LMFDB - Embedded newform 819.2.fm.f.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.f.748.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11595 + 0.299019i) q^{2} +(-0.576113 - 0.332619i) q^{4} +(0.549341 + 0.549341i) q^{5} +(0.347225 - 2.62287i) q^{7} +(-2.17732 - 2.17732i) q^{8} +O(q^{10})$	\(q+(1.11595 + 0.299019i) q^{2} +(-0.576113 - 0.332619i) q^{4} +(0.549341 + 0.549341i) q^{5} +(0.347225 - 2.62287i) q^{7} +(-2.17732 - 2.17732i) q^{8} +(0.448776 + 0.777302i) q^{10} +(0.824353 - 3.07653i) q^{11} +(-2.63686 + 2.45905i) q^{13} +(1.17177 - 2.82317i) q^{14} +(-1.11349 - 1.92862i) q^{16} +(1.74975 - 3.03065i) q^{17} +(-6.06267 + 1.62449i) q^{19} +(-0.133761 - 0.499204i) q^{20} +(1.83988 - 3.18676i) q^{22} +(4.89067 - 2.82363i) q^{23} -4.39645i q^{25} +(-3.67792 + 1.95572i) q^{26} +(-1.07246 + 1.39557i) q^{28} +(-4.54654 - 7.87483i) q^{29} +(0.888029 + 0.888029i) q^{31} +(0.928002 + 3.46335i) q^{32} +(2.85886 - 2.85886i) q^{34} +(1.63160 - 1.25010i) q^{35} +(0.151142 - 0.564068i) q^{37} -7.25141 q^{38} -2.39219i q^{40} +(0.704976 - 2.63101i) q^{41} +(6.60921 + 3.81583i) q^{43} +(-1.49823 + 1.49823i) q^{44} +(6.30208 - 1.68864i) q^{46} +(0.267009 - 0.267009i) q^{47} +(-6.75887 - 1.82145i) q^{49} +(1.31462 - 4.90623i) q^{50} +(2.33706 - 0.539622i) q^{52} +11.6025 q^{53} +(2.14292 - 1.23721i) q^{55} +(-6.46685 + 4.95481i) q^{56} +(-2.71900 - 10.1474i) q^{58} +(0.635122 + 2.37031i) q^{59} +(6.70242 + 3.86964i) q^{61} +(0.725461 + 1.25654i) q^{62} +8.59639i q^{64} +(-2.79940 - 0.0976783i) q^{65} +(-6.90457 - 1.85007i) q^{67} +(-2.01610 + 1.16400i) q^{68} +(2.19459 - 0.907181i) q^{70} +(2.51079 + 9.37039i) q^{71} +(7.71628 - 7.71628i) q^{73} +(0.337334 - 0.584279i) q^{74} +(4.03312 + 1.08067i) q^{76} +(-7.78309 - 3.23042i) q^{77} -10.8188 q^{79} +(0.447786 - 1.67116i) q^{80} +(1.57344 - 2.72528i) q^{82} +(10.3355 + 10.3355i) q^{83} +(2.62607 - 0.703654i) q^{85} +(6.23456 + 6.23456i) q^{86} +(-8.49348 + 4.90371i) q^{88} +(-7.02589 - 1.88258i) q^{89} +(5.53419 + 7.76999i) q^{91} -3.75677 q^{92} +(0.377810 - 0.218129i) q^{94} +(-4.22288 - 2.43808i) q^{95} +(0.704543 - 0.188782i) q^{97} +(-6.99793 - 4.05368i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 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} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+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 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * 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 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

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	0.819192	−	0.573519i	$-0.194422\pi$
$5$	0.549341	+	0.549341i	0.245673	+	0.245673i	−0.573519	+	0.819192i	$0.694422\pi$
$6$		0			0
$7$	0.347225	−	2.62287i	0.131239	−	0.991351i
$7$	0.347225	−	2.62287i	0.131239	−	0.991351i
$8$	−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	−0.571986	−	0.820263i	$-0.693827\pi$
$17$	1.74975	−	3.03065i	0.424376	−	0.735041i	0.996362	+	0.0852225i	$0.0271601\pi$
$18$		0			0
$19$	−6.06267	+	1.62449i	−1.39087	+	0.372683i	−0.875058	−	0.484017i	$-0.839177\pi$
$19$	−6.06267	+	1.62449i	−1.39087	+	0.372683i	−0.515814	+	0.856701i	$0.672510\pi$
$20$	−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
$28$	−1.07246	+	1.39557i	−0.202675	+	0.263739i
$29$	−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	0.782343	−	0.622848i	$-0.214025\pi$
$31$	0.888029	+	0.888029i	0.159495	+	0.159495i	−0.622848	+	0.782343i	$0.714025\pi$
$32$	0.928002	+	3.46335i	0.164049	+	0.612239i
$33$		0			0
$34$	2.85886	−	2.85886i	0.490290	−	0.490290i
