LMFDB - Embedded newform 405.2.r.a.197.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			197.12
Character	$\chi$	$=$	405.197
Dual form			405.2.r.a.368.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36666 - 0.119567i) q^{2} +(-0.116159 + 0.0204819i) q^{4} +(0.119339 + 2.23288i) q^{5} +(-2.68447 + 1.87969i) q^{7} +(-2.80657 + 0.752017i) q^{8} +O(q^{10})$	\(q+(1.36666 - 0.119567i) q^{2} +(-0.116159 + 0.0204819i) q^{4} +(0.119339 + 2.23288i) q^{5} +(-2.68447 + 1.87969i) q^{7} +(-2.80657 + 0.752017i) q^{8} +(0.430074 + 3.03731i) q^{10} +(1.85785 + 5.10439i) q^{11} +(0.215209 - 2.45985i) q^{13} +(-3.44400 + 2.88986i) q^{14} +(-3.52402 + 1.28264i) q^{16} +(3.45292 + 0.925208i) q^{17} +(0.417150 + 0.240842i) q^{19} +(-0.0595960 - 0.256925i) q^{20} +(3.14935 + 6.75381i) q^{22} +(4.01261 - 5.73060i) q^{23} +(-4.97152 + 0.532938i) q^{25} -3.38750i q^{26} +(0.273325 - 0.273325i) q^{28} +(-0.0993465 - 0.0833616i) q^{29} +(0.509526 + 2.88966i) q^{31} +(0.603911 - 0.281608i) q^{32} +(4.82959 + 0.851587i) q^{34} +(-4.51748 - 5.76978i) q^{35} +(1.67943 - 6.26774i) q^{37} +(0.598898 + 0.279271i) q^{38} +(-2.01410 - 6.17698i) q^{40} +(-0.215101 - 0.256347i) q^{41} +(-2.45933 + 5.27405i) q^{43} +(-0.320353 - 0.554867i) q^{44} +(4.79867 - 8.31155i) q^{46} +(6.80358 + 9.71652i) q^{47} +(1.27902 - 3.51408i) q^{49} +(-6.73064 + 1.32277i) q^{50} +(0.0253840 + 0.290141i) q^{52} +(0.167838 + 0.167838i) q^{53} +(-11.1758 + 4.75750i) q^{55} +(6.12058 - 7.29423i) q^{56} +(-0.145740 - 0.102048i) q^{58} +(3.62976 + 1.32113i) q^{59} +(-0.855508 + 4.85182i) q^{61} +(1.04186 + 3.88826i) q^{62} +(7.28718 - 4.20726i) q^{64} +(5.51823 + 0.186981i) q^{65} +(4.25953 + 0.372661i) q^{67} +(-0.420038 - 0.0367485i) q^{68} +(-6.86372 - 7.34518i) q^{70} +(-7.10207 + 4.10038i) q^{71} +(-3.51625 - 13.1228i) q^{73} +(1.54580 - 8.76665i) q^{74} +(-0.0533886 - 0.0194318i) q^{76} +(-14.5820 - 10.2104i) q^{77} +(6.44655 - 7.68270i) q^{79} +(-3.28453 - 7.71565i) q^{80} +(-0.324619 - 0.324619i) q^{82} +(-0.00128626 - 0.0147020i) q^{83} +(-1.65381 + 7.82038i) q^{85} +(-2.73046 + 7.50188i) q^{86} +(-9.05275 - 12.9287i) q^{88} +(2.55837 - 4.43123i) q^{89} +(4.04602 + 7.00791i) q^{91} +(-0.348726 + 0.747846i) q^{92} +(10.4599 + 12.4657i) q^{94} +(-0.487989 + 0.960188i) q^{95} +(3.77015 + 1.75805i) q^{97} +(1.32781 - 4.95547i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	1.36666	−	0.119567i	0.966373	−	0.0845467i	0.406969	−	0.913442i	$-0.366586\pi$
$2$	1.36666	−	0.119567i	0.966373	−	0.0845467i	0.559404	+	0.828895i	$0.311030\pi$
$3$		0			0
$3$		0			0
$4$	−0.116159	+	0.0204819i	−0.0580794	+	0.0102410i
$5$	0.119339	+	2.23288i	0.0533699	+	0.998575i
$5$	0.119339	+	2.23288i	0.0533699	+	0.998575i
$6$		0			0
$7$	−2.68447	+	1.87969i	−1.01463	+	0.710455i	−0.957654	−	0.287921i	$-0.907036\pi$
$7$	−2.68447	+	1.87969i	−1.01463	+	0.710455i	−0.0569801	+	0.998375i	$0.518147\pi$
$8$	−2.80657	+	0.752017i	−0.992271	+	0.265878i
$9$		0			0
$10$	0.430074	+	3.03731i	0.136001	+	0.960483i
$11$	1.85785	+	5.10439i	0.560161	+	1.53903i	0.819403	+	0.573218i	$0.194305\pi$
$11$	1.85785	+	5.10439i	0.560161	+	1.53903i	−0.259241	+	0.965813i	$0.583473\pi$
$12$		0			0
$13$	0.215209	−	2.45985i	0.0596882	−	0.682239i	−0.906127	−	0.423006i	$-0.860975\pi$
$13$	0.215209	−	2.45985i	0.0596882	−	0.682239i	0.965815	−	0.259233i	$-0.0834697\pi$
$14$	−3.44400	+	2.88986i	−0.920449	+	0.772348i
$15$		0			0
$16$	−3.52402	+	1.28264i	−0.881006	+	0.320660i
$17$	3.45292	+	0.925208i	0.837457	+	0.224396i	0.651964	−	0.758250i	$-0.273945\pi$
$17$	3.45292	+	0.925208i	0.837457	+	0.224396i	0.185493	+	0.982646i	$0.440612\pi$
$18$		0			0
$19$	0.417150	+	0.240842i	0.0957007	+	0.0552529i	0.547087	−	0.837076i	$-0.315737\pi$
$19$	0.417150	+	0.240842i	0.0957007	+	0.0552529i	−0.451386	+	0.892329i	$0.649070\pi$
$20$	−0.0595960	−	0.256925i	−0.0133261	−	0.0574501i
$21$		0			0
$22$	3.14935	+	6.75381i	0.671445	+	1.43992i
$23$	4.01261	−	5.73060i	0.836687	−	1.19491i	−0.142063	−	0.989858i	$-0.545374\pi$
$23$	4.01261	−	5.73060i	0.836687	−	1.19491i	0.978750	−	0.205055i	$-0.0657375\pi$
$24$		0			0
$25$	−4.97152	+	0.532938i	−0.994303	+	0.106588i
$26$		−	3.38750i		−	0.664344i
$27$		0			0
$28$	0.273325	−	0.273325i	0.0516536	−	0.0516536i
$29$	−0.0993465	−	0.0833616i	−0.0184482	−	0.0154799i	0.633517	−	0.773729i	$-0.281611\pi$
$29$	−0.0993465	−	0.0833616i	−0.0184482	−	0.0154799i	−0.651965	+	0.758249i	$0.726055\pi$
$30$		0			0
$31$	0.509526	+	2.88966i	0.0915135	+	0.518999i	0.995760	+	0.0919882i	$0.0293222\pi$
$31$	0.509526	+	2.88966i	0.0915135	+	0.518999i	−0.904247	+	0.427011i	$0.859567\pi$
$32$	0.603911	−	0.281608i	0.106757	−	0.0497818i
$33$		0			0
$34$	4.82959	+	0.851587i	0.828268	+	0.146046i
$35$	−4.51748	−	5.76978i	−0.763593	−	0.975271i
$36$		0			0
$37$	1.67943	−	6.26774i	0.276097	−	1.03041i	−0.679005	−	0.734134i	$-0.737589\pi$
$37$	1.67943	−	6.26774i	0.276097	−	1.03041i	0.955102	−	0.296276i	$-0.0957448\pi$
$38$	0.598898	+	0.279271i	0.0971540	+	0.0453037i
$39$		0			0
$40$	−2.01410	−	6.17698i	−0.318457	−	0.976667i
$41$	−0.215101	−	0.256347i	−0.0335931	−	0.0400346i	0.748986	−	0.662585i	$-0.230541\pi$
$41$	−0.215101	−	0.256347i	−0.0335931	−	0.0400346i	−0.782579	+	0.622551i	$0.786096\pi$
$42$		0			0
$43$	−2.45933	+	5.27405i	−0.375044	+	0.804285i	0.624682	+	0.780880i	$0.285229\pi$
$43$	−2.45933	+	5.27405i	−0.375044	+	0.804285i	−0.999726	+	0.0234058i	$0.992549\pi$
$44$	−0.320353	−	0.554867i	−0.0482950	−	0.0836494i
$45$		0			0
$46$	4.79867	−	8.31155i	0.707526	−	1.22547i
$47$	6.80358	+	9.71652i	0.992405	+	1.41730i	0.907085	+	0.420947i	$0.138302\pi$
$47$	6.80358	+	9.71652i	0.992405	+	1.41730i	0.0853195	+	0.996354i	$0.472809\pi$
$48$		0			0
$49$	1.27902	−	3.51408i	0.182717	−	0.502011i
$50$	−6.73064	+	1.32277i	−0.951856	+	0.187068i
$51$		0			0
$52$	0.0253840	+	0.290141i	0.00352013	+	0.0402353i
$53$	0.167838	+	0.167838i	0.0230543	+	0.0230543i	0.718540	−	0.695486i	$-0.244811\pi$
$53$	0.167838	+	0.167838i	0.0230543	+	0.0230543i	−0.695486	+	0.718540i	$0.744811\pi$
$54$		0			0
$55$	−11.1758	+	4.75750i	−1.50694	+	0.641501i
$56$	6.12058	−	7.29423i	0.817898	−	0.974732i
$57$		0			0
$58$	−0.145740	−	0.102048i	−0.0191366	−	0.0133996i
$59$	3.62976	+	1.32113i	0.472555	+	0.171996i	0.567309	−	0.823505i	$-0.307984\pi$
$59$	3.62976	+	1.32113i	0.472555	+	0.171996i	−0.0947544	+	0.995501i	$0.530207\pi$
$60$		0			0
$61$	−0.855508	+	4.85182i	−0.109537	+	0.621212i	0.879774	+	0.475391i	$0.157694\pi$
$61$	−0.855508	+	4.85182i	−0.109537	+	0.621212i	−0.989311	+	0.145821i	$0.953418\pi$
$62$	1.04186	+	3.88826i	0.132316	+	0.493809i
$63$		0			0
$64$	7.28718	−	4.20726i	0.910898	−	0.525907i
$65$	5.51823	+	0.186981i	0.684452	+	0.0231921i
$66$		0			0
$67$	4.25953	+	0.372661i	0.520385	+	0.0455277i	0.344323	−	0.938851i	$-0.388109\pi$
$67$	4.25953	+	0.372661i	0.520385	+	0.0455277i	0.176062	+	0.984379i	$0.443664\pi$
$68$	−0.420038	−	0.0367485i	−0.0509370	−	0.00445641i
$69$		0			0
$70$	−6.86372	−	7.34518i	−0.820372	−	0.877917i
$71$	−7.10207	+	4.10038i	−0.842861	+	0.486626i	−0.858236	−	0.513256i	$-0.828439\pi$
$71$	−7.10207	+	4.10038i	−0.842861	+	0.486626i	0.0153747	+	0.999882i	$0.495106\pi$
$72$		0			0
$73$	−3.51625	−	13.1228i	−0.411546	−	1.53591i	−0.791654	−	0.610969i	$-0.790780\pi$
$73$	−3.51625	−	13.1228i	−0.411546	−	1.53591i	0.380108	−	0.924942i	$-0.375887\pi$
$74$	1.54580	−	8.76665i	0.179695	−	1.01910i
$75$		0			0
$76$	−0.0533886	−	0.0194318i	−0.00612409	−	0.00222899i
$77$	−14.5820	−	10.2104i	−1.66177	−	1.16358i
$78$		0			0
$79$	6.44655	−	7.68270i	0.725293	−	0.864371i	−0.269840	−	0.962905i	$-0.586971\pi$
$79$	6.44655	−	7.68270i	0.725293	−	0.864371i	0.995134	+	0.0985341i	$0.0314153\pi$
$80$	−3.28453	−	7.71565i	−0.367222	−	0.862636i
$81$		0			0
