LMFDB - Embedded newform 441.2.bg.a.395.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			395.6
Character	$\chi$	$=$	441.395
Dual form			441.2.bg.a.278.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02327 - 0.401605i) q^{2} +(-0.580301 - 0.538441i) q^{4} +(-1.00842 - 0.687530i) q^{5} +(2.62056 - 0.364218i) q^{7} +(1.33147 + 2.76483i) q^{8} +O(q^{10})$	\(q+(-1.02327 - 0.401605i) q^{2} +(-0.580301 - 0.538441i) q^{4} +(-1.00842 - 0.687530i) q^{5} +(2.62056 - 0.364218i) q^{7} +(1.33147 + 2.76483i) q^{8} +(0.755775 + 1.10852i) q^{10} +(-0.0890350 - 0.590708i) q^{11} +(2.95451 - 2.35614i) q^{13} +(-2.82782 - 0.679737i) q^{14} +(-0.133773 - 1.78508i) q^{16} +(-2.61960 - 0.808039i) q^{17} +(0.127290 - 0.0734907i) q^{19} +(0.214994 + 0.941949i) q^{20} +(-0.146125 + 0.640213i) q^{22} +(-2.07095 - 6.71384i) q^{23} +(-1.28249 - 3.26773i) q^{25} +(-3.96951 + 1.22443i) q^{26} +(-1.71682 - 1.19966i) q^{28} +(-2.75551 + 0.628926i) q^{29} +(-4.54912 - 2.62644i) q^{31} +(1.22903 - 3.98443i) q^{32} +(2.35605 + 1.87889i) q^{34} +(-2.89304 - 1.43443i) q^{35} +(-0.323554 + 0.300214i) q^{37} +(-0.159766 + 0.0240809i) q^{38} +(0.558218 - 3.70353i) q^{40} +(4.98252 - 2.39945i) q^{41} +(1.07470 + 0.517549i) q^{43} +(-0.266394 + 0.390729i) q^{44} +(-0.577170 + 7.70180i) q^{46} +(-1.29597 + 3.30207i) q^{47} +(6.73469 - 1.90891i) q^{49} +3.85884i q^{50} +(-2.98315 - 0.223556i) q^{52} +(8.63323 - 9.30441i) q^{53} +(-0.316345 + 0.656897i) q^{55} +(4.49620 + 6.76045i) q^{56} +(3.07222 + 0.463062i) q^{58} +(1.25982 - 0.858928i) q^{59} +(-9.59443 - 10.3403i) q^{61} +(3.60020 + 4.51451i) q^{62} +(-5.09001 + 6.38267i) q^{64} +(-4.59931 + 0.344671i) q^{65} +(-1.69535 + 2.93644i) q^{67} +(1.08507 + 1.87940i) q^{68} +(2.38430 + 2.62968i) q^{70} +(6.84143 + 1.56151i) q^{71} +(-14.5201 + 5.69870i) q^{73} +(0.451652 - 0.177260i) q^{74} +(-0.113437 - 0.0258912i) q^{76} +(-0.448468 - 1.51556i) q^{77} +(5.62817 + 9.74827i) q^{79} +(-1.09240 + 1.89208i) q^{80} +(-6.06211 + 0.454292i) q^{82} +(4.09993 - 5.14115i) q^{83} +(2.08611 + 2.61590i) q^{85} +(-0.891863 - 0.961200i) q^{86} +(1.51466 - 1.03268i) q^{88} +(3.27093 + 0.493014i) q^{89} +(6.88433 - 7.25051i) q^{91} +(-2.41323 + 5.01113i) q^{92} +(2.65226 - 2.85845i) q^{94} +(-0.178888 - 0.0134058i) q^{95} +12.1414i q^{97} +(-7.65806 - 0.751350i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

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 $

$2$	−1.02327	−	0.401605i	−0.723564	−	0.283978i	−0.0251617	−	0.999683i	$-0.508010\pi$
$2$	−1.02327	−	0.401605i	−0.723564	−	0.283978i	−0.698402	+	0.715705i	$0.746105\pi$
$3$		0			0
$3$		0			0
$4$	−0.580301	−	0.538441i	−0.290151	−	0.269220i
$5$	−1.00842	−	0.687530i	−0.450980	−	0.307473i	0.316446	−	0.948610i	$-0.397510\pi$
$5$	−1.00842	−	0.687530i	−0.450980	−	0.307473i	−0.767426	+	0.641138i	$0.778463\pi$
$6$		0			0
$7$	2.62056	−	0.364218i	0.990479	−	0.137661i
$7$	2.62056	−	0.364218i	0.990479	−	0.137661i
$8$	1.33147	+	2.76483i	0.470746	+	0.977514i
$9$		0			0
$10$	0.755775	+	1.10852i	0.238997	+	0.350544i
$11$	−0.0890350	−	0.590708i	−0.0268450	−	0.178105i	0.971390	−	0.237489i	$-0.0763245\pi$
$11$	−0.0890350	−	0.590708i	−0.0268450	−	0.178105i	−0.998235	+	0.0593840i	$0.981086\pi$
$12$		0			0
$13$	2.95451	−	2.35614i	0.819434	−	0.653477i	−0.121302	−	0.992616i	$-0.538707\pi$
$13$	2.95451	−	2.35614i	0.819434	−	0.653477i	0.940736	+	0.339139i	$0.110136\pi$
$14$	−2.82782	−	0.679737i	−0.755768	−	0.181667i
$15$		0			0
$16$	−0.133773	−	1.78508i	−0.0334433	−	0.446270i
$17$	−2.61960	−	0.808039i	−0.635346	−	0.195978i	−0.0396825	−	0.999212i	$-0.512635\pi$
$17$	−2.61960	−	0.808039i	−0.635346	−	0.195978i	−0.595664	+	0.803234i	$0.703111\pi$
$18$		0			0
$19$	0.127290	−	0.0734907i	0.0292022	−	0.0168599i	−0.485328	−	0.874332i	$-0.661300\pi$
$19$	0.127290	−	0.0734907i	0.0292022	−	0.0168599i	0.514530	+	0.857472i	$0.327966\pi$
$20$	0.214994	+	0.941949i	0.0480741	+	0.210626i
$21$		0			0
$22$	−0.146125	+	0.640213i	−0.0311539	+	0.136494i
$23$	−2.07095	−	6.71384i	−0.431822	−	1.39993i	−0.866423	−	0.499310i	$-0.833587\pi$
$23$	−2.07095	−	6.71384i	−0.431822	−	1.39993i	0.434601	−	0.900623i	$-0.356889\pi$
$24$		0			0
$25$	−1.28249	−	3.26773i	−0.256498	−	0.653546i
$26$	−3.96951	+	1.22443i	−0.778486	+	0.240131i
$27$		0			0
$28$	−1.71682	−	1.19966i	−0.324449	−	0.226715i
$29$	−2.75551	+	0.628926i	−0.511684	+	0.116789i	−0.470565	−	0.882366i	$-0.655950\pi$
$29$	−2.75551	+	0.628926i	−0.511684	+	0.116789i	−0.0411199	+	0.999154i	$0.513093\pi$
$30$		0			0
$31$	−4.54912	−	2.62644i	−0.817046	−	0.471722i	0.0323508	−	0.999477i	$-0.489701\pi$
$31$	−4.54912	−	2.62644i	−0.817046	−	0.471722i	−0.849397	+	0.527755i	$0.823034\pi$
$32$	1.22903	−	3.98443i	0.217265	−	0.704355i
$33$		0			0
$34$	2.35605	+	1.87889i	0.404060	+	0.322227i
$35$	−2.89304	−	1.43443i	−0.489013	−	0.242463i
$36$		0			0
$37$	−0.323554	+	0.300214i	−0.0531919	+	0.0493549i	−0.706321	−	0.707892i	$-0.749646\pi$
$37$	−0.323554	+	0.300214i	−0.0531919	+	0.0493549i	0.653129	+	0.757247i	$0.273456\pi$
$38$	−0.159766	+	0.0240809i	−0.0259175	+	0.00390644i
$39$		0			0
$40$	0.558218	−	3.70353i	0.0882620	−	0.585580i
$41$	4.98252	−	2.39945i	0.778138	−	0.374732i	−0.00227370	−	0.999997i	$-0.500724\pi$
$41$	4.98252	−	2.39945i	0.778138	−	0.374732i	0.780412	+	0.625266i	$0.215009\pi$
$42$		0			0
$43$	1.07470	+	0.517549i	0.163890	+	0.0789254i	0.514031	−	0.857772i	$-0.328152\pi$
$43$	1.07470	+	0.517549i	0.163890	+	0.0789254i	−0.350140	+	0.936697i	$0.613866\pi$
$44$	−0.266394	+	0.390729i	−0.0401605	+	0.0589046i
$45$		0			0
$46$	−0.577170	+	7.70180i	−0.0850991	+	1.13557i
$47$	−1.29597	+	3.30207i	−0.189036	+	0.481656i	−0.993700	−	0.112075i	$-0.964250\pi$
$47$	−1.29597	+	3.30207i	−0.189036	+	0.481656i	0.804664	+	0.593731i	$0.202346\pi$
$48$		0			0
$49$	6.73469	−	1.90891i	0.962099	−	0.272702i
$50$			3.85884i			0.545722i
$51$		0			0
$52$	−2.98315	−	0.223556i	−0.413689	−	0.0310017i
$53$	8.63323	−	9.30441i	1.18586	−	1.27806i	0.233757	−	0.972295i	$-0.424898\pi$
$53$	8.63323	−	9.30441i	1.18586	−	1.27806i	0.952108	−	0.305763i	$-0.0989117\pi$
$54$		0			0
$55$	−0.316345	+	0.656897i	−0.0426559	+	0.0885760i
$56$	4.49620	+	6.76045i	0.600830	+	0.903403i
$57$		0			0
$58$	3.07222	+	0.463062i	0.403402	+	0.0608030i
$59$	1.25982	−	0.858928i	0.164014	−	0.111823i	−0.478531	−	0.878070i	$-0.658831\pi$
$59$	1.25982	−	0.858928i	0.164014	−	0.111823i	0.642546	+	0.766248i	$0.277878\pi$
$60$		0			0
$61$	−9.59443	−	10.3403i	−1.22844	−	1.32394i	−0.929114	−	0.369793i	$-0.879428\pi$
$61$	−9.59443	−	10.3403i	−1.22844	−	1.32394i	−0.299327	−	0.954151i	$-0.596762\pi$
$62$	3.60020	+	4.51451i	0.457226	+	0.573344i
$63$		0			0
$64$	−5.09001	+	6.38267i	−0.636251	+	0.797833i
$65$	−4.59931	+	0.344671i	−0.570474	+	0.0427511i
$66$		0			0
$67$	−1.69535	+	2.93644i	−0.207120	+	0.358743i	−0.950806	−	0.309786i	$-0.899742\pi$
$67$	−1.69535	+	2.93644i	−0.207120	+	0.358743i	0.743686	+	0.668529i	$0.233076\pi$
$68$	1.08507	+	1.87940i	0.131585	+	0.227911i
$69$		0			0
$70$	2.38430	+	2.62968i	0.284978	+	0.314306i
$71$	6.84143	+	1.56151i	0.811928	+	0.185317i	0.608275	−	0.793726i	$-0.291862\pi$
$71$	6.84143	+	1.56151i	0.811928	+	0.185317i	0.203652	+	0.979043i	$0.434719\pi$
$72$		0			0
$73$	−14.5201	+	5.69870i	−1.69944	+	0.666982i	−0.998912	−	0.0466388i	$-0.985149\pi$
$73$	−14.5201	+	5.69870i	−1.69944	+	0.666982i	−0.700532	+	0.713621i	$0.747054\pi$
$74$	0.451652	−	0.177260i	0.0525034	−	0.0206061i
$75$		0			0
$76$	−0.113437	−	0.0258912i	−0.0130121	−	0.00296992i
$77$	−0.448468	−	1.51556i	−0.0511077	−	0.172714i
$78$		0			0
$79$	5.62817	+	9.74827i	0.633218	+	1.09677i	0.986890	+	0.161396i	$0.0515998\pi$
