LMFDB - Embedded newform 576.2.bd.a.469.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [576,2,Mod(37,576)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("576.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(576, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 9, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bd (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,8,0,-8,8,0,-8,8,0,-8,8,0,-8,8,0,-8,8,0,-8,8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(22)] == traces)

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			469.1
Character	$\chi$	$=$	576.469
Dual form			576.2.bd.a.253.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26428 + 0.633715i) q^{2} +(1.19681 - 1.60239i) q^{4} +(2.78737 - 1.86246i) q^{5} +(-3.13672 - 1.29927i) q^{7} +(-0.497646 + 2.78430i) q^{8} +(-2.34375 + 4.12108i) q^{10} +(1.79402 + 0.356853i) q^{11} +(4.34710 + 2.90464i) q^{13} +(4.78906 - 0.345143i) q^{14} +(-1.13529 - 3.83551i) q^{16} +(1.16196 - 1.16196i) q^{17} +(-0.00265155 + 0.00396832i) q^{19} +(0.351568 - 6.69547i) q^{20} +(-2.49429 + 0.685737i) q^{22} +(-1.78945 - 4.32013i) q^{23} +(2.38726 - 5.76336i) q^{25} +(-7.33667 - 0.917455i) q^{26} +(-5.83599 + 3.47126i) q^{28} +(1.70191 - 0.338531i) q^{29} -9.42685i q^{31} +(3.86595 + 4.12970i) q^{32} +(-0.732694 + 2.20540i) q^{34} +(-11.1630 + 2.22047i) q^{35} +(-1.47130 - 2.20195i) q^{37} +(0.000837513 - 0.00669740i) q^{38} +(3.79854 + 8.68774i) q^{40} +(-0.497436 - 1.20092i) q^{41} +(0.104068 - 0.523183i) q^{43} +(2.71892 - 2.44763i) q^{44} +(5.00010 + 4.32785i) q^{46} +(0.378819 - 0.378819i) q^{47} +(3.20113 + 3.20113i) q^{49} +(0.634161 + 8.79935i) q^{50} +(9.85702 - 3.48944i) q^{52} +(3.63594 + 0.723233i) q^{53} +(5.66523 - 2.34662i) q^{55} +(5.17854 - 8.08699i) q^{56} +(-1.93716 + 1.50653i) q^{58} +(11.1857 - 7.47403i) q^{59} +(-1.29788 - 6.52488i) q^{61} +(5.97394 + 11.9182i) q^{62} +(-7.50470 - 2.77119i) q^{64} +17.5268 q^{65} +(1.46964 + 7.38837i) q^{67} +(-0.471267 - 3.25257i) q^{68} +(12.7061 - 9.88148i) q^{70} +(-5.03495 - 2.08554i) q^{71} +(-4.53632 + 1.87901i) q^{73} +(3.25554 + 1.85150i) q^{74} +(0.00318539 + 0.00899813i) q^{76} +(-5.16369 - 3.45027i) q^{77} +(11.3984 + 11.3984i) q^{79} +(-10.3080 - 8.57655i) q^{80} +(1.38994 + 1.20306i) q^{82} +(-3.35370 + 5.01916i) q^{83} +(1.07471 - 5.40294i) q^{85} +(0.199978 + 0.727399i) q^{86} +(-1.88637 + 4.81752i) q^{88} +(-4.25907 + 10.2823i) q^{89} +(-9.86171 - 14.7591i) q^{91} +(-9.06415 - 2.30297i) q^{92} +(-0.238870 + 0.718996i) q^{94} +0.0159996i q^{95} +12.2846i q^{97} +(-6.07574 - 2.01852i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32}+ \cdots - 128 q^{98}+O(q^{100}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{16}\right)$

Coefficient data

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

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

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

$2$	−1.26428	+	0.633715i	−0.893981	+	0.448104i
$2$	−1.26428	+	0.633715i	−0.893981	+	0.448104i
$3$		0			0
$3$		0			0
$4$	1.19681	−	1.60239i	0.598405	−	0.801194i
$5$	2.78737	−	1.86246i	1.24655	−	0.832919i	0.255553	−	0.966795i	$-0.417742\pi$
$5$	2.78737	−	1.86246i	1.24655	−	0.832919i	0.990998	+	0.133876i	$0.0427425\pi$
$6$		0			0
$7$	−3.13672	−	1.29927i	−1.18557	−	0.491078i	−0.299258	−	0.954172i	$-0.596739\pi$
$7$	−3.13672	−	1.29927i	−1.18557	−	0.491078i	−0.886309	+	0.463094i	$0.846739\pi$
$8$	−0.497646	+	2.78430i	−0.175944	+	0.984400i
$9$		0			0
$10$	−2.34375	+	4.12108i	−0.741159	+	1.30320i
$11$	1.79402	+	0.356853i	0.540918	+	0.107595i	0.457985	−	0.888960i	$-0.348571\pi$
$11$	1.79402	+	0.356853i	0.540918	+	0.107595i	0.0829328	+	0.996555i	$0.473571\pi$
$12$		0			0
$13$	4.34710	+	2.90464i	1.20567	+	0.805603i	0.985470	−	0.169852i	$-0.0543291\pi$
$13$	4.34710	+	2.90464i	1.20567	+	0.805603i	0.220200	+	0.975455i	$0.429329\pi$
$14$	4.78906	−	0.345143i	1.27993	−	0.0922433i
$15$		0			0
$16$	−1.13529	−	3.83551i	−0.283823	−	0.958877i
$17$	1.16196	−	1.16196i	0.281818	−	0.281818i	−0.552016	−	0.833834i	$-0.686141\pi$
$17$	1.16196	−	1.16196i	0.281818	−	0.281818i	0.833834	+	0.552016i	$0.186141\pi$
$18$		0			0
$19$	−0.00265155	+	0.00396832i	−0.000608307	+	0.000910395i	−0.831774	−	0.555115i	$-0.812674\pi$
$19$	−0.00265155	+	0.00396832i	−0.000608307	+	0.000910395i	0.831165	+	0.556025i	$0.187674\pi$
$20$	0.351568	−	6.69547i	0.0786129	−	1.49715i
$21$		0			0
$22$	−2.49429	+	0.685737i	−0.531784	+	0.146200i
$23$	−1.78945	−	4.32013i	−0.373127	−	0.900809i	−0.993217	−	0.116278i	$-0.962904\pi$
$23$	−1.78945	−	4.32013i	−0.373127	−	0.900809i	0.620090	−	0.784531i	$-0.287096\pi$
$24$		0			0
$25$	2.38726	−	5.76336i	0.477452	−	1.15267i
$26$	−7.33667	−	0.917455i	−1.43884	−	0.179928i
$27$		0			0
$28$	−5.83599	+	3.47126i	−1.10290	+	0.656006i
$29$	1.70191	−	0.338531i	0.316037	−	0.0628637i	−0.0345231	−	0.999404i	$-0.510991\pi$
$29$	1.70191	−	0.338531i	0.316037	−	0.0628637i	0.350560	+	0.936540i	$0.385991\pi$
$30$		0			0
$31$		−	9.42685i		−	1.69311i	−0.532300	−	0.846556i	$-0.678672\pi$
$31$		−	9.42685i		−	1.69311i	0.532300	−	0.846556i	$-0.321328\pi$
$32$	3.86595	+	4.12970i	0.683409	+	0.730035i
$33$		0			0
$34$	−0.732694	+	2.20540i	−0.125656	+	0.378224i
$35$	−11.1630	+	2.22047i	−1.88690	+	0.375327i
$36$		0			0
$37$	−1.47130	−	2.20195i	−0.241880	−	0.361999i	0.690590	−	0.723246i	$-0.257351\pi$
$37$	−1.47130	−	2.20195i	−0.241880	−	0.361999i	−0.932470	+	0.361248i	$0.882351\pi$
$38$	0.000837513	−	0.00669740i	0.000135863	−	0.00108646i
$39$		0			0
$40$	3.79854	+	8.68774i	0.600602	+	1.37365i
$41$	−0.497436	−	1.20092i	−0.0776864	−	0.187552i	0.880265	−	0.474483i	$-0.157365\pi$
$41$	−0.497436	−	1.20092i	−0.0776864	−	0.187552i	−0.957951	+	0.286931i	$0.907365\pi$
$42$		0			0
$43$	0.104068	−	0.523183i	0.0158702	−	0.0797847i	−0.972039	−	0.234821i	$-0.924550\pi$
$43$	0.104068	−	0.523183i	0.0158702	−	0.0797847i	0.987909	+	0.155037i	$0.0495495\pi$
$44$	2.71892	−	2.44763i	0.409893	−	0.368995i
$45$		0			0
$46$	5.00010	+	4.32785i	0.737225	+	0.638106i
$47$	0.378819	−	0.378819i	0.0552564	−	0.0552564i	−0.678939	−	0.734195i	$-0.737560\pi$
$47$	0.378819	−	0.378819i	0.0552564	−	0.0552564i	0.734195	+	0.678939i	$0.237560\pi$
$48$		0			0
$49$	3.20113	+	3.20113i	0.457305	+	0.457305i
$50$	0.634161	+	8.79935i	0.0896839	+	1.24442i
$51$		0			0
$52$	9.85702	−	3.48944i	1.36692	−	0.483898i
$53$	3.63594	+	0.723233i	0.499435	+	0.0993438i	0.438378	−	0.898791i	$-0.355553\pi$
$53$	3.63594	+	0.723233i	0.499435	+	0.0993438i	0.0610565	+	0.998134i	$0.480553\pi$
$54$		0			0
$55$	5.66523	−	2.34662i	0.763900	−	0.316418i
$56$	5.17854	−	8.08699i	0.692011	−	1.08067i
$57$		0			0
$58$	−1.93716	+	1.50653i	−0.254362	+	0.197816i
$59$	11.1857	−	7.47403i	1.45625	−	0.973036i	0.459874	−	0.887984i	$-0.347895\pi$
$59$	11.1857	−	7.47403i	1.45625	−	0.973036i	0.996377	−	0.0850514i	$-0.0271054\pi$
$60$		0			0
$61$	−1.29788	−	6.52488i	−0.166176	−	0.835425i	−0.970475	−	0.241200i	$-0.922459\pi$
$61$	−1.29788	−	6.52488i	−0.166176	−	0.835425i	0.804299	−	0.594225i	$-0.202541\pi$
$62$	5.97394	+	11.9182i	0.758691	+	1.51361i
$63$		0			0
$64$	−7.50470	−	2.77119i	−0.938087	−	0.346399i
$65$	17.5268			2.17393
$66$		0			0
$67$	1.46964	+	7.38837i	0.179545	+	0.902633i	0.960550	+	0.278108i	$0.0897074\pi$
$67$	1.46964	+	7.38837i	0.179545	+	0.902633i	−0.781005	+	0.624525i	$0.785293\pi$
$68$	−0.471267	−	3.25257i	−0.0571495	−	0.394432i
$69$		0			0
$70$	12.7061	−	9.88148i	1.51867	−	1.18106i
$71$	−5.03495	−	2.08554i	−0.597538	−	0.247508i	0.0633517	−	0.997991i	$-0.479821\pi$
$71$	−5.03495	−	2.08554i	−0.597538	−	0.247508i	−0.660890	+	0.750483i	$0.729821\pi$
$72$		0			0
