LMFDB - Embedded newform 361.2.k.a.4.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(4,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(342)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.k (of order $171$, degree $108$, 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:	$3348$
Relative dimension:	$31$ over $\Q(\zeta_{171})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{171}]$

Embedding invariants

Embedding label			4.17
Character	$\chi$	$=$	361.4
Dual form			361.2.k.a.271.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.126711 + 0.00232818i) q^{2} +(-0.167706 + 0.111779i) q^{3} +(-1.98260 - 0.0728810i) q^{4} +(-0.267723 - 0.554071i) q^{5} +(-0.0215104 + 0.0137732i) q^{6} +(1.97597 - 0.802569i) q^{7} +(-0.504126 - 0.0278134i) q^{8} +(-1.13878 + 2.73150i) q^{9} +(-0.0326333 - 0.0708300i) q^{10} +(1.59507 - 5.09972i) q^{11} +(0.340640 - 0.209391i) q^{12} +(4.56574 - 1.11167i) q^{13} +(0.252245 - 0.0970937i) q^{14} +(0.106832 + 0.0629951i) q^{15} +(3.89336 + 0.286629i) q^{16} +(-3.88995 - 6.19985i) q^{17} +(-0.150655 + 0.343459i) q^{18} +(0.324686 - 4.34679i) q^{19} +(0.490406 + 1.11801i) q^{20} +(-0.241671 + 0.355468i) q^{21} +(0.213986 - 0.642476i) q^{22} +(-3.14089 + 1.55340i) q^{23} +(0.0876539 - 0.0516863i) q^{24} +(2.87186 - 3.62065i) q^{25} +(0.581116 - 0.130231i) q^{26} +(-0.230259 - 1.17880i) q^{27} +(-3.97605 + 1.44716i) q^{28} +(7.80438 + 2.51995i) q^{29} +(0.0133901 + 0.00823088i) q^{30} +(-4.36730 + 3.80349i) q^{31} +(1.49819 + 0.138011i) q^{32} +(0.302540 + 1.03355i) q^{33} +(-0.478464 - 0.794643i) q^{34} +(-0.973691 - 0.879960i) q^{35} +(2.45682 - 5.33248i) q^{36} +(0.574852 + 0.624455i) q^{37} +(0.0512613 - 0.550029i) q^{38} +(-0.641439 + 0.696788i) q^{39} +(0.119555 + 0.286768i) q^{40} +(-0.967742 - 2.73681i) q^{41} +(-0.0314499 + 0.0444789i) q^{42} +(1.08853 + 1.53948i) q^{43} +(-3.53406 + 9.99446i) q^{44} +(1.81832 - 0.100320i) q^{45} +(-0.401601 + 0.189520i) q^{46} +(4.38676 + 2.27081i) q^{47} +(-0.684978 + 0.387127i) q^{48} +(-1.75714 + 1.70938i) q^{49} +(0.372325 - 0.452089i) q^{50} +(1.34538 + 0.604935i) q^{51} +(-9.13305 + 1.87125i) q^{52} +(0.392876 + 8.54784i) q^{53} +(-0.0264318 - 0.149902i) q^{54} +(-3.25264 + 0.481530i) q^{55} +(-1.01846 + 0.349638i) q^{56} +(0.431429 + 0.765275i) q^{57} +(0.983032 + 0.337475i) q^{58} +(-8.39024 - 1.55902i) q^{59} +(-0.207214 - 0.132680i) q^{60} +(-0.221562 + 1.84653i) q^{61} +(-0.562239 + 0.471775i) q^{62} +(-0.0579770 + 6.31131i) q^{63} +(-7.57088 - 0.837945i) q^{64} +(-1.83830 - 2.23212i) q^{65} +(0.0359288 + 0.131666i) q^{66} +(1.03701 - 4.43598i) q^{67} +(7.26036 + 12.5753i) q^{68} +(0.353108 - 0.611601i) q^{69} +(-0.121328 - 0.113767i) q^{70} +(-1.52356 - 12.6976i) q^{71} +(0.650062 - 1.34535i) q^{72} +(-2.15856 + 4.07772i) q^{73} +(0.0713860 + 0.0804635i) q^{74} +(-0.0769144 + 0.928219i) q^{75} +(-0.960522 + 8.59428i) q^{76} +(-0.941072 - 11.3570i) q^{77} +(-0.0828994 + 0.0867972i) q^{78} +(10.6913 - 0.984872i) q^{79} +(-0.883526 - 2.23393i) q^{80} +(-6.07851 - 6.13461i) q^{81} +(-0.116251 - 0.349036i) q^{82} +(0.562103 + 0.158948i) q^{83} +(0.505044 - 0.687137i) q^{84} +(-2.39372 + 3.81515i) q^{85} +(0.134344 + 0.197603i) q^{86} +(-1.59052 + 0.449756i) q^{87} +(-0.945958 + 2.52654i) q^{88} +(0.489170 + 0.924087i) q^{89} +(0.230635 - 0.00847820i) q^{90} +(8.12955 - 5.86095i) q^{91} +(6.34034 - 2.85086i) q^{92} +(0.307272 - 1.12604i) q^{93} +(0.550563 + 0.297950i) q^{94} +(-2.49535 + 0.983835i) q^{95} +(-0.266682 + 0.144321i) q^{96} +(2.32844 + 9.96025i) q^{97} +(-0.226629 + 0.212505i) q^{98} +(12.1135 + 10.1644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3348 q - 108 q^{2} - 111 q^{3} - 114 q^{4} - 108 q^{5} - 117 q^{6} - 111 q^{7} - 120 q^{8} - 117 q^{9} - 123 q^{10} - 111 q^{11} - 117 q^{12} - 111 q^{13} - 111 q^{14} - 117 q^{15} - 96 q^{16} - 3 q^{17}+ \cdots - 123 q^{99}+O(q^{100}) $ 3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{171}\right)$

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 $

$2$	0.126711	+	0.00232818i	0.0895980	+	0.00164627i	0.0631514	−	0.998004i	$-0.479885\pi$
$2$	0.126711	+	0.00232818i	0.0895980	+	0.00164627i	0.0264466	+	0.999650i	$0.491581\pi$
$3$	−0.167706	+	0.111779i	−0.0968250	+	0.0645357i	−0.602088	−	0.798430i	$-0.705664\pi$
$3$	−0.167706	+	0.111779i	−0.0968250	+	0.0645357i	0.505263	+	0.862965i	$0.331395\pi$
$4$	−1.98260	−	0.0728810i	−0.991300	−	0.0364405i
$5$	−0.267723	−	0.554071i	−0.119729	−	0.247788i	0.831970	−	0.554821i	$-0.187213\pi$
$5$	−0.267723	−	0.554071i	−0.119729	−	0.247788i	−0.951699	+	0.307033i	$0.900664\pi$
$6$	−0.0215104	+	0.0137732i	−0.00878157	+	0.00562287i
$7$	1.97597	−	0.802569i	0.746846	−	0.303343i	0.0290328	−	0.999578i	$-0.490757\pi$
$7$	1.97597	−	0.802569i	0.746846	−	0.303343i	0.717813	+	0.696236i	$0.245143\pi$
$8$	−0.504126	−	0.0278134i	−0.178236	−	0.00983353i
$9$	−1.13878	+	2.73150i	−0.379594	+	0.910501i
$10$	−0.0326333	−	0.0708300i	−0.0103196	−	0.0223984i
$11$	1.59507	−	5.09972i	0.480932	−	1.53762i	−0.325057	−	0.945694i	$-0.605384\pi$
$11$	1.59507	−	5.09972i	0.480932	−	1.53762i	0.805989	−	0.591930i	$-0.201634\pi$
$12$	0.340640	−	0.209391i	0.0983344	−	0.0604459i
$13$	4.56574	−	1.11167i	1.26631	−	0.308323i	0.453711	−	0.891149i	$-0.350100\pi$
$13$	4.56574	−	1.11167i	1.26631	−	0.308323i	0.812597	+	0.582826i	$0.198053\pi$
$14$	0.252245	−	0.0970937i	0.0674153	−	0.0259494i
$15$	0.106832	+	0.0629951i	0.0275840	+	0.0162653i
$16$	3.89336	+	0.286629i	0.973339	+	0.0716573i
$17$	−3.88995	−	6.19985i	−0.943451	−	1.50368i	−0.861940	−	0.507011i	$-0.830750\pi$
$17$	−3.88995	−	6.19985i	−0.943451	−	1.50368i	−0.0815117	−	0.996672i	$-0.525975\pi$
$18$	−0.150655	+	0.343459i	−0.0355098	+	0.0809541i
$19$	0.324686	−	4.34679i	0.0744882	−	0.997222i
$19$	0.324686	−	4.34679i	0.0744882	−	0.997222i
$20$	0.490406	+	1.11801i	0.109658	+	0.249995i
$21$	−0.241671	+	0.355468i	−0.0527369	+	0.0775694i
$22$	0.213986	−	0.642476i	0.0456219	−	0.136976i
$23$	−3.14089	+	1.55340i	−0.654921	+	0.323907i	−0.740137	−	0.672456i	$-0.765240\pi$
$23$	−3.14089	+	1.55340i	−0.654921	+	0.323907i	0.0852164	+	0.996362i	$0.472842\pi$
$24$	0.0876539	−	0.0516863i	0.0178923	−	0.0105504i
$25$	2.87186	−	3.62065i	0.574372	−	0.724130i
$26$	0.581116	−	0.130231i	0.113966	−	0.0255404i
$27$	−0.230259	−	1.17880i	−0.0443133	−	0.226860i
$28$	−3.97605	+	1.44716i	−0.751402	+	0.273488i
$29$	7.80438	+	2.51995i	1.44924	+	0.467944i	0.923796	−	0.382886i	$-0.125070\pi$
$29$	7.80438	+	2.51995i	1.44924	+	0.467944i	0.525441	+	0.850830i	$0.323900\pi$
$30$	0.0133901	+	0.00823088i	0.00244469	+	0.00150275i
$31$	−4.36730	+	3.80349i	−0.784391	+	0.683126i	−0.953139	−	0.302533i	$-0.902168\pi$
$31$	−4.36730	+	3.80349i	−0.784391	+	0.683126i	0.168748	+	0.985659i	$0.446027\pi$
$32$	1.49819	+	0.138011i	0.264845	+	0.0243972i
$33$	0.302540	+	1.03355i	0.0526655	+	0.179918i
$34$	−0.478464	−	0.794643i	−0.0820559	−	0.136280i
$35$	−0.973691	−	0.879960i	−0.164584	−	0.148740i
$36$	2.45682	−	5.33248i	0.409470	−	0.888747i
$37$	0.574852	+	0.624455i	0.0945050	+	0.102660i	0.781184	−	0.624301i	$-0.214616\pi$
$37$	0.574852	+	0.624455i	0.0945050	+	0.102660i	−0.686679	+	0.726961i	$0.740932\pi$
$38$	0.0512613	−	0.550029i	0.00831569	−	0.0892265i
$39$	−0.641439	+	0.696788i	−0.102712	+	0.111575i
$40$	0.119555	+	0.286768i	0.0189034	+	0.0453420i
$41$	−0.967742	−	2.73681i	−0.151136	−	0.427418i	0.842686	−	0.538405i	$-0.180973\pi$
$41$	−0.967742	−	2.73681i	−0.151136	−	0.427418i	−0.993822	+	0.110987i	$0.964599\pi$
$42$	−0.0314499	+	0.0444789i	−0.00485282	+	0.00686324i
$43$	1.08853	+	1.53948i	0.165999	+	0.234768i	0.891026	−	0.453951i	$-0.149986\pi$
$43$	1.08853	+	1.53948i	0.165999	+	0.234768i	−0.725028	+	0.688719i	$0.758173\pi$
$44$	−3.53406	+	9.99446i	−0.532780	+	1.50672i
$45$	1.81832	−	0.100320i	0.271060	−	0.0149548i
$46$	−0.401601	+	0.189520i	−0.0592128	+	0.0279432i
$47$	4.38676	+	2.27081i	0.639875	+	0.331232i	0.748779	−	0.662820i	$-0.230641\pi$
$47$	4.38676	+	2.27081i	0.639875	+	0.331232i	−0.108904	+	0.994052i	$0.534734\pi$
$48$	−0.684978	+	0.387127i	−0.0988680	+	0.0558769i
$49$	−1.75714	+	1.70938i	−0.251021	+	0.244197i
$50$	0.372325	−	0.452089i	0.0526547	−	0.0639351i
$51$	1.34538	+	0.604935i	0.188391	+	0.0847079i
$52$	−9.13305	+	1.87125i	−1.26653	+	0.259495i
$53$	0.392876	+	8.54784i	0.0539657	+	1.17414i	0.835217	+	0.549920i	$0.185342\pi$
$53$	0.392876	+	8.54784i	0.0539657	+	1.17414i	−0.781252	+	0.624216i	$0.785418\pi$
$54$	−0.0264318	−	0.149902i	−0.00359691	−	0.0203991i
$55$	−3.25264	+	0.481530i	−0.438586	+	0.0649295i
$56$	−1.01846	+	0.349638i	−0.136097	+	0.0467223i
$57$	0.431429	+	0.765275i	0.0571441	+	0.101363i
$58$	0.983032	+	0.337475i	0.129078	+	0.0443127i
$59$	−8.39024	−	1.55902i	−1.09232	−	0.202968i	−0.394251	−	0.919003i	$-0.628996\pi$
$59$	−8.39024	−	1.55902i	−1.09232	−	0.202968i	−0.698064	+	0.716035i	$0.745955\pi$
$60$	−0.207214	−	0.132680i	−0.0267513	−	0.0171289i
$61$	−0.221562	+	1.84653i	−0.0283681	+	0.236424i	−1.00000		7.43138e-5i	$-0.999976\pi$
$61$	−0.221562	+	1.84653i	−0.0283681	+	0.236424i	0.971632	+	0.236498i	$0.0759997\pi$
$62$	−0.562239	+	0.471775i	−0.0714044	+	0.0599154i
$63$	−0.0579770	+	6.31131i	−0.00730442	+	0.795151i
$64$	−7.57088	−	0.837945i	−0.946360	−	0.104743i
$65$	−1.83830	−	2.23212i	−0.228013	−	0.276860i
$66$	0.0359288	+	0.131666i	0.00442253	+	0.0162070i
$67$	1.03701	−	4.43598i	0.126691	−	0.541942i	−0.871939	−	0.489615i	$-0.837137\pi$
$67$	1.03701	−	4.43598i	0.126691	−	0.541942i	0.998630	−	0.0523269i	$-0.0166638\pi$
$68$	7.26036	+	12.5753i	0.880448	+	1.52498i
$69$	0.353108	−	0.611601i	0.0425092	−	0.0736281i
$70$	−0.121328	−	0.113767i	−0.0145015	−	0.0135978i
$71$	−1.52356	−	12.6976i	−0.180813	−	1.50692i	−0.737015	−	0.675877i	$-0.763765\pi$
