LMFDB - Embedded newform 361.2.i.a.7.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(7,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(114)) chi = DirichletCharacter(H, H._module([50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.i (of order $57$, degree $36$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$1080$
Relative dimension:	$30$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			7.11
Character	$\chi$	$=$	361.7
Dual form			361.2.i.a.258.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.166828 - 0.854065i) q^{2} +(2.73618 - 0.302840i) q^{3} +(1.15139 - 0.467655i) q^{4} +(0.510455 - 0.496579i) q^{5} +(-0.715115 - 2.28635i) q^{6} +(-1.32321 + 1.02989i) q^{7} +(-1.54341 - 2.36236i) q^{8} +(4.46756 - 1.00120i) q^{9} +(-0.509268 - 0.353119i) q^{10} +(-1.77342 + 1.92645i) q^{11} +(3.00879 - 1.62828i) q^{12} +(-0.382408 - 0.520285i) q^{13} +(1.10034 + 0.958289i) q^{14} +(1.24631 - 1.51331i) q^{15} +(0.0214243 - 0.0208419i) q^{16} +(-5.57085 - 2.26268i) q^{17} +(-1.60041 - 3.64856i) q^{18} +(0.165531 + 4.35575i) q^{19} +(0.355507 - 0.810474i) q^{20} +(-3.30863 + 3.21869i) q^{21} +(1.94117 + 1.19323i) q^{22} +(7.08301 + 0.783947i) q^{23} +(-4.93845 - 5.99643i) q^{24} +(-0.123797 + 4.49114i) q^{25} +(-0.380561 + 0.413399i) q^{26} +(4.10965 - 1.41085i) q^{27} +(-1.04189 + 1.80461i) q^{28} +(0.886158 + 6.39051i) q^{29} +(-1.50039 - 0.811969i) q^{30} +(-3.34168 + 1.14720i) q^{31} +(-4.65925 - 3.23065i) q^{32} +(-4.26899 + 5.80816i) q^{33} +(-1.00311 + 5.13535i) q^{34} +(-0.164015 + 1.18279i) q^{35} +(4.67570 - 3.24206i) q^{36} +(0.110996 - 0.120573i) q^{37} +(3.69248 - 0.868035i) q^{38} +(-1.20390 - 1.30778i) q^{39} +(-1.96094 - 0.439457i) q^{40} +(-2.85004 - 7.61213i) q^{41} +(3.30094 + 2.28882i) q^{42} +(9.56242 - 6.63043i) q^{43} +(-1.14099 + 3.04745i) q^{44} +(1.78331 - 2.72956i) q^{45} +(-0.512100 - 6.18013i) q^{46} +(-2.43391 - 7.78164i) q^{47} +(0.0523090 - 0.0635152i) q^{48} +(-1.02820 + 4.06028i) q^{49} +(3.85638 - 0.643516i) q^{50} +(-15.9281 - 4.50403i) q^{51} +(-0.683616 - 0.420217i) q^{52} +(1.76273 + 5.63576i) q^{53} +(-1.89056 - 3.27454i) q^{54} +(0.0513810 + 1.86401i) q^{55} +(4.47522 + 1.53635i) q^{56} +(1.77202 + 11.8680i) q^{57} +(5.31007 - 1.82295i) q^{58} +(-4.63414 - 12.3772i) q^{59} +(0.727286 - 2.32526i) q^{60} +(-0.679555 - 1.34284i) q^{61} +(1.53727 + 2.66263i) q^{62} +(-4.88037 + 5.92590i) q^{63} +(-1.95788 + 4.46352i) q^{64} +(-0.453565 - 0.0756865i) q^{65} +(5.67274 + 2.67703i) q^{66} +(6.25416 - 0.345052i) q^{67} -7.47239 q^{68} +19.6178 q^{69} +(1.03754 - 0.0572428i) q^{70} +(-1.83055 + 3.61727i) q^{71} +(-9.26047 - 9.00872i) q^{72} +(-2.20777 - 0.896719i) q^{73} +(-0.121495 - 0.0746825i) q^{74} +(1.02136 + 12.3260i) q^{75} +(2.22758 + 4.93777i) q^{76} +(0.362566 - 4.37552i) q^{77} +(-0.916088 + 1.24638i) q^{78} +(-2.81568 + 1.95235i) q^{79} +(0.000586516 - 0.0212777i) q^{80} +(-1.60398 + 0.756937i) q^{81} +(-6.02578 + 3.70404i) q^{82} +(-0.823013 + 3.25001i) q^{83} +(-2.30430 + 5.25327i) q^{84} +(-3.96727 + 1.61137i) q^{85} +(-7.25810 - 7.06079i) q^{86} +(4.35999 + 17.2172i) q^{87} +(7.28808 + 1.21616i) q^{88} +(5.56318 - 2.25957i) q^{89} +(-2.62873 - 1.06770i) q^{90} +(1.04184 + 0.294605i) q^{91} +(8.52194 - 2.40977i) q^{92} +(-8.79602 + 4.15094i) q^{93} +(-6.23999 + 3.37691i) q^{94} +(2.24747 + 2.14122i) q^{95} +(-13.7269 - 7.42862i) q^{96} +(-6.79664 - 0.374981i) q^{97} +(3.63928 + 0.200785i) q^{98} +(-5.99410 + 10.3821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1080 q - 38 q^{2} - 19 q^{3} - 8 q^{4} - 37 q^{5} - 38 q^{6} - 40 q^{7} - 38 q^{8} + 49 q^{9} + 19 q^{10} - 40 q^{11} - 38 q^{12} - 38 q^{13} - 38 q^{15} - 8 q^{16} - 94 q^{17} - 38 q^{18} - 38 q^{19} - 46 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) $ 1080 * q - 38 * q^2 - 19 * q^3 - 8 * q^4 - 37 * q^5 - 38 * q^6 - 40 * q^7 - 38 * q^8 + 49 * q^9 + 19 * q^10 - 40 * q^11 - 38 * q^12 - 38 * q^13 - 38 * q^15 - 8 * q^16 - 94 * q^17 - 38 * q^18 - 38 * q^19 - 46 * q^20 - 38 * q^21 - 19 * q^22 - 34 * q^23 - 30 * q^24 - 7 * q^25 + 41 * q^26 - 76 * q^27 - 15 * q^28 + 60 * q^30 - 38 * q^31 - 38 * q^32 - 114 * q^33 - 38 * q^34 - 33 * q^35 - 38 * q^37 - 76 * q^38 + 26 * q^39 - 38 * q^40 - 38 * q^41 - 32 * q^42 + 43 * q^43 - 26 * q^44 + 47 * q^45 + 26 * q^47 - 456 * q^48 - 32 * q^49 + 38 * q^50 + 38 * q^51 - 38 * q^52 - 38 * q^53 - 214 * q^54 - 29 * q^55 + 304 * q^56 - 38 * q^57 - 46 * q^58 - 38 * q^59 - 33 * q^61 - 13 * q^62 + 68 * q^63 - 110 * q^64 + 38 * q^65 - 26 * q^66 - 38 * q^67 - 96 * q^68 - 228 * q^69 - 342 * q^70 - 38 * q^71 - 38 * q^72 - 29 * q^73 + 50 * q^74 + 190 * q^75 + 323 * q^76 - 60 * q^77 + 228 * q^78 - 38 * q^79 + 322 * q^80 + 129 * q^81 + 48 * q^82 - 35 * q^83 + 19 * q^84 - 23 * q^85 - 684 * q^86 + 37 * q^87 - 38 * q^88 + 76 * q^89 - 722 * q^90 - 114 * q^91 - 22 * q^92 - 30 * q^93 + 228 * q^94 - 152 * q^95 + 142 * q^96 + 19 * q^97 + 57 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{25}{57}\right)$

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 $

$2$	−0.166828	−	0.854065i	−0.117965	−	0.603915i	−0.992829	−	0.119546i	$-0.961856\pi$
$2$	−0.166828	−	0.854065i	−0.117965	−	0.603915i	0.874864	−	0.484369i	$-0.160951\pi$
$3$	2.73618	−	0.302840i	1.57973	−	0.174845i	0.723089	−	0.690755i	$-0.242721\pi$
$3$	2.73618	−	0.302840i	1.57973	−	0.174845i	0.856643	+	0.515910i	$0.172546\pi$
$4$	1.15139	−	0.467655i	0.575696	−	0.233828i
$5$	0.510455	−	0.496579i	0.228283	−	0.222077i	−0.574258	−	0.818675i	$-0.694709\pi$
$5$	0.510455	−	0.496579i	0.228283	−	0.222077i	0.802540	+	0.596598i	$0.203481\pi$
$6$	−0.715115	−	2.28635i	−0.291945	−	0.933399i
$7$	−1.32321	+	1.02989i	−0.500125	+	0.389263i	−0.832622	−	0.553841i	$-0.813161\pi$
$7$	−1.32321	+	1.02989i	−0.500125	+	0.389263i	0.332497	+	0.943104i	$0.392109\pi$
$8$	−1.54341	−	2.36236i	−0.545677	−	0.835221i
$9$	4.46756	−	1.00120i	1.48919	−	0.333735i
$10$	−0.509268	−	0.353119i	−0.161045	−	0.111666i
$11$	−1.77342	+	1.92645i	−0.534706	+	0.580846i	−0.943330	−	0.331857i	$-0.892325\pi$
$11$	−1.77342	+	1.92645i	−0.534706	+	0.580846i	0.408623	+	0.912703i	$0.366009\pi$
$12$	3.00879	−	1.62828i	0.868563	−	0.470043i
$13$	−0.382408	−	0.520285i	−0.106061	−	0.144301i	0.749498	−	0.662007i	$-0.230295\pi$
$13$	−0.382408	−	0.520285i	−0.106061	−	0.144301i	−0.855559	+	0.517706i	$0.826786\pi$
$14$	1.10034	+	0.958289i	0.294079	+	0.256113i
$15$	1.24631	−	1.51331i	0.321796	−	0.390736i
$16$	0.0214243	−	0.0208419i	0.00535608	−	0.00521047i
$17$	−5.57085	−	2.26268i	−1.35113	−	0.548781i	−0.418041	−	0.908428i	$-0.637283\pi$
$17$	−5.57085	−	2.26268i	−1.35113	−	0.548781i	−0.933089	+	0.359647i	$0.882897\pi$
$18$	−1.60041	−	3.64856i	−0.377219	−	0.859973i
$19$	0.165531	+	4.35575i	0.0379755	+	0.999279i
$19$	0.165531	+	4.35575i	0.0379755	+	0.999279i
$20$	0.355507	−	0.810474i	0.0794938	−	0.181228i
$21$	−3.30863	+	3.21869i	−0.722003	+	0.702375i
$22$	1.94117	+	1.19323i	0.413858	+	0.254398i
$23$	7.08301	+	0.783947i	1.47691	+	0.163464i	0.812086	−	0.583537i	$-0.198332\pi$
$23$	7.08301	+	0.783947i	1.47691	+	0.163464i	0.664822	+	0.747001i	$0.268507\pi$
$24$	−4.93845	−	5.99643i	−1.00806	−	1.22402i
$25$	−0.123797	+	4.49114i	−0.0247595	+	0.898228i
$26$	−0.380561	+	0.413399i	−0.0746341	+	0.0810743i
$27$	4.10965	−	1.41085i	0.790903	−	0.271517i
$28$	−1.04189	+	1.80461i	−0.196900	+	0.341040i
$29$	0.886158	+	6.39051i	0.164555	+	1.18669i	0.875422	+	0.483360i	$0.160584\pi$
$29$	0.886158	+	6.39051i	0.164555	+	1.18669i	−0.710866	+	0.703327i	$0.751697\pi$
$30$	−1.50039	−	0.811969i	−0.273932	−	0.148245i
$31$	−3.34168	+	1.14720i	−0.600184	+	0.206043i	−0.608015	−	0.793926i	$-0.708034\pi$
$31$	−3.34168	+	1.14720i	−0.600184	+	0.206043i	0.00783046	+	0.999969i	$0.497507\pi$
$32$	−4.65925	−	3.23065i	−0.823646	−	0.571104i
$33$	−4.26899	+	5.80816i	−0.743135	+	1.01107i
$34$	−1.00311	+	5.13535i	−0.172031	+	0.880705i
$35$	−0.164015	+	1.18279i	−0.0277236	+	0.199928i
$36$	4.67570	−	3.24206i	0.779283	−	0.540343i
$37$	0.110996	−	0.120573i	0.0182476	−	0.0198222i	−0.726533	−	0.687131i	$-0.758870\pi$
$37$	0.110996	−	0.120573i	0.0182476	−	0.0198222i	0.744781	+	0.667309i	$0.232554\pi$
$38$	3.69248	−	0.868035i	0.599000	−	0.140814i
$39$	−1.20390	−	1.30778i	−0.192778	−	0.209413i
$40$	−1.96094	−	0.439457i	−0.310052	−	0.0694842i
$41$	−2.85004	−	7.61213i	−0.445102	−	1.18881i	−0.946245	−	0.323450i	$-0.895157\pi$
$41$	−2.85004	−	7.61213i	−0.445102	−	1.18881i	0.501143	−	0.865364i	$-0.332913\pi$
$42$	3.30094	+	2.28882i	0.509346	+	0.353173i
$43$	9.56242	−	6.63043i	1.45826	−	1.01113i	0.466288	−	0.884633i	$-0.345591\pi$
$43$	9.56242	−	6.63043i	1.45826	−	1.01113i	0.991967	−	0.126499i	$-0.0403740\pi$
$44$	−1.14099	+	3.04745i	−0.172011	+	0.459420i
$45$	1.78331	−	2.72956i	0.265841	−	0.406899i
$46$	−0.512100	−	6.18013i	−0.0755051	−	0.911211i
$47$	−2.43391	−	7.78164i	−0.355022	−	1.13507i	−0.944840	−	0.327533i	$-0.893783\pi$
$47$	−2.43391	−	7.78164i	−0.355022	−	1.13507i	0.589817	−	0.807537i	$-0.299200\pi$
$48$	0.0523090	−	0.0635152i	0.00755015	−	0.00916764i
$49$	−1.02820	+	4.06028i	−0.146886	+	0.580041i
$50$	3.85638	−	0.643516i	0.545374	−	0.0910068i
$51$	−15.9281	−	4.50403i	−2.23037	−	0.630690i
$52$	−0.683616	−	0.420217i	−0.0948005	−	0.0582736i
$53$	1.76273	+	5.63576i	0.242130	+	0.774132i	0.993457	+	0.114202i	$0.0364313\pi$
$53$	1.76273	+	5.63576i	0.242130	+	0.774132i	−0.751328	+	0.659929i	$0.770586\pi$
$54$	−1.89056	−	3.27454i	−0.257272	−	0.445609i
$55$	0.0513810	+	1.86401i	0.00692822	+	0.251343i
$56$	4.47522	+	1.53635i	0.598027	+	0.205303i
$57$	1.77202	+	11.8680i	0.234710	+	1.57195i
$58$	5.31007	−	1.82295i	0.697247	−	0.239365i
$59$	−4.63414	−	12.3772i	−0.603314	−	1.61138i	−0.779064	−	0.626945i	$-0.784305\pi$
$59$	−4.63414	−	12.3772i	−0.603314	−	1.61138i	0.175750	−	0.984435i	$-0.443765\pi$
