LMFDB - Embedded newform 261.2.x.a.101.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(2,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			101.6
Character	$\chi$	$=$	261.101
Dual form			261.2.x.a.230.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.697613 + 1.59895i) q^{2} +(-1.67727 - 0.432176i) q^{3} +(-0.709621 - 0.764789i) q^{4} +(-1.15314 - 0.173808i) q^{5} +(1.86111 - 2.38037i) q^{6} +(-1.39616 - 1.29545i) q^{7} +(-1.57532 + 0.551228i) q^{8} +(2.62645 + 1.44975i) q^{9} +(1.08236 - 1.72256i) q^{10} +(1.01917 - 0.877068i) q^{11} +(0.859699 + 1.58944i) q^{12} +(3.40307 - 4.99138i) q^{13} +(3.04533 - 1.32867i) q^{14} +(1.85901 + 0.789883i) q^{15} +(0.373510 - 4.98415i) q^{16} +(-4.84201 - 4.84201i) q^{17} +(-4.15032 + 3.18819i) q^{18} +(2.42324 + 1.52262i) q^{19} +(0.685366 + 1.00525i) q^{20} +(1.78187 + 2.77620i) q^{21} +(0.691398 + 2.24146i) q^{22} +(8.68782 + 3.40972i) q^{23} +(2.88046 - 0.243741i) q^{24} +(-3.47834 - 1.07293i) q^{25} +(5.60693 + 8.92337i) q^{26} +(-3.77871 - 3.56670i) q^{27} +1.98705i q^{28} +(-5.38516 - 0.00307224i) q^{29} +(-2.55985 + 2.42143i) q^{30} +(3.61087 - 2.66494i) q^{31} +(4.75769 + 2.51451i) q^{32} +(-2.08847 + 1.03062i) q^{33} +(11.1200 - 4.36426i) q^{34} +(1.38481 + 1.73650i) q^{35} +(-0.755029 - 3.03745i) q^{36} +(-2.95670 - 8.44975i) q^{37} +(-4.12507 + 2.81243i) q^{38} +(-7.86500 + 6.90115i) q^{39} +(1.91237 - 0.361841i) q^{40} +(-2.89074 - 0.774571i) q^{41} +(-5.68205 + 0.912406i) q^{42} +(-3.41519 + 4.62742i) q^{43} +(-1.39400 - 0.157066i) q^{44} +(-2.77669 - 2.12826i) q^{45} +(-11.5127 + 11.5127i) q^{46} +(-3.53637 - 4.10933i) q^{47} +(-2.78051 + 8.19833i) q^{48} +(-0.252031 - 3.36312i) q^{49} +(4.14208 - 4.81319i) q^{50} +(6.02874 + 10.2139i) q^{51} +(-6.23224 + 0.939359i) q^{52} +(-3.75928 - 2.99793i) q^{53} +(8.33904 - 3.55377i) q^{54} +(-1.32769 + 0.834243i) q^{55} +(2.91349 + 1.27114i) q^{56} +(-3.40638 - 3.60111i) q^{57} +(3.76167 - 8.60845i) q^{58} +(3.33276 - 1.92417i) q^{59} +(-0.715098 - 1.98227i) q^{60} +(-0.808853 + 0.0302651i) q^{61} +(1.74211 + 7.63268i) q^{62} +(-1.78887 - 5.42651i) q^{63} +(0.475788 - 0.379428i) q^{64} +(-4.79176 + 5.16429i) q^{65} +(-0.190955 - 4.05832i) q^{66} +(-7.70125 + 0.577129i) q^{67} +(-0.267126 + 7.13910i) q^{68} +(-13.0982 - 9.47367i) q^{69} +(-3.74263 + 1.00284i) q^{70} +(-2.36294 + 1.13793i) q^{71} +(-4.93664 - 0.836046i) q^{72} +(-1.13062 + 10.0345i) q^{73} +(15.5733 + 1.16706i) q^{74} +(5.37041 + 3.30284i) q^{75} +(-0.555095 - 2.93375i) q^{76} +(-2.55912 - 0.0957557i) q^{77} +(-5.54785 - 17.3901i) q^{78} +(-0.477589 + 2.52412i) q^{79} +(-1.29700 + 5.68251i) q^{80} +(4.79646 + 7.61538i) q^{81} +(3.25512 - 4.08179i) q^{82} +(4.79591 - 15.5480i) q^{83} +(0.858753 - 3.33281i) q^{84} +(4.74194 + 6.42510i) q^{85} +(-5.01651 - 8.68885i) q^{86} +(9.03103 + 2.33249i) q^{87} +(-1.12206 + 1.94346i) q^{88} +(0.181441 - 0.0204435i) q^{89} +(5.34003 - 2.95507i) q^{90} +(-11.2173 + 2.56028i) q^{91} +(-3.55734 - 9.06395i) q^{92} +(-7.20811 + 2.90929i) q^{93} +(9.03762 - 2.78774i) q^{94} +(-2.52969 - 2.17698i) q^{95} +(-6.89320 - 6.27367i) q^{96} +(2.49849 + 4.72738i) q^{97} +(5.55326 + 1.94317i) q^{98} +(3.94833 - 0.826031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.697613	+	1.59895i	−0.493287	+	1.13063i	0.474819	+	0.880084i	$0.342514\pi$
$2$	−0.697613	+	1.59895i	−0.493287	+	1.13063i	−0.968106	+	0.250542i	$0.919391\pi$
$3$	−1.67727	−	0.432176i	−0.968370	−	0.249517i
$3$	−1.67727	−	0.432176i	−0.968370	−	0.249517i
$4$	−0.709621	−	0.764789i	−0.354810	−	0.382395i
$5$	−1.15314	−	0.173808i	−0.515701	−	0.0777293i	−0.113964	−	0.993485i	$-0.536355\pi$
$5$	−1.15314	−	0.173808i	−0.515701	−	0.0777293i	−0.401736	+	0.915755i	$0.631593\pi$
$6$	1.86111	−	2.38037i	0.759795	−	0.971781i
$7$	−1.39616	−	1.29545i	−0.527699	−	0.489633i	0.370737	−	0.928738i	$-0.379105\pi$
$7$	−1.39616	−	1.29545i	−0.527699	−	0.489633i	−0.898436	+	0.439105i	$0.855296\pi$
$8$	−1.57532	+	0.551228i	−0.556959	+	0.194889i
$9$	2.62645	+	1.44975i	0.875483	+	0.483250i
$10$	1.08236	−	1.72256i	0.342271	−	0.544722i
$11$	1.01917	−	0.877068i	0.307292	−	0.264446i	−0.485100	−	0.874459i	$-0.661217\pi$
$11$	1.01917	−	0.877068i	0.307292	−	0.264446i	0.792392	+	0.610013i	$0.208836\pi$
$12$	0.859699	+	1.58944i	0.248174	+	0.458831i
$13$	3.40307	−	4.99138i	0.943841	−	1.38436i	0.0207469	−	0.999785i	$-0.493396\pi$
$13$	3.40307	−	4.99138i	0.943841	−	1.38436i	0.923094	−	0.384575i	$-0.125652\pi$
$14$	3.04533	−	1.32867i	0.813900	−	0.355101i
$15$	1.85901	+	0.789883i	0.479994	+	0.203947i
$16$	0.373510	−	4.98415i	0.0933776	−	1.24604i
$17$	−4.84201	−	4.84201i	−1.17436	−	1.17436i	−0.981159	−	0.193200i	$-0.938113\pi$
$17$	−4.84201	−	4.84201i	−1.17436	−	1.17436i	−0.193200	−	0.981159i	$-0.561887\pi$
$18$	−4.15032	+	3.18819i	−0.978239	+	0.751463i
$19$	2.42324	+	1.52262i	0.555929	+	0.349313i	0.780511	−	0.625142i	$-0.214959\pi$
$19$	2.42324	+	1.52262i	0.555929	+	0.349313i	−0.224582	+	0.974455i	$0.572102\pi$
$20$	0.685366	+	1.00525i	0.153253	+	0.224780i
$21$	1.78187	+	2.77620i	0.388837	+	0.605817i
$22$	0.691398	+	2.24146i	0.147406	+	0.477880i
$23$	8.68782	+	3.40972i	1.81154	+	0.710975i	0.990045	+	0.140753i	$0.0449522\pi$
$23$	8.68782	+	3.40972i	1.81154	+	0.710975i	0.821490	+	0.570223i	$0.193143\pi$
$24$	2.88046	−	0.243741i	0.587971	−	0.0497535i
$25$	−3.47834	−	1.07293i	−0.695668	−	0.214585i
$26$	5.60693	+	8.92337i	1.09961	+	1.75002i
$27$	−3.77871	−	3.56670i	−0.727212	−	0.686412i
$28$			1.98705i			0.375516i
$29$	−5.38516	−	0.00307224i	−1.00000	−	0.000570501i
$29$	−5.38516	−	0.00307224i	−1.00000	−	0.000570501i
$30$	−2.55985	+	2.42143i	−0.467363	+	0.442090i
$31$	3.61087	−	2.66494i	0.648531	−	0.478638i	−0.219195	−	0.975681i	$-0.570343\pi$
$31$	3.61087	−	2.66494i	0.648531	−	0.478638i	0.867726	+	0.497044i	$0.165581\pi$
$32$	4.75769	+	2.51451i	0.841048	+	0.444507i
$33$	−2.08847	+	1.03062i	−0.363556	+	0.179407i
$34$	11.1200	−	4.36426i	1.90706	−	0.748465i
$35$	1.38481	+	1.73650i	0.234076	+	0.293522i
$36$	−0.755029	−	3.03745i	−0.125838	−	0.506242i
$37$	−2.95670	−	8.44975i	−0.486078	−	1.38913i	−0.882175	−	0.470922i	$-0.843921\pi$
$37$	−2.95670	−	8.44975i	−0.486078	−	1.38913i	0.396097	−	0.918209i	$-0.370364\pi$
$38$	−4.12507	+	2.81243i	−0.669175	+	0.456236i
$39$	−7.86500	+	6.90115i	−1.25941	+	1.10507i
$40$	1.91237	−	0.361841i	0.302373	−	0.0572120i
$41$	−2.89074	−	0.774571i	−0.451458	−	0.120968i	0.0259237	−	0.999664i	$-0.491747\pi$
$41$	−2.89074	−	0.774571i	−0.451458	−	0.120968i	−0.477381	+	0.878696i	$0.658414\pi$
$42$	−5.68205	+	0.912406i	−0.876760	+	0.140787i
$43$	−3.41519	+	4.62742i	−0.520812	+	0.705675i	−0.983513	−	0.180840i	$-0.942118\pi$
$43$	−3.41519	+	4.62742i	−0.520812	+	0.705675i	0.462701	+	0.886514i	$0.346880\pi$
$44$	−1.39400	−	0.157066i	−0.210153	−	0.0236786i
$45$	−2.77669	−	2.12826i	−0.413924	−	0.317263i
$46$	−11.5127	+	11.5127i	−1.69745	+	1.69745i
$47$	−3.53637	−	4.10933i	−0.515832	−	0.599408i	0.438287	−	0.898835i	$-0.355585\pi$
$47$	−3.53637	−	4.10933i	−0.515832	−	0.599408i	−0.954119	+	0.299427i	$0.903204\pi$
$48$	−2.78051	+	8.19833i	−0.401332	+	1.18333i
$49$	−0.252031	−	3.36312i	−0.0360044	−	0.480445i
$50$	4.14208	−	4.81319i	0.585779	−	0.680688i
$51$	6.02874	+	10.2139i	0.844192	+	1.43024i
$52$	−6.23224	+	0.939359i	−0.864256	+	0.130266i
$53$	−3.75928	−	2.99793i	−0.516377	−	0.411797i	0.330323	−	0.943868i	$-0.392842\pi$
$53$	−3.75928	−	2.99793i	−0.516377	−	0.411797i	−0.846700	+	0.532071i	$0.821414\pi$
$54$	8.33904	−	3.55377i	1.13480	−	0.483607i
$55$	−1.32769	+	0.834243i	−0.179026	+	0.112489i
$56$	2.91349	+	1.27114i	0.389331	+	0.169863i
$57$	−3.40638	−	3.60111i	−0.451186	−	0.476978i
$58$	3.76167	−	8.60845i	0.493932	−	1.13034i
$59$	3.33276	−	1.92417i	0.433888	−	0.250505i	−0.267114	−	0.963665i	$-0.586070\pi$
$59$	3.33276	−	1.92417i	0.433888	−	0.250505i	0.701002	+	0.713160i	$0.252737\pi$
$60$	−0.715098	−	1.98227i	−0.0923188	−	0.255910i
$61$	−0.808853	+	0.0302651i	−0.103563	+	0.00387505i	−0.0891225	−	0.996021i	$-0.528406\pi$
$61$	−0.808853	+	0.0302651i	−0.103563	+	0.00387505i	−0.0144405	+	0.999896i	$0.504597\pi$
$62$	1.74211	+	7.63268i	0.221248	+	0.969352i
$63$	−1.78887	−	5.42651i	−0.225376	−	0.683676i
$64$	0.475788	−	0.379428i	0.0594735	−	0.0474285i
$65$	−4.79176	+	5.16429i	−0.594345	+	0.640551i
$66$	−0.190955	−	4.05832i	−0.0235049	−	0.499545i
$67$	−7.70125	+	0.577129i	−0.940857	+	0.0705075i	−0.536321	−	0.844014i	$-0.680186\pi$
$67$	−7.70125	+	0.577129i	−0.940857	+	0.0705075i	−0.404536	+	0.914522i	$0.632567\pi$
$68$	−0.267126	+	7.13910i	−0.0323938	+	0.865743i
$69$	−13.0982	−	9.47367i	−1.57684	−	1.14050i
$70$	−3.74263	+	1.00284i	−0.447330	+	0.119862i
$71$	−2.36294	+	1.13793i	−0.280429	+	0.135048i	−0.568812	−	0.822468i	$-0.692597\pi$
$71$	−2.36294	+	1.13793i	−0.280429	+	0.135048i	0.288383	+	0.957515i	$0.406882\pi$
$72$	−4.93664	−	0.836046i	−0.581788	−	0.0985289i
$73$	−1.13062	+	10.0345i	−0.132329	+	1.17445i	0.735479	+	0.677548i	$0.236957\pi$
$73$	−1.13062	+	10.0345i	−0.132329	+	1.17445i	−0.867807	+	0.496901i	$0.834471\pi$
$74$	15.5733	+	1.16706i	1.81036	+	0.135668i
$75$	5.37041	+	3.30284i	0.620121	+	0.381379i
$76$	−0.555095	−	2.93375i	−0.0636738	−	0.336524i
$77$	−2.55912	−	0.0957557i	−0.291639	−	0.0109124i
$78$	−5.54785	−	17.3901i	−0.628170	−	1.96904i
$79$	−0.477589	+	2.52412i	−0.0537329	+	0.283985i	−0.999119	−	0.0419675i	$-0.986637\pi$