$82$	−0.324619	−	0.324619i	−0.0358482	−	0.0358482i
$83$	−0.00128626	−	0.0147020i	−0.000141185	−	0.00161375i	0.996124	−	0.0879626i	$-0.0280356\pi$
$83$	−0.00128626	−	0.0147020i	−0.000141185	−	0.00161375i	−0.996265	+	0.0863488i	$0.972480\pi$
$84$		0			0
$85$	−1.65381	+	7.82038i	−0.179381	+	0.848239i
$86$	−2.73046	+	7.50188i	−0.294433	+	0.808948i
$87$		0			0
$88$	−9.05275	−	12.9287i	−0.965026	−	1.37820i
$89$	2.55837	−	4.43123i	0.271187	−	0.469709i	−0.697979	−	0.716118i	$-0.745917\pi$
$89$	2.55837	−	4.43123i	0.271187	−	0.469709i	0.969166	+	0.246409i	$0.0792506\pi$
$90$		0			0
$91$	4.04602	+	7.00791i	0.424138	+	0.734629i
$92$	−0.348726	+	0.747846i	−0.0363572	+	0.0779683i
$93$		0			0
$94$	10.4599	+	12.4657i	1.07886	+	1.28574i
$95$	−0.487989	+	0.960188i	−0.0500666	+	0.0985132i
$96$		0			0
$97$	3.77015	+	1.75805i	0.382800	+	0.178503i	0.604487	−	0.796615i	$-0.293378\pi$
$97$	3.77015	+	1.75805i	0.382800	+	0.178503i	−0.221686	+	0.975118i	$0.571156\pi$
$98$	1.32781	−	4.95547i	0.134129	−	0.500578i
$99$		0			0
$100$	0.566570	−	0.163732i	0.0566570	−	0.0163732i
$101$	−7.79700	−	1.37482i	−0.775831	−	0.136800i	−0.228306	−	0.973589i	$-0.573319\pi$
$101$	−7.79700	−	1.37482i	−0.775831	−	0.136800i	−0.547525	+	0.836789i	$0.684430\pi$
$102$		0			0
$103$	4.88597	−	2.27837i	0.481429	−	0.224494i	−0.166725	−	0.986004i	$-0.553319\pi$
$103$	4.88597	−	2.27837i	0.481429	−	0.224494i	0.648154	+	0.761509i	$0.275541\pi$
$104$	1.24585	+	7.06556i	0.122166	+	0.692836i
$105$		0			0
$106$	0.249444	+	0.209309i	0.0242282	+	0.0203299i
$107$	6.45665	−	6.45665i	0.624188	−	0.624188i	−0.322412	−	0.946600i	$-0.604494\pi$
$107$	6.45665	−	6.45665i	0.624188	−	0.624188i	0.946600	+	0.322412i	$0.104494\pi$
$108$		0			0
$109$			10.2697i			0.983654i	0.870693	+	0.491827i	$0.163671\pi$
$109$			10.2697i			0.983654i	−0.870693	+	0.491827i	$0.836329\pi$
$110$	−14.7046	+	7.83813i	−1.40203	+	0.747336i
$111$		0			0
$112$	7.04917	−	10.0673i	0.666084	−	0.951267i
$113$	4.39670	+	9.42875i	0.413607	+	0.886982i	0.997189	+	0.0749283i	$0.0238728\pi$
$113$	4.39670	+	9.42875i	0.413607	+	0.886982i	−0.583582	+	0.812054i	$0.698349\pi$
$114$		0			0
$115$	13.2746	+	8.27580i	1.23786	+	0.771722i
$116$	0.0132474	+	0.00764838i	0.00122999	+	0.000710134i
$117$		0			0
$118$	5.11861	+	1.37153i	0.471206	+	0.126259i
$119$	−11.0084	+	4.00672i	−1.00914	+	0.367295i
$120$		0			0
$121$	−14.1767	+	11.8957i	−1.28879	+	1.08142i
$122$	−0.589068	+	6.73307i	−0.0533317	+	0.609584i
$123$		0			0
$124$	−0.118372	−	0.325224i	−0.0106301	−	0.0292060i
$125$	−1.78328	−	11.0372i	−0.159502	−	0.987198i
$126$		0			0
$127$	12.6633	−	3.39311i	1.12368	−	0.301090i	0.351311	−	0.936259i	$-0.385736\pi$
$127$	12.6633	−	3.39311i	1.12368	−	0.301090i	0.772373	+	0.635169i	$0.219069\pi$
$128$	8.36436	−	5.85679i	0.739312	−	0.517672i
$129$		0			0
$130$	7.56389	−	0.404260i	0.663397	−	0.0354559i
$131$	3.19816	−	0.563922i	0.279425	−	0.0492701i	−0.0321796	−	0.999482i	$-0.510245\pi$
$131$	3.19816	−	0.563922i	0.279425	−	0.0492701i	0.311604	+	0.950212i	$0.399134\pi$
$132$		0			0
$133$	−1.57253	+	0.137579i	−0.136356	+	0.0119296i
$134$	5.86588			0.506735
$135$		0			0
$136$	−10.3866			−0.890646
$137$	4.68732	−	0.410087i	0.400465	−	0.0350361i	0.114855	−	0.993382i	$-0.463360\pi$
$137$	4.68732	−	0.410087i	0.400465	−	0.0350361i	0.285609	+	0.958346i	$0.407804\pi$
$138$		0			0
$139$	−11.3538	+	2.00197i	−0.963013	+	0.169805i	−0.632983	−	0.774165i	$-0.718170\pi$
$139$	−11.3538	+	2.00197i	−0.963013	+	0.169805i	−0.330030	+	0.943971i	$0.607059\pi$
$140$	0.642921	+	0.577685i	0.0543368	+	0.0488233i
$141$		0			0
$142$	−9.21583	+	6.45299i	−0.773375	+	0.541523i
$143$	12.9558	−	3.47151i	1.08342	−	0.290302i
$144$		0			0
$145$	0.174281	−	0.231777i	0.0144732	−	0.0192480i
$146$	−6.37457	−	17.5140i	−0.527563	−	1.44947i
$147$		0			0
$148$	−0.0667058	+	0.762451i	−0.00548319	+	0.0626731i
$149$	−8.56384	+	7.18592i	−0.701577	+	0.588693i	−0.922222	−	0.386661i	$-0.873628\pi$
$149$	−8.56384	+	7.18592i	−0.701577	+	0.588693i	0.220645	+	0.975354i	$0.429184\pi$
$150$		0			0
$151$	11.0074	−	4.00638i	0.895773	−	0.326035i	0.147215	−	0.989104i	$-0.452969\pi$
$151$	11.0074	−	4.00638i	0.895773	−	0.326035i	0.748558	+	0.663070i	$0.230747\pi$
$152$	−1.35188	−	0.362234i	−0.109652	−	0.0293810i
$153$		0			0
$154$	−21.1494	−	12.2106i	−1.70427	−	0.983959i
$155$	−6.39147	+	1.48256i	−0.513375	+	0.119082i
$156$		0			0
$157$	−8.59634	−	18.4349i	−0.686062	−	1.47127i	−0.872407	−	0.488781i	$-0.837442\pi$
$157$	−8.59634	−	18.4349i	−0.686062	−	1.47127i	0.186344	−	0.982485i	$-0.440336\pi$
$158$	7.89163	−	11.2704i	0.627824	−	0.896626i
$159$		0			0
$160$	0.700868	+	1.31486i	0.0554085	+	0.103948i
$161$			22.9261i			1.80683i
$162$		0			0
$163$	−6.89303	+	6.89303i	−0.539904	+	0.539904i	−0.923501	−	0.383597i	$-0.874685\pi$
$163$	−6.89303	+	6.89303i	−0.539904	+	0.539904i	0.383597	+	0.923501i	$0.374685\pi$
$164$	0.0302363	+	0.0253713i	0.00236106	+	0.00198116i
$165$		0			0
$166$	−0.00351574	−	0.0199388i	−0.000272875	−	0.00154755i
$167$	7.25712	−	3.38405i	0.561573	−	0.261866i	−0.121038	−	0.992648i	$-0.538622\pi$
$167$	7.25712	−	3.38405i	0.561573	−	0.261866i	0.682611	+	0.730782i	$0.260844\pi$
$168$		0			0
$169$	6.79796	+	1.19866i	0.522920	+	0.0922049i
$170$	−1.32514	+	10.8855i	−0.101633	+	0.834882i
$171$		0			0
$172$	0.177650	−	0.663000i	0.0135457	−	0.0505532i
$173$	−13.8817	−	6.47315i	−1.05541	−	0.492145i	−0.184113	−	0.982905i	$-0.558941\pi$
$173$	−13.8817	−	6.47315i	−1.05541	−	0.492145i	−0.871295	+	0.490760i	$0.836719\pi$
$174$		0			0
$175$	12.3441	−	10.7755i	0.933129	−	0.814555i
$176$	−13.0942	−	15.6050i	−0.987011	−	1.17627i
$177$		0			0
$178$	2.96659	−	6.36186i	0.222355	−	0.476842i
$179$	10.5577	+	18.2866i	0.789123	+	1.36680i	0.926505	+	0.376283i	$0.122798\pi$
$179$	10.5577	+	18.2866i	0.789123	+	1.36680i	−0.137382	+	0.990518i	$0.543869\pi$
$180$		0			0
$181$	5.12182	−	8.87125i	0.380702	−	0.659395i	−0.610461	−	0.792046i	$-0.709016\pi$
$181$	5.12182	−	8.87125i	0.380702	−	0.659395i	0.991163	+	0.132651i	$0.0423491\pi$
$182$	6.36744	+	9.09365i	0.471986	+	0.674066i
$183$		0			0
$184$	−6.95214	+	19.1009i	−0.512519	+	1.40813i
$185$	14.1955	+	3.00200i	1.04368	+	0.220711i
$186$		0			0
$187$	1.69238	+	19.3440i	0.123759	+	1.41457i
$188$	−0.989310	−	0.989310i	−0.0721528	−	0.0721528i
$189$		0			0
$190$	−0.552106	+	1.37060i	−0.0400540	+	0.0994334i
$191$	3.94811	−	4.70518i	0.285676	−	0.340455i	−0.604054	−	0.796944i	$-0.706449\pi$
$191$	3.94811	−	4.70518i	0.285676	−	0.340455i	0.889729	+	0.456489i	$0.150893\pi$
$192$		0			0
$193$	5.19711	+	3.63906i	0.374096	+	0.261945i	0.745471	−	0.666538i	$-0.232225\pi$
$193$	5.19711	+	3.63906i	0.374096	+	0.261945i	−0.371375	+	0.928483i	$0.621113\pi$
$194$	5.36270	+	1.95186i	0.385020	+	0.140136i
$195$		0			0
$196$	−0.0765943	+	0.434388i	−0.00547102	+	0.0310277i
$197$	0.0881812	+	0.329097i	0.00628265	+	0.0234472i	0.968996	−	0.247076i	$-0.0794699\pi$
$197$	0.0881812	+	0.329097i	0.00628265	+	0.0234472i	−0.962713	+	0.270524i	$0.912803\pi$
$198$		0			0
$199$	−17.6952	+	10.2163i	−1.25438	+	0.724216i	−0.971976	−	0.235079i	$-0.924465\pi$
$199$	−17.6952	+	10.2163i	−1.25438	+	0.724216i	−0.282404	+	0.959296i	$0.591132\pi$
$200$	13.5521	−	5.23439i	0.958279	−	0.370127i
$201$		0			0
$202$	−10.8202	−	0.946646i	−0.761308	−	0.0666058i
$203$	0.423386	+	0.0370415i	0.0297159	+	0.00259980i
$204$		0			0
$205$	0.546722	−	0.510886i	0.0381847	−	0.0356818i
$206$	6.40504	−	3.69795i	0.446260	−	0.257648i
$207$		0			0
$208$	2.39670	+	8.94459i	0.166181	+	0.620196i
$209$	−0.454349	+	2.57674i	−0.0314280	+	0.178237i
$210$		0			0
$211$	−5.48650	−	1.99692i	−0.377706	−	0.137474i	0.146189	−	0.989257i	$-0.453299\pi$
$211$	−5.48650	−	1.99692i	−0.377706	−	0.137474i	−0.523895	+	0.851783i	$0.675522\pi$
