LMFDB - Embedded newform 819.2.fm.e.496.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			496.5
Character	$\chi$	$=$	819.496
Dual form			819.2.fm.e.748.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11595 + 0.299019i) q^{2} +(-0.576113 - 0.332619i) q^{4} +(-0.549341 - 0.549341i) q^{5} +(1.61214 + 2.09786i) q^{7} +(-2.17732 - 2.17732i) q^{8} +O(q^{10})$	\(q+(1.11595 + 0.299019i) q^{2} +(-0.576113 - 0.332619i) q^{4} +(-0.549341 - 0.549341i) q^{5} +(1.61214 + 2.09786i) q^{7} +(-2.17732 - 2.17732i) q^{8} +(-0.448776 - 0.777302i) q^{10} +(0.824353 - 3.07653i) q^{11} +(2.63686 - 2.45905i) q^{13} +(1.17177 + 2.82317i) q^{14} +(-1.11349 - 1.92862i) q^{16} +(-1.74975 + 3.03065i) q^{17} +(6.06267 - 1.62449i) q^{19} +(0.133761 + 0.499204i) q^{20} +(1.83988 - 3.18676i) q^{22} +(4.89067 - 2.82363i) q^{23} -4.39645i q^{25} +(3.67792 - 1.95572i) q^{26} +(-0.230987 - 1.74483i) q^{28} +(-4.54654 - 7.87483i) q^{29} +(-0.888029 - 0.888029i) q^{31} +(0.928002 + 3.46335i) q^{32} +(-2.85886 + 2.85886i) q^{34} +(0.266825 - 2.03806i) q^{35} +(0.151142 - 0.564068i) q^{37} +7.25141 q^{38} +2.39219i q^{40} +(-0.704976 + 2.63101i) q^{41} +(6.60921 + 3.81583i) q^{43} +(-1.49823 + 1.49823i) q^{44} +(6.30208 - 1.68864i) q^{46} +(-0.267009 + 0.267009i) q^{47} +(-1.80201 + 6.76408i) q^{49} +(1.31462 - 4.90623i) q^{50} +(-2.33706 + 0.539622i) q^{52} +11.6025 q^{53} +(-2.14292 + 1.23721i) q^{55} +(1.05756 - 8.07786i) q^{56} +(-2.71900 - 10.1474i) q^{58} +(-0.635122 - 2.37031i) q^{59} +(-6.70242 - 3.86964i) q^{61} +(-0.725461 - 1.25654i) q^{62} +8.59639i q^{64} +(-2.79940 - 0.0976783i) q^{65} +(-6.90457 - 1.85007i) q^{67} +(2.01610 - 1.16400i) q^{68} +(0.907181 - 2.19459i) q^{70} +(2.51079 + 9.37039i) q^{71} +(-7.71628 + 7.71628i) q^{73} +(0.337334 - 0.584279i) q^{74} +(-4.03312 - 1.08067i) q^{76} +(7.78309 - 3.23042i) q^{77} -10.8188 q^{79} +(-0.447786 + 1.67116i) q^{80} +(-1.57344 + 2.72528i) q^{82} +(-10.3355 - 10.3355i) q^{83} +(2.62607 - 0.703654i) q^{85} +(6.23456 + 6.23456i) q^{86} +(-8.49348 + 4.90371i) q^{88} +(7.02589 + 1.88258i) q^{89} +(9.40974 + 1.56743i) q^{91} -3.75677 q^{92} +(-0.377810 + 0.218129i) q^{94} +(-4.22288 - 2.43808i) q^{95} +(-0.704543 + 0.188782i) q^{97} +(-4.03355 + 7.00956i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

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 $

$2$	1.11595	+	0.299019i	0.789098	+	0.211438i	0.630792	−	0.775952i	$-0.282730\pi$
$2$	1.11595	+	0.299019i	0.789098	+	0.211438i	0.158306	+	0.987390i	$0.449397\pi$
$3$		0			0
$3$		0			0
$4$	−0.576113	−	0.332619i	−0.288056	−	0.166309i
$5$	−0.549341	−	0.549341i	−0.245673	−	0.245673i	0.573519	−	0.819192i	$-0.305578\pi$
$5$	−0.549341	−	0.549341i	−0.245673	−	0.245673i	−0.819192	+	0.573519i	$0.805578\pi$
$6$		0			0
$7$	1.61214	+	2.09786i	0.609331	+	0.792916i
$7$	1.61214	+	2.09786i	0.609331	+	0.792916i
$8$	−2.17732	−	2.17732i	−0.769800	−	0.769800i
$9$		0			0
$10$	−0.448776	−	0.777302i	−0.141915	−	0.245805i
$11$	0.824353	−	3.07653i	0.248552	−	0.927608i	−0.723013	−	0.690834i	$-0.757243\pi$
$11$	0.824353	−	3.07653i	0.248552	−	0.927608i	0.971565	−	0.236774i	$-0.0760899\pi$
$12$		0			0
$13$	2.63686	−	2.45905i	0.731335	−	0.682019i
$13$	2.63686	−	2.45905i	0.731335	−	0.682019i
$14$	1.17177	+	2.82317i	0.313170	+	0.754524i
$15$		0			0
$16$	−1.11349	−	1.92862i	−0.278373	−	0.482156i
$17$	−1.74975	+	3.03065i	−0.424376	+	0.735041i	−0.996362	−	0.0852225i	$-0.972840\pi$
$17$	−1.74975	+	3.03065i	−0.424376	+	0.735041i	0.571986	+	0.820263i	$0.306173\pi$
$18$		0			0
$19$	6.06267	−	1.62449i	1.39087	−	0.372683i	0.515814	−	0.856701i	$-0.327490\pi$
$19$	6.06267	−	1.62449i	1.39087	−	0.372683i	0.875058	+	0.484017i	$0.160823\pi$
$20$	0.133761	+	0.499204i	0.0299099	+	0.111625i
$21$		0			0
$22$	1.83988	−	3.18676i	0.392263	−	0.679420i
$23$	4.89067	−	2.82363i	1.01978	−	0.588768i	0.105737	−	0.994394i	$-0.466280\pi$
$23$	4.89067	−	2.82363i	1.01978	−	0.588768i	0.914039	+	0.405626i	$0.132947\pi$
$24$		0			0
$25$		−	4.39645i		−	0.879290i
$26$	3.67792	−	1.95572i	0.721299	−	0.383548i
$27$		0			0
$28$	−0.230987	−	1.74483i	−0.0436525	−	0.329742i
$29$	−4.54654	−	7.87483i	−0.844271	−	1.46232i	−0.886253	−	0.463202i	$-0.846701\pi$
$29$	−4.54654	−	7.87483i	−0.844271	−	1.46232i	0.0419819	−	0.999118i	$-0.486633\pi$
$30$		0			0
$31$	−0.888029	−	0.888029i	−0.159495	−	0.159495i	0.622848	−	0.782343i	$-0.285975\pi$
$31$	−0.888029	−	0.888029i	−0.159495	−	0.159495i	−0.782343	+	0.622848i	$0.785975\pi$
$32$	0.928002	+	3.46335i	0.164049	+	0.612239i
$33$		0			0
$34$	−2.85886	+	2.85886i	−0.490290	+	0.490290i
$35$	0.266825	−	2.03806i	0.0451017	−	0.344494i
$36$		0			0
$37$	0.151142	−	0.564068i	0.0248475	−	0.0927322i	−0.952389	−	0.304887i	$-0.901381\pi$
$37$	0.151142	−	0.564068i	0.0248475	−	0.0927322i	0.977236	+	0.212155i	$0.0680480\pi$
$38$	7.25141			1.17633
$39$		0			0
$40$			2.39219i			0.378238i
$41$	−0.704976	+	2.63101i	−0.110099	+	0.410894i	−0.998874	−	0.0474499i	$-0.984891\pi$
$41$	−0.704976	+	2.63101i	−0.110099	+	0.410894i	0.888775	+	0.458344i	$0.151557\pi$
$42$		0			0
$43$	6.60921	+	3.81583i	1.00790	+	0.581909i	0.910575	−	0.413344i	$-0.135639\pi$
$43$	6.60921	+	3.81583i	1.00790	+	0.581909i	0.0973205	+	0.995253i	$0.468973\pi$
$44$	−1.49823	+	1.49823i	−0.225867	+	0.225867i
$45$		0			0
$46$	6.30208	−	1.68864i	0.929191	−	0.248976i
$47$	−0.267009	+	0.267009i	−0.0389472	+	0.0389472i	−0.726312	−	0.687365i	$-0.758767\pi$
$47$	−0.267009	+	0.267009i	−0.0389472	+	0.0389472i	0.687365	+	0.726312i	$0.258767\pi$
$48$		0			0
$49$	−1.80201	+	6.76408i	−0.257430	+	0.966297i
$50$	1.31462	−	4.90623i	0.185915	−	0.693845i
$51$		0			0
$52$	−2.33706	+	0.539622i	−0.324092	+	0.0748321i
$53$	11.6025			1.59372			0.796862	−	0.604161i	$-0.206492\pi$
$53$	11.6025			1.59372			0.796862	+	0.604161i	$0.206492\pi$
$54$		0			0
$55$	−2.14292	+	1.23721i	−0.288951	+	0.166826i
$56$	1.05756	−	8.07786i	0.141323	−	1.07945i
$57$		0			0
$58$	−2.71900	−	10.1474i	−0.357022	−	1.33242i
$59$	−0.635122	−	2.37031i	−0.0826858	−	0.308588i	0.912180	−	0.409790i	$-0.134398\pi$
$59$	−0.635122	−	2.37031i	−0.0826858	−	0.308588i	−0.994866	+	0.101202i	$0.967731\pi$
$60$		0			0
$61$	−6.70242	−	3.86964i	−0.858157	−	0.495457i	0.00523788	−	0.999986i	$-0.498333\pi$
$61$	−6.70242	−	3.86964i	−0.858157	−	0.495457i	−0.863395	+	0.504529i	$0.831666\pi$
$62$	−0.725461	−	1.25654i	−0.0921337	−	0.159580i
$63$		0			0
$64$			8.59639i			1.07455i
$65$	−2.79940	−	0.0976783i	−0.347223	−	0.0121155i
$66$		0			0
$67$	−6.90457	−	1.85007i	−0.843528	−	0.226023i	−0.188921	−	0.981992i	$-0.560499\pi$
$67$	−6.90457	−	1.85007i	−0.843528	−	0.226023i	−0.654607	+	0.755970i	$0.727166\pi$
$68$	2.01610	−	1.16400i	0.244488	−	0.141155i
$69$		0			0
$70$	0.907181	−	2.19459i	0.108429	−	0.262303i
$71$	2.51079	+	9.37039i	0.297976	+	1.11206i	0.938825	+	0.344394i	$0.111916\pi$
$71$	2.51079	+	9.37039i	0.297976	+	1.11206i	−0.640849	+	0.767667i	$0.721418\pi$
$72$		0			0
$73$	−7.71628	+	7.71628i	−0.903122	+	0.903122i	−0.995705	−	0.0925826i	$-0.970488\pi$
$73$	−7.71628	+	7.71628i	−0.903122	+	0.903122i	0.0925826	+	0.995705i	$0.470488\pi$
$74$	0.337334	−	0.584279i	0.0392142	−	0.0679210i
$75$		0			0
$76$	−4.03312	−	1.08067i	−0.462630	−	0.123961i
$77$	7.78309	−	3.23042i	0.886965	−	0.368140i
$78$		0			0
$79$	−10.8188			−1.21721			−0.608607	−	0.793472i	$-0.708271\pi$
$79$	−10.8188			−1.21721			−0.608607	+	0.793472i	$0.708271\pi$
$80$	−0.447786	+	1.67116i	−0.0500640	+	0.186841i
$81$		0			0