$35$	1.63160	−	1.25010i	0.275790	−	0.211306i
$36$		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	−0.888775	−	0.458344i	$-0.848443\pi$
$41$	0.704976	−	2.63101i	0.110099	−	0.410894i	0.998874	+	0.0474499i	$0.0151095\pi$
$42$		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	−0.687365	−	0.726312i	$-0.741233\pi$
$47$	0.267009	−	0.267009i	0.0389472	−	0.0389472i	0.726312	+	0.687365i	$0.241233\pi$
$48$		0			0
$49$	−6.75887	−	1.82145i	−0.965553	−	0.260207i
$50$	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
$56$	−6.46685	+	4.95481i	−0.864169	+	0.662114i
$57$		0			0
$58$	−2.71900	−	10.1474i	−0.357022	−	1.33242i
$59$	0.635122	+	2.37031i	0.0826858	+	0.308588i	0.994866	−	0.101202i	$-0.0322688\pi$
$59$	0.635122	+	2.37031i	0.0826858	+	0.308588i	−0.912180	+	0.409790i	$0.865602\pi$
$60$		0			0
$61$	6.70242	+	3.86964i	0.858157	+	0.495457i	0.863395	−	0.504529i	$-0.168334\pi$
$61$	6.70242	+	3.86964i	0.858157	+	0.495457i	−0.00523788	+	0.999986i	$0.501667\pi$
$62$	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
$70$	2.19459	−	0.907181i	0.262303	−	0.108429i
$71$	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	−0.0925826	−	0.995705i	$-0.529512\pi$
$73$	7.71628	−	7.71628i	0.903122	−	0.903122i	0.995705	+	0.0925826i	$0.0295122\pi$
$74$	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	$0.0463311\pi$
$83$	10.3355	+	10.3355i	1.13447	+	1.13447i	0.145040	+	0.989426i	$0.453669\pi$
$84$		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	−0.133558	−	0.991041i	$-0.542640\pi$
$89$	−7.02589	−	1.88258i	−0.744743	−	0.199553i	−0.611185	+	0.791488i	$0.709307\pi$
$90$		0			0
$91$	5.53419	+	7.76999i	0.580141	+	0.814516i
$92$	−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	−0.222874	−	0.974847i	$-0.571544\pi$
$97$	0.704543	−	0.188782i	0.0715355	−	0.0191679i	0.294409	+	0.955679i	$0.404877\pi$
$98$	−6.99793	−	4.05368i	−0.706898	−	0.409484i
$99$		0			0
$100$	−1.46234	+	2.53285i	−0.146234	+	0.253285i
$101$	−5.71320	−	9.89554i	−0.568484	−	0.984643i	−0.996716	−	0.0809746i	$-0.974197\pi$
$101$	−5.71320	−	9.89554i	−0.568484	−	0.984643i	0.428232	−	0.903669i	$-0.359137\pi$
$102$		0			0
$103$	−19.3170			−1.90336			−0.951679	−	0.307094i	$-0.900643\pi$
$103$	−19.3170			−1.90336			−0.951679	+	0.307094i	$0.900643\pi$
$104$	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
$112$	−5.44516	+	2.25088i	−0.514519	+	0.212688i
$113$	−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
$119$	−7.34144	−	5.64167i	−0.672989	−	0.517171i
$120$		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	$-0.868569\pi$
$131$		−	9.18546i		−	0.802537i	0.915960	−	0.401269i	$-0.131431\pi$
$132$		0			0
$133$	2.15571	+	16.4657i	0.186923	+	1.42775i
$134$	−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	0.995393	−	0.0958840i	$-0.0305678\pi$
$139$	16.6243	+	9.59802i	1.41005	+	0.814093i	0.414658	+	0.909977i	$0.363901\pi$
$140$	−1.35579	+	0.177502i	−0.114585	+	0.0150017i
$141$		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
$154$	−7.71960	−	5.93228i	−0.622063	−	0.478037i
$155$			0.975662i			0.0783671i
$156$		0			0
$157$			5.49387i			0.438459i	0.975673	+	0.219229i	$0.0703543\pi$
$157$			5.49387i			0.438459i	−0.975673	+	0.219229i	$0.929646\pi$
$158$	−12.0733	−	3.23503i	−0.960501	−	0.257365i
$159$		0			0
$160$	−1.39277	+	2.41235i	−0.110108	+	0.190713i
$161$	−5.70785	−	13.8080i	−0.449841	−	1.08822i
$162$		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	0.707969	−	0.706243i	$-0.249611\pi$
$167$	12.5089	+	3.35175i	0.967967	+	0.259366i	0.259998	+	0.965609i	$0.416278\pi$
