LMFDB - Embedded newform 115.2.l.a.107.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,2,Mod(7,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	115.107
Dual form			115.2.l.a.43.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23839 + 0.927048i) q^{2} +(-1.46916 - 0.547968i) q^{3} +(0.110730 - 0.377111i) q^{4} +(1.69332 + 1.46036i) q^{5} +(2.32738 - 0.683382i) q^{6} +(-4.02961 + 0.876587i) q^{7} +(-0.868729 - 2.32915i) q^{8} +(-0.409093 - 0.354481i) q^{9} +(-3.45082 - 0.238708i) q^{10} +(-4.51811 + 0.649606i) q^{11} +(-0.369324 + 0.493360i) q^{12} +(-0.844524 + 3.88221i) q^{13} +(4.17759 - 4.82120i) q^{14} +(-1.68753 - 3.07339i) q^{15} +(3.89634 + 2.50403i) q^{16} +(0.141248 - 0.258676i) q^{17} +(0.835238 + 0.0597374i) q^{18} +(3.49008 + 1.02478i) q^{19} +(0.738221 - 0.476866i) q^{20} +(6.40047 + 0.920248i) q^{21} +(4.99297 - 4.99297i) q^{22} +(-0.292826 - 4.78688i) q^{23} +3.89793i q^{24} +(0.734685 + 4.94573i) q^{25} +(-2.55315 - 5.59062i) q^{26} +(2.66120 + 4.87362i) q^{27} +(-0.115627 + 1.61667i) q^{28} +(0.403824 + 1.37530i) q^{29} +(4.93900 + 2.24164i) q^{30} +(-2.77678 + 6.08030i) q^{31} +(-2.18744 + 0.156449i) q^{32} +(6.99378 + 1.52140i) q^{33} +(0.0648851 + 0.451286i) q^{34} +(-8.10356 - 4.40034i) q^{35} +(-0.178977 + 0.115022i) q^{36} +(0.220858 + 3.08799i) q^{37} +(-5.27211 + 1.96640i) q^{38} +(3.36807 - 5.24081i) q^{39} +(1.93037 - 5.21266i) q^{40} +(-6.08818 - 7.02614i) q^{41} +(-8.77940 + 4.79391i) q^{42} +(0.482569 - 1.29382i) q^{43} +(-0.255316 + 1.77576i) q^{44} +(-0.175056 - 1.19767i) q^{45} +(4.80030 + 5.65657i) q^{46} +(9.04049 + 9.04049i) q^{47} +(-4.35221 - 5.81388i) q^{48} +(9.10189 - 4.15669i) q^{49} +(-5.49476 - 5.44366i) q^{50} +(-0.349262 + 0.302637i) q^{51} +(1.37051 + 0.748357i) q^{52} +(-0.184392 - 0.847638i) q^{53} +(-7.81368 - 3.56839i) q^{54} +(-8.59928 - 5.49808i) q^{55} +(5.54234 + 8.62405i) q^{56} +(-4.56593 - 3.41802i) q^{57} +(-1.77506 - 1.32879i) q^{58} +(-2.33805 - 3.63807i) q^{59} +(-1.34587 + 0.296070i) q^{60} +(-3.31298 - 1.51299i) q^{61} +(-2.19799 - 10.1040i) q^{62} +(1.95921 + 1.06981i) q^{63} +(-4.43677 + 3.84448i) q^{64} +(-7.09949 + 5.34053i) q^{65} +(-10.0714 + 4.59948i) q^{66} +(0.270684 + 0.361592i) q^{67} +(-0.0819094 - 0.0819094i) q^{68} +(-2.19285 + 7.19315i) q^{69} +(14.1147 - 2.06305i) q^{70} +(-0.537154 + 3.73599i) q^{71} +(-0.470249 + 1.26079i) q^{72} +(-3.83749 + 2.09543i) q^{73} +(-3.13623 - 3.61940i) q^{74} +(1.63073 - 7.66864i) q^{75} +(0.772913 - 1.20268i) q^{76} +(17.6368 - 6.57817i) q^{77} +(0.687502 + 9.61254i) q^{78} +(-8.40008 + 5.39840i) q^{79} +(2.94098 + 9.93019i) q^{80} +(-1.00803 - 7.01097i) q^{81} +(14.0531 + 3.05707i) q^{82} +(0.939647 - 0.0672048i) q^{83} +(1.05576 - 2.31179i) q^{84} +(0.616939 - 0.231749i) q^{85} +(0.601822 + 2.04962i) q^{86} +(0.160338 - 2.24181i) q^{87} +(5.43804 + 9.95903i) q^{88} +(1.99112 + 4.35995i) q^{89} +(1.32709 + 1.32090i) q^{90} -16.3841i q^{91} +(-1.83761 - 0.419623i) q^{92} +(7.41134 - 7.41134i) q^{93} +(-19.5766 - 2.81470i) q^{94} +(4.41329 + 6.83207i) q^{95} +(3.29943 + 0.968799i) q^{96} +(-7.77981 - 0.556423i) q^{97} +(-7.41825 + 13.5855i) q^{98} +(2.07860 + 1.33583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−1.23839	+	0.927048i	−0.875675	+	0.655522i	−0.939541	−	0.342436i	$-0.888748\pi$
$2$	−1.23839	+	0.927048i	−0.875675	+	0.655522i	0.0638660	+	0.997958i	$0.479657\pi$
$3$	−1.46916	−	0.547968i	−0.848219	−	0.316369i	−0.112496	−	0.993652i	$-0.535885\pi$
$3$	−1.46916	−	0.547968i	−0.848219	−	0.316369i	−0.735723	+	0.677283i	$0.763157\pi$
$4$	0.110730	−	0.377111i	0.0553649	−	0.188556i
$5$	1.69332	+	1.46036i	0.757277	+	0.653094i
$5$	1.69332	+	1.46036i	0.757277	+	0.653094i
$6$	2.32738	−	0.683382i	0.950151	−	0.278989i
$7$	−4.02961	+	0.876587i	−1.52305	+	0.331319i	−0.894719	−	0.446629i	$-0.852624\pi$
$7$	−4.02961	+	0.876587i	−1.52305	+	0.331319i	−0.628329	+	0.777948i	$0.716261\pi$
$8$	−0.868729	−	2.32915i	−0.307142	−	0.823480i
$9$	−0.409093	−	0.354481i	−0.136364	−	0.118160i
$10$	−3.45082	−	0.238708i	−1.09125	−	0.0754861i
$11$	−4.51811	+	0.649606i	−1.36226	+	0.195864i	−0.784392	−	0.620266i	$-0.787025\pi$
$11$	−4.51811	+	0.649606i	−1.36226	+	0.195864i	−0.577869	+	0.816129i	$0.696116\pi$
$12$	−0.369324	+	0.493360i	−0.106615	+	0.142421i
$13$	−0.844524	+	3.88221i	−0.234229	+	1.07673i	0.698347	+	0.715759i	$0.253919\pi$
$13$	−0.844524	+	3.88221i	−0.234229	+	1.07673i	−0.932576	+	0.360973i	$0.882444\pi$
$14$	4.17759	−	4.82120i	1.11651	−	1.28852i
$15$	−1.68753	−	3.07339i	−0.435718	−	0.793545i
$16$	3.89634	+	2.50403i	0.974085	+	0.626007i
$17$	0.141248	−	0.258676i	0.0342576	−	0.0627382i	−0.859989	−	0.510312i	$-0.829530\pi$
$17$	0.141248	−	0.258676i	0.0342576	−	0.0627382i	0.894247	+	0.447574i	$0.147712\pi$
$18$	0.835238	+	0.0597374i	0.196867	+	0.0140802i
$19$	3.49008	+	1.02478i	0.800680	+	0.235101i	0.656377	−	0.754433i	$-0.272088\pi$
$19$	3.49008	+	1.02478i	0.800680	+	0.235101i	0.144303	+	0.989534i	$0.453906\pi$
$20$	0.738221	−	0.476866i	0.165071	−	0.106630i
$21$	6.40047	+	0.920248i	1.39670	+	0.200815i
$22$	4.99297	−	4.99297i	1.06450	−	1.06450i
$23$	−0.292826	−	4.78688i	−0.0610583	−	0.998134i
$23$	−0.292826	−	4.78688i	−0.0610583	−	0.998134i
$24$			3.89793i			0.795661i
$25$	0.734685	+	4.94573i	0.146937	+	0.989146i
$26$	−2.55315	−	5.59062i	−0.500714	−	1.09641i
$27$	2.66120	+	4.87362i	0.512147	+	0.937928i
$28$	−0.115627	+	1.61667i	−0.0218514	+	0.305523i
$29$	0.403824	+	1.37530i	0.0749882	+	0.255386i	0.988452	−	0.151533i	$-0.0484211\pi$
$29$	0.403824	+	1.37530i	0.0749882	+	0.255386i	−0.913464	+	0.406920i	$0.866603\pi$
$30$	4.93900	+	2.24164i	0.901734	+	0.409265i
$31$	−2.77678	+	6.08030i	−0.498724	+	1.09205i	0.478157	+	0.878274i	$0.341305\pi$
$31$	−2.77678	+	6.08030i	−0.498724	+	1.09205i	−0.976882	+	0.213780i	$0.931422\pi$
$32$	−2.18744	+	0.156449i	−0.386689	+	0.0276565i
$33$	6.99378	+	1.52140i	1.21746	+	0.264842i
$34$	0.0648851	+	0.451286i	0.0111277	+	0.0773949i
$35$	−8.10356	−	4.40034i	−1.36975	−	0.743793i
$36$	−0.178977	+	0.115022i	−0.0298296	+	0.0191703i
$37$	0.220858	+	3.08799i	0.0363088	+	0.507663i	0.982768	+	0.184841i	$0.0591769\pi$
$37$	0.220858	+	3.08799i	0.0363088	+	0.507663i	−0.946460	+	0.322822i	$0.895369\pi$
$38$	−5.27211	+	1.96640i	−0.855249	+	0.318991i
$39$	3.36807	−	5.24081i	0.539322	−	0.839202i
$40$	1.93037	−	5.21266i	0.305218	−	0.824195i
$41$	−6.08818	−	7.02614i	−0.950814	−	1.09730i	−0.995159	−	0.0982818i	$-0.968665\pi$
$41$	−6.08818	−	7.02614i	−0.950814	−	1.09730i	0.0443444	−	0.999016i	$-0.485880\pi$
$42$	−8.77940	+	4.79391i	−1.35469	+	0.739717i
$43$	0.482569	−	1.29382i	0.0735911	−	0.197305i	−0.894946	−	0.446174i	$-0.852786\pi$
$43$	0.482569	−	1.29382i	0.0735911	−	0.197305i	0.968537	+	0.248869i	$0.0800589\pi$
$44$	−0.255316	+	1.77576i	−0.0384903	+	0.267706i
$45$	−0.175056	−	1.19767i	−0.0260958	−	0.178539i
