LMFDB - Embedded newform 990.2.bg.a.961.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(31,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 0, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,11,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			961.3
Character	$\chi$	$=$	990.961
Dual form			990.2.bg.a.751.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.913545 - 0.406737i) q^{2} +(-1.01237 + 1.40538i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.913545 + 0.406737i) q^{5} +(-0.353225 + 1.69565i) q^{6} +(-1.79977 - 0.382553i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.950211 - 2.84554i) q^{9} +1.00000 q^{10} +(-1.83620 + 2.76195i) q^{11} +(0.366996 + 1.69272i) q^{12} +(-0.355627 + 3.38356i) q^{13} +(-1.79977 + 0.382553i) q^{14} +(-1.49647 + 0.872114i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.0478740 + 0.0347825i) q^{17} +(-2.02545 - 2.21304i) q^{18} +(-1.28042 + 3.94074i) q^{19} +(0.913545 - 0.406737i) q^{20} +(2.35967 - 2.14209i) q^{21} +(-0.554071 + 3.27002i) q^{22} +(3.45785 + 5.98917i) q^{23} +(1.02376 + 1.39711i) q^{24} +(0.669131 + 0.743145i) q^{25} +(1.05134 + 3.23569i) q^{26} +(4.96104 + 1.54533i) q^{27} +(-1.48857 + 1.08151i) q^{28} +(-7.67575 - 1.63153i) q^{29} +(-1.01237 + 1.40538i) q^{30} +(-0.779832 + 7.41960i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.02268 - 5.37669i) q^{33} +(-0.0295877 + 0.0512475i) q^{34} +(-1.48857 - 1.08151i) q^{35} +(-2.75046 - 1.19789i) q^{36} +(-0.363903 - 1.11998i) q^{37} +(0.433118 + 4.12084i) q^{38} +(-4.39518 - 3.92521i) q^{39} +(0.669131 - 0.743145i) q^{40} +(-2.08813 + 0.443845i) q^{41} +(1.28440 - 2.91666i) q^{42} +(2.62307 - 4.54329i) q^{43} +(0.823866 + 3.21267i) q^{44} +(0.289324 - 2.98602i) q^{45} +(5.59492 + 4.06494i) q^{46} +(0.598083 + 0.664238i) q^{47} +(1.50351 + 0.859922i) q^{48} +(-3.30199 - 1.47014i) q^{49} +(0.913545 + 0.406737i) q^{50} +(-0.000416548 - 0.102494i) q^{51} +(2.27652 + 2.52833i) q^{52} +(0.197016 + 0.143141i) q^{53} +(5.16068 - 0.606110i) q^{54} +(-2.80084 + 1.77631i) q^{55} +(-0.919990 + 1.59347i) q^{56} +(-4.24199 - 5.78897i) q^{57} +(-7.67575 + 1.63153i) q^{58} +(-3.89766 + 4.32879i) q^{59} +(-0.353225 + 1.69565i) q^{60} +(1.19482 + 11.3680i) q^{61} +(2.30541 + 7.09533i) q^{62} +(0.621592 + 5.48483i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.70110 + 2.94639i) q^{65} +(-4.03470 - 4.08915i) q^{66} +(-1.08921 - 1.88657i) q^{67} +(-0.00618552 + 0.0588513i) q^{68} +(-11.9177 - 1.20365i) q^{69} +(-1.79977 - 0.382553i) q^{70} +(7.04819 - 5.12081i) q^{71} +(-2.99990 + 0.0243843i) q^{72} +(-3.27871 - 10.0908i) q^{73} +(-0.787977 - 0.875137i) q^{74} +(-1.72181 + 0.188048i) q^{75} +(2.07177 + 3.58841i) q^{76} +(4.36134 - 4.26843i) q^{77} +(-5.61173 - 1.79818i) q^{78} +(7.72055 - 3.43741i) q^{79} +(0.309017 - 0.951057i) q^{80} +(-7.19420 + 5.40773i) q^{81} +(-1.72707 + 1.25479i) q^{82} +(1.06155 + 10.1000i) q^{83} +(-0.0129520 - 3.18691i) q^{84} +(-0.0578824 + 0.0123033i) q^{85} +(0.548371 - 5.21740i) q^{86} +(10.0636 - 9.13566i) q^{87} +(2.05935 + 2.59982i) q^{88} -8.19011 q^{89} +(-0.950211 - 2.84554i) q^{90} +(1.93444 - 5.95360i) q^{91} +(6.76457 + 1.43785i) q^{92} +(-9.63792 - 8.60735i) q^{93} +(0.816546 + 0.363550i) q^{94} +(-2.77257 + 3.07925i) q^{95} +(1.72328 + 0.174046i) q^{96} +(16.2245 - 7.22360i) q^{97} -3.61447 q^{98} +(9.60401 + 2.60056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) $ 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$3$	−1.01237	+	1.40538i	−0.584492	+	0.811399i
$3$	−1.01237	+	1.40538i	−0.584492	+	0.811399i
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	0.913545	+	0.406737i	0.408550	+	0.181898i
$5$	0.913545	+	0.406737i	0.408550	+	0.181898i
$6$	−0.353225	+	1.69565i	−0.144204	+	0.692247i
$7$	−1.79977	−	0.382553i	−0.680250	−	0.144592i	−0.145187	−	0.989404i	$-0.546379\pi$
$7$	−1.79977	−	0.382553i	−0.680250	−	0.144592i	−0.535062	+	0.844813i	$0.679712\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.950211	−	2.84554i	−0.316737	−	0.948513i
$10$	1.00000			0.316228
$11$	−1.83620	+	2.76195i	−0.553636	+	0.832758i
$11$	−1.83620	+	2.76195i	−0.553636	+	0.832758i
$12$	0.366996	+	1.69272i	0.105943	+	0.488647i
$13$	−0.355627	+	3.38356i	−0.0986332	+	0.938432i	0.827559	+	0.561379i	$0.189729\pi$
$13$	−0.355627	+	3.38356i	−0.0986332	+	0.938432i	−0.926192	+	0.377053i	$0.876938\pi$
$14$	−1.79977	+	0.382553i	−0.481009	+	0.102242i
$15$	−1.49647	+	0.872114i	−0.386386	+	0.225179i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	−0.0478740	+	0.0347825i	−0.0116111	+	0.00843599i	−0.593576	−	0.804778i	$-0.702284\pi$
$17$	−0.0478740	+	0.0347825i	−0.0116111	+	0.00843599i	0.581965	+	0.813214i	$0.302284\pi$
$18$	−2.02545	−	2.21304i	−0.477402	−	0.521620i
$19$	−1.28042	+	3.94074i	−0.293749	+	0.904067i	0.689889	+	0.723915i	$0.257659\pi$
$19$	−1.28042	+	3.94074i	−0.293749	+	0.904067i	−0.983639	+	0.180153i	$0.942341\pi$
$20$	0.913545	−	0.406737i	0.204275	−	0.0909491i
$21$	2.35967	−	2.14209i	0.514922	−	0.467441i
$22$	−0.554071	+	3.27002i	−0.118128	+	0.697170i
$23$	3.45785	+	5.98917i	0.721011	+	1.24883i	0.960595	+	0.277952i	$0.0896557\pi$
$23$	3.45785	+	5.98917i	0.721011	+	1.24883i	−0.239584	+	0.970876i	$0.577011\pi$
$24$	1.02376	+	1.39711i	0.208974	+	0.285184i
$25$	0.669131	+	0.743145i	0.133826	+	0.148629i
$26$	1.05134	+	3.23569i	0.206184	+	0.634570i
$27$	4.96104	+	1.54533i	0.954753	+	0.297399i
$28$	−1.48857	+	1.08151i	−0.281314	+	0.204387i
$29$	−7.67575	−	1.63153i	−1.42535	−	0.302968i	−0.570268	−	0.821459i	$-0.693161\pi$
$29$	−7.67575	−	1.63153i	−1.42535	−	0.302968i	−0.855083	+	0.518491i	$0.826494\pi$
$30$	−1.01237	+	1.40538i	−0.184833	+	0.256587i
$31$	−0.779832	+	7.41960i	−0.140062	+	1.33260i	0.668290	+	0.743901i	$0.267026\pi$
$31$	−0.779832	+	7.41960i	−0.140062	+	1.33260i	−0.808352	+	0.588699i	$0.799640\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.02268	−	5.37669i	−0.352103	−	0.935961i
$34$	−0.0295877	+	0.0512475i	−0.00507426	+	0.00878887i
$35$	−1.48857	−	1.08151i	−0.251615	−	0.182809i
$36$	−2.75046	−	1.19789i	−0.458411	−	0.199649i
$37$	−0.363903	−	1.11998i	−0.0598252	−	0.184123i	0.916678	−	0.399627i	$-0.130860\pi$
$37$	−0.363903	−	1.11998i	−0.0598252	−	0.184123i	−0.976503	+	0.215504i	$0.930860\pi$
$38$	0.433118	+	4.12084i	0.0702609	+	0.668488i
$39$	−4.39518	−	3.92521i	−0.703792	−	0.628537i
$40$	0.669131	−	0.743145i	0.105799	−	0.117502i
$41$	−2.08813	+	0.443845i	−0.326111	+	0.0693169i	−0.368058	−	0.929803i	$-0.619977\pi$
$41$	−2.08813	+	0.443845i	−0.326111	+	0.0693169i	0.0419473	+	0.999120i	$0.486644\pi$
$42$	1.28440	−	2.91666i	0.198187	−	0.450050i
$43$	2.62307	−	4.54329i	0.400014	−	0.692845i	−0.593713	−	0.804677i	$-0.702338\pi$
$43$	2.62307	−	4.54329i	0.400014	−	0.692845i	0.993727	+	0.111832i	$0.0356718\pi$
$44$	0.823866	+	3.21267i	0.124203	+	0.484328i
$45$	0.289324	−	2.98602i	0.0431299	−	0.445129i
$46$	5.59492	+	4.06494i	0.824925	+	0.599343i
$47$	0.598083	+	0.664238i	0.0872393	+	0.0968891i	0.785184	−	0.619263i	$-0.212568\pi$
$47$	0.598083	+	0.664238i	0.0872393	+	0.0968891i	−0.697944	+	0.716152i	$0.745902\pi$
$48$	1.50351	+	0.859922i	0.217013	+	0.124119i
$49$	−3.30199	−	1.47014i	−0.471712	−	0.210020i
$50$	0.913545	+	0.406737i	0.129195	+	0.0575212i
$51$	−0.000416548	−	0.102494i	−5.83283e−5	−	0.0143520i
$52$	2.27652	+	2.52833i	0.315696	+	0.350616i
$53$	0.197016	+	0.143141i	0.0270623	+	0.0196619i	0.601234	−	0.799073i	$-0.294676\pi$
$53$	0.197016	+	0.143141i	0.0270623	+	0.0196619i	−0.574172	+	0.818735i	$0.694676\pi$
$54$	5.16068	−	0.606110i	0.702280	−	0.0824811i
$55$	−2.80084	+	1.77631i	−0.377665	+	0.239518i
$56$	−0.919990	+	1.59347i	−0.122939	+	0.212936i
$57$	−4.24199	−	5.78897i	−0.561865	−	0.766768i
$58$	−7.67575	+	1.63153i	−1.00788	+	0.214230i
$59$	−3.89766	+	4.32879i	−0.507432	+	0.563560i	−0.941367	−	0.337384i	$-0.890458\pi$
$59$	−3.89766	+	4.32879i	−0.507432	+	0.563560i	0.433935	+	0.900944i	$0.357125\pi$
$60$	−0.353225	+	1.69565i	−0.0456012	+	0.218908i
$61$	1.19482	+	11.3680i	0.152981	+	1.45552i	0.754311	+	0.656517i	$0.227971\pi$
$61$	1.19482	+	11.3680i	0.152981	+	1.45552i	−0.601330	+	0.799001i	$0.705362\pi$
$62$	2.30541	+	7.09533i	0.292788	+	0.901108i
$63$	0.621592	+	5.48483i	0.0783133	+	0.691023i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.70110	+	2.94639i	−0.210996	+	0.365455i
$66$	−4.03470	−	4.08915i	−0.496638	−	0.503340i
$67$	−1.08921	−	1.88657i	−0.133068	−	0.230481i	0.791790	−	0.610794i	$-0.209150\pi$
$67$	−1.08921	−	1.88657i	−0.133068	−	0.230481i	−0.924858	+	0.380313i	$0.875816\pi$
$68$	−0.00618552	+	0.0588513i	−0.000750105	+	0.00713677i
$69$	−11.9177	−	1.20365i	−1.43472	−	0.144903i
$70$	−1.79977	−	0.382553i	−0.215114	−	0.0457239i
$71$	7.04819	−	5.12081i	0.836467	−	0.607728i	−0.0849149	−	0.996388i	$-0.527062\pi$
$71$	7.04819	−	5.12081i	0.836467	−	0.607728i	0.921381	+	0.388660i	$0.127062\pi$
$72$	−2.99990	+	0.0243843i	−0.353542	+	0.00287371i
$73$	−3.27871	−	10.0908i	−0.383744	−	1.18104i	−0.937387	−	0.348289i	$-0.886763\pi$
$73$	−3.27871	−	10.0908i	−0.383744	−	1.18104i	0.553643	−	0.832754i	$-0.313237\pi$
$74$	−0.787977	−	0.875137i	−0.0916005	−	0.101733i
$75$	−1.72181	+	0.188048i	−0.198818	+	0.0217139i
$76$	2.07177	+	3.58841i	0.237648	+	0.411619i
$77$	4.36134	−	4.26843i	0.497021	−	0.486433i
$78$	−5.61173	−	1.79818i	−0.635403	−	0.203604i