$79$	5.62817	+	9.74827i	0.633218	+	1.09677i	−0.353671	+	0.935370i	$0.615067\pi$
$80$	−1.09240	+	1.89208i	−0.122134	+	0.211542i
$81$		0			0
$82$	−6.06211	+	0.454292i	−0.669448	+	0.0501682i
$83$	4.09993	−	5.14115i	0.450025	−	0.564314i	−0.504129	−	0.863628i	$-0.668186\pi$
$83$	4.09993	−	5.14115i	0.450025	−	0.564314i	0.954155	+	0.299314i	$0.0967579\pi$
$84$		0			0
$85$	2.08611	+	2.61590i	0.226270	+	0.283734i
$86$	−0.891863	−	0.961200i	−0.0961721	−	0.103649i
$87$		0			0
$88$	1.51466	−	1.03268i	0.161463	−	0.110084i
$89$	3.27093	+	0.493014i	0.346718	+	0.0522594i	0.320093	−	0.947386i	$-0.396286\pi$
$89$	3.27093	+	0.493014i	0.346718	+	0.0522594i	0.0266252	+	0.999645i	$0.491524\pi$
$90$		0			0
$91$	6.88433	−	7.25051i	0.721674	−	0.760060i
$92$	−2.41323	+	5.01113i	−0.251597	+	0.522447i
$93$		0			0
$94$	2.65226	−	2.85845i	0.273559	−	0.294827i
$95$	−0.178888	−	0.0134058i	−0.0183536	−	0.00137541i
$96$		0			0
$97$			12.1414i			1.23277i	0.787444	+	0.616387i	$0.211404\pi$
$97$			12.1414i			1.23277i	−0.787444	+	0.616387i	$0.788596\pi$
$98$	−7.65806	−	0.751350i	−0.773581	−	0.0758978i
$99$		0			0
$100$	−1.01525	+	2.58681i	−0.101525	+	0.258681i
$101$	−0.704604	+	9.40229i	−0.0701108	+	0.935563i	0.845624	+	0.533779i	$0.179229\pi$
$101$	−0.704604	+	9.40229i	−0.0701108	+	0.935563i	−0.915735	+	0.401784i	$0.868390\pi$
$102$		0			0
$103$	10.0187	−	14.6947i	0.987173	−	1.44792i	0.0953964	−	0.995439i	$-0.469588\pi$
$103$	10.0187	−	14.6947i	0.987173	−	1.44792i	0.891776	−	0.452477i	$-0.149459\pi$
$104$	10.4482	+	5.03157i	1.02453	+	0.493386i
$105$		0			0
$106$	−12.5709	+	6.05380i	−1.22099	+	0.587998i
$107$	1.12107	−	7.43778i	0.108377	−	0.719038i	−0.866970	−	0.498361i	$-0.833935\pi$
$107$	1.12107	−	7.43778i	0.108377	−	0.719038i	0.975347	−	0.220676i	$-0.0708265\pi$
$108$		0			0
$109$	8.76053	−	1.32044i	0.839107	−	0.126475i	0.284592	−	0.958649i	$-0.408142\pi$
$109$	8.76053	−	1.32044i	0.839107	−	0.126475i	0.554515	+	0.832174i	$0.312904\pi$
$110$	0.587521	−	0.545140i	0.0560179	−	0.0519770i
$111$		0			0
$112$	−1.00072	−	4.62919i	−0.0945590	−	0.437417i
$113$	6.41946	+	5.11935i	0.603892	+	0.481588i	0.877062	−	0.480378i	$-0.159500\pi$
$113$	6.41946	+	5.11935i	0.603892	+	0.481588i	−0.273169	+	0.961966i	$0.588072\pi$
$114$		0			0
$115$	−2.52758	+	8.19422i	−0.235698	+	0.764115i
$116$	1.93766	+	1.11871i	0.179907	+	0.103870i
$117$		0			0
$118$	−1.63409	+	0.372970i	−0.150430	+	0.0343346i
$119$	−7.15912	−	1.16341i	−0.656276	−	0.106650i
$120$		0			0
$121$	10.1703	−	3.13712i	0.924572	−	0.285193i
$122$	5.66499	+	14.4342i	0.512884	+	1.30681i
$123$		0			0
$124$	1.22568	+	3.97355i	0.110069	+	0.356836i
$125$	−2.31130	+	10.1265i	−0.206729	+	0.905739i
$126$		0			0
$127$	2.71555	+	11.8976i	0.240966	+	1.05574i	0.940140	+	0.340789i	$0.110694\pi$
$127$	2.71555	+	11.8976i	0.240966	+	1.05574i	−0.699174	+	0.714952i	$0.746449\pi$
$128$	0.549691	−	0.317364i	0.0485863	−	0.0280513i
$129$		0			0
$130$	4.84478	+	1.49442i	0.424915	+	0.131069i
$131$	0.334827	+	4.46795i	0.0292539	+	0.390367i	0.992543	+	0.121899i	$0.0388983\pi$
$131$	0.334827	+	4.46795i	0.0292539	+	0.390367i	−0.963289	+	0.268468i	$0.913483\pi$
$132$		0			0
$133$	0.306804	−	0.238948i	0.0266032	−	0.0207194i
$134$	2.91410	−	2.32392i	0.251740	−	0.200756i
$135$		0			0
$136$	−1.25383	−	8.31861i	−0.107515	−	0.713315i
$137$	6.27275	+	9.20044i	0.535917	+	0.786046i	0.994735	−	0.102484i	$-0.0326791\pi$
$137$	6.27275	+	9.20044i	0.535917	+	0.786046i	−0.458817	+	0.888531i	$0.651727\pi$
$138$		0			0
$139$	0.284202	+	0.590152i	0.0241057	+	0.0500560i	0.912674	−	0.408688i	$-0.134014\pi$
$139$	0.284202	+	0.590152i	0.0241057	+	0.0500560i	−0.888568	+	0.458744i	$0.848299\pi$
$140$	0.906479	+	2.39013i	0.0766115	+	0.202003i
$141$		0			0
$142$	−6.37354	−	4.34541i	−0.534856	−	0.364659i
$143$	−1.65485	−	1.53548i	−0.138385	−	0.128403i
$144$		0			0
$145$	3.21111	+	1.26027i	0.266669	+	0.104660i
$146$	17.1466			1.41906
$147$		0			0
$148$	0.349406			0.0287210
$149$	−8.98334	−	3.52570i	−0.735944	−	0.288837i	−0.0323867	−	0.999475i	$-0.510311\pi$
$149$	−8.98334	−	3.52570i	−0.735944	−	0.288837i	−0.703557	+	0.710639i	$0.748406\pi$
$150$		0			0
$151$	−0.969253	−	0.899335i	−0.0788767	−	0.0731868i	0.639749	−	0.768584i	$-0.279038\pi$
$151$	−0.969253	−	0.899335i	−0.0788767	−	0.0731868i	−0.718626	+	0.695397i	$0.755229\pi$
$152$	0.372671	+	0.254083i	0.0302276	+	0.0206088i
$153$		0			0
$154$	−0.149751	+	1.73094i	−0.0120673	+	0.139483i
$155$	2.78168	+	5.77621i	0.223430	+	0.463956i
$156$		0			0
$157$	−0.669063	−	0.981335i	−0.0533970	−	0.0783190i	0.798612	−	0.601847i	$-0.205568\pi$
$157$	−0.669063	−	0.981335i	−0.0533970	−	0.0783190i	−0.852009	+	0.523527i	$0.824616\pi$
$158$	−1.84420	−	12.2355i	−0.146717	−	0.973400i
$159$		0			0
$160$	−3.97880	+	3.17299i	−0.314552	+	0.250847i
$161$	−7.87234	−	16.8398i	−0.620428	−	1.32716i
$162$		0			0
$163$	1.18522	+	15.8157i	0.0928336	+	1.23878i	0.827936	+	0.560823i	$0.189515\pi$
$163$	1.18522	+	15.8157i	0.0928336	+	1.23878i	−0.735102	+	0.677956i	$0.762866\pi$
$164$	−4.18332	−	1.29038i	−0.326663	−	0.100762i
$165$		0			0
$166$	−6.26006	+	3.61425i	−0.485875	+	0.280520i
$167$	−2.67976	−	11.7408i	−0.207366	−	0.908531i	−0.966311	−	0.257376i	$-0.917142\pi$
$167$	−2.67976	−	11.7408i	−0.207366	−	0.908531i	0.758945	−	0.651155i	$-0.225715\pi$
$168$		0			0
$169$	0.284950	−	1.24845i	0.0219192	−	0.0960344i
$170$	−1.08410	−	3.51457i	−0.0831468	−	0.269555i
$171$		0			0
$172$	−0.344981	−	0.878997i	−0.0263045	−	0.0670229i
$173$	−23.7151	+	7.31513i	−1.80302	+	0.556159i	−0.999248	−	0.0387726i	$-0.987655\pi$
$173$	−23.7151	+	7.31513i	−1.80302	+	0.556159i	−0.803776	+	0.594932i	$0.797179\pi$
$174$		0			0
$175$	−4.55101	−	8.09618i	−0.344024	−	0.612014i
$176$	−1.04255	+	0.237955i	−0.0785852	+	0.0179366i
$177$		0			0
$178$	−3.14906	−	1.81811i	−0.236032	−	0.136273i
$179$	5.47310	−	17.7434i	0.409079	−	1.32620i	−0.483514	−	0.875337i	$-0.660640\pi$
$179$	5.47310	−	17.7434i	0.409079	−	1.32620i	0.892593	−	0.450864i	$-0.148884\pi$
$180$		0			0
$181$	−8.94857	−	7.13625i	−0.665142	−	0.530433i	0.231698	−	0.972788i	$-0.425572\pi$
$181$	−8.94857	−	7.13625i	−0.665142	−	0.530433i	−0.896840	+	0.442355i	$0.854143\pi$
$182$	−9.95640	+	4.65447i	−0.738017	+	0.345012i
$183$		0			0
$184$	15.8052	−	14.6651i	1.16517	−	1.08112i
$185$	0.532684	−	0.0802893i	0.0391637	−	0.00590298i
$186$		0			0
$187$	−0.244080	+	1.61936i	−0.0178489	+	0.118420i
$188$	2.53002	−	1.21839i	0.184521	−	0.0888605i
$189$		0			0
$190$	0.177668	+	0.0855604i	0.0128894	+	0.00620721i
$191$	13.2898	−	19.4926i	0.961618	−	1.41043i	0.0502992	−	0.998734i	$-0.483982\pi$
$191$	13.2898	−	19.4926i	0.961618	−	1.41043i	0.911319	−	0.411701i	$-0.135065\pi$
$192$		0			0
$193$	0.357297	−	4.76780i	0.0257188	−	0.343193i	−0.969469	−	0.245212i	$-0.921142\pi$
$193$	0.357297	−	4.76780i	0.0257188	−	0.343193i	0.995188	−	0.0979813i	$-0.0312386\pi$
$194$	4.87605	−	12.4240i	0.350080	−	0.891990i
$195$		0			0
$196$	−4.93598	−	2.51849i	−0.352570	−	0.179892i
$197$			10.3817i			0.739667i	0.929098	+	0.369833i	$0.120585\pi$
$197$			10.3817i			0.739667i	−0.929098	+	0.369833i	$0.879415\pi$
$198$		0			0
$199$	3.02679	+	0.226826i	0.214563	+	0.0160793i	0.181578	−	0.983377i	$-0.441880\pi$
$199$	3.02679	+	0.226826i	0.214563	+	0.0160793i	0.0329853	+	0.999456i	$0.489499\pi$
$200$	7.32711	−	7.89674i	0.518105	−	0.558384i
$201$		0			0
$202$	4.49702	−	9.33815i	0.316409	−	0.657030i
$203$	−6.99191	+	2.65174i	−0.490736	+	0.186116i
$204$		0			0
$205$	−6.67417	−	1.00597i	−0.466144	−	0.0702599i
$206$	−16.1534	+	11.0132i	−1.12546	+	0.767325i
$207$		0			0
$208$	−4.60114	−	4.95885i	−0.319032	−	0.343834i
$209$	−0.0547448	−	0.0686478i	−0.00378677	−	0.00474846i
$210$		0			0