$168$		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	−0.846449	−	0.532470i	$-0.821264\pi$
$173$	0.498608	−	0.863615i	0.0379085	−	0.0656594i	0.884357	+	0.466811i	$0.154597\pi$
$174$		0			0
$175$	−11.5313	−	1.52656i	−0.871684	−	0.115397i
$176$	−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	$-0.205156\pi$
$181$	21.5094			1.59878			0.799390	+	0.600813i	$0.205156\pi$
$182$	3.85252	+	10.3258i	0.285568	+	0.765397i
$183$		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	−0.823370	−	0.567505i	$-0.807909\pi$
$199$	1.12555	−	1.94951i	0.0797883	−	0.138197i	0.903159	+	0.429307i	$0.141242\pi$
$200$	−9.57249	+	9.57249i	−0.676877	+	0.676877i
$201$		0			0
$202$	−3.41670	−	12.7513i	−0.240398	−	0.897179i
$203$	−22.2333	+	9.19063i	−1.56047	+	0.645056i
$204$		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
$217$	2.63753	−	2.02084i	0.179047	−	0.137183i
$218$	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	$-0.638789\pi$
$223$	5.92307	−	22.1052i	0.396638	−	1.48027i	0.818972	−	0.573834i	$-0.194545\pi$
$224$	9.40613	−	1.23146i	0.628474	−	0.0822806i
$225$		0			0
$226$	−2.04971	+	2.04971i	−0.136345	+	0.136345i
$227$	−15.1087	+	4.04837i	−1.00280	+	0.268699i	−0.722618	−	0.691248i	$-0.757061\pi$
$227$	−15.1087	+	4.04837i	−1.00280	+	0.268699i	−0.280182	+	0.959947i	$0.590395\pi$
$228$		0			0
$229$	−3.61172	+	3.61172i	−0.238669	+	0.238669i	−0.816299	−	0.577630i	$-0.803978\pi$
$229$	−3.61172	+	3.61172i	−0.238669	+	0.238669i	0.577630	+	0.816299i	$0.303978\pi$
$230$	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
$238$	−6.50574	−	8.49107i	−0.421704	−	0.550394i
$239$	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	0.998434	−	0.0559344i	$-0.0178138\pi$
$241$	1.64242	+	6.12960i	0.105798	+	0.394842i	−0.892637	+	0.450777i	$0.851147\pi$
$242$	0.698823	+	0.698823i	0.0449221	+	0.0449221i
$243$		0			0
$244$	−2.57423	−	4.45870i	−0.164798	−	0.285439i
$245$	−2.71233	−	4.71353i	−0.173284	−	0.301136i
$246$		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	$-0.596480\pi$
$251$	10.7306	−	18.5859i	0.677308	−	1.17313i	0.975789	−	0.218716i	$-0.0701868\pi$
$252$		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	$-0.820666\pi$
$257$	−14.1914	−	24.5801i	−0.885232	−	1.53327i	−0.0397853	−	0.999208i	$-0.512667\pi$
$258$		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
$266$	−2.51787	+	19.0195i	−0.154381	+	1.16616i
$267$		0			0
$268$	3.36244	+	3.36244i	0.205394	+	0.205394i
$269$	5.62758	+	3.24908i	0.343120	+	0.198100i	0.661651	−	0.749812i	$-0.269856\pi$
$269$	5.62758	+	3.24908i	0.343120	+	0.198100i	−0.318531	+	0.947912i	$0.603190\pi$
$270$		0			0
$271$	6.14616	+	1.64686i	0.373353	+	0.100040i	0.440616	−	0.897696i	$-0.354760\pi$
$271$	6.14616	+	1.64686i	0.373353	+	0.100040i	−0.0672633	+	0.997735i	$0.521427\pi$
$272$	−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
$280$	−6.27439	−	0.830628i	−0.374967	−	0.0496395i
$281$	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	0.561240	−	0.827653i	$-0.310324\pi$
$283$	−7.33715	−	12.7083i	−0.436148	−	0.755431i	−0.997389	+	0.0722219i	$0.976991\pi$
$284$	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	0.997620	−	0.0689587i	$-0.0219677\pi$
$293$	1.69762	+	6.33562i	0.0991763	+	0.370131i	−0.898443	+	0.439090i	$0.855301\pi$
$294$		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
$301$	12.3033	−	16.0101i	0.709150	−	0.922809i
$302$	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	$0.650441\pi$
$307$	−23.5768	+	23.5768i	−1.34560	+	1.34560i	−0.890377	+	0.455225i	$0.849559\pi$
