532i	0.00356569	+	0.0339252i
$569$	−1.58439	−	1.75964i	−0.0664210	−	0.0737680i	0.709018	−	0.705190i	$-0.249138\pi$
$569$	−1.58439	−	1.75964i	−0.0664210	−	0.0737680i	−0.775439	+	0.631422i	$0.782472\pi$
$570$	−5.89549	−	2.62484i	−0.246935	−	0.109942i
$571$	−18.6016	+	8.28194i	−0.778451	+	0.346589i	−0.757198	−	0.653186i	$-0.773432\pi$
$571$	−18.6016	+	8.28194i	−0.778451	+	0.346589i	−0.0212528	+	0.999774i	$0.506765\pi$
$572$	13.7125	−	15.2293i	0.573350	−	0.636770i
$573$	−18.1136	−	13.1603i	−0.756705	−	0.549778i
$574$	−26.3517	−	19.1456i	−1.09990	−	0.799122i
$575$	1.15057	−	1.27783i	0.0479819	−	0.0532893i
$576$	−14.6251	+	6.51150i	−0.609378	+	0.271313i
$577$	23.3701	+	10.4050i	0.972910	+	0.433167i	0.830731	−	0.556674i	$-0.187923\pi$
$577$	23.3701	+	10.4050i	0.972910	+	0.433167i	0.142178	+	0.989841i	$0.454589\pi$
$578$	−17.2916	−	19.2043i	−0.719236	−	0.798792i
$579$	0.400438	+	3.80992i	0.0166416	+	0.158335i
$580$	−7.25581	−	1.54227i	−0.301281	−	0.0640392i
$581$	−5.88809	−	18.1217i	−0.244279	−	0.751814i
$582$	−29.1132	+	6.18821i	−1.20678	+	0.256509i
$583$	20.3516	+	35.2501i	0.842879	+	1.45991i
$584$	−4.31041	+	7.46585i	−0.178366	+	0.308939i
$585$	2.38813	−	7.34992i	0.0987371	−	0.303882i
$586$	−2.92654	+	27.8441i	−0.120894	+	1.15023i
$587$	32.3299	−	23.4890i	1.33440	−	0.969495i	0.334766	−	0.942301i	$-0.391343\pi$
$587$	32.3299	−	23.4890i	1.33440	−	0.969495i	0.999630	−	0.0271941i	$-0.00865722\pi$
$588$	31.9072			1.31583
$589$		0			0
$590$	−28.3514			−1.16721
$591$	11.0719	−	8.04419i	0.455436	−	0.330894i
$592$	−0.0954358	+	0.908011i	−0.00392239	+	0.0373190i
$593$	−6.48230	+	19.9505i	−0.266196	+	0.819268i	0.725219	+	0.688518i	$0.241738\pi$
$593$	−6.48230	+	19.9505i	−0.266196	+	0.819268i	−0.991415	+	0.130750i	$0.958262\pi$
$594$	13.5018	−	23.3857i	0.553984	−	0.959529i
$595$	−9.18005	−	15.9003i	−0.376345	−	0.651849i
$596$	−27.6294	+	5.87282i	−1.13175	+	0.240560i
$597$	−0.612951	−	1.88647i	−0.0250864	−	0.0772080i
$598$	−14.1883	−	3.01582i	−0.580203	−	0.123326i
$599$	−2.18897	−	20.8266i	−0.0894388	−	0.850954i	−0.943632	−	0.330997i	$-0.892615\pi$
$599$	−2.18897	−	20.8266i	−0.0894388	−	0.850954i	0.854193	−	0.519956i	$-0.174052\pi$
$600$	0.446638	+	0.496041i	0.0182339	+	0.0202508i
$601$	15.1819	+	6.75942i	0.619283	+	0.275723i	0.692302	−	0.721608i	$-0.256597\pi$
$601$	15.1819	+	6.75942i	0.619283	+	0.275723i	−0.0730189	+	0.997331i	$0.523263\pi$
$602$	1.87593	−	0.835219i	0.0764573	−	0.0340410i
$603$	−14.3661	+	15.9552i	−0.585034	+	0.649746i
$604$	−36.8843	−	26.7980i	−1.50080	−	1.09040i
$605$	−13.9117	−	10.1075i	−0.565592	−	0.410927i
$606$	−53.5793	+	59.5058i	−2.17651	+	2.41726i
$607$	26.9965	−	12.0196i	1.09575	−	0.487861i	0.222404	−	0.974955i	$-0.428610\pi$
$607$	26.9965	−	12.0196i	1.09575	−	0.487861i	0.873350	+	0.487093i	$0.161943\pi$
$608$	4.59347	+	2.04514i	0.186290	+	0.0829415i
$609$	−7.24552	−	8.04696i	−0.293603	−	0.326079i
$610$	1.13263	+	10.7763i	0.0458589	+	0.436318i
$611$	−10.9820	−	2.33430i	−0.444286	−	0.0944358i
$612$	−2.37869	−	7.32085i	−0.0961528	−	0.295928i
$613$	36.2891	−	7.71349i	1.46570	−	0.311545i	0.595149	−	0.803616i	$-0.297093\pi$
$613$	36.2891	−	7.71349i	1.46570	−	0.311545i	0.870555	+	0.492071i	$0.163760\pi$
$614$	23.5453	+	40.7817i	0.950212	+	1.64582i
$615$	10.7442	−	18.6095i	0.433248	−	0.750407i
$616$	−2.95798	+	9.10373i	−0.119180	+	0.366800i
$617$	2.75361	−	26.1988i	0.110856	−	1.05472i	−0.787758	−	0.615985i	$-0.788758\pi$
$617$	2.75361	−	26.1988i	0.110856	−	1.05472i	0.898614	−	0.438740i	$-0.144575\pi$
$618$	−14.0420	+	10.2021i	−0.564854	+	0.410390i
$619$	26.3796			1.06029			0.530144	−	0.847908i	$-0.322138\pi$
$619$	26.3796			1.06029			0.530144	+	0.847908i	$0.322138\pi$
$620$		0			0
$621$	−10.2104			−0.409730
$622$	−15.9144	+	11.5625i	−0.638109	+	0.463613i
$623$	−1.92530	+	18.3180i	−0.0771356	+	0.733897i
$624$	−4.58994	+	14.1264i	−0.183745	+	0.565508i
$625$	13.6503	−	23.6430i	0.546012	−	0.945720i
$626$	29.1103	+	50.4204i	1.16348	+	2.01521i
$627$	5.55400	−	1.18054i	0.221805	−	0.0471462i
$628$	−4.11425	−	12.6623i	−0.164176	−	0.505283i
$629$	−0.571348	−	0.121444i	−0.0227811	−	0.00484228i
$630$	2.94690	+	28.0379i	0.117407	+	1.11706i
$631$	−13.3634	−	14.8415i	−0.531987	−	0.590832i	0.415911	−	0.909405i	$-0.363463\pi$
$631$	−13.3634	−	14.8415i	−0.531987	−	0.590832i	−0.947898	+	0.318574i	$0.896796\pi$
