LMFDB - Embedded newform 552.2.n.a.91.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(91,552)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("552.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.n (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.19
Character	$\chi$	$=$	552.91
Dual form			552.2.n.a.91.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.869059 + 1.11568i) q^{2} +1.00000 q^{3} +(-0.489471 + 1.93918i) q^{4} -1.54212 q^{5} +(0.869059 + 1.11568i) q^{6} -2.92435 q^{7} +(-2.58888 + 1.13917i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.869059 + 1.11568i) q^{2} +1.00000 q^{3} +(-0.489471 + 1.93918i) q^{4} -1.54212 q^{5} +(0.869059 + 1.11568i) q^{6} -2.92435 q^{7} +(-2.58888 + 1.13917i) q^{8} +1.00000 q^{9} +(-1.34019 - 1.72051i) q^{10} +4.46647i q^{11} +(-0.489471 + 1.93918i) q^{12} +2.71706i q^{13} +(-2.54143 - 3.26263i) q^{14} -1.54212 q^{15} +(-3.52084 - 1.89835i) q^{16} +0.363371i q^{17} +(0.869059 + 1.11568i) q^{18} +1.20124i q^{19} +(0.754824 - 2.99045i) q^{20} -2.92435 q^{21} +(-4.98314 + 3.88163i) q^{22} +(3.23754 + 3.53813i) q^{23} +(-2.58888 + 1.13917i) q^{24} -2.62187 q^{25} +(-3.03136 + 2.36129i) q^{26} +1.00000 q^{27} +(1.43138 - 5.67084i) q^{28} -3.26887i q^{29} +(-1.34019 - 1.72051i) q^{30} +1.19384i q^{31} +(-0.941874 - 5.57789i) q^{32} +4.46647i q^{33} +(-0.405405 + 0.315791i) q^{34} +4.50969 q^{35} +(-0.489471 + 1.93918i) q^{36} +9.28288 q^{37} +(-1.34019 + 1.04395i) q^{38} +2.71706i q^{39} +(3.99236 - 1.75674i) q^{40} +3.65655 q^{41} +(-2.54143 - 3.26263i) q^{42} -8.22067i q^{43} +(-8.66128 - 2.18621i) q^{44} -1.54212 q^{45} +(-1.13380 + 6.68689i) q^{46} -2.10971i q^{47} +(-3.52084 - 1.89835i) q^{48} +1.55181 q^{49} +(-2.27856 - 2.92516i) q^{50} +0.363371i q^{51} +(-5.26887 - 1.32992i) q^{52} +8.60653 q^{53} +(0.869059 + 1.11568i) q^{54} -6.88783i q^{55} +(7.57078 - 3.33133i) q^{56} +1.20124i q^{57} +(3.64700 - 2.84084i) q^{58} +13.8664 q^{59} +(0.754824 - 2.99045i) q^{60} -5.63721 q^{61} +(-1.33194 + 1.03752i) q^{62} -2.92435 q^{63} +(5.40458 - 5.89835i) q^{64} -4.19004i q^{65} +(-4.98314 + 3.88163i) q^{66} +10.2726i q^{67} +(-0.704642 - 0.177860i) q^{68} +(3.23754 + 3.53813i) q^{69} +(3.91919 + 5.03136i) q^{70} +6.80616i q^{71} +(-2.58888 + 1.13917i) q^{72} -12.4268 q^{73} +(8.06738 + 10.3567i) q^{74} -2.62187 q^{75} +(-2.32942 - 0.587972i) q^{76} -13.0615i q^{77} +(-3.03136 + 2.36129i) q^{78} +2.37999 q^{79} +(5.42955 + 2.92748i) q^{80} +1.00000 q^{81} +(3.17776 + 4.07953i) q^{82} +16.3023i q^{83} +(1.43138 - 5.67084i) q^{84} -0.560362i q^{85} +(9.17162 - 7.14425i) q^{86} -3.26887i q^{87} +(-5.08807 - 11.5631i) q^{88} +2.99042i q^{89} +(-1.34019 - 1.72051i) q^{90} -7.94563i q^{91} +(-8.44575 + 4.54635i) q^{92} +1.19384i q^{93} +(2.35376 - 1.83347i) q^{94} -1.85245i q^{95} +(-0.941874 - 5.57789i) q^{96} -13.6119i q^{97} +(1.34861 + 1.73132i) q^{98} +4.46647i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9	$ 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 4 q^{24} + 24 q^{25} + 24 q^{27} - 4 q^{32} + 4 q^{36} + 4 q^{46} + 4 q^{48} - 8 q^{49} - 44 q^{50} - 4 q^{54} + 48 q^{58} - 40 q^{62} + 4 q^{64} - 4 q^{72} - 32 q^{73} + 24 q^{75} + 24 q^{81} - 40 q^{82} - 52 q^{92} + 40 q^{94} - 4 q^{96} - 20 q^{98}+O(q^{100}) $ 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 4 * q^24 + 24 * q^25 + 24 * q^27 - 4 * q^32 + 4 * q^36 + 4 * q^46 + 4 * q^48 - 8 * q^49 - 44 * q^50 - 4 * q^54 + 48 * q^58 - 40 * q^62 + 4 * q^64 - 4 * q^72 - 32 * q^73 + 24 * q^75 + 24 * q^81 - 40 * q^82 - 52 * q^92 + 40 * q^94 - 4 * q^96 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.869059	+	1.11568i	0.614518	+	0.788903i
$2$	0.869059	+	1.11568i	0.614518	+	0.788903i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.489471	+	1.93918i	−0.244736	+	0.969590i
$5$	−1.54212			−0.689657			−0.344829	−	0.938666i	$-0.612063\pi$
$5$	−1.54212			−0.689657			−0.344829	+	0.938666i	$0.612063\pi$
$6$	0.869059	+	1.11568i	0.354792	+	0.455473i
$7$	−2.92435			−1.10530			−0.552650	−	0.833414i	$-0.686383\pi$
$7$	−2.92435			−1.10530			−0.552650	+	0.833414i	$0.686383\pi$
$8$	−2.58888	+	1.13917i	−0.915307	+	0.402757i
$9$	1.00000			0.333333
$10$	−1.34019	−	1.72051i	−0.423807	−	0.544072i
$11$			4.46647i			1.34669i	0.739328	+	0.673345i	$0.235143\pi$
$11$			4.46647i			1.34669i	−0.739328	+	0.673345i	$0.764857\pi$
$12$	−0.489471	+	1.93918i	−0.141298	+	0.559793i
$13$			2.71706i			0.753577i	0.926299	+	0.376789i	$0.122972\pi$
$13$			2.71706i			0.753577i	−0.926299	+	0.376789i	$0.877028\pi$
$14$	−2.54143	−	3.26263i	−0.679226	−	0.871974i
$15$	−1.54212			−0.398174
$16$	−3.52084	−	1.89835i	−0.880209	−	0.474587i
$17$			0.363371i			0.0881305i	0.999029	+	0.0440652i	$0.0140309\pi$
$17$			0.363371i			0.0881305i	−0.999029	+	0.0440652i	$0.985969\pi$
$18$	0.869059	+	1.11568i	0.204839	+	0.262968i
$19$			1.20124i			0.275583i	0.990461	+	0.137791i	$0.0440004\pi$
$19$			1.20124i			0.275583i	−0.990461	+	0.137791i	$0.956000\pi$
$20$	0.754824	−	2.99045i	0.168784	−	0.668684i
$21$	−2.92435			−0.638145
$22$	−4.98314	+	3.88163i	−1.06241	+	0.827565i
$23$	3.23754	+	3.53813i	0.675073	+	0.737751i
$23$	3.23754	+	3.53813i	0.675073	+	0.737751i
$24$	−2.58888	+	1.13917i	−0.528453	+	0.232532i
$25$	−2.62187			−0.524373
$26$	−3.03136	+	2.36129i	−0.594499	+	0.463087i
$27$	1.00000			0.192450
$28$	1.43138	−	5.67084i	0.270506	−	1.07169i
$29$		−	3.26887i		−	0.607014i	−0.952829	−	0.303507i	$-0.901842\pi$
$29$		−	3.26887i		−	0.607014i	0.952829	−	0.303507i	$-0.0981576\pi$
$30$	−1.34019	−	1.72051i	−0.244685	−	0.314120i
$31$			1.19384i			0.214420i	0.994236	+	0.107210i	$0.0341917\pi$
$31$			1.19384i			0.214420i	−0.994236	+	0.107210i	$0.965808\pi$
$32$	−0.941874	−	5.57789i	−0.166501	−	0.986041i
$33$			4.46647i			0.777512i
$34$	−0.405405	+	0.315791i	−0.0695264	+	0.0541577i
$35$	4.50969			0.762278
$36$	−0.489471	+	1.93918i	−0.0815786	+	0.323197i
$37$	9.28288			1.52610			0.763048	−	0.646342i	$-0.223702\pi$
$37$	9.28288			1.52610			0.763048	+	0.646342i	$0.223702\pi$
$38$	−1.34019	+	1.04395i	−0.217408	+	0.169351i
$39$			2.71706i			0.435078i
$40$	3.99236	−	1.75674i	0.631248	−	0.277765i
$41$	3.65655			0.571057			0.285528	−	0.958370i	$-0.407831\pi$
$41$	3.65655			0.571057			0.285528	+	0.958370i	$0.407831\pi$
$42$	−2.54143	−	3.26263i	−0.392151	−	0.503434i
$43$		−	8.22067i		−	1.25364i	−0.779164	−	0.626820i	$-0.784356\pi$
$43$		−	8.22067i		−	1.25364i	0.779164	−	0.626820i	$-0.215644\pi$
$44$	−8.66128	−	2.18621i	−1.30574	−	0.329583i
$45$	−1.54212			−0.229886
$46$	−1.13380	+	6.68689i	−0.167169	+	0.985928i
$47$		−	2.10971i		−	0.307733i	−0.988092	−	0.153867i	$-0.950827\pi$
$47$		−	2.10971i		−	0.307733i	0.988092	−	0.153867i	$-0.0491726\pi$
$48$	−3.52084	−	1.89835i	−0.508189	−	0.274003i
$49$	1.55181			0.221687
$50$	−2.27856	−	2.92516i	−0.322237	−	0.413680i
$51$			0.363371i			0.0508822i
$52$	−5.26887	−	1.32992i	−0.730661	−	0.184427i
$53$	8.60653			1.18220			0.591099	−	0.806599i	$-0.298694\pi$
$53$	8.60653			1.18220			0.591099	+	0.806599i	$0.298694\pi$
$54$	0.869059	+	1.11568i	0.118264	+	0.151824i
$55$		−	6.88783i		−	0.928755i
$56$	7.57078	−	3.33133i	1.01169	−	0.445168i
$57$			1.20124i			0.159108i
$58$	3.64700	−	2.84084i	0.478875	−	0.373021i
$59$	13.8664			1.80526			0.902628	−	0.430422i	$-0.141635\pi$
$59$	13.8664			1.80526			0.902628	+	0.430422i	$0.141635\pi$
$60$	0.754824	−	2.99045i	0.0974473	−	0.386065i
$61$	−5.63721			−0.721771			−0.360885	−	0.932610i	$-0.617525\pi$
$61$	−5.63721			−0.721771			−0.360885	+	0.932610i	$0.617525\pi$
$62$	−1.33194	+	1.03752i	−0.169156	+	0.131765i
$63$	−2.92435			−0.368433
$64$	5.40458	−	5.89835i	0.675573	−	0.737293i
$65$		−	4.19004i		−	0.519710i
$66$	−4.98314	+	3.88163i	−0.613382	+	0.477795i
$67$			10.2726i			1.25500i	0.778616	+	0.627501i	$0.215922\pi$
$67$			10.2726i			1.25500i	−0.778616	+	0.627501i	$0.784078\pi$
$68$	−0.704642	−	0.177860i	−0.0854504	−	0.0215687i