$308$	3.40944	+	4.44988i	0.194271	+	0.253556i
$309$		0			0
$310$	−0.291741	+	1.08879i	−0.0165698	+	0.0618393i
$311$	−2.90579			−0.164772			−0.0823861	−	0.996600i	$-0.526254\pi$
$311$	−2.90579			−0.164772			−0.0823861	+	0.996600i	$0.526254\pi$
$312$		0			0
$313$			0.960626i			0.0542978i	0.999631	+	0.0271489i	$0.00864282\pi$
$313$			0.960626i			0.0542978i	−0.999631	+	0.0271489i	$0.991357\pi$
$314$	−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
$322$	−2.24083	−	17.1158i	−0.124877	−	0.953829i
$323$	−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
$329$	−0.607617	−	0.793041i	−0.0334990	−	0.0437218i
$330$		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
$343$	−7.12427	+	17.0952i	−0.384675	+	0.923052i
$344$	−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	0.380506	−	0.924779i	$-0.375750\pi$
$349$	4.62637	+	1.23963i	0.247644	+	0.0663560i	−0.132862	+	0.991135i	$0.542417\pi$
$350$	−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	$-0.809988\pi$
$353$	3.19876	−	11.9379i	0.170253	−	0.635392i	0.997312	−	0.0732769i	$-0.0233457\pi$
$354$		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
$364$	−0.603871	−	6.31716i	−0.0316514	−	0.331109i
$365$	8.47775			0.443746
$366$		0			0
$367$	5.05707	−	2.91970i	0.263977	−	0.152407i	−0.362170	−	0.932112i	$-0.617964\pi$
$367$	5.05707	−	2.91970i	0.263977	−	0.152407i	0.626147	+	0.779705i	$0.284631\pi$
$368$	−10.8914	−	6.28818i	−0.567756	−	0.327794i
$369$		0			0
$370$	0.506280	−	0.135657i	0.0263202	−	0.00705249i
$371$	4.02867	−	30.4318i	0.209158	−	1.57994i
$372$		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	−0.0717170	−	0.997425i	$-0.522848\pi$
$383$	7.14098	−	1.91342i	0.364887	−	0.0977711i	0.436604	+	0.899654i	$0.356181\pi$
$384$		0			0
$385$	−2.50097	−	6.05017i	−0.127461	−	0.308345i
$386$	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
$392$	10.7504	+	18.6821i	0.542975	+	0.943590i
$393$		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	$-0.832919\pi$
$397$	−7.30250	−	27.2533i	−0.366502	−	1.36780i	0.498872	−	0.866676i	$-0.333748\pi$
$398$	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
$406$	−27.5595	+	3.60813i	−1.36776	+	0.179068i
$407$	−1.61078	−	0.929982i	−0.0798432	−	0.0460975i
$408$		0			0
$409$	−30.3999	+	8.14562i	−1.50318	+	0.402775i	−0.914163	−	0.405348i	$-0.867150\pi$
$409$	−30.3999	+	8.14562i	−1.50318	+	0.402775i	−0.589014	+	0.808123i	$0.700484\pi$
$410$	2.36146	−	0.632752i	0.116624	−	0.0312494i
$411$		0			0
$412$	11.1288	+	6.42519i	0.548274	+	0.316546i
$413$	6.43753	−	0.842810i	0.316770	−	0.0414720i
$414$		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	0.0900058	−	0.995941i	$-0.471311\pi$
$419$	20.4187	−	11.7887i	0.997519	−	0.575918i	0.907513	+	0.420023i	$0.137978\pi$
$420$		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
$427$	12.4768	−	16.2359i	0.603795	−	0.785711i
$428$		−	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	−0.816179	−	0.577800i	$-0.803912\pi$
$433$	1.92063	−	3.32663i	0.0922998	−	0.159868i	0.908478	+	0.417932i	$0.137245\pi$
$434$	3.54763	−	1.46649i	0.170291	−	0.0703937i
$435$		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	0.637907	−	0.770113i	$-0.279800\pi$
$439$	−7.29107	−	12.6285i	−0.347984	−	0.602726i	−0.985891	+	0.167388i	$0.946467\pi$
$440$	−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
$448$	22.5472	+	2.98488i	1.06525	+	0.141022i
$449$	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
$455$	−1.22822	+	7.30854i	−0.0575798	+	0.342630i
$456$		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	−0.876540	−	0.481329i	$-0.840154\pi$