$632$	−4.82371	−	2.14766i	−0.191877	−	0.0854291i
$633$	−12.0812	+	5.37889i	−0.480184	+	0.213792i
$634$	−21.9303	+	24.3561i	−0.870965	+	0.967305i
$635$	−26.9696	−	19.5946i	−1.07026	−	0.777587i
$636$	37.7488	+	27.4261i	1.49684	+	1.08751i
$637$	9.08110	−	10.0856i	0.359806	−	0.399605i
$638$	11.1614	−	4.96938i	0.441885	−	0.196740i
$639$	−1.92461	−	0.856891i	−0.0761364	−	0.0338981i
$640$	−7.56616	−	8.40308i	−0.299079	−	0.332161i
$641$	2.43499	+	23.1673i	0.0961761	+	0.915055i	0.931118	+	0.364717i	$0.118834\pi$
$641$	2.43499	+	23.1673i	0.0961761	+	0.915055i	−0.834942	+	0.550338i	$0.814499\pi$
$642$	−48.1996	−	10.2451i	−1.90229	−	0.404344i
$643$	12.0189	+	36.9903i	0.473978	+	1.45875i	0.847332	+	0.531064i	$0.178208\pi$
$643$	12.0189	+	36.9903i	0.473978	+	1.45875i	−0.373354	+	0.927689i	$0.621792\pi$
$644$	27.6496	−	5.87710i	1.08955	−	0.231590i
$645$	0.677346	+	1.17320i	0.0266705	+	0.0461946i
$646$	−1.36703	+	2.36777i	−0.0537851	+	0.0931585i
$647$	0.689235	−	2.12125i	0.0270966	−	0.0833948i	−0.936594	−	0.350417i	$-0.886040\pi$
$647$	0.689235	−	2.12125i	0.0270966	−	0.0833948i	0.963690	+	0.267022i	$0.0860398\pi$
$648$	0.715252	−	6.80517i	0.0280978	−	0.267332i
$649$	20.1811	−	14.6624i	0.792176	−	0.575550i
$650$	2.21734			0.0869713
$651$		0			0
$652$	40.7894			1.59744
$653$	23.1162	−	16.7949i	0.904607	−	0.657235i	−0.0350384	−	0.999386i	$-0.511155\pi$
$653$	23.1162	−	16.7949i	0.904607	−	0.657235i	0.939645	+	0.342151i	$0.111155\pi$
$654$	−8.38416	+	79.7700i	−0.327847	+	3.11925i
$655$	5.21559	−	16.0519i	0.203790	−	0.627201i
$656$	−7.11497	+	12.3235i	−0.277793	+	0.481151i
$657$	−11.1699	−	19.3468i	−0.435778	−	0.754790i
$658$	40.0624	−	8.51553i	1.56180	−	0.331970i
$659$	1.58766	+	4.88632i	0.0618466	+	0.190344i	0.977206	−	0.212294i	$-0.0680934\pi$
$659$	1.58766	+	4.88632i	0.0618466	+	0.190344i	−0.915359	+	0.402638i	$0.868093\pi$
$660$	−48.2414	−	10.2540i	−1.87779	−	0.399137i
$661$	0.616242	+	5.86315i	0.0239690	+	0.228050i	0.999948	+	0.0101859i	$0.00324233\pi$
$661$	0.616242	+	5.86315i	0.0239690	+	0.228050i	−0.975979	+	0.217864i	$0.930091\pi$
$662$	−17.9473	−	19.9325i	−0.697541	−	0.774698i
$663$	−8.68110	−	3.86507i	−0.337146	−	0.150107i
$664$	2.88284	−	1.28352i	0.111876	−	0.0498103i
$665$	3.57930	−	3.97522i	0.138799	−	0.154152i
$666$	0.725620	+	0.527194i	0.0281172	+	0.0204284i
$667$	−3.73740	−	2.71538i	−0.144713	−	0.105140i
$668$	−3.34893	+	3.71936i	−0.129574	+	0.143906i
$669$	−31.0712	+	13.8338i	−1.20128	+	0.534845i
$670$	−60.5097	−	26.9407i	−2.33770	−	1.04081i
$671$	−6.37935	−	7.08499i	−0.246272	−	0.273513i
$672$	−6.66402	−	63.4039i	−0.257070	−	2.44586i
$673$	26.6675	+	5.66836i	1.02796	+	0.218499i	0.690874	−	0.722975i	$-0.257226\pi$
$673$	26.6675	+	5.66836i	1.02796	+	0.218499i	0.337084	+	0.941474i	$0.390559\pi$
$674$	17.8434	+	54.9163i	0.687301	+	2.11530i
$675$	1.52670	−	0.324510i	0.0587628	−	0.0124904i
$676$	9.91286	+	17.1696i	0.381264	+	0.660368i
$677$	−1.31511	+	2.27784i	−0.0505438	+	0.0875444i	−0.890190	−	0.455589i	$-0.849429\pi$
$677$	−1.31511	+	2.27784i	−0.0505438	+	0.0875444i	0.839647	+	0.543133i	$0.182762\pi$
$678$	24.0263	−	73.9453i	0.922724	−	2.83985i
$679$	2.57880	−	24.5357i	0.0989653	−	0.941592i
$680$	2.45997	−	1.78728i	0.0943357	−	0.0685389i
$681$	−9.93738			−0.380801
$682$		0			0
$683$	29.5859			1.13207			0.566037	−	0.824380i	$-0.308476\pi$
$683$	29.5859			1.13207			0.566037	+	0.824380i	$0.308476\pi$
$684$	1.81437	−	1.31821i	0.0693740	−	0.0504032i
$685$	1.85973	−	17.6942i	0.0710568	−	0.676060i
$686$	1.17114	−	3.60441i	0.0447145	−	0.137617i
$687$	−20.7717	+	35.9777i	−0.792492	+	1.37264i
$688$	−0.448549	−	0.776909i	−0.0171008	−	0.0296194i
$689$	19.4128	−	4.12632i	0.739570	−	0.157200i
$690$	10.7874	+	33.2002i	0.410669	+	1.26391i
$691$	−16.4777	−	3.50244i	−0.626841	−	0.133239i	−0.116471	−	0.993194i	$-0.537158\pi$
$691$	−16.4777	−	3.50244i	−0.626841	−	0.133239i	−0.510370	+	0.859955i	$0.670492\pi$
$692$	1.32056	+	12.5643i	0.0502000	+	0.477621i
$693$	−16.5979	−	18.4338i	−0.630502	−	0.700244i
$694$	−10.0773	−	4.48669i	−0.382528	−	0.170313i
$695$	43.1091	−	19.1934i	1.63522	−	0.728048i
$696$	1.19996	−	1.33269i	0.0454844	−	0.0505156i
$697$	−7.36512	−	5.35108i	−0.278974	−	0.202686i
$698$	6.86966	+	4.99110i	0.260020	+	0.188916i
$699$	−20.3972	+	22.6533i	−0.771491	+	0.856828i