$73$	−4.53632	+	1.87901i	−0.530936	+	0.219921i	−0.632013	−	0.774958i	$-0.717771\pi$
$73$	−4.53632	+	1.87901i	−0.530936	+	0.219921i	0.101077	+	0.994879i	$0.467771\pi$
$74$	3.25554	+	1.85150i	0.378449	+	0.215233i
$75$		0			0
$76$	0.00318539	+	0.00899813i	0.000365389	+	0.00103216i
$77$	−5.16369	−	3.45027i	−0.588457	−	0.393194i
$78$		0			0
$79$	11.3984	+	11.3984i	1.28242	+	1.28242i	0.939287	+	0.343133i	$0.111488\pi$
$79$	11.3984	+	11.3984i	1.28242	+	1.28242i	0.343133	+	0.939287i	$0.388512\pi$
$80$	−10.3080	−	8.57655i	−1.15247	−	0.958887i
$81$		0			0
$82$	1.38994	+	1.20306i	0.153493	+	0.132856i
$83$	−3.35370	+	5.01916i	−0.368116	+	0.550925i	−0.968572	−	0.248733i	$-0.919986\pi$
$83$	−3.35370	+	5.01916i	−0.368116	+	0.550925i	0.600456	+	0.799658i	$0.294986\pi$
$84$		0			0
$85$	1.07471	−	5.40294i	0.116569	−	0.586032i
$86$	0.199978	+	0.727399i	0.0215642	+	0.0784375i
$87$		0			0
$88$	−1.88637	+	4.81752i	−0.201088	+	0.513549i
$89$	−4.25907	+	10.2823i	−0.451460	+	1.08992i	0.520307	+	0.853980i	$0.325818\pi$
$89$	−4.25907	+	10.2823i	−0.451460	+	1.08992i	−0.971767	+	0.235942i	$0.924182\pi$
$90$		0			0
$91$	−9.86171	−	14.7591i	−1.03379	−	1.54717i
$92$	−9.06415	−	2.30297i	−0.945003	−	0.240101i
$93$		0			0
$94$	−0.238870	+	0.718996i	−0.0246375	+	0.0741588i
$95$			0.0159996i			0.00164152i
$96$		0			0
$97$			12.2846i			1.24731i	0.781698	+	0.623657i	$0.214354\pi$
$97$			12.2846i			1.24731i	−0.781698	+	0.623657i	$0.785646\pi$
$98$	−6.07574	−	2.01852i	−0.613742	−	0.203902i
$99$		0			0
$100$	−6.37804	−	10.7230i	−0.637804	−	1.07230i
$101$	1.04551	+	1.56472i	0.104032	+	0.155695i	0.879833	−	0.475282i	$-0.157654\pi$
$101$	1.04551	+	1.56472i	0.104032	+	0.155695i	−0.775801	+	0.630978i	$0.782654\pi$
$102$		0			0
$103$	−4.50995	+	10.8880i	−0.444379	+	1.07283i	0.530017	+	0.847987i	$0.322186\pi$
$103$	−4.50995	+	10.8880i	−0.444379	+	1.07283i	−0.974396	+	0.224839i	$0.927814\pi$
$104$	−10.2507	+	10.6582i	−1.00517	+	1.04512i
$105$		0			0
$106$	−5.05517	+	1.38978i	−0.491002	+	0.134987i
$107$	−2.90641	+	14.6115i	−0.280973	+	1.41255i	0.540042	+	0.841638i	$0.318408\pi$
$107$	−2.90641	+	14.6115i	−0.280973	+	1.41255i	−0.821014	+	0.570907i	$0.806592\pi$
$108$		0			0
$109$	8.04402	−	12.0387i	0.770478	−	1.15310i	−0.213870	−	0.976862i	$-0.568607\pi$
$109$	8.04402	−	12.0387i	0.770478	−	1.15310i	0.984347	−	0.176239i	$-0.0563932\pi$
$110$	−5.67536	+	6.55693i	−0.541124	+	0.625178i
$111$		0			0
$112$	−1.42227	+	13.5059i	−0.134392	+	1.27619i
$113$	−9.94034	−	9.94034i	−0.935109	−	0.935109i	0.0629105	−	0.998019i	$-0.479962\pi$
$113$	−9.94034	−	9.94034i	−0.935109	−	0.935109i	−0.998019	+	0.0629105i	$0.979962\pi$
$114$		0			0
$115$	−13.0340	−	8.70901i	−1.21542	−	0.812119i
$116$	1.49441	−	3.13228i	0.138752	−	0.290825i
$117$		0			0
$118$	−9.40542	+	16.5378i	−0.865839	+	1.52243i
$119$	−5.15446	+	2.13505i	−0.472508	+	0.195719i
$120$		0			0
$121$	−7.07151	−	2.92911i	−0.642864	−	0.266283i
$122$	5.77580	+	7.42679i	0.522916	+	0.672390i
$123$		0			0
$124$	−15.1055	−	11.2821i	−1.35651	−	1.01317i
$125$	−0.809807	−	4.07117i	−0.0724313	−	0.364137i
$126$		0			0
$127$	13.3100			1.18107			0.590534	−	0.807013i	$-0.298917\pi$
$127$	13.3100			1.18107			0.590534	+	0.807013i	$0.298917\pi$
$128$	11.2442	−	1.25228i	0.993855	−	0.110687i
$129$		0			0
$130$	−22.1588	+	11.1070i	−1.94345	+	0.974148i
$131$	−0.318596	−	1.60169i	−0.0278359	−	0.139940i	0.964368	−	0.264563i	$-0.0852279\pi$
$131$	−0.318596	−	1.60169i	−0.0278359	−	0.139940i	−0.992204	+	0.124623i	$0.960228\pi$
$132$		0			0
$133$	0.0134731	−	0.00900242i	0.00116826	−	0.000780609i
$134$	−6.54016	−	8.40964i	−0.564984	−	0.726482i
$135$		0			0
$136$	2.65702	+	3.81351i	0.227837	+	0.327006i
$137$	6.96260	−	2.88400i	0.594855	−	0.246397i	−0.0648827	−	0.997893i	$-0.520667\pi$
$137$	6.96260	−	2.88400i	0.594855	−	0.246397i	0.659738	+	0.751496i	$0.270667\pi$
$138$		0			0
$139$	−4.03376	−	0.802365i	−0.342139	−	0.0680557i	0.0210303	−	0.999779i	$-0.493305\pi$
$139$	−4.03376	−	0.802365i	−0.342139	−	0.0680557i	−0.363169	+	0.931723i	$0.618305\pi$
$140$	−9.80199	+	20.5450i	−0.828419	+	1.73637i
$141$		0			0
$142$	7.68722	−	0.554011i	0.645098	−	0.0464916i
$143$	6.76227	+	6.76227i	0.565489	+	0.565489i
$144$		0			0
$145$	4.11336	−	4.11336i	0.341596	−	0.341596i
$146$	4.54443	−	5.25033i	0.376100	−	0.434520i
$147$		0			0
$148$	−5.28924	−	0.277729i	−0.434773	−	0.0228292i
$149$	−0.992028	+	4.98726i	−0.0812701	+	0.408573i	0.918639	+	0.395098i	$0.129289\pi$
$149$	−0.992028	+	4.98726i	−0.0812701	+	0.408573i	−0.999909	+	0.0134748i	$0.995711\pi$
$150$		0			0
$151$	−0.957754	−	2.31222i	−0.0779409	−	0.188166i	0.880106	−	0.474777i	$-0.157471\pi$
$151$	−0.957754	−	2.31222i	−0.0779409	−	0.188166i	−0.958047	+	0.286611i	$0.907471\pi$
$152$	−0.00972948	−	0.00935753i	−0.000789165	−	0.000758996i
$153$		0			0
$154$	8.71483	+	1.08980i	0.702261	+	0.0878182i
$155$	−17.5572	−	26.2761i	−1.41022	−	2.11055i
$156$		0			0
$157$	−12.6061	+	2.50752i	−1.00608	+	0.200122i	−0.670515	−	0.741896i	$-0.733927\pi$
$157$	−12.6061	+	2.50752i	−1.00608	+	0.200122i	−0.335564	+	0.942017i	$0.608927\pi$
$158$	−21.6341	−	7.18743i	−1.72112	−	0.571801i
$159$		0			0
$160$	18.4673	+	4.31084i	1.45996	+	0.340802i
$161$			15.8760i			1.25120i
$162$		0			0
$163$	−12.1793	+	2.42260i	−0.953953	+	0.189753i	−0.647443	−	0.762114i	$-0.724161\pi$
$163$	−12.1793	+	2.42260i	−0.953953	+	0.189753i	−0.306510	+	0.951867i	$0.599161\pi$
$164$	−2.51967	−	0.640184i	−0.196753	−	0.0499899i
$165$		0			0
$166$	1.05929	−	8.47092i	0.0822171	−	0.657471i
$167$	−4.69682	+	11.3391i	−0.363451	+	0.877448i	0.631339	+	0.775507i	$0.282505\pi$
$167$	−4.69682	+	11.3391i	−0.363451	+	0.877448i	−0.994790	+	0.101942i	$0.967495\pi$
$168$		0			0
$169$	5.48548	+	13.2431i	0.421960	+	1.01870i
$170$	2.06519	+	7.51190i	0.158393	+	0.576136i
$171$		0			0
$172$	−0.713793	−	0.792907i	−0.0544262	−	0.0604586i
$173$	3.09606	−	4.63358i	0.235389	−	0.352285i	−0.694903	−	0.719103i	$-0.744553\pi$
$173$	3.09606	−	4.63358i	0.235389	−	0.352285i	0.930293	+	0.366818i	$0.119553\pi$
$174$		0			0
$175$	−14.9763	+	14.9763i	−1.13210	+	1.13210i
$176$	−0.668027	−	7.28611i	−0.0503544	−	0.549212i
$177$		0			0
$178$	−1.13139	−	15.6988i	−0.0848016	−	1.17667i
$179$	0.829076	+	0.553971i	0.0619681	+	0.0414057i	0.586168	−	0.810189i	$-0.300636\pi$
$179$	0.829076	+	0.553971i	0.0619681	+	0.0414057i	−0.524200	+	0.851595i	$0.675636\pi$
$180$		0			0
$181$	17.2786	+	3.43692i	1.28430	+	0.255464i	0.789613	−	0.613605i	$-0.210281\pi$
$181$	17.2786	+	3.43692i	1.28430	+	0.255464i	0.494691	+	0.869069i	$0.335281\pi$
$182$	21.8210	+	12.4101i	1.61748	+	0.919899i
$183$		0			0
$184$	12.9191	−	2.83249i	0.952406	−	0.208814i
$185$	−8.20211	−	3.39743i	−0.603031	−	0.249784i
$186$		0			0
$187$	2.49924	−	1.66994i	0.182763	−	0.122118i
$188$	−0.153640	−	1.06039i	−0.0112054	−	0.0773367i
$189$		0			0
$190$	−0.0101392	−	0.0202280i	−0.000735574	−	0.00146749i
$191$	6.00046			0.434178			0.217089	−	0.976152i	$-0.430344\pi$
$191$	6.00046			0.434178			0.217089	+	0.976152i	$0.430344\pi$
$192$		0			0
$193$	8.98517			0.646767			0.323383	−	0.946268i	$-0.395180\pi$
$193$	8.98517			0.646767			0.323383	+	0.946268i	$0.395180\pi$
$194$	−7.78496	−	15.5312i	−0.558927	−	1.11508i
$195$		0			0
$196$	8.96061	−	1.29831i	0.640043	−	0.0927364i
$197$	9.91120	−	6.62245i	0.706144	−	0.471830i	−0.149921	−	0.988698i	$-0.547902\pi$
$197$	9.91120	−	6.62245i	0.706144	−	0.471830i	0.856065	+	0.516868i	$0.172902\pi$
$198$		0			0
$199$	0.782393	+	0.324078i	0.0554624	+	0.0229733i	0.410242	−	0.911977i	$-0.365444\pi$
$199$	0.782393	+	0.324078i	0.0554624	+	0.0229733i	−0.354780	+	0.934950i	$0.615444\pi$
$200$	14.8589	+	9.51498i	1.05069	+	0.672810i
$201$		0			0
