LMFDB - Embedded newform 792.2.bp.d.19.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(19,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.bp (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 264)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	792.19
Dual form			792.2.bp.d.667.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40421 + 0.167908i) q^{2} +(1.94361 + 0.471557i) q^{4} +(1.03968 - 1.43099i) q^{5} +(-0.430909 + 1.32620i) q^{7} +(2.65006 + 0.988513i) q^{8} +(1.70020 - 1.83484i) q^{10} +(2.97889 + 1.45816i) q^{11} +(-2.66400 + 1.93551i) q^{13} +(-0.827766 + 1.78991i) q^{14} +(3.55527 + 1.83305i) q^{16} +(2.21773 - 3.05245i) q^{17} +(-0.399566 + 0.129827i) q^{19} +(2.69552 - 2.29103i) q^{20} +(3.93815 + 2.54775i) q^{22} -1.44940i q^{23} +(0.578275 + 1.77975i) q^{25} +(-4.06581 + 2.27056i) q^{26} +(-1.46290 + 2.37442i) q^{28} +(2.45128 - 7.54427i) q^{29} +(0.816325 + 1.12358i) q^{31} +(4.68456 + 3.17094i) q^{32} +(3.62669 - 3.91390i) q^{34} +(1.44978 + 1.99544i) q^{35} +(-8.91884 - 2.89791i) q^{37} +(-0.582873 + 0.115214i) q^{38} +(4.16976 - 2.76449i) q^{40} +(-3.29058 + 1.06918i) q^{41} -3.60336i q^{43} +(5.10220 + 4.23882i) q^{44} +(0.243367 - 2.03527i) q^{46} +(0.727433 - 0.236357i) q^{47} +(4.08999 + 2.97155i) q^{49} +(0.513186 + 2.59624i) q^{50} +(-6.09050 + 2.50566i) q^{52} +(-2.54374 - 3.50116i) q^{53} +(5.18369 - 2.74674i) q^{55} +(-2.45290 + 3.08856i) q^{56} +(4.70886 - 10.1821i) q^{58} +(-3.69578 + 11.3745i) q^{59} +(-8.45451 - 6.14256i) q^{61} +(0.957635 + 1.71480i) q^{62} +(6.04568 + 5.23925i) q^{64} +5.82447i q^{65} +9.95011 q^{67} +(5.74981 - 4.88699i) q^{68} +(1.70074 + 3.04545i) q^{70} +(-7.57332 + 10.4238i) q^{71} +(-9.14630 - 2.97181i) q^{73} +(-12.0373 - 5.56681i) q^{74} +(-0.837822 + 0.0639152i) q^{76} +(-3.21744 + 3.32227i) q^{77} +(-4.69761 + 3.41302i) q^{79} +(6.31940 - 3.18178i) q^{80} +(-4.80020 + 0.948832i) q^{82} +(8.86730 - 12.2048i) q^{83} +(-2.06230 - 6.34711i) q^{85} +(0.605033 - 5.05987i) q^{86} +(6.45283 + 6.80889i) q^{88} -10.9210 q^{89} +(-1.41893 - 4.36703i) q^{91} +(0.683476 - 2.81708i) q^{92} +(1.06116 - 0.209753i) q^{94} +(-0.229638 + 0.706752i) q^{95} +(-11.2144 + 8.14771i) q^{97} +(5.24426 + 4.85943i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{4} - 4 q^{11} + 16 q^{14} + 20 q^{16} - 25 q^{20} + 3 q^{22} - 4 q^{25} - 4 q^{26} - 25 q^{28} - 26 q^{38} - 65 q^{40} + 60 q^{41} + 43 q^{44} - 5 q^{46} - 12 q^{49} + 80 q^{50} - 15 q^{52}+ \cdots - 40 q^{97}+O(q^{100}) $ 48 * q + 4 * q^4 - 4 * q^11 + 16 * q^14 + 20 * q^16 - 25 * q^20 + 3 * q^22 - 4 * q^25 - 4 * q^26 - 25 * q^28 - 26 * q^38 - 65 * q^40 + 60 * q^41 + 43 * q^44 - 5 * q^46 - 12 * q^49 + 80 * q^50 - 15 * q^52 + 14 * q^56 + 73 * q^58 + 8 * q^59 + 45 * q^62 - 38 * q^64 + 8 * q^67 + 55 * q^68 - 40 * q^70 - 60 * q^74 - 35 * q^82 + 100 * q^83 - 81 * q^86 - 18 * q^88 - 96 * q^89 - 20 * q^91 - 59 * q^92 + 35 * q^94 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$	$-1$

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 $

$2$	1.40421	+	0.167908i	0.992927	+	0.118729i
$2$	1.40421	+	0.167908i	0.992927	+	0.118729i
$3$		0			0
$3$		0			0
$4$	1.94361	+	0.471557i	0.971807	+	0.235778i
$5$	1.03968	−	1.43099i	0.464957	−	0.639959i	−0.510570	−	0.859836i	$-0.670566\pi$
$5$	1.03968	−	1.43099i	0.464957	−	0.639959i	0.975528	+	0.219877i	$0.0705657\pi$
$6$		0			0
$7$	−0.430909	+	1.32620i	−0.162868	+	0.501257i	−0.998873	−	0.0474657i	$-0.984886\pi$
$7$	−0.430909	+	1.32620i	−0.162868	+	0.501257i	0.836005	+	0.548722i	$0.184886\pi$
$8$	2.65006	+	0.988513i	0.936939	+	0.349492i
$9$		0			0
$10$	1.70020	−	1.83484i	0.537650	−	0.580228i
$11$	2.97889	+	1.45816i	0.898168	+	0.439652i
$11$	2.97889	+	1.45816i	0.898168	+	0.439652i
$12$		0			0
$13$	−2.66400	+	1.93551i	−0.738862	+	0.536815i	−0.892355	−	0.451335i	$-0.850948\pi$
$13$	−2.66400	+	1.93551i	−0.738862	+	0.536815i	0.153493	+	0.988150i	$0.450948\pi$
$14$	−0.827766	+	1.78991i	−0.221230	+	0.478374i
$15$		0			0
$16$	3.55527	+	1.83305i	0.888817	+	0.458262i
$17$	2.21773	−	3.05245i	0.537879	−	0.740327i	−0.450427	−	0.892813i	$-0.648728\pi$
$17$	2.21773	−	3.05245i	0.537879	−	0.740327i	0.988306	+	0.152487i	$0.0487281\pi$
$18$		0			0
$19$	−0.399566	+	0.129827i	−0.0916666	+	0.0297843i	−0.354491	−	0.935059i	$-0.615346\pi$
$19$	−0.399566	+	0.129827i	−0.0916666	+	0.0297843i	0.262825	+	0.964844i	$0.415346\pi$
$20$	2.69552	−	2.29103i	0.602737	−	0.512289i
$21$		0			0
$22$	3.93815	+	2.54775i	0.839616	+	0.543181i
$23$		−	1.44940i		−	0.302222i	−0.988517	−	0.151111i	$-0.951715\pi$
$23$		−	1.44940i		−	0.302222i	0.988517	−	0.151111i	$-0.0482850\pi$
$24$		0			0
$25$	0.578275	+	1.77975i	0.115655	+	0.355950i
$26$	−4.06581	+	2.27056i	−0.797371	+	0.445293i
$27$		0			0
$28$	−1.46290	+	2.37442i	−0.276462	+	0.448724i
$29$	2.45128	−	7.54427i	0.455191	−	1.40094i	−0.415719	−	0.909493i	$-0.636470\pi$
$29$	2.45128	−	7.54427i	0.455191	−	1.40094i	0.870910	−	0.491442i	$-0.163530\pi$
$30$		0			0
$31$	0.816325	+	1.12358i	0.146616	+	0.201800i	0.876008	−	0.482296i	$-0.160197\pi$
$31$	0.816325	+	1.12358i	0.146616	+	0.201800i	−0.729392	+	0.684096i	$0.760197\pi$
$32$	4.68456	+	3.17094i	0.828121	+	0.560549i
$33$		0			0
$34$	3.62669	−	3.91390i	0.621972	−	0.671228i
$35$	1.44978	+	1.99544i	0.245057	+	0.337292i
$36$		0			0
$37$	−8.91884	−	2.89791i	−1.46625	−	0.476413i	−0.536276	−	0.844043i	$-0.680169\pi$
$37$	−8.91884	−	2.89791i	−1.46625	−	0.476413i	−0.929972	+	0.367630i	$0.880169\pi$
$38$	−0.582873	+	0.115214i	−0.0945545	+	0.0186901i
$39$		0			0
$40$	4.16976	−	2.76449i	0.659297	−	0.437104i
$41$	−3.29058	+	1.06918i	−0.513903	+	0.166977i	−0.554476	−	0.832199i	$-0.687081\pi$
$41$	−3.29058	+	1.06918i	−0.513903	+	0.166977i	0.0405736	+	0.999177i	$0.487081\pi$
$42$		0			0
$43$		−	3.60336i		−	0.549507i	−0.961515	−	0.274753i	$-0.911404\pi$
$43$		−	3.60336i		−	0.549507i	0.961515	−	0.274753i	$-0.0885962\pi$
$44$	5.10220	+	4.23882i	0.769185	+	0.639026i
$45$		0			0
$46$	0.243367	−	2.03527i	0.0358824	−	0.300084i
$47$	0.727433	−	0.236357i	0.106107	−	0.0344763i	−0.255482	−	0.966814i	$-0.582234\pi$
$47$	0.727433	−	0.236357i	0.106107	−	0.0344763i	0.361589	+	0.932337i	$0.382234\pi$
$48$		0			0
$49$	4.08999	+	2.97155i	0.584285	+	0.424508i
$50$	0.513186	+	2.59624i	0.0725754	+	0.367163i
$51$		0			0
$52$	−6.09050	+	2.50566i	−0.844600	+	0.347472i
$53$	−2.54374	−	3.50116i	−0.349410	−	0.480921i	0.597751	−	0.801682i	$-0.296061\pi$
$53$	−2.54374	−	3.50116i	−0.349410	−	0.480921i	−0.947160	+	0.320761i	$0.896061\pi$
$54$		0			0
$55$	5.18369	−	2.74674i	0.698969	−	0.370371i
$56$	−2.45290	+	3.08856i	−0.327783	+	0.412726i
$57$		0			0
$58$	4.70886	−	10.1821i	0.618303	−	1.33698i
$59$	−3.69578	+	11.3745i	−0.481150	+	1.48083i	0.356330	+	0.934360i	$0.384028\pi$
$59$	−3.69578	+	11.3745i	−0.481150	+	1.48083i	−0.837480	+	0.546468i	$0.815972\pi$
$60$		0			0
$61$	−8.45451	−	6.14256i	−1.08249	−	0.786474i	−0.104373	−	0.994538i	$-0.533284\pi$
$61$	−8.45451	−	6.14256i	−1.08249	−	0.786474i	−0.978115	+	0.208064i	$0.933284\pi$
$62$	0.957635	+	1.71480i	0.121620	+	0.217780i
$63$		0			0
$64$	6.04568	+	5.23925i	0.755710	+	0.654906i
$65$			5.82447i			0.722437i
$66$		0			0
$67$	9.95011			1.21560			0.607800	−	0.794090i	$-0.292052\pi$
$67$	9.95011			1.21560			0.607800	+	0.794090i	$0.292052\pi$
$68$	5.74981	−	4.88699i	0.697267	−	0.592634i
$69$		0			0
$70$	1.70074	+	3.04545i	0.203277	+	0.364001i
$71$	−7.57332	+	10.4238i	−0.898788	+	1.23708i	0.0720652	+	0.997400i	$0.477041\pi$
$71$	−7.57332	+	10.4238i	−0.898788	+	1.23708i	−0.970853	+	0.239675i	$0.922959\pi$
$72$		0			0
$73$	−9.14630	−	2.97181i	−1.07049	−	0.347824i	−0.279814	−	0.960054i	$-0.590273\pi$