$700$	−3.94749	+	1.75754i	−0.149201	+	0.0664286i
$701$	19.3894	+	8.63271i	0.732327	+	0.326053i	0.738799	−	0.673926i	$-0.235393\pi$
$701$	19.3894	+	8.63271i	0.732327	+	0.326053i	−0.00647177	+	0.999979i	$0.502060\pi$
$702$	−8.81021	−	9.78473i	−0.332520	−	0.369301i
$703$	−0.0177887	−	0.169248i	−0.000670912	−	0.00638330i
$704$	42.5060	+	9.03494i	1.60201	+	0.340517i
$705$	8.34966	+	25.6976i	0.314467	+	0.967828i
$706$	44.1636	−	9.38726i	1.66212	−	0.353294i
$707$	−33.1859	−	57.4796i	−1.24808	−	2.16174i
$708$	14.2979	−	24.7647i	0.537348	−	0.930714i
$709$	−15.8662	+	48.8313i	−0.595869	+	1.83390i	−0.0455172	+	0.998964i	$0.514494\pi$
$709$	−15.8662	+	48.8313i	−0.595869	+	1.83390i	−0.550352	+	0.834933i	$0.685506\pi$
$710$	0.679381	−	6.46388i	0.0254967	−	0.242585i
$711$	11.0698	−	8.04266i	0.415149	−	0.301623i
$712$	−3.05044			−0.114320
$713$		0			0
$714$	34.6656			1.29733
$715$	−16.9712	+	12.3303i	−0.634686	+	0.461127i
$716$	2.90917	−	27.6789i	0.108721	−	1.03441i
$717$	4.49654	−	13.8389i	0.167926	−	0.516824i
$718$	7.33679	−	12.7077i	0.273807	−	0.474247i
$719$	−20.0999	−	34.8141i	−0.749601	−	1.29835i	−0.948014	−	0.318229i	$-0.896912\pi$
$719$	−20.0999	−	34.8141i	−0.749601	−	1.29835i	0.198413	−	0.980119i	$-0.436421\pi$
$720$	12.0472	−	2.56072i	0.448974	−	0.0954324i
$721$	−4.44583	−	13.6829i	−0.165571	−	0.509576i
$722$	37.7308	+	8.01993i	1.40420	+	0.298471i
$723$	−2.57286	−	24.4791i	−0.0956857	−	0.910388i
$724$	−14.8058	−	16.4435i	−0.550253	−	0.611118i
$725$	0.645132	+	0.287231i	0.0239596	+	0.0106675i
$726$	29.6604	−	13.2057i	1.10080	−	0.490109i
$727$	−14.3755	+	15.9656i	−0.533158	+	0.592132i	−0.948201	−	0.317670i	$-0.897100\pi$
$727$	−14.3755	+	15.9656i	−0.533158	+	0.592132i	0.415044	+	0.909802i	$0.363766\pi$
$728$	3.77594	+	2.74338i	0.139946	+	0.101677i
$729$	−1.46222	−	1.06236i	−0.0541562	−	0.0393468i
$730$	46.1164	−	51.2175i	1.70685	−	1.89564i
$731$	0.524311	−	0.233438i	0.0193924	−	0.00863403i
$732$	−9.98416	−	4.44524i	−0.369025	−	0.164301i
$733$	15.0363	+	16.6995i	0.555377	+	0.616808i	0.953818	−	0.300386i	$-0.0971153\pi$
$733$	15.0363	+	16.6995i	0.555377	+	0.616808i	−0.398441	+	0.917194i	$0.630449\pi$
$734$	−3.49102	−	33.2148i	−0.128856	−	1.22598i
$735$	−31.9477	−	6.79070i	−1.17841	−	0.250479i
$736$	−8.40499	−	25.8679i	−0.309812	−	0.953504i
$737$	57.0048	−	12.1167i	2.09980	−	0.446326i
$738$	6.98953	+	12.1062i	0.257288	+	0.445636i
$739$	26.2750	−	45.5097i	0.966542	−	1.67410i	0.261129	−	0.965304i	$-0.415905\pi$
$739$	26.2750	−	45.5097i	0.966542	−	1.67410i	0.705413	−	0.708797i	$-0.250762\pi$
$740$	−0.456777	+	1.40582i	−0.0167915	+	0.0516788i
$741$	0.289395	−	2.75341i	0.0106312	−	0.101149i
$742$	−58.5729	+	42.5557i	−2.15028	+	1.56227i
$743$	17.4032			0.638460			0.319230	−	0.947677i	$-0.396576\pi$
$743$	17.4032			0.638460			0.319230	+	0.947677i	$0.396576\pi$
$744$		0			0
$745$	28.9145			1.05934
$746$	16.4603	−	11.9591i	0.602655	−	0.437854i
$747$	−0.854779	+	8.13268i	−0.0312747	+	0.297559i
$748$	−6.45678	+	19.8719i	−0.236083	+	0.726589i
$749$	20.4224	−	35.3727i	0.746219	−	1.29249i
$750$	23.3530	+	40.4487i	0.852732	+	1.47698i
$751$	21.9535	−	4.66636i	0.801095	−	0.170278i	0.210867	−	0.977515i	$-0.432371\pi$
$751$	21.9535	−	4.66636i	0.801095	−	0.170278i	0.590228	+	0.807237i	$0.299038\pi$
$752$	−5.52927	−	17.0173i	−0.201632	−	0.620559i
$753$	−15.2646	−	3.24459i	−0.556272	−	0.118239i
$754$	−0.622700	−	5.92460i	−0.0226774	−	0.215761i
$755$	31.2279	+	34.6821i	1.13650	+	1.26221i
$756$	23.4403	+	10.4363i	0.852517	+	0.379565i
$757$	13.5139	−	6.01679i	0.491172	−	0.218684i	−0.146178	−	0.989258i	$-0.546697\pi$
$757$	13.5139	−	6.01679i	0.491172	−	0.218684i	0.637350	+	0.770574i	$0.280031\pi$
$758$	−19.1556	+	21.2745i	−0.695764	+	0.772724i
$759$	−24.8487	−	18.0536i	−0.901951	−	0.655306i
$760$	0.716709	+	0.520719i	0.0259978	+	0.0188885i
$761$	13.3165	−	14.7895i	0.482724	−	0.536120i	−0.451753	−	0.892143i	$-0.649201\pi$
$761$	13.3165	−	14.7895i	0.482724	−	0.536120i	0.934477	+	0.356024i	$0.115868\pi$
$762$	57.5005	−	25.6009i	2.08302	−	0.927421i
$763$	−60.7370	−	27.0418i	−2.19883	−	0.978980i
$764$	16.0621	+	17.8387i	0.581105	+	0.645382i
$765$	0.823639	+	7.83641i	0.0297787	+	0.283326i
$766$	20.8887	+	4.44002i	0.754738	+	0.160425i
$767$	−3.75858	−	11.5677i	−0.135714	−	0.417686i
$768$	−21.6046	+	4.59219i	−0.779588	+	0.165706i