$212$	−0.0229335	−	0.0160582i	−0.00157508	−	0.00110288i
$213$		0			0
$214$	8.05203	−	9.59603i	0.550425	−	0.655971i
$215$	−12.0698	−	4.86199i	−0.823155	−	0.331585i
$216$		0			0
$217$	−6.79947	−	6.79947i	−0.461578	−	0.461578i
$218$	1.22791	+	14.0351i	0.0831647	+	0.950577i
$219$		0			0
$220$	1.20072	−	0.781527i	0.0809527	−	0.0526905i
$221$	3.01897	−	8.29455i	0.203078	−	0.557952i
$222$		0			0
$223$	−11.2233	−	16.0285i	−0.751567	−	1.07335i	−0.994646	−	0.103342i	$-0.967046\pi$
$223$	−11.2233	−	16.0285i	−0.751567	−	1.07335i	0.243079	−	0.970006i	$-0.421843\pi$
$224$	−1.09185	+	1.89113i	−0.0729521	+	0.126357i
$225$		0			0
$226$	7.13615	+	12.3602i	0.474690	+	0.822187i
$227$	−4.22532	+	9.06123i	−0.280444	+	0.601415i	−0.995189	−	0.0979701i	$-0.968765\pi$
$227$	−4.22532	+	9.06123i	−0.280444	+	0.601415i	0.714745	+	0.699385i	$0.246543\pi$
$228$		0			0
$229$	−8.12582	−	9.68397i	−0.536969	−	0.639935i	0.427536	−	0.903998i	$-0.359382\pi$
$229$	−8.12582	−	9.68397i	−0.536969	−	0.639935i	−0.964505	+	0.264063i	$0.914937\pi$
$230$	19.1314	+	9.72298i	1.26148	+	0.641114i
$231$		0			0
$232$	0.341512	+	0.159249i	0.0224213	+	0.0104552i
$233$	−0.393034	+	1.46682i	−0.0257485	+	0.0960947i	−0.977604	−	0.210451i	$-0.932507\pi$
$233$	−0.393034	+	1.46682i	−0.0257485	+	0.0960947i	0.951856	+	0.306546i	$0.0991733\pi$
$234$		0			0
$235$	−20.8839	+	16.3512i	−1.36232	+	1.06663i
$236$	−0.448688	−	0.0791159i	−0.0292071	−	0.00515000i
$237$		0			0
$238$	−14.5656	+	6.79205i	−0.944148	+	0.440263i
$239$	3.47433	+	19.7039i	0.224735	+	1.27454i	0.863190	+	0.504879i	$0.168463\pi$
$239$	3.47433	+	19.7039i	0.224735	+	1.27454i	−0.638455	+	0.769659i	$0.720426\pi$
$240$		0			0
$241$	−8.08193	−	6.78155i	−0.520603	−	0.436838i	0.344239	−	0.938882i	$-0.388137\pi$
$241$	−8.08193	−	6.78155i	−0.520603	−	0.436838i	−0.864842	+	0.502044i	$0.832581\pi$
$242$	−17.9524	+	17.9524i	−1.15402	+	1.15402i
$243$		0			0
$244$		−	0.581105i		−	0.0372014i
$245$	7.99915	+	2.43653i	0.511047	+	0.155664i
$246$		0			0
$247$	0.682208	−	0.974294i	0.0434079	−	0.0619929i
$248$	−3.60309	−	7.72686i	−0.228797	−	0.490656i
$249$		0			0
$250$	−3.75682	−	14.8709i	−0.237602	−	0.940516i
$251$	8.94339	+	5.16347i	0.564502	+	0.325915i	0.754950	−	0.655782i	$-0.227661\pi$
$251$	8.94339	+	5.16347i	0.564502	+	0.325915i	−0.190449	+	0.981697i	$0.560994\pi$
$252$		0			0
$253$	36.7060	+	9.83535i	2.30769	+	0.618343i
$254$	16.9007	−	6.15134i	1.06044	−	0.385969i
$255$		0			0
$256$	−2.16084	+	1.81316i	−0.135053	+	0.113323i
$257$	1.34587	−	15.3834i	0.0839533	−	0.959591i	−0.831064	−	0.556177i	$-0.812268\pi$
$257$	1.34587	−	15.3834i	0.0839533	−	0.959591i	0.915017	−	0.403414i	$-0.132177\pi$
$258$		0			0
$259$	7.27299	+	19.9824i	0.451921	+	1.24164i
$260$	−0.644821	+	0.0913046i	−0.0399901	+	0.00566247i
$261$		0			0
$262$	4.30336	−	1.15308i	0.265863	−	0.0712377i
$263$	−11.1530	+	7.80938i	−0.687721	+	0.481547i	−0.864454	−	0.502712i	$-0.832336\pi$
$263$	−11.1530	+	7.80938i	−0.687721	+	0.481547i	0.176734	+	0.984259i	$0.443447\pi$
$264$		0			0
$265$	−0.354732	+	0.394791i	−0.0217910	+	0.0242518i
$266$	−2.13266	+	0.376046i	−0.130762	+	0.0230569i
$267$		0			0
$268$	−0.502415	+	0.0439556i	−0.0306899	+	0.00268502i
$269$	11.6016			0.707363			0.353681	−	0.935366i	$-0.384930\pi$
$269$	11.6016			0.707363			0.353681	+	0.935366i	$0.384930\pi$
$270$		0			0
$271$	10.5393			0.640216			0.320108	−	0.947381i	$-0.396281\pi$
$271$	10.5393			0.640216			0.320108	+	0.947381i	$0.396281\pi$
$272$	−13.3549	+	1.16840i	−0.809759	+	0.0708447i
$273$		0			0
$274$	6.35693	−	1.12090i	0.384036	−	0.0677159i
$275$	−11.9566	−	24.3864i	−0.721012	−	1.47056i
$276$		0			0
$277$	13.5767	−	9.50648i	0.815743	−	0.571189i	−0.0895477	−	0.995983i	$-0.528542\pi$
$277$	13.5767	−	9.50648i	0.815743	−	0.571189i	0.905290	+	0.424793i	$0.139653\pi$
$278$	−15.2773	+	4.09355i	−0.916273	+	0.245515i
$279$		0			0
$280$	17.0176	+	12.7961i	1.01699	+	0.764711i
$281$	4.02535	+	11.0596i	0.240132	+	0.659758i	0.999954	+	0.00962623i	$0.00306417\pi$
$281$	4.02535	+	11.0596i	0.240132	+	0.659758i	−0.759821	+	0.650132i	$0.774714\pi$
$282$		0			0
$283$	0.637926	−	7.29153i	0.0379208	−	0.433437i	−0.953375	−	0.301787i	$-0.902417\pi$
$283$	0.637926	−	7.29153i	0.0379208	−	0.433437i	0.991296	−	0.131650i	$-0.0420275\pi$
$284$	0.740985	−	0.621760i	0.0439694	−	0.0368947i
$285$		0			0
$286$	17.2911	−	6.29345i	1.02245	−	0.372140i
$287$	1.05928	+	0.283834i	0.0625275	+	0.0167542i
$288$		0			0
$289$	−3.65576	−	2.11066i	−0.215045	−	0.124156i
$290$	0.210469	−	0.337598i	0.0123592	−	0.0198244i
$291$		0			0
$292$	0.677225	+	1.45231i	0.0396316	+	0.0849902i
$293$	4.56171	−	6.51480i	0.266498	−	0.380599i	−0.663492	−	0.748183i	$-0.730926\pi$
$293$	4.56171	−	6.51480i	0.266498	−	0.380599i	0.929990	+	0.367585i	$0.119815\pi$
$294$		0			0
$295$	−2.51675	+	8.26249i	−0.146531	+	0.481061i
$296$			18.8538i			1.09585i
$297$		0			0
$298$	−10.8446	+	10.8446i	−0.628213	+	0.628213i
$299$	−13.2329	−	11.1037i	−0.765276	−	0.642143i
$300$		0			0
$301$	−3.31156	−	18.7808i	−0.190875	−	1.08251i
$302$	14.5644	−	6.79148i	0.838086	−	0.390806i
$303$		0			0
$304$	−1.77896	−	0.313678i	−0.102030	−	0.0179907i
$305$	−10.9356	−	1.33124i	−0.626173	−	0.0762264i
$306$		0			0
$307$	−2.43216	+	9.07696i	−0.138811	+	0.518049i	0.861142	+	0.508364i	$0.169750\pi$
$307$	−2.43216	+	9.07696i	−0.138811	+	0.518049i	−0.999953	+	0.00968516i	$0.996917\pi$
$308$	1.90295	+	0.887362i	0.108431	+	0.0505622i
$309$		0			0
$310$	−8.55768	+	2.79036i	−0.486044	+	0.158482i
$311$	3.85633	+	4.59579i	0.218672	+	0.260603i	0.864217	−	0.503119i	$-0.167814\pi$
$311$	3.85633	+	4.59579i	0.218672	+	0.260603i	−0.645545	+	0.763722i	$0.723370\pi$
$312$		0			0
$313$	−3.90239	+	8.36871i	−0.220576	+	0.473027i	−0.985191	−	0.171460i	$-0.945151\pi$
$313$	−3.90239	+	8.36871i	−0.220576	+	0.473027i	0.764615	+	0.644488i	$0.222929\pi$
$314$	−13.9525	−	24.1664i	−0.787383	−	1.36379i
$315$		0			0
$316$	−0.591467	+	1.02445i	−0.0332726	+	0.0576299i
$317$	−18.3856	−	26.2573i	−1.03264	−	1.47476i	−0.873085	−	0.487568i	$-0.837884\pi$
$317$	−18.3856	−	26.2573i	−1.03264	−	1.47476i	−0.159551	−	0.987190i	$-0.551005\pi$
$318$		0			0
$319$	0.240939	−	0.661976i	0.0134900	−	0.0370635i
$320$	10.2639	+	15.7693i	0.573772	+	0.881532i
$321$		0			0
$322$	2.74120	+	31.3321i	0.152761	+	1.74607i
$323$	1.21756	+	1.21756i	0.0677467	+	0.0677467i
$324$		0			0
$325$	0.241032	+	12.3439i	0.0133701	+	0.684715i
$326$	−8.59623	+	10.2446i	−0.476101	+	0.567396i
$327$		0			0
$328$	0.796471	+	0.557695i	0.0439777	+	0.0307935i
$329$	−36.5280	−	13.2951i	−2.01386	−	0.732984i
$330$		0			0
$331$	−5.34763	+	30.3279i	−0.293932	+	1.66697i	0.377579	+	0.925977i	$0.376757\pi$
$331$	−5.34763	+	30.3279i	−0.293932	+	1.66697i	−0.671511	+	0.740995i	$0.734354\pi$
$332$	0.000450535		0.00168142i	2.47263e−5		9.22799e-5i
$333$		0			0
$334$	9.51338	−	5.49255i	0.520549	−	0.300539i
$335$	−0.323780	+	9.55550i	−0.0176900	+	0.522073i
$336$		0			0
$337$	3.15374	+	0.275916i	0.171795	+	0.0150301i	0.172729	−	0.984969i	$-0.444742\pi$
$337$	3.15374	+	0.275916i	0.171795	+	0.0150301i	−0.000933572		1.00000i	$0.500297\pi$
$338$	9.43381	+	0.825351i	0.513132	+	0.0448932i
$339$		0			0
$340$	0.0319284	−	0.942280i	0.00173156	−	0.0511023i
$341$	−13.8033	+	7.96936i	−0.747493	+	0.431565i
$342$		0			0
$343$	−2.76542	−	10.3207i	−0.149319	−	0.557265i
$344$	2.93610	−	16.6514i	0.158304	−	0.897785i
$345$		0			0
$346$	−19.7455	−	7.18679i	−1.06153	−	0.386364i
$347$	−23.8760	−	16.7182i	−1.28173	−	0.897479i	−0.283624	−	0.958936i	$-0.591537\pi$
$347$	−23.8760	−	16.7182i	−1.28173	−	0.897479i	−0.998110	+	0.0614562i	$0.980426\pi$
$348$		0			0
$349$	13.9918	−	16.6748i	0.748963	−	0.892579i	−0.248134	−	0.968726i	$-0.579817\pi$
