LMFDB - Embedded newform 972.2.l.b.215.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [972,2,Mod(107,972)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(972, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("972.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,-3,0,3,-6,0,0,9,0,-3,0,0,6,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			215.10
Character	$\chi$	$=$	972.215
Dual form			972.2.l.b.755.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.223817 + 1.39639i) q^{2} +(-1.89981 + 0.625071i) q^{4} +(-2.21508 + 2.63983i) q^{5} +(1.00203 - 2.75305i) q^{7} +(-1.29805 - 2.51298i) q^{8} +(-4.18200 - 2.50228i) q^{10} +(2.00243 - 1.68024i) q^{11} +(0.941927 - 5.34193i) q^{13} +(4.06860 + 0.783043i) q^{14} +(3.21857 - 2.37503i) q^{16} +(-1.15583 - 0.667320i) q^{17} +(0.0790760 - 0.0456546i) q^{19} +(2.55816 - 6.39976i) q^{20} +(2.79445 + 2.42011i) q^{22} +(0.797738 - 0.290353i) q^{23} +(-1.19388 - 6.77083i) q^{25} +(7.67024 + 0.119685i) q^{26} +(-0.182815 + 5.85661i) q^{28} +(-0.493578 + 0.0870310i) q^{29} +(2.27906 + 6.26168i) q^{31} +(4.03684 + 3.96281i) q^{32} +(0.673145 - 1.76335i) q^{34} +(5.04800 + 8.74340i) q^{35} +(2.75869 - 4.77819i) q^{37} +(0.0814501 + 0.100203i) q^{38} +(9.50912 + 2.13981i) q^{40} +(-2.81281 - 0.495975i) q^{41} +(-3.65343 - 4.35398i) q^{43} +(-2.75398 + 4.44381i) q^{44} +(0.583993 + 1.04897i) q^{46} +(6.20947 + 2.26006i) q^{47} +(-1.21289 - 1.01774i) q^{49} +(9.18751 - 3.18255i) q^{50} +(1.54960 + 10.7374i) q^{52} -7.37249i q^{53} +9.00795i q^{55} +(-8.21903 + 1.05553i) q^{56} +(-0.232000 - 0.669748i) q^{58} +(2.33273 + 1.95739i) q^{59} +(2.27868 + 0.829371i) q^{61} +(-8.23365 + 4.58393i) q^{62} +(-4.63012 + 6.52395i) q^{64} +(12.0154 + 14.3193i) q^{65} +(-4.74821 - 0.837237i) q^{67} +(2.61299 + 0.545306i) q^{68} +(-11.0794 + 9.00590i) q^{70} +(5.91940 - 10.2527i) q^{71} +(-5.83049 - 10.0987i) q^{73} +(7.28967 + 2.78277i) q^{74} +(-0.121692 + 0.136163i) q^{76} +(-2.61929 - 7.19644i) q^{77} +(1.66138 - 0.292946i) q^{79} +(-0.859714 + 13.7574i) q^{80} +(0.0630204 - 4.03879i) q^{82} +(0.375017 + 2.12683i) q^{83} +(4.32187 - 1.57303i) q^{85} +(5.26216 - 6.07610i) q^{86} +(-6.82167 - 2.85103i) q^{88} +(12.5801 - 7.26310i) q^{89} +(-13.7628 - 7.94593i) q^{91} +(-1.33406 + 1.05026i) q^{92} +(-1.76615 + 9.17668i) q^{94} +(-0.0546395 + 0.309876i) q^{95} +(5.05588 - 4.24238i) q^{97} +(1.14969 - 1.92146i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 + 12 * q^14 + 3 * q^16 + 18 * q^17 - 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 6 * q^29 + 57 * q^32 - 3 * q^34 - 6 * q^37 - 45 * q^38 - 12 * q^40 - 66 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 66 * q^50 - 24 * q^52 + 81 * q^56 - 24 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 + 42 * q^65 - 51 * q^68 - 30 * q^70 - 6 * q^73 + 96 * q^74 - 9 * q^76 - 30 * q^77 - 12 * q^82 + 66 * q^85 - 141 * q^86 - 45 * q^88 + 24 * q^92 - 51 * q^94 + 42 * q^97 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	0.223817	+	1.39639i	0.158262	+	0.987397i
$2$	0.223817	+	1.39639i	0.158262	+	0.987397i
$3$		0			0
$3$		0			0
$4$	−1.89981	+	0.625071i	−0.949906	+	0.312535i
$5$	−2.21508	+	2.63983i	−0.990614	+	1.18057i	−0.00705588	+	0.999975i	$0.502246\pi$
$5$	−2.21508	+	2.63983i	−0.990614	+	1.18057i	−0.983558	+	0.180593i	$0.942198\pi$
$6$		0			0
$7$	1.00203	−	2.75305i	0.378731	−	1.04055i	−0.593153	−	0.805090i	$-0.702117\pi$
$7$	1.00203	−	2.75305i	0.378731	−	1.04055i	0.971883	−	0.235464i	$-0.0756608\pi$
$8$	−1.29805	−	2.51298i	−0.458931	−	0.888472i
$9$		0			0
$10$	−4.18200	−	2.50228i	−1.32247	−	0.791290i
$11$	2.00243	−	1.68024i	0.603757	−	0.506612i	−0.288894	−	0.957361i	$-0.593288\pi$
$11$	2.00243	−	1.68024i	0.603757	−	0.506612i	0.892651	+	0.450749i	$0.148843\pi$
$12$		0			0
$13$	0.941927	−	5.34193i	0.261244	−	1.48159i	−0.518279	−	0.855212i	$-0.673427\pi$
$13$	0.941927	−	5.34193i	0.261244	−	1.48159i	0.779522	−	0.626374i	$-0.215462\pi$
$14$	4.06860	+	0.783043i	1.08738	+	0.209277i
$15$		0			0
$16$	3.21857	−	2.37503i	0.804643	−	0.593758i
$17$	−1.15583	−	0.667320i	−0.280330	−	0.161849i	0.353243	−	0.935532i	$-0.385079\pi$
$17$	−1.15583	−	0.667320i	−0.280330	−	0.161849i	−0.633573	+	0.773683i	$0.718412\pi$
$18$		0			0
$19$	0.0790760	−	0.0456546i	0.0181413	−	0.0104739i	−0.490902	−	0.871215i	$-0.663333\pi$
$19$	0.0790760	−	0.0456546i	0.0181413	−	0.0104739i	0.509043	+	0.860741i	$0.329999\pi$
$20$	2.55816	−	6.39976i	0.572021	−	1.43103i
$21$		0			0
$22$	2.79445	+	2.42011i	0.595779	+	0.515970i
$23$	0.797738	−	0.290353i	0.166340	−	0.0605428i	−0.257508	−	0.966276i	$-0.582901\pi$
$23$	0.797738	−	0.290353i	0.166340	−	0.0605428i	0.423848	+	0.905733i	$0.360679\pi$
$24$		0			0
$25$	−1.19388	−	6.77083i	−0.238776	−	1.35417i
$26$	7.67024	+	0.119685i	1.50426	+	0.0234721i
$27$		0			0
$28$	−0.182815	+	5.85661i	−0.0345487	+	1.10679i
$29$	−0.493578	+	0.0870310i	−0.0916551	+	0.0161613i	−0.219288	−	0.975660i	$-0.570373\pi$
$29$	−0.493578	+	0.0870310i	−0.0916551	+	0.0161613i	0.127633	+	0.991822i	$0.459262\pi$
$30$		0			0
$31$	2.27906	+	6.26168i	0.409332	+	1.12463i	0.957543	+	0.288290i	$0.0930868\pi$
$31$	2.27906	+	6.26168i	0.409332	+	1.12463i	−0.548211	+	0.836340i	$0.684691\pi$
$32$	4.03684	+	3.96281i	0.713620	+	0.700533i
$33$		0			0
$34$	0.673145	−	1.76335i	0.115443	−	0.302412i
$35$	5.04800	+	8.74340i	0.853268	+	1.47790i
$36$		0			0
$37$	2.75869	−	4.77819i	0.453526	−	0.785530i	−0.545076	−	0.838387i	$-0.683499\pi$
$37$	2.75869	−	4.77819i	0.453526	−	0.785530i	0.998602	+	0.0528563i	$0.0168325\pi$
$38$	0.0814501	+	0.100203i	0.0132130	+	0.0162550i
$39$		0			0
$40$	9.50912	+	2.13981i	1.50352	+	0.338334i
$41$	−2.81281	−	0.495975i	−0.439288	−	0.0774583i	−0.0503696	−	0.998731i	$-0.516040\pi$
$41$	−2.81281	−	0.495975i	−0.439288	−	0.0774583i	−0.388918	+	0.921272i	$0.627151\pi$
$42$		0			0
$43$	−3.65343	−	4.35398i	−0.557142	−	0.663976i	0.411797	−	0.911276i	$-0.364901\pi$
$43$	−3.65343	−	4.35398i	−0.557142	−	0.663976i	−0.968939	+	0.247299i	$0.920457\pi$
$44$	−2.75398	+	4.44381i	−0.415178	+	0.669929i
$45$		0			0
$46$	0.583993	+	1.04897i	0.0861051	+	0.154662i
$47$	6.20947	+	2.26006i	0.905744	+	0.329664i	0.752552	−	0.658533i	$-0.228823\pi$
$47$	6.20947	+	2.26006i	0.905744	+	0.329664i	0.153192	+	0.988197i	$0.451045\pi$
$48$		0			0
$49$	−1.21289	−	1.01774i	−0.173271	−	0.145391i
$50$	9.18751	−	3.18255i	1.29931	−	0.450080i
$51$		0			0
$52$	1.54960	+	10.7374i	0.214891	+	1.48902i
$53$		−	7.37249i		−	1.01269i	−0.862331	−	0.506345i	$-0.830996\pi$
$53$		−	7.37249i		−	1.01269i	0.862331	−	0.506345i	$-0.169004\pi$
$54$		0			0
$55$			9.00795i			1.21463i
$56$	−8.21903	+	1.05553i	−1.09831	+	0.141050i
$57$		0			0
$58$	−0.232000	−	0.669748i	−0.0304631	−	0.0879422i
$59$	2.33273	+	1.95739i	0.303696	+	0.254831i	0.781880	−	0.623428i	$-0.214261\pi$
$59$	2.33273	+	1.95739i	0.303696	+	0.254831i	−0.478185	+	0.878259i	$0.658705\pi$
$60$		0			0
$61$	2.27868	+	0.829371i	0.291755	+	0.106190i	0.483751	−	0.875206i	$-0.339274\pi$
$61$	2.27868	+	0.829371i	0.291755	+	0.106190i	−0.191996	+	0.981396i	$0.561496\pi$
$62$	−8.23365	+	4.58393i	−1.04568	+	0.582160i
$63$		0			0
$64$	−4.63012	+	6.52395i	−0.578765	+	0.815494i
$65$	12.0154	+	14.3193i	1.49032	+	1.77610i
$66$		0			0
$67$	−4.74821	−	0.837237i	−0.580086	−	0.102285i	−0.124097	−	0.992270i	$-0.539603\pi$
$67$	−4.74821	−	0.837237i	−0.580086	−	0.102285i	−0.455989	+	0.889985i	$0.650714\pi$
$68$	2.61299	+	0.545306i	0.316871	+	0.0661281i
$69$		0			0
$70$	−11.0794	+	9.00590i	−1.32424	+	1.07641i
$71$	5.91940	−	10.2527i	0.702504	−	1.21677i	−0.265081	−	0.964226i	$-0.585399\pi$
$71$	5.91940	−	10.2527i	0.702504	−	1.21677i	0.967585	−	0.252546i	$-0.0812678\pi$
$72$		0			0
$73$	−5.83049	−	10.0987i	−0.682408	−	1.18197i	−0.974244	−	0.225497i	$-0.927600\pi$
$73$	−5.83049	−	10.0987i	−0.682408	−	1.18197i	0.291836	−	0.956468i	$-0.405734\pi$