$73$	−9.14630	−	2.97181i	−1.07049	−	0.347824i	−0.790680	+	0.612230i	$0.790273\pi$
$74$	−12.0373	−	5.56681i	−1.39931	−	0.647129i
$75$		0			0
$76$	−0.837822	+	0.0639152i	−0.0961047	+	0.00733157i
$77$	−3.21744	+	3.32227i	−0.366662	+	0.378607i
$78$		0			0
$79$	−4.69761	+	3.41302i	−0.528523	+	0.383994i	−0.819805	−	0.572643i	$-0.805918\pi$
$79$	−4.69761	+	3.41302i	−0.528523	+	0.383994i	0.291282	+	0.956637i	$0.405918\pi$
$80$	6.31940	−	3.18178i	0.706531	−	0.355734i
$81$		0			0
$82$	−4.80020	+	0.948832i	−0.530093	+	0.104781i
$83$	8.86730	−	12.2048i	0.973313	−	1.33965i	0.0329578	−	0.999457i	$-0.489507\pi$
$83$	8.86730	−	12.2048i	0.973313	−	1.33965i	0.940355	−	0.340194i	$-0.110493\pi$
$84$		0			0
$85$	−2.06230	−	6.34711i	−0.223688	−	0.688441i
$86$	0.605033	−	5.05987i	0.0652424	−	0.545620i
$87$		0			0
$88$	6.45283	+	6.80889i	0.687874	+	0.725830i
$89$	−10.9210			−1.15763			−0.578814	−	0.815460i	$-0.696484\pi$
$89$	−10.9210			−1.15763			−0.578814	+	0.815460i	$0.696484\pi$
$90$		0			0
$91$	−1.41893	−	4.36703i	−0.148745	−	0.457789i
$92$	0.683476	−	2.81708i	0.0712573	−	0.293701i
$93$		0			0
$94$	1.06116	−	0.209753i	0.109450	−	0.0216344i
$95$	−0.229638	+	0.706752i	−0.0235603	+	0.0725113i
$96$		0			0
$97$	−11.2144	+	8.14771i	−1.13865	+	0.827275i	−0.986930	−	0.161149i	$-0.948480\pi$
$97$	−11.2144	+	8.14771i	−1.13865	+	0.827275i	−0.151716	+	0.988424i	$0.548480\pi$
$98$	5.24426	+	4.85943i	0.529751	+	0.490877i
$99$		0			0
$100$	0.284692	+	3.73183i	0.0284692	+	0.373183i
$101$	−6.49406	+	4.71821i	−0.646183	+	0.469480i	−0.861969	−	0.506961i	$-0.830769\pi$
$101$	−6.49406	+	4.71821i	−0.646183	+	0.469480i	0.215786	+	0.976441i	$0.430769\pi$
$102$		0			0
$103$	−11.7338	−	3.81254i	−1.15617	−	0.375661i	−0.332703	−	0.943032i	$-0.607961\pi$
$103$	−11.7338	−	3.81254i	−1.15617	−	0.375661i	−0.823463	+	0.567370i	$0.807961\pi$
$104$	−8.97306	+	2.49583i	−0.879881	+	0.244736i
$105$		0			0
$106$	−2.98407	−	5.34348i	−0.289839	−	0.519004i
$107$	6.82340	−	2.21706i	0.659643	−	0.214331i	0.0399817	−	0.999200i	$-0.487270\pi$
$107$	6.82340	−	2.21706i	0.659643	−	0.214331i	0.619661	+	0.784869i	$0.287270\pi$
$108$		0			0
$109$	9.38007			0.898448			0.449224	−	0.893419i	$-0.351700\pi$
$109$	9.38007			0.898448			0.449224	+	0.893419i	$0.351700\pi$
$110$	7.74020	−	2.98662i	0.737999	−	0.284763i
$111$		0			0
$112$	−3.96298	+	3.92512i	−0.374467	+	0.370889i
$113$	−0.566005	−	1.74198i	−0.0532452	−	0.163872i	0.920898	−	0.389804i	$-0.127457\pi$
$113$	−0.566005	−	1.74198i	−0.0532452	−	0.163872i	−0.974143	+	0.225932i	$0.927457\pi$
$114$		0			0
$115$	−2.07408	−	1.50691i	−0.193409	−	0.140520i
$116$	8.32189	−	13.5072i	0.772668	−	1.25411i
$117$		0			0
$118$	−7.09952	+	15.3516i	−0.653564	+	1.41323i
$119$	3.09251	+	4.25648i	0.283490	+	0.390191i
$120$		0			0
$121$	6.74753	+	8.68740i	0.613412	+	0.789763i
$122$	−10.8405	−	10.0450i	−0.981455	−	0.909434i
$123$		0			0
$124$	1.05679	+	2.56874i	0.0949027	+	0.230680i
$125$	11.5592	+	3.75580i	1.03388	+	0.335929i
$126$		0			0
$127$	5.77997	+	4.19940i	0.512890	+	0.372636i	0.813919	−	0.580979i	$-0.197330\pi$
$127$	5.77997	+	4.19940i	0.512890	+	0.372636i	−0.301029	+	0.953615i	$0.597330\pi$
$128$	7.60970	+	8.37213i	0.672609	+	0.739998i
$129$		0			0
$130$	−0.977976	+	8.17879i	−0.0857742	+	0.717327i
$131$		−	8.74918i		−	0.764420i	−0.924076	−	0.382210i	$-0.875163\pi$
$131$		−	8.74918i		−	0.764420i	0.924076	−	0.382210i	$-0.124837\pi$
$132$		0			0
$133$		−	0.585847i		−	0.0507994i
$134$	13.9721	+	1.67070i	1.20700	+	0.144327i
$135$		0			0
$136$	8.89451	−	5.89692i	0.762698	−	0.505657i
$137$	−6.84644	−	4.97423i	−0.584930	−	0.424977i	0.255568	−	0.966791i	$-0.417738\pi$
$137$	−6.84644	−	4.97423i	−0.584930	−	0.424977i	−0.840498	+	0.541814i	$0.817738\pi$
$138$		0			0
$139$	−5.45350	−	1.77195i	−0.462560	−	0.150295i	0.0684604	−	0.997654i	$-0.478191\pi$
$139$	−5.45350	−	1.77195i	−0.462560	−	0.150295i	−0.531021	+	0.847359i	$0.678191\pi$
$140$	1.87684	+	4.56203i	0.158622	+	0.385562i
$141$		0			0
$142$	−12.3848	+	13.3656i	−1.03931	+	1.12161i
$143$	−10.7581	+	1.88112i	−0.899634	+	0.157307i
$144$		0			0
$145$	−8.24724	−	11.3514i	−0.684896	−	0.942679i
$146$	−12.3443	−	5.70879i	−1.02162	−	0.472463i
$147$		0			0
$148$	−15.9682	−	9.83815i	−1.31258	−	0.808691i
$149$	−15.6781	−	11.3908i	−1.28440	−	0.933168i	−0.284720	−	0.958611i	$-0.591901\pi$
$149$	−15.6781	−	11.3908i	−1.28440	−	0.933168i	−0.999676	+	0.0254423i	$0.991901\pi$
$150$		0			0
$151$	−3.22214	−	9.91672i	−0.262214	−	0.807011i	−0.992322	−	0.123680i	$-0.960530\pi$
$151$	−3.22214	−	9.91672i	−0.262214	−	0.807011i	0.730108	−	0.683331i	$-0.239470\pi$
$152$	−1.18721	−	0.0509267i	−0.0962954	−	0.00413070i
$153$		0			0
$154$	−5.07580	+	4.12492i	−0.409020	+	0.332396i
$155$	2.45654			0.197314
$156$		0			0
$157$	16.9246	−	5.49914i	1.35073	−	0.438879i	0.457792	−	0.889059i	$-0.348640\pi$
$157$	16.9246	−	5.49914i	1.35073	−	0.438879i	0.892938	+	0.450180i	$0.148640\pi$
$158$	−7.16951	+	4.00383i	−0.570376	+	0.318527i
$159$		0			0
$160$	9.40802	−	3.40681i	0.743769	−	0.269332i
$161$	1.92220	+	0.624560i	0.151491	+	0.0492223i
$162$		0			0
$163$	−4.84269	+	3.51842i	−0.379308	+	0.275584i	−0.761060	−	0.648681i	$-0.775321\pi$
$163$	−4.84269	+	3.51842i	−0.379308	+	0.275584i	0.381752	+	0.924265i	$0.375321\pi$
$164$	−6.89980	+	0.526367i	−0.538784	+	0.0411024i
$165$		0			0
$166$	14.5008	−	15.6492i	1.12548	−	1.21461i
$167$	−4.20600	+	3.05584i	−0.325470	+	0.236468i	−0.738506	−	0.674247i	$-0.764468\pi$
$167$	−4.20600	+	3.05584i	−0.325470	+	0.236468i	0.413036	+	0.910715i	$0.364468\pi$
$168$		0			0
$169$	−0.666510	+	2.05131i	−0.0512700	+	0.157793i
$170$	−1.83017	−	9.25895i	−0.140368	−	0.710129i
$171$		0			0
$172$	1.69919	−	7.00353i	0.129562	−	0.534014i
$173$	−4.33891	−	13.3538i	−0.329881	−	1.01527i	−0.969189	−	0.246319i	$-0.920779\pi$
$173$	−4.33891	−	13.3538i	−0.329881	−	1.01527i	0.639307	−	0.768951i	$-0.279221\pi$
$174$		0			0
$175$	−2.60949			−0.197259
$176$	7.91786	+	10.6446i	0.596831	+	0.802367i
$177$		0			0
$178$	−15.3354	−	1.83373i	−1.14944	−	0.137444i
$179$	−7.11085	−	21.8849i	−0.531490	−	1.63576i	−0.751114	−	0.660173i	$-0.770483\pi$
$179$	−7.11085	−	21.8849i	−0.531490	−	1.63576i	0.219624	−	0.975585i	$-0.429517\pi$
$180$		0			0
$181$	−11.4700	+	15.7871i	−0.852559	+	1.17345i	0.130734	+	0.991418i	$0.458267\pi$
$181$	−11.4700	+	15.7871i	−0.852559	+	1.17345i	−0.983293	+	0.182030i	$0.941733\pi$
$182$	−1.25922	−	6.37048i	−0.0933398	−	0.472212i
$183$		0			0
$184$	1.43275	−	3.84101i	0.105624	−	0.283163i
$185$	−13.4196	+	9.74989i	−0.986627	+	0.716827i
$186$		0			0
$187$	11.0573	−	5.85908i	0.808592	−	0.428458i
$188$	1.52530	−	0.116361i	0.111244	−	0.00848653i
$189$		0			0
$190$	−0.441129	+	0.953871i	−0.0320029	+	0.0692011i
$191$	24.3481	+	7.91117i	1.76177	+	0.572432i	0.997381	−	0.0723280i	$-0.0230428\pi$
$191$	24.3481	+	7.91117i	1.76177	+	0.572432i	0.764385	+	0.644760i	$0.223043\pi$
$192$		0			0
$193$	12.9917	−	17.8816i	0.935166	−	1.28715i	−0.0226438	−	0.999744i	$-0.507208\pi$
$193$	12.9917	−	17.8816i	0.935166	−	1.28715i	0.957810	−	0.287402i	$-0.0927917\pi$
$194$	−17.1154	+	9.55812i	−1.22881	+	0.686233i
$195$		0			0
$196$	6.54811	+	7.70422i	0.467722	+	0.550301i
$197$	−18.2227			−1.29832			−0.649158	−	0.760653i	$-0.724879\pi$
$197$	−18.2227			−1.29832			−0.649158	+	0.760653i	$0.724879\pi$
$198$		0			0
$199$			13.2643i			0.940284i	0.882591	+	0.470142i	$0.155797\pi$
$199$			13.2643i			0.940284i	−0.882591	+	0.470142i	$0.844203\pi$
$200$	−0.226838	+	5.28808i	−0.0160399	+	0.373924i
$201$		0			0
$202$	−9.91125	+	5.53496i	−0.697353	+	0.389438i
$203$	8.94893	+	6.50178i	0.628092	+	0.456335i
$204$		0			0
$205$	−1.89116	+	5.82039i	−0.132084	+	0.406514i
$206$	−15.8366	−	7.32381i	−1.10339	−	0.510274i
