LMFDB - Embedded newform 361.2.k.a.4.16

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			4.16
Character	$\chi$	$=$	361.4
Dual form			361.2.k.a.271.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0510612 + 0.000938197i) q^{2} +(-1.90048 + 1.26671i) q^{3} +(-1.99604 - 0.0733752i) q^{4} +(-0.539848 - 1.11725i) q^{5} +(-0.0982292 + 0.0628965i) q^{6} +(0.439274 - 0.178418i) q^{7} +(-0.203836 - 0.0112460i) q^{8} +(0.852866 - 2.04570i) q^{9} +(-0.0265171 - 0.0575549i) q^{10} +(0.860613 - 2.75153i) q^{11} +(3.88638 - 2.38895i) q^{12} +(1.30343 - 0.317361i) q^{13} +(0.0225973 - 0.00869810i) q^{14} +(2.44120 + 1.43949i) q^{15} +(3.97360 + 0.292537i) q^{16} +(2.44607 + 3.89857i) q^{17} +(0.0454676 - 0.103656i) q^{18} +(1.52469 + 4.08354i) q^{19} +(0.995582 + 2.26970i) q^{20} +(-0.608828 + 0.895510i) q^{21} +(0.0465254 - 0.139689i) q^{22} +(4.47984 - 2.21561i) q^{23} +(0.401632 - 0.236828i) q^{24} +(2.15036 - 2.71103i) q^{25} +(0.0668524 - 0.0149820i) q^{26} +(-0.343119 - 1.75658i) q^{27} +(-0.889902 + 0.323898i) q^{28} +(-5.30516 - 1.71298i) q^{29} +(0.123300 + 0.0757924i) q^{30} +(7.13697 - 6.21559i) q^{31} +(0.609194 + 0.0561181i) q^{32} +(1.84980 + 6.31937i) q^{33} +(0.121242 + 0.201361i) q^{34} +(-0.436479 - 0.394462i) q^{35} +(-1.85246 + 4.02073i) q^{36} +(-4.48600 - 4.87309i) q^{37} +(0.0740213 + 0.209941i) q^{38} +(-2.07513 + 2.25420i) q^{39} +(0.0974761 + 0.233808i) q^{40} +(-2.28009 - 6.44819i) q^{41} +(-0.0319277 + 0.0451546i) q^{42} +(6.27575 + 8.87566i) q^{43} +(-1.91971 + 5.42903i) q^{44} +(-2.74598 + 0.151500i) q^{45} +(0.230825 - 0.108929i) q^{46} +(5.50470 + 2.84952i) q^{47} +(-7.92231 + 4.47743i) q^{48} +(-4.85635 + 4.72433i) q^{49} +(0.112343 - 0.136411i) q^{50} +(-9.58704 - 4.31070i) q^{51} +(-2.62498 + 0.537827i) q^{52} +(-0.475784 - 10.3517i) q^{53} +(-0.0158721 - 0.0900150i) q^{54} +(-3.53876 + 0.523887i) q^{55} +(-0.0915464 + 0.0314279i) q^{56} +(-8.07028 - 5.82936i) q^{57} +(-0.269281 - 0.0924442i) q^{58} +(8.95213 + 1.66343i) q^{59} +(-4.76712 - 3.05241i) q^{60} +(0.265097 - 2.20936i) q^{61} +(0.370254 - 0.310680i) q^{62} +(0.00965276 - 1.05079i) q^{63} +(-7.88930 - 0.873187i) q^{64} +(-1.05823 - 1.28493i) q^{65} +(0.0885245 + 0.324410i) q^{66} +(-1.11200 + 4.75676i) q^{67} +(-4.59640 - 7.96120i) q^{68} +(-5.70732 + 9.88536i) q^{69} +(-0.0219171 - 0.0205512i) q^{70} +(0.436637 + 3.63900i) q^{71} +(-0.196851 + 0.407396i) q^{72} +(5.54614 - 10.4772i) q^{73} +(-0.224489 - 0.253035i) q^{74} +(-0.652634 + 7.87613i) q^{75} +(-2.74371 - 8.26281i) q^{76} +(-0.112877 - 1.36223i) q^{77} +(-0.108074 + 0.113155i) q^{78} +(-5.24912 + 0.483542i) q^{79} +(-1.81831 - 4.59745i) q^{80} +(7.55713 + 7.62687i) q^{81} +(-0.110375 - 0.331392i) q^{82} +(-0.224397 - 0.0634533i) q^{83} +(1.28096 - 1.74280i) q^{84} +(3.03519 - 4.83751i) q^{85} +(0.312120 + 0.459090i) q^{86} +(12.2522 - 3.46459i) q^{87} +(-0.206368 + 0.551184i) q^{88} +(-0.0657750 - 0.124255i) q^{89} +(-0.140355 + 0.00515951i) q^{90} +(0.515939 - 0.371963i) q^{91} +(-9.10453 + 4.09375i) q^{92} +(-5.69033 + 20.8530i) q^{93} +(0.278404 + 0.150664i) q^{94} +(3.73926 - 3.90796i) q^{95} +(-1.22885 + 0.665018i) q^{96} +(1.41130 + 6.03706i) q^{97} +(-0.252404 + 0.236674i) q^{98} +(-4.89482 - 4.10724i) 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 $

$2$	0.0510612		0.000938197i	0.0361057		0.000663405i	0.0364207	−	0.999337i	$-0.488404\pi$
$2$	0.0510612		0.000938197i	0.0361057		0.000663405i	−0.000314984		1.00000i	$0.500100\pi$
$3$	−1.90048	+	1.26671i	−1.09724	+	0.731333i	−0.965618	−	0.259967i	$-0.916288\pi$
$3$	−1.90048	+	1.26671i	−1.09724	+	0.731333i	−0.131625	+	0.991300i	$0.542019\pi$
$4$	−1.99604	−	0.0733752i	−0.998022	−	0.0366876i
$5$	−0.539848	−	1.11725i	−0.241428	−	0.499651i	0.744332	−	0.667809i	$-0.232768\pi$
$5$	−0.539848	−	1.11725i	−0.241428	−	0.499651i	−0.985760	+	0.168158i	$0.946218\pi$
$6$	−0.0982292	+	0.0628965i	−0.0401019	+	0.0256774i
$7$	0.439274	−	0.178418i	0.166030	−	0.0674355i	−0.291781	−	0.956485i	$-0.594248\pi$
$7$	0.439274	−	0.178418i	0.166030	−	0.0674355i	0.457811	+	0.889050i	$0.348634\pi$
$8$	−0.203836	−	0.0112460i	−0.0720670	−	0.00397605i
$9$	0.852866	−	2.04570i	0.284289	−	0.681900i
$10$	−0.0265171	−	0.0575549i	−0.00838545	−	0.0182004i
$11$	0.860613	−	2.75153i	0.259485	−	0.829618i	−0.729806	−	0.683655i	$-0.760389\pi$
$11$	0.860613	−	2.75153i	0.259485	−	0.829618i	0.989290	−	0.145963i	$-0.0466281\pi$
$12$	3.88638	−	2.38895i	1.12190	−	0.689631i
$13$	1.30343	−	0.317361i	0.361506	−	0.0880201i	−0.0516878	−	0.998663i	$-0.516460\pi$
$13$	1.30343	−	0.317361i	0.361506	−	0.0880201i	0.413194	+	0.910643i	$0.364413\pi$
$14$	0.0225973	−	0.00869810i	0.00603937	−	0.00232467i
$15$	2.44120	+	1.43949i	0.630316	+	0.371674i
$16$	3.97360	+	0.292537i	0.993401	+	0.0731343i
$17$	2.44607	+	3.89857i	0.593258	+	0.945542i	0.999495	+	0.0317741i	$0.0101157\pi$
$17$	2.44607	+	3.89857i	0.593258	+	0.945542i	−0.406237	+	0.913768i	$0.633159\pi$
$18$	0.0454676	−	0.103656i	0.0107168	−	0.0244319i
$19$	1.52469	+	4.08354i	0.349787	+	0.936829i
$19$	1.52469	+	4.08354i	0.349787	+	0.936829i
$20$	0.995582	+	2.26970i	0.222619	+	0.507520i
$21$	−0.608828	+	0.895510i	−0.132857	+	0.195416i
$22$	0.0465254	−	0.139689i	0.00991926	−	0.0297818i
$23$	4.47984	−	2.21561i	0.934111	−	0.461987i	0.0886735	−	0.996061i	$-0.471737\pi$
$23$	4.47984	−	2.21561i	0.934111	−	0.461987i	0.845438	+	0.534074i	$0.179340\pi$
$24$	0.401632	−	0.236828i	0.0819828	−	0.0483423i
$25$	2.15036	−	2.71103i	0.430072	−	0.542206i
$26$	0.0668524	−	0.0149820i	0.0131108	−	0.00293821i
$27$	−0.343119	−	1.75658i	−0.0660333	−	0.338054i
$28$	−0.889902	+	0.323898i	−0.168176	+	0.0612109i
$29$	−5.30516	−	1.71298i	−0.985143	−	0.318093i	−0.229667	−	0.973269i	$-0.573764\pi$
$29$	−5.30516	−	1.71298i	−0.985143	−	0.318093i	−0.755476	+	0.655177i	$0.772594\pi$
$30$	0.123300	+	0.0757924i	0.0225115	+	0.0138377i
$31$	7.13697	−	6.21559i	1.28184	−	1.11635i	0.294852	−	0.955543i	$-0.404730\pi$
$31$	7.13697	−	6.21559i	1.28184	−	1.11635i	0.986985	−	0.160810i	$-0.0514106\pi$
$32$	0.609194	+	0.0561181i	0.107691	+	0.00992038i
$33$	1.84980	+	6.31937i	0.322010	+	1.10006i
$34$	0.121242	+	0.201361i	0.0207928	+	0.0345331i
$35$	−0.436479	−	0.394462i	−0.0737785	−	0.0666763i
$36$	−1.85246	+	4.02073i	−0.308743	+	0.670121i
$37$	−4.48600	−	4.87309i	−0.737493	−	0.801131i	0.248373	−	0.968664i	$-0.420104\pi$
$37$	−4.48600	−	4.87309i	−0.737493	−	0.801131i	−0.985866	+	0.167533i	$0.946420\pi$
$38$	0.0740213	+	0.209941i	0.0120078	+	0.0340570i
$39$	−2.07513	+	2.25420i	−0.332287	+	0.360960i
$40$	0.0974761	+	0.233808i	0.0154123	+	0.0369683i
$41$	−2.28009	−	6.44819i	−0.356090	−	1.00704i	−0.975121	−	0.221671i	$-0.928849\pi$
$41$	−2.28009	−	6.44819i	−0.356090	−	1.00704i	0.619031	−	0.785366i	$-0.287525\pi$
$42$	−0.0319277	+	0.0451546i	−0.00492655	+	0.00696751i
$43$	6.27575	+	8.87566i	0.957043	+	1.35352i	0.935336	+	0.353760i	$0.115097\pi$
$43$	6.27575	+	8.87566i	0.957043	+	1.35352i	0.0217068	+	0.999764i	$0.493090\pi$
$44$	−1.91971	+	5.42903i	−0.289408	+	0.818457i
$45$	−2.74598	+	0.151500i	−0.409347	+	0.0225843i
$46$	0.230825	−	0.108929i	0.0340333	−	0.0160607i
$47$	5.50470	+	2.84952i	0.802943	+	0.415645i	0.811525	−	0.584318i	$-0.198638\pi$
$47$	5.50470	+	2.84952i	0.802943	+	0.415645i	−0.00858124	+	0.999963i	$0.502732\pi$
$48$	−7.92231	+	4.47743i	−1.14349	+	0.646261i
$49$	−4.85635	+	4.72433i	−0.693764	+	0.674904i
$50$	0.112343	−	0.136411i	0.0158878	−	0.0192914i
$51$	−9.58704	−	4.31070i	−1.34245	−	0.603619i
$52$	−2.62498	+	0.537827i	−0.364020	+	0.0745832i
$53$	−0.475784	−	10.3517i	−0.0653540	−	1.42191i	−0.734413	−	0.678703i	$-0.762542\pi$
$53$	−0.475784	−	10.3517i	−0.0653540	−	1.42191i	0.669059	−	0.743209i	$-0.266697\pi$
$54$	−0.0158721	−	0.0900150i	−0.00215991	−	0.0122495i
$55$	−3.53876	+	0.523887i	−0.477166	+	0.0706410i
$56$	−0.0915464	+	0.0314279i	−0.0122334	+	0.00419973i
$57$	−8.07028	−	5.82936i	−1.06894	−	0.772118i
$58$	−0.269281	−	0.0924442i	−0.0353583	−	0.0121385i
$59$	8.95213	+	1.66343i	1.16547	+	0.216560i	0.729873	−	0.683582i	$-0.239579\pi$
$59$	8.95213	+	1.66343i	1.16547	+	0.216560i	0.435595	+	0.900143i	$0.356538\pi$
$60$	−4.76712	−	3.05241i	−0.615433	−	0.394064i
$61$	0.265097	−	2.20936i	0.0339422	−	0.282879i	−0.965781	−	0.259358i	$-0.916489\pi$
$61$	0.265097	−	2.20936i	0.0339422	−	0.282879i	0.999723	−	0.0235209i	$-0.00748764\pi$
$62$	0.370254	−	0.310680i	0.0470223	−	0.0394564i
$63$	0.00965276	−	1.05079i	0.00121613	−	0.132387i
$64$	−7.88930	−	0.873187i	−0.986162	−	0.109148i
$65$	−1.05823	−	1.28493i	−0.131257	−	0.159376i
$66$	0.0885245	+	0.324410i	0.0108966	+	0.0399322i
$67$	−1.11200	+	4.75676i	−0.135853	+	0.581131i	0.861457	+	0.507830i	$0.169552\pi$
$67$	−1.11200	+	4.75676i	−0.135853	+	0.581131i	−0.997310	+	0.0733011i	$0.976647\pi$
$68$	−4.59640	−	7.96120i	−0.557395	−	0.965437i
$69$	−5.70732	+	9.88536i	−0.687080	+	1.19006i
$70$	−0.0219171	−	0.0205512i	−0.00261959	−	0.00245634i
$71$	0.436637	+	3.63900i	0.0518193	+	0.431870i	0.995022	+	0.0996530i	$0.0317733\pi$
$71$	0.436637	+	3.63900i	0.0518193	+	0.431870i	−0.943203	+	0.332217i	$0.892203\pi$
$72$	−0.196851	+	0.407396i	−0.0231991	+	0.0480121i
$73$	5.54614	−	10.4772i	0.649126	−	1.22626i	−0.311982	−	0.950088i	$-0.600993\pi$
$73$	5.54614	−	10.4772i	0.649126	−	1.22626i	0.961109	−	0.276171i	$-0.0890655\pi$
$74$	−0.224489	−	0.253035i	−0.0260963	−	0.0294147i
$75$	−0.652634	+	7.87613i	−0.0753597	+	0.909457i
$76$	−2.74371	−	8.26281i	−0.314725	−	0.947809i
$77$	−0.112877	−	1.36223i	−0.0128635	−	0.155240i
$78$	−0.108074	+	0.113155i	−0.0122369	+	0.0128123i