$71$	−1.52356	−	12.6976i	−0.180813	−	1.50692i	0.556201	−	0.831048i	$-0.312258\pi$
$72$	0.650062	−	1.34535i	0.0766106	−	0.158551i
$73$	−2.15856	+	4.07772i	−0.252641	+	0.477261i	−0.977304	−	0.211842i	$-0.932054\pi$
$73$	−2.15856	+	4.07772i	−0.252641	+	0.477261i	0.724663	+	0.689103i	$0.241995\pi$
$74$	0.0713860	+	0.0804635i	0.00829846	+	0.00935370i
$75$	−0.0769144	+	0.928219i	−0.00888131	+	0.107181i
$76$	−0.960522	+	8.59428i	−0.110179	+	0.985832i
$77$	−0.941072	−	11.3570i	−0.107245	−	1.29426i
$78$	−0.0828994	+	0.0867972i	−0.00938651	+	0.00982784i
$79$	10.6913	−	0.984872i	1.20287	−	0.110807i	0.528326	−	0.849042i	$-0.322820\pi$
$79$	10.6913	−	0.984872i	1.20287	−	0.110807i	0.674544	+	0.738235i	$0.264340\pi$
$80$	−0.883526	−	2.23393i	−0.0987812	−	0.249761i
$81$	−6.07851	−	6.13461i	−0.675390	−	0.681623i
$82$	−0.116251	−	0.349036i	−0.0128378	−	0.0385446i
$83$	0.562103	+	0.158948i	0.0616989	+	0.0174468i	0.302813	−	0.953050i	$-0.402074\pi$
$83$	0.562103	+	0.158948i	0.0616989	+	0.0174468i	−0.241114	+	0.970497i	$0.577513\pi$
$84$	0.505044	−	0.687137i	0.0551048	−	0.0749728i
$85$	−2.39372	+	3.81515i	−0.259636	+	0.413811i
$86$	0.134344	+	0.197603i	0.0144866	+	0.0213080i
$87$	−1.59052	+	0.449756i	−0.170522	+	0.0482189i
$88$	−0.945958	+	2.52654i	−0.100839	+	0.269330i
$89$	0.489170	+	0.924087i	0.0518519	+	0.0979530i	0.908377	−	0.418153i	$-0.137322\pi$
$89$	0.489170	+	0.924087i	0.0518519	+	0.0979530i	−0.856525	+	0.516106i	$0.827381\pi$
$90$	0.230635	−	0.00847820i	0.0243110	−	0.000893681i
$91$	8.12955	−	5.86095i	0.852209	−	0.614394i
$92$	6.34034	−	2.85086i	0.661026	−	0.297223i
$93$	0.307272	−	1.12604i	0.0318626	−	0.116765i
$94$	0.550563	+	0.297950i	0.0567862	+	0.0307312i
$95$	−2.49535	+	0.983835i	−0.256018	+	0.100939i
$96$	−0.266682	+	0.144321i	−0.0272181	+	0.0147297i
$97$	2.32844	+	9.96025i	0.236417	+	1.01131i	0.950371	+	0.311118i	$0.100704\pi$
$97$	2.32844	+	9.96025i	0.236417	+	1.01131i	−0.713954	+	0.700192i	$0.753098\pi$
$98$	−0.226629	+	0.212505i	−0.0228930	+	0.0214663i
$99$	12.1135	+	10.1644i	1.21745	+	1.02156i
$100$	−5.95763	+	6.96900i	−0.595763	+	0.696900i
$101$	−1.95673	−	2.56222i	−0.194701	−	0.254950i	0.687109	−	0.726555i	$-0.258880\pi$
$101$	−1.95673	−	2.56222i	−0.194701	−	0.254950i	−0.881810	+	0.471605i	$0.843675\pi$
$102$	0.169066	+	0.0797841i	0.0167400	+	0.00789980i
$103$	6.54372	+	2.65783i	0.644772	+	0.261884i	0.675179	−	0.737654i	$-0.264066\pi$
$103$	6.54372	+	2.65783i	0.644772	+	0.261884i	−0.0304071	+	0.999538i	$0.509680\pi$
$104$	−2.33263	+	0.433435i	−0.228733	+	0.0425018i
$105$	0.261655	+	0.0387361i	0.0255349	+	0.00378025i
$106$	0.0298807	+	1.08402i	0.00290227	+	0.105289i
$107$	1.77698	−	9.09717i	0.171788	−	0.879457i	−0.791538	−	0.611120i	$-0.790719\pi$
$107$	1.77698	−	9.09717i	0.171788	−	0.879457i	0.963325	−	0.268336i	$-0.0864738\pi$
$108$	0.370599	+	2.35386i	0.0356609	+	0.226501i
$109$	−0.321462	+	6.99408i	−0.0307905	+	0.669911i	0.925719	+	0.378211i	$0.123461\pi$
$109$	−0.321462	+	6.99408i	−0.0307905	+	0.669911i	−0.956510	+	0.291700i	$0.905779\pi$
$110$	−0.413266	+	0.0534423i	−0.0394034	+	0.00509552i
$111$	−0.166207	−	0.0404684i	−0.0157757	−	0.00384109i
$112$	7.92319	−	2.55832i	0.748671	−	0.241738i
$113$	−14.5978	+	11.3620i	−1.37325	+	1.06884i	−0.383886	+	0.923381i	$0.625414\pi$
$113$	−14.5978	+	11.3620i	−1.37325	+	1.06884i	−0.989364	+	0.145462i	$0.953533\pi$
$114$	0.0528849	+	0.0979730i	0.00495313	+	0.00917601i
$115$	1.70158	+	1.32439i	0.158673	+	0.123500i
$116$	−15.2893	−	5.56485i	−1.41958	−	0.516684i
$117$	−2.16284	+	13.7373i	−0.199954	+	1.27001i
$118$	−1.05950	−	0.217079i	−0.0975352	−	0.0199837i
$119$	−12.6622	−	9.12875i	−1.16074	−	0.836831i
$120$	−0.0521048	−	0.0347288i	−0.00475650	−	0.00317030i
$121$	−14.4234	−	10.0009i	−1.31122	−	0.909177i
$122$	−0.0323733	+	0.233459i	−0.00293094	+	0.0211364i
$123$	0.468215	+	0.350806i	0.0422175	+	0.0316311i
$124$	8.93581	−	7.22250i	0.802460	−	0.648600i
$125$	−5.77729	−	1.29472i	−0.516737	−	0.115803i
$126$	−0.0220402	+	0.799576i	−0.00196349	+	0.0712319i
$127$	−1.15887	+	6.57228i	−0.102833	+	0.583195i	0.889231	+	0.457459i	$0.151240\pi$
$127$	−1.15887	+	6.57228i	−0.102833	+	0.583195i	−0.992064	+	0.125736i	$0.959871\pi$
$128$	−3.94158	−	0.509713i	−0.348390	−	0.0450527i
$129$	−0.354634	−	0.136505i	−0.0312237	−	0.0120186i
$130$	−0.227735	−	0.287113i	−0.0199737	−	0.0251815i
$131$	2.79340	+	2.25780i	0.244060	+	0.197265i	0.742850	−	0.669458i	$-0.233474\pi$
$131$	2.79340	+	2.25780i	0.244060	+	0.197265i	−0.498790	+	0.866723i	$0.666222\pi$
$132$	−0.524490	−	2.07116i	−0.0456510	−	0.180272i
$133$	−2.84703	−	8.84970i	−0.246869	−	0.767366i
$134$	0.141728	−	0.559672i	0.0122435	−	0.0483483i
$135$	−0.591491	+	0.443170i	−0.0509075	+	0.0381420i
$136$	1.78859	+	3.23370i	0.153370	+	0.277287i
$137$	5.29821	−	1.60387i	0.452657	−	0.137028i	−0.0551896	−	0.998476i	$-0.517576\pi$
$137$	5.29821	−	1.60387i	0.452657	−	0.137028i	0.507846	+	0.861448i	$0.330442\pi$
$138$	0.0461665	−	0.0766743i	0.00392995	−	0.00652695i
$139$	21.5388	+	5.66539i	1.82689	+	0.480532i	0.997001	−	0.0773900i	$-0.0246587\pi$
$139$	21.5388	+	5.66539i	1.82689	+	0.480532i	0.829893	+	0.557922i	$0.188401\pi$
$140$	1.86631	+	1.81557i	0.157732	+	0.153444i
$141$	−0.989515	+	0.109519i	−0.0833322	+	0.00922321i
$142$	−0.163489	−	1.61247i	−0.0137197	−	0.135315i
$143$	1.61344	−	25.0572i	0.134923	−	2.09539i
$144$	−5.21661	+	10.3083i	−0.434718	+	0.859025i
$145$	−0.693176	−	4.99883i	−0.0575652	−	0.415130i
$146$	−0.283006	+	0.511665i	−0.0234218	+	0.0423457i
$147$	0.103611	−	0.483084i	0.00854567	−	0.0398441i
$148$	−1.09419	−	1.27994i	−0.0899419	−	0.105211i
$149$	0.146531	+	15.9512i	0.0120043	+	1.30677i	0.762972	+	0.646431i	$0.223739\pi$
$149$	0.146531	+	15.9512i	0.0120043	+	1.30677i	−0.750968	+	0.660339i	$0.770413\pi$
$150$	−0.0119069	+	0.117436i	−0.000972197	+	0.00958862i
$151$	17.7287	+	2.95840i	1.44274	+	0.240752i	0.833627	−	0.552328i	$-0.186260\pi$
$151$	17.7287	+	2.95840i	1.44274	+	0.240752i	0.609118	+	0.793080i	$0.291524\pi$
$152$	−0.284582	+	2.18230i	−0.0230827	+	0.177008i
$153$	21.3647	−	3.56514i	1.72723	−	0.288224i
$154$	−0.0928027	−	1.44125i	−0.00747825	−	0.116139i
$155$	3.27663	+	1.40151i	0.263185	+	0.112572i
$156$	1.32250	−	1.33470i	0.105885	−	0.106862i
$157$	−6.36099	−	3.14598i	−0.507662	−	0.251076i	0.171341	−	0.985212i	$-0.445190\pi$
$157$	−6.36099	−	3.14598i	−0.507662	−	0.251076i	−0.679003	+	0.734136i	$0.737588\pi$
$158$	1.35700	−	0.0999025i	0.107957	−	0.00794782i
$159$	−1.02136	−	1.38961i	−0.0809990	−	0.110203i
$160$	−0.324632	−	0.867052i	−0.0256644	−	0.0685465i
$161$	−4.95959	+	5.59025i	−0.390870	+	0.440574i
$162$	−0.755930	−	0.791472i	−0.0593915	−	0.0621839i
$163$	−5.41945	−	4.71981i	−0.424484	−	0.369684i	0.417961	−	0.908465i	$-0.362745\pi$
$163$	−5.41945	−	4.71981i	−0.424484	−	0.369684i	−0.842446	+	0.538781i	$0.818885\pi$
$164$	1.71918	+	5.49653i	0.134246	+	0.429207i
$165$	0.491662	−	0.444333i	0.0382759	−	0.0345913i
$166$	0.0708545	+	0.0214490i	0.00549937	+	0.00166477i
$167$	−2.29697	−	10.7096i	−0.177745	−	0.828733i	−0.974492	−	0.224421i	$-0.927951\pi$
$167$	−2.29697	−	10.7096i	−0.177745	−	0.828733i	0.796748	−	0.604312i	$-0.206552\pi$
$168$	0.131719	−	0.172479i	0.0101624	−	0.0133070i
$169$	8.06523	−	4.17498i	0.620402	−	0.321152i
$170$	−0.312193	+	0.477847i	−0.0239441	+	0.0366492i
$171$	11.5035	+	5.83693i	0.879696	+	0.446361i
$172$	−2.04591	−	3.13150i	−0.155999	−	0.238775i
$173$	−3.17101	−	1.79215i	−0.241087	−	0.136254i	0.366741	−	0.930323i	$-0.380474\pi$
$173$	−3.17101	−	1.79215i	−0.241087	−	0.136254i	−0.607828	+	0.794069i	$0.707959\pi$
$174$	−0.202583	+	0.0532859i	−0.0153578	+	0.00403959i
$175$	2.76888	−	9.45916i	0.209308	−	0.715045i
$176$	7.67191	−	19.3978i	0.578292	−	1.46217i
$177$	1.58136	−	0.676396i	0.118862	−	0.0508410i
$178$	0.0598317	+	0.118231i	0.00448457	+	0.00886176i
$179$	12.6484	−	8.77024i	0.945389	−	0.655518i	0.00658837	−	0.999978i	$-0.497903\pi$
$179$	12.6484	−	8.77024i	0.945389	−	0.655518i	0.938801	+	0.344460i	$0.111938\pi$
$180$	−3.61232	+	0.0663726i	−0.269246	+	0.00494712i
$181$	−11.0722	+	0.203440i	−0.822991	+	0.0151216i	−0.428238	−	0.903666i	$-0.640866\pi$
$181$	−11.0722	+	0.203440i	−0.822991	+	0.0151216i	−0.394752	+	0.918788i	$0.629170\pi$
$182$	1.04375	−	0.723718i	0.0773677	−	0.0536455i
$183$	−0.169246	−	0.334440i	−0.0125110	−	0.0247225i
$184$	1.62661	−	0.695752i	0.119915	−	0.0512915i
$185$	0.192092	−	0.485689i	0.0141229	−	0.0357086i
$186$	0.0415562	−	0.141966i	0.00304705	−	0.0104095i
$187$	−37.8222	+	9.94848i	−2.76584	+	0.727505i
$188$	−8.53169	−	4.82183i	−0.622237	−	0.351668i
$189$	−1.40105	−	2.14447i	−0.101911	−	0.155987i
$190$	−0.318479	+	0.118853i	−0.0231049	+	0.00862249i
$191$	−0.538471	+	0.824191i	−0.0389624	+	0.0596364i	−0.856116	−	0.516783i	$-0.827129\pi$
$191$	−0.538471	+	0.824191i	−0.0389624	+	0.0596364i	0.817154	+	0.576419i	$0.195550\pi$
$192$	1.36335	−	0.705738i	0.0983910	−	0.0509323i
$193$	14.3716	−	18.8188i	1.03449	−	1.35461i	0.101448	−	0.994841i	$-0.467652\pi$
$193$	14.3716	−	18.8188i	1.03449	−	1.35461i	0.933043	−	0.359764i	$-0.117143\pi$
$194$	0.271848	+	1.26749i	0.0195176	+	0.0910006i
$195$	0.557798	+	0.168856i	0.0399447	+	0.0120921i
$196$	3.60829	−	3.26095i	0.257735	−	0.232925i
$197$	0.110693	+	0.353905i	0.00788654	+	0.0252147i	0.958265	−	0.285881i	$-0.0922863\pi$
$197$	0.110693	+	0.353905i	0.00788654	+	0.0252147i	−0.950378	+	0.311096i	$0.899304\pi$
$198$	1.51124	+	1.31614i	0.107399	+	0.0935341i
$199$	3.61517	+	3.78514i	0.256272	+	0.268322i	0.838740	−	0.544532i	$-0.183293\pi$
$199$	3.61517	+	3.78514i	0.256272	+	0.268322i	−0.582468	+	0.812854i	$0.697913\pi$
$200$	−1.54848	+	1.74539i	−0.109494	+	0.123418i