$69$	3.23754	+	3.53813i	0.389754	+	0.425941i
$70$	3.91919	+	5.03136i	0.468433	+	0.601363i
$71$			6.80616i			0.807743i	0.914816	+	0.403871i	$0.132336\pi$
$71$			6.80616i			0.807743i	−0.914816	+	0.403871i	$0.867664\pi$
$72$	−2.58888	+	1.13917i	−0.305102	+	0.134252i
$73$	−12.4268			−1.45445			−0.727223	−	0.686401i	$-0.759189\pi$
$73$	−12.4268			−1.45445			−0.727223	+	0.686401i	$0.759189\pi$
$74$	8.06738	+	10.3567i	0.937813	+	1.20394i
$75$	−2.62187			−0.302747
$76$	−2.32942	−	0.587972i	−0.267202	−	0.0674450i
$77$		−	13.0615i		−	1.48850i
$78$	−3.03136	+	2.36129i	−0.343234	+	0.267363i
$79$	2.37999			0.267769			0.133885	−	0.990997i	$-0.457255\pi$
$79$	2.37999			0.267769			0.133885	+	0.990997i	$0.457255\pi$
$80$	5.42955	+	2.92748i	0.607042	+	0.327302i
$81$	1.00000			0.111111
$82$	3.17776	+	4.07953i	0.350925	+	0.450508i
$83$			16.3023i			1.78941i	0.446656	+	0.894706i	$0.352615\pi$
$83$			16.3023i			1.78941i	−0.446656	+	0.894706i	$0.647385\pi$
$84$	1.43138	−	5.67084i	0.156177	−	0.618739i
$85$		−	0.560362i		−	0.0607798i
$86$	9.17162	−	7.14425i	0.989001	−	0.770385i
$87$		−	3.26887i		−	0.350460i
$88$	−5.08807	−	11.5631i	−0.542390	−	1.23264i
$89$			2.99042i			0.316984i	0.987360	+	0.158492i	$0.0506633\pi$
$89$			2.99042i			0.316984i	−0.987360	+	0.158492i	$0.949337\pi$
$90$	−1.34019	−	1.72051i	−0.141269	−	0.181357i
$91$		−	7.94563i		−	0.832929i
$92$	−8.44575	+	4.54635i	−0.880530	+	0.473990i
$93$			1.19384i			0.123795i
$94$	2.35376	−	1.83347i	0.242772	−	0.189108i
$95$		−	1.85245i		−	0.190058i
$96$	−0.941874	−	5.57789i	−0.0961296	−	0.569291i
$97$		−	13.6119i		−	1.38208i	−0.722815	−	0.691042i	$-0.757152\pi$
$97$		−	13.6119i		−	1.38208i	0.722815	−	0.691042i	$-0.242848\pi$
$98$	1.34861	+	1.73132i	0.136231	+	0.174890i
$99$			4.46647i			0.448897i
$100$	1.28333	−	5.08427i	0.128333	−	0.508427i
$101$		−	12.7451i		−	1.26819i	−0.773257	−	0.634093i	$-0.781374\pi$
$101$		−	12.7451i		−	1.26819i	0.773257	−	0.634093i	$-0.218626\pi$
$102$	−0.405405	+	0.315791i	−0.0401411	+	0.0312680i
$103$	−14.2608			−1.40516			−0.702580	−	0.711605i	$-0.747969\pi$
$103$	−14.2608			−1.40516			−0.702580	+	0.711605i	$0.747969\pi$
$104$	−3.09520	−	7.03414i	−0.303509	−	0.689754i
$105$	4.50969			0.440101
$106$	7.47959	+	9.60211i	0.726482	+	0.932640i
$107$			15.8754i			1.53473i	0.641209	+	0.767366i	$0.278433\pi$
$107$			15.8754i			1.53473i	−0.641209	+	0.767366i	$0.721567\pi$
$108$	−0.489471	+	1.93918i	−0.0470994	+	0.186598i
$109$	−4.48354			−0.429445			−0.214723	−	0.976675i	$-0.568885\pi$
$109$	−4.48354			−0.429445			−0.214723	+	0.976675i	$0.568885\pi$
$110$	7.68459	−	5.98593i	0.732697	−	0.570736i
$111$	9.28288			0.881092
$112$	10.2961	+	5.55142i	0.972894	+	0.524560i
$113$		−	1.06221i		−	0.0999242i	−0.998751	−	0.0499621i	$-0.984090\pi$
$113$		−	1.06221i		−	0.0999242i	0.998751	−	0.0499621i	$-0.0159101\pi$
$114$	−1.34019	+	1.04395i	−0.125521	+	0.0977746i
$115$	−4.99267	−	5.45622i	−0.465569	−	0.508795i
$116$	6.33893	+	1.60002i	0.588555	+	0.148558i
$117$			2.71706i			0.251192i
$118$	12.0508	+	15.4705i	1.10936	+	1.42417i
$119$		−	1.06262i		−	0.0974106i
$120$	3.99236	−	1.75674i	0.364451	−	0.160367i
$121$	−8.94933			−0.813576
$122$	−4.89907	−	6.28930i	−0.443541	−	0.569407i
$123$	3.65655			0.329700
$124$	−2.31507	−	0.584350i	−0.207899	−	0.0524762i
$125$	11.7538			1.05129
$126$	−2.54143	−	3.26263i	−0.226409	−	0.290658i
$127$			6.79761i			0.603190i	0.953436	+	0.301595i	$0.0975191\pi$
$127$			6.79761i			0.603190i	−0.953436	+	0.301595i	$0.902481\pi$
$128$	11.2776	+	0.903757i	0.996804	+	0.0798815i
$129$		−	8.22067i		−	0.723790i
$130$	4.67473	−	3.64139i	0.410001	−	0.319371i
$131$	6.25067			0.546124			0.273062	−	0.961996i	$-0.411964\pi$
$131$	6.25067			0.546124			0.273062	+	0.961996i	$0.411964\pi$
$132$	−8.66128	−	2.18621i	−0.753868	−	0.190285i
$133$		−	3.51284i		−	0.304602i
$134$	−11.4609	+	8.92753i	−0.990075	+	0.771221i
$135$	−1.54212			−0.132725
$136$	−0.413942	−	0.940724i	−0.0354952	−	0.0806664i
$137$		−	3.96407i		−	0.338673i	−0.985558	−	0.169337i	$-0.945838\pi$
$137$		−	3.96407i		−	0.338673i	0.985558	−	0.169337i	$-0.0541625\pi$
$138$	−1.13380	+	6.68689i	−0.0965152	+	0.569226i
$139$	7.53897			0.639447			0.319723	−	0.947511i	$-0.396410\pi$
$139$	7.53897			0.639447			0.319723	+	0.947511i	$0.396410\pi$
$140$	−2.20737	+	8.74511i	−0.186557	+	0.739097i
$141$		−	2.10971i		−	0.177670i
$142$	−7.59348	+	5.91496i	−0.637231	+	0.496372i
$143$	−12.1357			−1.01484
$144$	−3.52084	−	1.89835i	−0.293403	−	0.158196i
$145$			5.04099i			0.418632i
$146$	−10.7996	−	13.8643i	−0.893783	−	1.14742i
$147$	1.55181			0.127991
$148$	−4.54371	+	18.0012i	−0.373490	+	1.47969i
$149$	15.0167			1.23021			0.615107	−	0.788444i	$-0.289113\pi$
$149$	15.0167			1.23021			0.615107	+	0.788444i	$0.289113\pi$
$150$	−2.27856	−	2.92516i	−0.186043	−	0.238838i
$151$			21.5072i			1.75023i	0.483911	+	0.875117i	$0.339216\pi$
$151$			21.5072i			1.75023i	−0.483911	+	0.875117i	$0.660784\pi$
$152$	−1.36841	−	3.10986i	−0.110993	−	0.252243i
$153$			0.363371i			0.0293768i
$154$	14.5724	−	11.3512i	1.17428	−	0.914708i
$155$		−	1.84104i		−	0.147876i
$156$	−5.26887	−	1.32992i	−0.421847	−	0.106479i
$157$	3.34071			0.266617			0.133309	−	0.991075i	$-0.457440\pi$
$157$	3.34071			0.266617			0.133309	+	0.991075i	$0.457440\pi$
$158$	2.06835	+	2.65530i	0.164549	+	0.211244i
$159$	8.60653			0.682543
$160$	1.45248	+	8.60178i	0.114829	+	0.680030i
$161$	−9.46768	−	10.3467i	−0.746158	−	0.815436i
$162$	0.869059	+	1.11568i	0.0682798	+	0.0876559i
$163$	−4.58649			−0.359242			−0.179621	−	0.983736i	$-0.557487\pi$
$163$	−4.58649			−0.359242			−0.179621	+	0.983736i	$0.557487\pi$
$164$	−1.78978	+	7.09070i	−0.139758	+	0.553691i
$165$		−	6.88783i		−	0.536217i
$166$	−18.1881	+	14.1677i	−1.41167	+	1.09963i
$167$		−	1.30440i		−	0.100937i	−0.998726	−	0.0504686i	$-0.983929\pi$
$167$		−	1.30440i		−	0.100937i	0.998726	−	0.0504686i	$-0.0160715\pi$
$168$	7.57078	−	3.33133i	0.584098	−	0.257018i
$169$	5.61758			0.432121
$170$	0.625183	−	0.486988i	0.0479494	−	0.0373503i
$171$			1.20124i			0.0918610i
$172$	15.9414	+	4.02379i	1.21552	+	0.306811i
$173$		−	1.43712i		−	0.109262i	−0.998507	−	0.0546311i	$-0.982602\pi$
$173$		−	1.43712i		−	0.109262i	0.998507	−	0.0546311i	$-0.0173983\pi$
$174$	3.64700	−	2.84084i	0.276479	−	0.215364i
$175$	7.66725			0.579589
$176$	8.47890	−	15.7257i	0.639121	−	1.18537i
$177$	13.8664			1.04226
$178$	−3.33635	+	2.59886i	−0.250070	+	0.194792i
$179$	16.0065			1.19639			0.598193	−	0.801352i	$-0.295886\pi$
$179$	16.0065			1.19639			0.598193	+	0.801352i	$0.295886\pi$
$180$	0.754824	−	2.99045i	0.0562612	−	0.222895i
$181$	−17.7729			−1.32105			−0.660524	−	0.750805i	$-0.729666\pi$
$181$	−17.7729			−1.32105			−0.660524	+	0.750805i	$0.729666\pi$
$182$	8.86476	−	6.90523i	0.657100	−	0.511849i
$183$	−5.63721			−0.416714
$184$	−12.4121	−	5.47168i	−0.915034	−	0.403377i
$185$	−14.3153			−1.05248
$186$	−1.33194	+	1.03752i	−0.0976624	+	0.0760744i
$187$	−1.62299			−0.118684
$188$	4.09111	+	1.03264i	0.298375	+	0.0753134i
$189$	−2.92435			−0.212715
$190$	2.06674	−	1.60989i	0.149937	−	0.116794i
$191$	−8.65813			−0.626480			−0.313240	−	0.949674i	$-0.601414\pi$
$191$	−8.65813			−0.626480			−0.313240	+	0.949674i	$0.601414\pi$
$192$	5.40458	−	5.89835i	0.390042	−	0.425676i
$193$	−3.22385			−0.232058			−0.116029	−	0.993246i	$-0.537017\pi$
$193$	−3.22385			−0.232058			−0.116029	+	0.993246i	$0.537017\pi$
$194$	15.1865	−	11.8296i	1.09033	−	0.849315i
$195$		−	4.19004i		−	0.300055i
$196$	−0.759566	+	3.00924i	−0.0542547	+	0.214945i
$197$		−	4.82934i		−	0.344076i	−0.985090	−	0.172038i	$-0.944965\pi$
$197$		−	4.82934i		−	0.344076i	0.985090	−	0.172038i	$-0.0550352\pi$
$198$	−4.98314	+	3.88163i	−0.354136	+	0.275855i
$199$	10.7430			0.761550			0.380775	−	0.924668i	$-0.375657\pi$
$199$	10.7430			0.761550			0.380775	+	0.924668i	$0.375657\pi$
$200$	6.78769	−	2.98675i	0.479962	−	0.211195i
$201$			10.2726i			0.724576i