$79$	−0.477589	+	2.52412i	−0.0537329	+	0.283985i	0.945386	+	0.325953i	$0.105685\pi$
$80$	−1.29700	+	5.68251i	−0.145009	+	0.635324i
$81$	4.79646	+	7.61538i	0.532940	+	0.846153i
$82$	3.25512	−	4.08179i	0.359467	−	0.450758i
$83$	4.79591	−	15.5480i	0.526420	−	1.70661i	−0.166894	−	0.985975i	$-0.553374\pi$
$83$	4.79591	−	15.5480i	0.526420	−	1.70661i	0.693314	−	0.720636i	$-0.256150\pi$
$84$	0.858753	−	3.33281i	0.0936977	−	0.363639i
$85$	4.74194	+	6.42510i	0.514336	+	0.696900i
$86$	−5.01651	−	8.68885i	−0.540944	−	0.936943i
$87$	9.03103	+	2.33249i	0.968228	+	0.250069i
$88$	−1.12206	+	1.94346i	−0.119612	+	0.207173i
$89$	0.181441	−	0.0204435i	0.0192327	−	0.00216701i	−0.102343	−	0.994749i	$-0.532634\pi$
$89$	0.181441	−	0.0204435i	0.0192327	−	0.00216701i	0.121576	+	0.992582i	$0.461205\pi$
$90$	5.34003	−	2.95507i	0.562889	−	0.311492i
$91$	−11.2173	+	2.56028i	−1.17589	+	0.268390i
$92$	−3.55734	−	9.06395i	−0.370878	−	0.944982i
$93$	−7.20811	+	2.90929i	−0.747446	+	0.301679i
$94$	9.03762	−	2.78774i	0.932159	−	0.287533i
$95$	−2.52969	−	2.17698i	−0.259541	−	0.223353i
$96$	−6.89320	−	6.27367i	−0.703534	−	0.640303i
$97$	2.49849	+	4.72738i	0.253683	+	0.479993i	0.977760	−	0.209727i	$-0.0672576\pi$
$97$	2.49849	+	4.72738i	0.253683	+	0.479993i	−0.724076	+	0.689720i	$0.757734\pi$
$98$	5.55326	+	1.94317i	0.560964	+	0.196290i
$99$	3.94833	−	0.826031i	0.396822	−	0.0830192i
$100$	1.64774	+	3.42156i	0.164774	+	0.342156i
$101$	2.68488	+	1.98153i	0.267156	+	0.197170i	0.719158	−	0.694847i	$-0.244528\pi$
$101$	2.68488	+	1.98153i	0.267156	+	0.197170i	−0.452002	+	0.892017i	$0.649290\pi$
$102$	−20.5373	+	2.51425i	−2.03349	+	0.248948i
$103$	8.19594	+	5.58790i	0.807570	+	0.550592i	0.895254	−	0.445556i	$-0.146994\pi$
$103$	8.19594	+	5.58790i	0.807570	+	0.550592i	−0.0876837	+	0.996148i	$0.527946\pi$
$104$	−2.60953	+	9.73888i	−0.255885	+	0.954976i
$105$	−1.57223	−	3.51106i	−0.153434	−	0.342644i
$106$	7.41605	−	3.91950i	0.720310	−	0.380695i
$107$	0.524076	−	1.08825i	0.0506643	−	0.105206i	−0.874100	−	0.485746i	$-0.838548\pi$
$107$	0.524076	−	1.08825i	0.0506643	−	0.105206i	0.924764	+	0.380541i	$0.124262\pi$
$108$	−0.0463277	+	5.42092i	−0.00445789	+	0.521628i
$109$	10.0878	+	2.30248i	0.966238	+	0.220538i	0.676397	−	0.736537i	$-0.263540\pi$
$109$	10.0878	+	2.30248i	0.966238	+	0.220538i	0.289841	+	0.957075i	$0.406398\pi$
$110$	−0.407696	−	2.70489i	−0.0388723	−	0.257901i
$111$	1.30739	+	15.4503i	0.124092	+	1.46648i
$112$	−6.97819	+	6.47481i	−0.659377	+	0.611812i
$113$	9.33475	−	17.6622i	0.878140	−	1.66152i	0.136586	−	0.990628i	$-0.456387\pi$
$113$	9.33475	−	17.6622i	0.878140	−	1.66152i	0.741554	−	0.670893i	$-0.234089\pi$
$114$	8.13431	−	2.93443i	0.761848	−	0.274835i
$115$	−9.42565	−	5.44190i	−0.878946	−	0.507460i
$116$	3.81907	+	4.12069i	0.354592	+	0.382597i
$117$	16.1742	−	8.17601i	1.49531	−	0.755872i
$118$	0.751667	+	6.67123i	0.0691965	+	0.614136i
$119$	0.487653	+	13.0328i	0.0447031	+	1.19471i
$120$	−3.36394	−	0.219579i	−0.307084	−	0.0200447i
$121$	−1.37000	+	9.08937i	−0.124546	+	0.826307i
$122$	0.515874	−	1.31443i	0.0467051	−	0.119003i
$123$	4.51379	+	2.54847i	0.406995	+	0.229788i
$124$	−4.60046	−	0.870455i	−0.413134	−	0.0781691i
$125$	9.07793	+	4.37170i	0.811955	+	0.391017i
$126$	9.92464	+	0.925299i	0.884157	+	0.0824322i
$127$	−2.99995	+	8.57335i	−0.266202	+	0.760762i	0.730743	+	0.682653i	$0.239174\pi$
$127$	−2.99995	+	8.57335i	−0.266202	+	0.760762i	−0.996945	+	0.0781090i	$0.975112\pi$
$128$	3.06033	+	11.4213i	0.270498	+	1.00951i
$129$	7.72804	−	6.28545i	0.680416	−	0.553403i
$130$	−4.91463	−	11.2644i	−0.431041	−	0.987957i
$131$	−0.491715	−	1.12702i	−0.0429613	−	0.0984684i	0.893758	−	0.448549i	$-0.148059\pi$
$131$	−0.491715	−	1.12702i	−0.0429613	−	0.0984684i	−0.936720	+	0.350080i	$0.886154\pi$
$132$	2.27023	+	0.865893i	0.197598	+	0.0753663i
$133$	−1.41075	−	5.26500i	−0.122328	−	0.456534i
$134$	4.44969	−	12.7165i	0.384395	−	1.09854i
$135$	3.73746	+	4.76968i	0.321669	+	0.410509i
$136$	10.2968	+	4.95866i	0.882940	+	0.425201i
$137$	−2.85865	−	0.540885i	−0.244231	−	0.0462110i	0.0623548	−	0.998054i	$-0.480139\pi$
$137$	−2.85865	−	0.540885i	−0.244231	−	0.0462110i	−0.306586	+	0.951843i	$0.599187\pi$
$138$	24.2854	−	14.3343i	2.06731	−	1.22022i
$139$	4.85556	−	12.3718i	0.411843	−	1.04936i	−0.562998	−	0.826458i	$-0.690352\pi$
$139$	4.85556	−	12.3718i	0.411843	−	1.04936i	0.974841	−	0.222900i	$-0.0715525\pi$
$140$	0.345365	−	2.29134i	0.0291886	−	0.193654i
$141$	4.15548	+	8.42078i	0.349954	+	0.709158i
$142$	−0.171074	−	4.57205i	−0.0143562	−	0.383678i
$143$	−0.909473	−	8.07180i	−0.0760539	−	0.674997i
$144$	8.20677	−	12.5491i	0.683898	−	1.04576i
$145$	6.20932	+	0.939528i	0.515656	+	0.0780235i
$146$	−15.2559	−	8.80799i	−1.26259	−	0.728955i
$147$	−1.03074	+	5.74977i	−0.0850136	+	0.474233i
$148$	−4.36415	+	8.25737i	−0.358731	+	0.678751i
$149$	−10.1009	+	9.37224i	−0.827496	+	0.767804i	−0.975223	−	0.221224i	$-0.928995\pi$
$149$	−10.1009	+	9.37224i	−0.827496	+	0.767804i	0.147727	+	0.989028i	$0.452804\pi$
$150$	−9.02753	+	6.28289i	−0.737094	+	0.512996i
$151$	2.38797	+	15.8432i	0.194330	+	1.28930i	0.846974	+	0.531634i	$0.178422\pi$
$151$	2.38797	+	15.8432i	0.194330	+	1.28930i	−0.652644	+	0.757665i	$0.726340\pi$
$152$	−4.65668	−	1.06286i	−0.377707	−	0.0862092i
$153$	−5.69759	−	19.7370i	−0.460622	−	1.59564i
$154$	1.93839	−	4.02510i	0.156200	−	0.324352i
$155$	−4.62703	+	2.44546i	−0.371652	+	0.196424i
$156$	10.8591	+	1.11787i	0.869423	+	0.0895011i
$157$	−1.62668	+	6.07085i	−0.129823	+	0.484507i	−0.999966	−	0.00829351i	$-0.997360\pi$
$157$	−1.62668	+	6.07085i	−0.129823	+	0.484507i	0.870142	+	0.492800i	$0.164027\pi$
$158$	−3.70276	−	2.52450i	−0.294575	−	0.200838i
$159$	5.00968	+	6.65299i	0.397294	+	0.527617i
$160$	−5.04924	−	3.72651i	−0.399178	−	0.294607i
$161$	−7.71248	−	16.0151i	−0.607829	−	1.26217i
$162$	−15.5227	+	2.35669i	−1.21958	+	0.185159i
$163$	0.545549	+	0.190896i	0.0427307	+	0.0149521i	0.351560	−	0.936165i	$-0.385651\pi$
$163$	0.545549	+	0.190896i	0.0427307	+	0.0149521i	−0.308829	+	0.951118i	$0.599937\pi$
$164$	1.45894	+	2.76046i	0.113924	+	0.215555i
$165$	2.58743	−	0.825453i	0.201431	−	0.0642614i
$166$	21.5147	+	18.5149i	1.66986	+	1.43703i
$167$	−14.1172	+	4.35457i	−1.09242	+	0.336967i	−0.788065	−	0.615592i	$-0.788917\pi$
$167$	−14.1172	+	4.35457i	−1.09242	+	0.336967i	−0.304355	+	0.952559i	$0.598441\pi$
$168$	−4.33734	−	3.39118i	−0.334633	−	0.261635i
$169$	−8.58359	−	21.8706i	−0.660276	−	1.68236i
$170$	−13.5814	+	3.09987i	−1.04165	+	0.237749i
$171$	4.15709	+	7.51217i	0.317901	+	0.574470i
$172$	5.96249	−	0.671811i	0.454635	−	0.0512251i
$173$	6.71730	−	11.6347i	0.510707	−	0.884570i	−0.489216	−	0.872162i	$-0.662717\pi$
$173$	6.71730	−	11.6347i	0.510707	−	0.884570i	0.999923	−	0.0124075i	$-0.00394952\pi$
$174$	−10.0297	+	12.8130i	−0.760349	+	0.971348i
$175$	3.46640	+	6.00398i	0.262035	+	0.453859i
$176$	−3.99077	−	5.40730i	−0.300815	−	0.407590i
$177$	−6.42150	+	1.78701i	−0.482670	+	0.134320i
$178$	−0.0938877	+	0.304377i	−0.00703718	+	0.0228140i
$179$	6.17129	−	7.73855i	0.461264	−	0.578407i	−0.495744	−	0.868469i	$-0.665105\pi$
$179$	6.17129	−	7.73855i	0.461264	−	0.578407i	0.957008	+	0.290062i	$0.0936760\pi$
$180$	0.342722	+	3.63384i	0.0255450	+	0.270850i
$181$	4.42306	−	19.3787i	0.328764	−	1.44041i	−0.492726	−	0.870185i	$-0.663999\pi$
$181$	4.42306	−	19.3787i	0.328764	−	1.44041i	0.821489	−	0.570224i	$-0.193143\pi$
$182$	3.73160	−	19.7220i	0.276604	−	1.46189i
$183$	1.36974	+	0.298804i	0.101254	+	0.0220882i
$184$	−15.5656	−	0.582424i	−1.14751	−	0.0429369i
$185$	1.94085	+	10.2577i	0.142694	+	0.754158i
$186$	0.376679	−	13.5549i	0.0276194	−	0.993897i
$187$	−9.18161	−	0.688067i	−0.671426	−	0.0503164i
$188$	−0.633294	+	5.62064i	−0.0461877	+	0.409927i
$189$	0.655204	+	9.87481i	0.0476591	+	0.718287i
$190$	5.24562	−	2.52616i	0.380557	−	0.183267i
$191$	−5.75297	+	1.54150i	−0.416270	+	0.111539i	−0.460874	−	0.887465i	$-0.652464\pi$
$191$	−5.75297	+	1.54150i	−0.416270	+	0.111539i	0.0446039	+	0.999005i	$0.485797\pi$
$192$	−0.962003	+	0.430778i	−0.0694266	+	0.0310887i
$193$	−0.422653	+	11.2956i	−0.0304232	+	0.813078i	0.897656	+	0.440696i	$0.145268\pi$
$193$	−0.422653	+	11.2956i	−0.0304232	+	0.813078i	−0.928080	+	0.372382i	$0.878541\pi$
$194$	−9.30181	+	0.697074i	−0.667831	+	0.0500470i
$195$	10.2689	−	6.59101i	0.735374	−	0.471992i
$196$	−2.39323	+	2.57929i	−0.170945	+	0.184235i
$197$	7.08406	−	5.64935i	0.504718	−	0.402499i	−0.337758	−	0.941233i	$-0.609669\pi$
$197$	7.08406	−	5.64935i	0.504718	−	0.402499i	0.842476	+	0.538734i	$0.181097\pi$
$198$	−1.43363	+	6.88942i	−0.101884	+	0.489610i
$199$	−1.75876	−	7.70562i	−0.124675	−	0.546237i	−0.998228	−	0.0595075i	$-0.981047\pi$
$199$	−1.75876	−	7.70562i	−0.124675	−	0.546237i	0.873553	−	0.486729i	$-0.161810\pi$
$200$	6.07092	−	0.227158i	0.429279	−	0.0160625i
$201$	13.1665	+	2.36030i	0.928691	+	0.166482i
$202$	−5.04138	+	2.91064i	−0.354710	+	0.204792i
$203$	7.51458	+	6.98049i	0.527420	+	0.489934i
$204$	3.53339	−	11.8587i	0.247387	−	0.830278i
$205$	3.19880	+	1.39562i	0.223414	+	0.0974746i
$206$	−14.6524	+	9.20668i	−1.02088	+	0.641460i
$207$	17.8749	+	21.5506i	1.24239	+	1.49787i
$208$	−23.6067	−	18.8257i	−1.63683	−	1.30533i
$209$	3.80514	−	0.573532i	0.263207	−	0.0396721i
$210$	6.71080	−	0.0645465i	0.463089	−	0.00445413i
$211$	13.9472	−	16.2069i	0.960164	−	1.11573i	−0.0330525	−	0.999454i	$-0.510523\pi$