$46$	4.80030	+	5.65657i	0.707766	+	0.834016i
$47$	9.04049	+	9.04049i	1.31869	+	1.31869i	0.914812	+	0.403879i	$0.132338\pi$
$47$	9.04049	+	9.04049i	1.31869	+	1.31869i	0.403879	+	0.914812i	$0.367662\pi$
$48$	−4.35221	−	5.81388i	−0.628188	−	0.839161i
$49$	9.10189	−	4.15669i	1.30027	−	0.593813i
$50$	−5.49476	−	5.44366i	−0.777076	−	0.769850i
$51$	−0.349262	+	0.302637i	−0.0489064	+	0.0423776i
$52$	1.37051	+	0.748357i	0.190056	+	0.103778i
$53$	−0.184392	−	0.847638i	−0.0253282	−	0.116432i	0.962747	−	0.270404i	$-0.0871572\pi$
$53$	−0.184392	−	0.847638i	−0.0253282	−	0.116432i	−0.988075	+	0.153972i	$0.950794\pi$
$54$	−7.81368	−	3.56839i	−1.06331	−	0.485596i
$55$	−8.59928	−	5.49808i	−1.15953	−	0.741361i
$56$	5.54234	+	8.62405i	0.740626	+	1.15244i
$57$	−4.56593	−	3.41802i	−0.604773	−	0.452727i
$58$	−1.77506	−	1.32879i	−0.233077	−	0.174479i
$59$	−2.33805	−	3.63807i	−0.304388	−	0.473636i	0.655039	−	0.755595i	$-0.272652\pi$
$59$	−2.33805	−	3.63807i	−0.304388	−	0.473636i	−0.959427	+	0.281959i	$0.909016\pi$
$60$	−1.34587	+	0.296070i	−0.173751	+	0.0382225i
$61$	−3.31298	−	1.51299i	−0.424184	−	0.193718i	0.191873	−	0.981420i	$-0.438544\pi$
$61$	−3.31298	−	1.51299i	−0.424184	−	0.193718i	−0.616057	+	0.787701i	$0.711271\pi$
$62$	−2.19799	−	10.1040i	−0.279145	−	1.28321i
$63$	1.95921	+	1.06981i	0.246838	+	0.134784i
$64$	−4.43677	+	3.84448i	−0.554596	+	0.480561i
$65$	−7.09949	+	5.34053i	−0.880584	+	0.662411i
$66$	−10.0714	+	4.59948i	−1.23971	+	0.566156i
$67$	0.270684	+	0.361592i	0.0330694	+	0.0441755i	0.816771	−	0.576962i	$-0.195762\pi$
$67$	0.270684	+	0.361592i	0.0330694	+	0.0441755i	−0.783702	+	0.621137i	$0.786671\pi$
$68$	−0.0819094	−	0.0819094i	−0.00993297	−	0.00993297i
$69$	−2.19285	+	7.19315i	−0.263988	+	0.865953i
$70$	14.1147	−	2.06305i	1.68703	−	0.246581i
$71$	−0.537154	+	3.73599i	−0.0637485	+	0.443380i	0.932802	+	0.360390i	$0.117356\pi$
$71$	−0.537154	+	3.73599i	−0.0637485	+	0.443380i	−0.996550	+	0.0829907i	$0.973553\pi$
$72$	−0.470249	+	1.26079i	−0.0554194	+	0.148585i
$73$	−3.83749	+	2.09543i	−0.449145	+	0.245252i	−0.687868	−	0.725836i	$-0.741453\pi$
$73$	−3.83749	+	2.09543i	−0.449145	+	0.245252i	0.238723	+	0.971088i	$0.423271\pi$
$74$	−3.13623	−	3.61940i	−0.364579	−	0.420746i
$75$	1.63073	−	7.66864i	0.188301	−	0.885498i
$76$	0.772913	−	1.20268i	0.0886592	−	0.137956i
$77$	17.6368	−	6.57817i	2.00989	−	0.749652i
$78$	0.687502	+	9.61254i	0.0778443	+	1.08841i
$79$	−8.40008	+	5.39840i	−0.945083	+	0.607368i	−0.919832	−	0.392313i	$-0.871675\pi$
$79$	−8.40008	+	5.39840i	−0.945083	+	0.607368i	−0.0252511	+	0.999681i	$0.508039\pi$
$80$	2.94098	+	9.93019i	0.328811	+	1.11023i
$81$	−1.00803	−	7.01097i	−0.112003	−	0.778997i
$82$	14.0531	+	3.05707i	1.55191	+	0.337597i
$83$	0.939647	−	0.0672048i	0.103140	−	0.00737669i	−0.0196740	−	0.999806i	$-0.506263\pi$
$83$	0.939647	−	0.0672048i	0.103140	−	0.00737669i	0.122814	+	0.992430i	$0.460808\pi$
$84$	1.05576	−	2.31179i	0.115193	−	0.252237i
$85$	0.616939	−	0.231749i	0.0669165	−	0.0251367i
$86$	0.601822	+	2.04962i	0.0648961	+	0.221016i
$87$	0.160338	−	2.24181i	0.0171900	−	0.240347i
$88$	5.43804	+	9.95903i	0.579697	+	1.06164i
$89$	1.99112	+	4.35995i	0.211058	+	0.462153i	0.985321	−	0.170711i	$-0.0546064\pi$
$89$	1.99112	+	4.35995i	0.211058	+	0.462153i	−0.774263	+	0.632864i	$0.781879\pi$
$90$	1.32709	+	1.32090i	0.139887	+	0.139236i
$91$		−	16.3841i		−	1.71752i
$92$	−1.83761	−	0.419623i	−0.191584	−	0.0437487i
$93$	7.41134	−	7.41134i	0.768520	−	0.768520i
$94$	−19.5766	−	2.81470i	−2.01918	−	0.290314i
$95$	4.41329	+	6.83207i	0.452794	+	0.700955i
$96$	3.29943	+	0.968799i	0.336746	+	0.0988776i
$97$	−7.77981	−	0.556423i	−0.789920	−	0.0564962i	−0.329452	−	0.944172i	$-0.606864\pi$
$97$	−7.77981	−	0.556423i	−0.789920	−	0.0564962i	−0.460468	+	0.887676i	$0.652318\pi$
$98$	−7.41825	+	13.5855i	−0.749356	+	1.37234i
$99$	2.07860	+	1.33583i	0.208907	+	0.134256i
$100$	1.94644	+	0.270582i	0.194644	+	0.0270582i
$101$	−2.33404	+	2.69363i	−0.232246	+	0.268026i	−0.859896	−	0.510470i	$-0.829472\pi$
$101$	−2.33404	+	2.69363i	−0.232246	+	0.268026i	0.627650	+	0.778496i	$0.284017\pi$
$102$	0.151964	−	0.698565i	0.0150466	−	0.0691683i
$103$	7.99235	−	10.6765i	0.787510	−	1.05199i	−0.209731	−	0.977759i	$-0.567259\pi$
$103$	7.99235	−	10.6765i	0.787510	−	1.05199i	0.997241	−	0.0742312i	$-0.0236503\pi$
$104$	9.77593	−	1.40557i	0.958609	−	0.137827i
$105$	9.49416	+	10.9053i	0.926535	+	1.06425i
$106$	1.01415	+	0.878767i	0.0985031	+	0.0853534i
$107$	−5.23079	−	14.0243i	−0.505680	−	1.35578i	−0.899632	−	0.436649i	$-0.856165\pi$
$107$	−5.23079	−	14.0243i	−0.505680	−	1.35578i	0.393953	−	0.919131i	$-0.371107\pi$
$108$	2.13257	−	0.463912i	0.205207	−	0.0446400i
$109$	4.81925	−	1.41506i	0.461600	−	0.135538i	−0.0426604	−	0.999090i	$-0.513583\pi$
$109$	4.81925	−	1.41506i	0.461600	−	0.135538i	0.504260	+	0.863552i	$0.331765\pi$
$110$	15.7463	−	1.16317i	1.50135	−	0.110904i
$111$	1.36764	−	4.65777i	0.129811	−	0.442096i
$112$	−17.8957	−	6.67476i	−1.69099	−	0.630705i
$113$	−7.78815	+	5.83014i	−0.732647	+	0.548453i	−0.899178	−	0.437583i	$-0.855835\pi$
$113$	−7.78815	+	5.83014i	−0.732647	+	0.548453i	0.166530	+	0.986036i	$0.446744\pi$
$114$	8.82308			0.826357
$115$	6.49473	−	8.53337i	0.605637	−	0.795741i
$116$	0.563356			0.0523063
$117$	1.72166	−	1.28882i	0.159167	−	0.119151i
$118$	6.26808	+	2.33787i	0.577024	+	0.215219i
$119$	−0.342421	+	1.16618i	−0.0313897	+	0.106903i
$120$	−5.69238	+	6.60045i	−0.519641	+	0.602536i
$121$	9.43689	−	2.77092i	0.857899	−	0.251902i
$122$	5.50538	−	1.19762i	0.498434	−	0.108428i
$123$	5.09440	+	13.6586i	0.459347	+	1.23156i
$124$	1.98548	+	1.72043i	0.178301	+	0.154499i
$125$	−5.97850	+	9.44762i	−0.534733	+	0.845021i
$126$	−3.41804	+	0.491440i	−0.304503	+	0.0437810i
$127$	−8.38185	+	11.1968i	−0.743769	+	0.993559i	0.255870	+	0.966711i	$0.417638\pi$
$127$	−8.38185	+	11.1968i	−0.743769	+	0.993559i	−0.999640	+	0.0268482i	$0.991453\pi$
$128$	2.86276	−	13.1599i	0.253035	−	1.16318i
$129$	−1.41794	+	1.63639i	−0.124843	+	0.144076i
$130$	3.84102	−	13.1952i	0.336880	−	1.15730i
$131$	−1.30313	−	0.837474i	−0.113855	−	0.0731704i	0.482474	−	0.875910i	$-0.339738\pi$
$131$	−1.30313	−	0.837474i	−0.113855	−	0.0731704i	−0.596329	+	0.802740i	$0.703375\pi$
$132$	1.34816	−	2.46897i	0.117342	−	0.214896i
$133$	−14.9620	−	1.07010i	−1.29737	−	0.0927895i
$134$	−0.670426	−	0.196855i	−0.0579160	−	0.0170057i
$135$	−2.61098	+	12.1389i	−0.224717	+	1.04475i
$136$	−0.725202	−	0.104268i	−0.0621856	−	0.00894094i
$137$	−0.536442	+	0.536442i	−0.0458314	+	0.0458314i	−0.729651	−	0.683820i	$-0.760317\pi$
$137$	−0.536442	+	0.536442i	−0.0458314	+	0.0458314i	0.683820	+	0.729651i	$0.260317\pi$
$138$	−3.95279	−	10.9408i	−0.336484	−	0.931343i
$139$		−	1.53231i		−	0.129969i	−0.997886	−	0.0649844i	$-0.979300\pi$
$139$		−	1.53231i		−	0.129969i	0.997886	−	0.0649844i	$-0.0206998\pi$
$140$	−2.55672	+	2.56869i	−0.216083	+	0.217094i