$202$	14.2194	−	11.0763i	1.00048	−	0.779323i
$203$			9.55931i			0.670932i
$204$	−0.704642	−	0.177860i	−0.0493348	−	0.0124527i
$205$	−5.63883			−0.393833
$206$	−12.3935	−	15.9105i	−0.863496	−	1.10853i
$207$	3.23754	+	3.53813i	0.225024	+	0.245917i
$208$	5.15792	−	9.56633i	0.357638	−	0.663305i
$209$	−5.36529			−0.371125
$210$	3.91919	+	5.03136i	0.270450	+	0.347197i
$211$	−2.06691			−0.142292			−0.0711461	−	0.997466i	$-0.522666\pi$
$211$	−2.06691			−0.142292			−0.0711461	+	0.997466i	$0.522666\pi$
$212$	−4.21265	+	16.6896i	−0.289326	+	1.14625i
$213$			6.80616i			0.466351i
$214$	−17.7118	+	13.7967i	−1.21075	+	0.943120i
$215$			12.6773i			0.864582i
$216$	−2.58888	+	1.13917i	−0.176151	+	0.0775107i
$217$		−	3.49120i		−	0.236998i
$218$	−3.89646	−	5.00218i	−0.263902	−	0.338791i
$219$	−12.4268			−0.839725
$220$	13.3567	+	3.37140i	0.900511	+	0.227299i
$221$	−0.987302			−0.0664131
$222$	8.06738	+	10.3567i	0.541447	+	0.695096i
$223$			0.0731140i			0.00489608i	0.999997	+	0.00244804i	$0.000779236\pi$
$223$			0.0731140i			0.00489608i	−0.999997	+	0.00244804i	$0.999221\pi$
$224$	2.75437	+	16.3117i	0.184034	+	1.08987i
$225$	−2.62187			−0.174791
$226$	1.18508	−	0.923122i	0.0788305	−	0.0614052i
$227$		−	8.30924i		−	0.551504i	−0.961229	−	0.275752i	$-0.911073\pi$
$227$		−	8.30924i		−	0.551504i	0.961229	−	0.275752i	$-0.0889268\pi$
$228$	−2.32942	−	0.587972i	−0.154269	−	0.0389394i
$229$	21.0452			1.39071			0.695354	−	0.718668i	$-0.255248\pi$
$229$	21.0452			1.39071			0.695354	+	0.718668i	$0.255248\pi$
$230$	1.74845	−	10.3120i	0.115289	−	0.679952i
$231$		−	13.0615i		−	0.859384i
$232$	3.72380	+	8.46271i	0.244479	+	0.555604i
$233$	−9.22887			−0.604603			−0.302302	−	0.953212i	$-0.597755\pi$
$233$	−9.22887			−0.604603			−0.302302	+	0.953212i	$0.597755\pi$
$234$	−3.03136	+	2.36129i	−0.198166	+	0.154362i
$235$			3.25343i			0.212230i
$236$	−6.78722	+	26.8895i	−0.441811	+	1.75036i
$237$	2.37999			0.154597
$238$	1.18555	−	0.923483i	0.0768475	−	0.0598605i
$239$		−	6.75131i		−	0.436706i	−0.975870	−	0.218353i	$-0.929932\pi$
$239$		−	6.75131i		−	0.436706i	0.975870	−	0.218353i	$-0.0700684\pi$
$240$	5.42955	+	2.92748i	0.350476	+	0.188968i
$241$		−	14.5268i		−	0.935753i	−0.883794	−	0.467876i	$-0.845019\pi$
$241$		−	14.5268i		−	0.935753i	0.883794	−	0.467876i	$-0.154981\pi$
$242$	−7.77750	−	9.98457i	−0.499957	−	0.641832i
$243$	1.00000			0.0641500
$244$	2.75925	−	10.9316i	0.176643	−	0.699821i
$245$	−2.39308			−0.152888
$246$	3.17776	+	4.07953i	0.202606	+	0.260101i
$247$	−3.26384			−0.207673
$248$	−1.35998	−	3.09070i	−0.0863591	−	0.196260i
$249$			16.3023i			1.03312i
$250$	10.2148	+	13.1135i	0.646039	+	0.829369i
$251$		−	20.4199i		−	1.28889i	−0.764650	−	0.644446i	$-0.777088\pi$
$251$		−	20.4199i		−	1.28889i	0.764650	−	0.644446i	$-0.222912\pi$
$252$	1.43138	−	5.67084i	0.0901688	−	0.357229i
$253$	−15.8029	+	14.4604i	−0.993522	+	0.909115i
$254$	−7.58394	+	5.90753i	−0.475859	+	0.370671i
$255$		−	0.560362i		−	0.0350912i
$256$	8.79256	+	13.3675i	0.549535	+	0.835471i
$257$	−20.4408			−1.27506			−0.637530	−	0.770425i	$-0.720044\pi$
$257$	−20.4408			−1.27506			−0.637530	+	0.770425i	$0.720044\pi$
$258$	9.17162	−	7.14425i	0.571000	−	0.444782i
$259$	−27.1464			−1.68679
$260$	8.12523	+	2.05090i	0.503905	+	0.127192i
$261$		−	3.26887i		−	0.202338i
$262$	5.43220	+	6.97373i	0.335603	+	0.430839i
$263$	−15.7540			−0.971432			−0.485716	−	0.874117i	$-0.661441\pi$
$263$	−15.7540			−0.971432			−0.485716	+	0.874117i	$0.661441\pi$
$264$	−5.08807	−	11.5631i	−0.313149	−	0.711662i
$265$	−13.2723			−0.815311
$266$	3.91919	−	3.05286i	0.240301	−	0.187183i
$267$			2.99042i			0.183011i
$268$	−19.9205	−	5.02816i	−1.21684	−	0.307144i
$269$			25.4000i			1.54867i	0.632777	+	0.774334i	$0.281915\pi$
$269$			25.4000i			1.54867i	−0.632777	+	0.774334i	$0.718085\pi$
$270$	−1.34019	−	1.72051i	−0.0815616	−	0.104707i
$271$		−	19.1184i		−	1.16136i	−0.814132	−	0.580679i	$-0.802787\pi$
$271$		−	19.1184i		−	1.16136i	0.814132	−	0.580679i	$-0.197213\pi$
$272$	0.689804	−	1.27937i	0.0418255	−	0.0775732i
$273$		−	7.94563i		−	0.480892i
$274$	4.42262	−	3.44501i	0.267180	−	0.208121i
$275$		−	11.7105i		−	0.706168i
$276$	−8.44575	+	4.54635i	−0.508374	+	0.273658i
$277$		−	3.47221i		−	0.208625i	−0.994545	−	0.104312i	$-0.966736\pi$
$277$		−	3.47221i		−	0.208625i	0.994545	−	0.104312i	$-0.0332642\pi$
$278$	6.55181	+	8.41105i	0.392951	+	0.504461i
$279$			1.19384i			0.0714732i
$280$	−11.6751	+	5.13731i	−0.697718	+	0.307013i
$281$		−	28.2786i		−	1.68696i	−0.537161	−	0.843480i	$-0.680503\pi$
$281$		−	28.2786i		−	1.68696i	0.537161	−	0.843480i	$-0.319497\pi$
$282$	2.35376	−	1.83347i	0.140164	−	0.109181i
$283$		−	31.7425i		−	1.88689i	−0.331525	−	0.943446i	$-0.607563\pi$
$283$		−	31.7425i		−	1.88689i	0.331525	−	0.943446i	$-0.392437\pi$
$284$	−13.1984	−	3.33142i	−0.783179	−	0.197684i
$285$		−	1.85245i		−	0.109730i
$286$	−10.5466	−	13.5395i	−0.623635	−	0.800607i
$287$	−10.6930			−0.631189
$288$	−0.941874	−	5.57789i	−0.0555004	−	0.328680i
$289$	16.8680			0.992233
$290$	−5.62412	+	4.38092i	−0.330260	+	0.257257i
$291$		−	13.6119i		−	0.797946i
$292$	6.08256	−	24.0978i	0.355955	−	1.41022i
$293$	−3.79012			−0.221421			−0.110711	−	0.993853i	$-0.535313\pi$
$293$	−3.79012			−0.221421			−0.110711	+	0.993853i	$0.535313\pi$
$294$	1.34861	+	1.73132i	0.0786528	+	0.100973i
$295$	−21.3837			−1.24501
$296$	−24.0323	+	10.5748i	−1.39685	+	0.614647i
$297$			4.46647i			0.259171i
$298$	13.0504	+	16.7538i	0.755988	+	0.970519i
$299$	−9.61331	+	8.79659i	−0.555952	+	0.508720i
$300$	1.28333	−	5.08427i	0.0740930	−	0.293540i
$301$			24.0401i			1.38565i
$302$	−23.9951	+	18.6911i	−1.38076	+	1.07555i
$303$		−	12.7451i		−	0.732187i
$304$	2.28037	−	4.22936i	0.130788	−	0.242571i
$305$	8.69325			0.497774
$306$	−0.405405	+	0.315791i	−0.0231755	+	0.0180526i
$307$	−25.3014			−1.44402			−0.722012	−	0.691880i	$-0.756783\pi$
$307$	−25.3014			−1.44402			−0.722012	+	0.691880i	$0.756783\pi$
$308$	25.3286	+	6.39323i	1.44323	+	0.364288i
$309$	−14.2608			−0.811269
$310$	2.05401	−	1.59997i	0.116660	−	0.0908725i
$311$			22.5992i			1.28149i	0.767756	+	0.640743i	$0.221373\pi$
$311$			22.5992i			1.28149i	−0.767756	+	0.640743i	$0.778627\pi$
$312$	−3.09520	−	7.03414i	−0.175231	−	0.398230i
$313$		−	11.7264i		−	0.662813i	−0.943488	−	0.331406i	$-0.892477\pi$
$313$		−	11.7264i		−	0.662813i	0.943488	−	0.331406i	$-0.107523\pi$
$314$	2.90327	+	3.72715i	0.163841	+	0.210335i
$315$	4.50969			0.254093
$316$	−1.16494	+	4.61522i	−0.0655327	+	0.259627i
$317$			8.77236i			0.492705i	0.969180	+	0.246352i	$0.0792320\pi$
$317$			8.77236i			0.492705i	−0.969180	+	0.246352i	$0.920768\pi$
$318$	7.47959	+	9.60211i	0.419435	+	0.538460i
$319$	14.6003			0.817460
$320$	−8.33451	+	9.09596i	−0.465914	+	0.508479i
$321$			15.8754i			0.886078i
$322$	3.31562	−	19.5548i	0.184772	−	1.08975i
$323$	−0.436495			−0.0242873
$324$	−0.489471	+	1.93918i	−0.0271929	+	0.107732i
$325$		−	7.12377i		−	0.395156i
$326$	−3.98593	−	5.11704i	−0.220760	−	0.283407i
$327$	−4.48354			−0.247940
$328$	−9.46636	+	4.16543i	−0.522692	+	0.229997i
$329$			6.16954i			0.340138i
$330$	7.68459	−	5.98593i	0.423023	−	0.329515i
$331$	−13.7475			−0.755632			−0.377816	−	0.925881i	$-0.623325\pi$
$331$	−13.7475			−0.755632			−0.377816	+	0.925881i	$0.623325\pi$
$332$	−31.6131	−	7.97952i	−1.73500	−	0.437933i
$333$	9.28288			0.508699
$334$	1.45528	−	1.13360i	0.0796296	−	0.0620277i
$335$		−	15.8416i		−	0.865521i
$336$	10.2961	+	5.55142i	0.561701	+	0.302855i
$337$			7.26959i			0.396000i	0.980202	+	0.198000i	$0.0634446\pi$
$337$			7.26959i			0.396000i	−0.980202	+	0.198000i	$0.936555\pi$
$338$	4.88201	+	6.26740i	0.265546	+	0.340902i
$339$		−	1.06221i		−	0.0576912i
$340$	1.08664	+	0.274281i	0.0589315	+	0.0148750i
$341$	−5.33224			−0.288757
$342$	−1.34019	+	1.04395i	−0.0724694	+	0.0564502i
$343$	15.9324			0.860269
$344$	9.36475	+	21.2823i	0.504913	+	1.14747i
$345$	−4.99267	−	5.45622i	−0.268796	−	0.293753i