$211$	13.9472	−	16.2069i	0.960164	−	1.11573i	0.993217	−	0.116278i	$-0.0370962\pi$
$212$	0.374881	+	5.00245i	0.0257470	+	0.343569i
$213$	4.45506	−	0.887409i	0.305256	−	0.0608043i
$214$	1.37446	+	1.59715i	0.0939560	+	0.109179i
$215$	4.74248	−	4.74248i	0.323434	−	0.323434i
$216$	7.91874	+	3.53577i	0.538802	+	0.240578i
$217$	−8.49365	−	0.957004i	−0.576586	−	0.0649657i
$218$	−10.7189	+	14.5237i	−0.725978	+	0.983666i
$219$	6.23301	−	16.3419i	0.421188	−	1.10428i
$220$	1.58018	+	0.423407i	0.106536	+	0.0285461i
$221$	−40.6460	+	7.69063i	−2.73414	+	0.517328i
$222$	−25.6163	−	8.68789i	−1.71925	−	0.583093i
$223$	−11.7675	+	8.02295i	−0.788011	+	0.537257i	−0.889150	−	0.457616i	$-0.848704\pi$
$223$	−11.7675	+	8.02295i	−0.788011	+	0.537257i	0.101139	+	0.994872i	$0.467751\pi$
$224$	−3.38508	−	9.67400i	−0.226175	−	0.646372i
$225$	−7.58020	−	7.86070i	−0.505347	−	0.524047i
$226$	21.7289	+	27.2472i	1.44538	+	1.81245i
$227$	7.18928	−	2.82159i	0.477169	−	0.187275i	−0.114553	−	0.993417i	$-0.536543\pi$
$227$	7.18928	−	2.82159i	0.477169	−	0.187275i	0.591722	+	0.806142i	$0.298448\pi$
$228$	−0.336853	+	5.16058i	−0.0223086	+	0.341768i
$229$	−13.0603	−	6.90259i	−0.863051	−	0.456136i	−0.0236959	−	0.999719i	$-0.507543\pi$
$229$	−13.0603	−	6.90259i	−0.863051	−	0.456136i	−0.839355	+	0.543583i	$0.817067\pi$
$230$	15.2768	−	11.2748i	1.00732	−	0.743436i
$231$	4.25095	+	1.26660i	0.279692	+	0.0833362i
$232$	8.48505	−	2.96361i	0.557071	−	0.194571i
$233$			5.70123i			0.373500i	0.982407	+	0.186750i	$0.0597954\pi$
$233$			5.70123i			0.373500i	−0.982407	+	0.186750i	$0.940205\pi$
$234$	1.78965	+	31.5654i	0.116993	+	2.06350i
$235$	3.36370	+	5.35329i	0.219423	+	0.349210i
$236$	−3.83658	−	1.18343i	−0.249740	−	0.0770345i
$237$	1.89191	−	4.02721i	0.122893	−	0.261596i
$238$	−21.1789	−	8.31212i	−1.37283	−	0.538795i
$239$	1.41674	+	4.59295i	0.0916411	+	0.297093i	0.989777	−	0.142625i	$-0.0455544\pi$
$239$	1.41674	+	4.59295i	0.0916411	+	0.297093i	−0.898136	+	0.439718i	$0.855078\pi$
$240$	4.63125	−	8.97056i	0.298946	−	0.579047i
$241$	−2.54259	−	3.72930i	−0.163783	−	0.240225i	0.735570	−	0.677448i	$-0.236914\pi$
$241$	−2.54259	−	3.72930i	−0.163783	−	0.240225i	−0.899353	+	0.437223i	$0.855962\pi$
$242$	−13.5777	−	8.53143i	−0.872807	−	0.548421i
$243$	−4.75375	−	14.8459i	−0.304953	−	0.952367i
$244$	0.597125	+	0.597125i	0.0382270	+	0.0382270i
$245$	−0.293910	+	3.92195i	−0.0187772	+	0.250564i
$246$	−7.22375	+	5.43946i	−0.460569	+	0.346807i
$247$	15.8464	−	6.91372i	1.00828	−	0.439910i
$248$	−4.21928	+	6.18854i	−0.267924	+	0.392973i
$249$	−14.7635	+	24.0054i	−0.935598	+	1.52128i
$250$	−13.3230	+	11.4654i	−0.842621	+	0.725134i
$251$	1.65637	−	2.63611i	0.104549	−	0.166389i	−0.790352	−	0.612652i	$-0.790103\pi$
$251$	1.65637	−	2.63611i	0.104549	−	0.166389i	0.894902	+	0.446263i	$0.147245\pi$
$252$	−2.88072	+	5.21887i	−0.181468	+	0.328758i
$253$	11.8449	−	4.14472i	0.744685	−	0.260576i
$254$	−11.6155	−	10.7776i	−0.728823	−	0.676249i
$255$	−5.17672	−	12.8260i	−0.324179	−	0.803193i
$256$	−19.1935	−	2.89295i	−1.19959	−	0.180810i
$257$	3.46653	+	3.73604i	0.216236	+	0.233047i	0.831850	−	0.555001i	$-0.187282\pi$
$257$	3.46653	+	3.73604i	0.216236	+	0.233047i	−0.615613	+	0.788048i	$0.711092\pi$
$258$	4.65891	+	16.7415i	0.290051	+	1.04228i
$259$	−6.81819	+	15.6275i	−0.423662	+	0.971044i
$260$	7.34992			0.455823
$261$	−14.1394	−	7.81520i	−0.875207	−	0.483749i
$262$	2.14508			0.132523
$263$	−8.42590	+	19.3124i	−0.519563	+	1.19085i	0.437036	+	0.899444i	$0.356028\pi$
$263$	−8.42590	+	19.3124i	−0.519563	+	1.19085i	−0.956599	+	0.291407i	$0.905876\pi$
$264$	2.72190	−	2.77477i	0.167522	−	0.170775i
$265$	3.81392	+	4.11043i	0.234287	+	0.252501i
$266$	9.40262	+	1.41722i	0.576512	+	0.0868952i
$267$	−0.313161	−	0.0441253i	−0.0191651	−	0.00270043i
$268$	5.90634	+	5.48029i	0.360787	+	0.334762i
$269$	11.9573	−	4.18404i	0.729049	−	0.255105i	0.0598697	−	0.998206i	$-0.480931\pi$
$269$	11.9573	−	4.18404i	0.729049	−	0.255105i	0.669179	+	0.743101i	$0.266646\pi$
$270$	−10.2338	+	2.64861i	−0.622808	+	0.161189i
$271$	−10.5192	+	16.7412i	−0.638996	+	1.01696i	0.357548	+	0.933895i	$0.383613\pi$
$271$	−10.5192	+	16.7412i	−0.638996	+	1.01696i	−0.996544	+	0.0830620i	$0.973530\pi$
$272$	−25.9418	+	22.3248i	−1.57295	+	1.35364i
$273$	19.9209	+	0.553583i	1.20567	+	0.0335044i
$274$	2.85908	−	4.19350i	0.172723	−	0.253338i
$275$	−4.48605	+	1.95724i	−0.270519	+	0.118026i
$276$	2.04938	+	16.7401i	0.123358	+	1.00763i
$277$	2.16019	−	28.8257i	0.129793	−	1.73197i	−0.429559	−	0.903039i	$-0.641331\pi$
$277$	2.16019	−	28.8257i	0.129793	−	1.73197i	0.559352	−	0.828930i	$-0.311050\pi$
$278$	16.3945	+	16.3945i	0.983275	+	0.983275i
$279$	13.3473	−	1.76448i	0.799079	−	0.105637i
$280$	−3.13873	−	1.97219i	−0.187575	−	0.117861i
$281$	−4.35021	−	6.38058i	−0.259512	−	0.380634i	0.674265	−	0.738489i	$-0.264460\pi$
$281$	−4.35021	−	6.38058i	−0.259512	−	0.380634i	−0.933777	+	0.357855i	$0.883508\pi$
$282$	−16.3633	+	0.769935i	−0.974420	+	0.0458490i
$283$	4.87996	+	15.8204i	0.290084	+	0.940428i	0.976918	+	0.213614i	$0.0685235\pi$
$283$	4.87996	+	15.8204i	0.290084	+	0.940428i	−0.686835	+	0.726814i	$0.741000\pi$
$284$	2.54707	+	0.999650i	0.151141	+	0.0593183i
$285$	3.30213	+	4.74464i	0.195601	+	0.281048i
$286$	13.5408	+	4.17679i	0.800686	+	0.246979i
$287$	3.03252	+	4.82623i	0.179004	+	0.284883i
$288$	8.85041	+	13.5017i	0.521515	+	0.795594i
$289$			29.8901i			1.75824i
$290$	−5.83396	+	9.27295i	−0.342582	+	0.544526i
$291$	−2.14758	−	9.00886i	−0.125893	−	0.528109i
$292$	8.47658	−	6.25600i	0.496054	−	0.366105i
$293$	−1.96342	−	1.03770i	−0.114704	−	0.0606230i	0.408932	−	0.912565i	$-0.365901\pi$
$293$	−1.96342	−	1.03770i	−0.114704	−	0.0606230i	−0.523637	+	0.851942i	$0.675425\pi$
$294$	−8.47451	−	5.65920i	−0.494244	−	0.330051i
$295$	−4.17758	+	1.63958i	−0.243228	+	0.0954599i
$296$	9.31548	+	11.6812i	0.541451	+	0.678959i
$297$	−6.97939	−	0.320900i	−0.404986	−	0.0186205i
$298$	−7.93921	−	22.6890i	−0.459906	−	1.31434i
$299$	46.5844	−	31.7607i	2.69405	−	1.83677i
$300$	−1.28498	−	6.45099i	−0.0741883	−	0.372448i
$301$	10.7627	−	2.03642i	0.620354	−	0.117377i
$302$	−26.9983	−	7.23416i	−1.55357	−	0.416279i
$303$	−3.64689	−	4.48390i	−0.209509	−	0.257594i
$304$	8.49408	−	11.5091i	0.487169	−	0.660090i
$305$	0.937982	+	0.105685i	0.0537087	+	0.00605152i
$306$	35.5331	+	4.65864i	2.03129	+	0.266317i
$307$	−2.80044	+	2.80044i	−0.159830	+	0.159830i	−0.782491	−	0.622662i	$-0.786051\pi$
$307$	−2.80044	+	2.80044i	−0.159830	+	0.159830i	0.622662	+	0.782491i	$0.286051\pi$
$308$	1.74277	+	2.02514i	0.0993038	+	0.115393i
$309$	−11.3318	−	12.9145i	−0.644645	−	0.734680i
$310$	−0.682277	−	9.10436i	−0.0387507	−	0.517093i
$311$	5.83841	−	6.78436i	0.331066	−	0.384706i	−0.567626	−	0.823287i	$-0.692138\pi$
$311$	5.83841	−	6.78436i	0.331066	−	0.384706i	0.898692	+	0.438581i	$0.144519\pi$
$312$	8.58578	−	15.2069i	0.486074	−	0.860923i
$313$	0.625642	−	0.0943004i	0.0353634	−	0.00533018i	−0.131337	−	0.991338i	$-0.541927\pi$
$313$	0.625642	−	0.0943004i	0.0353634	−	0.00533018i	0.166700	+	0.986008i	$0.446689\pi$
$314$	−8.57218	−	6.83608i	−0.483756	−	0.385783i
$315$	1.11965	+	6.56846i	0.0630850	+	0.370091i
$316$	2.26932	−	1.42591i	0.127659	−	0.0802137i
$317$	24.4304	+	10.6589i	1.37215	+	0.598662i	0.951243	−	0.308443i	$-0.0998078\pi$
$317$	24.4304	+	10.6589i	1.37215	+	0.598662i	0.420905	+	0.907105i	$0.361713\pi$
$318$	−14.1326	+	3.36900i	−0.792517	+	0.188924i
$319$	−5.49110	+	4.72003i	−0.307443	+	0.264271i
$320$	−0.614599	+	0.354839i	−0.0343571	+	0.0198361i
$321$	−1.34933	+	1.59880i	−0.0753124	+	0.0892363i
$322$	30.9877	−	1.15948i	1.72688	−	0.0646151i
$323$	−4.36079	−	19.1059i	−0.242641	−	1.06308i
$324$	2.42050	−	9.07231i	0.134472	−	0.504017i
$325$	−17.1924	+	13.7105i	−0.953662	+	0.760520i
$326$	−0.685815	+	0.739133i	−0.0379838	+	0.0409368i
$327$	−15.9249	−	8.22159i	−0.880649	−	0.454655i
$328$	4.98080	−	0.373260i	0.275019	−	0.0206098i
$329$	−0.386090	+	10.3185i	−0.0212858	+	0.568876i
$330$	−0.485172	+	4.71301i	−0.0267078	+	0.259443i
$331$	1.77915	−	0.476721i	0.0977908	−	0.0262030i	−0.209592	−	0.977789i	$-0.567214\pi$
$331$	1.77915	−	0.476721i	0.0977908	−	0.0262030i	0.307383	+	0.951586i	$0.400547\pi$
$332$	−15.2942	+	7.36529i	−0.839378	+	0.404223i
$333$	4.48441	−	26.4793i	0.245744	−	1.45106i
$334$	2.88560	−	25.6104i	0.157893	−	1.40134i
$335$	8.98094	+	0.673028i	0.490681	+	0.0367715i
$336$	14.5025	−	7.84418i	0.791179	−	0.427935i
$337$	0.814721	+	4.30590i	0.0443807	+	0.234558i	0.997733	−	0.0673037i	$-0.0214397\pi$
$337$	0.814721	+	4.30590i	0.0443807	+	0.234558i	−0.953352	+	0.301861i	$0.902392\pi$
$338$	40.9580	+	1.53254i	2.22782	+	0.0833592i
$339$	−23.2901	+	25.5900i	−1.26494	+	1.38986i
$340$	1.54887	−	8.18597i	0.0839992	−	0.443946i
$341$	1.34276	−	5.88301i	0.0727145	−	0.318583i
$342$	−14.9116	+	1.40637i	−0.806327	+	0.0760479i
$343$	−12.3173	+	15.4454i	−0.665072	+	0.833974i
$344$	2.82925	−	9.17221i	0.152543	−	0.494532i
$345$	13.4575	+	13.2011i	0.724526	+	0.710721i
$346$	13.9172	+	18.8571i	0.748193	+	1.01377i
$347$	−1.70911	−	2.96026i	−0.0917496	−	0.158915i	0.816498	−	0.577349i	$-0.195913\pi$
$347$	−1.70911	−	2.96026i	−0.0917496	−	0.158915i	−0.908247	+	0.418434i	$0.862579\pi$
$348$	−4.62474	−	8.56202i	−0.247912	−	0.458972i
$349$	−7.11273	+	12.3196i	−0.380736	+	0.659453i	−0.991168	−	0.132615i	$-0.957663\pi$