$769$	−2.09853	−	3.63477i	−0.0756751	−	0.131073i	0.825705	−	0.564103i	$-0.190778\pi$
$769$	−2.09853	−	3.63477i	−0.0756751	−	0.131073i	−0.901380	+	0.433030i	$0.857445\pi$
$770$	38.2630	−	66.2734i	1.37890	−	2.38833i
$771$	−16.3001	+	50.1665i	−0.587033	+	1.80670i
$772$	0.429318	−	4.08469i	0.0154515	−	0.147011i
$773$	9.61002	−	6.98209i	0.345648	−	0.251128i	−0.401393	−	0.915906i	$-0.631474\pi$
$773$	9.61002	−	6.98209i	0.345648	−	0.251128i	0.747041	+	0.664778i	$0.231474\pi$
$774$	−0.881281			−0.0316770
$775$		0			0
$776$	4.08584			0.146673
$777$	−1.74565	+	1.26829i	−0.0626248	+	0.0454996i
$778$	−5.49404	+	52.2723i	−0.196971	+	1.87405i
$779$	0.819628	−	2.52256i	0.0293662	−	0.0903799i
$780$	−12.0238	+	20.8258i	−0.430519	+	0.745682i
$781$	2.85931	+	4.95246i	0.102314	+	0.177213i
$782$	14.4663	−	3.07490i	0.517313	−	0.109958i
$783$	−1.29582	−	3.98812i	−0.0463088	−	0.142524i
$784$	21.1563	+	4.49690i	0.755581	+	0.160604i
$785$	1.42459	+	13.5541i	0.0508458	+	0.483765i
$786$	21.3233	+	23.6820i	0.760579	+	0.844708i
$787$	−1.81250	−	0.806978i	−0.0646087	−	0.0287657i	0.374178	−	0.927357i	$-0.377925\pi$
$787$	−1.81250	−	0.806978i	−0.0646087	−	0.0287657i	−0.438787	+	0.898591i	$0.644592\pi$
$788$	−13.4041	+	5.96789i	−0.477502	+	0.212597i
$789$	37.6307	−	41.7931i	1.33969	−	1.48787i
$790$	34.1511	+	24.8122i	1.21504	+	0.882780i
$791$	52.1386	+	37.8809i	1.85384	+	1.34689i
$792$	2.74885	−	3.05291i	0.0976762	−	0.108480i
$793$	−4.24669	+	1.89075i	−0.150805	+	0.0671425i
$794$	31.7241	+	14.1245i	1.12584	+	0.501258i
$795$	−31.9597	−	35.4949i	−1.13350	−	1.25887i
$796$	0.222291	+	2.11496i	0.00787889	+	0.0749627i
$797$	−49.2853	−	10.4759i	−1.74577	−	0.371076i	−0.779063	−	0.626946i	$-0.784305\pi$
$797$	−49.2853	−	10.4759i	−1.74577	−	0.371076i	−0.966711	+	0.255870i	$0.917638\pi$
$798$	3.12100	+	9.60544i	0.110482	+	0.340029i
$799$	11.1972	−	2.38004i	0.396128	−	0.0841997i
$800$	2.07889	+	3.60074i	0.0734998	+	0.127305i
$801$	3.95241	−	6.84577i	0.139652	−	0.241884i
$802$	17.6879	−	54.4379i	0.624583	−	1.92227i
$803$	−6.33857	+	60.3075i	−0.223683	+	2.12820i
$804$	54.0481	−	39.2682i	1.90613	−	1.38488i
$805$	−28.9356			−1.01984
$806$		0			0
$807$	44.6701			1.57246
$808$	8.89281	−	6.46100i	0.312848	−	0.227297i
$809$	−1.62776	+	15.4871i	−0.0572290	+	0.544498i	0.927918	+	0.372784i	$0.121597\pi$
$809$	−1.62776	+	15.4871i	−0.0572290	+	0.544498i	−0.985147	+	0.171713i	$0.945070\pi$
$810$	−16.9045	+	52.0268i	−0.593964	+	1.82803i
$811$	−10.3694	+	17.9604i	−0.364119	+	0.630673i	−0.988634	−	0.150340i	$-0.951963\pi$
$811$	−10.3694	+	17.9604i	−0.364119	+	0.630673i	0.624515	+	0.781013i	$0.285297\pi$
$812$	5.80460	+	10.0539i	0.203702	+	0.352822i
$813$	−43.9682	+	9.34572i	−1.54203	+	0.327769i
$814$	−0.752337	−	2.31546i	−0.0263694	−	0.0811567i
$815$	−40.8413	−	8.68108i	−1.43061	−	0.304085i
$816$	−1.58302	−	15.0614i	−0.0554167	−	0.527255i
$817$	0.111888	+	0.124264i	0.00391445	+	0.00434744i
$818$	42.8015	+	19.0565i	1.49652	+	0.666293i
$819$	−11.0491	+	4.91939i	−0.386087	+	0.171897i
$820$	−15.4155	+	17.1207i	−0.538334	+	0.597881i
$821$	15.8525	+	11.5175i	0.553256	+	0.401964i	0.828984	−	0.559272i	$-0.188919\pi$
$821$	15.8525	+	11.5175i	0.553256	+	0.401964i	−0.275729	+	0.961235i	$0.588919\pi$
$822$	27.1768	+	19.7451i	0.947899	+	0.688689i
$823$	−1.40559	+	1.56106i	−0.0489958	+	0.0544153i	−0.767144	−	0.641474i	$-0.778323\pi$
$823$	−1.40559	+	1.56106i	−0.0489958	+	0.0544153i	0.718149	+	0.695890i	$0.244990\pi$
$824$	2.17670	−	0.969129i	0.0758289	−	0.0337612i
$825$	4.28926	+	1.90970i	0.149333	+	0.0664873i
$826$	29.6898	+	32.9738i	1.03304	+	1.14731i
$827$	−0.366387	−	3.48594i	−0.0127405	−	0.121218i	0.986303	−	0.164943i	$-0.0527441\pi$
$827$	−0.366387	−	3.48594i	−0.0127405	−	0.121218i	−0.999044	+	0.0437252i	$0.986077\pi$
$828$	−11.8663	−	2.52226i	−0.412383	−	0.0876548i
$829$	0.645411	+	1.98637i	0.0224161	+	0.0689895i	0.961639	−	0.274319i	$-0.0884524\pi$
$829$	0.645411	+	1.98637i	0.0224161	+	0.0689895i	−0.939223	+	0.343308i	$0.888452\pi$
$830$	−24.6769	+	5.24523i	−0.856547	+	0.182065i
$831$	−5.09098	−	8.81784i	−0.176604	−	0.305888i
$832$	10.5943	−	18.3498i	0.367290	−	0.636166i
$833$	−4.27599	+	13.1601i	−0.148154	+	0.455972i
$834$	−9.31317	+	88.6089i	−0.322489	+	3.06828i
$835$	4.14477	−	3.01135i	0.143436	−	0.104212i
$836$	−6.08759			−0.210544
$837$		0			0