$201$	0.321938	+	0.859857i	0.0227077	+	0.0606496i
$202$	−0.241973	−	0.329216i	−0.0170251	−	0.0231635i
$203$	17.4436	−	1.28420i	1.22430	−	0.0901334i
$204$	−2.62326	−	1.29740i	−0.183665	−	0.0908360i
$205$	−1.25730	+	1.26890i	−0.0878137	+	0.0886241i
$206$	0.822972	+	0.352010i	0.0573392	+	0.0245257i
$207$	−0.666333	−	10.3483i	−0.0463134	−	0.719259i
$208$	18.0947	−	3.01947i	1.25464	−	0.209362i
$209$	−21.6495	−	8.58925i	−1.49753	−	0.594131i
$210$	0.0330643	+	0.00551746i	0.00228165	+	0.000380741i
$211$	−2.49791	+	24.6365i	−0.171963	+	1.69605i	0.434289	+	0.900774i	$0.357000\pi$
$211$	−2.49791	+	24.6365i	−0.171963	+	1.69605i	−0.606252	+	0.795272i	$0.707328\pi$
$212$	−0.155941	−	16.9756i	−0.0107101	−	1.16589i
$213$	1.67483	+	1.95916i	0.114758	+	0.134239i
$214$	0.246343	−	1.14857i	0.0168396	−	0.0785147i
$215$	0.561556	−	1.01527i	0.0382978	−	0.0692410i
$216$	0.0832932	+	0.600667i	0.00566738	+	0.0408702i
$217$	−5.57709	+	11.0206i	−0.378598	+	0.748129i
$218$	−0.0570162	+	0.885477i	−0.00386162	+	0.0599720i
$219$	−0.0938005	−	0.925140i	−0.00633845	−	0.0625151i
$220$	6.48378	−	0.717625i	0.437137	−	0.0483823i
$221$	−24.6527	−	23.9825i	−1.65832	−	1.61324i
$222$	−0.0209660	−	0.00551474i	−0.00140715	−	0.000370125i
$223$	4.04887	−	6.72444i	0.271132	−	0.450302i	−0.691012	−	0.722843i	$-0.742835\pi$
$223$	4.04887	−	6.72444i	0.271132	−	0.450302i	0.962144	+	0.272541i	$0.0878641\pi$
$224$	3.07114	−	0.929695i	0.205199	−	0.0621179i
$225$	6.61940	+	11.9676i	0.441293	+	0.797842i
$226$	−1.87616	+	1.40570i	−0.124800	+	0.0935054i
$227$	1.11074	−	4.38620i	0.0737222	−	0.291122i	−0.921548	−	0.388263i	$-0.873075\pi$
$227$	1.11074	−	4.38620i	0.0737222	−	0.291122i	0.995271	+	0.0971411i	$0.0309698\pi$
$228$	−0.799576	−	1.54868i	−0.0529532	−	0.102564i
$229$	6.97194	+	27.5316i	0.460719	+	1.81934i	0.565380	+	0.824830i	$0.308729\pi$
$229$	6.97194	+	27.5316i	0.460719	+	1.81934i	−0.104662	+	0.994508i	$0.533376\pi$
$230$	0.212525	+	0.171777i	0.0140135	+	0.0113266i
$231$	1.42730	+	1.79945i	0.0939097	+	0.118395i
$232$	−3.86430	−	1.48744i	−0.253704	−	0.0976553i
$233$	20.5272	+	2.65452i	1.34478	+	0.173903i	0.766664	−	0.642049i	$-0.221915\pi$
$233$	20.5272	+	2.65452i	1.34478	+	0.173903i	0.578119	+	0.815952i	$0.303787\pi$
$234$	−0.306037	+	1.73562i	−0.0200063	+	0.113461i
$235$	0.0837563	−	3.03852i	0.00546366	−	0.198211i
$236$	16.5209	+	3.70241i	1.07542	+	0.241006i
$237$	−1.68291	+	1.36024i	−0.109317	+	0.0883569i
$238$	−1.58319	−	1.18619i	−0.102623	−	0.0768893i
$239$	0.374199	−	2.69853i	0.0242049	−	0.174553i	−0.974567	−	0.224096i	$-0.928057\pi$
$239$	0.374199	−	2.69853i	0.0242049	−	0.174553i	0.998772	+	0.0495427i	$0.0157764\pi$
$240$	0.397879	+	0.275883i	0.0256830	+	0.0178082i
$241$	8.68687	+	5.78996i	0.559570	+	0.372964i	0.802109	−	0.597177i	$-0.203711\pi$
$241$	8.68687	+	5.78996i	0.559570	+	0.372964i	−0.242539	+	0.970142i	$0.577980\pi$
$242$	−1.80431	−	1.30081i	−0.115986	−	0.0836191i
$243$	5.23502	+	1.07259i	0.335827	+	0.0688067i
$244$	0.573845	−	3.64478i	0.0367367	−	0.233333i
$245$	1.41754	+	0.515943i	0.0905634	+	0.0329624i
$246$	0.0585111	+	0.0455410i	0.00373053	+	0.00290359i
$247$	−3.34978	−	20.2072i	−0.213141	−	1.28576i
$248$	2.30746	−	1.79597i	0.146524	−	0.114044i
$249$	−0.112035	+	0.0361750i	−0.00709993	+	0.00229250i
$250$	−0.729031	−	0.177506i	−0.0461080	−	0.0112264i
$251$	−12.2657	+	1.58616i	−0.774204	+	0.100118i	−0.505178	−	0.863015i	$-0.668573\pi$
$251$	−12.2657	+	1.58616i	−0.774204	+	0.100118i	−0.269026	+	0.963133i	$0.586702\pi$
$252$	0.574920	−	12.5086i	0.0362166	−	0.787967i
$253$	2.91198	+	18.4955i	0.183075	+	1.16280i
$254$	−0.162143	+	0.830080i	−0.0101737	+	0.0520838i
$255$	−0.0250121	−	0.907391i	−0.00156632	−	0.0568230i
$256$	14.5717	+	2.15724i	0.910733	+	0.134827i
$257$	−6.18061	+	1.14844i	−0.385536	+	0.0716380i	−0.371909	−	0.928269i	$-0.621297\pi$
$257$	−6.18061	+	1.14844i	−0.385536	+	0.0716380i	−0.0136266	+	0.999907i	$0.504338\pi$
$258$	−0.0446181	−	0.0181223i	−0.00277780	−	0.00112824i
$259$	1.63706	+	0.772546i	0.101722	+	0.0480037i
$260$	3.48193	+	4.55938i	0.215940	+	0.282761i
$261$	−15.7707	+	18.4480i	−0.976185	+	1.14190i
$262$	0.348697	+	0.292591i	0.0215426	+	0.0180763i
$263$	−6.48821	+	6.08387i	−0.400080	+	0.375148i	−0.857830	−	0.513934i	$-0.828188\pi$
$263$	−6.48821	+	6.08387i	−0.400080	+	0.375148i	0.457750	+	0.889081i	$0.348656\pi$
$264$	−0.123772	−	0.529454i	−0.00761763	−	0.0325856i
$265$	4.63092	−	2.50613i	0.284475	−	0.153950i
$266$	−0.340145	−	1.12798i	−0.0208556	−	0.0691609i
$267$	−0.185330	−	0.100296i	−0.0113420	−	0.00613800i
$268$	−2.37928	+	8.71920i	−0.145338	+	0.532610i
$269$	9.66645	−	4.34641i	0.589374	−	0.265005i	−0.0934076	−	0.995628i	$-0.529776\pi$
$269$	9.66645	−	4.34641i	0.589374	−	0.265005i	0.682781	+	0.730623i	$0.260770\pi$
$270$	−0.0759801	+	0.0547773i	−0.00462400	+	0.00333364i
$271$	8.47868	−	0.311679i	0.515043	−	0.0189332i	0.222027	−	0.975041i	$-0.428733\pi$
$271$	8.47868	−	0.311679i	0.515043	−	0.0189332i	0.293017	+	0.956107i	$0.405341\pi$
$272$	−13.3679	−	25.2532i	−0.810548	−	1.53120i
$273$	−0.708242	+	1.89163i	−0.0428648	+	0.114487i
$274$	0.675074	−	0.190893i	0.0407827	−	0.0115323i
$275$	−13.8835	−	20.4209i	−0.837207	−	1.23143i
$276$	−0.744646	+	1.18682i	−0.0448224	+	0.0714384i
$277$	−9.65737	+	13.1393i	−0.580255	+	0.789465i	−0.992583	−	0.121570i	$-0.961207\pi$
$277$	−9.65737	+	13.1393i	−0.580255	+	0.789465i	0.412328	+	0.911036i	$0.364716\pi$
$278$	2.71600	+	0.768012i	0.162895	+	0.0460623i
$279$	−5.41583	−	16.2606i	−0.324237	−	0.973499i
$280$	0.466389	+	0.470693i	0.0278721	+	0.0281293i
$281$	8.56425	+	21.6541i	0.510901	+	1.29177i	0.924454	+	0.381294i	$0.124521\pi$
$281$	8.56425	+	21.6541i	0.510901	+	1.29177i	−0.413553	+	0.910480i	$0.635712\pi$
$282$	−0.125637	+	0.0115735i	−0.00748158	+	0.000689194i
$283$	−10.1424	+	10.6193i	−0.602906	+	0.631253i	−0.952096	−	0.305799i	$-0.901077\pi$
$283$	−10.1424	+	10.6193i	−0.602906	+	0.631253i	0.349190	+	0.937052i	$0.386457\pi$
$284$	2.09519	+	25.2852i	0.124327	+	1.50040i
$285$	0.308513	−	0.443923i	0.0182748	−	0.0262958i
$286$	0.262778	−	3.17126i	0.0155384	−	0.187520i
$287$	−4.10871	−	4.63117i	−0.242529	−	0.273370i
$288$	−2.08309	+	3.93515i	−0.122747	+	0.231881i
$289$	−15.9103	+	32.9274i	−0.935898	+	1.93691i
$290$	−0.0761947	−	0.635019i	−0.00447431	−	0.0372896i
$291$	−1.50384	−	1.41012i	−0.0881567	−	0.0826629i
$292$	4.57675	−	7.92717i	0.267834	−	0.463902i
$293$	−9.43183	−	16.3364i	−0.551013	−	0.954383i	−0.998202	−	0.0599435i	$-0.980908\pi$
$293$	−9.43183	−	16.3364i	−0.551013	−	0.954383i	0.447188	−	0.894440i	$-0.352425\pi$
$294$	0.0142533	−	0.0609708i	0.000831269	−	0.00355589i
$295$	1.38245	+	5.06617i	0.0804891	+	0.294964i
$296$	−0.272430	−	0.330793i	−0.0158346	−	0.0192270i
$297$	−6.37882	−	0.706008i	−0.370137	−	0.0409667i
$298$	−0.0185701	+	2.02152i	−0.00107574	+	0.117104i
$299$	−12.6136	+	10.5841i	−0.729463	+	0.612092i
$300$	0.220140	−	1.83468i	0.0127098	−	0.105925i
$301$	3.38643	+	2.16834i	0.195190	+	0.124981i
$302$	2.23953	+	0.416137i	0.128871	+	0.0239460i
$303$	0.614557	+	0.210978i	0.0353054	+	0.0121203i
$304$	2.51004	−	16.8305i	0.143960	−	0.965297i
$305$	1.08242	−	0.371597i	0.0619795	−	0.0212776i
$306$	2.71544	−	0.402000i	0.155231	−	0.0229808i
$307$	−3.09895	−	17.5750i	−0.176866	−	1.00306i	−0.935968	−	0.352086i	$-0.885473\pi$
$307$	−3.09895	−	17.5750i	−0.176866	−	1.00306i	0.759101	−	0.650972i	$-0.225639\pi$
$308$	1.03806	+	22.5851i	0.0591487	+	1.28690i
$309$	−1.39451	+	0.285718i	−0.0793309	+	0.0162539i
$310$	0.411921	+	0.185215i	0.0233955	+	0.0105195i
$311$	−7.14281	+	8.67304i	−0.405032	+	0.491803i	−0.934218	−	0.356703i	$-0.883901\pi$
$311$	−7.14281	+	8.67304i	−0.405032	+	0.491803i	0.529186	+	0.848506i	$0.322497\pi$
$312$	0.342746	−	0.333429i	0.0194042	−	0.0188767i
$313$	−26.7816	+	15.1361i	−1.51379	+	0.855542i	−0.999997	−	0.00237305i	$-0.999245\pi$
$313$	−26.7816	+	15.1361i	−1.51379	+	0.855542i	−0.513791	+	0.857915i	$0.671759\pi$
$314$	−0.798681	−	0.413438i	−0.0450722	−	0.0233317i
$315$	3.51243	−	1.65756i	0.197903	−	0.0933928i
$316$	−21.2684	+	1.17341i	−1.19644	+	0.0660096i
$317$	−2.03612	+	5.75823i	−0.114360	+	0.323414i	−0.986003	−	0.166726i	$-0.946680\pi$
$317$	−2.03612	+	5.75823i	−0.114360	+	0.323414i	0.871643	+	0.490141i	$0.163055\pi$
$318$	−0.126182	−	0.178456i	−0.00707592	−	0.0100073i
$319$	25.2996	−	35.7807i	1.41651	−	2.00333i
$320$	1.56262	+	4.41914i	0.0873528	+	0.247037i
$321$	0.718863	+	1.72428i	0.0401230	+	0.0962399i
$322$	−0.641448	+	0.696798i	−0.0357465	+	0.0388310i
$323$	−28.2124	+	14.8958i	−1.56978	+	0.828824i
$324$	11.6042	+	12.6055i	0.644676	+	0.700304i
$325$	9.08717	−	19.7235i	0.504066	−	1.09406i
$326$	−0.675714	−	0.610667i	−0.0374244	−	0.0338217i
$327$	−0.727881	−	1.20888i	−0.0402519	−	0.0668513i
$328$	0.411744	+	1.40662i	0.0227348	+	0.0776673i
$329$	10.4906	+	0.966379i	0.578365	+	0.0532782i
$330$	0.0633334	−	0.0551571i	0.00348639	−	0.00303630i
$331$	21.6821	+	13.3279i	1.19175	+	0.732568i	0.970135	−	0.242565i	$-0.0779887\pi$
$331$	21.6821	+	13.3279i	1.19175	+	0.732568i	0.221619	+	0.975133i	$0.428866\pi$
$332$	−1.10284	−	0.356096i	−0.0605263	−	0.0195433i
$333$	−2.36033	+	0.859091i	−0.129345	+	0.0470779i
$334$	−0.266116	−	1.36237i	−0.0145612	−	0.0745454i
$335$	−2.73548	+	0.613035i	−0.149455	+	0.0334937i
$336$	−1.04280	+	1.31469i	−0.0568893	+	0.0717223i
$337$	−1.05875	+	0.624307i	−0.0576738	+	0.0340082i	−0.536486	−	0.843909i	$-0.680249\pi$
$337$	−1.05875	+	0.624307i	−0.0576738	+	0.0340082i	0.478812	+	0.877917i	$0.341067\pi$
$338$	1.03167	−	0.510237i	0.0561155	−	0.0277533i
$339$	1.17811	−	3.53720i	0.0639864	−	0.192114i
$340$	5.02385	−	7.38945i	0.272456	−	0.400749i
$341$	12.4306	+	28.3389i	0.673154	+	1.53464i
$342$	1.44403	+	0.766383i	0.0780842	+	0.0414413i