$60$	0.727286	−	2.32526i	0.0938922	−	0.300190i
$61$	−0.679555	−	1.34284i	−0.0870081	−	0.171933i	0.844599	−	0.535399i	$-0.179839\pi$
$61$	−0.679555	−	1.34284i	−0.0870081	−	0.171933i	−0.931607	+	0.363466i	$0.881593\pi$
$62$	1.53727	+	2.66263i	0.195233	+	0.338154i
$63$	−4.88037	+	5.92590i	−0.614869	+	0.746594i
$64$	−1.95788	+	4.46352i	−0.244735	+	0.557940i
$65$	−0.453565	−	0.0756865i	−0.0562578	−	0.00938776i
$66$	5.67274	+	2.67703i	0.698265	+	0.329519i
$67$	6.25416	−	0.345052i	0.764067	−	0.0421548i	0.331138	−	0.943583i	$-0.392568\pi$
$67$	6.25416	−	0.345052i	0.764067	−	0.0421548i	0.432930	+	0.901428i	$0.357480\pi$
$68$	−7.47239			−0.906161
$69$	19.6178			2.36170
$70$	1.03754	−	0.0572428i	0.124010	−	0.00684182i
$71$	−1.83055	+	3.61727i	−0.217246	+	0.429291i	−0.974675	−	0.223628i	$-0.928210\pi$
$71$	−1.83055	+	3.61727i	−0.217246	+	0.429291i	0.757428	+	0.652918i	$0.226456\pi$
$72$	−9.26047	−	9.00872i	−1.09136	−	1.06169i
$73$	−2.20777	−	0.896719i	−0.258400	−	0.104953i	0.243432	−	0.969918i	$-0.421727\pi$
$73$	−2.20777	−	0.896719i	−0.258400	−	0.104953i	−0.501832	+	0.864965i	$0.667341\pi$
$74$	−0.121495	−	0.0746825i	−0.0141235	−	0.00868167i
$75$	1.02136	+	12.3260i	0.117937	+	1.42329i
$76$	2.22758	+	4.93777i	0.255521	+	0.566401i
$77$	0.362566	−	4.37552i	0.0413182	−	0.498637i
$78$	−0.916088	+	1.24638i	−0.103727	+	0.141125i
$79$	−2.81568	+	1.95235i	−0.316789	+	0.219657i	−0.717518	−	0.696540i	$-0.754722\pi$
$79$	−2.81568	+	1.95235i	−0.316789	+	0.219657i	0.400729	+	0.916197i	$0.368757\pi$
$80$	0.000586516	−	0.0212777i	6.55745e−5	−	0.00237892i
$81$	−1.60398	+	0.756937i	−0.178220	+	0.0841041i
$82$	−6.02578	+	3.70404i	−0.665437	+	0.409042i
$83$	−0.823013	+	3.25001i	−0.0903375	+	0.356735i	−0.998018	−	0.0629270i	$-0.979956\pi$
$83$	−0.823013	+	3.25001i	−0.0903375	+	0.356735i	0.907681	+	0.419662i	$0.137851\pi$
$84$	−2.30430	+	5.25327i	−0.251420	+	0.573179i
$85$	−3.96727	+	1.61137i	−0.430311	+	0.174777i
$86$	−7.25810	−	7.06079i	−0.782661	−	0.761384i
$87$	4.35999	+	17.2172i	0.467440	+	1.84588i
$88$	7.28808	+	1.21616i	0.776911	+	0.129644i
$89$	5.56318	−	2.25957i	0.589696	−	0.239514i	−0.0618971	−	0.998083i	$-0.519715\pi$
$89$	5.56318	−	2.25957i	0.589696	−	0.239514i	0.651593	+	0.758569i	$0.274101\pi$
$90$	−2.62873	−	1.06770i	−0.277093	−	0.112545i
$91$	1.04184	+	0.294605i	0.109215	+	0.0308830i
$92$	8.52194	−	2.40977i	0.888473	−	0.251236i
$93$	−8.79602	+	4.15094i	−0.912105	+	0.430433i
$94$	−6.23999	+	3.37691i	−0.643605	+	0.348302i
$95$	2.24747	+	2.14122i	0.230586	+	0.219684i
$96$	−13.7269	−	7.42862i	−1.40100	−	0.758181i
$97$	−6.79664	−	0.374981i	−0.690094	−	0.0380736i	−0.293353	−	0.956004i	$-0.594771\pi$
$97$	−6.79664	−	0.374981i	−0.690094	−	0.0380736i	−0.396741	+	0.917931i	$0.629859\pi$
$98$	3.63928	+	0.200785i	0.367623	+	0.0202823i
$99$	−5.99410	+	10.3821i	−0.602429	+	1.04344i
$100$	1.95777	+	5.22896i	0.195777	+	0.522896i
$101$	2.17034	−	0.486384i	0.215957	−	0.0483970i	−0.109360	−	0.994002i	$-0.534880\pi$
$101$	2.17034	−	0.486384i	0.215957	−	0.0483970i	0.325316	+	0.945605i	$0.394529\pi$
$102$	−1.18949	+	14.3550i	−0.117777	+	1.42136i
$103$	11.9779	+	9.32274i	1.18021	+	0.918597i	0.997908	−	0.0646451i	$-0.0205915\pi$
$103$	11.9779	+	9.32274i	1.18021	+	0.918597i	0.182305	+	0.983242i	$0.441644\pi$
$104$	−0.638889	+	1.70640i	−0.0626482	+	0.167326i
$105$	−0.0905777	+	3.28599i	−0.00883948	+	0.320680i
$106$	4.51924	−	2.44569i	0.438947	−	0.237546i
$107$	1.07806	+	0.370099i	0.104220	+	0.0357789i	0.376316	−	0.926491i	$-0.377191\pi$
$107$	1.07806	+	0.370099i	0.104220	+	0.0357789i	−0.272096	+	0.962270i	$0.587717\pi$
$108$	4.07203	−	3.54634i	0.391832	−	0.341246i
$109$	0.826371	−	2.64205i	0.0791520	−	0.253063i	−0.906404	−	0.422411i	$-0.861184\pi$
$109$	0.826371	−	2.64205i	0.0791520	−	0.253063i	0.985556	+	0.169348i	$0.0541663\pi$
$110$	1.58341	−	0.354851i	0.150972	−	0.0338337i
$111$	0.267189	−	0.363524i	0.0253605	−	0.0345042i
$112$	−0.00688387	+	0.0496429i	−0.000650464	+	0.00469081i
$113$	−10.3731	−	8.07373i	−0.975822	−	0.759513i	−0.00516622	−	0.999987i	$-0.501644\pi$
$113$	−10.3731	−	8.07373i	−0.975822	−	0.759513i	−0.970656	+	0.240474i	$0.922697\pi$
$114$	9.84041	−	3.49333i	0.921639	−	0.327180i
$115$	4.00485	−	3.11710i	0.373454	−	0.290671i
$116$	4.00887	+	6.94357i	0.372214	+	0.644694i
$117$	−2.22934	−	1.94154i	−0.206103	−	0.179495i
$118$	−9.79787	+	6.02273i	−0.901967	+	0.554437i
$119$	9.70170	−	2.74338i	0.889354	−	0.251485i
$120$	−5.49856	−	0.608580i	−0.501947	−	0.0555555i
$121$	0.342190	+	4.12962i	0.0311082	+	0.375420i
$122$	−1.03350	+	0.804407i	−0.0935688	+	0.0728276i
$123$	−10.1035	−	19.9650i	−0.911000	−	1.80018i
$124$	−3.31110	+	2.88364i	−0.297345	+	0.258958i
$125$	4.57863	+	4.97372i	0.409526	+	0.444863i
$126$	5.87529	+	3.17955i	0.523412	+	0.283257i
$127$	−6.15972	+	10.6689i	−0.546587	+	0.946716i	0.451918	+	0.892059i	$0.350740\pi$
$127$	−6.15972	+	10.6689i	−0.546587	+	0.946716i	−0.998505	+	0.0546569i	$0.982593\pi$
$128$	−6.92621	−	1.55220i	−0.612197	−	0.137196i
$129$	24.1565	−	21.0379i	2.12686	−	1.85229i
$130$	0.0110259	+	0.400000i	0.000967038	+	0.0350823i
$131$	−7.41834	−	6.46064i	−0.648143	−	0.564468i	0.268944	−	0.963156i	$-0.413325\pi$
$131$	−7.41834	−	6.46064i	−0.648143	−	0.564468i	−0.917087	+	0.398687i	$0.869466\pi$
$132$	−2.19906	+	8.68389i	−0.191404	+	0.755836i
$133$	−4.70499	−	5.59308i	−0.407974	−	0.484981i
$134$	−1.33806	−	5.28389i	−0.115591	−	0.456459i
$135$	1.39720	−	2.76094i	0.120252	−	0.237624i
$136$	3.25282	+	16.6526i	0.278927	+	1.42795i
$137$	13.3879	−	0.738631i	1.14381	−	0.0631055i	0.526747	−	0.850022i	$-0.323412\pi$
$137$	13.3879	−	0.738631i	1.14381	−	0.0631055i	0.617059	+	0.786917i	$0.288324\pi$
$138$	−3.27279	−	16.7548i	−0.278598	−	1.42627i
$139$	−7.91851	−	3.73684i	−0.671639	−	0.316954i	0.0604418	−	0.998172i	$-0.480749\pi$
$139$	−7.91851	−	3.73684i	−0.671639	−	0.316954i	−0.732081	+	0.681217i	$0.761451\pi$
$140$	0.364292	+	1.43856i	0.0307883	+	0.121580i
$141$	−9.01620	−	20.5549i	−0.759301	−	1.73103i
$142$	3.39477	+	0.959949i	0.284883	+	0.0805571i
$143$	1.68047	+	0.185995i	0.140528	+	0.0155536i
$144$	0.0748474	−	0.114563i	0.00623729	−	0.00954688i
$145$	3.62573	+	2.82202i	0.301101	+	0.234356i
$146$	−0.397539	+	2.03518i	−0.0329006	+	0.168432i
$147$	−1.58373	+	11.4210i	−0.130624	+	0.941991i
$148$	0.0714128	−	0.190735i	0.00587010	−	0.0156783i
$149$	4.69511	+	5.70095i	0.384638	+	0.467040i	0.928066	−	0.372416i	$-0.121470\pi$
$149$	4.69511	+	5.70095i	0.384638	+	0.467040i	−0.543428	+	0.839456i	$0.682874\pi$
$150$	10.3568	−	2.92864i	0.845633	−	0.239122i
$151$	−12.6781	+	2.11560i	−1.03173	+	0.172165i	−0.656154	−	0.754627i	$-0.727818\pi$
$151$	−12.6781	+	2.11560i	−1.03173	+	0.172165i	−0.375575	+	0.926792i	$0.622555\pi$
$152$	10.0344	−	7.11375i	0.813896	−	0.577001i
$153$	−27.1535	−	4.53112i	−2.19523	−	0.366319i
$154$	−3.79746	+	0.420303i	−0.306008	+	0.0338690i
$155$	−1.13610	+	2.24500i	−0.0912541	+	0.180323i
$156$	−1.99775	−	0.942762i	−0.159948	−	0.0754814i
$157$	14.3639	−	1.58980i	1.14636	−	0.126880i	0.483309	−	0.875450i	$-0.339435\pi$
$157$	14.3639	−	1.58980i	1.14636	−	0.126880i	0.663055	+	0.748570i	$0.269259\pi$
$158$	2.13717	+	2.07907i	0.170024	+	0.165402i
$159$	6.52988	+	14.8866i	0.517853	+	1.18059i
$160$	−3.98261	+	0.664580i	−0.314853	+	0.0525397i
$161$	−10.1797	+	6.25741i	−0.802269	+	0.493153i
$162$	0.914062	+	1.24363i	0.0718155	+	0.0977085i
$163$	−4.32623	−	1.48520i	−0.338856	−	0.116329i	0.150019	−	0.988683i	$-0.452066\pi$
$163$	−4.32623	−	1.48520i	−0.338856	−	0.116329i	−0.488875	+	0.872354i	$0.662593\pi$
$164$	−6.84137	−	7.43171i	−0.534221	−	0.580319i
$165$	0.705084	+	5.08470i	0.0548907	+	0.395843i
$166$	2.91302	+	0.160716i	0.226094	+	0.0124740i
$167$	−2.88548	−	20.8086i	−0.223285	−	1.61022i	−0.688648	−	0.725096i	$-0.741795\pi$
$167$	−2.88548	−	20.8086i	−0.223285	−	1.61022i	0.465363	−	0.885120i	$-0.345924\pi$
$168$	12.7103	+	2.84844i	0.980618	+	0.219762i
$169$	3.75623	−	12.0093i	0.288941	−	0.923796i
$170$	2.03806	+	3.11949i	0.156312	+	0.239254i
$171$	5.10052	+	19.2939i	0.390047	+	1.47544i
$172$	7.90934	−	12.1061i	0.603082	−	0.923085i
$173$	3.40826	+	4.13842i	0.259125	+	0.314638i	0.885278	−	0.465062i	$-0.153968\pi$
$173$	3.40826	+	4.13842i	0.259125	+	0.314638i	−0.626153	+	0.779700i	$0.715371\pi$
$174$	13.9772	−	6.59602i	1.05961	−	0.500043i
$175$	−4.46158	−	6.07020i	−0.337264	−	0.458864i
$176$	0.00215651	+	0.0782343i	0.000162553	+	0.00589713i
$177$	−16.4282	−	32.4629i	−1.23482	−	2.44006i
$178$	−2.85791	−	4.37436i	−0.214209	−	0.327872i
$179$	1.15512	−	13.9402i	0.0863378	−	1.04194i	−0.806401	−	0.591369i	$-0.798588\pi$
$179$	1.15512	−	13.9402i	0.0863378	−	1.04194i	0.892739	−	0.450574i	$-0.148781\pi$
$180$	0.776799	−	3.97678i	0.0578992	−	0.296411i
$181$	3.30308	−	16.9099i	0.245516	−	1.25691i	−0.631095	−	0.775706i	$-0.717394\pi$
$181$	3.30308	−	16.9099i	0.245516	−	1.25691i	0.876611	−	0.481200i	$-0.159799\pi$
$182$	0.0778035	−	0.938949i	0.00576718	−	0.0695995i
$183$	−2.26605	−	3.46844i	−0.167511	−	0.256395i
$184$	−9.08000	−	17.9426i	−0.669386	−	1.32274i
$185$	−0.00321586	−	0.116665i	−0.000236435	−	0.00857741i
$186$	5.01259	+	6.81988i	0.367541	+	0.500058i
$187$	14.2384	−	6.71926i	1.04122	−	0.491361i
$188$	−6.44151	−	7.82150i	−0.469796	−	0.570441i
$189$	−3.98490	+	6.09934i	−0.289859	+	0.443662i
$190$	1.45380	−	2.27670i	0.105470	−	0.165169i
$191$	−6.73583	−	10.3100i	−0.487388	−	0.746002i	0.505785	−	0.862660i	$-0.331203\pi$
$191$	−6.73583	−	10.3100i	−0.487388	−	0.746002i	−0.993172	+	0.116658i	$0.962782\pi$
$192$	−4.00537	+	12.8059i	−0.289063	+	0.924186i
$193$	−5.94587	−	1.33250i	−0.427993	−	0.0959155i	−0.000638827	−	1.00000i	$-0.500203\pi$
$193$	−5.94587	−	1.33250i	−0.427993	−	0.0959155i	−0.427354	+	0.904084i	$0.640554\pi$