$207$		0			0
$208$	−13.0191	+	1.99802i	−0.902715	+	0.138538i
$209$	−1.37957	−	0.195892i	−0.0954268	−	0.0135501i
$210$		0			0
$211$	11.2460	+	15.4787i	0.774204	+	1.06560i	0.995898	+	0.0904841i	$0.0288414\pi$
$211$	11.2460	+	15.4787i	0.774204	+	1.06560i	−0.221694	+	0.975116i	$0.571159\pi$
$212$	−3.29305	−	8.00442i	−0.226168	−	0.549746i
$213$		0			0
$214$	9.95375	−	1.96751i	0.680424	−	0.134496i
$215$	−5.15637	−	3.74632i	−0.351662	−	0.255497i
$216$		0			0
$217$	−1.84185	+	0.598452i	−0.125033	+	0.0406256i
$218$	13.1716	+	1.57499i	0.892093	+	0.106672i
$219$		0			0
$220$	11.3703	−	2.89421i	0.766588	−	0.195127i
$221$			12.4242i			0.835740i
$222$		0			0
$223$	−1.64768	+	0.535364i	−0.110337	+	0.0358507i	−0.363665	−	0.931530i	$-0.618475\pi$
$223$	−1.64768	+	0.535364i	−0.110337	+	0.0358507i	0.253328	+	0.967380i	$0.418475\pi$
$224$	−6.22392	+	4.84628i	−0.415853	+	0.323806i
$225$		0			0
$226$	−0.502296	−	2.54115i	−0.0334123	−	0.169035i
$227$	−5.99045	−	1.94642i	−0.397600	−	0.129188i	0.103390	−	0.994641i	$-0.467031\pi$
$227$	−5.99045	−	1.94642i	−0.397600	−	0.129188i	−0.500991	+	0.865453i	$0.667031\pi$
$228$		0			0
$229$	−2.03611	−	2.80246i	−0.134550	−	0.185192i	0.736426	−	0.676519i	$-0.236512\pi$
$229$	−2.03611	−	2.80246i	−0.134550	−	0.185192i	−0.870975	+	0.491327i	$0.836512\pi$
$230$	−2.65943	−	2.46427i	−0.175357	−	0.162489i
$231$		0			0
$232$	13.9537	−	17.5697i	0.916103	−	1.15351i
$233$	8.63879	+	11.8903i	0.565946	+	0.778958i	0.992067	−	0.125708i	$-0.0401203\pi$
$233$	8.63879	+	11.8903i	0.565946	+	0.778958i	−0.426121	+	0.904666i	$0.640120\pi$
$234$		0			0
$235$	0.418069	−	1.28669i	0.0272718	−	0.0839341i
$236$	−12.5469	+	20.3648i	−0.816732	+	1.32563i
$237$		0			0
$238$	3.62784	+	6.49625i	0.235158	+	0.421089i
$239$	6.25422	+	19.2485i	0.404552	+	1.24508i	0.921269	+	0.388927i	$0.127154\pi$
$239$	6.25422	+	19.2485i	0.404552	+	1.24508i	−0.516717	+	0.856156i	$0.672846\pi$
$240$		0			0
$241$		−	8.76302i		−	0.564476i	−0.959344	−	0.282238i	$-0.908923\pi$
$241$		−	8.76302i		−	0.564476i	0.959344	−	0.282238i	$-0.0910768\pi$
$242$	8.01626	+	13.3319i	0.515305	+	0.857007i
$243$		0			0
$244$	−13.5357	−	15.9255i	−0.866536	−	1.01953i
$245$	8.50454	−	2.76329i	0.543335	−	0.176540i
$246$		0			0
$247$	0.813163	−	1.11922i	0.0517403	−	0.0712145i
$248$	1.05265	+	3.78450i	0.0668430	+	0.240316i
$249$		0			0
$250$	15.6009	+	7.21482i	0.986687	+	0.456305i
$251$	4.24381	−	3.08331i	0.267867	−	0.194617i	−0.445741	−	0.895162i	$-0.647060\pi$
$251$	4.24381	−	3.08331i	0.267867	−	0.194617i	0.713608	+	0.700545i	$0.247060\pi$
$252$		0			0
$253$	2.11346	−	4.31761i	0.132872	−	0.271446i
$254$	7.41118	+	6.86734i	0.465019	+	0.430895i
$255$		0			0
$256$	9.27987	+	13.0340i	0.579992	+	0.814622i
$257$	1.45063	−	4.46459i	0.0904879	−	0.278493i	−0.895564	−	0.444933i	$-0.853227\pi$
$257$	1.45063	−	4.46459i	0.0904879	−	0.278493i	0.986052	+	0.166440i	$0.0532273\pi$
$258$		0			0
$259$	7.68641	−	10.5794i	0.477610	−	0.657374i
$260$	−2.74657	+	11.3205i	−0.170335	+	0.702069i
$261$		0			0
$262$	1.46906	−	12.2857i	0.0907588	−	0.759013i
$263$	23.0463			1.42110			0.710548	−	0.703648i	$-0.248447\pi$
$263$	23.0463			1.42110			0.710548	+	0.703648i	$0.248447\pi$
$264$		0			0
$265$	−7.65479			−0.470230
$266$	0.0983685	−	0.822653i	0.00603136	−	0.0504401i
$267$		0			0
$268$	19.3392	+	4.69204i	1.18133	+	0.286612i
$269$	5.66339	−	7.79498i	0.345303	−	0.475268i	−0.600678	−	0.799491i	$-0.705103\pi$
$269$	5.66339	−	7.79498i	0.345303	−	0.475268i	0.945981	+	0.324223i	$0.105103\pi$
$270$		0			0
$271$	−7.25330	+	22.3234i	−0.440607	+	1.35605i	0.446624	+	0.894722i	$0.352626\pi$
$271$	−7.25330	+	22.3234i	−0.440607	+	1.35605i	−0.887230	+	0.461326i	$0.847374\pi$
$272$	13.4799	−	6.78705i	0.817340	−	0.411526i
$273$		0			0
$274$	−8.77862	−	8.13443i	−0.530336	−	0.491419i
$275$	−0.872544	+	6.14489i	−0.0526164	+	0.370551i
$276$		0			0
$277$	16.1312	−	11.7200i	0.969227	−	0.704185i	0.0139521	−	0.999903i	$-0.495559\pi$
$277$	16.1312	−	11.7200i	0.969227	−	0.704185i	0.955275	+	0.295718i	$0.0955588\pi$
$278$	−7.36034	−	3.40388i	−0.441444	−	0.204151i
$279$		0			0
$280$	1.86947	+	6.72118i	0.111722	+	0.401667i
$281$	3.73754	−	5.14428i	0.222963	−	0.306882i	−0.682851	−	0.730557i	$-0.739260\pi$
$281$	3.73754	−	5.14428i	0.222963	−	0.306882i	0.905814	+	0.423675i	$0.139260\pi$
$282$		0			0
$283$	−8.30006	+	2.69685i	−0.493387	+	0.160311i	−0.545134	−	0.838349i	$-0.683521\pi$
$283$	−8.30006	+	2.69685i	−0.493387	+	0.160311i	0.0517465	+	0.998660i	$0.483521\pi$
$284$	−19.6350	+	16.6886i	−1.16512	+	0.990284i
$285$		0			0
$286$	−15.4224	+	0.835126i	−0.911948	+	0.0493821i
$287$		−	4.82469i		−	0.284792i
$288$		0			0
$289$	0.854199	+	2.62895i	0.0502470	+	0.154644i
$290$	−9.67488	−	17.3245i	−0.568128	−	1.01733i
$291$		0			0
$292$	−16.3755	−	10.0891i	−0.958303	−	0.590417i
$293$	6.37463	−	19.6191i	0.372410	−	1.14616i	−0.572799	−	0.819696i	$-0.694143\pi$
$293$	6.37463	−	19.6191i	0.372410	−	1.14616i	0.945209	−	0.326465i	$-0.105857\pi$
$294$		0			0
$295$	12.4343	+	17.1144i	0.723955	+	0.996438i
$296$	−20.7709	−	16.4960i	−1.20728	−	0.958812i
$297$		0			0
$298$	−20.1027	−	18.6275i	−1.16452	−	1.07906i
$299$	2.80534	+	3.86122i	0.162237	+	0.223300i
$300$		0			0
$301$	4.77877	+	1.55272i	0.275444	+	0.0894971i
$302$	−2.85946	−	14.4662i	−0.164543	−	0.832435i
$303$		0			0
$304$	−1.65854	−	0.270854i	−0.0951239	−	0.0155345i
$305$	−17.5799	+	5.71205i	−1.00662	+	0.327071i
$306$		0			0
$307$			24.6574i			1.40727i	0.710560	+	0.703637i	$0.248442\pi$
$307$			24.6574i			1.40727i	−0.710560	+	0.703637i	$0.751558\pi$
$308$	−7.82010	+	4.93999i	−0.445592	+	0.281482i
$309$		0			0
$310$	3.44950	+	0.412473i	0.195918	+	0.0234269i
$311$	24.3504	−	7.91194i	1.38079	−	0.448645i	0.477859	−	0.878437i	$-0.341413\pi$
$311$	24.3504	−	7.91194i	1.38079	−	0.448645i	0.902928	+	0.429792i	$0.141413\pi$
$312$		0			0
$313$	3.15731	+	2.29392i	0.178462	+	0.129660i	0.673430	−	0.739251i	$-0.264820\pi$
$313$	3.15731	+	2.29392i	0.178462	+	0.129660i	−0.494968	+	0.868911i	$0.664820\pi$
$314$	24.6890	−	4.88017i	1.39328	−	0.275404i
$315$		0			0
$316$	−10.7398	+	4.41839i	−0.604160	+	0.248554i
$317$	3.74958	+	5.16085i	0.210597	+	0.289862i	0.901228	−	0.433345i	$-0.142667\pi$
$317$	3.74958	+	5.16085i	0.210597	+	0.289862i	−0.690631	+	0.723208i	$0.742667\pi$
$318$		0			0
$319$	18.3028	−	18.8991i	1.02476	−	1.05815i
$320$	13.7829	−	3.20420i	0.770486	−	0.179120i
$321$		0			0
$322$	2.59430	+	1.19977i	0.144575	+	0.0668604i
$323$	−0.489840	+	1.50757i	−0.0272554	+	0.0838836i
$324$		0			0
$325$	−4.98525	−	3.62200i	−0.276532	−	0.200912i
$326$	−7.39092	+	4.12747i	−0.409345	+	0.228600i
$327$		0			0
$328$	−9.77715	−	0.419402i	−0.539853	−	0.0231576i
$329$			1.06657i			0.0588019i
$330$		0			0
$331$	−4.34773			−0.238973			−0.119486	−	0.992836i	$-0.538125\pi$
$331$	−4.34773			−0.238973			−0.119486	+	0.992836i	$0.538125\pi$
$332$	22.9899	−	19.5400i	1.26173	−	1.07240i
$333$		0			0
$334$	−6.41922	+	3.58482i	−0.351244	+	0.196153i
$335$	10.3449	−	14.2385i	0.565202	−	0.777934i
$336$		0			0
$337$	9.71778	+	3.15750i	0.529361	+	0.172000i	0.561490	−	0.827484i	$-0.310229\pi$
$337$	9.71778	+	3.15750i	0.529361	+	0.172000i	−0.0321283	+	0.999484i	$0.510229\pi$
$338$	−1.28035	+	2.76855i	−0.0696419	+	0.150589i
$339$		0			0
$340$	−1.01529	−	13.3088i	−0.0550621	−	0.721772i
$341$	0.793386	+	4.53734i	0.0429642	+	0.245711i
$342$		0			0
$343$	−13.6002	+	9.88114i	−0.734343	+	0.533531i
$344$	3.56197	−	9.54913i	0.192048	−	0.514854i
$345$		0			0
$346$	−3.85054	−	19.4801i	−0.207006	−	1.04726i
$347$	−4.37155	+	6.01692i	−0.234677	+	0.323005i	−0.910071	−	0.414452i	$-0.863973\pi$
$347$	−4.37155	+	6.01692i	−0.234677	+	0.323005i	0.675394	+	0.737457i	$0.263973\pi$