$141$	−8.32801	−	18.2358i	−0.701345	−	1.53573i
$142$	−2.79823	−	5.12458i	−0.234823	−	0.430046i
$143$	1.29374	−	18.0889i	0.108188	−	1.51267i
$144$	−0.706335	−	2.40556i	−0.0588613	−	0.200463i
$145$	−1.32463	+	2.91855i	−0.110004	+	0.242373i
$146$	2.80975	−	6.15250i	0.232537	−	0.509185i
$147$	−15.6498	+	1.11930i	−1.29078	+	0.0923182i
$148$	1.18897	+	0.258645i	0.0977329	+	0.0212605i
$149$	1.08165	+	7.52305i	0.0886123	+	0.616312i	0.984937	+	0.172914i	$0.0553182\pi$
$149$	1.08165	+	7.52305i	0.0886123	+	0.616312i	−0.896325	+	0.443398i	$0.853773\pi$
$150$	5.08972	+	11.0085i	0.415574	+	0.898844i
$151$	−1.59008	+	1.02188i	−0.129399	+	0.0831597i	−0.603739	−	0.797182i	$-0.706323\pi$
$151$	−1.59008	+	1.02188i	−0.129399	+	0.0831597i	0.474340	+	0.880342i	$0.342687\pi$
$152$	−0.645065	−	9.01919i	−0.0523217	−	0.731553i
$153$	−0.149479	+	0.0557529i	−0.0120847	+	0.00450735i
$154$	−15.7429	+	24.4965i	−1.26860	+	1.97398i
$155$	−13.5814	+	6.24081i	−1.09089	+	0.501274i
$156$	−1.60342	−	1.85045i	−0.128377	−	0.148155i
$157$	3.36717	−	1.83862i	0.268730	−	0.146738i	−0.339235	−	0.940702i	$-0.610168\pi$
$157$	3.36717	−	1.83862i	0.268730	−	0.146738i	0.607964	+	0.793964i	$0.291986\pi$
$158$	5.39801	−	14.4726i	0.429442	−	1.15138i
$159$	−0.193577	+	1.34635i	−0.0153516	+	0.106773i
$160$	−3.93252	−	2.92954i	−0.310893	−	0.231600i
$161$	5.37609	+	19.0326i	0.423695	+	1.49998i
$162$	7.74784	+	7.74784i	0.608728	+	0.608728i
$163$	13.6798	+	18.2741i	1.07149	+	1.43134i	0.894470	+	0.447129i	$0.147553\pi$
$163$	13.6798	+	18.2741i	1.07149	+	1.43134i	0.177016	+	0.984208i	$0.443356\pi$
$164$	−3.32378	+	1.51792i	−0.259544	+	0.118530i
$165$	9.62092	+	12.7897i	0.748988	+	0.995675i
$166$	−1.10135	+	0.954324i	−0.0854812	+	0.0740699i
$167$	2.50524	+	1.36796i	0.193861	+	0.105856i	0.573248	−	0.819382i	$-0.305683\pi$
$167$	2.50524	+	1.36796i	0.193861	+	0.105856i	−0.379387	+	0.925238i	$0.623865\pi$
$168$	−3.41687	−	15.7071i	−0.263617	−	1.21183i
$169$	−2.53315	−	1.15685i	−0.194858	−	0.0889887i
$170$	−0.549169	+	0.858929i	−0.0421194	+	0.0658768i
$171$	−1.06450	−	1.65640i	−0.0814045	−	0.126668i
$172$	−0.434478	−	0.325246i	−0.0331287	−	0.0247998i
$173$	10.6307	+	7.95803i	0.808236	+	0.605038i	0.921434	−	0.388534i	$-0.127019\pi$
$173$	10.6307	+	7.95803i	0.808236	+	0.605038i	−0.113198	+	0.993572i	$0.536109\pi$
$174$	1.87971	+	2.92488i	0.142500	+	0.221735i
$175$	−7.29585	−	19.2853i	−0.551515	−	1.45783i
$176$	−19.2307	−	8.78238i	−1.44957	−	0.661997i
$177$	1.44141	+	6.62607i	0.108343	+	0.498046i
$178$	−6.50767	−	3.55345i	−0.487770	−	0.266343i
$179$	−1.30949	+	1.13468i	−0.0978757	+	0.0848098i	−0.702424	−	0.711759i	$-0.747899\pi$
$179$	−1.30949	+	1.13468i	−0.0978757	+	0.0848098i	0.604548	+	0.796568i	$0.293354\pi$
$180$	−0.471040	−	0.0666028i	−0.0351093	−	0.00496428i
$181$	22.3917	−	10.2259i	1.66436	−	0.760089i	0.664444	−	0.747338i	$-0.268669\pi$
$181$	22.3917	−	10.2259i	1.66436	−	0.760089i	0.999919	−	0.0127505i	$-0.00405872\pi$
$182$	15.1888	+	20.2899i	1.12587	+	1.50399i
$183$	4.03822	+	4.03822i	0.298514	+	0.298514i
$184$	−10.8950	+	4.84054i	−0.803189	+	0.356849i
$185$	−4.13560	+	5.55150i	−0.304056	+	0.408154i
$186$	−2.30747	+	16.0488i	−0.169192	+	1.17676i
$187$	−0.470136	+	1.26048i	−0.0343797	+	0.0921756i
$188$	4.41032	−	2.40822i	0.321656	−	0.175637i
$189$	−14.9957	−	17.3060i	−1.09078	−	1.25883i
$190$	−11.7990	−	4.36945i	−0.855992	−	0.316993i
$191$	−3.32253	+	5.16996i	−0.240410	+	0.374085i	−0.940402	−	0.340066i	$-0.889551\pi$
$191$	−3.32253	+	5.16996i	−0.240410	+	0.374085i	0.699992	+	0.714151i	$0.253187\pi$
$192$	8.62497	−	3.21695i	0.622454	−	0.232163i
$193$	−0.261218	−	3.65231i	−0.0188029	−	0.262899i	−0.998154	−	0.0607326i	$-0.980656\pi$
$193$	−0.261218	−	3.65231i	−0.0188029	−	0.262899i	0.979351	−	0.202167i	$-0.0647982\pi$
$194$	10.1503	−	6.52319i	0.728748	−	0.468338i
$195$	13.3567	−	3.95579i	0.956494	−	0.283280i
$196$	−0.559685	−	3.89270i	−0.0399775	−	0.278050i
$197$	−19.7898	−	4.30500i	−1.40996	−	0.306719i	−0.557792	−	0.829981i	$-0.688351\pi$
$197$	−19.7898	−	4.30500i	−1.40996	−	0.306719i	−0.852172	+	0.523262i	$0.824715\pi$
$198$	−3.81250	+	0.272675i	−0.270943	+	0.0193782i
$199$	2.56663	−	5.62014i	0.181944	−	0.398401i	−0.796581	−	0.604532i	$-0.793360\pi$
$199$	2.56663	−	5.62014i	0.181944	−	0.398401i	0.978524	+	0.206131i	$0.0660873\pi$
$200$	10.8811	−	6.00769i	0.769411	−	0.424808i
$201$	−0.199537	−	0.679562i	−0.0140743	−	0.0479326i
$202$	0.393335	−	5.49954i	0.0276749	−	0.386946i
$203$	−2.83282	−	5.18792i	−0.198825	−	0.364121i
$204$	0.0754541	+	0.165221i	0.00528284	+	0.0115678i
$205$	−0.0485548	−	20.7885i	−0.00339122	−	1.45193i
$206$			20.6310i			1.43743i
$207$	−1.57707	+	2.06208i	−0.109614	+	0.143324i
$208$	−13.0117	+	13.0117i	−0.902201	+	0.902201i
$209$	−16.4343	−	2.36289i	−1.13678	−	0.163445i
$210$	−21.8672	−	4.70346i	−1.50898	−	0.324569i
$211$	16.0626	+	4.71640i	1.10579	+	0.324690i	0.783152	−	0.621831i	$-0.213611\pi$
$211$	16.0626	+	4.71640i	1.10579	+	0.324690i	0.322642	+	0.946521i	$0.395429\pi$
$212$	−0.340072	−	0.0243224i	−0.0233562	−	0.00167047i
$213$	2.83636	−	5.19441i	0.194344	−	0.355915i
$214$	19.4790	+	12.5184i	1.33155	+	0.855738i
$215$	2.70659	−	1.48613i	0.184588	−	0.101353i
$216$	9.03954	−	10.4322i	0.615063	−	0.709820i
$217$	5.85942	−	26.9353i	0.397763	−	1.82849i
$218$	−4.65629	+	6.22007i	−0.315363	+	0.421276i
$219$	6.78611	−	0.975695i	0.458563	−	0.0659314i
$220$	−3.02559	+	2.63408i	−0.203985	+	0.177590i
$221$	0.884949	+	0.766813i	0.0595281	+	0.0515814i
$222$	2.62430	+	7.03601i	0.176131	+	0.472226i
$223$	−10.8134	+	2.35231i	−0.724119	+	0.157523i	−0.559495	−	0.828834i	$-0.689005\pi$
$223$	−10.8134	+	2.35231i	−0.724119	+	0.157523i	−0.164625	+	0.986356i	$0.552641\pi$
$224$	8.67738	−	2.54791i	0.579782	−	0.170239i
$225$	1.45261	−	2.28369i	0.0968408	−	0.152246i
$226$	4.23996	−	14.4400i	0.282038	−	0.960533i
$227$	−13.8979	−	5.18363i	−0.922433	−	0.344050i	−0.157025	−	0.987595i	$-0.550190\pi$
$227$	−13.8979	−	5.18363i	−0.922433	−	0.344050i	−0.765408	+	0.643545i	$0.777463\pi$
$228$	−1.79456	+	1.34339i	−0.118848	+	0.0889681i
$229$	5.58663			0.369175			0.184588	−	0.982816i	$-0.440905\pi$
$229$	5.58663			0.369175			0.184588	+	0.982816i	$0.440905\pi$
$230$	−0.132178	+	16.5886i	−0.00871555	+	1.09382i
$231$	−29.5158			−1.94200
$232$	2.85246	−	2.13533i	0.187273	−	0.140191i
$233$	12.7049	+	4.73869i	0.832327	+	0.310442i	0.729264	−	0.684233i	$-0.239863\pi$
$233$	12.7049	+	4.73869i	0.832327	+	0.310442i	0.103064	+	0.994675i	$0.467135\pi$
$234$	−0.937292	+	3.19212i	−0.0612727	+	0.208676i
$235$	2.10608	+	28.5109i	0.137386	+	1.85984i
$236$	−1.63085	+	0.478861i	−0.106159	+	0.0311712i
$237$	15.2992	−	3.32814i	0.993789	−	0.216186i
$238$	−0.657053	−	1.76163i	−0.0425904	−	0.114189i
$239$	17.9625	+	15.5646i	1.16190	+	1.00679i	0.999800	+	0.0200143i	$0.00637119\pi$
$239$	17.9625	+	15.5646i	1.16190	+	1.00679i	0.162097	+	0.986775i	$0.448174\pi$