$74$	7.28967	+	2.78277i	0.847406	+	0.323491i
$75$		0			0
$76$	−0.121692	+	0.136163i	−0.0139591	+	0.0156190i
$77$	−2.61929	−	7.19644i	−0.298496	−	0.820110i
$78$		0			0
$79$	1.66138	−	0.292946i	0.186920	−	0.0329590i	−0.0794047	−	0.996842i	$-0.525302\pi$
$79$	1.66138	−	0.292946i	0.186920	−	0.0329590i	0.266324	+	0.963884i	$0.414191\pi$
$80$	−0.859714	+	13.7574i	−0.0961190	+	1.53812i
$81$		0			0
$82$	0.0630204	−	4.03879i	0.00695944	−	0.446010i
$83$	0.375017	+	2.12683i	0.0411635	+	0.233450i	0.998448	−	0.0556992i	$-0.0177388\pi$
$83$	0.375017	+	2.12683i	0.0411635	+	0.233450i	−0.957284	+	0.289149i	$0.906628\pi$
$84$		0			0
$85$	4.32187	−	1.57303i	0.468773	−	0.170619i
$86$	5.26216	−	6.07610i	0.567434	−	0.655203i
$87$		0			0
$88$	−6.82167	−	2.85103i	−0.727193	−	0.303921i
$89$	12.5801	−	7.26310i	1.33348	−	0.769887i	0.347652	−	0.937624i	$-0.386979\pi$
$89$	12.5801	−	7.26310i	1.33348	−	0.769887i	0.985832	+	0.167737i	$0.0536458\pi$
$90$		0			0
$91$	−13.7628	−	7.94593i	−1.44273	−	0.832960i
$92$	−1.33406	+	1.05026i	−0.139086	+	0.109497i
$93$		0			0
$94$	−1.76615	+	9.17668i	−0.182164	+	0.946502i
$95$	−0.0546395	+	0.309876i	−0.00560589	+	0.0317926i
$96$		0			0
$97$	5.05588	−	4.24238i	0.513347	−	0.430749i	−0.348958	−	0.937138i	$-0.613465\pi$
$97$	5.05588	−	4.24238i	0.513347	−	0.430749i	0.862305	+	0.506389i	$0.169020\pi$
$98$	1.14969	−	1.92146i	0.116137	−	0.194097i
$99$		0			0
$100$	6.50039	+	12.1170i	0.650039	+	1.21170i
$101$	2.82004	−	7.74801i	0.280605	−	0.770956i	−0.716686	−	0.697396i	$-0.754342\pi$
$101$	2.82004	−	7.74801i	0.280605	−	0.770956i	0.997291	−	0.0735595i	$-0.0234359\pi$
$102$		0			0
$103$	10.3468	−	12.3309i	1.01950	−	1.21500i	0.0430954	−	0.999071i	$-0.486278\pi$
$103$	10.3468	−	12.3309i	1.01950	−	1.21500i	0.976409	−	0.215928i	$-0.0692775\pi$
$104$	−14.6468	+	4.56707i	−1.43624	+	0.447838i
$105$		0			0
$106$	10.2949	−	1.65009i	0.999927	−	0.160271i
$107$	−9.71808			−0.939482			−0.469741	−	0.882804i	$-0.655653\pi$
$107$	−9.71808			−0.939482			−0.469741	+	0.882804i	$0.655653\pi$
$108$		0			0
$109$	−4.69860			−0.450044			−0.225022	−	0.974354i	$-0.572245\pi$
$109$	−4.69860			−0.450044			−0.225022	+	0.974354i	$0.572245\pi$
$110$	−12.5786	+	2.01613i	−1.19932	+	0.192230i
$111$		0			0
$112$	−3.31348	−	11.2407i	−0.313094	−	1.06215i
$113$	0.362829	−	0.432403i	0.0341321	−	0.0406770i	−0.748708	−	0.662900i	$-0.769326\pi$
$113$	0.362829	−	0.432403i	0.0341321	−	0.0406770i	0.782840	+	0.622222i	$0.213770\pi$
$114$		0			0
$115$	−1.00057	+	2.74905i	−0.0933038	+	0.256350i
$116$	0.883304	−	0.473863i	0.0820127	−	0.0439971i
$117$		0			0
$118$	−2.21118	+	3.69550i	−0.203556	+	0.340198i
$119$	−2.99534	+	2.51339i	−0.274582	+	0.230402i
$120$		0			0
$121$	−0.723600	+	4.10374i	−0.0657818	+	0.373067i
$122$	−0.648119	+	3.36755i	−0.0586780	+	0.304884i
$123$		0			0
$124$	−8.24378	−	10.4714i	−0.740314	−	0.940363i
$125$	5.59652	+	3.23116i	0.500568	+	0.289003i
$126$		0			0
$127$	9.63141	−	5.56070i	0.854649	−	0.493432i	−0.00756758	−	0.999971i	$-0.502409\pi$
$127$	9.63141	−	5.56070i	0.854649	−	0.493432i	0.862217	+	0.506539i	$0.169076\pi$
$128$	−10.1463	−	5.00529i	−0.896813	−	0.442409i
$129$		0			0
$130$	−17.3062	+	19.9830i	−1.51785	+	1.75263i
$131$	2.91519	−	1.06104i	0.254701	−	0.0927037i	−0.211514	−	0.977375i	$-0.567839\pi$
$131$	2.91519	−	1.06104i	0.254701	−	0.0927037i	0.466215	+	0.884671i	$0.345617\pi$
$132$		0			0
$133$	−0.0464528	−	0.263447i	−0.00402797	−	0.0228438i
$134$	0.106382	−	6.81774i	0.00919004	−	0.588963i
$135$		0			0
$136$	−0.176631	+	3.77080i	−0.0151459	+	0.323343i
$137$	−17.0059	+	2.99860i	−1.45291	+	0.256188i	−0.843698	−	0.536818i	$-0.819626\pi$
$137$	−17.0059	+	2.99860i	−1.45291	+	0.256188i	−0.609214	+	0.793006i	$0.708515\pi$
$138$		0			0
$139$	3.82721	+	10.5152i	0.324620	+	0.891885i	0.989448	+	0.144889i	$0.0462825\pi$
$139$	3.82721	+	10.5152i	0.324620	+	0.891885i	−0.664828	+	0.746996i	$0.731495\pi$
$140$	−15.0555	−	13.4555i	−1.27242	−	1.13719i
$141$		0			0
$142$	15.6416	+	5.97107i	1.31262	+	0.501081i
$143$	−7.08959	−	12.2795i	−0.592862	−	1.02687i
$144$		0			0
$145$	0.863567	−	1.49574i	0.0717153	−	0.124215i
$146$	12.7968	−	10.4019i	1.05907	−	0.860868i
$147$		0			0
$148$	−2.25429	+	10.8020i	−0.185301	+	0.887923i
$149$	−17.9746	−	3.16940i	−1.47253	−	0.259647i	−0.620943	−	0.783855i	$-0.713250\pi$
$149$	−17.9746	−	3.16940i	−1.47253	−	0.259647i	−0.851590	+	0.524208i	$0.824361\pi$
$150$		0			0
$151$	12.3734	+	14.7460i	1.00693	+	1.20001i	0.979718	+	0.200383i	$0.0642187\pi$
$151$	12.3734	+	14.7460i	1.00693	+	1.20001i	0.0272126	+	0.999630i	$0.491337\pi$
$152$	−0.217374	−	0.139454i	−0.0176313	−	0.0113112i
$153$		0			0
$154$	9.46280	−	5.26823i	0.762534	−	0.424526i
$155$	−21.5781	−	7.85378i	−1.73319	−	0.630830i
$156$		0			0
$157$	−12.9003	−	10.8246i	−1.02955	−	0.863897i	−0.0387551	−	0.999249i	$-0.512339\pi$
$157$	−12.9003	−	10.8246i	−1.02955	−	0.863897i	−0.990798	+	0.135351i	$0.956784\pi$
$158$	0.780910	+	2.25436i	0.0621259	+	0.179348i
$159$		0			0
$160$	−19.4031	+	1.87863i	−1.53395	+	0.148519i
$161$		−	2.48715i		−	0.196015i
$162$		0			0
$163$		−	8.02606i		−	0.628650i	−0.949315	−	0.314325i	$-0.898222\pi$
$163$		−	8.02606i		−	0.628650i	0.949315	−	0.314325i	$-0.101778\pi$
$164$	5.65384	−	0.815948i	0.441490	−	0.0637148i
$165$		0			0
$166$	−2.88595	+	0.999690i	−0.223993	+	0.0775910i
$167$	−1.00020	−	0.839268i	−0.0773979	−	0.0649445i	0.603268	−	0.797539i	$-0.293865\pi$
$167$	−1.00020	−	0.839268i	−0.0773979	−	0.0649445i	−0.680666	+	0.732594i	$0.738309\pi$
$168$		0			0
$169$	−15.4330	−	5.61716i	−1.18716	−	0.432090i
$170$	3.16387	+	5.68295i	0.242658	+	0.435862i
$171$		0			0
$172$	9.66237	+	5.98810i	0.736749	+	0.456588i
$173$	7.36046	+	8.77186i	0.559606	+	0.666912i	0.969463	−	0.245238i	$-0.0788660\pi$
$173$	7.36046	+	8.77186i	0.559606	+	0.666912i	−0.409857	+	0.912150i	$0.634422\pi$
$174$		0			0
$175$	−19.8367	−	3.49775i	−1.49951	−	0.264405i
$176$	2.45435	−	10.1638i	0.185004	−	0.766127i
$177$		0			0
$178$	12.9578	+	15.9411i	0.971224	+	1.19483i
$179$	−10.7064	+	18.5441i	−0.800237	+	1.38605i	0.119222	+	0.992868i	$0.461960\pi$
$179$	−10.7064	+	18.5441i	−0.800237	+	1.38605i	−0.919460	+	0.393184i	$0.871373\pi$
$180$		0			0
$181$	7.31416	+	12.6685i	0.543657	+	0.941641i	0.998690	+	0.0511670i	$0.0162941\pi$
$181$	7.31416	+	12.6685i	0.543657	+	0.941641i	−0.455033	+	0.890474i	$0.650373\pi$
$182$	8.01529	−	20.9966i	0.594133	−	1.55637i
$183$		0			0
$184$	−1.76516	−	1.62781i	−0.130129	−	0.120003i
$185$	6.50290	+	17.8666i	0.478102	+	1.31358i
$186$		0			0
$187$	−3.43574	+	0.605813i	−0.251246	+	0.0443014i
$188$	−13.2095	−	0.412337i	−0.963403	−	0.0300728i
$189$		0			0
$190$	−0.444937	−	0.00694269i	−0.0322791	−	0.000503676i
$191$	−0.333749	−	1.89278i	−0.0241492	−	0.136957i	0.970349	−	0.241706i	$-0.0777071\pi$
$191$	−0.333749	−	1.89278i	−0.0241492	−	0.136957i	−0.994499	+	0.104749i	$0.966596\pi$
$192$		0			0
$193$	5.88386	−	2.14155i	0.423530	−	0.154152i	−0.121457	−	0.992597i	$-0.538757\pi$
$193$	5.88386	−	2.14155i	0.423530	−	0.154152i	0.544987	+	0.838444i	$0.316535\pi$
$194$	7.05561	+	6.11046i	0.506564	+	0.438706i
$195$		0			0
$196$	2.94043	+	1.17537i	0.210031	+	0.0839549i
$197$	−13.1022	+	7.56456i	−0.933494	+	0.538953i	−0.887915	−	0.460008i	$-0.847847\pi$
$197$	−13.1022	+	7.56456i	−0.933494	+	0.538953i	−0.0455788	+	0.998961i	$0.514513\pi$
$198$		0			0
$199$	22.4427	+	12.9573i	1.59092	+	0.918517i	0.993150	+	0.116849i	$0.0372792\pi$
$199$	22.4427	+	12.9573i	1.59092	+	0.918517i	0.597769	+	0.801669i	$0.296054\pi$
$200$	−15.4652	+	11.7891i	−1.09356	+	0.833614i
$201$		0			0
$202$	11.4504	+	2.20375i	0.805648	+	0.155055i
$203$	−0.254977	+	1.44605i	−0.0178959	+	0.101493i
$204$		0			0
$205$	7.53990	−	6.32672i	0.526609	−	0.441878i
$206$	19.5345	+	11.6884i	1.36104	+	0.814368i
$207$		0			0
$208$	−9.65561	−	19.4305i	−0.669496	−	1.34726i
$209$	0.0816338	−	0.224287i	0.00564673	−	0.0155143i