$194$	0.813610	+	5.86733i	0.0584138	+	0.421250i
$195$	−1.26395	−	0.0697343i	−0.0905136	−	0.00499377i
$196$	0.714947	+	5.15583i	0.0510677	+	0.368273i
$197$	14.7389	+	16.0108i	1.05011	+	1.14072i	0.989789	+	0.142541i	$0.0455271\pi$
$197$	14.7389	+	16.0108i	1.05011	+	1.14072i	0.0603175	+	0.998179i	$0.480789\pi$
$198$	9.86695	+	3.38733i	0.701214	+	0.240727i
$199$	10.3614	+	14.0972i	0.734500	+	0.999324i	0.999386	+	0.0350439i	$0.0111571\pi$
$199$	10.3614	+	14.0972i	0.734500	+	0.999324i	−0.264885	+	0.964280i	$0.585334\pi$
$200$	10.8008	−	6.63920i	0.763729	−	0.469463i
$201$	17.0080	−	2.83813i	1.19965	−	0.200186i
$202$	−0.777476	−	1.77247i	−0.0547030	−	0.124710i
$203$	−7.75410	−	7.54331i	−0.544231	−	0.529436i
$204$	−20.4458	+	2.26294i	−1.43149	+	0.158437i
$205$	−5.23484	−	2.47038i	−0.365617	−	0.172539i
$206$	5.96399	−	11.7852i	0.415531	−	0.821111i
$207$	32.4286	−	3.58920i	2.25395	−	0.249467i
$208$	−0.0190366	−	0.00317664i	−0.00131995	−	0.000220260i
$209$	−8.68469	−	7.40570i	−0.600733	−	0.512263i
$210$	2.82156	−	0.470835i	0.194706	−	0.0324907i
$211$	15.0953	−	4.26856i	1.03921	−	0.293860i	0.290579	−	0.956851i	$-0.406152\pi$
$211$	15.0953	−	4.26856i	1.03921	−	0.293860i	0.748627	+	0.662991i	$0.230713\pi$
$212$	4.66519	+	5.66463i	0.320407	+	0.389048i
$213$	−3.91326	+	10.4518i	−0.268132	+	0.716149i
$214$	0.136238	−	0.982478i	0.00931305	−	0.0671608i
$215$	1.58866	−	8.13303i	0.108345	−	0.554668i
$216$	−9.67579	−	7.53097i	−0.658354	−	0.512418i
$217$	3.24024	−	4.95956i	0.219962	−	0.336677i
$218$	−2.39435	−	0.265006i	−0.162166	−	0.0179485i
$219$	−6.31241	−	1.78498i	−0.426553	−	0.120618i
$220$	0.930873	+	2.12218i	0.0627594	+	0.143077i
$221$	0.953098	+	3.76370i	0.0641123	+	0.253174i
$222$	−0.355048	−	0.167551i	−0.0238292	−	0.0112453i
$223$	−1.14285	−	5.85078i	−0.0765312	−	0.391797i	−0.999968	−	0.00804561i	$-0.997439\pi$
$223$	−1.14285	−	5.85078i	−0.0765312	−	0.391797i	0.923436	−	0.383751i	$-0.125368\pi$
$224$	9.49236	−	0.523708i	0.634235	−	0.0349917i
$225$	3.94347	+	20.1884i	0.262898	+	1.34589i
$226$	−5.16496	+	10.2062i	−0.343568	+	0.678909i
$227$	−0.336122	−	1.32731i	−0.0223092	−	0.0880969i	0.957244	−	0.289280i	$-0.0934160\pi$
$227$	−0.336122	−	1.32731i	−0.0223092	−	0.0880969i	−0.979554	+	0.201183i	$0.935521\pi$
$228$	7.59042	+	12.8360i	0.502688	+	0.850086i
$229$	−6.86357	+	27.1036i	−0.453557	+	1.79106i	0.144389	+	0.989521i	$0.453878\pi$
$229$	−6.86357	+	27.1036i	−0.453557	+	1.79106i	−0.597947	+	0.801536i	$0.704017\pi$
$230$	−3.33033	−	2.90038i	−0.219595	−	0.191246i
$231$	−0.333038	−	12.0820i	−0.0219123	−	0.794937i
$232$	13.7290	−	11.9566i	0.901352	−	0.784988i
$233$	−16.8226	−	3.77003i	−1.10208	−	0.246983i	−0.370566	−	0.928806i	$-0.620836\pi$
$233$	−16.8226	−	3.77003i	−1.10208	−	0.246983i	−0.731517	+	0.681823i	$0.761187\pi$
$234$	−1.28628	+	2.22791i	−0.0840869	+	0.145643i
$235$	−5.10660	−	2.76355i	−0.333118	−	0.180274i
$236$	−11.1240	−	12.0839i	−0.724111	−	0.786594i
$237$	−7.11296	+	6.19468i	−0.462036	+	0.402388i
$238$	−3.96154	−	7.82821i	−0.256788	−	0.507428i
$239$	5.97263	−	4.64869i	0.386338	−	0.300699i	−0.402358	−	0.915482i	$-0.631809\pi$
$239$	5.97263	−	4.64869i	0.386338	−	0.300699i	0.788696	+	0.614784i	$0.210757\pi$
$240$	−0.00483893	−	0.0583972i	−0.000312352	−	0.00376952i
$241$	6.81111	+	0.753853i	0.438742	+	0.0485600i	0.326666	−	0.945140i	$-0.394075\pi$
$241$	6.81111	+	0.753853i	0.438742	+	0.0485600i	0.112076	+	0.993700i	$0.464250\pi$
$242$	3.46988	−	0.981189i	0.223052	−	0.0630732i
$243$	−15.2645	+	9.38307i	−0.979220	+	0.601924i
$244$	−1.41042	−	1.22834i	−0.0902929	−	0.0786361i
$245$	1.49140	+	2.58318i	0.0952819	+	0.165033i
$246$	−15.3659	+	11.9597i	−0.979693	+	0.762526i
$247$	2.20293	−	1.75180i	0.140169	−	0.111464i
$248$	7.86768	+	6.12366i	0.499598	+	0.388853i
$249$	−1.26768	+	9.14183i	−0.0803358	+	0.579340i
$250$	3.48404	−	4.74021i	0.220350	−	0.299797i
$251$	−27.3583	+	6.13113i	−1.72684	+	0.386994i	−0.965304	−	0.261130i	$-0.915905\pi$
$251$	−27.3583	+	6.13113i	−1.72684	+	0.386994i	−0.761535	+	0.648123i	$0.775554\pi$
$252$	−2.84794	+	9.10537i	−0.179403	+	0.573585i
$253$	−14.0714	+	12.2548i	−0.884660	+	0.770451i
$254$	10.1396	+	3.48093i	0.636214	+	0.218413i
$255$	−10.3672	+	5.61043i	−0.649217	+	0.351339i
$256$	−0.438798	+	15.9188i	−0.0274249	+	0.994923i
$257$	1.98047	−	5.28961i	0.123538	−	0.329957i	−0.860096	−	0.510132i	$-0.829596\pi$
$257$	1.98047	−	5.28961i	0.123538	−	0.329957i	0.983634	+	0.180176i	$0.0576666\pi$
$258$	−21.9977	−	17.1215i	−1.36952	−	1.06594i
$259$	−0.0226924	+	0.273857i	−0.00141004	+	0.0170166i
$260$	−0.557626	+	0.124967i	−0.0345825	+	0.00775012i
$261$	10.3572	+	27.6628i	0.641092	+	1.71228i
$262$	−4.28022	+	7.41356i	−0.264433	+	0.458011i
$263$	−21.1985	−	1.16955i	−1.30716	−	0.0721178i	−0.611932	−	0.790911i	$-0.709607\pi$
$263$	−21.1985	−	1.16955i	−1.30716	−	0.0721178i	−0.695224	+	0.718793i	$0.744695\pi$
$264$	20.3098	+	1.12052i	1.24998	+	0.0689633i
$265$	3.69839	+	2.00147i	0.227191	+	0.122949i
$266$	−3.99193	+	4.95145i	−0.244761	+	0.303593i
$267$	14.5376	−	7.86733i	0.889684	−	0.481473i
$268$	7.03963	−	3.32208i	0.430014	−	0.202928i
$269$	5.77870	−	1.63406i	0.352334	−	0.0996304i	−0.0913379	−	0.995820i	$-0.529114\pi$
$269$	5.77870	−	1.63406i	0.352334	−	0.0996304i	0.443671	+	0.896190i	$0.353676\pi$
$270$	−2.59111	−	0.732697i	−0.157690	−	0.0445905i
$271$	18.6207	+	7.56306i	1.13113	+	0.459423i	0.863625	−	0.504134i	$-0.168188\pi$
$271$	18.6207	+	7.56306i	1.13113	+	0.459423i	0.267500	+	0.963558i	$0.413802\pi$
$272$	−0.166510	+	0.0676306i	−0.0100962	+	0.00410071i
$273$	2.93988	+	0.490579i	0.177930	+	0.0296912i
$274$	−2.86431	−	11.3109i	−0.173040	−	0.683318i
$275$	−8.43240	−	8.20317i	−0.508493	−	0.494670i
$276$	22.5877	−	9.17435i	1.35962	−	0.552231i
$277$	−1.84821	+	4.21349i	−0.111048	+	0.253164i	−0.962507	−	0.271258i	$-0.912560\pi$
$277$	−1.84821	+	4.21349i	−0.111048	+	0.253164i	0.851459	+	0.524422i	$0.175718\pi$
$278$	−1.87047	+	7.38633i	−0.112184	+	0.443003i
$279$	−13.7806	+	8.47090i	−0.825022	+	0.507139i
$280$	3.04732	−	1.43806i	0.182112	−	0.0859407i
$281$	0.158625	−	5.75462i	0.00946278	−	0.343292i	−0.980042	−	0.198791i	$-0.936298\pi$
$281$	0.158625	−	5.75462i	0.00946278	−	0.343292i	0.989505	−	0.144501i	$-0.0461577\pi$
$282$	−16.0510	+	11.1295i	−0.955825	+	0.662755i
$283$	14.0129	−	19.0653i	0.832982	−	1.13331i	−0.156360	−	0.987700i	$-0.549976\pi$
$283$	14.0129	−	19.0653i	0.832982	−	1.13331i	0.989342	−	0.145612i	$-0.0465152\pi$
$284$	−0.416049	+	5.02096i	−0.0246879	+	0.297939i
$285$	6.79792	+	5.17813i	0.402674	+	0.306726i
$286$	−0.121498	−	1.46626i	−0.00718432	−	0.0867019i
$287$	11.6109	+	7.13717i	0.685368	+	0.421294i
$288$	−24.0500	−	9.76827i	−1.41716	−	0.575601i
$289$	13.7293	+	13.3561i	0.807608	+	0.785653i
$290$	1.80532	−	3.56740i	0.106012	−	0.209485i
$291$	−18.7104	+	1.03228i	−1.09682	+	0.0605133i
$292$	−2.96137			−0.173301
$293$	15.9429			0.931393			0.465697	−	0.884944i	$-0.345804\pi$
$293$	15.9429			0.931393			0.465697	+	0.884944i	$0.345804\pi$
$294$	10.0185	−	0.552737i	0.584292	−	0.0322363i
$295$	−8.51180	−	4.01681i	−0.495576	−	0.233868i
$296$	−0.456149	−	0.0761179i	−0.0265132	−	0.00442426i
$297$	−4.57022	+	10.4191i	−0.265191	+	0.604575i
$298$	4.08571	−	4.96100i	0.236679	−	0.287383i
$299$	−2.30072	−	3.98497i	−0.133054	−	0.230457i
$300$	6.94033	+	13.7145i	0.400700	+	0.791805i
$301$	−5.82441	+	18.6217i	−0.335714	+	1.07334i
$302$	3.92192	+	10.4750i	0.225681	+	0.602768i
$303$	5.79113	−	1.98810i	0.332692	−	0.114213i
$304$	0.0943286	+	0.0898691i	0.00541012	+	0.00515435i
$305$	−1.01371	−	0.348006i	−0.0580447	−	0.0199268i
$306$	0.660089	+	23.9468i	0.0377348	+	1.36895i
$307$	−14.2276	−	24.6429i	−0.812010	−	1.40644i	−0.911455	−	0.411399i	$-0.865040\pi$
$307$	−14.2276	−	24.6429i	−0.812010	−	1.40644i	0.0994453	−	0.995043i	$-0.468293\pi$
$308$	−1.62878	−	5.20750i	−0.0928083	−	0.296725i
$309$	35.5968	+	21.8813i	2.02503	+	1.24478i
$310$	2.10691	+	0.595778i	0.119665	+	0.0338379i
$311$	10.5107	−	1.75393i	0.596008	−	0.0994562i	0.141101	−	0.989995i	$-0.454936\pi$
$311$	10.5107	−	1.75393i	0.596008	−	0.0994562i	0.454907	+	0.890539i	$0.349673\pi$
$312$	−1.23135	+	4.86249i	−0.0697114	+	0.275284i
$313$	8.68365	−	10.5440i	0.490829	−	0.595980i	−0.466665	−	0.884434i	$-0.654545\pi$
$313$	8.68365	−	10.5440i	0.490829	−	0.595980i	0.957494	+	0.288454i	$0.0931412\pi$
$314$	−3.75409	−	12.0025i	−0.211855	−	0.677339i
$315$	0.451467	+	5.44840i	0.0254373	+	0.306982i
$316$	−2.32893	+	3.56469i	−0.131013	+	0.200530i
$317$	−6.06354	+	16.1950i	−0.340563	+	0.909602i	0.648382	+	0.761315i	$0.275446\pi$
$317$	−6.06354	+	16.1950i	−0.340563	+	0.909602i	−0.988944	+	0.148287i	$0.952624\pi$
$318$	11.6248	−	8.06044i	0.651885	−	0.452007i
$319$	−13.8825	−	9.62592i	−0.777271	−	0.538948i
$320$	1.21708	+	3.25067i	0.0680367	+	0.181718i
$321$	3.06185	+	0.686177i	0.170896	+	0.0382987i
$322$	7.04248	+	7.65018i	0.392462	+	0.426328i
$323$	8.93355	−	24.6398i	0.497076	−	1.37100i
$324$	−1.49283	+	1.62164i	−0.0829348	+	0.0900912i
$325$	2.38401	−	1.65304i	0.132241	−	0.0916940i
$326$	−0.546719	+	3.94265i	−0.0302799	+	0.218363i
$327$	1.46098	−	7.47939i	0.0807922	−	0.413611i
$328$	−13.5838	+	18.4814i	−0.750041	+	1.02047i
$329$	11.2348	+	7.79005i	0.619396	+	0.429479i
$330$	4.22503	−	1.45046i	0.232580	−	0.0798449i
$331$	−17.9841	−	9.73251i	−0.988496	−	0.534947i	−0.100568	−	0.994930i	$-0.532066\pi$
$331$	−17.9841	−	9.73251i	−0.988496	−	0.534947i	−0.887928	+	0.459983i	$0.847855\pi$
$332$	0.572271	+	4.12692i	0.0314075	+	0.226494i
$333$	0.375161	−	0.649798i	0.0205587	−	0.0356087i
$334$	−17.2905	+	5.93583i	−0.946094	+	0.324794i
$335$	3.02112	−	3.28181i	0.165062	−	0.179305i
$336$	−0.00380164	+	0.137916i	−0.000207396	+	0.00752395i
$337$	3.46684	+	4.20955i	0.188851	+	0.229309i	0.857780	−	0.514018i	$-0.171843\pi$