$79$	7.72055	−	3.43741i	0.868630	−	0.386739i	0.0764839	−	0.997071i	$-0.475631\pi$
$79$	7.72055	−	3.43741i	0.868630	−	0.386739i	0.792146	+	0.610332i	$0.208964\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	−7.19420	+	5.40773i	−0.799355	+	0.600859i
$82$	−1.72707	+	1.25479i	−0.190723	+	0.138568i
$83$	1.06155	+	10.1000i	0.116520	+	1.10862i	0.883982	+	0.467522i	$0.154853\pi$
$83$	1.06155	+	10.1000i	0.116520	+	1.10862i	−0.767461	+	0.641095i	$0.778480\pi$
$84$	−0.0129520	−	3.18691i	−0.00141318	−	0.347721i
$85$	−0.0578824	+	0.0123033i	−0.00627822	+	0.00133448i
$86$	0.548371	−	5.21740i	0.0591324	−	0.562607i
$87$	10.0636	−	9.13566i	1.07893	−	0.979446i
$88$	2.05935	+	2.59982i	0.219527	+	0.277142i
$89$	−8.19011			−0.868150			−0.434075	−	0.900877i	$-0.642925\pi$
$89$	−8.19011			−0.868150			−0.434075	+	0.900877i	$0.642925\pi$
$90$	−0.950211	−	2.84554i	−0.100161	−	0.299946i
$91$	1.93444	−	5.95360i	0.202784	−	0.624106i
$92$	6.76457	+	1.43785i	0.705255	+	0.149907i
$93$	−9.63792	−	8.60735i	−0.999405	−	0.892541i
$94$	0.816546	+	0.363550i	0.0842202	+	0.0374973i
$95$	−2.77257	+	3.07925i	−0.284459	+	0.315924i
$96$	1.72328	+	0.174046i	0.175882	+	0.0177635i
$97$	16.2245	−	7.22360i	1.64734	−	0.733445i	0.647748	−	0.761854i	$-0.275711\pi$
$97$	16.2245	−	7.22360i	1.64734	−	0.733445i	0.999596	+	0.0284091i	$0.00904413\pi$
$98$	−3.61447			−0.365117
$99$	9.60401	+	2.60056i	0.965240	+	0.261366i
$100$	1.00000			0.100000
$101$	−11.6700	+	5.19584i	−1.16121	+	0.517005i	−0.894630	−	0.446807i	$-0.852561\pi$
$101$	−11.6700	+	5.19584i	−1.16121	+	0.517005i	−0.266582	+	0.963812i	$0.585894\pi$
$102$	−0.0420686	−	0.0934636i	−0.00416542	−	0.00925427i
$103$	−7.62786	+	8.47159i	−0.751595	+	0.834731i	−0.990672	−	0.136270i	$-0.956489\pi$
$103$	−7.62786	+	8.47159i	−0.751595	+	0.834731i	0.239077	+	0.971001i	$0.423155\pi$
$104$	3.10807	+	1.38380i	0.304771	+	0.135693i
$105$	3.02693	−	0.997128i	0.295398	−	0.0973097i
$106$	0.238204	+	0.0506318i	0.0231364	+	0.00491779i
$107$	−2.53552	+	7.80352i	−0.245118	+	0.754395i	0.750499	+	0.660871i	$0.229813\pi$
$107$	−2.53552	+	7.80352i	−0.245118	+	0.754395i	−0.995617	+	0.0935236i	$0.970187\pi$
$108$	4.46799	−	2.65275i	0.429933	−	0.255261i
$109$	13.9729			1.33836			0.669181	−	0.743100i	$-0.266645\pi$
$109$	13.9729			1.33836			0.669181	+	0.743100i	$0.266645\pi$
$110$	−1.83620	+	2.76195i	−0.175075	+	0.263341i
$111$	1.94240	+	0.622409i	0.184365	+	0.0590764i
$112$	−0.192330	+	1.82990i	−0.0181735	+	0.172909i
$113$	15.2200	−	3.23511i	1.43177	−	0.304333i	0.574209	−	0.818708i	$-0.305309\pi$
$113$	15.2200	−	3.23511i	1.43177	−	0.304333i	0.857565	+	0.514375i	$0.171976\pi$
$114$	−6.22984	−	3.56312i	−0.583478	−	0.333717i
$115$	0.722887	+	6.87781i	0.0674096	+	0.641359i
$116$	−6.34854	+	4.61249i	−0.589447	+	0.428259i
$117$	9.96599	−	2.20315i	0.921356	−	0.203681i
$118$	−1.80001	+	5.53987i	−0.165705	+	0.509986i
$119$	0.0994684	−	0.0442862i	0.00911825	−	0.00405971i
$120$	0.366996	+	1.69272i	0.0335020	+	0.154524i
$121$	−4.25671	−	10.1430i	−0.386973	−	0.922091i
$122$	5.71529	+	9.89917i	0.517438	+	0.896229i
$123$	1.49019	−	3.38396i	0.134365	−	0.305121i
$124$	4.99203	+	5.54421i	0.448298	+	0.497885i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	2.79873	+	4.75782i	0.249331	+	0.423860i
$127$	14.5326	−	10.5586i	1.28956	−	0.936922i	0.289766	−	0.957098i	$-0.406423\pi$
$127$	14.5326	−	10.5586i	1.28956	−	0.936922i	0.999796	+	0.0201756i	$0.00642254\pi$
$128$	−0.978148	−	0.207912i	−0.0864569	−	0.0183770i
$129$	3.72955	+	8.28592i	0.328369	+	0.729534i
$130$	−0.355627	+	3.38356i	−0.0311905	+	0.296758i
$131$	1.35199	+	2.34171i	0.118124	+	0.204596i	0.919024	−	0.394201i	$-0.128979\pi$
$131$	1.35199	+	2.34171i	0.118124	+	0.204596i	−0.800900	+	0.598798i	$0.795645\pi$
$132$	−5.34909	−	2.09456i	−0.465579	−	0.182308i
$133$	3.81201	−	6.60260i	0.330543	−	0.572518i
$134$	−1.76238	−	1.28044i	−0.152246	−	0.110613i
$135$	3.90360	+	3.42957i	0.335968	+	0.295170i
$136$	0.0182862	+	0.0562792i	0.00156803	+	0.00482590i
$137$	0.226922	+	2.15902i	0.0193872	+	0.184457i	0.999930	−	0.0118493i	$-0.00377185\pi$
$137$	0.226922	+	2.15902i	0.0193872	+	0.184457i	−0.980543	+	0.196307i	$0.937105\pi$
$138$	−11.3769	+	3.74778i	−0.968469	+	0.319032i
$139$	2.62936	−	2.92020i	0.223020	−	0.247688i	−0.621243	−	0.783618i	$-0.713372\pi$
$139$	2.62936	−	2.92020i	0.223020	−	0.247688i	0.844263	+	0.535930i	$0.180039\pi$
$140$	−1.79977	+	0.382553i	−0.152108	+	0.0323317i
$141$	−1.53899	+	0.168081i	−0.129606	+	0.0141550i
$142$	4.35602	−	7.54485i	0.365549	−	0.633150i
$143$	−8.69222	−	7.19514i	−0.726880	−	0.601688i
$144$	−2.73063	+	1.24245i	−0.227552	+	0.103537i
$145$	−6.34854	−	4.61249i	−0.527218	−	0.383046i
$146$	−7.09957	−	7.88487i	−0.587564	−	0.652556i
$147$	5.40895	−	3.15224i	0.446122	−	0.259992i
$148$	−1.07580	−	0.478978i	−0.0884305	−	0.0393718i
$149$	1.38786	+	0.617917i	0.113698	+	0.0506218i	0.462798	−	0.886464i	$-0.346846\pi$
$149$	1.38786	+	0.617917i	0.113698	+	0.0506218i	−0.349099	+	0.937086i	$0.613512\pi$
$150$	−1.49647	+	0.872114i	−0.122186	+	0.0712078i
$151$	−15.1990	−	16.8802i	−1.23687	−	1.37369i	−0.902179	−	0.431362i	$-0.858033\pi$
$151$	−15.1990	−	16.8802i	−1.23687	−	1.37369i	−0.334696	−	0.942326i	$-0.608634\pi$
$152$	3.35219	+	2.43551i	0.271899	+	0.197546i
$153$	0.144465	+	0.103177i	0.0116793	+	0.00834133i
$154$	2.24816	−	5.67332i	0.181162	−	0.457169i
$155$	−3.73024	+	6.46096i	−0.299620	+	0.518957i
$156$	−5.85795	+	0.639776i	−0.469012	+	0.0512231i
$157$	17.3932	−	3.69704i	1.38813	−	0.295056i	0.547562	−	0.836765i	$-0.315556\pi$
$157$	17.3932	−	3.69704i	1.38813	−	0.295056i	0.840566	+	0.541710i	$0.182223\pi$
$158$	5.65495	−	6.28046i	0.449884	−	0.499647i
$159$	−0.400621	+	0.131972i	−0.0317713	+	0.0104661i
$160$	−0.104528	−	0.994522i	−0.00826370	−	0.0786239i
$161$	−3.93216	−	12.1019i	−0.309898	−	0.953767i
$162$	−4.37271	+	7.86635i	−0.343552	+	0.618039i
$163$	−0.527811	−	0.383477i	−0.0413413	−	0.0300362i	0.566923	−	0.823771i	$-0.308134\pi$
$163$	−0.527811	−	0.383477i	−0.0413413	−	0.0300362i	−0.608264	+	0.793735i	$0.708134\pi$
$164$	−1.06739	+	1.84877i	−0.0833490	+	0.144365i
$165$	0.339087	−	5.73455i	0.0263979	−	0.446434i
$166$	5.07781	+	8.79502i	0.394114	+	0.682626i
$167$	0.401590	−	3.82087i	0.0310760	−	0.295668i	−0.967935	−	0.251201i	$-0.919174\pi$
$167$	0.401590	−	3.82087i	0.0310760	−	0.295668i	0.999011	−	0.0444668i	$-0.0141589\pi$
$168$	−1.30807	−	2.90612i	−0.100919	−	0.224212i
$169$	1.39388	+	0.296279i	0.107222	+	0.0227907i
$170$	−0.0478740	+	0.0347825i	−0.00367177	+	0.00266769i
$171$	12.4302	−	0.101037i	0.950561	−	0.00772650i
$172$	−1.62115	−	4.98938i	−0.123611	−	0.380436i
$173$	0.334927	+	0.371974i	0.0254640	+	0.0282807i	0.755742	−	0.654869i	$-0.227276\pi$
$173$	0.334927	+	0.371974i	0.0254640	+	0.0282807i	−0.730278	+	0.683150i	$0.760610\pi$
$174$	5.47777	−	12.4391i	0.415269	−	0.943005i
$175$	−0.919990	−	1.59347i	−0.0695447	−	0.120455i
$176$	2.93875	+	1.53744i	0.221517	+	0.115889i
$177$	−2.13774	−	9.86005i	−0.160682	−	0.741127i
$178$	−7.48204	+	3.33122i	−0.560802	+	0.249685i
$179$	−1.20978	+	3.72333i	−0.0904235	+	0.278295i	−0.986034	−	0.166544i	$-0.946739\pi$
$179$	−1.20978	+	3.72333i	−0.0904235	+	0.278295i	0.895610	+	0.444839i	$0.146739\pi$
$180$	−2.02545	−	2.21304i	−0.150968	−	0.164951i
$181$	10.3795	−	7.54114i	0.771501	−	0.560528i	−0.130915	−	0.991394i	$-0.541792\pi$
$181$	10.3795	−	7.54114i	0.771501	−	0.560528i	0.902416	+	0.430865i	$0.141792\pi$
$182$	−0.654346	−	6.22569i	−0.0485034	−	0.461479i
$183$	−17.1860	−	9.82941i	−1.27042	−	0.726611i
$184$	6.76457	−	1.43785i	0.498691	−	0.106000i
$185$	0.123094	−	1.17116i	0.00905006	−	0.0861056i
$186$	−12.3056	−	3.94311i	−0.902290	−	0.289123i
$187$	−0.00816097	−	0.196093i	−0.000596790	−	0.0143397i
$188$	0.893820			0.0651886
$189$	−8.33758	−	4.67910i	−0.606469	−	0.340355i
$190$	−1.28042	+	3.94074i	−0.0928917	+	0.285891i
$191$	−6.17144	−	1.31178i	−0.446550	−	0.0949170i	−0.0208521	−	0.999783i	$-0.506638\pi$
$191$	−6.17144	−	1.31178i	−0.446550	−	0.0949170i	−0.425698	+	0.904866i	$0.639971\pi$
$192$	1.64509	−	0.541923i	0.118724	−	0.0391100i
$193$	−9.66933	−	4.30506i	−0.696014	−	0.309885i	0.0280615	−	0.999606i	$-0.491067\pi$
$193$	−9.66933	−	4.30506i	−0.696014	−	0.309885i	−0.724075	+	0.689721i	$0.757733\pi$
$194$	11.8837	−	13.1982i	0.853199	−	0.947573i
$195$	−2.41867	−	5.37354i	−0.173205	−	0.384807i
$196$	−3.30199	+	1.47014i	−0.235856	+	0.105010i
$197$	−0.496020			−0.0353400			−0.0176700	−	0.999844i	$-0.505625\pi$
$197$	−0.496020			−0.0353400			−0.0176700	+	0.999844i	$0.505625\pi$
$198$	9.83145	−	1.53057i	0.698690	−	0.108773i
$199$	8.05807			0.571221			0.285611	−	0.958346i	$-0.407804\pi$
$199$	8.05807			0.571221			0.285611	+	0.958346i	$0.407804\pi$
$200$	0.913545	−	0.406737i	0.0645974	−	0.0287606i
$201$	3.75403	+	0.379146i	0.264789	+	0.0267429i
$202$	−8.54778	+	9.49327i	−0.601419	+	0.667944i
$203$	13.1904	+	5.87277i	0.925788	+	0.412187i
$204$	−0.0764467	−	0.0682724i	−0.00535234	−	0.00478002i
$205$	−2.08813	−	0.443845i	−0.145841	−	0.0309995i
$206$	−3.52269	+	10.8417i	−0.245437	+	0.755378i
$207$	13.7567	−	15.5304i	0.956159	−	1.07944i
$208$	3.40220			0.235900
$209$	−8.53299	−	10.7725i	−0.590239	−	0.745147i
$210$	2.35967	−	2.14209i	0.162833	−	0.147818i
$211$	−2.15623	+	20.5151i	−0.148441	+	1.41232i	0.626074	+	0.779764i	$0.284661\pi$