$210$		0			0
$211$	11.2158	−	13.3665i	0.772127	−	0.920186i	−0.226422	−	0.974029i	$-0.572703\pi$
$211$	11.2158	−	13.3665i	0.772127	−	0.920186i	0.998549	+	0.0538436i	$0.0171473\pi$
$212$	4.60833	+	14.0064i	0.316501	+	0.961960i
$213$		0			0
$214$	−2.17507	−	13.5702i	−0.148685	−	0.927642i
$215$	19.5864			1.33578
$216$		0			0
$217$	19.5224			1.32526
$218$	−1.05162	−	6.56108i	−0.0712250	−	0.444373i
$219$		0			0
$220$	−5.63061	−	17.1134i	−0.379615	−	1.15379i
$221$	−4.65349	+	5.54581i	−0.313028	+	0.373052i
$222$		0			0
$223$	−6.04555	+	16.6100i	−0.404840	+	1.11229i	0.555027	+	0.831832i	$0.312708\pi$
$223$	−6.04555	+	16.6100i	−0.404840	+	1.11229i	−0.959867	+	0.280456i	$0.909514\pi$
$224$	14.9548	−	7.14277i	0.999212	−	0.477247i
$225$		0			0
$226$	0.685010	+	0.409872i	0.0455662	+	0.0272643i
$227$	−7.14681	+	5.99689i	−0.474351	+	0.398027i	−0.848379	−	0.529390i	$-0.822421\pi$
$227$	−7.14681	+	5.99689i	−0.474351	+	0.398027i	0.374028	+	0.927417i	$0.377976\pi$
$228$		0			0
$229$	2.92027	−	16.5617i	0.192977	−	1.09442i	−0.722294	−	0.691586i	$-0.756912\pi$
$229$	2.92027	−	16.5617i	0.192977	−	1.09442i	0.915271	−	0.402839i	$-0.131977\pi$
$230$	−4.06269	−	0.781906i	−0.267886	−	0.0515574i
$231$		0			0
$232$	0.859396	+	1.12738i	0.0564221	+	0.0740161i
$233$	−15.2659	−	8.81379i	−1.00010	−	0.577410i	−0.0918250	−	0.995775i	$-0.529270\pi$
$233$	−15.2659	−	8.81379i	−1.00010	−	0.577410i	−0.908279	+	0.418365i	$0.862603\pi$
$234$		0			0
$235$	−19.7206	+	11.3857i	−1.28643	+	0.742722i
$236$	−5.65526	−	2.26056i	−0.368126	−	0.147150i
$237$		0			0
$238$	−4.18007	−	3.62012i	−0.270954	−	0.234658i
$239$	−8.65868	+	3.15150i	−0.560084	+	0.203854i	−0.606521	−	0.795067i	$-0.707435\pi$
$239$	−8.65868	+	3.15150i	−0.560084	+	0.203854i	0.0464374	+	0.998921i	$0.485213\pi$
$240$		0			0
$241$	1.08125	+	6.13209i	0.0696496	+	0.395003i	0.999625	+	0.0273809i	$0.00871671\pi$
$241$	1.08125	+	6.13209i	0.0696496	+	0.395003i	−0.929975	+	0.367622i	$0.880172\pi$
$242$	−5.89238	−	0.0919433i	−0.378776	−	0.00591034i
$243$		0			0
$244$	−4.84747	−	0.151315i	−0.310328	−	0.00968692i
$245$	5.37331	−	0.947460i	0.343288	−	0.0605310i
$246$		0			0
$247$	−0.169400	−	0.465422i	−0.0107787	−	0.0296141i
$248$	12.7771	−	13.8552i	0.811348	−	0.879807i
$249$		0			0
$250$	−3.25936	+	8.53812i	−0.206140	+	0.539998i
$251$	−14.1765	−	24.5545i	−0.894814	−	1.54986i	−0.834034	−	0.551713i	$-0.813974\pi$
$251$	−14.1765	−	24.5545i	−0.894814	−	1.54986i	−0.0607805	−	0.998151i	$-0.519359\pi$
$252$		0			0
$253$	1.10955	−	1.92181i	0.0697571	−	0.120823i
$254$	9.92057	+	12.2046i	0.622472	+	0.765787i
$255$		0			0
$256$	4.71843	−	15.2884i	0.294902	−	0.955528i
$257$	16.2474	+	2.86485i	1.01348	+	0.178705i	0.655638	−	0.755076i	$-0.272400\pi$
$257$	16.2474	+	2.86485i	1.01348	+	0.178705i	0.357847	+	0.933780i	$0.383511\pi$
$258$		0			0
$259$	−10.3903	−	12.3827i	−0.645622	−	0.769423i
$260$	−31.7775	−	19.6936i	−1.97076	−	1.22135i
$261$		0			0
$262$	2.13410	+	3.83326i	0.131845	+	0.236820i
$263$	22.7564	+	8.28265i	1.40322	+	0.510730i	0.929132	−	0.369748i	$-0.120556\pi$
$263$	22.7564	+	8.28265i	1.40322	+	0.510730i	0.474087	+	0.880478i	$0.342778\pi$
$264$		0			0
$265$	19.4621	+	16.3307i	1.19555	+	1.00318i
$266$	0.357478	−	0.123830i	0.0219184	−	0.00759251i
$267$		0			0
$268$	9.54404	−	1.37737i	0.582995	−	0.0841364i
$269$			12.1956i			0.743578i	0.928317	+	0.371789i	$0.121255\pi$
$269$			12.1956i			0.743578i	−0.928317	+	0.371789i	$0.878745\pi$
$270$		0			0
$271$		−	25.0009i		−	1.51870i	−0.650683	−	0.759349i	$-0.725517\pi$
$271$		−	25.0009i		−	1.51870i	0.650683	−	0.759349i	$-0.274483\pi$
$272$	−5.30504	+	0.597322i	−0.321665	+	0.0362179i
$273$		0			0
$274$	−7.99342	−	23.0757i	−0.482900	−	1.39406i
$275$	−13.7673	−	11.5521i	−0.830199	−	0.696620i
$276$		0			0
$277$	8.21089	+	2.98852i	0.493345	+	0.179563i	0.576698	−	0.816957i	$-0.304341\pi$
$277$	8.21089	+	2.98852i	0.493345	+	0.179563i	−0.0833536	+	0.996520i	$0.526563\pi$
$278$	−13.8267	+	7.69775i	−0.829270	+	0.461680i
$279$		0			0
$280$	15.4194	−	24.0349i	0.921485	−	1.43636i
$281$	−14.0693	−	16.7671i	−0.839303	−	1.00024i	−0.999913	−	0.0132243i	$-0.995790\pi$
$281$	−14.0693	−	16.7671i	−0.839303	−	1.00024i	0.160610	−	0.987018i	$-0.448654\pi$
$282$		0			0
$283$	−29.6450	−	5.22722i	−1.76221	−	0.310726i	−0.803543	−	0.595246i	$-0.797055\pi$
$283$	−29.6450	−	5.22722i	−1.76221	−	0.310726i	−0.958670	+	0.284520i	$0.908166\pi$
$284$	−4.83709	+	23.1783i	−0.287028	+	1.37538i
$285$		0			0
$286$	15.5603	−	12.6482i	0.920097	−	0.747904i
$287$	−4.18396	+	7.24682i	−0.246971	+	0.427766i
$288$		0			0
$289$	−7.60937	−	13.1798i	−0.447610	−	0.775283i
$290$	2.28192	+	0.871105i	0.133999	+	0.0511530i
$291$		0			0
$292$	17.3893	+	15.5412i	1.01763	+	0.909479i
$293$	−4.52797	−	12.4405i	−0.264527	−	0.726782i	−0.998848	−	0.0479801i	$-0.984722\pi$
$293$	−4.52797	−	12.4405i	−0.264527	−	0.726782i	0.734321	−	0.678802i	$-0.237501\pi$
$294$		0			0
$295$	−10.3344	+	1.82223i	−0.601690	+	0.106094i
$296$	−15.5884	−	0.730189i	−0.906059	−	0.0424413i
$297$		0			0
$298$	0.402716	−	25.8089i	0.0233287	−	1.49507i
$299$	−0.799635	−	4.53496i	−0.0462441	−	0.262263i
$300$		0			0
$301$	−15.6475	+	5.69524i	−0.901910	+	0.328268i
$302$	−17.8218	+	20.5784i	−1.02553	+	1.18416i
$303$		0			0
$304$	0.146081	−	0.334751i	0.00837831	−	0.0191993i
$305$	−7.23685	+	4.17820i	−0.414381	+	0.239243i
$306$		0			0
$307$	11.4064	+	6.58546i	0.650995	+	0.375852i	0.788837	−	0.614602i	$-0.210683\pi$
$307$	11.4064	+	6.58546i	0.650995	+	0.375852i	−0.137842	+	0.990454i	$0.544017\pi$
$308$	9.47444	+	12.0346i	0.539856	+	0.685738i
$309$		0			0
$310$	6.13741	−	31.8892i	0.348581	−	1.81119i
$311$	1.07244	−	6.08211i	0.0608125	−	0.344885i	−0.939186	−	0.343408i	$-0.888419\pi$
$311$	1.07244	−	6.08211i	0.0608125	−	0.344885i	0.999999	−	0.00147712i	$-0.000470181\pi$
$312$		0			0
$313$	−16.4217	+	13.7794i	−0.928207	+	0.778858i	−0.975495	−	0.220023i	$-0.929387\pi$
$313$	−16.4217	+	13.7794i	−0.928207	+	0.778858i	0.0472879	+	0.998881i	$0.484942\pi$
$314$	12.2281	−	20.4365i	0.690070	−	1.15330i
$315$		0			0
$316$	−2.97319	+	1.59502i	−0.167255	+	0.0897269i
$317$	5.02856	−	13.8159i	0.282432	−	0.775976i	−0.714639	−	0.699494i	$-0.753409\pi$
$317$	5.02856	−	13.8159i	0.282432	−	0.775976i	0.997071	−	0.0764825i	$-0.0243689\pi$
$318$		0			0
$319$	−0.842123	+	1.00360i	−0.0471499	+	0.0561910i
$320$	−6.96603	−	26.6738i	−0.389413	−	1.49111i
$321$		0			0
$322$	3.47303	−	0.556666i	0.193545	−	0.0310218i
$323$	−0.121865			−0.00678074
$324$		0			0
$325$	−37.2939			−2.06869
$326$	11.2075	−	1.79637i	0.620727	−	0.0994915i
$327$		0			0
$328$	2.40480	+	7.71234i	0.132783	+	0.425843i
$329$	12.4441	−	14.8303i	0.686066	−	0.817621i
$330$		0			0
$331$	9.07166	−	24.9242i	0.498624	−	1.36996i	−0.393982	−	0.919118i	$-0.628903\pi$
$331$	9.07166	−	24.9242i	0.498624	−	1.36996i	0.892605	−	0.450839i	$-0.148875\pi$
$332$	−2.04188	−	3.80616i	−0.112063	−	0.208890i
$333$		0			0
$334$	0.948085	−	1.58451i	0.0518769	−	0.0867007i
$335$	12.7278	−	10.6799i	0.695395	−	0.583506i
$336$		0			0
$337$	−2.67934	+	15.1953i	−0.145953	+	0.827740i	0.820644	+	0.571439i	$0.193615\pi$
$337$	−2.67934	+	15.1953i	−0.145953	+	0.827740i	−0.966597	+	0.256300i	$0.917496\pi$
$338$	4.38959	−	22.8077i	0.238762	−	1.24058i
$339$		0			0
$340$	−7.22749	+	5.68994i	−0.391966	+	0.308580i
$341$	15.0848	+	8.70922i	0.816888	+	0.471631i
$342$		0			0
$343$	13.7433	−	7.93471i	0.742069	−	0.428434i
$344$	−6.19913	+	14.8327i	−0.334235	+	0.799724i
$345$		0			0
$346$	−10.6015	+	12.2414i	−0.569943	+	0.658100i
$347$	−20.2264	+	7.36182i	−1.08581	+	0.395203i	−0.822068	−	0.569390i	$-0.807180\pi$
$347$	−20.2264	+	7.36182i	−1.08581	+	0.395203i	−0.263744	+	0.964593i	$0.584957\pi$
$348$		0			0
$349$	2.19509	+	12.4490i	0.117501	+	0.666379i	0.985482	+	0.169782i	$0.0543063\pi$
$349$	2.19509	+	12.4490i	0.117501	+	0.666379i	−0.867981	+	0.496597i	$0.834583\pi$