$349$	−7.11273	+	12.3196i	−0.380736	+	0.659453i	0.610432	+	0.792069i	$0.290996\pi$
$350$	−12.0183	+	1.35413i	−0.642403	+	0.0723814i
$351$	−30.6620	+	6.72324i	−1.63661	+	0.358860i
$352$	7.05430	−	1.61010i	0.375995	−	0.0858185i
$353$	7.59527	+	19.3524i	0.404256	+	1.03003i	0.977555	+	0.210681i	$0.0675680\pi$
$353$	7.59527	+	19.3524i	0.404256	+	1.03003i	−0.573299	+	0.819346i	$0.694337\pi$
$354$	1.62240	−	11.5143i	0.0862295	−	0.611977i
$355$	2.92258	−	0.901498i	0.155115	−	0.0478465i
$356$	−0.144389	−	0.124257i	−0.00765262	−	0.00658561i
$357$	4.81454	−	22.0702i	0.254812	−	1.16808i
$358$	8.06836	+	15.2661i	0.426426	+	0.806838i
$359$	13.7024	+	4.79467i	0.723184	+	0.253053i	0.666674	−	0.745349i	$-0.267717\pi$
$359$	13.7024	+	4.79467i	0.723184	+	0.253053i	0.0565094	+	0.998402i	$0.482003\pi$
$360$	5.54733	+	1.82211i	0.292370	+	0.0960334i
$361$	−4.69008	−	9.73906i	−0.246847	−	0.512582i
$362$	27.8999	+	20.5911i	1.46639	+	1.08224i
$363$	6.22607	−	14.6532i	0.326784	−	0.769095i
$364$	9.91810	+	6.76205i	0.519850	+	0.354428i
$365$	3.04784	−	11.3747i	0.159531	−	0.595378i
$366$	−1.43332	+	1.98169i	−0.0749210	+	0.103585i
$367$	−0.796460	+	0.420941i	−0.0415748	+	0.0219729i	−0.487927	−	0.872885i	$-0.662247\pi$
$367$	−0.796460	+	0.420941i	−0.0415748	+	0.0219729i	0.446352	+	0.894857i	$0.352723\pi$
$368$	20.2395	−	42.0278i	1.05506	−	2.19085i
$369$	−6.46944	−	6.22522i	−0.336786	−	0.324072i
$370$	−17.7554	−	4.05256i	−0.923060	−	0.210682i
$371$	1.36490	+	9.05554i	0.0708622	+	0.470140i
$372$	7.34002	+	3.44819i	0.380562	+	0.178781i
$373$	−16.2868	+	15.1119i	−0.843297	+	0.782465i	−0.978040	−	0.208415i	$-0.933169\pi$
$373$	−16.2868	+	15.1119i	−0.843297	+	0.782465i	0.134744	+	0.990880i	$0.456979\pi$
$374$	7.50539	−	14.2009i	0.388095	−	0.734311i
$375$	−13.3368	−	11.2558i	−0.688708	−	0.581246i
$376$	7.83609	+	4.52417i	0.404115	+	0.233316i
$377$	−18.3414	+	26.8689i	−0.944630	+	1.38382i
$378$	−16.2464	−	5.84116i	−0.835624	−	0.300437i
$379$	−3.00447	−	26.6654i	−0.154329	−	1.36971i	−0.797190	−	0.603728i	$-0.793681\pi$
$379$	−3.00447	−	26.6654i	−0.154329	−	1.36971i	0.642861	−	0.765983i	$-0.277747\pi$
$380$	0.130194	+	3.47951i	0.00667881	+	0.178495i
$381$	8.73691	−	13.0833i	0.447605	−	0.670277i
$382$	1.54857	−	10.2741i	0.0792316	−	0.525667i
$383$	0.234825	−	0.598323i	0.0119990	−	0.0305729i	−0.924749	−	0.380578i	$-0.875725\pi$
$383$	0.234825	−	0.598323i	0.0119990	−	0.0305729i	0.936748	+	0.350005i	$0.113820\pi$
$384$	−0.196975	−	20.4792i	−0.0100519	−	1.04508i
$385$	2.93439	+	0.555217i	0.149550	+	0.0282965i
$386$	−17.7663	−	8.55578i	−0.904279	−	0.435478i
$387$	−15.6784	+	7.20250i	−0.796978	+	0.366124i
$388$	1.84247	−	5.26546i	0.0935370	−	0.267313i
$389$	−6.18018	−	23.0648i	−0.313348	−	1.16943i	−0.925518	−	0.378704i	$-0.876370\pi$
$389$	−6.18018	−	23.0648i	−0.313348	−	1.16943i	0.612170	−	0.790726i	$-0.290297\pi$
$390$	3.37492	+	21.0175i	0.170896	+	1.06426i
$391$	−25.5566	−	58.5764i	−1.29245	−	2.96233i
$392$	2.25087	+	5.15906i	0.113686	+	0.260572i
$393$	0.337665	+	2.10283i	0.0170330	+	0.106074i
$394$	4.09107	+	15.2681i	0.206105	+	0.769195i
$395$	0.989439	−	2.82765i	0.0497841	−	0.142275i
$396$	−3.43356	−	2.43347i	−0.172543	−	0.122287i
$397$	0.782814	+	0.376983i	0.0392883	+	0.0189203i	0.453425	−	0.891295i	$-0.350202\pi$
$397$	0.782814	+	0.376983i	0.0392883	+	0.0189203i	−0.414136	+	0.910215i	$0.635916\pi$
$398$	13.5478	+	2.56338i	0.679090	+	0.128491i
$399$	0.0908017	+	9.44051i	0.00454577	+	0.472617i
$400$	−6.64682	+	16.9358i	−0.332341	+	0.846790i
$401$	4.77618	−	31.6879i	0.238511	−	1.58242i	−0.473852	−	0.880605i	$-0.657137\pi$
$401$	4.77618	−	31.6879i	0.238511	−	1.58242i	0.712362	−	0.701812i	$-0.247625\pi$
$402$	−12.9591	+	19.4059i	−0.646341	+	0.967879i
$403$	−1.01372	−	27.0922i	−0.0504969	−	1.34956i
$404$	−0.389793	−	3.45951i	−0.0193929	−	0.172117i
$405$	−4.20738	−	9.61527i	−0.209066	−	0.477787i
$406$	−16.4037	+	7.14573i	−0.814102	+	0.354636i
$407$	−10.4244	−	6.01853i	−0.516718	−	0.298327i
$408$	−15.1274	−	12.7670i	−0.748918	−	0.632061i
$409$	12.4079	−	23.4769i	0.613532	−	1.16086i	−0.360138	−	0.932899i	$-0.617271\pi$
$409$	12.4079	−	23.4769i	0.613532	−	1.16086i	0.973670	−	0.227960i	$-0.0732056\pi$
$410$	−4.46306	+	4.14111i	−0.220415	+	0.204515i
$411$	4.56096	+	2.14265i	0.224975	+	0.105689i
$412$	−1.54245	−	10.2335i	−0.0759908	−	0.504166i
$413$	−7.14573	−	1.63097i	−0.351618	−	0.0802546i
$414$	−46.9280	+	13.5470i	−2.30639	+	0.665797i
$415$	−8.23273	+	17.0954i	−0.404129	+	0.839182i
$416$	28.7416	−	15.1904i	1.40917	−	0.744770i
$417$	−13.4908	+	18.6523i	−0.660649	+	0.913406i
$418$	−1.73747	+	6.48432i	−0.0849823	+	0.317158i
$419$	16.9971	+	11.5884i	0.830361	+	0.566131i	0.902216	−	0.431284i	$-0.141939\pi$
$419$	16.9971	+	11.5884i	0.830361	+	0.566131i	−0.0718547	+	0.997415i	$0.522892\pi$
$420$	−1.56953	+	3.69394i	−0.0765854	+	0.180246i
$421$	21.1515	+	15.6105i	1.03086	+	0.760810i	0.971407	−	0.237421i	$-0.0763020\pi$
$421$	21.1515	+	15.6105i	1.03086	+	0.760810i	0.0594546	+	0.998231i	$0.481064\pi$
$422$	16.1843	+	33.6070i	0.787838	+	1.63596i
$423$	−3.33058	−	15.9198i	−0.161938	−	0.774047i
$424$	7.57461	+	2.65047i	0.367855	+	0.128718i
$425$	11.6470	+	22.0373i	0.564964	+	1.06896i
$426$	−1.68899	+	7.74248i	−0.0818320	+	0.375124i
$427$	1.16850	+	1.00557i	0.0565475	+	0.0486631i
$428$	−1.20418	+	0.371440i	−0.0582062	+	0.0179542i
$429$	−1.96301	+	13.9316i	−0.0947749	+	0.672624i
$430$	4.27455	+	10.8914i	0.206137	+	0.525229i
$431$	11.6197	−	2.65212i	0.559700	−	0.127748i	0.0666938	−	0.997773i	$-0.478755\pi$
$431$	11.6197	−	2.65212i	0.559700	−	0.127748i	0.493007	+	0.870026i	$0.335898\pi$
$432$	−19.1884	+	17.5014i	−0.923201	+	0.842038i
$433$	32.9250	−	3.70975i	1.58227	−	0.178279i	0.723386	−	0.690444i	$-0.242585\pi$
$433$	32.9250	−	3.70975i	1.58227	−	0.178279i	0.858887	+	0.512164i	$0.171156\pi$
$434$	7.45548	−	12.9133i	0.357875	−	0.619857i
$435$	−10.0086	−	4.25936i	−0.479878	−	0.204221i
$436$	−5.39762	−	9.34894i	−0.258499	−	0.447733i
$437$	15.8609	+	21.4908i	0.758732	+	1.02804i
$438$	21.7816	+	21.3666i	1.04076	+	1.02093i
$439$	3.21368	−	10.4185i	0.153381	−	0.497248i	−0.845972	−	0.533227i	$-0.820979\pi$
$439$	3.21368	−	10.4185i	0.153381	−	0.497248i	0.999353	+	0.0359798i	$0.0114552\pi$
$440$	1.63168	−	2.04606i	0.0777872	−	0.0975421i
$441$	4.21373	−	9.19843i	0.200654	−	0.438021i
$442$	16.0583	−	70.3558i	0.763814	−	3.34649i
$443$	−4.16437	+	22.0092i	−0.197855	+	1.04569i	0.732979	+	0.680251i	$0.238129\pi$
$443$	−4.16437	+	22.0092i	−0.197855	+	1.04569i	−0.930835	+	0.365440i	$0.880918\pi$
$444$	10.8885	−	11.9637i	0.516744	−	0.567773i
$445$	−0.212781	−	0.00796169i	−0.0100868	−	0.000377420i
$446$	−4.61910	−	24.4125i	−0.218721	−	1.15597i
$447$	20.9923	−	11.3544i	0.992903	−	0.537044i
$448$	−1.15581	−	0.0866157i	−0.0546067	−	0.00409221i
$449$	−2.83162	+	25.1313i	−0.133632	+	1.18602i	0.730556	+	0.682853i	$0.239261\pi$
$449$	−2.83162	+	25.1313i	−0.133632	+	1.18602i	−0.864189	+	0.503168i	$0.832168\pi$
$450$	17.8569	−	6.63661i	0.841782	−	0.312853i
$451$	−3.62551	+	1.74595i	−0.170719	+	0.0822138i
$452$	−20.1320	+	5.39435i	−0.946930	+	0.253729i
$453$	2.84177	−	27.6052i	0.133518	−	1.29701i
$454$	−0.503774	+	13.4637i	−0.0236433	+	0.631881i
$455$	13.3801	−	1.00270i	0.627270	−	0.0470074i
$456$	7.35116	+	3.79520i	0.344250	+	0.177727i
$457$	−11.9830	+	12.9146i	−0.560540	+	0.604118i	−0.948196	−	0.317686i	$-0.897094\pi$
$457$	−11.9830	+	12.9146i	−0.560540	+	0.604118i	0.387656	+	0.921804i	$0.373285\pi$
$458$	20.1479	−	16.0674i	0.941451	−	0.750782i
$459$	1.02652	+	35.5665i	0.0479140	+	1.66010i
$460$	2.52673	+	11.0703i	0.117809	+	0.516156i
$461$	−10.9861	+	0.411070i	−0.511673	+	0.0191454i	−0.291981	−	0.956424i	$-0.594315\pi$
$461$	−10.9861	+	0.411070i	−0.511673	+	0.0191454i	−0.219691	+	0.975569i	$0.570505\pi$
$462$	−4.99075	+	5.91345i	−0.232191	+	0.275119i
$463$	−18.8922	+	10.9074i	−0.877993	+	0.506910i	−0.869996	−	0.493058i	$-0.835879\pi$
$463$	−18.8922	+	10.9074i	−0.877993	+	0.506910i	−0.00799706	+	0.999968i	$0.502546\pi$
$464$	−2.02673	+	26.8393i	−0.0940884	+	1.24598i
$465$	8.81763	−	2.10199i	0.408908	−	0.0974775i
$466$	−9.11596	−	3.97725i	−0.422289	−	0.184243i
$467$	−3.85913	+	2.42485i	−0.178579	+	0.112209i	−0.618355	−	0.785899i	$-0.712201\pi$
$467$	−3.85913	+	2.42485i	−0.178579	+	0.112209i	0.439776	+	0.898108i	$0.355058\pi$
$468$	−17.7305	−	6.56800i	−0.819592	−	0.303606i
$469$	11.4998	+	9.17080i	0.531013	+	0.423468i
$470$	−10.9062	+	1.64384i	−0.503065	+	0.0758248i
$471$	5.35205	−	9.47943i	0.246610	−	0.436789i
$472$	−4.18950	+	4.86829i	−0.192837	+	0.224081i
$473$	0.577896	+	7.71149i	0.0265717	+	0.354575i
$474$	5.11948	+	5.83449i	0.235146	+	0.267987i
$475$	−6.79518	−	7.89614i	−0.311784	−	0.362300i
$476$	9.62129	−	9.62129i	0.440991	−	0.440991i
$477$	−5.52731	−	13.3239i	−0.253078	−	0.610060i
$478$	−8.33221	−	0.938815i	−0.381107	−	0.0429404i
$479$	−16.8048	+	22.7696i	−0.767829	+	1.04037i	0.229913	+	0.973211i	$0.426156\pi$
$479$	−16.8048	+	22.7696i	−0.767829	+	1.04037i	−0.997742	+	0.0671606i	$0.978606\pi$
$480$	6.85842	+	8.43252i	0.313043	+	0.384890i
$481$	−52.2378	−	13.9971i	−2.38184	−	0.638211i
$482$	7.73669	−	1.46386i	0.352397	−	0.0666770i
$483$	6.01453	+	30.1948i	0.273671	+	1.37391i
$484$	7.92363	−	5.40224i	0.360165	−	0.245556i
$485$	−2.05946	−	5.88559i	−0.0935152	−	0.267251i
$486$	27.0541	+	2.75573i	1.22720	+	0.125002i
$487$	−17.7963	−	22.3159i	−0.806429	−	1.01123i	−0.999548	−	0.0300546i	$-0.990432\pi$