$348$		0			0
$349$	1.81469	+	5.58504i	0.0971382	+	0.298961i	0.987805	−	0.155696i	$-0.0497620\pi$
$349$	1.81469	+	5.58504i	0.0971382	+	0.298961i	−0.890667	+	0.454657i	$0.849762\pi$
$350$	−3.66427	−	0.438154i	−0.195863	−	0.0234203i
$351$		0			0
$352$	9.33103	+	16.2767i	0.497345	+	0.867553i
$353$	26.3624			1.40313			0.701565	−	0.712605i	$-0.252485\pi$
$353$	26.3624			1.40313			0.701565	+	0.712605i	$0.252485\pi$
$354$		0			0
$355$	7.04254	+	21.6747i	0.373779	+	1.15037i
$356$	−21.2263	−	5.14989i	−1.12499	−	0.272944i
$357$		0			0
$358$	−6.31047	−	31.9250i	−0.333519	−	1.68729i
$359$	1.23260	−	3.79354i	0.0650539	−	0.200215i	−0.913246	−	0.407408i	$-0.866433\pi$
$359$	1.23260	−	3.79354i	0.0650539	−	0.200215i	0.978300	+	0.207193i	$0.0664327\pi$
$360$		0			0
$361$	−15.2285	+	11.0642i	−0.801501	+	0.582325i
$362$	−18.7571	+	20.2425i	−0.985851	+	1.06392i
$363$		0			0
$364$	−0.698558	−	9.15693i	−0.0366144	−	0.479954i
$365$	−13.7618	+	9.99855i	−0.720327	+	0.523348i
$366$		0			0
$367$	31.5697	+	10.2576i	1.64792	+	0.535443i	0.978288	−	0.207248i	$-0.0664509\pi$
$367$	31.5697	+	10.2576i	1.64792	+	0.535443i	0.669634	+	0.742691i	$0.266451\pi$
$368$	2.65683	−	5.15302i	0.138497	−	0.268620i
$369$		0			0
$370$	−20.4810	+	11.4376i	−1.06476	+	0.594615i
$371$	5.73936	−	1.86483i	0.297973	−	0.0968171i
$372$		0			0
$373$	30.7237			1.59081			0.795407	−	0.606075i	$-0.207257\pi$
$373$	30.7237			1.59081			0.795407	+	0.606075i	$0.207257\pi$
$374$	16.5106	−	6.37076i	0.853743	−	0.329424i
$375$		0			0
$376$	2.16139	+	0.0927151i	0.111465	+	0.00478142i
$377$	8.07180	+	24.8424i	0.415719	+	1.27945i
$378$		0			0
$379$	−29.7001	−	21.5784i	−1.52559	−	1.10841i	−0.958626	−	0.284667i	$-0.908117\pi$
$379$	−29.7001	−	21.5784i	−1.52559	−	1.10841i	−0.566967	−	0.823741i	$-0.691883\pi$
$380$	−0.779601	+	1.26537i	−0.0399927	+	0.0649119i
$381$		0			0
$382$	32.8615	+	15.1972i	1.68134	+	0.777556i
$383$	−7.33813	−	10.1001i	−0.374961	−	0.516090i	0.579280	−	0.815129i	$-0.303334\pi$
$383$	−7.33813	−	10.1001i	−0.374961	−	0.516090i	−0.954241	+	0.299039i	$0.903334\pi$
$384$		0			0
$385$	1.40904	+	8.05821i	0.0718111	+	0.410684i
$386$	21.2456	−	22.9281i	1.08137	−	1.16701i
$387$		0			0
$388$	−25.6385	+	10.5478i	−1.30160	+	0.535483i
$389$	31.6936	+	10.2979i	1.60693	+	0.522122i	0.968807	−	0.247815i	$-0.0797124\pi$
$389$	31.6936	+	10.2979i	1.60693	+	0.522122i	0.638120	+	0.769937i	$0.279712\pi$
$390$		0			0
$391$	−4.42422	−	3.21439i	−0.223743	−	0.162559i
$392$	7.90133	+	11.9178i	0.399077	+	0.601941i
$393$		0			0
$394$	−25.5886	−	3.05975i	−1.28913	−	0.154148i
$395$			10.2707i			0.516774i
$396$		0			0
$397$			14.1022i			0.707767i	0.935289	+	0.353884i	$0.115139\pi$
$397$			14.1022i			0.707767i	−0.935289	+	0.353884i	$0.884861\pi$
$398$	−2.22719	+	18.6259i	−0.111639	+	0.933633i
$399$		0			0
$400$	−1.20644	+	7.38749i	−0.0603220	+	0.369374i
$401$	−9.67496	−	7.02927i	−0.483145	−	0.351025i	0.319397	−	0.947621i	$-0.396520\pi$
$401$	−9.67496	−	7.02927i	−0.483145	−	0.351025i	−0.802542	+	0.596596i	$0.796520\pi$
$402$		0			0
$403$	−4.34939	−	1.41320i	−0.216658	−	0.0703966i
$404$	−14.8469	+	6.10806i	−0.738658	+	0.303887i
$405$		0			0
$406$	11.4745	+	10.6325i	0.569469	+	0.527680i
$407$	−22.3426	−	21.6376i	−1.10748	−	1.07254i
$408$		0			0
$409$	−9.59791	−	13.2104i	−0.474586	−	0.653212i	0.502867	−	0.864364i	$-0.332279\pi$
$409$	−9.59791	−	13.2104i	−0.474586	−	0.653212i	−0.977453	+	0.211152i	$0.932279\pi$
$410$	−3.63288	+	7.85552i	−0.179415	+	0.387956i
$411$		0			0
$412$	−21.0082	−	12.9433i	−1.03500	−	0.637669i
$413$	−13.4923	−	9.80270i	−0.663911	−	0.482359i
$414$		0			0
$415$	−8.24584	−	25.3781i	−0.404772	−	1.24576i
$416$	−18.6171	+	0.619620i	−0.912778	+	0.0303794i
$417$		0			0
$418$	−1.90431	−	0.506715i	−0.0931430	−	0.0247842i
$419$	−5.36954			−0.262319			−0.131159	−	0.991361i	$-0.541870\pi$
$419$	−5.36954			−0.262319			−0.131159	+	0.991361i	$0.541870\pi$
$420$		0			0
$421$	8.90313	−	2.89280i	0.433912	−	0.140987i	−0.0839132	−	0.996473i	$-0.526742\pi$
$421$	8.90313	−	2.89280i	0.433912	−	0.140987i	0.517825	+	0.855487i	$0.326742\pi$
$422$	13.1927	+	23.6237i	0.642210	+	1.14998i
$423$		0			0
$424$	−3.28013	−	11.7928i	−0.159297	−	0.572710i
$425$	6.71504	+	2.18185i	0.325727	+	0.105835i
$426$		0			0
$427$	11.7894	−	8.56549i	0.570528	−	0.414513i
$428$	14.3075	−	1.09148i	0.691580	−	0.0527588i
$429$		0			0
$430$	−6.61159	−	6.12642i	−0.318839	−	0.295442i
$431$	−30.9429	+	22.4813i	−1.49047	+	1.08289i	−0.516477	+	0.856301i	$0.672757\pi$
$431$	−30.9429	+	22.4813i	−1.49047	+	1.08289i	−0.973991	+	0.226587i	$0.927243\pi$
$432$		0			0
$433$	3.07438	−	9.46196i	0.147745	−	0.454713i	−0.849609	−	0.527414i	$-0.823162\pi$
$433$	3.07438	−	9.46196i	0.147745	−	0.454713i	0.997354	+	0.0727008i	$0.0231618\pi$
$434$	−2.68683	+	0.531092i	−0.128972	+	0.0254932i
$435$		0			0
$436$	18.2312	+	4.42324i	0.873118	+	0.211835i
$437$	0.188171	+	0.579132i	0.00900145	+	0.0277036i
$438$		0			0
$439$	15.8844			0.758122			0.379061	−	0.925372i	$-0.376247\pi$
$439$	15.8844			0.758122			0.379061	+	0.925372i	$0.376247\pi$
$440$	16.4523	−	2.15490i	0.784333	−	0.102731i
$441$		0			0
$442$	−2.08612	+	17.4462i	−0.0992266	+	0.829829i
$443$	1.67612	+	5.15857i	0.0796349	+	0.245091i	0.982946	−	0.183895i	$-0.0588708\pi$
$443$	1.67612	+	5.15857i	0.0796349	+	0.245091i	−0.903311	+	0.428986i	$0.858871\pi$
$444$		0			0
$445$	−11.3543	+	15.6279i	−0.538247	+	0.740834i
$446$	−2.40358	+	0.475105i	−0.113813	+	0.0224969i
$447$		0			0
$448$	−9.55343	+	5.76015i	−0.451357	+	0.272141i
$449$	8.05234	−	5.85037i	0.380013	−	0.276096i	−0.381338	−	0.924436i	$-0.624536\pi$
$449$	8.05234	−	5.85037i	0.380013	−	0.276096i	0.761351	+	0.648340i	$0.224536\pi$
$450$		0			0
$451$	−11.3613	−	1.61325i	−0.534983	−	0.0759650i
$452$	−0.278651	−	3.65264i	−0.0131066	−	0.171806i
$453$		0			0
$454$	−8.08504	−	3.73902i	−0.379450	−	0.175481i
$455$	−7.72442	−	2.50982i	−0.362126	−	0.117662i
$456$		0			0
$457$	−14.7492	+	20.3005i	−0.689939	+	0.949619i	−0.999999	−	0.00109777i	$-0.999651\pi$
$457$	−14.7492	+	20.3005i	−0.689939	+	0.949619i	0.310061	+	0.950717i	$0.399651\pi$
$458$	−2.38857	−	4.27713i	−0.111611	−	0.199857i
$459$		0			0
$460$	−3.32062	−	3.90690i	−0.154825	−	0.182160i
$461$	34.5074			1.60717			0.803585	−	0.595190i	$-0.202923\pi$
$461$	34.5074			1.60717			0.803585	+	0.595190i	$0.202923\pi$
$462$		0			0
$463$		−	22.7879i		−	1.05905i	−0.848296	−	0.529523i	$-0.822371\pi$
$463$		−	22.7879i		−	1.05905i	0.848296	−	0.529523i	$-0.177629\pi$
$464$	22.5440	−	22.3286i	1.04658	−	1.03658i
$465$		0			0
$466$	10.1342	+	18.1470i	0.469458	+	0.840642i
$467$	−4.94788	−	3.59484i	−0.228960	−	0.166349i	0.467390	−	0.884051i	$-0.345194\pi$
$467$	−4.94788	−	3.59484i	−0.228960	−	0.166349i	−0.696351	+	0.717702i	$0.745194\pi$
$468$		0			0
$469$	−4.28759	+	13.1958i	−0.197982	+	0.609327i
$470$	0.803102	−	1.73658i	0.0370443	−	0.0801024i
$471$		0			0
$472$	−21.0379	+	26.4897i	−0.968346	+	1.21929i
$473$	5.25428	−	10.7340i	0.241592	−	0.493549i
$474$		0			0
$475$	−0.462118	−	0.636050i	−0.0212034	−	0.0291840i
$476$	4.00348	+	9.73125i	0.183499	+	0.446031i
$477$		0			0
$478$	5.55026	+	28.0791i	0.253863	+	1.28431i
$479$	−2.50936	−	1.82316i	−0.114656	−	0.0833022i	0.528980	−	0.848634i	$-0.322575\pi$
$479$	−2.50936	−	1.82316i	−0.114656	−	0.0833022i	−0.643635	+	0.765332i	$0.722575\pi$
$480$		0			0
$481$	29.3688	−	9.54249i	1.33910	−	0.435100i
$482$	1.47138	−	12.3051i	0.0670197	−	0.560483i
$483$		0			0
$484$	9.01799	+	20.0668i	0.409909	+	0.912127i
$485$			24.5186i			1.11333i
$486$		0			0
$487$	20.1262	−	6.53939i	0.912003	−	0.296328i	0.184821	−	0.982772i	$-0.440829\pi$
$487$	20.1262	−	6.53939i	0.912003	−	0.296328i	0.727182	+	0.686444i	$0.240829\pi$