$461$	−29.9515	+	8.02549i	−1.39498	+	0.373784i	−0.518441	+	0.855113i	$0.673488\pi$
$462$		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	$-0.634125\pi$
$467$	−17.6775			−0.818017			−0.409009	+	0.912530i	$0.634125\pi$
$468$		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
$476$	2.35297	+	5.69214i	0.107848	+	0.260899i
$477$		0			0
$478$	2.29110	−	1.32276i	0.104792	−	0.0605018i
$479$	19.1281	+	5.12537i	0.873987	+	0.234184i	0.667811	−	0.744331i	$-0.267231\pi$
$479$	19.1281	+	5.12537i	0.873987	+	0.234184i	0.206176	+	0.978515i	$0.433898\pi$
$480$		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
$490$	−1.61740	−	6.07111i	−0.0730666	−	0.274265i
$491$	−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
$497$	25.4491	−	3.33183i	1.14155	−	0.149453i
$498$		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	0.431989	−	0.901879i	$-0.357812\pi$
$503$	−2.98438	−	1.72303i	−0.133067	−	0.0768262i	−0.565056	+	0.825053i	$0.691145\pi$
$504$		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	$-0.678862\pi$
$509$	7.93556	−	29.6159i	0.351737	−	1.31270i	0.884541	−	0.466463i	$-0.154472\pi$
$510$		0			0
$511$	−17.5595	−	22.9181i	−0.776786	−	1.01384i
$512$	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
$518$	−1.41536	−	1.08766i	−0.0621872	−	0.0477889i
$519$		0			0
$520$	5.88252	+	6.30787i	0.257966	+	0.276619i
$521$		−	13.0906i		−	0.573510i	−0.958004	−	0.286755i	$-0.907423\pi$
$521$		−	13.0906i		−	0.573510i	0.958004	−	0.286755i	$-0.0925766\pi$
$522$		0			0
$523$	29.9435	−	17.2879i	1.30934	−	0.755946i	0.327351	−	0.944903i	$-0.393844\pi$
$523$	29.9435	−	17.2879i	1.30934	−	0.755946i	0.981985	+	0.188957i	$0.0605106\pi$
$524$	−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
$539$	−11.1754	+	19.2923i	−0.481360	+	0.830979i
$540$		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
$553$	−3.75657	+	28.3764i	−0.159746	+	1.20669i
$554$	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	−0.888047	−	0.459753i	$-0.847938\pi$
$563$	−1.08829	+	1.88498i	−0.0458661	+	0.0794424i	0.842181	+	0.539195i	$0.181271\pi$
$564$		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
$574$	−6.60170	−	5.07321i	−0.275550	−	0.211752i
$575$	−12.4139	−	21.5016i	−0.517697	−	0.896678i
$576$		0			0
$577$	−1.10520	−	1.10520i	−0.0460102	−	0.0460102i	0.683727	−	0.729738i	$-0.260358\pi$
$577$	−1.10520	−	1.10520i	−0.0460102	−	0.0460102i	−0.729738	+	0.683727i	$0.760358\pi$
$578$	1.42140	+	5.30472i	0.0591223	+	0.220647i
$579$		0			0
$580$	−3.32300	+	3.32300i	−0.137980	+	0.137980i
$581$	30.6973	−	23.5198i	1.27354	−	0.975768i
$582$		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	$0.258880\pi$
$587$	−6.57121	+	24.5241i	−0.271223	+	1.01222i	−0.958331	+	0.285662i	$0.907787\pi$
$588$		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	−0.928641	−	0.370981i	$-0.879022\pi$
$593$	−13.5799	+	13.5799i	−0.557660	+	0.557660i	0.370981	+	0.928641i	$0.379022\pi$
$594$		0			0
$595$	−0.933753	−	7.13216i	−0.0382801	−	0.292390i
$596$	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	−0.0289030	−	0.999582i	$-0.509201\pi$
$601$	20.1592	−	11.6389i	0.822309	−	0.474760i	0.851212	+	0.524822i	$0.175868\pi$
$602$	18.5172	−	14.1876i	0.754706	−	0.578245i
$603$		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	0.673040	−	0.739607i	$-0.264988\pi$
$607$	9.09221	+	5.24939i	0.369041	+	0.213066i	−0.303998	+	0.952673i	$0.598322\pi$
$608$	−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
$616$	9.91264	+	23.9800i	0.399392	+	0.966180i
$617$	−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	−0.659108	−	0.752048i	$-0.729066\pi$