$349$	13.9918	−	16.6748i	0.748963	−	0.892579i	0.997097	+	0.0761464i	$0.0242616\pi$
$350$	15.5818	−	16.2024i	0.832882	−	0.866057i
$351$		0			0
$352$	2.55941	+	2.55941i	0.136417	+	0.136417i
$353$	0.350221	+	4.00305i	0.0186404	+	0.213061i	0.999802	+	0.0198744i	$0.00632664\pi$
$353$	0.350221	+	4.00305i	0.0186404	+	0.213061i	−0.981162	+	0.193186i	$0.938118\pi$
$354$		0			0
$355$	−10.0032	−	15.3687i	−0.530916	−	0.815689i
$356$	−0.206417	+	0.567126i	−0.0109401	+	0.0300576i
$357$		0			0
$358$	16.6153	+	23.7291i	0.878146	+	1.25412i
$359$	4.90370	−	8.49346i	0.258807	−	0.448268i	−0.707115	−	0.707098i	$-0.750004\pi$
$359$	4.90370	−	8.49346i	0.258807	−	0.448268i	0.965923	+	0.258831i	$0.0833372\pi$
$360$		0			0
$361$	−9.38399	−	16.2535i	−0.493894	−	0.855450i
$362$	5.93907	−	12.7364i	0.312150	−	0.669409i
$363$		0			0
$364$	−0.613517	−	0.731161i	−0.0321570	−	0.0383232i
$365$	28.8821	−	9.41743i	1.51176	−	0.492931i
$366$		0			0
$367$	−33.4836	−	15.6137i	−1.74783	−	0.815027i	−0.985893	−	0.167377i	$-0.946470\pi$
$367$	−33.4836	−	15.6137i	−1.74783	−	0.815027i	−0.761938	−	0.647650i	$-0.775752\pi$
$368$	−6.79023	+	25.3415i	−0.353965	+	1.32102i
$369$		0			0
$370$	19.7594	+	2.40538i	1.02724	+	0.125050i
$371$	−0.766037	−	0.135073i	−0.0397707	−	0.00701264i
$372$		0			0
$373$	23.6061	−	11.0077i	1.22228	−	0.569958i	0.299061	−	0.954234i	$-0.403327\pi$
$373$	23.6061	−	11.0077i	1.22228	−	0.569958i	0.923218	+	0.384276i	$0.125549\pi$
$374$	4.62580	+	26.2342i	0.239194	+	1.35654i
$375$		0			0
$376$	−26.4017	−	22.1537i	−1.36156	−	1.14249i
$377$	−0.226437	+	0.226437i	−0.0116621	+	0.0116621i
$378$		0			0
$379$		−	25.9056i		−	1.33068i	−0.746541	−	0.665340i	$-0.768287\pi$
$379$		−	25.9056i		−	1.33068i	0.746541	−	0.665340i	$-0.231713\pi$
$380$	0.0370177	−	0.121529i	0.00189897	−	0.00623432i
$381$		0			0
$382$	4.83314	−	6.90243i	0.247285	−	0.353159i
$383$	−4.13501	−	8.86756i	−0.211289	−	0.453111i	0.771890	−	0.635757i	$-0.219312\pi$
$383$	−4.13501	−	8.86756i	−0.211289	−	0.453111i	−0.983179	+	0.182645i	$0.941534\pi$
$384$		0			0
$385$	21.0584	−	33.7783i	1.07324	−	1.72150i
$386$	7.53778	+	4.35194i	0.383663	+	0.221508i
$387$		0			0
$388$	−0.473944	−	0.126993i	−0.0240609	−	0.00644709i
$389$	−11.3841	+	4.14348i	−0.577198	+	0.210083i	−0.614089	−	0.789236i	$-0.710477\pi$
$389$	−11.3841	+	4.14348i	−0.577198	+	0.210083i	0.0368917	+	0.999319i	$0.488254\pi$
$390$		0			0
$391$	19.1572	−	16.0748i	0.968823	−	0.812939i
$392$	−0.947006	+	10.8243i	−0.0478310	+	0.546711i
$393$		0			0
$394$	0.159863	+	0.439219i	0.00805376	+	0.0221275i
$395$	17.9239	+	13.4775i	0.901848	+	0.678128i
$396$		0			0
$397$	−11.4729	+	3.07416i	−0.575810	+	0.154288i	−0.534960	−	0.844878i	$-0.679673\pi$
$397$	−11.4729	+	3.07416i	−0.575810	+	0.154288i	−0.0408499	+	0.999165i	$0.513007\pi$
$398$	−22.9617	+	16.0780i	−1.15097	+	0.805917i
$399$		0			0
$400$	16.8362	−	8.25475i	0.841808	−	0.412737i
$401$	31.8998	−	5.62479i	1.59300	−	0.280889i	0.694377	−	0.719612i	$-0.255680\pi$
$401$	31.8998	−	5.62479i	1.59300	−	0.280889i	0.898622	+	0.438723i	$0.144569\pi$
$402$		0			0
$403$	7.21779	−	0.631475i	0.359544	−	0.0314560i
$404$	0.933850			0.0464608
$405$		0			0
$406$	0.583053			0.0289364
$407$	35.1131	−	3.07200i	1.74049	−	0.152273i
$408$		0			0
$409$	4.62791	−	0.816026i	0.228836	−	0.0403499i	−0.0580544	−	0.998313i	$-0.518490\pi$
$409$	4.62791	−	0.816026i	0.228836	−	0.0403499i	0.286890	+	0.957964i	$0.407379\pi$
$410$	0.686097	−	0.763576i	0.0338839	−	0.0377103i
$411$		0			0
$412$	−0.520884	+	0.364727i	−0.0256621	+	0.0179688i
$413$	−12.2273	+	3.27629i	−0.601666	+	0.161216i
$414$		0			0
$415$	0.0326743	−	0.00462657i	0.00160392	−	0.000227109i
$416$	−0.562747	−	1.54613i	−0.0275909	−	0.0758055i
$417$		0			0
$418$	−0.312846	+	3.57585i	−0.0153018	+	0.174900i
$419$	16.7939	−	14.0917i	0.820435	−	0.688427i	−0.132639	−	0.991164i	$-0.542345\pi$
$419$	16.7939	−	14.0917i	0.820435	−	0.688427i	0.953074	+	0.302737i	$0.0979005\pi$
$420$		0			0
$421$	26.6703	−	9.70721i	1.29983	−	0.473101i	0.402891	−	0.915248i	$-0.368005\pi$
$421$	26.6703	−	9.70721i	1.29983	−	0.473101i	0.896942	+	0.442148i	$0.145783\pi$
$422$	−7.73694	−	2.07311i	−0.376628	−	0.100917i
$423$		0			0
$424$	−0.597264	−	0.344831i	−0.0290057	−	0.0167465i
$425$	−17.6593	−	2.75949i	−0.856604	−	0.133855i
$426$		0			0
$427$	−6.82332	−	14.6327i	−0.330204	−	0.708124i
$428$	−0.617752	+	0.882242i	−0.0298602	+	0.0426448i
$429$		0			0
$430$	−17.0767	−	5.20153i	−0.823509	−	0.250840i
$431$		−	34.6874i		−	1.67083i	−0.549617	−	0.835417i	$-0.685226\pi$
$431$		−	34.6874i		−	1.67083i	0.549617	−	0.835417i	$-0.314774\pi$
$432$		0			0
$433$	−3.65895	+	3.65895i	−0.175838	+	0.175838i	−0.789539	−	0.613701i	$-0.789680\pi$
$433$	−3.65895	+	3.65895i	−0.175838	+	0.175838i	0.613701	+	0.789539i	$0.289680\pi$
$434$	−10.1055	−	8.47955i	−0.485081	−	0.407031i
$435$		0			0
$436$	−0.210342	−	1.19291i	−0.0100736	−	0.0571301i
$437$	3.05403	−	1.42412i	0.146094	−	0.0681247i
$438$		0			0
$439$	−30.7144	−	5.41577i	−1.46592	−	0.258481i	−0.616982	−	0.786977i	$-0.711645\pi$
$439$	−30.7144	−	5.41577i	−1.46592	−	0.258481i	−0.848935	+	0.528496i	$0.822756\pi$
$440$	27.7878	−	21.7566i	1.32473	−	1.03721i
$441$		0			0
$442$	3.13414	−	11.6968i	0.149076	−	0.556359i
$443$	28.1594	+	13.1309i	1.33789	+	0.623869i	0.954083	−	0.299544i	$-0.0968344\pi$
$443$	28.1594	+	13.1309i	1.33789	+	0.623869i	0.383809	+	0.923413i	$0.374612\pi$
$444$		0			0
$445$	10.1997	+	5.18372i	0.483513	+	0.245732i
$446$	−17.2549	−	20.5636i	−0.817042	−	0.973712i
$447$		0			0
$448$	−11.6539	+	24.9919i	−0.550595	+	1.18075i
$449$	−5.46364	−	9.46330i	−0.257845	−	0.446601i	0.707819	−	0.706394i	$-0.249679\pi$
$449$	−5.46364	−	9.46330i	−0.257845	−	0.446601i	−0.965664	+	0.259793i	$0.916346\pi$
$450$		0			0
$451$	0.908870	−	1.57421i	0.0427970	−	0.0741266i
$452$	−0.703835	−	1.00518i	−0.0331056	−	0.0472797i
$453$		0			0
$454$	−4.69114	+	12.8888i	−0.220166	+	0.604902i
$455$	−15.1650	+	9.87060i	−0.710946	+	0.462741i
$456$		0			0
$457$	−2.25825	−	25.8119i	−0.105637	−	1.20743i	−0.845239	−	0.534388i	$-0.820542\pi$
$457$	−2.25825	−	25.8119i	−0.105637	−	1.20743i	0.739603	−	0.673044i	$-0.235013\pi$
$458$	−12.2631	−	12.2631i	−0.573017	−	0.573017i
$459$		0			0
$460$	−1.71147	−	0.689418i	−0.0797976	−	0.0321443i
$461$	10.5103	−	12.5256i	0.489512	−	0.583377i	−0.463582	−	0.886054i	$-0.653436\pi$
$461$	10.5103	−	12.5256i	0.489512	−	0.583377i	0.953093	+	0.302677i	$0.0978804\pi$
$462$		0			0
$463$	0.973401	+	0.681583i	0.0452378	+	0.0316758i	0.595977	−	0.803002i	$-0.296765\pi$
$463$	0.973401	+	0.681583i	0.0452378	+	0.0316758i	−0.550739	+	0.834678i	$0.685654\pi$
$464$	0.457022	+	0.166342i	0.0212167	+	0.00772225i
$465$		0			0
$466$	−0.361759	+	2.05164i	−0.0167582	+	0.0950403i
$467$	4.13206	+	15.4210i	0.191209	+	0.713601i	0.993216	+	0.116286i	$0.0370989\pi$
$467$	4.13206	+	15.4210i	0.191209	+	0.713601i	−0.802007	+	0.597315i	$0.796234\pi$
$468$		0			0
$469$	−12.1351	+	7.00619i	−0.560345	+	0.323516i
$470$	−26.5861	+	24.8435i	−1.22633	+	1.14594i
$471$		0			0
$472$	−11.1807	−	0.978183i	−0.514632	−	0.0450245i
$473$	−31.4899	−	2.75501i	−1.44791	−	0.126675i
$474$		0			0
$475$	−2.20222	−	0.975033i	−0.101045	−	0.0447376i
$476$	1.19665	−	0.690889i	0.0548486	−	0.0316668i
$477$		0			0
$478$	7.10415	+	26.5130i	0.324936	+	1.21268i
$479$	1.29177	−	7.32601i	0.0590226	−	0.334734i	−0.940970	−	0.338489i	$-0.890084\pi$
$479$	1.29177	−	7.32601i	0.0590226	−	0.334734i	0.999993	+	0.00375516i	$0.00119531\pi$
$480$		0			0
$481$	−15.0563	−	5.48003i	−0.686506	−	0.249868i
$482$	−11.8561	−	8.30172i	−0.540030	−	0.378133i
$483$		0			0
$484$	1.40310	−	1.67215i	0.0637774	−	0.0760069i
$485$	−3.47559	+	8.62809i	−0.157818	+	0.391782i
$486$		0			0
$487$	13.2649	+	13.2649i	0.601090	+	0.601090i	0.940602	−	0.339512i	$-0.110262\pi$