$82$	−1.57344	+	2.72528i	−0.173757	+	0.300956i
$83$	−10.3355	−	10.3355i	−1.13447	−	1.13447i	−0.989426	−	0.145040i	$-0.953669\pi$
$83$	−10.3355	−	10.3355i	−1.13447	−	1.13447i	−0.145040	−	0.989426i	$-0.546331\pi$
$84$		0			0
$85$	2.62607	−	0.703654i	0.284837	−	0.0763220i
$86$	6.23456	+	6.23456i	0.672290	+	0.672290i
$87$		0			0
$88$	−8.49348	+	4.90371i	−0.905408	+	0.522737i
$89$	7.02589	+	1.88258i	0.744743	+	0.199553i	0.611185	−	0.791488i	$-0.290693\pi$
$89$	7.02589	+	1.88258i	0.744743	+	0.199553i	0.133558	+	0.991041i	$0.457360\pi$
$90$		0			0
$91$	9.40974	+	1.56743i	0.986409	+	0.164311i
$92$	−3.75677			−0.391670
$93$		0			0
$94$	−0.377810	+	0.218129i	−0.0389681	+	0.0224983i
$95$	−4.22288	−	2.43808i	−0.433258	−	0.250142i
$96$		0			0
$97$	−0.704543	+	0.188782i	−0.0715355	+	0.0191679i	−0.294409	−	0.955679i	$-0.595123\pi$
$97$	−0.704543	+	0.188782i	−0.0715355	+	0.0191679i	0.222874	+	0.974847i	$0.428456\pi$
$98$	−4.03355	+	7.00956i	−0.407450	+	0.708072i
$99$		0			0
$100$	−1.46234	+	2.53285i	−0.146234	+	0.253285i
$101$	5.71320	+	9.89554i	0.568484	+	0.984643i	0.996716	+	0.0809746i	$0.0258033\pi$
$101$	5.71320	+	9.89554i	0.568484	+	0.984643i	−0.428232	+	0.903669i	$0.640863\pi$
$102$		0			0
$103$	19.3170			1.90336			0.951679	−	0.307094i	$-0.0993568\pi$
$103$	19.3170			1.90336			0.951679	+	0.307094i	$0.0993568\pi$
$104$	−11.0955	−	0.387150i	−1.08800	−	0.0379631i
$105$		0			0
$106$	12.9478	+	3.46936i	1.25760	+	0.336974i
$107$	4.59094	+	7.95175i	0.443823	+	0.768724i	0.997969	−	0.0636951i	$-0.0202885\pi$
$107$	4.59094	+	7.95175i	0.443823	+	0.768724i	−0.554146	+	0.832419i	$0.686955\pi$
$108$		0			0
$109$	1.79167	−	1.79167i	0.171610	−	0.171610i	−0.616076	−	0.787687i	$-0.711279\pi$
$109$	1.79167	−	1.79167i	0.171610	−	0.171610i	0.787687	+	0.616076i	$0.211279\pi$
$110$	−2.76134	+	0.739899i	−0.263284	+	0.0705466i
$111$		0			0
$112$	2.25088	−	5.44516i	0.212688	−	0.514519i
$113$	−1.25451	+	2.17288i	−0.118015	+	0.204407i	−0.918981	−	0.394302i	$-0.870986\pi$
$113$	−1.25451	+	2.17288i	−0.118015	+	0.204407i	0.800966	+	0.598710i	$0.204320\pi$
$114$		0			0
$115$	−4.23779	−	1.13551i	−0.395176	−	0.105887i
$116$			6.04906i			0.561641i
$117$		0			0
$118$		−	2.83506i		−	0.260989i
$119$	−9.17871	+	1.21511i	−0.841411	+	0.111389i
$120$		0			0
$121$	0.740817	+	0.427711i	0.0673470	+	0.0388828i
$122$	−6.32249	−	6.32249i	−0.572411	−	0.572411i
$123$		0			0
$124$	0.216230	+	0.806980i	0.0194180	+	0.0724689i
$125$	−5.16186	+	5.16186i	−0.461691	+	0.461691i
$126$		0			0
$127$	−14.6248	+	8.44360i	−1.29774	+	0.749249i	−0.980013	−	0.198934i	$-0.936252\pi$
$127$	−14.6248	+	8.44360i	−1.29774	+	0.749249i	−0.317724	+	0.948183i	$0.602919\pi$
$128$	−0.714478	+	2.66647i	−0.0631515	+	0.235685i
$129$		0			0
$130$	−3.09479	−	0.946077i	−0.271431	−	0.0829764i
$131$			9.18546i			0.802537i	0.915960	+	0.401269i	$0.131431\pi$
$131$			9.18546i			0.802537i	−0.915960	+	0.401269i	$0.868569\pi$
$132$		0			0
$133$	13.1818	+	10.0997i	1.14301	+	0.875757i
$134$	−7.15197	−	4.12919i	−0.617836	−	0.356708i
$135$		0			0
$136$	10.4085	−	2.78894i	0.892519	−	0.239150i
$137$	−6.08217	+	1.62971i	−0.519635	+	0.139236i	−0.509098	−	0.860709i	$-0.670021\pi$
$137$	−6.08217	+	1.62971i	−0.519635	+	0.139236i	−0.0105372	+	0.999944i	$0.503354\pi$
$138$		0			0
$139$	−16.6243	−	9.59802i	−1.41005	−	0.814093i	−0.414658	−	0.909977i	$-0.636099\pi$
$139$	−16.6243	−	9.59802i	−1.41005	−	0.814093i	−0.995393	+	0.0958840i	$0.969432\pi$
$140$	−0.831617	+	1.08540i	−0.0702844	+	0.0917329i
$141$		0			0
$142$			11.2077i			0.940528i
$143$	−5.39164	−	10.1395i	−0.450872	−	0.847909i
$144$		0			0
$145$	−1.82837	+	6.82358i	−0.151838	+	0.566667i
$146$	−10.9183	+	6.30369i	−0.903606	+	0.521697i
$147$		0			0
$148$	−0.274694	+	0.274694i	−0.0225797	+	0.0225797i
$149$	2.99088	+	11.1621i	0.245022	+	0.914435i	0.973372	+	0.229230i	$0.0736207\pi$
$149$	2.99088	+	11.1621i	0.245022	+	0.914435i	−0.728350	+	0.685205i	$0.759713\pi$
$150$		0			0
$151$	8.90574	+	8.90574i	0.724738	+	0.724738i	0.969567	−	0.244828i	$-0.0787315\pi$
$151$	8.90574	+	8.90574i	0.724738	+	0.724738i	−0.244828	+	0.969567i	$0.578732\pi$
$152$	−16.7374	−	9.66336i	−1.35759	−	0.783802i
$153$		0			0
$154$	9.65151	−	1.27770i	0.777741	−	0.102960i
$155$			0.975662i			0.0783671i
$156$		0			0
$157$		−	5.49387i		−	0.438459i	−0.975673	−	0.219229i	$-0.929646\pi$
$157$		−	5.49387i		−	0.438459i	0.975673	−	0.219229i	$-0.0703543\pi$
$158$	−12.0733	−	3.23503i	−0.960501	−	0.257365i
$159$		0			0
$160$	1.39277	−	2.41235i	0.110108	−	0.190713i
$161$	13.8080	+	5.70785i	1.08822	+	0.449841i
$162$		0			0
$163$	10.2964	−	2.75892i	0.806480	−	0.216096i	0.168053	−	0.985778i	$-0.446252\pi$
$163$	10.2964	−	2.75892i	0.806480	−	0.216096i	0.638427	+	0.769682i	$0.279585\pi$
$164$	1.28127	−	1.28127i	0.100050	−	0.100050i
$165$		0			0
$166$	−8.44340	−	14.6244i	−0.655335	−	1.13507i
$167$	−12.5089	−	3.35175i	−0.967967	−	0.259366i	−0.259998	−	0.965609i	$-0.583722\pi$
$167$	−12.5089	−	3.35175i	−0.967967	−	0.259366i	−0.707969	+	0.706243i	$0.750389\pi$
$168$		0			0
$169$	0.906105	−	12.9684i	0.0697004	−	0.997568i
$170$	3.14098			0.240902
$171$		0			0
$172$	−2.53843	−	4.39670i	−0.193554	−	0.335245i
$173$	−0.498608	+	0.863615i	−0.0379085	+	0.0656594i	−0.884357	−	0.466811i	$-0.845403\pi$
$173$	−0.498608	+	0.863615i	−0.0379085	+	0.0656594i	0.846449	+	0.532470i	$0.178736\pi$
$174$		0			0
$175$	9.22312	−	7.08769i	0.697202	−	0.535779i
$176$	−6.85138	+	1.83582i	−0.516442	+	0.138380i
$177$		0			0
$178$	7.27763	+	4.20174i	0.545482	+	0.314934i
$179$	4.88304	−	2.81922i	0.364975	−	0.210719i	−0.306286	−	0.951940i	$-0.599086\pi$
$179$	4.88304	−	2.81922i	0.364975	−	0.210719i	0.671261	+	0.741221i	$0.265753\pi$
$180$		0			0
$181$	−21.5094			−1.59878			−0.799390	−	0.600813i	$-0.794844\pi$
$181$	−21.5094			−1.59878			−0.799390	+	0.600813i	$0.794844\pi$
$182$	10.0321	+	4.56286i	0.743631	+	0.338222i
$183$		0			0
$184$	−16.7965	−	4.50062i	−1.23826	−	0.331790i
$185$	−0.392894	+	0.226838i	−0.0288862	+	0.0166774i
$186$		0			0
$187$	7.88147	+	7.88147i	0.576350	+	0.576350i
$188$	0.242639	−	0.0650150i	0.0176963	−	0.00474171i
$189$		0			0
$190$	−3.98350	−	3.98350i	−0.288993	−	0.288993i
$191$	4.39198	−	7.60714i	0.317793	−	0.550433i	−0.662234	−	0.749297i	$-0.730392\pi$
$191$	4.39198	−	7.60714i	0.317793	−	0.550433i	0.980027	+	0.198863i	$0.0637250\pi$
$192$		0			0
$193$	0.249296	−	0.930384i	0.0179447	−	0.0669705i	−0.956373	−	0.292149i	$-0.905630\pi$
$193$	0.249296	−	0.930384i	0.0179447	−	0.0669705i	0.974318	+	0.225178i	$0.0722964\pi$
$194$	−0.842685			−0.0605013
$195$		0			0
$196$	3.28802	−	3.29749i	0.234859	−	0.235535i
$197$	16.6329	+	4.45678i	1.18505	+	0.317532i	0.796926	−	0.604076i	$-0.206458\pi$
$197$	16.6329	+	4.45678i	1.18505	+	0.317532i	0.388120	+	0.921609i	$0.373124\pi$
$198$		0			0
$199$	−1.12555	+	1.94951i	−0.0797883	+	0.138197i	−0.903159	−	0.429307i	$-0.858758\pi$
$199$	−1.12555	+	1.94951i	−0.0797883	+	0.138197i	0.823370	+	0.567505i	$0.192091\pi$
$200$	−9.57249	+	9.57249i	−0.676877	+	0.676877i
$201$		0			0
$202$	3.41670	+	12.7513i	0.240398	+	0.897179i
$203$	9.19063	−	22.2333i	0.645056	−	1.56047i
$204$		0			0
$205$	1.83259	−	1.05805i	0.127994	−	0.0738973i
$206$	21.5568	+	5.77613i	1.50194	+	0.402442i
$207$		0			0
$208$	−7.67872	−	2.34738i	−0.532423	−	0.162762i
$209$		−	19.9911i		−	1.38282i
$210$		0			0
$211$	−10.3549	−	17.9352i	−0.712859	−	1.23471i	−0.963780	−	0.266700i	$-0.914067\pi$
$211$	−10.3549	−	17.9352i	−0.712859	−	1.23471i	0.250921	−	0.968008i	$-0.419267\pi$