$346$	1.60336	−	1.24894i	0.0861973	−	0.0671436i
$347$	31.6982			1.70165			0.850824	−	0.525451i	$-0.176103\pi$
$347$	31.6982			1.70165			0.850824	+	0.525451i	$0.176103\pi$
$348$	6.33893	+	1.60002i	0.339802	+	0.0857700i
$349$			19.2070i			1.02813i	0.857753	+	0.514063i	$0.171860\pi$
$349$			19.2070i			1.02813i	−0.857753	+	0.514063i	$0.828140\pi$
$350$	6.66329	+	8.55417i	0.356168	+	0.457240i
$351$			2.71706i			0.145026i
$352$	24.9135	−	4.20685i	1.32789	−	0.224226i
$353$	−14.0523			−0.747926			−0.373963	−	0.927444i	$-0.622001\pi$
$353$	−14.0523			−0.747926			−0.373963	+	0.927444i	$0.622001\pi$
$354$	12.0508	+	15.4705i	0.640490	+	0.822246i
$355$		−	10.4959i		−	0.557065i
$356$	−5.79897	−	1.46373i	−0.307345	−	0.0775774i
$357$		−	1.06262i		−	0.0562400i
$358$	13.9106	+	17.8581i	0.735200	+	0.943832i
$359$	−26.0902			−1.37699			−0.688494	−	0.725242i	$-0.741728\pi$
$359$	−26.0902			−1.37699			−0.688494	+	0.725242i	$0.741728\pi$
$360$	3.99236	−	1.75674i	0.210416	−	0.0925882i
$361$	17.5570			0.924054
$362$	−15.4457	−	19.8288i	−0.811807	−	1.04218i
$363$	−8.94933			−0.469718
$364$	15.4080	+	3.88916i	0.807599	+	0.203847i
$365$	19.1636			1.00307
$366$	−4.89907	−	6.28930i	−0.256078	−	0.328747i
$367$	11.4514			0.597757			0.298879	−	0.954291i	$-0.403387\pi$
$367$	11.4514			0.597757			0.298879	+	0.954291i	$0.403387\pi$
$368$	−4.68224	−	18.6031i	−0.244079	−	0.969755i
$369$	3.65655			0.190352
$370$	−12.4409	−	15.9713i	−0.646770	−	0.830307i
$371$	−25.1685			−1.30668
$372$	−2.31507	−	0.584350i	−0.120031	−	0.0302971i
$373$	1.15765			0.0599409			0.0299705	−	0.999551i	$-0.490459\pi$
$373$	1.15765			0.0599409			0.0299705	+	0.999551i	$0.490459\pi$
$374$	−1.41047	−	1.81073i	−0.0729337	−	0.0936305i
$375$	11.7538			0.606965
$376$	2.40332	+	5.46179i	0.123942	+	0.281670i
$377$	8.88172			0.457432
$378$	−2.54143	−	3.26263i	−0.130717	−	0.167811i
$379$			11.5124i			0.591353i	0.955288	+	0.295677i	$0.0955451\pi$
$379$			11.5124i			0.591353i	−0.955288	+	0.295677i	$0.904455\pi$
$380$	3.59224	+	0.906723i	0.184278	+	0.0465139i
$381$			6.79761i			0.348252i
$382$	−7.52443	−	9.65968i	−0.384983	−	0.494232i
$383$	26.8009			1.36946			0.684731	−	0.728795i	$-0.259919\pi$
$383$	26.8009			1.36946			0.684731	+	0.728795i	$0.259919\pi$
$384$	11.2776	+	0.903757i	0.575505	+	0.0461196i
$385$			20.1424i			1.02655i
$386$	−2.80172	−	3.59677i	−0.142604	−	0.183071i
$387$		−	8.22067i		−	0.417880i
$388$	26.3960	+	6.66266i	1.34005	+	0.338245i
$389$	−12.0562			−0.611272			−0.305636	−	0.952148i	$-0.598869\pi$
$389$	−12.0562			−0.611272			−0.305636	+	0.952148i	$0.598869\pi$
$390$	4.67473	−	3.64139i	0.236714	−	0.184389i
$391$	−1.28565	+	1.17643i	−0.0650183	+	0.0594945i
$392$	−4.01744	+	1.76777i	−0.202912	+	0.0892861i
$393$	6.25067			0.315305
$394$	5.38798	−	4.19698i	0.271443	−	0.211441i
$395$	−3.67022			−0.184669
$396$	−8.66128	−	2.18621i	−0.435246	−	0.109861i
$397$		−	34.9302i		−	1.75310i	−0.481312	−	0.876549i	$-0.659840\pi$
$397$		−	34.9302i		−	1.75310i	0.481312	−	0.876549i	$-0.340160\pi$
$398$	9.33629	+	11.9857i	0.467986	+	0.600789i
$399$		−	3.51284i		−	0.175862i
$400$	9.23116	+	4.97721i	0.461558	+	0.248860i
$401$			30.6293i			1.52955i	0.644295	+	0.764777i	$0.277151\pi$
$401$			30.6293i			1.52955i	−0.644295	+	0.764777i	$0.722849\pi$
$402$	−11.4609	+	8.92753i	−0.571620	+	0.445265i
$403$	−3.24373			−0.161582
$404$	24.7151	+	6.23837i	1.22962	+	0.310370i
$405$	−1.54212			−0.0766286
$406$	−10.6651	+	8.30761i	−0.529301	+	0.412300i
$407$			41.4617i			2.05518i
$408$	−0.413942	−	0.940724i	−0.0204932	−	0.0465728i
$409$	33.5284			1.65787			0.828936	−	0.559343i	$-0.188946\pi$
$409$	33.5284			1.65787			0.828936	+	0.559343i	$0.188946\pi$
$410$	−4.90048	−	6.29112i	−0.242018	−	0.310696i
$411$		−	3.96407i		−	0.195533i
$412$	6.98026	−	27.6543i	0.343893	−	1.36243i
$413$	−40.5503			−1.99535
$414$	−1.13380	+	6.68689i	−0.0557231	+	0.328643i
$415$		−	25.1401i		−	1.23408i
$416$	15.1555	−	2.55913i	0.743058	−	0.125472i
$417$	7.53897			0.369185
$418$	−4.66276	−	5.98593i	−0.228063	−	0.292782i
$419$			4.92881i			0.240788i	0.992726	+	0.120394i	$0.0384158\pi$
$419$			4.92881i			0.240788i	−0.992726	+	0.120394i	$0.961584\pi$
$420$	−2.20737	+	8.74511i	−0.107708	+	0.426718i
$421$	−23.5566			−1.14808			−0.574040	−	0.818827i	$-0.694625\pi$
$421$	−23.5566			−1.14808			−0.574040	+	0.818827i	$0.694625\pi$
$422$	−1.79627	−	2.30601i	−0.0874411	−	0.112255i
$423$		−	2.10971i		−	0.102578i
$424$	−22.2813	+	9.80431i	−1.08207	+	0.476139i
$425$		−	0.952711i		−	0.0462133i
$426$	−7.59348	+	5.91496i	−0.367905	+	0.286581i
$427$	16.4852			0.797773
$428$	−30.7852	−	7.77055i	−1.48806	−	0.375604i
$429$	−12.1357			−0.585916
$430$	−14.1437	+	11.0173i	−0.682072	+	0.531301i
$431$	27.4570			1.32256			0.661278	−	0.750141i	$-0.270014\pi$
$431$	27.4570			1.32256			0.661278	+	0.750141i	$0.270014\pi$
$432$	−3.52084	−	1.89835i	−0.169396	−	0.0913342i
$433$			1.12287i			0.0539616i	0.999636	+	0.0269808i	$0.00858930\pi$
$433$			1.12287i			0.0539616i	−0.999636	+	0.0269808i	$0.991411\pi$
$434$	3.89505	−	3.03406i	0.186968	−	0.145639i
$435$			5.04099i			0.241697i
$436$	2.19457	−	8.69439i	0.105101	−	0.416386i
$437$	−4.25013	+	3.88905i	−0.203311	+	0.186039i
$438$	−10.7996	−	13.8643i	−0.516026	−	0.662461i
$439$			2.83686i			0.135396i	0.997706	+	0.0676979i	$0.0215654\pi$
$439$			2.83686i			0.135396i	−0.997706	+	0.0676979i	$0.978435\pi$
$440$	7.84641	+	17.8318i	0.374063	+	0.850095i
$441$	1.55181			0.0738957
$442$	−0.858024	−	1.10151i	−0.0408121	−	0.0523935i
$443$	−12.6439			−0.600730			−0.300365	−	0.953824i	$-0.597108\pi$
$443$	−12.6439			−0.600730			−0.300365	+	0.953824i	$0.597108\pi$
$444$	−4.54371	+	18.0012i	−0.215635	+	0.854298i
$445$		−	4.61159i		−	0.218610i
$446$	−0.0815717	+	0.0635404i	−0.00386253	+	0.00300873i
$447$	15.0167			0.710264
$448$	−15.8049	+	17.2488i	−0.746710	+	0.814930i
$449$	16.6649			0.786466			0.393233	−	0.919439i	$-0.371357\pi$
$449$	16.6649			0.786466			0.393233	+	0.919439i	$0.371357\pi$
$450$	−2.27856	−	2.92516i	−0.107412	−	0.137893i
$451$			16.3318i			0.769037i
$452$	2.05981	+	0.519921i	0.0968855	+	0.0244550i
$453$			21.5072i			1.01050i
$454$	9.27043	−	7.22122i	0.435083	−	0.338909i
$455$			12.2531i			0.574435i
$456$	−1.36841	−	3.10986i	−0.0640819	−	0.145632i
$457$			9.23670i			0.432075i	0.976385	+	0.216037i	$0.0693133\pi$
$457$			9.23670i			0.432075i	−0.976385	+	0.216037i	$0.930687\pi$
$458$	18.2895	+	23.4797i	0.854614	+	1.09713i
$459$			0.363371i			0.0169607i
$460$	13.0244	−	7.01102i	0.607264	−	0.326891i
$461$		−	4.64180i		−	0.216190i	−0.994141	−	0.108095i	$-0.965525\pi$
$461$		−	4.64180i		−	0.216190i	0.994141	−	0.108095i	$-0.0344751\pi$
$462$	14.5724	−	11.3512i	0.677970	−	0.528107i
$463$		−	14.9526i		−	0.694905i	−0.937698	−	0.347452i	$-0.887047\pi$
$463$		−	14.9526i		−	0.694905i	0.937698	−	0.347452i	$-0.112953\pi$
$464$	−6.20545	+	11.5092i	−0.288081	+	0.534299i
$465$		−	1.84104i		−	0.0853763i
$466$	−8.02043	−	10.2964i	−0.371539	−	0.476973i
$467$			18.0049i			0.833167i	0.909097	+	0.416584i	$0.136773\pi$
$467$			18.0049i			0.833167i	−0.909097	+	0.416584i	$0.863227\pi$
$468$	−5.26887	−	1.32992i	−0.243554	−	0.0614758i
$469$		−	30.0407i		−	1.38715i
$470$	−3.62978	+	2.82743i	−0.167429	+	0.130419i
$471$	3.34071			0.153932
$472$	−35.8985	+	15.7962i	−1.65236	+	0.727080i
$473$	36.7174			1.68827
$474$	2.06835	+	2.65530i	0.0950025	+	0.121962i
$475$		−	3.14949i		−	0.144508i
$476$	2.06062	+	0.520124i	0.0944483	+	0.0238398i
$477$	8.60653			0.394066
$478$	7.53228	−	5.86729i	0.344519	−	0.268364i
$479$	8.53964			0.390186			0.195093	−	0.980785i	$-0.437499\pi$
$479$	8.53964			0.390186			0.195093	+	0.980785i	$0.437499\pi$
$480$	1.45248	+	8.60178i	0.0662964	+	0.392616i
$481$			25.2222i			1.15003i
$482$	16.2072	−	12.6246i	0.738218	−	0.575037i
$483$	−9.46768	−	10.3467i	−0.430795	−	0.470792i
$484$	4.38044	−	17.3544i	0.199111	−	0.788835i
$485$			20.9913i			0.953164i
$486$	0.869059	+	1.11568i	0.0394213	+	0.0506081i