$202$	−2.31341	−	1.31569i	−0.162771	−	0.0925714i
$203$	−5.77826	−	1.14937i	−0.405554	−	0.0806697i
$204$		0			0
$205$	−3.62320	−	2.42095i	−0.253055	−	0.169086i
$206$	−1.19804	−	16.6235i	−0.0834715	−	1.15821i
$207$		0			0
$208$	6.20554	−	19.9710i	0.430277	−	1.38474i
$209$	−0.00617304	+	0.00617304i	−0.000426998	+	0.000426998i
$210$		0			0
$211$	−4.82250	+	7.21737i	−0.331994	+	0.496865i	−0.959485	−	0.281759i	$-0.909082\pi$
$211$	−4.82250	+	7.21737i	−0.331994	+	0.496865i	0.627491	+	0.778624i	$0.284082\pi$
$212$	5.51043	−	4.96061i	0.378458	−	0.340696i
$213$		0			0
$214$	−5.58501	−	20.3149i	−0.381784	−	1.38869i
$215$	−0.684334	−	1.65213i	−0.0466712	−	0.112674i
$216$		0			0
$217$	−12.2480	+	29.5693i	−0.831450	+	2.00730i
$218$	−2.54077	+	20.3180i	−0.172083	+	1.37611i
$219$		0			0
$220$	3.02002	−	11.8864i	0.203610	−	0.801378i
$221$	8.42627	−	1.67609i	0.566812	−	0.112746i
$222$		0			0
$223$			10.1030i			0.676547i	0.941048	+	0.338273i	$0.109843\pi$
$223$			10.1030i			0.676547i	−0.941048	+	0.338273i	$0.890157\pi$
$224$	−6.76078	−	17.9766i	−0.451723	−	1.20111i
$225$		0			0
$226$	18.8667	+	6.26803i	1.25500	+	0.416943i
$227$	−17.3254	+	3.44624i	−1.14993	+	0.228735i	−0.733016	−	0.680212i	$-0.761888\pi$
$227$	−17.3254	+	3.44624i	−1.14993	+	0.228735i	−0.416912	+	0.908947i	$0.636888\pi$
$228$		0			0
$229$	3.76160	+	5.62963i	0.248574	+	0.372017i	0.934683	−	0.355481i	$-0.115683\pi$
$229$	3.76160	+	5.62963i	0.248574	+	0.372017i	−0.686110	+	0.727498i	$0.740683\pi$
$230$	21.9976	+	2.75081i	1.45048	+	0.181383i
$231$		0			0
$232$	0.0956249	+	4.90711i	0.00627808	+	0.322167i
$233$	11.2794	+	27.2309i	0.738939	+	1.78396i	0.610152	+	0.792285i	$0.291108\pi$
$233$	11.2794	+	27.2309i	0.738939	+	1.78396i	0.128787	+	0.991672i	$0.458892\pi$
$234$		0			0
$235$	0.350373	−	1.76144i	0.0228558	−	0.114904i
$236$	1.41083	−	26.8688i	0.0918375	−	1.74901i
$237$		0			0
$238$	5.16367	−	5.96576i	0.334711	−	0.386703i
$239$	−4.91117	+	4.91117i	−0.317677	+	0.317677i	−0.847874	−	0.530197i	$-0.822118\pi$
$239$	−4.91117	+	4.91117i	−0.317677	+	0.317677i	0.530197	+	0.847874i	$0.322118\pi$
$240$		0			0
$241$	−15.9105	−	15.9105i	−1.02488	−	1.02488i	−0.999682	−	0.0252016i	$-0.991977\pi$
$241$	−15.9105	−	15.9105i	−1.02488	−	1.02488i	−0.0252016	−	0.999682i	$-0.508023\pi$
$242$	10.7966	−	0.778100i	0.694031	−	0.0500182i
$243$		0			0
$244$	−12.0087	−	5.72933i	−0.768778	−	0.366783i
$245$	14.8848	+	2.96076i	0.950952	+	0.189156i
$246$		0			0
$247$	−0.0230531	+	0.00954890i	−0.00146683	+	0.000607582i
$248$	26.2472	+	4.69123i	1.66670	+	0.297893i
$249$		0			0
$250$	3.60379	+	4.63392i	0.227923	+	0.293075i
$251$	−13.4114	+	8.96124i	−0.846523	+	0.565628i	−0.901461	−	0.432861i	$-0.857504\pi$
$251$	−13.4114	+	8.96124i	−0.846523	+	0.565628i	0.0549377	+	0.998490i	$0.482504\pi$
$252$		0			0
$253$	−1.66867	−	8.38897i	−0.104908	−	0.527410i
$254$	−16.8275	+	8.43472i	−1.05585	+	0.529242i
$255$		0			0
$256$	−13.4222	+	8.70884i	−0.838889	+	0.544303i
$257$	−13.4126			−0.836653			−0.418327	−	0.908297i	$-0.637383\pi$
$257$	−13.4126			−0.836653			−0.418327	+	0.908297i	$0.637383\pi$
$258$		0			0
$259$	1.75411	+	8.81851i	0.108995	+	0.547956i
$260$	20.9762	−	28.0847i	1.30089	−	1.74174i
$261$		0			0
$262$	1.41781	+	1.82309i	0.0875927	+	0.112631i
$263$	5.51629	+	2.28492i	0.340149	+	0.140894i	0.546218	−	0.837643i	$-0.316067\pi$
$263$	5.51629	+	2.28492i	0.340149	+	0.140894i	−0.206069	+	0.978538i	$0.566067\pi$
$264$		0			0
$265$	11.4817	−	4.75588i	0.705316	−	0.292152i
$266$	−0.0113288	+	0.0199197i	−0.000694611	+	0.00122135i
$267$		0			0
$268$	13.5979	+	6.48755i	0.830625	+	0.396290i
$269$	7.39748	+	4.94284i	0.451032	+	0.301370i	0.760261	−	0.649617i	$-0.225071\pi$
$269$	7.39748	+	4.94284i	0.451032	+	0.301370i	−0.309229	+	0.950988i	$0.600071\pi$
$270$		0			0
$271$	3.27670	+	3.27670i	0.199046	+	0.199046i	0.799591	−	0.600545i	$-0.205050\pi$
$271$	3.27670	+	3.27670i	0.199046	+	0.199046i	−0.600545	+	0.799591i	$0.705050\pi$
$272$	−5.77589	−	3.13755i	−0.350215	−	0.190242i
$273$		0			0
$274$	−6.97504	+	8.05850i	−0.421378	+	0.486832i
$275$	6.33947	−	9.48769i	0.382285	−	0.572129i
$276$		0			0
$277$	−1.81203	+	9.10969i	−0.108874	+	0.547348i	0.887392	+	0.461016i	$0.152515\pi$
$277$	−1.81203	+	9.10969i	−0.108874	+	0.547348i	−0.996266	+	0.0863327i	$0.972485\pi$
$278$	5.60827	−	1.54184i	0.336362	−	0.0924735i
$279$		0			0
$280$	−0.627215	−	32.1863i	−0.0374833	−	1.92350i
$281$	−7.02651	+	16.9635i	−0.419166	+	1.01196i	0.563424	+	0.826168i	$0.309484\pi$
$281$	−7.02651	+	16.9635i	−0.419166	+	1.01196i	−0.982590	+	0.185789i	$0.940516\pi$
$282$		0			0
$283$	2.58111	+	3.86291i	0.153431	+	0.229626i	0.900220	−	0.435435i	$-0.143405\pi$
$283$	2.58111	+	3.86291i	0.153431	+	0.229626i	−0.746789	+	0.665061i	$0.768405\pi$
$284$	−9.36772	+	5.57194i	−0.555872	+	0.330634i
$285$		0			0
$286$	−12.8348	−	4.26405i	−0.758935	−	0.252139i
$287$			4.41324i			0.260505i
$288$		0			0
$289$			14.2997i			0.841158i
$290$	−2.59374	+	7.80714i	−0.152310	+	0.458451i
$291$		0			0
$292$	−2.41822	+	9.51776i	−0.141516	+	0.556985i
$293$	−4.12834	−	6.17849i	−0.241180	−	0.360951i	0.691057	−	0.722801i	$-0.257146\pi$
$293$	−4.12834	−	6.17849i	−0.241180	−	0.360951i	−0.932237	+	0.361849i	$0.882146\pi$
$294$		0			0
$295$	17.2585	−	41.6658i	1.00483	−	2.42588i
$296$	6.86309	−	3.00075i	0.398909	−	0.174415i
$297$		0			0
$298$	−1.90630	−	6.93396i	−0.110429	−	0.401674i
$299$	4.76947	−	23.9778i	0.275826	−	1.38667i
$300$		0			0
$301$	−1.00619	+	1.50586i	−0.0579956	+	0.0867966i
$302$	2.67616	+	2.31635i	0.153996	+	0.133291i
$303$		0			0
$304$	0.0182308	+	0.00566482i	0.00104561	+	0.000324900i
$305$	−15.7700	−	15.7700i	−0.902988	−	0.902988i
$306$		0			0
$307$	−4.22026	−	2.81989i	−0.240863	−	0.160939i	0.429280	−	0.903171i	$-0.358767\pi$
$307$	−4.22026	−	2.81989i	−0.240863	−	0.160939i	−0.670143	+	0.742232i	$0.733767\pi$
$308$	−11.7086	+	4.14492i	−0.667160	+	0.236179i
$309$		0			0
$310$	38.8488	+	22.0942i	2.20646	+	1.25486i
$311$	28.5642	−	11.8317i	1.61972	−	0.670912i	0.625699	−	0.780064i	$-0.284814\pi$
$311$	28.5642	−	11.8317i	1.61972	−	0.670912i	0.994025	+	0.109152i	$0.0348136\pi$
$312$		0			0
$313$	−8.76475	−	3.63048i	−0.495413	−	0.205207i	0.120966	−	0.992657i	$-0.461401\pi$
$313$	−8.76475	−	3.63048i	−0.495413	−	0.205207i	−0.616379	+	0.787450i	$0.711401\pi$
$314$	14.3486	−	11.1589i	0.809740	−	0.629733i
$315$		0			0
$316$	31.9064	−	4.62294i	1.79487	−	0.260060i
$317$	−3.95679	−	19.8921i	−0.222235	−	1.11725i	−0.917267	−	0.398274i	$-0.869609\pi$
$317$	−3.95679	−	19.8921i	−0.222235	−	1.11725i	0.695031	−	0.718980i	$-0.255391\pi$
$318$		0			0
$319$	3.17407			0.177714
$320$	−26.0796	+	6.25287i	−1.45790	+	0.349546i
$321$		0			0
$322$	−10.0609	−	20.0717i	−0.560670	−	1.11855i
$323$	0.00153004	+	0.00769205i	8.51339e−5	+	0.000427997i
$324$		0			0
$325$	27.1182	−	18.1198i	1.50425	−	1.00510i
$326$	13.8628	−	10.7810i	0.767787	−	0.597106i
$327$		0			0
$328$	3.59126	−	0.787382i	0.198294	−	0.0434759i
$329$	−1.68043	+	0.696058i	−0.0926453	+	0.0383749i
$330$		0			0
$331$	25.0847	+	4.98965i	1.37878	+	0.274256i	0.828155	−	0.560498i	$-0.189390\pi$
$331$	25.0847	+	4.98965i	1.37878	+	0.274256i	0.550622	+	0.834754i	$0.314390\pi$
$332$	4.02891	+	11.3809i	0.221115	+	0.624608i
$333$		0			0
$334$	−1.24768	−	17.3123i	−0.0682701	−	0.947286i
$335$	17.8570	+	17.8570i	0.975632	+	0.975632i
$336$		0			0
$337$	1.30903	−	1.30903i	0.0713075	−	0.0713075i	−0.670554	−	0.741861i	$-0.733943\pi$
$337$	1.30903	−	1.30903i	0.0713075	−	0.0713075i	0.741861	+	0.670554i	$0.233943\pi$
$338$	−15.3275	−	13.2668i	−0.833709	−	0.721618i
$339$		0			0
$340$	−7.37138	−	8.18840i	−0.399769	−	0.444078i
$341$	3.36400	−	16.9120i	0.182171	−	0.915834i
$342$		0			0