$212$	−6.68434	−	3.85920i	−0.459082	−	0.265051i
$213$		0			0
$214$	2.74555	+	10.2465i	0.187682	+	0.700440i
$215$	−1.53452	−	5.72691i	−0.104653	−	0.390572i
$216$		0			0
$217$	0.431332	−	3.29459i	0.0292807	−	0.223651i
$218$	2.53516	−	1.46367i	0.171702	−	0.0991325i
$219$		0			0
$220$	1.64608			0.110979
$221$	2.83869	+	12.2941i	0.190951	+	0.826993i
$222$		0			0
$223$	−5.92307	+	22.1052i	−0.396638	+	1.48027i	0.422333	+	0.906441i	$0.361211\pi$
$223$	−5.92307	+	22.1052i	−0.396638	+	1.48027i	−0.818972	+	0.573834i	$0.805455\pi$
$224$	−5.76954	+	7.53022i	−0.385494	+	0.503134i
$225$		0			0
$226$	−2.04971	+	2.04971i	−0.136345	+	0.136345i
$227$	15.1087	−	4.04837i	1.00280	−	0.268699i	0.280182	−	0.959947i	$-0.409605\pi$
$227$	15.1087	−	4.04837i	1.00280	−	0.268699i	0.722618	+	0.691248i	$0.242939\pi$
$228$		0			0
$229$	3.61172	−	3.61172i	0.238669	−	0.238669i	−0.577630	−	0.816299i	$-0.696022\pi$
$229$	3.61172	−	3.61172i	0.238669	−	0.238669i	0.816299	+	0.577630i	$0.196022\pi$
$230$	−4.38963	−	2.53435i	−0.289444	−	0.167110i
$231$		0			0
$232$	−7.24678	+	27.0453i	−0.475774	+	1.77561i
$233$			3.18656i			0.208758i	0.994538	+	0.104379i	$0.0332855\pi$
$233$			3.18656i			0.208758i	−0.994538	+	0.104379i	$0.966714\pi$
$234$		0			0
$235$	0.293358			0.0191366
$236$	−0.422507	+	1.57682i	−0.0275029	+	0.102642i
$237$		0			0
$238$	−10.6063	−	1.38860i	−0.687508	−	0.0900094i
$239$	1.61918	−	1.61918i	0.104736	−	0.104736i	−0.652797	−	0.757533i	$-0.726404\pi$
$239$	1.61918	−	1.61918i	0.104736	−	0.104736i	0.757533	+	0.652797i	$0.226404\pi$
$240$		0			0
$241$	−1.64242	−	6.12960i	−0.105798	−	0.394842i	0.892637	−	0.450777i	$-0.148853\pi$
$241$	−1.64242	−	6.12960i	−0.105798	−	0.394842i	−0.998434	+	0.0559344i	$0.982186\pi$
$242$	0.698823	+	0.698823i	0.0449221	+	0.0449221i
$243$		0			0
$244$	2.57423	+	4.45870i	0.164798	+	0.285439i
$245$	4.70571	−	2.72587i	0.300637	−	0.174149i
$246$		0			0
$247$	11.9917	−	19.1920i	0.763016	−	1.22116i
$248$			3.86705i			0.245558i
$249$		0			0
$250$	−7.30388	+	4.21690i	−0.461938	+	0.266700i
$251$	−10.7306	+	18.5859i	−0.677308	+	1.17313i	0.298481	+	0.954416i	$0.403520\pi$
$251$	−10.7306	+	18.5859i	−0.677308	+	1.17313i	−0.975789	+	0.218716i	$0.929813\pi$
$252$		0			0
$253$	−4.65534	−	17.3740i	−0.292679	−	1.09229i
$254$	−18.8453	+	5.04959i	−1.18246	+	0.316839i
$255$		0			0
$256$	7.00174	−	12.1274i	0.437609	−	0.757961i
$257$	14.1914	+	24.5801i	0.885232	+	1.53327i	0.845447	+	0.534059i	$0.179334\pi$
$257$	14.1914	+	24.5801i	0.885232	+	1.53327i	0.0397853	+	0.999208i	$0.487333\pi$
$258$		0			0
$259$	1.42700	−	0.592283i	0.0886692	−	0.0368027i
$260$	1.58028	+	0.987406i	0.0980048	+	0.0612364i
$261$		0			0
$262$	−2.74662	+	10.2505i	−0.169687	+	0.633280i
$263$	−6.33755	−	10.9770i	−0.390790	−	0.676868i	0.601764	−	0.798674i	$-0.294465\pi$
$263$	−6.33755	−	10.9770i	−0.390790	−	0.676868i	−0.992554	+	0.121806i	$0.961131\pi$
$264$		0			0
$265$	−6.37373	−	6.37373i	−0.391535	−	0.391535i
$266$	11.6903	+	15.2124i	0.716777	+	0.932733i
$267$		0			0
$268$	3.36244	+	3.36244i	0.205394	+	0.205394i
$269$	−5.62758	−	3.24908i	−0.343120	−	0.198100i	0.318531	−	0.947912i	$-0.396810\pi$
$269$	−5.62758	−	3.24908i	−0.343120	−	0.198100i	−0.661651	+	0.749812i	$0.730144\pi$
$270$		0			0
$271$	−6.14616	−	1.64686i	−0.373353	−	0.100040i	0.0672633	−	0.997735i	$-0.478573\pi$
$271$	−6.14616	−	1.64686i	−0.373353	−	0.100040i	−0.440616	+	0.897696i	$0.645240\pi$
$272$	7.79332			0.472539
$273$		0			0
$274$	−7.27473			−0.439482
$275$	−13.5258	−	3.62423i	−0.815636	−	0.218549i
$276$		0			0
$277$	15.6622	+	9.04260i	0.941053	+	0.543317i	0.890290	−	0.455394i	$-0.150501\pi$
$277$	15.6622	+	9.04260i	0.941053	+	0.543317i	0.0507626	+	0.998711i	$0.483835\pi$
$278$	−15.6819	−	15.6819i	−0.940538	−	0.940538i
$279$		0			0
$280$	−5.01847	+	3.85654i	−0.299911	+	0.230472i
$281$	6.43538	+	6.43538i	0.383903	+	0.383903i	0.872506	−	0.488603i	$-0.162493\pi$
$281$	6.43538	+	6.43538i	0.383903	+	0.383903i	−0.488603	+	0.872506i	$0.662493\pi$
$282$		0			0
$283$	7.33715	+	12.7083i	0.436148	+	0.755431i	0.997389	−	0.0722219i	$-0.0230090\pi$
$283$	7.33715	+	12.7083i	0.436148	+	0.755431i	−0.561240	+	0.827653i	$0.689676\pi$
$284$	1.67027	−	6.23354i	0.0991124	−	0.369892i
$285$		0			0
$286$	−2.98491	−	12.9274i	−0.176502	−	0.764414i
$287$	−6.65599	+	2.76261i	−0.392891	+	0.163072i
$288$		0			0
$289$	2.37677	+	4.11668i	0.139810	+	0.242158i
$290$	−4.08075	+	7.06807i	−0.239630	+	0.415051i
$291$		0			0
$292$	7.01203	−	1.87887i	0.410348	−	0.109952i
$293$	−1.69762	−	6.33562i	−0.0991763	−	0.370131i	0.898443	−	0.439090i	$-0.144699\pi$
$293$	−1.69762	−	6.33562i	−0.0991763	−	0.370131i	−0.997620	+	0.0689587i	$0.978032\pi$
$294$		0			0
$295$	−0.953209	+	1.65101i	−0.0554980	+	0.0961253i
$296$	−1.55724	+	0.899074i	−0.0905129	+	0.0522576i
$297$		0			0
$298$			13.3507i			0.773385i
$299$	5.95258	−	19.4720i	0.344246	−	1.12609i
$300$		0			0
$301$	2.64990	+	20.0168i	0.152738	+	1.15375i
$302$	7.27540	+	12.6014i	0.418652	+	0.725127i
$303$		0			0
$304$	−9.88377	−	9.88377i	−0.566873	−	0.566873i
$305$	1.55616	+	5.80767i	0.0891055	+	0.332546i
$306$		0			0
$307$	23.5768	−	23.5768i	1.34560	−	1.34560i	0.455225	−	0.890377i	$-0.349559\pi$
$307$	23.5768	−	23.5768i	1.34560	−	1.34560i	0.890377	−	0.455225i	$-0.150441\pi$
$308$	−5.55843	−	0.727718i	−0.316721	−	0.0414656i
$309$		0			0
$310$	−0.291741	+	1.08879i	−0.0165698	+	0.0618393i
$311$	2.90579			0.164772			0.0823861	−	0.996600i	$-0.473746\pi$
$311$	2.90579			0.164772			0.0823861	+	0.996600i	$0.473746\pi$
$312$		0			0
$313$		−	0.960626i		−	0.0542978i	−0.999631	−	0.0271489i	$-0.991357\pi$
$313$		−	0.960626i		−	0.0542978i	0.999631	−	0.0271489i	$-0.00864282\pi$
$314$	1.64277	−	6.13090i	0.0927069	−	0.345987i
$315$		0			0
$316$	6.23287	+	3.59855i	0.350626	+	0.202434i
$317$	23.7216	−	23.7216i	1.33234	−	1.33234i	0.429064	−	0.903274i	$-0.358844\pi$
$317$	23.7216	−	23.7216i	1.33234	−	1.33234i	0.903274	−	0.429064i	$-0.141156\pi$
$318$		0			0
$319$	−27.9751	+	7.49590i	−1.56630	+	0.419690i
$320$	4.72235	−	4.72235i	0.263988	−	0.263988i
$321$		0			0
$322$	13.7023	+	10.4985i	0.763602	+	0.585061i
$323$	−5.68489	+	21.2163i	−0.316316	+	1.18051i
$324$		0			0
$325$	−10.8111	−	11.5928i	−0.599692	−	0.643055i
$326$	12.3153			0.682082
$327$		0			0
$328$	7.26351	−	4.19359i	0.401060	−	0.231552i
$329$	−0.990602	−	0.129691i	−0.0546137	−	0.00715010i
$330$		0			0
$331$	3.27417	+	12.2194i	0.179965	+	0.671637i	0.995653	+	0.0931447i	$0.0296919\pi$
$331$	3.27417	+	12.2194i	0.179965	+	0.671637i	−0.815688	+	0.578492i	$0.803641\pi$
$332$	2.51662	+	9.39217i	0.138118	+	0.515462i
$333$		0			0
$334$	−12.9571	−	7.48078i	−0.708981	−	0.409330i
$335$	2.77665	+	4.80929i	0.151704	+	0.262760i
$336$		0			0
$337$		−	12.8172i		−	0.698196i	−0.937086	−	0.349098i	$-0.886488\pi$
$337$		−	12.8172i		−	0.698196i	0.937086	−	0.349098i	$-0.113512\pi$
$338$	4.88896	−	14.2012i	0.265924	−	0.772441i
$339$		0			0
$340$	−1.74696	−	0.468097i	−0.0947423	−	0.0253861i
$341$	−3.46410	+	2.00000i	−0.187591	+	0.108306i
$342$		0			0
$343$	−17.0952	+	7.12427i	−0.923052	+	0.384675i
$344$	−6.08209	−	22.6987i	−0.327925	−	1.22383i
$345$		0			0
$346$	−0.814660	+	0.814660i	−0.0437964	+	0.0437964i
$347$	9.29372	−	16.0972i	0.498913	−	0.864143i	−0.501086	−	0.865397i	$-0.667066\pi$
$347$	9.29372	−	16.0972i	0.498913	−	0.864143i	0.999999	+	0.00125445i	$0.000399304\pi$
$348$		0			0
$349$	−4.62637	−	1.23963i	−0.247644	−	0.0663560i	0.132862	−	0.991135i	$-0.457583\pi$