$350$	0.444436	−	28.4826i	0.0237561	−	1.52246i
$351$		0			0
$352$	14.7420	+	1.15240i	0.785751	+	0.0614231i
$353$	11.0190	−	1.94295i	0.586484	−	0.103413i	0.127471	−	0.991842i	$-0.459314\pi$
$353$	11.0190	−	1.94295i	0.586484	−	0.103413i	0.459013	+	0.888429i	$0.348203\pi$
$354$		0			0
$355$	13.9534	+	38.3368i	0.740572	+	2.03470i
$356$	−19.3598	+	21.6620i	−1.02607	+	1.14808i
$357$		0			0
$358$	−28.2911	−	10.7999i	−1.49523	−	0.570793i
$359$	16.1699	+	28.0070i	0.853413	+	1.47816i	0.878109	+	0.478460i	$0.158805\pi$
$359$	16.1699	+	28.0070i	0.853413	+	1.47816i	−0.0246959	+	0.999695i	$0.507862\pi$
$360$		0			0
$361$	−9.49583	+	16.4473i	−0.499781	+	0.865645i
$362$	−16.0531	+	13.0488i	−0.843734	+	0.685832i
$363$		0			0
$364$	31.1134	+	6.49308i	1.63079	+	0.340330i
$365$	39.5739	+	6.97795i	2.07139	+	0.365242i
$366$		0			0
$367$	−0.428395	−	0.510541i	−0.0223620	−	0.0266500i	0.754748	−	0.656015i	$-0.227759\pi$
$367$	−0.428395	−	0.510541i	−0.0223620	−	0.0266500i	−0.777110	+	0.629365i	$0.783315\pi$
$368$	1.87798	−	2.82918i	0.0978965	−	0.147481i
$369$		0			0
$370$	−23.4932	+	13.0794i	−1.22136	+	0.679966i
$371$	−20.2968	−	7.38744i	−1.05376	−	0.383537i
$372$		0			0
$373$	15.9574	+	13.3899i	0.826243	+	0.693300i	0.954425	−	0.298450i	$-0.0964697\pi$
$373$	15.9574	+	13.3899i	0.826243	+	0.693300i	−0.128182	+	0.991751i	$0.540914\pi$
$374$	−1.61493	−	4.66204i	−0.0835058	−	0.241068i
$375$		0			0
$376$	−2.38073	−	18.5379i	−0.122777	−	0.956021i
$377$			2.71864i			0.140017i
$378$		0			0
$379$			19.1904i			0.985744i	0.870102	+	0.492872i	$0.164053\pi$
$379$			19.1904i			0.985744i	−0.870102	+	0.492872i	$0.835947\pi$
$380$	−0.0898895	−	0.622859i	−0.00461123	−	0.0319520i
$381$		0			0
$382$	2.56837	−	0.889680i	0.131409	−	0.0455200i
$383$	6.07655	+	5.09883i	0.310497	+	0.260538i	0.784697	−	0.619879i	$-0.212818\pi$
$383$	6.07655	+	5.09883i	0.310497	+	0.260538i	−0.474200	+	0.880417i	$0.657263\pi$
$384$		0			0
$385$	24.7993	+	9.02621i	1.26389	+	0.460018i
$386$	4.30735	+	7.73685i	0.219238	+	0.393795i
$387$		0			0
$388$	−6.95343	+	11.2200i	−0.353007	+	0.569610i
$389$	−7.93591	−	9.45764i	−0.402366	−	0.479522i	0.526374	−	0.850253i	$-0.323551\pi$
$389$	−7.93591	−	9.45764i	−0.402366	−	0.479522i	−0.928740	+	0.370732i	$0.879107\pi$
$390$		0			0
$391$	−1.11581	−	0.196747i	−0.0564289	−	0.00994994i
$392$	−0.983156	+	4.36905i	−0.0496569	+	0.220671i
$393$		0			0
$394$	−13.4956	−	16.6027i	−0.679897	−	0.836433i
$395$	−2.90676	+	5.03465i	−0.146255	+	0.253321i
$396$		0			0
$397$	11.5959	+	20.0847i	0.581982	+	1.00802i	0.995244	+	0.0974099i	$0.0310558\pi$
$397$	11.5959	+	20.0847i	0.581982	+	1.00802i	−0.413263	+	0.910612i	$0.635611\pi$
$398$	−13.0704	+	34.2388i	−0.655159	+	1.71623i
$399$		0			0
$400$	−19.9235	−	18.9569i	−0.996177	−	0.947845i
$401$	−2.32432	−	6.38601i	−0.116071	−	0.318902i	0.868030	−	0.496511i	$-0.165386\pi$
$401$	−2.32432	−	6.38601i	−0.116071	−	0.318902i	−0.984101	+	0.177609i	$0.943164\pi$
$402$		0			0
$403$	35.5962	−	6.27657i	1.77317	−	0.312658i
$404$	−0.514503	+	16.4825i	−0.0255975	+	0.820034i
$405$		0			0
$406$	−2.07632	−	0.0323984i	−0.103046	−	0.00160790i
$407$	−2.50442	−	14.2033i	−0.124140	−	0.704031i
$408$		0			0
$409$	−17.0717	+	6.21358i	−0.844140	+	0.307242i	−0.727649	−	0.685950i	$-0.759387\pi$
$409$	−17.0717	+	6.21358i	−0.844140	+	0.307242i	−0.116491	+	0.993192i	$0.537165\pi$
$410$	10.5221	+	9.11261i	0.519651	+	0.450040i
$411$		0			0
$412$	−11.9494	+	29.8939i	−0.588704	+	1.47277i
$413$	7.72625	−	4.46075i	0.380184	−	0.219499i
$414$		0			0
$415$	−6.44516	−	3.72111i	−0.316380	−	0.182662i
$416$	24.9715	−	17.8319i	1.22433	−	0.874280i
$417$		0			0
$418$	0.331463	+	0.0637935i	0.0162124	+	0.00312024i
$419$	−0.854595	+	4.84665i	−0.0417497	+	0.236774i	−0.998541	−	0.0540017i	$-0.982802\pi$
$419$	−0.854595	+	4.84665i	−0.0417497	+	0.236774i	0.956791	+	0.290776i	$0.0939135\pi$
$420$		0			0
$421$	−9.01524	+	7.56468i	−0.439376	+	0.368680i	−0.835476	−	0.549527i	$-0.814808\pi$
$421$	−9.01524	+	7.56468i	−0.439376	+	0.368680i	0.396100	+	0.918207i	$0.370363\pi$
$422$	21.1751	+	12.6700i	1.03079	+	0.616766i
$423$		0			0
$424$	−18.5269	+	9.56988i	−0.899747	+	0.464754i
$425$	−3.13838	+	8.62264i	−0.152234	+	0.418259i
$426$		0			0
$427$	4.56659	−	5.44225i	0.220993	−	0.263369i
$428$	18.4625	−	6.07449i	0.892420	−	0.293621i
$429$		0			0
$430$	4.38376	+	27.3503i	0.211404	+	1.31895i
$431$	−4.40894			−0.212371			−0.106186	−	0.994346i	$-0.533864\pi$
$431$	−4.40894			−0.212371			−0.106186	+	0.994346i	$0.533864\pi$
$432$		0			0
$433$	28.5232			1.37074			0.685369	−	0.728196i	$-0.259641\pi$
$433$	28.5232			1.37074			0.685369	+	0.728196i	$0.259641\pi$
$434$	4.36943	+	27.2608i	0.209739	+	1.30856i
$435$		0			0
$436$	8.92646	−	2.93696i	0.427500	−	0.140655i
$437$	0.0498260	−	0.0593804i	0.00238350	−	0.00284055i
$438$		0			0
$439$	−1.65430	+	4.54515i	−0.0789555	+	0.216928i	−0.972890	−	0.231270i	$-0.925712\pi$
$439$	−1.65430	+	4.54515i	−0.0789555	+	0.216928i	0.893934	+	0.448198i	$0.147934\pi$
$440$	22.6368	−	11.6928i	1.07917	−	0.557432i
$441$		0			0
$442$	−8.78565	−	5.25684i	−0.417891	−	0.250042i
$443$	5.56660	−	4.67093i	0.264477	−	0.221923i	−0.500899	−	0.865506i	$-0.666997\pi$
$443$	5.56660	−	4.67093i	0.264477	−	0.221923i	0.765376	+	0.643583i	$0.222553\pi$
$444$		0			0
$445$	−8.69249	+	49.2976i	−0.412064	+	2.33693i
$446$	−24.5472	−	4.72435i	−1.16234	−	0.223705i
$447$		0			0
$448$	13.3212	+	19.2841i	0.629369	+	0.911089i
$449$	5.50442	+	3.17798i	0.259769	+	0.149978i	0.624229	−	0.781241i	$-0.285413\pi$
$449$	5.50442	+	3.17798i	0.259769	+	0.149978i	−0.364460	+	0.931219i	$0.618746\pi$
$450$		0			0
$451$	−6.46583	+	3.73305i	−0.304464	+	0.175782i
$452$	−0.419025	+	1.04828i	−0.0197093	+	0.0493068i
$453$		0			0
$454$	−9.97357	−	8.63754i	−0.468083	−	0.405380i
$455$	51.4615	−	18.7305i	2.41255	−	0.878097i
$456$		0			0
$457$	−0.155269	−	0.880575i	−0.00726318	−	0.0411916i	0.980961	−	0.194206i	$-0.0622130\pi$
$457$	−0.155269	−	0.880575i	−0.00726318	−	0.0411916i	−0.988224	+	0.153014i	$0.951102\pi$
$458$	23.7801	+	0.371060i	1.11117	+	0.0173385i
$459$		0			0
$460$	0.182549	−	5.84810i	0.00851140	−	0.272669i
$461$	−12.9026	+	2.27507i	−0.600934	+	0.105961i	−0.465835	−	0.884871i	$-0.654246\pi$
$461$	−12.9026	+	2.27507i	−0.600934	+	0.105961i	−0.135098	+	0.990832i	$0.543135\pi$
$462$		0			0
$463$	−0.461244	−	1.26726i	−0.0214358	−	0.0588945i	0.928513	−	0.371299i	$-0.121088\pi$
$463$	−0.461244	−	1.26726i	−0.0214358	−	0.0588945i	−0.949949	+	0.312405i	$0.898865\pi$
$464$	−1.38191	+	1.45238i	−0.0641537	+	0.0674250i
$465$		0			0
$466$	8.89072	−	23.2899i	0.411855	−	1.07888i
$467$	9.81172	+	16.9944i	0.454032	+	0.786407i	0.998632	−	0.0522890i	$-0.0166517\pi$
$467$	9.81172	+	16.9944i	0.454032	+	0.786407i	−0.544600	+	0.838696i	$0.683318\pi$
$468$		0			0
$469$	−7.06278	+	12.2331i	−0.326129	+	0.564872i
$470$	−20.3127	−	24.9894i	−0.936955	−	1.15267i
$471$		0			0
$472$	1.89088	−	8.40290i	0.0870349	−	0.386775i
$473$	−14.6315	−	2.57993i	−0.672756	−	0.118625i
$474$		0			0
$475$	−0.403527	−	0.480904i	−0.0185151	−	0.0220654i
$476$	4.11953	−	6.64726i	0.188819	−	0.304677i
$477$		0			0
$478$	−6.33869	−	11.3855i	−0.289925	−	0.520763i
$479$	17.9117	+	6.51932i	0.818405	+	0.297875i	0.717091	−	0.696979i	$-0.245473\pi$
$479$	17.9117	+	6.51932i	0.818405	+	0.297875i	0.101314	+	0.994854i	$0.467695\pi$
$480$		0			0
$481$	−22.9263	−	19.2375i	−1.04535	−	0.877153i
$482$	−8.32079	+	2.88231i	−0.379001	+	0.131286i
$483$		0			0
$484$	−1.19042	−	8.24864i	−0.0541101	−	0.374938i
$485$			22.7439i			1.03275i
$486$		0			0
$487$			12.7440i			0.577486i	0.957407	+	0.288743i	$0.0932373\pi$
$487$			12.7440i			0.577486i	−0.957407	+	0.288743i	$0.906763\pi$
$488$	−0.873651	−	6.80283i	−0.0395483	−	0.307950i
$489$		0			0
$490$	2.52566	+	7.29119i	0.114098	+	0.329382i
$491$	18.9461	+	15.8977i	0.855027	+	0.717453i	0.960891	−	0.276928i	$-0.0893162\pi$