$211$	8.83991	−	11.0849i	0.608564	−	0.763115i	−0.378121	−	0.925756i	$-0.623430\pi$
$211$	8.83991	−	11.0849i	0.608564	−	0.763115i	0.986685	+	0.162641i	$0.0520012\pi$
$212$	−10.0197	+	0.750876i	−0.688159	+	0.0515704i
$213$		0			0
$214$	−4.13421	+	7.16066i	−0.282609	+	0.489493i
$215$	−0.727921	−	1.26080i	−0.0496438	−	0.0859856i
$216$		0			0
$217$	−12.8778	−	5.22587i	−0.874205	−	0.354755i
$218$	−9.49472	−	2.16711i	−0.643063	−	0.146775i
$219$		0			0
$220$	0.537275	−	0.210865i	0.0362231	−	0.0142165i
$221$	−9.64349	+	3.78479i	−0.648691	+	0.254593i
$222$		0			0
$223$	20.8492	+	4.75870i	1.39617	+	0.318666i	0.853418	−	0.521228i	$-0.174526\pi$
$223$	20.8492	+	4.75870i	1.39617	+	0.318666i	0.542750	+	0.839894i	$0.317383\pi$
$224$	1.76956	−	10.8891i	0.118234	−	0.727558i
$225$		0			0
$226$	−4.51291	−	7.81659i	−0.300194	−	0.519952i
$227$	−8.57972	+	14.8605i	−0.569456	+	0.986327i	0.427164	+	0.904174i	$0.359513\pi$
$227$	−8.57972	+	14.8605i	−0.569456	+	0.986327i	−0.996620	+	0.0821526i	$0.973821\pi$
$228$		0			0
$229$	−13.6062	+	1.01964i	−0.899122	+	0.0673799i	−0.516266	−	0.856428i	$-0.672678\pi$
$229$	−13.6062	+	1.01964i	−0.899122	+	0.0673799i	−0.382856	+	0.923808i	$0.625059\pi$
$230$	5.87725	−	7.36984i	0.387534	−	0.485953i
$231$		0			0
$232$	−5.40774	−	6.78110i	−0.355036	−	0.445201i
$233$	7.71223	+	8.31180i	0.505245	+	0.544524i	0.933239	−	0.359257i	$-0.116970\pi$
$233$	7.71223	+	8.31180i	0.505245	+	0.544524i	−0.427994	+	0.903782i	$0.640779\pi$
$234$		0			0
$235$	3.57715	−	2.43886i	0.233348	−	0.159094i
$236$	−1.19355	−	0.179899i	−0.0776938	−	0.0117104i
$237$		0			0
$238$	6.85851	+	4.06563i	0.444571	+	0.263536i
$239$	7.61533	−	15.8134i	0.492595	−	1.02288i	−0.495439	−	0.868643i	$-0.664993\pi$
$239$	7.61533	−	15.8134i	0.492595	−	1.02288i	0.988033	−	0.154240i	$-0.0492930\pi$
$240$		0			0
$241$	3.98556	−	4.29542i	0.256733	−	0.276692i	−0.591512	−	0.806296i	$-0.701469\pi$
$241$	3.98556	−	4.29542i	0.256733	−	0.276692i	0.848245	+	0.529604i	$0.177659\pi$
$242$	−11.6669	−	0.874312i	−0.749975	−	0.0562029i
$243$		0			0
$244$			11.1665i			0.714864i
$245$	−8.10384	−	2.70532i	−0.517735	−	0.172836i
$246$		0			0
$247$	0.202924	−	0.517042i	0.0129117	−	0.0328986i
$248$	1.20462	−	16.0745i	0.0764935	−	1.02073i
$249$		0			0
$250$	6.43194	−	9.43393i	0.406792	−	0.596654i
$251$	−1.45893	−	0.702581i	−0.0920865	−	0.0443465i	0.387274	−	0.921965i	$-0.373417\pi$
$251$	−1.45893	−	0.702581i	−0.0920865	−	0.0443465i	−0.479360	+	0.877618i	$0.659131\pi$
$252$		0			0
$253$	−3.78154	+	1.82109i	−0.237743	+	0.114491i
$254$	1.99939	−	13.2651i	0.125453	−	0.832325i
$255$		0			0
$256$	15.4552	−	2.32949i	0.965948	−	0.145593i
$257$	−21.2854	+	19.7500i	−1.32775	+	1.23197i	−0.375433	+	0.926849i	$0.622506\pi$
$257$	−21.2854	+	19.7500i	−1.32775	+	1.23197i	−0.952314	+	0.305120i	$0.901303\pi$
$258$		0			0
$259$	−0.738549	+	0.904573i	−0.0458912	+	0.0562074i
$260$	2.85457	+	2.27644i	0.177033	+	0.141179i
$261$		0			0
$262$	1.45173	−	4.70641i	0.0896884	−	0.290763i
$263$	10.7065	+	6.18139i	0.660190	+	0.381161i	0.792349	−	0.610067i	$-0.208858\pi$
$263$	10.7065	+	6.18139i	0.660190	+	0.381161i	−0.132159	+	0.991229i	$0.542191\pi$
$264$		0			0
$265$	−15.1030	+	3.44716i	−0.927769	+	0.211757i
$266$	−0.409907	+	0.121295i	−0.0251330	+	0.00743709i
$267$		0			0
$268$	2.56491	−	0.791171i	0.156677	−	0.0483284i
$269$	3.80395	+	9.69230i	0.231931	+	0.590950i	0.998700	−	0.0509729i	$-0.0162322\pi$
$269$	3.80395	+	9.69230i	0.231931	+	0.590950i	−0.766769	+	0.641923i	$0.778137\pi$
$270$		0			0
$271$	5.16634	+	16.7489i	0.313833	+	1.01742i	0.965825	+	0.259195i	$0.0834572\pi$
$271$	5.16634	+	16.7489i	0.313833	+	1.01742i	−0.651992	+	0.758225i	$0.726067\pi$
$272$	−1.09198	+	4.78429i	−0.0662111	+	0.290090i
$273$		0			0
$274$	−2.72380	−	11.9337i	−0.164551	−	0.720944i
$275$	−1.81609	+	1.04852i	−0.109514	+	0.0632281i
$276$		0			0
$277$	8.46264	+	2.61038i	0.508471	+	0.156842i	0.538367	−	0.842711i	$-0.319041\pi$
$277$	8.46264	+	2.61038i	0.508471	+	0.156842i	−0.0298962	+	0.999553i	$0.509518\pi$
$278$	−0.0538085	−	0.718024i	−0.00322722	−	0.0430642i
$279$		0			0
$280$	0.113952	−	9.90865i	0.00680991	−	0.592155i
$281$	9.01577	−	7.18984i	0.537836	−	0.428910i	−0.316529	−	0.948583i	$-0.602518\pi$
$281$	9.01577	−	7.18984i	0.537836	−	0.428910i	0.854365	+	0.519673i	$0.173946\pi$
$282$		0			0
$283$	0.320975	+	2.12953i	0.0190800	+	0.126587i	0.996343	−	0.0854430i	$-0.0272305\pi$
$283$	0.320975	+	2.12953i	0.0190800	+	0.126587i	−0.977263	+	0.212030i	$0.931992\pi$
$284$	−3.12931	−	4.58985i	−0.185690	−	0.272357i
$285$		0			0
$286$	1.07671	+	2.23581i	0.0636671	+	0.132206i
$287$	12.1831	−	8.10264i	0.719144	−	0.478283i
$288$		0			0
$289$	−7.83669	−	5.34296i	−0.460982	−	0.314292i
$290$	−2.77972	−	2.57920i	−0.163231	−	0.151456i
$291$		0			0
$292$	11.4944	+	4.51123i	0.672660	+	0.264000i
$293$	−28.4472			−1.66190			−0.830952	−	0.556344i	$-0.812204\pi$
$293$	−28.4472			−1.66190			−0.830952	+	0.556344i	$0.812204\pi$
$294$		0			0
$295$	−1.86096			−0.108349
$296$	−1.26084	−	0.494844i	−0.0732849	−	0.0287622i
$297$		0			0
$298$	7.77648	+	7.21551i	0.450479	+	0.417984i
$299$	−21.9374	−	14.9567i	−1.26867	−	0.864967i
$300$		0			0
$301$	3.00482	+	0.964843i	0.173195	+	0.0556126i
$302$	0.630633	+	1.30952i	0.0362889	+	0.0753546i
$303$		0			0
$304$	−0.148215	−	0.217391i	−0.00850069	−	0.0124682i
$305$	2.56594	+	17.0239i	0.146925	+	0.974784i
$306$		0			0
$307$	−19.3774	+	15.4529i	−1.10592	+	0.881946i	−0.993737	−	0.111741i	$-0.964357\pi$
$307$	−19.3774	+	15.4529i	−1.10592	+	0.881946i	−0.112187	+	0.993687i	$0.535786\pi$
$308$	−0.555793	+	1.12095i	−0.0316692	+	0.0638723i
$309$		0			0
$310$	−0.526659	−	7.02778i	−0.0299122	−	0.399151i
$311$	30.0487	+	9.26878i	1.70390	+	0.525584i	0.985446	−	0.169987i	$-0.0543726\pi$
$311$	30.0487	+	9.26878i	1.70390	+	0.525584i	0.718457	+	0.695572i	$0.244849\pi$
$312$		0			0
$313$	13.3170	−	7.68856i	0.752720	−	0.434583i	−0.0739557	−	0.997262i	$-0.523562\pi$
$313$	13.3170	−	7.68856i	0.752720	−	0.434583i	0.826676	+	0.562678i	$0.190229\pi$
$314$	0.290525	+	1.27287i	0.0163953	+	0.0718324i
$315$		0			0
$316$	1.98284	−	8.68737i	0.111543	−	0.488703i
$317$	6.56746	+	21.2912i	0.368865	+	1.19583i	0.929829	+	0.367992i	$0.119955\pi$
$317$	6.56746	+	21.2912i	0.368865	+	1.19583i	−0.560963	+	0.827841i	$0.689569\pi$
$318$		0			0
$319$	0.616848	+	1.57170i	0.0345369	+	0.0879985i
$320$	9.52114	−	2.93688i	0.532248	−	0.164177i
$321$		0			0
$322$	1.29262	+	20.3933i	0.0720351	+	1.13647i
$323$	−0.392831	+	0.0896611i	−0.0218577	+	0.00498888i
$324$		0			0
$325$	−11.4884	−	6.63281i	−0.637260	−	0.367922i
$326$	5.13885	−	16.6597i	0.284615	−	0.922698i
$327$		0			0
$328$	13.2681	+	10.5810i	0.732610	+	0.584237i
$329$	−2.19349	+	9.12529i	−0.120931	+	0.503094i
$330$		0			0
$331$	21.9476	−	20.3644i	1.20635	−	1.11933i	0.216635	−	0.976253i	$-0.430492\pi$
$331$	21.9476	−	20.3644i	1.20635	−	1.11933i	0.989712	−	0.143074i	$-0.0456986\pi$
$332$	−5.14740	+	0.775845i	−0.282500	+	0.0425800i
$333$		0			0
$334$	−1.97304	+	13.0903i	−0.107960	+	0.716268i
$335$	3.72852	−	1.79556i	0.203711	−	0.0981019i
$336$		0			0
$337$	−7.76079	−	3.73740i	−0.422757	−	0.203589i	0.210395	−	0.977616i	$-0.432525\pi$
$337$	−7.76079	−	3.73740i	−0.422757	−	0.203589i	−0.633152	+	0.774027i	$0.718239\pi$
$338$	−0.792965	+	1.16307i	−0.0431316	+	0.0632624i
$339$		0			0
$340$	0.197935	−	2.64125i	0.0107345	−	0.143242i
$341$	−1.14643	+	2.92105i	−0.0620825	+	0.158184i
$342$		0			0
$343$	16.9534	−	7.45531i	0.915398	−	0.402549i
$344$			3.66046i			0.197359i
$345$		0			0
$346$	27.2048	+	2.03872i	1.46254	+	0.109602i
$347$	−21.8259	+	23.5228i	−1.17168	+	1.26277i	−0.213389	+	0.976967i	$0.568450\pi$