$343$	−8.09714	+	18.4596i	−0.437205	+	0.996726i
$344$	−0.505936	−	0.806367i	−0.0272782	−	0.0434764i
$345$	−0.433405	−	0.0319073i	−0.0233337	−	0.00171783i
$346$	−0.397628	−	0.234467i	−0.0213766	−	0.0126050i
$347$	16.6155	−	6.39561i	0.891967	−	0.343334i	0.130431	−	0.991457i	$-0.458364\pi$
$347$	16.6155	−	6.39561i	0.891967	−	0.343334i	0.761536	+	0.648123i	$0.224446\pi$
$348$	3.18614	−	0.775767i	0.170795	−	0.0415855i
$349$	−15.5441	+	9.55492i	−0.832056	+	0.511463i	−0.873012	−	0.487698i	$-0.837837\pi$
$349$	−15.5441	+	9.55492i	−0.832056	+	0.511463i	0.0409562	+	0.999161i	$0.486960\pi$
$350$	0.372869	−	1.19213i	0.0199307	−	0.0637220i
$351$	−2.36174	−	5.12610i	−0.126060	−	0.273611i
$352$	3.09354	−	7.42022i	0.164886	−	0.395499i
$353$	27.3506	+	1.50897i	1.45572	+	0.0803145i	0.765572	−	0.643350i	$-0.222456\pi$
$353$	27.3506	+	1.50897i	1.45572	+	0.0803145i	0.690151	+	0.723665i	$0.257544\pi$
$354$	0.201950	−	0.0820249i	0.0107335	−	0.00435958i
$355$	−6.62746	+	4.24359i	−0.351749	+	0.225226i
$356$	−0.902480	−	1.86775i	−0.0478314	−	0.0989903i
$357$	3.14393	+	0.115572i	0.166395	+	0.00611672i
$358$	1.62311	−	1.08184i	0.0857842	−	0.0571768i
$359$	−19.5618	−	0.359427i	−1.03243	−	0.0189698i	−0.500483	−	0.865746i	$-0.666844\pi$
$359$	−19.5618	−	0.359427i	−1.03243	−	0.0189698i	−0.531949	+	0.846777i	$0.678540\pi$
$360$	−0.919455			−0.0484595
$361$	−18.7892	−	2.82269i	−0.988903	−	0.148562i
$362$	−1.40344			−0.0737632
$363$	3.53678	+	0.0649847i	0.185633	+	0.00341081i
$364$	−16.5448	+	11.0274i	−0.867183	+	0.577994i
$365$	2.83724	+	0.104298i	0.148508	+	0.00545920i
$366$	−0.0206667	−	0.0427711i	−0.00108026	−	0.00223568i
$367$	−13.2120	+	8.45968i	−0.689660	+	0.441592i	−0.836789	−	0.547526i	$-0.815570\pi$
$367$	−13.2120	+	8.45968i	−0.689660	+	0.441592i	0.147129	+	0.989117i	$0.452997\pi$
$368$	−12.6739	+	5.14767i	−0.660670	+	0.268341i
$369$	8.57766	+	0.473243i	0.446535	+	0.0246360i
$370$	0.0254708	−	0.0610948i	0.00132417	−	0.00317617i
$371$	7.63654	+	16.5750i	0.396469	+	0.860529i
$372$	−0.691264	+	2.21009i	−0.0358404	+	0.114588i
$373$	27.8818	−	17.1389i	1.44367	−	0.887418i	0.443704	−	0.896174i	$-0.353664\pi$
$373$	27.8818	−	17.1389i	1.44367	−	0.887418i	0.999962	+	0.00875574i	$0.00278707\pi$
$374$	−4.81565	+	1.17252i	−0.249011	+	0.0606297i
$375$	1.11361	−	0.428649i	0.0575065	−	0.0221353i
$376$	−2.14832	−	1.26679i	−0.110791	−	0.0653296i
$377$	38.4341	+	2.82952i	1.97946	+	0.145728i
$378$	−0.172535	−	0.274989i	−0.00887426	−	0.0141439i
$379$	−12.8771	+	29.3568i	−0.661453	+	1.50796i	0.189038	+	0.981970i	$0.439463\pi$
$379$	−12.8771	+	29.3568i	−0.661453	+	1.50796i	−0.850491	+	0.525990i	$0.823695\pi$
$380$	5.01899	−	1.76869i	0.257469	−	0.0907317i
$381$	−0.540294	−	1.23175i	−0.0276801	−	0.0631043i
$382$	−0.0701489	+	0.103180i	−0.00358913	+	0.00527916i
$383$	10.3747	−	31.1492i	0.530120	−	1.59165i	−0.251476	−	0.967864i	$-0.580916\pi$
$383$	10.3747	−	31.1492i	0.530120	−	1.59165i	0.781596	−	0.623784i	$-0.214406\pi$
$384$	0.718001	−	0.355105i	0.0366404	−	0.0181214i
$385$	−6.04066	+	3.56196i	−0.307861	+	0.181534i
$386$	1.86485	−	2.35108i	0.0949184	−	0.119667i
$387$	−5.44468	+	1.22018i	−0.276769	+	0.0620253i
$388$	−3.89044	−	19.9169i	−0.197507	−	1.01113i
$389$	−20.8873	+	7.60237i	−1.05903	+	0.385455i	−0.812064	−	0.583569i	$-0.801656\pi$
$389$	−20.8873	+	7.60237i	−1.05903	+	0.385455i	−0.246966	+	0.969024i	$0.579434\pi$
$390$	0.0702858	+	0.0226946i	0.00355906	+	0.00114918i
$391$	21.8488	+	13.4304i	1.10494	+	0.679204i
$392$	0.933366	−	0.812869i	0.0471421	−	0.0410561i
$393$	−0.720844	−	0.0664032i	−0.0363618	−	0.00334960i
$394$	0.0132020	+	0.0451013i	0.000665108	+	0.00227217i
$395$	−3.40800	−	5.66008i	−0.171475	−	0.284790i
$396$	−23.2754	−	21.0348i	−1.16963	−	1.05704i
$397$	8.51995	−	18.4924i	0.427604	−	0.928106i	−0.566937	−	0.823761i	$-0.691872\pi$
$397$	8.51995	−	18.4924i	0.427604	−	0.928106i	0.994541	−	0.104345i	$-0.0332745\pi$
$398$	0.449268	+	0.488035i	0.0225198	+	0.0244630i
$399$	1.46668	+	1.16591i	0.0734256	+	0.0583684i
$400$	12.2190	−	13.2733i	0.610948	−	0.663666i
$401$	−2.42605	−	5.81916i	−0.121151	−	0.290595i	0.850915	−	0.525304i	$-0.176048\pi$
$401$	−2.42605	−	5.81916i	−0.121151	−	0.290595i	−0.972066	+	0.234709i	$0.924586\pi$
$402$	0.0387910	+	0.109703i	0.00193472	+	0.00547147i
$403$	−15.7117	+	22.2207i	−0.782656	+	1.10689i
$404$	3.69267	+	5.22246i	0.183717	+	0.259827i
$405$	−1.77165	+	5.01030i	−0.0880340	+	0.248964i
$406$	2.21329	−	0.122110i	0.109844	−	0.00606024i
$407$	4.10148	−	1.93553i	0.203303	−	0.0959409i
$408$	−0.661417	−	0.342383i	−0.0327450	−	0.0169505i
$409$	23.7268	−	13.4096i	1.17322	−	0.663063i	0.223050	−	0.974807i	$-0.428399\pi$
$409$	23.7268	−	13.4096i	1.17322	−	0.663063i	0.950166	+	0.311744i	$0.100913\pi$
$410$	−0.162268	+	0.157856i	−0.00801383	+	0.00779598i
$411$	−0.709261	+	0.861208i	−0.0349853	+	0.0424803i
$412$	−12.7799	−	5.74633i	−0.629619	−	0.283101i
$413$	−17.8301	+	3.65316i	−0.877360	+	0.179760i
$414$	−0.0603388	−	1.31280i	−0.00296549	−	0.0645204i
$415$	−0.0624195	−	0.353999i	−0.00306405	−	0.0173771i
$416$	6.99377	−	1.03538i	0.342898	−	0.0507635i
$417$	−4.24545	+	1.45746i	−0.207901	+	0.0713724i
$418$	−2.72323	−	1.13875i	−0.133198	−	0.0556983i
$419$	−32.1838	−	11.0487i	−1.57228	−	0.539766i	−0.605607	−	0.795764i	$-0.707069\pi$
$419$	−32.1838	−	11.0487i	−1.57228	−	0.539766i	−0.966677	+	0.255998i	$0.917596\pi$
$420$	−0.515934	−	0.0958678i	−0.0251750	−	0.00467787i
$421$	−2.33952	−	1.49801i	−0.114021	−	0.0730083i	0.480987	−	0.876728i	$-0.340278\pi$
$421$	−2.33952	−	1.49801i	−0.114021	−	0.0730083i	−0.595009	+	0.803719i	$0.702851\pi$
$422$	−0.373870	+	3.11589i	−0.0181997	+	0.151679i
$423$	−11.1983	+	9.39649i	−0.544480	+	0.456873i
$424$	0.0396855	−	4.32012i	0.00192730	−	0.209803i
$425$	−33.6189	−	3.72094i	−1.63075	−	0.180492i
$426$	0.207658	+	0.252145i	0.0100611	+	0.0122165i
$427$	1.04417	+	3.82650i	0.0505309	+	0.185177i
$428$	−4.18606	+	17.9065i	−0.202341	+	0.865545i
$429$	2.53029	+	4.38259i	0.122163	+	0.211593i
$430$	0.0735189	−	0.127339i	0.00354540	−	0.00614081i
$431$	17.2016	+	16.1296i	0.828571	+	0.776935i	0.977281	−	0.211946i	$-0.0679800\pi$
$431$	17.2016	+	16.1296i	0.828571	+	0.776935i	−0.148710	+	0.988881i	$0.547512\pi$
$432$	−0.558602	−	4.65547i	−0.0268757	−	0.223987i
$433$	−10.6678	+	22.0778i	−0.512663	+	1.06099i	0.471193	+	0.882030i	$0.343824\pi$
$433$	−10.6678	+	22.0778i	−0.512663	+	1.06099i	−0.983856	+	0.178962i	$0.942726\pi$
$434$	−0.732335	+	1.38345i	−0.0351532	+	0.0664076i
$435$	0.675014	+	0.760850i	0.0323645	+	0.0364800i
$436$	1.14707	−	13.8430i	0.0549345	−	0.662961i
$437$	5.73251	+	14.1572i	0.274223	+	0.677229i
$438$	−0.00973164	−	0.117443i	−0.000464996	−	0.00561167i
$439$	8.40345	−	8.79856i	0.401075	−	0.419932i	−0.491468	−	0.870896i	$-0.663539\pi$
$439$	8.40345	−	8.79856i	0.401075	−	0.419932i	0.892542	+	0.450963i	$0.148920\pi$
$440$	1.65314	−	0.152285i	0.0788102	−	0.00725989i
$441$	−2.66816	−	6.74625i	−0.127055	−	0.321250i
$442$	−3.06792	−	3.09624i	−0.145926	−	0.147273i
$443$	10.2793	+	30.8628i	0.488383	+	1.46633i	0.846364	+	0.532605i	$0.178787\pi$
$443$	10.2793	+	30.8628i	0.488383	+	1.46633i	−0.357981	+	0.933729i	$0.616535\pi$
$444$	0.326573	+	0.0923460i	0.0154985	+	0.00438255i
$445$	0.381047	−	0.518434i	0.0180634	−	0.0245761i
$446$	0.528690	−	0.842633i	0.0250342	−	0.0398998i
$447$	−1.80758	−	2.65872i	−0.0854957	−	0.125753i
$448$	−15.6323	+	4.42040i	−0.738558	+	0.208844i
$449$	−5.52887	+	14.7670i	−0.260923	+	0.696896i	0.738812	+	0.673911i	$0.235387\pi$
$449$	−5.52887	+	14.7670i	−0.260923	+	0.696896i	−0.999736	+	0.0229844i	$0.992683\pi$
$450$	0.810886	+	1.53184i	0.0382255	+	0.0722115i
$451$	−15.5006	+	0.569807i	−0.729895	+	0.0268312i
$452$	29.7697	−	21.4623i	1.40025	−	1.00950i
$453$	−3.30390	+	1.48556i	−0.155231	+	0.0697978i
$454$	0.150954	−	0.553193i	0.00708463	−	0.0259626i
$455$	−5.42384	−	2.93524i	−0.254274	−	0.137606i
$456$	−0.196210	−	0.397795i	−0.00918836	−	0.0186285i
$457$	12.8337	−	6.94523i	0.600333	−	0.324884i	−0.147202	−	0.989106i	$-0.547027\pi$
$457$	12.8337	−	6.94523i	0.600333	−	0.324884i	0.747535	+	0.664222i	$0.231237\pi$
$458$	0.819321	+	3.50478i	0.0382844	+	0.163768i
$459$	−6.41266	+	6.01303i	−0.299318	+	0.280664i
$460$	−3.27703	−	2.74976i	−0.152792	−	0.128208i
$461$	−0.474378	+	0.554909i	−0.0220940	+	0.0258447i	−0.771045	−	0.636781i	$-0.780266\pi$
$461$	−0.474378	+	0.554909i	−0.0220940	+	0.0258447i	0.748951	+	0.662626i	$0.230558\pi$
$462$	0.176665	+	0.231333i	0.00821921	+	0.0107626i
$463$	10.4012	+	4.90844i	0.483385	+	0.228115i	0.652945	−	0.757405i	$-0.273533\pi$
$463$	10.4012	+	4.90844i	0.483385	+	0.228115i	−0.169561	+	0.985520i	$0.554235\pi$
$464$	29.6629	+	12.0480i	1.37707	+	0.559316i
$465$	−0.706169	+	0.131216i	−0.0327478	+	0.00608501i
$466$	2.59484	+	0.384147i	0.120204	+	0.0177953i
$467$	1.09099	+	39.5790i	0.0504849	+	1.83150i	0.426048	+	0.904700i	$0.359905\pi$
$467$	1.09099	+	39.5790i	0.0504849	+	1.83150i	−0.375563	+	0.926797i	$0.622551\pi$
$468$	5.28923	−	27.0779i	0.244495	−	1.25168i
$469$	−1.51108	−	9.59764i	−0.0697752	−	0.443178i
$470$	0.0176870	−	0.384818i	0.000815842	−	0.0177503i
$471$	1.41843	−	0.183427i	0.0653578	−	0.00845187i
$472$	4.18638	+	1.01931i	0.192694	+	0.0469174i
$473$	9.58718	−	3.09560i	0.440819	−	0.142336i
$474$	−0.216410	+	0.168439i	−0.00994004	+	0.00773664i
$475$	−14.8058	−	13.6589i	−0.679335	−	0.626715i
$476$	24.4388	+	19.0215i	1.12015	+	0.871848i
$477$	−23.7958	−	8.66098i	−1.08954	−	0.396559i
$478$	0.0536977	−	0.341061i	0.00245607	−	0.0155998i
$479$	28.1920	+	5.77619i	1.28813	+	0.263921i	0.795305	−	0.606210i	$-0.207311\pi$
$479$	28.1920	+	5.77619i	1.28813	+	0.263921i	0.492821	+	0.870131i	$0.335966\pi$
$480$	0.151361	+	0.109123i	0.00690865	+	0.00498075i