$349$	−4.62637	−	1.23963i	−0.247644	−	0.0663560i	−0.380506	+	0.924779i	$0.624250\pi$
$350$	12.4119	−	5.15164i	0.663445	−	0.275367i
$351$		0			0
$352$	11.4201			0.608693
$353$	−3.19876	+	11.9379i	−0.170253	+	0.635392i	0.827059	+	0.562116i	$0.190012\pi$
$353$	−3.19876	+	11.9379i	−0.170253	+	0.635392i	−0.997312	+	0.0732769i	$0.976654\pi$
$354$		0			0
$355$	3.76826	−	6.52683i	0.199999	−	0.346408i
$356$	−3.42152	−	3.42152i	−0.181340	−	0.181340i
$357$		0			0
$358$	6.29224	−	1.68600i	0.332555	−	0.0891079i
$359$	−4.20137	−	4.20137i	−0.221740	−	0.221740i	0.587491	−	0.809231i	$-0.300116\pi$
$359$	−4.20137	−	4.20137i	−0.221740	−	0.221740i	−0.809231	+	0.587491i	$0.800116\pi$
$360$		0			0
$361$	17.6626	−	10.1975i	0.929608	−	0.536710i
$362$	−24.0035	−	6.43171i	−1.26159	−	0.338043i
$363$		0			0
$364$	−4.89971	−	4.03287i	−0.256815	−	0.211380i
$365$	8.47775			0.443746
$366$		0			0
$367$	−5.05707	+	2.91970i	−0.263977	+	0.152407i	−0.626147	−	0.779705i	$-0.715369\pi$
$367$	−5.05707	+	2.91970i	−0.263977	+	0.152407i	0.362170	+	0.932112i	$0.382036\pi$
$368$	−10.8914	−	6.28818i	−0.567756	−	0.327794i
$369$		0			0
$370$	−0.506280	+	0.135657i	−0.0263202	+	0.00705249i
$371$	18.7048	+	24.3404i	0.971106	+	1.26369i
$372$		0			0
$373$	−5.17801	+	8.96858i	−0.268107	+	0.464375i	−0.968373	−	0.249507i	$-0.919731\pi$
$373$	−5.17801	+	8.96858i	−0.268107	+	0.464375i	0.700266	+	0.713882i	$0.253065\pi$
$374$	6.43864	+	11.1521i	0.332934	+	0.576659i
$375$		0			0
$376$	1.16273			0.0599632
$377$	−31.3532	−	9.58469i	−1.61477	−	0.493636i
$378$		0			0
$379$	6.76845	+	1.81360i	0.347672	+	0.0931584i	0.428429	−	0.903575i	$-0.359067\pi$
$379$	6.76845	+	1.81360i	0.347672	+	0.0931584i	−0.0807572	+	0.996734i	$0.525734\pi$
$380$	1.62190	+	2.80922i	0.0832018	+	0.144110i
$381$		0			0
$382$	7.17592	−	7.17592i	0.367152	−	0.367152i
$383$	−7.14098	+	1.91342i	−0.364887	+	0.0977711i	−0.436604	−	0.899654i	$-0.643819\pi$
$383$	−7.14098	+	1.91342i	−0.364887	+	0.0977711i	0.0717170	+	0.997425i	$0.477152\pi$
$384$		0			0
$385$	−6.05017	−	2.50097i	−0.308345	−	0.127461i
$386$	0.556404	−	0.963720i	0.0283202	−	0.0490521i
$387$		0			0
$388$	0.468688	+	0.125585i	0.0237940	+	0.00637559i
$389$			10.2280i			0.518581i	0.965799	+	0.259290i	$0.0834886\pi$
$389$			10.2280i			0.518581i	−0.965799	+	0.259290i	$0.916511\pi$
$390$		0			0
$391$			19.7626i			0.999436i
$392$	18.6511	−	10.8040i	0.942025	−	0.545686i
$393$		0			0
$394$	17.2289	+	9.94711i	0.867979	+	0.501128i
$395$	5.94323	+	5.94323i	0.299037	+	0.299037i
$396$		0			0
$397$	7.30250	+	27.2533i	0.366502	+	1.36780i	0.865373	+	0.501128i	$0.167081\pi$
$397$	7.30250	+	27.2533i	0.366502	+	1.36780i	−0.498872	+	0.866676i	$0.666252\pi$
$398$	−1.83900	+	1.83900i	−0.0921810	+	0.0921810i
$399$		0			0
$400$	−8.47910	+	4.89541i	−0.423955	+	0.244770i
$401$	1.82731	−	6.81960i	0.0912514	−	0.340555i	−0.905173	−	0.425043i	$-0.860259\pi$
$401$	1.82731	−	6.81960i	0.0912514	−	0.340555i	0.996424	+	0.0844884i	$0.0269256\pi$
$402$		0			0
$403$	−4.52532	−	0.157900i	−0.225422	−	0.00786558i
$404$		−	7.60126i		−	0.378177i
$405$		0			0
$406$	16.9045	−	22.0632i	0.838955	−	1.09498i
$407$	−1.61078	−	0.929982i	−0.0798432	−	0.0460975i
$408$		0			0
$409$	30.3999	−	8.14562i	1.50318	−	0.402775i	0.589014	−	0.808123i	$-0.299516\pi$
$409$	30.3999	−	8.14562i	1.50318	−	0.402775i	0.914163	+	0.405348i	$0.132850\pi$
$410$	2.36146	−	0.632752i	0.116624	−	0.0312494i
$411$		0			0
$412$	−11.1288	−	6.42519i	−0.548274	−	0.316546i
$413$	3.94866	−	5.15366i	0.194301	−	0.253595i
$414$		0			0
$415$			11.3554i			0.557415i
$416$	10.9636	+	6.85037i	0.537534	+	0.335867i
$417$		0			0
$418$	5.97772	−	22.3092i	0.292380	−	1.09118i
$419$	−20.4187	+	11.7887i	−0.997519	+	0.575918i	−0.907513	−	0.420023i	$-0.862022\pi$
$419$	−20.4187	+	11.7887i	−0.997519	+	0.575918i	−0.0900058	+	0.995941i	$0.528689\pi$
$420$		0			0
$421$	4.63273	−	4.63273i	0.225785	−	0.225785i	−0.585144	−	0.810929i	$-0.698962\pi$
$421$	4.63273	−	4.63273i	0.225785	−	0.225785i	0.810929	+	0.585144i	$0.198962\pi$
$422$	−6.19260	−	23.1111i	−0.301451	−	1.12503i
$423$		0			0
$424$	−25.2624	−	25.2624i	−1.22685	−	1.22685i
$425$	13.3241	+	7.69267i	0.646314	+	0.373149i
$426$		0			0
$427$	−2.68727	−	20.2991i	−0.130046	−	0.982343i
$428$		−	6.10813i		−	0.295248i
$429$		0			0
$430$		−	6.84981i		−	0.330327i
$431$	−27.8082	−	7.45118i	−1.33947	−	0.358911i	−0.483234	−	0.875491i	$-0.660538\pi$
$431$	−27.8082	−	7.45118i	−1.33947	−	0.358911i	−0.856239	+	0.516580i	$0.827205\pi$
$432$		0			0
$433$	−1.92063	+	3.32663i	−0.0922998	+	0.159868i	−0.908478	−	0.417932i	$-0.862755\pi$
$433$	−1.92063	+	3.32663i	−0.0922998	+	0.159868i	0.816179	+	0.577800i	$0.196088\pi$
$434$	1.46649	−	3.54763i	0.0703937	−	0.170291i
$435$		0			0
$436$	−1.62814	+	0.436260i	−0.0779739	+	0.0208930i
$437$	25.0636	−	25.0636i	1.19895	−	1.19895i
$438$		0			0
$439$	7.29107	+	12.6285i	0.347984	+	0.602726i	0.985891	−	0.167388i	$-0.0535331\pi$
$439$	7.29107	+	12.6285i	0.347984	+	0.602726i	−0.637907	+	0.770113i	$0.720200\pi$
$440$	7.35963	+	1.97201i	0.350857	+	0.0940118i
$441$		0			0
$442$	−0.508333	+	14.5685i	−0.0241789	+	0.692953i
$443$	−32.2060			−1.53015			−0.765076	−	0.643940i	$-0.777299\pi$
$443$	−32.2060			−1.53015			−0.765076	+	0.643940i	$0.777299\pi$
$444$		0			0
$445$	−2.82543	−	4.89379i	−0.133938	−	0.231988i
$446$	−13.2197	+	22.8973i	−0.625973	+	1.08422i
$447$		0			0
$448$	−18.0340	+	13.8586i	−0.852027	+	0.654756i
$449$	19.3546	−	5.18606i	0.913402	−	0.244745i	0.228639	−	0.973511i	$-0.426572\pi$
$449$	19.3546	−	5.18606i	0.913402	−	0.244745i	0.684763	+	0.728766i	$0.259906\pi$
$450$		0			0
$451$	7.51321	+	4.33776i	0.353783	+	0.204257i
$452$	1.44548	−	0.834549i	0.0679897	−	0.0392539i
$453$		0			0
$454$	18.0711			0.848120
$455$	−4.30811	−	6.03021i	−0.201967	−	0.282701i
$456$		0			0
$457$	14.5061	+	3.88690i	0.678567	+	0.181822i	0.581611	−	0.813467i	$-0.302423\pi$
$457$	14.5061	+	3.88690i	0.678567	+	0.181822i	0.0969563	+	0.995289i	$0.469089\pi$
$458$	5.11049	−	2.95054i	0.238797	−	0.137870i
$459$		0			0
$460$	2.06375	+	2.06375i	0.0962228	+	0.0962228i
$461$	29.9515	−	8.02549i	1.39498	−	0.373784i	0.518441	−	0.855113i	$-0.326512\pi$
$461$	29.9515	−	8.02549i	1.39498	−	0.373784i	0.876540	+	0.481329i	$0.159846\pi$
$462$		0			0
$463$	3.61564	+	3.61564i	0.168033	+	0.168033i	0.786114	−	0.618081i	$-0.212090\pi$
$463$	3.61564	+	3.61564i	0.168033	+	0.168033i	−0.618081	+	0.786114i	$0.712090\pi$
$464$	−10.1251	+	17.5371i	−0.470044	+	0.814141i
$465$		0			0
$466$	−0.952840	+	3.55605i	−0.0441395	+	0.164731i
$467$	17.6775			0.818017			0.409009	−	0.912530i	$-0.365875\pi$
$467$	17.6775			0.818017			0.409009	+	0.912530i	$0.365875\pi$
$468$		0			0
$469$	−7.24994	−	17.4674i	−0.334771	−	0.806569i
$470$	0.327374	+	0.0877195i	0.0151006	+	0.00404620i
$471$		0			0
$472$	−3.77806	+	6.54379i	−0.173899	+	0.301202i
$473$	17.1878	−	17.1878i	0.790297	−	0.790297i
$474$		0			0
$475$	−7.14198	−	26.6542i	−0.327696	−	1.22298i
$476$	5.69214	+	2.35297i	0.260899	+	0.107848i
$477$		0			0
$478$	2.29110	−	1.32276i	0.104792	−	0.0605018i
$479$	−19.1281	−	5.12537i	−0.873987	−	0.234184i	−0.206176	−	0.978515i	$-0.566102\pi$
$479$	−19.1281	−	5.12537i	−0.873987	−	0.234184i	−0.667811	+	0.744331i	$0.732769\pi$
$480$		0			0
$481$	−0.988534	−	1.85904i	−0.0450733	−	0.0847647i
$482$		−	7.33146i		−	0.333939i
$483$		0			0
$484$	−0.284529	−	0.492819i	−0.0129332	−	0.0224009i
$485$	0.490740	+	0.283329i	0.0222834	+	0.0128653i