$487$	−17.7963	−	22.3159i	−0.806429	−	1.01123i	0.193119	−	0.981175i	$-0.438140\pi$
$488$	1.25752	−	0.493540i	0.0569252	−	0.0223415i
$489$	−0.832531	−	0.555957i	−0.0376483	−	0.0251412i
$490$	−6.06596	−	3.20595i	−0.274032	−	0.144830i
$491$	7.65438	−	5.64919i	0.345438	−	0.254944i	−0.407258	−	0.913313i	$-0.633515\pi$
$491$	7.65438	−	5.64919i	0.345438	−	0.254944i	0.752696	+	0.658369i	$0.228753\pi$
$492$	−1.25404	−	5.26054i	−0.0565363	−	0.237164i
$493$	26.0601	+	26.0899i	1.17369	+	1.17503i
$494$			30.1607i			1.35699i
$495$	−4.69655	+	0.266278i	−0.211094	+	0.0119683i
$496$	−11.9338	−	18.9925i	−0.535842	−	0.852788i
$497$	4.77317	+	1.47233i	0.214106	+	0.0660430i
$498$	−28.0842	−	40.3525i	−1.25848	−	1.80824i
$499$	29.8813	+	11.7275i	1.33767	+	0.524997i	0.922939	−	0.384946i	$-0.125780\pi$
$499$	29.8813	+	11.7275i	1.33767	+	0.524997i	0.414732	+	0.909944i	$0.363875\pi$
$500$	−3.09846	−	10.0450i	−0.138567	−	0.449224i
$501$	25.5602	−	1.20267i	1.14195	−	0.0537315i
$502$	3.05948	+	4.48744i	0.136551	+	0.200284i
$503$	18.6965	+	11.7478i	0.833635	+	0.523808i	0.879921	−	0.475121i	$-0.157596\pi$
$503$	18.6965	+	11.7478i	0.833635	+	0.523808i	−0.0462857	+	0.998928i	$0.514738\pi$
$504$	5.80929	+	7.56241i	0.258766	+	0.336857i
$505$	−2.75164	−	2.75164i	−0.122447	−	0.122447i
$506$	−1.63599	+	21.8308i	−0.0727288	+	0.970499i
$507$	4.94501	+	40.3925i	0.219616	+	1.79389i
$508$	8.68563	−	3.78950i	0.385362	−	0.168132i
$509$	−9.35968	+	13.7281i	−0.414860	+	0.608488i	−0.975614	−	0.219494i	$-0.929559\pi$
$509$	−9.35968	+	13.7281i	−0.414860	+	0.608488i	0.560753	+	0.827983i	$0.310512\pi$
$510$	24.1194	+	0.670255i	1.06802	+	0.0296794i
$511$	14.5777	−	12.5451i	0.644879	−	0.554963i
$512$	5.43359	−	8.64750i	0.240133	−	0.382169i
$513$	−3.72597	−	14.3965i	−0.164505	−	0.635621i
$514$	−8.39202	+	2.93650i	−0.370156	+	0.129523i
$515$	−8.47986	−	7.86816i	−0.373667	−	0.346713i
$516$	−10.2910	−	1.45004i	−0.453037	−	0.0638343i
$517$	−7.20833	−	1.08648i	−0.317022	−	0.0477834i
$518$	−20.2310	−	21.8039i	−0.888900	−	0.958007i
$519$	−16.2949	+	16.6114i	−0.715268	+	0.729161i
$520$	4.70185	−	10.7768i	0.206190	−	0.472592i
$521$	−1.80355			−0.0790152			−0.0395076	−	0.999219i	$-0.512579\pi$
$521$	−1.80355			−0.0790152			−0.0395076	+	0.999219i	$0.512579\pi$
$522$	22.3599	−	17.1562i	0.978667	−	0.750904i
$523$	20.8531			0.911843			0.455921	−	0.890020i	$-0.349310\pi$
$523$	20.8531			0.911843			0.455921	+	0.890020i	$0.349310\pi$
$524$	−0.513004	+	1.17582i	−0.0224107	+	0.0513658i
$525$	−3.21930	−	11.5684i	−0.140502	−	0.504885i
$526$	−25.0014	−	26.9451i	−1.09011	−	1.17486i
$527$	−30.3875	−	4.58018i	−1.32370	−	0.199516i
$528$	4.35668	+	10.7942i	0.189600	+	0.469757i
$529$	46.9918	+	43.6020i	2.04312	+	1.89574i
$530$	−9.23299	+	3.23076i	−0.401055	+	0.140335i
$531$	11.5429	−	0.222066i	0.500918	−	0.00963686i
$532$	−3.02552	+	4.81508i	−0.131173	+	0.208760i
$533$	−13.7036	+	11.7929i	−0.593567	+	0.510806i
$534$	0.289019	−	0.469945i	0.0125071	−	0.0203365i
$535$	−0.793481	+	1.16382i	−0.0343052	+	0.0503164i
$536$	11.8138	−	5.15430i	0.510278	−	0.222632i
$537$	−13.6953	+	10.3125i	−0.590997	+	0.445019i
$538$	−1.65151	+	22.0379i	−0.0712018	+	0.950122i
$539$	−3.20655	−	3.20655i	−0.138116	−	0.138116i
$540$	0.995622	−	6.24303i	0.0428448	−	0.268657i
$541$	13.5254	+	8.49856i	0.581501	+	0.365382i	0.790433	−	0.612549i	$-0.209856\pi$
$541$	13.5254	+	8.49856i	0.581501	+	0.365382i	−0.208931	+	0.977930i	$0.566999\pi$
$542$	−19.4300	−	28.4985i	−0.834589	−	1.22412i
$543$	−15.7937	+	30.5917i	−0.677771	+	1.31282i
$544$	−10.8615	−	35.2120i	−0.465682	−	1.50970i
$545$	−11.2325	−	4.40843i	−0.481147	−	0.188836i
$546$	−14.7822	+	31.4663i	−0.632621	+	1.34663i
$547$	−2.84456	−	0.877431i	−0.121625	−	0.0375162i	0.233345	−	0.972394i	$-0.425033\pi$
$547$	−2.84456	−	0.877431i	−0.121625	−	0.0375162i	−0.354970	+	0.934878i	$0.615509\pi$
$548$	1.61489	+	2.57009i	0.0689848	+	0.109789i
$549$	−2.16829	−	1.09314i	−0.0925402	−	0.0466542i
$550$		−	8.53836i		−	0.364077i
$551$	−13.0449	−	8.20701i	−0.555730	−	0.349630i
$552$	25.8560	+	7.70397i	1.10050	+	0.327903i
$553$	3.93665	−	2.90538i	0.167404	−	0.123549i
$554$	44.5838	+	23.5632i	1.89418	+	1.00111i
$555$	1.17778	−	18.0436i	0.0499942	−	0.765909i
$556$	−12.9074	+	5.06577i	−0.547395	+	0.214837i
$557$	0.0782381	+	0.0981075i	0.00331506	+	0.00415695i	0.783486	−	0.621409i	$-0.213439\pi$
$557$	0.0782381	+	0.0981075i	0.00331506	+	0.00415695i	−0.780171	+	0.625566i	$0.784868\pi$
$558$	−6.48991	+	22.5725i	−0.274740	+	0.955569i
$559$	11.4751	+	32.7939i	0.485345	+	1.38703i
$560$	9.17222	−	6.25351i	0.387597	−	0.264259i
$561$	15.1026	+	5.12214i	0.637634	+	0.216257i
$562$	13.2370	−	2.50457i	0.558368	−	0.105649i
$563$	−2.93255	−	0.785774i	−0.123592	−	0.0331164i	0.196493	−	0.980505i	$-0.437045\pi$
$563$	−2.93255	−	0.785774i	−0.123592	−	0.0331164i	−0.320085	+	0.947389i	$0.603711\pi$
$564$	3.49131	−	9.15362i	0.147011	−	0.385437i
$565$	−13.8341	+	18.7446i	−0.582006	+	0.788590i
$566$	−28.7004	−	3.23376i	−1.20637	−	0.135925i
$567$	3.16871	−	16.8459i	0.133073	−	0.707460i
$568$	3.09512	−	3.09512i	0.129868	−	0.129868i
$569$	−16.4002	−	19.0574i	−0.687532	−	0.798927i	0.300400	−	0.953813i	$-0.402880\pi$
$569$	−16.4002	−	19.0574i	−0.687532	−	0.798927i	−0.987932	+	0.154886i	$0.950499\pi$
$570$	−9.89004	+	1.97001i	−0.414248	+	0.0825145i
$571$	0.728814	+	9.72535i	0.0304999	+	0.406993i	0.991469	+	0.130339i	$0.0416066\pi$
$571$	0.728814	+	9.72535i	0.0304999	+	0.406993i	−0.960970	+	0.276654i	$0.910774\pi$
$572$	−5.52784	+	6.42347i	−0.231131	+	0.268579i
$573$	10.3155	−	0.0992173i	0.430935	−	0.00414486i
$574$	−9.83241	+	1.48200i	−0.410397	+	0.0618574i
$575$	−26.5608	−	21.1815i	−1.10766	−	0.883331i
$576$	1.79971	−	0.306775i	0.0749878	−	0.0127823i
$577$	23.5628	−	14.8055i	0.980931	−	0.616360i	0.0567799	−	0.998387i	$-0.481917\pi$
$577$	23.5628	−	14.8055i	0.980931	−	0.616360i	0.924151	+	0.382027i	$0.124774\pi$
$578$	−47.7926	−	20.8517i	−1.98791	−	0.867317i
$579$	5.59060	−	18.7631i	0.232338	−	0.779769i
$580$	−3.68772	−	5.41553i	−0.153124	−	0.224868i
$581$	−26.8375	+	15.4946i	−1.11341	+	0.642825i
$582$	15.9029	+	2.85084i	0.659195	+	0.118171i
$583$	−6.46074	+	0.241744i	−0.267576	+	0.0100120i
$584$	−3.75021	−	16.4308i	−0.155185	−	0.679910i
$585$	−20.0722	+	6.61688i	−0.829884	+	0.273575i
$586$	3.02894	−	2.41550i	0.125124	−	0.0997832i
$587$	−11.3159	+	12.1957i	−0.467059	+	0.503370i	−0.922020	−	0.387141i	$-0.873463\pi$
$587$	−11.3159	+	12.1957i	−0.467059	+	0.503370i	0.454961	+	0.890511i	$0.349653\pi$
$588$	5.12879	−	3.29186i	0.211508	−	0.135754i
$589$	12.8077	−	0.959804i	0.527732	−	0.0395480i
$590$	0.292735	−	7.82351i	0.0120517	−	0.322089i
$591$	−14.3234	+	6.41390i	−0.589184	+	0.263833i
$592$	−43.2192	+	11.5805i	−1.77630	+	0.475958i
$593$	10.9745	−	5.28503i	0.450668	−	0.217030i	−0.194761	−	0.980851i	$-0.562393\pi$
$593$	10.9745	−	5.28503i	0.450668	−	0.217030i	0.645429	+	0.763821i	$0.276679\pi$
$594$	5.38202	−	10.9358i	0.220827	−	0.448702i
$595$	1.70287	−	15.1134i	0.0698110	−	0.619590i
$596$	14.3356	+	1.07430i	0.587208	+	0.0440052i
$597$	−0.380278	+	13.6845i	−0.0155638	+	0.560068i
$598$	18.2858	+	96.6427i	0.747761	+	3.95201i
$599$	44.8250	+	1.67723i	1.83150	+	0.0685299i	0.930718	−	0.365738i	$-0.119184\pi$
$599$	44.8250	+	1.67723i	1.83150	+	0.0685299i	0.900784	+	0.434268i	$0.142993\pi$
$600$	−10.2807	−	2.24270i	−0.419709	−	0.0915579i
$601$	8.91453	−	47.1144i	0.363631	−	1.92184i	−0.0232994	−	0.999729i	$-0.507417\pi$
$601$	8.91453	−	47.1144i	0.363631	−	1.92184i	0.386931	−	0.922109i	$-0.373535\pi$
$602$	−4.25210	+	18.6297i	−0.173303	+	0.759289i
$603$	−21.0636	−	9.64908i	−0.857777	−	0.392941i
$604$	10.4221	−	13.0689i	0.424070	−	0.531767i
$605$	3.15961	−	10.2432i	0.128457	−	0.416446i
$606$	9.71365	−	2.70316i	0.394590	−	0.109808i
$607$	−8.48121	−	11.4916i	−0.344242	−	0.466431i	0.597936	−	0.801544i	$-0.295988\pi$
$607$	−8.48121	−	11.4916i	−0.344242	−	0.466431i	−0.942178	+	0.335113i	$0.891226\pi$
$608$	7.70036	+	13.3374i	0.312291	+	0.540904i
$609$	−9.58715	−	14.9558i	−0.388491	−	0.606038i
$610$	−0.823334	+	1.42606i	−0.0333358	+	0.0577393i
$611$	−32.5457	+	3.66702i	−1.31666	+	0.148352i
$612$	−11.0515	+	18.3632i	−0.446730	+	0.742289i
$613$	1.61956	−	0.369655i	0.0654136	−	0.0149302i	−0.189689	−	0.981844i	$-0.560748\pi$
$613$	1.61956	−	0.369655i	0.0654136	−	0.0149302i	0.255102	+	0.966914i	$0.417891\pi$
$614$	−2.52413	−	6.43139i	−0.101866	−	0.259550i
$615$	−4.76209	−	3.72328i	−0.192026	−	0.150137i
$616$	4.08422	−	1.25982i	0.164558	−	0.0507594i
$617$	12.6171	+	10.8579i	0.507945	+	0.437122i	0.868554	−	0.495595i	$-0.165050\pi$
$617$	12.6171	+	10.8579i	0.507945	+	0.437122i	−0.360609	+	0.932717i	$0.617431\pi$
$618$	28.5548	−	9.10967i	1.14864	−	0.366445i
$619$	−22.8793	−	43.2897i	−0.919596	−	1.73996i	−0.617262	−	0.786757i	$-0.711758\pi$
$619$	−22.8793	−	43.2897i	−0.919596	−	1.73996i	−0.302333	−	0.953202i	$-0.597766\pi$
$620$	5.15369	+	1.80336i	0.206977	+	0.0724245i
$621$	−20.6673	−	43.8712i	−0.829349	−	1.76049i
$622$	6.77487	+	14.0682i	0.271648	+	0.564082i
$623$	−0.279805	−	0.206505i	−0.0112101	−	0.00827346i
$624$	31.4587	+	41.7780i	1.25936	+	1.67246i
$625$	5.32947	+	3.63357i	0.213179	+	0.145343i
$626$	−0.285675	+	1.06615i	−0.0114179	+	0.0426121i
$627$	−6.63010	−	0.682523i	−0.264781	−	0.0272573i
$628$	5.79725	−	3.06394i	0.231335	−	0.122264i