$487$	13.2649	+	13.2649i	0.601090	+	0.601090i	−0.339512	+	0.940602i	$0.610262\pi$
$488$	−1.24762	−	14.2603i	−0.0564769	−	0.645534i
$489$		0			0
$490$	11.2234	+	2.37347i	0.507023	+	0.107222i
$491$	−12.3391	+	33.9013i	−0.556855	+	1.52995i	0.267319	+	0.963608i	$0.413862\pi$
$491$	−12.3391	+	33.9013i	−0.556855	+	1.52995i	−0.824173	+	0.566337i	$0.808360\pi$
$492$		0			0
$493$	−0.265909	−	0.379757i	−0.0119759	−	0.0171034i
$494$	0.815851	−	1.41310i	0.0367069	−	0.0635782i
$495$		0			0
$496$	−5.50198	−	9.52970i	−0.247046	−	0.427896i
$497$	11.3579	−	24.3570i	0.509470	−	1.09256i
$498$		0			0
$499$	20.6192	+	24.5730i	0.923042	+	1.10004i	0.994722	+	0.102610i	$0.0327195\pi$
$499$	20.6192	+	24.5730i	0.923042	+	1.10004i	−0.0716800	+	0.997428i	$0.522836\pi$
$500$	0.433207	+	1.24554i	0.0193736	+	0.0557024i
$501$		0			0
$502$	12.8399	+	5.98736i	0.573074	+	0.267229i
$503$	9.15328	−	34.1605i	0.408124	−	1.52314i	−0.390095	−	0.920775i	$-0.627558\pi$
$503$	9.15328	−	34.1605i	0.408124	−	1.52314i	0.798220	−	0.602367i	$-0.205775\pi$
$504$		0			0
$505$	2.13933	−	17.5739i	0.0951990	−	0.782026i
$506$	51.3405	+	9.05272i	2.28237	+	0.402443i
$507$		0			0
$508$	−1.40145	+	0.653509i	−0.0621795	+	0.0289948i
$509$	−3.11515	−	17.6669i	−0.138077	−	0.783072i	−0.972668	−	0.232202i	$-0.925407\pi$
$509$	−3.11515	−	17.6669i	−0.138077	−	0.783072i	0.834591	−	0.550870i	$-0.185704\pi$
$510$		0			0
$511$	34.1061	+	28.6184i	1.50876	+	1.26600i
$512$	−17.1769	+	17.1769i	−0.759118	+	0.759118i
$513$		0			0
$514$		−	21.1848i		−	0.934420i
$515$	5.67041	+	10.6379i	0.249868	+	0.468762i
$516$		0			0
$517$	−36.9569	+	52.7799i	−1.62536	+	2.32126i
$518$	12.3289	+	26.4394i	0.541701	+	1.16168i
$519$		0			0
$520$	−15.6279	+	3.62503i	−0.685328	+	0.158968i
$521$	−5.38399	−	3.10845i	−0.235877	−	0.136184i	0.377403	−	0.926049i	$-0.376817\pi$
$521$	−5.38399	−	3.10845i	−0.235877	−	0.136184i	−0.613280	+	0.789865i	$0.710150\pi$
$522$		0			0
$523$	−41.3195	−	11.0715i	−1.80677	−	0.484124i	−0.811771	−	0.583975i	$-0.801497\pi$
$523$	−41.3195	−	11.0715i	−1.80677	−	0.484124i	−0.995002	+	0.0998516i	$0.968163\pi$
$524$	−0.359944	+	0.131009i	−0.0157242	+	0.00572316i
$525$		0			0
$526$	−14.3085	+	12.0063i	−0.623881	+	0.523499i
$527$	−0.914187	+	10.4492i	−0.0398226	+	0.455174i
$528$		0			0
$529$	−8.87229	−	24.3764i	−0.385752	−	1.05984i
$530$	−0.437593	+	0.581958i	−0.0190078	+	0.0252787i
$531$		0			0
$532$	0.179846	−	0.0481895i	0.00779730	−	0.00208928i
$533$	−0.676866	+	0.473947i	−0.0293183	+	0.0205289i
$534$		0			0
$535$	15.1875	+	13.6464i	0.656611	+	0.589986i
$536$	−12.2349	+	2.15734i	−0.528467	+	0.0931830i
$537$		0			0
$538$	15.8554	−	1.38717i	0.683576	−	0.0598052i
$539$	20.3134			0.874961
$540$		0			0
$541$	16.3822			0.704326			0.352163	−	0.935939i	$-0.385446\pi$
$541$	16.3822			0.704326			0.352163	+	0.935939i	$0.385446\pi$
$542$	14.4036	−	1.26015i	0.618687	−	0.0541281i
$543$		0			0
$544$	2.34581	−	0.413629i	0.100576	−	0.0177342i
$545$	−22.9309	+	1.22557i	−0.982252	+	0.0524975i
$546$		0			0
$547$	17.4002	−	12.1838i	0.743980	−	0.520940i	−0.139034	−	0.990288i	$-0.544400\pi$
$547$	17.4002	−	12.1838i	0.743980	−	0.520940i	0.883014	+	0.469347i	$0.155511\pi$
$548$	−0.536074	+	0.143641i	−0.0228999	+	0.00613602i
$549$		0			0
$550$	−19.2564	−	31.8983i	−0.821097	−	1.36015i
$551$	−0.0213654	−	0.0587010i	−0.000910198	−	0.00250075i
$552$		0			0
$553$	−2.86451	+	32.7415i	−0.121811	+	1.39231i
$554$	17.4180	−	14.6154i	0.740019	−	0.620950i
$555$		0			0
$556$	1.27783	−	0.465094i	0.0541923	−	0.0197244i
$557$	−16.5180	−	4.42599i	−0.699891	−	0.187535i	−0.108709	−	0.994074i	$-0.534672\pi$
$557$	−16.5180	−	4.42599i	−0.699891	−	0.187535i	−0.591182	+	0.806538i	$0.701338\pi$
$558$		0			0
$559$	12.4441	+	7.18460i	0.526329	+	0.303876i
$560$	23.3202	+	14.5386i	0.985460	+	0.614366i
$561$		0			0
$562$	6.82364	+	14.6333i	0.287838	+	0.617270i
$563$	−25.1939	+	35.9806i	−1.06180	+	1.51640i	−0.220829	+	0.975313i	$0.570876\pi$
$563$	−25.1939	+	35.9806i	−1.06180	+	1.51640i	−0.840966	+	0.541088i	$0.818013\pi$
$564$		0			0
$565$	−20.5286	+	10.9425i	−0.863644	+	0.460355i
$566$		−	10.0413i		−	0.422067i
$567$		0			0
$568$	16.8489	−	16.8489i	0.706963	−	0.706963i
$569$	−31.1911	−	26.1725i	−1.30760	−	1.09721i	−0.988778	−	0.149393i	$-0.952268\pi$
$569$	−31.1911	−	26.1725i	−1.30760	−	1.09721i	−0.318823	−	0.947814i	$-0.603288\pi$
$570$		0			0
$571$	6.97321	+	39.5470i	0.291820	+	1.65499i	0.679855	+	0.733347i	$0.262043\pi$
$571$	6.97321	+	39.5470i	0.291820	+	1.65499i	−0.388035	+	0.921645i	$0.626846\pi$
$572$	−1.43383	+	0.668607i	−0.0599515	+	0.0279559i
$573$		0			0
$574$	1.48161	+	0.261248i	0.0618414	+	0.0109043i
$575$	−16.8947	+	30.6283i	−0.704558	+	1.27729i
$576$		0			0
$577$	−3.00476	+	11.2139i	−0.125090	+	0.466841i	−0.999843	−	0.0177276i	$-0.994357\pi$
$577$	−3.00476	+	11.2139i	−0.125090	+	0.466841i	0.874753	+	0.484569i	$0.161024\pi$
$578$	−5.24854	−	2.44743i	−0.218311	−	0.101800i
$579$		0			0
$580$	−0.0154970	+	0.0304926i	−0.000643477	+	0.00126613i
$581$	0.0310880	+	0.0370492i	0.00128975	+	0.00153706i
$582$		0			0
$583$	−0.544892	+	1.16852i	−0.0225671	+	0.0483953i
$584$	19.7372	+	34.1858i	0.816730	+	1.41462i
$585$		0			0
$586$	5.45534	−	9.44893i	0.225358	−	0.390332i
$587$	24.1649	+	34.5111i	0.997393	+	1.42442i	0.903374	+	0.428855i	$0.141083\pi$
$587$	24.1649	+	34.5111i	0.997393	+	1.42442i	0.0940196	+	0.995570i	$0.470028\pi$
$588$		0			0
$589$	−0.483403	+	1.32814i	−0.0199183	+	0.0547250i
$590$	−2.45161	+	11.5929i	−0.100931	+	0.477273i
$591$		0			0
$592$	2.12088	+	24.2418i	0.0871676	+	0.996330i
$593$	10.2163	+	10.2163i	0.419534	+	0.419534i	0.885043	−	0.465509i	$-0.154129\pi$
$593$	10.2163	+	10.2163i	0.419534	+	0.419534i	−0.465509	+	0.885043i	$0.654129\pi$
$594$		0			0
$595$	−10.2603	−	24.1022i	−0.420629	−	0.988095i
$596$	0.847584	−	1.01011i	0.0347184	−	0.0413758i
$597$		0			0
$598$	−19.4124	−	13.5927i	−0.793833	−	0.555848i
$599$	4.58046	+	1.66715i	0.187153	+	0.0681180i	0.433896	−	0.900963i	$-0.357138\pi$
$599$	4.58046	+	1.66715i	0.187153	+	0.0681180i	−0.246744	+	0.969081i	$0.579361\pi$
$600$		0			0
$601$	−6.94695	+	39.3981i	−0.283372	+	1.60708i	0.427671	+	0.903935i	$0.359334\pi$
$601$	−6.94695	+	39.3981i	−0.283372	+	1.60708i	−0.711043	+	0.703149i	$0.751777\pi$
$602$	−6.77134	−	25.2710i	−0.275979	−	1.02997i
$603$		0			0
$604$	−1.19655	+	0.690830i	−0.0486871	+	0.0281095i
$605$	−28.2534	−	30.2353i	−1.14866	−	1.22924i
$606$		0			0
$607$	−9.47967	−	0.829363i	−0.384768	−	0.0336628i	−0.106869	−	0.994273i	$-0.534083\pi$
$607$	−9.47967	−	0.829363i	−0.384768	−	0.0336628i	−0.277899	+	0.960610i	$0.589638\pi$
$608$	0.319745	+	0.0279740i	0.0129674	+	0.00113450i
$609$		0			0
$610$	−15.1045	−	0.511802i	−0.611561	−	0.0207223i
$611$	25.3654	−	14.6447i	1.02617	−	0.592461i
$612$		0			0
$613$	5.22613	+	19.5042i	0.211081	+	0.787766i	0.987509	+	0.157560i	$0.0503628\pi$
$613$	5.22613	+	19.5042i	0.211081	+	0.787766i	−0.776428	+	0.630206i	$0.782971\pi$
$614$	−2.23863	+	12.6959i	−0.0903437	+	0.512365i
$615$		0			0
$616$	48.6037	+	17.6903i	1.95830	+	0.712762i
$617$	24.4398	+	17.1129i	0.983908	+	0.688940i	0.950572	−	0.310505i	$-0.100498\pi$
$617$	24.4398	+	17.1129i	0.983908	+	0.688940i	0.0333358	+	0.999444i	$0.489387\pi$
$618$		0			0
$619$	1.44832	−	1.72604i	0.0582129	−	0.0693754i	−0.736152	−	0.676816i	$-0.763359\pi$
$619$	1.44832	−	1.72604i	0.0582129	−	0.0693754i	0.794365	+	0.607441i	$0.207804\pi$
$620$	0.712060	−	0.303122i	0.0285970	−	0.0121737i
$621$		0			0
$622$	5.81978	+	5.81978i	0.233352	+	0.233352i
$623$	1.46145	+	16.7044i	0.0585517	+	0.669249i
$624$		0			0
$625$	24.4320	−	5.29902i	0.977278	−	0.211961i
$626$	−4.33261	+	11.9038i	−0.173166	+	0.475770i
$627$		0			0
$628$	1.37612	+	1.96531i	0.0549133	+	0.0784243i