$211$	−2.15623	+	20.5151i	−0.148441	+	1.41232i	−0.774515	+	0.632556i	$0.782006\pi$
$212$	0.238204	−	0.0506318i	0.0163599	−	0.00347741i
$213$	0.0613258	+	15.0896i	0.00420197	+	1.03392i
$214$	0.857667	+	8.16016i	0.0586289	+	0.557817i
$215$	4.24422	−	3.08360i	0.289453	−	0.210300i
$216$	3.00274	−	4.24070i	0.204311	−	0.288543i
$217$	4.24191	−	13.0553i	0.287960	−	0.886249i
$218$	12.7649	−	5.68329i	0.864547	−	0.384921i
$219$	17.5008	+	5.60782i	1.18259	+	0.378941i
$220$	−0.554071	+	3.27002i	−0.0373555	+	0.220464i
$221$	−0.100663	−	0.174354i	−0.00677136	−	0.0117283i
$222$	2.02763	−	0.221448i	0.136086	−	0.0148626i
$223$	16.9069	+	18.7770i	1.13217	+	1.25740i	0.962317	+	0.271930i	$0.0876619\pi$
$223$	16.9069	+	18.7770i	1.13217	+	1.25740i	0.169851	+	0.985470i	$0.445671\pi$
$224$	0.568585	+	1.74992i	0.0379902	+	0.116922i
$225$	1.47883	−	2.61018i	0.0985889	−	0.174012i
$226$	12.5883	−	9.14594i	0.837361	−	0.608379i
$227$	−3.25027	−	0.690866i	−0.215728	−	0.0458544i	0.0987797	−	0.995109i	$-0.468506\pi$
$227$	−3.25027	−	0.690866i	−0.215728	−	0.0458544i	−0.314508	+	0.949255i	$0.601839\pi$
$228$	−7.14049	−	0.721168i	−0.472891	−	0.0477605i
$229$	1.89369	−	18.0172i	0.125138	−	1.19061i	−0.734102	−	0.679039i	$-0.762397\pi$
$229$	1.89369	−	18.0172i	0.125138	−	1.19061i	0.859240	−	0.511572i	$-0.170937\pi$
$230$	3.45785	+	5.98917i	0.228004	+	0.394914i
$231$	1.58349	+	10.4506i	0.104186	+	0.687599i
$232$	−3.92361	+	6.79590i	−0.257598	+	0.446173i
$233$	−3.39105	−	2.46374i	−0.222155	−	0.161405i	0.471141	−	0.882058i	$-0.343842\pi$
$233$	−3.39105	−	2.46374i	−0.222155	−	0.161405i	−0.693296	+	0.720653i	$0.743842\pi$
$234$	8.20828	−	6.06621i	0.536592	−	0.396561i
$235$	0.276206	+	0.850074i	0.0180177	+	0.0554527i
$236$	0.608874	+	5.79305i	0.0396343	+	0.377096i
$237$	−2.98518	+	14.3303i	−0.193908	+	0.930851i
$238$	0.0728561	−	0.0809149i	0.00472256	−	0.00524493i
$239$	−7.46497	+	1.58673i	−0.482869	+	0.102637i	−0.442913	−	0.896565i	$-0.646055\pi$
$239$	−7.46497	+	1.58673i	−0.482869	+	0.102637i	−0.0399556	+	0.999201i	$0.512722\pi$
$240$	1.02376	+	1.39711i	0.0660834	+	0.0901830i
$241$	9.18066	−	15.9014i	0.591378	−	1.02430i	−0.402669	−	0.915346i	$-0.631917\pi$
$241$	9.18066	−	15.9014i	0.591378	−	1.02430i	0.994047	−	0.108952i	$-0.0347494\pi$
$242$	−8.01423	−	7.53473i	−0.515174	−	0.484351i
$243$	−0.316743	−	15.5852i	−0.0203191	−	0.999794i
$244$	9.24753	+	6.71873i	0.592013	+	0.430122i
$245$	−2.41856	−	2.68608i	−0.154516	−	0.171607i
$246$	−0.0150271	−	3.69751i	−0.000958093	−	0.235745i
$247$	−12.8784	−	5.73383i	−0.819432	−	0.364835i
$248$	6.81548	+	3.03445i	0.432783	+	0.192688i
$249$	−15.2690	−	8.73304i	−0.967636	−	0.553434i
$250$	0.669131	+	0.743145i	0.0423195	+	0.0470006i
$251$	16.5695	+	12.0384i	1.04585	+	0.759858i	0.971420	−	0.237368i	$-0.0762848\pi$
$251$	16.5695	+	12.0384i	1.04585	+	0.759858i	0.0744347	+	0.997226i	$0.476285\pi$
$252$	4.49195	+	3.20813i	0.282966	+	0.202093i
$253$	−22.8911	−	1.44694i	−1.43915	−	0.0909685i
$254$	8.98166	−	15.5567i	0.563559	−	0.976114i
$255$	0.0413076	−	0.0938024i	0.00258678	−	0.00587414i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	14.7851	−	16.4205i	0.922268	−	1.02428i	−0.0773596	−	0.997003i	$-0.524649\pi$
$257$	14.7851	−	16.4205i	0.922268	−	1.02428i	0.999628	−	0.0272794i	$-0.00868438\pi$
$258$	6.77730	+	6.05262i	0.421936	+	0.376819i
$259$	0.226491	+	2.15491i	0.0140734	+	0.133900i
$260$	1.05134	+	3.23569i	0.0652012	+	0.200669i
$261$	2.65100	+	23.3919i	0.164093	+	1.44793i
$262$	2.18756	+	1.58936i	0.135148	+	0.0981908i
$263$	−9.09464	+	15.7524i	−0.560799	+	0.971333i	0.436628	+	0.899642i	$0.356173\pi$
$263$	−9.09464	+	15.7524i	−0.560799	+	0.971333i	−0.997427	+	0.0716905i	$0.977161\pi$
$264$	−5.73858	+	0.262194i	−0.353185	+	0.0161369i
$265$	0.121763	+	0.210899i	0.00747982	+	0.0129554i
$266$	0.796927	−	7.58226i	0.0488628	−	0.464898i
$267$	8.29143	−	11.5103i	0.507427	−	0.704416i
$268$	−2.13081	−	0.452919i	−0.130160	−	0.0276664i
$269$	−14.2368	+	10.3437i	−0.868034	+	0.630664i	−0.930059	−	0.367411i	$-0.880244\pi$
$269$	−14.2368	+	10.3437i	−0.868034	+	0.630664i	0.0620244	+	0.998075i	$0.480244\pi$
$270$	4.96104	+	1.54533i	0.301920	+	0.0940458i
$271$	−8.91756	−	27.4454i	−0.541703	−	1.66719i	−0.728702	−	0.684831i	$-0.759876\pi$
$271$	−8.91756	−	27.4454i	−0.541703	−	1.66719i	0.186999	−	0.982360i	$-0.440124\pi$
$272$	0.0395961	+	0.0439760i	0.00240087	+	0.00266643i
$273$	6.40872	+	8.74588i	0.387873	+	0.529325i
$274$	1.08546	+	1.88006i	0.0655747	+	0.113579i
$275$	−3.28119	+	0.483538i	−0.197863	+	0.0291584i
$276$	−8.86899	+	8.05118i	−0.533851	+	0.484624i
$277$	1.01709	−	0.452839i	0.0611113	−	0.0272085i	−0.375953	−	0.926639i	$-0.622685\pi$
$277$	1.01709	−	0.452839i	0.0611113	−	0.0272085i	0.437065	+	0.899430i	$0.356018\pi$
$278$	1.21429	−	3.73719i	0.0728282	−	0.224142i
$279$	21.8538	−	4.83115i	1.30835	−	0.289233i
$280$	−1.48857	+	1.08151i	−0.0889594	+	0.0646328i
$281$	2.91351	+	27.7202i	0.173806	+	1.65365i	0.639564	+	0.768738i	$0.279115\pi$
$281$	2.91351	+	27.7202i	0.173806	+	1.65365i	−0.465758	+	0.884912i	$0.654218\pi$
$282$	−1.33757	+	0.779514i	−0.0796513	+	0.0464194i
$283$	14.1282	−	3.00304i	0.839832	−	0.178512i	0.232138	−	0.972683i	$-0.425428\pi$
$283$	14.1282	−	3.00304i	0.839832	−	0.178512i	0.607694	+	0.794171i	$0.292095\pi$
$284$	0.910657	−	8.66432i	0.0540375	−	0.514133i
$285$	−1.52066	−	7.01386i	−0.0900762	−	0.415465i
$286$	−10.8673	−	3.03764i	−0.642595	−	0.179619i
$287$	3.92795			0.231859
$288$	−1.98920	+	2.24568i	−0.117215	+	0.132328i
$289$	−5.25221	+	16.1646i	−0.308953	+	0.950861i
$290$	−7.67575	−	1.63153i	−0.450735	−	0.0958068i
$291$	−6.27324	+	30.1146i	−0.367744	+	1.76535i
$292$	−9.69284	−	4.31553i	−0.567231	−	0.252547i
$293$	−5.65923	+	6.28521i	−0.330615	+	0.367186i	−0.885417	−	0.464797i	$-0.846127\pi$
$293$	−5.65923	+	6.28521i	−0.330615	+	0.367186i	0.554802	+	0.831982i	$0.312794\pi$
$294$	3.65919	−	5.07973i	0.213408	−	0.296256i
$295$	−5.32137	+	2.36923i	−0.309822	+	0.137942i
$296$	−1.17761			−0.0684474
$297$	−13.3776	+	10.8646i	−0.776248	+	0.630428i
$298$	1.51921			0.0880053
$299$	−21.4944	+	9.56994i	−1.24306	+	0.553444i
$300$	−1.01237	+	1.40538i	−0.0584492	+	0.0811399i
$301$	−6.45898	+	7.17342i	−0.372289	+	0.413469i
$302$	−20.7507	−	9.23882i	−1.19407	−	0.531634i
$303$	4.51226	−	21.6610i	0.259223	−	1.24439i
$304$	4.05299	+	0.861490i	0.232455	+	0.0494098i
$305$	−3.53224	+	10.8711i	−0.202256	+	0.622479i
$306$	0.173941	+	0.0354972i	0.00994356	+	0.00202924i
$307$	1.46285			0.0834890			0.0417445	−	0.999128i	$-0.486708\pi$
$307$	1.46285			0.0834890			0.0417445	+	0.999128i	$0.486708\pi$
$308$	−0.253754	−	6.09724i	−0.0144590	−	0.347423i
$309$	−4.18363	−	19.2965i	−0.237998	−	1.09774i
$310$	−0.779832	+	7.41960i	−0.0442915	+	0.421405i
$311$	−24.7624	+	5.26341i	−1.40415	+	0.298461i	−0.846841	−	0.531846i	$-0.821498\pi$
$311$	−24.7624	+	5.26341i	−1.40415	+	0.298461i	−0.557306	+	0.830307i	$0.688165\pi$
$312$	−5.09129	+	2.96711i	−0.288237	+	0.167979i
$313$	0.532874	+	5.06995i	0.0301198	+	0.286571i	0.999206	+	0.0398474i	$0.0126872\pi$
$313$	0.532874	+	5.06995i	0.0301198	+	0.286571i	−0.969086	+	0.246723i	$0.920646\pi$
$314$	14.3857	−	10.4519i	0.811835	−	0.589832i
$315$	−1.66303	+	5.26346i	−0.0937010	+	0.296563i
$316$	2.61156	−	8.03756i	0.146912	−	0.452148i
$317$	−10.7908	+	4.80436i	−0.606070	+	0.269840i	−0.686742	−	0.726901i	$-0.740960\pi$
$317$	−10.7908	+	4.80436i	−0.606070	+	0.269840i	0.0806723	+	0.996741i	$0.474293\pi$
$318$	−0.312308	+	0.283510i	−0.0175133	+	0.0158984i
$319$	18.6004	−	18.2042i	1.04143	−	1.01924i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−8.40006	−	11.4634i	−0.468846	−	0.639826i
$322$	−8.51451	−	9.45632i	−0.474495	−	0.526980i
$323$	−0.0757697	−	0.233195i	−0.00421594	−	0.0129753i
$324$	−0.795133	+	8.96481i	−0.0441740	+	0.498045i
$325$	−2.75244	+	1.99976i	−0.152678	+	0.110927i
$326$	−0.638153	−	0.135644i	−0.0353440	−	0.00751261i
$327$	−14.1458	+	19.6373i	−0.782262	+	1.08595i
$328$	−0.223145	+	2.12308i	−0.0123211	+	0.117228i
$329$	−0.822306	−	1.42428i	−0.0453352	−	0.0785228i
$330$	−2.02268	−	5.37669i	−0.111345	−	0.295977i
$331$	−1.99365	+	3.45310i	−0.109581	+	0.189799i	−0.915600	−	0.402089i	$-0.868284\pi$
$331$	−1.99365	+	3.45310i	−0.109581	+	0.189799i	0.806020	+	0.591889i	$0.201617\pi$
$332$	8.21607	+	5.96932i	0.450915	+	0.327609i
$333$	−2.84115	+	2.09971i	−0.155694	+	0.115064i
$334$	−1.18722	−	3.65388i	−0.0649617	−	0.199932i
$335$	−0.227707	−	2.16648i	−0.0124409	−	0.118368i
$336$	−2.37700	−	2.12284i	−0.129676	−	0.115810i
$337$	−12.5855	+	13.9776i	−0.685574	+	0.761407i	−0.981010	−	0.193955i	$-0.937868\pi$
$337$	−12.5855	+	13.9776i	−0.685574	+	0.761407i	0.295436	+	0.955362i	$0.404535\pi$
$338$	1.39388	−	0.296279i	0.0758173	−	0.0161155i
$339$	−10.8617	+	24.6650i	−0.589926	+	1.33962i
$340$	−0.0295877	+	0.0512475i	−0.00160462	+	0.00277928i
$341$	−19.0606	−	15.7778i	−1.03219	−	0.854414i
$342$	11.3145	−	5.14812i	0.611816	−	0.278378i
$343$	15.8004	+	11.4797i	0.853144	+	0.619845i
$344$	−3.51035	−	3.89864i	−0.189266	−	0.210201i
$345$	−10.3978	−	5.94696i	−0.559799	−	0.320174i
$346$	0.457267	+	0.203588i	0.0245828	+	0.0109450i
$347$	−27.7436	−	12.3523i	−1.48936	−	0.663104i	−0.509077	−	0.860721i	$-0.670013\pi$
$347$	−27.7436	−	12.3523i	−1.48936	−	0.663104i	−0.980279	+	0.197617i	$0.936680\pi$
$348$	−0.0552382	−	13.5917i	−0.00296108	−	0.728591i