$337$	3.46684	+	4.20955i	0.188851	+	0.229309i	−0.668929	+	0.743327i	$0.733247\pi$
$338$	−10.8834	−	1.20457i	−0.591979	−	0.0655202i
$339$	−30.8278	−	18.9498i	−1.67433	−	1.02921i
$340$	−3.81432	+	3.71063i	−0.206861	+	0.201237i
$341$	3.71619	−	8.47205i	0.201243	−	0.458787i
$342$	15.6273	−	7.57493i	0.845028	−	0.409605i
$343$	−7.53598	−	17.1803i	−0.406905	−	0.927649i
$344$	−30.4222	−	12.3564i	−1.64025	−	0.666214i
$345$	10.0140	−	9.74176i	0.539135	−	0.524479i
$346$	2.96589	−	3.60128i	0.159447	−	0.193606i
$347$	22.7514	+	19.8142i	1.22136	+	1.06368i	0.995995	+	0.0894070i	$0.0284972\pi$
$347$	22.7514	+	19.8142i	1.22136	+	1.06368i	0.225363	+	0.974275i	$0.427643\pi$
$348$	13.0718	+	17.7848i	0.700720	+	0.953364i
$349$	−19.9516	+	10.7973i	−1.06798	+	0.577964i	−0.912166	−	0.409822i	$-0.865591\pi$
$349$	−19.9516	+	10.7973i	−1.06798	+	0.577964i	−0.155819	+	0.987786i	$0.549802\pi$
$350$	−4.44003	+	4.82316i	−0.237330	+	0.257809i
$351$	−2.30561	−	1.59867i	−0.123064	−	0.0853308i
$352$	14.4865	−	3.24650i	0.772132	−	0.173039i
$353$	16.8767	+	25.8316i	0.898254	+	1.37488i	0.926907	+	0.375290i	$0.122457\pi$
$353$	16.8767	+	25.8316i	0.898254	+	1.37488i	−0.0286539	+	0.999589i	$0.509122\pi$
$354$	−24.9848	+	19.4464i	−1.32793	+	1.03357i
$355$	0.861843	+	2.75547i	0.0457419	+	0.146245i
$356$	5.34870	−	5.20330i	0.283481	−	0.275774i
$357$	25.7148	−	10.4444i	1.36097	−	0.552778i
$358$	−12.0986	+	1.33907i	−0.639430	+	0.0707721i
$359$	−0.338613	−	1.73351i	−0.0178713	−	0.0914912i	0.971449	−	0.237248i	$-0.0762454\pi$
$359$	−0.338613	−	1.73351i	−0.0178713	−	0.0914912i	−0.989320	+	0.145757i	$0.953438\pi$
$360$	−9.20060			−0.484914
$361$	−18.9452	+	1.44203i	−0.997116	+	0.0758963i
$362$	−14.9932			−0.788027
$363$	2.18691	+	11.1958i	0.114783	+	0.587625i
$364$	1.33734	−	0.148017i	0.0700958	−	0.00775820i
$365$	−1.57226	+	0.638597i	−0.0822958	+	0.0334257i
$366$	−2.58424	+	2.51398i	−0.135080	+	0.131408i
$367$	−5.89650	−	18.8522i	−0.307795	−	0.984075i	−0.971692	−	0.236251i	$-0.924081\pi$
$367$	−5.89650	−	18.8522i	−0.307795	−	0.984075i	0.663897	−	0.747824i	$-0.268901\pi$
$368$	0.168087	−	0.130828i	0.00876217	−	0.00681987i
$369$	−20.3540	−	31.1542i	−1.05959	−	1.62182i
$370$	−0.0991034	+	0.0222096i	−0.00515214	+	0.00115462i
$371$	−8.13668	−	5.64185i	−0.422436	−	0.292910i
$372$	−8.18646	+	8.89287i	−0.424448	+	0.461074i
$373$	13.5708	−	7.34413i	0.702667	−	0.380264i	−0.0849871	−	0.996382i	$-0.527085\pi$
$373$	13.5708	−	7.34413i	0.702667	−	0.380264i	0.787654	+	0.616118i	$0.211295\pi$
$374$	−8.11405	−	11.0396i	−0.419567	−	0.570842i
$375$	14.0342	+	12.2224i	0.724723	+	0.631162i
$376$	−14.6265	+	17.7600i	−0.754306	+	0.915903i
$377$	2.98601	−	2.90484i	0.153787	−	0.149607i
$378$	5.87402	+	2.38582i	0.302127	+	0.122713i
$379$	−1.74134	−	3.96985i	−0.0894465	−	0.203917i	0.865357	−	0.501157i	$-0.167092\pi$
$379$	−1.74134	−	3.96985i	−0.0894465	−	0.203917i	−0.954803	+	0.297239i	$0.903934\pi$
$380$	3.58907	+	1.41434i	0.184116	+	0.0725542i
$381$	−13.6231	+	31.0575i	−0.697933	+	1.59113i
$382$	−7.68165	+	7.47282i	−0.393027	+	0.382343i
$383$	33.1738	+	20.3918i	1.69510	+	1.04197i	0.900519	+	0.434817i	$0.143187\pi$
$383$	33.1738	+	20.3918i	1.69510	+	1.04197i	0.794581	+	0.607158i	$0.207690\pi$
$384$	−19.4214	−	2.14956i	−0.991095	−	0.109694i
$385$	−1.98772	−	2.41355i	−0.101303	−	0.123006i
$386$	−0.146106	+	5.30046i	−0.00743660	+	0.269786i
$387$	36.0823	−	39.1958i	1.83416	−	1.99243i
$388$	−8.00096	+	2.74673i	−0.406187	+	0.139444i
$389$	−8.05233	+	13.9470i	−0.408269	+	0.707143i	−0.994696	−	0.102859i	$-0.967201\pi$
$389$	−8.05233	+	13.9470i	−0.408269	+	0.707143i	0.586426	+	0.810002i	$0.300534\pi$
$390$	0.151305	+	1.09113i	0.00766162	+	0.0552516i
$391$	−37.6845	−	20.3939i	−1.90579	−	1.03136i
$392$	11.1788	−	3.83768i	0.564614	−	0.193832i
$393$	−22.2544	−	15.4309i	−1.12259	−	0.778385i
$394$	11.2154	−	15.2591i	0.565022	−	0.768740i
$395$	−0.467785	+	2.39480i	−0.0235368	+	0.120495i
$396$	−2.04632	+	14.7570i	−0.102832	+	0.741568i
$397$	18.7949	−	13.0321i	0.943287	−	0.654061i	0.00502570	−	0.999987i	$-0.498400\pi$
$397$	18.7949	−	13.0321i	0.943287	−	0.654061i	0.938262	+	0.345927i	$0.112435\pi$
$398$	10.3114	−	11.2011i	0.516861	−	0.561461i
$399$	−14.5675	−	13.8788i	−0.729287	−	0.694809i
$400$	0.0909516	+	0.0987998i	0.00454758	+	0.00493999i
$401$	−16.3757	−	3.66987i	−0.817762	−	0.183265i	−0.210324	−	0.977632i	$-0.567452\pi$
$401$	−16.3757	−	3.66987i	−0.817762	−	0.183265i	−0.607438	+	0.794367i	$0.707803\pi$
$402$	−5.26135	−	14.0524i	−0.262412	−	0.700872i
$403$	1.87476	+	1.29993i	0.0933884	+	0.0647540i
$404$	2.27145	−	1.57499i	0.113009	−	0.0783586i
$405$	−0.442882	+	1.18289i	−0.0220070	+	0.0587781i
$406$	−5.14888	+	7.88094i	−0.255534	+	0.391125i
$407$	0.0354365	+	0.427655i	0.00175652	+	0.0211981i
$408$	13.9434	+	44.5794i	0.690299	+	2.20701i
$409$	−7.70423	+	9.35473i	−0.380950	+	0.462561i	−0.926929	−	0.375237i	$-0.877561\pi$
$409$	−7.70423	+	9.35473i	−0.380950	+	0.462561i	0.545979	+	0.837799i	$0.316158\pi$
$410$	−1.23655	+	4.88302i	−0.0610688	+	0.241155i
$411$	36.4080	−	6.07542i	1.79587	−	0.299678i
$412$	18.1510	+	5.13263i	0.894238	+	0.252866i
$413$	18.8791	+	11.6050i	0.928982	+	0.571043i
$414$	−8.47541	−	27.0974i	−0.416544	−	1.33176i
$415$	1.19377	+	2.06767i	0.0586000	+	0.101498i
$416$	0.100875	+	3.65956i	0.00494581	+	0.179425i
$417$	−22.7981	−	7.82660i	−1.11643	−	0.383270i
$418$	−4.87610	+	8.65277i	−0.238498	+	0.423221i
$419$	−8.36819	+	2.87280i	−0.408813	+	0.140346i	−0.521432	−	0.853293i	$-0.674602\pi$
$419$	−8.36819	+	2.87280i	−0.408813	+	0.140346i	0.112620	+	0.993638i	$0.464076\pi$
$420$	1.43242	+	3.82583i	0.0698950	+	0.186681i
$421$	4.45739	−	14.2511i	0.217240	−	0.694554i	−0.780361	−	0.625329i	$-0.784965\pi$
$421$	4.45739	−	14.2511i	0.217240	−	0.694554i	0.997601	−	0.0692253i	$-0.0220527\pi$
$422$	−6.16395	−	12.1803i	−0.300056	−	0.592927i
$423$	−18.6647	−	32.3281i	−0.907506	−	1.57185i
$424$	10.5931	−	12.8625i	0.514446	−	0.624657i
$425$	10.8517	−	24.7394i	0.526384	−	1.20003i
$426$	9.57939	+	1.59852i	0.464123	+	0.0774484i
$427$	2.28217	+	1.07698i	0.110442	+	0.0521188i
$428$	1.41435	−	0.0780320i	0.0683653	−	0.00377182i
$429$	4.65439			0.224716
$430$	−7.21117			−0.347753
$431$	16.5984	−	0.915762i	0.799519	−	0.0441107i	0.349280	−	0.937019i	$-0.386426\pi$
$431$	16.5984	−	0.915762i	0.799519	−	0.0441107i	0.450239	+	0.892908i	$0.351339\pi$
$432$	0.0586418	−	0.115879i	0.00282140	−	0.00557525i
$433$	−16.8967	−	16.4373i	−0.812002	−	0.789928i	0.168652	−	0.985676i	$-0.446058\pi$
$433$	−16.8967	−	16.4373i	−0.812002	−	0.789928i	−0.980654	+	0.195748i	$0.937287\pi$
$434$	−4.77635	−	1.93998i	−0.229272	−	0.0931222i
$435$	10.7753	+	6.62353i	0.516635	+	0.317574i
$436$	−0.284094	−	3.42850i	−0.0136056	−	0.164195i
$437$	−2.24222	+	30.9816i	−0.107260	+	1.48205i
$438$	−0.471404	+	5.68899i	−0.0225245	+	0.271831i
$439$	13.3037	−	18.1004i	0.634952	−	0.863884i	−0.362733	−	0.931893i	$-0.618156\pi$
$439$	13.3037	−	18.1004i	0.634952	−	0.863884i	0.997685	+	0.0680098i	$0.0216649\pi$
$440$	4.32416	−	2.99830i	0.206146	−	0.142939i
$441$	−0.528390	+	19.1690i	−0.0251614	+	0.912810i
$442$	3.05544	−	1.44190i	0.145332	−	0.0685840i
$443$	12.6731	−	7.79013i	0.602117	−	0.370120i	−0.188825	−	0.982011i	$-0.560468\pi$
$443$	12.6731	−	7.79013i	0.602117	−	0.370120i	0.790942	+	0.611891i	$0.209591\pi$
$444$	0.137636	−	0.543511i	0.00653191	−	0.0257939i
$445$	1.71770	−	3.91596i	0.0814268	−	0.185635i
$446$	−4.80628	+	1.95214i	−0.227584	+	0.0924367i
$447$	14.5731	+	14.1770i	0.689285	+	0.670547i
$448$	−2.00626	−	7.92256i	−0.0947871	−	0.374306i
$449$	−18.4664	−	3.08150i	−0.871484	−	0.145425i	−0.288079	−	0.957607i	$-0.593017\pi$
$449$	−18.4664	−	3.08150i	−0.871484	−	0.145425i	−0.583405	+	0.812182i	$0.698280\pi$
$450$	16.5843	−	6.73596i	0.781792	−	0.317536i
$451$	19.7187	+	8.00904i	0.928517	+	0.377131i
$452$	−15.7193	−	4.44498i	−0.739372	−	0.209074i
$453$	−34.0489	+	9.62810i	−1.59975	+	0.452367i
$454$	−1.07754	+	0.508502i	−0.0505714	+	0.0238652i
$455$	0.678108	−	0.366974i	0.0317902	−	0.0172040i
$456$	25.3015	−	22.5033i	1.18485	−	1.05381i
$457$	25.2149	+	13.6456i	1.17950	+	0.638316i	0.942830	−	0.333273i	$-0.108153\pi$
$457$	25.2149	+	13.6456i	1.17950	+	0.638316i	0.236674	+	0.971589i	$0.423943\pi$
$458$	24.2933	+	1.34030i	1.13515	+	0.0626280i
$459$	−26.0866	−	1.43924i	−1.21762	−	0.0671778i
$460$	3.15343	−	5.46189i	0.147029	−	0.254662i
$461$	12.9266	+	34.5254i	0.602051	+	1.60801i	0.781267	+	0.624198i	$0.214574\pi$
$461$	12.9266	+	34.5254i	0.602051	+	1.60801i	−0.179215	+	0.983810i	$0.557356\pi$
$462$	−10.2632	+	2.30005i	−0.477489	+	0.107008i
$463$	−2.23639	+	26.9892i	−0.103934	+	1.25429i	0.722544	+	0.691325i	$0.242972\pi$
$463$	−2.23639	+	26.9892i	−0.103934	+	1.25429i	−0.826478	+	0.562969i	$0.809659\pi$
$464$	0.152176	+	0.118443i	0.00706458	+	0.00549858i
$465$	−2.42871	+	6.48678i	−0.112629	+	0.300817i
$466$	−0.413376	+	14.9965i	−0.0191493	+	0.694700i
$467$	−36.3776	+	19.6866i	−1.68336	+	0.910987i	−0.703650	+	0.710547i	$0.748448\pi$
$467$	−36.3776	+	19.6866i	−1.68336	+	0.910987i	−0.979706	+	0.200440i	$0.935763\pi$
$468$	−3.47482	−	1.19291i	−0.160624	−	0.0551421i
$469$	−7.92017	+	6.89768i	−0.365720	+	0.318505i
$470$	−1.50833	+	4.82241i	−0.0695742	+	0.222441i
$471$	38.8207	−	8.69992i	1.78876	−	0.400871i
$472$	−22.0871	+	30.0506i	−1.01664	+	1.38319i
$473$	−4.18500	+	30.1800i	−0.192427	+	1.38768i
$474$	6.47730	+	5.04148i	0.297512	+	0.231563i
$475$	−19.5828	+	0.204194i	−0.898520	+	0.00936905i
$476$	9.88751	−	7.69576i	0.453193	−	0.352735i
$477$	13.5177	+	23.4133i	0.618931	+	1.07202i
$478$	−4.96668	−	4.32549i	−0.227171	−	0.197843i
$479$	−16.3807	+	10.0692i	−0.748454	+	0.460073i	−0.844670	−	0.535287i	$-0.820203\pi$
$479$	−16.3807	+	10.0692i	−0.748454	+	0.460073i	0.0962158	+	0.995360i	$0.469326\pi$