$343$	3.21298	+	7.75682i	0.173485	+	0.418829i
$344$	1.40491	+	0.550116i	0.0757478	+	0.0296602i
$345$		0			0
$346$	−0.977917	+	7.82017i	−0.0525732	+	0.420415i
$347$	17.1922	+	25.7299i	0.922925	+	1.38125i	0.924470	+	0.381256i	$0.124508\pi$
$347$	17.1922	+	25.7299i	0.922925	+	1.38125i	−0.00154489	+	0.999999i	$0.500492\pi$
$348$		0			0
$349$	−0.252228	+	0.0501713i	−0.0135015	+	0.00268561i	−0.201836	−	0.979419i	$-0.564691\pi$
$349$	−0.252228	+	0.0501713i	−0.0135015	+	0.00268561i	0.188335	+	0.982105i	$0.439691\pi$
$350$	9.44355	−	28.4250i	0.504779	−	1.51938i
$351$		0			0
$352$	5.46189	+	8.78835i	0.291120	+	0.468421i
$353$		−	6.17608i		−	0.328719i	−0.986400	−	0.164360i	$-0.947444\pi$
$353$		−	6.17608i		−	0.328719i	0.986400	−	0.164360i	$-0.0525558\pi$
$354$		0			0
$355$	−17.9185	+	3.56422i	−0.951016	+	0.189169i
$356$	11.3789	+	19.1306i	0.603083	+	1.01392i
$357$		0			0
$358$	−1.39924	−	0.174976i	−0.0739524	−	0.00924779i
$359$	10.7708	−	26.0029i	0.568459	−	1.37238i	−0.334395	−	0.942433i	$-0.608532\pi$
$359$	10.7708	−	26.0029i	0.568459	−	1.37238i	0.902854	−	0.429948i	$-0.141468\pi$
$360$		0			0
$361$	7.27098	+	17.5537i	0.382683	+	0.923878i
$362$	−24.0230	+	6.60445i	−1.26262	+	0.347122i
$363$		0			0
$364$	−35.4524	−	1.86155i	−1.85821	−	0.0975715i
$365$	−9.14484	+	13.6862i	−0.478663	+	0.716370i
$366$		0			0
$367$	6.85490	−	6.85490i	0.357823	−	0.357823i	−0.505187	−	0.863010i	$-0.668576\pi$
$367$	6.85490	−	6.85490i	0.357823	−	0.357823i	0.863010	+	0.505187i	$0.168576\pi$
$368$	−14.5383	+	11.7681i	−0.757862	+	0.613453i
$369$		0			0
$370$	12.5228	−	0.902504i	0.651028	−	0.0469190i
$371$	−10.4652	−	6.99265i	−0.543328	−	0.363040i
$372$		0			0
$373$	−15.4393	−	3.07108i	−0.799419	−	0.159014i	−0.221555	−	0.975148i	$-0.571113\pi$
$373$	−15.4393	−	3.07108i	−0.799419	−	0.159014i	−0.577863	+	0.816133i	$0.696113\pi$
$374$	−2.10147	+	3.69508i	−0.108665	+	0.191068i
$375$		0			0
$376$	0.866229	+	1.24326i	0.0446723	+	0.0641164i
$377$	8.38169	+	3.47181i	0.431679	+	0.178807i
$378$		0			0
$379$	−25.8812	+	17.2933i	−1.32943	+	0.888295i	−0.998467	−	0.0553495i	$-0.982373\pi$
$379$	−25.8812	+	17.2933i	−1.32943	+	0.888295i	−0.330961	+	0.943645i	$0.607373\pi$
$380$	0.0256376	+	0.0191485i	0.00131518	+	0.000982296i
$381$		0			0
$382$	−7.58627	+	3.80259i	−0.388147	+	0.194557i
$383$	26.3304			1.34542			0.672711	−	0.739905i	$-0.265130\pi$
$383$	26.3304			1.34542			0.672711	+	0.739905i	$0.265130\pi$
$384$		0			0
$385$	−20.8191			−1.06104
$386$	−11.3598	+	5.69404i	−0.578198	+	0.289819i
$387$		0			0
$388$	19.6847	+	14.7024i	0.999341	+	0.746399i
$389$	−20.4392	+	13.6570i	−1.03631	+	0.692439i	−0.952654	−	0.304056i	$-0.901659\pi$
$389$	−20.4392	+	13.6570i	−1.03631	+	0.692439i	−0.0836539	+	0.996495i	$0.526659\pi$
$390$		0			0
$391$	−7.09912	−	2.94055i	−0.359018	−	0.148710i
$392$	−10.5060	+	7.31990i	−0.530631	+	0.369711i
$393$		0			0
$394$	−8.33379	+	14.6535i	−0.419850	+	0.738234i
$395$	53.0007	+	10.5425i	2.66675	+	0.530450i
$396$		0			0
$397$	−22.8836	−	15.2903i	−1.14850	−	0.767400i	−0.172461	−	0.985016i	$-0.555172\pi$
$397$	−22.8836	−	15.2903i	−1.14850	−	0.767400i	−0.976034	+	0.217616i	$0.930172\pi$
$398$	−1.19454	+	0.0860892i	−0.0598768	+	0.00431526i
$399$		0			0
$400$	−24.8157	−	2.61326i	−1.24078	−	0.130663i
$401$	24.4437	−	24.4437i	1.22066	−	1.22066i	0.253263	−	0.967398i	$-0.418496\pi$
$401$	24.4437	−	24.4437i	1.22066	−	1.22066i	0.967398	−	0.253263i	$-0.0815037\pi$
$402$		0			0
$403$	27.3816	−	40.9795i	1.36397	−	2.04133i
$404$	3.75857	+	0.197356i	0.186996	+	0.00981883i
$405$		0			0
$406$	8.03371	−	2.20865i	0.398706	−	0.109613i
$407$	−1.85377	−	4.47539i	−0.0918878	−	0.221837i
$408$		0			0
$409$	−12.0633	+	29.1234i	−0.596492	+	1.44006i	0.280641	+	0.959813i	$0.409453\pi$
$409$	−12.0633	+	29.1234i	−0.596492	+	1.44006i	−0.877134	+	0.480247i	$0.840547\pi$
$410$	6.11494	+	0.764676i	0.301995	+	0.0377647i
$411$		0			0
$412$	12.0492	+	20.2576i	0.593623	+	0.998018i
$413$	−44.7971	+	8.91069i	−2.20432	+	0.438466i
$414$		0			0
$415$			20.2364i			0.993367i
$416$	4.81036	+	29.1814i	0.235847	+	1.43074i
$417$		0			0
$418$	0.00389250	−	0.0117164i	0.000190389	−	0.000573068i
$419$	11.3813	−	2.26388i	0.556012	−	0.110598i	0.0909169	−	0.995858i	$-0.471020\pi$
$419$	11.3813	−	2.26388i	0.556012	−	0.110598i	0.465095	+	0.885261i	$0.346020\pi$
$420$		0			0
$421$	−3.35311	−	5.01829i	−0.163421	−	0.244576i	0.740717	−	0.671817i	$-0.234486\pi$
$421$	−3.35311	−	5.01829i	−0.163421	−	0.244576i	−0.904138	+	0.427240i	$0.859486\pi$
$422$	1.52323	−	12.1809i	0.0741495	−	0.592956i
$423$		0			0
$424$	−3.82311	+	9.76365i	−0.185667	+	0.474165i
$425$	−3.92291	−	9.47073i	−0.190289	−	0.459398i
$426$		0			0
$427$	−4.40650	+	22.1530i	−0.213246	+	1.07206i
$428$	19.9349	+	22.1444i	0.963587	+	1.07039i
$429$		0			0
$430$	1.91217	+	1.65508i	0.0922130	+	0.0798151i
$431$	−19.6711	+	19.6711i	−0.947521	+	0.947521i	−0.998690	−	0.0511686i	$-0.983705\pi$
$431$	−19.6711	+	19.6711i	−0.947521	+	0.947521i	0.0511686	+	0.998690i	$0.483705\pi$
$432$		0			0
$433$	−18.2910	−	18.2910i	−0.879011	−	0.879011i	0.114421	−	0.993432i	$-0.463499\pi$
$433$	−18.2910	−	18.2910i	−0.879011	−	0.879011i	−0.993432	+	0.114421i	$0.963499\pi$
$434$	−3.25361	−	45.1457i	−0.156178	−	2.16706i
$435$		0			0
$436$	−9.66355	−	27.2977i	−0.462800	−	1.30732i
$437$	0.0218885	+	0.00435389i	0.00104707	+	0.000208275i
$438$		0			0
$439$	10.7707	−	4.46137i	0.514057	−	0.212929i	−0.110547	−	0.993871i	$-0.535260\pi$
$439$	10.7707	−	4.46137i	0.514057	−	0.212929i	0.624604	+	0.780941i	$0.285260\pi$
$440$	3.71441	+	16.9415i	0.177078	+	0.807655i
$441$		0			0
$442$	−9.59100	+	7.45890i	−0.456197	+	0.354784i
$443$	−9.77026	+	6.52828i	−0.464199	+	0.310168i	−0.765586	−	0.643334i	$-0.777551\pi$
$443$	−9.77026	+	6.52828i	−0.464199	+	0.310168i	0.301386	+	0.953502i	$0.402551\pi$
$444$		0			0
$445$	7.27880	+	36.5930i	0.345048	+	1.73467i
$446$	−6.40242	−	12.7730i	−0.303164	−	0.604820i
$447$		0			0
$448$	19.9396	+	18.4431i	0.942056	+	0.871353i
$449$	−26.5341			−1.25222			−0.626111	−	0.779734i	$-0.715354\pi$
$449$	−26.5341			−1.25222			−0.626111	+	0.779734i	$0.715354\pi$
$450$		0			0
$451$	−0.463860	−	2.33198i	−0.0218423	−	0.109809i
$452$	−27.8250	+	4.03158i	−1.30878	+	0.189630i
$453$		0			0
$454$	19.7202	−	15.3364i	0.925517	−	0.719773i
$455$	−54.9765	−	22.7720i	−2.57734	−	1.06757i
$456$		0			0
$457$	23.9069	−	9.90258i	1.11832	−	0.463223i	0.254525	−	0.967066i	$-0.418081\pi$
$457$	23.9069	−	9.90258i	1.11832	−	0.463223i	0.863795	+	0.503843i	$0.168081\pi$
$458$	−8.32330	−	4.73365i	−0.388922	−	0.221189i
$459$		0			0
$460$	−29.5544	+	10.4624i	−1.37798	+	0.487813i
$461$	−23.9755	−	16.0199i	−1.11665	−	0.746121i	−0.146640	−	0.989190i	$-0.546846\pi$
$461$	−23.9755	−	16.0199i	−1.11665	−	0.746121i	−0.970009	+	0.243069i	$0.921846\pi$
$462$		0			0
$463$	−19.4799	−	19.4799i	−0.905307	−	0.905307i	0.0905817	−	0.995889i	$-0.471127\pi$
$463$	−19.4799	−	19.4799i	−0.905307	−	0.905307i	−0.995889	+	0.0905817i	$0.971127\pi$
$464$	−3.23061	−	6.14336i	−0.149977	−	0.285198i
$465$		0			0
$466$	−31.5170	−	27.2796i	−1.46000	−	1.26370i
$467$	−11.7398	+	17.5698i	−0.543252	+	0.813035i	−0.996944	−	0.0781243i	$-0.975107\pi$
$467$	−11.7398	+	17.5698i	−0.543252	+	0.813035i	0.453691	+	0.891159i	$0.350107\pi$
$468$		0			0
$469$	4.98965	−	25.0847i	0.230401	−	1.15830i
$470$	0.673284	+	2.44900i	0.0310563	+	0.112964i
$471$		0			0
$472$	15.2435	+	34.8637i	0.701637	+	1.60473i
$473$	0.373399	−	0.901465i	0.0171689	−	0.0414494i
$474$		0			0
$475$	0.0165409	+	0.0247552i	0.000758950	+	0.00113585i
$476$	−2.74773	+	10.8147i	−0.125942	+	0.495690i
$477$		0			0
$478$	3.09681	−	9.32138i	0.141645	−	0.426350i