$240$	1.12066	−	16.2006i	0.0723384	−	1.04574i
$241$	−24.0576	+	3.45897i	−1.54969	+	0.222812i	−0.863401	−	0.504519i	$-0.831670\pi$
$241$	−24.0576	+	3.45897i	−1.54969	+	0.222812i	−0.686288	+	0.727330i	$0.740761\pi$
$242$	−9.11779	+	12.1799i	−0.586114	+	0.782956i
$243$	1.18019	−	5.42526i	0.0757094	−	0.348030i
$244$	−0.937411	+	1.08183i	−0.0600116	+	0.0692570i
$245$	21.4827	+	6.25343i	1.37248	+	0.399517i
$246$	−18.9711	−	12.1920i	−1.20955	−	0.777332i
$247$	−6.92588	+	12.6838i	−0.440683	+	0.807051i
$248$	16.5742	+	1.18541i	1.05246	+	0.0752737i
$249$	−1.41732	−	0.416161i	−0.0898187	−	0.0263731i
$250$	−1.35468	−	17.2422i	−0.0856777	−	1.09049i
$251$	21.9423	+	3.15483i	1.38499	+	0.199131i	0.794181	−	0.607681i	$-0.207900\pi$
$251$	21.9423	+	3.15483i	1.38499	+	0.199131i	0.590807	+	0.806813i	$0.298809\pi$
$252$	0.620382	−	0.620382i	0.0390804	−	0.0390804i
$253$	4.43261	+	21.4374i	0.278676	+	1.34776i
$254$		−	21.6365i		−	1.35759i
$255$	−1.03337	+	0.00241361i	−0.0647123	+	0.000151146i
$256$	3.77710	+	8.27069i	0.236069	+	0.516918i
$257$	5.30228	+	9.71040i	0.330747	+	0.605718i	0.989143	−	0.146953i	$-0.0469467\pi$
$257$	5.30228	+	9.71040i	0.330747	+	0.605718i	−0.658396	+	0.752671i	$0.728765\pi$
$258$	0.238952	−	3.34099i	0.0148765	−	0.208001i
$259$	−3.59686	−	12.2498i	−0.223498	−	0.761165i
$260$	1.22785	+	3.26866i	0.0761480	+	0.202713i
$261$	0.322315	−	0.705772i	0.0199508	−	0.0436862i
$262$	2.39017	−	0.170948i	0.147665	−	0.0105612i
$263$	−25.8864	−	5.63125i	−1.59623	−	0.347238i	−0.675473	−	0.737384i	$-0.736061\pi$
$263$	−25.8864	−	5.63125i	−1.59623	−	0.347238i	−0.920753	+	0.390147i	$0.872424\pi$
$264$	−2.53212	−	17.6113i	−0.155841	−	1.08390i
$265$	0.925623	−	1.70460i	0.0568605	−	0.104713i
$266$	19.5208	−	12.5453i	1.19690	−	0.769199i
$267$	−0.536161	−	7.49652i	−0.0328125	−	0.458779i
$268$	0.166333	−	0.0620391i	0.0101604	−	0.00378964i
$269$	12.9958	−	20.2218i	0.792366	−	1.23295i	−0.176240	−	0.984347i	$-0.556394\pi$
$269$	12.9958	−	20.2218i	0.792366	−	1.23295i	0.968607	−	0.248599i	$-0.0799701\pi$
$270$	−8.01995	−	17.4532i	−0.488078	−	1.06217i
$271$	13.9638	+	16.1151i	0.848239	+	0.978920i	0.999955	−	0.00950404i	$-0.00302527\pi$
$271$	13.9638	+	16.1151i	0.848239	+	0.978920i	−0.151716	+	0.988424i	$0.548480\pi$
$272$	1.19808	−	0.654202i	0.0726444	−	0.0396668i
$273$	−8.97795	+	24.0708i	−0.543370	+	1.45683i
$274$	0.167018	−	1.16163i	0.0100899	−	0.0701768i
$275$	−6.53216	−	21.8681i	−0.393904	−	1.31870i
$276$	2.46980	+	1.62344i	0.148665	+	0.0977199i
$277$	8.95749	+	8.95749i	0.538203	+	0.538203i	0.923001	−	0.384798i	$-0.125729\pi$
$277$	8.95749	+	8.95749i	0.538203	+	0.538203i	−0.384798	+	0.923001i	$0.625729\pi$
$278$	1.42052	+	1.89760i	0.0851974	+	0.113810i
$279$	3.29131	−	1.50309i	0.197046	−	0.0899877i
$280$	−3.20926	+	22.6971i	−0.191790	+	1.35641i
$281$	−18.3424	+	15.8938i	−1.09422	+	0.948143i	−0.998881	−	0.0473018i	$-0.984938\pi$
$281$	−18.3424	+	15.8938i	−1.09422	+	0.948143i	−0.0953352	+	0.995445i	$0.530392\pi$
$282$	27.2188	+	14.8626i	1.62086	+	0.885055i
$283$	0.288784	+	1.32752i	0.0171664	+	0.0789127i	0.984933	−	0.172936i	$-0.0553253\pi$
$283$	0.288784	+	1.32752i	0.0171664	+	0.0789127i	−0.967767	+	0.251848i	$0.918962\pi$
$284$	1.34940	+	0.616252i	0.0800724	+	0.0365679i
$285$	−2.74006	−	12.4557i	−0.162307	−	0.737813i
$286$	15.1671	+	23.6005i	0.896849	+	1.39552i
$287$	30.6920	+	22.9757i	1.81169	+	1.35621i
$288$	0.950324	+	0.711404i	0.0559984	+	0.0419199i
$289$	9.14393	+	14.2282i	0.537878	+	0.836955i
$290$	−1.06523	−	4.84230i	−0.0625525	−	0.284350i
$291$	11.1249	+	5.08056i	0.652151	+	0.297827i
$292$	0.365285	+	1.67919i	0.0213767	+	0.0982671i
$293$	−1.68047	−	0.917604i	−0.0981738	−	0.0536070i	0.429412	−	0.903109i	$-0.358721\pi$
$293$	−1.68047	−	0.917604i	−0.0981738	−	0.0536070i	−0.527586	+	0.849502i	$0.676903\pi$
$294$	18.3430	−	15.8943i	1.06978	−	0.926974i
$295$	1.35383	−	9.57482i	0.0788232	−	0.557468i
$296$	7.00054	−	3.19704i	0.406898	−	0.185824i
$297$	−15.1895	−	20.2908i	−0.881384	−	1.17739i
$298$	−8.31374	−	8.31374i	−0.481602	−	0.481602i
$299$	18.8310	+	2.90583i	1.08903	+	0.168048i
$300$	−2.71136	−	1.46411i	−0.156540	−	0.0845307i
$301$	−0.810419	+	5.63659i	−0.0467118	+	0.324887i
$302$	1.02181	−	2.73957i	0.0587984	−	0.157645i
$303$	4.90510	−	2.67839i	0.281790	−	0.153869i
$304$	11.0325	+	12.7322i	0.632756	+	0.730239i
$305$	−3.40044	−	7.40013i	−0.194708	−	0.423730i
$306$	0.133428	−	0.207618i	0.00762758	−	0.0118687i
$307$	−7.56378	+	2.82114i	−0.431688	+	0.161011i	−0.555909	−	0.831243i	$-0.687630\pi$
$307$	−7.56378	+	2.82114i	−0.431688	+	0.161011i	0.124221	+	0.992255i	$0.460357\pi$
$308$	−0.527787	−	7.37942i	−0.0300734	−	0.420482i
$309$	−17.5924	+	11.3060i	−1.00080	+	0.643174i
$310$	11.0336	−	20.3192i	0.626666	−	1.15405i
$311$	−0.592979	−	4.12426i	−0.0336248	−	0.233865i	0.966078	−	0.258251i	$-0.0831462\pi$
$311$	−0.592979	−	4.12426i	−0.0336248	−	0.233865i	−0.999703	+	0.0243856i	$0.992237\pi$
$312$	−15.1326	−	3.29189i	−0.856714	−	0.186367i
$313$	−18.7944	+	1.34420i	−1.06232	+	0.0759788i	−0.591544	−	0.806273i	$-0.701481\pi$
$313$	−18.7944	+	1.34420i	−1.06232	+	0.0759788i	−0.470778	+	0.882251i	$0.656027\pi$
$314$	−2.46539	+	5.39846i	−0.139130	+	0.304653i
$315$	1.75527	+	4.67270i	0.0988983	+	0.263277i
$316$	1.10566	+	3.76553i	0.0621982	+	0.211828i
$317$	−1.46950	+	20.5464i	−0.0825356	+	1.15400i	0.772355	+	0.635191i	$0.219078\pi$
$317$	−1.46950	+	20.5464i	−0.0825356	+	1.15400i	−0.854891	+	0.518808i	$0.826376\pi$
$318$	−1.00841	−	1.84677i	−0.0565490	−	0.103562i
$319$	−2.71792	−	5.95142i	−0.152174	−	0.333215i
$320$	−13.1272	+	0.0306608i	−0.733834	+	0.00171399i
$321$			23.4702i			1.30998i
$322$	−24.3018	−	18.5859i	−1.35429	−	1.03575i
$323$	0.758053	−	0.758053i	0.0421792	−	0.0421792i
$324$	−2.75553	−	0.396186i	−0.153085	−	0.0220103i
$325$	−19.8208	−	1.32458i	−1.09946	−	0.0734746i
$326$	−33.8819	−	9.94863i	−1.87655	−	0.551004i
$327$	−7.85564	−	0.561846i	−0.434418	−	0.0310702i
$328$	−11.0760	+	20.2841i	−0.611568	+	1.12000i
$329$	−44.3544	−	28.5048i	−2.44534	−	1.57152i
$330$	−23.7711	−	6.91956i	−1.30856	−	0.380909i
$331$	1.39492	−	1.60982i	0.0766715	−	0.0884836i	−0.716118	−	0.697979i	$-0.754083\pi$
$331$	1.39492	−	1.60982i	0.0766715	−	0.0884836i	0.792789	+	0.609496i	$0.208628\pi$
$332$	0.0787032	−	0.361793i	0.00431940	−	0.0198560i
$333$	1.00428	−	1.34156i	0.0550343	−	0.0735173i
$334$	−4.37063	+	0.628402i	−0.239150	+	0.0343847i
$335$	−0.0696992	+	1.00759i	−0.00380807	+	0.0550505i
$336$	22.6341	+	19.6125i	1.23479	+	1.06995i
$337$	3.49472	+	9.36970i	0.190369	+	0.510400i	0.996710	−	0.0810514i	$-0.0258278\pi$
$337$	3.49472	+	9.36970i	0.190369	+	0.510400i	−0.806340	+	0.591452i	$0.798555\pi$
$338$	4.20949	−	0.915719i	0.228966	−	0.0498086i
$339$	14.6367	−	4.29774i	0.794959	−	0.233421i
$340$	−0.0190817	−	0.258316i	−0.00103485	−	0.0140092i
$341$	8.59599	−	29.2753i	0.465499	−	1.58534i