$487$		−	34.9348i		−	1.58305i	−0.611139	−	0.791523i	$-0.709288\pi$
$487$		−	34.9348i		−	1.58305i	0.611139	−	0.791523i	$-0.290712\pi$
$488$	14.5940	−	6.42174i	0.660641	−	0.290698i
$489$	−4.58649			−0.207408
$490$	−2.07973	−	2.66990i	−0.0939524	−	0.120614i
$491$	−19.8556			−0.896071			−0.448036	−	0.894016i	$-0.647876\pi$
$491$	−19.8556			−0.896071			−0.448036	+	0.894016i	$0.647876\pi$
$492$	−1.78978	+	7.09070i	−0.0806893	+	0.319674i
$493$	1.18781			0.0534964
$494$	−2.83647	−	3.64139i	−0.127619	−	0.163834i
$495$		−	6.88783i		−	0.309585i
$496$	2.26632	−	4.20331i	0.101761	−	0.188734i
$497$		−	19.9036i		−	0.892798i
$498$	−18.1881	+	14.1677i	−0.815029	+	0.634869i
$499$	18.7678			0.840164			0.420082	−	0.907486i	$-0.362001\pi$
$499$	18.7678			0.840164			0.420082	+	0.907486i	$0.362001\pi$
$500$	−5.75317	+	22.7928i	−0.257289	+	1.01932i
$501$		−	1.30440i		−	0.0582761i
$502$	22.7820	−	17.7461i	1.01681	−	0.792047i
$503$	−1.28243			−0.0571809			−0.0285905	−	0.999591i	$-0.509102\pi$
$503$	−1.28243			−0.0571809			−0.0285905	+	0.999591i	$0.509102\pi$
$504$	7.57078	−	3.33133i	0.337229	−	0.148389i
$505$			19.6545i			0.874613i
$506$	−29.8668	−	5.06407i	−1.32774	−	0.225125i
$507$	5.61758			0.249485
$508$	−13.1818	−	3.32724i	−0.584847	−	0.147622i
$509$		−	30.2587i		−	1.34119i	−0.741821	−	0.670597i	$-0.766038\pi$
$509$		−	30.2587i		−	1.34119i	0.741821	−	0.670597i	$-0.233962\pi$
$510$	0.625183	−	0.486988i	0.0276836	−	0.0215642i
$511$	36.3403			1.60760
$512$	−7.27259	+	21.4268i	−0.321406	+	0.946941i
$513$			1.20124i			0.0530360i
$514$	−17.7642	−	22.8053i	−0.783547	−	1.00590i
$515$	21.9919			0.969078
$516$	15.9414	+	4.02379i	0.701779	+	0.177137i
$517$	9.42297			0.414422
$518$	−23.5918	−	30.2866i	−1.03656	−	1.33072i
$519$		−	1.43712i		−	0.0630825i
$520$	4.77316	+	10.8475i	0.209317	+	0.475694i
$521$			20.7953i			0.911059i	0.890221	+	0.455529i	$0.150550\pi$
$521$			20.7953i			0.911059i	−0.890221	+	0.455529i	$0.849450\pi$
$522$	3.64700	−	2.84084i	0.159625	−	0.124340i
$523$		−	40.3973i		−	1.76645i	−0.468948	−	0.883226i	$-0.655367\pi$
$523$		−	40.3973i		−	1.76645i	0.468948	−	0.883226i	$-0.344633\pi$
$524$	−3.05953	+	12.1212i	−0.133656	+	0.529516i
$525$	7.66725			0.334626
$526$	−13.6911	−	17.5763i	−0.596962	−	0.766365i
$527$	−0.433806			−0.0188969
$528$	8.47890	−	15.7257i	0.368997	−	0.684373i
$529$	−2.03670	+	22.9096i	−0.0885523	+	0.996072i
$530$	−11.5344	−	14.8076i	−0.501023	−	0.643202i
$531$	13.8664			0.601752
$532$	6.81202	+	1.71943i	0.295339	+	0.0745469i
$533$			9.93506i			0.430335i
$534$	−3.33635	+	2.59886i	−0.144378	+	0.112463i
$535$		−	24.4818i		−	1.05844i
$536$	−11.7023	−	26.5946i	−0.505461	−	1.14871i
$537$	16.0065			0.690733
$538$	−28.3382	+	22.0741i	−1.22175	+	0.951684i
$539$			6.93110i			0.298544i
$540$	0.754824	−	2.99045i	0.0324824	−	0.128688i
$541$			41.3501i			1.77778i	0.458119	+	0.888891i	$0.348523\pi$
$541$			41.3501i			1.77778i	−0.458119	+	0.888891i	$0.651477\pi$
$542$	21.3299	−	16.6150i	0.916199	−	0.713675i
$543$	−17.7729			−0.762707
$544$	2.02685	−	0.342250i	0.0869003	−	0.0146738i
$545$	6.91416			0.296170
$546$	8.86476	−	6.90523i	0.379377	−	0.295516i
$547$	17.7586			0.759301			0.379650	−	0.925130i	$-0.376044\pi$
$547$	17.7586			0.759301			0.379650	+	0.925130i	$0.376044\pi$
$548$	7.68704	+	1.94030i	0.328374	+	0.0828854i
$549$	−5.63721			−0.240590
$550$	13.0651	−	10.1771i	0.557098	−	0.433953i
$551$	3.92669			0.167283
$552$	−12.4121	−	5.47168i	−0.528295	−	0.232890i
$553$	−6.95991			−0.295965
$554$	3.87387	−	3.01756i	0.164585	−	0.128204i
$555$	−14.3153			−0.607651
$556$	−3.69011	+	14.6194i	−0.156495	+	0.620001i
$557$	29.6990			1.25839			0.629193	−	0.777249i	$-0.283385\pi$
$557$	29.6990			1.25839			0.629193	+	0.777249i	$0.283385\pi$
$558$	−1.33194	+	1.03752i	−0.0563854	+	0.0439216i
$559$	22.3361			0.944715
$560$	−15.8779	−	8.56096i	−0.670963	−	0.361767i
$561$	−1.62299			−0.0685225
$562$	31.5498	−	24.5758i	1.33085	−	1.03667i
$563$			7.78195i			0.327970i	0.986463	+	0.163985i	$0.0524349\pi$
$563$			7.78195i			0.327970i	−0.986463	+	0.163985i	$0.947565\pi$
$564$	4.09111	+	1.03264i	0.172267	+	0.0434822i
$565$			1.63805i			0.0689134i
$566$	35.4143	−	27.5861i	1.48858	−	1.15953i
$567$	−2.92435			−0.122811
$568$	−7.75338	−	17.6203i	−0.325324	−	0.739332i
$569$		−	42.2668i		−	1.77191i	−0.463767	−	0.885957i	$-0.653502\pi$
$569$		−	42.2668i		−	1.77191i	0.463767	−	0.885957i	$-0.346498\pi$
$570$	2.06674	−	1.60989i	0.0865662	−	0.0674309i
$571$			34.2699i			1.43415i	0.696995	+	0.717076i	$0.254520\pi$
$571$			34.2699i			1.43415i	−0.696995	+	0.717076i	$0.745480\pi$
$572$	5.94006	−	23.5332i	0.248367	−	0.983974i
$573$	−8.65813			−0.361699
$574$	−9.29287	−	11.9300i	−0.387877	−	0.497947i
$575$	−8.48839	−	9.27650i	−0.353990	−	0.386857i
$576$	5.40458	−	5.89835i	0.225191	−	0.245764i
$577$	28.6093			1.19102			0.595510	−	0.803348i	$-0.296950\pi$
$577$	28.6093			1.19102			0.595510	+	0.803348i	$0.296950\pi$
$578$	14.6593	+	18.8192i	0.609745	+	0.782776i
$579$	−3.22385			−0.133979
$580$	−9.77539	−	2.46742i	−0.405901	−	0.102454i
$581$		−	47.6736i		−	1.97784i
$582$	15.1865	−	11.8296i	0.629502	−	0.490352i
$583$			38.4408i			1.59206i
$584$	32.1715	−	14.1562i	1.33126	−	0.585789i
$585$		−	4.19004i		−	0.173237i
$586$	−3.29384	−	4.22855i	−0.136067	−	0.174680i
$587$	−15.7214			−0.648892			−0.324446	−	0.945904i	$-0.605178\pi$
$587$	−15.7214			−0.648892			−0.324446	+	0.945904i	$0.605178\pi$
$588$	−0.759566	+	3.00924i	−0.0313240	+	0.124099i
$589$	−1.43408			−0.0590904
$590$	−18.5837	−	23.8573i	−0.765079	−	0.982190i
$591$		−	4.82934i		−	0.198652i
$592$	−32.6835	−	17.6221i	−1.34328	−	0.724265i
$593$	−2.98451			−0.122559			−0.0612795	−	0.998121i	$-0.519518\pi$
$593$	−2.98451			−0.122559			−0.0612795	+	0.998121i	$0.519518\pi$
$594$	−4.98314	+	3.88163i	−0.204461	+	0.159265i
$595$			1.63869i			0.0671799i
$596$	−7.35023	+	29.1200i	−0.301077	+	1.19280i
$597$	10.7430			0.439681
$598$	−18.1687	−	3.08060i	−0.742973	−	0.125975i
$599$		−	44.6517i		−	1.82442i	−0.409722	−	0.912210i	$-0.634374\pi$
$599$		−	44.6517i		−	1.82442i	0.409722	−	0.912210i	$-0.365626\pi$
$600$	6.78769	−	2.98675i	0.277106	−	0.121934i
$601$	35.0051			1.42789			0.713945	−	0.700202i	$-0.246907\pi$
$601$	35.0051			1.42789			0.713945	+	0.700202i	$0.246907\pi$
$602$	−26.8210	+	20.8923i	−1.09314	+	0.851506i
$603$			10.2726i			0.418334i
$604$	−41.7064	−	10.5272i	−1.69701	−	0.428345i
$605$	13.8009			0.561088
$606$	14.2194	−	11.0763i	0.577625	−	0.449942i
$607$		−	33.4183i		−	1.35641i	−0.734874	−	0.678204i	$-0.762759\pi$
$607$		−	33.4183i		−	1.35641i	0.734874	−	0.678204i	$-0.237241\pi$
$608$	6.70038	−	1.13141i	0.271736	−	0.0458849i
$609$			9.55931i			0.387363i
$610$	7.55495	+	9.69886i	0.305891	+	0.392695i
$611$	5.73222			0.231901
$612$	−0.704642	−	0.177860i	−0.0284835	−	0.00718956i
$613$	29.4958			1.19133			0.595663	−	0.803234i	$-0.296889\pi$
$613$	29.4958			1.19133			0.595663	+	0.803234i	$0.296889\pi$
$614$	−21.9884	−	28.2281i	−0.887379	−	1.13920i
$615$	−5.63883			−0.227380
$616$	14.8793	+	33.8146i	0.599503	+	1.36243i
$617$		−	30.9541i		−	1.24617i	−0.782155	−	0.623083i	$-0.785880\pi$
$617$		−	30.9541i		−	1.24617i	0.782155	−	0.623083i	$-0.214120\pi$
$618$	−12.3935	−	15.9105i	−0.498540	−	0.640013i
$619$			26.0112i			1.04548i	0.852493	+	0.522739i	$0.175090\pi$
$619$			26.0112i			1.04548i	−0.852493	+	0.522739i	$0.824910\pi$
$620$	3.57011	+	0.901137i	0.143379	+	0.0361905i
$621$	3.23754	+	3.53813i	0.129918	+	0.141980i
$622$	−25.2135	+	19.6401i	−1.01097	+	0.787495i
$623$		−	8.74504i		−	0.350363i
$624$	5.15792	−	9.56633i	0.206482	−	0.382960i
$625$	−5.01649			−0.200660
$626$	13.0828	−	10.1909i	0.522895	−	0.407310i
$627$	−5.36529			−0.214269
$628$	−1.63518	+	6.47823i	−0.0652508	+	0.258509i
$629$			3.37313i			0.134496i
$630$	3.91919	+	5.03136i	0.156144	+	0.200454i
$631$	2.75385			0.109629			0.0548146	−	0.998497i	$-0.482543\pi$