$479$			12.7073i			0.580611i	0.956934	+	0.290305i	$0.0937569\pi$
$479$			12.7073i			0.580611i	−0.956934	+	0.290305i	$0.906243\pi$
$480$		0			0
$481$		−	13.8457i		−	0.631310i
$482$	30.1980	+	10.0326i	1.37548	+	0.456972i
$483$		0			0
$484$	−13.1568	+	7.82570i	−0.598037	+	0.355714i
$485$	22.8797	+	34.2418i	1.03891	+	1.55484i
$486$		0			0
$487$	−5.38031	+	12.9892i	−0.243805	+	0.588597i	−0.997655	−	0.0684497i	$-0.978195\pi$
$487$	−5.38031	+	12.9892i	−0.243805	+	0.588597i	0.753850	+	0.657047i	$0.228195\pi$
$488$	18.8131	−	0.366612i	0.851630	−	0.0165957i
$489$		0			0
$490$	−20.6948	+	5.68946i	−0.934895	+	0.257024i
$491$	2.14334	−	10.7753i	0.0967275	−	0.486282i	−0.901806	−	0.432141i	$-0.857758\pi$
$491$	2.14334	−	10.7753i	0.0967275	−	0.486282i	0.998533	−	0.0541404i	$-0.0172419\pi$
$492$		0			0
$493$	1.58420	−	2.37092i	0.0713487	−	0.106781i
$494$	0.0230943	−	0.0266816i	0.00103906	−	0.00120046i
$495$		0			0
$496$	−36.1567	+	10.7022i	−1.62349	+	0.480544i
$497$	13.0835	+	13.0835i	0.586876	+	0.586876i
$498$		0			0
$499$	7.97175	+	5.32655i	0.356864	+	0.238449i	0.721059	−	0.692874i	$-0.243656\pi$
$499$	7.97175	+	5.32655i	0.356864	+	0.238449i	−0.364195	+	0.931323i	$0.618656\pi$
$500$	−7.49278	−	3.57480i	−0.335087	−	0.159870i
$501$		0			0
$502$	11.2769	−	19.8286i	0.503315	−	0.884992i
$503$	7.63705	−	3.16337i	0.340519	−	0.141048i	−0.205869	−	0.978579i	$-0.566002\pi$
$503$	7.63705	−	3.16337i	0.340519	−	0.141048i	0.546389	+	0.837532i	$0.316002\pi$
$504$		0			0
$505$	5.82846	+	2.41423i	0.259363	+	0.107432i
$506$	7.42589	+	9.54855i	0.330121	+	0.424485i
$507$		0			0
$508$	15.9295	−	21.3277i	0.706757	−	0.946264i
$509$	2.95926	+	14.8772i	0.131167	+	0.659420i	0.989288	+	0.145974i	$0.0466314\pi$
$509$	2.95926	+	14.8772i	0.131167	+	0.659420i	−0.858122	+	0.513446i	$0.828369\pi$
$510$		0			0
$511$	16.6705			0.737459
$512$	11.4505	−	19.5163i	0.506047	−	0.862506i
$513$		0			0
$514$	16.9573	−	8.49975i	0.747952	−	0.374908i
$515$	7.70756	+	38.7485i	0.339636	+	1.70746i
$516$		0			0
$517$	0.814791	−	0.544426i	0.0358345	−	0.0239438i
$518$	−7.80611	−	10.0375i	−0.342981	−	0.441021i
$519$		0			0
$520$	−8.72213	+	48.7999i	−0.382491	+	2.14002i
$521$	−10.0424	+	4.15970i	−0.439966	+	0.182240i	−0.591660	−	0.806188i	$-0.701527\pi$
$521$	−10.0424	+	4.15970i	−0.439966	+	0.182240i	0.151694	+	0.988427i	$0.451527\pi$
$522$		0			0
$523$	−3.45679	−	0.687599i	−0.151155	−	0.0300666i	0.118933	−	0.992902i	$-0.462053\pi$
$523$	−3.45679	−	0.687599i	−0.151155	−	0.0300666i	−0.270088	+	0.962836i	$0.587053\pi$
$524$	−2.94783	−	1.40641i	−0.128777	−	0.0614391i
$525$		0			0
$526$	−8.42213	+	0.606976i	−0.367222	+	0.0264654i
$527$	−10.9537	−	10.9537i	−0.477149	−	0.477149i
$528$		0			0
$529$	0.802117	−	0.802117i	0.0348746	−	0.0348746i
$530$	−11.5022	+	13.2889i	−0.499625	+	0.577233i
$531$		0			0
$532$	0.00169934	−	0.0323633i	7.36757e−5	−	0.00140313i
$533$	1.32583	−	6.66538i	0.0574279	−	0.288710i
$534$		0			0
$535$	19.1121	+	46.1407i	0.826289	+	1.99484i
$536$	−21.3028	+	0.415129i	−0.920142	+	0.0179308i
$537$		0			0
$538$	−12.4848	−	1.56124i	−0.538260	−	0.0673097i
$539$	4.60057	+	6.88524i	0.198161	+	0.296568i
$540$		0			0
$541$	−4.58170	+	0.911357i	−0.196983	+	0.0391823i	−0.292595	−	0.956236i	$-0.594519\pi$
$541$	−4.58170	+	0.911357i	−0.196983	+	0.0391823i	0.0956128	+	0.995419i	$0.469519\pi$
$542$	−6.21917	−	2.06618i	−0.267136	−	0.0887498i
$543$		0			0
$544$	9.29066	+	0.306476i	0.398334	+	0.0131401i
$545$		−	48.5381i		−	2.07915i
$546$		0			0
$547$	7.46021	−	1.48393i	0.318975	−	0.0634482i	−0.0330060	−	0.999455i	$-0.510508\pi$
$547$	7.46021	−	1.48393i	0.318975	−	0.0634482i	0.351981	+	0.936007i	$0.385508\pi$
$548$	3.71162	−	14.6084i	0.158552	−	0.624040i
$549$		0			0
$550$	−2.00238	+	16.0125i	−0.0853816	+	0.682776i
$551$	−0.00316930	+	0.00765136i	−0.000135017	+	0.000325959i
$552$		0			0
$553$	−20.9439	−	50.5631i	−0.890626	−	2.15016i
$554$	−3.48204	−	12.6655i	−0.147938	−	0.538106i
$555$		0			0
$556$	−6.11334	+	5.50337i	−0.259263	+	0.233395i
$557$	−8.06578	+	12.0713i	−0.341758	+	0.511477i	−0.962042	−	0.272900i	$-0.912017\pi$
$557$	−8.06578	+	12.0713i	−0.341758	+	0.511477i	0.620284	+	0.784377i	$0.287017\pi$
$558$		0			0
$559$	1.97205	−	1.97205i	0.0834089	−	0.0834089i
$560$	21.1899	+	40.2950i	0.895438	+	1.70278i
$561$		0			0
$562$	−1.86655	−	25.8994i	−0.0787355	−	1.09250i
$563$	−13.7599	−	9.19410i	−0.579912	−	0.387485i	0.230738	−	0.973016i	$-0.425886\pi$
$563$	−13.7599	−	9.19410i	−0.579912	−	0.387485i	−0.810650	+	0.585531i	$0.800886\pi$
$564$		0			0
$565$	−46.2210	−	9.19392i	−1.94453	−	0.386791i
$566$	−5.71123	−	3.24811i	−0.240061	−	0.136528i
$567$		0			0
$568$	8.31241	−	12.9810i	0.348781	−	0.544669i
$569$	−10.7745	−	4.46295i	−0.451691	−	0.187097i	0.145228	−	0.989398i	$-0.453609\pi$
$569$	−10.7745	−	4.46295i	−0.451691	−	0.187097i	−0.596919	+	0.802302i	$0.703609\pi$
$570$		0			0
$571$	38.3434	−	25.6202i	1.60462	−	1.07217i	0.656471	−	0.754351i	$-0.272049\pi$
$571$	38.3434	−	25.6202i	1.60462	−	1.07217i	0.948150	−	0.317822i	$-0.102951\pi$
$572$	18.9289	−	2.74262i	0.791458	−	0.114675i
$573$		0			0
$574$	−2.79674	−	5.57957i	−0.116734	−	0.232887i
$575$	−29.1703			−1.21649
$576$		0			0
$577$	5.30739			0.220949			0.110475	−	0.993879i	$-0.464763\pi$
$577$	5.30739			0.220949			0.110475	+	0.993879i	$0.464763\pi$
$578$	−9.06192	−	18.0788i	−0.376926	−	0.751979i
$579$		0			0
$580$	−1.66829	−	11.5141i	−0.0692719	−	0.478097i
$581$	17.0408	−	11.3863i	0.706973	−	0.472384i
$582$		0			0
$583$	6.26487	+	2.59499i	0.259464	+	0.107474i
$584$	−2.97424	−	13.5656i	−0.123075	−	0.561348i
$585$		0			0
$586$	9.13478	+	5.19516i	0.377354	+	0.214610i
$587$	1.07653	+	0.214135i	0.0444331	+	0.00883830i	0.217257	−	0.976114i	$-0.430289\pi$
$587$	1.07653	+	0.214135i	0.0444331	+	0.00883830i	−0.172824	+	0.984953i	$0.555289\pi$
$588$		0			0
$589$	0.0374087	+	0.0249957i	0.00154140	+	0.00102993i
$590$	4.58462	+	63.6143i	0.188746	+	2.61896i
$591$		0			0
$592$	−6.77525	+	8.14303i	−0.278461	+	0.334677i
$593$	9.71203	−	9.71203i	0.398825	−	0.398825i	−0.478993	−	0.877819i	$-0.658998\pi$
$593$	9.71203	−	9.71203i	0.398825	−	0.398825i	0.877819	+	0.478993i	$0.158998\pi$
$594$		0			0
$595$	−10.3910	+	15.5512i	−0.425987	+	0.637535i
$596$	6.80426	+	7.55842i	0.278713	+	0.309605i
$597$		0			0
$598$	9.16512	+	33.3371i	0.374790	+	1.36326i
$599$	−1.51141	−	3.64886i	−0.0617545	−	0.149088i	0.889990	−	0.455980i	$-0.150711\pi$
$599$	−1.51141	−	3.64886i	−0.0617545	−	0.149088i	−0.951745	+	0.306891i	$0.900711\pi$
$600$		0			0
$601$	−4.10853	+	9.91887i	−0.167591	+	0.404599i	−0.985254	−	0.171097i	$-0.945269\pi$
$601$	−4.10853	+	9.91887i	−0.167591	+	0.404599i	0.817664	+	0.575696i	$0.195269\pi$
$602$	0.317812	−	2.54147i	0.0129531	−	0.103583i
$603$		0			0
$604$	−4.85133	−	1.23260i	−0.197398	−	0.0501537i
$605$	−25.1663	+	5.00589i	−1.02316	+	0.203518i
$606$		0			0
$607$		−	43.0657i		−	1.74798i	−0.485943	−	0.873991i	$-0.661524\pi$
$607$		−	43.0657i		−	1.74798i	0.485943	−	0.873991i	$-0.338476\pi$
$608$	−0.0266387	+	0.00439121i	−0.00108034	+	0.000178087i
$609$		0			0
$610$	29.9314	+	9.94402i	1.21189	+	0.402622i
$611$	2.74710	−	0.546431i	0.111136	−	0.0221062i
$612$		0			0
$613$	25.9537	+	38.8424i	1.04826	+	1.56883i	0.799872	+	0.600170i	$0.204901\pi$
$613$	25.9537	+	38.8424i	1.04826	+	1.56883i	0.248387	+	0.968661i	$0.420099\pi$
$614$	7.12260	+	0.890685i	0.287445	+	0.0359451i
$615$		0			0
$616$	12.1763	−	12.6603i	0.490596	−	0.510097i
$617$	10.4503	+	25.2293i	0.420715	+	1.01570i	0.982137	+	0.188166i	$0.0602543\pi$
$617$	10.4503	+	25.2293i	0.420715	+	1.01570i	−0.561422	+	0.827529i	$0.689746\pi$
$618$		0			0
$619$	7.81639	−	39.2957i	0.314167	−	1.57943i	−0.424546	−	0.905406i	$-0.639566\pi$