$342$	2.85383	+	1.06442i	0.154317	+	0.0575574i
$343$	−9.92415	+	7.42912i	−0.535854	+	0.401135i
$344$	−3.43272			−0.185080
$345$	−14.2178	+	8.97796i	−0.765461	+	0.483357i
$346$	−20.5424			−1.10437
$347$	11.9521	−	8.94725i	0.641624	−	0.480313i	−0.228241	−	0.973605i	$-0.573297\pi$
$347$	11.9521	−	8.94725i	0.641624	−	0.480313i	0.869864	+	0.493291i	$0.164206\pi$
$348$	−0.827658	−	0.308701i	−0.0443671	−	0.0165481i
$349$	9.92356	−	33.7965i	0.531196	−	1.80909i	−0.0544443	−	0.998517i	$-0.517339\pi$
$349$	9.92356	−	33.7965i	0.531196	−	1.80909i	0.585640	−	0.810571i	$-0.300843\pi$
$350$	26.9135	+	17.1192i	1.43859	+	0.915058i
$351$	−21.1679	+	6.21545i	−1.12986	+	0.331756i
$352$	9.78147	−	2.12783i	0.521354	−	0.113414i
$353$	1.49372	+	4.00481i	0.0795025	+	0.213154i	0.970620	−	0.240619i	$-0.0773503\pi$
$353$	1.49372	+	4.00481i	0.0795025	+	0.213154i	−0.891117	+	0.453773i	$0.850078\pi$
$354$	−7.92772	−	6.86941i	−0.421354	−	0.365105i
$355$	−6.36547	+	5.54180i	−0.337844	+	0.294128i
$356$	1.86466	−	0.268098i	0.0988268	−	0.0142092i
$357$	1.14210	−	1.52567i	0.0604463	−	0.0807468i
$358$	0.569758	−	2.61913i	0.0301126	−	0.138426i
$359$	−11.5833	+	13.3679i	−0.611344	+	0.705529i	−0.974039	−	0.226379i	$-0.927311\pi$
$359$	−11.5833	+	13.3679i	−0.611344	+	0.705529i	0.362695	+	0.931908i	$0.381857\pi$
$360$	−2.63749	+	1.44818i	−0.139008	+	0.0763260i
$361$	−4.85332	−	3.11904i	−0.255438	−	0.164160i
$362$	−18.2497	+	33.4219i	−0.959186	+	1.75662i
$363$	−15.3827	−	1.10019i	−0.807380	−	0.0577450i
$364$	−6.17863	−	1.81421i	−0.323848	−	0.0950904i
$365$	−9.55820	−	2.05589i	−0.500299	−	0.107610i
$366$	−8.74453	−	1.25727i	−0.457084	−	0.0657187i
$367$	−6.48917	+	6.48917i	−0.338732	+	0.338732i	−0.855890	−	0.517158i	$-0.826990\pi$
$367$	−6.48917	+	6.48917i	−0.338732	+	0.338732i	0.517158	+	0.855890i	$0.326990\pi$
$368$	10.8455	−	19.3846i	0.565363	−	1.01049i
$369$			5.03248i			0.261981i
$370$	−0.0250122	−	10.7088i	−0.00130032	−	0.556726i
$371$	1.48606	+	3.25401i	0.0771522	+	0.168940i
$372$	−1.97424	−	3.61555i	−0.102360	−	0.187458i
$373$	2.49193	−	34.8417i	0.129027	−	1.80404i	−0.361250	−	0.932469i	$-0.617650\pi$
$373$	2.49193	−	34.8417i	0.129027	−	1.80404i	0.490277	−	0.871567i	$-0.336896\pi$
$374$	−0.586316	−	1.99681i	−0.0303177	−	0.103253i
$375$	13.9603	−	10.6040i	0.720909	−	0.547590i
$376$	13.2029	−	28.9104i	0.680890	−	1.49094i
$377$	−5.68024	+	0.406259i	−0.292547	+	0.0209234i
$378$	34.6141	+	7.52983i	1.78035	+	0.387292i
$379$	3.53302	+	24.5727i	0.181479	+	1.26221i	0.853268	+	0.521472i	$0.174617\pi$
$379$	3.53302	+	24.5727i	0.181479	+	1.26221i	−0.671789	+	0.740742i	$0.734474\pi$
$380$	3.06513	−	0.907786i	0.157238	−	0.0465684i
$381$	18.4498	−	11.8569i	0.945210	−	0.607450i
$382$	−0.678207	−	9.48258i	−0.0347001	−	0.485171i
$383$	13.0566	−	4.86987i	0.667162	−	0.248839i	0.00701537	−	0.999975i	$-0.497767\pi$
$383$	13.0566	−	4.86987i	0.667162	−	0.248839i	0.660146	+	0.751137i	$0.270494\pi$
$384$	−11.4170	+	17.7653i	−0.582624	+	0.906580i
$385$	39.4712	+	14.6171i	2.01164	+	0.744956i
$386$	3.70936	+	4.28083i	0.188801	+	0.217888i
$387$	−0.656049	+	0.358230i	−0.0333488	+	0.0182098i
$388$	−1.07129	+	2.87224i	−0.0543865	+	0.145816i
$389$	0.192013	−	1.33548i	0.00973544	−	0.0677115i	−0.984375	−	0.176087i	$-0.943656\pi$
$389$	0.192013	−	1.33548i	0.00973544	−	0.0677115i	0.994110	+	0.108376i	$0.0345650\pi$
$390$	−12.8736	+	17.2811i	−0.651881	+	0.875064i
$391$	−1.27961	−	0.600390i	−0.0647129	−	0.0303630i
$392$	−17.5886	−	17.5886i	−0.888361	−	0.888361i
$393$	1.45560	+	1.94446i	0.0734254	+	0.0980849i
$394$	28.4984	−	13.0148i	1.43573	−	0.655676i
$395$	−22.1077	−	3.12592i	−1.11236	−	0.157282i
$396$	0.733921	−	0.635946i	0.0368809	−	0.0319575i
$397$	5.25618	+	2.87009i	0.263800	+	0.144046i	0.605706	−	0.795688i	$-0.292891\pi$
$397$	5.25618	+	2.87009i	0.263800	+	0.144046i	−0.341906	+	0.939734i	$0.611072\pi$
$398$	2.03165	+	9.33933i	0.101837	+	0.468138i
$399$	21.3951	+	9.77082i	1.07109	+	0.489153i
$400$	−9.52165	+	21.1099i	−0.476083	+	1.05550i
$401$	5.04254	+	7.84635i	0.251813	+	0.391828i	0.944029	−	0.329862i	$-0.107002\pi$
$401$	5.04254	+	7.84635i	0.251813	+	0.391828i	−0.692217	+	0.721690i	$0.743366\pi$
$402$	0.877092	+	0.656583i	0.0437454	+	0.0327474i
$403$	−21.2600	−	15.9150i	−1.05903	−	0.792783i
$404$	0.757350	+	1.17846i	0.0376795	+	0.0586305i
$405$	8.53164	−	13.3439i	0.423941	−	0.663065i
$406$	8.31759	+	3.79852i	0.412795	+	0.188517i
$407$	−3.00384	−	13.8084i	−0.148895	−	0.684457i
$408$	1.00830	+	0.550574i	0.0499183	+	0.0272575i
$409$	−22.9218	+	19.8618i	−1.13341	+	0.982104i	−0.999960	−	0.00895179i	$-0.997151\pi$
$409$	−22.9218	+	19.8618i	−1.13341	+	0.982104i	−0.133448	+	0.991056i	$0.542605\pi$
$410$	19.3320	+	25.6992i	0.954742	+	1.26920i
$411$	1.08207	−	0.494165i	0.0533746	−	0.0243754i
$412$	−3.14125	−	4.19622i	−0.154758	−	0.206733i
$413$	12.6105	+	12.6105i	0.620522	+	0.620522i
$414$	0.0413769	−	4.01568i	0.00203357	−	0.197360i
$415$	1.68927	+	1.25842i	0.0829229	+	0.0617736i
$416$	1.23998	−	8.62424i	0.0607950	−	0.422838i
$417$	−0.839656	+	2.25120i	−0.0411181	+	0.110242i
$418$	22.5426	−	12.3092i	1.10259	−	0.602062i
$419$	−1.71447	−	1.97861i	−0.0837575	−	0.0966613i	0.712324	−	0.701851i	$-0.247643\pi$
$419$	−1.71447	−	1.97861i	−0.0837575	−	0.0966613i	−0.796081	+	0.605190i	$0.793097\pi$
$420$	5.16379	−	2.37282i	0.251967	−	0.115782i
$421$	11.2076	−	17.4394i	0.546225	−	0.849942i	−0.452909	−	0.891557i	$-0.649614\pi$
$421$	11.2076	−	17.4394i	0.546225	−	0.849942i	0.999134	+	0.0416143i	$0.0132501\pi$
$422$	−24.2641	+	9.05004i	−1.18116	+	0.440549i
$423$	−0.493718	−	6.90308i	−0.0240054	−	0.335639i
$424$	−1.81409	+	1.16585i	−0.0881000	+	0.0566185i
$425$	1.38312	+	0.508528i	0.0670909	+	0.0246672i
$426$	1.30294	+	9.06216i	0.0631278	+	0.439063i
$427$	14.6763	+	3.19263i	0.710234	+	0.154502i
$428$	−5.86792	+	0.419682i	−0.283637	+	0.0202861i
$429$	−11.8128	+	25.8665i	−0.570329	+	1.24885i
$430$	−1.97410	+	4.34954i	−0.0951998	+	0.209754i
$431$	−10.0073	−	34.0817i	−0.482034	−	1.64166i	−0.737875	−	0.674937i	$-0.764171\pi$
$431$	−10.0073	−	34.0817i	−0.482034	−	1.64166i	0.255842	−	0.966719i	$-0.417647\pi$
$432$	−1.83474	+	25.6530i	−0.0882739	+	1.23423i
$433$	−17.0124	−	31.1559i	−0.817565	−	1.49726i	−0.866903	−	0.498477i	$-0.833893\pi$
$433$	−17.0124	−	31.1559i	−0.817565	−	1.49726i	0.0493377	−	0.998782i	$-0.484289\pi$
$434$	17.7141	+	38.7884i	0.850303	+	1.86190i
$435$	3.54536	−	3.56196i	0.169987	−	0.170783i
$436$		−	1.97408i		−	0.0945413i
$437$	3.88352	−	17.0067i	0.185774	−	0.813541i
$438$	−7.49935	+	7.49935i	−0.358333	+	0.358333i
$439$	26.4790	+	3.80711i	1.26378	+	0.181703i	0.741430	−	0.671030i	$-0.234148\pi$
$439$	26.4790	+	3.80711i	1.26378	+	0.181703i	0.522346	+	0.852734i	$0.325057\pi$
$440$	−5.33543	+	24.8054i	−0.254357	+	1.18255i
$441$	−5.19698	−	1.52597i	−0.247475	−	0.0726653i
$442$	−1.80679	−	0.129224i	−0.0859401	−	0.00614655i