$629$	11.5979	−	20.0882i	0.462439	−	0.800968i
$630$		0			0
$631$	−10.8829	−	18.8498i	−0.433243	−	0.750399i	0.563907	−	0.825838i	$-0.309298\pi$
$631$	−10.8829	−	18.8498i	−0.433243	−	0.750399i	−0.997150	+	0.0754390i	$0.975964\pi$
$632$	−12.3151	+	26.4099i	−0.489870	+	1.05053i
$633$		0			0
$634$	−28.2663	−	33.6864i	−1.12260	−	1.33786i
$635$	9.08764	+	27.8707i	0.360632	+	1.10601i
$636$		0			0
$637$	−8.36884	−	3.90245i	−0.331585	−	0.154621i
$638$	0.250131	−	0.933502i	0.00990279	−	0.0369577i
$639$		0			0
$640$	14.0757	+	17.9777i	0.556391	+	0.710630i
$641$	15.8779	+	2.79971i	0.627141	+	0.110582i	0.478181	−	0.878261i	$-0.341296\pi$
$641$	15.8779	+	2.79971i	0.627141	+	0.110582i	0.148960	+	0.988843i	$0.452407\pi$
$642$		0			0
$643$	14.8423	−	6.92110i	0.585325	−	0.272941i	−0.107315	−	0.994225i	$-0.534225\pi$
$643$	14.8423	−	6.92110i	0.585325	−	0.272941i	0.692640	+	0.721284i	$0.256448\pi$
$644$	−0.469571	−	2.66307i	−0.0185037	−	0.104940i
$645$		0			0
$646$	1.80956	+	1.51841i	0.0711964	+	0.0597408i
$647$	11.6159	−	11.6159i	0.456669	−	0.456669i	−0.440892	−	0.897560i	$-0.645338\pi$
$647$	11.6159	−	11.6159i	0.456669	−	0.456669i	0.897560	+	0.440892i	$0.145338\pi$
$648$		0			0
$649$			20.9822i			0.823622i
$650$	1.80533	+	16.8410i	0.0708108	+	0.660559i
$651$		0			0
$652$	0.659504	−	0.941869i	0.0258282	−	0.0368864i
$653$	18.8657	+	40.4576i	0.738271	+	1.58323i	0.810432	+	0.585833i	$0.199233\pi$
$653$	18.8657	+	40.4576i	0.738271	+	1.58323i	−0.0721611	+	0.997393i	$0.522990\pi$
$654$		0			0
$655$	1.64083	+	7.07381i	0.0641127	+	0.276397i
$656$	1.08682	+	0.627476i	0.0424332	+	0.0244988i
$657$		0			0
$658$	−51.5110	−	13.8023i	−2.00811	−	0.538071i
$659$	0.617551	−	0.224770i	0.0240564	−	0.00875580i	−0.329964	−	0.943994i	$-0.607037\pi$
$659$	0.617551	−	0.224770i	0.0240564	−	0.00875580i	0.354020	+	0.935238i	$0.384814\pi$
$660$		0			0
$661$	29.7997	−	25.0049i	1.15907	−	0.972578i	0.159181	−	0.987249i	$-0.449115\pi$
$661$	29.7997	−	25.0049i	1.15907	−	0.972578i	0.999892	+	0.0146714i	$0.00467022\pi$
$662$	−3.68216	+	42.0873i	−0.143111	+	1.63577i
$663$		0			0
$664$	0.0146661	+	0.0402948i	0.000569155	+	0.00156374i
$665$	−0.494861	−	3.49486i	−0.0191899	−	0.135525i
$666$		0			0
$667$	−0.876351	+	0.234817i	−0.0339324	+	0.00909217i
$668$	−0.773667	+	0.541728i	−0.0299341	+	0.0209601i
$669$		0			0
$670$	0.700026	+	13.0978i	0.0270444	+	0.506013i
$671$	−26.3550	+	4.64710i	−1.01742	+	0.179399i
$672$		0			0
$673$	−4.00299	+	0.350216i	−0.154304	+	0.0134998i	−0.164046	−	0.986453i	$-0.552455\pi$
$673$	−4.00299	+	0.350216i	−0.154304	+	0.0134998i	0.00974205	+	0.999953i	$0.496899\pi$
$674$	4.34307			0.167289
$675$		0			0
$676$	−0.814194			−0.0313152
$677$	−29.2823	+	2.56187i	−1.12541	+	0.0984607i	−0.634626	−	0.772820i	$-0.718846\pi$
$677$	−29.2823	+	2.56187i	−1.12541	+	0.0984607i	−0.490786	+	0.871280i	$0.663290\pi$
$678$		0			0
$679$	−13.4254	+	2.36727i	−0.515221	+	0.0908473i
$680$	−1.23953	−	23.1921i	−0.0475337	−	0.889377i
$681$		0			0
$682$	−17.9116	+	12.5418i	−0.685869	+	0.480251i
$683$	−7.44976	+	1.99616i	−0.285057	+	0.0763808i	−0.398515	−	0.917162i	$-0.630474\pi$
$683$	−7.44976	+	1.99616i	−0.285057	+	0.0763808i	0.113457	+	0.993543i	$0.463807\pi$
$684$		0			0
$685$	1.47505	+	10.4173i	0.0563589	+	0.398024i
$686$	−5.01340	−	13.7742i	−0.191412	−	0.525901i
$687$		0			0
$688$	1.90203	−	21.7403i	0.0725142	−	0.828841i
$689$	0.448975	−	0.376735i	0.0171046	−	0.0143525i
$690$		0			0
$691$	−32.4494	+	11.8106i	−1.23443	+	0.449297i	−0.875114	−	0.483918i	$-0.839213\pi$
$691$	−32.4494	+	11.8106i	−1.23443	+	0.449297i	−0.359320	+	0.933215i	$0.616991\pi$
$692$	1.74507	+	0.467589i	0.0663375	+	0.0177751i
$693$		0			0
$694$	−34.6293	−	19.9933i	−1.31451	−	0.758933i
$695$	−5.82511	−	25.1127i	−0.220959	−	0.952578i
$696$		0			0
$697$	−0.505551	−	1.08416i	−0.0191491	−	0.0410654i
$698$	17.1282	−	24.4616i	0.648313	−	0.925887i
$699$		0			0
$700$	−1.21318	+	1.50451i	−0.0458537	+	0.0568650i
$701$		−	2.02183i		−	0.0763636i	−0.999271	−	0.0381818i	$-0.987843\pi$
$701$		−	2.02183i		−	0.0763636i	0.999271	−	0.0381818i	$-0.0121566\pi$
$702$		0			0
$703$	2.21011	−	2.21011i	0.0833558	−	0.0833558i
$704$	35.0139	+	29.3802i	1.31964	+	1.10731i
$705$		0			0
$706$	0.957265	+	5.42892i	0.0360272	+	0.204320i
$707$	23.5151	−	10.9653i	0.884375	−	0.412391i
$708$		0			0
$709$	0.162501	+	0.0286532i	0.00610284	+	0.00107609i	0.176699	−	0.984265i	$-0.443458\pi$
$709$	0.162501	+	0.0286532i	0.00610284	+	0.00107609i	−0.170596	+	0.985341i	$0.554569\pi$
$710$	−15.5086	−	19.8078i	−0.582026	−	0.743372i
$711$		0			0
$712$	−3.84787	+	14.3605i	−0.144205	+	0.538181i
$713$	18.6040	+	8.67521i	0.696727	+	0.324889i
$714$		0			0
$715$	9.29760	+	28.5146i	0.347710	+	1.06638i
$716$	−1.60092	−	1.90790i	−0.0598292	−	0.0713017i
$717$		0			0
$718$	5.68614	−	12.1940i	0.212205	−	0.455075i
$719$	−0.704484	−	1.22020i	−0.0262728	−	0.0455059i	0.852590	−	0.522580i	$-0.175031\pi$
$719$	−0.704484	−	1.22020i	−0.0262728	−	0.0455059i	−0.878863	+	0.477074i	$0.841697\pi$
$720$		0			0
$721$	−8.83364	+	15.3003i	−0.328982	+	0.569813i
$722$	−14.7681	−	21.0910i	−0.549611	−	0.784926i
$723$		0			0
$724$	−0.413244	+	1.13538i	−0.0153581	+	0.0421960i
$725$	0.538329	+	0.361488i	0.0199930	+	0.0134253i
$726$		0			0
$727$	−2.88007	−	32.9194i	−0.106816	−	1.22091i	−0.840648	−	0.541581i	$-0.817826\pi$
$727$	−2.88007	−	32.9194i	−0.106816	−	1.22091i	0.733832	−	0.679330i	$-0.237730\pi$
$728$	−16.6255	−	16.6255i	−0.616182	−	0.616182i
$729$		0			0
$730$	38.3459	−	16.3238i	1.41925	−	0.604169i
$731$	−13.3715	+	15.9355i	−0.494562	+	0.589396i
$732$		0			0
$733$	12.1269	+	8.49132i	0.447916	+	0.313634i	0.775681	−	0.631125i	$-0.217407\pi$
$733$	12.1269	+	8.49132i	0.447916	+	0.313634i	−0.327765	+	0.944759i	$0.606295\pi$
$734$	−47.6275	−	17.3350i	−1.75796	−	0.639847i
$735$		0			0
$736$	0.809475	−	4.59076i	0.0298376	−	0.169218i
$737$	6.01134	+	22.4346i	0.221431	+	0.826391i
$738$		0			0
$739$	10.7323	−	6.19632i	0.394796	−	0.227935i	−0.289440	−	0.957196i	$-0.593469\pi$
$739$	10.7323	−	6.19632i	0.394796	−	0.227935i	0.684236	+	0.729261i	$0.260136\pi$
$740$	−1.71042	−	0.0579563i	−0.0628764	−	0.00213052i
$741$		0			0
$742$	−1.06306	−	0.0930058i	−0.0390262	−	0.00341435i
$743$	−3.75974	−	0.328934i	−0.137931	−	0.0120674i	0.0179809	−	0.999838i	$-0.494276\pi$
$743$	−3.75974	−	0.328934i	−0.137931	−	0.0120674i	−0.155912	+	0.987771i	$0.549832\pi$
$744$		0			0
$745$	−17.0673	−	18.2645i	−0.625297	−	0.669159i
$746$	30.9454	−	17.8663i	1.13299	−	0.654132i
$747$		0			0
$748$	−0.592786	−	2.21231i	−0.0216744	−	0.0808900i
$749$	−5.19621	+	29.4692i	−0.189865	+	1.07678i
$750$		0			0
$751$	−11.6339	−	4.23440i	−0.424528	−	0.154516i	0.120916	−	0.992663i	$-0.461417\pi$
$751$	−11.6339	−	4.23440i	−0.424528	−	0.154516i	−0.545444	+	0.838147i	$0.683639\pi$
$752$	−36.4388	−	25.5147i	−1.32879	−	0.930426i
$753$		0			0
$754$	−0.282387	+	0.336536i	−0.0102839	+	0.0122559i
$755$	10.2594	+	24.1002i	0.373377	+	0.877096i
$756$		0			0
$757$	14.6821	+	14.6821i	0.533632	+	0.533632i	0.921651	−	0.388019i	$-0.126841\pi$
$757$	14.6821	+	14.6821i	0.533632	+	0.533632i	−0.388019	+	0.921651i	$0.626841\pi$
$758$	−3.09745	−	35.4040i	−0.112505	−	1.28593i
$759$		0			0
$760$	0.647494	−	3.06181i	0.0234871	−	0.111063i
$761$	0.142795	−	0.392327i	0.00517632	−	0.0142218i	−0.937078	−	0.349121i	$-0.886480\pi$
$761$	0.142795	−	0.392327i	0.00517632	−	0.0142218i	0.942254	+	0.334899i	$0.108702\pi$
$762$		0			0
$763$	−19.3037	−	27.5686i	−0.698842	−	0.998050i
$764$	−0.362237	+	0.627413i	−0.0131053	+	0.0226990i
$765$		0			0
$766$	−6.71141	−	11.6245i	−0.242493	−	0.420010i
$767$	4.03093	−	8.64435i	0.145548	−	0.312129i
$768$		0			0
$769$	11.9703	+	14.2656i	0.431660	+	0.514432i	0.937400	−	0.348254i	$-0.113225\pi$