$629$	−26.5974	+	55.2301i	−1.06051	+	2.20217i
$630$	−11.2837	−	2.79198i	−0.449553	−	0.111235i
$631$	19.2099	+	4.38452i	0.764732	+	0.174545i	0.587059	−	0.809544i	$-0.300286\pi$
$631$	19.2099	+	4.38452i	0.764732	+	0.174545i	0.177674	+	0.984089i	$0.443143\pi$
$632$	−0.639009	−	4.23955i	−0.0254184	−	0.168640i
$633$	−30.3974	+	21.1557i	−1.20819	+	0.840864i
$634$	−34.0859	+	31.6271i	−1.35373	+	1.25607i
$635$	4.94948	−	9.36487i	0.196414	−	0.371634i
$636$	1.53316	−	8.55245i	0.0607938	−	0.339127i
$637$	−17.6443	−	10.1869i	−0.699091	−	0.403621i
$638$	−3.71640	−	12.0727i	−0.147134	−	0.477964i
$639$	−7.85585	−	0.436951i	−0.310773	−	0.0172855i
$640$	−1.54388	−	13.7023i	−0.0610272	−	0.541631i
$641$	−0.599083	−	16.0108i	−0.0236623	−	0.632390i	−0.959788	−	0.280725i	$-0.909425\pi$
$641$	−0.599083	−	16.0108i	−0.0236623	−	0.632390i	0.936126	−	0.351665i	$-0.114384\pi$
$642$	−1.61508	−	3.27285i	−0.0637423	−	0.129169i
$643$	3.65790	−	24.2686i	0.144253	−	0.957059i	−0.793203	−	0.608957i	$-0.791588\pi$
$643$	3.65790	−	24.2686i	0.144253	−	0.957059i	0.937457	−	0.348102i	$-0.113174\pi$
$644$	−6.77526	+	17.2631i	−0.266983	+	0.680261i
$645$	−10.0040	+	5.90482i	−0.393907	+	0.232502i
$646$	33.5914	+	6.35584i	1.32164	+	0.250067i
$647$	36.5590	+	17.6059i	1.43728	+	0.692159i	0.980336	−	0.197335i	$-0.0632287\pi$
$647$	36.5590	+	17.6059i	1.43728	+	0.692159i	0.456947	+	0.889494i	$0.348943\pi$
$648$	−11.7538	−	9.35271i	−0.461731	−	0.367409i
$649$	1.70903	−	4.88411i	0.0670851	−	0.191718i
$650$	−9.92868	−	37.0543i	−0.389435	−	1.45339i
$651$	13.8325	+	5.27590i	0.542139	+	0.206779i
$652$	−0.241138	−	0.552694i	−0.00944369	−	0.0216452i
$653$	−13.1755	−	30.1985i	−0.515596	−	1.18176i	−0.958475	−	0.285178i	$-0.907947\pi$
$653$	−13.1755	−	30.1985i	−0.515596	−	1.18176i	0.442878	−	0.896582i	$-0.353957\pi$
$654$	24.2553	−	19.7276i	0.948457	−	0.771409i
$655$	0.371131	+	1.38508i	0.0145013	+	0.0541196i
$656$	−4.94030	+	14.1186i	−0.192886	+	0.551237i
$657$	−17.5170	+	24.7160i	−0.683403	+	0.964262i
$658$	−16.2293	−	7.81564i	−0.632686	−	0.304685i
$659$	−47.8164	−	9.04734i	−1.86266	−	0.352435i	−0.872080	−	0.489363i	$-0.837229\pi$
$659$	−47.8164	−	9.04734i	−1.86266	−	0.352435i	−0.990581	+	0.136928i	$0.956277\pi$
$660$	−2.46739	−	1.39308i	−0.0960431	−	0.0542256i
$661$	−10.0081	+	25.5002i	−0.389269	+	0.991841i	0.593140	+	0.805099i	$0.297888\pi$
$661$	−10.0081	+	25.5002i	−0.389269	+	0.991841i	−0.982409	+	0.186742i	$0.940207\pi$
$662$	−0.478905	+	3.17733i	−0.0186132	+	0.123490i
$663$	71.4979	+	4.66697i	2.77675	+	0.181250i
$664$	1.01538	+	27.1366i	0.0394045	+	1.05311i
$665$	0.711698	+	6.31650i	0.0275985	+	0.244943i
$666$	39.2106	+	25.6426i	1.51938	+	0.993632i
$667$	−46.7748	−	18.3886i	−1.81113	−	0.712008i
$668$	13.3482	+	7.70657i	0.516456	+	0.298176i
$669$	23.2046	−	8.37100i	0.897141	−	0.323642i
$670$	−7.34136	+	13.8905i	−0.283621	+	0.536638i
$671$	−0.797816	+	0.740265i	−0.0307993	+	0.0285776i
$672$	1.49681	+	17.6888i	0.0577407	+	0.682362i
$673$	−5.39345	−	35.7832i	−0.207902	−	1.37934i	−0.812571	−	0.582863i	$-0.801932\pi$
$673$	−5.39345	−	35.7832i	−0.207902	−	1.37934i	0.604669	−	0.796477i	$-0.293306\pi$
$674$	−7.45327	−	1.70116i	−0.287089	−	0.0655263i
$675$	9.31681	+	16.4605i	0.358604	+	0.633564i
$676$	−10.6353	+	22.0845i	−0.409051	+	0.849403i
$677$	−14.1079	+	7.45623i	−0.542210	+	0.286566i	−0.715863	−	0.698241i	$-0.753967\pi$
$677$	−14.1079	+	7.45623i	−0.542210	+	0.286566i	0.173653	+	0.984807i	$0.444443\pi$
$678$	−24.6696	−	55.0915i	−0.947429	−	2.11578i
$679$	2.63578	−	9.83685i	0.101152	−	0.377504i
$680$	−11.0118	−	7.50769i	−0.422282	−	0.287907i
$681$	−13.2778	+	1.62552i	−0.508805	+	0.0622899i
$682$	8.46989	+	6.25107i	0.324329	+	0.239366i
$683$	−4.84873	−	10.0685i	−0.185531	−	0.385260i	0.787370	−	0.616481i	$-0.211442\pi$
$683$	−4.84873	−	10.0685i	−0.185531	−	0.385260i	−0.972901	+	0.231221i	$0.925728\pi$
$684$	2.79527	−	8.51009i	0.106880	−	0.325391i
$685$	3.20242	+	1.12057i	0.122358	+	0.0428149i
$686$	−16.1037	−	30.4696i	−0.614841	−	1.16334i
$687$	18.9225	+	17.2218i	0.721940	+	0.657054i
$688$	21.7881	+	18.7502i	0.830665	+	0.714845i
$689$	−27.7569	+	8.56186i	−1.05745	+	0.326181i
$690$	−30.4959	+	12.3085i	−1.16096	+	0.468578i
$691$	0.705140	+	1.79667i	0.0268248	+	0.0683485i	0.943659	−	0.330921i	$-0.107359\pi$
$691$	0.705140	+	1.79667i	0.0268248	+	0.0683485i	−0.916834	+	0.399269i	$0.869264\pi$
$692$	−13.6648	+	3.11891i	−0.519459	+	0.118563i
$693$	−6.58259	−	3.96159i	−0.250052	−	0.150488i
$694$	5.92559	−	0.667653i	0.224932	−	0.0253438i
$695$	−7.74945	+	13.4224i	−0.293954	+	0.509142i
$696$	−15.5125	+	1.30374i	−0.587999	+	0.0494180i
$697$	10.2465	+	17.7475i	0.388114	+	0.672233i
$698$	−14.7365	−	19.9672i	−0.557783	−	0.755769i
$699$	2.46393	−	9.56248i	0.0931946	−	0.361686i
$700$	2.13195	−	6.91162i	0.0805802	−	0.261235i
$701$	−4.59251	+	5.75882i	−0.173457	+	0.217508i	−0.860959	−	0.508674i	$-0.830136\pi$
$701$	−4.59251	+	5.75882i	−0.173457	+	0.217508i	0.687502	+	0.726182i	$0.258707\pi$
$702$	10.6401	−	53.7171i	0.401584	−	2.02742i
$703$	5.70100	−	24.9777i	0.215017	−	0.942052i
$704$	0.152125	−	0.804001i	0.00573343	−	0.0303019i
$705$	−3.32825	−	10.4326i	−0.125349	−	0.392915i
$706$	−36.2421	−	1.35608i	−1.36399	−	0.0510369i
$707$	−1.18156	−	6.24467i	−0.0444370	−	0.234855i
$708$	5.92351	+	3.64300i	0.222619	+	0.136912i
$709$	−12.9134	−	0.967726i	−0.484973	−	0.0363437i	−0.170000	−	0.985444i	$-0.554377\pi$
$709$	−12.9134	−	0.967726i	−0.484973	−	0.0363437i	−0.314974	+	0.949100i	$0.601996\pi$
$710$	−0.597387	+	5.30195i	−0.0224195	+	0.198979i
$711$	−4.91370	+	5.93708i	−0.184278	+	0.222658i
$712$	−0.274559	+	0.132221i	−0.0102895	+	0.00495517i
$713$	40.4573	−	10.8405i	1.51514	−	0.405979i
$714$	31.9304	+	23.0947i	1.19497	+	0.864296i
$715$	−0.354193	+	9.46600i	−0.0132461	+	0.354008i
$716$	−10.2976	+	0.771701i	−0.384841	+	0.0288398i
$717$	−0.391284	−	8.31588i	−0.0146128	−	0.310562i
$718$	−17.2254	+	18.5645i	−0.642845	+	0.692823i
$719$	−0.335819	+	0.267807i	−0.0125239	+	0.00998751i	−0.629732	−	0.776813i	$-0.716835\pi$
$719$	−0.335819	+	0.267807i	−0.0125239	+	0.00998751i	0.617208	+	0.786800i	$0.288264\pi$
$720$	−11.6447	+	13.0445i	−0.433973	+	0.486140i
$721$	−4.20402	−	18.4190i	−0.156566	−	0.685961i
$722$	18.8441	−	0.705097i	0.701305	−	0.0262410i
$723$	2.65289	+	7.35387i	0.0986621	+	0.273493i
$724$	−17.9593	+	10.3688i	−0.667453	+	0.385354i
$725$	18.7281	+	5.78856i	0.695545	+	0.214982i
$726$	19.0863	+	20.1774i	0.708360	+	0.748855i
$727$	36.8293	+	16.0684i	1.36592	+	0.595945i	0.949655	−	0.313297i	$-0.101434\pi$
$727$	36.8293	+	16.0684i	1.36592	+	0.595945i	0.416266	+	0.909243i	$0.363338\pi$
$728$	16.2595	−	10.2165i	0.602619	−	0.378650i
$729$	1.55725	+	26.9551i	0.0576760	+	0.998335i
$730$	16.0613	+	12.8085i	0.594455	+	0.474062i
$731$	38.9424	−	5.86962i	1.44034	−	0.217096i
$732$	−0.743475	−	1.25960i	−0.0274796	−	0.0465562i
$733$	−10.3313	+	12.0052i	−0.381595	+	0.443422i	−0.915619	−	0.402048i	$-0.868298\pi$
$733$	−10.3313	+	12.0052i	−0.381595	+	0.443422i	0.534023	+	0.845470i	$0.320679\pi$
$734$	−0.117442	−	1.56715i	−0.00433485	−	0.0578446i
$735$	2.18794	−	6.45114i	0.0807034	−	0.237954i
$736$	32.7601	+	38.0680i	1.20756	+	1.40320i
$737$	−7.34271	+	7.34271i	−0.270472	+	0.270472i
$738$	14.4670	−	6.00150i	0.532536	−	0.220918i
$739$	−14.6912	−	1.65530i	−0.540423	−	0.0608911i	−0.162466	−	0.986714i	$-0.551945\pi$
$739$	−14.6912	−	1.65530i	−0.540423	−	0.0608911i	−0.377957	+	0.925823i	$0.623373\pi$
$740$	6.46768	−	8.76339i	0.237756	−	0.322149i
$741$	−29.5666	+	4.74771i	−1.08616	+	0.174412i
$742$	−15.4315	−	4.13486i	−0.566508	−	0.151795i
$743$	51.7815	−	9.79758i	1.89968	−	0.359438i	0.902256	−	0.431200i	$-0.141910\pi$
$743$	51.7815	−	9.79758i	1.89968	−	0.359438i	0.997422	+	0.0717616i	$0.0228621\pi$
$744$	9.75140	−	8.55637i	0.357504	−	0.313692i
$745$	13.2767	−	9.05191i	0.486421	−	0.331636i
$746$	−12.8013	−	36.5839i	−0.468688	−	1.33943i
$747$	35.1369	−	33.8831i	1.28559	−	1.23972i
$748$	5.98923	+	7.51026i	0.218988	+	0.274602i
$749$	−2.14147	+	0.840466i	−0.0782477	+	0.0307099i
$750$	27.3013	−	13.4726i	0.996902	−	0.491950i
$751$	−36.7254	−	19.4099i	−1.34013	−	0.708279i	−0.365228	−	0.930918i	$-0.619009\pi$
$751$	−36.7254	−	19.4099i	−1.34013	−	0.708279i	−0.974901	+	0.222639i	$0.928533\pi$
$752$	−21.8024	+	16.0909i	−0.795052	+	0.586775i
$753$	−3.91744	+	3.70561i	−0.142760	+	0.135040i
$754$	−30.1668	−	48.0711i	−1.09861	−	1.75064i
$755$		−	18.6845i		−	0.679997i
$756$	7.08720	−	7.50846i	0.257759	−	0.273080i
$757$	−1.02193	−	1.62639i	−0.0371426	−	0.0591121i	0.827637	−	0.561264i	$-0.189685\pi$
$757$	−1.02193	−	1.62639i	−0.0371426	−	0.0591121i	−0.864780	+	0.502152i	$0.832542\pi$
$758$	44.7326	+	13.7982i	1.62476	+	0.501172i
$759$	−21.6584	+	1.83271i	−0.786149	+	0.0665231i
$760$	5.18508	+	2.03500i	0.188083	+	0.0738170i
$761$	−6.14364	−	19.9172i	−0.222707	−	0.721998i	−0.996113	−	0.0880868i	$-0.971925\pi$
$761$	−6.14364	−	19.9172i	−0.222707	−	0.721998i	0.773406	−	0.633911i	$-0.218551\pi$
$762$	14.8245	+	23.0969i	0.537035	+	0.836713i
$763$	−11.1015	−	16.2829i	−0.401901	−	0.589480i
$764$	5.26135	+	3.30593i	0.190349	+	0.119604i
$765$	3.13968	+	23.7498i	0.113515	+	0.858676i
$766$	0.792870	+	0.792870i	0.0286476	+	0.0286476i
$767$	1.73734	−	23.1831i	0.0627316	−	0.837095i
$768$	30.9423	+	13.1472i	1.11654	+	0.474410i
$769$	31.2972	−	13.6548i	1.12860	−	0.492405i	0.249187	−	0.968455i	$-0.419837\pi$