$488$	−16.3330	−	24.6356i	−0.739360	−	1.11520i
$489$		0			0
$490$	12.4061	−	2.45226i	0.560452	−	0.110782i
$491$	4.96607	+	1.61357i	0.224116	+	0.0728195i	0.418922	−	0.908022i	$-0.362408\pi$
$491$	4.96607	+	1.61357i	0.224116	+	0.0728195i	−0.194807	+	0.980842i	$0.562408\pi$
$492$		0			0
$493$	−17.5922	−	24.2136i	−0.792312	−	1.09052i
$494$	1.32978	−	1.43509i	0.0598296	−	0.0645677i
$495$		0			0
$496$	0.842688	+	5.49098i	0.0378378	+	0.246552i
$497$	−10.5606	−	14.5354i	−0.473708	−	0.652003i
$498$		0			0
$499$	−9.84802	+	30.3091i	−0.440858	+	1.35682i	0.446105	+	0.894980i	$0.352811\pi$
$499$	−9.84802	+	30.3091i	−0.440858	+	1.35682i	−0.886963	+	0.461840i	$0.847189\pi$
$500$	20.6955	+	12.7506i	0.925531	+	0.570226i
$501$		0			0
$502$	6.47691	−	3.61704i	0.289079	−	0.161437i
$503$	4.38495	+	13.4955i	0.195515	+	0.601734i	0.999970	+	0.00772063i	$0.00245758\pi$
$503$	4.38495	+	13.4955i	0.195515	+	0.601734i	−0.804455	+	0.594014i	$0.797542\pi$
$504$		0			0
$505$			14.1984i			0.631819i
$506$	3.69271	−	5.70796i	0.164161	−	0.253750i
$507$		0			0
$508$	9.25378	+	10.8876i	0.410570	+	0.483059i
$509$	8.45834	−	2.74828i	0.374909	−	0.121815i	−0.115500	−	0.993307i	$-0.536847\pi$
$509$	8.45834	−	2.74828i	0.374909	−	0.121815i	0.490410	+	0.871492i	$0.336847\pi$
$510$		0			0
$511$	7.88244	−	10.8492i	0.348699	−	0.479942i
$512$	10.8424	+	19.8606i	0.479170	+	0.877722i
$513$		0			0
$514$	2.78663	−	6.02564i	0.122913	−	0.265780i
$515$	−17.6551	+	12.8272i	−0.777975	+	0.565232i
$516$		0			0
$517$	2.51159	+	0.356633i	0.110459	+	0.0156847i
$518$	12.5697	−	13.5651i	0.552281	−	0.596018i
$519$		0			0
$520$	−5.75757	+	15.4352i	−0.252486	+	0.676880i
$521$	8.34024	−	25.6686i	0.365393	−	1.12456i	−0.584342	−	0.811507i	$-0.698647\pi$
$521$	8.34024	−	25.6686i	0.365393	−	1.12456i	0.949735	−	0.313056i	$-0.101353\pi$
$522$		0			0
$523$	25.2868	−	34.8043i	1.10571	−	1.52188i	0.278129	−	0.960544i	$-0.410286\pi$
$523$	25.2868	−	34.8043i	1.10571	−	1.52188i	0.827585	−	0.561341i	$-0.189714\pi$
$524$	4.12574	−	17.0050i	0.180234	−	0.742868i
$525$		0			0
$526$	32.3619	+	3.86966i	1.41105	+	0.168725i
$527$	5.24004			0.228260
$528$		0			0
$529$	20.8992			0.908662
$530$	−10.7489	−	1.28530i	−0.466904	−	0.0558299i
$531$		0			0
$532$	0.276260	−	1.13866i	0.0119774	−	0.0493672i
$533$	6.69673	−	9.21726i	0.290067	−	0.399244i
$534$		0			0
$535$	3.92154	−	12.0692i	0.169543	−	0.521799i
$536$	26.3684	+	9.83582i	1.13894	+	0.424843i
$537$		0			0
$538$	9.26143	−	9.99487i	0.399288	−	0.430909i
$539$	7.85062	+	14.8158i	0.338150	+	0.638162i
$540$		0			0
$541$	16.3673	−	11.8916i	0.703686	−	0.511258i	−0.177444	−	0.984131i	$-0.556783\pi$
$541$	16.3673	−	11.8916i	0.703686	−	0.511258i	0.881131	+	0.472873i	$0.156783\pi$
$542$	−13.9334	+	30.1288i	−0.598493	+	1.29414i
$543$		0			0
$544$	20.0682	−	7.26707i	0.860418	−	0.311573i
$545$	9.75224	−	13.4228i	0.417740	−	0.574970i
$546$		0			0
$547$	13.6380	−	4.43124i	0.583117	−	0.189466i	−0.00257925	−	0.999997i	$-0.500821\pi$
$547$	13.6380	−	4.43124i	0.583117	−	0.189466i	0.585697	+	0.810530i	$0.300821\pi$
$548$	−10.9612	−	12.8965i	−0.468239	−	0.550909i
$549$		0			0
$550$	−2.25701	+	8.48220i	−0.0962393	+	0.361682i
$551$			3.33267i			0.141977i
$552$		0			0
$553$	−2.50210	−	7.70067i	−0.106400	−	0.327466i
$554$	24.6194	−	13.7488i	1.04598	−	0.584129i
$555$		0			0
$556$	−9.76393	−	6.01562i	−0.414083	−	0.255119i
$557$	−9.72693	+	29.9364i	−0.412143	+	1.26845i	0.502638	+	0.864497i	$0.332363\pi$
$557$	−9.72693	+	29.9364i	−0.412143	+	1.26845i	−0.914781	+	0.403949i	$0.867637\pi$
$558$		0			0
$559$	6.97434	+	9.59936i	0.294983	+	0.406010i
$560$	1.49660	+	9.75185i	0.0632427	+	0.412091i
$561$		0			0
$562$	6.11206	−	6.59609i	0.257822	−	0.278239i
$563$	−11.5320	−	15.8725i	−0.486017	−	0.668946i	0.493630	−	0.869672i	$-0.335670\pi$
$563$	−11.5320	−	15.8725i	−0.486017	−	0.668946i	−0.979647	+	0.200726i	$0.935670\pi$
$564$		0			0
$565$	−3.08122	−	1.00115i	−0.129628	−	0.0421187i
$566$	−12.1079	+	2.39330i	−0.508931	+	0.100598i
$567$		0			0
$568$	−30.3738	+	20.1374i	−1.27446	+	0.844945i
$569$	−25.2020	+	8.18862i	−1.05652	+	0.343285i	−0.785225	−	0.619211i	$-0.787453\pi$
$569$	−25.2020	+	8.18862i	−1.05652	+	0.343285i	−0.271297	+	0.962496i	$0.587453\pi$
$570$		0			0
$571$		−	15.2004i		−	0.636116i	−0.948071	−	0.318058i	$-0.896969\pi$
$571$		−	15.2004i		−	0.636116i	0.948071	−	0.318058i	$-0.103031\pi$
$572$	−21.7966	−	1.41686i	−0.911360	−	0.0592418i
$573$		0			0
$574$	0.810105	−	6.77488i	0.0338131	−	0.282778i
$575$	2.57957	−	0.838154i	0.107576	−	0.0349534i
$576$		0			0
$577$	17.6624	+	12.8325i	0.735296	+	0.534224i	0.891234	−	0.453543i	$-0.149840\pi$
$577$	17.6624	+	12.8325i	0.735296	+	0.534224i	−0.155939	+	0.987767i	$0.549840\pi$
$578$	0.758053	+	3.83503i	0.0315308	+	0.159516i
$579$		0			0
$580$	−10.6766	−	25.9517i	−0.443324	−	1.07759i
$581$	12.3650	+	17.0190i	0.512987	+	0.706066i
$582$		0			0
$583$	−2.47226	−	14.1387i	−0.102390	−	0.585567i
$584$	−21.3006	−	16.9167i	−0.881425	−	0.700019i
$585$		0			0
$586$	12.2455	−	26.4790i	0.505858	−	1.09384i
$587$	−7.06883	+	21.7556i	−0.291762	+	0.897951i	0.692528	+	0.721391i	$0.256497\pi$
$587$	−7.06883	+	21.7556i	−0.291762	+	0.897951i	−0.984290	+	0.176560i	$0.943503\pi$
$588$		0			0
$589$	−0.472045	−	0.342961i	−0.0194503	−	0.0141315i
$590$	14.5868	+	26.1200i	0.600528	+	1.07534i
$591$		0			0
$592$	−26.3969	−	26.6515i	−1.08490	−	1.09537i
$593$		−	13.3772i		−	0.549336i	−0.961539	−	0.274668i	$-0.911432\pi$
$593$		−	13.3772i		−	0.549336i	0.961539	−	0.274668i	$-0.0885679\pi$
$594$		0			0
$595$	9.30620			0.381517
$596$	−25.1007	−	29.5324i	−1.02816	−	1.20969i
$597$		0			0
$598$	3.29096	+	5.89300i	0.134577	+	0.240983i
$599$	−13.8109	+	19.0091i	−0.564300	+	0.776692i	−0.991865	−	0.127292i	$-0.959371\pi$
$599$	−13.8109	+	19.0091i	−0.564300	+	0.776692i	0.427565	+	0.903984i	$0.359371\pi$
$600$		0			0
$601$	11.5910	+	3.76616i	0.472809	+	0.153625i	0.535722	−	0.844394i	$-0.320039\pi$
$601$	11.5910	+	3.76616i	0.472809	+	0.153625i	−0.0629138	+	0.998019i	$0.520039\pi$
$602$	6.44969	+	2.98274i	0.262870	+	0.121567i
$603$		0			0
$604$	−1.58630	−	20.7937i	−0.0645454	−	0.846083i
$605$	19.4468	−	0.623576i	0.790626	−	0.0253520i
$606$		0			0
$607$	−33.2882	+	24.1853i	−1.35113	+	0.981652i	−0.352173	+	0.935935i	$0.614557\pi$
$607$	−33.2882	+	24.1853i	−1.35113	+	0.981652i	−0.998954	+	0.0457169i	$0.985443\pi$
$608$	−2.28346	−	0.658819i	−0.0926066	−	0.0267186i
$609$		0			0
$610$	−25.6450	+	5.06912i	−1.03833	+	0.205243i
$611$	−1.48041	+	2.03761i	−0.0598911	+	0.0824330i
$612$		0			0
$613$	−3.01493	−	9.27900i	−0.121772	−	0.374775i	0.871527	−	0.490347i	$-0.163130\pi$
$613$	−3.01493	−	9.27900i	−0.121772	−	0.374775i	−0.993299	+	0.115572i	$0.963130\pi$
$614$	−4.14018	+	34.6242i	−0.167084	+	1.39732i
$615$		0			0
$616$	−11.8105	+	5.62373i	−0.475860	+	0.226587i
$617$	19.8476			0.799035			0.399518	−	0.916725i	$-0.369178\pi$
$617$	19.8476			0.799035			0.399518	+	0.916725i	$0.369178\pi$
$618$		0			0
$619$	0.849909	+	2.61575i	0.0341607	+	0.105136i	0.966683	−	0.255977i	$-0.0823970\pi$
$619$	0.849909	+	2.61575i	0.0341607	+	0.105136i	−0.932522	+	0.361113i	$0.882397\pi$
$620$	4.77457	+	1.15840i	0.191751	+	0.0465224i
$621$		0			0
$622$	35.5216	−	7.02139i	1.42429	−	0.281532i
$623$	4.70597	−	14.4835i	0.188541	−	0.580269i
$624$		0			0
$625$	9.82260	−	7.13654i	0.392904	−	0.285462i
$626$	4.04837	+	3.75129i	0.161805	+	0.149932i
$627$		0			0
$628$	35.4880	−	2.70729i	1.41613	−	0.108033i
$629$	−28.6253	+	20.7975i	−1.14136	+	0.829250i
$630$		0			0
$631$	−5.16849	−	1.67934i	−0.205754	−	0.0668536i	0.204327	−	0.978903i	$-0.434500\pi$
$631$	−5.16849	−	1.67934i	−0.205754	−	0.0668536i	−0.410081	+	0.912049i	$0.634500\pi$