$349$	18.2310	+	20.2475i	0.975881	+	1.08383i	0.996463	+	0.0840371i	$0.0267814\pi$
$349$	18.2310	+	20.2475i	0.975881	+	1.08383i	−0.0205820	+	0.999788i	$0.506552\pi$
$350$	−1.48857	−	1.08151i	−0.0795677	−	0.0578093i
$351$	−6.99300	+	16.2364i	−0.373259	+	0.866638i
$352$	3.31002	+	0.209226i	0.176425	+	0.0111518i
$353$	8.22771	−	14.2508i	0.437917	−	0.758495i	−0.559612	−	0.828755i	$-0.689050\pi$
$353$	8.22771	−	14.2508i	0.437917	−	0.758495i	0.997529	+	0.0702604i	$0.0223830\pi$
$354$	−5.96336	−	8.13811i	−0.316949	−	0.432536i
$355$	8.52167	−	1.81134i	0.452283	−	0.0961357i
$356$	−5.48025	+	6.08644i	−0.290453	+	0.322581i
$357$	−0.0384598	+	0.184625i	−0.00203551	+	0.00977141i
$358$	0.409223	+	3.89350i	0.0216281	+	0.205778i
$359$	4.48206	+	13.7943i	0.236554	+	0.728038i	0.996911	+	0.0785333i	$0.0250237\pi$
$359$	4.48206	+	13.7943i	0.236554	+	0.728038i	−0.760358	+	0.649505i	$0.774976\pi$
$360$	−2.75046	−	1.19789i	−0.144962	−	0.0631345i
$361$	1.48139	+	1.07629i	0.0779680	+	0.0566470i
$362$	6.41487	−	11.1109i	0.337158	−	0.583975i
$363$	18.5642	+	4.28617i	0.974367	+	0.224965i
$364$	−3.12999	−	5.42130i	−0.164056	−	0.284154i
$365$	1.10906	−	10.5520i	0.0580509	−	0.552318i
$366$	−19.6981	−	1.98945i	−1.02964	−	0.103990i
$367$	11.7560	+	2.49881i	0.613657	+	0.130437i	0.504246	−	0.863560i	$-0.331770\pi$
$367$	11.7560	+	2.49881i	0.613657	+	0.130437i	0.109410	+	0.993997i	$0.465104\pi$
$368$	5.59492	−	4.06494i	0.291655	−	0.211900i
$369$	3.24714	+	5.52010i	0.169039	+	0.287365i
$370$	−0.363903	−	1.11998i	−0.0189184	−	0.0582248i
$371$	−0.299825	−	0.332990i	−0.0155662	−	0.0172880i
$372$	−12.8455	+	1.40292i	−0.666010	+	0.0727383i
$373$	−6.90703	−	11.9633i	−0.357633	−	0.619438i	0.629932	−	0.776650i	$-0.283083\pi$
$373$	−6.90703	−	11.9633i	−0.357633	−	0.619438i	−0.987565	+	0.157212i	$0.949749\pi$
$374$	−0.0872137	−	0.175821i	−0.00450971	−	0.00909147i
$375$	−1.64944	−	0.528534i	−0.0851767	−	0.0272934i
$376$	0.816546	−	0.363550i	0.0421101	−	0.0187486i
$377$	8.25009	−	25.3912i	0.424901	−	1.30771i
$378$	−9.51992	−	0.883376i	−0.489652	−	0.0454360i
$379$	0.661011	−	0.480253i	0.0339539	−	0.0246689i	−0.570679	−	0.821173i	$-0.693320\pi$
$379$	0.661011	−	0.480253i	0.0339539	−	0.0246689i	0.604633	+	0.796504i	$0.293320\pi$
$380$	0.433118	+	4.12084i	0.0222185	+	0.211395i
$381$	0.126447	+	31.1131i	0.00647809	+	1.59397i
$382$	−6.17144	+	1.31178i	−0.315758	+	0.0671165i
$383$	−0.912491	+	8.68177i	−0.0466261	+	0.443618i	0.946158	+	0.323704i	$0.104928\pi$
$383$	−0.912491	+	8.68177i	−0.0466261	+	0.443618i	−0.992784	+	0.119913i	$0.961738\pi$
$384$	1.28244	−	1.16419i	0.0654444	−	0.0594098i
$385$	5.72041	−	2.12549i	0.291539	−	0.108325i
$386$	−10.5844			−0.538732
$387$	−15.4206	−	3.14697i	−0.783872	−	0.159969i
$388$	5.48811	−	16.8907i	0.278616	−	0.857493i
$389$	27.1632	+	5.77372i	1.37723	+	0.292739i	0.836274	−	0.548312i	$-0.184730\pi$
$389$	27.1632	+	5.77372i	1.37723	+	0.292739i	0.540955	+	0.841051i	$0.318063\pi$
$390$	−4.39518	−	3.92521i	−0.222559	−	0.198761i
$391$	−0.373859	−	0.166453i	−0.0189069	−	0.00841788i
$392$	−2.41856	+	2.68608i	−0.122156	+	0.135667i
$393$	−4.65972	−	0.470617i	−0.235052	−	0.0237395i
$394$	−0.453137	+	0.201750i	−0.0228287	+	0.0101640i
$395$	8.45119			0.425226
$396$	8.35893	−	5.39706i	0.420052	−	0.271212i
$397$	15.3874			0.772271			0.386136	−	0.922442i	$-0.373810\pi$
$397$	15.3874			0.772271			0.386136	+	0.922442i	$0.373810\pi$
$398$	7.36141	−	3.27751i	0.368994	−	0.164287i
$399$	5.42002	+	12.0416i	0.271340	+	0.602835i
$400$	0.669131	−	0.743145i	0.0334565	−	0.0371572i
$401$	−32.4424	−	14.4443i	−1.62009	−	0.721313i	−0.622000	−	0.783017i	$-0.713680\pi$
$401$	−32.4424	−	14.4443i	−1.62009	−	0.721313i	−0.998094	+	0.0617045i	$0.980346\pi$
$402$	3.58369	−	1.18054i	0.178738	−	0.0588798i
$403$	−24.8274	−	5.27722i	−1.23674	−	0.262877i
$404$	−3.94752	+	12.1492i	−0.196397	+	0.604447i
$405$	−8.77175	+	2.01406i	−0.435872	+	0.100080i
$406$	14.4387			0.716583
$407$	3.76152	+	1.05143i	0.186451	+	0.0521173i
$408$	−0.0976064	−	0.0312763i	−0.00483224	−	0.00154841i
$409$	−3.53382	+	33.6221i	−0.174736	+	1.66250i	0.458611	+	0.888637i	$0.348347\pi$
$409$	−3.53382	+	33.6221i	−0.174736	+	1.66250i	−0.633348	+	0.773867i	$0.718320\pi$
$410$	−2.08813	+	0.443845i	−0.103125	+	0.0219199i
$411$	−3.26398	−	1.86681i	−0.161000	−	0.0920831i
$412$	1.19159	+	11.3372i	0.0587053	+	0.558544i
$413$	8.67089	−	6.29977i	0.426667	−	0.309991i
$414$	6.25061	−	19.7831i	0.307201	−	0.972287i
$415$	−3.13826	+	9.65856i	−0.154051	+	0.474120i
$416$	3.10807	−	1.38380i	0.152385	−	0.0678464i
$417$	1.44212	+	6.65159i	0.0706208	+	0.325730i
$418$	−12.1768	−	6.37045i	−0.595588	−	0.311589i
$419$	−4.56087	−	7.89966i	−0.222813	−	0.385924i	0.732848	−	0.680392i	$-0.238191\pi$
$419$	−4.56087	−	7.89966i	−0.222813	−	0.385924i	−0.955661	+	0.294469i	$0.904857\pi$
$420$	1.28440	−	2.91666i	0.0626724	−	0.142318i
$421$	16.1682	+	17.9566i	0.787988	+	0.875149i	0.994654	−	0.103262i	$-0.0329281\pi$
$421$	16.1682	+	17.9566i	0.787988	+	0.875149i	−0.206666	+	0.978412i	$0.566261\pi$
$422$	6.37444	+	19.6185i	0.310303	+	0.955015i
$423$	1.32181	−	2.33303i	0.0642687	−	0.113436i
$424$	0.197016	−	0.143141i	0.00956795	−	0.00695152i
$425$	−0.0578824	−	0.0123033i	−0.00280771	−	0.000596796i
$426$	6.19351	+	13.7601i	0.300076	+	0.666678i
$427$	2.19845	−	20.9168i	0.106390	−	1.01224i
$428$	4.10255	+	7.10583i	0.198304	+	0.343473i
$429$	18.9117	−	4.93177i	0.913065	−	0.238108i
$430$	2.62307	−	4.54329i	0.126496	−	0.219097i
$431$	−2.37533	−	1.72578i	−0.114416	−	0.0831280i	0.529106	−	0.848556i	$-0.322527\pi$
$431$	−2.37533	−	1.72578i	−0.114416	−	0.0831280i	−0.643522	+	0.765428i	$0.722527\pi$
$432$	1.01829	−	5.09540i	0.0489927	−	0.245152i
$433$	3.53014	+	10.8647i	0.169648	+	0.522122i	0.999349	−	0.0360862i	$-0.0114891\pi$
$433$	3.53014	+	10.8647i	0.169648	+	0.522122i	−0.829701	+	0.558208i	$0.811489\pi$
$434$	−1.43487	−	13.6519i	−0.0688762	−	0.655313i
$435$	12.9094	−	4.25260i	0.618958	−	0.203896i
$436$	9.34970	−	10.3839i	0.447769	−	0.497298i
$437$	−28.0293	+	5.95780i	−1.34082	+	0.285000i
$438$	18.2687	−	1.99521i	0.872911	−	0.0953349i
$439$	−3.66993	+	6.35651i	−0.175156	+	0.303380i	−0.940215	−	0.340580i	$-0.889376\pi$
$439$	−3.66993	+	6.35651i	−0.175156	+	0.303380i	0.765059	+	0.643960i	$0.222710\pi$
$440$	0.823866	+	3.21267i	0.0392763	+	0.153158i
$441$	−1.04576	+	10.7929i	−0.0497979	+	0.513947i
$442$	−0.162877	−	0.118337i	−0.00774726	−	0.00562872i
$443$	20.4289	+	22.6886i	0.970607	+	1.07797i	0.996929	+	0.0783149i	$0.0249539\pi$
$443$	20.4289	+	22.6886i	0.970607	+	1.07797i	−0.0263216	+	0.999654i	$0.508379\pi$
$444$	1.76226	−	1.02701i	0.0836332	−	0.0487399i
$445$	−7.48204	−	3.33122i	−0.354683	−	0.157915i
$446$	23.0825	+	10.2770i	1.09299	+	0.486629i
$447$	−2.27345	+	1.32492i	−0.107530	+	0.0626667i
$448$	1.23119	+	1.36737i	0.0581681	+	0.0646022i
$449$	18.5288	+	13.4620i	0.874429	+	0.635310i	0.931772	−	0.363045i	$-0.118263\pi$
$449$	18.5288	+	13.4620i	0.874429	+	0.635310i	−0.0573425	+	0.998355i	$0.518263\pi$
$450$	0.289324	−	2.98602i	0.0136389	−	0.140762i
$451$	2.60835	−	6.58229i	0.122822	−	0.309948i
$452$	7.78000	−	13.4754i	0.365940	−	0.633827i
$453$	39.1101	−	4.27141i	1.83755	−	0.200688i
$454$	−3.25027	+	0.690866i	−0.152543	+	0.0324240i
$455$	4.18875	−	4.65207i	0.196371	−	0.218093i
$456$	−6.81649	+	2.24548i	−0.319211	+	0.105154i
$457$	−1.35604	−	12.9019i	−0.0634330	−	0.603525i	−0.979352	−	0.202162i	$-0.935203\pi$
$457$	−1.35604	−	12.9019i	−0.0634330	−	0.603525i	0.915919	−	0.401363i	$-0.131463\pi$
$458$	−5.59830	−	17.2298i	−0.261591	−	0.805095i
$459$	−0.291255	+	0.0985763i	−0.0135946	+	0.00460115i
$460$	5.59492	+	4.06494i	0.260864	+	0.189529i
$461$	17.4901	−	30.2937i	0.814593	−	1.41092i	−0.0950261	−	0.995475i	$-0.530293\pi$
$461$	17.4901	−	30.2937i	0.814593	−	1.41092i	0.909620	−	0.415442i	$-0.136373\pi$
$462$	5.69723	+	8.90303i	0.265059	+	0.414206i
$463$	−10.5004	−	18.1873i	−0.487996	−	0.845234i	0.511909	−	0.859040i	$-0.328939\pi$
$463$	−10.5004	−	18.1873i	−0.487996	−	0.845234i	−0.999905	+	0.0138059i	$0.995605\pi$
$464$	−0.820259	+	7.80424i	−0.0380796	+	0.362303i
$465$	−5.30375	−	11.7833i	−0.245955	−	0.546437i
$466$	−4.09997	−	0.871475i	−0.189927	−	0.0403703i
$467$	−13.5456	+	9.84147i	−0.626817	+	0.455409i	−0.855296	−	0.518140i	$-0.826625\pi$
$467$	−13.5456	+	9.84147i	−0.626817	+	0.455409i	0.228479	+	0.973549i	$0.426625\pi$
$468$	5.03129	−	8.88037i	0.232571	−	0.410495i
$469$	1.23862	+	3.81207i	0.0571940	+	0.176025i
$470$	0.598083	+	0.664238i	0.0275875	+	0.0306390i
$471$	−12.4126	+	28.1869i	−0.571942	+	1.29878i
$472$	2.91248	+	5.04456i	0.134058	+	0.232195i
$473$	7.73184	+	15.5872i	0.355510	+	0.716700i
$474$	3.10155	+	14.3055i	0.142459	+	0.657075i
$475$	−3.78531	+	1.68533i	−0.173682	+	0.0773282i
$476$	0.0336463	−	0.103553i	0.00154218	−	0.00474633i
$477$	0.220105	−	0.696631i	0.0100779	−	0.0318966i
$478$	−6.17421	+	4.48582i	−0.282402	+	0.205177i
$479$	1.08261	+	10.3003i	0.0494657	+	0.470634i	0.991014	+	0.133757i	$0.0427041\pi$
$479$	1.08261	+	10.3003i	0.0494657	+	0.470634i	−0.941549	+	0.336877i	$0.890629\pi$
$480$	1.50351	+	0.859922i	0.0686254	+	0.0392499i
$481$	3.91893	−	0.832994i	0.178688	−	0.0379812i
$482$	1.91928	−	18.2607i	0.0874208	−	0.831754i
$483$	20.9887	+	6.72546i	0.955019	+	0.306019i
$484$	−10.3860	−	3.62364i	−0.472091	−	0.164711i
$485$	17.7599			0.806435