$79$	−5.24912	+	0.483542i	−0.590572	+	0.0544027i	−0.382890	−	0.923794i	$-0.625071\pi$
$79$	−5.24912	+	0.483542i	−0.590572	+	0.0544027i	−0.207681	+	0.978197i	$0.566592\pi$
$80$	−1.81831	−	4.59745i	−0.203293	−	0.514011i
$81$	7.55713	+	7.62687i	0.839681	+	0.847430i
$82$	−0.110375	−	0.331392i	−0.0121888	−	0.0365961i
$83$	−0.224397	−	0.0634533i	−0.0246307	−	0.00696490i	0.259766	−	0.965672i	$-0.416355\pi$
$83$	−0.224397	−	0.0634533i	−0.0246307	−	0.00696490i	−0.284397	+	0.958707i	$0.591793\pi$
$84$	1.28096	−	1.74280i	0.139764	−	0.190155i
$85$	3.03519	−	4.83751i	0.329212	−	0.524702i
$86$	0.312120	+	0.459090i	0.0336568	+	0.0495049i
$87$	12.2522	−	3.46459i	1.31357	−	0.371443i
$88$	−0.206368	+	0.551184i	−0.0219989	+	0.0587564i
$89$	−0.0657750	−	0.124255i	−0.00697214	−	0.0131710i	0.880298	−	0.474421i	$-0.157343\pi$
$89$	−0.0657750	−	0.124255i	−0.00697214	−	0.0131710i	−0.887270	+	0.461250i	$0.847401\pi$
$90$	−0.140355	+	0.00515951i	−0.0147948	+	0.000543860i
$91$	0.515939	−	0.371963i	0.0540851	−	0.0389923i
$92$	−9.10453	+	4.09375i	−0.949213	+	0.426803i
$93$	−5.69033	+	20.8530i	−0.590060	+	2.16236i
$94$	0.278404	+	0.150664i	0.0287151	+	0.0155399i
$95$	3.73926	−	3.90796i	0.383639	−	0.400948i
$96$	−1.22885	+	0.665018i	−0.125418	+	0.0678731i
$97$	1.41130	+	6.03706i	0.143296	+	0.612971i	0.995904	+	0.0904196i	$0.0288208\pi$
$97$	1.41130	+	6.03706i	0.143296	+	0.612971i	−0.852608	+	0.522551i	$0.824980\pi$
$98$	−0.252404	+	0.236674i	−0.0254966	+	0.0239077i
$99$	−4.89482	−	4.10724i	−0.491948	−	0.412793i
$100$	−4.49113	+	5.25355i	−0.449113	+	0.525355i
$101$	−4.85172	−	6.35304i	−0.482765	−	0.632152i	0.487811	−	0.872949i	$-0.337796\pi$
$101$	−4.85172	−	6.35304i	−0.482765	−	0.632152i	−0.970575	+	0.240798i	$0.922591\pi$
$102$	−0.485482	−	0.229104i	−0.0480699	−	0.0226847i
$103$	9.31028	+	3.78151i	0.917369	+	0.372603i	0.785641	−	0.618683i	$-0.212333\pi$
$103$	9.31028	+	3.78151i	0.917369	+	0.372603i	0.131728	+	0.991286i	$0.457947\pi$
$104$	−0.269255	+	0.0500314i	−0.0264026	+	0.00490598i
$105$	1.32919	+	0.196776i	0.129715	+	0.0192034i
$106$	−0.0145822	−	0.529016i	−0.00141635	−	0.0513826i
$107$	2.01296	−	10.3052i	0.194600	−	0.996245i	−0.748348	−	0.663306i	$-0.769153\pi$
$107$	2.01296	−	10.3052i	0.194600	−	0.996245i	0.942948	−	0.332939i	$-0.108040\pi$
$108$	0.555991	+	3.53138i	0.0535003	+	0.339807i
$109$	−0.249371	+	5.42559i	−0.0238854	+	0.519677i	0.952617	+	0.304172i	$0.0983797\pi$
$109$	−0.249371	+	5.42559i	−0.0238854	+	0.519677i	−0.976503	+	0.215506i	$0.930860\pi$
$110$	−0.181185	+	0.0234303i	−0.0172753	+	0.00223399i
$111$	14.6983	+	3.57877i	1.39510	+	0.339682i
$112$	1.79769	−	0.580457i	0.169866	−	0.0548481i
$113$	2.51543	−	1.95784i	0.236632	−	0.184178i	−0.488954	−	0.872310i	$-0.662621\pi$
$113$	2.51543	−	1.95784i	0.236632	−	0.184178i	0.725586	+	0.688132i	$0.241569\pi$
$114$	−0.406610	−	0.305226i	−0.0380825	−	0.0285870i
$115$	−4.89384	−	3.80903i	−0.456353	−	0.355193i
$116$	10.4636	+	3.80845i	0.971524	+	0.353606i
$117$	0.462424	−	2.93709i	0.0427511	−	0.271534i
$118$	0.455546	+	0.0933358i	0.0419364	+	0.00859226i
$119$	1.77007	+	1.27612i	0.162262	+	0.116982i
$120$	−0.481417	−	0.320874i	−0.0439472	−	0.0292916i
$121$	2.20928	+	1.53188i	0.200844	+	0.139262i
$122$	0.0156090	−	0.112564i	0.00141317	−	0.0101910i
$123$	12.5012	+	9.36644i	1.12720	+	0.844544i
$124$	−14.7018	+	11.8829i	−1.32026	+	1.06712i
$125$	−10.2438	−	2.29570i	−0.916236	−	0.205333i
$126$	0.00147873	−	0.0536455i	0.000131736	−	0.00477912i
$127$	−1.33333	+	7.56167i	−0.118314	+	0.670990i	0.866742	+	0.498756i	$0.166210\pi$
$127$	−1.33333	+	7.56167i	−0.118314	+	0.670990i	−0.985056	+	0.172234i	$0.944901\pi$
$128$	−1.61546	−	0.208906i	−0.142788	−	0.0184649i
$129$	−23.1698	−	8.91847i	−2.03998	−	0.785228i
$130$	−0.0528288	−	0.0666031i	−0.00463339	−	0.00584148i
$131$	8.77663	+	7.09383i	0.766817	+	0.619791i	0.930319	−	0.366752i	$-0.119530\pi$
$131$	8.77663	+	7.09383i	0.766817	+	0.619791i	−0.163501	+	0.986543i	$0.552279\pi$
$132$	−3.22860	−	12.7495i	−0.281014	−	1.10970i
$133$	1.39833	+	1.52176i	0.121251	+	0.131954i
$134$	−0.0612430	+	0.241843i	−0.00529059	+	0.0208921i
$135$	−1.77731	+	1.33164i	−0.152967	+	0.114609i
$136$	−0.454754	−	0.822178i	−0.0389948	−	0.0705012i
$137$	17.9954	−	5.44756i	1.53745	−	0.465416i	0.596117	−	0.802897i	$-0.296709\pi$
$137$	17.9954	−	5.44756i	1.53745	−	0.465416i	0.941332	+	0.337481i	$0.109575\pi$
$138$	−0.300697	+	0.499404i	−0.0255970	+	0.0425121i
$139$	−4.45857	−	1.17275i	−0.378171	−	0.0994712i	0.0603850	−	0.998175i	$-0.480767\pi$
$139$	−4.45857	−	1.17275i	−0.378171	−	0.0994712i	−0.438556	+	0.898704i	$0.644510\pi$
$140$	0.842288	+	0.819390i	0.0711863	+	0.0692511i
$141$	−14.0711	+	1.55739i	−1.18500	+	0.131156i
$142$	0.0188811	+	0.186222i	0.00158447	+	0.0156274i
$143$	0.248518	−	3.85955i	0.0207821	−	0.322752i
$144$	3.98739	−	7.87931i	0.332283	−	0.656609i
$145$	0.950146	+	6.85196i	0.0789054	+	0.569024i
$146$	0.293022	−	0.529773i	0.0242507	−	0.0438443i
$147$	3.24506	−	15.1301i	0.267648	−	1.24791i
$148$	8.59668	+	10.0561i	0.706643	+	0.826603i
$149$	−0.114835	−	12.5008i	−0.00940765	−	1.02411i	−0.863608	−	0.504163i	$-0.831801\pi$
$149$	−0.114835	−	12.5008i	−0.00940765	−	1.02411i	0.854201	−	0.519944i	$-0.174047\pi$
$150$	−0.0407137	+	0.401552i	−0.00332426	+	0.0327866i
$151$	−6.93815	−	1.15777i	−0.564619	−	0.0942182i	−0.124600	−	0.992207i	$-0.539765\pi$
$151$	−6.93815	−	1.15777i	−0.564619	−	0.0942182i	−0.440018	+	0.897989i	$0.645028\pi$
$152$	−0.264863	−	0.849521i	−0.0214832	−	0.0689052i
$153$	10.0615	−	1.67896i	0.813421	−	0.135736i
$154$	−0.00448561	−	0.0696628i	−0.000361461	−	0.00561359i
$155$	−10.7973	−	4.61833i	−0.867258	−	0.370953i
$156$	4.30746	−	4.34721i	0.344873	−	0.348055i
$157$	20.5112	+	10.1443i	1.63697	+	0.809602i	0.999225	+	0.0393533i	$0.0125298\pi$
$157$	20.5112	+	10.1443i	1.63697	+	0.809602i	0.637744	+	0.770249i	$0.279868\pi$
$158$	−0.268480	+	0.0197655i	−0.0213591	+	0.00157246i
$159$	14.0167	+	19.0705i	1.11160	+	1.51239i
$160$	−0.266174	−	0.710919i	−0.0210429	−	0.0562031i
$161$	1.57257	−	1.77254i	0.123936	−	0.139696i
$162$	0.378721	+	0.396528i	0.0297551	+	0.0311541i
$163$	−0.945878	−	0.823766i	−0.0740869	−	0.0645223i	0.618916	−	0.785457i	$-0.287572\pi$
$163$	−0.945878	−	0.823766i	−0.0740869	−	0.0645223i	−0.693003	+	0.720935i	$0.743713\pi$
$164$	4.07802	+	13.0382i	0.318440	+	1.01811i
$165$	6.06173	−	5.47820i	0.471905	−	0.426478i
$166$	−0.0113984	−	0.00345053i	−0.000884690	−	0.000267813i
$167$	−2.94575	−	13.7346i	−0.227949	−	1.06281i	−0.934724	−	0.355374i	$-0.884354\pi$
$167$	−2.94575	−	13.7346i	−0.227949	−	1.06281i	0.706775	−	0.707438i	$-0.250149\pi$
$168$	0.134172	−	0.175691i	0.0103516	−	0.0135548i
$169$	−9.94669	+	5.14892i	−0.765130	+	0.396071i
$170$	0.159519	−	0.244162i	0.0122345	−	0.0187264i
$171$	9.65406	+	0.363662i	0.738264	+	0.0278099i
$172$	−11.8754	−	18.1767i	−0.905492	−	1.38596i
$173$	−9.24589	−	5.22547i	−0.702952	−	0.397285i	0.0986669	−	0.995121i	$-0.468542\pi$
$173$	−9.24589	−	5.22547i	−0.702952	−	0.397285i	−0.801619	+	0.597836i	$0.796028\pi$
$174$	0.628862	−	0.165411i	0.0476739	−	0.0125398i
$175$	0.460901	−	1.57455i	0.0348408	−	0.119025i
$176$	4.22466	−	10.6817i	0.318446	−	0.805166i
$177$	−19.1204	+	8.17839i	−1.43718	+	0.614726i
$178$	−0.00324198	−	0.00640633i	−0.000242997	−	0.000480174i
$179$	9.28126	−	6.43549i	0.693714	−	0.481011i	−0.169707	−	0.985495i	$-0.554282\pi$
$179$	9.28126	−	6.43549i	0.693714	−	0.481011i	0.863421	+	0.504484i	$0.168317\pi$
$180$	5.49222	−	0.100914i	0.409366	−	0.00752167i
$181$	−9.30537	+	0.170976i	−0.691663	+	0.0127086i	−0.363068	−	0.931763i	$-0.618271\pi$
$181$	−9.30537	+	0.170976i	−0.691663	+	0.0127086i	−0.328594	+	0.944471i	$0.606575\pi$
$182$	0.0266935	−	0.0185088i	0.00197865	−	0.00137197i
$183$	2.29479	+	4.53464i	0.169636	+	0.335210i
$184$	−0.938071	+	0.401242i	−0.0691555	+	0.0295799i
$185$	−3.02272	+	7.64273i	−0.222235	+	0.561904i
$186$	−0.310120	+	1.05944i	−0.0227391	+	0.0776821i
$187$	12.8322	−	3.37527i	0.938380	−	0.246824i
$188$	−10.7785	−	6.09167i	−0.786106	−	0.444281i
$189$	−0.464128	−	0.710401i	−0.0337603	−	0.0516740i
$190$	0.194597	−	0.196037i	0.0141176	−	0.0142220i
$191$	−1.36801	+	2.09390i	−0.0989860	+	0.151509i	−0.883225	−	0.468950i	$-0.844633\pi$
$191$	−1.36801	+	2.09390i	−0.0989860	+	0.151509i	0.784239	+	0.620459i	$0.213054\pi$
$192$	16.0995	−	8.33394i	1.16188	−	0.601450i
$193$	−3.93346	+	5.15063i	−0.283137	+	0.370751i	−0.914396	−	0.404821i	$-0.867334\pi$
$193$	−3.93346	+	5.15063i	−0.283137	+	0.370751i	0.631259	+	0.775572i	$0.282538\pi$
$194$	0.0663988	+	0.309584i	0.00476716	+	0.0222268i
$195$	3.63877	+	1.10153i	0.260578	+	0.0788820i
$196$	10.0401	−	9.07363i	0.717152	−	0.648117i
$197$	−1.01388	−	3.24155i	−0.0722359	−	0.230951i	0.911275	−	0.411797i	$-0.135099\pi$
$197$	−1.01388	−	3.24155i	−0.0722359	−	0.230951i	−0.983511	+	0.180846i	$0.942116\pi$
$198$	−0.246082	−	0.214313i	−0.0174883	−	0.0152306i
$199$	−1.54997	−	1.62285i	−0.109875	−	0.115041i	0.665929	−	0.746015i	$-0.268035\pi$
$199$	−1.54997	−	1.62285i	−0.109875	−	0.115041i	−0.775804	+	0.630974i	$0.782655\pi$
$200$	−0.468809	+	0.528423i	−0.0331498	+	0.0373652i
$201$	−3.91208	−	10.4487i	−0.275937	−	0.736995i
$202$	−0.241775	−	0.328946i	−0.0170112	−	0.0231446i
$203$	−2.63604	+	0.194066i	−0.185014	+	0.0136208i
$204$	18.8198	+	9.30780i	1.31765	+	0.651677i
$205$	−5.97336	+	6.02848i	−0.417198	+	0.421048i
$206$	0.471847	+	0.201823i	0.0328751	+	0.0140617i
$207$	−0.711773	−	11.0540i	−0.0494716	−	0.768308i
$208$	5.27215	−	0.879765i	0.365558	−	0.0610008i
$209$	12.5482	−	0.680877i	0.867975	−	0.0470972i
$210$	0.0676853	+	0.0112947i	0.00467073	+	0.000779407i