$480$	−10.6959	+	3.02450i	−0.488197	+	0.138049i
$481$	−0.105178	−	0.0116411i	−0.00479571	−	0.000530789i
$482$	−0.492442	−	5.94289i	−0.0224301	−	0.270691i
$483$	−25.9583	+	20.2042i	−1.18115	+	0.919322i
$484$	2.32524	+	4.59479i	0.105693	+	0.208854i
$485$	−3.65559	+	3.18365i	−0.165992	+	0.144562i
$486$	10.5603	+	11.4715i	0.479025	+	0.520360i
$487$	−30.5709	−	16.5442i	−1.38530	−	0.749687i	−0.399362	−	0.916793i	$-0.630768\pi$
$487$	−30.5709	−	16.5442i	−1.38530	−	0.749687i	−0.985939	+	0.167106i	$0.946558\pi$
$488$	−2.12344	+	3.67790i	−0.0961234	+	0.166491i
$489$	−12.2871	−	2.75360i	−0.555642	−	0.124522i
$490$	1.95739	−	1.70470i	0.0884261	−	0.0770103i
$491$	−0.117606	−	4.26652i	−0.00530747	−	0.192545i	−0.997627	−	0.0688464i	$-0.978068\pi$
$491$	−0.117606	−	4.26652i	−0.00530747	−	0.192545i	0.992320	−	0.123699i	$-0.0394757\pi$
$492$	−20.9698	−	18.2626i	−0.945392	−	0.823343i
$493$	9.52305	−	37.6057i	0.428896	−	1.69367i
$494$	−1.86366	−	1.58920i	−0.0838501	−	0.0715014i
$495$	2.09580	+	8.27613i	0.0941992	+	0.371984i
$496$	−0.0476834	+	0.0942250i	−0.00214105	+	0.00423083i
$497$	−1.30320	−	6.67166i	−0.0584565	−	0.299265i
$498$	8.01920	−	0.442432i	0.359349	−	0.0198258i
$499$	−2.23782	−	11.4564i	−0.100178	−	0.512858i	−0.997449	−	0.0713775i	$-0.977260\pi$
$499$	−2.23782	−	11.4564i	−0.100178	−	0.512858i	0.897271	−	0.441480i	$-0.145547\pi$
$500$	7.59779	+	3.58549i	0.339784	+	0.160348i
$501$	−14.1968	−	56.0621i	−0.634268	−	2.50467i
$502$	9.80050	+	22.3429i	0.437418	+	0.997212i
$503$	7.81503	+	2.20988i	0.348455	+	0.0985337i	0.441834	−	0.897097i	$-0.354328\pi$
$503$	7.81503	+	2.20988i	0.348455	+	0.0985337i	−0.0933786	+	0.995631i	$0.529767\pi$
$504$	21.5315	+	2.38311i	0.959090	+	0.106152i
$505$	0.866332	−	1.32602i	0.0385513	−	0.0590071i
$506$	12.8139	+	9.97344i	0.569646	+	0.443373i
$507$	6.64081	−	33.9972i	0.294929	−	1.50987i
$508$	−2.10287	+	15.1648i	−0.0932996	+	0.672828i
$509$	4.31748	−	11.5315i	0.191369	−	0.511124i	−0.805283	−	0.592891i	$-0.797986\pi$
$509$	4.31748	−	11.5315i	0.191369	−	0.511124i	0.996651	+	0.0817677i	$0.0260565\pi$
$510$	6.52120	+	7.91826i	0.288764	+	0.350626i
$511$	3.84486	−	1.08722i	0.170087	−	0.0480959i
$512$	−0.333541	+	0.0556582i	−0.0147406	+	0.00245977i
$513$	6.82557	+	17.6671i	0.301356	+	0.780021i
$514$	−4.84807	−	0.808999i	−0.213839	−	0.0356834i
$515$	10.7436	−	1.18911i	0.473421	−	0.0523982i
$516$	17.9751	−	35.5198i	0.791311	−	1.56367i
$517$	19.3073	+	9.11132i	0.849133	+	0.400716i
$518$	0.237677	−	0.0263061i	0.0104429	−	0.00115583i
$519$	10.5789	+	10.2913i	0.464361	+	0.451738i
$520$	0.521236	+	1.18830i	0.0228577	+	0.0521103i
$521$	11.5650	−	1.92986i	0.506671	−	0.0845485i	0.0942625	−	0.995547i	$-0.469951\pi$
$521$	11.5650	−	1.92986i	0.506671	−	0.0845485i	0.412409	+	0.910999i	$0.364688\pi$
$522$	21.8979	−	13.4606i	0.958446	−	0.589155i
$523$	17.3259	+	23.5728i	0.757610	+	1.03077i	0.998190	+	0.0601360i	$0.0191535\pi$
$523$	17.3259	+	23.5728i	0.757610	+	1.03077i	−0.240580	+	0.970629i	$0.577338\pi$
$524$	−11.5628	−	3.96950i	−0.505122	−	0.173409i
$525$	−14.0460	−	15.2580i	−0.613016	−	0.665913i
$526$	2.53762	+	18.3000i	0.110646	+	0.797919i
$527$	21.2118	+	1.17029i	0.923999	+	0.0509785i
$528$	0.0295931	+	0.213410i	0.00128787	+	0.00928747i
$529$	27.1111	+	6.07573i	1.17874	+	0.264162i
$530$	1.09239	−	3.49257i	0.0474505	−	0.151708i
$531$	−33.0954	−	50.6564i	−1.43622	−	2.19830i
$532$	−8.03292	−	4.23952i	−0.348271	−	0.183806i
$533$	−2.87060	+	4.39377i	−0.124339	+	0.190315i
$534$	−9.14448	−	11.1035i	−0.395720	−	0.480497i
$535$	0.734086	−	0.346424i	0.0317373	−	0.0149772i
$536$	−10.4679	−	14.2420i	−0.452142	−	0.615162i
$537$	−1.06105	−	38.4928i	−0.0457875	−	1.66109i
$538$	−2.35964	−	4.66278i	−0.101731	−	0.201027i
$539$	−5.99849	−	9.18137i	−0.258373	−	0.395470i
$540$	0.317556	−	3.83233i	0.0136654	−	0.164917i
$541$	−7.09060	+	36.2999i	−0.304849	+	1.56066i	0.442837	+	0.896602i	$0.353972\pi$
$541$	−7.09060	+	36.2999i	−0.304849	+	1.56066i	−0.747685	+	0.664053i	$0.768835\pi$
$542$	3.35290	−	17.1650i	0.144020	−	0.737300i
$543$	3.91681	−	47.2689i	0.168086	−	2.02850i
$544$	18.6460	+	28.5399i	0.799442	+	1.22364i
$545$	−0.890163	−	1.75901i	−0.0381304	−	0.0753477i
$546$	−0.0714671	−	2.59269i	−0.00305851	−	0.110957i
$547$	1.92986	+	2.62567i	0.0825150	+	0.112266i	0.845065	−	0.534664i	$-0.179562\pi$
$547$	1.92986	+	2.62567i	0.0825150	+	0.112266i	−0.762550	+	0.646929i	$0.776053\pi$
$548$	15.0693	−	7.11138i	0.643729	−	0.303783i
$549$	−4.38041	−	5.31883i	−0.186951	−	0.227002i
$550$	−5.59928	+	8.57033i	−0.238754	+	0.365440i
$551$	−27.6888	+	4.91772i	−1.17958	+	0.209502i
$552$	−30.2782	−	46.3442i	−1.28873	−	1.97254i
$553$	1.71502	−	5.48321i	0.0729299	−	0.233170i
$554$	3.90693	+	0.875563i	0.165989	+	0.0371991i
$555$	−0.0441301	−	0.318243i	−0.00187322	−	0.0135087i
$556$	−10.8649	−	0.599431i	−0.460773	−	0.0254216i
$557$	1.14177	+	8.23384i	0.0483783	+	0.348879i	0.999230	+	0.0392327i	$0.0124914\pi$
$557$	1.14177	+	8.23384i	0.0483783	+	0.348879i	−0.950852	+	0.309646i	$0.899789\pi$
$558$	9.53368	+	10.3563i	0.403593	+	0.438419i
$559$	−7.10646	−	2.43965i	−0.300571	−	0.103186i
$560$	0.0211377	+	0.0287588i	0.000893230	+	0.00121528i
$561$	36.9239	−	22.6971i	1.55893	−	0.958270i
$562$	−4.94129	+	0.824555i	−0.208436	+	0.0347817i
$563$	6.87905	+	15.6826i	0.289917	+	0.660945i	0.999025	−	0.0441557i	$-0.0140598\pi$
$563$	6.87905	+	15.6826i	0.289917	+	0.660945i	−0.709107	+	0.705100i	$0.750902\pi$
$564$	−19.9938	−	19.4502i	−0.841890	−	0.819003i
$565$	−9.30426	+	1.02980i	−0.391433	+	0.0433238i
$566$	−18.6207	−	8.78733i	−0.782687	−	0.369359i
$567$	1.34283	−	2.65351i	0.0563937	−	0.111437i
$568$	11.3706	−	1.25849i	0.477099	−	0.0528053i
$569$	23.4570	+	3.91428i	0.983368	+	0.164095i	0.634371	−	0.773029i	$-0.281259\pi$
$569$	23.4570	+	3.91428i	0.983368	+	0.164095i	0.348997	+	0.937124i	$0.386522\pi$
$570$	3.28838	−	6.66972i	0.137735	−	0.279364i
$571$	28.9774	−	4.83547i	1.21267	−	0.202358i	0.476509	−	0.879169i	$-0.341902\pi$
$571$	28.9774	−	4.83547i	1.21267	−	0.202358i	0.736156	+	0.676811i	$0.236639\pi$
$572$	2.02186	−	0.571729i	0.0845384	−	0.0239052i
$573$	−21.5527	−	26.1700i	−0.900376	−	1.09327i
$574$	4.15859	−	11.1071i	0.173576	−	0.463602i
$575$	−4.39767	+	31.7137i	−0.183396	+	1.32255i
$576$	−4.27806	+	21.9013i	−0.178252	+	0.912553i
$577$	24.8684	+	19.3559i	1.03529	+	0.805796i	0.981249	−	0.192743i	$-0.0617383\pi$
$577$	24.8684	+	19.3559i	1.03529	+	0.805796i	0.0540376	+	0.998539i	$0.482791\pi$
$578$	9.11655	−	13.9539i	0.379198	−	0.580406i
$579$	−16.6725	−	1.84531i	−0.692884	−	0.0766884i
$580$	5.49438	+	1.55366i	0.228142	+	0.0645123i
$581$	−2.25814	−	5.14804i	−0.0936835	−	0.213577i
$582$	4.00304	+	15.8077i	0.165931	+	0.655248i
$583$	−13.9831	−	6.59877i	−0.579119	−	0.273293i
$584$	1.28912	+	6.59955i	0.0533440	+	0.273091i
$585$	−2.10210	+	0.115976i	−0.0869113	+	0.00479503i
$586$	−2.65972	−	13.6163i	−0.109872	−	0.562482i
$587$	−3.84094	+	7.58989i	−0.158532	+	0.313268i	−0.957664	−	0.287887i	$-0.907047\pi$
$587$	−3.84094	+	7.58989i	−0.158532	+	0.313268i	0.799132	+	0.601156i	$0.205293\pi$
$588$	3.51761	+	13.8907i	0.145064	+	0.572844i
$589$	−5.55008	−	14.3657i	−0.228687	−	0.591927i
$590$	−2.01062	+	7.93974i	−0.0827757	+	0.326874i
$591$	45.1771	+	39.3447i	1.85834	+	1.61843i
$592$	−0.000134973	−	0.00489656i	−5.54735e−6	−	0.000201248i
$593$	−24.3039	+	21.1663i	−0.998042	+	0.869196i	−0.991411	−	0.130782i	$-0.958251\pi$
$593$	−24.3039	+	21.1663i	−0.998042	+	0.869196i	−0.00663093	+	0.999978i	$0.502111\pi$
$594$	9.66099	+	2.16508i	0.396395	+	0.0888342i
$595$	3.58998	−	6.21803i	0.147175	−	0.254914i
$596$	8.07199	+	4.36834i	0.330642	+	0.178934i
$597$	32.6198	+	35.4346i	1.33504	+	1.45024i
$598$	−3.01960	+	2.62977i	−0.123481	+	0.107539i
$599$	−15.0898	−	29.8182i	−0.616552	−	1.21834i	−0.960219	−	0.279248i	$-0.909915\pi$
$599$	−15.0898	−	29.8182i	−0.616552	−	1.21834i	0.343667	−	0.939092i	$-0.388331\pi$
$600$	27.5422	−	21.4369i	1.12440	−	0.875159i
$601$	−2.27781	−	27.4890i	−0.0929137	−	1.12130i	−0.870381	−	0.492378i	$-0.836128\pi$
$601$	−2.27781	−	27.4890i	−0.0929137	−	1.12130i	0.777468	−	0.628923i	$-0.216504\pi$
$602$	16.8758	+	1.86781i	0.687806	+	0.0761264i
$603$	27.5954	−	7.80323i	1.12377	−	0.317772i
$604$	−13.6081	+	8.36487i	−0.553706	+	0.340362i
$605$	2.22536	+	1.93806i	0.0904736	+	0.0787935i
$606$	−2.66408	−	4.61433i	−0.108221	−	0.187444i
$607$	31.3119	−	24.3710i	1.27091	−	0.989188i	0.271265	−	0.962505i	$-0.412558\pi$
$607$	31.3119	−	24.3710i	1.27091	−	0.989188i	0.999644	−	0.0266835i	$-0.00849462\pi$
$608$	13.3007	−	20.8293i	0.539413	−	0.844740i
$609$	−23.5010	−	18.2916i	−0.952309	−	0.741212i
$610$	−0.128105	+	0.923828i	−0.00518683	+	0.0374047i
$611$	−3.11792	+	4.24209i	−0.126138	+	0.171617i
$612$	−33.3834	+	7.48139i	−1.34944	+	0.302417i
$613$	−2.44874	+	7.82907i	−0.0989038	+	0.316213i	−0.990670	−	0.136284i	$-0.956484\pi$
$613$	−2.44874	+	7.82907i	−0.0989038	+	0.316213i	0.891766	+	0.452497i	$0.149467\pi$
$614$	−18.6731	+	16.2624i	−0.753583	+	0.656296i
$615$	−15.0716	−	5.17408i	−0.607745	−	0.208639i
$616$	−10.8961	+	5.89670i	−0.439018	+	0.237585i
$617$	−0.725216	+	26.3095i	−0.0291961	+	1.05918i	0.833208	+	0.552960i	$0.186502\pi$
$617$	−0.725216	+	26.3095i	−0.0291961	+	1.05918i	−0.862404	+	0.506221i	$0.831042\pi$
$618$	12.7495	−	34.0524i	0.512860	−	1.36979i
$619$	7.13794	+	5.55568i	0.286898	+	0.223302i	0.747429	−	0.664342i	$-0.231288\pi$
$619$	7.13794	+	5.55568i	0.286898	+	0.223302i	−0.460531	+	0.887644i	$0.652341\pi$
$620$	−0.258215	+	3.11619i	−0.0103701	+	0.125149i
$621$	30.2147	−	6.77128i	1.21247	−	0.271722i
$622$	−3.25145	−	8.68423i	−0.130371	−	0.348206i
$623$	−5.03412	+	8.71935i	−0.201688	+	0.349333i
$624$	−0.0530494	−	0.00292682i	−0.00212368	−	0.000117166i
$625$	−17.6231	−	0.972292i	−0.704923	−	0.0388917i