$486$	−6.62845	−	14.1090i	−0.300672	−	0.639997i
$487$	11.3536	−	34.9427i	0.514480	−	1.58341i	−0.269747	−	0.962931i	$-0.586940\pi$
$487$	11.3536	−	34.9427i	0.514480	−	1.58341i	0.784227	−	0.620474i	$-0.213060\pi$
$488$	11.1808	+	2.37655i	0.506131	+	0.107581i
$489$	1.07327	−	0.353556i	0.0485351	−	0.0159884i
$490$	−3.30199	−	1.47014i	−0.149169	−	0.0664141i
$491$	−7.18506	+	7.97981i	−0.324257	+	0.360124i	−0.883129	−	0.469130i	$-0.844568\pi$
$491$	−7.18506	+	7.97981i	−0.324257	+	0.360124i	0.558872	+	0.829254i	$0.311234\pi$
$492$	−1.51764	−	3.37173i	−0.0684205	−	0.152009i
$493$	0.424217	−	0.188874i	0.0191058	−	0.00850644i
$494$	−14.0971			−0.634261
$495$	7.71596	+	6.28203i	0.346807	+	0.282356i
$496$	7.46047			0.334985
$497$	−14.6441	+	6.51998i	−0.656879	+	0.292461i
$498$	−17.5010	−	1.76755i	−0.784239	−	0.0792058i
$499$	−3.93910	+	4.37481i	−0.176338	+	0.195843i	−0.824834	−	0.565375i	$-0.808732\pi$
$499$	−3.93910	+	4.37481i	−0.176338	+	0.195843i	0.648496	+	0.761218i	$0.275398\pi$
$500$	0.913545	+	0.406737i	0.0408550	+	0.0181898i
$501$	4.96324	+	4.43253i	0.221741	+	0.198031i
$502$	20.0334	+	4.25823i	0.894135	+	0.190054i
$503$	5.20108	−	16.0073i	0.231905	−	0.713730i	−0.765612	−	0.643303i	$-0.777564\pi$
$503$	5.20108	−	16.0073i	0.231905	−	0.713730i	0.997517	−	0.0704272i	$-0.0224362\pi$
$504$	5.40846	+	1.10374i	0.240912	+	0.0491643i
$505$	−12.7745			−0.568456
$506$	−21.5006	+	7.98879i	−0.955817	+	0.355145i
$507$	−1.82751	+	1.65900i	−0.0811627	+	0.0736787i
$508$	1.87768	−	17.8649i	0.0833085	−	0.792627i
$509$	−6.05949	+	1.28798i	−0.268582	+	0.0570889i	−0.340234	−	0.940341i	$-0.610506\pi$
$509$	−6.05949	+	1.28798i	−0.268582	+	0.0570889i	0.0716518	+	0.997430i	$0.477173\pi$
$510$	−0.000416548	−	0.102494i	−1.84450e−5	−	0.00453851i
$511$	2.04065	+	19.4155i	0.0902731	+	0.858891i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−12.4420	+	17.5715i	−0.549327	+	0.775801i
$514$	6.82803	−	21.0145i	0.301171	−	0.926910i
$515$	−10.4141	+	4.63666i	−0.458900	+	0.204316i
$516$	8.65319	+	2.77276i	0.380936	+	0.122064i
$517$	−2.93279	+	0.432196i	−0.128984	+	0.0190080i
$518$	1.08339	+	1.87649i	0.0476015	+	0.0824483i
$519$	−0.861837	+	0.0941255i	−0.0378305	+	0.00413165i
$520$	2.27652	+	2.52833i	0.0998319	+	0.110875i
$521$	7.83916	+	24.1265i	0.343440	+	1.05700i	0.962414	+	0.271588i	$0.0875487\pi$
$521$	7.83916	+	24.1265i	0.343440	+	1.05700i	−0.618974	+	0.785412i	$0.712451\pi$
$522$	11.9362	+	20.2914i	0.522432	+	0.888128i
$523$	−19.4029	+	14.0970i	−0.848430	+	0.616421i	−0.924713	−	0.380666i	$-0.875695\pi$
$523$	−19.4029	+	14.0970i	−0.848430	+	0.616421i	0.0762827	+	0.997086i	$0.475695\pi$
$524$	2.64489	+	0.562188i	0.115542	+	0.0245593i
$525$	3.17081	+	0.320242i	0.138385	+	0.0139765i
$526$	−1.90130	+	18.0896i	−0.0829005	+	0.788745i
$527$	−0.220739	−	0.382330i	−0.00961552	−	0.0166546i
$528$	−5.13581	+	2.57362i	−0.223507	+	0.112002i
$529$	−12.4134	+	21.5007i	−0.539714	+	0.934812i
$530$	0.197016	+	0.143141i	0.00855784	+	0.00621763i
$531$	16.0213	+	6.97768i	0.695267	+	0.302806i
$532$	−2.35595	−	7.25088i	−0.102144	−	0.314365i
$533$	−0.759184	−	7.22315i	−0.0328839	−	0.312870i
$534$	2.89295	−	13.8876i	0.125190	−	0.600974i
$535$	−5.49029	+	6.09758i	−0.237366	+	0.263622i
$536$	−2.13081	+	0.452919i	−0.0920372	+	0.0195631i
$537$	−4.00796	−	5.46960i	−0.172956	−	0.236031i
$538$	−8.79884	+	15.2400i	−0.379345	+	0.657045i
$539$	10.1236	−	6.42044i	0.436053	−	0.276548i
$540$	5.16068	−	0.606110i	0.222080	−	0.0260828i
$541$	−32.1227	−	23.3385i	−1.38106	−	1.00340i	−0.996780	−	0.0801830i	$-0.974450\pi$
$541$	−32.1227	−	23.3385i	−1.38106	−	1.00340i	−0.384281	−	0.923216i	$-0.625550\pi$
$542$	−19.3097	−	21.4455i	−0.829421	−	0.921165i
$543$	0.0903111	+	22.2216i	0.00387562	+	0.953620i
$544$	0.0540595	+	0.0240688i	0.00231778	+	0.00103194i
$545$	12.7649	+	5.68329i	0.546788	+	0.243445i
$546$	9.41193	+	5.38310i	0.402793	+	0.230375i
$547$	8.26341	+	9.17744i	0.353318	+	0.392399i	0.893436	−	0.449190i	$-0.148287\pi$
$547$	8.26341	+	9.17744i	0.353318	+	0.392399i	−0.540119	+	0.841589i	$0.681621\pi$
$548$	1.75630	+	1.27603i	0.0750256	+	0.0545093i
$549$	31.2127	−	14.2019i	1.33212	−	0.606121i
$550$	−2.80084	+	1.77631i	−0.119428	+	0.0757422i
$551$	16.2576	−	28.1591i	0.692599	−	1.19962i
$552$	−4.82752	+	10.9625i	−0.205473	+	0.466594i
$553$	−15.2102	+	3.23303i	−0.646804	+	0.137482i
$554$	0.744975	−	0.827379i	0.0316510	−	0.0351520i
$555$	1.52132	+	1.35864i	0.0645763	+	0.0576713i
$556$	−0.410747	−	3.90799i	−0.0174195	−	0.165736i
$557$	−3.82569	−	11.7743i	−0.162100	−	0.498891i	0.836711	−	0.547644i	$-0.184475\pi$
$557$	−3.82569	−	11.7743i	−0.162100	−	0.498891i	−0.998811	+	0.0487530i	$0.984475\pi$
$558$	17.9994	−	13.3022i	0.761976	−	0.563127i
$559$	14.4397	+	10.4910i	0.610733	+	0.443724i
$560$	−0.919990	+	1.59347i	−0.0388767	+	0.0673364i
$561$	0.283848	+	0.187050i	0.0119841	+	0.00789724i
$562$	13.9365	+	24.1387i	0.587874	+	1.01823i
$563$	−2.15345	+	20.4887i	−0.0907572	+	0.863497i	0.850538	+	0.525913i	$0.176276\pi$
$563$	−2.15345	+	20.4887i	−0.0907572	+	0.863497i	−0.941295	+	0.337584i	$0.890390\pi$
$564$	−0.904878	+	1.25616i	−0.0381022	+	0.0528939i
$565$	15.2200	+	3.23511i	0.640309	+	0.136102i
$566$	11.6853	−	8.48985i	0.491169	−	0.356855i
$567$	15.0167	−	6.98051i	0.630640	−	0.293154i
$568$	−2.69217	−	8.28565i	−0.112961	−	0.347658i
$569$	−23.4119	−	26.0016i	−0.981480	−	1.09004i	−0.995928	−	0.0901478i	$-0.971266\pi$
$569$	−23.4119	−	26.0016i	−0.981480	−	1.09004i	0.0144489	−	0.999896i	$-0.495401\pi$
$570$	−4.24199	−	5.78897i	−0.177677	−	0.242473i
$571$	−18.2089	−	31.5387i	−0.762018	−	1.31985i	−0.941809	−	0.336149i	$-0.890875\pi$
$571$	−18.2089	−	31.5387i	−0.762018	−	1.31985i	0.179790	−	0.983705i	$-0.442458\pi$
$572$	−11.1633	+	1.64509i	−0.466759	+	0.0687848i
$573$	8.09134	−	7.34524i	0.338020	−	0.306852i
$574$	3.58836	−	1.59764i	0.149775	−	0.0666842i
$575$	−2.13707	+	6.57722i	−0.0891219	+	0.274289i
$576$	−0.903830	+	2.86061i	−0.0376596	+	0.119192i
$577$	−34.5968	+	25.1361i	−1.44028	+	1.04643i	−0.452302	+	0.891865i	$0.649397\pi$
$577$	−34.5968	+	25.1361i	−1.44028	+	1.04643i	−0.987983	+	0.154563i	$0.950603\pi$
$578$	1.77662	+	16.9034i	0.0738976	+	0.703088i
$579$	15.8392	−	9.23081i	0.658256	−	0.383619i
$580$	−7.67575	+	1.63153i	−0.318718	+	0.0677456i
$581$	1.95323	−	18.5838i	0.0810337	−	0.770984i
$582$	6.51781	+	30.0626i	0.270172	+	1.24613i
$583$	−0.757109	+	0.281313i	−0.0313562	+	0.0116508i
$584$	−10.6101			−0.439051
$585$	10.0005	+	2.04086i	0.413469	+	0.0843790i
$586$	−2.61354	+	8.04364i	−0.107964	+	0.332280i
$587$	45.2183	+	9.61144i	1.86636	+	0.396706i	0.995494	−	0.0948200i	$-0.0302276\pi$
$587$	45.2183	+	9.61144i	1.86636	+	0.396706i	0.870863	+	0.491526i	$0.163561\pi$
$588$	1.27672	−	6.12889i	0.0526512	−	0.252751i
$589$	−28.2402	−	12.5733i	−1.16362	−	0.518076i
$590$	−3.89766	+	4.32879i	−0.160464	+	0.178213i
$591$	0.502156	−	0.697099i	0.0206560	−	0.0286748i
$592$	−1.07580	+	0.478978i	−0.0442152	+	0.0196859i
$593$	19.4576			0.799027			0.399513	−	0.916727i	$-0.369179\pi$
$593$	19.4576			0.799027			0.399513	+	0.916727i	$0.369179\pi$
$594$	−7.80202	+	15.3665i	−0.320121	+	0.630494i
$595$	0.108882			0.00446371
$596$	1.38786	−	0.617917i	0.0568492	−	0.0253109i
$597$	−8.15775	+	11.3247i	−0.333874	+	0.463488i
$598$	−15.7437	+	17.4852i	−0.643808	+	0.715021i
$599$	−9.18093	−	4.08761i	−0.375123	−	0.167015i	0.210511	−	0.977592i	$-0.432487\pi$
$599$	−9.18093	−	4.08761i	−0.375123	−	0.167015i	−0.585633	+	0.810576i	$0.699154\pi$
$600$	−0.353225	+	1.69565i	−0.0144204	+	0.0692247i
$601$	18.4865	+	3.92943i	0.754080	+	0.160285i	0.568885	−	0.822417i	$-0.307375\pi$
$601$	18.4865	+	3.92943i	0.754080	+	0.160285i	0.185195	+	0.982702i	$0.440708\pi$
$602$	−2.98288	+	9.18035i	−0.121573	+	0.374163i
$603$	−4.33332	+	4.89202i	−0.176466	+	0.199219i
$604$	−22.7145			−0.924240
$605$	0.236834	−	10.9975i	0.00962868	−	0.447110i
$606$	−4.68817	−	21.6236i	−0.190444	−	0.878400i
$607$	−2.82139	+	26.8437i	−0.114517	+	1.08955i	0.774783	+	0.632227i	$0.217859\pi$
$607$	−2.82139	+	26.8437i	−0.114517	+	1.08955i	−0.889300	+	0.457325i	$0.848808\pi$
$608$	4.05299	−	0.861490i	0.164370	−	0.0349380i
$609$	−21.6071	+	12.5922i	−0.875565	+	0.510263i
$610$	1.19482	+	11.3680i	0.0483769	+	0.460275i
$611$	−2.46019	+	1.78743i	−0.0995285	+	0.0723117i
$612$	0.173341	−	0.0383200i	0.00700691	−	0.00154900i
$613$	−8.82241	+	27.1526i	−0.356334	+	1.09668i	0.598898	+	0.800825i	$0.295605\pi$
$613$	−8.82241	+	27.1526i	−0.356334	+	1.09668i	−0.955232	+	0.295858i	$0.904395\pi$
$614$	1.33638	−	0.594993i	0.0539317	−	0.0240120i
$615$	2.73773	−	2.48529i	0.110396	−	0.100216i
$616$	−2.71179	−	5.46690i	−0.109261	−	0.220268i
$617$	22.9901	+	39.8201i	0.925548	+	1.60310i	0.790677	+	0.612234i	$0.209729\pi$
$617$	22.9901	+	39.8201i	0.925548	+	1.60310i	0.134872	+	0.990863i	$0.456938\pi$
$618$	−11.6705	−	15.9266i	−0.469457	−	0.640660i
$619$	−18.9554	−	21.0522i	−0.761884	−	0.846157i	0.230015	−	0.973187i	$-0.426122\pi$
$619$	−18.9554	−	21.0522i	−0.761884	−	0.846157i	−0.991899	+	0.127030i	$0.959456\pi$
$620$	2.30541	+	7.09533i	0.0925876	+	0.284955i
$621$	7.89930	+	35.0560i	0.316988	+	1.40675i
$622$	−20.4808	+	14.8801i	−0.821204	+	0.596639i
$623$	14.7403	+	3.13315i	0.590559	+	0.125527i
$624$	−3.44429	+	4.78140i	−0.137882	+	0.191409i
$625$	−0.104528	+	0.994522i	−0.00418114	+	0.0397809i