$491$	18.9461	+	15.8977i	0.855027	+	0.717453i	−0.105864	+	0.994381i	$0.533761\pi$
$492$		0			0
$493$	0.628570	+	0.228781i	0.0283094	+	0.0103038i
$494$	0.611997	−	0.340718i	0.0275350	−	0.0153296i
$495$		0			0
$496$	22.2070	+	14.7408i	0.997125	+	0.661882i
$497$	−22.2948	−	26.5699i	−1.00006	−	1.19182i
$498$		0			0
$499$	38.9086	+	6.86064i	1.74179	+	0.307124i	0.951964	−	0.306209i	$-0.0990608\pi$
$499$	38.9086	+	6.86064i	1.74179	+	0.307124i	0.789824	+	0.613334i	$0.210172\pi$
$500$	−12.6520	−	2.64037i	−0.565817	−	0.118081i
$501$		0			0
$502$	31.1147	−	25.2917i	1.38872	−	1.12882i
$503$	18.2058	−	31.5334i	0.811757	−	1.40600i	−0.0998757	−	0.995000i	$-0.531845\pi$
$503$	18.2058	−	31.5334i	0.811757	−	1.40600i	0.911633	−	0.411005i	$-0.134822\pi$
$504$		0			0
$505$	14.2068	+	24.6069i	0.632194	+	1.09499i
$506$	2.93193	+	1.11924i	0.130340	+	0.0497563i
$507$		0			0
$508$	−14.8220	+	16.5846i	−0.657622	+	0.735822i
$509$	1.23919	+	3.40464i	0.0549260	+	0.150908i	0.964121	−	0.265462i	$-0.0855244\pi$
$509$	1.23919	+	3.40464i	0.0549260	+	0.150908i	−0.909195	+	0.416370i	$0.863302\pi$
$510$		0			0
$511$	−33.6445	+	5.93244i	−1.48835	+	0.262436i
$512$	22.4047	+	3.16697i	0.990157	+	0.139961i
$513$		0			0
$514$	−0.364019	+	23.3289i	−0.0160562	+	1.02899i
$515$	9.63236	+	54.6278i	0.424452	+	2.40719i
$516$		0			0
$517$	16.2315	−	5.90778i	0.713860	−	0.259824i
$518$	14.9655	−	17.2804i	0.657548	−	0.759256i
$519$		0			0
$520$	20.3876	−	48.7816i	0.894057	−	2.13921i
$521$	−18.0443	+	10.4179i	−0.790534	+	0.456415i	−0.840151	−	0.542353i	$-0.817534\pi$
$521$	−18.0443	+	10.4179i	−0.790534	+	0.456415i	0.0496162	+	0.998768i	$0.484200\pi$
$522$		0			0
$523$	−19.0780	−	11.0147i	−0.834223	−	0.481639i	0.0210733	−	0.999778i	$-0.493292\pi$
$523$	−19.0780	−	11.0147i	−0.834223	−	0.481639i	−0.855296	+	0.518139i	$0.826625\pi$
$524$	−4.87509	+	3.83798i	−0.212969	+	0.167663i
$525$		0			0
$526$	−6.47255	+	33.6306i	−0.282217	+	1.46636i
$527$	1.54433	−	8.75831i	0.0672719	−	0.381518i
$528$		0			0
$529$	−17.0669	+	14.3209i	−0.742041	+	0.622646i
$530$	−18.4480	+	30.8318i	−0.801331	+	1.33925i
$531$		0			0
$532$	0.252925	+	0.471464i	0.0109657	+	0.0204405i
$533$	−5.29893	+	14.5587i	−0.229522	+	0.630607i
$534$		0			0
$535$	21.5263	−	25.6541i	0.930664	−	1.10912i
$536$	4.05946	+	13.0189i	0.175342	+	0.562332i
$537$		0			0
$538$	−17.0298	+	2.72957i	−0.734207	+	0.117680i
$539$	−4.13879			−0.178270
$540$		0			0
$541$	−13.2610			−0.570135			−0.285067	−	0.958507i	$-0.592016\pi$
$541$	−13.2610			−0.570135			−0.285067	+	0.958507i	$0.592016\pi$
$542$	34.9111	−	5.59562i	1.49956	−	0.240353i
$543$		0			0
$544$	−2.02145	−	7.27421i	−0.0866689	−	0.311879i
$545$	10.4078	−	12.4035i	0.445820	−	0.531308i
$546$		0			0
$547$	4.89178	−	13.4401i	0.209157	−	0.574655i	−0.790108	−	0.612967i	$-0.789976\pi$
$547$	4.89178	−	13.4401i	0.209157	−	0.574655i	0.999266	+	0.0383119i	$0.0121980\pi$
$548$	30.4337	−	16.3267i	1.30006	−	0.697440i
$549$		0			0
$550$	13.0499	−	21.8101i	0.556451	−	0.929985i
$551$	−0.0350568	+	0.0294161i	−0.00149347	+	0.00125317i
$552$		0			0
$553$	0.858252	−	4.86739i	0.0364966	−	0.206982i
$554$	−2.33541	+	12.1345i	−0.0992219	+	0.515545i
$555$		0			0
$556$	−13.8437	−	17.5846i	−0.587104	−	0.745752i
$557$	−6.40425	−	3.69750i	−0.271357	−	0.156668i	0.358147	−	0.933665i	$-0.383409\pi$
$557$	−6.40425	−	3.69750i	−0.271357	−	0.156668i	−0.629504	+	0.776997i	$0.716742\pi$
$558$		0			0
$559$	−26.6999	+	15.4152i	−1.12929	+	0.651994i
$560$	37.0132	+	16.1521i	1.56409	+	0.682550i
$561$		0			0
$562$	20.2645	−	23.3990i	0.854806	−	0.987026i
$563$	−19.9054	+	7.24497i	−0.838912	+	0.305339i	−0.725511	−	0.688210i	$-0.758397\pi$
$563$	−19.9054	+	7.24497i	−0.838912	+	0.305339i	−0.113401	+	0.993549i	$0.536174\pi$
$564$		0			0
$565$	0.337774	+	1.91561i	0.0142103	+	0.0805905i
$566$	0.664189	−	42.5660i	0.0279180	−	1.78918i
$567$		0			0
$568$	−33.4485	−	1.56679i	−1.40347	−	0.0657409i
$569$	−4.38899	+	0.773898i	−0.183996	+	0.0324435i	−0.264887	−	0.964279i	$-0.585335\pi$
$569$	−4.38899	+	0.773898i	−0.183996	+	0.0324435i	0.0808907	+	0.996723i	$0.474224\pi$
$570$		0			0
$571$	0.735560	+	2.02093i	0.0307822	+	0.0845734i	0.954132	−	0.299387i	$-0.0967821\pi$
$571$	0.735560	+	2.02093i	0.0307822	+	0.0845734i	−0.923350	+	0.383960i	$0.874560\pi$
$572$	21.1445	+	18.8973i	0.884095	+	0.790137i
$573$		0			0
$574$	−11.0558	−	4.22048i	−0.461462	−	0.176159i
$575$	−2.91833	−	5.05470i	−0.121703	−	0.210796i
$576$		0			0
$577$	−16.0706	+	27.8351i	−0.669028	+	1.15879i	0.309148	+	0.951014i	$0.399956\pi$
$577$	−16.0706	+	27.8351i	−0.669028	+	1.15879i	−0.978176	+	0.207777i	$0.933377\pi$
$578$	16.7011	−	13.5755i	0.694673	−	0.564667i
$579$		0			0
$580$	−0.705671	+	3.38142i	−0.0293014	+	0.140406i
$581$	6.23104	+	1.09870i	0.258507	+	0.0455817i
$582$		0			0
$583$	−12.3876	−	14.7629i	−0.513041	−	0.611418i
$584$	−17.8096	+	27.7606i	−0.736965	+	1.14874i
$585$		0			0
$586$	16.3584	−	9.10721i	0.675758	−	0.376215i
$587$	33.8753	+	12.3296i	1.39818	+	0.508897i	0.927639	−	0.373478i	$-0.121835\pi$
$587$	33.8753	+	12.3296i	1.39818	+	0.508897i	0.470545	+	0.882376i	$0.344057\pi$
$588$		0			0
$589$	0.466094	+	0.391099i	0.0192051	+	0.0161150i
$590$	−4.85754	−	14.0230i	−0.199982	−	0.577316i
$591$		0			0
$592$	−2.46932	−	21.9310i	−0.101488	−	0.901357i
$593$			4.09387i			0.168115i	0.996461	+	0.0840576i	$0.0267880\pi$
$593$			4.09387i			0.168115i	−0.996461	+	0.0840576i	$0.973212\pi$
$594$		0			0
$595$		−	13.4745i		−	0.552402i
$596$	36.1294	−	5.21410i	1.47992	−	0.213578i
$597$		0			0
$598$	6.15360	−	2.13160i	0.251639	−	0.0871676i
$599$	6.47708	+	5.43491i	0.264646	+	0.222065i	0.765449	−	0.643497i	$-0.222517\pi$
$599$	6.47708	+	5.43491i	0.264646	+	0.222065i	−0.500802	+	0.865562i	$0.666962\pi$
$600$		0			0
$601$	−27.4438	−	9.98874i	−1.11946	−	0.407449i	−0.285003	−	0.958527i	$-0.591995\pi$
$601$	−27.4438	−	9.98874i	−1.11946	−	0.407449i	−0.834454	+	0.551078i	$0.814217\pi$
$602$	−11.4550	−	20.5754i	−0.466869	−	0.838590i
$603$		0			0
$604$	−32.7244	−	20.2804i	−1.33154	−	0.825198i
$605$	−9.23034	−	11.0003i	−0.375267	−	0.447225i
$606$		0			0
$607$	−38.2139	−	6.73814i	−1.55105	−	0.273493i	−0.668503	−	0.743710i	$-0.733064\pi$
$607$	−38.2139	−	6.73814i	−1.55105	−	0.273493i	−0.882551	+	0.470217i	$0.844176\pi$
$608$	0.500138	+	0.129063i	0.0202833	+	0.00523420i
$609$		0			0
$610$	−7.45412	−	9.17032i	−0.301808	−	0.371295i
$611$	17.9220	−	31.0417i	0.725045	−	1.25581i
$612$		0			0
$613$	−0.677216	−	1.17297i	−0.0273525	−	0.0473759i	0.852025	−	0.523501i	$-0.175374\pi$
$613$	−0.677216	−	1.17297i	−0.0273525	−	0.0473759i	−0.879378	+	0.476125i	$0.842041\pi$
$614$	−6.64294	+	17.4017i	−0.268087	+	0.702274i
$615$		0			0
$616$	−14.6845	+	15.9236i	−0.591656	+	0.641579i
$617$	7.59537	+	20.8681i	0.305778	+	0.840118i	0.993468	+	0.114114i	$0.0364028\pi$
$617$	7.59537	+	20.8681i	0.305778	+	0.840118i	−0.687690	+	0.726005i	$0.741375\pi$
$618$		0			0
$619$	2.18009	−	0.384409i	0.0876253	−	0.0154507i	−0.129664	−	0.991558i	$-0.541390\pi$
$619$	2.18009	−	0.384409i	0.0876253	−	0.0154507i	0.217289	+	0.976107i	$0.430279\pi$
$620$	45.9034	+	1.43288i	1.84353	+	0.0575459i
$621$		0			0
$622$	8.73303	+	0.136268i	0.350163	+	0.00546386i
$623$	−7.39009	−	41.9113i	−0.296078	−	1.67914i
$624$		0			0
$625$	11.3768	−	4.14082i	0.455072	−	0.165633i
$626$	−22.9169	−	19.8470i	−0.915942	−	0.793245i
$627$		0			0
$628$	31.2742	+	12.5011i	1.24798	+	0.498850i
$629$	−6.37717	+	3.68186i	−0.254274	+	0.146805i
$630$		0			0
$631$	−10.3534	−	5.97752i	−0.412161	−	0.237961i	0.279557	−	0.960129i	$-0.409813\pi$
$631$	−10.3534	−	5.97752i	−0.412161	−	0.237961i	−0.691718	+	0.722168i	$0.743146\pi$
$632$	−2.89272	−	3.79475i	−0.115066	−	0.150947i
$633$		0			0
$634$	20.4178	+	3.92962i	0.810895	+	0.156065i
$635$	−6.65505	+	37.7427i	−0.264098	+	1.49777i
$636$		0			0
$637$	−6.57915	+	5.52056i	−0.260675	+	0.218733i
$638$	−1.58990	−	0.951310i	−0.0629449	−	0.0376627i
