LMFDB - Embedded newform 552.2.n.a.91.18

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			91.18
Character	$\chi$	$=$	552.91
Dual form			552.2.n.a.91.20

$q$-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} +(-6.76102 + 0.537203i) 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} +(-5.27638 + 8.00998i) 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	$-0.387937\pi$
$5$	1.54212			0.689657			0.344829	+	0.938666i	$0.387937\pi$
$6$	0.869059	−	1.11568i	0.354792	−	0.455473i
$7$	2.92435			1.10530			0.552650	−	0.833414i	$-0.313617\pi$
$7$	2.92435			1.10530			0.552650	+	0.833414i	$0.313617\pi$
$8$	−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	$-0.877028\pi$
$13$		−	2.71706i		−	0.753577i	0.926299	−	0.376789i	$-0.122972\pi$
$14$	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	$0.0981576\pi$
$29$			3.26887i			0.607014i	−0.952829	+	0.303507i	$0.901842\pi$
$30$	1.34019	−	1.72051i	0.244685	−	0.314120i
$31$		−	1.19384i		−	0.214420i	−0.994236	−	0.107210i	$-0.965808\pi$
$31$		−	1.19384i		−	0.214420i	0.994236	−	0.107210i	$-0.0341917\pi$
$32$	−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	$-0.776298\pi$
$37$	−9.28288			−1.52610			−0.763048	+	0.646342i	$0.776298\pi$
$38$	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
$46$	−6.76102	+	0.537203i	−0.996858	+	0.0792063i
$47$			2.10971i			0.307733i	0.988092	+	0.153867i	$0.0491726\pi$
$47$			2.10971i			0.307733i	−0.988092	+	0.153867i	$0.950827\pi$
$48$	−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	$-0.701306\pi$
$53$	−8.60653			−1.18220			−0.591099	+	0.806599i	$0.701306\pi$
$54$	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	$-0.382475\pi$
$61$	5.63721			0.721771			0.360885	+	0.932610i	$0.382475\pi$
$62$	−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	$-0.867664\pi$
$71$		−	6.80616i		−	0.807743i	0.914816	−	0.403871i	$-0.132336\pi$
$72$	−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	$-0.542745\pi$
$79$	−2.37999			−0.267769			−0.133885	+	0.990997i	$0.542745\pi$
$80$	−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
$92$	−5.27638	+	8.00998i	−0.550101	+	0.835098i
$93$		−	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	$0.218626\pi$
$101$			12.7451i			1.26819i	−0.773257	+	0.634093i	$0.781374\pi$
$102$	0.405405	+	0.315791i	0.0401411	+	0.0312680i
$103$	14.2608			1.40516			0.702580	−	0.711605i	$-0.252031\pi$
$103$	14.2608			1.40516			0.702580	+	0.711605i	$0.252031\pi$
$104$	−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	$-0.431115\pi$
$109$	4.48354			0.429445			0.214723	+	0.976675i	$0.431115\pi$
$110$	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	$-0.902481\pi$
$127$		−	6.79761i		−	0.603190i	0.953436	−	0.301595i	$-0.0975191\pi$
$128$	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	$-0.0541625\pi$
$138$	−6.76102	+	0.537203i	−0.575536	+	0.0457298i
$139$	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	$-0.710887\pi$
$149$	−15.0167			−1.23021			−0.615107	+	0.788444i	$0.710887\pi$
$150$	−2.27856	+	2.92516i	−0.186043	+	0.238838i
$151$		−	21.5072i		−	1.75023i	−0.483911	−	0.875117i	$-0.660784\pi$
$151$		−	21.5072i		−	1.75023i	0.483911	−	0.875117i	$-0.339216\pi$
$152$	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	$-0.542560\pi$
$157$	−3.34071			−0.266617			−0.133309	+	0.991075i	$0.542560\pi$
$158$	−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	$0.0160715\pi$
$167$			1.30440i			0.100937i	−0.998726	+	0.0504686i	$0.983929\pi$
$168$	−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	$0.0173983\pi$
$173$			1.43712i			0.109262i	−0.998507	+	0.0546311i	$0.982602\pi$
$174$	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	$-0.270334\pi$
$181$	17.7729			1.32105			0.660524	+	0.750805i	$0.270334\pi$
$182$	−8.86476	−	6.90523i	−0.657100	−	0.511849i
$183$	5.63721			0.416714
$184$	4.35106	+	12.8479i	0.320764	+	0.947159i
$185$	−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	$-0.398586\pi$