$632$	−15.8228	+	4.40106i	−0.629397	+	0.175065i
$633$		0			0
$634$	4.39865	+	7.87651i	0.174693	+	0.312816i
$635$	12.0186	−	3.90508i	0.476943	−	0.154968i
$636$		0			0
$637$	−16.6472			−0.659588
$638$	28.8744	−	23.4652i	1.14315	−	0.928996i
$639$		0			0
$640$	19.8921	−	2.18511i	0.786303	−	0.0863742i
$641$	5.69933	+	17.5407i	0.225110	+	0.692817i	0.998280	+	0.0586191i	$0.0186697\pi$
$641$	5.69933	+	17.5407i	0.225110	+	0.692817i	−0.773170	+	0.634198i	$0.781330\pi$
$642$		0			0
$643$	−36.3473	−	26.4078i	−1.43340	−	1.04142i	−0.989372	−	0.145408i	$-0.953551\pi$
$643$	−36.3473	−	26.4078i	−1.43340	−	1.04142i	−0.444024	−	0.896015i	$-0.646449\pi$
$644$	3.44150	+	2.12033i	0.135614	+	0.0835527i
$645$		0			0
$646$	−0.940972	+	2.03470i	−0.0370221	+	0.0800542i
$647$	−12.0677	−	16.6098i	−0.474430	−	0.652997i	0.502993	−	0.864291i	$-0.332232\pi$
$647$	−12.0677	−	16.6098i	−0.474430	−	0.652997i	−0.977423	+	0.211294i	$0.932232\pi$
$648$		0			0
$649$	−27.5951	+	28.4942i	−1.08320	+	1.11849i
$650$	−6.39218	−	5.92311i	−0.250722	−	0.232324i
$651$		0			0
$652$	−11.0714	+	4.55484i	−0.433591	+	0.178381i
$653$	−4.82108	−	1.56646i	−0.188664	−	0.0613005i	0.213161	−	0.977017i	$-0.431624\pi$
$653$	−4.82108	−	1.56646i	−0.188664	−	0.0613005i	−0.401825	+	0.915717i	$0.631624\pi$
$654$		0			0
$655$	−12.5200	−	9.09632i	−0.489197	−	0.355423i
$656$	−13.6588	−	2.23059i	−0.533285	−	0.0870900i
$657$		0			0
$658$	−0.179086	+	1.49769i	−0.00698149	+	0.0583860i
$659$			24.6770i			0.961279i	0.876918	+	0.480640i	$0.159595\pi$
$659$			24.6770i			0.961279i	−0.876918	+	0.480640i	$0.840405\pi$
$660$		0			0
$661$			29.9755i			1.16591i	0.812504	+	0.582956i	$0.198104\pi$
$661$			29.9755i			1.16591i	−0.812504	+	0.582956i	$0.801896\pi$
$662$	−6.10513	−	0.730019i	−0.237282	−	0.0283730i
$663$		0			0
$664$	35.5635	−	23.5781i	1.38013	−	0.915006i
$665$	−0.838342	−	0.609091i	−0.0325095	−	0.0236196i
$666$		0			0
$667$	−10.9347	−	3.55289i	−0.423393	−	0.137569i
$668$	−9.61585	+	3.95601i	−0.372048	+	0.153062i
$669$		0			0
$670$	16.9172	−	18.2569i	0.653567	−	0.705325i
$671$	−16.2282	−	30.6260i	−0.626482	−	1.18230i
$672$		0			0
$673$	−0.00676354	−	0.00930921i	−0.000260715	−	0.000358844i	0.808887	−	0.587965i	$-0.200071\pi$
$673$	−0.00676354	−	0.00930921i	−0.000260715	−	0.000358844i	−0.809147	+	0.587606i	$0.800071\pi$
$674$	13.1156	+	6.06549i	0.505196	+	0.233634i
$675$		0			0
$676$	−2.26274	+	3.67265i	−0.0870286	+	0.141256i
$677$	−0.292248	−	0.212331i	−0.0112320	−	0.00816054i	0.582155	−	0.813078i	$-0.302210\pi$
$677$	−0.292248	−	0.212331i	−0.0112320	−	0.00816054i	−0.593387	+	0.804917i	$0.702210\pi$
$678$		0			0
$679$	−5.97313	−	18.3834i	−0.229228	−	0.705491i
$680$	0.808972	−	18.8589i	0.0310227	−	0.723204i
$681$		0			0
$682$	0.352224	+	6.50459i	0.0134874	+	0.249074i
$683$	−16.8584			−0.645070			−0.322535	−	0.946557i	$-0.604535\pi$
$683$	−16.8584			−0.645070			−0.322535	+	0.946557i	$0.604535\pi$
$684$		0			0
$685$	−14.2362	+	4.62561i	−0.543935	+	0.176735i
$686$	−20.7567	+	11.5916i	−0.792494	+	0.442570i
$687$		0			0
$688$	6.60513	−	12.8109i	0.251818	−	0.488411i
$689$	13.5531	+	4.40366i	0.516331	+	0.167766i
$690$		0			0
$691$	33.4931	−	24.3341i	1.27414	−	0.925714i	0.274777	−	0.961508i	$-0.411396\pi$
$691$	33.4931	−	24.3341i	1.27414	−	0.925714i	0.999359	+	0.0357938i	$0.0113959\pi$
$692$	−2.13610	−	28.0007i	−0.0812022	−	1.06443i
$693$		0			0
$694$	−7.14886	+	7.71500i	−0.271367	+	0.292857i
$695$	−8.20552	+	5.96166i	−0.311253	+	0.226139i
$696$		0			0
$697$	−4.03403	+	12.4155i	−0.152800	+	0.470269i
$698$	1.61043	+	8.14728i	0.0609558	+	0.308379i
$699$		0			0
$700$	−5.07183	−	1.23052i	−0.191697	−	0.0465093i
$701$	−9.88537	−	30.4240i	−0.373365	−	1.14910i	−0.944575	−	0.328296i	$-0.893526\pi$
$701$	−9.88537	−	30.4240i	−0.373365	−	1.14910i	0.571210	−	0.820804i	$-0.306474\pi$
$702$		0			0
$703$	3.93989			0.148596
$704$	10.3697	+	24.4227i	0.390824	+	0.920465i
$705$		0			0
$706$	37.0184	+	4.42647i	1.39321	+	0.166592i
$707$	−3.45895	−	10.6455i	−0.130087	−	0.400367i
$708$		0			0
$709$	−20.2031	+	27.8072i	−0.758743	+	1.04432i	0.238574	+	0.971124i	$0.423320\pi$
$709$	−20.2031	+	27.8072i	−0.758743	+	1.04432i	−0.997318	+	0.0731963i	$0.976680\pi$
$710$	6.24985	+	31.6184i	0.234553	+	1.18662i
$711$		0			0
$712$	−28.9415	−	10.7956i	−1.08463	−	0.404582i
$713$	1.62851	−	1.18318i	0.0609883	−	0.0443106i
$714$		0			0
$715$	−8.49302	+	17.3504i	−0.317621	+	0.648870i
$716$	−3.50075	−	45.8890i	−0.130829	−	1.71495i
$717$		0			0
$718$	2.36779	−	5.11997i	0.0883652	−	0.191075i
$719$	−25.4856	−	8.28077i	−0.950452	−	0.308821i	−0.207553	−	0.978224i	$-0.566550\pi$
$719$	−25.4856	−	8.28077i	−0.950452	−	0.308821i	−0.742899	+	0.669403i	$0.766550\pi$
$720$		0			0
$721$	10.1124	−	13.9185i	0.376605	−	0.518353i
$722$	−23.2418	+	12.9794i	−0.864971	+	0.483044i
$723$		0			0
$724$	−29.7378	+	25.2753i	−1.10520	+	0.939349i
$725$	14.8444			0.551307
$726$		0			0
$727$			26.4551i			0.981165i	0.871395	+	0.490583i	$0.163216\pi$
$727$			26.4551i			0.981165i	−0.871395	+	0.490583i	$0.836784\pi$
$728$	0.556601	−	12.9756i	0.0206290	−	0.480906i
$729$		0			0
$730$	−21.0033	+	11.7293i	−0.777368	+	0.434123i
$731$	−10.9990	−	7.99128i	−0.406814	−	0.295568i
$732$		0			0
$733$	0.587267	−	1.80742i	0.0216912	−	0.0667586i	−0.939625	−	0.342206i	$-0.888826\pi$
$733$	0.587267	−	1.80742i	0.0216912	−	0.0667586i	0.961316	+	0.275447i	$0.0888260\pi$
$734$	42.6081	+	19.7046i	1.57269	+	0.727311i
$735$		0			0
$736$	4.59598	−	6.78982i	0.169410	−	0.250276i
$737$	29.6403	+	14.5089i	1.09181	+	0.534441i
$738$		0			0
$739$	8.35357	+	11.4977i	0.307291	+	0.422950i	0.934534	−	0.355874i	$-0.115817\pi$
$739$	8.35357	+	11.4977i	0.307291	+	0.422950i	−0.627243	+	0.778824i	$0.715817\pi$
$740$	−30.6801	+	12.6219i	−1.12782	+	0.463992i
$741$		0			0
$742$	8.37238	−	1.65493i	0.307360	−	0.0607544i
$743$	−19.8113	−	14.3937i	−0.726806	−	0.528055i	0.161746	−	0.986832i	$-0.448288\pi$
$743$	−19.8113	−	14.3937i	−0.726806	−	0.528055i	−0.888551	+	0.458777i	$0.848288\pi$
$744$		0			0
$745$	−32.6002	+	10.5924i	−1.19438	+	0.388077i
$746$	43.1426	+	5.15876i	1.57956	+	0.188876i
$747$		0			0
$748$	24.2541	−	6.17362i	0.886816	−	0.225730i
$749$			10.0045i			0.365558i
$750$		0			0
$751$	−38.6132	+	12.5462i	−1.40901	+	0.457817i	−0.912095	−	0.409980i	$-0.865536\pi$
$751$	−38.6132	+	12.5462i	−1.40901	+	0.457817i	−0.496920	+	0.867796i	$0.665536\pi$
$752$	3.01947	+	0.493106i	0.110109	+	0.0179817i
$753$		0			0
$754$	7.16326	+	36.2393i	0.260870	+	1.31976i
$755$	−17.5407	−	5.69932i	−0.638372	−	0.207420i
$756$		0			0
$757$	−7.32712	−	10.0849i	−0.266309	−	0.366542i	0.654831	−	0.755776i	$-0.272740\pi$
$757$	−7.32712	−	10.0849i	−0.266309	−	0.366542i	−0.921139	+	0.389233i	$0.872740\pi$
$758$	−38.0820	−	35.2875i	−1.38320	−	1.28170i
$759$		0			0
$760$	−1.30719	+	1.64594i	−0.0474167	+	0.0597045i
$761$	−19.4146	−	26.7219i	−0.703779	−	0.968668i	−0.999909	−	0.0135207i	$-0.995696\pi$
$761$	−19.4146	−	26.7219i	−0.703779	−	0.968668i	0.296130	−	0.955148i	$-0.404304\pi$
$762$		0			0
$763$	−4.04195	+	12.4399i	−0.146329	+	0.450353i
$764$	43.5927	+	26.8578i	1.57713	+	0.971680i
$765$		0			0
$766$	−8.60840	−	15.4148i	−0.311034	−	0.556958i
$767$	−12.1698	−	37.4548i	−0.439427	−	1.35242i
$768$		0			0
$769$		−	45.9291i		−	1.65625i	−0.560546	−	0.828123i	$-0.689409\pi$
$769$		−	45.9291i		−	1.65625i	0.560546	−	0.828123i	$-0.310591\pi$
$770$	0.625543	+	11.5520i	0.0225430	+	0.416306i
$771$		0			0
$772$	33.6831	−	28.6286i	1.21228	−	1.03037i
$773$	−13.4151	+	4.35884i	−0.482509	+	0.156777i	−0.540164	−	0.841560i	$-0.681638\pi$
$773$	−13.4151	+	4.35884i	−0.482509	+	0.156777i	0.0576547	+	0.998337i	$0.481638\pi$
$774$		0			0
$775$	−1.52762	+	2.10259i	−0.0548737	+	0.0755272i