$639$		0			0
$640$	35.6879	−	15.6973i	1.41069	−	0.620492i
$641$	−4.61107	+	12.6688i	−0.182126	+	0.500388i	−0.996836	−	0.0794805i	$-0.974674\pi$
$641$	−4.61107	+	12.6688i	−0.182126	+	0.500388i	0.814710	+	0.579868i	$0.196896\pi$
$642$		0			0
$643$	−17.7513	+	21.1552i	−0.700044	+	0.834280i	−0.992531	−	0.121989i	$-0.961073\pi$
$643$	−17.7513	+	21.1552i	−0.700044	+	0.834280i	0.292487	+	0.956269i	$0.405517\pi$
$644$	1.55465	+	4.72512i	0.0612616	+	0.186196i
$645$		0			0
$646$	−0.0272754	−	0.170171i	−0.00107313	−	0.00669528i
$647$	15.2634			0.600064			0.300032	−	0.953929i	$-0.403003\pi$
$647$	15.2634			0.600064			0.300032	+	0.953929i	$0.403003\pi$
$648$		0			0
$649$	7.96003			0.312458
$650$	−8.34698	−	52.0768i	−0.327396	−	2.04262i
$651$		0			0
$652$	5.01685	+	15.2480i	0.196475	+	0.597158i
$653$	−19.6661	+	23.4372i	−0.769595	+	0.917167i	−0.998414	−	0.0563018i	$-0.982069\pi$
$653$	−19.6661	+	23.4372i	−0.769595	+	0.917167i	0.228819	+	0.973469i	$0.426514\pi$
$654$		0			0
$655$	−3.65641	+	10.0459i	−0.142868	+	0.392526i
$656$	−10.2312	+	5.08419i	−0.399461	+	0.198504i
$657$		0			0
$658$	23.4941	+	14.0576i	0.915895	+	0.548021i
$659$	−32.0036	+	26.8542i	−1.24668	+	1.04609i	−0.249714	+	0.968320i	$0.580337\pi$
$659$	−32.0036	+	26.8542i	−1.24668	+	1.04609i	−0.996971	+	0.0777732i	$0.975219\pi$
$660$		0			0
$661$	5.68117	−	32.2195i	0.220972	−	1.25319i	−0.649265	−	0.760562i	$-0.724924\pi$
$661$	5.68117	−	32.2195i	0.220972	−	1.25319i	0.870237	−	0.492633i	$-0.163965\pi$
$662$	36.8343	+	7.08914i	1.43160	+	0.275527i
$663$		0			0
$664$	4.85788	−	3.70315i	0.188522	−	0.143710i
$665$	0.798352	+	0.460929i	0.0309588	+	0.0178741i
$666$		0			0
$667$	−0.368476	+	0.212740i	−0.0142674	+	0.00823731i
$668$	2.42480	+	0.969256i	0.0938182	+	0.0375016i
$669$		0			0
$670$	17.7620	+	15.3827i	0.686207	+	0.594284i
$671$	5.95644	−	2.16797i	0.229946	−	0.0836935i
$672$		0			0
$673$	4.92417	+	27.9264i	0.189813	+	1.07648i	0.919614	+	0.392823i	$0.128501\pi$
$673$	4.92417	+	27.9264i	0.189813	+	1.07648i	−0.729801	+	0.683659i	$0.760387\pi$
$674$	−21.8182	−	0.340446i	−0.840407	−	0.0131135i
$675$		0			0
$676$	32.8310	+	1.02482i	1.26273	+	0.0394163i
$677$	39.6598	−	6.99309i	1.52425	−	0.268766i	0.652148	−	0.758092i	$-0.273868\pi$
$677$	39.6598	−	6.99309i	1.52425	−	0.268766i	0.872101	+	0.489326i	$0.162757\pi$
$678$		0			0
$679$	−6.61336	−	18.1700i	−0.253797	−	0.697302i
$680$	−9.56301	−	8.81889i	−0.366725	−	0.338189i
$681$		0			0
$682$	−8.78524	+	23.0135i	−0.336404	+	0.881234i
$683$	2.35647	+	4.08153i	0.0901678	+	0.156175i	0.907582	−	0.419876i	$-0.137926\pi$
$683$	2.35647	+	4.08153i	0.0901678	+	0.156175i	−0.817414	+	0.576051i	$0.804593\pi$
$684$		0			0
$685$	29.7536	−	51.5348i	1.13683	−	1.96904i
$686$	14.1559	+	17.4151i	0.540476	+	0.664912i
$687$		0			0
$688$	−22.0997	−	5.33661i	−0.842542	−	0.203456i
$689$	−39.3834	−	6.94435i	−1.50039	−	0.264559i
$690$		0			0
$691$	31.2420	+	37.2328i	1.18850	+	1.41640i	0.886270	+	0.463169i	$0.153288\pi$
$691$	31.2420	+	37.2328i	1.18850	+	1.41640i	0.302234	+	0.953234i	$0.402268\pi$
$692$	−19.4665	−	12.0641i	−0.740006	−	0.458607i
$693$		0			0
$694$	−14.8070	−	26.5963i	−0.562065	−	1.00958i
$695$	−36.2358	−	13.1888i	−1.37450	−	0.500278i
$696$		0			0
$697$	2.92017	+	2.45031i	0.110609	+	0.0928121i
$698$	−16.8923	+	5.85150i	−0.639385	+	0.221482i
$699$		0			0
$700$	39.8723	−	5.75428i	1.50703	−	0.217491i
$701$		−	5.10945i		−	0.192981i	−0.995334	−	0.0964906i	$-0.969238\pi$
$701$		−	5.10945i		−	0.192981i	0.995334	−	0.0964906i	$-0.0307618\pi$
$702$		0			0
$703$		−	0.503788i		−	0.0190007i
$704$	1.69030	+	20.8435i	0.0637057	+	0.785569i
$705$		0			0
$706$	5.17937	+	14.9520i	0.194928	+	0.562727i
$707$	−18.5049	−	15.5274i	−0.695947	−	0.583969i
$708$		0			0
$709$	8.59158	+	3.12708i	0.322663	+	0.117440i	0.498273	−	0.867020i	$-0.333968\pi$
$709$	8.59158	+	3.12708i	0.322663	+	0.117440i	−0.175610	+	0.984460i	$0.556190\pi$
$710$	−50.4101	+	28.0649i	−1.89186	+	1.05326i
$711$		0			0
$712$	−34.5816	−	22.1855i	−1.29600	−	0.831438i
$713$	3.63619	+	4.33345i	0.136176	+	0.162289i
$714$		0			0
$715$	48.1199	+	8.48484i	1.79958	+	0.317315i
$716$	8.74886	−	41.9226i	0.326960	−	1.56672i
$717$		0			0
$718$	−35.4897	+	28.8479i	−1.32446	+	1.07659i
$719$	−11.2528	+	19.4904i	−0.419658	+	0.726869i	−0.995905	−	0.0904064i	$-0.971183\pi$
$719$	−11.2528	+	19.4904i	−0.419658	+	0.726869i	0.576247	+	0.817276i	$0.304517\pi$
$720$		0			0
$721$	−23.5797	−	40.8412i	−0.878153	−	1.52101i
$722$	−25.0921	−	9.57872i	−0.933832	−	0.356483i
$723$		0			0
$724$	−21.8142	−	19.4959i	−0.810719	−	0.724559i
$725$	1.17854	+	3.23802i	0.0437700	+	0.120257i
$726$		0			0
$727$	17.2598	−	3.04338i	0.640132	−	0.112873i	0.155845	−	0.987782i	$-0.450190\pi$
$727$	17.2598	−	3.04338i	0.640132	−	0.112873i	0.484287	+	0.874909i	$0.339079\pi$
$728$	−2.10318	+	44.8997i	−0.0779491	+	1.66409i
$729$		0			0
$730$	−0.886643	+	56.8224i	−0.0328161	+	2.10309i
$731$	1.31725	+	7.47048i	0.0487201	+	0.276306i
$732$		0			0
$733$	21.1222	−	7.68786i	0.780167	−	0.283958i	0.0789247	−	0.996881i	$-0.474851\pi$
$733$	21.1222	−	7.68786i	0.780167	−	0.283958i	0.701242	+	0.712923i	$0.252629\pi$
$734$	0.617033	−	0.712474i	0.0227751	−	0.0262979i
$735$		0			0
$736$	4.37096	+	1.98918i	0.161116	+	0.0733221i
$737$	−10.9147	+	6.30162i	−0.402049	+	0.232123i
$738$		0			0
$739$	−7.76664	−	4.48407i	−0.285700	−	0.164949i	0.350301	−	0.936637i	$-0.386079\pi$
$739$	−7.76664	−	4.48407i	−0.285700	−	0.164949i	−0.636001	+	0.771688i	$0.719413\pi$
$740$	−23.5221	−	29.8783i	−0.864691	−	1.09835i
$741$		0			0
$742$	5.77298	−	29.9957i	0.211933	−	1.10118i
$743$	8.24486	−	46.7589i	0.302474	−	1.71542i	−0.332686	−	0.943038i	$-0.607955\pi$
$743$	8.24486	−	46.7589i	0.302474	−	1.71542i	0.635161	−	0.772380i	$-0.280934\pi$
$744$		0			0
$745$	48.1818	−	40.4293i	1.76524	−	1.48122i
$746$	−15.1259	+	25.2796i	−0.553800	+	0.925554i
$747$		0			0
$748$	6.14858	−	3.29851i	0.224814	−	0.120605i
$749$	−9.73778	+	26.7543i	−0.355811	+	0.977582i
$750$		0			0
$751$	−8.95708	+	10.6746i	−0.326848	+	0.389523i	−0.904297	−	0.426904i	$-0.859604\pi$
$751$	−8.95708	+	10.6746i	−0.326848	+	0.389523i	0.577448	+	0.816427i	$0.304049\pi$
$752$	25.3533	−	7.47352i	0.924541	−	0.272531i
$753$		0			0
$754$	−3.79628	+	0.608476i	−0.138252	+	0.0221594i
$755$	−66.3349			−2.41418
$756$		0			0
$757$	12.8098			0.465582			0.232791	−	0.972527i	$-0.425214\pi$
$757$	12.8098			0.465582			0.232791	+	0.972527i	$0.425214\pi$
$758$	−26.7973	+	4.29513i	−0.973321	+	0.156006i
$759$		0			0
$760$	0.849636	−	0.264927i	0.0308195	−	0.00960992i
$761$	19.9205	−	23.7403i	0.722117	−	0.860586i	−0.272718	−	0.962094i	$-0.587922\pi$
$761$	19.9205	−	23.7403i	0.722117	−	0.860586i	0.994835	+	0.101509i	$0.0323669\pi$
$762$		0			0
$763$	−4.70813	+	12.9355i	−0.170446	+	0.468295i
$764$	1.81718	+	3.38732i	0.0657434	+	0.122549i
$765$		0			0
$766$	−5.75993	+	9.62644i	−0.208115	+	0.347817i
$767$	12.6535	−	10.6176i	0.456892	−	0.383378i
$768$		0			0
$769$	2.97310	−	16.8613i	0.107213	−	0.608034i	−0.883101	−	0.469184i	$-0.844548\pi$
$769$	2.97310	−	16.8613i	0.107213	−	0.608034i	0.990313	−	0.138850i	$-0.0443406\pi$
$770$	−7.05362	+	36.6497i	−0.254195	+	1.32076i
$771$		0			0
$772$	−9.83961	+	7.74637i	−0.354135	+	0.278798i
$773$	−37.1476	−	21.4472i	−1.33610	−	0.771401i	−0.349877	−	0.936795i	$-0.613777\pi$
$773$	−37.1476	−	21.4472i	−1.33610	−	0.771401i	−0.986227	+	0.165395i	$0.947110\pi$
$774$		0			0
$775$	39.6758	−	22.9068i	1.42520	−	0.822838i
$776$	−17.2238	−	7.19848i	−0.618299	−	0.258410i
$777$		0			0
$778$	11.4304	−	13.1984i	0.409799	−	0.473186i
$779$	−0.245070	+	0.0891981i	−0.00878053	+	0.00319585i
$780$		0			0
$781$	−5.37381	−	30.4764i	−0.192290	−	1.09053i
$782$	0.0249994	−	1.60214i	0.000893978	−	0.0572924i
$783$		0			0
$784$	−6.32095	−	0.395004i	−0.225748	−	0.0141073i
$785$	57.1502	−	10.0771i	2.03978	−	0.359668i
$786$		0			0