$619$	7.81639	−	39.2957i	0.314167	−	1.57943i	0.738713	−	0.674020i	$-0.235434\pi$
$620$	−63.1171	−	3.31417i	−2.53484	−	0.133100i
$621$		0			0
$622$	−28.6152	+	33.0601i	−1.14736	+	1.32559i
$623$	26.7190	−	26.7190i	1.07047	−	1.07047i
$624$		0			0
$625$	12.2158	+	12.2158i	0.488631	+	0.488631i
$626$	13.3818	−	0.964414i	0.534844	−	0.0385457i
$627$		0			0
$628$	−11.0691	+	23.2009i	−0.441706	+	0.925818i
$629$	−4.26819	−	0.848995i	−0.170184	−	0.0338516i
$630$		0			0
$631$	−30.5309	+	12.6463i	−1.21542	+	0.503442i	−0.895950	−	0.444155i	$-0.853504\pi$
$631$	−30.5309	+	12.6463i	−1.21542	+	0.503442i	−0.319467	+	0.947597i	$0.603504\pi$
$632$	−37.4090	+	26.0642i	−1.48805	+	1.03678i
$633$		0			0
$634$	17.6084	+	22.6417i	0.699320	+	0.899219i
$635$	37.0998	−	24.7893i	1.47226	−	0.983733i
$636$		0			0
$637$	4.61751	+	23.2138i	0.182953	+	0.919765i
$638$	−4.01292	+	2.01146i	−0.158873	+	0.0796344i
$639$		0			0
$640$	29.0094	−	24.4324i	1.14670	−	0.965777i
$641$	30.0254			1.18593			0.592966	−	0.805227i	$-0.297957\pi$
$641$	30.0254			1.18593			0.592966	+	0.805227i	$0.297957\pi$
$642$		0			0
$643$	−1.92684	−	9.68687i	−0.0759871	−	0.382013i	0.924013	−	0.382361i	$-0.124889\pi$
$643$	−1.92684	−	9.68687i	−0.0759871	−	0.382013i	−1.00000		0.000348458i	$0.999889\pi$
$644$	25.4395	+	19.0005i	1.00246	+	0.748726i
$645$		0			0
$646$	−0.00680897	−	0.00875530i	−0.000267896	−	0.000344473i
$647$	32.0095	+	13.2588i	1.25842	+	0.521257i	0.909426	−	0.415867i	$-0.136522\pi$
$647$	32.0095	+	13.2588i	1.25842	+	0.521257i	0.348999	+	0.937123i	$0.386522\pi$
$648$		0			0
$649$	22.7345	−	9.41693i	0.892406	−	0.369647i
$650$	−22.8022	+	40.0937i	−0.894375	+	1.57260i
$651$		0			0
$652$	−10.6943	+	22.4153i	−0.418821	+	0.877850i
$653$	−30.9545	−	20.6832i	−1.21134	−	0.809394i	−0.225043	−	0.974349i	$-0.572252\pi$
$653$	−30.9545	−	20.6832i	−1.21134	−	0.809394i	−0.986301	+	0.164954i	$0.947252\pi$
$654$		0			0
$655$	−3.87114	−	3.87114i	−0.151258	−	0.151258i
$656$	−4.04139	+	3.27131i	−0.157790	+	0.127723i
$657$		0			0
$658$	1.68344	−	1.94493i	0.0656272	−	0.0758213i
$659$	6.96386	−	10.4222i	0.271273	−	0.405989i	−0.670673	−	0.741753i	$-0.733994\pi$
$659$	6.96386	−	10.4222i	0.271273	−	0.405989i	0.941946	+	0.335764i	$0.108994\pi$
$660$		0			0
$661$	4.07042	−	20.4634i	0.158321	−	0.795934i	−0.817256	−	0.576275i	$-0.804506\pi$
$661$	4.07042	−	20.4634i	0.158321	−	0.795934i	0.975577	−	0.219659i	$-0.0704944\pi$
$662$	−34.8761	+	9.58822i	−1.35550	+	0.372657i
$663$		0			0
$664$	−12.3059	−	11.8355i	−0.477562	−	0.459306i
$665$	0.0207878	−	0.0501862i	0.000806116	−	0.00194614i
$666$		0			0
$667$	−4.50799	−	6.74668i	−0.174550	−	0.261233i
$668$	12.5485	+	21.0969i	0.485515	+	0.816264i
$669$		0			0
$670$	−33.8925	−	11.2600i	−1.30938	−	0.435012i
$671$		−	12.1689i		−	0.469776i
$672$		0			0
$673$			3.76884i			0.145278i	0.997358	+	0.0726390i	$0.0231421\pi$
$673$			3.76884i			0.145278i	−0.997358	+	0.0726390i	$0.976858\pi$
$674$	−0.825430	+	2.48454i	−0.0317944	+	0.0957008i
$675$		0			0
$676$	27.7857	+	7.05963i	1.06868	+	0.271524i
$677$	12.4716	+	18.6650i	0.479321	+	0.717354i	0.989789	−	0.142543i	$-0.0455278\pi$
$677$	12.4716	+	18.6650i	0.479321	+	0.717354i	−0.510468	+	0.859897i	$0.670528\pi$
$678$		0			0
$679$	15.9610	−	38.5334i	0.612529	−	1.47878i
$680$	14.5086	+	5.68108i	0.556380	+	0.217859i
$681$		0			0
$682$	6.46433	+	23.5133i	0.247532	+	0.900370i
$683$	7.81275	−	39.2773i	0.298946	−	1.50291i	−0.480811	−	0.876824i	$-0.659658\pi$
$683$	7.81275	−	39.2773i	0.298946	−	1.50291i	0.779758	−	0.626081i	$-0.215342\pi$
$684$		0			0
$685$	14.0360	−	21.0064i	0.536289	−	0.802613i
$686$	−8.97773	−	7.77068i	−0.342771	−	0.296686i
$687$		0			0
$688$	−2.12482	+	0.194814i	−0.0810080	+	0.00742721i
$689$	13.7051	+	13.7051i	0.522122	+	0.522122i
$690$		0			0
$691$	28.3968	+	18.9741i	1.08027	+	0.721811i	0.962514	−	0.271232i	$-0.0874312\pi$
$691$	28.3968	+	18.9741i	1.08027	+	0.721811i	0.117752	+	0.993043i	$0.462431\pi$
$692$	−3.71940	−	10.5066i	−0.141390	−	0.399401i
$693$		0			0
$694$	−38.0412	−	21.6349i	−1.44402	−	0.821249i
$695$	−12.7380	+	5.27624i	−0.483179	+	0.200139i
$696$		0			0
$697$	−1.97343	−	0.817420i	−0.0747488	−	0.0309620i
$698$	0.287093	−	0.223272i	0.0108666	−	0.00845095i
$699$		0			0
$700$	6.07407	+	41.9217i	0.229578	+	1.58449i
$701$	3.21632	+	16.1695i	0.121479	+	0.610715i	0.992778	+	0.119963i	$0.0382777\pi$
$701$	3.21632	+	16.1695i	0.121479	+	0.610715i	−0.871300	+	0.490752i	$0.836722\pi$
$702$		0			0
$703$	0.0126393			0.000476699
$704$	−12.4747	−	7.64966i	−0.470157	−	0.288307i
$705$		0			0
$706$	3.91387	+	7.80829i	0.147301	+	0.293869i
$707$	−1.24648	−	6.26648i	−0.0468787	−	0.235675i
$708$		0			0
$709$	−2.10981	+	1.40973i	−0.0792355	+	0.0529435i	−0.594557	−	0.804053i	$-0.702673\pi$
$709$	−2.10981	+	1.40973i	−0.0792355	+	0.0529435i	0.515321	+	0.856997i	$0.327673\pi$
$710$	20.3953	−	15.8614i	0.765423	−	0.595268i
$711$		0			0
$712$	−26.5096	−	16.9755i	−0.993487	−	0.636183i
$713$	−40.7252	+	16.8689i	−1.52517	+	0.631746i
$714$		0			0
$715$	31.4434	+	6.25449i	1.17592	+	0.233905i
$716$	1.87992	−	0.665504i	0.0702560	−	0.0248710i
$717$		0			0
$718$	2.86118	+	39.7005i	0.106778	+	1.48161i
$719$	13.6165	+	13.6165i	0.507809	+	0.507809i	0.913854	−	0.406044i	$-0.133092\pi$
$719$	13.6165	+	13.6165i	0.507809	+	0.507809i	−0.406044	+	0.913854i	$0.633092\pi$
$720$		0			0
$721$	28.2929	−	28.2929i	1.05368	−	1.05368i
$722$	−20.3166	−	17.5851i	−0.756105	−	0.654448i
$723$		0			0
$724$	26.1864	−	23.5736i	0.973210	−	0.876106i
$725$	2.11183	−	10.6169i	0.0784314	−	0.394301i
$726$		0			0
$727$	−7.57477	−	18.2871i	−0.280933	−	0.678231i	0.718925	−	0.695087i	$-0.244634\pi$
$727$	−7.57477	−	18.2871i	−0.280933	−	0.678231i	−0.999858	+	0.0168560i	$0.994634\pi$
$728$	46.0014	−	20.1132i	1.70493	−	0.745445i
$729$		0			0
$730$	2.88848	−	23.0985i	0.106907	−	0.854912i
$731$	−0.486997	−	0.728843i	−0.0180122	−	0.0269572i
$732$		0			0
$733$	−34.5625	+	6.87491i	−1.27660	+	0.253931i	−0.786420	−	0.617693i	$-0.788068\pi$
$733$	−34.5625	+	6.87491i	−1.27660	+	0.253931i	−0.490176	+	0.871623i	$0.663068\pi$
$734$	−4.32246	+	13.0106i	−0.159545	+	0.480229i
$735$		0			0
$736$	10.9229	−	24.0913i	0.402624	−	0.888017i
$737$			13.7793i			0.507569i
$738$		0			0
$739$	−25.3933	+	5.05105i	−0.934109	+	0.185806i	−0.638604	−	0.769535i	$-0.720488\pi$
$739$	−25.3933	+	5.05105i	−0.934109	+	0.185806i	−0.295505	+	0.955341i	$0.595488\pi$
$740$	−15.2604	+	9.07689i	−0.560982	+	0.333673i
$741$		0			0
$742$	17.6623	+	2.20869i	0.648405	+	0.0810834i
$743$	10.2227	−	24.6798i	0.375034	−	0.905413i	−0.617846	−	0.786299i	$-0.711995\pi$
$743$	10.2227	−	24.6798i	0.375034	−	0.905413i	0.992881	−	0.119114i	$-0.0380054\pi$
$744$		0			0
$745$	6.52344	+	15.7490i	0.239000	+	0.576998i
$746$	21.4658	−	5.90145i	0.785920	−	0.216067i
$747$		0			0
$748$	0.315226	−	6.00335i	0.0115258	−	0.219504i
$749$	28.1008	−	42.0559i	1.02678	−	1.53669i
$750$		0			0
$751$	−18.2054	+	18.2054i	−0.664326	+	0.664326i	−0.956397	−	0.292071i	$-0.905656\pi$
$751$	−18.2054	+	18.2054i	−0.664326	+	0.664326i	0.292071	+	0.956397i	$0.405656\pi$
$752$	−1.88303	−	1.02289i	−0.0686671	−	0.0373010i
$753$		0			0
$754$	−12.7970	+	0.922265i	−0.466038	+	0.0335869i
$755$	−6.97605	−	4.66124i	−0.253884	−	0.169640i
$756$		0			0
$757$	−8.14973	−	1.62108i	−0.296207	−	0.0589192i	0.0447498	−	0.998998i	$-0.485751\pi$
$757$	−8.14973	−	1.62108i	−0.296207	−	0.0589192i	−0.340957	+	0.940079i	$0.610751\pi$
$758$	21.7621	−	38.2648i	0.790434	−	1.38984i
$759$		0			0
$760$	−0.0445477	−	0.00796213i	−0.00161592	−	0.000288817i
$761$	−37.0579	−	15.3499i	−1.34335	−	0.556433i	−0.408916	−	0.912572i	$-0.634093\pi$
$761$	−37.0579	−	15.3499i	−1.34335	−	0.556433i	−0.934433	+	0.356139i	$0.884093\pi$