$619$	2.31233	−	2.31233i	0.0929403	−	0.0929403i	0.752048	+	0.659108i	$0.229066\pi$
$620$	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
$637$	22.3013	−	11.8175i	0.883608	−	0.468227i
$638$	−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	0.527120	−	0.849791i	$-0.323272\pi$
$643$	35.7163	−	9.57017i	1.40852	−	0.377411i	0.881395	+	0.472380i	$0.156605\pi$
$644$	−1.30444	+	9.85351i	−0.0514023	+	0.388283i
$645$		0			0
$646$	−12.6881	+	21.9765i	−0.499208	+	0.864653i
$647$	24.0363	+	41.6322i	0.944966	+	1.63673i	0.755819	+	0.654780i	$0.227239\pi$
$647$	24.0363	+	41.6322i	0.944966	+	1.63673i	0.189147	+	0.981949i	$0.439428\pi$
$648$		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
$658$	−0.440938	−	1.06669i	−0.0171895	−	0.0415837i
$659$	−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	−0.176537	−	0.984294i	$-0.556490\pi$
$661$	−21.1225	−	5.65976i	−0.821570	−	0.220139i	−0.645033	+	0.764155i	$0.723156\pi$
$662$			14.6153i			0.568038i
$663$		0			0
$664$		−	45.0073i		−	1.74662i
$665$	−7.86105	+	10.2295i	−0.304838	+	0.396682i
$666$		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	$-0.798763\pi$
$677$		−	30.7509i		−	1.18185i	0.806726	−	0.590926i	$-0.201237\pi$
$678$		0			0
$679$	−0.250514	−	1.91347i	−0.00961386	−	0.0734323i
$680$	−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
$686$	−13.0621	+	16.9471i	−0.498714	+	0.647044i
$687$		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	$0.466768\pi$
$691$	−12.7049	+	47.4152i	−0.483316	+	1.80376i	−0.587528	+	0.809204i	$0.699899\pi$
$692$	−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
$700$	6.13557	+	4.71500i	0.231903	+	0.178210i
$701$			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
$707$	−27.9385	+	11.5490i	−1.05073	+	0.434344i
$708$		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	−0.718954	−	0.695058i	$-0.755379\pi$
$719$	6.50138	−	11.2607i	0.242461	−	0.419954i	0.961415	+	0.275103i	$0.0887121\pi$
$720$		0			0
$721$	−6.70734	+	50.6659i	−0.249794	+	1.88690i
$722$	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	$-0.553949\pi$
$727$	−9.09604			−0.337353			−0.168677	+	0.985671i	$0.553949\pi$
$728$	4.86806	−	28.9675i	0.180422	−	1.07361i
$729$		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	0.0899161	−	0.995949i	$-0.471340\pi$
$733$	−24.5299	−	24.5299i	−0.906033	−	0.906033i	−0.995949	+	0.0899161i	$0.971340\pi$
$734$	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
$749$	22.4505	−	9.28039i	0.820322	−	0.339098i
$750$		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	$0.183368\pi$
$761$	10.6129	+	39.6079i	0.384718	+	1.43579i	−0.453893	+	0.891056i	$0.649965\pi$
$762$		0			0
$763$	−4.07719	−	5.32141i	−0.147604	−	0.192648i
$764$	−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	−0.949189	−	0.314707i	$-0.898094\pi$
$769$	0.837092	−	3.12407i	0.0301863	−	0.112657i	0.979375	+	0.202050i	$0.0647604\pi$
$770$	−0.981851	−	7.49955i	−0.0353834	−	0.270265i
$771$		0			0
$772$	−0.453085	+	0.453085i	−0.0163069	+	0.0163069i
$773$	20.3857	−	5.46232i	0.733221	−	0.196466i	0.127158	−	0.991882i	$-0.459415\pi$
$773$	20.3857	−	5.46232i	0.733221	−	0.196466i	0.606063	+	0.795417i	$0.292748\pi$
$774$		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
$784$	4.01305	+	15.0635i	0.143323	+	0.537982i
$785$	−3.01801	+	3.01801i	−0.107718	+	0.107718i
$786$		0			0
$787$	12.5317	+	46.7690i	0.446707	+	1.66713i	0.711389	+	0.702798i	$0.248066\pi$
$787$	12.5317	+	46.7690i	0.446707	+	1.66713i	−0.264682	+	0.964336i	$0.585267\pi$
$788$	−8.10003	−	8.10003i	−0.288552	−	0.288552i