$838$	−12.8284			−0.443151
$839$	8.71583	−	6.33242i	0.300904	−	0.218620i	−0.427080	−	0.904214i	$-0.640458\pi$
$839$	8.71583	−	6.33242i	0.300904	−	0.218620i	0.727984	+	0.685594i	$0.240458\pi$
$840$	1.17411	−	11.1710i	0.0405108	−	0.385435i
$841$	−8.37520	+	25.7762i	−0.288800	+	0.888835i
$842$	−6.79587	+	11.7708i	−0.234201	+	0.405648i
$843$	7.11863	+	12.3298i	0.245178	+	0.424662i
$844$	13.8685	−	2.94783i	0.477372	−	0.101469i
$845$	−6.27132	−	19.3011i	−0.215740	−	0.663979i
$846$	−17.1935	−	3.65460i	−0.591125	−	0.125648i
$847$	2.81306	+	26.7645i	0.0966580	+	0.919640i
$848$	21.1642	+	23.5052i	0.726782	+	0.807173i
$849$	−14.1623	−	6.30546i	−0.486049	−	0.216403i
$850$	−2.06533	+	0.919543i	−0.0708402	+	0.0315401i
$851$	−0.615976	+	0.684111i	−0.0211154	+	0.0234510i
$852$	5.30352	+	3.85323i	0.181695	+	0.132010i
$853$	−26.4147	−	19.1914i	−0.904423	−	0.657102i	0.0351753	−	0.999381i	$-0.488801\pi$
$853$	−26.4147	−	19.1914i	−0.904423	−	0.657102i	−0.939598	+	0.342280i	$0.888801\pi$
$854$	11.3471	−	12.6023i	0.388291	−	0.431241i
$855$	−2.09722	+	0.933744i	−0.0717236	+	0.0319334i
$856$	6.17967	+	2.75136i	0.211217	+	0.0940397i
$857$	−29.2636	−	32.5005i	−0.999626	−	1.11020i	−0.993908	−	0.110214i	$-0.964846\pi$
$857$	−29.2636	−	32.5005i	−0.999626	−	1.11020i	−0.00571842	−	0.999984i	$-0.501820\pi$
$858$	−4.14012	−	39.3906i	−0.141341	−	1.34477i
$859$	−23.8338	−	5.06604i	−0.813200	−	0.172851i	−0.217503	−	0.976060i	$-0.569791\pi$
$859$	−23.8338	−	5.06604i	−0.813200	−	0.172851i	−0.595698	+	0.803209i	$0.703124\pi$
$860$	−0.448815	−	1.38131i	−0.0153045	−	0.0471023i
$861$	−32.8950	+	6.99205i	−1.12106	+	0.238288i
$862$	−24.3140	−	42.1130i	−0.828137	−	1.43438i
$863$	−21.7570	+	37.6842i	−0.740616	+	1.28279i	0.211599	+	0.977357i	$0.432133\pi$
$863$	−21.7570	+	37.6842i	−0.740616	+	1.28279i	−0.952215	+	0.305429i	$0.901200\pi$
$864$	7.62934	−	23.4807i	0.259555	−	0.798829i
$865$	1.35178	−	12.8613i	0.0459617	−	0.437297i
$866$	40.7578	−	29.6123i	1.38501	−	1.00627i
$867$	−26.6808			−0.906129
$868$		0			0
$869$	−37.1415			−1.25994
$870$	−11.5987	+	8.42696i	−0.393233	+	0.285701i
$871$	2.97027	−	28.2603i	0.100644	−	0.957563i
$872$	3.40254	−	10.4719i	0.115224	−	0.354625i
$873$	−5.29396	+	9.16941i	−0.179173	+	0.310338i
$874$	2.15444	+	3.73160i	0.0728751	+	0.126223i
$875$	−37.8683	+	8.04915i	−1.28018	+	0.272111i
$876$	21.4810	+	66.1118i	0.725776	+	2.23371i
$877$	37.4081	+	7.95134i	1.26318	+	0.268498i	0.790350	−	0.612655i	$-0.209899\pi$
$877$	37.4081	+	7.95134i	1.26318	+	0.268498i	0.472832	+	0.881153i	$0.343232\pi$
$878$	−3.14201	−	29.8943i	−0.106038	−	1.00888i
$879$	19.3422	+	21.4817i	0.652395	+	0.724559i
$880$	−30.5416	−	13.5980i	−1.02956	−	0.458388i
$881$	−37.2191	+	16.5710i	−1.25394	+	0.558292i	−0.922797	−	0.385287i	$-0.874102\pi$
$881$	−37.2191	+	16.5710i	−1.25394	+	0.558292i	−0.331148	+	0.943579i	$0.607436\pi$
$882$	14.2174	−	15.7900i	0.478725	−	0.531678i
$883$	26.7914	+	19.4651i	0.901604	+	0.655054i	0.938877	−	0.344252i	$-0.111867\pi$
$883$	26.7914	+	19.4651i	0.901604	+	0.655054i	−0.0372736	+	0.999305i	$0.511867\pi$
$884$	8.24226	+	5.98835i	0.277217	+	0.201410i
$885$	−19.5867	+	21.7532i	−0.658399	+	0.731226i
$886$	−31.3590	+	13.9619i	−1.05353	+	0.469061i
$887$	11.3896	+	5.07100i	0.382427	+	0.170267i	0.588941	−	0.808176i	$-0.299545\pi$
$887$	11.3896	+	5.07100i	0.382427	+	0.170267i	−0.206514	+	0.978444i	$0.566212\pi$
$888$	−0.239116	−	0.265565i	−0.00802420	−	0.00891178i
$889$	5.45348	+	51.8864i	0.182904	+	1.74021i
$890$	23.8541	+	5.07034i	0.799591	+	0.169958i
$891$	−14.8736	−	45.7761i	−0.498283	−	1.53356i
$892$	35.6678	−	7.58142i	1.19425	−	0.253845i
$893$	1.66758	+	2.88834i	0.0558035	+	0.0966545i
$894$	−27.2966	+	47.2791i	−0.912936	+	1.58125i
$895$	−8.80368	+	27.0949i	−0.294274	+	0.905684i
$896$	−1.84978	+	17.5995i	−0.0617969	+	0.587958i
$897$	−12.1160	+	8.80278i	−0.404541	+	0.293916i
$898$	−14.1263			−0.471401
$899$		0			0
$900$	1.85446			0.0618154
$901$	−16.3707	+	11.8940i	−0.545389	+	0.396248i
$902$	3.96635	−	37.7373i	0.132065	−	1.25651i
$903$	0.655156	−	2.01636i	0.0218022	−	0.0671003i
$904$	−5.33666	+	9.24337i	−0.177495	+	0.307430i
$905$	11.3250	+	19.6155i	0.376456	+	0.652041i
$906$	−86.1906	+	18.3204i	−2.86349	+	0.608654i
$907$	5.22278	+	16.0741i	0.173419	+	0.533730i	0.999558	−	0.0297372i	$-0.00946703\pi$