$211$	−2.19378	+	21.6369i	−0.151026	+	1.48955i	0.584135	+	0.811657i	$0.301434\pi$
$211$	−2.19378	+	21.6369i	−0.151026	+	1.48955i	−0.735161	+	0.677892i	$0.762894\pi$
$212$	0.190130	+	20.6973i	0.0130582	+	1.42150i
$213$	−5.43936	−	6.36276i	−0.372699	−	0.435969i
$214$	0.112453	−	0.524309i	0.00768710	−	0.0358411i
$215$	6.52841	−	11.8031i	0.445234	−	0.804966i
$216$	0.0501857	+	0.361913i	0.00341470	+	0.0246251i
$217$	2.02611	−	4.00371i	0.137542	−	0.271789i
$218$	−0.0178235	+	0.276803i	−0.00120716	+	0.0187475i
$219$	2.73115	+	26.9369i	0.184554	+	1.82023i
$220$	7.10196	−	0.786045i	0.478814	−	0.0529951i
$221$	4.42552	+	4.30522i	0.297693	+	0.289600i
$222$	0.747156	+	0.196526i	0.0501458	+	0.0131900i
$223$	0.749638	−	1.24502i	0.0501995	−	0.0833724i	−0.830579	−	0.556900i	$-0.811990\pi$
$223$	0.749638	−	1.24502i	0.0501995	−	0.0833724i	0.880779	+	0.473528i	$0.157020\pi$
$224$	0.277615	−	0.0840397i	0.0185490	−	0.00561514i
$225$	−3.71199	−	6.71113i	−0.247466	−	0.447409i
$226$	0.130278	−	0.0976097i	0.00866595	−	0.00649290i
$227$	5.73768	−	22.6576i	0.380823	−	1.50384i	−0.421434	−	0.906859i	$-0.638473\pi$
$227$	5.73768	−	22.6576i	0.380823	−	1.50384i	0.802257	−	0.596979i	$-0.203632\pi$
$228$	15.6809	+	12.2278i	1.03849	+	0.809807i
$229$	3.19702	+	12.6247i	0.211265	+	0.834265i	0.980696	+	0.195536i	$0.0626448\pi$
$229$	3.19702	+	12.6247i	0.211265	+	0.834265i	−0.769432	+	0.638729i	$0.779460\pi$
$230$	−0.246312	−	0.199085i	−0.0162413	−	0.0131273i
$231$	1.94006	+	2.44590i	0.127646	+	0.160928i
$232$	1.06212	+	0.408829i	0.0697316	+	0.0268410i
$233$	−13.2411	−	1.71230i	−0.867454	−	0.112176i	−0.318393	−	0.947959i	$-0.603143\pi$
$233$	−13.2411	−	1.71230i	−0.867454	−	0.112176i	−0.549061	+	0.835782i	$0.685015\pi$
$234$	0.0263675	−	0.149537i	0.00172370	−	0.00977557i
$235$	0.211931	−	7.68846i	0.0138248	−	0.501540i
$236$	−17.7468	−	3.97715i	−1.15522	−	0.258890i
$237$	9.36333	−	7.56805i	0.608214	−	0.491597i
$238$	0.0891846	+	0.0668209i	0.00578098	+	0.00433135i
$239$	0.196287	−	1.41552i	0.0126967	−	0.0915622i	−0.983115	−	0.182988i	$-0.941423\pi$
$239$	0.196287	−	1.41552i	0.0126967	−	0.0915622i	0.995812	+	0.0914257i	$0.0291424\pi$
$240$	9.27927	+	6.43410i	0.598974	+	0.415319i
$241$	−1.67461	−	1.11616i	−0.107871	−	0.0718983i	0.499513	−	0.866306i	$-0.333512\pi$
$241$	−1.67461	−	1.11616i	−0.107871	−	0.0718983i	−0.607384	+	0.794408i	$0.707781\pi$
$242$	0.111371	+	0.0802925i	0.00715923	+	0.00516140i
$243$	−18.7631	−	3.84433i	−1.20365	−	0.246614i
$244$	−0.691257	+	4.39052i	−0.0442532	+	0.281074i
$245$	7.89997	+	2.87535i	0.504710	+	0.183700i
$246$	0.629540	+	0.489991i	0.0401380	+	0.0312407i
$247$	3.28328	+	4.83873i	0.208910	+	0.307881i
$248$	−1.52467	+	1.18670i	−0.0968168	+	0.0753556i
$249$	0.506837	−	0.163653i	0.0321195	−	0.0103711i
$250$	−0.520909	−	0.126832i	−0.0329452	−	0.00802155i
$251$	8.78427	−	1.13595i	0.554458	−	0.0717008i	0.154093	−	0.988056i	$-0.450755\pi$
$251$	8.78427	−	1.13595i	0.554458	−	0.0717008i	0.400365	+	0.916356i	$0.368883\pi$
$252$	−0.0963692	+	2.09671i	−0.00607069	+	0.132080i
$253$	−2.24092	−	14.2332i	−0.140885	−	0.894834i
$254$	−0.0751757	+	0.384858i	−0.00471694	+	0.0241481i
$255$	0.359398	+	13.0383i	0.0225064	+	0.816489i
$256$	15.6215	+	2.31265i	0.976344	+	0.144540i
$257$	5.25915	−	0.977224i	0.328057	−	0.0609576i	−0.0160983	−	0.999870i	$-0.505124\pi$
$257$	5.25915	−	0.977224i	0.328057	−	0.0609576i	0.344155	+	0.938913i	$0.388165\pi$
$258$	−1.17471	−	0.477126i	−0.0731343	−	0.0297046i
$259$	−2.84003	−	1.34024i	−0.176471	−	0.0832785i
$260$	2.01798	+	2.64243i	0.125150	+	0.163877i
$261$	−8.02883	+	9.39182i	−0.496972	+	0.581339i
$262$	0.441490	+	0.370454i	0.0272753	+	0.0228867i
$263$	13.1336	−	12.3151i	0.809854	−	0.759384i	−0.164024	−	0.986456i	$-0.552448\pi$
$263$	13.1336	−	12.3151i	0.809854	−	0.759384i	0.973878	+	0.227072i	$0.0729154\pi$
$264$	−0.305990	−	1.30892i	−0.0188324	−	0.0805584i
$265$	−11.3086	+	6.11991i	−0.694682	+	0.375943i
$266$	0.0699728	+	0.0790150i	0.00429031	+	0.00484472i
$267$	0.282399	+	0.152826i	0.0172825	+	0.00935283i
$268$	2.56863	−	9.41312i	0.156904	−	0.574998i
$269$	−28.7444	+	12.9246i	−1.75258	+	0.788027i	−0.762590	+	0.646882i	$0.776073\pi$
$269$	−28.7444	+	12.9246i	−1.75258	+	0.788027i	−0.989989	+	0.141146i	$0.954921\pi$
$270$	−0.0920011	+	0.0663276i	−0.00559901	+	0.00403657i
$271$	−29.9454	+	1.10080i	−1.81905	+	0.0668690i	−0.924746	−	0.380585i	$-0.875723\pi$
$271$	−29.9454	+	1.10080i	−1.81905	+	0.0668690i	−0.894307	+	0.447454i	$0.852331\pi$
$272$	8.57923	+	16.2069i	0.520192	+	0.982690i
$273$	−0.509364	+	1.36045i	−0.0308281	+	0.0823382i
$274$	0.923978	−	0.261276i	0.0558195	−	0.0157843i
$275$	−5.60886	−	8.24993i	−0.338227	−	0.497489i
$276$	12.1174	−	19.3128i	0.729381	−	1.16250i
$277$	−1.84374	+	2.50850i	−0.110780	+	0.150721i	−0.857623	−	0.514279i	$-0.828060\pi$
$277$	−1.84374	+	2.50850i	−0.110780	+	0.150721i	0.746843	+	0.665000i	$0.231568\pi$
$278$	−0.226560	−	0.0640650i	−0.0135881	−	0.00384236i
$279$	−6.62836	−	19.9012i	−0.396829	−	1.19145i
$280$	0.0845342	+	0.0853143i	0.00505188	+	0.00509850i
$281$	9.87935	+	24.9792i	0.589352	+	1.49013i	0.851103	+	0.524998i	$0.175934\pi$
$281$	9.87935	+	24.9792i	0.589352	+	1.49013i	−0.261751	+	0.965136i	$0.584300\pi$
$282$	−0.719948	+	0.0663206i	−0.0428723	+	0.00394934i
$283$	−1.96196	+	2.05420i	−0.116626	+	0.122110i	−0.778889	−	0.627162i	$-0.784216\pi$
$283$	−1.96196	+	2.05420i	−0.116626	+	0.122110i	0.662262	+	0.749272i	$0.269596\pi$
$284$	−0.604534	−	7.29564i	−0.0358725	−	0.432917i
$285$	−2.15614	+	12.1635i	−0.127719	+	0.720505i
$286$	0.0163106	−	0.196840i	0.000964468	−	0.0116394i
$287$	−2.15206	−	2.42571i	−0.127032	−	0.143185i
$288$	0.634361	−	1.19837i	0.0373801	−	0.0706144i
$289$	−1.81948	+	3.76554i	−0.107028	+	0.221503i
$290$	0.0420872	+	0.350761i	0.00247144	+	0.0205974i
$291$	−10.3293	−	9.68561i	−0.605516	−	0.567780i
$292$	−11.8391	+	20.5059i	−0.692831	+	1.20002i
$293$	−4.93973	−	8.55587i	−0.288582	−	0.499839i	0.684889	−	0.728647i	$-0.259851\pi$
$293$	−4.93973	−	8.55587i	−0.288582	−	0.499839i	−0.973472	+	0.228808i	$0.926517\pi$
$294$	0.179892	−	0.769515i	0.0104915	−	0.0448790i
$295$	−2.97432	−	10.8998i	−0.173171	−	0.634611i
$296$	0.859606	+	1.04376i	0.0499636	+	0.0606674i
$297$	−5.12857	−	0.567630i	−0.297590	−	0.0329373i
$298$	0.00586461	−	0.638415i	0.000339728	−	0.0369824i
$299$	5.13600	−	4.30962i	0.297023	−	0.249232i
$300$	1.88060	−	15.6732i	0.108576	−	0.904893i
$301$	4.34035	+	2.77914i	0.250173	+	0.160187i
$302$	−0.353184	−	0.0656267i	−0.0203235	−	0.00377639i
$303$	17.2680	+	5.92812i	0.992023	+	0.340562i
$304$	4.86392	+	16.6724i	0.278965	+	0.956229i
$305$	−2.61152	+	0.896538i	−0.149535	+	0.0513356i
$306$	0.515326	−	0.0762902i	0.0294592	−	0.00436122i
$307$	0.108313	+	0.614271i	0.00618172	+	0.0350583i	0.987743	−	0.156092i	$-0.0498895\pi$
$307$	0.108313	+	0.614271i	0.00618172	+	0.0350583i	−0.981561	+	0.191150i	$0.938778\pi$
$308$	0.125354	+	2.72734i	0.00714272	+	0.155405i
$309$	−22.4840	+	4.60670i	−1.27907	+	0.262066i
$310$	−0.546989	−	0.245948i	−0.0310669	−	0.0139689i
$311$	13.3024	−	16.1522i	0.754310	−	0.915908i	−0.244241	−	0.969714i	$-0.578539\pi$
$311$	13.3024	−	16.1522i	0.754310	−	0.915908i	0.998551	+	0.0538066i	$0.0171354\pi$
$312$	0.448338	−	0.436150i	0.0253821	−	0.0246921i
$313$	5.00516	−	2.82875i	0.282908	−	0.159890i	−0.344031	−	0.938958i	$-0.611793\pi$
$313$	5.00516	−	2.82875i	0.282908	−	0.159890i	0.626940	+	0.779068i	$0.284307\pi$
$314$	1.03781	+	0.537223i	0.0585669	+	0.0303173i
$315$	−1.17921	+	0.556482i	−0.0664409	+	0.0313542i
$316$	10.5129	−	0.580015i	0.591399	−	0.0326284i
$317$	3.04445	−	8.60984i	0.170994	−	0.483577i	−0.825766	−	0.564013i	$-0.809257\pi$
$317$	3.04445	−	8.60984i	0.170994	−	0.483577i	0.996760	+	0.0804359i	$0.0256312\pi$
$318$	0.697821	+	0.986912i	0.0391318	+	0.0553433i
$319$	−9.27901	+	13.1231i	−0.519525	+	0.734753i
$320$	3.28345	+	9.28574i	0.183551	+	0.519089i
$321$	9.22811	+	22.1347i	0.515063	+	1.23544i
$322$	0.0819605	−	0.0890329i	0.00456748	−	0.00496161i
$323$	−12.1905	+	15.9327i	−0.678297	+	0.886520i
$324$	−14.5247	−	15.7781i	−0.806930	−	0.876560i
$325$	1.94246	−	4.21607i	0.107748	−	0.233866i
$326$	−0.0475249	−	0.0429499i	−0.00263216	−	0.00237878i
$327$	−6.39870	−	10.6271i	−0.353849	−	0.587680i
$328$	0.392249	+	1.34002i	0.0216583	+	0.0739900i
$329$	2.92648	+	0.269583i	0.161342	+	0.0148626i
$330$	0.314659	−	0.274037i	0.0173214	−	0.0150852i
$331$	−27.6940	−	17.0234i	−1.52220	−	0.935692i	−0.996372	−	0.0851009i	$-0.972879\pi$
$331$	−27.6940	−	17.0234i	−1.52220	−	0.935692i	−0.525827	−	0.850592i	$-0.676244\pi$
$332$	0.443249	+	0.143121i	0.0243265	+	0.00785477i
$333$	−13.7948	+	5.02091i	−0.755952	+	0.275144i
$334$	−0.137528	−	0.704067i	−0.00752520	−	0.0385248i
$335$	5.91483	−	1.32554i	0.323161	−	0.0724222i
$336$	−2.68121	+	3.38030i	−0.146272	+	0.184410i
$337$	15.7027	−	9.25934i	0.855383	−	0.504388i	−0.0132113	−	0.999913i	$-0.504205\pi$
$337$	15.7027	−	9.25934i	0.855383	−	0.504388i	0.868594	+	0.495525i	$0.165024\pi$
$338$	−0.512721	+	0.253578i	−0.0278883	+	0.0137928i
$339$	−2.30052	+	6.90714i	−0.124947	+	0.375144i
$340$	−6.41332	+	9.43318i	−0.347811	+	0.511586i
$341$	−10.9602	−	24.9868i	−0.593530	−	1.35311i
$342$	0.492607	+	0.0276264i	0.0266371	+	0.00149387i
$343$	−2.62354	+	5.98107i	−0.141658	+	0.322947i
$344$	−1.17941	−	1.87976i	−0.0635895	−	0.101350i
$345$	14.1255	+	1.03992i	0.760494	+	0.0559877i
$346$	−0.467204	−	0.275493i	−0.0251170	−	0.0148106i
$347$	−34.5712	+	13.3071i	−1.85588	+	0.714361i	−0.889666	+	0.456611i	$0.849063\pi$
$347$	−34.5712	+	13.3071i	−1.85588	+	0.714361i	−0.966212	+	0.257750i	$0.917019\pi$