$769$	11.9703	+	14.2656i	0.431660	+	0.514432i	−0.505741	+	0.862685i	$0.668781\pi$
$770$	24.7409	−	48.6813i	0.891600	−	1.75435i
$771$		0			0
$772$	−0.678225	−	0.316262i	−0.0244099	−	0.0113825i
$773$	−4.48345	+	16.7325i	−0.161259	+	0.601825i	0.837229	+	0.546852i	$0.184174\pi$
$773$	−4.48345	+	16.7325i	−0.161259	+	0.601825i	−0.998488	+	0.0549731i	$0.982493\pi$
$774$		0			0
$775$	−4.07313	−	14.0945i	−0.146311	−	0.506288i
$776$	−11.9032	−	2.09886i	−0.427302	−	0.0753448i
$777$		0			0
$778$	−15.0628	+	7.02388i	−0.540026	+	0.251818i
$779$	−0.0279902	−	0.158740i	−0.00100285	−	0.00568746i
$780$		0			0
$781$	−34.1245	−	28.6339i	−1.22107	−	1.02460i
$782$	24.2594	−	24.2594i	0.867513	−	0.867513i
$783$		0			0
$784$			14.0242i			0.500864i
$785$	40.1371	−	21.3946i	1.43255	−	0.763606i
$786$		0			0
$787$	19.6926	−	28.1240i	0.701966	−	1.00251i	−0.296900	−	0.954909i	$-0.595953\pi$
$787$	19.6926	−	28.1240i	0.701966	−	1.00251i	0.998866	−	0.0476032i	$-0.0151583\pi$
$788$	−0.0169836	−	0.0364214i	−0.000605014	−	0.00129746i
$789$		0			0
$790$	26.1073	+	16.2761i	0.928855	+	0.579077i
$791$	−29.5259	−	17.0468i	−1.04982	−	0.606114i
$792$		0			0
$793$	11.7506	+	3.14857i	0.417277	+	0.111809i
$794$	−15.3120	+	5.57311i	−0.543402	+	0.197782i
$795$		0			0
$796$	1.84620	−	1.54915i	0.0654370	−	0.0549081i
$797$	−3.24062	+	37.0405i	−0.114789	+	1.31204i	0.692300	+	0.721610i	$0.256598\pi$
$797$	−3.24062	+	37.0405i	−0.114789	+	1.31204i	−0.807088	+	0.590431i	$0.798958\pi$
$798$		0			0
$799$	14.5024	+	39.8451i	0.513060	+	1.40962i
$800$	−2.85228	+	1.72187i	−0.100843	+	0.0608772i
$801$		0			0
$802$	42.9235	−	11.5013i	1.51568	−	0.406126i
$803$	60.4514	−	42.3285i	2.13328	−	1.49374i
$804$		0			0
$805$	−51.1912	+	2.73597i	−1.80425	+	0.0964302i
$806$	9.78874	−	1.72602i	0.344794	−	0.0607964i
$807$		0			0
$808$	22.9167	−	2.00495i	0.806206	−	0.0705339i
$809$	−38.7711			−1.36312			−0.681560	−	0.731763i	$-0.738698\pi$
$809$	−38.7711			−1.36312			−0.681560	+	0.731763i	$0.738698\pi$
$810$		0			0
$811$	−15.0813			−0.529577			−0.264789	−	0.964307i	$-0.585302\pi$
$811$	−15.0813			−0.529577			−0.264789	+	0.964307i	$0.585302\pi$
$812$	−0.0499387	+	0.00436907i	−0.00175251	+	0.000153324i
$813$		0			0
$814$	47.6203	−	8.39674i	1.66909	−	0.294305i
$815$	−16.2139	−	14.5687i	−0.567949	−	0.510320i
$816$		0			0
$817$	−2.29612	+	1.60776i	−0.0803311	+	0.0562484i
$818$	6.22720	−	1.66857i	0.217729	−	0.0583403i
$819$		0			0
$820$	−0.0530427	+	0.0705419i	−0.00185233	+	0.00246343i
$821$	5.23862	+	14.3930i	0.182829	+	0.502318i	0.996921	−	0.0784180i	$-0.0249869\pi$
$821$	5.23862	+	14.3930i	0.182829	+	0.502318i	−0.814092	+	0.580736i	$0.802765\pi$
$822$		0			0
$823$	3.01659	−	34.4798i	0.105152	−	1.20189i	−0.741948	−	0.670458i	$-0.766098\pi$
$823$	3.01659	−	34.4798i	0.105152	−	1.20189i	0.847100	−	0.531434i	$-0.178347\pi$
$824$	−11.9994	+	10.0687i	−0.418020	+	0.350761i
$825$		0			0
$826$	−16.3188	+	5.93955i	−0.567803	+	0.206664i
$827$	8.57712	+	2.29823i	0.298256	+	0.0799174i	0.404844	−	0.914386i	$-0.367326\pi$
$827$	8.57712	+	2.29823i	0.298256	+	0.0799174i	−0.106588	+	0.994303i	$0.533993\pi$
$828$		0			0
$829$	45.2184	+	26.1068i	1.57050	+	0.906728i	0.996108	+	0.0881465i	$0.0280944\pi$
$829$	45.2184	+	26.1068i	1.57050	+	0.906728i	0.574391	+	0.818581i	$0.305239\pi$
$830$	0.0441013	−	0.0102297i	0.00153078	−	0.000355078i
$831$		0			0
$832$	−8.78095	−	18.8308i	−0.304425	−	0.652840i
$833$	7.66760	−	10.9505i	0.265667	−	0.379411i
$834$		0			0
$835$	8.42224	+	15.8004i	0.291464	+	0.546797i
$836$		−	0.308617i		−	0.0106737i
$837$		0			0
$838$	21.2666	−	21.2666i	0.734642	−	0.734642i
$839$	11.8964	+	9.98230i	0.410711	+	0.344627i	0.824616	−	0.565693i	$-0.191391\pi$
$839$	11.8964	+	9.98230i	0.410711	+	0.344627i	−0.413905	+	0.910320i	$0.635836\pi$
$840$		0			0
$841$	−5.03288	−	28.5429i	−0.173547	−	0.984237i
$842$	35.2886	−	16.4553i	1.21612	−	0.567088i
$843$		0			0
$844$	0.678207	+	0.119586i	0.0233448	+	0.00411632i
$845$	−1.86522	+	15.3221i	−0.0641654	+	0.527096i
$846$		0			0
$847$	15.6968	−	58.5813i	0.539349	−	2.01288i
$848$	−0.806739	−	0.376188i	−0.0277035	−	0.0129184i
$849$		0			0
$850$	−24.4642	−	1.65981i	−0.839116	−	0.0569309i
$851$	−29.1790	−	34.7742i	−1.00024	−	1.19204i
$852$		0			0
$853$	−11.3970	+	24.4409i	−0.390225	+	0.836841i	0.608826	+	0.793303i	$0.291641\pi$
$853$	−11.3970	+	24.4409i	−0.390225	+	0.836841i	−0.999052	+	0.0435376i	$0.986137\pi$
$854$	−11.0747	−	19.1820i	−0.378969	−	0.656394i
$855$		0			0
$856$	−13.2655	+	22.9765i	−0.453405	+	0.785321i
$857$	−13.4716	−	19.2394i	−0.460181	−	0.657206i	0.520263	−	0.854006i	$-0.325834\pi$
$857$	−13.4716	−	19.2394i	−0.460181	−	0.657206i	−0.980444	+	0.196800i	$0.936945\pi$
$858$		0			0
$859$	−1.36480	+	3.74977i	−0.0465665	+	0.127940i	−0.960796	−	0.277257i	$-0.910575\pi$
$859$	−1.36480	+	3.74977i	−0.0465665	+	0.127940i	0.914229	+	0.405197i	$0.132797\pi$
$860$	1.50160	+	0.317550i	0.0512041	+	0.0108284i
$861$		0			0
$862$	−4.14747	−	47.4058i	−0.141263	−	1.61465i
$863$	−20.0386	−	20.0386i	−0.682123	−	0.682123i	0.278355	−	0.960478i	$-0.410211\pi$
$863$	−20.0386	−	20.0386i	−0.682123	−	0.682123i	−0.960478	+	0.278355i	$0.910211\pi$
$864$		0			0
$865$	12.7972	−	31.7687i	0.435116	−	1.08017i
$866$	−4.56305	+	5.43803i	−0.155059	+	0.184792i
$867$		0			0
$868$	0.929084	+	0.650552i	0.0315352	+	0.0220812i
$869$	51.1922	+	18.6324i	1.73657	+	0.632062i
$870$		0			0
$871$	1.83338	−	10.3976i	0.0621216	−	0.352309i
$872$	−7.72295	−	28.8225i	−0.261532	−	0.976051i
$873$		0			0
$874$	4.00353	−	2.31144i	0.135421	−	0.0781856i
$875$	25.5337	+	26.2770i	0.863195	+	0.888326i
$876$		0			0
$877$	8.35740	+	0.731178i	0.282209	+	0.0246901i	0.227382	−	0.973806i	$-0.426984\pi$
$877$	8.35740	+	0.731178i	0.282209	+	0.0246901i	0.0548277	+	0.998496i	$0.482539\pi$
$878$	−42.6236	−	3.72908i	−1.43848	−	0.125850i
$879$		0			0
$880$	33.2815	−	31.1000i	1.12192	−	1.04838i
$881$	−35.8317	+	20.6875i	−1.20720	+	0.696978i	−0.962147	−	0.272531i	$-0.912139\pi$
$881$	−35.8317	+	20.6875i	−1.20720	+	0.696978i	−0.245055	+	0.969509i	$0.578806\pi$
$882$		0			0
$883$	12.7078	+	47.4262i	0.427652	+	1.59602i	0.758063	+	0.652181i	$0.226146\pi$
$883$	12.7078	+	47.4262i	0.427652	+	1.59602i	−0.330411	+	0.943837i	$0.607187\pi$
$884$	−0.180792	+	1.02532i	−0.00608068	+	0.0344852i
$885$		0			0
$886$	40.0542	+	14.5785i	1.34565	+	0.489776i
$887$	−29.4925	−	20.6509i	−0.990261	−	0.693389i	−0.0381920	−	0.999270i	$-0.512160\pi$
$887$	−29.4925	−	20.6509i	−0.990261	−	0.693389i	−0.952069	+	0.305882i	$0.901049\pi$
$888$		0			0
$889$	−27.6162	+	32.9117i	−0.926218	+	1.10382i
$890$	14.5593	+	5.86482i	0.488029	+	0.196589i
$891$		0			0
$892$	1.63198	+	1.63198i	0.0546427	+	0.0546427i
$893$	0.497971	+	5.69183i	0.0166640	+	0.190470i
$894$		0			0
$895$	−39.5718	+	25.7565i	−1.32274	+	0.860945i
$896$	−11.4450	+	31.4448i	−0.382349	+	1.05050i
$897$		0			0
$898$	−8.59842	−	12.2798i	−0.286933	−	0.409783i
$899$	0.190267	−	0.329553i	0.00634577	−	0.0109912i
$900$		0			0
$901$	0.424246	+	0.734815i	0.0141337	+	0.0244802i
$902$	1.05389	−	2.26008i	0.0350907	−	0.0752523i
$903$		0			0
$904$	−19.4302	−	23.1560i	−0.646239	−	0.770158i
$905$	20.4197	+	10.3777i	0.678773	+	0.344968i
$906$		0			0
$907$	26.5638	+	12.3869i	0.882035	+	0.411300i	0.810225	−	0.586118i	$-0.199345\pi$
$907$	26.5638	+	12.3869i	0.882035	+	0.411300i	0.0718100	+	0.997418i	$0.477122\pi$
$908$	0.305217	−	1.13909i	0.0101290	−	0.0378019i
$909$		0			0
$910$	−19.5452	+	15.3030i	−0.647916	+	0.507288i
$911$	−6.24634	−	1.10140i	−0.206950	−	0.0364909i	0.0692118	−	0.997602i	$-0.477952\pi$
$911$	−6.24634	−	1.10140i	−0.206950	−	0.0364909i	−0.276162	+	0.961111i	$0.589063\pi$
$912$		0			0
$913$	0.0726549	−	0.0338795i	0.00240453	−	0.00112125i
$914$	−6.17252	−	35.0061i	−0.204169	−	1.15790i