$907$	5.22278	+	16.0741i	0.173419	+	0.533730i	−0.826138	+	0.563467i	$0.809467\pi$
$908$	10.4213	+	2.21511i	0.345842	+	0.0735109i
$909$	2.97746	+	28.3286i	0.0987560	+	0.939600i
$910$	−24.9675	−	27.7292i	−0.827664	−	0.919214i
$911$	49.7605	+	22.1548i	1.64864	+	0.734021i	0.999642	−	0.0267695i	$-0.00852200\pi$
$911$	49.7605	+	22.1548i	1.64864	+	0.734021i	0.648997	+	0.760791i	$0.275189\pi$
$912$	4.03082	−	1.79464i	0.133474	−	0.0594264i
$913$	14.8528	−	16.4957i	0.491556	−	0.545929i
$914$	35.9211	+	26.0982i	1.18816	+	0.863251i
$915$	9.05079	+	6.57578i	0.299210	+	0.217389i
$916$	29.8029	−	33.0994i	0.984714	−	1.09364i
$917$	−24.1308	+	10.7437i	−0.796870	+	0.354790i
$918$	12.2640	+	5.46028i	0.404772	+	0.180216i
$919$	−5.86648	−	6.51539i	−0.193517	−	0.214923i	0.638575	−	0.769559i	$-0.279524\pi$
$919$	−5.86648	−	6.51539i	−0.193517	−	0.214923i	−0.832093	+	0.554636i	$0.812857\pi$
$920$	−0.500915	−	4.76589i	−0.0165147	−	0.157127i
$921$	47.5570	+	10.1085i	1.56706	+	0.333088i
$922$	5.55447	+	17.0949i	0.182927	+	0.562990i
$923$	2.72741	−	0.579728i	0.0897737	−	0.0190820i
$924$	38.5928	+	66.8447i	1.26961	+	2.19903i
$925$	0.0703606	−	0.121868i	0.00231344	−	0.00400700i
$926$	−2.33709	+	7.19283i	−0.0768016	+	0.236371i
$927$	−0.645405	+	6.14062i	−0.0211979	+	0.201684i
$928$	9.03714	−	6.56587i	0.296659	−	0.215535i
$929$	44.2868			1.45300			0.726501	−	0.687165i	$-0.241145\pi$
$929$	44.2868			1.45300			0.726501	+	0.687165i	$0.241145\pi$
$930$		0			0
$931$	−4.03150			−0.132127
$932$	26.4399	−	19.2097i	0.866069	−	0.629236i
$933$	−2.12296	+	20.1986i	−0.0695026	+	0.661273i
$934$	−1.97290	+	6.07196i	−0.0645552	+	0.198681i
$935$	10.6943	−	18.5230i	0.349740	−	0.605767i
$936$	−1.00153	−	1.73471i	−0.0327361	−	0.0567006i
$937$	50.3908	−	10.7109i	1.64620	−	0.349910i	0.710768	−	0.703427i	$-0.248348\pi$
$937$	50.3908	−	10.7109i	1.64620	−	0.349910i	0.935428	+	0.353517i	$0.115014\pi$
$938$	32.0331	+	98.5877i	1.04592	+	3.21900i
$939$	58.7970	+	12.4977i	1.91877	+	0.407847i
$940$	−3.02807	−	28.8101i	−0.0987646	−	0.939682i
$941$	−26.2279	−	29.1291i	−0.855006	−	0.949580i	0.144195	−	0.989549i	$-0.453941\pi$
$941$	−26.2279	−	29.1291i	−0.855006	−	0.949580i	−0.999201	+	0.0399692i	$0.987274\pi$
$942$	−23.5077	−	10.4663i	−0.765921	−	0.341010i
$943$	−13.1072	+	5.83569i	−0.426828	+	0.190036i
$944$	12.9706	−	14.4053i	0.422156	−	0.468852i
$945$	−21.2490	−	15.4383i	−0.691231	−	0.502208i
$946$	1.93531	+	1.40608i	0.0629223	+	0.0457158i
$947$	−38.0845	+	42.2971i	−1.23758	+	1.37447i	−0.335996	+	0.941864i	$0.609073\pi$
$947$	−38.0845	+	42.2971i	−1.23758	+	1.37447i	−0.901583	+	0.432606i	$0.857594\pi$
$948$	−38.8960	+	17.3176i	−1.26328	+	0.562450i
$949$	27.0111	+	12.0261i	0.876817	+	0.390384i
$950$	−0.440739	−	0.489491i	−0.0142995	−	0.0158812i
$951$	3.53707	+	33.6530i	0.114697	+	1.09127i
$952$	−4.65478	−	0.989403i	−0.150862	−	0.0320667i
$953$	4.71987	+	14.5263i	0.152892	+	0.470552i	0.997941	−	0.0641360i	$-0.0204292\pi$
$953$	4.71987	+	14.5263i	0.152892	+	0.470552i	−0.845050	+	0.534688i	$0.820429\pi$
$954$	30.3928	−	6.46019i	0.984003	−	0.209156i
$955$	−12.2859	−	21.2798i	−0.397563	−	0.688599i
$956$	−7.80028	+	13.5105i	−0.252279	+	0.436960i
$957$	3.89804	−	11.9969i	0.126006	−	0.387806i
$958$	3.77098	−	35.8785i	0.121835	−	1.15918i
$959$	−22.5266	+	16.3665i	−0.727421	+	0.528503i
$960$	−50.9928			−1.64579
$961$		0			0
$962$	−1.18709			−0.0382735
$963$	−14.1815	+	10.3035i	−0.456992	+	0.332024i
$964$	−2.75842	+	26.2446i	−0.0888427	+	0.845281i
$965$	−1.29920	+	3.99852i	−0.0418226	+	0.128717i
$966$	27.3165	−	47.3136i	0.878895	−	1.52229i
$967$	5.64979	+	9.78573i	0.181685	+	0.314688i	0.942455	−	0.334334i	$-0.108511\pi$
$967$	5.64979	+	9.78573i	0.181685	+	0.314688i	−0.760769	+	0.649022i	$0.775178\pi$
$968$	−4.35961	+	0.926663i	−0.140123	+	0.0297841i
$969$	0.872299	+	2.68466i	0.0280223	+	0.0862437i
$970$	−31.9508	−	6.79135i	−1.02588	−	0.218057i
$971$	1.65868	+	15.7813i	0.0532296	+	0.506446i	0.988359	+	0.152139i	$0.0486163\pi$
$971$	1.65868	+	15.7813i	0.0532296	+	0.506446i	−0.935129	+	0.354306i	$0.884717\pi$
$972$	−22.9025	−	25.4358i	−0.734599	−	0.815855i
$973$	−67.4669	−	30.0382i	−2.16289	−	0.962981i
$974$	−54.4678	+	24.2506i	−1.74526	+	0.777040i
$975$	1.53186	−	1.70130i	0.0490587	−	0.0544852i
$976$	−5.99357	−	4.35458i	−0.191849	−	0.139387i