$769$	31.2972	−	13.6548i	1.12860	−	0.492405i	0.879418	+	0.476050i	$0.157932\pi$
$770$	−2.93483	+	4.30461i	−0.105764	+	0.155127i
$771$	−4.19968	−	7.76448i	−0.151248	−	0.279631i
$772$	8.93870	−	7.69237i	0.321711	−	0.276855i
$773$	18.3006	−	29.1252i	0.658227	−	1.04756i	−0.336165	−	0.941803i	$-0.609130\pi$
$773$	18.3006	−	29.1252i	0.658227	−	1.04756i	0.994392	−	0.105759i	$-0.0337271\pi$
$774$	−0.578951	−	30.0935i	−0.0208099	−	1.08169i
$775$	−15.4191	+	5.39538i	−0.553870	+	0.193808i
$776$	−6.54179	−	6.06989i	−0.234836	−	0.217896i
$777$	18.1897	−	23.2648i	0.652554	−	0.834619i
$778$	41.1907	+	6.20850i	1.47676	+	0.222585i
$779$	−5.82557	−	6.27847i	−0.208723	−	0.224950i
$780$	−12.3278	−	3.17646i	−0.441405	−	0.113735i
$781$	−1.41020	+	3.23221i	−0.0504608	+	0.115657i
$782$	111.489			3.98684
$783$	20.3380	+	19.2189i	0.726821	+	0.686827i
$784$	−16.8564			−0.602015
$785$	2.93096	−	6.71782i	0.104610	−	0.239769i
$786$	−3.59787	−	0.927051i	−0.128332	−	0.0330668i
$787$	28.7302	+	30.9638i	1.02412	+	1.10374i	0.994559	+	0.104177i	$0.0332207\pi$
$787$	28.7302	+	30.9638i	1.02412	+	1.10374i	0.0295618	+	0.999563i	$0.490589\pi$
$788$	−9.34755	−	1.40892i	−0.332993	−	0.0501906i
$789$	22.4788	−	28.7505i	0.800267	−	1.02355i
$790$	3.83102	+	3.55467i	0.136302	+	0.126469i
$791$	−35.9133	+	12.5666i	−1.27693	+	0.446817i
$792$	−5.76455	+	3.47769i	−0.204834	+	0.123574i
$793$	−2.60152	+	4.14029i	−0.0923825	+	0.147026i
$794$	−1.14888	+	0.988689i	−0.0407721	+	0.0350873i
$795$	−4.62053	−	8.54256i	−0.163873	−	0.302974i
$796$	−4.64512	+	6.81314i	−0.164642	+	0.241485i
$797$	26.8528	−	11.7157i	0.951174	−	0.414993i	0.133741	−	0.991016i	$-0.457301\pi$
$797$	26.8528	−	11.7157i	0.951174	−	0.414993i	0.817433	+	0.576024i	$0.195396\pi$
$798$	−15.1582	−	6.44064i	−0.536595	−	0.227996i
$799$	−2.77431	+	37.0205i	−0.0981479	+	1.30969i
$800$	−13.8510	−	13.8510i	−0.489706	−	0.489706i
$801$	0.506184	+	0.209350i	0.0178851	+	0.00739703i
$802$	47.3353	+	29.7427i	1.67147	+	1.05025i
$803$	7.64864	+	11.2185i	0.269915	+	0.395892i
$804$	−7.53807	−	11.7445i	−0.265847	−	0.414196i
$805$	6.11002	+	19.8082i	0.215350	+	0.698148i
$806$	44.0261	+	17.2790i	1.55075	+	0.608626i
$807$	−21.8638	+	1.85009i	−0.769643	+	0.0651264i
$808$	−5.32183	−	1.64157i	−0.187221	−	0.0577501i
$809$	2.44015	+	3.88347i	0.0857909	+	0.136535i	0.886863	−	0.462032i	$-0.152880\pi$
$809$	2.44015	+	3.88347i	0.0857909	+	0.136535i	−0.801072	+	0.598568i	$0.795737\pi$
$810$	18.3094	−	0.0196299i	0.643328	−	0.000689724i
$811$			50.2870i			1.76581i	0.469548	+	0.882907i	$0.344417\pi$
$811$			50.2870i			1.76581i	−0.469548	+	0.882907i	$0.655583\pi$
$812$	0.00610468	−	10.7006i	0.000214232	−	0.375516i
$813$	24.8787	−	23.5333i	0.872533	−	0.825350i
$814$	16.8955	−	12.4694i	0.592187	−	0.437054i
$815$	−0.595916	−	0.314951i	−0.0208740	−	0.0110322i
$816$	53.1596	−	26.2331i	1.86096	−	0.918343i
$817$	−15.3216	+	6.01329i	−0.536036	+	0.210379i
$818$	28.8824	+	36.2174i	1.00985	+	1.26631i
$819$	−33.1734	−	9.53784i	−1.15917	−	0.333279i
$820$	−1.20258	−	3.43677i	−0.0419959	−	0.120017i
$821$	−29.7765	+	20.3013i	−1.03921	+	0.708519i	−0.957587	−	0.288145i	$-0.906961\pi$
$821$	−29.7765	+	20.3013i	−1.03921	+	0.708519i	−0.0816191	+	0.996664i	$0.526009\pi$
$822$	−6.60776	+	5.79799i	−0.230472	+	0.202228i
$823$	31.3052	−	5.92327i	1.09123	−	0.206472i	0.391002	−	0.920390i	$-0.372129\pi$
$823$	31.3052	−	5.92327i	1.09123	−	0.206472i	0.700229	+	0.713918i	$0.253081\pi$
$824$	−15.9914	−	4.28489i	−0.557088	−	0.149271i
$825$	8.37018	−	1.34406i	0.291412	−	0.0467941i
$826$	7.59278	−	10.2879i	0.264187	−	0.357960i
$827$	−3.23614	−	0.364625i	−0.112532	−	0.0126793i	0.0555191	−	0.998458i	$-0.482319\pi$
$827$	−3.23614	−	0.364625i	−0.112532	−	0.0126793i	−0.168051	+	0.985778i	$0.553747\pi$
$828$	3.79729	−	28.9632i	0.131965	−	1.00654i
$829$	30.9466	−	30.9466i	1.07482	−	1.07482i	0.0778547	−	0.996965i	$-0.475193\pi$
$829$	30.9466	−	30.9466i	1.07482	−	1.07482i	0.996965	−	0.0778547i	$-0.0248070\pi$
$830$	−21.5914	−	25.0897i	−0.749449	−	0.870876i
$831$	−16.0810	+	47.4148i	−0.557843	+	1.64480i
$832$	−0.274733	−	3.66606i	−0.00952466	−	0.127098i
$833$	−15.0639	+	17.5046i	−0.521933	+	0.606497i
$834$	−20.4126	−	34.5832i	−0.706831	−	1.19752i
$835$	17.0360	−	2.56776i	0.589554	−	0.0888609i
$836$	−3.13884	−	2.50314i	−0.108559	−	0.0865728i
$837$	−23.1495	−	2.80886i	−0.800163	−	0.0970884i
$838$	−30.3866	+	19.0932i	−1.04969	+	0.659563i
$839$	0.545702	+	0.238087i	0.0188397	+	0.00821969i	0.409291	−	0.912404i	$-0.365776\pi$
$839$	0.545702	+	0.238087i	0.0188397	+	0.00821969i	−0.390451	+	0.920624i	$0.627681\pi$
$840$	4.41215	+	4.66438i	0.152234	+	0.160936i
$841$	29.0000	+	0.0330890i	0.999999	+	0.00114100i
$842$	−39.7160	+	22.9300i	−1.36870	+	0.790221i
$843$	4.53892	+	12.5820i	0.156329	+	0.433347i
$844$	−22.2921	+	0.834111i	−0.767326	+	0.0287113i
$845$	6.09680	+	26.7118i	0.209736	+	0.918915i
$846$	27.7784	+	5.78044i	0.955040	+	0.198735i
$847$	13.6876	−	10.9155i	0.470310	−	0.375060i
$848$	−16.3462	+	17.6171i	−0.561332	+	0.604972i
$849$	−1.34778	−	28.6441i	−0.0462557	−	0.983063i
$850$	−43.3615	+	3.24950i	−1.48729	+	0.111457i
$851$	3.12403	−	83.4914i	0.107090	−	2.86205i
$852$	−3.84009	−	2.77746i	−0.131559	−	0.0951542i
$853$	6.20756	−	1.66331i	0.212543	−	0.0569507i	−0.150976	−	0.988537i	$-0.548242\pi$
$853$	6.20756	−	1.66331i	0.212543	−	0.0569507i	0.363519	+	0.931587i	$0.381575\pi$
$854$	−2.42301	+	1.16686i	−0.0829139	+	0.0399292i
$855$	−3.48804	−	9.38513i	−0.119288	−	0.320965i
$856$	−0.225710	+	2.00323i	−0.00771461	+	0.0684691i
$857$	43.2317	+	3.23976i	1.47677	+	0.110668i	0.788609	−	0.614895i	$-0.210801\pi$
$857$	43.2317	+	3.23976i	1.47677	+	0.110668i	0.688156	+	0.725563i	$0.258421\pi$
$858$	−20.9065	−	12.8576i	−0.713735	−	0.438952i
$859$	−8.17519	−	43.2069i	−0.278934	−	1.47420i	−0.789174	−	0.614169i	$-0.789491\pi$
$859$	−8.17519	−	43.2069i	−0.278934	−	1.47420i	0.510241	−	0.860032i	$-0.329556\pi$
$860$	−6.99236	−	0.261636i	−0.238437	−	0.00892170i
$861$	−3.00057	−	9.40546i	−0.102259	−	0.320537i
$862$	−3.86545	+	20.4294i	−0.131658	+	0.695828i
$863$	−9.09567	+	39.8508i	−0.309620	+	1.35654i	0.545502	+	0.838109i	$0.316339\pi$
$863$	−9.09567	+	39.8508i	−0.309620	+	1.35654i	−0.855123	+	0.518426i	$0.826518\pi$
$864$	−9.00939	−	26.4709i	−0.306506	−	0.900557i
$865$	−9.76820	+	12.2489i	−0.332129	+	0.416476i
$866$	−17.0372	+	55.2333i	−0.578948	+	1.87690i
$867$	12.9178	−	50.1336i	0.438711	−	1.70263i
$868$	5.29536	+	7.17496i	0.179736	+	0.243534i
$869$	1.72708	+	2.99139i	0.0585871	+	0.101476i
$870$	13.7927	−	13.0319i	0.467615	−	0.441823i
$871$	−23.3272	+	40.4039i	−0.790411	+	1.36903i
$872$	−17.1607	+	1.93355i	−0.581136	+	0.0654783i
$873$	−0.291352	+	16.0384i	−0.00986077	+	0.542818i
$874$	−45.4275	+	10.3685i	−1.53661	+	0.350720i
$875$	−7.01094	−	17.8636i	−0.237013	−	0.603900i
$876$	−16.9212	+	6.82961i	−0.571714	+	0.230751i
$877$	18.4655	−	5.69585i	0.623535	−	0.192335i	0.0331415	−	0.999451i	$-0.489449\pi$
$877$	18.4655	−	5.69585i	0.623535	−	0.192335i	0.590393	+	0.807116i	$0.298973\pi$
$878$	14.4167	+	12.4066i	0.486540	+	0.418702i
$879$	2.84472	+	2.58904i	0.0959499	+	0.0873262i
$880$	3.66209	+	6.92901i	0.123449	+	0.233577i
$881$	6.78699	+	2.37487i	0.228660	+	0.0800115i	0.442177	−	0.896928i	$-0.354206\pi$
$881$	6.78699	+	2.37487i	0.228660	+	0.0800115i	−0.213517	+	0.976939i	$0.568492\pi$
$882$	11.7682	+	13.1545i	0.396257	+	0.442934i
$883$	15.8825	+	32.9804i	0.534489	+	1.10988i	0.977024	+	0.213127i	$0.0683649\pi$
$883$	15.8825	+	32.9804i	0.534489	+	1.10988i	−0.442535	+	0.896751i	$0.645921\pi$
$884$	34.7249	+	25.6282i	1.16793	+	0.861969i
$885$	7.71550	−	0.944562i	0.259354	−	0.0317511i
$886$	−32.2865	−	22.0126i	−1.08469	−	0.739526i
$887$	1.63158	−	6.08915i	0.0547832	−	0.204454i	−0.933109	−	0.359592i	$-0.882916\pi$
$887$	1.63158	−	6.08915i	0.0547832	−	0.204454i	0.987893	+	0.155139i	$0.0495824\pi$
$888$	−10.5762	−	23.6185i	−0.354914	−	0.792585i
$889$	15.2947	−	8.08351i	0.512969	−	0.271112i
$890$	0.161169	−	0.334671i	0.00540239	−	0.0112182i
$891$	11.5676	+	3.55456i	0.387530	+	0.119082i
$892$	14.4863	+	3.30641i	0.485038	+	0.110707i
$893$	−2.31250	−	15.3424i	−0.0773849	−	0.513415i
$894$	3.51055	+	41.4866i	0.117410	+	1.38752i
$895$	−8.46140	+	7.85103i	−0.282833	+	0.262431i
$896$	10.5230	−	19.9105i	0.351549	−	0.665164i
$897$	−91.8607	+	33.1385i	−3.06714	+	1.10646i
$898$	−38.2083	−	22.0596i	−1.27503	−	0.736137i
$899$	−19.4533	+	14.3401i	−0.648804	+	0.478268i
$900$	−0.632710	+	11.3754i	−0.0210903	+	0.379179i
$901$	3.68648	+	32.7184i	0.122815	+	1.09001i
$902$	−0.262483	−	7.01500i	−0.00873972	−	0.233574i
$903$	−18.9321	−	1.23578i	−0.630020	−	0.0411241i
$904$	−4.96931	+	32.9692i	−0.165277	+	1.09654i
$905$	−8.46860	+	21.5776i	−0.281506	+	0.717265i
$906$	42.1568	+	23.8016i	1.40057	+	0.790756i
$907$	−4.91895	−	0.930715i	−0.163331	−	0.0309039i	0.103603	−	0.994619i	$-0.466963\pi$
$907$	−4.91895	−	0.930715i	−0.163331	−	0.0309039i	−0.266934	+	0.963715i	$0.586011\pi$
$908$	−7.25958	−	3.49603i	−0.240918	−	0.116020i
$909$	4.17898	+	9.09680i	0.138608	+	0.301722i
$910$	−7.73089	+	22.0936i	−0.256277	+	0.732396i
$911$	−7.99810	−	29.8493i	−0.264989	−	0.988952i	−0.962257	−	0.272142i	$-0.912268\pi$
$911$	−7.99810	−	29.8493i	−0.264989	−	0.988952i	0.697268	−	0.716810i	$-0.254399\pi$
$912$	−19.2208	+	15.6328i	−0.636464	+	0.517655i
$913$	−8.74877	−	20.0524i	−0.289542	−	0.663637i