$626$	−10.4539	−	5.65737i	−0.417822	−	0.226114i
$627$	−26.0056	−	17.6332i	−1.03856	−	0.704203i
$628$	15.7950	−	8.54783i	0.630290	−	0.341096i
$629$	−0.891160	+	0.420548i	−0.0355329	+	0.0167684i
$630$	4.57797	−	1.29453i	0.182391	−	0.0515751i
$631$	−23.6478	−	6.68696i	−0.941404	−	0.266204i	−0.233375	−	0.972387i	$-0.574977\pi$
$631$	−23.6478	−	6.68696i	−0.941404	−	0.266204i	−0.708029	+	0.706183i	$0.750416\pi$
$632$	8.95791	+	3.63839i	0.356326	+	0.144727i
$633$	40.0108	−	16.2510i	1.59029	−	0.645919i
$634$	14.8432	+	2.47688i	0.589497	+	0.0983697i
$635$	2.15371	+	8.50481i	0.0854674	+	0.337503i
$636$	14.4803	+	14.0866i	0.574180	+	0.558570i
$637$	2.50570	−	1.01773i	0.0992793	−	0.0403238i
$638$	−5.90517	+	13.4624i	−0.233788	+	0.532983i
$639$	−4.55647	+	17.9931i	−0.180251	+	0.711796i
$640$	−4.30631	+	2.64708i	−0.170222	+	0.104635i
$641$	3.35444	−	1.58300i	0.132493	−	0.0625247i	−0.359384	−	0.933190i	$-0.617013\pi$
$641$	3.35444	−	1.58300i	0.132493	−	0.0625247i	0.491876	+	0.870665i	$0.336311\pi$
$642$	0.0752379	−	2.72949i	0.00296940	−	0.107724i
$643$	25.5781	−	17.7355i	1.00870	−	0.699419i	0.0544802	−	0.998515i	$-0.482650\pi$
$643$	25.5781	−	17.7355i	1.00870	−	0.699419i	0.954223	+	0.299095i	$0.0966849\pi$
$644$	−8.79447	+	11.9653i	−0.346551	+	0.471499i
$645$	1.88384	−	22.7345i	0.0741760	−	0.895171i
$646$	−22.5344	−	3.51923i	−0.886602	−	0.138462i
$647$	−0.440687	−	5.31830i	−0.0173252	−	0.209084i	−0.999749	−	0.0224183i	$-0.992863\pi$
$647$	−0.440687	−	5.31830i	−0.0173252	−	0.209084i	0.982423	−	0.186666i	$-0.0597681\pi$
$648$	4.26376	+	2.62092i	0.167496	+	0.102960i
$649$	32.0624	+	13.0226i	1.25856	+	0.511183i
$650$	−1.80952	−	1.76033i	−0.0709753	−	0.0690458i
$651$	7.36392	−	14.5515i	0.288615	−	0.570318i
$652$	−5.67574	+	0.313140i	−0.222279	+	0.0122635i
$653$	−37.1208			−1.45265			−0.726324	−	0.687353i	$-0.758773\pi$
$653$	−37.1208			−1.45265			−0.726324	+	0.687353i	$0.758773\pi$
$654$	−6.63161			−0.259317
$655$	−6.99494	+	0.385922i	−0.273315	+	0.0150792i
$656$	−0.219711	−	0.103684i	−0.00857829	−	0.00404819i
$657$	−10.7611	−	1.79572i	−0.419832	−	0.0700576i
$658$	4.77893	−	10.8949i	0.186302	−	0.424726i
$659$	−29.3483	+	35.6357i	−1.14325	+	1.38817i	−0.233836	+	0.972276i	$0.575128\pi$
$659$	−29.3483	+	35.6357i	−1.14325	+	1.38817i	−0.909413	+	0.415894i	$0.863469\pi$
$660$	3.18971	+	5.52474i	0.124159	+	0.215050i
$661$	−2.98963	−	5.90768i	−0.116283	−	0.229782i	0.826685	−	0.562665i	$-0.190224\pi$
$661$	−2.98963	−	5.90768i	−0.116283	−	0.229782i	−0.942968	+	0.332883i	$0.891978\pi$
$662$	−5.31195	+	16.9832i	−0.206455	+	0.660073i
$663$	3.74764	+	10.0095i	0.145546	+	0.388737i
$664$	8.94793	−	3.07183i	0.347247	−	0.119210i
$665$	−5.17909	−	0.518620i	−0.200837	−	0.0201112i
$666$	−0.617557	−	0.212008i	−0.0239299	−	0.00821513i
$667$	1.26684	+	45.9587i	0.0490524	+	1.77953i
$668$	−13.0536	−	22.6094i	−0.505057	−	0.874785i
$669$	−4.89890	−	15.6627i	−0.189402	−	0.605553i
$670$	−3.30689	−	2.03274i	−0.127756	−	0.0785315i
$671$	3.79204	+	1.07229i	0.146390	+	0.0413952i
$672$	25.8142	−	4.30762i	0.995804	−	0.166170i
$673$	−1.37000	+	5.41001i	−0.0528096	+	0.208540i	−0.990181	−	0.139791i	$-0.955357\pi$
$673$	−1.37000	+	5.41001i	−0.0528096	+	0.208540i	0.937371	+	0.348332i	$0.113252\pi$
$674$	3.01687	−	3.66318i	0.116205	−	0.141100i
$675$	5.82754	+	18.6317i	0.224302	+	0.717134i
$676$	−1.29133	−	15.5841i	−0.0496667	−	0.599388i
$677$	6.60997	−	10.1173i	0.254042	−	0.388840i	−0.687257	−	0.726414i	$-0.741185\pi$
$677$	6.60997	−	10.1173i	0.254042	−	0.388840i	0.941299	+	0.337574i	$0.109606\pi$
$678$	−11.0414	+	29.4903i	−0.424042	+	1.13257i
$679$	9.37954	−	6.50363i	0.359954	−	0.249586i
$680$	9.92974	+	6.88513i	0.380788	+	0.264033i
$681$	−1.32165	−	3.52997i	−0.0506458	−	0.135269i
$682$	−7.85564	−	1.76049i	−0.300808	−	0.0674127i
$683$	21.3053	+	23.1437i	0.815224	+	0.885569i	0.995176	−	0.0981061i	$-0.0312785\pi$
$683$	21.3053	+	23.1437i	0.815224	+	0.885569i	−0.179952	+	0.983675i	$0.557594\pi$
$684$	14.8956	+	19.8295i	0.569547	+	0.758201i
$685$	6.46714	−	7.02519i	0.247097	−	0.268419i
$686$	−13.4159	+	9.30237i	−0.512221	+	0.355166i
$687$	−10.5719	+	76.2388i	−0.403342	+	2.90869i
$688$	0.0666775	−	0.341351i	0.00254205	−	0.0130139i
$689$	2.25812	−	3.07228i	0.0860275	−	0.117045i
$690$	−9.99071	−	6.92740i	−0.380340	−	0.263722i
$691$	13.8792	−	4.76474i	0.527990	−	0.181259i	−0.0477998	−	0.998857i	$-0.515221\pi$
$691$	13.8792	−	4.76474i	0.527990	−	0.181259i	0.575790	+	0.817598i	$0.304695\pi$
$692$	5.85960	+	3.17106i	0.222749	+	0.120546i
$693$	−2.76100	−	19.9109i	−0.104882	−	0.756352i
$694$	13.1270	−	22.7367i	0.498296	−	0.863074i
$695$	−5.89768	+	2.02468i	−0.223712	+	0.0768003i
$696$	33.9440	−	36.8730i	1.28664	−	1.39767i
$697$	−1.34667	+	48.8548i	−0.0510089	+	1.85051i
$698$	12.5500	+	15.2387i	0.475026	+	0.576792i
$699$	−47.1712	−	5.22091i	−1.78418	−	0.197473i
$700$	−7.97579	−	4.90270i	−0.301457	−	0.185305i
$701$	1.88201	−	1.83085i	0.0710827	−	0.0691503i	−0.660898	−	0.750476i	$-0.729824\pi$
$701$	1.88201	−	1.83085i	0.0710827	−	0.0691503i	0.731980	+	0.681326i	$0.238596\pi$
$702$	−0.980730	+	2.23584i	−0.0370153	+	0.0843863i
$703$	0.543562	+	0.463511i	0.0205008	+	0.0174817i
$704$	−5.12659	−	11.6874i	−0.193216	−	0.440487i
$705$	−14.8095	−	6.01509i	−0.557757	−	0.226541i
$706$	19.2464	−	18.7232i	0.724348	−	0.704657i
$707$	−2.37088	+	2.87880i	−0.0891661	+	0.108268i
$708$	−34.0967	−	29.6948i	−1.28143	−	1.11600i
$709$	−27.0262	−	36.7705i	−1.01499	−	1.38095i	−0.922832	−	0.385202i	$-0.874132\pi$
$709$	−27.0262	−	36.7705i	−1.01499	−	1.38095i	−0.0921597	−	0.995744i	$-0.529377\pi$
$710$	2.20957	−	1.19576i	0.0829236	−	0.0448760i
$711$	−10.6245	+	11.5413i	−0.398451	+	0.432833i
$712$	−13.9242	−	9.65480i	−0.521830	−	0.361829i
$713$	−24.5685	+	5.50593i	−0.920098	+	0.206199i
$714$	−13.2102	−	20.2197i	−0.494378	−	0.756702i
$715$	0.950167	−	0.739545i	0.0355342	−	0.0276574i
$716$	−5.18923	−	16.5909i	−0.193931	−	0.620031i
$717$	14.9344	−	14.5284i	0.557734	−	0.542572i
$718$	−1.42404	+	0.578396i	−0.0531448	+	0.0215855i
$719$	−2.68969	+	0.297695i	−0.100309	+	0.0111022i	−0.160022	−	0.987113i	$-0.551157\pi$
$719$	−2.68969	+	0.297695i	−0.100309	+	0.0111022i	0.0597138	+	0.998216i	$0.480981\pi$
$720$	−0.0186830	−	0.0956467i	−0.000696275	−	0.00356454i
$721$	−25.4506			−0.947829
$722$	4.39217	+	15.9399i	0.163460	+	0.593220i
$723$	18.8647			0.701585
$724$	−4.10488	−	21.0147i	−0.152557	−	0.781004i
$725$	−28.8104	+	3.18873i	−1.06999	+	0.118426i
$726$	9.19706	−	3.73552i	0.341335	−	0.138638i
$727$	13.6577	−	13.2864i	0.506536	−	0.492766i	−0.399050	−	0.916929i	$-0.630660\pi$
$727$	13.6577	−	13.2864i	0.506536	−	0.492766i	0.905586	+	0.424164i	$0.139432\pi$
$728$	−0.912023	−	2.91590i	−0.0338018	−	0.108070i
$729$	−34.7260	+	27.0283i	−1.28615	+	1.00105i
$730$	0.807700	+	1.23628i	0.0298943	+	0.0457566i
$731$	−68.2734	+	15.3004i	−2.52518	+	0.565907i
$732$	−4.23115	−	2.93381i	−0.156388	−	0.108437i
$733$	15.4593	−	16.7932i	0.571001	−	0.620273i	−0.381661	−	0.924302i	$-0.624648\pi$
$733$	15.4593	−	16.7932i	0.571001	−	0.620273i	0.952663	+	0.304029i	$0.0983321\pi$
$734$	−15.1173	+	8.18106i	−0.557989	+	0.301968i
$735$	4.86302	+	6.61637i	0.179375	+	0.244049i
$736$	−30.4688	−	26.5353i	−1.12310	−	0.978105i
$737$	−10.4265	+	12.6602i	−0.384066	+	0.466346i
$738$	−23.2121	+	22.5810i	−0.854448	+	0.831220i
$739$	10.1595	+	4.12642i	0.373722	+	0.151793i	0.555437	−	0.831559i	$-0.312551\pi$
$739$	10.1595	+	4.12642i	0.373722	+	0.151793i	−0.181715	+	0.983351i	$0.558165\pi$
$740$	−0.0582619	−	0.132824i	−0.00214175	−	0.00488270i
$741$	5.49710	−	5.46037i	0.201941	−	0.200592i
$742$	−3.46108	+	7.89047i	−0.127060	+	0.289668i
$743$	−1.89682	+	1.84525i	−0.0695874	+	0.0676957i	−0.731269	−	0.682090i	$-0.761071\pi$
$743$	−1.89682	+	1.84525i	−0.0695874	+	0.0676957i	0.661681	+	0.749785i	$0.269843\pi$
$744$	23.3819	+	14.3728i	0.857221	+	0.526931i
$745$	5.22761	+	0.578592i	0.191525	+	0.0211980i
$746$	−8.53634	−	10.3651i	−0.312538	−	0.379493i
$747$	−0.422944	+	15.3436i	−0.0154747	+	0.561393i
$748$	13.2517	−	14.3952i	0.484530	−	0.526340i
$749$	−1.80766	+	0.620571i	−0.0660505	+	0.0226752i
$750$	8.09742	−	14.0251i	0.295676	−	0.512126i
$751$	6.84628	+	49.3718i	0.249824	+	1.80160i	0.536848	+	0.843679i	$0.319615\pi$
$751$	6.84628	+	49.3718i	0.249824	+	1.80160i	−0.287023	+	0.957924i	$0.592666\pi$
$752$	−0.214329	−	0.115989i	−0.00781578	−	0.00422969i
$753$	−73.0003	+	25.0610i	−2.66028	+	0.913275i
$754$	−2.97907	−	2.06564i	−0.108491	−	0.0752262i
$755$	−5.42104	+	7.37560i	−0.197292	+	0.268425i
$756$	−1.73579	+	8.88629i	−0.0631302	+	0.323191i
$757$	−3.92041	+	28.2719i	−0.142490	+	1.02756i	0.775610	+	0.631212i	$0.217442\pi$
$757$	−3.92041	+	28.2719i	−0.142490	+	1.02756i	−0.918100	+	0.396349i	$0.870277\pi$
$758$	−3.10001	+	2.14950i	−0.112597	+	0.0780732i
$759$	−34.7905	+	37.7926i	−1.26282	+	1.37178i
$760$	1.58957	−	8.61411i	0.0576597	−	0.312467i
$761$	25.0351	+	27.1954i	0.907523	+	0.985832i	0.999951	−	0.00988703i	$-0.00314719\pi$
$761$	25.0351	+	27.1954i	0.907523	+	0.985832i	−0.0924286	+	0.995719i	$0.529463\pi$
$762$	28.7979	+	6.45375i	1.04324	+	0.233795i
$763$	1.62757	+	4.34705i	0.0589221	+	0.157374i
$764$	−12.5771	−	8.72076i	−0.455023	−	0.315506i
$765$	−16.1107	+	11.1709i	−0.582484	+	0.403886i
$766$	11.8817	−	31.7345i	0.429302	−	1.14661i
$767$	−4.66756	+	7.14423i	−0.168536	+	0.257963i
$768$	3.62021	+	43.6894i	0.130633	+	1.57651i
$769$	5.20541	+	16.6426i	0.187712	+	0.600149i	0.999861	+	0.0166981i	$0.00531542\pi$
$769$	5.20541	+	16.6426i	0.187712	+	0.600149i	−0.812149	+	0.583451i	$0.801702\pi$
$770$	−1.72972	+	2.10028i	−0.0623348	+	0.0756890i
$771$	3.81702	−	15.0731i	0.137467	−	0.542843i
$772$	−7.46918	+	1.24639i	−0.268822	+	0.0448584i
$773$	31.7310	+	8.97268i	1.14129	+	0.322725i	0.789738	−	0.613445i	$-0.210217\pi$