$631$	2.75385			0.109629			0.0548146	+	0.998497i	$0.482543\pi$
$632$	−6.16150	+	2.71121i	−0.245091	+	0.107846i
$633$	−2.06691			−0.0821525
$634$	−9.78712	+	7.62370i	−0.388696	+	0.302776i
$635$		−	10.4827i		−	0.415994i
$636$	−4.21265	+	16.6896i	−0.167043	+	0.661786i
$637$			4.21636i			0.167058i
$638$	12.6885	+	16.2892i	0.502344	+	0.644897i
$639$			6.80616i			0.269248i
$640$	−17.3913	−	1.39370i	−0.687453	−	0.0550909i
$641$			36.9099i			1.45785i	0.684592	+	0.728926i	$0.259980\pi$
$641$			36.9099i			1.45785i	−0.684592	+	0.728926i	$0.740020\pi$
$642$	−17.7118	+	13.7967i	−0.699030	+	0.544511i
$643$		−	3.44130i		−	0.135712i	−0.997695	−	0.0678558i	$-0.978384\pi$
$643$		−	3.44130i		−	0.135712i	0.997695	−	0.0678558i	$-0.0216158\pi$
$644$	24.6983	−	13.2951i	0.973250	−	0.523901i
$645$			12.6773i			0.499167i
$646$	−0.379340	−	0.486988i	−0.0149249	−	0.0191603i
$647$			15.2137i			0.598113i	0.954235	+	0.299057i	$0.0966719\pi$
$647$			15.2137i			0.598113i	−0.954235	+	0.299057i	$0.903328\pi$
$648$	−2.58888	+	1.13917i	−0.101701	+	0.0447508i
$649$			61.9340i			2.43112i
$650$	7.94783	−	6.19098i	0.311740	−	0.242830i
$651$		−	3.49120i		−	0.136831i
$652$	2.24496	−	8.89403i	0.0879193	−	0.348317i
$653$			19.7643i			0.773436i	0.922198	+	0.386718i	$0.126391\pi$
$653$			19.7643i			0.773436i	−0.922198	+	0.386718i	$0.873609\pi$
$654$	−3.89646	−	5.00218i	−0.152364	−	0.195601i
$655$	−9.63929			−0.376638
$656$	−12.8741	−	6.94139i	−0.502649	−	0.271016i
$657$	−12.4268			−0.484815
$658$	−6.88321	+	5.36169i	−0.268336	+	0.209021i
$659$		−	23.1718i		−	0.902646i	−0.892361	−	0.451323i	$-0.850952\pi$
$659$		−	23.1718i		−	0.902646i	0.892361	−	0.451323i	$-0.149048\pi$
$660$	13.3567	+	3.37140i	0.519910	+	0.131231i
$661$	13.7175			0.533547			0.266774	−	0.963759i	$-0.414042\pi$
$661$	13.7175			0.533547			0.266774	+	0.963759i	$0.414042\pi$
$662$	−11.9474	−	15.3378i	−0.464349	−	0.596120i
$663$	−0.987302			−0.0383436
$664$	−18.5711	−	42.2047i	−0.720699	−	1.63786i
$665$			5.41722i			0.210071i
$666$	8.06738	+	10.3567i	0.312604	+	0.401314i
$667$	11.5657	−	10.5831i	0.447825	−	0.409779i
$668$	2.52946	+	0.638464i	0.0978677	+	0.0247029i
$669$			0.0731140i			0.00282675i
$670$	17.6741	−	13.7673i	0.682812	−	0.531878i
$671$		−	25.1784i		−	0.972002i
$672$	2.75437	+	16.3117i	0.106252	+	0.629237i
$673$	−32.0097			−1.23388			−0.616941	−	0.787009i	$-0.711628\pi$
$673$	−32.0097			−1.23388			−0.616941	+	0.787009i	$0.711628\pi$
$674$	−8.11052	+	6.31771i	−0.312405	+	0.243349i
$675$	−2.62187			−0.100916
$676$	−2.74964	+	10.8935i	−0.105755	+	0.418980i
$677$	−4.81157			−0.184924			−0.0924618	−	0.995716i	$-0.529474\pi$
$677$	−4.81157			−0.184924			−0.0924618	+	0.995716i	$0.529474\pi$
$678$	1.18508	−	0.923122i	0.0455128	−	0.0354523i
$679$			39.8061i			1.52762i
$680$	0.638348	+	1.45071i	0.0244795	+	0.0556322i
$681$		−	8.30924i		−	0.318411i
$682$	−4.63403	−	5.94906i	−0.177446	−	0.227801i
$683$	4.85580			0.185802			0.0929009	−	0.995675i	$-0.470386\pi$
$683$	4.85580			0.185802			0.0929009	+	0.995675i	$0.470386\pi$
$684$	−2.32942	−	0.587972i	−0.0890675	−	0.0224817i
$685$			6.11307i			0.233568i
$686$	13.8462	+	17.7754i	0.528651	+	0.678669i
$687$	21.0452			0.802925
$688$	−15.6057	+	28.9436i	−0.594961	+	1.10347i
$689$			23.3845i			0.890878i
$690$	1.74845	−	10.3120i	0.0665624	−	0.392571i
$691$	18.2656			0.694855			0.347428	−	0.937707i	$-0.387055\pi$
$691$	18.2656			0.694855			0.347428	+	0.937707i	$0.387055\pi$
$692$	2.78683	+	0.703429i	0.105939	+	0.0267404i
$693$		−	13.0615i		−	0.496166i
$694$	27.5476	+	35.3649i	1.04569	+	1.34243i
$695$	−11.6260			−0.440999
$696$	3.72380	+	8.46271i	0.141150	+	0.320778i
$697$			1.32868i			0.0503275i
$698$	−21.4288	+	16.6920i	−0.811091	+	0.631802i
$699$	−9.22887			−0.349068
$700$	−3.75290	+	14.8682i	−0.141846	+	0.561964i
$701$	−11.1332			−0.420496			−0.210248	−	0.977648i	$-0.567427\pi$
$701$	−11.1332			−0.420496			−0.210248	+	0.977648i	$0.567427\pi$
$702$	−3.03136	+	2.36129i	−0.114411	+	0.0891211i
$703$			11.1510i			0.420566i
$704$	26.3448	+	24.1394i	0.992906	+	0.909788i
$705$			3.25343i			0.122531i
$706$	−12.2122	−	15.6778i	−0.459614	−	0.590041i
$707$			37.2711i			1.40173i
$708$	−6.78722	+	26.8895i	−0.255079	+	1.01057i
$709$	−0.387202			−0.0145417			−0.00727083	−	0.999974i	$-0.502314\pi$
$709$	−0.387202			−0.0145417			−0.00727083	+	0.999974i	$0.502314\pi$
$710$	11.7101	−	9.12158i	0.439471	−	0.342327i
$711$	2.37999			0.0892565
$712$	−3.40660	−	7.74184i	−0.127668	−	0.290138i
$713$	−4.22395	+	3.86510i	−0.158188	+	0.144749i
$714$	1.18555	−	0.923483i	0.0443679	−	0.0345605i
$715$	18.7147			0.699888
$716$	−7.83475	+	31.0396i	−0.292798	+	1.16000i
$717$		−	6.75131i		−	0.252132i
$718$	−22.6739	−	29.1082i	−0.846183	−	1.08631i
$719$		−	39.2143i		−	1.46245i	−0.682138	−	0.731224i	$-0.738950\pi$
$719$		−	39.2143i		−	1.46245i	0.682138	−	0.731224i	$-0.261050\pi$
$720$	5.42955	+	2.92748i	0.202347	+	0.109101i
$721$	41.7036			1.55312
$722$	15.2581	+	19.5880i	0.567848	+	0.728989i
$723$		−	14.5268i		−	0.540257i
$724$	8.69932	−	34.4648i	0.323308	−	1.28087i
$725$			8.57054i			0.318302i
$726$	−7.77750	−	9.98457i	−0.288650	−	0.370562i
$727$	−38.1247			−1.41397			−0.706983	−	0.707231i	$-0.749944\pi$
$727$	−38.1247			−1.41397			−0.706983	+	0.707231i	$0.749944\pi$
$728$	9.05143	+	20.5703i	0.335468	+	0.762385i
$729$	1.00000			0.0370370
$730$	16.6543	+	21.3804i	0.616404	+	0.791324i
$731$	2.98716			0.110484
$732$	2.75925	−	10.9316i	0.101985	−	0.404042i
$733$	−10.3840			−0.383541			−0.191771	−	0.981440i	$-0.561423\pi$
$733$	−10.3840			−0.383541			−0.191771	+	0.981440i	$0.561423\pi$
$734$	9.95193	+	12.7760i	0.367332	+	0.471572i
$735$	−2.39308			−0.0882699
$736$	16.6859	−	21.3911i	0.615052	−	0.788486i
$737$	−45.8824			−1.69010
$738$	3.17776	+	4.07953i	0.116975	+	0.150169i
$739$	53.2532			1.95895			0.979475	−	0.201565i	$-0.0646026\pi$
$739$	53.2532			1.95895			0.979475	+	0.201565i	$0.0646026\pi$
$740$	7.00694	−	27.7600i	0.257580	−	1.02048i
$741$	−3.26384			−0.119900
$742$	−21.8729	−	28.0799i	−0.802980	−	1.03085i
$743$	−34.2222			−1.25549			−0.627745	−	0.778419i	$-0.716022\pi$
$743$	−34.2222			−1.25549			−0.627745	+	0.778419i	$0.716022\pi$
$744$	−1.35998	−	3.09070i	−0.0498595	−	0.113311i
$745$	−23.1575			−0.848425
$746$	1.00607	+	1.29157i	0.0368348	+	0.0472876i
$747$			16.3023i			0.596471i
$748$	0.794405	−	3.14726i	0.0290463	−	0.115075i
$749$		−	46.4252i		−	1.69634i
$750$	10.2148	+	13.1135i	0.372991	+	0.478837i
$751$	−41.9687			−1.53146			−0.765731	−	0.643161i	$-0.777622\pi$
$751$	−41.9687			−1.53146			−0.765731	+	0.643161i	$0.777622\pi$
$752$	−4.00497	+	7.42796i	−0.146046	+	0.270870i
$753$		−	20.4199i		−	0.744142i
$754$	7.71875	+	9.90914i	0.281100	+	0.360869i
$755$		−	33.1667i		−	1.20706i
$756$	1.43138	−	5.67084i	0.0520590	−	0.206246i
$757$	11.7725			0.427880			0.213940	−	0.976847i	$-0.431370\pi$
$757$	11.7725			0.427880			0.213940	+	0.976847i	$0.431370\pi$
$758$	−12.8441	+	10.0050i	−0.466520	+	0.363397i
$759$	−15.8029	+	14.4604i	−0.573610	+	0.524878i
$760$	2.11026	+	4.79578i	0.0765472	+	0.173961i
$761$	10.2905			0.373030			0.186515	−	0.982452i	$-0.440281\pi$
$761$	10.2905			0.373030			0.186515	+	0.982452i	$0.440281\pi$
$762$	−7.58394	+	5.90753i	−0.274737	+	0.214007i
$763$	13.1114			0.474666
$764$	4.23791	−	16.7897i	0.153322	−	0.607429i
$765$		−	0.560362i		−	0.0202599i
$766$	23.2916	+	29.9012i	0.841559	+	1.08037i
$767$			37.6760i			1.36040i
$768$	8.79256	+	13.3675i	0.317274	+	0.482359i
$769$		−	49.9328i		−	1.80062i	−0.435246	−	0.900312i	$-0.643339\pi$
$769$		−	49.9328i		−	1.80062i	0.435246	−	0.900312i	$-0.356661\pi$
$770$	−22.4724	+	17.5049i	−0.809850	+	0.630835i
$771$	−20.4408			−0.736156
$772$	1.57798	−	6.25162i	0.0567928	−	0.225001i
$773$	14.5916			0.524823			0.262411	−	0.964956i	$-0.415482\pi$
$773$	14.5916			0.524823			0.262411	+	0.964956i	$0.415482\pi$
$774$	9.17162	−	7.14425i	0.329667	−	0.256795i
$775$		−	3.13008i		−	0.112436i