$486$		0			0
$487$	10.1291	+	37.8022i	0.458992	+	1.71298i	0.676080	+	0.736828i	$0.263677\pi$
$487$	10.1291	+	37.8022i	0.458992	+	1.71298i	−0.217089	+	0.976152i	$0.569656\pi$
$488$	6.16787	+	23.0188i	0.279206	+	1.04201i
$489$		0			0
$490$	6.06643	−	1.63485i	0.274054	−	0.0738548i
$491$	−16.0715	+	9.27889i	−0.725297	+	0.418750i	−0.816699	−	0.577064i	$-0.804198\pi$
$491$	−16.0715	+	9.27889i	−0.725297	+	0.418750i	0.0914021	+	0.995814i	$0.470865\pi$
$492$		0			0
$493$	31.8212			1.43315
$494$	19.1210	−	17.8316i	0.860293	−	0.802282i
$495$		0			0
$496$	−0.723862	+	2.70149i	−0.0325023	+	0.121300i
$497$	−15.6100	+	20.3737i	−0.700204	+	0.913883i
$498$		0			0
$499$	3.54363	−	3.54363i	0.158635	−	0.158635i	−0.623327	−	0.781962i	$-0.714219\pi$
$499$	3.54363	−	3.54363i	0.158635	−	0.158635i	0.781962	+	0.623327i	$0.214219\pi$
$500$	4.69074	−	1.25688i	0.209776	−	0.0562094i
$501$		0			0
$502$	−17.5323	+	17.5323i	−0.782507	+	0.782507i
$503$	2.98438	+	1.72303i	0.133067	+	0.0768262i	0.565056	−	0.825053i	$-0.308855\pi$
$503$	2.98438	+	1.72303i	0.133067	+	0.0768262i	−0.431989	+	0.901879i	$0.642188\pi$
$504$		0			0
$505$	2.29754	−	8.57453i	0.102239	−	0.381561i
$506$		−	20.7805i		−	0.923808i
$507$		0			0
$508$	11.2340			0.498428
$509$	−7.93556	+	29.6159i	−0.351737	+	1.31270i	0.532803	+	0.846239i	$0.321138\pi$
$509$	−7.93556	+	29.6159i	−0.351737	+	1.31270i	−0.884541	+	0.466463i	$0.845528\pi$
$510$		0			0
$511$	−28.6274	−	3.74794i	−1.26640	−	0.165799i
$512$	15.3439	−	15.3439i	0.678111	−	0.678111i
$513$		0			0
$514$	8.48696	+	31.6738i	0.374344	+	1.39707i
$515$	−10.6116	−	10.6116i	−0.467604	−	0.467604i
$516$		0			0
$517$	0.601351	+	1.04157i	0.0264474	+	0.0458082i
$518$	1.76956	−	0.234261i	0.0777501	−	0.0102929i
$519$		0			0
$520$	5.88252	+	6.30787i	0.257966	+	0.276619i
$521$			13.0906i			0.573510i	0.958004	+	0.286755i	$0.0925766\pi$
$521$			13.0906i			0.573510i	−0.958004	+	0.286755i	$0.907423\pi$
$522$		0			0
$523$	−29.9435	+	17.2879i	−1.30934	+	0.755946i	−0.981985	−	0.188957i	$-0.939489\pi$
$523$	−29.9435	+	17.2879i	−1.30934	+	0.755946i	−0.327351	+	0.944903i	$0.606156\pi$
$524$	3.05526	−	5.29186i	0.133469	−	0.231176i
$525$		0			0
$526$	−3.79009	−	14.1448i	−0.165256	−	0.616743i
$527$	4.24513	−	1.13748i	0.184921	−	0.0495494i
$528$		0			0
$529$	4.44578	−	7.70032i	0.193295	−	0.334797i
$530$	−5.20691	−	9.01864i	−0.226174	−	0.391745i
$531$		0			0
$532$	−4.23486	−	10.2031i	−0.183604	−	0.442360i
$533$	4.61086	+	8.67118i	0.199719	+	0.375590i
$534$		0			0
$535$	1.84623	−	6.89022i	0.0798194	−	0.297890i
$536$	11.0053	+	19.0617i	0.475355	+	0.823340i
$537$		0			0
$538$	−5.30857	−	5.30857i	−0.228869	−	0.228869i
$539$	19.3244	+	11.1199i	0.832360	+	0.478969i
$540$		0			0
$541$	23.6775	+	23.6775i	1.01797	+	1.01797i	0.999835	+	0.0181382i	$0.00577388\pi$
$541$	23.6775	+	23.6775i	1.01797	+	1.01797i	0.0181382	+	0.999835i	$0.494226\pi$
$542$	−6.36638	−	3.67563i	−0.273460	−	0.157882i
$543$		0			0
$544$	−12.1200	−	3.24754i	−0.519640	−	0.139237i
$545$	−1.96847			−0.0843201
$546$		0			0
$547$	−9.25725			−0.395811			−0.197906	−	0.980221i	$-0.563414\pi$
$547$	−9.25725			−0.395811			−0.197906	+	0.980221i	$0.563414\pi$
$548$	4.04609	+	1.08415i	0.172840	+	0.0463124i
$549$		0			0
$550$	−14.0104	−	8.08893i	−0.597407	−	0.344913i
$551$	−40.3567	−	40.3567i	−1.71926	−	1.71926i
$552$		0			0
$553$	−17.4415	−	22.6964i	−0.741687	−	0.965148i
$554$	14.7744	+	14.7744i	0.627705	+	0.627705i
$555$		0			0
$556$	6.38496	+	11.0591i	0.270783	+	0.469009i
$557$	−2.46966	+	9.21689i	−0.104643	+	0.390532i	−0.998304	−	0.0582092i	$-0.981461\pi$
$557$	−2.46966	+	9.21689i	−0.104643	+	0.390532i	0.893662	+	0.448742i	$0.148128\pi$
$558$		0			0
$559$	26.8109	−	6.19058i	1.13398	−	0.261834i
$560$	−4.22775	+	1.75475i	−0.178655	+	0.0741518i
$561$		0			0
$562$	5.25728	+	9.10588i	0.221765	+	0.384108i
$563$	1.08829	−	1.88498i	0.0458661	−	0.0794424i	−0.842181	−	0.539195i	$-0.818729\pi$
$563$	1.08829	−	1.88498i	0.0458661	−	0.0794424i	0.888047	+	0.459753i	$0.152062\pi$
$564$		0			0
$565$	1.88281	−	0.504497i	0.0792104	−	0.0212244i
$566$	4.38789	+	16.3758i	0.184437	+	0.688327i
$567$		0			0
$568$	14.9356	−	25.8692i	0.626683	−	1.08545i
$569$	−20.3648	+	11.7576i	−0.853738	+	0.492906i	−0.861910	−	0.507061i	$-0.830732\pi$
$569$	−20.3648	+	11.7576i	−0.853738	+	0.492906i	0.00817222	+	0.999967i	$0.497399\pi$
$570$		0			0
$571$		−	13.2414i		−	0.554134i	−0.960851	−	0.277067i	$-0.910638\pi$
$571$		−	13.2414i		−	0.554134i	0.960851	−	0.277067i	$-0.0893624\pi$
$572$	−0.266400	+	7.63486i	−0.0111388	+	0.319230i
$573$		0			0
$574$	−8.25385	+	1.09268i	−0.344509	+	0.0456074i
$575$	−12.4139	−	21.5016i	−0.517697	−	0.896678i
$576$		0			0
$577$	1.10520	+	1.10520i	0.0460102	+	0.0460102i	0.729738	−	0.683727i	$-0.239642\pi$
$577$	1.10520	+	1.10520i	0.0460102	+	0.0460102i	−0.683727	+	0.729738i	$0.739642\pi$
$578$	1.42140	+	5.30472i	0.0591223	+	0.220647i
$579$		0			0
$580$	3.32300	−	3.32300i	0.137980	−	0.137980i
$581$	5.02013	−	38.3446i	0.208270	−	1.59080i
$582$		0			0
$583$	9.56454	−	35.6954i	0.396123	−	1.47835i
$584$	33.6017			1.39045
$585$		0			0
$586$		−	7.57788i		−	0.313039i
$587$	6.57121	−	24.5241i	0.271223	−	1.01222i	−0.687108	−	0.726556i	$-0.741120\pi$
$587$	6.57121	−	24.5241i	0.271223	−	1.01222i	0.958331	−	0.285662i	$-0.0922133\pi$
$588$		0			0
$589$	−6.82642	−	3.94124i	−0.281278	−	0.162396i
$590$	−1.55742	+	1.55742i	−0.0641179	+	0.0641179i
$591$		0			0
$592$	−1.25617	+	0.336590i	−0.0516283	+	0.0138338i
$593$	13.5799	−	13.5799i	0.557660	−	0.557660i	−0.370981	−	0.928641i	$-0.620978\pi$
$593$	13.5799	−	13.5799i	0.557660	−	0.557660i	0.928641	+	0.370981i	$0.120978\pi$
$594$		0			0
$595$	5.70976	+	4.37474i	0.234077	+	0.179347i
$596$	1.98964	−	7.42545i	0.0814989	−	0.304158i
$597$		0			0
$598$	12.4653	−	19.9499i	0.509743	−	0.815810i
$599$	6.33246			0.258737			0.129369	−	0.991597i	$-0.458705\pi$
$599$	6.33246			0.258737			0.129369	+	0.991597i	$0.458705\pi$
$600$		0			0
$601$	−20.1592	+	11.6389i	−0.822309	+	0.474760i	−0.851212	−	0.524822i	$-0.824132\pi$
$601$	−20.1592	+	11.6389i	−0.822309	+	0.474760i	0.0289030	+	0.999582i	$0.490799\pi$
$602$	−3.02824	+	23.1302i	−0.123422	+	0.942717i
$603$		0			0
$604$	−2.16849	−	8.09292i	−0.0882347	−	0.329296i
$605$	−0.172002	−	0.641921i	−0.00699288	−	0.0260978i
$606$		0			0
$607$	−9.09221	−	5.24939i	−0.369041	−	0.213066i	0.303998	−	0.952673i	$-0.401678\pi$
$607$	−9.09221	−	5.24939i	−0.369041	−	0.213066i	−0.673040	+	0.739607i	$0.735012\pi$
$608$	11.2523	+	19.4896i	0.456343	+	0.790409i
$609$		0			0
$610$			6.94641i			0.281252i
$611$	−0.0474768	+	1.36066i	−0.00192071	+	0.0550462i
$612$		0			0
$613$	−8.40441	−	2.25196i	−0.339451	−	0.0909556i	0.0850667	−	0.996375i	$-0.472890\pi$
$613$	−8.40441	−	2.25196i	−0.339451	−	0.0909556i	−0.424518	+	0.905420i	$0.639556\pi$
$614$	33.3606	−	19.2607i	1.34632	−	0.777300i
$615$		0			0
$616$	−23.9800	−	9.91264i	−0.966180	−	0.399392i
$617$	−7.98973	−	29.8181i	−0.321654	−	1.20043i	−0.917633	−	0.397430i	$-0.869902\pi$
$617$	−7.98973	−	29.8181i	−0.321654	−	1.20043i	0.595978	−	0.803000i	$-0.296764\pi$
$618$		0			0
$619$	−2.31233	+	2.31233i	−0.0929403	+	0.0929403i	−0.752048	−	0.659108i	$-0.770934\pi$
$619$	−2.31233	+	2.31233i	−0.0929403	+	0.0929403i	0.659108	+	0.752048i	$0.270934\pi$
$620$	0.324524	−	0.562091i	0.0130332	−	0.0225741i
$621$		0			0
$622$	3.24272	+	0.868885i	0.130021	+	0.0348391i
$623$	7.37733	+	17.7743i	0.295566	+	0.712112i
$624$		0			0