$626$	2.54894	+	4.41489i	0.101876	+	0.176455i
$627$	23.7780	−	1.08641i	0.949602	−	0.0433870i
$628$	8.89088	−	15.3995i	0.354785	−	0.614505i
$629$	0.0563770	+	0.0409603i	0.00224790	+	0.00163319i
$630$	0.621592	+	5.48483i	0.0247648	+	0.218521i
$631$	5.39955	+	16.6181i	0.214953	+	0.661556i	0.999157	+	0.0410536i	$0.0130714\pi$
$631$	5.39955	+	16.6181i	0.214953	+	0.661556i	−0.784204	+	0.620503i	$0.786929\pi$
$632$	−0.883390	−	8.40490i	−0.0351394	−	0.334329i
$633$	−26.6487	−	23.7992i	−1.05919	−	0.945935i
$634$	−7.90375	+	8.77800i	−0.313898	+	0.348619i
$635$	17.5708	−	3.73478i	0.697275	−	0.148210i
$636$	−0.169993	+	0.386026i	−0.00674068	+	0.0153069i
$637$	6.14859	−	10.6497i	0.243616	−	0.421955i
$638$	9.58804	−	24.1958i	0.379594	−	0.957922i
$639$	−21.2687	−	15.1901i	−0.841379	−	0.600910i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	−29.8880	−	33.1940i	−1.18051	−	1.31108i	−0.940294	−	0.340365i	$-0.889450\pi$
$641$	−29.8880	−	33.1940i	−1.18051	−	1.31108i	−0.240213	−	0.970720i	$-0.577217\pi$
$642$	−12.3364	−	7.05575i	−0.486880	−	0.278468i
$643$	−8.54544	−	3.80467i	−0.336999	−	0.150042i	0.231259	−	0.972892i	$-0.425716\pi$
$643$	−8.54544	−	3.80467i	−0.336999	−	0.150042i	−0.568258	+	0.822851i	$0.692382\pi$
$644$	−11.6246	−	5.17562i	−0.458075	−	0.203948i
$645$	0.0369286	+	9.08651i	0.00145406	+	0.357781i
$646$	−0.164068	−	0.182216i	−0.00645517	−	0.00716919i
$647$	−14.6295	−	10.6289i	−0.575144	−	0.417866i	0.261826	−	0.965115i	$-0.415675\pi$
$647$	−14.6295	−	10.6289i	−0.575144	−	0.417866i	−0.836970	+	0.547249i	$0.815675\pi$
$648$	2.91993	+	8.51317i	0.114706	+	0.334429i
$649$	−4.79899	−	18.7137i	−0.188377	−	0.734576i
$650$	−1.70110	+	2.94639i	−0.0667227	+	0.115567i
$651$	14.0533	+	19.1783i	0.550791	+	0.751656i
$652$	−0.638153	+	0.135644i	−0.0249920	+	0.00531222i
$653$	27.3225	−	30.3447i	1.06921	−	1.18748i	0.0876873	−	0.996148i	$-0.472052\pi$
$653$	27.3225	−	30.3447i	1.06921	−	1.18748i	0.981525	−	0.191333i	$-0.0612810\pi$
$654$	−4.93558	+	23.6932i	−0.192997	+	0.926476i
$655$	0.282642	+	2.68916i	0.0110438	+	0.105074i
$656$	0.659682	+	2.03029i	0.0257563	+	0.0792696i
$657$	−25.5984	+	18.9181i	−0.998690	+	0.738067i
$658$	−1.33052	−	0.966678i	−0.0518690	−	0.0376850i
$659$	−7.78311	+	13.4807i	−0.303187	+	0.525135i	−0.976856	−	0.213898i	$-0.931384\pi$
$659$	−7.78311	+	13.4807i	−0.303187	+	0.525135i	0.673669	+	0.739033i	$0.264717\pi$
$660$	−4.03470	−	4.08915i	−0.157051	−	0.159170i
$661$	1.30737	+	2.26444i	0.0508510	+	0.0880765i	0.890330	−	0.455315i	$-0.150473\pi$
$661$	1.30737	+	2.26444i	0.0508510	+	0.0880765i	−0.839479	+	0.543391i	$0.817140\pi$
$662$	−0.416785	+	3.96545i	−0.0161988	+	0.154122i
$663$	0.346943	+	0.0350402i	0.0134742	+	0.00136085i
$664$	9.93369	+	2.11147i	0.385502	+	0.0819410i
$665$	6.16796	−	4.48129i	0.239183	−	0.173777i
$666$	−1.74149	+	3.07379i	−0.0674815	+	0.119107i
$667$	−16.7701	−	51.6129i	−0.649339	−	1.99846i
$668$	−2.57075	−	2.85510i	−0.0994651	−	0.110467i
$669$	−43.5049	+	4.75139i	−1.68200	+	0.183699i
$670$	−1.08921	−	1.88657i	−0.0420798	−	0.0728844i
$671$	−33.5916	−	17.5739i	−1.29679	−	0.678432i
$672$	−3.03494	−	0.972492i	−0.117075	−	0.0375147i
$673$	−4.18855	+	1.86486i	−0.161457	+	0.0718851i	−0.485874	−	0.874029i	$-0.661499\pi$
$673$	−4.18855	+	1.86486i	−0.161457	+	0.0718851i	0.324417	+	0.945914i	$0.394832\pi$
$674$	−5.81220	+	17.8881i	−0.223878	+	0.689025i
$675$	2.17118	+	4.72080i	0.0835689	+	0.181704i
$676$	1.15287	−	0.837608i	0.0443411	−	0.0322157i
$677$	3.37860	+	32.1453i	0.129850	+	1.23544i	0.844344	+	0.535801i	$0.179990\pi$
$677$	3.37860	+	32.1453i	0.129850	+	1.23544i	−0.714494	+	0.699642i	$0.753343\pi$
$678$	0.109530	+	26.9505i	0.00420647	+	1.03503i
$679$	−31.9637	+	6.79410i	−1.22666	+	0.260734i
$680$	−0.00618552	+	0.0588513i	−0.000237204	+	0.00225684i
$681$	4.26141	−	3.86847i	0.163298	−	0.148240i
$682$	−23.8301	−	6.66105i	−0.912503	−	0.255065i
$683$	42.6656			1.63255			0.816276	−	0.577662i	$-0.196035\pi$
$683$	42.6656			1.63255			0.816276	+	0.577662i	$0.196035\pi$
$684$	8.24234	−	9.30505i	0.315154	−	0.355787i
$685$	−0.670848	+	2.06466i	−0.0256318	+	0.0788865i
$686$	19.1036	+	4.06060i	0.729380	+	0.155035i
$687$	23.4040	+	20.9015i	0.892919	+	0.797441i
$688$	−4.79259	−	2.13380i	−0.182716	−	0.0813503i
$689$	−0.554390	+	0.615712i	−0.0211206	+	0.0234568i
$690$	−11.9177	−	1.20365i	−0.453699	−	0.0458223i
$691$	−20.3350	+	9.05373i	−0.773581	+	0.344420i	−0.755271	−	0.655412i	$-0.772495\pi$
$691$	−20.3350	+	9.05373i	−0.773581	+	0.344420i	−0.0183091	+	0.999832i	$0.505828\pi$
$692$	0.500541			0.0190277
$693$	−16.2902	−	8.35446i	−0.618813	−	0.317360i
$694$	−30.3692			−1.15280
$695$	3.58979	−	1.59828i	0.136169	−	0.0606262i
$696$	−5.57870	−	12.3942i	−0.211460	−	0.469799i
$697$	0.0845289	−	0.0938788i	0.00320176	−	0.00355591i
$698$	24.8902	+	11.0818i	0.942109	+	0.419454i
$699$	6.89550	−	2.27151i	0.260812	−	0.0859163i
$700$	−1.79977	−	0.382553i	−0.0680250	−	0.0144592i
$701$	8.49329	−	26.1396i	0.320787	−	0.987281i	−0.652520	−	0.757772i	$-0.726288\pi$
$701$	8.49329	−	26.1396i	0.320787	−	0.987281i	0.973307	−	0.229509i	$-0.0737120\pi$
$702$	0.215534	+	17.6770i	0.00813481	+	0.667177i
$703$	4.87948			0.184033
$704$	3.10895	−	1.15517i	0.117173	−	0.0435371i
$705$	−1.47430	−	0.472415i	−0.0555255	−	0.0177922i
$706$	1.72006	−	16.3653i	0.0647353	−	0.615916i
$707$	22.9911	−	4.88691i	0.864669	−	0.183791i
$708$	−8.75787	−	5.00901i	−0.329141	−	0.188250i
$709$	2.08460	+	19.8336i	0.0782888	+	0.744868i	0.961298	+	0.275512i	$0.0888473\pi$
$709$	2.08460	+	19.8336i	0.0782888	+	0.744868i	−0.883009	+	0.469356i	$0.844486\pi$
$710$	7.04819	−	5.12081i	0.264514	−	0.192181i
$711$	−17.1174	−	18.7029i	−0.641954	−	0.701412i
$712$	−2.53088	+	7.78926i	−0.0948488	+	0.291915i
$713$	−47.1338	+	20.9853i	−1.76517	+	0.785906i
$714$	0.0399591	+	0.184307i	0.00149543	+	0.00689750i
$715$	−5.01421	−	10.1085i	−0.187521	−	0.378038i
$716$	1.95747	+	3.39044i	0.0731541	+	0.126707i
$717$	5.32735	−	12.0975i	0.198954	−	0.451790i
$718$	9.70523	+	10.7787i	0.362196	+	0.402259i
$719$	15.6310	+	48.1073i	0.582939	+	1.79410i	0.607395	+	0.794400i	$0.292214\pi$
$719$	15.6310	+	48.1073i	0.582939	+	1.79410i	−0.0244567	+	0.999701i	$0.507786\pi$
$720$	−2.99990	+	0.0243843i	−0.111800	+	0.000908748i
$721$	16.9692	−	12.3289i	0.631967	−	0.459151i
$722$	1.79109	+	0.380707i	0.0666573	+	0.0141685i
$723$	13.0533	+	29.0004i	0.485458	+	1.07854i
$724$	1.34107	−	12.7595i	0.0498406	−	0.474202i
$725$	−3.92361	−	6.79590i	−0.145719	−	0.252393i
$726$	18.7026	−	3.63513i	0.694117	−	0.134912i
$727$	10.0253	−	17.3643i	0.371817	−	0.644006i	−0.618028	−	0.786156i	$-0.712068\pi$
$727$	10.0253	−	17.3643i	0.371817	−	0.644006i	0.989845	+	0.142150i	$0.0454016\pi$
$728$	−5.06443	−	3.67953i	−0.187700	−	0.136372i
$729$	22.2239	+	15.3329i	0.823108	+	0.567885i
$730$	−3.27871	−	10.0908i	−0.121351	−	0.373479i
$731$	0.0324501	+	0.308742i	0.00120021	+	0.0114192i
$732$	−18.8043	+	6.19450i	−0.695028	+	0.228955i
$733$	−1.91206	+	2.12356i	−0.0706237	+	0.0784355i	−0.777421	−	0.628980i	$-0.783473\pi$
$733$	−1.91206	+	2.12356i	−0.0706237	+	0.0784355i	0.706797	+	0.707416i	$0.250139\pi$
$734$	11.7560	−	2.49881i	0.433921	−	0.0922327i
$735$	6.22345	−	0.679694i	0.229555	−	0.0250709i
$736$	3.45785	−	5.98917i	0.127458	−	0.220764i
$737$	7.21060	+	0.455782i	0.265606	+	0.0167889i
$738$	5.21164	+	3.72213i	0.191843	+	0.137014i
$739$	13.9563	+	10.1398i	0.513389	+	0.372999i	0.814108	−	0.580714i	$-0.197226\pi$
$739$	13.9563	+	10.1398i	0.513389	+	0.372999i	−0.300718	+	0.953713i	$0.597226\pi$
$740$	−0.787977	−	0.875137i	−0.0289666	−	0.0321707i
$741$	21.0959	−	12.2943i	0.774978	−	0.451643i
$742$	−0.409343	−	0.182251i	−0.0150275	−	0.00669066i
$743$	7.32329	+	3.26054i	0.268665	+	0.119618i	0.536648	−	0.843806i	$-0.319690\pi$
$743$	7.32329	+	3.26054i	0.268665	+	0.119618i	−0.267983	+	0.963424i	$0.586357\pi$
$744$	−11.1644	+	6.50638i	−0.409305	+	0.238536i
$745$	1.01655	+	1.12899i	0.0372434	+	0.0413630i
$746$	−11.1758	−	8.11970i	−0.409176	−	0.297283i
$747$	27.7312	−	12.6178i	1.01463	−	0.461661i
$748$	−0.151186	−	0.125147i	−0.00552792	−	0.00457583i
$749$	7.54862	−	13.0746i	0.275820	−	0.477735i
$750$	−1.72181	+	0.188048i	−0.0628717	+	0.00686653i
$751$	−37.9773	+	8.07232i	−1.38581	+	0.294563i	−0.839655	−	0.543121i	$-0.817243\pi$
$751$	−37.9773	+	8.07232i	−1.38581	+	0.294563i	−0.546156	+	0.837684i	$0.683909\pi$
$752$	0.598083	−	0.664238i	0.0218098	−	0.0242223i
$753$	−33.6930	+	11.0991i	−1.22784	+	0.404474i
$754$	−2.79069	−	26.5516i	−0.101631	−	0.966952i
$755$	−7.01917	−	21.6028i	−0.255454	−	0.786206i
$756$	−9.05618	+	3.06509i	−0.329370	+	0.111476i
$757$	−25.5859	−	18.5892i	−0.929935	−	0.675637i	0.0160418	−	0.999871i	$-0.494894\pi$
$757$	−25.5859	−	18.5892i	−0.929935	−	0.675637i	−0.945977	+	0.324234i	$0.894894\pi$
$758$	0.408527	−	0.707590i	0.0148384	−	0.0257008i
$759$	25.2078	−	30.7059i	0.914984	−	1.11455i
$760$	2.07177	+	3.58841i	0.0751509	+	0.130165i
$761$	2.48939	−	23.6849i	0.0902402	−	0.858578i	−0.851978	−	0.523578i	$-0.824597\pi$
$761$	2.48939	−	23.6849i	0.0902402	−	0.858578i	0.942218	−	0.335000i	$-0.108736\pi$
$762$	12.7704	+	28.3718i	0.462621	+	1.02780i
$763$	−25.1480	−	5.34538i	−0.910420	−	0.193516i
$764$	−5.10434	+	3.70852i	−0.184669	+	0.134170i
$765$	0.0900099	+	0.153016i	0.00325432	+	0.00553230i
$766$	2.69759	+	8.30233i	0.0974679	+	0.299975i