$347$	−21.8259	+	23.5228i	−1.17168	+	1.26277i	−0.958289	+	0.285801i	$0.907740\pi$
$348$		0			0
$349$	3.66405	−	7.60847i	0.196132	−	0.407272i	−0.779588	−	0.626292i	$-0.784572\pi$
$349$	3.66405	−	7.60847i	0.196132	−	0.407272i	0.975720	+	0.219020i	$0.0702860\pi$
$350$	1.40546	+	10.1123i	0.0751248	+	0.540526i
$351$		0			0
$352$	−2.46306	−	0.371247i	−0.131282	−	0.0197875i
$353$	16.7385	−	11.4121i	0.890900	−	0.607405i	−0.0289908	−	0.999580i	$-0.509229\pi$
$353$	16.7385	−	11.4121i	0.890900	−	0.607405i	0.919891	+	0.392174i	$0.128277\pi$
$354$		0			0
$355$	−5.82545	−	6.27835i	−0.309183	−	0.333220i
$356$	−1.63267	−	2.04730i	−0.0865312	−	0.108507i
$357$		0			0
$358$	−12.7263	+	15.9583i	−0.672606	+	0.843422i
$359$	9.92008	−	0.743407i	0.523562	−	0.0392355i	0.189672	−	0.981848i	$-0.439258\pi$
$359$	9.92008	−	0.743407i	0.523562	−	0.0392355i	0.333890	+	0.942612i	$0.391639\pi$
$360$		0			0
$361$	−9.48920	+	16.4358i	−0.499431	+	0.865041i
$362$	6.29088	+	10.8961i	0.330642	+	0.572688i
$363$		0			0
$364$	−7.89895	+	0.500674i	−0.414018	+	0.0262424i
$365$	18.5604	+	4.23628i	0.971493	+	0.221737i
$366$		0			0
$367$	−7.78931	+	3.05708i	−0.406599	+	0.159578i	−0.559821	−	0.828613i	$-0.689130\pi$
$367$	−7.78931	+	3.05708i	−0.406599	+	0.159578i	0.153222	+	0.988192i	$0.451035\pi$
$368$	−11.7077	+	4.59494i	−0.610306	+	0.239528i
$369$		0			0
$370$	−0.577327	−	0.131771i	−0.0300138	−	0.00685045i
$371$	19.2351	−	27.5271i	0.998635	−	1.42914i
$372$		0			0
$373$	5.90695	+	10.2311i	0.305850	+	0.529748i	0.977450	−	0.211166i	$-0.0677260\pi$
$373$	5.90695	+	10.2311i	0.305850	+	0.529748i	−0.671600	+	0.740914i	$0.734393\pi$
$374$	0.900105	−	1.55903i	0.0465433	−	0.0806154i
$375$		0			0
$376$	−10.8552	+	0.813484i	−0.559813	+	0.0419522i
$377$	−6.65933	+	8.35054i	−0.342973	+	0.430075i
$378$		0			0
$379$	2.27986	+	2.85885i	0.117108	+	0.146849i	0.836930	−	0.547309i	$-0.184348\pi$
$379$	2.27986	+	2.85885i	0.117108	+	0.146849i	−0.719822	+	0.694159i	$0.755777\pi$
$380$	0.0965910	+	0.104100i	0.00495501	+	0.00534023i
$381$		0			0
$382$	−21.4275	+	14.6090i	−1.09632	+	0.747462i
$383$	33.7006	+	5.07955i	1.72202	+	0.259553i	0.934302	−	0.356482i	$-0.116024\pi$
$383$	33.7006	+	5.07955i	1.72202	+	0.259553i	0.787719	+	0.616035i	$0.211262\pi$
$384$		0			0
$385$	−0.589748	+	1.83666i	−0.0300563	+	0.0936047i
$386$	−2.28039	+	4.73527i	−0.116069	+	0.241019i
$387$		0			0
$388$	6.53743	−	7.04567i	0.331888	−	0.357690i
$389$	−1.57422	−	0.117972i	−0.0798162	−	0.00598139i	0.0347621	−	0.999396i	$-0.488933\pi$
$389$	−1.57422	−	0.117972i	−0.0798162	−	0.00598139i	−0.114578	+	0.993414i	$0.536552\pi$
$390$		0			0
$391$			19.2610i			0.974070i
$392$	14.2448	+	16.0786i	0.719473	+	0.812091i
$393$		0			0
$394$	4.16936	−	10.6233i	0.210049	−	0.535196i
$395$	1.02667	−	13.6999i	0.0516571	−	0.689317i
$396$		0			0
$397$	−16.7864	+	24.6211i	−0.842486	+	1.23570i	0.127330	+	0.991860i	$0.459359\pi$
$397$	−16.7864	+	24.6211i	−0.842486	+	1.23570i	−0.969816	+	0.243839i	$0.921593\pi$
$398$	−3.00614	−	1.44768i	−0.150684	−	0.0725656i
$399$		0			0
$400$	−5.66159	+	2.72648i	−0.283080	+	0.136324i
$401$	−2.37414	+	15.7514i	−0.118559	+	0.786588i	0.847972	+	0.530040i	$0.177823\pi$
$401$	−2.37414	+	15.7514i	−0.118559	+	0.786588i	−0.966531	+	0.256548i	$0.917415\pi$
$402$		0			0
$403$	−19.6287	+	2.95855i	−0.977774	+	0.147376i
$404$	5.47146	−	5.07677i	0.272215	−	0.252579i
$405$		0			0
$406$	8.21959	+	0.0945271i	0.407931	+	0.00469130i
$407$	0.206146	+	0.164396i	0.0102183	+	0.00814882i
$408$		0			0
$409$	−3.27118	+	10.6049i	−0.161749	+	0.524379i	−0.999774	−	0.0212535i	$-0.993234\pi$
$409$	−3.27118	+	10.6049i	−0.161749	+	0.524379i	0.838025	+	0.545632i	$0.183710\pi$
$410$	6.42550	+	3.70976i	0.317333	+	0.183212i
$411$		0			0
$412$	−13.7261	+	3.13290i	−0.676237	+	0.154347i
$413$	2.98859	−	2.70972i	0.147059	−	0.133337i
$414$		0			0
$415$	−7.66915	+	2.36562i	−0.376464	+	0.116124i
$416$	−5.75670	−	14.6678i	−0.282245	−	0.719149i
$417$		0			0
$418$	0.0284496	+	0.0922313i	0.00139151	+	0.00451118i
$419$	0.448076	−	1.96315i	0.0218900	−	0.0959062i	−0.962803	−	0.270205i	$-0.912909\pi$
$419$	0.448076	−	1.96315i	0.0218900	−	0.0959062i	0.984693	+	0.174299i	$0.0557658\pi$
$420$		0			0
$421$	−2.65745	−	11.6431i	−0.129516	−	0.567448i	−0.997488	−	0.0708345i	$-0.977434\pi$
$421$	−2.65745	−	11.6431i	−0.129516	−	0.567448i	0.867972	−	0.496614i	$-0.165423\pi$
$422$	−13.4974	+	7.79273i	−0.657043	+	0.379344i
$423$		0			0
$424$	37.2199	+	11.4808i	1.80756	+	0.557558i
$425$	0.719154	+	9.59644i	0.0348841	+	0.465496i
$426$		0			0
$427$	−28.9089	−	23.6030i	−1.39900	−	1.14223i
$428$	−4.65536	+	3.71253i	−0.225025	+	0.179452i
$429$		0			0
$430$	0.238520	+	1.58248i	0.0115025	+	0.0763138i
$431$	20.0900	+	29.4666i	0.967701	+	1.41936i	0.906966	+	0.421203i	$0.138392\pi$
$431$	20.0900	+	29.4666i	0.967701	+	1.41936i	0.0607346	+	0.998154i	$0.480656\pi$
$432$		0			0
$433$	−15.3199	−	31.8121i	−0.736228	−	1.52879i	−0.845024	−	0.534728i	$-0.820414\pi$
$433$	−15.3199	−	31.8121i	−0.736228	−	1.52879i	0.108797	−	0.994064i	$-0.465300\pi$
$434$	11.0788	+	10.5193i	0.531801	+	0.504943i
$435$		0			0
$436$	−5.79472	−	3.95078i	−0.277517	−	0.189208i
$437$	−0.757014	−	0.702407i	−0.0362129	−	0.0336007i
$438$		0			0
$439$	22.5761	+	8.86048i	1.07750	+	0.422887i	0.836685	−	0.547684i	$-0.184490\pi$
$439$	22.5761	+	8.86048i	1.07750	+	0.422887i	0.240814	+	0.970571i	$0.422586\pi$
$440$	−2.23741			−0.106664
$441$		0			0
$442$	11.3879			0.541668
$443$	15.6618	+	6.14681i	0.744115	+	0.292044i	0.706948	−	0.707265i	$-0.250071\pi$
$443$	15.6618	+	6.14681i	0.744115	+	0.292044i	0.0371671	+	0.999309i	$0.488167\pi$
$444$		0			0
$445$	−2.95952	−	2.74603i	−0.140295	−	0.130174i
$446$	−19.4234	−	13.2426i	−0.919723	−	0.627056i
$447$		0			0
$448$	−11.0140	+	18.5800i	−0.520363	+	0.877825i
$449$	−4.11154	−	8.53770i	−0.194036	−	0.402919i	0.781139	−	0.624357i	$-0.214639\pi$
$449$	−4.11154	−	8.53770i	−0.194036	−	0.402919i	−0.975174	+	0.221438i	$0.928925\pi$
$450$		0			0
$451$	−1.86099	−	2.72958i	−0.0876308	−	0.128531i
$452$	−0.968754	−	6.42727i	−0.0455664	−	0.302313i
$453$		0			0
$454$	14.7475	−	11.7607i	0.692133	−	0.551958i
$455$	−11.9272	+	2.57838i	−0.559158	+	0.120876i
$456$		0			0
$457$	1.35220	+	18.0438i	0.0632531	+	0.844054i	0.935124	+	0.354319i	$0.115287\pi$
$457$	1.35220	+	18.0438i	0.0632531	+	0.844054i	−0.871871	+	0.489735i	$0.837094\pi$
$458$	14.3323	+	4.42094i	0.669707	+	0.206577i
$459$		0			0
$460$	5.87886	−	3.39416i	0.274103	−	0.158254i
$461$	−5.09445	−	22.3202i	−0.237272	−	1.03956i	−0.943448	−	0.331520i	$-0.892438\pi$
$461$	−5.09445	−	22.3202i	−0.237272	−	1.03956i	0.706176	−	0.708036i	$-0.250419\pi$
$462$		0			0
$463$	−0.225238	+	0.986834i	−0.0104677	+	0.0458621i	−0.979892	−	0.199528i	$-0.936059\pi$
$463$	−0.225238	+	0.986834i	−0.0104677	+	0.0458621i	0.969424	+	0.245390i	$0.0789161\pi$
$464$	1.49130	+	4.83466i	0.0692317	+	0.224444i
$465$		0			0
$466$	−4.55365	−	11.6025i	−0.210944	−	0.537477i
$467$	−11.4864	+	3.54309i	−0.531528	+	0.163955i	−0.548890	−	0.835895i	$-0.684949\pi$
$467$	−11.4864	+	3.54309i	−0.531528	+	0.163955i	0.0173621	+	0.999849i	$0.494473\pi$
$468$		0			0
$469$	−3.37327	+	8.31259i	−0.155763	+	0.383840i
$470$	−4.63987	+	1.05902i	−0.214021	+	0.0488489i
$471$		0			0
$472$	4.05219	+	2.33953i	0.186517	+	0.107686i
$473$	0.210034	−	0.680915i	0.00965739	−	0.0313085i
$474$		0			0
$475$	−0.403395	−	0.321697i	−0.0185090	−	0.0147605i
$476$	3.52802	+	4.52989i	0.161706	+	0.207627i
$477$		0			0
$478$	−14.1433	+	13.1231i	−0.646900	+	0.600236i
$479$	−11.7948	+	1.77777i	−0.538917	+	0.0812286i	−0.412860	−	0.910794i	$-0.635470\pi$
$479$	−11.7948	+	1.77777i	−0.538917	+	0.0812286i	−0.126056	+	0.992023i	$0.540232\pi$