$443$	−7.32859	+	13.4213i	−0.348192	+	0.637665i	−0.991816	−	0.127676i	$-0.959248\pi$
$443$	−7.32859	+	13.4213i	−0.348192	+	0.637665i	0.643624	+	0.765342i	$0.277430\pi$
$444$	−1.60506	−	1.03151i	−0.0761727	−	0.0489532i
$445$	−2.99549	+	10.2906i	−0.142000	+	0.487819i
$446$	11.2105	−	12.9376i	0.530834	−	0.612615i
$447$	2.53327	−	11.6453i	0.119820	−	0.550802i
$448$	14.5084	−	19.3810i	0.685458	−	0.915665i
$449$	12.7619	−	1.83489i	0.602272	−	0.0865937i	0.165567	−	0.986198i	$-0.447054\pi$
$449$	12.7619	−	1.83489i	0.602272	−	0.0865937i	0.436705	+	0.899605i	$0.356145\pi$
$450$	0.318192	+	4.17475i	0.0149997	+	0.196799i
$451$	32.0713	+	27.7899i	1.51018	+	1.30858i
$452$	1.33623	+	3.58257i	0.0628509	+	0.168510i
$453$	2.89604	−	0.629995i	0.136068	−	0.0295997i
$454$	22.0165	−	6.46462i	1.03328	−	0.303400i
$455$	23.9267	−	27.7436i	1.12170	−	1.30064i
$456$	−3.99452	+	13.6041i	−0.187061	+	0.637070i
$457$	31.9481	+	11.9160i	1.49447	+	0.557408i	0.958064	−	0.286554i	$-0.0925097\pi$
$457$	31.9481	+	11.9160i	1.49447	+	0.557408i	0.536404	+	0.843962i	$0.319782\pi$
$458$	−6.91844	+	5.17908i	−0.323277	+	0.242002i
$459$	1.63658			0.0763889
$460$	−2.49887	−	3.39414i	−0.116510	−	0.158252i
$461$	−0.104891			−0.00488528			−0.00244264	−	0.999997i	$-0.500778\pi$
$461$	−0.104891			−0.00488528			−0.00244264	+	0.999997i	$0.500778\pi$
$462$	36.5521	−	27.3626i	1.70056	−	1.27302i
$463$	33.8185	+	12.6136i	1.57168	+	0.586206i	0.976144	−	0.217123i	$-0.0696674\pi$
$463$	33.8185	+	12.6136i	1.57168	+	0.586206i	0.595535	+	0.803329i	$0.296940\pi$
$464$	−1.87035	+	6.36981i	−0.0868286	+	0.295711i
$465$	23.3730	−	1.72655i	1.08390	−	0.0800669i
$466$	−20.1267	+	5.90972i	−0.932350	+	0.273763i
$467$	−30.0225	+	6.53100i	−1.38928	+	0.302219i	−0.844137	−	0.536127i	$-0.819887\pi$
$467$	−30.0225	+	6.53100i	−1.38928	+	0.302219i	−0.545139	+	0.838346i	$0.683523\pi$
$468$	−0.295389	−	0.791968i	−0.0136543	−	0.0366087i
$469$	−1.40772	−	1.21979i	−0.0650024	−	0.0563249i
$470$	−29.0391	−	33.3552i	−1.33947	−	1.53856i
$471$	−5.95441	+	0.856115i	−0.274365	+	0.0394477i
$472$	−6.44249	+	8.60616i	−0.296540	+	0.396131i
$473$	−1.33983	+	6.15909i	−0.0616053	+	0.283195i
$474$	−15.8610	+	18.3046i	−0.728522	+	0.840759i
$475$	−2.50418	+	18.0139i	−0.114899	+	0.826534i
$476$	0.401863	+	0.258262i	0.0184194	+	0.0118374i
$477$	−0.225038	+	0.412126i	−0.0103038	+	0.0188700i
$478$	−36.6737	−	2.62296i	−1.67742	−	0.119971i
$479$	20.2802	+	5.95481i	0.926627	+	0.272082i	0.710024	−	0.704178i	$-0.248684\pi$
$479$	20.2802	+	5.95481i	0.926627	+	0.272082i	0.216603	+	0.976260i	$0.430502\pi$
$480$	4.17220	+	6.45884i	0.190434	+	0.294805i
$481$	−12.1748	−	1.75047i	−0.555122	−	0.0798144i
$482$	26.5861	−	26.5861i	1.21097	−	1.21097i
$483$	2.53090	−	30.9078i	0.115160	−	1.40635i
$484$		−	3.86558i		−	0.175708i
$485$	−12.3612	−	12.3035i	−0.561291	−	0.558675i
$486$	3.56793	+	7.81269i	0.161845	+	0.354391i
$487$	−3.97800	−	7.28517i	−0.180260	−	0.330122i	0.771888	−	0.635759i	$-0.219313\pi$
$487$	−3.97800	−	7.28517i	−0.180260	−	0.330122i	−0.952148	+	0.305636i	$0.901131\pi$
$488$	−0.645896	+	9.03081i	−0.0292384	+	0.408806i
$489$	−10.0842	−	34.3436i	−0.456023	−	1.55307i
$490$	−32.4012	+	12.1713i	−1.46374	+	0.549844i
$491$	−10.6070	+	23.2262i	−0.478689	+	1.04818i	0.504133	+	0.863626i	$0.331812\pi$
$491$	−10.6070	+	23.2262i	−0.478689	+	1.04818i	−0.982822	+	0.184556i	$0.940915\pi$
$492$	5.71493	−	0.408740i	0.257649	−	0.0184274i
$493$	0.412796	+	0.0897983i	0.0185914	+	0.00404431i
$494$	−3.18154	−	22.1281i	−0.143144	−	0.995592i
$495$	1.56894	+	5.29750i	0.0705184	+	0.238105i
$496$	−26.0445	+	16.7378i	−1.16943	+	0.751549i
$497$	−1.11040	−	15.5254i	−0.0498083	−	0.696410i
$498$	2.14099	−	0.798549i	0.0959402	−	0.0357838i
$499$	15.2280	−	23.6952i	0.681699	−	1.06074i	−0.312153	−	0.950032i	$-0.601050\pi$
$499$	15.2280	−	23.6952i	0.681699	−	1.06074i	0.993852	−	0.110713i	$-0.0353134\pi$
$500$	2.90081	+	3.30069i	0.129728	+	0.147611i
$501$	−2.93099	−	3.38254i	−0.130947	−	0.151121i
$502$	−30.0979	+	16.4347i	−1.34333	+	0.733516i
$503$	−3.16395	+	8.48288i	−0.141074	+	0.378233i	−0.988202	−	0.153155i	$-0.951057\pi$
$503$	−3.16395	+	8.48288i	−0.141074	+	0.378233i	0.847129	+	0.531388i	$0.178329\pi$
$504$	0.789729	−	5.49269i	0.0351773	−	0.244664i
$505$	−7.88596	+	1.15264i	−0.350921	+	0.0512916i
$506$	−25.3628	−	22.4387i	−1.12752	−	0.997522i
$507$	3.08769	+	3.08769i	0.137129	+	0.137129i
$508$	3.29434	+	4.40072i	0.146162	+	0.195250i
$509$	−38.1610	+	17.4276i	−1.69146	+	0.772463i	−0.692775	+	0.721154i	$0.743612\pi$
$509$	−38.1610	+	17.4276i	−1.69146	+	0.772463i	−0.998683	+	0.0513092i	$0.983661\pi$
$510$	1.27748	−	0.960975i	0.0565678	−	0.0425527i
$511$	13.6268	−	11.8077i	0.602812	−	0.522340i
$512$	11.2957	+	6.16794i	0.499206	+	0.272587i
$513$	4.29341	+	19.7365i	0.189559	+	0.871386i
$514$	−15.5683	−	7.10981i	−0.686689	−	0.313600i
$515$	29.1252	−	6.40709i	1.28341	−	0.282330i
$516$	0.460093	+	0.715918i	0.0202545	+	0.0315165i
$517$	−46.7187	−	34.9732i	−2.05469	−	1.53812i
$518$	15.8105	+	11.8356i	0.694672	+	0.520025i
$519$	−11.2574	−	17.5169i	−0.494146	−	0.768905i
$520$	18.6064	+	11.8963i	0.815946	+	0.521688i
$521$	−11.9238	−	5.44540i	−0.522389	−	0.238567i	0.136726	−	0.990609i	$-0.456342\pi$
$521$	−11.9238	−	5.44540i	−0.522389	−	0.238567i	−0.659115	+	0.752042i	$0.729069\pi$
$522$	0.255132	+	1.17282i	0.0111668	+	0.0513331i
$523$	−1.19449	−	0.652242i	−0.0522315	−	0.0285205i	0.452921	−	0.891551i	$-0.350382\pi$
$523$	−1.19449	−	0.652242i	−0.0522315	−	0.0285205i	−0.505153	+	0.863030i	$0.668564\pi$
$524$	−0.460117	+	0.398694i	−0.0201003	+	0.0174170i
$525$	0.151030	+	32.3311i	0.00659148	+	1.41104i
$526$	37.2780	−	17.0243i	1.62540	−	0.742294i
$527$	1.18061	+	1.57712i	0.0514284	+	0.0687003i
$528$	23.4405	+	23.4405i	1.02012	+	1.02012i
$529$	−22.8285	+	2.80344i	−0.992544	+	0.121889i
$530$	0.433967	+	2.96906i	0.0188503	+	0.128968i
$531$	−0.333149	+	2.31710i	−0.0144574	+	0.100554i
$532$	−2.06028	+	5.52383i	−0.0893246	+	0.239489i
$533$	32.4186	−	17.7019i	1.40420	−	0.766754i
$534$	7.61361	+	8.78657i	0.329473	+	0.380232i
$535$	11.6231	−	31.3865i	0.502512	−	1.35696i
$536$	0.607051	−	0.944590i	0.0262206	−	0.0408001i
$537$	2.54561	−	0.949464i	0.109851	−	0.0409724i
$538$	2.65275	+	37.0902i	0.114368	+	1.59907i
$539$	−38.4231	+	24.6930i	−1.65500	+	1.06360i
$540$	4.28861	+	2.32877i	0.184552	+	0.100214i
$541$	−1.96647	−	13.6771i	−0.0845453	−	0.588025i	−0.987420	−	0.158121i	$-0.949456\pi$
$541$	−1.96647	−	13.6771i	−0.0845453	−	0.588025i	0.902874	−	0.429904i	$-0.141453\pi$
$542$	−32.2321	−	7.01166i	−1.38449	−	0.301176i
$543$	−38.5004	+	2.75361i	−1.65221	+	0.118169i
$544$	−0.268502	+	0.587937i	−0.0115119	+	0.0252076i
$545$	10.2270	+	4.64169i	0.438078	+	0.198828i
$546$	−11.1966	−	38.1321i	−0.479170	−	1.63190i
$547$	0.597899	−	8.35972i	0.0255643	−	0.357436i	−0.968528	−	0.248903i	$-0.919930\pi$