$481$	3.31881	+	2.21205i	0.151325	+	0.100861i
$482$	1.08724	+	0.753875i	0.0495224	+	0.0343381i
$483$	0.206878	−	1.49190i	0.00941328	−	0.0678837i
$484$	27.8669	+	20.8791i	1.26668	+	0.949049i
$485$	4.89531	−	3.95670i	0.222285	−	0.179665i
$486$	0.660836	+	0.148097i	0.0299761	+	0.00671781i
$487$	0.867179	−	31.4596i	0.0392956	−	1.42557i	−0.681192	−	0.732104i	$-0.738538\pi$
$487$	0.867179	−	31.4596i	0.0392956	−	1.42557i	0.720488	−	0.693467i	$-0.243918\pi$
$488$	0.163053	−	0.924722i	0.00738108	−	0.0418602i
$489$	1.43645	+	0.185757i	0.0649585	+	0.00840024i
$490$	0.178417	+	0.0686758i	0.00806004	+	0.00310246i
$491$	−5.32443	−	6.71269i	−0.240288	−	0.302940i	0.648540	−	0.761181i	$-0.275380\pi$
$491$	−5.32443	−	6.71269i	−0.240288	−	0.302940i	−0.888828	+	0.458241i	$0.848480\pi$
$492$	−0.902715	−	0.729632i	−0.0406975	−	0.0328944i
$493$	−14.7353	−	58.1884i	−0.663645	−	2.62068i
$494$	−0.377407	−	2.56827i	−0.0169803	−	0.115552i
$495$	2.38875	−	9.43296i	0.107366	−	0.423980i
$496$	−18.0936	+	13.5565i	−0.812429	+	0.608706i
$497$	−13.2012	−	23.8672i	−0.592154	−	1.07059i
$498$	−0.0142803	+	0.00432292i	−0.000639914	+	0.000193715i
$499$	9.52611	−	15.8212i	0.426447	−	0.708253i	−0.566853	−	0.823819i	$-0.691839\pi$
$499$	9.52611	−	15.8212i	0.426447	−	0.708253i	0.993300	+	0.115567i	$0.0368683\pi$
$500$	11.3597	+	2.98797i	0.508021	+	0.133626i
$501$	1.58232	+	1.53931i	0.0706930	+	0.0687712i
$502$	−1.55789	+	0.172427i	−0.0695319	+	0.00769579i
$503$	−1.00790	−	9.94074i	−0.0449400	−	0.443236i	−0.992372	−	0.123279i	$-0.960659\pi$
$503$	−1.00790	−	9.94074i	−0.0449400	−	0.443236i	0.947432	−	0.319957i	$-0.103668\pi$
$504$	0.204767	−	3.18009i	0.00912104	−	0.141652i
$505$	−0.895789	+	1.77013i	−0.0398621	+	0.0787696i
$506$	0.325918	+	2.35035i	0.0144888	+	0.104486i
$507$	−0.885911	+	1.60169i	−0.0393447	+	0.0711337i
$508$	2.77657	−	12.9457i	0.123190	−	0.574374i
$509$	8.68745	+	10.1622i	0.385065	+	0.450434i	0.918508	−	0.395402i	$-0.129395\pi$
$509$	8.68745	+	10.1622i	0.385065	+	0.450434i	−0.533444	+	0.845836i	$0.679102\pi$
$510$	−0.00105673	−	0.115034i	−4.67927e−5	−	0.00509381i
$511$	−0.992598	+	9.78984i	−0.0439100	+	0.433077i
$512$	9.68176	+	1.61560i	0.427877	+	0.0714001i
$513$	−5.19874	+	0.618148i	−0.229530	+	0.0272919i
$514$	−0.785823	+	0.131131i	−0.0346612	+	0.00578392i
$515$	−0.279277	−	4.33724i	−0.0123064	−	0.191122i
$516$	0.693148	+	0.296481i	0.0305141	+	0.0130518i
$517$	18.5777	−	18.7492i	0.817047	−	0.824587i
$518$	0.205634	+	0.101701i	0.00903504	+	0.00446849i
$519$	0.732121	−	0.0538989i	0.0321366	−	0.00236590i
$520$	0.864651	+	1.17640i	0.0379174	+	0.0515885i
$521$	−3.03775	−	8.11346i	−0.133086	−	0.355457i	0.852949	−	0.521994i	$-0.174812\pi$
$521$	−3.03775	−	8.11346i	−0.133086	−	0.355457i	−0.986035	+	0.166537i	$0.946742\pi$
$522$	−2.04127	+	2.30084i	−0.0893441	+	0.100705i
$523$	−31.1434	−	32.6077i	−1.36181	−	1.42584i	−0.802165	−	0.597102i	$-0.796319\pi$
$523$	−31.1434	−	32.6077i	−1.36181	−	1.42584i	−0.559642	−	0.828734i	$-0.689061\pi$
$524$	−5.37364	−	4.67990i	−0.234748	−	0.204443i
$525$	0.592979	+	1.89586i	0.0258797	+	0.0827421i
$526$	−0.836290	+	0.755786i	−0.0364640	+	0.0329538i
$527$	40.5696	+	12.2812i	1.76724	+	0.534979i
$528$	0.881651	+	4.11069i	0.0383689	+	0.178895i
$529$	−6.50744	+	8.52110i	−0.282932	+	0.370483i
$530$	0.592622	−	0.306772i	0.0257419	−	0.0133253i
$531$	13.8131	−	21.1426i	0.599439	−	0.917509i
$532$	4.99954	+	17.7529i	0.216758	+	0.769686i
$533$	−7.46089	−	11.4197i	−0.323167	−	0.494644i
$534$	−0.0232498	−	0.0131400i	−0.00100612	−	0.000568625i
$535$	−5.51621	+	1.45094i	−0.238487	+	0.0627297i
$536$	−0.646165	+	2.20745i	−0.0279101	+	0.0953475i
$537$	−1.14089	+	2.88465i	−0.0492330	+	0.124482i
$538$	1.23496	−	0.528231i	0.0532430	−	0.0227737i
$539$	5.91458	+	11.6875i	0.254759	+	0.503417i
$540$	1.20499	−	0.835521i	0.0518545	−	0.0359551i
$541$	−1.24246	+	0.0228290i	−0.0534177	+	0.000981494i	−0.0450731	−	0.998984i	$-0.514352\pi$
$541$	−1.24246	+	0.0228290i	−0.0534177	+	0.000981494i	−0.00834453	+	0.999965i	$0.502656\pi$
$542$	1.07507	−	0.0197532i	0.0461780	−	0.000848473i
$543$	1.83413	−	1.27176i	0.0787102	−	0.0545764i
$544$	−4.97224	−	9.82541i	−0.213183	−	0.421261i
$545$	3.96128	−	1.69436i	0.169682	−	0.0725784i
$546$	−0.0941459	+	0.238041i	−0.00402907	+	0.0101872i
$547$	8.00529	−	27.3480i	0.342282	−	1.16932i	−0.589946	−	0.807443i	$-0.700851\pi$
$547$	8.00529	−	27.3480i	0.342282	−	1.16932i	0.932227	−	0.361873i	$-0.117863\pi$
$548$	−10.6211	+	2.79370i	−0.453712	+	0.119341i
$549$	−4.79149	−	2.70799i	−0.204496	−	0.115574i
$550$	−1.71165	−	2.61987i	−0.0729848	−	0.111712i
$551$	13.4877	−	33.1058i	0.574595	−	1.41035i
$552$	−0.195022	+	0.298503i	−0.00830067	+	0.0127051i
$553$	20.3353	−	10.5266i	0.864746	−	0.447637i
$554$	−1.25428	+	1.64241i	−0.0532894	+	0.0697793i
$555$	0.0220750	+	0.102925i	0.000937034	+	0.00436891i
$556$	−42.2898	−	12.8020i	−1.79349	−	0.542925i
$557$	8.39282	−	7.58490i	0.355615	−	0.321382i	−0.473147	−	0.880984i	$-0.656882\pi$
$557$	8.39282	−	7.58490i	0.355615	−	0.321382i	0.828762	+	0.559601i	$0.189046\pi$
$558$	−0.648386	−	2.07301i	−0.0274484	−	0.0877573i
$559$	6.68131	+	5.81876i	0.282590	+	0.246107i
$560$	−3.53870	−	3.70509i	−0.149538	−	0.156568i
$561$	5.23098	−	5.89616i	0.220852	−	0.248936i
$562$	1.03477	+	2.76374i	0.0436491	+	0.116581i
$563$	−6.96289	−	9.47335i	−0.293451	−	0.399254i	0.633919	−	0.773399i	$-0.281445\pi$
$563$	−6.96289	−	9.47335i	−0.293451	−	0.399254i	−0.927370	+	0.374145i	$0.877936\pi$
$564$	1.96979	−	0.145016i	0.0829433	−	0.00610630i
$565$	10.2035	+	5.04638i	0.429264	+	0.212303i
$566$	−1.30988	+	1.32197i	−0.0550584	+	0.0555665i
$567$	−16.9344	−	7.24336i	−0.711178	−	0.304193i
$568$	0.414903	+	6.44355i	0.0174089	+	0.270366i
$569$	0.616000	−	0.102792i	0.0258240	−	0.00430927i	−0.151668	−	0.988431i	$-0.548465\pi$
$569$	0.616000	−	0.102792i	0.0258240	−	0.00430927i	0.177493	+	0.984122i	$0.443201\pi$
$570$	0.0401255	−	0.0555316i	0.00168067	−	0.00232596i
$571$	20.7821	+	3.46792i	0.869704	+	0.145128i	0.582588	−	0.812768i	$-0.302040\pi$
$571$	20.7821	+	3.46792i	0.869704	+	0.145128i	0.287116	+	0.957896i	$0.407303\pi$
$572$	−5.02500	+	49.5608i	−0.210106	+	2.07224i
$573$	−0.00182265	−	0.198412i	−7.61422e−5	−	0.00828876i
$574$	−0.509835	−	0.596385i	−0.0212801	−	0.0248926i
$575$	−3.39587	+	15.8332i	−0.141618	+	0.660291i
$576$	10.9104	−	19.7256i	0.454601	−	0.821902i
$577$	−4.68240	−	33.7670i	−0.194931	−	1.40574i	−0.795397	−	0.606089i	$-0.792738\pi$
$577$	−4.68240	−	33.7670i	−0.194931	−	1.40574i	0.600466	−	0.799650i	$-0.294982\pi$
$578$	−2.09266	+	4.13521i	−0.0870432	+	0.172002i
$579$	−0.306657	+	4.76247i	−0.0127442	+	0.197921i
$580$	1.00997	+	9.96119i	0.0419368	+	0.413616i
$581$	1.23826	−	0.137051i	0.0513719	−	0.00568584i
$582$	−0.187270	−	0.182179i	−0.00776258	−	0.00755156i
$583$	44.2183	+	11.6308i	1.83133	+	0.481700i
$584$	1.20160	−	1.99565i	0.0497227	−	0.0825805i
$585$	8.19046	−	2.47941i	0.338634	−	0.102511i
$586$	−1.15708	−	2.09196i	−0.0477985	−	0.0864180i
$587$	4.56734	−	3.42205i	0.188514	−	0.141243i	−0.501181	−	0.865342i	$-0.667101\pi$
$587$	4.56734	−	3.42205i	0.188514	−	0.141243i	0.689696	+	0.724099i	$0.257744\pi$
$588$	−0.240626	+	0.950212i	−0.00992326	+	0.0391861i
$589$	15.1150	+	20.2187i	0.622801	+	0.833096i
$590$	0.163376	+	0.645156i	0.00672607	+	0.0265607i
$591$	−0.0581230	−	0.0469788i	−0.00239086	−	0.00193245i
$592$	2.05911	+	2.59600i	0.0846291	+	0.106695i
$593$	−24.4850	−	9.42472i	−1.00548	−	0.387027i	−0.200092	−	0.979777i	$-0.564124\pi$
$593$	−24.4850	−	9.42472i	−1.00548	−	0.387027i	−0.805386	+	0.592750i	$0.798042\pi$
$594$	−0.806621	−	0.104310i	−0.0330961	−	0.00427988i
$595$	−1.66801	+	9.45973i	−0.0683816	+	0.387811i
$596$	0.872025	−	31.6354i	0.0357195	−	1.29584i
$597$	−1.02938	−	0.230690i	−0.0421299	−	0.00944153i
$598$	−1.62292	+	1.31175i	−0.0663661	+	0.0536414i
$599$	−0.511605	−	0.383316i	−0.0209036	−	0.0156619i	0.589109	−	0.808054i	$-0.299479\pi$
$599$	−0.511605	−	0.383316i	−0.0209036	−	0.0156619i	−0.610013	+	0.792392i	$0.708836\pi$
$600$	0.0645915	−	0.465800i	0.00263694	−	0.0190162i
$601$	20.6960	+	14.3503i	0.844208	+	0.585361i	0.911000	−	0.412406i	$-0.135312\pi$
$601$	20.6960	+	14.3503i	0.844208	+	0.585361i	−0.0667923	+	0.997767i	$0.521276\pi$
$602$	0.424048	+	0.282636i	0.0172829	+	0.0115194i
$603$	10.9360	+	7.88422i	0.445347	+	0.321070i
$604$	−34.9334	−	7.15742i	−1.42142	−	0.291231i
$605$	−1.67977	+	10.6691i	−0.0682922	+	0.433759i
$606$	0.0773797	+	0.0281639i	0.00314334	+	0.00114408i
$607$	15.0728	+	11.7316i	0.611785	+	0.476172i	0.872084	−	0.489356i	$-0.162768\pi$
$607$	15.0728	+	11.7316i	0.611785	+	0.476172i	−0.260298	+	0.965528i	$0.583821\pi$
$608$	1.08635	−	6.46751i	0.0440573	−	0.262292i
$609$	−2.78185	+	2.16520i	−0.112726	+	0.0877385i
$610$	0.138020	−	0.0445652i	0.00558826	−	0.00180439i
$611$	22.5532	+	5.49129i	0.912404	+	0.222154i
$612$	−42.6175	+	5.51116i	−1.72271	+	0.222775i
$613$	1.22370	−	26.6241i	0.0494247	−	1.07534i	−0.817193	−	0.576365i	$-0.804471\pi$
$613$	1.22370	−	26.6241i	0.0494247	−	1.07534i	0.866617	−	0.498973i	$-0.166289\pi$
$614$	−0.351752	−	2.23416i	−0.0141956	−	0.0901632i
$615$	0.0690198	−	0.353343i	0.00278315	−	0.0142481i
$616$	0.158541	+	5.75156i	0.00638779	+	0.231737i
$617$	0.685385	+	0.101466i	0.0275926	+	0.00408488i	0.160229	−	0.987080i	$-0.448777\pi$
$617$	0.685385	+	0.101466i	0.0275926	+	0.00408488i	−0.132636	+	0.991165i	$0.542344\pi$
$618$	−0.177365	+	0.0329569i	−0.00713465	+	0.00132572i
$619$	−2.32200	−	0.943114i	−0.0933289	−	0.0379069i	0.329167	−	0.944272i	$-0.393232\pi$
$619$	−2.32200	−	0.943114i	−0.0933289	−	0.0379069i	−0.422496	+	0.906365i	$0.638846\pi$
$620$	−6.39409	−	3.01745i	−0.256793	−	0.121184i
$621$	2.55436	+	3.34479i	0.102503	+	0.134222i