$773$	31.7310	+	8.97268i	1.14129	+	0.322725i	0.351548	+	0.936170i	$0.385655\pi$
$774$	−39.4953	−	24.2777i	−1.41963	−	0.872642i
$775$	−4.73855	−	15.1500i	−0.170214	−	0.544204i
$776$	9.60414	+	16.6349i	0.344769	+	0.597157i
$777$	0.0208443	+	0.756193i	0.000747786	+	0.0271283i
$778$	13.2550	+	4.55046i	0.475216	+	0.163142i
$779$	32.6848	−	13.6741i	1.17105	−	0.489927i
$780$	−1.48792	+	0.510803i	−0.0532760	+	0.0182897i
$781$	−3.72214	−	9.94139i	−0.133189	−	0.355731i
$782$	−11.1308	+	35.5873i	−0.398038	+	1.27260i
$783$	12.6578	+	25.0125i	0.452354	+	0.893875i
$784$	0.0625955	+	0.108419i	0.00223555	+	0.00387209i
$785$	6.54267	−	7.94432i	0.233518	−	0.283545i
$786$	−9.46631	+	21.5810i	−0.337652	+	0.769769i
$787$	−18.8289	−	3.14199i	−0.671178	−	0.112000i	−0.180813	−	0.983517i	$-0.557873\pi$
$787$	−18.8289	−	3.14199i	−0.671178	−	0.112000i	−0.490364	+	0.871518i	$0.663136\pi$
$788$	24.4578	+	11.5419i	0.871274	+	0.411164i
$789$	−58.3570	+	3.21965i	−2.07757	+	0.114622i
$790$	2.12335			0.0755455
$791$	22.0409			0.783682
$792$	33.7775	−	1.86356i	1.20023	−	0.0662187i
$793$	−0.438791	+	0.867074i	−0.0155819	+	0.0307907i
$794$	−14.2657	−	13.8779i	−0.506272	−	0.492509i
$795$	10.7256	+	4.35636i	0.380397	+	0.154504i
$796$	18.5227	+	11.3858i	0.656519	+	0.403561i
$797$	2.79976	+	33.7881i	0.0991727	+	1.19684i	0.846503	+	0.532384i	$0.178704\pi$
$797$	2.79976	+	33.7881i	0.0991727	+	1.19684i	−0.747330	+	0.664453i	$0.768665\pi$
$798$	−9.42313	+	14.7570i	−0.333575	+	0.522390i
$799$	−4.04845	+	48.8575i	−0.143224	+	1.72846i
$800$	15.0861	−	20.5254i	0.533374	−	0.725682i
$801$	22.5916	−	15.6646i	0.798233	−	0.553483i
$802$	−0.402395	+	14.5981i	−0.0142090	+	0.515478i
$803$	5.64279	−	2.66290i	0.199130	−	0.0939716i
$804$	18.2556	−	11.2217i	0.643826	−	0.395758i
$805$	−2.08896	+	8.24913i	−0.0736262	+	0.290743i
$806$	0.797462	−	1.81803i	0.0280894	−	0.0640374i
$807$	15.3167	−	6.22110i	0.539173	−	0.218993i
$808$	−4.49873	−	4.37643i	−0.158265	−	0.153962i
$809$	9.14544	+	36.1145i	0.321537	+	1.26972i	0.893360	+	0.449342i	$0.148342\pi$
$809$	9.14544	+	36.1145i	0.321537	+	1.26972i	−0.571823	+	0.820377i	$0.693764\pi$
$810$	1.08415	+	0.180912i	0.0380930	+	0.00635660i
$811$	−32.9483	+	13.3824i	−1.15697	+	0.469921i	−0.872428	−	0.488742i	$-0.837456\pi$
$811$	−32.9483	+	13.3824i	−1.15697	+	0.469921i	−0.284543	+	0.958663i	$0.591842\pi$
$812$	−12.4557	−	5.05906i	−0.437109	−	0.177538i
$813$	53.2398	+	15.0548i	1.86720	+	0.527995i
$814$	0.359333	−	0.101610i	0.0125946	−	0.00356142i
$815$	−2.94586	+	1.39019i	−0.103189	+	0.0486961i
$816$	−0.435120	+	0.235475i	−0.0152323	+	0.00824329i
$817$	30.4634	+	40.5540i	1.06578	+	1.41881i
$818$	9.27482	+	5.01928i	0.324287	+	0.175495i
$819$	4.94945	+	0.273069i	0.172948	+	0.00954180i
$820$	−7.18264	−	0.396277i	−0.250829	−	0.0138386i
$821$	−12.4799	+	21.6158i	−0.435550	+	0.754396i	−0.997340	−	0.0728844i	$-0.976780\pi$
$821$	−12.4799	+	21.6158i	−0.435550	+	0.754396i	0.561790	+	0.827280i	$0.310113\pi$
$822$	−11.2627	−	30.0812i	−0.392831	−	1.04920i
$823$	10.5710	−	2.36901i	0.368480	−	0.0825784i	−0.0305076	−	0.999535i	$-0.509712\pi$
$823$	10.5710	−	2.36901i	0.368480	−	0.0825784i	0.398988	+	0.916956i	$0.369362\pi$
$824$	3.53696	−	42.6848i	0.123216	−	1.48700i
$825$	−25.5568	−	19.8916i	−0.889773	−	0.692538i
$826$	6.76183	−	18.0600i	0.235274	−	0.628389i
$827$	−0.908139	+	32.9456i	−0.0315791	+	1.14563i	0.803432	+	0.595397i	$0.203005\pi$
$827$	−0.908139	+	32.9456i	−0.0315791	+	1.14563i	−0.835011	+	0.550234i	$0.814539\pi$
$828$	35.6596	−	19.2980i	1.23926	−	0.670652i
$829$	28.5801	+	9.81157i	0.992629	+	0.340770i	0.772718	−	0.634750i	$-0.218897\pi$
$829$	28.5801	+	9.81157i	0.992629	+	0.340770i	0.219911	+	0.975520i	$0.429423\pi$
$830$	1.56677	−	1.36450i	0.0543835	−	0.0473626i
$831$	−3.78101	+	12.0886i	−0.131162	+	0.419348i
$832$	3.07101	−	0.688229i	0.106468	−	0.0238601i
$833$	14.9151	−	20.2927i	0.516778	−	0.703102i
$834$	−2.88107	+	20.7768i	−0.0997632	+	0.719440i
$835$	−11.8060	−	9.18898i	−0.408563	−	0.317998i
$836$	−13.4628	−	4.46542i	−0.465621	−	0.154440i
$837$	−12.1146	+	9.42920i	−0.418743	+	0.325921i
$838$	3.84960	+	6.66771i	0.132982	+	0.230332i
$839$	−6.07806	−	5.29339i	−0.209838	−	0.182748i	0.545445	−	0.838146i	$-0.316360\pi$
$839$	−6.07806	−	5.29339i	−0.209838	−	0.182748i	−0.755284	+	0.655398i	$0.772501\pi$
$840$	7.90250	−	4.85765i	0.272662	−	0.167605i
$841$	−12.1475	+	3.43500i	−0.418881	+	0.118448i
$842$	−12.9149	−	1.42943i	−0.445078	−	0.0492613i
$843$	−1.30870	−	15.7937i	−0.0450742	−	0.543964i
$844$	15.3845	−	11.9742i	0.529555	−	0.412169i
$845$	−4.04619	−	7.99550i	−0.139193	−	0.275053i
$846$	−24.4965	+	21.3341i	−0.842208	+	0.733480i
$847$	−4.70586	−	5.11192i	−0.161695	−	0.175648i
$848$	0.155225	+	0.0840037i	0.00533046	+	0.00288470i
$849$	32.5681	−	56.4096i	1.11773	−	1.93597i
$850$	−22.9394	−	5.14083i	−0.786814	−	0.176329i
$851$	0.880706	−	0.767008i	0.0301902	−	0.0262927i
$852$	0.382165	+	13.8642i	0.0130928	+	0.474981i
$853$	−36.6694	−	31.9355i	−1.25554	−	1.09345i	−0.991658	−	0.128893i	$-0.958858\pi$
$853$	−36.6694	−	31.9355i	−1.25554	−	1.09345i	−0.263880	−	0.964556i	$-0.585002\pi$
$854$	0.539083	−	2.12879i	0.0184470	−	0.0728457i
$855$	12.1845	+	7.31585i	0.416701	+	0.250197i
$856$	−0.789582	−	3.11799i	−0.0269873	−	0.106571i
$857$	−8.20848	+	16.2204i	−0.280396	+	0.554078i	−0.988353	−	0.152177i	$-0.951372\pi$
$857$	−8.20848	+	16.2204i	−0.280396	+	0.554078i	0.707957	+	0.706256i	$0.249617\pi$
$858$	−0.776482	−	3.97516i	−0.0265087	−	0.135710i
$859$	−27.7761	+	1.53245i	−0.947710	+	0.0522866i	−0.522344	−	0.852735i	$-0.674942\pi$
$859$	−27.7761	+	1.53245i	−0.947710	+	0.0522866i	−0.425366	+	0.905021i	$0.639855\pi$
$860$	−1.97429	−	10.1073i	−0.0673227	−	0.344655i
$861$	33.9308	+	16.0123i	1.15636	+	0.545699i
$862$	−3.55120	−	14.0234i	−0.120954	−	0.477638i
$863$	−6.10248	−	13.9123i	−0.207731	−	0.473579i	0.780765	−	0.624824i	$-0.214829\pi$
$863$	−6.10248	−	13.9123i	−0.207731	−	0.473579i	−0.988496	+	0.151246i	$0.951672\pi$
$864$	−23.7058	−	6.70337i	−0.806489	−	0.228053i
$865$	3.79482	+	0.420010i	0.129028	+	0.0142808i
$866$	−11.2197	+	17.1731i	−0.381261	+	0.583564i
$867$	41.6106	+	32.3869i	1.41317	+	1.09992i
$868$	1.41143	−	7.22571i	0.0479069	−	0.245257i
$869$	1.23229	−	8.88661i	0.0418025	−	0.301458i
$870$	3.85931	−	10.3078i	0.130843	−	0.349466i
$871$	−2.57117	−	3.12199i	−0.0871206	−	0.105785i
$872$	−7.51691	+	2.12558i	−0.254555	+	0.0719812i
$873$	−30.7398	+	5.12957i	−1.04039	+	0.173610i
$874$	26.8344	−	3.25359i	0.907686	−	0.110054i
$875$	−11.1809	−	1.86576i	−0.377983	−	0.0630741i
$876$	−8.10282	+	0.896820i	−0.273769	+	0.0303007i
$877$	−3.86525	+	7.63794i	−0.130520	+	0.257915i	−0.948146	−	0.317835i	$-0.897044\pi$
$877$	−3.86525	+	7.63794i	−0.130520	+	0.257915i	0.817626	+	0.575750i	$0.195290\pi$
$878$	−17.6783	−	8.34260i	−0.596614	−	0.281549i
$879$	43.6225	−	4.82814i	1.47135	−	0.162849i
$880$	0.0399503	+	0.0388642i	0.00134672	+	0.00131011i
$881$	17.0095	+	38.7779i	0.573066	+	1.30646i	0.928352	+	0.371702i	$0.121226\pi$
$881$	17.0095	+	38.7779i	0.573066	+	1.30646i	−0.355286	+	0.934758i	$0.615616\pi$
$882$	16.4597	−	2.74664i	0.554228	−	0.0924843i
$883$	36.1200	−	22.2029i	1.21553	−	0.747185i	0.240804	−	0.970574i	$-0.422589\pi$
$883$	36.1200	−	22.2029i	1.21553	−	0.747185i	0.974730	+	0.223388i	$0.0717118\pi$
$884$	2.85750	+	3.88777i	0.0961082	+	0.130760i
$885$	−24.5062	−	8.41300i	−0.823768	−	0.282800i
$886$	−8.76750	−	9.52404i	−0.294550	−	0.319966i
$887$	−1.29459	−	9.33590i	−0.0434680	−	0.313469i	−0.999777	−	0.0211112i	$-0.993280\pi$
$887$	−1.29459	−	9.33590i	−0.0434680	−	0.313469i	0.956309	−	0.292357i	$-0.0944397\pi$
$888$	−1.27116	−	0.0701317i	−0.0426572	−	0.00235347i
$889$	−2.83729	−	20.4611i	−0.0951597	−	0.686242i
$890$	−3.63105	−	0.813737i	−0.121713	−	0.0272765i
$891$	1.38633	−	4.43236i	0.0464439	−	0.148489i
$892$	−4.05202	−	6.20208i	−0.135672	−	0.207661i
$893$	33.4920	−	11.8896i	1.12077	−	0.397871i
$894$	9.67684	−	14.8115i	0.323642	−	0.495371i
$895$	−6.33279	−	7.68948i	−0.211682	−	0.257031i
$896$	10.7634	−	5.07937i	0.359580	−	0.169690i
$897$	−7.50199	−	10.2068i	−0.250484	−	0.340796i
$898$	0.448909	+	16.2856i	0.0149803	+	0.543457i
$899$	−10.2925	−	20.3385i	−0.343273	−	0.678325i
$900$	13.9817	+	21.4006i	0.466056	+	0.713352i
$901$	2.93204	−	35.3845i	0.0976805	−	1.17883i
$902$	3.55062	−	18.1772i	0.118223	−	0.605234i
$903$	−10.2972	+	52.7161i	−0.342670	+	1.75428i
$904$	−3.06310	+	36.9661i	−0.101877	+	1.22948i
$905$	−6.71104	−	10.2720i	−0.223082	−	0.341453i
$906$	13.9033	+	27.4737i	0.461907	+	0.912752i
$907$	−0.764677	−	27.7411i	−0.0253907	−	0.921127i	−0.899894	−	0.436108i	$-0.856357\pi$
$907$	−0.764677	−	27.7411i	−0.0253907	−	0.921127i	0.874504	−	0.485019i	$-0.161187\pi$
$908$	−1.00773	−	1.37107i	−0.0334428	−	0.0455006i
$909$	9.20914	−	4.34590i	0.305448	−	0.144144i
$910$	−0.426547	−	0.517927i	−0.0141399	−	0.0171691i
$911$	−9.47357	+	14.5004i	−0.313874	+	0.480419i	−0.958901	−	0.283740i	$-0.908425\pi$
$911$	−9.47357	+	14.5004i	−0.313874	+	0.480419i	0.645028	+	0.764159i	$0.276846\pi$
$912$	0.285316	+	0.217331i	0.00944774	+	0.00719655i
$913$	−4.80142	−	7.34912i	−0.158904	−	0.243220i
$914$	7.44771	−	23.8117i	0.246348	−	0.787620i
$915$	−2.87907	−	0.645215i	−0.0951791	−	0.0213301i
$916$	4.77249	+	34.4167i	0.157687	+	1.13716i
$917$	16.4697	+	0.908661i	0.543879	+	0.0300066i
$918$	3.12276	+	22.5197i	0.103066	+	0.743261i
$919$	19.0780	+	20.7243i	0.629326	+	0.683631i	0.966163	−	0.257933i	$-0.0830412\pi$
$919$	19.0780	+	20.7243i	0.629326	+	0.683631i	−0.336837	+	0.941563i	$0.609357\pi$
$920$	−13.5448	−	4.64994i	−0.446560	−	0.153304i
$921$	−46.3920	−	63.1185i	−1.52867	−	2.07983i
$922$	27.3304	−	16.7999i	0.900079	−	0.553277i
$923$	2.58203	−	0.430864i	0.0849884	−	0.0141821i
$924$	−6.03366	−	13.7554i	−0.198493	−	0.452518i