$480$		0			0
$481$	−0.248596	+	1.64932i	−0.0113350	+	0.0752027i
$482$	−5.80339	+	2.79476i	−0.264337	+	0.127298i
$483$		0			0
$484$	−7.59099	−	3.65563i	−0.345045	−	0.166165i
$485$	8.34758	−	12.2437i	0.379044	−	0.555956i
$486$		0			0
$487$	2.35956	−	31.4861i	0.106922	−	1.42677i	−0.643314	−	0.765602i	$-0.722441\pi$
$487$	2.35956	−	31.4861i	0.106922	−	1.42677i	0.750236	−	0.661170i	$-0.229940\pi$
$488$	15.8145	−	40.2948i	0.715890	−	1.82406i
$489$		0			0
$490$	7.20598	+	6.02282i	0.325533	+	0.272083i
$491$		−	27.7128i		−	1.25066i	−0.780360	−	0.625331i	$-0.784964\pi$
$491$		−	27.7128i		−	1.25066i	0.780360	−	0.625331i	$-0.215036\pi$
$492$		0			0
$493$	7.72651	+	0.579022i	0.347985	+	0.0260778i
$494$	−0.415293	+	0.447580i	−0.0186849	+	0.0201376i
$495$		0			0
$496$	−4.07985	+	8.47189i	−0.183190	+	0.380399i
$497$	18.4971	+	1.60027i	0.829709	+	0.0717818i
$498$		0			0
$499$	−15.6910	−	2.36504i	−0.702427	−	0.105874i	−0.211889	−	0.977294i	$-0.567962\pi$
$499$	−15.6910	−	2.36504i	−0.702427	−	0.105874i	−0.490538	+	0.871420i	$0.663200\pi$
$500$	6.79376	−	4.63191i	0.303826	−	0.207145i
$501$		0			0
$502$	1.21072	+	1.30485i	0.0540371	+	0.0582381i
$503$	4.07333	+	5.10779i	0.181621	+	0.227745i	0.864305	−	0.502969i	$-0.167759\pi$
$503$	4.07333	+	5.10779i	0.181621	+	0.227745i	−0.682684	+	0.730714i	$0.739187\pi$
$504$		0			0
$505$	7.17490	−	8.99703i	0.319279	−	0.400363i
$506$	4.60091	−	0.344790i	0.204535	−	0.0153278i
$507$		0			0
$508$	4.83031	−	8.36635i	0.214311	−	0.371197i
$509$	21.9330	+	37.9891i	0.972164	+	1.68384i	0.688993	+	0.724768i	$0.258053\pi$
$509$	21.9330	+	37.9891i	0.972164	+	1.68384i	0.283171	+	0.959069i	$0.408613\pi$
$510$		0			0
$511$	−35.9751	+	20.2223i	−1.59145	+	0.894580i
$512$	−17.9880	−	4.10565i	−0.794967	−	0.181446i
$513$		0			0
$514$	29.7125	−	11.6613i	1.31056	−	0.514358i
$515$	−20.2062	+	7.93033i	−0.890389	+	0.349452i
$516$		0			0
$517$	2.06595	+	0.471539i	0.0908602	+	0.0207382i
$518$	1.11902	−	0.629021i	0.0491669	−	0.0276376i
$519$		0			0
$520$	−7.07680	−	12.2574i	−0.310338	−	0.537521i
$521$	−5.19339	+	8.99522i	−0.227527	+	0.394088i	−0.957074	−	0.289842i	$-0.906397\pi$
$521$	−5.19339	+	8.99522i	−0.227527	+	0.394088i	0.729548	+	0.683930i	$0.239731\pi$
$522$		0			0
$523$	−17.4606	+	1.30849i	−0.763501	+	0.0572165i	−0.450788	−	0.892631i	$-0.648857\pi$
$523$	−17.4606	+	1.30849i	−0.763501	+	0.0572165i	−0.312713	+	0.949848i	$0.601238\pi$
$524$	2.21143	−	2.77304i	0.0966066	−	0.121141i
$525$		0			0
$526$	−8.47319	−	10.6250i	−0.369449	−	0.463274i
$527$	9.79460	+	10.5561i	0.426660	+	0.459830i
$528$		0			0
$529$	−21.7834	+	14.8516i	−0.947103	+	0.645724i
$530$	16.8389	+	2.53805i	0.731435	+	0.110246i
$531$		0			0
$532$	−0.306698	−	0.0265338i	−0.0132970	−	0.00115039i
$533$	9.06744	−	18.8287i	0.392754	−	0.815563i
$534$		0			0
$535$	−6.24420	+	6.72965i	−0.269960	+	0.290948i
$536$	−10.3760	−	0.777577i	−0.448177	−	0.0335862i
$537$		0			0
$538$		−	11.4456i		−	0.493453i
$539$	−1.72723	−	3.80828i	−0.0743972	−	0.164034i
$540$		0			0
$541$	−6.58030	+	16.7663i	−0.282909	+	0.720841i	0.716813	+	0.697266i	$0.245600\pi$
$541$	−6.58030	+	16.7663i	−0.282909	+	0.720841i	−0.999722	+	0.0235754i	$0.992495\pi$
$542$	1.43985	−	19.2135i	0.0618469	−	0.825290i
$543$		0			0
$544$	−6.43915	+	9.44450i	−0.276076	+	0.404930i
$545$	−9.74214	−	4.69157i	−0.417308	−	0.200965i
$546$		0			0
$547$	23.9587	−	11.5379i	1.02440	−	0.493325i	0.155251	−	0.987875i	$-0.450381\pi$
$547$	23.9587	−	11.5379i	1.02440	−	0.493325i	0.869149	+	0.494550i	$0.164667\pi$
$548$	1.31381	−	8.71653i	0.0561230	−	0.372352i
$549$		0			0
$550$	2.27945	−	0.343571i	0.0971960	−	0.0146499i
$551$	−0.304527	+	0.282560i	−0.0129733	+	0.0120374i
$552$		0			0
$553$	18.2995	+	23.4961i	0.778172	+	0.999155i
$554$	−7.61125	−	6.06977i	−0.323371	−	0.257880i
$555$		0			0
$556$	0.152839	−	0.495492i	0.00648182	−	0.0210135i
$557$	30.2571	+	17.4690i	1.28204	+	0.740184i	0.977220	−	0.212228i	$-0.0680719\pi$
$557$	30.2571	+	17.4690i	1.28204	+	0.740184i	0.304815	+	0.952411i	$0.401405\pi$
$558$		0			0
$559$	4.39463	−	1.00305i	0.185873	−	0.0424244i
$560$	−2.17356	+	5.35620i	−0.0918497	+	0.226341i
$561$		0			0
$562$	−12.1131	+	3.73639i	−0.510959	+	0.157610i
$563$	11.8233	+	30.1254i	0.498294	+	1.26963i	0.929981	+	0.367609i	$0.119823\pi$
$563$	11.8233	+	30.1254i	0.498294	+	1.26963i	−0.431686	+	0.902024i	$0.642081\pi$
$564$		0			0
$565$	−2.95382	−	9.57603i	−0.124268	−	0.402867i
$566$	0.526785	−	2.30800i	0.0221424	−	0.0970123i
$567$		0			0
$568$	4.79185	+	20.9945i	0.201061	+	0.880908i
$569$	−5.09419	+	2.94113i	−0.213560	+	0.123299i	−0.602965	−	0.797768i	$-0.706014\pi$
$569$	−5.09419	+	2.94113i	−0.213560	+	0.123299i	0.389405	+	0.921067i	$0.372681\pi$
$570$		0			0
$571$	−9.47090	−	2.92138i	−0.396345	−	0.122256i	0.0901746	−	0.995926i	$-0.471257\pi$
$571$	−9.47090	−	2.92138i	−0.396345	−	0.122256i	−0.486519	+	0.873670i	$0.661734\pi$
$572$	0.133548	+	1.78208i	0.00558393	+	0.0745123i
$573$		0			0
$574$	−15.7207	+	3.39843i	−0.656168	+	0.141848i
$575$	−19.2831	+	15.3777i	−0.804159	+	0.641295i
$576$		0			0
$577$	−1.86601	−	12.3801i	−0.0776829	−	0.515392i	−0.993503	−	0.113804i	$-0.963696\pi$
$577$	−1.86601	−	12.3801i	−0.0776829	−	0.515392i	0.915820	−	0.401588i	$-0.131542\pi$
$578$	5.87332	+	8.61457i	0.244298	+	0.358319i
$579$		0			0
$580$	−1.18483	−	2.46033i	−0.0491975	−	0.102160i
$581$	8.87162	−	14.9660i	0.368057	−	0.620893i
$582$		0			0
$583$	−6.26485	−	4.27130i	−0.259464	−	0.176899i
$584$	−35.0889	−	32.5578i	−1.45199	−	1.34725i
$585$		0			0
$586$	29.1093	+	11.4246i	1.20249	+	0.471944i
$587$	−42.3771			−1.74909			−0.874545	−	0.484944i	$-0.838840\pi$
$587$	−42.3771			−1.74909			−0.874545	+	0.484944i	$0.838840\pi$
$588$		0			0
$589$	−0.772074			−0.0318127
$590$	1.90427	+	0.747373i	0.0783978	+	0.0307689i
$591$		0			0
$592$	0.579189	+	0.537408i	0.0238045	+	0.0220874i
$593$	−32.0983	−	21.8843i	−1.31812	−	0.898680i	−0.319321	−	0.947647i	$-0.603455\pi$
$593$	−32.0983	−	21.8843i	−1.31812	−	0.898680i	−0.998800	+	0.0489669i	$0.984407\pi$
$594$		0			0
$595$	6.41953	+	6.09532i	0.263175	+	0.249884i
$596$	3.31466	+	6.88296i	0.135774	+	0.281937i
$597$		0			0
$598$	16.4413	+	24.1150i	0.672335	+	0.986134i
$599$	−5.22634	−	34.6745i	−0.213543	−	1.41676i	−0.796686	−	0.604393i	$-0.793416\pi$
$599$	−5.22634	−	34.6745i	−0.213543	−	1.41676i	0.583143	−	0.812369i	$-0.301823\pi$
$600$		0			0
$601$	27.7268	−	22.1114i	1.13100	−	0.901941i	0.134958	−	0.990851i	$-0.456910\pi$
$601$	27.7268	−	22.1114i	1.13100	−	0.901941i	0.996040	+	0.0889104i	$0.0283385\pi$
$602$	−2.68727	−	2.19405i	−0.109525	−	0.0894228i
$603$		0			0
$604$	0.0782198	+	1.04377i	0.00318272	+	0.0424704i
$605$	−12.4128	−	3.82884i	−0.504652	−	0.155665i
$606$		0			0
$607$	7.36201	−	4.25046i	0.298815	−	0.172521i	−0.343095	−	0.939301i	$-0.611475\pi$
$607$	7.36201	−	4.25046i	0.298815	−	0.172521i	0.641910	+	0.766780i	$0.278142\pi$
$608$	−0.136375	−	0.597499i	−0.00553075	−	0.0242318i
$609$		0			0
$610$	4.21122	−	18.4506i	0.170507	−	0.747042i
$611$	3.95120	+	12.8095i	0.159849	+	0.518216i
$612$		0			0
$613$	−16.1317	−	41.1030i	−0.651555	−	1.66013i	−0.747102	−	0.664709i	$-0.768555\pi$
$613$	−16.1317	−	41.1030i	−0.651555	−	1.66013i	0.0955474	−	0.995425i	$-0.469540\pi$
$614$	26.0343	−	8.03053i	1.05066	−	0.324086i
$615$		0			0
$616$	3.59314	−	3.25786i	0.144772	−	0.131263i
$617$	0.434012	−	0.0990604i	0.0174727	−	0.00398802i	−0.213776	−	0.976883i	$-0.568576\pi$
$617$	0.434012	−	0.0990604i	0.0174727	−	0.00398802i	0.231248	+	0.972895i	$0.425719\pi$
$618$		0			0
$619$	29.1881	+	16.8517i	1.17317	+	0.677328i	0.954424	−	0.298454i	$-0.0964710\pi$
$619$	29.1881	+	16.8517i	1.17317	+	0.677328i	0.218743	+	0.975782i	$0.429804\pi$