$191$	8.65813			0.626480			0.313240	+	0.949674i	$0.398586\pi$
$192$	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	$0.0550352\pi$
$197$			4.82934i			0.344076i	−0.985090	+	0.172038i	$0.944965\pi$
$198$	4.98314	+	3.88163i	0.354136	+	0.275855i
$199$	−10.7430			−0.761550			−0.380775	−	0.924668i	$-0.624343\pi$
$199$	−10.7430			−0.761550			−0.380775	+	0.924668i	$0.624343\pi$
$200$	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	$-0.999221\pi$
$223$		−	0.0731140i		−	0.00489608i	0.999997	−	0.00244804i	$-0.000779236\pi$
$224$	−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	$-0.744752\pi$
$229$	−21.0452			−1.39071			−0.695354	+	0.718668i	$0.744752\pi$
$230$	−10.4263	+	0.828432i	−0.687490	+	0.0546252i
$231$			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	$0.0700684\pi$
$239$			6.75131i			0.436706i	−0.975870	+	0.218353i	$0.929932\pi$
$240$	−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	$-0.338559\pi$
$263$	15.7540			0.971432			0.485716	+	0.874117i	$0.338559\pi$
$264$	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	$-0.718085\pi$
$269$		−	25.4000i		−	1.54867i	0.632777	−	0.774334i	$-0.281915\pi$
$270$	1.34019	−	1.72051i	0.0815616	−	0.104707i
$271$			19.1184i			1.16136i	0.814132	+	0.580679i	$0.197213\pi$
$271$			19.1184i			1.16136i	−0.814132	+	0.580679i	$0.802787\pi$
$272$	−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
$276$	−5.27638	+	8.00998i	−0.317601	+	0.482144i
$277$			3.47221i			0.208625i	0.994545	+	0.104312i	$0.0332642\pi$
$277$			3.47221i			0.208625i	−0.994545	+	0.104312i	$0.966736\pi$
$278$	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	$-0.464687\pi$
$293$	3.79012			0.221421			0.110711	+	0.993853i	$0.464687\pi$
$294$	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	$-0.778627\pi$
$311$		−	22.5992i		−	1.28149i	0.767756	−	0.640743i	$-0.221373\pi$
$312$	−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	$-0.920768\pi$
$317$		−	8.77236i		−	0.492705i	0.969180	−	0.246352i	$-0.0792320\pi$
$318$	−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
$322$	−19.7716	+	1.57097i	−1.10183	+	0.0875466i
$323$	−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	$-0.828140\pi$
$349$		−	19.2070i		−	1.02813i	0.857753	−	0.514063i	$-0.171860\pi$
$350$	−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	$-0.258272\pi$
$359$	26.0902			1.37699			0.688494	+	0.725242i	$0.258272\pi$
$360$	−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	$-0.596613\pi$
$367$	−11.4514			−0.597757			−0.298879	+	0.954291i	$0.596613\pi$
$368$	18.1154	+	6.31120i	0.944332	+	0.328994i
$369$	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	$-0.509541\pi$
$373$	−1.15765			−0.0599409			−0.0299705	+	0.999551i	$0.509541\pi$
$374$	−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	$-0.740081\pi$
$383$	−26.8009			−1.36946			−0.684731	+	0.728795i	$0.740081\pi$
$384$	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	$-0.401131\pi$
$389$	12.0562			0.611272			0.305636	+	0.952148i	$0.401131\pi$
$390$	−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	$0.340160\pi$
$397$			34.9302i			1.75310i	−0.481312	+	0.876549i	$0.659840\pi$
$398$	−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
$414$	−6.76102	+	0.537203i	−0.332286	+	0.0264021i
$415$			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	$-0.305375\pi$
$421$	23.5566			1.14808			0.574040	+	0.818827i	$0.305375\pi$
$422$	−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	$-0.729986\pi$
$431$	−27.4570			−1.32256			−0.661278	+	0.750141i	$0.729986\pi$
$432$	−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	$-0.978435\pi$
$439$		−	2.83686i		−	0.135396i	0.997706	−	0.0676979i	$-0.0215654\pi$
$440$	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
$460$	−8.13682	+	12.3523i	−0.379381	+	0.575931i
$461$			4.64180i			0.216190i	0.994141	+	0.108095i	$0.0344751\pi$