$789$		0			0
$790$	−4.85523	−	8.40951i	−0.172741	−	0.299197i
$791$	5.26358	+	4.04490i	0.187151	+	0.143820i
$792$		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	$-0.531230\pi$
$797$	22.9487	−	39.7483i	0.812884	−	1.40796i	0.910837	−	0.412765i	$-0.135437\pi$
$798$		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	0.927186	−	0.374602i	$-0.122221\pi$
$811$	15.7365	+	15.7365i	0.552584	+	0.552584i	−0.374602	+	0.927186i	$0.622221\pi$
$812$	15.8659	+	2.10038i	0.556783	+	0.0737090i
$813$		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
$826$	7.43600	+	0.984405i	0.258731	+	0.0342518i
$827$	−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	0.901634	−	0.432499i	$-0.142368\pi$
$829$	2.19576	+	3.80317i	0.0762620	+	0.132090i	−0.825372	+	0.564589i	$0.809035\pi$
$830$	−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	0.966387	−	0.257093i	$-0.0827646\pi$
$839$	0.0267890	+	0.0999778i	0.000924858	+	0.00345162i	−0.965462	+	0.260544i	$0.916098\pi$
$840$		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
$847$	1.37906	−	1.79455i	0.0473850	−	0.0616616i
$848$	−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	$0.516780\pi$
$853$	−30.7045	+	30.7045i	−1.05130	+	1.05130i	−0.998611	+	0.0526924i	$0.983220\pi$
$854$	18.7784	−	14.3877i	0.642583	−	0.492338i
$855$		0			0
$856$	7.31756	−	27.3095i	0.250109	−	0.933419i
$857$	46.5367			1.58966			0.794831	−	0.606831i	$-0.207559\pi$
$857$	46.5367			1.58966			0.794831	+	0.606831i	$0.207559\pi$
$858$		0			0
$859$			34.8981i			1.19071i	0.803464	+	0.595354i	$0.202988\pi$
$859$			34.8981i			1.19071i	−0.803464	+	0.595354i	$0.797012\pi$
$860$	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
$868$	−2.19168	+	0.286938i	−0.0743905	+	0.00973931i
$869$	−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
$875$	−11.7465	−	15.3312i	−0.397106	−	0.518289i
$876$		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	$0.0458597\pi$
$881$	18.3777	+	31.8310i	0.619159	+	1.07242i	−0.370480	+	0.928840i	$0.620807\pi$
$882$		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	−0.934388	−	0.356258i	$-0.884052\pi$
$887$	−32.5539	+	18.7950i	−1.09305	+	0.631074i	−0.158665	+	0.987332i	$0.550719\pi$
$888$		0			0
$889$	17.0684	+	41.2906i	0.572455	+	1.38484i
$890$	−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
$910$	−3.55602	+	7.78872i	−0.117881	+	0.258194i
$911$	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
$917$	−24.0922	−	3.18942i	−0.795596	−	0.105324i
$918$		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	−0.262132	−	0.965032i	$-0.584426\pi$
$929$	−0.202032	+	0.0541344i	−0.00662846	+	0.00177609i	0.255503	+	0.966808i	$0.417759\pi$
$930$		0			0
$931$	43.9357	+	0.0631567i	1.43994	+	0.00206988i
$932$	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	$0.0375470\pi$
$937$			7.20471i			0.235368i	−0.993051	+	0.117684i	$0.962453\pi$
$938$	−13.3137	+	17.3249i	−0.434707	+	0.565678i
$939$		0			0
$940$	−0.169007	−	0.0975764i	−0.00551241	−	0.00318259i
$941$	27.6042	+	27.6042i	0.899870	+	0.899870i	0.995424	−	0.0955544i	$-0.0304624\pi$
$941$	27.6042	+	27.6042i	0.899870	+	0.899870i	−0.0955544	+	0.995424i	$0.530462\pi$
$942$		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
$952$	3.70094	+	28.2684i	0.119948	+	0.916185i
$953$	−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
$959$	2.16264	+	16.5186i	0.0698352	+	0.533414i
$960$		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	0.0267525	−	0.999642i	$-0.491483\pi$
$971$	−25.7260	−	14.8529i	−0.825587	−	0.476653i	−0.852339	+	0.522989i	$0.824817\pi$