$547$	0.597899	−	8.35972i	0.0255643	−	0.357436i	0.994093	−	0.108533i	$-0.0346154\pi$
$548$	0.142898	+	0.261699i	0.00610431	+	0.0111792i
$549$	0.818991	+	1.79334i	0.0349537	+	0.0765379i
$550$	28.3621	+	21.0256i	1.20937	+	0.896535i
$551$			5.21373i			0.222112i
$552$	18.6589	−	1.14141i	0.794176	−	0.0485817i
$553$	29.1168	−	29.1168i	1.23817	−	1.23817i
$554$	−19.3969	−	2.78885i	−0.824095	−	0.118487i
$555$	9.11789	−	5.88985i	0.387033	−	0.250010i
$556$	−0.577851	−	0.169672i	−0.0245063	−	0.00719571i
$557$	27.8131	+	1.98924i	1.17848	+	0.0842866i	0.646801	−	0.762659i	$-0.276106\pi$
$557$	27.8131	+	1.98924i	1.17848	+	0.0842866i	0.531680	+	0.846945i	$0.321561\pi$
$558$	−2.68249	+	4.91262i	−0.113559	+	0.207968i
$559$	4.61534	+	2.96610i	0.195208	+	0.125453i
$560$	−20.5557	−	37.4367i	−0.868635	−	1.58199i
$561$	1.38141	−	1.59423i	0.0583230	−	0.0673084i
$562$	7.98077	−	36.6870i	0.336648	−	1.54755i
$563$	−19.2393	+	25.7007i	−0.810840	+	1.08316i	0.184122	+	0.982903i	$0.441056\pi$
$563$	−19.2393	+	25.7007i	−0.810840	+	1.08316i	−0.994962	+	0.100253i	$0.968035\pi$
$564$	−7.79909	+	1.12134i	−0.328401	+	0.0472169i
$565$	−21.7020	−	1.50122i	−0.913008	−	0.0631566i
$566$	−1.58830	−	1.37627i	−0.0667612	−	0.0578489i
$567$	10.2077	+	27.3678i	0.428682	+	1.14934i
$568$	9.16833	−	1.99445i	0.384694	−	0.0836851i
$569$	−26.3665	+	7.74190i	−1.10534	+	0.324557i	−0.782972	−	0.622057i	$-0.786297\pi$
$569$	−26.3665	+	7.74190i	−1.10534	+	0.324557i	−0.322368	+	0.946614i	$0.604479\pi$
$570$	14.9403	+	12.8849i	0.625781	+	0.539689i
$571$	−1.99692	+	6.80090i	−0.0835686	+	0.284609i	−0.990666	−	0.136312i	$-0.956475\pi$
$571$	−1.99692	+	6.80090i	−0.0835686	+	0.284609i	0.907097	+	0.420921i	$0.138293\pi$
$572$	−6.67826	−	2.49086i	−0.279232	−	0.104148i
$573$	7.71429	−	5.77484i	0.322269	−	0.241248i
$574$	−59.3083			−2.47548
$575$	23.4595	−	4.96509i	0.978329	−	0.207058i
$576$	3.17785			0.132410
$577$	28.8776	−	21.6175i	1.20219	−	0.899949i	0.205297	−	0.978700i	$-0.434184\pi$
$577$	28.8776	−	21.6175i	1.20219	−	0.899949i	0.996894	+	0.0787505i	$0.0250930\pi$
$578$	−24.5140	−	9.14326i	−1.01965	−	0.380309i
$579$	−1.61758	+	5.50896i	−0.0672242	+	0.228945i
$580$	0.953943	+	0.822703i	0.0396103	+	0.0341609i
$581$	−3.72749	+	1.09449i	−0.154643	+	0.0454071i
$582$	−18.4869	+	4.02157i	−0.766305	+	0.166699i
$583$	1.38374	+	3.70994i	0.0573085	+	0.153650i
$584$	8.21432	+	7.11774i	0.339911	+	0.294534i
$585$	4.79747	+	0.331861i	0.198351	+	0.0137208i
$586$	2.93174	−	0.421520i	0.121109	−	0.0174128i
$587$	−2.14671	+	2.86767i	−0.0886043	+	0.118361i	−0.842653	−	0.538457i	$-0.819007\pi$
$587$	−2.14671	+	2.86767i	−0.0886043	+	0.118361i	0.754049	+	0.656819i	$0.228098\pi$
$588$	−1.31081	+	6.02567i	−0.0540567	+	0.248495i
$589$	−15.9222	+	18.3752i	−0.656061	+	0.757135i
$590$	7.19975	+	13.1124i	0.296409	+	0.539831i
$591$	26.7153	+	17.1689i	1.09892	+	0.706234i
$592$	−6.87188	+	12.5849i	−0.282432	+	0.517236i
$593$	2.62487	+	0.187734i	0.107790	+	0.00770933i	0.125130	−	0.992140i	$-0.460065\pi$
$593$	2.62487	+	0.187734i	0.107790	+	0.00770933i	−0.0173397	+	0.999850i	$0.505520\pi$
$594$	37.6211	+	11.0466i	1.54361	+	0.453246i
$595$	−2.28287	+	1.47466i	−0.0935887	+	0.0604551i
$596$	2.95680	+	0.425123i	0.121115	+	0.0174137i
$597$	−6.85044	+	6.85044i	−0.280370	+	0.280370i
$598$	−26.0140	+	13.8587i	−1.06379	+	0.566724i
$599$		−	30.0749i		−	1.22883i	−0.788984	−	0.614413i	$-0.789393\pi$
$599$		−	30.0749i		−	1.22883i	0.788984	−	0.614413i	$-0.210607\pi$
$600$	−19.2781	+	2.86375i	−0.787025	+	0.116912i
$601$	1.25891	+	2.75664i	0.0513522	+	0.112446i	0.933569	−	0.358398i	$-0.116677\pi$
$601$	1.25891	+	2.75664i	0.0513522	+	0.112446i	−0.882217	+	0.470844i	$0.843950\pi$
$602$	−4.22177	−	7.73160i	−0.172067	−	0.315116i
$603$	0.0174424	−	0.243877i	0.000710310	−	0.00993144i
$604$	0.209294	+	0.712791i	0.00851606	+	0.0290030i
$605$	20.0263	+	9.08921i	0.814183	+	0.369529i
$606$	−3.59144	+	7.86415i	−0.145892	+	0.319459i
$607$	20.7870	−	1.48672i	0.843719	−	0.0603440i	0.357215	−	0.934022i	$-0.383726\pi$
$607$	20.7870	−	1.48672i	0.843719	−	0.0603440i	0.486504	+	0.873678i	$0.338272\pi$
$608$	−7.79468	−	1.69563i	−0.316116	−	0.0687668i
$609$	1.31905	+	9.17416i	0.0534504	+	0.371756i
$610$	11.0713	+	6.01189i	0.448266	+	0.243414i
$611$	−42.7320	+	27.4622i	−1.72875	+	1.11100i
$612$	0.00447322	+	0.0625438i	0.000180819	+	0.00252818i
$613$	−28.3756	+	10.5836i	−1.14608	+	0.427466i	−0.849524	−	0.527549i	$-0.823111\pi$
$613$	−28.3756	+	10.5836i	−1.14608	+	0.427466i	−0.296556	+	0.955015i	$0.595838\pi$
$614$	6.75158	−	10.5057i	0.272472	−	0.423974i
$615$	−11.3201	+	30.5681i	−0.456469	+	1.23263i
$616$	−30.6431	−	35.3640i	−1.23465	−	1.42486i
$617$	−22.7868	+	12.4425i	−0.917361	+	0.500917i	−0.867276	−	0.497828i	$-0.834131\pi$
$617$	−22.7868	+	12.4425i	−0.917361	+	0.500917i	−0.0500850	+	0.998745i	$0.515949\pi$
$618$	11.3051	−	30.3102i	0.454759	−	1.21926i
$619$	−2.74672	+	19.1039i	−0.110400	+	0.767849i	0.857131	+	0.515098i	$0.172244\pi$
$619$	−2.74672	+	19.1039i	−0.110400	+	0.767849i	−0.967531	+	0.252751i	$0.918665\pi$
$620$	0.849610	+	5.81275i	0.0341211	+	0.233446i
$621$	22.5502	−	14.1660i	0.904907	−	0.568460i
$622$	4.55773	+	4.55773i	0.182748	+	0.182748i
$623$	−11.8453	−	15.8235i	−0.474572	−	0.633954i
$624$	26.2463	−	11.9863i	1.05069	−	0.479835i
$625$	−23.9205	+	7.26711i	−0.956819	+	0.290684i
$626$	22.0287	−	19.0880i	0.880444	−	0.762909i
$627$	22.8498	+	12.4769i	0.912531	+	0.498280i
$628$	−0.320516	−	1.47339i	−0.0127900	−	0.0587946i
$629$	0.829986	+	0.379042i	0.0330937	+	0.0151134i
$630$	−6.50553	−	4.15941i	−0.259187	−	0.165715i
$631$	11.9260	+	18.5573i	0.474768	+	0.738753i	0.993207	−	0.116361i	$-0.0371230\pi$
$631$	11.9260	+	18.5573i	0.474768	+	0.738753i	−0.518439	+	0.855115i	$0.673487\pi$
$632$	19.8711	+	14.8753i	0.790430	+	0.591708i
$633$	−21.0140	−	15.7309i	−0.835233	−	0.625248i
$634$	−17.2276	−	26.8067i	−0.684197	−	1.06463i
$635$	−30.5446	+	6.71933i	−1.21213	+	0.266649i
$636$	0.486291	+	0.222082i	0.0192827	+	0.00880611i
$637$	8.45041	+	38.8459i	0.334818	+	1.53913i
$638$	8.88310	+	4.85054i	0.351685	+	0.192035i
$639$	1.54408	−	1.33795i	0.0610829	−	0.0529287i
$640$	24.0658	−	18.1033i	0.951284	−	0.715595i
$641$	−23.3854	+	10.6797i	−0.923667	+	0.421824i	−0.819724	−	0.572759i	$-0.805873\pi$
$641$	−23.3854	+	10.6797i	−0.923667	+	0.421824i	−0.103943	+	0.994583i	$0.533146\pi$
$642$	−21.7580	−	29.0653i	−0.858720	−	1.14712i
$643$	9.34906	+	9.34906i	0.368691	+	0.368691i	0.867000	−	0.498309i	$-0.166045\pi$
$643$	9.34906	+	9.34906i	0.368691	+	0.368691i	−0.498309	+	0.867000i	$0.666045\pi$
$644$	7.77269	+	0.0800886i	0.306287	+	0.00315593i
$645$	−4.79075	+	0.700231i	−0.188636	+	0.0275716i
$646$	−0.236015	+	1.64152i	−0.00928587	+	0.0645847i
$647$	10.6757	−	28.6226i	0.419705	−	1.12527i	−0.539357	−	0.842077i	$-0.681333\pi$
$647$	10.6757	−	28.6226i	0.419705	−	1.12527i	0.959062	−	0.283195i	$-0.0913945\pi$