$977$	13.3973	+	9.73371i	0.428617	+	0.311409i	0.781096	−	0.624411i	$-0.214661\pi$
$977$	13.3973	+	9.73371i	0.428617	+	0.311409i	−0.352478	+	0.935820i	$0.614661\pi$
$978$	52.7508	−	58.5857i	1.68679	−	1.87337i
$979$	−19.6020	+	8.72737i	−0.626483	+	0.278928i
$980$	31.9897	+	14.2427i	1.02187	+	0.454967i
$981$	19.0924	+	21.2043i	0.609574	+	0.677001i
$982$	−2.12820	−	20.2485i	−0.0679136	−	0.646155i
$983$	21.1767	+	4.50125i	0.675432	+	0.143568i	0.532843	−	0.846214i	$-0.321124\pi$
$983$	21.1767	+	4.50125i	0.675432	+	0.143568i	0.142590	+	0.989782i	$0.454457\pi$
$984$	−1.72110	−	5.29699i	−0.0548666	−	0.168862i
$985$	14.6913	−	3.12273i	0.468103	−	0.0994984i
$986$	3.03697	+	5.26019i	0.0967169	+	0.167519i
$987$	21.1436	−	36.6217i	0.673007	−	1.16568i
$988$	−0.917240	+	2.82297i	−0.0291813	+	0.0898108i
$989$	0.0945475	−	0.899560i	0.00300644	−	0.0286043i
$990$	−26.5701	+	19.3043i	−0.844455	+	0.613532i
$991$	−32.3028			−1.02613			−0.513066	−	0.858349i	$-0.671490\pi$
$991$	−32.3028			−1.02613			−0.513066	+	0.858349i	$0.671490\pi$
$992$		0			0
$993$	−27.6925			−0.878796
$994$	−8.22920	+	5.97887i	−0.261014	+	0.189638i
$995$	0.227546	−	2.16496i	0.00721369	−	0.0686337i
$996$	7.86314	−	24.2002i	0.249153	−	0.766814i
$997$	5.74360	−	9.94821i	0.181902	−	0.315063i	−0.760626	−	0.649190i	$-0.775108\pi$
$997$	5.74360	−	9.94821i	0.181902	−	0.315063i	0.942528	+	0.334127i	$0.108441\pi$
$998$	−11.2392	−	19.4669i	−0.355771	−	0.616213i
$999$	−0.817348	+	0.173733i	−0.0258597	+	0.00549666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.n.338.1		16
31.2	even	5		961.2.g.m.732.1		16
31.3	odd	30		961.2.d.o.531.4		16
31.4	even	5		961.2.g.l.448.2		16
31.5	even	3		961.2.g.m.235.1		16
31.6	odd	6		961.2.d.p.388.1		16
31.7	even	15		961.2.d.n.628.4		16
31.8	even	5		961.2.c.i.521.7		16
31.9	even	15		961.2.c.i.439.7		16
31.10	even	15	inner	961.2.g.n.816.1		16
31.11	odd	30		961.2.g.k.846.2		16
31.12	odd	30		961.2.d.p.374.1		16
31.13	odd	30		31.2.g.a.20.2	yes	16
31.14	even	15		961.2.a.j.1.7		8
31.15	odd	10		961.2.g.k.844.2		16
31.16	even	5		961.2.g.j.844.2		16
31.17	odd	30		961.2.a.i.1.7		8
31.18	even	15		961.2.g.l.547.2		16
31.19	even	15		961.2.d.q.374.1		16
31.20	even	15		961.2.g.j.846.2		16
31.21	odd	30		961.2.g.t.816.1		16
31.22	odd	30		961.2.c.j.439.7		16
31.23	odd	10		961.2.c.j.521.7		16
31.24	odd	30		961.2.d.o.628.4		16
31.25	even	3		961.2.d.q.388.1		16
31.26	odd	6		961.2.g.s.235.1		16
31.27	odd	10		31.2.g.a.14.2	✓	16
31.28	even	15		961.2.d.n.531.4		16
31.29	odd	10		961.2.g.s.732.1		16
31.30	odd	2		961.2.g.t.338.1		16
93.14	odd	30		8649.2.a.be.1.2		8
93.17	even	30		8649.2.a.bf.1.2		8
93.44	even	30		279.2.y.c.82.1		16
93.89	even	10		279.2.y.c.262.1		16
124.27	even	10		496.2.bg.c.417.2		16
124.75	even	30		496.2.bg.c.113.2		16
155.13	even	60		775.2.ck.a.299.3		32
155.27	even	20		775.2.ck.a.324.3		32
155.44	odd	30		775.2.bl.a.51.1		16
155.58	even	20		775.2.ck.a.324.2		32
155.89	odd	10		775.2.bl.a.76.1		16
155.137	even	60		775.2.ck.a.299.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.2	✓	16	31.27	odd	10
31.2.g.a.20.2	yes	16	31.13	odd	30
279.2.y.c.82.1		16	93.44	even	30
279.2.y.c.262.1		16	93.89	even	10
496.2.bg.c.113.2		16	124.75	even	30
496.2.bg.c.417.2		16	124.27	even	10
775.2.bl.a.51.1		16	155.44	odd	30
775.2.bl.a.76.1		16	155.89	odd	10
775.2.ck.a.299.2		32	155.137	even	60
775.2.ck.a.299.3		32	155.13	even	60
775.2.ck.a.324.2		32	155.58	even	20
775.2.ck.a.324.3		32	155.27	even	20
961.2.a.i.1.7		8	31.17	odd	30
961.2.a.j.1.7		8	31.14	even	15
961.2.c.i.439.7		16	31.9	even	15
961.2.c.i.521.7		16	31.8	even	5
961.2.c.j.439.7		16	31.22	odd	30
961.2.c.j.521.7		16	31.23	odd	10
961.2.d.n.531.4		16	31.28	even	15
961.2.d.n.628.4		16	31.7	even	15
961.2.d.o.531.4		16	31.3	odd	30
961.2.d.o.628.4		16	31.24	odd	30
961.2.d.p.374.1		16	31.12	odd	30
961.2.d.p.388.1		16	31.6	odd	6
961.2.d.q.374.1		16	31.19	even	15
961.2.d.q.388.1		16	31.25	even	3
961.2.g.j.844.2		16	31.16	even	5
961.2.g.j.846.2		16	31.20	even	15
961.2.g.k.844.2		16	31.15	odd	10
961.2.g.k.846.2		16	31.11	odd	30
961.2.g.l.448.2		16	31.4	even	5
961.2.g.l.547.2		16	31.18	even	15
961.2.g.m.235.1		16	31.5	even	3
961.2.g.m.732.1		16	31.2	even	5
961.2.g.n.338.1		16	1.1	even	1	trivial
961.2.g.n.816.1		16	31.10	even	15	inner
961.2.g.s.235.1		16	31.26	odd	6
961.2.g.s.732.1		16	31.29	odd	10
961.2.g.t.338.1		16	31.30	odd	2