$787$	2.03832	+	5.60024i	0.0726582	+	0.199627i	0.970706	−	0.240272i	$-0.0772366\pi$
$787$	2.03832	+	5.60024i	0.0726582	+	0.199627i	−0.898047	+	0.439899i	$0.855014\pi$
$788$	20.1633	−	22.5611i	0.718290	−	0.803704i
$789$		0			0
$790$	−7.68092	−	2.93213i	−0.273275	−	0.104320i
$791$	−0.826860	−	1.43216i	−0.0293998	−	0.0509219i
$792$		0			0
$793$	6.57679	−	11.3913i	0.233549	−	0.404518i
$794$	−25.4507	+	20.6877i	−0.903212	+	0.734179i
$795$		0			0
$796$	−50.7361	−	10.5881i	−1.79829	−	0.375287i
$797$	40.7435	+	7.18417i	1.44321	+	0.254477i	0.839774	−	0.542936i	$-0.182688\pi$
$797$	40.7435	+	7.18417i	1.44321	+	0.254477i	0.603434	+	0.797413i	$0.293799\pi$
$798$		0			0
$799$	−5.66892	−	6.75595i	−0.200552	−	0.239008i
$800$	22.0120	−	32.0639i	0.778243	−	1.13363i
$801$		0			0
$802$	8.39715	−	4.67495i	0.296514	−	0.165078i
$803$	−28.6435	−	10.4254i	−1.01081	−	0.367903i
$804$		0			0
$805$	6.56566	+	5.50924i	0.231409	+	0.194175i
$806$	16.7316	+	48.3014i	0.589344	+	1.70134i
$807$		0			0
$808$	−23.1311	+	2.97061i	−0.813751	+	0.104506i
$809$		−	45.8780i		−	1.61298i	−0.591245	−	0.806492i	$-0.701363\pi$
$809$		−	45.8780i		−	1.61298i	0.591245	−	0.806492i	$-0.298637\pi$
$810$		0			0
$811$			25.4302i			0.892974i	0.894790	+	0.446487i	$0.147325\pi$
$811$			25.4302i			0.892974i	−0.894790	+	0.446487i	$0.852675\pi$
$812$	−0.419473	−	2.90660i	−0.0147206	−	0.102002i
$813$		0			0
$814$	19.2728	−	6.67608i	0.675511	−	0.233997i
$815$	21.1874	+	17.7784i	0.742163	+	0.622749i
$816$		0			0
$817$	−0.487678	−	0.177500i	−0.0170617	−	0.00620994i
$818$	−12.4975	−	22.4480i	−0.436965	−	0.784877i
$819$		0			0
$820$	−10.3697	+	16.7326i	−0.362127	+	0.584326i
$821$	−5.04053	−	6.00706i	−0.175916	−	0.209648i	0.670881	−	0.741565i	$-0.265916\pi$
$821$	−5.04053	−	6.00706i	−0.175916	−	0.209648i	−0.846796	+	0.531917i	$0.821472\pi$
$822$		0			0
$823$	−8.63034	−	1.52176i	−0.300835	−	0.0530453i	0.0211934	−	0.999775i	$-0.493253\pi$
$823$	−8.63034	−	1.52176i	−0.300835	−	0.0530453i	−0.322028	+	0.946730i	$0.604365\pi$
$824$	−44.4180	−	9.99526i	−1.54737	−	0.348201i
$825$		0			0
$826$	7.95821	+	9.79047i	0.276902	+	0.340654i
$827$	−9.57006	+	16.5758i	−0.332784	+	0.576398i	−0.983057	−	0.183303i	$-0.941321\pi$
$827$	−9.57006	+	16.5758i	−0.332784	+	0.576398i	0.650273	+	0.759701i	$0.274655\pi$
$828$		0			0
$829$	−0.0258029	−	0.0446919i	−0.000896172	−	0.00155222i	0.865577	−	0.500776i	$-0.166952\pi$
$829$	−0.0258029	−	0.0446919i	−0.000896172	−	0.00155222i	−0.866473	+	0.499224i	$0.833619\pi$
$830$	3.75360	−	9.83281i	0.130289	−	0.341302i
$831$		0			0
$832$	30.4893	+	30.8789i	1.05703	+	1.07053i
$833$	0.722744	+	1.98572i	0.0250416	+	0.0688012i
$834$		0			0
$835$	4.43105	−	0.781314i	0.153343	−	0.0270385i
$836$	−0.0148937	+	0.477130i	−0.000515109	+	0.0165019i
$837$		0			0
$838$	−6.95909	−	0.108588i	−0.240398	−	0.00375111i
$839$	1.86814	+	10.5948i	0.0644954	+	0.365771i	0.999925	+	0.0122581i	$0.00390198\pi$
$839$	1.86814	+	10.5948i	0.0644954	+	0.365771i	−0.935429	+	0.353513i	$0.884987\pi$
$840$		0			0
$841$	−27.0150	+	9.83267i	−0.931553	+	0.339058i
$842$	−12.5810	−	10.8957i	−0.433570	−	0.375490i
$843$		0			0
$844$	−12.9529	+	32.4044i	−0.445858	+	1.11541i
$845$	49.0137	−	28.2981i	1.68612	−	0.973484i
$846$		0			0
$847$	10.5727	+	6.10416i	0.363283	+	0.209741i
$848$	−17.5099	−	23.7289i	−0.601293	−	0.814854i
$849$		0			0
$850$	−12.7430	−	2.45252i	−0.437081	−	0.0841207i
$851$	0.813351	−	4.61274i	0.0278813	−	0.158123i
$852$		0			0
$853$	30.2999	−	25.4247i	1.03745	−	0.870524i	0.0457315	−	0.998954i	$-0.485438\pi$
$853$	30.2999	−	25.4247i	1.03745	−	0.870524i	0.991719	+	0.128430i	$0.0409937\pi$
$854$	8.62159	+	5.15868i	0.295025	+	0.176526i
$855$		0			0
$856$	12.6146	+	24.4213i	0.431157	+	0.834704i
$857$	3.50870	−	9.64007i	0.119855	−	0.329299i	−0.865228	−	0.501378i	$-0.832826\pi$
$857$	3.50870	−	9.64007i	0.119855	−	0.329299i	0.985083	+	0.172080i	$0.0550487\pi$
$858$		0			0
$859$	−2.27840	+	2.71529i	−0.0777381	+	0.0926446i	−0.803512	−	0.595289i	$-0.797038\pi$
$859$	−2.27840	+	2.71529i	−0.0777381	+	0.0926446i	0.725774	+	0.687934i	$0.241482\pi$
$860$	−37.2105	+	12.2429i	−1.26887	+	0.417479i
$861$		0			0
$862$	−0.986794	−	6.15661i	−0.0336104	−	0.209695i
$863$	6.36151			0.216548			0.108274	−	0.994121i	$-0.465468\pi$
$863$	6.36151			0.216548			0.108274	+	0.994121i	$0.465468\pi$
$864$		0			0
$865$	−39.4602			−1.34169
$866$	6.38397	+	39.8296i	0.216936	+	1.35346i
$867$		0			0
$868$	−37.0888	+	12.2029i	−1.25888	+	0.414192i
$869$	2.83458	−	3.37812i	0.0961565	−	0.114595i
$870$		0			0
$871$	−8.94493	+	24.5760i	−0.303087	+	0.832726i
$872$	6.09903	+	11.8075i	0.206539	+	0.399852i
$873$		0			0
$874$	0.0940700	+	0.0562863i	0.00318197	+	0.00190391i
$875$	14.5034	−	12.1698i	0.490304	−	0.411414i
$876$		0			0
$877$	−2.83565	+	16.0818i	−0.0957531	+	0.543043i	0.898761	+	0.438439i	$0.144468\pi$
$877$	−2.83565	+	16.0818i	−0.0957531	+	0.543043i	−0.994514	+	0.104604i	$0.966643\pi$
$878$	−6.71707	−	1.29277i	−0.226690	−	0.0436288i
$879$		0			0
$880$	21.3942	+	28.9928i	0.721198	+	0.977346i
$881$	43.1593	+	24.9180i	1.45407	+	0.839509i	0.998709	−	0.0507963i	$-0.0161759\pi$
$881$	43.1593	+	24.9180i	1.45407	+	0.839509i	0.455364	+	0.890306i	$0.349509\pi$
$882$		0			0
$883$	38.2077	−	22.0592i	1.28579	−	0.742352i	0.307890	−	0.951422i	$-0.400377\pi$
$883$	38.2077	−	22.0592i	1.28579	−	0.742352i	0.977901	+	0.209070i	$0.0670437\pi$
$884$	5.37423	−	13.4448i	0.180755	−	0.452196i
$885$		0			0
$886$	7.76834	+	6.72771i	0.260982	+	0.226022i
$887$	2.25857	−	0.822052i	0.0758353	−	0.0276018i	−0.303824	−	0.952728i	$-0.598263\pi$
$887$	2.25857	−	0.822052i	0.0758353	−	0.0276018i	0.379659	+	0.925126i	$0.376041\pi$
$888$		0			0
$889$	−5.65792	−	32.0877i	−0.189761	−	1.07619i
$890$	−70.7842	−	1.10450i	−2.37269	−	0.0370229i
$891$		0			0
$892$	1.10298	−	35.3348i	0.0369305	−	1.18310i
$893$	0.594202	−	0.104774i	0.0198842	−	0.00350612i
$894$		0			0
$895$	−25.2377	−	69.3399i	−0.843602	−	2.31778i
$896$	−23.9466	+	22.9178i	−0.800001	+	0.765628i
$897$		0			0
$898$	−3.20572	+	8.39760i	−0.106976	+	0.280231i
$899$	−1.66986	−	2.89227i	−0.0556928	−	0.0964627i
$900$		0			0
$901$	−4.91981	+	8.52136i	−0.163903	+	0.283888i
$902$	−6.65995	−	8.19331i	−0.221752	−	0.272807i
$903$		0			0
$904$	−1.55759	−	0.350500i	−0.0518047	−	0.0116575i
$905$	−49.6441	−	8.75359i	−1.65023	−	0.290979i
$906$		0			0
$907$	−22.5530	−	26.8776i	−0.748858	−	0.892455i	0.248231	−	0.968701i	$-0.420151\pi$
$907$	−22.5530	−	26.8776i	−0.748858	−	0.892455i	−0.997089	+	0.0762463i	$0.975706\pi$
$908$	9.82912	−	15.8602i	0.326191	−	0.526340i
$909$		0			0
$910$	37.6730	+	67.6682i	1.24885	+	2.24318i
$911$	10.1501	+	3.69433i	0.336287	+	0.122399i	0.504644	−	0.863328i	$-0.331624\pi$
$911$	10.1501	+	3.69433i	0.336287	+	0.122399i	−0.168357	+	0.985726i	$0.553846\pi$
$912$		0			0
$913$	4.32453	+	3.62872i	0.143121	+	0.120093i
$914$	1.19487	−	0.413904i	0.0395229	−	0.0136907i
$915$		0			0
$916$	4.80424	+	33.2894i	0.158737	+	1.09991i
$917$		−	9.08884i		−	0.300140i
$918$		0			0
$919$			20.9319i			0.690481i	0.938514	+	0.345241i	$0.112203\pi$
$919$			20.9319i			0.690481i	−0.938514	+	0.345241i	$0.887797\pi$
$920$	8.20709	−	1.05399i	0.270580	−	0.0347491i
$921$		0			0
$922$	−6.06471	−	17.5079i	−0.199730	−	0.576591i
$923$	−49.1936	−	41.2783i	−1.61923	−	1.35869i
$924$		0			0
$925$	−35.6459	−	12.9740i	−1.17203	−	0.426584i
$926$	1.66635	−	0.927710i	0.0547598	−	0.0304865i
$927$		0			0
$928$	−2.33738	−	1.60463i	−0.0767284	−	0.0526744i
$929$	21.6205	+	25.7663i	0.709345	+	0.845365i	0.993550	−	0.113399i	$-0.0361738\pi$
$929$	21.6205	+	25.7663i	0.709345	+	0.845365i	−0.284204	+	0.958764i	$0.591729\pi$
$930$		0			0
$931$	−0.142375	−	0.0251046i	−0.00466616	−	0.000822770i
$932$	34.5116	+	7.20226i	1.13047	+	0.235918i
$933$		0			0
$934$	−21.5348	+	17.5046i	−0.704640	+	0.572769i
$935$	6.01119	−	10.4117i	0.196587	−	0.340498i
$936$		0			0