$776$	15.5063	+	35.2397i	0.556645	+	1.26503i
$777$	−27.1464			−0.973871
$778$	−10.4775	−	13.4508i	−0.375638	−	0.482234i
$779$			4.39238i			0.157373i
$780$	8.12523	+	2.05090i	0.290930	+	0.0734341i
$781$	−30.3995			−1.08778
$782$	−2.42982	−	0.411989i	−0.0868903	−	0.0147327i
$783$		−	3.26887i		−	0.116820i
$784$	−5.46366	−	2.94587i	−0.195131	−	0.105210i
$785$	−5.15177			−0.183875
$786$	5.43220	+	6.97373i	0.193760	+	0.248745i
$787$			5.70206i			0.203257i	0.994822	+	0.101628i	$0.0324052\pi$
$787$			5.70206i			0.203257i	−0.994822	+	0.101628i	$0.967595\pi$
$788$	9.36495	+	2.36382i	0.333613	+	0.0842077i
$789$	−15.7540			−0.560856
$790$	−3.18964	−	4.09479i	−0.113482	−	0.145686i
$791$			3.10627i			0.110446i
$792$	−5.08807	−	11.5631i	−0.180797	−	0.410878i
$793$		−	15.3166i		−	0.543910i
$794$	38.9709	−	30.3565i	1.38302	−	1.07731i
$795$	−13.2723			−0.470720
$796$	−5.25838	+	20.8326i	−0.186378	+	0.738391i
$797$	−27.8701			−0.987209			−0.493604	−	0.869687i	$-0.664321\pi$
$797$	−27.8701			−0.987209			−0.493604	+	0.869687i	$0.664321\pi$
$798$	3.91919	−	3.05286i	0.138738	−	0.108070i
$799$	0.766609			0.0271207
$800$	2.46947	+	14.6245i	0.0873088	+	0.517054i
$801$			2.99042i			0.105661i
$802$	−34.1724	+	26.6187i	−1.20667	+	0.939939i
$803$		−	55.5039i		−	1.95869i
$804$	−19.9205	−	5.02816i	−0.702541	−	0.177330i
$805$	14.6003	+	15.9559i	0.514593	+	0.562371i
$806$	−2.81900	−	3.61896i	−0.0992949	−	0.127472i
$807$			25.4000i			0.894124i
$808$	14.5188	+	32.9955i	0.510771	+	1.16078i
$809$	−24.5770			−0.864081			−0.432040	−	0.901854i	$-0.642206\pi$
$809$	−24.5770			−0.864081			−0.432040	+	0.901854i	$0.642206\pi$
$810$	−1.34019	−	1.72051i	−0.0470896	−	0.0604525i
$811$	−30.3892			−1.06711			−0.533554	−	0.845766i	$-0.679144\pi$
$811$	−30.3892			−1.06711			−0.533554	+	0.845766i	$0.679144\pi$
$812$	−18.5372	−	4.67901i	−0.650529	−	0.164201i
$813$		−	19.1184i		−	0.670511i
$814$	−46.2579	+	36.0327i	−1.62134	+	1.26294i
$815$	7.07292			0.247754
$816$	0.689804	−	1.27937i	0.0241480	−	0.0447869i
$817$	9.87499			0.345482
$818$	29.1382	+	37.4069i	1.01879	+	1.30790i
$819$		−	7.94563i		−	0.277643i
$820$	2.76005	−	10.9347i	0.0963851	−	0.381857i
$821$			43.0718i			1.50322i	0.659610	+	0.751608i	$0.270722\pi$
$821$			43.0718i			1.50322i	−0.659610	+	0.751608i	$0.729278\pi$
$822$	4.42262	−	3.44501i	0.154257	−	0.120159i
$823$			43.9947i			1.53356i	0.641911	+	0.766779i	$0.278142\pi$
$823$			43.9947i			1.53356i	−0.641911	+	0.766779i	$0.721858\pi$
$824$	36.9195	−	16.2455i	1.28615	−	0.565939i
$825$		−	11.7105i		−	0.407707i
$826$	−35.2406	−	45.2410i	−1.22618	−	1.57414i
$827$			14.6739i			0.510262i	0.966906	+	0.255131i	$0.0821186\pi$
$827$			14.6739i			0.510262i	−0.966906	+	0.255131i	$0.917881\pi$
$828$	−8.44575	+	4.54635i	−0.293510	+	0.157997i
$829$			15.6549i			0.543716i	0.962337	+	0.271858i	$0.0876382\pi$
$829$			15.6549i			0.543716i	−0.962337	+	0.271858i	$0.912362\pi$
$830$	28.0483	−	21.8483i	0.973570	−	0.758364i
$831$		−	3.47221i		−	0.120450i
$832$	16.0262	+	14.6846i	0.555607	+	0.509096i
$833$			0.563883i			0.0195374i
$834$	6.55181	+	8.41105i	0.226871	+	0.291251i
$835$			2.01153i			0.0696120i
$836$	2.62616	−	10.4043i	0.0908275	−	0.359839i
$837$			1.19384i			0.0412651i
$838$	−5.49896	+	4.28343i	−0.189958	+	0.147969i
$839$	56.0576			1.93532			0.967661	−	0.252253i	$-0.0811714\pi$
$839$	56.0576			1.93532			0.967661	+	0.252253i	$0.0811714\pi$
$840$	−11.6751	+	5.13731i	−0.402828	+	0.177254i
$841$	18.3145			0.631534
$842$	−20.4721	−	26.2816i	−0.705515	−	0.905723i
$843$		−	28.2786i		−	0.973966i
$844$	1.01170	−	4.00812i	0.0348240	−	0.137965i
$845$	−8.66298			−0.298015
$846$	2.35376	−	1.83347i	0.0809239	−	0.0630359i
$847$	26.1710			0.899245
$848$	−30.3022	−	16.3382i	−1.04058	−	0.561055i
$849$		−	31.7425i		−	1.08940i
$850$	1.06292	−	0.827962i	0.0364578	−	0.0283989i
$851$	30.0537	+	32.8440i	1.03023	+	1.12588i
$852$	−13.1984	−	3.33142i	−0.452169	−	0.114133i
$853$			50.5636i			1.73126i	0.500681	+	0.865632i	$0.333083\pi$
$853$			50.5636i			1.73126i	−0.500681	+	0.865632i	$0.666917\pi$
$854$	14.3266	+	18.3921i	0.490245	+	0.629365i
$855$		−	1.85245i		−	0.0633526i
$856$	−18.0848	−	41.0995i	−0.618125	−	1.40475i
$857$	−26.7777			−0.914710			−0.457355	−	0.889284i	$-0.651203\pi$
$857$	−26.7777			−0.914710			−0.457355	+	0.889284i	$0.651203\pi$
$858$	−10.5466	−	13.5395i	−0.360056	−	0.462231i
$859$	−25.0671			−0.855279			−0.427639	−	0.903949i	$-0.640655\pi$
$859$	−25.0671			−0.855279			−0.427639	+	0.903949i	$0.640655\pi$
$860$	−24.5835	−	6.20516i	−0.838290	−	0.211594i
$861$	−10.6930			−0.364417
$862$	23.8617	+	30.6331i	0.812734	+	1.04337i
$863$			36.0014i			1.22550i	0.790276	+	0.612751i	$0.209937\pi$
$863$			36.0014i			1.22550i	−0.790276	+	0.612751i	$0.790063\pi$
$864$	−0.941874	−	5.57789i	−0.0320432	−	0.189764i
$865$			2.21621i			0.0753534i
$866$	−1.25276	+	0.975839i	−0.0425705	+	0.0331604i
$867$	16.8680			0.572866
$868$	6.77006	+	1.70884i	0.229791	+	0.0580019i
$869$			10.6301i			0.360603i
$870$	−5.62412	+	4.38092i	−0.190675	+	0.148527i
$871$	−27.9114			−0.945741
$872$	11.6073	−	5.10752i	0.393074	−	0.172962i
$873$		−	13.6119i		−	0.460695i
$874$	−8.03255	−	1.36196i	−0.271705	−	0.0460690i
$875$	−34.3723			−1.16200
$876$	6.08256	−	24.0978i	0.205511	−	0.814189i
$877$		−	32.5996i		−	1.10081i	−0.834898	−	0.550405i	$-0.814473\pi$
$877$		−	32.5996i		−	1.10081i	0.834898	−	0.550405i	$-0.185527\pi$
$878$	−3.16502	+	2.46540i	−0.106814	+	0.0832031i
$879$	−3.79012			−0.127838
$880$	−13.0755	+	24.2509i	−0.440774	+	0.817498i
$881$		−	31.7442i		−	1.06949i	−0.845014	−	0.534745i	$-0.820408\pi$
$881$		−	31.7442i		−	1.06949i	0.845014	−	0.534745i	$-0.179592\pi$
$882$	1.34861	+	1.73132i	0.0454102	+	0.0582965i
$883$	−42.1494			−1.41844			−0.709220	−	0.704988i	$-0.750953\pi$
$883$	−42.1494			−1.41844			−0.709220	+	0.704988i	$0.750953\pi$
$884$	0.483256	−	1.91456i	0.0162537	−	0.0643935i
$885$	−21.3837			−0.718805
$886$	−10.9883	−	14.1065i	−0.369159	−	0.473918i
$887$		−	30.1148i		−	1.01115i	−0.862781	−	0.505577i	$-0.831280\pi$
$887$		−	30.1148i		−	1.01115i	0.862781	−	0.505577i	$-0.168720\pi$
$888$	−24.0323	+	10.5748i	−0.806470	+	0.354866i
$889$		−	19.8786i		−	0.666706i
$890$	5.14505	−	4.00775i	0.172462	−	0.134340i
$891$			4.46647i			0.149632i
$892$	−0.141781	−	0.0357872i	−0.00474719	−	0.00119825i
$893$	2.53427			0.0848061
$894$	13.0504	+	16.7538i	0.436470	+	0.560329i
$895$	−24.6840			−0.825096
$896$	−32.9795	−	2.64290i	−1.10177	−	0.0882930i
$897$	−9.61331	+	8.79659i	−0.320979	+	0.293710i
$898$	14.4828	+	18.5927i	0.483297	+	0.620445i
$899$	3.90250			0.130156
$900$	1.28333	−	5.08427i	0.0427776	−	0.169476i
$901$			3.12737i			0.104188i
$902$	−18.2211	+	14.1933i	−0.606695	+	0.472587i
$903$			24.0401i			0.800005i
$904$	1.21004	+	2.74993i	0.0402452	+	0.0914613i
$905$	27.4079			0.911070
$906$	−23.9951	+	18.6911i	−0.797185	+	0.620969i
$907$			53.7974i			1.78631i	0.449745	+	0.893157i	$0.351515\pi$
$907$			53.7974i			1.78631i	−0.449745	+	0.893157i	$0.648485\pi$
$908$	16.1131	+	4.06714i	0.534732	+	0.134973i
$909$		−	12.7451i		−	0.422729i
$910$	−13.6705	+	10.6487i	−0.453174	+	0.353001i
$911$	52.4946			1.73922			0.869611	−	0.493737i	$-0.164370\pi$
$911$	52.4946			1.73922			0.869611	+	0.493737i	$0.164370\pi$
$912$	2.28037	−	4.22936i	0.0755104	−	0.140048i
$913$	−72.8138			−2.40978
$914$	−10.3052	+	8.02724i	−0.340865	+	0.265518i
$915$	8.69325			0.287390
$916$	−10.3010	+	40.8105i	−0.340356	+	1.34842i
$917$	−18.2791			−0.603630
$918$	−0.405405	+	0.315791i	−0.0133804	+	0.0104227i
$919$	−6.52504			−0.215241			−0.107621	−	0.994192i	$-0.534323\pi$
$919$	−6.52504			−0.215241			−0.107621	+	0.994192i	$0.534323\pi$
$920$	19.1410	+	8.43798i	0.631059	+	0.278192i
$921$	−25.3014			−0.833708
$922$	5.17875	−	4.03400i	0.170553	−	0.132853i
$923$	−18.4928			−0.608697
$924$	25.3286	+	6.39323i	0.833250	+	0.210322i
$925$	−24.3385			−0.800244
$926$	16.6822	−	12.9947i	0.548212	−	0.427031i
$927$	−14.2608			−0.468387