$767$	−13.2606	−	14.7274i	−0.478813	−	0.531776i
$768$	0.698052	−	1.58516i	0.0251888	−	0.0571994i
$769$	−4.88460	−	8.46037i	−0.176143	−	0.305089i	0.764413	−	0.644727i	$-0.223029\pi$
$769$	−4.88460	−	8.46037i	−0.176143	−	0.305089i	−0.940556	+	0.339638i	$0.889695\pi$
$770$	4.36134	−	4.26843i	0.157172	−	0.153823i
$771$	8.10913	+	37.4024i	0.292043	+	1.34701i
$772$	−9.66933	+	4.30506i	−0.348007	+	0.154943i
$773$	7.32474	−	22.5432i	0.263452	−	0.810823i	−0.728593	−	0.684946i	$-0.759826\pi$
$773$	7.32474	−	22.5432i	0.263452	−	0.810823i	0.992046	−	0.125877i	$-0.0401744\pi$
$774$	−15.3674	+	3.39722i	−0.552369	+	0.122111i
$775$	−6.03565	+	4.38516i	−0.216807	+	0.157519i
$776$	−1.85641	−	17.6626i	−0.0666414	−	0.634050i
$777$	−3.25778	−	1.86327i	−0.116872	−	0.0668443i
$778$	27.1632	−	5.77372i	0.973848	−	0.206998i
$779$	0.924609	−	8.79707i	0.0331276	−	0.315188i
$780$	−5.61173	−	1.79818i	−0.200932	−	0.0643852i
$781$	1.20149	+	28.8696i	0.0429927	+	1.03304i
$782$	−0.409240			−0.0146344
$783$	−35.5585	−	19.9557i	−1.27076	−	0.713157i
$784$	−1.11693	+	3.43757i	−0.0398905	+	0.122770i
$785$	17.3932	+	3.69704i	0.620789	+	0.131953i
$786$	−4.44828	+	1.46535i	−0.158665	+	0.0522672i
$787$	9.57792	+	4.26437i	0.341416	+	0.152008i	0.570280	−	0.821450i	$-0.306835\pi$
$787$	9.57792	+	4.26437i	0.341416	+	0.152008i	−0.228864	+	0.973458i	$0.573501\pi$
$788$	−0.331902	+	0.368615i	−0.0118235	+	0.0131314i
$789$	−12.9310	−	28.7287i	−0.460356	−	1.02277i
$790$	7.72055	−	3.43741i	0.274685	−	0.122298i
$791$	−28.6301			−1.01797
$792$	5.44108	−	8.33034i	0.193340	−	0.296006i
$793$	−38.8891			−1.38099
$794$	14.0571	−	6.25862i	0.498867	−	0.222110i
$795$	−0.419663	−	0.0423847i	−0.0148839	−	0.00150323i
$796$	5.39190	−	5.98831i	0.191111	−	0.212250i
$797$	−36.4665	−	16.2359i	−1.29171	−	0.575106i	−0.358195	−	0.933647i	$-0.616608\pi$
$797$	−36.4665	−	16.2359i	−1.29171	−	0.575106i	−0.933514	+	0.358541i	$0.883274\pi$
$798$	9.84920	+	8.79605i	0.348658	+	0.311377i
$799$	−0.0517364	−	0.0109969i	−0.00183030	−	0.000389043i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$	7.78233	+	23.3053i	0.274975	+	0.823452i
$802$	−35.5126			−1.25399
$803$	33.8908	+	9.47321i	1.19598	+	0.334302i
$804$	2.79370	−	2.53609i	0.0985262	−	0.0894411i
$805$	1.33010	−	12.6550i	0.0468798	−	0.446031i
$806$	−24.8274	+	5.27722i	−0.874507	+	0.185882i
$807$	−0.123873	−	30.4798i	−0.00436055	−	1.07294i
$808$	1.33529	+	12.7045i	0.0469755	+	0.446942i
$809$	−19.2713	+	14.0014i	−0.677543	+	0.492264i	−0.872542	−	0.488539i	$-0.837530\pi$
$809$	−19.2713	+	14.0014i	−0.677543	+	0.492264i	0.194998	+	0.980804i	$0.437530\pi$
$810$	−7.19420	+	5.40773i	−0.252778	+	0.190008i
$811$	12.1317	−	37.3377i	0.426003	−	1.31110i	−0.476027	−	0.879431i	$-0.657924\pi$
$811$	12.1317	−	37.3377i	0.426003	−	1.31110i	0.902030	−	0.431673i	$-0.142076\pi$
$812$	13.1904	−	5.87277i	0.462894	−	0.206094i
$813$	47.5993	+	15.2523i	1.66938	+	0.534923i
$814$	3.86397	−	0.569421i	0.135432	−	0.0199582i
$815$	−0.326205	−	0.565004i	−0.0114265	−	0.0197912i
$816$	−0.101889	+	0.0111278i	−0.00356683	+	0.000389551i
$817$	14.5453	+	16.1542i	0.508875	+	0.565163i
$818$	10.4470	+	32.1526i	0.365272	+	1.12419i
$819$	−18.7793	+	0.152645i	−0.656203	+	0.00533385i
$820$	−1.72707	+	1.25479i	−0.0603119	+	0.0438192i
$821$	35.4220	+	7.52918i	1.23624	+	0.262770i	0.779256	−	0.626706i	$-0.215597\pi$
$821$	35.4220	+	7.52918i	1.23624	+	0.262770i	0.456981	+	0.889476i	$0.348931\pi$
$822$	−3.74109	−	0.377839i	−0.130486	−	0.0131787i
$823$	−1.54403	+	14.6905i	−0.0538215	+	0.512078i	0.934088	+	0.357044i	$0.116215\pi$
$823$	−1.54403	+	14.6905i	−0.0538215	+	0.512078i	−0.987909	+	0.155034i	$0.950451\pi$
$824$	5.69983	+	9.87239i	0.198563	+	0.343921i
$825$	2.64222	−	5.10085i	0.0919903	−	0.177589i
$826$	5.35891	−	9.28190i	0.186460	−	0.322958i
$827$	−27.7418	−	20.1556i	−0.964677	−	0.700879i	−0.0104446	−	0.999945i	$-0.503325\pi$
$827$	−27.7418	−	20.1556i	−0.964677	−	0.700879i	−0.954232	+	0.299067i	$0.903325\pi$
$828$	−2.33630	−	20.6151i	−0.0811920	−	0.716425i
$829$	3.33907	+	10.2766i	0.115971	+	0.356921i	0.992148	−	0.125068i	$-0.0399148\pi$
$829$	3.33907	+	10.2766i	0.115971	+	0.356921i	−0.876178	+	0.481988i	$0.839915\pi$
$830$	1.06155	+	10.1000i	0.0368470	+	0.350575i
$831$	−0.393263	+	1.88785i	−0.0136421	+	0.0654888i
$832$	2.27652	−	2.52833i	0.0789240	−	0.0876540i
$833$	0.209214	−	0.0444699i	0.00724885	−	0.00154079i
$834$	4.02289	+	5.48997i	0.139301	+	0.190102i
$835$	1.92096	−	3.32720i	0.0664775	−	0.115142i
$836$	−13.7152	−	0.866935i	−0.474350	−	0.0299836i
$837$	−15.3345	+	35.6039i	−0.530038	+	1.23065i
$838$	−7.37965	−	5.36163i	−0.254926	−	0.185214i
$839$	−21.4311	−	23.8017i	−0.739884	−	0.821725i	0.249296	−	0.968427i	$-0.419801\pi$
$839$	−21.4311	−	23.8017i	−0.739884	−	0.821725i	−0.989181	+	0.146702i	$0.953134\pi$
$840$	−0.0129520	−	3.18691i	−0.000446885	−	0.109959i
$841$	29.7624	+	13.2511i	1.02629	+	0.456934i
$842$	22.0739	+	9.82795i	0.760718	+	0.338694i
$843$	−41.9071	−	23.9685i	−1.44336	−	0.825520i
$844$	13.8029	+	15.3297i	0.475116	+	0.527670i
$845$	1.15287	+	0.837608i	0.0396599	+	0.0288146i
$846$	0.258604	−	2.66896i	0.00889099	−	0.0917608i
$847$	3.78086	+	19.8835i	0.129912	+	0.683205i
$848$	0.121763	−	0.210899i	0.00418135	−	0.00724231i
$849$	−10.0825	+	22.8957i	−0.346031	+	0.785778i
$850$	−0.0578824	+	0.0123033i	−0.00198535	+	0.000421999i
$851$	5.44941	−	6.05218i	0.186803	−	0.207466i
$852$	11.2548	+	10.0513i	0.385582	+	0.344353i
$853$	1.63595	+	15.5651i	0.0560140	+	0.532938i	0.986166	+	0.165762i	$0.0530084\pi$
$853$	1.63595	+	15.5651i	0.0560140	+	0.532938i	−0.930152	+	0.367175i	$0.880325\pi$
$854$	−6.49926	−	20.0027i	−0.222400	−	0.684477i
$855$	11.3966	+	4.96352i	0.389757	+	0.169749i
$856$	6.63807	+	4.82284i	0.226885	+	0.164841i
$857$	−8.16092	+	14.1351i	−0.278772	+	0.482847i	−0.971080	−	0.238755i	$-0.923261\pi$
$857$	−8.16092	+	14.1351i	−0.278772	+	0.482847i	0.692308	+	0.721602i	$0.256594\pi$
$858$	15.2708	−	12.1975i	0.521335	−	0.416415i
$859$	15.8280	+	27.4149i	0.540045	+	0.935385i	0.998901	+	0.0468742i	$0.0149260\pi$
$859$	15.8280	+	27.4149i	0.540045	+	0.935385i	−0.458856	+	0.888511i	$0.651741\pi$
$860$	0.548371	−	5.21740i	0.0186993	−	0.177912i
$861$	−3.97654	+	5.52027i	−0.135520	+	0.188130i
$862$	−2.87191	−	0.610444i	−0.0978178	−	0.0207918i
$863$	−6.88978	+	5.00572i	−0.234531	+	0.170397i	−0.698843	−	0.715275i	$-0.746302\pi$
$863$	−6.88978	+	5.00572i	−0.234531	+	0.170397i	0.464312	+	0.885672i	$0.346302\pi$
$864$	−1.14223	−	5.06905i	−0.0388594	−	0.172453i
$865$	0.154676	+	0.476042i	0.00525913	+	0.0161859i
$866$	7.64399	+	8.48952i	0.259754	+	0.288486i
$867$	−17.4003	−	23.7460i	−0.590947	−	0.806455i
$868$	−6.86356	−	11.8880i	−0.232964	−	0.403506i
$869$	−4.68256	+	27.6355i	−0.158845	+	0.937471i
$870$	10.0636	−	9.13566i	0.341189	−	0.309728i
$871$	6.77067	−	3.01450i	0.229415	−	0.102142i
$872$	4.31786	−	13.2890i	0.146221	−	0.450023i
$873$	−35.9717	−	39.3034i	−1.21746	−	1.33022i
$874$	−23.1827	+	16.8432i	−0.784168	+	0.569731i
$875$	−0.192330	−	1.82990i	−0.00650195	−	0.0618619i
$876$	15.8777	−	9.25325i	0.536459	−	0.312638i
$877$	23.1864	−	4.92842i	0.782949	−	0.166421i	0.200940	−	0.979604i	$-0.435600\pi$
$877$	23.1864	−	4.92842i	0.782949	−	0.166421i	0.582009	+	0.813183i	$0.302267\pi$
$878$	−0.767225	+	7.29966i	−0.0258926	+	0.246352i
$879$	−3.10390	−	14.3163i	−0.104692	−	0.482878i
$880$	2.05935	+	2.59982i	0.0694207	+	0.0876400i
$881$	25.2116			0.849400			0.424700	−	0.905334i	$-0.360380\pi$
$881$	25.2116			0.849400			0.424700	+	0.905334i	$0.360380\pi$
$882$	3.43451	+	10.2851i	0.115646	+	0.346318i
$883$	−9.85752	+	30.3383i	−0.331732	+	1.02097i	0.636578	+	0.771213i	$0.280350\pi$
$883$	−9.85752	+	30.3383i	−0.331732	+	1.02097i	−0.968309	+	0.249753i	$0.919650\pi$
$884$	−0.196927	−	0.0418582i	−0.00662339	−	0.00140784i
$885$	2.05752	−	9.87710i	0.0691629	−	0.332015i
$886$	27.8910	+	12.4179i	0.937018	+	0.417187i
$887$	22.3816	−	24.8573i	0.751502	−	0.834628i	−0.239158	−	0.970981i	$-0.576871\pi$
$887$	22.3816	−	24.8573i	0.751502	−	0.834628i	0.990660	+	0.136353i	$0.0435381\pi$
$888$	1.19218	−	1.65500i	0.0400070	−	0.0555381i
$889$	−30.1946	+	13.4435i	−1.01270	+	0.450881i
$890$	−8.19011			−0.274533
$891$	−1.72584	−	29.7997i	−0.0578179	−	0.998327i
$892$	25.2669			0.845999
$893$	−3.38339	+	1.50638i	−0.113221	+	0.0504091i
$894$	−1.53800	+	2.13507i	−0.0514384	+	0.0714074i
$895$	−2.61961	+	2.90937i	−0.0875638	+	0.0972495i
$896$	1.68091	+	0.748387i	0.0561551	+	0.0250019i
$897$	8.31089	−	39.8963i	0.277493	−	1.33210i
$898$	22.4024	+	4.76178i	0.747578	+	0.158903i
$899$	18.0911	−	55.6787i	0.603372	−	1.85699i
$900$	−0.950211	−	2.84554i	−0.0316737	−	0.0948513i
$901$	−0.0144107			−0.000480091
$902$	−0.294410	−	7.07413i	−0.00980278	−	0.235543i
$903$	−3.54254	−	16.3395i	−0.117888	−	0.543745i
$904$	1.62646	−	15.4748i	0.0540953	−	0.514683i
$905$	12.5494	−	2.66745i	0.417156	−	0.0886692i
$906$	33.9915	−	19.8096i	1.12929	−	0.658131i
$907$	1.11153	+	10.5755i	0.0369079	+	0.351155i	0.997355	+	0.0726908i	$0.0231586\pi$
$907$	1.11153	+	10.5755i	0.0369079	+	0.351155i	−0.960447	+	0.278464i	$0.910175\pi$
$908$	−2.68827	+	1.95314i	−0.0892133	+	0.0648173i
$909$	25.8740	+	28.2704i	0.858185	+	0.937671i
$910$	1.93444	−	5.95360i	0.0641261	−	0.197360i
$911$	39.2205	−	17.4621i	1.29943	−	0.578545i	0.363787	−	0.931482i	$-0.381484\pi$