$937$	−12.5767	−	21.7834i	−0.410862	−	0.711634i	0.584122	−	0.811666i	$-0.301439\pi$
$937$	−12.5767	−	21.7834i	−0.410862	−	0.711634i	−0.994984	+	0.100032i	$0.968106\pi$
$938$	−18.6630	−	7.12443i	−0.609367	−	0.232621i
$939$		0			0
$940$	30.3486	−	33.9575i	0.989863	−	1.10757i
$941$	−14.1661	−	38.9209i	−0.461801	−	1.26879i	−0.924130	−	0.382078i	$-0.875208\pi$
$941$	−14.1661	−	38.9209i	−0.461801	−	1.26879i	0.462329	−	0.886708i	$-0.347014\pi$
$942$		0			0
$943$	−2.38790	+	0.421051i	−0.0777606	+	0.0137113i
$944$	12.1569	+	0.759701i	0.395675	+	0.0247262i
$945$		0			0
$946$	0.327815	−	21.0087i	0.0106582	−	0.683052i
$947$	−9.81759	−	55.6783i	−0.319029	−	1.80930i	−0.548684	−	0.836030i	$-0.684871\pi$
$947$	−9.81759	−	55.6783i	−0.319029	−	1.80930i	0.229656	−	0.973272i	$-0.426240\pi$
$948$		0			0
$949$	−59.4386	+	21.6339i	−1.92946	+	0.702265i
$950$	0.581214	−	0.671115i	0.0188571	−	0.0217738i
$951$		0			0
$952$	10.2042	+	4.26471i	0.330720	+	0.138220i
$953$	31.8569	−	18.3926i	1.03195	−	0.595795i	0.114405	−	0.993434i	$-0.463504\pi$
$953$	31.8569	−	18.3926i	1.03195	−	0.595795i	0.917542	+	0.397639i	$0.130170\pi$
$954$		0			0
$955$	5.73591	+	3.31163i	0.185610	+	0.107162i
$956$	14.4800	−	11.3996i	0.468315	−	0.368688i
$957$		0			0
$958$	−5.09458	+	26.4708i	−0.164598	+	0.855234i
$959$	−8.78509	+	49.8227i	−0.283685	+	1.60886i
$960$		0			0
$961$	−10.2671	+	8.61511i	−0.331196	+	0.277907i
$962$	21.7317	−	36.3197i	0.700659	−	1.17100i
$963$		0			0
$964$	−5.88716	−	10.9740i	−0.189613	−	0.353447i
$965$	−7.37989	+	20.2761i	−0.237567	+	0.652711i
$966$		0			0
$967$	−28.9550	+	34.5072i	−0.931129	+	1.10968i	0.0626196	+	0.998037i	$0.480055\pi$
$967$	−28.9550	+	34.5072i	−0.931129	+	1.10968i	−0.993749	+	0.111639i	$0.964390\pi$
$968$	11.2519	−	3.50848i	0.361649	−	0.112767i
$969$		0			0
$970$	−31.7593	+	5.09046i	−1.01973	+	0.163445i
$971$	40.1053			1.28704			0.643520	−	0.765429i	$-0.277473\pi$
$971$	40.1053			1.28704			0.643520	+	0.765429i	$0.277473\pi$
$972$		0			0
$973$	32.7837			1.05100
$974$	−17.7956	+	2.85232i	−0.570208	+	0.0913942i
$975$		0			0
$976$	9.30387	−	2.74254i	0.297810	−	0.0877867i
$977$	−23.6105	+	28.1379i	−0.755368	+	0.900213i	−0.997546	−	0.0700194i	$-0.977694\pi$
$977$	−23.6105	+	28.1379i	−0.755368	+	0.900213i	0.242178	+	0.970232i	$0.422138\pi$
$978$		0			0
$979$	12.9870	−	35.6814i	0.415066	−	1.14038i
$980$	−9.61606	+	5.15870i	−0.307174	+	0.164788i
$981$		0			0
$982$	−17.9589	+	30.0144i	−0.573093	+	0.957797i
$983$	14.5073	−	12.1730i	0.462710	−	0.388259i	−0.381417	−	0.924403i	$-0.624564\pi$
$983$	14.5073	−	12.1730i	0.462710	−	0.388259i	0.844127	+	0.536144i	$0.180119\pi$
$984$		0			0
$985$	9.05328	−	51.3437i	0.288462	−	1.63595i
$986$	−0.178783	+	0.928934i	−0.00569361	+	0.0295833i
$987$		0			0
$988$	0.612750	+	0.778328i	0.0194942	+	0.0247619i
$989$	−4.17867	−	2.41256i	−0.132874	−	0.0767148i
$990$		0			0
$991$	30.3997	−	17.5513i	0.965680	−	0.557535i	0.0677633	−	0.997701i	$-0.478414\pi$
$991$	30.3997	−	17.5513i	0.965680	−	0.557535i	0.897916	+	0.440166i	$0.145080\pi$
$992$	−15.6136	+	34.3089i	−0.495733	+	1.08931i
$993$		0			0
$994$	32.1120	−	37.0790i	1.01853	−	1.17607i
$995$	−83.9173	+	30.5434i	−2.66036	+	0.968291i
$996$		0			0
$997$	4.16898	+	23.6435i	0.132033	+	0.748796i	0.976880	+	0.213788i	$0.0685803\pi$
$997$	4.16898	+	23.6435i	0.132033	+	0.748796i	−0.844847	+	0.535008i	$0.820309\pi$
$998$	−0.871737	+	55.8671i	−0.0275944	+	1.76844i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.b.215.10		96
3.2	odd	2		972.2.l.c.215.7		96
4.3	odd	2	inner	972.2.l.b.215.8		96
9.2	odd	6		972.2.l.d.863.5		96
9.4	even	3		324.2.l.a.179.2		96
9.5	odd	6		108.2.l.a.23.15	yes	96
9.7	even	3		972.2.l.a.863.12		96
12.11	even	2		972.2.l.c.215.9		96
27.2	odd	18	inner	972.2.l.b.755.8		96
27.7	even	9		972.2.l.d.107.13		96
27.11	odd	18		324.2.l.a.143.15		96
27.16	even	9		108.2.l.a.47.2	yes	96
27.20	odd	18		972.2.l.a.107.4		96
27.25	even	9		972.2.l.c.755.9		96
36.7	odd	6		972.2.l.a.863.4		96
36.11	even	6		972.2.l.d.863.13		96
36.23	even	6		108.2.l.a.23.2	✓	96
36.31	odd	6		324.2.l.a.179.15		96
108.7	odd	18		972.2.l.d.107.5		96
108.11	even	18		324.2.l.a.143.2		96
108.43	odd	18		108.2.l.a.47.15	yes	96
108.47	even	18		972.2.l.a.107.12		96
108.79	odd	18		972.2.l.c.755.7		96
108.83	even	18	inner	972.2.l.b.755.10		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.2	✓	96	36.23	even	6
108.2.l.a.23.15	yes	96	9.5	odd	6
108.2.l.a.47.2	yes	96	27.16	even	9
108.2.l.a.47.15	yes	96	108.43	odd	18
324.2.l.a.143.2		96	108.11	even	18
324.2.l.a.143.15		96	27.11	odd	18
324.2.l.a.179.2		96	9.4	even	3
324.2.l.a.179.15		96	36.31	odd	6
972.2.l.a.107.4		96	27.20	odd	18
972.2.l.a.107.12		96	108.47	even	18
972.2.l.a.863.4		96	36.7	odd	6
972.2.l.a.863.12		96	9.7	even	3
972.2.l.b.215.8		96	4.3	odd	2	inner
972.2.l.b.215.10		96	1.1	even	1	trivial
972.2.l.b.755.8		96	27.2	odd	18	inner
972.2.l.b.755.10		96	108.83	even	18	inner
972.2.l.c.215.7		96	3.2	odd	2
972.2.l.c.215.9		96	12.11	even	2
972.2.l.c.755.7		96	108.79	odd	18
972.2.l.c.755.9		96	27.25	even	9
972.2.l.d.107.5		96	108.7	odd	18
972.2.l.d.107.13		96	27.7	even	9
972.2.l.d.863.5		96	9.2	odd	6
972.2.l.d.863.13		96	36.11	even	6

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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.223817 + 1.39639i) q^{2} +(-1.89981 + 0.625071i) q^{4} +(-2.21508 + 2.63983i) q^{5} +(1.00203 - 2.75305i) q^{7} +(-1.29805 - 2.51298i) q^{8} +(-4.18200 - 2.50228i) q^{10} +(2.00243 - 1.68024i) q^{11} +(0.941927 - 5.34193i) q^{13} +(4.06860 + 0.783043i) q^{14} +(3.21857 - 2.37503i) q^{16} +(-1.15583 - 0.667320i) q^{17} +(0.0790760 - 0.0456546i) q^{19} +(2.55816 - 6.39976i) q^{20} +(2.79445 + 2.42011i) q^{22} +(0.797738 - 0.290353i) q^{23} +(-1.19388 - 6.77083i) q^{25} +(7.67024 + 0.119685i) q^{26} +(-0.182815 + 5.85661i) q^{28} +(-0.493578 + 0.0870310i) q^{29} +(2.27906 + 6.26168i) q^{31} +(4.03684 + 3.96281i) q^{32} +(0.673145 - 1.76335i) q^{34} +(5.04800 + 8.74340i) q^{35} +(2.75869 - 4.77819i) q^{37} +(0.0814501 + 0.100203i) q^{38} +(9.50912 + 2.13981i) q^{40} +(-2.81281 - 0.495975i) q^{41} +(-3.65343 - 4.35398i) q^{43} +(-2.75398 + 4.44381i) q^{44} +(0.583993 + 1.04897i) q^{46} +(6.20947 + 2.26006i) q^{47} +(-1.21289 - 1.01774i) q^{49} +(9.18751 - 3.18255i) q^{50} +(1.54960 + 10.7374i) q^{52} -7.37249i q^{53} +9.00795i q^{55} +(-8.21903 + 1.05553i) q^{56} +(-0.232000 - 0.669748i) q^{58} +(2.33273 + 1.95739i) q^{59} +(2.27868 + 0.829371i) q^{61} +(-8.23365 + 4.58393i) q^{62} +(-4.63012 + 6.52395i) q^{64} +(12.0154 + 14.3193i) q^{65} +(-4.74821 - 0.837237i) q^{67} +(2.61299 + 0.545306i) q^{68} +(-11.0794 + 9.00590i) q^{70} +(5.91940 - 10.2527i) q^{71} +(-5.83049 - 10.0987i) q^{73} +(7.28967 + 2.78277i) q^{74} +(-0.121692 + 0.136163i) q^{76} +(-2.61929 - 7.19644i) q^{77} +(1.66138 - 0.292946i) q^{79} +(-0.859714 + 13.7574i) q^{80} +(0.0630204 - 4.03879i) q^{82} +(0.375017 + 2.12683i) q^{83} +(4.32187 - 1.57303i) q^{85} +(5.26216 - 6.07610i) q^{86} +(-6.82167 - 2.85103i) q^{88} +(12.5801 - 7.26310i) q^{89} +(-13.7628 - 7.94593i) q^{91} +(-1.33406 + 1.05026i) q^{92} +(-1.76615 + 9.17668i) q^{94} +(-0.0546395 + 0.309876i) q^{95} +(5.05588 - 4.24238i) q^{97} +(1.14969 - 1.92146i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 + 12 * q^14 + 3 * q^16 + 18 * q^17 - 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 6 * q^29 + 57 * q^32 - 3 * q^34 - 6 * q^37 - 45 * q^38 - 12 * q^40 - 66 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 66 * q^50 - 24 * q^52 + 81 * q^56 - 24 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 + 42 * q^65 - 51 * q^68 - 30 * q^70 - 6 * q^73 + 96 * q^74 - 9 * q^76 - 30 * q^77 - 12 * q^82 + 66 * q^85 - 141 * q^86 - 45 * q^88 + 24 * q^92 - 51 * q^94 + 42 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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