$620$	1.49594	−	4.84971i	0.0600783	−	0.194769i
$621$		0			0
$622$	−27.0256	−	21.5522i	−1.08363	−	0.864165i
$623$	8.75125	+	0.100641i	0.350611	+	0.00403211i
$624$		0			0
$625$	−3.57347	+	3.31569i	−0.142939	+	0.132628i
$626$	−16.7147	+	2.51933i	−0.668053	+	0.100693i
$627$		0			0
$628$	−0.140133	+	0.929720i	−0.00559191	+	0.0370999i
$629$	1.09017	−	0.524996i	0.0434677	−	0.0209330i
$630$		0			0
$631$	35.6887	+	17.1868i	1.42075	+	0.684195i	0.977252	−	0.212082i	$-0.0680244\pi$
$631$	35.6887	+	17.1868i	1.42075	+	0.684195i	0.443494	+	0.896277i	$0.353739\pi$
$632$	−19.4585	+	28.5404i	−0.774019	+	1.13528i
$633$		0			0
$634$	1.83034	−	24.4243i	0.0726923	−	0.970011i
$635$	5.44154	−	13.8648i	0.215941	−	0.550208i
$636$		0			0
$637$	15.4001	−	21.5078i	0.610172	−	0.852170i
$638$		−	1.85601i		−	0.0734802i
$639$		0			0
$640$	−0.772517	−	0.0578921i	−0.0305364	−	0.00228839i
$641$	−15.2531	+	16.4390i	−0.602463	+	0.649300i	−0.958474	−	0.285182i	$-0.907946\pi$
$641$	−15.2531	+	16.4390i	−0.602463	+	0.649300i	0.356011	+	0.934482i	$0.384137\pi$
$642$		0			0
$643$	17.6815	−	36.7159i	0.697289	−	1.44794i	−0.187654	−	0.982235i	$-0.560088\pi$
$643$	17.6815	−	36.7159i	0.697289	−	1.44794i	0.884943	−	0.465700i	$-0.154197\pi$
$644$	−4.49889	+	14.0109i	−0.177281	+	0.552108i
$645$		0			0
$646$	0.437982	+	0.0660152i	0.0172322	+	0.00259733i
$647$	29.0910	−	19.8339i	1.14368	−	0.779750i	0.165238	−	0.986254i	$-0.447161\pi$
$647$	29.0910	−	19.8339i	1.14368	−	0.779750i	0.978446	+	0.206503i	$0.0662085\pi$
$648$		0			0
$649$	−0.619543	−	0.667709i	−0.0243192	−	0.0262099i
$650$	9.09198	+	11.4010i	0.356617	+	0.447183i
$651$		0			0
$652$	7.82802	−	9.81602i	0.306569	−	0.384425i
$653$	−30.3295	+	2.27288i	−1.18688	+	0.0889447i	−0.653499	−	0.756927i	$-0.726700\pi$
$653$	−30.3295	+	2.27288i	−1.18688	+	0.0889447i	−0.533386	+	0.845872i	$0.679081\pi$
$654$		0			0
$655$	2.73420	−	4.73578i	0.106834	−	0.185042i
$656$	−4.94974	−	8.57320i	−0.193255	−	0.334727i
$657$		0			0
$658$	5.90931	−	8.45676i	0.230369	−	0.329679i
$659$	−45.9980	−	10.4987i	−1.79183	−	0.408973i	−0.808160	−	0.588963i	$-0.799536\pi$
$659$	−45.9980	−	10.4987i	−1.79183	−	0.408973i	−0.983668	+	0.179990i	$0.942394\pi$
$660$		0			0
$661$	−6.83240	+	2.68152i	−0.265749	+	0.104299i	−0.494475	−	0.869192i	$-0.664640\pi$
$661$	−6.83240	+	2.68152i	−0.265749	+	0.104299i	0.228725	+	0.973491i	$0.426544\pi$
$662$	−30.6368	+	12.0241i	−1.19073	+	0.467328i
$663$		0			0
$664$	19.6733	+	4.49030i	0.763472	+	0.174258i
$665$	−0.473671	+	0.0300235i	−0.0183682	+	0.00116426i
$666$		0			0
$667$	9.92901	+	17.1976i	0.384453	+	0.665892i
$668$	−4.76666	+	8.25610i	−0.184428	+	0.319438i
$669$		0			0
$670$	−4.53640	+	0.339956i	−0.175256	+	0.0131337i
$671$	−5.25388	+	6.58816i	−0.202824	+	0.254333i
$672$		0			0
$673$	13.7235	+	17.2087i	0.529001	+	0.663346i	0.972493	−	0.232932i	$-0.0748320\pi$
$673$	13.7235	+	17.2087i	0.529001	+	0.663346i	−0.443492	+	0.896278i	$0.646261\pi$
$674$	6.44045	+	6.94116i	0.248077	+	0.267363i
$675$		0			0
$676$	−0.837572	+	0.571047i	−0.0322143	+	0.0219633i
$677$	42.7750	+	6.44729i	1.64398	+	0.247789i	0.904835	−	0.425762i	$-0.139994\pi$
$677$	42.7750	+	6.44729i	1.64398	+	0.247789i	0.739140	+	0.673551i	$0.235232\pi$
$678$		0			0
$679$	4.42212	+	31.8173i	0.169705	+	1.22104i
$680$	−4.45491	+	9.25071i	−0.170838	+	0.354749i
$681$		0			0
$682$	2.34622	−	2.52862i	0.0898413	−	0.0968259i
$683$	−34.9513	−	2.61923i	−1.33737	−	0.100222i	−0.613248	−	0.789891i	$-0.710137\pi$
$683$	−34.9513	−	2.61923i	−1.33737	−	0.100222i	−0.724125	+	0.689669i	$0.757756\pi$
$684$		0			0
$685$		−	13.5906i		−	0.519271i
$686$	−20.3421	+	0.820244i	−0.776664	+	0.0313171i
$687$		0			0
$688$	0.780099	−	1.98766i	0.0297410	−	0.0757788i
$689$	3.58445	−	47.8311i	0.136556	−	1.82222i
$690$		0			0
$691$	20.4381	−	29.9772i	0.777502	−	1.14039i	−0.209205	−	0.977872i	$-0.567087\pi$
$691$	20.4381	−	29.9772i	0.777502	−	1.14039i	0.986706	−	0.162514i	$-0.0519602\pi$
$692$	17.7007	+	8.52419i	0.672878	+	0.324041i
$693$		0			0
$694$	31.7808	−	15.3048i	1.20638	−	0.580963i
$695$	0.119152	−	0.790519i	0.00451968	−	0.0299861i
$696$		0			0
$697$	−14.9910	+	2.25954i	−0.567826	+	0.0855860i
$698$	−6.80492	+	6.31405i	−0.257570	+	0.238990i
$699$		0			0
$700$	−1.71836	+	7.14867i	−0.0649479	+	0.270194i
$701$	−12.3967	−	9.88606i	−0.468218	−	0.373391i	0.360773	−	0.932654i	$-0.382513\pi$
$701$	−12.3967	−	9.88606i	−0.468218	−	0.373391i	−0.828991	+	0.559262i	$0.811084\pi$
$702$		0			0
$703$	−0.0191221	+	0.0619923i	−0.000721203	+	0.00233808i
$704$	4.22348	+	2.43843i	0.159179	+	0.0919018i
$705$		0			0
$706$	−21.7112	+	4.95545i	−0.817113	+	0.186501i
$707$	1.57802	+	24.8959i	0.0593477	+	0.936307i
$708$		0			0
$709$	19.9754	−	6.16161i	0.750193	−	0.231404i	0.104000	−	0.994577i	$-0.466836\pi$
$709$	19.9754	−	6.16161i	0.750193	−	0.231404i	0.646194	+	0.763173i	$0.276360\pi$
$710$	3.43962	+	8.76400i	0.129087	+	0.328907i
$711$		0			0
$712$	2.99205	+	9.69999i	0.112132	+	0.363523i
$713$	−8.21249	+	35.9813i	−0.307560	+	1.34751i
$714$		0			0
$715$	0.613099	+	2.68616i	0.0229286	+	0.100457i
$716$	−12.7298	+	7.34955i	−0.475735	+	0.274666i
$717$		0			0
$718$	−10.4495	−	3.22325i	−0.389972	−	0.120291i
$719$	−2.28617	−	30.5069i	−0.0852599	−	1.13771i	−0.861664	−	0.507479i	$-0.830577\pi$
$719$	−2.28617	−	30.5069i	−0.0852599	−	1.13771i	0.776404	−	0.630235i	$-0.217042\pi$
$720$		0			0
$721$	20.9026	−	42.1575i	0.778452	−	1.57003i
$722$	16.3107	−	13.0074i	0.607023	−	0.484085i
$723$		0			0
$724$	1.35042	+	8.95945i	0.0501879	+	0.332975i
$725$	5.58907	+	8.19765i	0.207573	+	0.304453i
$726$		0			0
$727$	−5.02146	−	10.4272i	−0.186236	−	0.386722i	0.786857	−	0.617135i	$-0.211707\pi$
$727$	−5.02146	−	10.4272i	−0.186236	−	0.386722i	−0.973093	+	0.230413i	$0.925992\pi$
$728$	29.2127	+	9.38014i	1.08269	+	0.347651i
$729$		0			0
$730$	−17.2910	−	11.7888i	−0.639969	−	0.436324i
$731$	−2.39709	−	2.22417i	−0.0886594	−	0.0822639i
$732$		0			0
$733$	8.21013	+	3.22224i	0.303248	+	0.119016i	0.512086	−	0.858934i	$-0.328873\pi$
$733$	8.21013	+	3.22224i	0.303248	+	0.119016i	−0.208838	+	0.977950i	$0.566968\pi$
$734$	9.19834			0.339517
$735$		0			0
$736$	−29.2961			−1.07987
$737$	1.88552	+	0.740013i	0.0694541	+	0.0272587i
$738$		0			0
$739$	6.75975	+	6.27213i	0.248661	+	0.230724i	0.794649	−	0.607069i	$-0.207655\pi$
$739$	6.75975	+	6.27213i	0.248661	+	0.230724i	−0.545988	+	0.837793i	$0.683845\pi$
$740$	−0.352348	−	0.240227i	−0.0129526	−	0.00883092i
$741$		0			0
$742$	−30.7378	+	20.4429i	−1.12842	+	0.750482i
$743$	−20.2631	−	42.0767i	−0.743379	−	1.54364i	−0.836487	−	0.547987i	$-0.815394\pi$
$743$	−20.2631	−	42.0767i	−0.743379	−	1.54364i	0.0931076	−	0.995656i	$-0.470320\pi$
$744$		0			0
$745$	6.63496	+	9.73170i	0.243086	+	0.356542i
$746$	−1.93555	−	12.8415i	−0.0708654	−	0.470161i
$747$		0			0
$748$	1.01357	−	0.808296i	0.0370598	−	0.0295542i
$749$	0.228848	−	19.8995i	0.00836194	−	0.727111i
$750$		0			0
$751$	3.43092	+	45.7824i	0.125196	+	1.67062i	0.607271	+	0.794495i	$0.292264\pi$
$751$	3.43092	+	45.7824i	0.125196	+	1.67062i	−0.482075	+	0.876130i	$0.660117\pi$
$752$	6.06782	+	1.87168i	0.221271	+	0.0682530i
$753$		0			0
$754$	10.1679	−	5.87046i	0.370295	−	0.213790i
$755$	0.359095	+	1.57330i	0.0130688	+	0.0572582i
$756$		0			0
$757$	−3.22626	+	14.1352i	−0.117261	+	0.513752i	0.881848	+	0.471534i	$0.156300\pi$
$757$	−3.22626	+	14.1352i	−0.117261	+	0.513752i	−0.999108	+	0.0422180i	$0.986558\pi$
$758$	−1.18479	−	3.84099i	−0.0430335	−	0.139511i
$759$		0			0
$760$	−0.201120	−	0.512445i	−0.00729538	−	0.0185883i
$761$	18.9984	−	5.86022i	0.688690	−	0.212433i	0.0693930	−	0.997589i	$-0.477894\pi$