$762$		0			0
$763$	−40.8734	+	27.3107i	−1.47972	+	0.988714i
$764$	7.18142	−	9.61507i	0.259814	−	0.347861i
$765$		0			0
$766$	−33.2890	+	16.6860i	−1.20278	+	0.602889i
$767$	70.3346			2.53964
$768$		0			0
$769$	44.7180			1.61257			0.806287	−	0.591525i	$-0.201474\pi$
$769$	44.7180			1.61257			0.806287	+	0.591525i	$0.201474\pi$
$770$	26.3212	−	13.1934i	0.948550	−	0.475457i
$771$		0			0
$772$	10.7535	−	14.3977i	0.387029	−	0.518186i
$773$	29.7197	−	19.8581i	1.06894	−	0.714245i	0.108887	−	0.994054i	$-0.465271\pi$
$773$	29.7197	−	19.8581i	1.06894	−	0.714245i	0.960056	+	0.279809i	$0.0902712\pi$
$774$		0			0
$775$	−54.3303	−	22.5044i	−1.95160	−	0.808380i
$776$	−34.2041	−	6.11339i	−1.22786	−	0.219458i
$777$		0			0
$778$	17.1862	−	30.2189i	0.616155	−	1.08340i
$779$	0.00608460	+	0.00121030i	0.000218003	+	4.33636e-5i
$780$		0			0
$781$	−8.28857	−	5.53825i	−0.296588	−	0.198174i
$782$	10.8387	−	0.781138i	0.387593	−	0.0279335i
$783$		0			0
$784$	8.64375	−	15.9122i	0.308705	−	0.568293i
$785$	−30.4678	+	30.4678i	−1.08744	+	1.08744i
$786$		0			0
$787$	12.8406	−	19.2173i	0.457717	−	0.685022i	−0.528788	−	0.848754i	$-0.677353\pi$
$787$	12.8406	−	19.2173i	0.457717	−	0.685022i	0.986505	+	0.163732i	$0.0523533\pi$
$788$	1.25009	−	23.8074i	0.0445325	−	0.848104i
$789$		0			0
$790$	−73.6886	+	20.2587i	−2.62172	+	0.720771i
$791$	18.2648	+	44.0952i	0.649423	+	1.56785i
$792$		0			0
$793$	13.3104	−	32.1342i	0.472667	−	1.14112i
$794$	38.6210	+	4.82958i	1.37061	+	0.171395i
$795$		0			0
$796$	1.45567	−	0.865838i	0.0515950	−	0.0306888i
$797$	9.16130	−	1.82230i	0.324510	−	0.0645491i	−0.0301471	−	0.999545i	$-0.509598\pi$
$797$	9.16130	−	1.82230i	0.324510	−	0.0645491i	0.354657	+	0.934996i	$0.384598\pi$
$798$		0			0
$799$		−	0.880347i		−	0.0311445i
$800$	33.0300	−	12.4222i	1.16779	−	0.439190i
$801$		0			0
$802$	−15.4133	+	46.3940i	−0.544264	+	1.63823i
$803$	−8.80879	+	1.75218i	−0.310856	+	0.0618330i
$804$		0			0
$805$	29.5684	+	44.2523i	1.04215	+	1.55969i
$806$	−8.64871	+	69.1617i	−0.304638	+	2.43612i
$807$		0			0
$808$	−4.87695	+	2.13235i	−0.171570	+	0.0750157i
$809$	−10.1941	−	24.6108i	−0.358406	−	0.865268i	−0.995525	−	0.0945027i	$-0.969874\pi$
$809$	−10.1941	−	24.6108i	−0.358406	−	0.865268i	0.637119	−	0.770766i	$-0.280126\pi$
$810$		0			0
$811$	2.07144	−	10.4138i	0.0727380	−	0.365679i	−0.927223	−	0.374510i	$-0.877811\pi$
$811$	2.07144	−	10.4138i	0.0727380	−	0.365679i	0.999961	+	0.00883095i	$0.00281102\pi$
$812$	−8.75720	+	7.88343i	−0.307318	+	0.276654i
$813$		0			0
$814$	5.17980	+	4.48338i	0.181552	+	0.157143i
$815$	−29.4361	+	29.4361i	−1.03110	+	1.03110i
$816$		0			0
$817$	0.00180022	+	0.00180022i	6.29816e−5	+	6.29816e-5i
$818$	−3.20454	−	44.4648i	−0.112044	−	1.55468i
$819$		0			0
$820$	−8.21558	+	2.90836i	−0.286900	+	0.101564i
$821$	−53.6020	−	10.6621i	−1.87072	−	0.372110i	−0.876677	−	0.481079i	$-0.840245\pi$
$821$	−53.6020	−	10.6621i	−1.87072	−	0.372110i	−0.994045	+	0.108969i	$0.965245\pi$
$822$		0			0
$823$	25.4170	−	10.5281i	0.885982	−	0.366986i	0.107168	−	0.994241i	$-0.465822\pi$
$823$	25.4170	−	10.5281i	0.885982	−	0.366986i	0.778814	+	0.627255i	$0.215822\pi$
$824$	−28.0711	−	17.9754i	−0.977904	−	0.626204i
$825$		0			0
$826$	50.9892	−	39.6542i	1.77414	−	1.37975i
$827$	−22.6824	+	15.1559i	−0.788743	+	0.527021i	−0.883473	−	0.468482i	$-0.844801\pi$
$827$	−22.6824	+	15.1559i	−0.788743	+	0.527021i	0.0947301	+	0.995503i	$0.469801\pi$
$828$		0			0
$829$	2.14763	+	10.7969i	0.0745902	+	0.374990i	0.999992	−	0.00399713i	$-0.00127233\pi$
$829$	2.14763	+	10.7969i	0.0745902	+	0.374990i	−0.925402	+	0.378988i	$0.876272\pi$
$830$	−12.8241	−	25.5845i	−0.445132	−	0.888051i
$831$		0			0
$832$	−24.5744	−	33.8451i	−0.851963	−	1.17337i
$833$	7.43921			0.257753
$834$		0			0
$835$	8.02692	+	40.3540i	0.277783	+	1.39651i
$836$	0.00250365	+	0.0172796i	8.65905e−5	+	0.000597626i
$837$		0			0
$838$	−12.9545	+	10.0747i	−0.447505	+	0.348023i
$839$	−17.6575	−	7.31397i	−0.609604	−	0.252506i	0.0564551	−	0.998405i	$-0.482020\pi$
$839$	−17.6575	−	7.31397i	−0.609604	−	0.252506i	−0.666059	+	0.745899i	$0.732020\pi$
$840$		0			0
$841$	−24.0106	+	9.94552i	−0.827952	+	0.342949i
$842$	7.41944	+	4.21960i	0.255691	+	0.145417i
$843$		0			0
$844$	5.79342	+	16.3653i	0.199418	+	0.563318i
$845$	39.9549	+	26.6970i	1.37449	+	0.918405i
$846$		0			0
$847$	18.3756	+	18.3756i	0.631393	+	0.631393i
$848$	−1.35389	−	14.7668i	−0.0464927	−	0.507092i
$849$		0			0
$850$	10.9614	+	9.48766i	0.375973	+	0.325424i
$851$	−6.87989	+	10.2965i	−0.235840	+	0.352959i
$852$		0			0
$853$	−8.92566	+	44.8723i	−0.305609	+	1.53640i	0.456957	+	0.889489i	$0.348939\pi$
$853$	−8.92566	+	44.8723i	−0.305609	+	1.53640i	−0.762566	+	0.646911i	$0.776061\pi$
$854$	−8.46763	−	30.8000i	−0.289756	−	1.05396i
$855$		0			0
$856$	−39.2365	−	15.3637i	−1.34107	−	0.525119i
$857$	−4.18475	+	10.1029i	−0.142948	+	0.345108i	−0.979097	−	0.203396i	$-0.934802\pi$
$857$	−4.18475	+	10.1029i	−0.142948	+	0.345108i	0.836148	+	0.548503i	$0.184802\pi$
$858$		0			0
$859$	3.25686	+	4.87424i	0.111123	+	0.166307i	0.882862	−	0.469632i	$-0.155613\pi$
$859$	3.25686	+	4.87424i	0.111123	+	0.166307i	−0.771740	+	0.635938i	$0.780613\pi$
$860$	−3.46637	−	0.880715i	−0.118202	−	0.0300321i
$861$		0			0
$862$	12.4039	−	37.3356i	0.422478	−	1.27165i
$863$			1.43064i			0.0486996i	0.999704	+	0.0243498i	$0.00775154\pi$
$863$			1.43064i			0.0486996i	−0.999704	+	0.0243498i	$0.992248\pi$
$864$		0			0
$865$		−	18.6818i		−	0.635201i
$866$	34.7163	+	11.5337i	1.17971	+	0.391931i
$867$		0			0
$868$	32.7230	+	55.0149i	1.11069	+	1.86733i
$869$	16.3814	+	24.5165i	0.555701	+	0.831666i
$870$		0			0
$871$	−15.0719	+	36.3868i	−0.510692	+	1.23292i
$872$	29.5164	+	28.3880i	0.999552	+	0.961340i
$873$		0			0
$874$	−0.0304323	+	0.00836652i	−0.00102939	+	0.000283002i
$875$	−2.74942	+	13.8223i	−0.0929474	+	0.467278i
$876$		0			0
$877$	20.5649	−	30.7776i	0.694428	−	1.03929i	−0.301872	−	0.953348i	$-0.597612\pi$
$877$	20.5649	−	30.7776i	0.694428	−	1.03929i	0.996301	−	0.0859368i	$-0.0273883\pi$
$878$	−10.7899	+	12.4660i	−0.364143	+	0.420706i
$879$		0			0
$880$	−15.4322	−	19.0649i	−0.520218	−	0.642679i
$881$	−10.5814	−	10.5814i	−0.356496	−	0.356496i	0.506023	−	0.862520i	$-0.331115\pi$
$881$	−10.5814	−	10.5814i	−0.356496	−	0.356496i	−0.862520	+	0.506023i	$0.831115\pi$
$882$		0			0
$883$	−46.6957	−	31.2011i	−1.57144	−	1.05000i	−0.967469	−	0.252991i	$-0.918586\pi$
$883$	−46.6957	−	31.2011i	−1.57144	−	1.05000i	−0.603968	−	0.797009i	$-0.706414\pi$
$884$	7.39890	−	15.5081i	0.248852	−	0.521594i
$885$		0			0
$886$	8.21528	−	14.4451i	0.275998	−	0.485294i
$887$	−47.8447	+	19.8179i	−1.60647	+	0.665421i	−0.992312	−	0.123764i	$-0.960503\pi$
$887$	−47.8447	+	19.8179i	−1.60647	+	0.665421i	−0.614156	+	0.789185i	$0.710503\pi$
$888$		0			0
$889$	−41.7495	−	17.2932i	−1.40023	−	0.579996i
$890$	−32.3920	−	41.6511i	−1.08578	−	1.39615i
$891$		0			0
$892$	16.1889	+	12.0914i	0.542045	+	0.404849i
$893$	0.000498818		0.00250773i	1.66923e−5		8.39179e-5i
$894$		0			0
$895$	3.34270			0.111734
$896$	−36.8969	−	10.6812i	−1.23264	−	0.356834i
$897$		0			0
$898$	33.5465	−	16.8151i	1.11946	−	0.561126i
$899$	−3.19128	−	16.0437i	−0.106435	−	0.535086i
$900$		0			0
$901$	5.06520	−	3.38446i	0.168746	−	0.112753i
$902$	2.06426	+	2.65432i	0.0687324	+	0.0883793i
$903$		0			0
$904$	32.6237	−	22.7302i	1.08505	−	0.755994i
$905$	54.5629	−	22.6007i	1.81373	−	0.751272i
$906$		0			0
$907$	39.2228	+	7.80190i	1.30237	+	0.259058i	0.797071	−	0.603886i	$-0.206382\pi$
$907$	39.2228	+	7.80190i	1.30237	+	0.259058i	0.505300	+	0.862943i	$0.331382\pi$
$908$	−15.2130	+	31.8865i	−0.504862	+	1.05819i
$909$		0			0