$776$	−37.7729	+	10.5064i	−1.35597	+	0.377158i
$777$		0			0
$778$	42.7753	+	19.7820i	1.53357	+	0.709218i
$779$	1.17600	−	0.854411i	0.0421344	−	0.0306125i
$780$		0			0
$781$	−37.7596	+	20.0081i	−1.35115	+	0.715947i
$782$	−5.67282	−	5.25654i	−0.202860	−	0.187973i
$783$		0			0
$784$	9.09403	+	18.0618i	0.324787	+	0.645065i
$785$	9.72688	−	29.9363i	0.347167	−	1.06847i
$786$		0			0
$787$	−18.5090	+	25.4755i	−0.659776	+	0.908104i	−0.999474	−	0.0324309i	$-0.989675\pi$
$787$	−18.5090	+	25.4755i	−0.659776	+	0.908104i	0.339698	+	0.940535i	$0.389675\pi$
$788$	−35.4180	−	8.59306i	−1.26171	−	0.306115i
$789$		0			0
$790$	−1.72453	+	14.4222i	−0.0613560	+	0.513118i
$791$	2.55411			0.0908138
$792$		0			0
$793$	34.4118			1.22200
$794$	−2.36787	+	19.8024i	−0.0840325	+	0.702761i
$795$		0			0
$796$	−6.25489	+	25.7808i	−0.221699	+	0.913775i
$797$	−19.3111	+	26.5794i	−0.684033	+	0.941490i	−0.999973	−	0.00728889i	$-0.997680\pi$
$797$	−19.3111	+	26.5794i	−0.684033	+	0.941490i	0.315941	+	0.948779i	$0.397680\pi$
$798$		0			0
$799$	0.891783	−	2.74463i	0.0315490	−	0.0970979i
$800$	−2.93451	+	10.1710i	−0.103751	+	0.359600i
$801$		0			0
$802$	−12.4054	−	11.4951i	−0.438050	−	0.405906i
$803$	−22.9124	−	22.1895i	−0.808561	−	0.783050i
$804$		0			0
$805$	2.89220	−	2.10131i	0.101937	−	0.0740614i
$806$	−5.87017	−	2.71473i	−0.206768	−	0.0956223i
$807$		0			0
$808$	−21.8737	+	6.08410i	−0.769514	+	0.214038i
$809$	−3.52470	+	4.85134i	−0.123922	+	0.170564i	−0.866470	−	0.499228i	$-0.833617\pi$
$809$	−3.52470	+	4.85134i	−0.123922	+	0.170564i	0.742549	+	0.669792i	$0.233617\pi$
$810$		0			0
$811$	−39.0150	+	12.6767i	−1.37000	+	0.445140i	−0.899369	−	0.437189i	$-0.855974\pi$
$811$	−39.0150	+	12.6767i	−1.37000	+	0.445140i	−0.470632	+	0.882330i	$0.655974\pi$
$812$	14.3273	+	16.8569i	0.502790	+	0.591560i
$813$		0			0
$814$	−27.7406	−	34.1353i	−0.972306	−	1.19644i
$815$			10.5879i			0.370876i
$816$		0			0
$817$	0.467812	+	1.43978i	0.0163667	+	0.0503714i
$818$	−11.2594	−	20.1617i	−0.393674	−	0.704939i
$819$		0			0
$820$	−6.42033	+	10.4208i	−0.224208	+	0.363910i
$821$	7.86487	−	24.2056i	0.274486	−	0.844781i	−0.714869	−	0.699258i	$-0.753514\pi$
$821$	7.86487	−	24.2056i	0.274486	−	0.844781i	0.989355	−	0.145523i	$-0.0464863\pi$
$822$		0			0
$823$	−8.33462	−	11.4716i	−0.290526	−	0.399875i	0.638659	−	0.769490i	$-0.279490\pi$
$823$	−8.33462	−	11.4716i	−0.290526	−	0.399875i	−0.929185	+	0.369615i	$0.879490\pi$
$824$	−27.3266	−	21.7025i	−0.951967	−	0.756043i
$825$		0			0
$826$	−17.3000	−	16.0305i	−0.601945	−	0.557773i
$827$	−16.3323	−	22.4795i	−0.567931	−	0.781690i	0.424377	−	0.905486i	$-0.360493\pi$
$827$	−16.3323	−	22.4795i	−0.567931	−	0.781690i	−0.992308	+	0.123796i	$0.960493\pi$
$828$		0			0
$829$	47.9834	+	15.5908i	1.66653	+	0.541490i	0.982226	−	0.187703i	$-0.0601044\pi$
$829$	47.9834	+	15.5908i	1.66653	+	0.541490i	0.684308	+	0.729193i	$0.260104\pi$
$830$	−7.31770	−	37.0207i	−0.254001	−	1.28501i
$831$		0			0
$832$	−26.2464	−	2.25589i	−0.909929	−	0.0782087i
$833$	18.1410	−	5.89437i	0.628549	−	0.204228i
$834$		0			0
$835$			9.19584i			0.318235i
$836$	−2.58897	−	1.03128i	−0.0895415	−	0.0356677i
$837$		0			0
$838$	−7.53996	−	0.901589i	−0.260464	−	0.0311449i
$839$	44.3548	−	14.4117i	1.53130	−	0.497548i	0.582337	−	0.812947i	$-0.302138\pi$
$839$	44.3548	−	14.4117i	1.53130	−	0.497548i	0.948959	+	0.315399i	$0.102138\pi$
$840$		0			0
$841$	−27.4457	−	19.9405i	−0.946403	−	0.687602i
$842$	12.9876	−	2.56719i	0.447582	−	0.0884714i
$843$		0			0
$844$	14.5587	+	35.3878i	0.501131	+	1.21810i
$845$	2.24245	+	3.08646i	0.0771425	+	0.106178i
$846$		0			0
$847$	−14.4288	+	5.20510i	−0.495779	+	0.178849i
$848$	−2.62589	−	17.1104i	−0.0901734	−	0.587572i
$849$		0			0
$850$	9.06298	+	4.19129i	0.310858	+	0.143760i
$851$	−4.20023	+	12.9270i	−0.143982	+	0.443132i
$852$		0			0
$853$	−41.5877	−	30.2152i	−1.42394	−	1.03455i	−0.991106	−	0.133073i	$-0.957515\pi$
$853$	−41.5877	−	30.2152i	−1.42394	−	1.03455i	−0.432829	−	0.901476i	$-0.642485\pi$
$854$	17.9930	−	10.0482i	0.615707	−	0.343843i
$855$		0			0
$856$	20.2740	+	0.869678i	0.692952	+	0.0297250i
$857$			17.4541i			0.596221i	0.954531	+	0.298111i	$0.0963565\pi$
$857$			17.4541i			0.596221i	−0.954531	+	0.298111i	$0.903644\pi$
$858$		0			0
$859$	−35.3164			−1.20498			−0.602489	−	0.798127i	$-0.705824\pi$
$859$	−35.3164			−1.20498			−0.602489	+	0.798127i	$0.705824\pi$
$860$	−8.25539	−	9.71293i	−0.281506	−	0.331208i
$861$		0			0
$862$	−47.2252	+	26.3730i	−1.60850	+	0.898267i
$863$	3.84304	−	5.28949i	0.130819	−	0.180056i	−0.738583	−	0.674163i	$-0.764505\pi$
$863$	3.84304	−	5.28949i	0.130819	−	0.180056i	0.869401	+	0.494106i	$0.164505\pi$
$864$		0			0
$865$	−23.6202	−	7.67468i	−0.803112	−	0.260947i
$866$	5.90581	−	12.7704i	0.200688	−	0.433955i
$867$		0			0
$868$	−3.86204	+	0.294625i	−0.131086	+	0.0100002i
$869$	−18.9704	+	3.31711i	−0.643526	+	0.112525i
$870$		0			0
$871$	−26.5071	+	19.2586i	−0.898160	+	0.652552i
$872$	24.8578	+	9.27233i	0.841791	+	0.314001i
$873$		0			0
$874$	0.166991	+	0.844818i	0.00564856	+	0.0285764i
$875$	−9.96190	+	13.7114i	−0.336774	+	0.463529i
$876$		0			0
$877$	9.06904	+	27.9116i	0.306240	+	0.942509i	0.979212	+	0.202841i	$0.0650175\pi$
$877$	9.06904	+	27.9116i	0.306240	+	0.942509i	−0.672972	+	0.739668i	$0.734982\pi$
$878$	22.3051	+	2.66712i	0.752759	+	0.0900110i
$879$		0			0
$880$	23.4643	−	0.263455i	0.790983	−	0.00888108i
$881$	−1.12915			−0.0380420			−0.0190210	−	0.999819i	$-0.506055\pi$
$881$	−1.12915			−0.0380420			−0.0190210	+	0.999819i	$0.506055\pi$
$882$		0			0
$883$	4.24530	+	13.0657i	0.142866	+	0.439695i	0.996730	−	0.0807999i	$-0.0257475\pi$
$883$	4.24530	+	13.0657i	0.142866	+	0.439695i	−0.853865	+	0.520495i	$0.825747\pi$
$884$	−5.85870	+	24.1478i	−0.197049	+	0.812178i
$885$		0			0
$886$	1.48746	+	7.52515i	0.0499722	+	0.252812i
$887$	−1.98190	+	6.09967i	−0.0665458	+	0.204807i	−0.978800	−	0.204817i	$-0.934340\pi$
$887$	−1.98190	+	6.09967i	−0.0665458	+	0.204807i	0.912254	+	0.409624i	$0.134340\pi$
$888$		0			0
$889$	−8.05988	+	5.85584i	−0.270320	+	0.196399i
$890$	−18.5679	+	20.0384i	−0.622399	+	0.671688i
$891$		0			0
$892$	−3.45491	+	0.263566i	−0.115679	+	0.00882485i
$893$	−0.259972	+	0.188880i	−0.00869962	+	0.00632064i
$894$		0			0
$895$	−38.7101	−	12.5777i	−1.29394	−	0.420426i
$896$	−14.3822	+	6.48436i	−0.480476	+	0.216627i
$897$		0			0
$898$	12.2895	−	6.86309i	0.410106	−	0.229024i
$899$	10.4776	−	3.40438i	0.349447	−	0.113542i
$900$		0			0
$901$	−16.3284			−0.543979
$902$	−15.6828	−	4.17300i	−0.522180	−	0.138946i
$903$		0			0
$904$	0.222025	−	5.17587i	0.00738443	−	0.172147i
$905$	10.6661	+	32.8270i	0.354554	+	1.09121i
$906$		0			0
$907$	9.91808	+	7.20591i	0.329325	+	0.239268i	0.740144	−	0.672448i	$-0.234757\pi$
$907$	9.91808	+	7.20591i	0.329325	+	0.239268i	−0.410819	+	0.911717i	$0.634757\pi$
$908$	−10.7253	−	6.60792i	−0.355931	−	0.219291i
$909$		0			0
$910$	−10.4253	−	4.82130i	−0.345595	−	0.159825i
$911$	21.4231	+	29.4864i	0.709779	+	0.976927i	0.999802	+	0.0199074i	$0.00633714\pi$
$911$	21.4231	+	29.4864i	0.709779	+	0.976927i	−0.290023	+	0.957020i	$0.593663\pi$
$912$		0			0
$913$	44.2113	−	23.4267i	1.46318	−	0.775312i
$914$	−24.1196	+	26.0297i	−0.797806	+	0.860986i
$915$		0			0
$916$	−2.63589	−	6.40705i	−0.0870923	−	0.211695i
$917$	11.6032	+	3.77010i	0.383170	+	0.124500i
$918$		0			0
$919$	−10.4315	−	7.57891i	−0.344103	−	0.250005i	0.402288	−	0.915513i	$-0.368215\pi$
$919$	−10.4315	−	7.57891i	−0.344103	−	0.250005i	−0.746391	+	0.665508i	$0.768215\pi$
$920$	−4.00685	−	6.04367i	−0.132102	−	0.199254i
$921$		0			0
$922$	48.4557	+	5.79407i	1.59580	+	0.190818i
$923$		−	42.4273i		−	1.39651i
$924$		0			0
$925$		−	17.5491i		−	0.577010i