$461$			4.64180i			0.216190i	−0.994141	+	0.108095i	$0.965525\pi$
$462$	14.5724	+	11.3512i	0.677970	+	0.528107i
$463$			14.9526i			0.694905i	0.937698	+	0.347452i	$0.112953\pi$
$463$			14.9526i			0.694905i	−0.937698	+	0.347452i	$0.887047\pi$
$464$	−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	$-0.562501\pi$
$479$	−8.53964			−0.390186			−0.195093	+	0.980785i	$0.562501\pi$
$480$	−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	$0.290712\pi$
$487$			34.9348i			1.58305i	−0.611139	+	0.791523i	$0.709288\pi$
$488$	−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	$-0.490898\pi$
$503$	1.28243			0.0571809			0.0285905	+	0.999591i	$0.490898\pi$
$504$	−7.57078	−	3.33133i	−0.337229	−	0.148389i
$505$			19.6545i			0.874613i
$506$	−2.39940	−	30.1979i	−0.106666	−	1.34246i
$507$	5.61758			0.249485
$508$	−13.1818	+	3.32724i	−0.584847	+	0.147622i
$509$			30.2587i			1.34119i	0.741821	+	0.670597i	$0.233962\pi$
$509$			30.2587i			1.34119i	−0.741821	+	0.670597i	$0.766038\pi$
$510$	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	$-0.651477\pi$
$541$		−	41.3501i		−	1.77778i	0.458119	−	0.888891i	$-0.348523\pi$
$542$	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
$552$	4.35106	+	12.8479i	0.185193	+	0.546843i
$553$	−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	$-0.716615\pi$
$557$	−29.6990			−1.25839			−0.629193	+	0.777249i	$0.716615\pi$
$558$	−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
$598$	1.45961	+	18.3701i	0.0596880	+	0.751210i
$599$			44.6517i			1.82442i	0.409722	+	0.912210i	$0.365626\pi$
$599$			44.6517i			1.82442i	−0.409722	+	0.912210i	$0.634374\pi$
$600$	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	$0.237241\pi$
$607$			33.4183i			1.35641i	−0.734874	+	0.678204i	$0.762759\pi$
$608$	−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	$-0.703111\pi$
$613$	−29.4958			−1.19133			−0.595663	+	0.803234i	$0.703111\pi$
$614$	−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	$-0.517457\pi$
$631$	−2.75385			−0.109629			−0.0548146	+	0.998497i	$0.517457\pi$
$632$	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	$-0.0216158\pi$
$644$	−15.4300	+	23.4240i	−0.608026	+	0.923033i
$645$		−	12.6773i		−	0.499167i
$646$	−0.379340	+	0.486988i	−0.0149249	+	0.0191603i
$647$		−	15.2137i		−	0.598113i	−0.954235	−	0.299057i	$-0.903328\pi$
$647$		−	15.2137i		−	0.598113i	0.954235	−	0.299057i	$-0.0966719\pi$
$648$	−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	$-0.873609\pi$
$653$		−	19.7643i		−	0.773436i	0.922198	−	0.386718i	$-0.126391\pi$
$654$	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	$-0.585958\pi$
$661$	−13.7175			−0.533547			−0.266774	+	0.963759i	$0.585958\pi$
$662$	−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	$-0.470526\pi$
$677$	4.81157			0.184924			0.0924618	+	0.995716i	$0.470526\pi$
$678$	−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
$690$	−10.4263	+	0.828432i	−0.396923	+	0.0315378i
$691$	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	$-0.432573\pi$
$701$	11.1332			0.420496			0.210248	+	0.977648i	$0.432573\pi$
$702$	−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	$-0.497686\pi$
$709$	0.387202			0.0145417			0.00727083	+	0.999974i	$0.497686\pi$
$710$	−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	$0.261050\pi$
$719$			39.2143i			1.46245i	−0.682138	+	0.731224i	$0.738950\pi$
$720$	−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	$-0.250056\pi$
$727$	38.1247			1.41397			0.706983	+	0.707231i	$0.250056\pi$
$728$	−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	$-0.438577\pi$
$733$	10.3840			0.383541			0.191771	+	0.981440i	$0.438577\pi$
$734$	−9.95193	+	12.7760i	−0.367332	+	0.471572i
$735$	2.39308			0.0882699
$736$	22.7846	−	14.7262i	0.839853	−	0.542814i
$737$	−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	$-0.283978\pi$
$743$	34.2222			1.25549			0.627745	+	0.778419i	$0.283978\pi$