$914$	−12.2902	−	28.1695i	−0.406525	−	0.931765i
$915$	−1.52757	−	0.582636i	−0.0505000	−	0.0192613i
$916$	3.98886	+	14.8866i	0.131796	+	0.491868i
$917$	−0.773486	+	2.21050i	−0.0255428	+	0.0729971i
$918$	−57.5851	−	23.1703i	−1.90059	−	0.764735i
$919$	20.7552	+	9.99517i	0.684651	+	0.329710i	0.743670	−	0.668546i	$-0.233083\pi$
$919$	20.7552	+	9.99517i	0.684651	+	0.329710i	−0.0590198	+	0.998257i	$0.518798\pi$
$920$	17.8481	+	3.37705i	0.588435	+	0.111338i
$921$	5.90738	−	3.48681i	0.194655	−	0.114894i
$922$	7.00676	−	17.8529i	0.230755	−	0.587955i
$923$	−2.36139	+	15.6668i	−0.0777260	+	0.515678i
$924$	−2.04788	−	4.14989i	−0.0673703	−	0.136521i
$925$	1.21844	+	32.5634i	0.0400620	+	1.07068i
$926$	−4.26092	−	37.8167i	−0.140022	−	1.24273i
$927$	13.4252	+	26.5584i	0.440940	+	0.872292i
$928$	−25.6132	−	13.5557i	−0.840795	−	0.444987i
$929$	−23.2933	−	13.4484i	−0.764228	−	0.441227i	0.0665840	−	0.997781i	$-0.478790\pi$
$929$	−23.2933	−	13.4484i	−0.764228	−	0.441227i	−0.830812	+	0.556554i	$0.812123\pi$
$930$	−2.79032	+	15.5653i	−0.0914983	+	0.510406i
$931$	4.51002	−	8.53338i	0.147810	−	0.279670i
$932$	4.36024	−	4.04571i	0.142824	−	0.132522i
$933$	−12.7246	+	8.85596i	−0.416585	+	0.289931i
$934$	−1.18503	−	7.86216i	−0.0387754	−	0.257258i
$935$	10.4681	+	2.38928i	0.342344	+	0.0781377i
$936$	−20.9727	+	21.7955i	−0.685515	+	0.712409i
$937$	8.99142	−	18.6709i	0.293737	−	0.609951i	−0.700914	−	0.713246i	$-0.747224\pi$
$937$	8.99142	−	18.6709i	0.293737	−	0.609951i	0.994651	+	0.103295i	$0.0329386\pi$
$938$	−22.6861	+	11.9899i	−0.740726	+	0.391485i
$939$	−1.09012	−	0.112221i	−0.0355748	−	0.00366218i
$940$	1.70719	−	6.37132i	0.0556824	−	0.207810i
$941$	−33.0831	−	22.5556i	−1.07848	−	0.735293i	−0.112430	−	0.993660i	$-0.535863\pi$
$941$	−33.0831	−	22.5556i	−1.07848	−	0.735293i	−0.966047	+	0.258367i	$0.916816\pi$
$942$	11.4234	+	15.1706i	0.372196	+	0.494286i
$943$	−22.4731	−	16.5859i	−0.731826	−	0.540112i
$944$	−8.34552	−	17.3297i	−0.271624	−	0.564032i
$945$	0.960780	−	11.5009i	0.0312542	−	0.374126i
$946$	−12.7334	−	4.45561i	−0.413999	−	0.144864i
$947$	13.1935	+	24.9634i	0.428732	+	0.811201i	0.999954	−	0.00959510i	$-0.00305426\pi$
$947$	13.1935	+	24.9634i	0.428732	+	0.811201i	−0.571222	+	0.820796i	$0.693530\pi$
$948$	−4.42250	+	1.41088i	−0.143636	+	0.0458234i
$949$	46.2384	+	39.7914i	1.50096	+	1.29168i
$950$	17.3659	−	5.35668i	0.563425	−	0.173794i
$951$	−36.3698	−	28.4360i	−1.17937	−	0.922101i
$952$	−7.95225	−	20.2620i	−0.257734	−	0.656695i
$953$	3.67235	−	0.838191i	0.118959	−	0.0271517i	−0.162627	−	0.986688i	$-0.551997\pi$
$953$	3.67235	−	0.838191i	0.118959	−	0.0271517i	0.281586	+	0.959536i	$0.409140\pi$
$954$	25.1601	+	0.457057i	0.814590	+	0.0147978i
$955$	6.90192	−	0.777659i	0.223341	−	0.0251645i
$956$	2.50729	−	4.34275i	0.0810916	−	0.140455i
$957$	11.2499	−	5.54362i	0.363658	−	0.179200i
$958$	−24.6842	−	42.7543i	−0.797511	−	1.38133i
$959$	3.29044	+	4.45839i	0.106254	+	0.143969i
$960$	1.18420	−	0.329544i	0.0382198	−	0.0106360i
$961$	−3.20096	+	10.3773i	−0.103257	+	0.334750i
$962$	58.8223	−	73.7609i	1.89651	−	2.37815i
$963$	2.95415	−	2.09847i	0.0951963	−	0.0676221i
$964$	−1.04785	+	4.59093i	−0.0337490	+	0.147864i
$965$	2.45065	−	12.9520i	0.0788893	−	0.416940i
$966$	−52.4757	−	11.4474i	−1.68838	−	0.368313i
$967$	35.0122	+	1.31006i	1.12591	+	0.0421288i	0.593851	−	0.804575i	$-0.297607\pi$
$967$	35.0122	+	1.31006i	1.12591	+	0.0421288i	0.532064	+	0.846704i	$0.321416\pi$
$968$	−2.85213	−	15.0738i	−0.0916708	−	0.484492i
$969$	−0.942891	+	33.9303i	−0.0302900	+	1.09000i
$970$	10.8475	+	0.812904i	0.348291	+	0.0261008i
$971$	3.63582	−	32.2688i	0.116679	−	1.03555i	−0.789818	−	0.613342i	$-0.789825\pi$
$971$	3.63582	−	32.2688i	0.116679	−	1.03555i	0.906497	−	0.422213i	$-0.138746\pi$
$972$	−7.98065	+	14.1706i	−0.255979	+	0.454522i
$973$	−22.8061	+	10.9828i	−0.731130	+	0.352094i
$974$	48.0969	−	12.8875i	1.54112	−	0.412943i
$975$	34.7616	−	15.5660i	1.11326	−	0.498510i
$976$	−0.151269	+	4.04275i	−0.00484200	+	0.129405i
$977$	−9.72628	+	0.728884i	−0.311171	+	0.0233191i	−0.229401	−	0.973332i	$-0.573677\pi$
$977$	−9.72628	+	0.728884i	−0.311171	+	0.0233191i	−0.0817707	+	0.996651i	$0.526058\pi$
$978$	1.46973	−	0.943330i	0.0469968	−	0.0301644i
$979$	0.166989	−	0.179972i	0.00533701	−	0.00575192i
$980$	3.20803	−	2.55832i	0.102477	−	0.0817225i
$981$	23.1571	+	20.6722i	0.739350	+	0.660011i
$982$	3.69296	+	16.1799i	0.117847	+	0.516321i
$983$	4.91194	−	0.183792i	0.156667	−	0.00586205i	0.0410572	−	0.999157i	$-0.486927\pi$
$983$	4.91194	−	0.183792i	0.156667	−	0.00586205i	0.115609	+	0.993295i	$0.463118\pi$
$984$	−8.51545	−	1.52653i	−0.271463	−	0.0486639i
$985$	−9.15082	+	5.28323i	−0.291569	+	0.168338i
$986$	−59.8962	+	23.4681i	−1.90748	+	0.747377i
$987$	5.10697	−	17.1400i	0.162557	−	0.545571i
$988$	−16.5325	−	7.21305i	−0.525968	−	0.229478i
$989$	−45.4487	+	28.5573i	−1.44519	+	0.908070i
$990$	2.85061	−	7.69530i	0.0905984	−	0.244573i
$991$	12.0749	+	9.62938i	0.383571	+	0.305887i	0.796225	−	0.605000i	$-0.206827\pi$
$991$	12.0749	+	9.62938i	0.383571	+	0.305887i	−0.412655	+	0.910887i	$0.635398\pi$
$992$	23.8804	−	3.59939i	0.758204	−	0.114281i
$993$	−3.19013	+	0.0306837i	−0.101236	+	0.000973717i
$994$	−5.68401	+	6.60493i	−0.180286	+	0.209496i
$995$	0.688797	+	9.19135i	0.0218363	+	0.291385i
$996$	28.8355	−	5.74378i	0.913689	−	0.181999i
$997$	−7.84259	−	9.11325i	−0.248377	−	0.288620i	0.619919	−	0.784666i	$-0.287166\pi$
$997$	−7.84259	−	9.11325i	−0.248377	−	0.288620i	−0.868296	+	0.496046i	$0.834785\pi$
$998$	−39.5973	+	39.5973i	−1.25343	+	1.25343i
$999$	−18.9653	+	42.4748i	−0.600035	+	1.34384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.101.6	yes	672
3.2	odd	2		783.2.be.a.710.23		672
9.4	even	3		783.2.be.a.449.6		672
9.5	odd	6	inner	261.2.x.a.14.23	✓	672
29.27	odd	28	inner	261.2.x.a.56.23	yes	672
87.56	even	28		783.2.be.a.143.6		672
261.85	odd	84		783.2.be.a.665.23		672
261.230	even	84	inner	261.2.x.a.230.6	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.23	✓	672	9.5	odd	6	inner
261.2.x.a.56.23	yes	672	29.27	odd	28	inner
261.2.x.a.101.6	yes	672	1.1	even	1	trivial
261.2.x.a.230.6	yes	672	261.230	even	84	inner
783.2.be.a.143.6		672	87.56	even	28
783.2.be.a.449.6		672	9.4	even	3
783.2.be.a.665.23		672	261.85	odd	84
783.2.be.a.710.23		672	3.2	odd	2

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.697613 + 1.59895i) q^{2} +(-1.67727 - 0.432176i) q^{3} +(-0.709621 - 0.764789i) q^{4} +(-1.15314 - 0.173808i) q^{5} +(1.86111 - 2.38037i) q^{6} +(-1.39616 - 1.29545i) q^{7} +(-1.57532 + 0.551228i) q^{8} +(2.62645 + 1.44975i) q^{9} +(1.08236 - 1.72256i) q^{10} +(1.01917 - 0.877068i) q^{11} +(0.859699 + 1.58944i) q^{12} +(3.40307 - 4.99138i) q^{13} +(3.04533 - 1.32867i) q^{14} +(1.85901 + 0.789883i) q^{15} +(0.373510 - 4.98415i) q^{16} +(-4.84201 - 4.84201i) q^{17} +(-4.15032 + 3.18819i) q^{18} +(2.42324 + 1.52262i) q^{19} +(0.685366 + 1.00525i) q^{20} +(1.78187 + 2.77620i) q^{21} +(0.691398 + 2.24146i) q^{22} +(8.68782 + 3.40972i) q^{23} +(2.88046 - 0.243741i) q^{24} +(-3.47834 - 1.07293i) q^{25} +(5.60693 + 8.92337i) q^{26} +(-3.77871 - 3.56670i) q^{27} +1.98705i q^{28} +(-5.38516 - 0.00307224i) q^{29} +(-2.55985 + 2.42143i) q^{30} +(3.61087 - 2.66494i) q^{31} +(4.75769 + 2.51451i) q^{32} +(-2.08847 + 1.03062i) q^{33} +(11.1200 - 4.36426i) q^{34} +(1.38481 + 1.73650i) q^{35} +(-0.755029 - 3.03745i) q^{36} +(-2.95670 - 8.44975i) q^{37} +(-4.12507 + 2.81243i) q^{38} +(-7.86500 + 6.90115i) q^{39} +(1.91237 - 0.361841i) q^{40} +(-2.89074 - 0.774571i) q^{41} +(-5.68205 + 0.912406i) q^{42} +(-3.41519 + 4.62742i) q^{43} +(-1.39400 - 0.157066i) q^{44} +(-2.77669 - 2.12826i) q^{45} +(-11.5127 + 11.5127i) q^{46} +(-3.53637 - 4.10933i) q^{47} +(-2.78051 + 8.19833i) q^{48} +(-0.252031 - 3.36312i) q^{49} +(4.14208 - 4.81319i) q^{50} +(6.02874 + 10.2139i) q^{51} +(-6.23224 + 0.939359i) q^{52} +(-3.75928 - 2.99793i) q^{53} +(8.33904 - 3.55377i) q^{54} +(-1.32769 + 0.834243i) q^{55} +(2.91349 + 1.27114i) q^{56} +(-3.40638 - 3.60111i) q^{57} +(3.76167 - 8.60845i) q^{58} +(3.33276 - 1.92417i) q^{59} +(-0.715098 - 1.98227i) q^{60} +(-0.808853 + 0.0302651i) q^{61} +(1.74211 + 7.63268i) q^{62} +(-1.78887 - 5.42651i) q^{63} +(0.475788 - 0.379428i) q^{64} +(-4.79176 + 5.16429i) q^{65} +(-0.190955 - 4.05832i) q^{66} +(-7.70125 + 0.577129i) q^{67} +(-0.267126 + 7.13910i) q^{68} +(-13.0982 - 9.47367i) q^{69} +(-3.74263 + 1.00284i) q^{70} +(-2.36294 + 1.13793i) q^{71} +(-4.93664 - 0.836046i) q^{72} +(-1.13062 + 10.0345i) q^{73} +(15.5733 + 1.16706i) q^{74} +(5.37041 + 3.30284i) q^{75} +(-0.555095 - 2.93375i) q^{76} +(-2.55912 - 0.0957557i) q^{77} +(-5.54785 - 17.3901i) q^{78} +(-0.477589 + 2.52412i) q^{79} +(-1.29700 + 5.68251i) q^{80} +(4.79646 + 7.61538i) q^{81} +(3.25512 - 4.08179i) q^{82} +(4.79591 - 15.5480i) q^{83} +(0.858753 - 3.33281i) q^{84} +(4.74194 + 6.42510i) q^{85} +(-5.01651 - 8.68885i) q^{86} +(9.03103 + 2.33249i) q^{87} +(-1.12206 + 1.94346i) q^{88} +(0.181441 - 0.0204435i) q^{89} +(5.34003 - 2.95507i) q^{90} +(-11.2173 + 2.56028i) q^{91} +(-3.55734 - 9.06395i) q^{92} +(-7.20811 + 2.90929i) q^{93} +(9.03762 - 2.78774i) q^{94} +(-2.52969 - 2.17698i) q^{95} +(-6.89320 - 6.27367i) q^{96} +(2.49849 + 4.72738i) q^{97} +(5.55326 + 1.94317i) q^{98} +(3.94833 - 0.826031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more