$761$	18.9984	−	5.86022i	0.688690	−	0.212433i	0.619297	+	0.785157i	$0.287418\pi$
$762$		0			0
$763$	22.4766	−	6.65103i	0.813707	−	0.240783i
$764$	−18.2077	+	4.15579i	−0.658732	+	0.150351i
$765$		0			0
$766$	−32.4450	−	18.7321i	−1.17228	−	0.676819i
$767$	1.69838	−	5.50602i	0.0613250	−	0.198811i
$768$		0			0
$769$	−9.19228	−	7.33060i	−0.331482	−	0.264348i	0.443578	−	0.896236i	$-0.353709\pi$
$769$	−9.19228	−	7.33060i	−0.331482	−	0.264348i	−0.775060	+	0.631888i	$0.782280\pi$
$770$	1.34109	−	1.64256i	0.0483294	−	0.0591937i
$771$		0			0
$772$	−2.77452	+	2.57437i	−0.0998570	+	0.0926537i
$773$	−5.23175	+	0.788560i	−0.188173	+	0.0283625i	−0.242453	−	0.970163i	$-0.577952\pi$
$773$	−5.23175	+	0.788560i	−0.188173	+	0.0283625i	0.0542795	+	0.998526i	$0.482714\pi$
$774$		0			0
$775$	−2.74828	+	18.2337i	−0.0987212	+	0.654973i
$776$	−33.5689	+	16.1659i	−1.20505	+	0.580323i
$777$		0			0
$778$	1.56348	+	0.752933i	0.0560535	+	0.0269939i
$779$	0.457885	−	0.671594i	0.0164054	−	0.0240623i
$780$		0			0
$781$	0.313271	−	4.18032i	0.0112097	−	0.149583i
$782$	7.73531	−	19.7093i	0.276614	−	0.704802i
$783$		0			0
$784$	−4.30848	−	11.7666i	−0.153874	−	0.420236i
$785$			1.44960i			0.0517384i
$786$		0			0
$787$	−28.4751	−	2.13391i	−1.01503	−	0.0760658i	−0.443186	−	0.896430i	$-0.646152\pi$
$787$	−28.4751	−	2.13391i	−1.01503	−	0.0760658i	−0.571842	+	0.820364i	$0.693771\pi$
$788$	5.58994	−	6.02452i	0.199133	−	0.214615i
$789$		0			0
$790$	−6.55251	+	13.6064i	−0.233128	+	0.484095i
$791$	18.6872	+	11.0775i	0.664439	+	0.393870i
$792$		0			0
$793$	−52.7102	−	7.94478i	−1.87179	−	0.282127i
$794$	27.0651	−	18.4527i	0.960503	−	0.654860i
$795$		0			0
$796$	−1.63432	−	1.76137i	−0.0579268	−	0.0624302i
$797$	−27.1272	−	34.0164i	−0.960893	−	1.20492i	−0.978745	−	0.205082i	$-0.934254\pi$
$797$	−27.1272	−	34.0164i	−0.960893	−	1.20492i	0.0178515	−	0.999841i	$-0.494317\pi$
$798$		0			0
$799$	6.06311	−	7.60290i	0.214498	−	0.268971i
$800$	−14.5963	+	1.09384i	−0.516056	+	0.0386730i
$801$		0			0
$802$	8.75526	−	15.1645i	0.309159	−	0.535479i
$803$	4.65906	+	8.06973i	0.164415	+	0.284775i
$804$		0			0
$805$	−3.63920	+	22.3940i	−0.128265	+	0.789286i
$806$	21.2737	+	4.85558i	0.749334	+	0.171031i
$807$		0			0
$808$	−26.9339	+	10.5708i	−0.947530	+	0.371878i
$809$	−27.5258	+	10.8031i	−0.967756	+	0.379816i	−0.795982	−	0.605320i	$-0.793045\pi$
$809$	−27.5258	+	10.8031i	−0.967756	+	0.379816i	−0.171774	+	0.985136i	$0.554950\pi$
$810$		0			0
$811$	−6.61452	−	1.50972i	−0.232267	−	0.0530135i	0.104803	−	0.994493i	$-0.466579\pi$
$811$	−6.61452	−	1.50972i	−0.232267	−	0.0530135i	−0.337070	+	0.941480i	$0.609436\pi$
$812$	5.48522	+	2.22592i	0.192493	+	0.0781144i
$813$		0			0
$814$	−0.144922	−	0.251012i	−0.00507951	−	0.00879797i
$815$	9.67854	−	16.7637i	0.339025	−	0.587208i
$816$		0			0
$817$	0.174833	−	0.0131019i	0.00611664	−	0.000458379i
$818$	7.60630	−	9.53800i	0.265948	−	0.333488i
$819$		0			0
$820$	3.33137	+	4.17741i	0.116337	+	0.145881i
$821$	15.0794	+	16.2517i	0.526273	+	0.567188i	0.939110	−	0.343618i	$-0.111652\pi$
$821$	15.0794	+	16.2517i	0.526273	+	0.567188i	−0.412836	+	0.910805i	$0.635462\pi$
$822$		0			0
$823$	−43.6296	+	29.7461i	−1.52083	+	1.03689i	−0.540083	+	0.841612i	$0.681607\pi$
$823$	−43.6296	+	29.7461i	−1.52083	+	1.03689i	−0.980749	+	0.195274i	$0.937440\pi$
$824$	53.9680	+	8.13437i	1.88006	+	0.283374i
$825$		0			0
$826$	−4.14638	+	1.57255i	−0.144271	+	0.0547161i
$827$	−5.83012	+	12.1064i	−0.202733	+	0.420979i	−0.977402	−	0.211387i	$-0.932202\pi$
$827$	−5.83012	+	12.1064i	−0.202733	+	0.420979i	0.774669	+	0.632366i	$0.217916\pi$
$828$		0			0
$829$	26.0997	−	28.1288i	0.906479	−	0.976952i	−0.0933464	−	0.995634i	$-0.529756\pi$
$829$	26.0997	−	28.1288i	0.906479	−	0.976952i	0.999825	+	0.0186815i	$0.00594687\pi$
$830$	8.79768	+	0.659295i	0.305372	+	0.0228845i
$831$		0			0
$832$			30.8505i			1.06955i
$833$	−19.1847	−	0.441314i	−0.664709	−	0.0152906i
$834$		0			0
$835$	−5.36983	+	13.6821i	−0.185831	+	0.473488i
$836$	−0.00519431	+	0.0693132i	−0.000179649	+	0.00239725i
$837$		0			0
$838$	−1.24692	+	1.82889i	−0.0430740	+	0.0631780i
$839$	14.1317	+	6.80546i	0.487880	+	0.234951i	0.661618	−	0.749841i	$-0.269870\pi$
$839$	14.1317	+	6.80546i	0.487880	+	0.234951i	−0.173738	+	0.984792i	$0.555585\pi$
$840$		0			0
$841$	−18.9308	+	9.11661i	−0.652787	+	0.314366i
$842$	−1.95661	+	12.9813i	−0.0674294	+	0.447365i
$843$		0			0
$844$	−11.0984	+	1.67281i	−0.382021	+	0.0575805i
$845$	−1.14569	+	1.06305i	−0.0394131	+	0.0365700i
$846$		0			0
$847$	25.5093	−	11.9252i	0.876509	−	0.409755i
$848$	−17.7640	−	14.1663i	−0.610018	−	0.486473i
$849$		0			0
$850$	3.11809	−	10.1086i	0.106950	−	0.346722i
$851$	2.68565	+	1.55056i	0.0920629	+	0.0531526i
$852$		0			0
$853$	46.1579	−	10.5352i	1.58042	−	0.360720i	0.659878	−	0.751373i	$-0.270608\pi$
$853$	46.1579	−	10.5352i	1.58042	−	0.360720i	0.920538	+	0.390653i	$0.127751\pi$
$854$	20.1026	+	35.7623i	0.687898	+	1.22376i
$855$		0			0
$856$	22.0568	−	6.80363i	0.753887	−	0.232543i
$857$	−9.13000	−	23.2629i	−0.311875	−	0.794644i	−0.997758	−	0.0669320i	$-0.978679\pi$
$857$	−9.13000	−	23.2629i	−0.311875	−	0.794644i	0.685883	−	0.727712i	$-0.259416\pi$
$858$		0			0
$859$	−7.42565	−	24.0734i	−0.253360	−	0.821372i	−0.989499	−	0.144542i	$-0.953829\pi$
$859$	−7.42565	−	24.0734i	−0.253360	−	0.821372i	0.736139	−	0.676831i	$-0.236647\pi$
$860$	−0.256451	+	1.12358i	−0.00874489	+	0.0383139i
$861$		0			0
$862$	−8.72362	−	38.2207i	−0.297128	−	1.30180i
$863$	46.0397	−	26.5810i	1.56721	−	0.904829i	0.570716	−	0.821147i	$-0.306666\pi$
$863$	46.0397	−	26.5810i	1.56721	−	0.904829i	0.996493	−	0.0836813i	$-0.0266678\pi$
$864$		0			0
$865$	28.9442	+	8.92809i	0.984131	+	0.303564i
$866$	2.90054	+	38.7051i	0.0985645	+	1.31525i
$867$		0			0
$868$	4.65921	+	9.96653i	0.158144	+	0.338286i
$869$	5.25728	−	4.19254i	0.178341	−	0.142222i
$870$		0			0
$871$	1.90973	+	12.6702i	0.0647087	+	0.429314i
$872$	15.3152	+	22.4632i	0.518637	+	0.760701i
$873$		0			0
$874$	0.492543	+	1.02278i	0.0166605	+	0.0345959i
$875$	−2.36867	+	27.3789i	−0.0800756	+	0.925575i
$876$		0			0
$877$	2.84755	+	1.94142i	0.0961548	+	0.0655573i	0.610443	−	0.792060i	$-0.290991\pi$
$877$	2.84755	+	1.94142i	0.0961548	+	0.0655573i	−0.514288	+	0.857617i	$0.671944\pi$
$878$	−19.5431	−	18.1334i	−0.659549	−	0.611972i
$879$		0			0
$880$	1.21493	+	0.476826i	0.0409553	+	0.0160738i
$881$	−26.1175			−0.879919			−0.439960	−	0.898018i	$-0.645007\pi$
$881$	−26.1175			−0.879919			−0.439960	+	0.898018i	$0.645007\pi$
$882$		0			0
$883$	18.2669			0.614728			0.307364	−	0.951592i	$-0.400553\pi$
$883$	18.2669			0.614728			0.307364	+	0.951592i	$0.400553\pi$
$884$	7.63402	+	2.99613i	0.256760	+	0.100771i
$885$		0			0
$886$	−13.5577	−	12.5797i	−0.455481	−	0.422625i
$887$	−20.3623	−	13.8828i	−0.683699	−	0.466138i	0.170994	−	0.985272i	$-0.445302\pi$
$887$	−20.3623	−	13.8828i	−0.683699	−	0.466138i	−0.854693	+	0.519134i	$0.826255\pi$
$888$		0			0
$889$	11.4496	+	30.1893i	0.384007	+	1.01252i
$890$	1.92558	+	3.99850i	0.0645454	+	0.134030i
$891$		0			0
$892$	−9.53656	−	13.9876i	−0.319308	−	0.468338i
$893$	0.0777082	+	0.515560i	0.00260041	+	0.0172526i
$894$		0			0
$895$	−17.7183	+	14.1299i	−0.592257	+	0.472309i
$896$	1.32491	−	1.03188i	0.0442621	−	0.0344727i
$897$		0			0
$898$	0.778445	+	10.3876i	0.0259770	+	0.346640i
$899$	14.1870	+	4.37610i	0.473161	+	0.145951i
$900$		0			0
$901$	−30.1339	+	17.3978i	−1.00391	+	0.579606i
$902$	0.808094	+	3.54049i	0.0269066	+	0.117885i
$903$		0			0
$904$	−5.60679	+	24.5650i	−0.186479	+	0.817018i
$905$	4.11755	+	13.3488i	0.136872	+	0.443728i
$906$		0			0
$907$	−17.1969	−	43.8170i	−0.571013	−	1.45492i	−0.866307	−	0.499512i	$-0.833513\pi$