$972$		0			0
$973$	30.9467	−	40.2705i	0.992105	−	1.29101i
$974$			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
$980$	−0.00520036	+	3.61769i	−0.000166119	+	0.115563i
$981$		0			0
$982$	−20.7096	+	5.54912i	−0.660870	+	0.177080i
$983$	−36.4493	+	36.4493i	−1.16255	+	1.16255i	−0.178637	+	0.983915i	$0.557169\pi$
$983$	−36.4493	+	36.4493i	−1.16255	+	1.16255i	−0.983915	+	0.178637i	$0.942831\pi$
$984$		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
$994$	29.3963	+	3.89159i	0.932393	+	0.123434i
$995$	1.68926	−	0.452636i	0.0535532	−	0.0143495i
$996$		0			0
$997$	9.41930	+	5.43824i	0.298312	+	0.172231i	0.641684	−	0.766969i	$-0.278236\pi$
$997$	9.41930	+	5.43824i	0.298312	+	0.172231i	−0.343372	+	0.939199i	$0.611569\pi$
$998$	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.f.496.5		32
3.2	odd	2		273.2.by.c.223.4	yes	32
7.6	odd	2		819.2.fm.e.496.5		32
13.7	odd	12		819.2.fm.e.748.5		32
21.20	even	2		273.2.by.d.223.4	yes	32
39.20	even	12		273.2.by.d.202.4	yes	32
91.20	even	12	inner	819.2.fm.f.748.5		32
273.20	odd	12		273.2.by.c.202.4	✓	32

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

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)

\(f(q)\)	\(=\)	\(q+(1.11595 + 0.299019i) q^{2} +(-0.576113 - 0.332619i) q^{4} +(0.549341 + 0.549341i) q^{5} +(0.347225 - 2.62287i) q^{7} +(-2.17732 - 2.17732i) q^{8} +O(q^{10})\)	\(q+(1.11595 + 0.299019i) q^{2} +(-0.576113 - 0.332619i) q^{4} +(0.549341 + 0.549341i) q^{5} +(0.347225 - 2.62287i) q^{7} +(-2.17732 - 2.17732i) q^{8} +(0.448776 + 0.777302i) q^{10} +(0.824353 - 3.07653i) q^{11} +(-2.63686 + 2.45905i) q^{13} +(1.17177 - 2.82317i) q^{14} +(-1.11349 - 1.92862i) q^{16} +(1.74975 - 3.03065i) q^{17} +(-6.06267 + 1.62449i) q^{19} +(-0.133761 - 0.499204i) q^{20} +(1.83988 - 3.18676i) q^{22} +(4.89067 - 2.82363i) q^{23} -4.39645i q^{25} +(-3.67792 + 1.95572i) q^{26} +(-1.07246 + 1.39557i) q^{28} +(-4.54654 - 7.87483i) q^{29} +(0.888029 + 0.888029i) q^{31} +(0.928002 + 3.46335i) q^{32} +(2.85886 - 2.85886i) q^{34} +(1.63160 - 1.25010i) q^{35} +(0.151142 - 0.564068i) q^{37} -7.25141 q^{38} -2.39219i q^{40} +(0.704976 - 2.63101i) q^{41} +(6.60921 + 3.81583i) q^{43} +(-1.49823 + 1.49823i) q^{44} +(6.30208 - 1.68864i) q^{46} +(0.267009 - 0.267009i) q^{47} +(-6.75887 - 1.82145i) q^{49} +(1.31462 - 4.90623i) q^{50} +(2.33706 - 0.539622i) q^{52} +11.6025 q^{53} +(2.14292 - 1.23721i) q^{55} +(-6.46685 + 4.95481i) q^{56} +(-2.71900 - 10.1474i) q^{58} +(0.635122 + 2.37031i) q^{59} +(6.70242 + 3.86964i) q^{61} +(0.725461 + 1.25654i) q^{62} +8.59639i q^{64} +(-2.79940 - 0.0976783i) q^{65} +(-6.90457 - 1.85007i) q^{67} +(-2.01610 + 1.16400i) q^{68} +(2.19459 - 0.907181i) q^{70} +(2.51079 + 9.37039i) q^{71} +(7.71628 - 7.71628i) q^{73} +(0.337334 - 0.584279i) q^{74} +(4.03312 + 1.08067i) q^{76} +(-7.78309 - 3.23042i) q^{77} -10.8188 q^{79} +(0.447786 - 1.67116i) q^{80} +(1.57344 - 2.72528i) q^{82} +(10.3355 + 10.3355i) q^{83} +(2.62607 - 0.703654i) q^{85} +(6.23456 + 6.23456i) q^{86} +(-8.49348 + 4.90371i) q^{88} +(-7.02589 - 1.88258i) q^{89} +(5.53419 + 7.76999i) q^{91} -3.75677 q^{92} +(0.377810 - 0.218129i) q^{94} +(-4.22288 - 2.43808i) q^{95} +(0.704543 - 0.188782i) q^{97} +(-6.99793 - 4.05368i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 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 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * 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 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

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