$348$	−24.7101	+	6.01646i	−1.32460	+	0.322516i
$349$	5.59049	−	3.43646i	0.299252	−	0.183950i	−0.365907	−	0.930652i	$-0.619241\pi$
$349$	5.59049	−	3.43646i	0.299252	−	0.183950i	0.665159	+	0.746702i	$0.268364\pi$
$350$	0.0250114	−	0.0799659i	0.00133692	−	0.00427436i
$351$	−1.00470	−	2.18068i	−0.0536269	−	0.116396i
$352$	0.678691	−	1.62792i	0.0361743	−	0.0867684i
$353$	4.26239	+	0.235163i	0.226864	+	0.0125165i	0.168163	−	0.985759i	$-0.446216\pi$
$353$	4.26239	+	0.235163i	0.226864	+	0.0125165i	0.0587010	+	0.998276i	$0.481304\pi$
$354$	−0.983985	+	0.399660i	−0.0522982	+	0.0212417i
$355$	3.82997	−	2.45234i	0.203274	−	0.130157i
$356$	0.122173	+	0.252845i	0.00647514	+	0.0134007i
$357$	−4.98044	−	0.183083i	−0.263593	−	0.00968976i
$358$	0.479951	−	0.319896i	0.0253662	−	0.0169070i
$359$	−7.73560	−	0.142134i	−0.408269	−	0.00750152i	−0.186151	−	0.982521i	$-0.559601\pi$
$359$	−7.73560	−	0.142134i	−0.408269	−	0.00750152i	−0.222119	+	0.975020i	$0.571297\pi$
$360$	0.561435			0.0295902
$361$	−14.3507	+	12.4523i	−0.755298	+	0.655382i
$362$	−0.475304			−0.0249814
$363$	−6.13914	−	0.112800i	−0.322221	−	0.00592047i
$364$	−1.05713	+	0.704597i	−0.0554087	+	0.0369309i
$365$	−14.6997	−	0.540366i	−0.769419	−	0.0282841i
$366$	0.112921	+	0.233697i	0.00590246	+	0.0122155i
$367$	7.48052	−	4.78980i	0.390480	−	0.250026i	−0.329304	−	0.944224i	$-0.606814\pi$
$367$	7.48052	−	4.78980i	0.390480	−	0.250026i	0.719784	+	0.694198i	$0.244241\pi$
$368$	18.4493	−	7.49344i	0.961734	−	0.390623i
$369$	−15.1357	−	0.835058i	−0.787931	−	0.0434714i
$370$	−0.161514	+	0.387411i	−0.00839673	+	0.0201405i
$371$	−2.05592	−	4.46234i	−0.106738	−	0.231673i
$372$	12.8883	−	41.2060i	0.668225	−	2.13643i
$373$	−26.5799	+	16.3386i	−1.37626	+	0.845982i	−0.996855	−	0.0792499i	$-0.974747\pi$
$373$	−26.5799	+	16.3386i	−1.37626	+	0.845982i	−0.379402	+	0.925232i	$0.623870\pi$
$374$	0.658392	−	0.160307i	0.0340447	−	0.00828925i
$375$	22.3762	−	8.61299i	1.15550	−	0.444773i
$376$	−1.09001	−	0.642741i	−0.0562131	−	0.0331468i
$377$	−7.45852	−	0.549097i	−0.384133	−	0.0282800i
$378$	−0.0230324	−	0.0367094i	−0.00118466	−	0.00188813i
$379$	−12.6088	+	28.7453i	−0.647673	+	1.47655i	0.218007	+	0.975947i	$0.430045\pi$
$379$	−12.6088	+	28.7453i	−0.647673	+	1.47655i	−0.865680	+	0.500598i	$0.833113\pi$
$380$	−7.75046	+	7.52609i	−0.397590	+	0.386080i
$381$	−7.04445	−	16.0597i	−0.360898	−	0.822765i
$382$	−0.0718169	+	0.105634i	−0.00367447	+	0.00540469i
$383$	−4.73607	+	14.2197i	−0.242002	+	0.726593i	0.755447	+	0.655210i	$0.227420\pi$
$383$	−4.73607	+	14.2197i	−0.242002	+	0.726593i	−0.997449	+	0.0713834i	$0.977259\pi$
$384$	3.33477	−	1.64929i	0.170177	−	0.0841650i
$385$	−1.46101	+	0.861508i	−0.0744602	+	0.0439065i
$386$	−0.205680	+	0.259307i	−0.0104688	+	0.0131984i
$387$	23.5093	−	5.26856i	1.19504	−	0.267816i
$388$	−2.37405	−	12.1538i	−0.120524	−	0.617015i
$389$	−27.4438	+	9.98874i	−1.39146	+	0.506449i	−0.925631	−	0.378427i	$-0.876465\pi$
$389$	−27.4438	+	9.98874i	−1.39146	+	0.506449i	−0.465827	+	0.884876i	$0.654243\pi$
$390$	0.184767	+	0.0596592i	0.00935602	+	0.00302096i
$391$	19.5957	+	12.0454i	0.990997	+	0.609164i
$392$	1.04303	−	0.908375i	0.0526809	−	0.0458799i
$393$	−25.6656	−	2.36428i	−1.29466	−	0.119262i
$394$	−0.0487287	−	0.166469i	−0.00245492	−	0.00838658i
$395$	3.37397	+	5.60356i	0.169763	+	0.281946i
$396$	9.46891	+	8.55739i	0.475830	+	0.430025i
$397$	14.3892	−	31.2314i	0.722171	−	1.56746i	−0.0979002	−	0.995196i	$-0.531213\pi$
$397$	14.3892	−	31.2314i	0.722171	−	1.56746i	0.820072	−	0.572261i	$-0.193934\pi$
$398$	−0.0776211	−	0.0843190i	−0.00389079	−	0.00422653i
$399$	−4.58513	−	1.12080i	−0.229543	−	0.0561104i
$400$	9.33775	−	10.1435i	0.466888	−	0.507175i
$401$	10.7842	+	25.8672i	0.538537	+	1.29175i	0.928643	+	0.370976i	$0.120977\pi$
$401$	10.7842	+	25.8672i	0.538537	+	1.29175i	−0.390105	+	0.920770i	$0.627561\pi$
$402$	−0.189953	−	0.537194i	−0.00947399	−	0.0267928i
$403$	7.32994	−	10.3666i	0.365130	−	0.516395i
$404$	9.21810	+	13.0370i	0.458617	+	0.648613i
$405$	4.44145	−	12.5606i	0.220697	−	0.624141i
$406$	−0.134782	+	0.00743612i	−0.00668911	+	0.000369048i
$407$	−17.2692	+	8.14952i	−0.856001	+	0.403957i
$408$	1.90571	+	0.986493i	0.0943466	+	0.0488387i
$409$	31.0715	−	17.5606i	1.53639	−	0.868315i	0.536688	−	0.843780i	$-0.319675\pi$
$409$	31.0715	−	17.5606i	1.53639	−	0.868315i	0.999699	−	0.0245344i	$-0.00781032\pi$
$410$	−0.310663	+	0.302218i	−0.0153426	+	0.0149255i
$411$	−27.2994	+	33.1478i	−1.34658	+	1.63506i
$412$	−18.3063	−	8.23120i	−0.901884	−	0.405522i
$413$	4.22922	−	0.866516i	0.208107	−	0.0426385i
$414$	−0.0259732	−	0.565100i	−0.00127651	−	0.0277732i
$415$	0.0502467	+	0.284963i	0.00246651	+	0.0139883i
$416$	0.811850	−	0.120188i	0.0398042	−	0.00589272i
$417$	9.95894	−	3.41891i	0.487691	−	0.167425i
$418$	0.641364	−	0.0229938i	0.0313701	−	0.00112466i
$419$	−9.02943	−	3.09981i	−0.441116	−	0.151435i	0.0951895	−	0.995459i	$-0.469654\pi$
$419$	−9.02943	−	3.09981i	−0.441116	−	0.151435i	−0.536306	+	0.844024i	$0.680181\pi$
$420$	−2.63868	−	0.490304i	−0.128754	−	0.0239244i
$421$	5.96097	+	3.81683i	0.290520	+	0.186021i	0.676413	−	0.736523i	$-0.263533\pi$
$421$	5.96097	+	3.81683i	0.290520	+	0.186021i	−0.385893	+	0.922544i	$0.626107\pi$
$422$	−0.132317	+	1.10275i	−0.00644109	+	0.0536811i
$423$	10.5240	−	8.83071i	0.511696	−	0.429364i
$424$	−0.0194325	+	2.11540i	−0.000943724	+	0.102733i
$425$	15.8291	+	1.75196i	0.767822	+	0.0849825i
$426$	−0.271771	−	0.329993i	−0.0131674	−	0.0159882i
$427$	−0.277738	−	1.01781i	−0.0134407	−	0.0492553i
$428$	−4.77411	+	20.4220i	−0.230765	+	0.987134i
$429$	4.41661	+	7.64979i	0.213236	+	0.369335i
$430$	0.344422	−	0.596557i	0.0166095	−	0.0287685i
$431$	−3.02695	−	2.83831i	−0.145803	−	0.136717i	0.607685	−	0.794178i	$-0.292098\pi$
$431$	−3.02695	−	2.83831i	−0.145803	−	0.136717i	−0.753488	+	0.657461i	$0.771630\pi$
$432$	−0.849555	−	7.08032i	−0.0408742	−	0.340652i
$433$	2.64155	−	5.46687i	0.126945	−	0.262721i	−0.827293	−	0.561771i	$-0.810120\pi$
$433$	2.64155	−	5.46687i	0.126945	−	0.262721i	0.954237	+	0.299050i	$0.0966698\pi$
$434$	0.107212	−	0.202533i	0.00514635	−	0.00972192i
$435$	−10.4851	−	11.8185i	−0.502724	−	0.566651i
$436$	0.895860	−	10.8114i	0.0429039	−	0.517773i
$437$	15.8779	+	14.9155i	0.759543	+	0.713506i
$438$	0.114184	+	1.37800i	0.00545592	+	0.0658432i
$439$	27.7246	−	29.0282i	1.32323	−	1.38544i	0.454018	−	0.890993i	$-0.349990\pi$
$439$	27.7246	−	29.0282i	1.32323	−	1.38544i	0.869208	−	0.494447i	$-0.164630\pi$
$440$	0.727219	−	0.0669905i	0.0346688	−	0.00319365i
$441$	5.52274	+	13.9638i	0.262988	+	0.664945i
$442$	0.221934	+	0.223982i	0.0105563	+	0.0106537i
$443$	−1.57369	−	4.72488i	−0.0747681	−	0.224486i	0.904713	−	0.426021i	$-0.140085\pi$
$443$	−1.57369	−	4.72488i	−0.0747681	−	0.224486i	−0.979481	+	0.201536i	$0.935407\pi$
$444$	−29.0759	−	8.22187i	−1.37988	−	0.390193i
$445$	−0.103316	+	0.140566i	−0.00489764	+	0.00666348i
$446$	0.0394455	−	0.0628687i	0.00186780	−	0.00297692i
$447$	16.0531	+	23.6121i	0.759286	+	1.11681i
$448$	−3.62136	+	1.02402i	−0.171093	+	0.0483805i
$449$	−11.6430	+	31.0970i	−0.549466	+	1.46756i	0.307180	+	0.951652i	$0.400615\pi$
$449$	−11.6430	+	31.0970i	−0.549466	+	1.46756i	−0.856645	+	0.515906i	$0.827455\pi$
$450$	−0.183242	−	0.346161i	−0.00863812	−	0.0163182i
$451$	−19.7047	+	0.724350i	−0.927857	+	0.0341083i
$452$	−5.16457	+	3.72336i	−0.242921	+	0.175132i
$453$	14.6524	−	6.58827i	0.688428	−	0.309544i
$454$	0.314231	−	1.15154i	0.0147476	−	0.0540445i
$455$	−0.694106	−	0.375631i	−0.0325402	−	0.0176099i
$456$	1.57946	+	1.27899i	0.0739650	+	0.0598943i
$457$	−4.15027	+	2.24602i	−0.194142	+	0.105064i	−0.570110	−	0.821568i	$-0.693100\pi$
$457$	−4.15027	+	2.24602i	−0.194142	+	0.105064i	0.375969	+	0.926632i	$0.377310\pi$
$458$	0.151399	+	0.647634i	0.00707441	+	0.0302619i
$459$	6.00885	−	5.63438i	0.280469	−	0.262990i
$460$	9.48882	+	7.96207i	0.442419	+	0.371233i
$461$	7.28561	−	8.52243i	0.339325	−	0.396929i	−0.564078	−	0.825721i	$-0.690768\pi$
$461$	7.28561	−	8.52243i	0.339325	−	0.396929i	0.903403	+	0.428792i	$0.141061\pi$
$462$	0.0967671	+	0.126711i	0.00450201	+	0.00589512i
$463$	36.0058	+	16.9916i	1.67333	+	0.789665i	0.998671	+	0.0515387i	$0.0164126\pi$
$463$	36.0058	+	16.9916i	1.67333	+	0.789665i	0.674662	+	0.738126i	$0.264289\pi$
$464$	−20.5795	−	8.35867i	−0.955379	−	0.388041i
$465$	26.3701	−	4.89993i	1.22288	−	0.227229i
$466$	−0.674501	−	0.0998549i	−0.0312457	−	0.00462569i
$467$	0.654684	+	23.7507i	0.0302952	+	1.09905i	0.850169	+	0.526509i	$0.176499\pi$
$467$	0.654684	+	23.7507i	0.0302952	+	1.09905i	−0.819874	+	0.572544i	$0.805957\pi$
$468$	−1.13853	+	5.82862i	−0.0526284	+	0.269428i
$469$	0.360217	+	2.28792i	0.0166333	+	0.105646i
$470$	0.0180347	−	0.392383i	0.000831881	−	0.0180993i
$471$	−51.8309	+	6.70261i	−2.38824	+	0.308840i
$472$	−1.80606	−	0.439743i	−0.0831307	−	0.0202408i
$473$	29.8226	−	9.62943i	1.37125	−	0.442761i
$474$	0.485204	−	0.377649i	0.0222861	−	0.0173460i
$475$	14.3492	+	4.64761i	0.658388	+	0.213247i
$476$	−3.43950	−	2.67707i	−0.157649	−	0.122703i
$477$	−21.5822	−	7.85528i	−0.988181	−	0.359669i
$478$	0.0113507	−	0.0720939i	0.000519168	−	0.00329750i
$479$	20.8916	+	4.28043i	0.954561	+	0.195578i	0.652566	−	0.757732i	$-0.273693\pi$
$479$	20.8916	+	4.28043i	0.954561	+	0.195578i	0.301995	+	0.953310i	$0.402347\pi$
$480$	1.40638	+	1.01392i	0.0641923	+	0.0462791i
$481$	−7.39370	−	4.92804i	−0.337124	−	0.224699i
$482$	−0.0844606	−	0.0585637i	−0.00384708	−	0.00266750i
$483$	−0.743352	+	5.36067i	−0.0338237	+	0.243919i
$484$	−4.29742	−	3.21981i	−0.195337	−	0.146355i