$625$	−16.3110			−0.652440
$626$	0.287245	−	1.07201i	0.0114806	−	0.0428462i
$627$		0			0
$628$	−1.82737	+	3.16509i	−0.0729198	+	0.126301i
$629$	1.44503	+	1.44503i	0.0576173	+	0.0576173i
$630$		0			0
$631$	5.07213	−	1.35907i	0.201918	−	0.0541039i	−0.156442	−	0.987687i	$-0.550003\pi$
$631$	5.07213	−	1.35907i	0.201918	−	0.0541039i	0.358361	+	0.933583i	$0.383336\pi$
$632$	23.5561	+	23.5561i	0.937011	+	0.937011i
$633$		0			0
$634$	33.5654	−	19.3790i	1.33305	−	0.769638i
$635$	12.6724	+	3.39556i	0.502889	+	0.134749i
$636$		0			0
$637$	11.8816	+	22.2672i	0.470765	+	0.882259i
$638$	−33.4603			−1.32471
$639$		0			0
$640$	1.85729	−	1.07231i	0.0734160	−	0.0423867i
$641$	28.4420	+	16.4210i	1.12339	+	0.648589i	0.942264	−	0.334871i	$-0.108693\pi$
$641$	28.4420	+	16.4210i	1.12339	+	0.648589i	0.181126	+	0.983460i	$0.442026\pi$
$642$		0			0
$643$	−35.7163	+	9.57017i	−1.40852	+	0.377411i	−0.881395	−	0.472380i	$-0.843395\pi$
$643$	−35.7163	+	9.57017i	−1.40852	+	0.377411i	−0.527120	+	0.849791i	$0.676728\pi$
$644$	−6.05644	−	7.88117i	−0.238657	−	0.310562i
$645$		0			0
$646$	−12.6881	+	21.9765i	−0.499208	+	0.864653i
$647$	−24.0363	−	41.6322i	−0.944966	−	1.63673i	−0.755819	−	0.654780i	$-0.772761\pi$
$647$	−24.0363	−	41.6322i	−0.944966	−	1.63673i	−0.189147	−	0.981949i	$-0.560572\pi$
$648$		0			0
$649$	−7.81588			−0.306800
$650$	−8.59821	−	16.1698i	−0.337249	−	0.634231i
$651$		0			0
$652$	−6.84958	−	1.83534i	−0.268250	−	0.0718775i
$653$	−17.6801	−	30.6228i	−0.691876	−	1.19836i	−0.971223	−	0.238174i	$-0.923451\pi$
$653$	−17.6801	−	30.6228i	−0.691876	−	1.19836i	0.279347	−	0.960190i	$-0.409882\pi$
$654$		0			0
$655$	5.04595	−	5.04595i	0.197162	−	0.197162i
$656$	5.85921	−	1.56997i	0.228764	−	0.0612970i
$657$		0			0
$658$	−1.06669	−	0.440938i	−0.0415837	−	0.0171895i
$659$	−14.6210	+	25.3243i	−0.569554	+	0.986496i	0.427056	+	0.904225i	$0.359551\pi$
$659$	−14.6210	+	25.3243i	−0.569554	+	0.986496i	−0.996610	+	0.0822711i	$0.973783\pi$
$660$		0			0
$661$	21.1225	+	5.65976i	0.821570	+	0.220139i	0.645033	−	0.764155i	$-0.276844\pi$
$661$	21.1225	+	5.65976i	0.821570	+	0.220139i	0.176537	+	0.984294i	$0.443510\pi$
$662$			14.6153i			0.568038i
$663$		0			0
$664$			45.0073i			1.74662i
$665$	−1.69312	−	12.7895i	−0.0656565	−	0.495956i
$666$		0			0
$667$	−44.4713	−	25.6755i	−1.72193	−	0.994159i
$668$	6.09168	+	6.09168i	0.235694	+	0.235694i
$669$		0			0
$670$	1.66054	+	6.19721i	0.0641521	+	0.239419i
$671$	−17.4302	+	17.4302i	−0.672886	+	0.672886i
$672$		0			0
$673$	−6.52213	+	3.76555i	−0.251409	+	0.145151i	−0.620409	−	0.784278i	$-0.713034\pi$
$673$	−6.52213	+	3.76555i	−0.251409	+	0.145151i	0.369000	+	0.929429i	$0.379700\pi$
$674$	3.83258	−	14.3034i	0.147625	−	0.550945i
$675$		0			0
$676$	−4.83555	+	7.16986i	−0.185983	+	0.275764i
$677$			30.7509i			1.18185i	0.806726	+	0.590926i	$0.201237\pi$
$677$			30.7509i			1.18185i	−0.806726	+	0.590926i	$0.798763\pi$
$678$		0			0
$679$	−1.53186	−	1.17369i	−0.0587873	−	0.0450420i
$680$	−7.24989	−	4.18573i	−0.278021	−	0.160515i
$681$		0			0
$682$	−4.46380	+	1.19607i	−0.170928	+	0.0458000i
$683$	−14.8258	+	3.97256i	−0.567293	+	0.152006i	−0.531055	−	0.847338i	$-0.678204\pi$
$683$	−14.8258	+	3.97256i	−0.567293	+	0.152006i	−0.0362380	+	0.999343i	$0.511537\pi$
$684$		0			0
$685$	4.23646	+	2.44592i	0.161867	+	0.0934538i
$686$	−21.2077	+	2.83858i	−0.809713	+	0.108377i
$687$		0			0
$688$		−	16.9956i		−	0.647951i
$689$	30.5942	−	28.5311i	1.16555	−	1.08695i
$690$		0			0
$691$	12.7049	−	47.4152i	0.483316	−	1.80376i	−0.104212	−	0.994555i	$-0.533232\pi$
$691$	12.7049	−	47.4152i	0.483316	−	1.80376i	0.587528	−	0.809204i	$-0.300101\pi$
$692$	0.574509	−	0.331693i	0.0218396	−	0.0126091i
$693$		0			0
$694$	15.1847	−	15.1847i	0.576404	−	0.576404i
$695$	3.85980	+	14.4050i	0.146411	+	0.546412i
$696$		0			0
$697$	−6.74013	−	6.74013i	−0.255301	−	0.255301i
$698$	−4.79214	−	2.76674i	−0.181385	−	0.104723i
$699$		0			0
$700$	−7.67105	+	1.01552i	−0.289939	+	0.0383832i
$701$			40.9218i			1.54559i	0.634653	+	0.772797i	$0.281143\pi$
$701$			40.9218i			1.54559i	−0.634653	+	0.772797i	$0.718857\pi$
$702$		0			0
$703$		−	3.66529i		−	0.138239i
$704$	26.4470	+	7.08646i	0.996760	+	0.267081i
$705$		0			0
$706$	−7.13933	+	12.3657i	−0.268692	+	0.465389i
$707$	−11.5490	+	27.9385i	−0.434344	+	1.05073i
$708$		0			0
$709$	−20.0521	+	5.37294i	−0.753071	+	0.201785i	−0.614880	−	0.788621i	$-0.710796\pi$
$709$	−20.0521	+	5.37294i	−0.753071	+	0.201785i	−0.138191	+	0.990406i	$0.544129\pi$
$710$	6.15685	−	6.15685i	0.231062	−	0.231062i
$711$		0			0
$712$	−11.1986	−	19.3966i	−0.419687	−	0.726919i
$713$	−6.85053	−	1.83559i	−0.256554	−	0.0687435i
$714$		0			0
$715$	−2.60820	+	8.53191i	−0.0975413	+	0.319075i
$716$	−3.75090			−0.140178
$717$		0			0
$718$	−3.43224	−	5.94482i	−0.128090	−	0.221859i
$719$	−6.50138	+	11.2607i	−0.242461	+	0.419954i	−0.961415	−	0.275103i	$-0.911288\pi$
$719$	−6.50138	+	11.2607i	−0.242461	+	0.419954i	0.718954	+	0.695058i	$0.244621\pi$
$720$		0			0
$721$	31.1417	+	40.5243i	1.15978	+	1.50920i
$722$	22.7598	−	6.09847i	0.847033	−	0.226962i
$723$		0			0
$724$	12.3918	+	7.15442i	0.460539	+	0.265892i
$725$	−34.6213	+	19.9886i	−1.28580	+	0.742359i
$726$		0			0
$727$	9.09604			0.337353			0.168677	−	0.985671i	$-0.446051\pi$
$727$	9.09604			0.337353			0.168677	+	0.985671i	$0.446051\pi$
$728$	−17.0752	−	23.9008i	−0.632851	−	0.885824i
$729$		0			0
$730$	9.46076	+	2.53500i	0.350159	+	0.0938247i
$731$	−23.1289	+	13.3535i	−0.855453	+	0.493896i
$732$		0			0
$733$	24.5299	+	24.5299i	0.906033	+	0.906033i	0.995949	−	0.0899161i	$-0.0286599\pi$
$733$	24.5299	+	24.5299i	0.906033	+	0.906033i	−0.0899161	+	0.995949i	$0.528660\pi$
$734$	−6.51649	+	1.74609i	−0.240528	+	0.0644493i
$735$		0			0
$736$	14.3178	+	14.3178i	0.527760	+	0.527760i
$737$	−11.3836	+	19.7170i	−0.419321	+	0.726285i
$738$		0			0
$739$	−12.5301	+	46.7628i	−0.460926	+	1.72020i	0.209130	+	0.977888i	$0.432937\pi$
$739$	−12.5301	+	46.7628i	−0.460926	+	1.72020i	−0.670056	+	0.742311i	$0.733730\pi$
$740$	0.301802			0.0110945
$741$		0			0
$742$	13.5955	+	32.7558i	0.499106	+	1.20250i
$743$	11.2679	+	3.01923i	0.413379	+	0.110765i	0.459514	−	0.888171i	$-0.348024\pi$
$743$	11.2679	+	3.01923i	0.413379	+	0.110765i	−0.0461346	+	0.998935i	$0.514690\pi$
$744$		0			0
$745$	4.48879	−	7.77482i	0.164457	−	0.284847i
$746$	−8.46019	+	8.46019i	−0.309749	+	0.309749i
$747$		0			0
$748$	−1.91909	−	7.16214i	−0.0701689	−	0.261874i
$749$	−9.28039	+	22.4505i	−0.339098	+	0.820322i
$750$		0			0
$751$	−12.9544	+	7.47922i	−0.472712	+	0.272921i	−0.717374	−	0.696688i	$-0.754656\pi$
$751$	−12.9544	+	7.47922i	−0.472712	+	0.272921i	0.244662	+	0.969608i	$0.421323\pi$
$752$	0.812272	+	0.217648i	0.0296205	+	0.00793679i
$753$		0			0
$754$	−32.1227	−	20.0713i	−1.16984	−	0.730952i
$755$		−	9.78458i		−	0.356097i
$756$		0			0
$757$	13.2377	+	22.9284i	0.481134	+	0.833348i	0.999766	−	0.0216496i	$-0.00689182\pi$
$757$	13.2377	+	22.9284i	0.481134	+	0.833348i	−0.518632	+	0.854998i	$0.673558\pi$
$758$	7.01097	+	4.04778i	0.254650	+	0.147022i
$759$		0			0
$760$	3.88608	+	14.5031i	0.140963	+	0.526081i
$761$	−10.6129	−	39.6079i	−0.384718	−	1.43579i	−0.838611	−	0.544731i	$-0.816632\pi$
$761$	−10.6129	−	39.6079i	−0.384718	−	1.43579i	0.453893	−	0.891056i	$-0.350035\pi$
$762$		0			0
$763$	6.64708	+	0.870244i	0.240640	+	0.0315050i
$764$	−5.06055	+	2.92171i	−0.183084	+	0.105704i
$765$		0			0
$766$	−8.54114			−0.308604
$767$	−7.50344	−	4.68838i	−0.270934	−	0.169288i
$768$		0			0