$622$	−0.925263	+	1.08234i	−0.0370997	+	0.0433978i
$623$	1.70823	+	1.43337i	0.0684387	+	0.0574269i
$624$	−2.69707	+	2.52899i	−0.107969	+	0.101241i
$625$	−4.43055	−	18.9524i	−0.177222	−	0.758095i
$626$	−3.42876	+	1.85555i	−0.137041	+	0.0741628i
$627$	4.59085	−	0.979499i	0.183341	−	0.0391174i
$628$	12.3820	+	6.70081i	0.494096	+	0.267391i
$629$	1.63538	−	5.99309i	0.0652070	−	0.238960i
$630$	0.448922	−	0.201853i	0.0178855	−	0.00804201i
$631$	9.94715	−	7.17133i	0.395990	−	0.285486i	−0.369126	−	0.929380i	$-0.620343\pi$
$631$	9.94715	−	7.17133i	0.395990	−	0.285486i	0.765115	+	0.643893i	$0.222682\pi$
$632$	−5.41718	+	0.199137i	−0.215484	+	0.00792125i
$633$	−2.33493	−	4.41090i	−0.0928052	−	0.175317i
$634$	−0.271404	+	0.724888i	−0.0107788	+	0.0287890i
$635$	3.95176	−	1.11745i	0.156821	−	0.0443447i
$636$	1.92367	+	2.82947i	0.0762784	+	0.112196i
$637$	−6.12239	+	9.75793i	−0.242578	+	0.386623i
$638$	3.28904	−	4.47489i	0.130214	−	0.177163i
$639$	36.4184	+	10.2982i	1.44069	+	0.407389i
$640$	0.772833	+	2.32038i	0.0305489	+	0.0917209i
$641$	−22.5071	−	22.7148i	−0.888978	−	0.897182i	0.106291	−	0.994335i	$-0.466102\pi$
$641$	−22.5071	−	22.7148i	−0.888978	−	0.897182i	−0.995269	+	0.0971528i	$0.969026\pi$
$642$	0.0870732	+	0.220158i	0.00343651	+	0.00868895i
$643$	−37.7153	+	3.47428i	−1.48735	+	0.137012i	−0.804675	−	0.593715i	$-0.797661\pi$
$643$	−37.7153	+	3.47428i	−1.48735	+	0.137012i	−0.682670	+	0.730727i	$0.739181\pi$
$644$	10.2403	−	10.7218i	0.403524	−	0.422497i
$645$	0.0193100	+	0.233037i	0.000760332	+	0.00917584i
$646$	−3.60950	+	1.82177i	−0.142014	+	0.0716767i
$647$	2.46516	−	29.7501i	0.0969154	−	1.16960i	−0.758507	−	0.651665i	$-0.774071\pi$
$647$	2.46516	−	29.7501i	0.0969154	−	1.16960i	0.855423	−	0.517931i	$-0.173297\pi$
$648$	2.89371	+	3.26168i	0.113676	+	0.128131i
$649$	−21.3336	+	40.3011i	−0.837418	+	1.58196i
$650$	1.19736	−	2.47802i	0.0469644	−	0.0971961i
$651$	−0.296566	−	2.47163i	−0.0116233	−	0.0968707i
$652$	10.4006	+	9.75246i	0.407320	+	0.381936i
$653$	−21.1811	+	36.6867i	−0.828880	+	1.43566i	0.0700383	+	0.997544i	$0.477688\pi$
$653$	−21.1811	+	36.6867i	−0.828880	+	1.43566i	−0.898918	+	0.438117i	$0.855645\pi$
$654$	−0.0894159	−	0.154873i	−0.00349644	−	0.00605601i
$655$	0.503126	−	2.15220i	0.0196588	−	0.0840935i
$656$	−2.98331	−	10.9328i	−0.116479	−	0.426853i
$657$	−8.68017	−	10.5397i	−0.338646	−	0.411195i
$658$	1.32702	+	0.146874i	0.0517326	+	0.00572576i
$659$	0.253149	−	27.5575i	0.00986128	−	1.07349i	−0.838764	−	0.544495i	$-0.816721\pi$
$659$	0.253149	−	27.5575i	0.00986128	−	1.07349i	0.848626	−	0.528994i	$-0.177431\pi$
$660$	−1.00715	+	0.845102i	−0.0392034	+	0.0328955i
$661$	1.27079	−	10.5909i	0.0494278	−	0.411939i	−0.946566	−	0.322512i	$-0.895473\pi$
$661$	1.27079	−	10.5909i	0.0494278	−	0.411939i	0.995993	−	0.0894275i	$-0.0285037\pi$
$662$	2.71632	+	1.73927i	0.105573	+	0.0675986i
$663$	6.81514	+	1.26635i	0.264678	+	0.0491810i
$664$	−0.278950	−	0.0957637i	−0.0108254	−	0.00371635i
$665$	−4.14115	+	3.94672i	−0.160587	+	0.153047i
$666$	−0.301079	+	0.103361i	−0.0116666	+	0.00400515i
$667$	−28.4272	+	4.20844i	−1.10071	+	0.162951i
$668$	3.77344	+	21.4002i	0.145999	+	0.828000i
$669$	0.0726342	+	1.58031i	0.00280820	+	0.0610982i
$670$	−0.348042	+	0.0713095i	−0.0134460	+	0.00275493i
$671$	9.06338	+	4.07525i	0.349888	+	0.157323i
$672$	−0.411128	+	0.499205i	−0.0158596	+	0.0192573i
$673$	−29.8220	+	29.0113i	−1.14955	+	1.11830i	−0.158155	+	0.987414i	$0.550555\pi$
$673$	−29.8220	+	29.0113i	−1.14955	+	1.11830i	−0.991397	+	0.130888i	$0.958217\pi$
$674$	−0.135609	+	0.0766414i	−0.00522345	+	0.00295212i
$675$	−4.92928	−	2.55165i	−0.189728	−	0.0982132i
$676$	−16.2944	+	7.68951i	−0.626708	+	0.295750i
$677$	2.47115	−	0.136337i	0.0949741	−	0.00523987i	−0.00753835	−	0.999972i	$-0.502400\pi$
$677$	2.47115	−	0.136337i	0.0949741	−	0.00523987i	0.102512	+	0.994732i	$0.467312\pi$
$678$	0.157515	−	0.445458i	0.00604932	−	0.0171077i
$679$	12.5947	+	17.8124i	0.483340	+	0.683578i
$680$	1.31285	−	1.85674i	0.0503456	−	0.0712026i
$681$	0.304009	+	0.859749i	0.0116496	+	0.0329457i
$682$	1.50911	+	3.61978i	0.0577868	+	0.138608i
$683$	−10.0981	+	10.9695i	−0.386394	+	0.419736i	−0.898353	−	0.439274i	$-0.855236\pi$
$683$	−10.0981	+	10.9695i	−0.386394	+	0.419736i	0.511959	+	0.859010i	$0.328920\pi$
$684$	−22.3815	−	12.4107i	−0.855777	−	0.474534i
$685$	−2.30711	−	2.50619i	−0.0881501	−	0.0957566i
$686$	−1.06897	+	2.32018i	−0.0408135	+	0.0885849i
$687$	−4.24669	−	3.83789i	−0.162021	−	0.146425i
$688$	3.79676	+	6.30574i	0.144750	+	0.240404i
$689$	11.2962	+	38.5904i	0.430350	+	1.47018i
$690$	−0.0548428	−	0.00505204i	−0.00208783	−	0.000192328i
$691$	−4.23922	+	3.69194i	−0.161267	+	0.140448i	−0.733621	−	0.679559i	$-0.762171\pi$
$691$	−4.23922	+	3.69194i	−0.161267	+	0.140448i	0.572353	+	0.820007i	$0.306031\pi$
$692$	6.15623	+	3.78422i	0.234025	+	0.143854i
$693$	32.0935	+	10.3627i	1.21913	+	0.393645i
$694$	2.12025	−	0.771708i	0.0804836	−	0.0292937i
$695$	−2.62739	−	13.4507i	−0.0996624	−	0.510216i
$696$	0.814332	−	0.182496i	0.0308672	−	0.00691749i
$697$	−13.2033	+	16.6459i	−0.500112	+	0.630509i
$698$	−1.99185	+	1.17452i	−0.0753926	+	0.0444563i
$699$	−3.73926	+	1.84934i	−0.141432	+	0.0699484i
$700$	−6.17898	+	18.5519i	−0.233543	+	0.701197i
$701$	−5.44423	+	8.00778i	−0.205626	+	0.302450i	−0.915846	−	0.401530i	$-0.868478\pi$
$701$	−5.44423	+	8.00778i	−0.205626	+	0.302450i	0.710220	+	0.703980i	$0.248595\pi$
$702$	−0.287323	−	0.655031i	−0.0108443	−	0.0247225i
$703$	2.90102	−	2.29601i	0.109414	−	0.0865955i
$704$	−16.3494	+	37.2728i	−0.616190	+	1.40477i
$705$	0.325597	+	0.518940i	0.0122627	+	0.0195444i
$706$	3.46210	+	0.254880i	0.130298	+	0.00959253i
$707$	−5.92278	−	3.49245i	−0.222749	−	0.131347i
$708$	−3.18450	+	1.22577i	−0.119681	+	0.0460673i
$709$	−39.4854	+	9.61398i	−1.48291	+	0.361061i	−0.894340	−	0.447388i	$-0.852354\pi$
$709$	−39.4854	+	9.61398i	−1.48291	+	0.361061i	−0.588566	+	0.808449i	$0.700307\pi$
$710$	−0.849650	+	0.522278i	−0.0318868	+	0.0196007i
$711$	−9.48492	+	30.3250i	−0.355712	+	1.13728i
$712$	−0.220901	−	0.479462i	−0.00827863	−	0.0179686i
$713$	7.80887	−	18.7305i	0.292445	−	0.701463i
$714$	0.398101	+	0.0219638i	0.0148985	+	0.000821976i
$715$	−14.3154	+	5.81442i	−0.535366	+	0.217447i
$716$	−25.7160	+	16.4660i	−0.961052	+	0.615365i
$717$	0.238884	+	0.494387i	0.00892128	+	0.0184632i
$718$	−2.47785	−	0.0910866i	−0.0924726	−	0.00339932i
$719$	31.1930	−	20.7907i	1.16330	−	0.775363i	0.185039	−	0.982731i	$-0.440759\pi$
$719$	31.1930	−	20.7907i	1.16330	−	0.775363i	0.978263	+	0.207369i	$0.0664900\pi$
$720$	7.10813	+	0.130604i	0.264904	+	0.00486734i
$721$	15.0633			0.560986
$722$	−2.37422	−	0.401409i	−0.0883592	−	0.0149389i
$723$	−2.10404			−0.0782499
$724$	21.9666	+	0.403613i	0.816382	+	0.0150002i
$725$	31.5370	−	21.0200i	1.17125	−	0.780663i
$726$	0.447997	+	0.0164685i	0.0166267	+	0.000611204i
$727$	−13.6003	−	28.1467i	−0.504406	−	1.04390i	−0.985882	−	0.167444i	$-0.946449\pi$
$727$	−13.6003	−	28.1467i	−0.504406	−	1.04390i	0.481476	−	0.876459i	$-0.340101\pi$
$728$	−4.26133	+	2.72855i	−0.157936	+	0.101127i
$729$	23.0060	−	9.34422i	0.852073	−	0.346082i
$730$	0.359266	+	0.0198212i	0.0132970	+	0.000733617i
$731$	5.31021	−	12.7372i	0.196405	−	0.471102i
$732$	0.311173	+	0.675395i	0.0115013	+	0.0249633i
$733$	9.63373	−	30.8008i	0.355830	−	1.13765i	−0.588457	−	0.808529i	$-0.700264\pi$
$733$	9.63373	−	30.8008i	0.355830	−	1.13765i	0.944287	−	0.329123i	$-0.106753\pi$
$734$	−1.69380	+	1.04117i	−0.0625192	+	0.0384304i
$735$	−0.295402	+	0.0719250i	−0.0108961	+	0.00265299i
$736$	−4.92004	+	1.89381i	−0.181355	+	0.0698069i
$737$	−20.9682	−	12.3642i	−0.772373	−	0.455441i
$738$	1.08578	+	0.0799352i	0.0399681	+	0.00294246i
$739$	16.6686	+	26.5667i	0.613166	+	0.977271i	0.998514	+	0.0544994i	$0.0173563\pi$
$739$	16.6686	+	26.5667i	0.613166	+	0.977271i	−0.385348	+	0.922771i	$0.625919\pi$
$740$	−0.416238	+	0.948928i	−0.0153012	+	0.0348833i
$741$	2.82053	+	3.01444i	0.103615	+	0.110738i
$742$	0.929042	+	2.11800i	0.0341062	+	0.0777543i
$743$	7.94884	−	11.6917i	0.291615	−	0.428929i	−0.652877	−	0.757464i	$-0.726438\pi$
$743$	7.94884	−	11.6917i	0.291615	−	0.428929i	0.944492	+	0.328535i	$0.106555\pi$
$744$	−0.186223	+	0.559120i	−0.00682726	+	0.0204983i
$745$	8.79884	−	4.35167i	0.322364	−	0.159433i
$746$	3.57283	−	2.10677i	0.130810	−	0.0771342i
$747$	−1.07428	+	1.35438i	−0.0393058	+	0.0495542i
$748$	75.7114	−	16.9673i	2.76828	−	0.620387i
$749$	−3.78984	−	19.4019i	−0.138478	−	0.708929i
$750$	0.142104	−	0.0517217i	0.00518891	−	0.00188861i
$751$	1.39969	+	0.451947i	0.0510756	+	0.0164918i	0.332696	−	0.943034i	$-0.392042\pi$
$751$	1.39969	+	0.451947i	0.0510756	+	0.0164918i	−0.281621	+	0.959526i	$0.590872\pi$
$752$	16.4283	+	10.0985i	0.599080	+	0.368253i
$753$	1.87973	−	1.63706i	0.0685011	−	0.0596577i
$754$	4.86343	+	0.448012i	0.177116	+	0.0163156i
$755$	−3.10722	−	10.6150i	−0.113083	−	0.386320i
$756$	2.62143	+	4.35373i	0.0953405	+	0.158344i
$757$	25.9737	+	23.4734i	0.944030	+	0.853154i	0.989311	−	0.145820i	$-0.0465820\pi$
$757$	25.9737	+	23.4734i	0.944030	+	0.853154i	−0.0452808	+	0.998974i	$0.514418\pi$
$758$	−1.70002	+	3.68985i	−0.0617473	+	0.134021i
$759$	−2.55576	−	2.77630i	−0.0927683	−	0.100773i
$760$	1.28534	−	0.426573i	0.0466241	−	0.0154734i
$761$	4.13199	−	4.48854i	0.149785	−	0.162709i	−0.656320	−	0.754483i	$-0.727888\pi$
$761$	4.13199	−	4.48854i	0.149785	−	0.162709i	0.806104	+	0.591773i	$0.201572\pi$
$762$	−0.0655933	−	0.157333i	−0.00237620	−	0.00569959i
$763$	4.97803	+	14.0781i	0.180217	+	0.509661i
$764$	1.12764	−	1.59480i	0.0407966	−	0.0576977i
$765$	−7.69515	−	10.8831i	−0.278219	−	0.393479i
$766$	1.38710	−	3.92278i	0.0501180	−	0.141736i