$925$	0.527771	+	0.513424i	0.0173530	+	0.0168813i
$926$	23.4236	−	2.59252i	0.769747	−	0.0851956i
$927$	62.8458	+	29.6576i	2.06413	+	0.974084i
$928$	16.5167	−	32.6378i	0.542186	−	1.07139i
$929$	−27.1573	+	3.00577i	−0.891003	+	0.0986161i	−0.543840	−	0.839189i	$-0.683030\pi$
$929$	−27.1573	+	3.00577i	−0.891003	+	0.0986161i	−0.347162	+	0.937805i	$0.612855\pi$
$930$	5.94531	+	0.992097i	0.194954	+	0.0325321i
$931$	−17.8558	−	3.80650i	−0.585200	−	0.124753i
$932$	−21.1325	+	3.52638i	−0.692217	+	0.115511i
$933$	28.2280	−	7.98212i	0.924144	−	0.261323i
$934$	22.8824	+	27.7846i	0.748736	+	0.909140i
$935$	3.93143	−	10.5004i	0.128571	−	0.343399i
$936$	−1.14583	+	8.26309i	−0.0374525	+	0.270088i
$937$	3.72712	−	19.0808i	0.121760	−	0.623342i	−0.869770	−	0.493458i	$-0.835733\pi$
$937$	3.72712	−	19.0808i	0.121760	−	0.623342i	0.991529	−	0.129884i	$-0.0414603\pi$
$938$	7.21237	+	5.61362i	0.235492	+	0.183291i
$939$	20.5669	−	31.4799i	0.671174	−	1.02731i
$940$	−7.17209	−	0.793807i	−0.233928	−	0.0258911i
$941$	−46.9364	−	13.2723i	−1.53008	−	0.432666i	−0.599994	−	0.800004i	$-0.704831\pi$
$941$	−46.9364	−	13.2723i	−1.53008	−	0.432666i	−0.930087	+	0.367338i	$0.880269\pi$
$942$	−13.9067	−	31.7040i	−0.453104	−	1.03297i
$943$	−14.2194	−	56.1510i	−0.463046	−	1.82853i
$944$	−0.357249	−	0.168590i	−0.0116274	−	0.00548713i
$945$	0.994689	+	5.09225i	0.0323572	+	0.165651i
$946$	26.4739	−	1.46061i	0.860741	−	0.0474884i
$947$	−9.42332	−	48.2422i	−0.306217	−	1.56766i	−0.743750	−	0.668457i	$-0.766955\pi$
$947$	−9.42332	−	48.2422i	−0.306217	−	1.56766i	0.437534	−	0.899202i	$-0.355852\pi$
$948$	−5.29283	+	10.4589i	−0.171903	+	0.339690i
$949$	0.377720	+	1.49158i	0.0122613	+	0.0484188i
$950$	3.44135	+	16.6909i	0.111652	+	0.541525i
$951$	−11.6864	+	46.1487i	−0.378959	+	1.49647i
$952$	−21.4545	−	18.6848i	−0.695345	−	0.605577i
$953$	1.24330	+	45.1047i	0.0402745	+	1.46108i	0.702449	+	0.711734i	$0.252090\pi$
$953$	1.24330	+	45.1047i	0.0402745	+	1.46108i	−0.662175	+	0.749350i	$0.730366\pi$
$954$	17.7413	−	15.4509i	0.574397	−	0.500242i
$955$	−8.55804	−	1.91790i	−0.276932	−	0.0620619i
$956$	4.70286	−	8.14560i	0.152101	−	0.263447i
$957$	−40.9001	−	22.1340i	−1.32211	−	0.715492i
$958$	11.3325	+	12.3104i	0.366137	+	0.397730i
$959$	−16.9542	+	14.7655i	−0.547481	+	0.476802i
$960$	4.31457	+	8.52582i	0.139252	+	0.275170i
$961$	−14.6126	+	11.3734i	−0.471373	+	0.366885i
$962$	0.00760437	+	0.0917711i	0.000245175	+	0.00295882i
$963$	5.18686	+	0.574081i	0.167144	+	0.0184995i
$964$	8.19480	−	2.31727i	0.263937	−	0.0746342i
$965$	−3.69679	+	2.27241i	−0.119004	+	0.0731514i
$966$	21.5863	+	18.7995i	0.694526	+	0.604864i
$967$	−3.70914	−	6.42441i	−0.119278	−	0.206595i	0.800204	−	0.599728i	$-0.204725\pi$
$967$	−3.70914	−	6.42441i	−0.119278	−	0.206595i	−0.919482	+	0.393133i	$0.871391\pi$
$968$	9.22752	−	7.18207i	0.296584	−	0.230840i
$969$	16.9818	−	70.1243i	0.545535	−	2.25272i
$970$	3.32890	+	2.59099i	0.106885	+	0.0831916i
$971$	2.55762	−	18.4442i	0.0820778	−	0.591902i	−0.904237	−	0.427030i	$-0.859560\pi$
$971$	2.55762	−	18.4442i	0.0820778	−	0.591902i	0.986315	−	0.164872i	$-0.0527210\pi$
$972$	−13.1874	+	17.9421i	−0.422987	+	0.575494i
$973$	14.3264	−	3.21061i	0.459282	−	0.102927i
$974$	−9.02971	+	28.8696i	−0.289331	+	0.925041i
$975$	6.02247	−	5.24498i	0.192874	−	0.167974i
$976$	−0.0425463	−	0.0146062i	−0.00136187	−	0.000467532i
$977$	41.0590	−	22.2200i	1.31359	−	0.710882i	0.340273	−	0.940327i	$-0.389480\pi$
$977$	41.0590	−	22.2200i	1.31359	−	0.710882i	0.973322	+	0.229445i	$0.0736910\pi$
$978$	−0.301927	+	10.9534i	−0.00965456	+	0.350250i
$979$	−5.51291	+	14.7243i	−0.176194	+	0.470592i
$980$	2.92522	+	2.27679i	0.0934428	+	0.0727294i
$981$	1.04663	−	12.6309i	0.0334162	−	0.403274i
$982$	−3.62426	+	0.812216i	−0.115655	+	0.0259189i
$983$	−15.2343	−	40.6891i	−0.485899	−	1.29778i	−0.918224	−	0.396062i	$-0.870377\pi$
$983$	−15.2343	−	40.6891i	−0.485899	−	1.29778i	0.432324	−	0.901718i	$-0.357694\pi$
$984$	−31.5708	+	54.6822i	−1.00644	+	1.74321i
$985$	15.4742	+	0.853734i	0.493048	+	0.0272022i
$986$	−33.7064	−	1.85963i	−1.07343	−	0.0592228i
$987$	33.0996	+	17.9126i	1.05357	+	0.570164i
$988$	1.71720	−	3.04722i	0.0546315	−	0.0969450i
$989$	72.9286	−	39.4670i	2.31899	−	1.25498i
$990$	6.71871	−	3.17064i	0.213535	−	0.100769i
$991$	23.7913	−	6.72752i	0.755754	−	0.213707i	0.127632	−	0.991822i	$-0.459262\pi$
$991$	23.7913	−	6.72752i	0.755754	−	0.213707i	0.628122	+	0.778115i	$0.283824\pi$
$992$	19.2759	+	5.45072i	0.612012	+	0.173060i
$993$	−52.1551	−	21.1836i	−1.65509	−	0.672240i
$994$	−5.48062	+	2.22603i	−0.173835	+	0.0706055i
$995$	12.2894	+	2.05074i	0.389600	+	0.0650128i
$996$	2.81563	+	11.1187i	0.0892167	+	0.352309i
$997$	19.2785	+	18.7544i	0.610555	+	0.593957i	0.936171	−	0.351545i	$-0.114344\pi$
$997$	19.2785	+	18.7544i	0.610555	+	0.593957i	−0.325616	+	0.945502i	$0.605572\pi$
$998$	−9.41116	+	3.82248i	−0.297905	+	0.120999i
$999$	0.286043	−	0.652113i	0.00905000	−	0.0206319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.i.a.7.11	✓	1080
361.258	even	57	inner	361.2.i.a.258.11	yes	1080

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.i.a.7.11	✓	1080	1.1	even	1	trivial
361.2.i.a.258.11	yes	1080	361.258	even	57	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.166828 - 0.854065i) q^{2} +(2.73618 - 0.302840i) q^{3} +(1.15139 - 0.467655i) q^{4} +(0.510455 - 0.496579i) q^{5} +(-0.715115 - 2.28635i) q^{6} +(-1.32321 + 1.02989i) q^{7} +(-1.54341 - 2.36236i) q^{8} +(4.46756 - 1.00120i) q^{9} +(-0.509268 - 0.353119i) q^{10} +(-1.77342 + 1.92645i) q^{11} +(3.00879 - 1.62828i) q^{12} +(-0.382408 - 0.520285i) q^{13} +(1.10034 + 0.958289i) q^{14} +(1.24631 - 1.51331i) q^{15} +(0.0214243 - 0.0208419i) q^{16} +(-5.57085 - 2.26268i) q^{17} +(-1.60041 - 3.64856i) q^{18} +(0.165531 + 4.35575i) q^{19} +(0.355507 - 0.810474i) q^{20} +(-3.30863 + 3.21869i) q^{21} +(1.94117 + 1.19323i) q^{22} +(7.08301 + 0.783947i) q^{23} +(-4.93845 - 5.99643i) q^{24} +(-0.123797 + 4.49114i) q^{25} +(-0.380561 + 0.413399i) q^{26} +(4.10965 - 1.41085i) q^{27} +(-1.04189 + 1.80461i) q^{28} +(0.886158 + 6.39051i) q^{29} +(-1.50039 - 0.811969i) q^{30} +(-3.34168 + 1.14720i) q^{31} +(-4.65925 - 3.23065i) q^{32} +(-4.26899 + 5.80816i) q^{33} +(-1.00311 + 5.13535i) q^{34} +(-0.164015 + 1.18279i) q^{35} +(4.67570 - 3.24206i) q^{36} +(0.110996 - 0.120573i) q^{37} +(3.69248 - 0.868035i) q^{38} +(-1.20390 - 1.30778i) q^{39} +(-1.96094 - 0.439457i) q^{40} +(-2.85004 - 7.61213i) q^{41} +(3.30094 + 2.28882i) q^{42} +(9.56242 - 6.63043i) q^{43} +(-1.14099 + 3.04745i) q^{44} +(1.78331 - 2.72956i) q^{45} +(-0.512100 - 6.18013i) q^{46} +(-2.43391 - 7.78164i) q^{47} +(0.0523090 - 0.0635152i) q^{48} +(-1.02820 + 4.06028i) q^{49} +(3.85638 - 0.643516i) q^{50} +(-15.9281 - 4.50403i) q^{51} +(-0.683616 - 0.420217i) q^{52} +(1.76273 + 5.63576i) q^{53} +(-1.89056 - 3.27454i) q^{54} +(0.0513810 + 1.86401i) q^{55} +(4.47522 + 1.53635i) q^{56} +(1.77202 + 11.8680i) q^{57} +(5.31007 - 1.82295i) q^{58} +(-4.63414 - 12.3772i) q^{59} +(0.727286 - 2.32526i) q^{60} +(-0.679555 - 1.34284i) q^{61} +(1.53727 + 2.66263i) q^{62} +(-4.88037 + 5.92590i) q^{63} +(-1.95788 + 4.46352i) q^{64} +(-0.453565 - 0.0756865i) q^{65} +(5.67274 + 2.67703i) q^{66} +(6.25416 - 0.345052i) q^{67} -7.47239 q^{68} +19.6178 q^{69} +(1.03754 - 0.0572428i) q^{70} +(-1.83055 + 3.61727i) q^{71} +(-9.26047 - 9.00872i) q^{72} +(-2.20777 - 0.896719i) q^{73} +(-0.121495 - 0.0746825i) q^{74} +(1.02136 + 12.3260i) q^{75} +(2.22758 + 4.93777i) q^{76} +(0.362566 - 4.37552i) q^{77} +(-0.916088 + 1.24638i) q^{78} +(-2.81568 + 1.95235i) q^{79} +(0.000586516 - 0.0212777i) q^{80} +(-1.60398 + 0.756937i) q^{81} +(-6.02578 + 3.70404i) q^{82} +(-0.823013 + 3.25001i) q^{83} +(-2.30430 + 5.25327i) q^{84} +(-3.96727 + 1.61137i) q^{85} +(-7.25810 - 7.06079i) q^{86} +(4.35999 + 17.2172i) q^{87} +(7.28808 + 1.21616i) q^{88} +(5.56318 - 2.25957i) q^{89} +(-2.62873 - 1.06770i) q^{90} +(1.04184 + 0.294605i) q^{91} +(8.52194 - 2.40977i) q^{92} +(-8.79602 + 4.15094i) q^{93} +(-6.23999 + 3.37691i) q^{94} +(2.24747 + 2.14122i) q^{95} +(-13.7269 - 7.42862i) q^{96} +(-6.79664 - 0.374981i) q^{97} +(3.63928 + 0.200785i) q^{98} +(-5.99410 + 10.3821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1080 q - 38 q^{2} - 19 q^{3} - 8 q^{4} - 37 q^{5} - 38 q^{6} - 40 q^{7} - 38 q^{8} + 49 q^{9} + 19 q^{10} - 40 q^{11} - 38 q^{12} - 38 q^{13} - 38 q^{15} - 8 q^{16} - 94 q^{17} - 38 q^{18} - 38 q^{19} - 46 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) \) 1080 * q - 38 * q^2 - 19 * q^3 - 8 * q^4 - 37 * q^5 - 38 * q^6 - 40 * q^7 - 38 * q^8 + 49 * q^9 + 19 * q^10 - 40 * q^11 - 38 * q^12 - 38 * q^13 - 38 * q^15 - 8 * q^16 - 94 * q^17 - 38 * q^18 - 38 * q^19 - 46 * q^20 - 38 * q^21 - 19 * q^22 - 34 * q^23 - 30 * q^24 - 7 * q^25 + 41 * q^26 - 76 * q^27 - 15 * q^28 + 60 * q^30 - 38 * q^31 - 38 * q^32 - 114 * q^33 - 38 * q^34 - 33 * q^35 - 38 * q^37 - 76 * q^38 + 26 * q^39 - 38 * q^40 - 38 * q^41 - 32 * q^42 + 43 * q^43 - 26 * q^44 + 47 * q^45 + 26 * q^47 - 456 * q^48 - 32 * q^49 + 38 * q^50 + 38 * q^51 - 38 * q^52 - 38 * q^53 - 214 * q^54 - 29 * q^55 + 304 * q^56 - 38 * q^57 - 46 * q^58 - 38 * q^59 - 33 * q^61 - 13 * q^62 + 68 * q^63 - 110 * q^64 + 38 * q^65 - 26 * q^66 - 38 * q^67 - 96 * q^68 - 228 * q^69 - 342 * q^70 - 38 * q^71 - 38 * q^72 - 29 * q^73 + 50 * q^74 + 190 * q^75 + 323 * q^76 - 60 * q^77 + 228 * q^78 - 38 * q^79 + 322 * q^80 + 129 * q^81 + 48 * q^82 - 35 * q^83 + 19 * q^84 - 23 * q^85 - 684 * q^86 + 37 * q^87 - 38 * q^88 + 76 * q^89 - 722 * q^90 - 114 * q^91 - 22 * q^92 - 30 * q^93 + 228 * q^94 - 152 * q^95 + 142 * q^96 + 19 * q^97 + 57 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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