$485$	5.98304	−	4.83588i	0.271676	−	0.219586i
$486$	−0.954461	−	0.213900i	−0.0432952	−	0.00970269i
$487$	0.415271	−	15.0653i	0.0188177	−	0.682672i	−0.930128	−	0.367234i	$-0.880305\pi$
$487$	0.415271	−	15.0653i	0.0188177	−	0.682672i	0.948946	−	0.315438i	$-0.102151\pi$
$488$	−0.0788826	+	0.447366i	−0.00357085	+	0.0202513i
$489$	2.84109	+	0.367401i	0.128479	+	0.0166145i
$490$	0.400685	+	0.154231i	0.0181011	+	0.00696744i
$491$	−23.0706	−	29.0859i	−1.04116	−	1.31263i	−0.948447	−	0.316935i	$-0.897346\pi$
$491$	−23.0706	−	29.0859i	−1.04116	−	1.31263i	−0.0927141	−	0.995693i	$-0.529554\pi$
$492$	−24.2657	−	19.6131i	−1.09398	−	0.884227i
$493$	−6.29860	−	24.8726i	−0.283675	−	1.12021i
$494$	0.163108	+	0.250152i	0.00733860	+	0.0112549i
$495$	−1.94637	+	7.68605i	−0.0874829	+	0.345462i
$496$	30.1778	−	22.6105i	1.35502	−	1.01524i
$497$	0.841066	+	1.52061i	0.0377269	+	0.0682089i
$498$	0.0260333	−	0.00788079i	0.00116658	−	0.000353147i
$499$	−0.0446173	+	0.0741014i	−0.00199734	+	0.00331723i	−0.857691	−	0.514166i	$-0.828102\pi$
$499$	−0.0446173	+	0.0741014i	−0.00199734	+	0.00331723i	0.855694	+	0.517483i	$0.173131\pi$
$500$	20.2787	+	5.33395i	0.906890	+	0.238542i
$501$	22.9960	+	22.3708i	1.02738	+	0.999455i
$502$	0.449601	−	0.0497619i	0.0200667	−	0.00222098i
$503$	1.66799	+	16.4511i	0.0743719	+	0.733518i	0.962017	+	0.272990i	$0.0880126\pi$
$503$	1.66799	+	16.4511i	0.0743719	+	0.733518i	−0.887645	+	0.460528i	$0.847660\pi$
$504$	−0.0137847	+	0.214080i	−0.000614020	+	0.00953590i
$505$	−4.47877	+	8.85029i	−0.199303	+	0.393833i
$506$	−0.101071	−	0.728868i	−0.00449313	−	0.0324021i
$507$	12.3813	−	22.3849i	0.549873	−	0.994150i
$508$	3.21622	−	14.9956i	0.142697	−	0.665322i
$509$	8.92103	+	10.4355i	0.395418	+	0.462544i	0.921778	−	0.387717i	$-0.126736\pi$
$509$	8.92103	+	10.4355i	0.395418	+	0.462544i	−0.526361	+	0.850261i	$0.676444\pi$
$510$	0.00611882	+	0.666088i	0.000270946	+	0.0294949i
$511$	0.566964	−	5.59187i	0.0250810	−	0.247370i
$512$	4.00887	+	0.668963i	0.177169	+	0.0295643i
$513$	6.64991	−	4.07937i	0.293601	−	0.180109i
$514$	0.269456	−	0.0449642i	0.0118852	−	0.00198328i
$515$	−0.801234	−	12.4434i	−0.0353066	−	0.548321i
$516$	45.5935	+	19.5017i	2.00714	+	0.858516i
$517$	12.5780	−	12.6940i	0.553178	−	0.558283i
$518$	−0.143758	−	0.0710989i	−0.00631636	−	0.00312390i
$519$	24.1907	−	1.78093i	1.06186	−	0.0781739i
$520$	0.201255	+	0.273817i	0.00882560	+	0.0120077i
$521$	13.5583	+	36.2127i	0.594001	+	1.58651i	0.794798	+	0.606874i	$0.207577\pi$
$521$	13.5583	+	36.2127i	0.594001	+	1.58651i	−0.200797	+	0.979633i	$0.564353\pi$
$522$	−0.418774	+	0.472025i	−0.0183292	+	0.0206600i
$523$	19.0217	+	19.9160i	0.831761	+	0.870868i	0.993248	−	0.116007i	$-0.0370094\pi$
$523$	19.0217	+	19.9160i	0.831761	+	0.870868i	−0.161488	+	0.986875i	$0.551629\pi$
$524$	−16.9980	−	14.8036i	−0.742562	−	0.646698i
$525$	1.11855	+	3.57622i	0.0488177	+	0.156079i
$526$	0.682173	−	0.616504i	0.0297441	−	0.0268809i
$527$	41.6894	+	12.6202i	1.81602	+	0.549745i
$528$	5.50174	+	25.6518i	0.239432	+	1.11635i
$529$	1.20047	−	1.57194i	0.0521942	−	0.0683453i
$530$	−0.583173	+	0.301880i	−0.0253314	+	0.0131129i
$531$	11.0378	−	16.8947i	0.479002	−	0.733167i
$532$	−2.67947	−	3.14011i	−0.116170	−	0.136141i
$533$	−5.01834	−	7.68113i	−0.217368	−	0.332707i
$534$	0.0142762	+	0.00806845i	0.000617793	+	0.000349156i
$535$	−12.6003	+	3.31428i	−0.544757	+	0.143289i
$536$	0.280161	−	0.957095i	0.0121011	−	0.0413402i
$537$	−9.48698	+	23.9871i	−0.409394	+	1.03512i
$538$	−1.47985	+	0.632979i	−0.0638010	+	0.0272896i
$539$	8.81971	+	17.4282i	0.379892	+	0.750686i
$540$	3.64530	−	2.52760i	0.156869	−	0.108770i
$541$	−36.1689	+	0.664566i	−1.55502	+	0.0285719i	−0.789061	−	0.614314i	$-0.789433\pi$
$541$	−36.1689	+	0.664566i	−1.55502	+	0.0285719i	−0.765962	+	0.642886i	$0.777737\pi$
$542$	−1.53008	+	0.0281136i	−0.0657226	+	0.00120758i
$543$	17.4681	−	12.1121i	0.749627	−	0.519780i
$544$	1.27135	+	2.51225i	0.0545086	+	0.107712i
$545$	6.19639	−	2.65039i	0.265424	−	0.113530i
$546$	−0.0272851	+	0.0689884i	−0.00116770	+	0.00295243i
$547$	−3.46951	+	11.8527i	−0.148345	+	0.506784i	−0.999846	−	0.0175708i	$-0.994407\pi$
$547$	−3.46951	+	11.8527i	−0.148345	+	0.506784i	0.851500	+	0.524354i	$0.175693\pi$
$548$	−36.3193	+	9.55315i	−1.55148	+	0.408090i
$549$	−4.29359	−	2.42659i	−0.183246	−	0.103564i
$550$	−0.278655	−	0.426514i	−0.0118819	−	0.0181866i
$551$	−1.09367	−	24.2756i	−0.0465921	−	1.03418i
$552$	1.27453	−	1.95081i	0.0542475	−	0.0830320i
$553$	−2.21953	+	1.14894i	−0.0943839	+	0.0488580i
$554$	−0.0964973	+	0.126358i	−0.00409978	+	0.00536842i
$555$	−3.93646	−	18.3537i	−0.167094	−	0.779073i
$556$	8.81344	+	2.66800i	0.373773	+	0.113149i
$557$	25.7281	−	23.2514i	1.09014	−	0.985195i	0.0901928	−	0.995924i	$-0.471252\pi$
$557$	25.7281	−	23.2514i	1.09014	−	0.985195i	0.999942	+	0.0107297i	$0.00341543\pi$
$558$	−0.319781	−	1.02240i	−0.0135374	−	0.0432815i
$559$	10.9968	+	9.57710i	0.465114	+	0.405068i
$560$	−1.61900	−	1.69512i	−0.0684153	−	0.0716320i
$561$	−20.1118	+	22.6692i	−0.849119	+	0.957094i
$562$	0.481016	+	1.28474i	0.0202905	+	0.0541934i
$563$	−20.0223	−	27.2414i	−0.843841	−	1.14809i	−0.987369	−	0.158440i	$-0.949353\pi$
$563$	−20.0223	−	27.2414i	−0.843841	−	1.14809i	0.143528	−	0.989646i	$-0.454155\pi$
$564$	28.2008	−	2.07614i	1.18747	−	0.0874214i
$565$	−3.54535	−	1.75344i	−0.149154	−	0.0737677i
$566$	−0.102107	+	0.103050i	−0.00429189	+	0.00433150i
$567$	4.68042	+	2.00196i	0.196559	+	0.0840744i
$568$	−0.0480784	−	0.746671i	−0.00201733	−	0.0313296i
$569$	30.1921	−	5.03817i	1.26572	−	0.211211i	0.506611	−	0.862175i	$-0.330898\pi$
$569$	30.1921	−	5.03817i	1.26572	−	0.211211i	0.759109	+	0.650964i	$0.225635\pi$
$570$	−0.121507	+	0.619062i	−0.00508938	+	0.0259296i
$571$	0.784658	+	0.130936i	0.0328369	+	0.00547951i	0.180990	−	0.983485i	$-0.442070\pi$
$571$	0.784658	+	0.130936i	0.0328369	+	0.00547951i	−0.148153	+	0.988964i	$0.547333\pi$
$572$	−0.779247	+	7.68559i	−0.0325820	+	0.321351i
$573$	−0.0524742	−	5.71228i	−0.00219214	−	0.238634i
$574$	−0.107611	−	0.125879i	−0.00449159	−	0.00525409i
$575$	3.62667	−	16.9093i	0.151243	−	0.705168i
$576$	−8.51479	+	15.3944i	−0.354783	+	0.641434i
$577$	−1.37481	−	9.91441i	−0.0572341	−	0.412742i	−0.997402	−	0.0720319i	$-0.977052\pi$
$577$	−1.37481	−	9.91441i	−0.0572341	−	0.412742i	0.940168	−	0.340711i	$-0.110668\pi$
$578$	−0.0964378	+	0.190566i	−0.00401129	+	0.00792652i
$579$	0.951123	−	14.7712i	0.0395273	−	0.613870i
$580$	−1.39377	−	13.7465i	−0.0578731	−	0.570793i
$581$	−0.109893	+	0.0121629i	−0.00455912	+	0.000504603i
$582$	−0.518341	−	0.504250i	−0.0214859	−	0.0209018i
$583$	−28.8924	−	7.59965i	−1.19660	−	0.314745i
$584$	−1.24833	+	2.07325i	−0.0516562	+	0.0857918i
$585$	−3.53111	+	1.06894i	−0.145993	+	0.0441951i
$586$	−0.244202	−	0.441508i	−0.0100879	−	0.0182385i
$587$	−22.2056	+	16.6374i	−0.916523	+	0.686698i	−0.949837	−	0.312747i	$-0.898751\pi$
$587$	−22.2056	+	16.6374i	−0.916523	+	0.686698i	0.0333131	+	0.999445i	$0.489394\pi$
$588$	−7.58744	+	29.9621i	−0.312901	+	1.23562i
$589$	36.2633	+	19.6673i	1.49420	+	0.810376i
$590$	−0.141646	−	0.559348i	−0.00583148	−	0.0230280i
$591$	6.03295	+	4.87622i	0.248162	+	0.200581i
$592$	−16.4000	−	20.6761i	−0.674036	−	0.849780i
$593$	−1.61485	−	0.621584i	−0.0663138	−	0.0255254i	0.325842	−	0.945424i	$-0.394352\pi$
$593$	−1.61485	−	0.621584i	−0.0663138	−	0.0255254i	−0.392155	+	0.919899i	$0.628270\pi$
$594$	−0.261339	−	0.0337955i	−0.0107229	−	0.00138665i
$595$	0.470180	−	2.66653i	0.0192755	−	0.109317i
$596$	−0.688034	+	24.9606i	−0.0281830	+	1.02243i
$597$	5.00137	+	1.12083i	0.204692	+	0.0458726i
$598$	0.266294	−	0.215236i	0.0108896	−	0.00880164i
$599$	−31.2989	−	23.4505i	−1.27884	−	0.958161i	−0.278842	−	0.960337i	$-0.589951\pi$
$599$	−31.2989	−	23.4505i	−1.27884	−	0.958161i	−0.999998	+	0.00217607i	$0.999307\pi$
$600$	0.221605	−	1.59810i	0.00904699	−	0.0652422i
$601$	−6.26070	−	4.34107i	−0.255379	−	0.177076i	0.435198	−	0.900335i	$-0.356678\pi$
$601$	−6.26070	−	4.34107i	−0.255379	−	0.177076i	−0.690577	+	0.723259i	$0.742643\pi$
$602$	0.219016	+	0.145978i	0.00892643	+	0.00594964i
$603$	8.78252	+	6.33170i	0.357652	+	0.257847i
$604$	13.7639	+	2.82005i	0.560045	+	0.114746i
$605$	0.518824	−	3.29531i	0.0210932	−	0.133973i
$606$	0.876166	+	0.318898i	0.0355918	+	0.0129544i
$607$	−5.68402	−	4.42405i	−0.230707	−	0.179567i	0.492262	−	0.870447i	$-0.336170\pi$
$607$	−5.68402	−	4.42405i	−0.230707	−	0.179567i	−0.722969	+	0.690881i	$0.757223\pi$
$608$	0.699669	+	2.57323i	0.0283753	+	0.104358i
$609$	4.76392	−	3.70791i	0.193044	−	0.150252i
$610$	−0.134189	+	0.0433282i	−0.00543315	+	0.00175431i
$611$	8.07931	+	1.96716i	0.326854	+	0.0795830i
$612$	−20.2063	+	2.61302i	−0.816792	+	0.105625i
$613$	1.07515	−	23.3922i	0.0434250	−	0.944801i	−0.858475	−	0.512856i	$-0.828588\pi$
$613$	1.07515	−	23.3922i	0.0434250	−	0.944801i	0.901900	−	0.431945i	$-0.142173\pi$
$614$	0.00495427	+	0.0314671i	0.000199938	+	0.00126991i
$615$	3.71593	−	19.0235i	0.149841	−	0.767101i
$616$	0.00768893	+	0.278940i	0.000309796	+	0.0112388i
$617$	39.9382	+	5.91256i	1.60785	+	0.238031i	0.889260	−	0.457402i	$-0.151220\pi$
$617$	39.9382	+	5.91256i	1.60785	+	0.238031i	0.718591	+	0.695432i	$0.244787\pi$
$618$	−1.15239	+	0.214130i	−0.0463557	+	0.00861355i
$619$	−1.17101	−	0.475624i	−0.0470669	−	0.0191169i	0.352655	−	0.935754i	$-0.385279\pi$
$619$	−1.17101	−	0.475624i	−0.0470669	−	0.0191169i	−0.399721	+	0.916637i	$0.630893\pi$
$620$	21.2130	+	10.0106i	0.851933	+	0.402037i
$621$	−5.42901	−	7.10897i	−0.217859	−	0.285273i
$622$	0.694391	−	0.812272i	0.0278425	−	0.0325691i