$769$	−0.837092	+	3.12407i	−0.0301863	+	0.112657i	−0.979375	−	0.202050i	$-0.935240\pi$
$769$	−0.837092	+	3.12407i	−0.0301863	+	0.112657i	0.949189	+	0.314707i	$0.101906\pi$
$770$	−6.00387	−	4.60008i	−0.216365	−	0.165775i
$771$		0			0
$772$	−0.453085	+	0.453085i	−0.0163069	+	0.0163069i
$773$	−20.3857	+	5.46232i	−0.733221	+	0.196466i	−0.606063	−	0.795417i	$-0.707252\pi$
$773$	−20.3857	+	5.46232i	−0.733221	+	0.196466i	−0.127158	+	0.991882i	$0.540585\pi$
$774$		0			0
$775$	−3.90417	+	3.90417i	−0.140242	+	0.140242i
$776$	1.94506	+	1.12298i	0.0698234	+	0.0403126i
$777$		0			0
$778$	−3.05836	+	11.4140i	−0.109648	+	0.409211i
$779$			17.0962i			0.612533i
$780$		0			0
$781$	30.8980			1.10562
$782$	−5.90937	+	22.0541i	−0.211319	+	0.788652i
$783$		0			0
$784$	15.0519	−	4.05634i	0.537568	−	0.144869i
$785$	−3.01801	+	3.01801i	−0.107718	+	0.107718i
$786$		0			0
$787$	−12.5317	−	46.7690i	−0.446707	−	1.66713i	−0.711389	−	0.702798i	$-0.751934\pi$
$787$	−12.5317	−	46.7690i	−0.446707	−	1.66713i	0.264682	−	0.964336i	$-0.414733\pi$
$788$	−8.10003	−	8.10003i	−0.288552	−	0.288552i
$789$		0			0
$790$	4.85523	+	8.40951i	0.172741	+	0.299197i
$791$	−6.58084	+	0.871197i	−0.233988	+	0.0309762i
$792$		0			0
$793$	−27.1890	+	6.27789i	−0.965511	+	0.222934i
$794$			32.5970i			1.15682i
$795$		0			0
$796$	1.29689	−	0.748760i	0.0459671	−	0.0265391i
$797$	−22.9487	+	39.7483i	−0.812884	+	1.40796i	0.0979535	+	0.995191i	$0.468770\pi$
$797$	−22.9487	+	39.7483i	−0.812884	+	1.40796i	−0.910837	+	0.412765i	$0.864563\pi$
$798$		0			0
$799$	−0.342013	−	1.27641i	−0.0120995	−	0.0451561i
$800$	15.2264	−	4.07991i	0.538336	−	0.144247i
$801$		0			0
$802$	4.07838	−	7.06395i	0.144012	−	0.249437i
$803$	17.3784	+	30.1003i	0.613271	+	1.06222i
$804$		0			0
$805$	−4.44976	−	10.7209i	−0.156834	−	0.377861i
$806$	−5.00283	−	1.52937i	−0.176217	−	0.0538696i
$807$		0			0
$808$	9.10633	−	33.9853i	0.320359	−	1.19560i
$809$	−22.7833	−	39.4619i	−0.801019	−	1.38740i	−0.918946	−	0.394383i	$-0.870958\pi$
$809$	−22.7833	−	39.4619i	−0.801019	−	1.38740i	0.117928	−	0.993022i	$-0.462375\pi$
$810$		0			0
$811$	−15.7365	−	15.7365i	−0.552584	−	0.552584i	0.374602	−	0.927186i	$-0.377779\pi$
$811$	−15.7365	−	15.7365i	−0.552584	−	0.552584i	−0.927186	+	0.374602i	$0.877779\pi$
$812$	−12.6901	+	9.75192i	−0.445334	+	0.342225i
$813$		0			0
$814$	−1.51947	−	1.51947i	−0.0532573	−	0.0532573i
$815$	−7.17186	−	4.14067i	−0.251219	−	0.145041i
$816$		0			0
$817$	46.2683	+	12.3975i	1.61872	+	0.433735i
$818$	36.3605			1.27132
$819$		0			0
$820$	−1.40771			−0.0491592
$821$	51.3616	+	13.7623i	1.79253	+	0.480307i	0.992772	−	0.120014i	$-0.0382941\pi$
$821$	51.3616	+	13.7623i	1.79253	+	0.480307i	0.799759	+	0.600322i	$0.204961\pi$
$822$		0			0
$823$	0.0980900	+	0.0566323i	0.00341920	+	0.00197408i	0.501709	−	0.865037i	$-0.332705\pi$
$823$	0.0980900	+	0.0566323i	0.00341920	+	0.00197408i	−0.498289	+	0.867011i	$0.666038\pi$
$824$	−42.0593	−	42.0593i	−1.46521	−	1.46521i
$825$		0			0
$826$	5.94756	−	4.57052i	0.206942	−	0.159029i
$827$	−5.18917	−	5.18917i	−0.180445	−	0.180445i	0.611105	−	0.791550i	$-0.290725\pi$
$827$	−5.18917	−	5.18917i	−0.180445	−	0.180445i	−0.791550	+	0.611105i	$0.790725\pi$
$828$		0			0
$829$	−2.19576	−	3.80317i	−0.0762620	−	0.132090i	0.825372	−	0.564589i	$-0.190965\pi$
$829$	−2.19576	−	3.80317i	−0.0762620	−	0.132090i	−0.901634	+	0.432499i	$0.857632\pi$
$830$	−3.39548	+	12.6721i	−0.117859	+	0.439855i
$831$		0			0
$832$	21.1390	+	22.6675i	0.732863	+	0.785855i
$833$	−17.3465	−	17.2967i	−0.601021	−	0.599295i
$834$		0			0
$835$	5.03040	+	8.71291i	0.174084	+	0.301523i
$836$	−6.64943	+	11.5171i	−0.229975	+	0.398329i
$837$		0			0
$838$	−26.3114	+	7.05011i	−0.908911	+	0.243542i
$839$	−0.0267890	−	0.0999778i	−0.000924858	−	0.00345162i	0.965462	−	0.260544i	$-0.0839021\pi$
$839$	−0.0267890	−	0.0999778i	−0.000924858	−	0.00345162i	−0.966387	+	0.257093i	$0.917235\pi$
$840$		0			0
$841$	−26.8420	+	46.4917i	−0.925587	+	1.60316i
$842$	6.55517	−	3.78463i	0.225906	−	0.130427i
$843$		0			0
$844$			13.7769i			0.474220i
$845$	−7.62183	+	6.62631i	−0.262199	+	0.227952i
$846$		0			0
$847$	0.297024	+	2.24366i	0.0102059	+	0.0770930i
$848$	−12.9193	−	22.3768i	−0.443650	−	0.768424i
$849$		0			0
$850$	12.5688	+	12.5688i	0.431107	+	0.431107i
$851$	−0.853536	−	3.18544i	−0.0292588	−	0.109195i
$852$		0			0
$853$	30.7045	−	30.7045i	1.05130	−	1.05130i	0.0526924	−	0.998611i	$-0.483220\pi$
$853$	30.7045	−	30.7045i	1.05130	−	1.05130i	0.998611	−	0.0526924i	$-0.0167803\pi$
$854$	3.07094	−	23.4564i	0.105086	−	0.802662i
$855$		0			0
$856$	7.31756	−	27.3095i	0.250109	−	0.933419i
$857$	−46.5367			−1.58966			−0.794831	−	0.606831i	$-0.792441\pi$
$857$	−46.5367			−1.58966			−0.794831	+	0.606831i	$0.792441\pi$
$858$		0			0
$859$		−	34.8981i		−	1.19071i	−0.803464	−	0.595354i	$-0.797012\pi$
$859$		−	34.8981i		−	1.19071i	0.803464	−	0.595354i	$-0.202988\pi$
$860$	−1.02082	+	3.80975i	−0.0348097	+	0.129912i
$861$		0			0
$862$	−28.8046	−	16.6303i	−0.981088	−	0.566431i
$863$	−33.6057	+	33.6057i	−1.14395	+	1.14395i	−0.156232	+	0.987720i	$0.549935\pi$
$863$	−33.6057	+	33.6057i	−1.14395	+	1.14395i	−0.987720	+	0.156232i	$0.950065\pi$
$864$		0			0
$865$	0.748326	−	0.200513i	0.0254438	−	0.00681766i
$866$	−3.13806	+	3.13806i	−0.106636	+	0.106636i
$867$		0			0
$868$	−1.34434	+	1.75458i	−0.0456298	+	0.0595544i
$869$	−8.91854	+	33.2844i	−0.302541	+	1.12910i
$870$		0			0
$871$	−22.7559	+	12.1003i	−0.771053	+	0.410004i
$872$	−7.80207			−0.264212
$873$		0			0
$874$	35.4643	−	20.4753i	1.19960	−	0.692587i
$875$	−19.1505	−	2.50721i	−0.647404	−	0.0847591i
$876$		0			0
$877$	0.133090	+	0.496699i	0.00449413	+	0.0167723i	0.968136	−	0.250423i	$-0.0805697\pi$
$877$	0.133090	+	0.496699i	0.00449413	+	0.0167723i	−0.963642	+	0.267195i	$0.913903\pi$
$878$	4.36033	+	16.2730i	0.147154	+	0.549186i
$879$		0			0
$880$	4.77224	+	2.75525i	0.160872	+	0.0928796i
$881$	−18.3777	−	31.8310i	−0.619159	−	1.07242i	−0.989639	−	0.143575i	$-0.954140\pi$
$881$	−18.3777	−	31.8310i	−0.619159	−	1.07242i	0.370480	−	0.928840i	$-0.379193\pi$
$882$		0			0
$883$			25.7950i			0.868071i	0.900896	+	0.434036i	$0.142911\pi$
$883$			25.7950i			0.868071i	−0.900896	+	0.434036i	$0.857089\pi$
$884$	2.45386	−	8.02701i	0.0825321	−	0.269978i
$885$		0			0
$886$	−35.9403	−	9.63019i	−1.20744	−	0.323532i
$887$	32.5539	−	18.7950i	1.09305	−	0.631074i	0.158665	−	0.987332i	$-0.449281\pi$
$887$	32.5539	−	18.7950i	1.09305	−	0.631074i	0.934388	+	0.356258i	$0.115948\pi$
$888$		0			0
$889$	−41.2906	−	17.0684i	−1.38484	−	0.572455i
$890$	−1.68971	−	6.30610i	−0.0566393	−	0.211381i
$891$		0			0
$892$	10.7650	−	10.7650i	0.360438	−	0.360438i
$893$	−1.18503	+	2.05254i	−0.0396557	+	0.0686856i
$894$		0			0
$895$	−4.23117	−	1.13374i	−0.141432	−	0.0378967i
$896$	−6.74571	+	2.79985i	−0.225358	+	0.0935363i
$897$		0			0
$898$	23.1496			0.772512
$899$	−2.95562	+	11.0305i	−0.0985756	+	0.367889i
$900$		0			0
$901$	−20.3014	+	35.1631i	−0.676338	+	1.17145i
$902$	7.08732	+	7.08732i	0.235982	+	0.235982i
$903$		0			0
$904$	7.46254	−	1.99958i	0.248200	−	0.0665051i
$905$	11.8160	+	11.8160i	0.392777	+	0.392777i
$906$		0			0
$907$	−25.7384	+	14.8601i	−0.854631	+	0.493421i	−0.862211	−	0.506550i	$-0.830921\pi$
$907$	−25.7384	+	14.8601i	−0.854631	+	0.493421i	0.00757996	+	0.999971i	$0.497587\pi$
$908$	−10.0509	−	2.69312i	−0.333550	−	0.0893745i
$909$		0			0
$910$	−3.00450	−	8.01764i	−0.0995981	−	0.265782i
$911$	35.4837			1.17563			0.587814	−	0.808996i	$-0.299989\pi$