$767$	−40.0407	+	2.20911i	−1.44579	+	0.0797663i
$768$	−2.68490	+	1.26703i	−0.0968829	+	0.0457201i
$769$	−12.3638	−	6.40015i	−0.445850	−	0.230795i	0.222066	−	0.975032i	$-0.428720\pi$
$769$	−12.3638	−	6.40015i	−0.445850	−	0.230795i	−0.667916	+	0.744236i	$0.732814\pi$
$770$	−0.773709	+	0.437275i	−0.0278825	+	0.0157583i
$771$	0.908152	−	0.883464i	0.0327063	−	0.0318172i
$772$	−29.8647	+	36.2627i	−1.07485	+	1.30512i
$773$	26.0944	+	11.7330i	0.938549	+	0.422008i	0.820916	−	0.571049i	$-0.193463\pi$
$773$	26.0944	+	11.7330i	0.938549	+	0.422008i	0.117633	+	0.993057i	$0.462469\pi$
$774$	−0.692740	+	0.141934i	−0.0249000	+	0.00510171i
$775$	1.22882	+	26.7356i	0.0441405	+	0.960370i
$776$	−0.896797	−	5.08599i	−0.0321931	−	0.182576i
$777$	−0.360899	+	0.0534284i	−0.0129472	+	0.00191673i
$778$	−2.66435	+	0.914672i	−0.0955215	+	0.0327926i
$779$	−12.2106	+	3.31796i	−0.437489	+	0.118878i
$780$	−1.09358	−	0.375427i	−0.0391565	−	0.0134425i
$781$	−67.1843	−	12.4838i	−2.40404	−	0.446705i
$782$	2.73720	+	1.75264i	0.0978822	+	0.0626743i
$783$	1.17349	−	9.78002i	0.0419370	−	0.349510i
$784$	−7.33114	+	6.15156i	−0.261827	+	0.219699i
$785$	−0.0401132	+	4.36668i	−0.00143170	+	0.155854i
$786$	−0.0911841	−	0.0100923i	−0.00325243	−	0.000359979i
$787$	−25.2929	−	30.7115i	−0.901595	−	1.09475i	−0.995075	−	0.0991250i	$-0.968396\pi$
$787$	−25.2929	−	30.7115i	−0.901595	−	1.09475i	0.0934801	−	0.995621i	$-0.470201\pi$
$788$	−0.193667	−	0.709719i	−0.00689909	−	0.0252827i
$789$	0.408062	−	1.74555i	0.0145274	−	0.0621432i
$790$	−0.418653	−	0.725128i	−0.0148950	−	0.0257989i
$791$	−19.7261	+	34.1666i	−0.701380	+	1.21483i
$792$	−5.82401	−	5.46106i	−0.206947	−	0.194050i
$793$	1.04115	+	8.67707i	0.0369722	+	0.308132i
$794$	1.12262	−	2.32335i	0.0398404	−	0.0824525i
$795$	−0.496500	+	0.937934i	−0.0176090	+	0.0332651i
$796$	−6.89156	−	7.76790i	−0.244265	−	0.275326i
$797$	−3.59100	+	43.3369i	−0.127200	+	1.53507i	0.572064	+	0.820209i	$0.306143\pi$
$797$	−3.59100	+	43.3369i	−0.127200	+	1.53507i	−0.699264	+	0.714864i	$0.746489\pi$
$798$	0.183129	+	0.151148i	0.00648270	+	0.00535057i
$799$	−2.98558	−	36.0306i	−0.105622	−	1.27467i
$800$	4.80229	−	5.02808i	0.169786	−	0.177769i
$801$	−3.08120	+	0.283836i	−0.108869	+	0.0100289i
$802$	−0.293858	−	0.742999i	−0.0103765	−	0.0262362i
$803$	17.3522	+	17.5123i	0.612345	+	0.617996i
$804$	−0.575606	−	1.72822i	−0.0203001	−	0.0609495i
$805$	4.42519	+	1.25132i	0.155967	+	0.0441034i
$806$	−2.04258	+	2.77902i	−0.0719467	+	0.0978870i
$807$	−1.13528	+	1.80943i	−0.0399638	+	0.0636948i
$808$	0.915172	+	1.34610i	0.0321957	+	0.0473558i
$809$	−16.7822	+	4.74556i	−0.590031	+	0.166845i	−0.554016	−	0.832506i	$-0.686905\pi$
$809$	−16.7822	+	4.74556i	−0.590031	+	0.166845i	−0.0360155	+	0.999351i	$0.511467\pi$
$810$	−0.236152	+	0.630734i	−0.00829753	+	0.0221617i
$811$	−2.11020	−	3.98636i	−0.0740991	−	0.139980i	0.843983	−	0.536369i	$-0.180205\pi$
$811$	−2.11020	−	3.98636i	−0.0740991	−	0.139980i	−0.918083	+	0.396389i	$0.870263\pi$
$812$	−34.6774	+	1.27475i	−1.21694	+	0.0447350i
$813$	−1.38709	+	1.00001i	−0.0486472	+	0.0350719i
$814$	0.524208	−	0.235704i	0.0183735	−	0.00826142i
$815$	−1.16420	+	4.26636i	−0.0407800	+	0.149444i
$816$	5.06465	+	2.74085i	0.177298	+	0.0959491i
$817$	7.04521	−	4.23174i	0.246481	−	0.148050i
$818$	3.03766	−	1.64390i	0.106209	−	0.0574777i
$819$	6.75141	+	28.8802i	0.235913	+	1.00916i
$820$	2.58520	−	2.42409i	0.0902792	−	0.0846531i
$821$	30.5762	+	25.6565i	1.06712	+	0.895417i	0.994788	−	0.101963i	$-0.0325125\pi$
$821$	30.5762	+	25.6565i	1.06712	+	0.895417i	0.0723288	+	0.997381i	$0.476957\pi$
$822$	−0.0918761	+	0.107473i	−0.00320455	+	0.00374855i
$823$	−4.10870	−	5.38010i	−0.143220	−	0.187538i	0.717588	−	0.696468i	$-0.245246\pi$
$823$	−4.10870	−	5.38010i	−0.143220	−	0.187538i	−0.860808	+	0.508929i	$0.830041\pi$
$824$	−3.22494	−	1.52189i	−0.112346	−	0.0530174i
$825$	4.61097	+	1.87282i	0.160534	+	0.0652031i
$826$	−2.26777	+	0.421383i	−0.0789056	+	0.0146618i
$827$	−7.14140	−	1.05723i	−0.248331	−	0.0367635i	0.0211229	−	0.999777i	$-0.493276\pi$
$827$	−7.14140	−	1.05723i	−0.248331	−	0.0367635i	−0.269454	+	0.963013i	$0.586843\pi$
$828$	0.566875	+	20.5652i	0.0197003	+	0.714689i
$829$	−3.85206	+	19.7204i	−0.133787	+	0.684917i	0.852872	+	0.522120i	$0.174859\pi$
$829$	−3.85206	+	19.7204i	−0.133787	+	0.684917i	−0.986660	+	0.162797i	$0.947948\pi$
$830$	−0.00708505	−	0.0450008i	−0.000245926	−	0.00156200i
$831$	0.150895	−	3.28303i	0.00523449	−	0.113887i
$832$	−35.4982	+	4.59051i	−1.23068	+	0.159147i
$833$	17.4331	+	4.24463i	0.604020	+	0.147068i
$834$	−0.541337	+	0.174792i	−0.0187450	+	0.00605256i
$835$	−5.31892	+	4.13988i	−0.184069	+	0.143266i
$836$	42.2964	+	18.6069i	1.46285	+	0.643532i
$837$	5.48915	+	4.27238i	0.189733	+	0.147675i
$838$	−4.05231	−	1.47492i	−0.139985	−	0.0509503i
$839$	−0.00103592	+	0.00657963i	−3.57638e−5	+	0.000227154i	−0.987849	−	0.155414i	$-0.950329\pi$
$839$	−0.00103592	+	0.00657963i	−3.57638e−5	+	0.000227154i	0.987814	+	0.155641i	$0.0497442\pi$
$840$	−0.130830	−	0.0268054i	−0.00451405	−	0.000924874i
$841$	31.0342	+	22.3739i	1.07015	+	0.771514i
$842$	−0.292955	−	0.195260i	−0.0100959	−	0.00672911i
$843$	−3.85675	−	2.67421i	−0.132834	−	0.0921047i
$844$	6.74789	−	48.6623i	0.232272	−	1.67502i
$845$	−4.47248	−	3.35097i	−0.153858	−	0.115277i
$846$	−1.44082	+	1.16456i	−0.0495364	+	0.0400385i
$847$	−36.5266	−	8.18580i	−1.25507	−	0.281267i
$848$	−0.920455	+	33.3924i	−0.0316085	+	1.14670i
$849$	0.513929	−	2.91464i	0.0176380	−	0.100030i
$850$	−4.25121	−	0.549753i	−0.145815	−	0.0188564i
$851$	−2.77558	−	1.06837i	−0.0951455	−	0.0366233i
$852$	−3.17774	−	4.00628i	−0.108868	−	0.137253i
$853$	−40.4245	−	32.6736i	−1.38411	−	1.11872i	−0.978863	−	0.204516i	$-0.934438\pi$
$853$	−40.4245	−	32.6736i	−1.38411	−	1.11872i	−0.405244	−	0.914209i	$-0.632813\pi$
$854$	0.123399	+	0.487290i	0.00422261	+	0.0166747i
$855$	0.154316	−	7.93644i	0.00527750	−	0.271420i
$856$	−1.14885	+	4.53670i	−0.0392668	+	0.155061i
$857$	29.0881	−	21.7940i	0.993629	−	0.744469i	0.0267341	−	0.999643i	$-0.491489\pi$
$857$	29.0881	−	21.7940i	0.993629	−	0.744469i	0.966895	+	0.255173i	$0.0821325\pi$
$858$	0.310411	+	0.561212i	0.0105973	+	0.0191595i
$859$	21.5442	−	6.52185i	0.735078	−	0.222523i	0.100018	−	0.994986i	$-0.468110\pi$
$859$	21.5442	−	6.52185i	0.735078	−	0.222523i	0.635060	+	0.772463i	$0.280975\pi$
$860$	−1.18734	+	1.97195i	−0.0404878	+	0.0672430i
$861$	1.20672	+	0.317407i	0.0411250	+	0.0108172i
$862$	2.14207	+	2.08384i	0.0729593	+	0.0709759i
$863$	−41.8861	+	4.63596i	−1.42582	+	0.157810i	−0.789564	−	0.613668i	$-0.789693\pi$
$863$	−41.8861	+	4.63596i	−1.42582	+	0.157810i	−0.636256	+	0.771478i	$0.719518\pi$
$864$	−0.182284	−	1.79784i	−0.00620144	−	0.0611638i
$865$	−0.144026	+	2.23676i	−0.00489703	+	0.0760521i
$866$	−1.40313	+	2.77266i	−0.0476803	+	0.0942188i
$867$	−1.01235	−	7.30055i	−0.0343813	−	0.247940i
$868$	11.8603	−	21.4430i	0.402566	−	0.727824i
$869$	12.0309	−	56.0938i	0.408119	−	1.90285i
$870$	0.0837602	+	0.0979794i	0.00283974	+	0.00332181i
$871$	−0.196643	−	21.4064i	−0.00666300	−	0.725327i
$872$	0.356587	−	3.51696i	0.0120756	−	0.119099i
$873$	−29.8580	−	4.98243i	−1.01054	−	0.168630i
$874$	0.693410	+	1.80721i	0.0234549	+	0.0611298i
$875$	−12.4549	+	2.07835i	−0.421051	+	0.0702610i
$876$	0.118544	+	1.84102i	0.00400522	+	0.0622022i
$877$	41.5569	+	17.7752i	1.40328	+	0.600225i	0.955786	−	0.294063i	$-0.0950076\pi$
$877$	41.5569	+	17.7752i	1.40328	+	0.600225i	0.447491	+	0.894288i	$0.352318\pi$
$878$	1.08529	−	1.09531i	0.0366268	−	0.0369648i
$879$	3.40784	+	1.68543i	0.114944	+	0.0568481i
$880$	−12.8017	+	0.942464i	−0.431546	+	0.0317705i
$881$	25.8262	+	35.1378i	0.870106	+	1.18382i	0.981770	+	0.190075i	$0.0608732\pi$
$881$	25.8262	+	35.1378i	0.870106	+	1.18382i	−0.111664	+	0.993746i	$0.535618\pi$
$882$	−0.322378	−	0.861034i	−0.0108550	−	0.0289925i
$883$	11.9395	−	13.4578i	0.401797	−	0.452889i	−0.512046	−	0.858958i	$-0.671112\pi$
$883$	11.9395	−	13.4578i	0.401797	−	0.452889i	0.913843	+	0.406069i	$0.133101\pi$
$884$	47.1285	+	49.3444i	1.58510	+	1.65963i
$885$	−0.798136	−	0.695098i	−0.0268291	−	0.0233655i
$886$	1.23064	+	3.93457i	0.0413441	+	0.132185i
$887$	−11.3737	+	10.2788i	−0.381891	+	0.345129i	−0.838854	−	0.544357i	$-0.816774\pi$
$887$	−11.3737	+	10.2788i	−0.381891	+	0.345129i	0.456962	+	0.889486i	$0.348937\pi$
$888$	0.0826638	+	0.0250240i	0.00277402	+	0.000839750i
$889$	2.98482	+	13.9167i	0.100107	+	0.466751i
$890$	0.0494898	−	0.0648040i	0.00165890	−	0.00217223i
$891$	−40.9805	+	21.2136i	−1.37290	+	0.710683i
$892$	−8.51736	+	13.0368i	−0.285182	+	0.436504i
$893$	11.2951	−	18.3310i	0.377975	−	0.613424i
$894$	−0.222850	−	0.341097i	−0.00745322	−	0.0114080i
$895$	−8.24561	−	4.66014i	−0.275620	−	0.155771i
$896$	−8.19752	+	2.15621i	−0.273860	+	0.0720340i
$897$	0.932297	−	3.18495i	0.0311285	−	0.106342i
$898$	−0.734947	+	1.85826i	−0.0245255	+	0.0620109i
$899$	−43.6687	+	18.6785i	−1.45643	+	0.622961i
$900$	−12.2514	−	24.2094i	−0.408380	−	0.806981i
$901$	51.4670	−	35.6864i	1.71461	−	1.18889i
$902$	−1.96542	+	0.0361125i	−0.0654413	+	0.00120242i
$903$	−0.810299	+	0.0148884i	−0.0269651	+	0.000495455i
$904$	7.67517	−	5.32184i	0.255272	−	0.177002i
$905$	3.07700	+	6.08032i	0.102283	+	0.202117i
$906$	−0.422098	+	0.180545i	−0.0140233	+	0.00599819i
$907$	−0.457914	+	1.15780i	−0.0152048	+	0.0384441i	−0.937315	−	0.348482i	$-0.886697\pi$
$907$	−0.457914	+	1.15780i	−0.0152048	+	0.0384441i	0.922111	+	0.386926i	$0.126463\pi$
$908$	−2.52182	+	8.61513i	−0.0836895	+	0.285903i
$909$	9.22698	−	2.42700i	0.306040	−	0.0804984i
$910$	−0.680425	−	0.384554i	−0.0225559	−	0.0127478i
$911$	15.1843	+	23.2414i	0.503080	+	0.770021i	0.994920	−	0.100664i	$-0.0320968\pi$