$910$	83.9367	−	6.04924i	2.78248	−	0.200530i
$911$	−28.9692	−	28.9692i	−0.959794	−	0.959794i	0.0394285	−	0.999222i	$-0.487446\pi$
$911$	−28.9692	−	28.9692i	−0.959794	−	0.959794i	−0.999222	+	0.0394285i	$0.987446\pi$
$912$		0			0
$913$	−7.80771	+	7.80771i	−0.258397	+	0.258397i
$914$	−23.9497	+	27.6698i	−0.792184	+	0.915237i
$915$		0			0
$916$	13.5228	+	0.710058i	0.446805	+	0.0234610i
$917$	−1.08168	+	5.43799i	−0.0357204	+	0.179578i
$918$		0			0
$919$	4.60437	+	11.1159i	0.151884	+	0.366681i	0.981447	−	0.191732i	$-0.0614105\pi$
$919$	4.60437	+	11.1159i	0.151884	+	0.366681i	−0.829563	+	0.558413i	$0.811411\pi$
$920$	30.7348	−	31.9565i	1.01330	−	1.05357i
$921$		0			0
$922$	40.4638	+	5.06002i	1.33260	+	0.166643i
$923$	−15.8297	−	23.6908i	−0.521040	−	0.779792i
$924$		0			0
$925$	−16.2030	+	3.22298i	−0.532752	+	0.105971i
$926$	36.9727	+	12.2833i	1.21500	+	0.403656i
$927$		0			0
$928$	7.97753	+	5.71965i	0.261875	+	0.187757i
$929$			27.6140i			0.905987i	0.891514	+	0.452994i	$0.149644\pi$
$929$			27.6140i			0.905987i	−0.891514	+	0.452994i	$0.850356\pi$
$930$		0			0
$931$	−0.0211911	+	0.00421517i	−0.000694510	+	0.000138147i
$932$	57.1338	+	14.5162i	1.87148	+	0.475495i
$933$		0			0
$934$	3.70811	−	29.6529i	0.121333	−	0.970271i
$935$	3.85611	−	9.30948i	0.126108	−	0.304453i
$936$		0			0
$937$	8.53902	+	20.6150i	0.278958	+	0.673464i	0.999807	−	0.0196280i	$-0.00624818\pi$
$937$	8.53902	+	20.6150i	0.278958	+	0.673464i	−0.720850	+	0.693091i	$0.756248\pi$
$938$	9.58823	+	34.8761i	0.313067	+	1.13874i
$939$		0			0
$940$	−2.40319	−	2.66955i	−0.0783833	−	0.0870710i
$941$	21.1132	−	31.5981i	0.688270	−	1.03007i	−0.308614	−	0.951187i	$-0.599865\pi$
$941$	21.1132	−	31.5981i	0.688270	−	1.03007i	0.996884	−	0.0788810i	$-0.0251347\pi$
$942$		0			0
$943$	−4.29797	+	4.29797i	−0.139961	+	0.139961i
$944$	−41.3657	−	34.4175i	−1.34634	−	1.12019i
$945$		0			0
$946$	0.0991911	+	1.37633i	0.00322498	+	0.0447484i
$947$	23.9627	+	16.0114i	0.778683	+	0.520299i	0.880239	−	0.474531i	$-0.157382\pi$
$947$	23.9627	+	16.0114i	0.778683	+	0.520299i	−0.101556	+	0.994830i	$0.532382\pi$
$948$		0			0
$949$	−25.1777	−	5.00816i	−0.817303	−	0.162572i
$950$	−0.0366001	−	0.0208153i	−0.00118747	−	0.000675339i
$951$		0			0
$952$	−3.37952	−	15.4141i	−0.109531	−	0.499573i
$953$	46.7611	+	19.3691i	1.51474	+	0.627426i	0.976529	−	0.215385i	$-0.0691005\pi$
$953$	46.7611	+	19.3691i	1.51474	+	0.627426i	0.538211	+	0.842810i	$0.319101\pi$
$954$		0			0
$955$	16.7255	−	11.1756i	0.541226	−	0.361635i
$956$	1.99186	+	13.7473i	0.0644214	+	0.444621i
$957$		0			0
$958$	−8.05280	−	16.0656i	−0.260174	−	0.519055i
$959$	−25.5868			−0.826241
$960$		0			0
$961$	−57.8654			−1.86663
$962$	8.77424	+	17.5049i	0.282893	+	0.564379i
$963$		0			0
$964$	−44.5366	+	6.45294i	−1.43443	+	0.207835i
$965$	25.0450	−	16.7346i	0.806228	−	0.538704i
$966$		0			0
$967$	−49.7556	−	20.6095i	−1.60003	−	0.662755i	−0.608612	−	0.793468i	$-0.708274\pi$
$967$	−49.7556	−	20.6095i	−1.60003	−	0.662755i	−0.991420	+	0.130712i	$0.958274\pi$
$968$	11.6746	−	18.2316i	0.375237	−	0.585985i
$969$		0			0
$970$	−50.6259	−	28.7921i	−1.62550	−	0.924458i
$971$	−20.0337	−	3.98496i	−0.642913	−	0.127883i	−0.137142	−	0.990551i	$-0.543792\pi$
$971$	−20.0337	−	3.98496i	−0.642913	−	0.127883i	−0.505771	+	0.862668i	$0.668792\pi$
$972$		0			0
$973$	11.6103	+	7.75773i	0.372208	+	0.248701i
$974$	−1.42924	−	19.8316i	−0.0457959	−	0.635445i
$975$		0			0
$976$	−23.5527	+	12.3857i	−0.753905	+	0.396455i
$977$	−8.15858	+	8.15858i	−0.261016	+	0.261016i	−0.825467	−	0.564451i	$-0.809088\pi$
$977$	−8.15858	+	8.15858i	−0.261016	+	0.261016i	0.564451	+	0.825467i	$0.309088\pi$
$978$		0			0
$979$	−11.3101	+	16.9268i	−0.361473	+	0.540983i
$980$	22.5585	−	20.3077i	0.720605	−	0.648705i
$981$		0			0
$982$	4.11868	+	14.9812i	0.131432	+	0.478071i
$983$	−3.28561	−	7.93217i	−0.104795	−	0.252997i	0.862781	−	0.505578i	$-0.168721\pi$
$983$	−3.28561	−	7.93217i	−0.104795	−	0.252997i	−0.967576	+	0.252581i	$0.918721\pi$
$984$		0			0
$985$	15.2921	−	36.9185i	0.487248	−	1.17632i
$986$	−0.500383	+	4.00144i	−0.0159354	+	0.127432i
$987$		0			0
$988$	−0.0122891	+	0.0483682i	−0.000390969	+	0.00153880i
$989$	−2.44644	+	0.486627i	−0.0777923	+	0.0154738i
$990$		0			0
$991$			21.7977i			0.692427i	0.938156	+	0.346213i	$0.112533\pi$
$991$			21.7977i			0.692427i	−0.938156	+	0.346213i	$0.887467\pi$
$992$	38.9301	−	36.4437i	1.23603	−	1.15709i
$993$		0			0
$994$	−24.8324	−	8.25001i	−0.787637	−	0.261674i
$995$	2.78441	−	0.553853i	0.0882716	−	0.0175583i
$996$		0			0
$997$	8.81651	+	13.1948i	0.279222	+	0.417885i	0.944400	−	0.328800i	$-0.106644\pi$
$997$	8.81651	+	13.1948i	0.279222	+	0.417885i	−0.665178	+	0.746685i	$0.731644\pi$
$998$	−13.4540	−	1.68244i	−0.425880	−	0.0532566i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.a.469.1		56
3.2	odd	2		64.2.i.a.21.7	✓	56
12.11	even	2		256.2.i.a.177.3		56
24.5	odd	2		512.2.i.b.97.3		56
24.11	even	2		512.2.i.a.97.5		56
64.61	even	16	inner	576.2.bd.a.253.1		56
192.29	odd	16		512.2.i.b.417.3		56
192.35	even	16		512.2.i.a.417.5		56
192.125	odd	16		64.2.i.a.61.7	yes	56
192.131	even	16		256.2.i.a.81.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.7	✓	56	3.2	odd	2
64.2.i.a.61.7	yes	56	192.125	odd	16
256.2.i.a.81.3		56	192.131	even	16
256.2.i.a.177.3		56	12.11	even	2
512.2.i.a.97.5		56	24.11	even	2
512.2.i.a.417.5		56	192.35	even	16
512.2.i.b.97.3		56	24.5	odd	2
512.2.i.b.417.3		56	192.29	odd	16
576.2.bd.a.253.1		56	64.61	even	16	inner
576.2.bd.a.469.1		56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26428 + 0.633715i) q^{2} +(1.19681 - 1.60239i) q^{4} +(2.78737 - 1.86246i) q^{5} +(-3.13672 - 1.29927i) q^{7} +(-0.497646 + 2.78430i) q^{8} +(-2.34375 + 4.12108i) q^{10} +(1.79402 + 0.356853i) q^{11} +(4.34710 + 2.90464i) q^{13} +(4.78906 - 0.345143i) q^{14} +(-1.13529 - 3.83551i) q^{16} +(1.16196 - 1.16196i) q^{17} +(-0.00265155 + 0.00396832i) q^{19} +(0.351568 - 6.69547i) q^{20} +(-2.49429 + 0.685737i) q^{22} +(-1.78945 - 4.32013i) q^{23} +(2.38726 - 5.76336i) q^{25} +(-7.33667 - 0.917455i) q^{26} +(-5.83599 + 3.47126i) q^{28} +(1.70191 - 0.338531i) q^{29} -9.42685i q^{31} +(3.86595 + 4.12970i) q^{32} +(-0.732694 + 2.20540i) q^{34} +(-11.1630 + 2.22047i) q^{35} +(-1.47130 - 2.20195i) q^{37} +(0.000837513 - 0.00669740i) q^{38} +(3.79854 + 8.68774i) q^{40} +(-0.497436 - 1.20092i) q^{41} +(0.104068 - 0.523183i) q^{43} +(2.71892 - 2.44763i) q^{44} +(5.00010 + 4.32785i) q^{46} +(0.378819 - 0.378819i) q^{47} +(3.20113 + 3.20113i) q^{49} +(0.634161 + 8.79935i) q^{50} +(9.85702 - 3.48944i) q^{52} +(3.63594 + 0.723233i) q^{53} +(5.66523 - 2.34662i) q^{55} +(5.17854 - 8.08699i) q^{56} +(-1.93716 + 1.50653i) q^{58} +(11.1857 - 7.47403i) q^{59} +(-1.29788 - 6.52488i) q^{61} +(5.97394 + 11.9182i) q^{62} +(-7.50470 - 2.77119i) q^{64} +17.5268 q^{65} +(1.46964 + 7.38837i) q^{67} +(-0.471267 - 3.25257i) q^{68} +(12.7061 - 9.88148i) q^{70} +(-5.03495 - 2.08554i) q^{71} +(-4.53632 + 1.87901i) q^{73} +(3.25554 + 1.85150i) q^{74} +(0.00318539 + 0.00899813i) q^{76} +(-5.16369 - 3.45027i) q^{77} +(11.3984 + 11.3984i) q^{79} +(-10.3080 - 8.57655i) q^{80} +(1.38994 + 1.20306i) q^{82} +(-3.35370 + 5.01916i) q^{83} +(1.07471 - 5.40294i) q^{85} +(0.199978 + 0.727399i) q^{86} +(-1.88637 + 4.81752i) q^{88} +(-4.25907 + 10.2823i) q^{89} +(-9.86171 - 14.7591i) q^{91} +(-9.06415 - 2.30297i) q^{92} +(-0.238870 + 0.718996i) q^{94} +0.0159996i q^{95} +12.2846i q^{97} +(-6.07574 - 2.01852i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32}+ \cdots - 128 q^{98}+O(q^{100}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Introduction

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