$744$	−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	$-0.222378\pi$
$751$	41.9687			1.53146			0.765731	+	0.643161i	$0.222378\pi$
$752$	−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	$-0.568630\pi$
$757$	−11.7725			−0.427880			−0.213940	+	0.976847i	$0.568630\pi$
$758$	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	$-0.584518\pi$
$773$	−14.5916			−0.524823			−0.262411	+	0.964956i	$0.584518\pi$
$774$	−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
$782$	−0.195204	−	2.45676i	−0.00698049	−	0.0878536i
$783$			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	$-0.335679\pi$
$797$	27.8701			0.987209			0.493604	+	0.869687i	$0.335679\pi$
$798$	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	$-0.729278\pi$
$821$		−	43.0718i		−	1.50322i	0.659610	−	0.751608i	$-0.270722\pi$
$822$	−4.42262	−	3.44501i	−0.154257	−	0.120159i
$823$		−	43.9947i		−	1.53356i	−0.641911	−	0.766779i	$-0.721858\pi$
$823$		−	43.9947i		−	1.53356i	0.641911	−	0.766779i	$-0.278142\pi$
$824$	−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	$0.917881\pi$
$828$	−5.27638	+	8.00998i	−0.183367	+	0.278366i
$829$		−	15.6549i		−	0.543716i	−0.962337	−	0.271858i	$-0.912362\pi$
$829$		−	15.6549i		−	0.543716i	0.962337	−	0.271858i	$-0.0876382\pi$
$830$	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	$-0.918829\pi$
$839$	−56.0576			−1.93532			−0.967661	+	0.252253i	$0.918829\pi$
$840$	−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	$-0.666917\pi$
$853$		−	50.5636i		−	1.73126i	0.500681	−	0.865632i	$-0.333083\pi$
$854$	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	$-0.790063\pi$
$863$		−	36.0014i		−	1.22550i	0.790276	−	0.612751i	$-0.209937\pi$
$864$	−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
$874$	−0.645309	−	8.12160i	−0.0218279	−	0.274717i
$875$	−34.3723			−1.16200
$876$	6.08256	+	24.0978i	0.205511	+	0.814189i
$877$			32.5996i			1.10081i	0.834898	+	0.550405i	$0.185527\pi$
$877$			32.5996i			1.10081i	−0.834898	+	0.550405i	$0.814473\pi$
$878$	−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	$0.168720\pi$
$887$			30.1148i			1.01115i	−0.862781	+	0.505577i	$0.831280\pi$
$888$	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	$-0.835630\pi$
$911$	−52.4946			−1.73922			−0.869611	+	0.493737i	$0.835630\pi$
$912$	−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	$-0.465677\pi$
$919$	6.52504			0.215241			0.107621	+	0.994192i	$0.465677\pi$
$920$	6.70986	+	19.8130i	0.221217	+	0.653215i
$921$	−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	$-0.758102\pi$
$941$	−44.4720			−1.44975			−0.724874	+	0.688882i	$0.758102\pi$
$942$	−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
$966$	−19.7716	+	1.57097i	−0.636140	+	0.0505451i
$967$		−	52.1381i		−	1.67665i	−0.545173	−	0.838324i	$-0.683536\pi$
$967$		−	52.1381i		−	1.67665i	0.545173	−	0.838324i	$-0.316464\pi$
$968$	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	$-0.285308\pi$
$983$	39.1588			1.24897			0.624486	+	0.781036i	$0.285308\pi$
$984$	−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	$0.0384529\pi$
$991$			7.58733i			0.241019i	−0.992712	+	0.120510i	$0.961547\pi$
$992$	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	$0.254854\pi$
$997$			45.3300i			1.43561i	−0.696242	+	0.717807i	$0.745146\pi$
$998$	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.91.18	yes	24
4.3	odd	2		2208.2.n.a.367.17		24
8.3	odd	2	inner	552.2.n.a.91.19	yes	24
8.5	even	2		2208.2.n.a.367.7		24
23.22	odd	2	inner	552.2.n.a.91.17	✓	24
92.91	even	2		2208.2.n.a.367.8		24
184.45	odd	2		2208.2.n.a.367.18		24
184.91	even	2	inner	552.2.n.a.91.20	yes	24

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

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} +(-6.76102 + 0.537203i) 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} +(-5.27638 + 8.00998i) 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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