$623$	−0.0510626	−	0.0428466i	−0.00204578	−	0.00171661i
$624$	−8.90520	+	8.35023i	−0.356493	+	0.334277i
$625$	−0.973200	−	4.16302i	−0.0389280	−	0.166521i
$626$	0.258224	−	0.139744i	0.0103207	−	0.00558528i
$627$	−22.9851	+	17.1888i	−0.917935	+	0.686455i
$628$	−40.1968	−	21.7534i	−1.60403	−	0.868057i
$629$	8.02503	−	29.4089i	0.319979	−	1.17261i
$630$	−0.0607340	+	0.0273083i	−0.00241970	+	0.00108799i
$631$	−17.6957	+	12.7576i	−0.704454	+	0.507872i	−0.879027	−	0.476773i	$-0.841806\pi$
$631$	−17.6957	+	12.7576i	−0.704454	+	0.507872i	0.174572	+	0.984644i	$0.444146\pi$
$632$	1.07540	−	0.0395320i	0.0427770	−	0.00157250i
$633$	−23.2384	−	43.8994i	−0.923643	−	1.74485i
$634$	0.163531	−	0.436773i	0.00649466	−	0.0173465i
$635$	9.16811	−	2.59249i	0.363825	−	0.102880i
$636$	−26.5787	−	39.0940i	−1.05392	−	1.55018i
$637$	−4.83058	+	7.69904i	−0.191395	+	0.305047i
$638$	−0.486110	+	0.661376i	−0.0192453	+	0.0261841i
$639$	7.81670	+	2.21035i	0.309224	+	0.0874401i
$640$	0.638702	+	1.91766i	0.0252469	+	0.0758021i
$641$	−10.7638	−	10.8631i	−0.425144	−	0.429067i	0.464605	−	0.885518i	$-0.346196\pi$
$641$	−10.7638	−	10.8631i	−0.425144	−	0.429067i	−0.889749	+	0.456451i	$0.849120\pi$
$642$	0.450432	+	1.13888i	0.0177771	+	0.0449481i
$643$	38.8583	−	3.57957i	1.53242	−	0.141164i	0.707622	−	0.706592i	$-0.249768\pi$
$643$	38.8583	−	3.57957i	1.53242	−	0.141164i	0.824798	+	0.565427i	$0.191289\pi$
$644$	−3.26899	+	3.42269i	−0.128816	+	0.134873i
$645$	2.54397	+	30.7011i	0.100169	+	1.20886i
$646$	−0.637410	+	0.802107i	−0.0250785	+	0.0315585i
$647$	−2.53323	+	30.5715i	−0.0995914	+	1.20189i	0.745218	+	0.666821i	$0.232346\pi$
$647$	−2.53323	+	30.5715i	−0.0995914	+	1.20189i	−0.844809	+	0.535068i	$0.820286\pi$
$648$	−1.45465	−	1.63962i	−0.0571439	−	0.0644103i
$649$	12.2813	−	23.2005i	0.482083	−	0.910699i
$650$	0.103140	−	0.213455i	0.00404548	−	0.00837241i
$651$	1.22093	+	10.1755i	0.0478522	+	0.398807i
$652$	1.82757	+	1.71368i	0.0715732	+	0.0671128i
$653$	−24.4315	+	42.3167i	−0.956080	+	1.65598i	−0.224204	+	0.974542i	$0.571978\pi$
$653$	−24.4315	+	42.3167i	−0.956080	+	1.65598i	−0.731876	+	0.681437i	$0.761355\pi$
$654$	−0.316755	−	0.548636i	−0.0123861	−	0.0214534i
$655$	3.18756	−	13.6353i	0.124548	−	0.532776i
$656$	−7.17384	−	26.2896i	−0.280091	−	1.02643i
$657$	−16.7030	−	20.2813i	−0.651646	−	0.791250i
$658$	0.149177	+	0.0165109i	0.00581551	+	0.000643661i
$659$	−0.0247851	+	2.69807i	−0.000965489	+	0.105102i	0.998093	+	0.0617242i	$0.0196599\pi$
$659$	−0.0247851	+	2.69807i	−0.000965489	+	0.105102i	−0.999059	+	0.0433779i	$0.986188\pi$
$660$	−12.5014	+	10.4900i	−0.486618	+	0.408321i
$661$	−0.110042	+	0.917106i	−0.00428013	+	0.0356713i	−0.994858	−	0.101279i	$-0.967707\pi$
$661$	−0.110042	+	0.917106i	−0.00428013	+	0.0356713i	0.990578	+	0.136950i	$0.0437300\pi$
$662$	−1.39812	−	0.895220i	−0.0543394	−	0.0347937i
$663$	−13.8641	−	2.57614i	−0.538435	−	0.100049i
$664$	0.0450265	+	0.0154576i	0.00174737	+	0.000599873i
$665$	0.945309	−	2.38381i	0.0366575	−	0.0924403i
$666$	−0.709092	+	0.243431i	−0.0274767	+	0.00943278i
$667$	−27.5616	+	4.08029i	−1.06719	+	0.157989i
$668$	4.87208	+	27.6309i	0.188506	+	1.06907i
$669$	0.152396	+	3.31570i	0.00589198	+	0.128192i
$670$	0.303262	−	0.0621346i	0.0117160	−	0.00240047i
$671$	−5.85097	−	2.63082i	−0.225874	−	0.101562i
$672$	−0.421149	+	0.511373i	−0.0162462	+	0.0197266i
$673$	−16.6753	+	16.2220i	−0.642786	+	0.625312i	−0.944666	−	0.328034i	$-0.893614\pi$
$673$	−16.6753	+	16.2220i	−0.642786	+	0.625312i	0.301880	+	0.953346i	$0.402386\pi$
$674$	0.810488	−	0.458061i	0.0312188	−	0.0176438i
$675$	−5.49997	−	2.84707i	−0.211694	−	0.109584i
$676$	20.2318	−	9.54763i	0.778147	−	0.367217i
$677$	26.3447	−	1.45348i	1.01251	−	0.0558617i	0.458773	−	0.888553i	$-0.348289\pi$
$677$	26.3447	−	1.45348i	1.01251	−	0.0558617i	0.553737	+	0.832692i	$0.313201\pi$
$678$	−0.123948	+	0.350529i	−0.00476018	+	0.0134620i
$679$	1.69707	+	2.40012i	0.0651274	+	0.0921083i
$680$	−0.673084	+	0.951927i	−0.0258116	+	0.0365047i
$681$	17.7962	+	50.3283i	0.681950	+	1.92858i
$682$	−0.536200	−	1.28614i	−0.0205322	−	0.0492489i
$683$	2.42842	−	2.63797i	0.0929209	−	0.100939i	−0.687530	−	0.726156i	$-0.741305\pi$
$683$	2.42842	−	2.63797i	0.0929209	−	0.100939i	0.780451	+	0.625217i	$0.214989\pi$
$684$	−19.2432	−	1.43425i	−0.735784	−	0.0548401i
$685$	−15.8011	−	17.1646i	−0.603729	−	0.655824i
$686$	−0.139573	+	0.302939i	−0.00532891	+	0.0115663i
$687$	−22.0677	−	19.9434i	−0.841934	−	0.760886i
$688$	22.3409	+	37.1042i	0.851738	+	1.41459i
$689$	−3.90537	−	13.3417i	−0.148783	−	0.508277i
$690$	0.720292	+	0.0663524i	0.0274211	+	0.00252599i
$691$	−19.8060	+	17.2490i	−0.753454	+	0.656184i	−0.945655	−	0.325172i	$-0.894578\pi$
$691$	−19.8060	+	17.2490i	−0.753454	+	0.656184i	0.192201	+	0.981356i	$0.438437\pi$
$692$	18.0718	+	11.1087i	0.686986	+	0.422289i
$693$	−2.88297	−	0.930882i	−0.109515	−	0.0353613i
$694$	−1.77773	+	0.647041i	−0.0674818	+	0.0245614i
$695$	1.09669	+	5.61446i	0.0416000	+	0.212969i
$696$	−2.53640	+	0.568421i	−0.0961421	+	0.0215459i
$697$	19.5615	−	24.6618i	0.740943	−	0.934132i
$698$	0.288681	−	0.170225i	0.0109268	−	0.00644311i
$699$	27.3334	−	13.5184i	1.03385	−	0.511313i
$700$	−1.03551	+	3.10905i	−0.0391386	+	0.117511i
$701$	−10.6034	+	15.5963i	−0.400487	+	0.589065i	−0.972993	−	0.230835i	$-0.925854\pi$
$701$	−10.6034	+	15.5963i	−0.400487	+	0.589065i	0.572506	+	0.819900i	$0.305971\pi$
$702$	−0.0492553	−	0.112291i	−0.00185902	−	0.00423814i
$703$	13.0597	−	25.7487i	0.492557	−	0.971130i
$704$	−9.19223	+	20.9562i	−0.346445	+	0.789816i
$705$	9.33624	+	14.8802i	0.351623	+	0.560421i
$706$	0.217422	+	0.0160067i	0.00818280	+	0.000602419i
$707$	−3.26473	−	1.92509i	−0.122783	−	0.0724006i
$708$	38.7653	−	14.9215i	1.45689	−	0.560783i
$709$	−1.95334	+	0.475602i	−0.0733591	+	0.0178616i	−0.273081	−	0.961991i	$-0.588043\pi$
$709$	−1.95334	+	0.475602i	−0.0733591	+	0.0178616i	0.199722	+	0.979853i	$0.435996\pi$
$710$	0.197864	−	0.121626i	0.00742570	−	0.00456456i
$711$	−3.48761	+	11.1505i	−0.130796	+	0.418177i
$712$	0.0120100	+	0.0260674i	0.000450093	+	0.000976916i
$713$	18.2011	−	43.6576i	0.681638	−	1.63499i
$714$	−0.254136	−	0.0140211i	−0.00951079	−	0.000524725i
$715$	−4.44626	+	1.80591i	−0.166281	+	0.0675373i
$716$	−18.9980	+	12.1645i	−0.709989	+	0.454609i
$717$	1.42000	+	2.93880i	0.0530310	+	0.109751i
$718$	−0.394856	−	0.0145150i	−0.0147359	−	0.000541696i
$719$	−1.81847	+	1.21204i	−0.0678175	+	0.0452016i	−0.588063	−	0.808815i	$-0.700109\pi$
$719$	−1.81847	+	1.21204i	−0.0678175	+	0.0452016i	0.520246	+	0.854017i	$0.325840\pi$
$720$	−10.9558	−	0.201301i	−0.408298	−	0.00750204i
$721$	4.76445			0.177437
$722$	−0.744445	+	0.622364i	−0.0277054	+	0.0231620i
$723$	4.59641			0.170942
$724$	18.5865	+	0.341507i	0.690761	+	0.0126920i
$725$	−16.0519	+	10.6989i	−0.596154	+	0.397348i
$726$	−0.313366	−	0.0115194i	−0.0116301	−	0.000427526i
$727$	3.91234	+	8.09686i	0.145101	+	0.300296i	0.960342	−	0.278826i	$-0.0899452\pi$
$727$	3.91234	+	8.09686i	0.145101	+	0.300296i	−0.815241	+	0.579122i	$0.803396\pi$
$728$	−0.109350	+	0.0700173i	−0.00405279	+	0.00259501i
$729$	10.6857	−	4.34017i	0.395767	−	0.160747i
$730$	−0.750079	−	0.0413830i	−0.0277617	−	0.00153165i
$731$	−19.2515	+	46.1769i	−0.712041	+	1.70791i
$732$	−4.24778	−	9.21971i	−0.157002	−	0.340770i
$733$	−5.12353	+	16.3808i	−0.189242	+	0.605040i	0.810570	+	0.585642i	$0.199158\pi$
$733$	−5.12353	+	16.3808i	−0.189242	+	0.605040i	−0.999812	+	0.0193984i	$0.993825\pi$
$734$	0.386458	−	0.237555i	0.0142644	−	0.00876832i
$735$	−18.6559	+	4.54238i	−0.688135	+	0.167548i
$736$	2.85343	−	1.09834i	0.105179	−	0.0404852i
$737$	12.1314	+	7.15344i	0.446865	+	0.263500i
$738$	−0.772062	−	0.0568393i	−0.0284200	−	0.00209228i
$739$	17.9660	+	28.6345i	0.660892	+	1.05334i	0.993886	+	0.110408i	$0.0352158\pi$
$739$	17.9660	+	28.6345i	0.660892	+	1.05334i	−0.332995	+	0.942929i	$0.608059\pi$
$740$	6.59427	−	15.0334i	0.242410	−	0.552640i
$741$	−12.3690	−	5.03696i	−0.454388	−	0.185037i
$742$	−0.100791	−	0.229781i	−0.00370017	−	0.00843553i
$743$	−19.3568	+	28.4714i	−0.710132	+	1.04451i	0.286135	+	0.958189i	$0.407629\pi$
$743$	−19.3568	+	28.4714i	−0.710132	+	1.04451i	−0.996267	+	0.0863256i	$0.972487\pi$
$744$	1.39441	−	4.18661i	0.0511215	−	0.153489i
$745$	−13.9046	+	6.87685i	−0.509425	+	0.251948i
$746$	−1.37253	+	0.809333i	−0.0502520	+	0.0296318i
$747$	−0.321186	+	0.404931i	−0.0117516	+	0.0148156i
$748$	−25.8612	+	5.79563i	−0.945579	+	0.211909i
$749$	−0.954395	−	4.88597i	−0.0348728	−	0.178529i
$750$	1.15063	−	0.418797i	0.0420152	−	0.0152923i
$751$	22.1993	+	7.16793i	0.810065	+	0.261562i	0.683081	−	0.730343i	$-0.260640\pi$
$751$	22.1993	+	7.16793i	0.810065	+	0.261562i	0.126984	+	0.991905i	$0.459470\pi$
$752$	21.0399	+	12.9332i	0.767247	+	0.471625i
$753$	−15.2554	+	13.2859i	−0.555938	+	0.484167i
$754$	−0.380326	−	0.0350352i	−0.0138507	−	0.00127591i
$755$	2.45202	+	8.37670i	0.0892383	+	0.304859i
$756$	0.874294	+	1.45205i	0.0317978	+	0.0528104i
$757$	−36.6742	−	33.1438i	−1.33295	−	1.20463i	−0.961056	−	0.276355i	$-0.910874\pi$
$757$	−36.6742	−	33.1438i	−1.33295	−	1.20463i	−0.371890	−	0.928277i	$-0.621290\pi$
$758$	−0.670792	+	1.45594i	−0.0243643	+	0.0528821i
$759$	22.2881	+	24.2113i	0.809007	+	0.878816i
$760$	−0.806144	+	0.754532i	−0.0292419	+	0.0273697i
$761$	15.9724	−	17.3507i	0.578999	−	0.628961i	−0.375626	−	0.926772i	$-0.622572\pi$
$761$	15.9724	−	17.3507i	0.578999	−	0.628961i	0.954625	+	0.297810i	$0.0962563\pi$
$762$	−0.344631	−	0.826639i	−0.0124847	−	0.0299460i
$763$	0.858479	+	2.42781i	0.0310790	+	0.0878927i
$764$	2.88425	−	4.07914i	0.104349	−	0.147578i