$907$	−17.1969	−	43.8170i	−0.571013	−	1.45492i	0.295294	−	0.955407i	$-0.404583\pi$
$908$	12.9803	−	4.00390i	0.430767	−	0.132874i
$909$		0			0
$910$	13.2403	+	2.15166i	0.438913	+	0.0713267i
$911$	24.2803	−	5.54182i	0.804442	−	0.183609i	0.199520	−	0.979894i	$-0.436062\pi$
$911$	24.2803	−	5.54182i	0.804442	−	0.183609i	0.604922	+	0.796285i	$0.293204\pi$
$912$		0			0
$913$	−3.40195	−	1.96412i	−0.112588	−	0.0650029i
$914$	5.86283	−	19.0068i	0.193925	−	0.628690i
$915$		0			0
$916$	8.44470	+	6.73442i	0.279021	+	0.222512i
$917$	2.50474	+	11.5866i	0.0827138	+	0.382623i
$918$		0			0
$919$	−1.73172	+	1.60681i	−0.0571243	+	0.0530036i	−0.708218	−	0.705993i	$-0.750501\pi$
$919$	−1.73172	+	1.60681i	−0.0571243	+	0.0530036i	0.651094	+	0.758997i	$0.274310\pi$
$920$	−26.0210	+	3.92203i	−0.857886	+	0.129306i
$921$		0			0
$922$	−3.75091	+	24.8857i	−0.123530	+	0.819566i
$923$	23.8922	−	11.5059i	0.786422	−	0.378721i
$924$		0			0
$925$	1.39597	+	0.672265i	0.0458993	+	0.0221039i
$926$	0.626799	−	0.919345i	0.0205979	−	0.0302115i
$927$		0			0
$928$	−0.880698	+	11.7521i	−0.0289103	+	0.385781i
$929$	14.4284	−	36.7630i	0.473382	−	1.20616i	−0.472409	−	0.881379i	$-0.656615\pi$
$929$	14.4284	−	36.7630i	0.473382	−	1.20616i	0.945791	−	0.324777i	$-0.105289\pi$
$930$		0			0
$931$	0.716969	−	0.737921i	0.0234977	−	0.0241844i
$932$		−	8.97593i		−	0.294016i
$933$		0			0
$934$	13.1767	+	0.987455i	0.431154	+	0.0323105i
$935$	1.35950	−	1.46519i	0.0444602	−	0.0479167i
$936$		0			0
$937$	17.2515	−	35.8232i	0.563583	−	1.17029i	−0.403299	−	0.915068i	$-0.632136\pi$
$937$	17.2515	−	35.8232i	0.563583	−	1.17029i	0.966882	−	0.255224i	$-0.0821493\pi$
$938$	6.79017	−	7.15133i	0.221707	−	0.233499i
$939$		0			0
$940$	−3.38901	−	0.510811i	−0.110537	−	0.0166608i
$941$	10.8066	−	7.36780i	0.352284	−	0.240183i	−0.374228	−	0.927337i	$-0.622092\pi$
$941$	10.8066	−	7.36780i	0.352284	−	0.240183i	0.726512	+	0.687153i	$0.241140\pi$
$942$		0			0
$943$	−26.4281	−	28.4827i	−0.860616	−	0.927524i
$944$	−1.70178	−	2.13397i	−0.0553883	−	0.0694548i
$945$		0			0
$946$	−0.488382	+	0.612411i	−0.0158787	+	0.0199112i
$947$	−10.5439	+	0.790153i	−0.342629	+	0.0256765i	−0.244934	−	0.969540i	$-0.578766\pi$
$947$	−10.5439	+	0.790153i	−0.342629	+	0.0256765i	−0.0976955	+	0.995216i	$0.531147\pi$
$948$		0			0
$949$	−29.4727	+	51.0482i	−0.956724	+	1.65710i
$950$	0.283588	+	0.491190i	0.00920082	+	0.0159363i
$951$		0			0
$952$	−6.31552	−	21.3428i	−0.204687	−	0.691723i
$953$	18.6372	+	4.25382i	0.603719	+	0.137795i	0.513445	−	0.858122i	$-0.328369\pi$
$953$	18.6372	+	4.25382i	0.603719	+	0.137795i	0.0902731	+	0.995917i	$0.471226\pi$
$954$		0			0
$955$	−26.8035	+	10.5196i	−0.867341	+	0.340406i
$956$	−12.9338	+	5.07613i	−0.418308	+	0.164174i
$957$		0			0
$958$	12.7832	+	2.91769i	0.413008	+	0.0942663i
$959$	19.7891	+	21.8257i	0.639023	+	0.704788i
$960$		0			0
$961$	−1.70368	−	2.95085i	−0.0549573	−	0.0951888i
$962$	0.916759	−	1.58787i	0.0295575	−	0.0511951i
$963$		0			0
$964$	−4.62566	+	0.346645i	−0.148982	+	0.0111647i
$965$	−3.63831	+	4.56229i	−0.117121	+	0.146865i
$966$		0			0
$967$	6.62198	+	8.30370i	0.212949	+	0.267029i	0.876821	−	0.480817i	$-0.159660\pi$
$967$	6.62198	+	8.30370i	0.212949	+	0.267029i	−0.663873	+	0.747846i	$0.731088\pi$
$968$	22.2150	+	23.9421i	0.714018	+	0.769528i
$969$		0			0
$970$	−13.4590	+	9.17618i	−0.432142	+	0.294629i
$971$	−9.85954	−	1.48609i	−0.316408	−	0.0476908i	−0.0110815	−	0.999939i	$-0.503527\pi$
$971$	−9.85954	−	1.48609i	−0.316408	−	0.0476908i	−0.305326	+	0.952248i	$0.598766\pi$
$972$		0			0
$973$	0.959713	+	1.44302i	0.0307670	+	0.0462610i
$974$	−15.0595	+	31.2713i	−0.482537	+	1.00200i
$975$		0			0
$976$	−17.1748	+	18.5101i	−0.549753	+	0.592493i
$977$	13.5691	+	1.01687i	0.434115	+	0.0325325i	0.289996	−	0.957028i	$-0.406346\pi$
$977$	13.5691	+	1.01687i	0.434115	+	0.0325325i	0.144119	+	0.989560i	$0.453965\pi$
$978$		0			0
$979$		−	1.97606i		−	0.0631552i
$980$	3.24601	+	5.93333i	0.103690	+	0.189533i
$981$		0			0
$982$	−11.1296	+	28.3578i	−0.355160	+	0.904934i
$983$	−2.48034	+	33.0979i	−0.0791106	+	1.05566i	0.806501	+	0.591232i	$0.201358\pi$
$983$	−2.48034	+	33.0979i	−0.0791106	+	1.05566i	−0.885612	+	0.464426i	$0.846261\pi$
$984$		0			0
$985$	7.13774	−	10.4691i	0.227427	−	0.333575i
$986$	−7.67380	−	3.69551i	−0.244384	−	0.117689i
$987$		0			0
$988$	−0.396153	+	0.190777i	−0.0126033	+	0.00606944i
$989$	1.24909	−	8.28719i	0.0397188	−	0.263517i
$990$		0			0
$991$	22.6040	−	3.40700i	0.718038	−	0.108227i	0.220147	−	0.975467i	$-0.429346\pi$
$991$	22.6040	−	3.40700i	0.718038	−	0.108227i	0.497891	+	0.867240i	$0.334108\pi$
$992$	−16.0559	+	14.8977i	−0.509774	+	0.473002i
$993$		0			0
$994$	−18.2849	−	9.06605i	−0.579963	−	0.287558i
$995$	−2.89633	−	2.30974i	−0.0918197	−	0.0732238i
$996$		0			0
$997$	−15.1742	+	49.1935i	−0.480571	+	1.55797i	0.313156	+	0.949702i	$0.398614\pi$
$997$	−15.1742	+	49.1935i	−0.480571	+	1.55797i	−0.793728	+	0.608273i	$0.791863\pi$
$998$	15.1064	+	8.72169i	0.478185	+	0.276080i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.395.6	yes	216
3.2	odd	2	inner	441.2.bg.a.395.13	yes	216
49.33	odd	42	inner	441.2.bg.a.278.13	yes	216
147.131	even	42	inner	441.2.bg.a.278.6	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.278.6	✓	216	147.131	even	42	inner
441.2.bg.a.278.13	yes	216	49.33	odd	42	inner
441.2.bg.a.395.6	yes	216	1.1	even	1	trivial
441.2.bg.a.395.13	yes	216	3.2	odd	2	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02327 - 0.401605i) q^{2} +(-0.580301 - 0.538441i) q^{4} +(-1.00842 - 0.687530i) q^{5} +(2.62056 - 0.364218i) q^{7} +(1.33147 + 2.76483i) q^{8} +O(q^{10})\)	\(q+(-1.02327 - 0.401605i) q^{2} +(-0.580301 - 0.538441i) q^{4} +(-1.00842 - 0.687530i) q^{5} +(2.62056 - 0.364218i) q^{7} +(1.33147 + 2.76483i) q^{8} +(0.755775 + 1.10852i) q^{10} +(-0.0890350 - 0.590708i) q^{11} +(2.95451 - 2.35614i) q^{13} +(-2.82782 - 0.679737i) q^{14} +(-0.133773 - 1.78508i) q^{16} +(-2.61960 - 0.808039i) q^{17} +(0.127290 - 0.0734907i) q^{19} +(0.214994 + 0.941949i) q^{20} +(-0.146125 + 0.640213i) q^{22} +(-2.07095 - 6.71384i) q^{23} +(-1.28249 - 3.26773i) q^{25} +(-3.96951 + 1.22443i) q^{26} +(-1.71682 - 1.19966i) q^{28} +(-2.75551 + 0.628926i) q^{29} +(-4.54912 - 2.62644i) q^{31} +(1.22903 - 3.98443i) q^{32} +(2.35605 + 1.87889i) q^{34} +(-2.89304 - 1.43443i) q^{35} +(-0.323554 + 0.300214i) q^{37} +(-0.159766 + 0.0240809i) q^{38} +(0.558218 - 3.70353i) q^{40} +(4.98252 - 2.39945i) q^{41} +(1.07470 + 0.517549i) q^{43} +(-0.266394 + 0.390729i) q^{44} +(-0.577170 + 7.70180i) q^{46} +(-1.29597 + 3.30207i) q^{47} +(6.73469 - 1.90891i) q^{49} +3.85884i q^{50} +(-2.98315 - 0.223556i) q^{52} +(8.63323 - 9.30441i) q^{53} +(-0.316345 + 0.656897i) q^{55} +(4.49620 + 6.76045i) q^{56} +(3.07222 + 0.463062i) q^{58} +(1.25982 - 0.858928i) q^{59} +(-9.59443 - 10.3403i) q^{61} +(3.60020 + 4.51451i) q^{62} +(-5.09001 + 6.38267i) q^{64} +(-4.59931 + 0.344671i) q^{65} +(-1.69535 + 2.93644i) q^{67} +(1.08507 + 1.87940i) q^{68} +(2.38430 + 2.62968i) q^{70} +(6.84143 + 1.56151i) q^{71} +(-14.5201 + 5.69870i) q^{73} +(0.451652 - 0.177260i) q^{74} +(-0.113437 - 0.0258912i) q^{76} +(-0.448468 - 1.51556i) q^{77} +(5.62817 + 9.74827i) q^{79} +(-1.09240 + 1.89208i) q^{80} +(-6.06211 + 0.454292i) q^{82} +(4.09993 - 5.14115i) q^{83} +(2.08611 + 2.61590i) q^{85} +(-0.891863 - 0.961200i) q^{86} +(1.51466 - 1.03268i) q^{88} +(3.27093 + 0.493014i) q^{89} +(6.88433 - 7.25051i) q^{91} +(-2.41323 + 5.01113i) q^{92} +(2.65226 - 2.85845i) q^{94} +(-0.178888 - 0.0134058i) q^{95} +12.1414i q^{97} +(-7.65806 - 0.751350i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

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