$915$		0			0
$916$	1.14223	+	0.958446i	0.0377404	+	0.0316680i
$917$	−7.52537	+	7.52537i	−0.248510	+	0.248510i
$918$		0			0
$919$		−	32.7220i		−	1.07940i	−0.841858	−	0.539699i	$-0.818538\pi$
$919$		−	32.7220i		−	1.07940i	0.841858	−	0.539699i	$-0.181462\pi$
$920$	−43.4796	−	13.2438i	−1.43348	−	0.436636i
$921$		0			0
$922$	12.8663	−	18.3749i	0.423728	−	0.605146i
$923$	8.55789	+	18.3525i	0.281686	+	0.604079i
$924$		0			0
$925$	−5.00902	+	32.0552i	−0.164696	+	1.05397i
$926$	1.41180	+	0.815104i	0.0463947	+	0.0267860i
$927$		0			0
$928$	−0.0834718	−	0.0223662i	−0.00274010	−	0.000734206i
$929$	43.8241	−	15.9507i	1.43782	−	0.523324i	0.498659	−	0.866798i	$-0.333826\pi$
$929$	43.8241	−	15.9507i	1.43782	−	0.523324i	0.939162	+	0.343474i	$0.111604\pi$
$930$		0			0
$931$	1.37988	−	1.15786i	0.0452237	−	0.0379472i
$932$	0.0156110	−	0.178434i	0.000511355	−	0.00584481i
$933$		0			0
$934$	7.49095	+	20.5812i	0.245111	+	0.673438i
$935$	−42.9908	+	6.08736i	−1.40595	+	0.199078i
$936$		0			0
$937$	−35.0118	+	9.38138i	−1.14379	+	0.306476i	−0.780472	−	0.625191i	$-0.785021\pi$
$937$	−35.0118	+	9.38138i	−1.14379	+	0.306476i	−0.363313	+	0.931667i	$0.618355\pi$
$938$	−15.7468	+	11.0260i	−0.514150	+	0.360012i
$939$		0			0
$940$	2.09095	−	2.32707i	0.0681992	−	0.0759008i
$941$	57.6114	−	10.1585i	1.87808	−	0.331156i	0.886718	−	0.462312i	$-0.152980\pi$
$941$	57.6114	−	10.1585i	1.87808	−	0.331156i	0.991362	+	0.131155i	$0.0418687\pi$
$942$		0			0
$943$	−2.33214	+	0.204035i	−0.0759448	+	0.00664431i
$944$	−14.4859			−0.471476
$945$		0			0
$946$	−43.3653			−1.40993
$947$	−35.5094	+	3.10667i	−1.15390	+	0.100953i	−0.648001	−	0.761639i	$-0.724395\pi$
$947$	−35.5094	+	3.10667i	−1.15390	+	0.100953i	−0.505900	+	0.862592i	$0.668839\pi$
$948$		0			0
$949$	−33.0369	+	5.82530i	−1.07242	+	0.189097i
$950$	−3.12626	−	1.06922i	−0.101429	−	0.0346902i
$951$		0			0
$952$	27.8826	−	19.5236i	0.903680	−	0.632763i
$953$	31.6489	−	8.48031i	1.02521	−	0.274704i	0.293238	−	0.956039i	$-0.405267\pi$
$953$	31.6489	−	8.48031i	1.02521	−	0.274704i	0.731971	+	0.681335i	$0.238600\pi$
$954$		0			0
$955$	10.9773	+	8.25416i	0.355216	+	0.267098i
$956$	−0.807147	−	2.21762i	−0.0261050	−	0.0717229i
$957$		0			0
$958$	0.889462	−	10.1666i	0.0287372	−	0.328468i
$959$	−11.8121	+	9.91155i	−0.381434	+	0.320061i
$960$		0			0
$961$	21.0399	−	7.65791i	0.678708	−	0.247029i
$962$	−21.2320	−	5.68909i	−0.684546	−	0.183424i
$963$		0			0
$964$	1.07769	+	0.622203i	0.0347100	+	0.0200398i
$965$	−7.50536	+	12.0388i	−0.241606	+	0.387543i
$966$		0			0
$967$	9.66112	+	20.7183i	0.310681	+	0.666257i	0.998204	−	0.0599053i	$-0.0190799\pi$
$967$	9.66112	+	20.7183i	0.310681	+	0.666257i	−0.687523	+	0.726162i	$0.741302\pi$
$968$	30.8421	−	44.0471i	0.991302	−	1.41573i
$969$		0			0
$970$	−3.71830	+	12.2072i	−0.119388	+	0.391950i
$971$		−	15.4621i		−	0.496202i	−0.968734	−	0.248101i	$-0.920193\pi$
$971$		−	15.4621i		−	0.496202i	0.968734	−	0.248101i	$-0.0798065\pi$
$972$		0			0
$973$	26.7157	−	26.7157i	0.856467	−	0.856467i
$974$	19.7146	+	16.5425i	0.631697	+	0.530057i
$975$		0			0
$976$	−3.20831	−	18.1952i	−0.102696	−	0.582416i
$977$	27.0270	−	12.6029i	0.864672	−	0.403203i	0.0609021	−	0.998144i	$-0.480602\pi$
$977$	27.0270	−	12.6029i	0.864672	−	0.403203i	0.803770	+	0.594941i	$0.202824\pi$
$978$		0			0
$979$	27.3717	+	4.82638i	0.874805	+	0.154252i
$980$	−0.979077	−	0.119187i	−0.0312755	−	0.00380728i
$981$		0			0
$982$	−12.8098	+	47.8069i	−0.408777	+	1.52558i
$983$	−18.4209	−	8.58979i	−0.587535	−	0.273972i	0.106034	−	0.994363i	$-0.466185\pi$
$983$	−18.4209	−	8.58979i	−0.587535	−	0.273972i	−0.693569	+	0.720391i	$0.743963\pi$
$984$		0			0
$985$	−0.724310	+	0.236172i	−0.0230784	+	0.00752507i
$986$	−0.408813	−	0.487204i	−0.0130193	−	0.0155157i
$987$		0			0
$988$	−0.0592891	+	0.127146i	−0.00188624	+	0.00404505i
$989$	20.3552	+	35.2562i	0.647256	+	1.12108i
$990$		0			0
$991$	−13.3395	+	23.1047i	−0.423743	+	0.733944i	−0.996302	−	0.0859191i	$-0.972617\pi$
$991$	−13.3395	+	23.1047i	−0.423743	+	0.733944i	0.572559	+	0.819863i	$0.305951\pi$
$992$	1.12146	+	1.60161i	0.0356065	+	0.0508513i
$993$		0			0
$994$	12.6100	−	34.6457i	0.399965	−	1.09890i
$995$	−24.9236	−	38.2921i	−0.790130	−	1.21394i
$996$		0			0
$997$	−0.716120	−	8.18529i	−0.0226798	−	0.259231i	−0.999066	−	0.0432005i	$-0.986245\pi$
$997$	−0.716120	−	8.18529i	−0.0226798	−	0.259231i	0.976387	−	0.216030i	$-0.0693110\pi$
$998$	31.1175	+	31.1175i	0.985007	+	0.985007i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.197.12		192
3.2	odd	2		135.2.q.a.92.5	yes	192
5.3	odd	4	inner	405.2.r.a.278.5		192
15.2	even	4		675.2.ba.b.443.5		192
15.8	even	4		135.2.q.a.38.12	yes	192
15.14	odd	2		675.2.ba.b.632.12		192
27.5	odd	18	inner	405.2.r.a.287.5		192
27.22	even	9		135.2.q.a.32.12	✓	192
135.22	odd	36		675.2.ba.b.518.12		192
135.49	even	18		675.2.ba.b.32.5		192
135.103	odd	36		135.2.q.a.113.5	yes	192
135.113	even	36	inner	405.2.r.a.368.12		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.12	✓	192	27.22	even	9
135.2.q.a.38.12	yes	192	15.8	even	4
135.2.q.a.92.5	yes	192	3.2	odd	2
135.2.q.a.113.5	yes	192	135.103	odd	36
405.2.r.a.197.12		192	1.1	even	1	trivial
405.2.r.a.278.5		192	5.3	odd	4	inner
405.2.r.a.287.5		192	27.5	odd	18	inner
405.2.r.a.368.12		192	135.113	even	36	inner
675.2.ba.b.32.5		192	135.49	even	18
675.2.ba.b.443.5		192	15.2	even	4
675.2.ba.b.518.12		192	135.22	odd	36
675.2.ba.b.632.12		192	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36666 - 0.119567i) q^{2} +(-0.116159 + 0.0204819i) q^{4} +(0.119339 + 2.23288i) q^{5} +(-2.68447 + 1.87969i) q^{7} +(-2.80657 + 0.752017i) q^{8} +O(q^{10})\)	\(q+(1.36666 - 0.119567i) q^{2} +(-0.116159 + 0.0204819i) q^{4} +(0.119339 + 2.23288i) q^{5} +(-2.68447 + 1.87969i) q^{7} +(-2.80657 + 0.752017i) q^{8} +(0.430074 + 3.03731i) q^{10} +(1.85785 + 5.10439i) q^{11} +(0.215209 - 2.45985i) q^{13} +(-3.44400 + 2.88986i) q^{14} +(-3.52402 + 1.28264i) q^{16} +(3.45292 + 0.925208i) q^{17} +(0.417150 + 0.240842i) q^{19} +(-0.0595960 - 0.256925i) q^{20} +(3.14935 + 6.75381i) q^{22} +(4.01261 - 5.73060i) q^{23} +(-4.97152 + 0.532938i) q^{25} -3.38750i q^{26} +(0.273325 - 0.273325i) q^{28} +(-0.0993465 - 0.0833616i) q^{29} +(0.509526 + 2.88966i) q^{31} +(0.603911 - 0.281608i) q^{32} +(4.82959 + 0.851587i) q^{34} +(-4.51748 - 5.76978i) q^{35} +(1.67943 - 6.26774i) q^{37} +(0.598898 + 0.279271i) q^{38} +(-2.01410 - 6.17698i) q^{40} +(-0.215101 - 0.256347i) q^{41} +(-2.45933 + 5.27405i) q^{43} +(-0.320353 - 0.554867i) q^{44} +(4.79867 - 8.31155i) q^{46} +(6.80358 + 9.71652i) q^{47} +(1.27902 - 3.51408i) q^{49} +(-6.73064 + 1.32277i) q^{50} +(0.0253840 + 0.290141i) q^{52} +(0.167838 + 0.167838i) q^{53} +(-11.1758 + 4.75750i) q^{55} +(6.12058 - 7.29423i) q^{56} +(-0.145740 - 0.102048i) q^{58} +(3.62976 + 1.32113i) q^{59} +(-0.855508 + 4.85182i) q^{61} +(1.04186 + 3.88826i) q^{62} +(7.28718 - 4.20726i) q^{64} +(5.51823 + 0.186981i) q^{65} +(4.25953 + 0.372661i) q^{67} +(-0.420038 - 0.0367485i) q^{68} +(-6.86372 - 7.34518i) q^{70} +(-7.10207 + 4.10038i) q^{71} +(-3.51625 - 13.1228i) q^{73} +(1.54580 - 8.76665i) q^{74} +(-0.0533886 - 0.0194318i) q^{76} +(-14.5820 - 10.2104i) q^{77} +(6.44655 - 7.68270i) q^{79} +(-3.28453 - 7.71565i) q^{80} +(-0.324619 - 0.324619i) q^{82} +(-0.00128626 - 0.0147020i) q^{83} +(-1.65381 + 7.82038i) q^{85} +(-2.73046 + 7.50188i) q^{86} +(-9.05275 - 12.9287i) q^{88} +(2.55837 - 4.43123i) q^{89} +(4.04602 + 7.00791i) q^{91} +(-0.348726 + 0.747846i) q^{92} +(10.4599 + 12.4657i) q^{94} +(-0.487989 + 0.960188i) q^{95} +(3.77015 + 1.75805i) q^{97} +(1.32781 - 4.95547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

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