$765$	−7.30750	−	10.3348i	−0.264203	−	0.373657i
$766$	−0.255171	+	0.721632i	−0.00921969	+	0.0260736i
$767$	12.1964	−	0.672892i	0.440385	−	0.0242967i
$768$	−32.6178	+	15.3927i	−1.17699	+	0.555436i
$769$	−13.1265	−	6.79493i	−0.473352	−	0.245032i	0.206408	−	0.978466i	$-0.433823\pi$
$769$	−13.1265	−	6.79493i	−0.473352	−	0.245032i	−0.679760	+	0.733434i	$0.737916\pi$
$770$	−0.0754095	+	0.0426189i	−0.00271757	+	0.00153588i
$771$	−8.75705	+	8.51899i	−0.315377	+	0.306804i
$772$	8.22928	−	9.99227i	0.296178	−	0.359630i
$773$	9.34591	+	4.20228i	0.336149	+	0.151146i	0.571142	−	0.820852i	$-0.306501\pi$
$773$	9.34591	+	4.20228i	0.336149	+	0.151146i	−0.234993	+	0.971997i	$0.575507\pi$
$774$	1.20536	−	0.246963i	0.0433257	−	0.00887689i
$775$	−1.50362	−	32.7143i	−0.0540114	−	1.17513i
$776$	−0.219782	−	1.24644i	−0.00788970	−	0.0447447i
$777$	7.09510	−	1.05038i	0.254535	−	0.0376821i
$778$	−1.41069	+	0.484290i	−0.0505756	+	0.0173626i
$779$	22.8550	−	19.1423i	0.818866	−	0.685845i
$780$	−7.18232	−	2.46569i	−0.257168	−	0.0882859i
$781$	10.3886	+	1.93035i	0.371734	+	0.0690733i
$782$	0.989280	+	0.633439i	0.0353766	+	0.0226517i
$783$	−1.18868	+	9.90668i	−0.0424801	+	0.354036i
$784$	−20.6793	+	17.3520i	−0.738545	+	0.619713i
$785$	0.260820	−	28.3926i	0.00930906	−	1.01337i
$786$	−1.30830	−	0.144802i	−0.0466655	−	0.00516493i
$787$	−6.34128	−	7.69978i	−0.226042	−	0.274468i	0.646599	−	0.762830i	$-0.276191\pi$
$787$	−6.34128	−	7.69978i	−0.226042	−	0.274468i	−0.872641	+	0.488363i	$0.837594\pi$
$788$	1.78590	+	6.54467i	0.0636200	+	0.233144i
$789$	−9.36051	+	40.0411i	−0.333243	+	1.42550i
$790$	0.167022	+	0.289290i	0.00594236	+	0.0102925i
$791$	0.755650	−	1.30882i	0.0268678	−	0.0465364i
$792$	0.951552	+	0.892252i	0.0338119	+	0.0317048i
$793$	−0.355629	−	2.96387i	−0.0126288	−	0.105250i
$794$	0.764030	−	1.58121i	0.0271144	−	0.0561151i
$795$	13.7396	−	25.9554i	0.487295	−	0.920544i
$796$	2.97474	+	3.35301i	0.105437	+	0.118844i
$797$	0.936474	−	11.3016i	0.0331716	−	0.400322i	−0.959691	−	0.281057i	$-0.909315\pi$
$797$	0.936474	−	11.3016i	0.0331716	−	0.400322i	0.992863	−	0.119264i	$-0.0380536\pi$
$798$	−0.233071	−	0.0615314i	−0.00825061	−	0.00217819i
$799$	2.35583	+	28.4306i	0.0833431	+	1.00580i
$800$	1.46212	−	1.53087i	0.0516938	−	0.0541244i
$801$	−0.310286	+	0.0285831i	−0.0109634	+	0.00100993i
$802$	0.526386	+	1.33093i	0.0185873	+	0.0469967i
$803$	−24.0552	−	24.2772i	−0.848888	−	0.856722i
$804$	7.04201	+	21.1431i	0.248353	+	0.745661i
$805$	−2.82933	−	0.800059i	−0.0997209	−	0.0281984i
$806$	0.384001	−	0.522453i	0.0135259	−	0.0184026i
$807$	38.2565	−	60.9737i	1.34669	−	2.14638i
$808$	0.917511	+	1.34954i	0.0322779	+	0.0474768i
$809$	−51.5260	+	14.5702i	−1.81156	+	0.512260i	−0.997636	−	0.0687146i	$-0.978110\pi$
$809$	−51.5260	+	14.5702i	−1.81156	+	0.512260i	−0.813922	+	0.580974i	$0.802672\pi$
$810$	0.238570	−	0.637192i	0.00838250	−	0.0223887i
$811$	18.4005	+	34.7603i	0.646130	+	1.22060i	0.962324	+	0.271904i	$0.0876534\pi$
$811$	18.4005	+	34.7603i	0.646130	+	1.22060i	−0.316194	+	0.948695i	$0.602405\pi$
$812$	5.27590	−	0.193944i	0.185148	−	0.00680609i
$813$	55.5162	−	40.0240i	1.94704	−	1.40370i
$814$	−0.889431	+	0.399923i	−0.0311745	+	0.0140173i
$815$	−0.409725	+	1.50150i	−0.0143520	+	0.0525951i
$816$	−36.8341	−	19.9336i	−1.28945	−	0.697815i
$817$	−26.6756	+	39.1599i	−0.933260	+	1.37003i
$818$	1.60303	−	0.867514i	0.0560485	−	0.0303319i
$819$	−0.320898	−	1.37269i	−0.0112131	−	0.0479657i
$820$	12.3654	−	11.5948i	0.431820	−	0.404909i
$821$	−9.76470	−	8.19356i	−0.340790	−	0.285957i	0.456289	−	0.889832i	$-0.349178\pi$
$821$	−9.76470	−	8.19356i	−0.340790	−	0.285957i	−0.797079	+	0.603875i	$0.793623\pi$
$822$	−1.42504	+	1.66696i	−0.0497040	+	0.0581418i
$823$	17.5707	+	23.0078i	0.612476	+	0.802001i	0.992405	−	0.123015i	$-0.0392563\pi$
$823$	17.5707	+	23.0078i	0.612476	+	0.802001i	−0.379929	+	0.925016i	$0.624052\pi$
$824$	−1.85525	−	0.875511i	−0.0646305	−	0.0304999i
$825$	21.1097	+	8.57404i	0.734947	+	0.298510i
$826$	0.216762	−	0.0402775i	0.00754213	−	0.00140143i
$827$	−8.58902	−	1.27154i	−0.298670	−	0.0442158i	−0.00456665	−	0.999990i	$-0.501454\pi$
$827$	−8.58902	−	1.27154i	−0.298670	−	0.0442158i	−0.294103	+	0.955774i	$0.595021\pi$
$828$	0.609638	+	22.1165i	0.0211864	+	0.768603i
$829$	4.35839	−	22.3125i	0.151373	−	0.774947i	−0.826040	−	0.563611i	$-0.809412\pi$
$829$	4.35839	−	22.3125i	0.151373	−	0.774947i	0.977414	−	0.211336i	$-0.0677813\pi$
$830$	0.00229831	+	0.0145977i	7.97754e−5	+	0.000506694i
$831$	0.326461	−	7.10284i	0.0113248	−	0.246395i
$832$	−10.5602	+	1.36562i	−0.366111	+	0.0473443i
$833$	−30.2971	−	7.37679i	−1.04973	−	0.255591i
$834$	0.511723	−	0.165230i	0.0177195	−	0.00572146i
$835$	−13.7547	+	10.7057i	−0.476002	+	0.370487i
$836$	−25.0966	+	0.438335i	−0.867986	+	0.0151601i
$837$	−13.3670	−	10.4040i	−0.462031	−	0.359613i
$838$	−0.458145	−	0.166751i	−0.0158264	−	0.00576033i
$839$	−0.219231	+	1.39244i	−0.00756868	+	0.0480725i	−0.991323	−	0.131445i	$-0.958038\pi$
$839$	−0.219231	+	1.39244i	−0.00756868	+	0.0480725i	0.983755	+	0.179517i	$0.0574536\pi$
$840$	−0.268724	−	0.0550581i	−0.00927184	−	0.00189969i
$841$	1.68643	+	1.21582i	0.0581528	+	0.0419249i
$842$	0.300794	+	0.200485i	0.0103660	+	0.00690916i
$843$	−50.4168	−	34.9582i	−1.73645	−	1.20402i
$844$	5.96651	−	43.0273i	0.205376	−	1.48106i
$845$	11.1224	+	8.33334i	0.382621	+	0.286676i
$846$	0.545655	−	0.441033i	0.0187600	−	0.0151630i
$847$	1.24379	+	0.278741i	0.0427373	+	0.00957765i
$848$	1.13767	−	41.2727i	0.0390679	−	1.41731i
$849$	1.12659	−	6.38920i	0.0386644	−	0.219277i
$850$	0.806608	+	0.104308i	0.0276664	+	0.00357774i
$851$	−30.8934	−	11.8914i	−1.05901	−	0.407633i
$852$	10.3903	+	13.0995i	0.355967	+	0.448780i
$853$	20.5107	+	16.5781i	0.702273	+	0.567622i	0.912026	−	0.410132i	$-0.134517\pi$
$853$	20.5107	+	16.5781i	0.702273	+	0.567622i	−0.209753	+	0.977754i	$0.567266\pi$
$854$	−0.0132268	−	0.0522313i	−0.000452610	−	0.00178732i
$855$	−4.80543	−	10.9824i	−0.164342	−	0.375589i
$856$	−0.526207	+	2.07794i	−0.0179854	+	0.0710226i
$857$	−36.3983	+	27.2711i	−1.24334	+	0.931564i	−0.999270	−	0.0381937i	$-0.987840\pi$
$857$	−36.3983	+	27.2711i	−1.24334	+	0.931564i	−0.244071	+	0.969757i	$0.578483\pi$
$858$	0.218340	+	0.394751i	0.00745402	+	0.0134766i
$859$	19.1869	−	5.80827i	0.654650	−	0.198176i	0.0550602	−	0.998483i	$-0.482465\pi$
$859$	19.1869	−	5.80827i	0.654650	−	0.198176i	0.599590	+	0.800307i	$0.295330\pi$
$860$	−13.8970	+	23.0805i	−0.473885	+	0.787039i
$861$	7.16260	+	1.88400i	0.244101	+	0.0642064i
$862$	−0.151897	−	0.147768i	−0.00517363	−	0.00503298i
$863$	2.73430	−	0.302632i	0.0930765	−	0.0103017i	−0.0633493	−	0.997991i	$-0.520178\pi$
$863$	2.73430	−	0.302632i	0.0930765	−	0.0103017i	0.156426	+	0.987690i	$0.450003\pi$
$864$	−0.110450	−	1.08935i	−0.00375759	−	0.0370605i
$865$	−0.846795	+	13.1510i	−0.0287919	+	0.447146i
$866$	0.140010	−	0.276667i	0.00475773	−	0.00940153i
$867$	−1.31195	−	9.46109i	−0.0445561	−	0.321315i
$868$	−4.33798	+	7.84291i	−0.147241	+	0.266206i
$869$	−3.18698	+	14.8593i	−0.108111	+	0.504066i
$870$	−0.524297	−	0.613302i	−0.0177753	−	0.0207929i
$871$	0.0601972	+	6.55300i	0.00203970	+	0.222040i
$872$	0.111847	−	1.10313i	0.00378761	−	0.0373566i
$873$	13.5537	+	2.26171i	0.458722	+	0.0765472i
$874$	0.796752	+	0.776501i	0.0269505	+	0.0262655i
$875$	−4.90944	+	0.819241i	−0.165969	+	0.0276954i
$876$	−3.47500	−	53.9677i	−0.117409	−	1.82340i
$877$	5.97996	+	2.55781i	0.201929	+	0.0863712i	0.491852	−	0.870679i	$-0.336320\pi$
$877$	5.97996	+	2.55781i	0.201929	+	0.0863712i	−0.289924	+	0.957050i	$0.593630\pi$
$878$	1.44289	−	1.45620i	0.0486951	−	0.0491445i
$879$	20.2256	+	10.0031i	0.682193	+	0.337395i
$880$	−14.2149	+	1.04650i	−0.479184	+	0.0352776i
$881$	−15.8522	−	21.5677i	−0.534074	−	0.726633i	0.452170	−	0.891932i	$-0.350650\pi$
$881$	−15.8522	−	21.5677i	−0.534074	−	0.726633i	−0.986244	+	0.165298i	$0.947141\pi$
$882$	0.268897	+	0.718193i	0.00905424	+	0.0241828i
$883$	−24.4536	+	27.5631i	−0.822928	+	0.927572i	−0.998379	−	0.0569158i	$-0.981873\pi$
$883$	−24.4536	+	27.5631i	−0.822928	+	0.927572i	0.175451	+	0.984488i	$0.443862\pi$
$884$	−8.51764	−	8.91812i	−0.286479	−	0.299949i
$885$	19.4595	+	16.9473i	0.654123	+	0.569676i
$886$	−0.0759215	−	0.242734i	−0.00255063	−	0.00815482i
$887$	7.08048	−	6.39889i	0.237739	−	0.214854i	−0.542963	−	0.839756i	$-0.682698\pi$
$887$	7.08048	−	6.39889i	0.237739	−	0.214854i	0.780702	+	0.624903i	$0.214861\pi$
$888$	−2.95580	−	0.894780i	−0.0991902	−	0.0300268i
$889$	0.763440	+	3.55954i	0.0256050	+	0.119383i
$890$	−0.00540732	+	0.00708056i	−0.000181254	+	0.000237341i
$891$	27.4893	−	14.2299i	0.920928	−	0.476720i
$892$	−1.58766	+	2.43010i	−0.0531589	+	0.0813658i
$893$	−3.24318	+	26.8233i	−0.108529	+	0.897608i
$894$	0.797538	+	1.22072i	0.0266737	+	0.0408271i
$895$	−12.2005	−	6.89534i	−0.407819	−	0.230486i
$896$	−0.746902	+	0.196460i	−0.0249523	+	0.00656325i
$897$	−4.30185	+	14.6961i	−0.143634	+	0.490690i
$898$	−0.623679	+	1.57693i	−0.0208125	+	0.0526227i
$899$	−48.5099	+	20.7492i	−1.61790	+	0.692025i
$900$	6.91686	+	13.6681i	0.230562	+	0.455603i
$901$	39.1929	−	27.1758i	1.30571	−	0.905356i
$902$	−1.00682	+	0.0184993i	−0.0335236	+	0.000615961i
$903$	−11.7691	+	0.216245i	−0.391651	+	0.00719617i
$904$	−0.534754	+	0.370790i	−0.0177856	+	0.0123323i
$905$	5.21451	+	10.3042i	0.173336	+	0.342522i
$906$	0.754349	−	0.322658i	0.0250616	−	0.0107196i
$907$	8.80970	−	22.2747i	0.292521	−	0.739618i	−0.706955	−	0.707259i	$-0.749932\pi$
$907$	8.80970	−	22.2747i	0.292521	−	0.739618i	0.999476	−	0.0323599i	$-0.0103023\pi$
$908$	−13.1152	+	44.8046i	−0.435242	+	1.48689i