$928$	−18.2334	+	3.07886i	−0.598541	+	0.101069i
$929$	14.7989			0.485538			0.242769	−	0.970084i	$-0.421944\pi$
$929$	14.7989			0.485538			0.242769	+	0.970084i	$0.421944\pi$
$930$	2.05401	−	1.59997i	0.0673536	−	0.0524652i
$931$			1.86409i			0.0610931i
$932$	4.51727	−	17.8964i	0.147968	−	0.586217i
$933$			22.5992i			0.739866i
$934$	−20.0877	+	15.6473i	−0.657288	+	0.511996i
$935$	2.50284			0.0818516
$936$	−3.09520	−	7.03414i	−0.101170	−	0.229918i
$937$			15.5914i			0.509350i	0.967027	+	0.254675i	$0.0819686\pi$
$937$			15.5914i			0.509350i	−0.967027	+	0.254675i	$0.918031\pi$
$938$	33.5158	−	26.1072i	1.09433	−	0.852430i
$939$		−	11.7264i		−	0.382675i
$940$	−6.30899	−	1.59246i	−0.205777	−	0.0519404i
$941$	44.4720			1.44975			0.724874	−	0.688882i	$-0.241898\pi$
$941$	44.4720			1.44975			0.724874	+	0.688882i	$0.241898\pi$
$942$	2.90327	+	3.72715i	0.0945937	+	0.121437i
$943$	11.8382	+	12.9373i	0.385505	+	0.421298i
$944$	−48.8214	−	26.3233i	−1.58900	−	0.856750i
$945$	4.50969			0.146700
$946$	31.9096	+	40.9647i	1.03747	+	1.33188i
$947$	2.07216			0.0673361			0.0336681	−	0.999433i	$-0.489281\pi$
$947$	2.07216			0.0673361			0.0336681	+	0.999433i	$0.489281\pi$
$948$	−1.16494	+	4.61522i	−0.0378353	+	0.149895i
$949$		−	33.7644i		−	1.09604i
$950$	3.51381	−	2.73709i	0.114003	−	0.0888029i
$951$			8.77236i			0.284463i
$952$	1.21051	+	2.75100i	0.0392328	+	0.0891606i
$953$		−	11.7267i		−	0.379865i	−0.981797	−	0.189932i	$-0.939173\pi$
$953$		−	11.7267i		−	0.379865i	0.981797	−	0.189932i	$-0.0608269\pi$
$954$	7.47959	+	9.60211i	0.242161	+	0.310880i
$955$	13.3519			0.432056
$956$	13.0920	+	3.30457i	0.423426	+	0.106878i
$957$	14.6003			0.471961
$958$	7.42145	+	9.52748i	0.239776	+	0.307819i
$959$			11.5923i			0.374335i
$960$	−8.33451	+	9.09596i	−0.268995	+	0.293571i
$961$	29.5748			0.954024
$962$	−28.1398	+	21.9196i	−0.907263	+	0.706715i
$963$			15.8754i			0.511577i
$964$	28.1701	+	7.11045i	0.907296	+	0.229012i
$965$	4.97156			0.160040
$966$	3.31562	−	19.5548i	0.106678	−	0.629165i
$967$			52.1381i			1.67665i	0.545173	+	0.838324i	$0.316464\pi$
$967$			52.1381i			1.67665i	−0.545173	+	0.838324i	$0.683536\pi$
$968$	23.1687	−	10.1948i	0.744671	−	0.327674i
$969$	−0.436495			−0.0140223
$970$	−23.4195	+	18.2426i	−0.751954	+	0.585736i
$971$		−	15.9862i		−	0.513020i	−0.966542	−	0.256510i	$-0.917427\pi$
$971$		−	15.9862i		−	0.513020i	0.966542	−	0.256510i	$-0.0825727\pi$
$972$	−0.489471	+	1.93918i	−0.0156998	+	0.0621992i
$973$	−22.0466			−0.706780
$974$	38.9759	−	30.3604i	1.24887	−	0.972810i
$975$		−	7.12377i		−	0.228143i
$976$	19.8477	+	10.7014i	0.635309	+	0.342543i
$977$		−	4.91411i		−	0.157216i	−0.996906	−	0.0786082i	$-0.974952\pi$
$977$		−	4.91411i		−	0.157216i	0.996906	−	0.0786082i	$-0.0250476\pi$
$978$	−3.98593	−	5.11704i	−0.127456	−	0.163625i
$979$	−13.3566			−0.426880
$980$	1.17134	−	4.64060i	0.0374172	−	0.148239i
$981$	−4.48354			−0.143148
$982$	−17.2557	−	22.1525i	−0.550652	−	0.706913i
$983$	−39.1588			−1.24897			−0.624486	−	0.781036i	$-0.714692\pi$
$983$	−39.1588			−1.24897			−0.624486	+	0.781036i	$0.714692\pi$
$984$	−9.46636	+	4.16543i	−0.301776	+	0.132789i
$985$			7.44742i			0.237294i
$986$	1.03228	+	1.32522i	0.0328745	+	0.0422035i
$987$			6.16954i			0.196379i
$988$	1.59756	−	6.32917i	0.0508250	−	0.201358i
$989$	29.0858	−	26.6147i	0.924875	−	0.846299i
$990$	7.68459	−	5.98593i	0.244232	−	0.190245i
$991$		−	7.58733i		−	0.241019i	−0.992712	−	0.120510i	$-0.961547\pi$
$991$		−	7.58733i		−	0.241019i	0.992712	−	0.120510i	$-0.0384529\pi$
$992$	6.65910	−	1.12444i	0.211427	−	0.0357012i
$993$	−13.7475			−0.436264
$994$	22.2060	−	17.2974i	0.704331	−	0.548640i
$995$	−16.5670			−0.525208
$996$	−31.6131	−	7.97952i	−1.00170	−	0.252841i
$997$		−	45.3300i		−	1.43561i	−0.696242	−	0.717807i	$-0.745146\pi$
$997$		−	45.3300i		−	1.43561i	0.696242	−	0.717807i	$-0.254854\pi$
$998$	16.3104	+	20.9388i	0.516295	+	0.662807i
$999$	9.28288			0.293697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.a.91.19	yes	24
4.3	odd	2		2208.2.n.a.367.7		24
8.3	odd	2	inner	552.2.n.a.91.18	yes	24
8.5	even	2		2208.2.n.a.367.17		24
23.22	odd	2	inner	552.2.n.a.91.20	yes	24
92.91	even	2		2208.2.n.a.367.18		24
184.45	odd	2		2208.2.n.a.367.8		24
184.91	even	2	inner	552.2.n.a.91.17	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.a.91.17	✓	24	184.91	even	2	inner
552.2.n.a.91.18	yes	24	8.3	odd	2	inner
552.2.n.a.91.19	yes	24	1.1	even	1	trivial
552.2.n.a.91.20	yes	24	23.22	odd	2	inner
2208.2.n.a.367.7		24	4.3	odd	2
2208.2.n.a.367.8		24	184.45	odd	2
2208.2.n.a.367.17		24	8.5	even	2
2208.2.n.a.367.18		24	92.91	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.869059 + 1.11568i) q^{2} +1.00000 q^{3} +(-0.489471 + 1.93918i) q^{4} -1.54212 q^{5} +(0.869059 + 1.11568i) q^{6} -2.92435 q^{7} +(-2.58888 + 1.13917i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.869059 + 1.11568i) q^{2} +1.00000 q^{3} +(-0.489471 + 1.93918i) q^{4} -1.54212 q^{5} +(0.869059 + 1.11568i) q^{6} -2.92435 q^{7} +(-2.58888 + 1.13917i) q^{8} +1.00000 q^{9} +(-1.34019 - 1.72051i) q^{10} +4.46647i q^{11} +(-0.489471 + 1.93918i) q^{12} +2.71706i q^{13} +(-2.54143 - 3.26263i) q^{14} -1.54212 q^{15} +(-3.52084 - 1.89835i) q^{16} +0.363371i q^{17} +(0.869059 + 1.11568i) q^{18} +1.20124i q^{19} +(0.754824 - 2.99045i) q^{20} -2.92435 q^{21} +(-4.98314 + 3.88163i) q^{22} +(3.23754 + 3.53813i) q^{23} +(-2.58888 + 1.13917i) q^{24} -2.62187 q^{25} +(-3.03136 + 2.36129i) q^{26} +1.00000 q^{27} +(1.43138 - 5.67084i) q^{28} -3.26887i q^{29} +(-1.34019 - 1.72051i) q^{30} +1.19384i q^{31} +(-0.941874 - 5.57789i) q^{32} +4.46647i q^{33} +(-0.405405 + 0.315791i) q^{34} +4.50969 q^{35} +(-0.489471 + 1.93918i) q^{36} +9.28288 q^{37} +(-1.34019 + 1.04395i) q^{38} +2.71706i q^{39} +(3.99236 - 1.75674i) q^{40} +3.65655 q^{41} +(-2.54143 - 3.26263i) q^{42} -8.22067i q^{43} +(-8.66128 - 2.18621i) q^{44} -1.54212 q^{45} +(-1.13380 + 6.68689i) q^{46} -2.10971i q^{47} +(-3.52084 - 1.89835i) q^{48} +1.55181 q^{49} +(-2.27856 - 2.92516i) q^{50} +0.363371i q^{51} +(-5.26887 - 1.32992i) q^{52} +8.60653 q^{53} +(0.869059 + 1.11568i) q^{54} -6.88783i q^{55} +(7.57078 - 3.33133i) q^{56} +1.20124i q^{57} +(3.64700 - 2.84084i) q^{58} +13.8664 q^{59} +(0.754824 - 2.99045i) q^{60} -5.63721 q^{61} +(-1.33194 + 1.03752i) q^{62} -2.92435 q^{63} +(5.40458 - 5.89835i) q^{64} -4.19004i q^{65} +(-4.98314 + 3.88163i) q^{66} +10.2726i q^{67} +(-0.704642 - 0.177860i) q^{68} +(3.23754 + 3.53813i) q^{69} +(3.91919 + 5.03136i) q^{70} +6.80616i q^{71} +(-2.58888 + 1.13917i) q^{72} -12.4268 q^{73} +(8.06738 + 10.3567i) q^{74} -2.62187 q^{75} +(-2.32942 - 0.587972i) q^{76} -13.0615i q^{77} +(-3.03136 + 2.36129i) q^{78} +2.37999 q^{79} +(5.42955 + 2.92748i) q^{80} +1.00000 q^{81} +(3.17776 + 4.07953i) q^{82} +16.3023i q^{83} +(1.43138 - 5.67084i) q^{84} -0.560362i q^{85} +(9.17162 - 7.14425i) q^{86} -3.26887i q^{87} +(-5.08807 - 11.5631i) q^{88} +2.99042i q^{89} +(-1.34019 - 1.72051i) q^{90} -7.94563i q^{91} +(-8.44575 + 4.54635i) q^{92} +1.19384i q^{93} +(2.35376 - 1.83347i) q^{94} -1.85245i q^{95} +(-0.941874 - 5.57789i) q^{96} -13.6119i q^{97} +(1.34861 + 1.73132i) q^{98} +4.46647i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9	\( 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 4 q^{24} + 24 q^{25} + 24 q^{27} - 4 q^{32} + 4 q^{36} + 4 q^{46} + 4 q^{48} - 8 q^{49} - 44 q^{50} - 4 q^{54} + 48 q^{58} - 40 q^{62} + 4 q^{64} - 4 q^{72} - 32 q^{73} + 24 q^{75} + 24 q^{81} - 40 q^{82} - 52 q^{92} + 40 q^{94} - 4 q^{96} - 20 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 4 * q^24 + 24 * q^25 + 24 * q^27 - 4 * q^32 + 4 * q^36 + 4 * q^46 + 4 * q^48 - 8 * q^49 - 44 * q^50 - 4 * q^54 + 48 * q^58 - 40 * q^62 + 4 * q^64 - 4 * q^72 - 32 * q^73 + 24 * q^75 + 24 * q^81 - 40 * q^82 - 52 * q^92 + 40 * q^94 - 4 * q^96 - 20 * q^98

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