$926$	3.82628	−	31.9991i	0.125739	−	1.05155i
$927$		0			0
$928$	35.4056	−	27.5687i	1.16225	−	0.904987i
$929$	−11.5280	−	8.37561i	−0.378223	−	0.274795i	0.382390	−	0.924001i	$-0.375101\pi$
$929$	−11.5280	−	8.37561i	−0.378223	−	0.274795i	−0.760612	+	0.649206i	$0.775101\pi$
$930$		0			0
$931$	−2.02001	−	0.656340i	−0.0662031	−	0.0215107i
$932$	11.1835	+	27.1838i	0.366329	+	0.890435i
$933$		0			0
$934$	−6.34426	−	5.87870i	−0.207590	−	0.192357i
$935$	3.11175	−	21.9145i	0.101765	−	0.716680i
$936$		0			0
$937$	−29.3763	−	40.4330i	−0.959681	−	1.32089i	−0.947090	−	0.320967i	$-0.895992\pi$
$937$	−29.3763	−	40.4330i	−0.959681	−	1.32089i	−0.0125913	−	0.999921i	$-0.504008\pi$
$938$	−8.23637	+	17.8098i	−0.268927	+	0.581511i
$939$		0			0
$940$	1.41931	−	2.30368i	0.0462928	−	0.0751376i
$941$	3.47674	+	2.52600i	0.113338	+	0.0823452i	0.643011	−	0.765857i	$-0.277685\pi$
$941$	3.47674	+	2.52600i	0.113338	+	0.0823452i	−0.529672	+	0.848202i	$0.677685\pi$
$942$		0			0
$943$	1.54967	+	4.76938i	0.0504641	+	0.155312i
$944$	−33.9894	+	33.6647i	−1.10626	+	1.09569i
$945$		0			0
$946$	9.18043	−	14.1905i	0.298482	−	0.461374i
$947$	−0.231238			−0.00751424			−0.00375712	−	0.999993i	$-0.501196\pi$
$947$	−0.231238			−0.00751424			−0.00375712	+	0.999993i	$0.501196\pi$
$948$		0			0
$949$	30.1178	−	9.78586i	0.977664	−	0.317662i
$950$	−0.542112	−	0.970742i	−0.0175884	−	0.0314950i
$951$		0			0
$952$	3.98777	+	14.3369i	0.129244	+	0.464663i
$953$	−50.8341	−	16.5170i	−1.64668	−	0.535039i	−0.668663	−	0.743566i	$-0.733133\pi$
$953$	−50.8341	−	16.5170i	−1.64668	−	0.535039i	−0.978017	+	0.208527i	$0.933133\pi$
$954$		0			0
$955$	36.6349	−	26.6168i	1.18548	−	0.861301i
$956$	3.07903	+	40.3609i	0.0995828	+	1.30536i
$957$		0			0
$958$	−3.21755	−	2.98144i	−0.103954	−	0.0963259i
$959$	9.54701	−	6.93631i	0.308289	−	0.223985i
$960$		0			0
$961$	8.98349	−	27.6483i	0.289790	−	0.891882i
$962$	42.8422	−	8.46841i	1.38129	−	0.273032i
$963$		0			0
$964$	4.13226	−	17.0319i	0.133091	−	0.548562i
$965$	−12.0812	−	37.1821i	−0.388908	−	1.19694i
$966$		0			0
$967$	1.08508			0.0348938			0.0174469	−	0.999848i	$-0.494446\pi$
$967$	1.08508			0.0348938			0.0174469	+	0.999848i	$0.494446\pi$
$968$	9.29378	+	29.6922i	0.298713	+	0.954343i
$969$		0			0
$970$	−4.11688	+	34.4293i	−0.132185	+	1.10546i
$971$	10.1034	+	31.0950i	0.324233	+	0.997887i	0.971786	+	0.235866i	$0.0757927\pi$
$971$	10.1034	+	31.0950i	0.324233	+	0.997887i	−0.647552	+	0.762021i	$0.724207\pi$
$972$		0			0
$973$	4.69992	−	6.46889i	0.150673	−	0.207383i
$974$	29.3594	−	5.80333i	0.940735	−	0.185951i
$975$		0			0
$976$	−18.7984	−	37.3360i	−0.601723	−	1.19510i
$977$	40.9534	−	29.7544i	1.31021	−	0.951926i	0.310215	−	0.950667i	$-0.399599\pi$
$977$	40.9534	−	29.7544i	1.31021	−	0.951926i	0.999999	−	0.00125964i	$-0.000400956\pi$
$978$		0			0
$979$	−32.5325	−	15.9246i	−1.03974	−	0.508954i
$980$	17.8326	−	1.36040i	0.569641	−	0.0434564i
$981$		0			0
$982$	6.70247	+	3.09964i	0.213884	+	0.0989135i
$983$	−23.1688	−	7.52801i	−0.738971	−	0.240106i	−0.0847421	−	0.996403i	$-0.527007\pi$
$983$	−23.1688	−	7.52801i	−0.738971	−	0.240106i	−0.654229	+	0.756297i	$0.727007\pi$
$984$		0			0
$985$	−18.9457	+	26.0766i	−0.603662	+	0.830869i
$986$	−20.6375	−	36.9548i	−0.657231	−	1.17688i
$987$		0			0
$988$	2.10825	−	1.79188i	0.0670724	−	0.0570074i
$989$	−5.22272			−0.166073
$990$		0			0
$991$		−	27.0358i		−	0.858821i	−0.903110	−	0.429410i	$-0.858721\pi$
$991$		−	27.0358i		−	0.858821i	0.903110	−	0.429410i	$-0.141279\pi$
$992$	0.261332	+	7.85198i	0.00829730	+	0.249301i
$993$		0			0
$994$	−12.3887	−	22.1840i	−0.392946	−	0.703635i
$995$	18.9812	+	13.7906i	0.601743	+	0.437192i
$996$		0			0
$997$	4.82347	−	14.8451i	0.152761	−	0.470149i	−0.845166	−	0.534503i	$-0.820499\pi$
$997$	4.82347	−	14.8451i	0.152761	−	0.470149i	0.997927	+	0.0643542i	$0.0204987\pi$
$998$	−18.9178	+	40.9068i	−0.598833	+	1.29488i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.bp.d.19.12		48
3.2	odd	2		264.2.z.b.19.1	✓	48
8.3	odd	2	inner	792.2.bp.d.19.6		48
11.7	odd	10	inner	792.2.bp.d.667.6		48
12.11	even	2		1056.2.bp.a.943.4		48
24.5	odd	2		1056.2.bp.a.943.9		48
24.11	even	2		264.2.z.b.19.7	yes	48
33.29	even	10		264.2.z.b.139.7	yes	48
88.51	even	10	inner	792.2.bp.d.667.12		48
132.95	odd	10		1056.2.bp.a.271.9		48
264.29	even	10		1056.2.bp.a.271.4		48
264.227	odd	10		264.2.z.b.139.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.z.b.19.1	✓	48	3.2	odd	2
264.2.z.b.19.7	yes	48	24.11	even	2
264.2.z.b.139.1	yes	48	264.227	odd	10
264.2.z.b.139.7	yes	48	33.29	even	10
792.2.bp.d.19.6		48	8.3	odd	2	inner
792.2.bp.d.19.12		48	1.1	even	1	trivial
792.2.bp.d.667.6		48	11.7	odd	10	inner
792.2.bp.d.667.12		48	88.51	even	10	inner
1056.2.bp.a.271.4		48	264.29	even	10
1056.2.bp.a.271.9		48	132.95	odd	10
1056.2.bp.a.943.4		48	12.11	even	2
1056.2.bp.a.943.9		48	24.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.bp (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40421 + 0.167908i) q^{2} +(1.94361 + 0.471557i) q^{4} +(1.03968 - 1.43099i) q^{5} +(-0.430909 + 1.32620i) q^{7} +(2.65006 + 0.988513i) q^{8} +(1.70020 - 1.83484i) q^{10} +(2.97889 + 1.45816i) q^{11} +(-2.66400 + 1.93551i) q^{13} +(-0.827766 + 1.78991i) q^{14} +(3.55527 + 1.83305i) q^{16} +(2.21773 - 3.05245i) q^{17} +(-0.399566 + 0.129827i) q^{19} +(2.69552 - 2.29103i) q^{20} +(3.93815 + 2.54775i) q^{22} -1.44940i q^{23} +(0.578275 + 1.77975i) q^{25} +(-4.06581 + 2.27056i) q^{26} +(-1.46290 + 2.37442i) q^{28} +(2.45128 - 7.54427i) q^{29} +(0.816325 + 1.12358i) q^{31} +(4.68456 + 3.17094i) q^{32} +(3.62669 - 3.91390i) q^{34} +(1.44978 + 1.99544i) q^{35} +(-8.91884 - 2.89791i) q^{37} +(-0.582873 + 0.115214i) q^{38} +(4.16976 - 2.76449i) q^{40} +(-3.29058 + 1.06918i) q^{41} -3.60336i q^{43} +(5.10220 + 4.23882i) q^{44} +(0.243367 - 2.03527i) q^{46} +(0.727433 - 0.236357i) q^{47} +(4.08999 + 2.97155i) q^{49} +(0.513186 + 2.59624i) q^{50} +(-6.09050 + 2.50566i) q^{52} +(-2.54374 - 3.50116i) q^{53} +(5.18369 - 2.74674i) q^{55} +(-2.45290 + 3.08856i) q^{56} +(4.70886 - 10.1821i) q^{58} +(-3.69578 + 11.3745i) q^{59} +(-8.45451 - 6.14256i) q^{61} +(0.957635 + 1.71480i) q^{62} +(6.04568 + 5.23925i) q^{64} +5.82447i q^{65} +9.95011 q^{67} +(5.74981 - 4.88699i) q^{68} +(1.70074 + 3.04545i) q^{70} +(-7.57332 + 10.4238i) q^{71} +(-9.14630 - 2.97181i) q^{73} +(-12.0373 - 5.56681i) q^{74} +(-0.837822 + 0.0639152i) q^{76} +(-3.21744 + 3.32227i) q^{77} +(-4.69761 + 3.41302i) q^{79} +(6.31940 - 3.18178i) q^{80} +(-4.80020 + 0.948832i) q^{82} +(8.86730 - 12.2048i) q^{83} +(-2.06230 - 6.34711i) q^{85} +(0.605033 - 5.05987i) q^{86} +(6.45283 + 6.80889i) q^{88} -10.9210 q^{89} +(-1.41893 - 4.36703i) q^{91} +(0.683476 - 2.81708i) q^{92} +(1.06116 - 0.209753i) q^{94} +(-0.229638 + 0.706752i) q^{95} +(-11.2144 + 8.14771i) q^{97} +(5.24426 + 4.85943i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4} - 4 q^{11} + 16 q^{14} + 20 q^{16} - 25 q^{20} + 3 q^{22} - 4 q^{25} - 4 q^{26} - 25 q^{28} - 26 q^{38} - 65 q^{40} + 60 q^{41} + 43 q^{44} - 5 q^{46} - 12 q^{49} + 80 q^{50} - 15 q^{52}+ \cdots - 40 q^{97}+O(q^{100}) \) 48 * q + 4 * q^4 - 4 * q^11 + 16 * q^14 + 20 * q^16 - 25 * q^20 + 3 * q^22 - 4 * q^25 - 4 * q^26 - 25 * q^28 - 26 * q^38 - 65 * q^40 + 60 * q^41 + 43 * q^44 - 5 * q^46 - 12 * q^49 + 80 * q^50 - 15 * q^52 + 14 * q^56 + 73 * q^58 + 8 * q^59 + 45 * q^62 - 38 * q^64 + 8 * q^67 + 55 * q^68 - 40 * q^70 - 60 * q^74 - 35 * q^82 + 100 * q^83 - 81 * q^86 - 18 * q^88 - 96 * q^89 - 20 * q^91 - 59 * q^92 + 35 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

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Database

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