961.2.g.t.816.1		16	31.21	odd	30
8649.2.a.be.1.2		8	93.14	odd	30
8649.2.a.bf.1.2		8	93.17	even	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.67638 + 1.21796i) q^{2} +(-0.223627 + 2.12767i) q^{3} +(0.708788 - 2.18143i) q^{4} +(-1.17396 + 2.03335i) q^{5} +(-2.21654 - 3.83916i) q^{6} +(3.59424 - 0.763980i) q^{7} +(0.188054 + 0.578772i) q^{8} +(-1.54253 - 0.327876i) q^{9} +(-0.508547 - 4.83851i) q^{10} +(2.86431 + 3.18114i) q^{11} +(4.48286 + 1.99590i) q^{12} +(1.90675 - 0.848940i) q^{13} +(-5.09482 + 5.65838i) q^{14} +(-4.06377 - 2.95251i) q^{15} +(2.69109 + 1.95519i) q^{16} +(-1.42397 + 1.58148i) q^{17} +(2.98522 - 1.32910i) q^{18} +(-0.566412 - 0.252183i) q^{19} +(3.60352 + 4.00211i) q^{20} +(0.821728 + 7.81822i) q^{21} +(-8.67618 - 1.84418i) q^{22} +(1.03640 + 3.18973i) q^{23} +(-1.27349 + 0.270689i) q^{24} +(-0.256344 - 0.444001i) q^{25} +(-2.16247 + 3.74550i) q^{26} +(-0.940760 + 2.89536i) q^{27} +(0.880992 - 8.38208i) q^{28} +(-1.11435 + 0.809625i) q^{29} +10.4085 q^{30} -8.10976 q^{32} +(-7.40895 + 5.38292i) q^{33} +(0.460935 - 4.38551i) q^{34} +(-2.66604 + 8.20524i) q^{35} +(-1.80857 + 3.13253i) q^{36} +(0.137239 + 0.237704i) q^{37} +(1.25667 - 0.267114i) q^{38} +(1.37986 + 4.24679i) q^{39} +(-1.39761 - 0.297072i) q^{40} +(0.447164 + 4.25448i) q^{41} +(-10.8998 - 12.1055i) q^{42} +(-0.246376 - 0.109694i) q^{43} +(8.96960 - 3.99353i) q^{44} +(2.47755 - 2.75160i) q^{45} +(-5.62238 - 4.08489i) q^{46} +(-4.35183 - 3.16179i) q^{47} +(-4.76181 + 5.28853i) q^{48} +(5.94010 - 2.64470i) q^{49} +(0.970507 + 0.432098i) q^{50} +(-3.04643 - 3.38341i) q^{51} +(-0.500418 - 4.76116i) q^{52} +(9.30090 + 1.97697i) q^{53} +(-1.94937 - 5.99954i) q^{54} +(-9.83094 + 2.08963i) q^{55} +(1.11808 + 1.93658i) q^{56} +(0.663228 - 1.14874i) q^{57} +(0.881988 - 2.71448i) q^{58} +(0.609133 - 5.79551i) q^{59} +(-9.32103 + 6.77212i) q^{60} -2.22719 q^{61} -5.79474 q^{63} +(8.21287 - 5.96700i) q^{64} +(-0.512248 + 4.87371i) q^{65} +(5.86404 - 18.0477i) q^{66} +(6.80719 - 11.7904i) q^{67} +(2.44059 + 4.22722i) q^{68} +(-7.01846 + 1.49182i) q^{69} +(-5.52437 - 17.0022i) q^{70} +(1.30673 + 0.277754i) q^{71} +(-0.100315 - 0.954434i) q^{72} +(9.47892 + 10.5274i) q^{73} +(-0.519579 - 0.231331i) q^{74} +(1.00201 - 0.446125i) q^{75} +(-0.951585 + 1.05684i) q^{76} +(12.7253 + 9.24551i) q^{77} +(-7.48561 - 5.43861i) q^{78} +(-5.80579 + 6.44798i) q^{79} +(-7.13482 + 3.17662i) q^{80} +(-10.2720 - 4.57338i) q^{81} +(-5.93141 - 6.58750i) q^{82} +(-0.542030 - 5.15707i) q^{83} +(17.6373 + 3.74892i) q^{84} +(-1.54403 - 4.75202i) q^{85} +(0.546623 - 0.116188i) q^{86} +(-1.47342 - 2.55203i) q^{87} +(-1.30251 + 2.25601i) q^{88} +(-1.54897 + 4.76725i) q^{89} +(-0.801977 + 7.63030i) q^{90} +(6.20475 - 4.50802i) q^{91} +7.69274 q^{92} +11.1463 q^{94} +(1.17772 - 0.855663i) q^{95} +(1.81356 - 17.2549i) q^{96} +(2.07474 - 6.38538i) q^{97} +(-6.73673 + 11.6684i) q^{98} +(-3.37528 - 5.84615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} + 12 q^{7} - 8 q^{8} + 5 q^{9} - 12 q^{10} + 2 q^{11} - 25 q^{12} - 18 q^{13} + 24 q^{14} - 4 q^{15} - 2 q^{16} + q^{17} - 8 q^{18} + 11 q^{19} - 18 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 11 * q^6 + 12 * q^7 - 8 * q^8 + 5 * q^9 - 12 * q^10 + 2 * q^11 - 25 * q^12 - 18 * q^13 + 24 * q^14 - 4 * q^15 - 2 * q^16 + q^17 - 8 * q^18 + 11 * q^19 - 18 * q^20 + 31 * q^21 - 4 * q^22 - 21 * q^23 - 20 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 - 28 * q^34 + 21 * q^35 + q^36 + 8 * q^37 + 3 * q^38 + 2 * q^39 + 29 * q^40 - 3 * q^41 - 39 * q^42 - 8 * q^43 + 41 * q^44 - 20 * q^45 + 16 * q^46 + 4 * q^47 - 49 * q^48 + 12 * q^49 + 48 * q^50 - 2 * q^51 + 6 * q^52 + 69 * q^53 - 39 * q^54 - 23 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 54 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 + 27 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 27 * q^69 + 27 * q^70 + 6 * q^71 + 2 * q^72 + 18 * q^73 + 92 * q^74 - 13 * q^75 - 27 * q^76 + 42 * q^77 + 15 * q^78 + 22 * q^79 + 21 * q^80 - 22 * q^81 - 61 * q^82 + 71 * q^83 + 12 * q^84 + 63 * q^85 + 11 * q^86 + 15 * q^87 + 17 * q^88 - 26 * q^89 - 33 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 58 * q^96 - 37 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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