$911$	39.2205	−	17.4621i	1.29943	−	0.578545i	0.935647	+	0.352937i	$0.114817\pi$
$912$	−5.31385	+	4.82386i	−0.175959	+	0.159734i
$913$	−29.8448	−	15.6137i	−0.987720	−	0.516737i
$914$	−6.48648	−	11.2349i	−0.214554	−	0.371618i
$915$	−11.7022	−	15.9698i	−0.386862	−	0.527944i
$916$	−12.1223	−	13.4632i	−0.400532	−	0.444835i
$917$	−1.53744	−	4.73175i	−0.0507707	−	0.156256i
$918$	−0.225980	+	0.208518i	−0.00745846	+	0.00688212i
$919$	22.8991	−	16.6372i	0.755372	−	0.548810i	−0.142115	−	0.989850i	$-0.545390\pi$
$919$	22.8991	−	16.6372i	0.755372	−	0.548810i	0.897487	+	0.441040i	$0.145390\pi$
$920$	6.76457	+	1.43785i	0.223021	+	0.0474046i
$921$	−1.48094	+	2.05586i	−0.0487987	+	0.0677429i
$922$	3.65642	−	34.7885i	0.120418	−	1.14570i
$923$	14.8201	+	25.6691i	0.487808	+	0.844909i
$924$	8.82587	+	5.81605i	0.290350	+	0.191334i
$925$	0.588807	−	1.01984i	0.0193598	−	0.0335322i
$926$	−16.9900	−	12.3440i	−0.558327	−	0.405649i
$927$	31.3543	+	13.6556i	1.02981	+	0.448508i
$928$	2.42493	+	7.46316i	0.0796021	+	0.244990i
$929$	2.23845	+	21.2974i	0.0734412	+	0.698747i	0.967855	+	0.251507i	$0.0809262\pi$
$929$	2.23845	+	21.2974i	0.0734412	+	0.698747i	−0.894414	+	0.447240i	$0.852407\pi$
$930$	−9.63792	−	8.60735i	−0.316040	−	0.282246i
$931$	10.0214	−	11.1299i	0.328437	−	0.364767i
$932$	−4.09997	+	0.871475i	−0.134299	+	0.0285461i
$933$	17.6716	−	40.1292i	0.578543	−	1.31377i
$934$	−8.37165	+	14.5001i	−0.273929	+	0.474459i
$935$	0.0723028	−	0.182459i	0.00236456	−	0.00596706i
$936$	0.984340	−	10.1590i	0.0321742	−	0.332058i
$937$	18.3866	+	13.3587i	0.600665	+	0.436409i	0.846115	−	0.533000i	$-0.178936\pi$
$937$	18.3866	+	13.3587i	0.600665	+	0.436409i	−0.245450	+	0.969409i	$0.578936\pi$
$938$	2.68204	+	2.97871i	0.0875717	+	0.0972582i
$939$	−7.66470	−	4.38378i	−0.250128	−	0.143059i
$940$	0.816546	+	0.363550i	0.0266328	+	0.0118577i
$941$	−12.5303	−	5.57883i	−0.408475	−	0.181865i	0.192204	−	0.981355i	$-0.438436\pi$
$941$	−12.5303	−	5.57883i	−0.408475	−	0.181865i	−0.600679	+	0.799490i	$0.705103\pi$
$942$	0.125169	+	30.7987i	0.00407823	+	1.00347i
$943$	−9.87869	−	10.9714i	−0.321694	−	0.357278i
$944$	4.71249	+	3.42383i	0.153379	+	0.111436i
$945$	−5.71359	−	7.66577i	−0.185863	−	0.249368i
$946$	13.4033	+	11.0948i	0.435778	+	0.360723i
$947$	15.0566	−	26.0787i	0.489272	−	0.847444i	−0.510652	−	0.859788i	$-0.670596\pi$
$947$	15.0566	−	26.0787i	0.489272	−	0.847444i	0.999924	+	0.0123434i	$0.00392913\pi$
$948$	8.65200	+	11.8072i	0.281004	+	0.383481i
$949$	35.3090	−	7.50516i	1.14618	−	0.243628i
$950$	−2.77257	+	3.07925i	−0.0899540	+	0.0999040i
$951$	4.17229	−	20.0290i	0.135296	−	0.649484i
$952$	−0.0113812	−	0.108285i	−0.000368868	−	0.00350954i
$953$	−3.91644	−	12.0536i	−0.126866	−	0.390453i	0.867370	−	0.497663i	$-0.165808\pi$
$953$	−3.91644	−	12.0536i	−0.126866	−	0.390453i	−0.994236	+	0.107210i	$0.965808\pi$
$954$	−0.0822692	−	0.725929i	−0.00266356	−	0.0235028i
$955$	−5.10434	−	3.70852i	−0.165173	−	0.120005i
$956$	−3.81587	+	6.60928i	−0.123414	+	0.213759i
$957$	6.75334	+	44.5702i	0.218305	+	1.44075i
$958$	5.17854	+	8.96949i	0.167311	+	0.289791i
$959$	0.417532	−	3.97255i	0.0134828	−	0.128280i
$960$	1.72328	+	0.174046i	0.0556188	+	0.00561733i
$961$	−24.1198	−	5.12682i	−0.778058	−	0.165381i
$962$	3.24131	−	2.35495i	0.104504	−	0.0759266i
$963$	24.6145	−	0.200076i	0.793191	−	0.00644735i
$964$	−5.67396	−	17.4627i	−0.182746	−	0.562434i
$965$	−7.08235	−	7.86575i	−0.227989	−	0.253207i
$966$	21.9096	−	2.39286i	0.704930	−	0.0769890i
$967$	15.8046	+	27.3744i	0.508242	+	0.880300i	0.999954	+	0.00954284i	$0.00303763\pi$
$967$	15.8046	+	27.3744i	0.508242	+	0.880300i	−0.491713	+	0.870757i	$0.663629\pi$
$968$	−10.9620	+	0.914010i	−0.352331	+	0.0293774i
$969$	0.404436	+	0.129594i	0.0129923	+	0.00416317i
$970$	16.2245	−	7.22360i	0.520936	−	0.231936i
$971$	−14.9331	+	45.9593i	−0.479225	+	1.47490i	0.360949	+	0.932586i	$0.382453\pi$
$971$	−14.9331	+	45.9593i	−0.479225	+	1.47490i	−0.840174	+	0.542317i	$0.817547\pi$
$972$	−11.7940	−	10.1932i	−0.378294	−	0.326946i
$973$	−5.84938	+	4.24983i	−0.187523	+	0.136243i
$974$	−3.84047	−	36.5397i	−0.123057	−	1.17081i
$975$	−0.0239488	−	5.89274i	−0.000766974	−	0.188719i
$976$	11.1808	−	2.37655i	0.357888	−	0.0760715i
$977$	−3.27870	+	31.1947i	−0.104895	+	0.998008i	0.807825	+	0.589422i	$0.200645\pi$
$977$	−3.27870	+	31.1947i	−0.104895	+	0.998008i	−0.912720	+	0.408586i	$0.866022\pi$
$978$	0.836679	−	0.759529i	0.0267541	−	0.0242871i
$979$	15.0387	−	22.6207i	0.480639	−	0.722959i
$980$	−3.61447			−0.115460
$981$	−13.2772	−	39.7605i	−0.423909	−	1.26945i
$982$	−3.31819	+	10.2123i	−0.105888	+	0.325889i
$983$	54.1711	+	11.5144i	1.72779	+	0.367253i	0.961407	−	0.275132i	$-0.0887215\pi$
$983$	54.1711	+	11.5144i	1.72779	+	0.367253i	0.766382	+	0.642385i	$0.222055\pi$
$984$	−2.75784	−	2.46295i	−0.0879168	−	0.0785160i
$985$	−0.453137	−	0.201750i	−0.0144382	−	0.00642828i
$986$	0.310720	−	0.345089i	0.00989534	−	0.0109899i
$987$	2.83413	+	0.286239i	0.0902114	+	0.00911108i
$988$	−12.8784	+	5.73383i	−0.409716	+	0.182417i
$989$	36.2807			1.15366
$990$	9.60401	+	2.60056i	0.305236	+	0.0826512i
$991$	22.1307			0.703006			0.351503	−	0.936187i	$-0.385671\pi$
$991$	22.1307			0.703006			0.351503	+	0.936187i	$0.385671\pi$
$992$	6.81548	−	3.03445i	0.216392	−	0.0963438i
$993$	−2.83462	−	6.29765i	−0.0899539	−	0.199850i
$994$	−10.7262	+	11.9126i	−0.340213	+	0.377845i
$995$	7.36141	+	3.27751i	0.233372	+	0.103904i
$996$	−16.7069	+	5.50357i	−0.529378	+	0.174387i
$997$	38.5096	+	8.18546i	1.21961	+	0.259236i	0.772367	−	0.635177i	$-0.219073\pi$
$997$	38.5096	+	8.18546i	1.21961	+	0.259236i	0.447243	+	0.894413i	$0.352406\pi$
$998$	−1.81915	+	5.59876i	−0.0575841	+	0.177226i
$999$	−0.0746034	−	6.11860i	−0.00236035	−	0.193584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bg.a.961.3	yes	88
9.4	even	3	inner	990.2.bg.a.301.7	✓	88
11.3	even	5	inner	990.2.bg.a.421.7	yes	88
99.58	even	15	inner	990.2.bg.a.751.3	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bg.a.301.7	✓	88	9.4	even	3	inner
990.2.bg.a.421.7	yes	88	11.3	even	5	inner
990.2.bg.a.751.3	yes	88	99.58	even	15	inner
990.2.bg.a.961.3	yes	88	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 - 0.406737i) q^{2} +(-1.01237 + 1.40538i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.913545 + 0.406737i) q^{5} +(-0.353225 + 1.69565i) q^{6} +(-1.79977 - 0.382553i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.950211 - 2.84554i) q^{9} +1.00000 q^{10} +(-1.83620 + 2.76195i) q^{11} +(0.366996 + 1.69272i) q^{12} +(-0.355627 + 3.38356i) q^{13} +(-1.79977 + 0.382553i) q^{14} +(-1.49647 + 0.872114i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.0478740 + 0.0347825i) q^{17} +(-2.02545 - 2.21304i) q^{18} +(-1.28042 + 3.94074i) q^{19} +(0.913545 - 0.406737i) q^{20} +(2.35967 - 2.14209i) q^{21} +(-0.554071 + 3.27002i) q^{22} +(3.45785 + 5.98917i) q^{23} +(1.02376 + 1.39711i) q^{24} +(0.669131 + 0.743145i) q^{25} +(1.05134 + 3.23569i) q^{26} +(4.96104 + 1.54533i) q^{27} +(-1.48857 + 1.08151i) q^{28} +(-7.67575 - 1.63153i) q^{29} +(-1.01237 + 1.40538i) q^{30} +(-0.779832 + 7.41960i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.02268 - 5.37669i) q^{33} +(-0.0295877 + 0.0512475i) q^{34} +(-1.48857 - 1.08151i) q^{35} +(-2.75046 - 1.19789i) q^{36} +(-0.363903 - 1.11998i) q^{37} +(0.433118 + 4.12084i) q^{38} +(-4.39518 - 3.92521i) q^{39} +(0.669131 - 0.743145i) q^{40} +(-2.08813 + 0.443845i) q^{41} +(1.28440 - 2.91666i) q^{42} +(2.62307 - 4.54329i) q^{43} +(0.823866 + 3.21267i) q^{44} +(0.289324 - 2.98602i) q^{45} +(5.59492 + 4.06494i) q^{46} +(0.598083 + 0.664238i) q^{47} +(1.50351 + 0.859922i) q^{48} +(-3.30199 - 1.47014i) q^{49} +(0.913545 + 0.406737i) q^{50} +(-0.000416548 - 0.102494i) q^{51} +(2.27652 + 2.52833i) q^{52} +(0.197016 + 0.143141i) q^{53} +(5.16068 - 0.606110i) q^{54} +(-2.80084 + 1.77631i) q^{55} +(-0.919990 + 1.59347i) q^{56} +(-4.24199 - 5.78897i) q^{57} +(-7.67575 + 1.63153i) q^{58} +(-3.89766 + 4.32879i) q^{59} +(-0.353225 + 1.69565i) q^{60} +(1.19482 + 11.3680i) q^{61} +(2.30541 + 7.09533i) q^{62} +(0.621592 + 5.48483i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.70110 + 2.94639i) q^{65} +(-4.03470 - 4.08915i) q^{66} +(-1.08921 - 1.88657i) q^{67} +(-0.00618552 + 0.0588513i) q^{68} +(-11.9177 - 1.20365i) q^{69} +(-1.79977 - 0.382553i) q^{70} +(7.04819 - 5.12081i) q^{71} +(-2.99990 + 0.0243843i) q^{72} +(-3.27871 - 10.0908i) q^{73} +(-0.787977 - 0.875137i) q^{74} +(-1.72181 + 0.188048i) q^{75} +(2.07177 + 3.58841i) q^{76} +(4.36134 - 4.26843i) q^{77} +(-5.61173 - 1.79818i) q^{78} +(7.72055 - 3.43741i) q^{79} +(0.309017 - 0.951057i) q^{80} +(-7.19420 + 5.40773i) q^{81} +(-1.72707 + 1.25479i) q^{82} +(1.06155 + 10.1000i) q^{83} +(-0.0129520 - 3.18691i) q^{84} +(-0.0578824 + 0.0123033i) q^{85} +(0.548371 - 5.21740i) q^{86} +(10.0636 - 9.13566i) q^{87} +(2.05935 + 2.59982i) q^{88} -8.19011 q^{89} +(-0.950211 - 2.84554i) q^{90} +(1.93444 - 5.95360i) q^{91} +(6.76457 + 1.43785i) q^{92} +(-9.63792 - 8.60735i) q^{93} +(0.816546 + 0.363550i) q^{94} +(-2.77257 + 3.07925i) q^{95} +(1.72328 + 0.174046i) q^{96} +(16.2245 - 7.22360i) q^{97} -3.61447 q^{98} +(9.60401 + 2.60056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) \) 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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