$911$	35.4837			1.17563			0.587814	+	0.808996i	$0.299989\pi$
$912$		0			0
$913$	−40.3175	+	23.2773i	−1.33431	+	0.770366i
$914$	15.0259	+	8.67519i	0.497012	+	0.286950i
$915$		0			0
$916$	−3.28209	+	0.879433i	−0.108443	+	0.0290573i
$917$	−19.2698	+	14.8082i	−0.636344	+	0.489011i
$918$		0			0
$919$	0.276560	−	0.479016i	0.00912288	−	0.0158013i	−0.861428	−	0.507880i	$-0.830429\pi$
$919$	0.276560	−	0.479016i	0.00912288	−	0.0158013i	0.870551	+	0.492079i	$0.163763\pi$
$920$	6.75466	+	11.6994i	0.222694	+	0.385718i
$921$		0			0
$922$	35.8242			1.17981
$923$	29.6629	+	18.5343i	0.976367	+	0.610063i
$924$		0			0
$925$	−2.47990	−	0.664486i	−0.0815384	−	0.0218482i
$926$	2.95374	+	5.11603i	0.0970659	+	0.168123i
$927$		0			0
$928$	23.0541	−	23.0541i	0.756788	−	0.756788i
$929$	0.202032	−	0.0541344i	0.00662846	−	0.00177609i	−0.255503	−	0.966808i	$-0.582241\pi$
$929$	0.202032	−	0.0541344i	0.00662846	−	0.00177609i	0.262132	+	0.965032i	$0.415574\pi$
$930$		0			0
$931$	0.0631567	+	43.9357i	0.00206988	+	1.43994i
$932$	1.05991	−	1.83582i	0.0347185	−	0.0601341i
$933$		0			0
$934$	19.7273	+	5.28590i	0.645496	+	0.172960i
$935$		−	8.65924i		−	0.283187i
$936$		0			0
$937$		−	7.20471i		−	0.235368i	−0.993051	−	0.117684i	$-0.962453\pi$
$937$		−	7.20471i		−	0.235368i	0.993051	−	0.117684i	$-0.0375470\pi$
$938$	−2.86752	−	21.6606i	−0.0936278	−	0.707245i
$939$		0			0
$940$	−0.169007	−	0.0975764i	−0.00551241	−	0.00318259i
$941$	−27.6042	−	27.6042i	−0.899870	−	0.899870i	0.0955544	−	0.995424i	$-0.469538\pi$
$941$	−27.6042	−	27.6042i	−0.899870	−	0.899870i	−0.995424	+	0.0955544i	$0.969538\pi$
$942$		0			0
$943$	3.98118	+	14.8580i	0.129645	+	0.483842i
$944$	−3.86423	+	3.86423i	−0.125770	+	0.125770i
$945$		0			0
$946$	24.3203	−	14.0413i	0.790721	−	0.456523i
$947$	−10.3004	+	38.4417i	−0.334719	+	1.24919i	0.569455	+	0.822022i	$0.307154\pi$
$947$	−10.3004	+	38.4417i	−0.334719	+	1.24919i	−0.904174	+	0.427164i	$0.859513\pi$
$948$		0			0
$949$	−1.37203	+	39.3215i	−0.0445380	+	1.27643i
$950$		−	31.8804i		−	1.03434i
$951$		0			0
$952$	22.6307	+	17.3393i	0.733466	+	0.561971i
$953$	−32.2352	−	18.6110i	−1.04420	−	0.602870i	−0.123181	−	0.992384i	$-0.539310\pi$
$953$	−32.2352	−	18.6110i	−1.04420	−	0.602870i	−0.921020	+	0.389514i	$0.872643\pi$
$954$		0			0
$955$	−6.59162	+	1.76622i	−0.213300	+	0.0571535i
$956$	−1.47140	+	0.394261i	−0.0475885	+	0.0127513i
$957$		0			0
$958$	−19.8135	−	11.4393i	−0.640145	−	0.369588i
$959$	−13.2242	−	10.1322i	−0.427032	−	0.327186i
$960$		0			0
$961$		−	29.4228i		−	0.949123i
$962$	−0.547271	−	2.37019i	−0.0176447	−	0.0764179i
$963$		0			0
$964$	−1.09260	+	4.07764i	−0.0351903	+	0.131332i
$965$	−0.648047	+	0.374150i	−0.0208614	+	0.0120443i
$966$		0			0
$967$	3.64583	−	3.64583i	0.117242	−	0.117242i	−0.646052	−	0.763294i	$-0.723581\pi$
$967$	3.64583	−	3.64583i	0.117242	−	0.117242i	0.763294	+	0.646052i	$0.223581\pi$
$968$	−0.681733	−	2.54426i	−0.0219117	−	0.0817757i
$969$		0			0
$970$	0.462922	+	0.462922i	0.0148635	+	0.0148635i
$971$	25.7260	+	14.8529i	0.825587	+	0.476653i	0.852339	−	0.522989i	$-0.175183\pi$
$971$	25.7260	+	14.8529i	0.825587	+	0.476653i	−0.0267525	+	0.999642i	$0.508517\pi$
$972$		0			0
$973$	−6.66534	−	50.3487i	−0.213681	−	1.61410i
$974$			45.2142i			1.44876i
$975$		0			0
$976$			17.2353i			0.551687i
$977$	−44.1801	−	11.8380i	−1.41345	−	0.378732i	−0.530293	−	0.847815i	$-0.677918\pi$
$977$	−44.1801	−	11.8380i	−1.41345	−	0.378732i	−0.883154	+	0.469083i	$0.844585\pi$
$978$		0			0
$979$	11.5836	−	20.0634i	0.370214	−	0.641230i
$980$	−3.61769	+	0.00520036i	−0.115563	+	0.000166119i
$981$		0			0
$982$	−20.7096	+	5.54912i	−0.660870	+	0.177080i
$983$	36.4493	−	36.4493i	1.16255	−	1.16255i	0.178637	−	0.983915i	$-0.442831\pi$
$983$	36.4493	−	36.4493i	1.16255	−	1.16255i	0.983915	−	0.178637i	$-0.0571687\pi$
$984$		0			0
$985$	−6.68886	−	11.5854i	−0.213125	−	0.369143i
$986$	35.5109	+	9.51512i	1.13090	+	0.303023i
$987$		0			0
$988$	−13.2922	+	7.06807i	−0.422882	+	0.224865i
$989$	43.0980			1.37044
$990$		0			0
$991$	−1.36323	−	2.36118i	−0.0433043	−	0.0750052i	0.843561	−	0.537034i	$-0.180455\pi$
$991$	−1.36323	−	2.36118i	−0.0433043	−	0.0750052i	−0.886865	+	0.462028i	$0.847122\pi$
$992$	2.25146	−	3.89965i	0.0714840	−	0.123814i
$993$		0			0
$994$	−23.5121	+	18.0684i	−0.745759	+	0.573093i
$995$	1.68926	−	0.452636i	0.0535532	−	0.0143495i
$996$		0			0
$997$	−9.41930	−	5.43824i	−0.298312	−	0.172231i	0.343372	−	0.939199i	$-0.388431\pi$
$997$	−9.41930	−	5.43824i	−0.298312	−	0.172231i	−0.641684	+	0.766969i	$0.721764\pi$
$998$	5.01414	−	2.89492i	0.158720	−	0.0916370i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.e.496.5		32
3.2	odd	2		273.2.by.d.223.4	yes	32
7.6	odd	2		819.2.fm.f.496.5		32
13.7	odd	12		819.2.fm.f.748.5		32
21.20	even	2		273.2.by.c.223.4	yes	32
39.20	even	12		273.2.by.c.202.4	✓	32
91.20	even	12	inner	819.2.fm.e.748.5		32
273.20	odd	12		273.2.by.d.202.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.4	✓	32	39.20	even	12
273.2.by.c.223.4	yes	32	21.20	even	2
273.2.by.d.202.4	yes	32	273.20	odd	12
273.2.by.d.223.4	yes	32	3.2	odd	2
819.2.fm.e.496.5		32	1.1	even	1	trivial
819.2.fm.e.748.5		32	91.20	even	12	inner
819.2.fm.f.496.5		32	7.6	odd	2
819.2.fm.f.748.5		32	13.7	odd	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11595 + 0.299019i) q^{2} +(-0.576113 - 0.332619i) q^{4} +(-0.549341 - 0.549341i) q^{5} +(1.61214 + 2.09786i) q^{7} +(-2.17732 - 2.17732i) q^{8} +O(q^{10})\)	\(q+(1.11595 + 0.299019i) q^{2} +(-0.576113 - 0.332619i) q^{4} +(-0.549341 - 0.549341i) q^{5} +(1.61214 + 2.09786i) q^{7} +(-2.17732 - 2.17732i) q^{8} +(-0.448776 - 0.777302i) q^{10} +(0.824353 - 3.07653i) q^{11} +(2.63686 - 2.45905i) q^{13} +(1.17177 + 2.82317i) q^{14} +(-1.11349 - 1.92862i) q^{16} +(-1.74975 + 3.03065i) q^{17} +(6.06267 - 1.62449i) q^{19} +(0.133761 + 0.499204i) q^{20} +(1.83988 - 3.18676i) q^{22} +(4.89067 - 2.82363i) q^{23} -4.39645i q^{25} +(3.67792 - 1.95572i) q^{26} +(-0.230987 - 1.74483i) q^{28} +(-4.54654 - 7.87483i) q^{29} +(-0.888029 - 0.888029i) q^{31} +(0.928002 + 3.46335i) q^{32} +(-2.85886 + 2.85886i) q^{34} +(0.266825 - 2.03806i) q^{35} +(0.151142 - 0.564068i) q^{37} +7.25141 q^{38} +2.39219i q^{40} +(-0.704976 + 2.63101i) q^{41} +(6.60921 + 3.81583i) q^{43} +(-1.49823 + 1.49823i) q^{44} +(6.30208 - 1.68864i) q^{46} +(-0.267009 + 0.267009i) q^{47} +(-1.80201 + 6.76408i) q^{49} +(1.31462 - 4.90623i) q^{50} +(-2.33706 + 0.539622i) q^{52} +11.6025 q^{53} +(-2.14292 + 1.23721i) q^{55} +(1.05756 - 8.07786i) q^{56} +(-2.71900 - 10.1474i) q^{58} +(-0.635122 - 2.37031i) q^{59} +(-6.70242 - 3.86964i) q^{61} +(-0.725461 - 1.25654i) q^{62} +8.59639i q^{64} +(-2.79940 - 0.0976783i) q^{65} +(-6.90457 - 1.85007i) q^{67} +(2.01610 - 1.16400i) q^{68} +(0.907181 - 2.19459i) q^{70} +(2.51079 + 9.37039i) q^{71} +(-7.71628 + 7.71628i) q^{73} +(0.337334 - 0.584279i) q^{74} +(-4.03312 - 1.08067i) q^{76} +(7.78309 - 3.23042i) q^{77} -10.8188 q^{79} +(-0.447786 + 1.67116i) q^{80} +(-1.57344 + 2.72528i) q^{82} +(-10.3355 - 10.3355i) q^{83} +(2.62607 - 0.703654i) q^{85} +(6.23456 + 6.23456i) q^{86} +(-8.49348 + 4.90371i) q^{88} +(7.02589 + 1.88258i) q^{89} +(9.40974 + 1.56743i) q^{91} -3.75677 q^{92} +(-0.377810 + 0.218129i) q^{94} +(-4.22288 - 2.43808i) q^{95} +(-0.704543 + 0.188782i) q^{97} +(-4.03355 + 7.00956i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

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