$909$	−17.1343	+	4.50687i	−0.568309	+	0.149484i
$910$	−0.0350895	−	0.0198314i	−0.00116321	−	0.000657405i
$911$	17.8207	+	27.2766i	0.590426	+	0.903714i	0.999963	−	0.00857943i	$-0.00273095\pi$
$911$	17.8207	+	27.2766i	0.590426	+	0.903714i	−0.409537	+	0.912293i	$0.634310\pi$
$912$	−30.3628	−	25.5244i	−1.00541	−	0.845198i
$913$	−0.367712	+	0.562825i	−0.0121695	+	0.0186268i
$914$	−0.214025	+	0.110791i	−0.00707933	+	0.00366463i
$915$	3.82750	−	5.01188i	0.126533	−	0.165688i
$916$	−5.45504	−	25.4341i	−0.180240	−	0.840366i
$917$	5.12101	+	1.55023i	0.169111	+	0.0511931i
$918$	0.312105	−	0.282061i	0.0103010	−	0.00930940i
$919$	−12.0757	−	38.6081i	−0.398340	−	1.27356i	−0.910083	−	0.414425i	$-0.863983\pi$
$919$	−12.0757	−	38.6081i	−0.398340	−	1.27356i	0.511744	−	0.859138i	$-0.329000\pi$
$920$	0.954705	+	0.831453i	0.0314757	+	0.0274122i
$921$	−0.983946	−	1.03021i	−0.0324221	−	0.0339465i
$922$	0.380008	−	0.428330i	0.0125149	−	0.0141063i
$923$	1.72400	+	4.60460i	0.0567462	+	0.151562i
$924$	−3.69297	−	5.02447i	−0.121490	−	0.165293i
$925$	−22.8576	+	1.68278i	−0.751553	+	0.0553294i
$926$	1.82256	+	0.901391i	0.0598931	+	0.0296215i
$927$	15.6762	−	15.8209i	0.514876	−	0.519627i
$928$	−3.13574	−	1.34125i	−0.102936	−	0.0440288i
$929$	2.06589	+	32.0839i	0.0677798	+	1.05264i	0.881745	+	0.471726i	$0.156369\pi$
$929$	2.06589	+	32.0839i	0.0677798	+	1.05264i	−0.813966	+	0.580913i	$0.802696\pi$
$930$	1.35108	−	0.225456i	0.0443038	−	0.00739300i
$931$	−26.6964	−	12.6280i	−0.874940	−	0.413866i
$932$	26.3042	+	4.38939i	0.861622	+	0.143779i
$933$	−4.82084	+	47.5472i	−0.157827	+	1.55662i
$934$	0.0111461	+	1.21336i	0.000364713	+	0.0397022i
$935$	−10.6985	−	12.5146i	−0.349877	−	0.409273i
$936$	−0.127289	+	0.593484i	−0.00416057	+	0.0193986i
$937$	−10.5394	+	19.0549i	−0.344309	+	0.622497i	−0.989995	−	0.141106i	$-0.954934\pi$
$937$	−10.5394	+	19.0549i	−0.344309	+	0.622497i	0.645686	+	0.763603i	$0.276572\pi$
$938$	0.0162466	+	0.117162i	0.000530471	+	0.00382548i
$939$	−5.92901	+	11.7160i	−0.193486	+	0.382339i
$940$	−0.987166	+	15.3310i	−0.0321978	+	0.500041i
$941$	−0.883996	−	8.71871i	−0.0288174	−	0.284222i	−0.999106	−	0.0422717i	$-0.986540\pi$
$941$	−0.883996	−	8.71871i	−0.0288174	−	0.284222i	0.970289	−	0.241950i	$-0.0777870\pi$
$942$	−2.65284	+	0.293616i	−0.0864341	+	0.00956652i
$943$	−24.5011	−	23.8351i	−0.797866	−	0.776176i
$944$	35.0856	+	9.22865i	1.14194	+	0.300367i
$945$	−0.543139	+	0.902057i	−0.0176683	+	0.0293439i
$946$	1.53182	−	0.463711i	0.0498036	−	0.0150765i
$947$	0.0701515	+	0.126831i	0.00227962	+	0.00412146i	0.876202	−	0.481944i	$-0.160069\pi$
$947$	0.0701515	+	0.126831i	0.00227962	+	0.00412146i	−0.873922	+	0.486065i	$0.838432\pi$
$948$	−19.2449	+	14.4191i	−0.625046	+	0.468311i
$949$	3.90395	−	15.4163i	0.126728	−	0.500436i
$950$	0.728329	+	0.250775i	0.0236301	+	0.00813622i
$951$	5.12021	+	20.2192i	0.166034	+	0.655654i
$952$	−0.346453	−	0.280025i	−0.0112286	−	0.00907567i
$953$	−36.7840	−	46.3748i	−1.19155	−	1.50223i	−0.818590	−	0.574379i	$-0.805244\pi$
$953$	−36.7840	−	46.3748i	−1.19155	−	1.50223i	−0.372959	−	0.927848i	$-0.621657\pi$
$954$	−1.09464	−	0.421349i	−0.0354404	−	0.0136417i
$955$	3.07794	+	0.398030i	0.0995998	+	0.0128799i
$956$	−0.495661	+	2.81103i	−0.0160308	+	0.0909152i
$957$	1.01146	−	36.6939i	0.0326959	−	1.18615i
$958$	1.06273	+	0.238164i	0.0343354	+	0.00769474i
$959$	6.93296	−	5.60367i	0.223877	−	0.180952i
$960$	−18.0024	−	13.4882i	−0.581026	−	0.435329i
$961$	8.04478	−	58.0147i	0.259509	−	1.87144i
$962$	−0.372908	−	0.258569i	−0.0120230	−	0.00833659i
$963$	−19.3646	−	12.9069i	−0.624016	−	0.415919i
$964$	3.26070	+	2.35078i	0.105020	+	0.0757136i
$965$	7.87803	+	1.61411i	0.253603	+	0.0519601i
$966$	−0.0429859	+	0.273025i	−0.00138305	+	0.00878443i
$967$	38.5741	+	14.0398i	1.24046	+	0.451490i	0.877167	−	0.480186i	$-0.159431\pi$
$967$	38.5741	+	14.0398i	1.24046	+	0.451490i	0.363291	+	0.931676i	$0.381653\pi$
$968$	−0.433104	−	0.337098i	−0.0139205	−	0.0108348i
$969$	2.98571	−	45.7216i	0.0959147	−	1.46879i
$970$	0.310039	−	0.241313i	0.00995474	−	0.00774808i
$971$	54.0083	−	17.4387i	1.73321	−	0.559636i	0.739655	−	0.672986i	$-0.234989\pi$
$971$	54.0083	−	17.4387i	1.73321	−	0.559636i	0.993555	+	0.113351i	$0.0361584\pi$
$972$	37.1699	+	9.05020i	1.19223	+	0.290285i
$973$	−2.16777	+	0.280330i	−0.0694956	+	0.00898695i
$974$	0.0353385	−	0.768862i	0.00113232	−	0.0246359i
$975$	1.64891	+	10.4731i	0.0528075	+	0.335407i
$976$	1.69971	−	8.70156i	0.0544063	−	0.278530i
$977$	0.634135	+	23.0053i	0.0202878	+	0.736003i	0.939561	+	0.342382i	$0.111234\pi$
$977$	0.634135	+	23.0053i	0.0202878	+	0.736003i	−0.919273	+	0.393621i	$0.871222\pi$
$978$	0.144725	+	0.0214255i	0.00462779	+	0.000685111i
$979$	−0.398499	+	0.0740467i	−0.0127361	+	0.00236654i
$980$	−15.5577	−	6.31899i	−0.496973	−	0.201853i
$981$	10.8864	+	5.13744i	0.347578	+	0.164026i
$982$	−1.15072	−	1.50681i	−0.0367211	−	0.0480841i
$983$	−30.0219	+	35.1185i	−0.957551	+	1.12011i	0.0351357	+	0.999383i	$0.488814\pi$
$983$	−30.0219	+	35.1185i	−0.957551	+	1.12011i	−0.992686	+	0.120723i	$0.961479\pi$
$984$	−2.44287	−	2.04981i	−0.0778758	−	0.0653455i
$985$	−3.07430	+	2.88271i	−0.0979552	+	0.0918507i
$986$	−0.298279	−	1.27593i	−0.00949913	−	0.0406340i
$987$	−5.90319	+	3.19465i	−0.187901	+	0.101687i
$988$	−6.19852	−	9.89922i	−0.197201	−	0.314936i
$989$	47.7794	+	25.8569i	1.51930	+	0.822202i
$990$	−0.106595	+	0.390633i	−0.00338782	+	0.0124151i
$991$	−30.5973	+	13.7577i	−0.971956	+	0.437029i	−0.833002	−	0.553270i	$-0.813380\pi$
$991$	−30.5973	+	13.7577i	−0.971956	+	0.437029i	−0.138954	+	0.990299i	$0.544374\pi$
$992$	4.69660	−	3.38599i	0.149117	−	0.107505i
$993$	74.1955	−	2.72745i	2.35452	−	0.0865530i
$994$	0.0415192	+	0.0784336i	0.00131691	+	0.00248776i
$995$	−0.976385	+	2.60781i	−0.0309535	+	0.0826731i
$996$	−1.02368	+	0.289469i	−0.0324365	+	0.00917216i
$997$	12.5702	+	18.4892i	0.398103	+	0.585559i	0.972467	−	0.233041i	$-0.0748677\pi$
$997$	12.5702	+	18.4892i	0.398103	+	0.585559i	−0.574364	+	0.818600i	$0.694751\pi$
$998$	−0.00234774	+	0.00374185i	−7.43163e−5	+	0.000118446i
$999$	−7.02073	+	9.55205i	−0.222126	+	0.302214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.k.a.4.16	✓	3348
361.271	even	171	inner	361.2.k.a.271.16	yes	3348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.k.a.4.16	✓	3348	1.1	even	1	trivial
361.2.k.a.271.16	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+(0.0510612 + 0.000938197i) q^{2} +(-1.90048 + 1.26671i) q^{3} +(-1.99604 - 0.0733752i) q^{4} +(-0.539848 - 1.11725i) q^{5} +(-0.0982292 + 0.0628965i) q^{6} +(0.439274 - 0.178418i) q^{7} +(-0.203836 - 0.0112460i) q^{8} +(0.852866 - 2.04570i) q^{9} +(-0.0265171 - 0.0575549i) q^{10} +(0.860613 - 2.75153i) q^{11} +(3.88638 - 2.38895i) q^{12} +(1.30343 - 0.317361i) q^{13} +(0.0225973 - 0.00869810i) q^{14} +(2.44120 + 1.43949i) q^{15} +(3.97360 + 0.292537i) q^{16} +(2.44607 + 3.89857i) q^{17} +(0.0454676 - 0.103656i) q^{18} +(1.52469 + 4.08354i) q^{19} +(0.995582 + 2.26970i) q^{20} +(-0.608828 + 0.895510i) q^{21} +(0.0465254 - 0.139689i) q^{22} +(4.47984 - 2.21561i) q^{23} +(0.401632 - 0.236828i) q^{24} +(2.15036 - 2.71103i) q^{25} +(0.0668524 - 0.0149820i) q^{26} +(-0.343119 - 1.75658i) q^{27} +(-0.889902 + 0.323898i) q^{28} +(-5.30516 - 1.71298i) q^{29} +(0.123300 + 0.0757924i) q^{30} +(7.13697 - 6.21559i) q^{31} +(0.609194 + 0.0561181i) q^{32} +(1.84980 + 6.31937i) q^{33} +(0.121242 + 0.201361i) q^{34} +(-0.436479 - 0.394462i) q^{35} +(-1.85246 + 4.02073i) q^{36} +(-4.48600 - 4.87309i) q^{37} +(0.0740213 + 0.209941i) q^{38} +(-2.07513 + 2.25420i) q^{39} +(0.0974761 + 0.233808i) q^{40} +(-2.28009 - 6.44819i) q^{41} +(-0.0319277 + 0.0451546i) q^{42} +(6.27575 + 8.87566i) q^{43} +(-1.91971 + 5.42903i) q^{44} +(-2.74598 + 0.151500i) q^{45} +(0.230825 - 0.108929i) q^{46} +(5.50470 + 2.84952i) q^{47} +(-7.92231 + 4.47743i) q^{48} +(-4.85635 + 4.72433i) q^{49} +(0.112343 - 0.136411i) q^{50} +(-9.58704 - 4.31070i) q^{51} +(-2.62498 + 0.537827i) q^{52} +(-0.475784 - 10.3517i) q^{53} +(-0.0158721 - 0.0900150i) q^{54} +(-3.53876 + 0.523887i) q^{55} +(-0.0915464 + 0.0314279i) q^{56} +(-8.07028 - 5.82936i) q^{57} +(-0.269281 - 0.0924442i) q^{58} +(8.95213 + 1.66343i) q^{59} +(-4.76712 - 3.05241i) q^{60} +(0.265097 - 2.20936i) q^{61} +(0.370254 - 0.310680i) q^{62} +(0.00965276 - 1.05079i) q^{63} +(-7.88930 - 0.873187i) q^{64} +(-1.05823 - 1.28493i) q^{65} +(0.0885245 + 0.324410i) q^{66} +(-1.11200 + 4.75676i) q^{67} +(-4.59640 - 7.96120i) q^{68} +(-5.70732 + 9.88536i) q^{69} +(-0.0219171 - 0.0205512i) q^{70} +(0.436637 + 3.63900i) q^{71} +(-0.196851 + 0.407396i) q^{72} +(5.54614 - 10.4772i) q^{73} +(-0.224489 - 0.253035i) q^{74} +(-0.652634 + 7.87613i) q^{75} +(-2.74371 - 8.26281i) q^{76} +(-0.112877 - 1.36223i) q^{77} +(-0.108074 + 0.113155i) q^{78} +(-5.24912 + 0.483542i) q^{79} +(-1.81831 - 4.59745i) q^{80} +(7.55713 + 7.62687i) q^{81} +(-0.110375 - 0.331392i) q^{82} +(-0.224397 - 0.0634533i) q^{83} +(1.28096 - 1.74280i) q^{84} +(3.03519 - 4.83751i) q^{85} +(0.312120 + 0.459090i) q^{86} +(12.2522 - 3.46459i) q^{87} +(-0.206368 + 0.551184i) q^{88} +(-0.0657750 - 0.124255i) q^{89} +(-0.140355 + 0.00515951i) q^{90} +(0.515939 - 0.371963i) q^{91} +(-9.10453 + 4.09375i) q^{92} +(-5.69033 + 20.8530i) q^{93} +(0.278404 + 0.150664i) q^{94} +(3.73926 - 3.90796i) q^{95} +(-1.22885 + 0.665018i) q^{96} +(1.41130 + 6.03706i) q^{97} +(-0.252404 + 0.236674i) q^{98} +(-4.89482 - 4.10724i) 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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