$911$	15.1843	+	23.2414i	0.503080	+	0.770021i	−0.491841	+	0.870685i	$0.663676\pi$
$912$	1.46035	+	3.10315i	0.0483572	+	0.102756i
$913$	1.70718	−	2.61304i	0.0564995	−	0.0864790i
$914$	1.64233	−	0.850156i	0.0543235	−	0.0281207i
$915$	−0.139992	+	0.183312i	−0.00462800	+	0.00606009i
$916$	−11.8160	−	55.0922i	−0.390413	−	1.82030i
$917$	7.33170	+	2.21945i	0.242114	+	0.0732928i
$918$	−0.826553	+	0.746986i	−0.0272803	+	0.0246542i
$919$	2.16668	+	6.92727i	0.0714723	+	0.228510i	0.983278	−	0.182113i	$-0.0582937\pi$
$919$	2.16668	+	6.92727i	0.0714723	+	0.228510i	−0.911805	+	0.410623i	$0.865311\pi$
$920$	−0.820976	−	0.714989i	−0.0270668	−	0.0235725i
$921$	2.48423	+	2.60103i	0.0818582	+	0.0857069i
$922$	−0.0614007	+	0.0692084i	−0.00202212	+	0.00227926i
$923$	−21.0717	−	56.2801i	−0.693584	−	1.85248i
$924$	−2.69863	−	3.67162i	−0.0887783	−	0.120787i
$925$	3.91183	−	0.287989i	0.128620	−	0.00946903i
$926$	1.30652	+	0.646168i	0.0429347	+	0.0212344i
$927$	−14.7117	+	14.8475i	−0.483197	+	0.487656i
$928$	11.3447	+	4.85247i	0.372407	+	0.159290i
$929$	−2.10052	−	32.6216i	−0.0689158	−	1.07028i	−0.876774	−	0.480903i	$-0.840309\pi$
$929$	−2.10052	−	32.6216i	−0.0689158	−	1.07028i	0.807858	−	0.589377i	$-0.200627\pi$
$930$	−0.0897847	+	0.0149824i	−0.00294416	+	0.000491293i
$931$	6.85978	+	8.19295i	0.224820	+	0.268513i
$932$	−40.5038	−	6.75889i	−1.32675	−	0.221395i
$933$	0.228427	−	2.25294i	0.00747836	−	0.0737579i
$934$	0.0460929	+	5.01762i	0.00150821	+	0.164182i
$935$	15.6380	+	18.2928i	0.511418	+	0.598237i
$936$	1.47242	−	6.86516i	0.0481277	−	0.224395i
$937$	12.5734	−	22.7322i	0.410754	−	0.742628i	−0.587002	−	0.809586i	$-0.699692\pi$
$937$	12.5734	−	22.7322i	0.410754	−	0.742628i	0.997756	+	0.0669576i	$0.0213292\pi$
$938$	−0.169125	−	1.21964i	−0.00552213	−	0.0398227i
$939$	2.79954	−	5.53204i	0.0913595	−	0.180531i
$940$	−0.387506	+	6.01807i	−0.0126390	+	0.196288i
$941$	5.12636	+	50.5605i	0.167115	+	1.64822i	0.640929	+	0.767600i	$0.278549\pi$
$941$	5.12636	+	50.5605i	0.167115	+	1.64822i	−0.473814	+	0.880625i	$0.657123\pi$
$942$	0.180157	−	0.0199398i	0.00586984	−	0.000649674i
$943$	7.29094	+	7.09274i	0.237426	+	0.230971i
$944$	−32.2193	−	8.47472i	−1.04865	−	0.275829i
$945$	−0.813093	+	1.35040i	−0.0264499	+	0.0439286i
$946$	1.22201	−	0.369925i	0.0397308	−	0.0120273i
$947$	11.4130	+	20.6343i	0.370872	+	0.670523i	0.993729	−	0.111812i	$-0.0356656\pi$
$947$	11.4130	+	20.6343i	0.370872	+	0.670523i	−0.622857	+	0.782336i	$0.714028\pi$
$948$	3.43568	−	2.57416i	0.111586	−	0.0836047i
$949$	−5.32233	+	21.0174i	−0.172770	+	0.682254i
$950$	−1.84425	−	1.76521i	−0.0598353	−	0.0572708i
$951$	−0.302181	−	1.19328i	−0.00979888	−	0.0386949i
$952$	6.12946	+	4.95422i	0.198657	+	0.160567i
$953$	−18.8255	−	23.7339i	−0.609817	−	0.768817i	0.377769	−	0.925900i	$-0.376691\pi$
$953$	−18.8255	−	23.7339i	−0.609817	−	0.768817i	−0.987585	+	0.157083i	$0.949791\pi$
$954$	−2.99502	−	1.15284i	−0.0969675	−	0.0373246i
$955$	0.600821	+	0.0776963i	0.0194421	+	0.00251419i
$956$	−0.938558	+	5.32283i	−0.0303551	+	0.172153i
$957$	−0.243359	+	8.82860i	−0.00786667	+	0.285388i
$958$	3.55878	+	0.797541i	0.114979	+	0.0257674i
$959$	9.18188	−	7.42138i	0.296498	−	0.239649i
$960$	−0.756027	−	0.566448i	−0.0244007	−	0.0182820i
$961$	0.348855	−	2.51576i	0.0112534	−	0.0811536i
$962$	0.415379	+	0.288017i	0.0133924	+	0.00928605i
$963$	22.8253	+	15.2135i	0.735537	+	0.490249i
$964$	−16.8006	−	12.1123i	−0.541111	−	0.390111i
$965$	−14.2745	−	2.92468i	−0.459514	−	0.0941486i
$966$	0.0296871	−	0.188558i	0.000955166	−	0.00606674i
$967$	33.3073	+	12.1229i	1.07109	+	0.389845i	0.816584	−	0.577226i	$-0.195865\pi$
$967$	33.3073	+	12.1229i	1.07109	+	0.389845i	0.254506	+	0.967071i	$0.418087\pi$
$968$	6.99304	+	5.44290i	0.224765	+	0.174942i
$969$	3.06635	−	5.65167i	0.0985055	−	0.181558i
$970$	0.629500	−	0.489959i	0.0202120	−	0.0157317i
$971$	32.6324	−	10.5367i	1.04722	−	0.338138i	0.267039	−	0.963686i	$-0.413955\pi$
$971$	32.6324	−	10.5367i	1.04722	−	0.338138i	0.780186	+	0.625548i	$0.215124\pi$
$972$	−10.3008	−	2.50805i	−0.330398	−	0.0804458i
$973$	47.1068	−	6.09170i	1.51017	−	0.195291i
$974$	0.183124	−	3.98425i	0.00586768	−	0.127664i
$975$	0.680705	+	4.32350i	0.0218000	+	0.138463i
$976$	−1.39189	+	7.12569i	−0.0445532	+	0.228088i
$977$	0.919131	+	33.3443i	0.0294056	+	1.06678i	0.860123	+	0.510086i	$0.170387\pi$
$977$	0.919131	+	33.3443i	0.0294056	+	1.06678i	−0.830718	+	0.556694i	$0.812070\pi$
$978$	0.181581	+	0.0268818i	0.00580633	+	0.000859584i
$979$	5.49285	−	1.02065i	0.175552	−	0.0326201i
$980$	−2.77282	−	1.12622i	−0.0885744	−	0.0359758i
$981$	−18.7383	−	8.84281i	−0.598267	−	0.282329i
$982$	−0.659034	−	0.862966i	−0.0210306	−	0.0275384i
$983$	−23.3462	+	27.3095i	−0.744627	+	0.871036i	−0.995280	−	0.0970408i	$-0.969062\pi$
$983$	−23.3462	+	27.3095i	−0.744627	+	0.871036i	0.250653	+	0.968077i	$0.419355\pi$
$984$	−0.226282	−	0.189873i	−0.00721361	−	0.00605294i
$985$	0.166453	−	0.156080i	0.00530364	−	0.00497312i
$986$	−1.73165	−	7.40741i	−0.0551470	−	0.235900i
$987$	−1.86735	+	1.01056i	−0.0594385	+	0.0321665i
$988$	5.16855	+	40.3070i	0.164433	+	1.28234i
$989$	−5.81037	−	3.14441i	−0.184759	−	0.0999865i
$990$	0.324642	−	1.18970i	0.0103178	−	0.0378110i
$991$	−27.9435	+	12.5645i	−0.887655	+	0.399124i	−0.802086	−	0.597208i	$-0.796277\pi$
$991$	−27.9435	+	12.5645i	−0.887655	+	0.399124i	−0.0855688	+	0.996332i	$0.527271\pi$
$992$	−7.06798	+	5.09561i	−0.224408	+	0.161786i
$993$	−5.12599	+	0.188433i	−0.162668	+	0.00597974i
$994$	−1.61716	−	3.05497i	−0.0512933	−	0.0968977i
$995$	1.12937	−	3.01642i	0.0358036	−	0.0956271i
$996$	0.224757	−	0.0635553i	0.00712170	−	0.00201383i
$997$	−18.1587	−	26.7091i	−0.575091	−	0.845886i	0.423096	−	0.906085i	$-0.360943\pi$
$997$	−18.1587	−	26.7091i	−0.575091	−	0.845886i	−0.998186	+	0.0601990i	$0.980826\pi$
$998$	1.24389	−	1.98253i	0.0393748	−	0.0627560i
$999$	0.603741	−	0.821420i	0.0191015	−	0.0259886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.k.a.4.17	✓	3348
361.271	even	171	inner	361.2.k.a.271.17	yes	3348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.k.a.4.17	✓	3348	1.1	even	1	trivial
361.2.k.a.271.17	yes	3348	361.271	even	171	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.k (of order \(171\), degree \(108\), minimal)

\(f(q)\)	\(=\)	\(q+(0.126711 + 0.00232818i) q^{2} +(-0.167706 + 0.111779i) q^{3} +(-1.98260 - 0.0728810i) q^{4} +(-0.267723 - 0.554071i) q^{5} +(-0.0215104 + 0.0137732i) q^{6} +(1.97597 - 0.802569i) q^{7} +(-0.504126 - 0.0278134i) q^{8} +(-1.13878 + 2.73150i) q^{9} +(-0.0326333 - 0.0708300i) q^{10} +(1.59507 - 5.09972i) q^{11} +(0.340640 - 0.209391i) q^{12} +(4.56574 - 1.11167i) q^{13} +(0.252245 - 0.0970937i) q^{14} +(0.106832 + 0.0629951i) q^{15} +(3.89336 + 0.286629i) q^{16} +(-3.88995 - 6.19985i) q^{17} +(-0.150655 + 0.343459i) q^{18} +(0.324686 - 4.34679i) q^{19} +(0.490406 + 1.11801i) q^{20} +(-0.241671 + 0.355468i) q^{21} +(0.213986 - 0.642476i) q^{22} +(-3.14089 + 1.55340i) q^{23} +(0.0876539 - 0.0516863i) q^{24} +(2.87186 - 3.62065i) q^{25} +(0.581116 - 0.130231i) q^{26} +(-0.230259 - 1.17880i) q^{27} +(-3.97605 + 1.44716i) q^{28} +(7.80438 + 2.51995i) q^{29} +(0.0133901 + 0.00823088i) q^{30} +(-4.36730 + 3.80349i) q^{31} +(1.49819 + 0.138011i) q^{32} +(0.302540 + 1.03355i) q^{33} +(-0.478464 - 0.794643i) q^{34} +(-0.973691 - 0.879960i) q^{35} +(2.45682 - 5.33248i) q^{36} +(0.574852 + 0.624455i) q^{37} +(0.0512613 - 0.550029i) q^{38} +(-0.641439 + 0.696788i) q^{39} +(0.119555 + 0.286768i) q^{40} +(-0.967742 - 2.73681i) q^{41} +(-0.0314499 + 0.0444789i) q^{42} +(1.08853 + 1.53948i) q^{43} +(-3.53406 + 9.99446i) q^{44} +(1.81832 - 0.100320i) q^{45} +(-0.401601 + 0.189520i) q^{46} +(4.38676 + 2.27081i) q^{47} +(-0.684978 + 0.387127i) q^{48} +(-1.75714 + 1.70938i) q^{49} +(0.372325 - 0.452089i) q^{50} +(1.34538 + 0.604935i) q^{51} +(-9.13305 + 1.87125i) q^{52} +(0.392876 + 8.54784i) q^{53} +(-0.0264318 - 0.149902i) q^{54} +(-3.25264 + 0.481530i) q^{55} +(-1.01846 + 0.349638i) q^{56} +(0.431429 + 0.765275i) q^{57} +(0.983032 + 0.337475i) q^{58} +(-8.39024 - 1.55902i) q^{59} +(-0.207214 - 0.132680i) q^{60} +(-0.221562 + 1.84653i) q^{61} +(-0.562239 + 0.471775i) q^{62} +(-0.0579770 + 6.31131i) q^{63} +(-7.57088 - 0.837945i) q^{64} +(-1.83830 - 2.23212i) q^{65} +(0.0359288 + 0.131666i) q^{66} +(1.03701 - 4.43598i) q^{67} +(7.26036 + 12.5753i) q^{68} +(0.353108 - 0.611601i) q^{69} +(-0.121328 - 0.113767i) q^{70} +(-1.52356 - 12.6976i) q^{71} +(0.650062 - 1.34535i) q^{72} +(-2.15856 + 4.07772i) q^{73} +(0.0713860 + 0.0804635i) q^{74} +(-0.0769144 + 0.928219i) q^{75} +(-0.960522 + 8.59428i) q^{76} +(-0.941072 - 11.3570i) q^{77} +(-0.0828994 + 0.0867972i) q^{78} +(10.6913 - 0.984872i) q^{79} +(-0.883526 - 2.23393i) q^{80} +(-6.07851 - 6.13461i) q^{81} +(-0.116251 - 0.349036i) q^{82} +(0.562103 + 0.158948i) q^{83} +(0.505044 - 0.687137i) q^{84} +(-2.39372 + 3.81515i) q^{85} +(0.134344 + 0.197603i) q^{86} +(-1.59052 + 0.449756i) q^{87} +(-0.945958 + 2.52654i) q^{88} +(0.489170 + 0.924087i) q^{89} +(0.230635 - 0.00847820i) q^{90} +(8.12955 - 5.86095i) q^{91} +(6.34034 - 2.85086i) q^{92} +(0.307272 - 1.12604i) q^{93} +(0.550563 + 0.297950i) q^{94} +(-2.49535 + 0.983835i) q^{95} +(-0.266682 + 0.144321i) q^{96} +(2.32844 + 9.96025i) q^{97} +(-0.226629 + 0.212505i) q^{98} +(12.1135 + 10.1644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3348 q - 108 q^{2} - 111 q^{3} - 114 q^{4} - 108 q^{5} - 117 q^{6} - 111 q^{7} - 120 q^{8} - 117 q^{9} - 123 q^{10} - 111 q^{11} - 117 q^{12} - 111 q^{13} - 111 q^{14} - 117 q^{15} - 96 q^{16} - 3 q^{17}+ \cdots - 123 q^{99}+O(q^{100}) \) 3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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