$648$	−15.4539	+	8.43847i	−0.607087	+	0.331495i
$649$	12.9269	+	14.9184i	0.507424	+	0.585598i
$650$	25.7739	−	16.7345i	1.01094	−	0.656382i
$651$	−23.3681	+	36.3614i	−0.915867	+	1.42512i
$652$	8.40613	−	3.13532i	0.329209	−	0.122789i
$653$	−0.358746	−	5.01593i	−0.0140388	−	0.196288i	−0.999631	−	0.0271512i	$-0.991356\pi$
$653$	−0.358746	−	5.01593i	−0.0140388	−	0.196288i	0.985593	−	0.169137i	$-0.0540981\pi$
$654$	10.2492	−	6.58677i	0.400776	−	0.257563i
$655$	−0.983613	−	3.32116i	−0.0384329	−	0.129769i
$656$	−6.12800	−	42.6212i	−0.239258	−	1.66408i
$657$	2.31268	+	0.503093i	0.0902262	+	0.0196275i
$658$	81.3535	−	5.81851i	3.17149	−	0.226829i
$659$	9.90689	−	21.6931i	0.385918	−	0.845042i	−0.612588	−	0.790402i	$-0.709872\pi$
$659$	9.90689	−	21.6931i	0.385918	−	0.845042i	0.998506	−	0.0546397i	$-0.0174010\pi$
$660$	5.88845	−	2.21196i	0.229208	−	0.0861004i
$661$	4.03122	+	13.7291i	0.156796	+	0.533999i	0.999994	−	0.00360508i	$-0.00114754\pi$
$661$	4.03122	+	13.7291i	0.156796	+	0.533999i	−0.843197	+	0.537605i	$0.819329\pi$
$662$	−0.235072	+	3.28674i	−0.00913634	+	0.127743i
$663$	−0.879942	−	1.61149i	−0.0341741	−	0.0625852i
$664$	−0.972828	−	2.13020i	−0.0377531	−	0.0826677i
$665$	−23.7727	−	23.6619i	−0.921866	−	0.917570i
$666$			2.59240i			0.100453i
$667$	6.46514	−	2.33578i	0.250331	−	0.0904418i
$668$	0.793279	−	0.793279i	0.0306929	−	0.0306929i
$669$	17.1756	+	2.46948i	0.664047	+	0.0954755i
$670$	−0.847769	−	1.31240i	−0.0327522	−	0.0507026i
$671$	15.9513	+	4.68371i	0.615791	+	0.180813i
$672$	−14.1446	−	1.01164i	−0.545640	−	0.0390250i
$673$	−0.265687	+	0.486570i	−0.0102415	+	0.0187559i	−0.882750	−	0.469844i	$-0.844310\pi$
$673$	−0.265687	+	0.486570i	−0.0102415	+	0.0187559i	0.872508	+	0.488600i	$0.162492\pi$
$674$	−13.0140	−	8.36359i	−0.501280	−	0.322153i
$675$	−22.1485	+	16.7421i	−0.852494	+	0.644405i
$676$	−0.716758	+	0.827183i	−0.0275676	+	0.0318147i
$677$	5.69936	−	26.1995i	0.219044	−	1.00693i	−0.727938	−	0.685643i	$-0.759521\pi$
$677$	5.69936	−	26.1995i	0.219044	−	1.00693i	0.946982	−	0.321287i	$-0.104115\pi$
$678$	−14.1418	+	18.8912i	−0.543113	+	0.725514i
$679$	31.8373	−	4.57751i	1.22180	−	0.175669i
$680$	−1.07573	−	1.23562i	−0.0412524	−	0.0473838i
$681$	17.5777	+	15.2312i	0.673578	+	0.583659i
$682$	16.4944	+	44.2231i	0.631602	+	1.69339i
$683$	7.37951	−	1.60531i	0.282369	−	0.0614256i	−0.0691502	−	0.997606i	$-0.522029\pi$
$683$	7.37951	−	1.60531i	0.282369	−	0.0614256i	0.351519	+	0.936181i	$0.385665\pi$
$684$	−0.742518	+	0.218023i	−0.0283909	+	0.00833632i
$685$	−1.69177	+	0.124970i	−0.0646392	+	0.00477486i
$686$	5.40282	−	18.4003i	0.206281	−	0.702528i
$687$	−8.20765	−	3.06129i	−0.313141	−	0.116796i
$688$	5.12001	−	3.83279i	0.195198	−	0.146124i
$689$	3.44644			0.131299
$690$	9.28420	−	24.2988i	0.353443	−	0.925040i
$691$	−29.9436			−1.13911			−0.569555	−	0.821953i	$-0.692884\pi$
$691$	−29.9436			−1.13911			−0.569555	+	0.821953i	$0.692884\pi$
$692$	4.17820	−	3.12776i	0.158831	−	0.118900i
$693$	−9.54690	−	3.56081i	−0.362657	−	0.135264i
$694$	−6.50688	+	22.1604i	−0.246998	+	0.841197i
$695$	2.23773	−	2.59469i	0.0848818	−	0.0984224i
$696$	−5.36081	+	1.57408i	−0.203201	+	0.0596652i
$697$	−2.67744	+	0.582441i	−0.101415	+	0.0220615i
$698$	19.0418	+	51.0530i	0.720742	+	1.93238i
$699$	−16.0689	−	13.9238i	−0.607781	−	0.526645i
$700$	−8.08058	+	0.615888i	−0.305417	+	0.0232784i
$701$	−12.9369	+	1.86004i	−0.488620	+	0.0702529i	−0.382222	−	0.924071i	$-0.624841\pi$
$701$	−12.9369	+	1.86004i	−0.488620	+	0.0702529i	−0.106398	+	0.994324i	$0.533932\pi$
$702$	20.4521	−	27.3208i	0.771915	−	1.03116i
$703$	−2.39370	+	11.0037i	−0.0902802	+	0.415011i
$704$	17.5484	−	20.2519i	0.661381	−	0.763274i
$705$	12.5289	−	43.0410i	0.471864	−	1.62102i
$706$	−5.56246	−	3.57477i	−0.209346	−	0.134538i
$707$	7.04407	−	12.9002i	0.264919	−	0.485164i
$708$	2.65837	+	0.190131i	0.0999078	+	0.00714555i
$709$	−3.21911	−	0.945215i	−0.120896	−	0.0354983i	0.220725	−	0.975336i	$-0.429158\pi$
$709$	−3.21911	−	0.945215i	−0.120896	−	0.0354983i	−0.341621	+	0.939838i	$0.610976\pi$
$710$	2.74543	−	12.7640i	0.103034	−	0.479025i
$711$	5.35004	+	0.769220i	0.200642	+	0.0288480i
$712$	8.42523	−	8.42523i	0.315749	−	0.315749i
$713$	29.9188	+	11.5117i	1.12047	+	0.431115i
$714$			2.94815i			0.110332i
$715$	28.6070	−	28.7410i	1.06984	−	1.07485i
$716$	0.282900	+	0.619465i	0.0105725	+	0.0231505i
$717$	−17.8608	−	32.7097i	−0.667025	−	1.22157i
$718$	1.95203	−	27.2929i	0.0728491	−	1.01856i
$719$	12.1438	+	41.3579i	0.452887	+	1.54239i	0.797306	+	0.603575i	$0.206258\pi$
$719$	12.1438	+	41.3579i	0.452887	+	1.54239i	−0.344420	+	0.938816i	$0.611924\pi$
$720$	2.31693	−	5.10489i	0.0863469	−	0.190248i
$721$	−22.8471	+	50.0282i	−0.850871	+	1.86315i
$722$	8.90181	−	0.636670i	0.331291	−	0.0236944i
$723$	37.2399	+	8.10103i	1.38497	+	0.301281i
$724$	−1.37689	−	9.57648i	−0.0511717	−	0.355907i
$725$	−6.50517	+	3.00761i	−0.241596	+	0.111700i
$726$	20.0697	−	12.8980i	0.744856	−	0.478690i
$727$	−0.160401	−	2.24270i	−0.00594895	−	0.0831772i	0.993610	−	0.112866i	$-0.0360030\pi$
$727$	−0.160401	−	2.24270i	−0.00594895	−	0.0831772i	−0.999559	+	0.0296885i	$0.990548\pi$
$728$	−38.1610	+	14.2333i	−1.41434	+	0.527522i
$729$	−16.1949	+	25.1998i	−0.599812	+	0.933326i
$730$	13.7427	−	6.31492i	0.508640	−	0.233726i
$731$	−0.266518	−	0.307578i	−0.00985752	−	0.0113762i
$732$	1.97001	−	1.07571i	0.0728137	−	0.0397593i
$733$	−2.47619	+	6.63893i	−0.0914603	+	0.245215i	−0.974623	−	0.223852i	$-0.928137\pi$
$733$	−2.47619	+	6.63893i	−0.0914603	+	0.245215i	0.883163	+	0.469066i	$0.155410\pi$
$734$	2.02036	−	14.0519i	0.0745728	−	0.518665i
$735$	−28.1348	−	20.9591i	−1.03777	−	0.773088i
$736$	1.38944	+	10.4252i	0.0512155	+	0.384278i
$737$	−1.45787	−	1.45787i	−0.0537015	−	0.0537015i
$738$	−4.66536	−	6.23219i	−0.171734	−	0.229410i
$739$	−30.6945	+	14.0177i	−1.12912	+	0.515650i	−0.890282	−	0.455411i	$-0.849492\pi$
$739$	−30.6945	+	14.0177i	−1.12912	+	0.515650i	−0.238834	+	0.971060i	$0.576765\pi$
$740$	1.63560	+	2.17430i	0.0601258	+	0.0799288i
$741$	17.1255	−	14.8393i	0.629121	−	0.545137i
$742$	−4.85695	−	2.65209i	−0.178304	−	0.0973614i
$743$	−0.386449	−	1.77648i	−0.0141774	−	0.0651726i	0.969515	−	0.245033i	$-0.0787989\pi$
$743$	−0.386449	−	1.77648i	−0.0141774	−	0.0651726i	−0.983692	+	0.179861i	$0.942435\pi$
$744$	−23.7006	−	10.8237i	−0.868905	−	0.396816i
$745$	−9.15479	+	14.3186i	−0.335406	+	0.524591i
$746$	29.2140	+	45.4578i	1.06960	+	1.66433i
$747$	−0.408225	−	0.305594i	−0.0149362	−	0.0111811i
$748$	0.423284	+	0.316867i	0.0154768	+	0.0115858i
$749$	33.3715	+	51.9271i	1.21937	+	1.89738i
$750$	−7.45793	+	26.0738i	−0.272325	+	0.952082i
$751$	−14.4073	−	6.57958i	−0.525729	−	0.240092i	0.134827	−	0.990869i	$-0.456952\pi$
$751$	−14.4073	−	6.57958i	−0.525729	−	0.240092i	−0.660556	+	0.750777i	$0.729679\pi$
$752$	12.5872	+	57.8625i	0.459008	+	2.11003i
$753$	−30.5080	−	16.6586i	−1.11177	−	0.607074i
$754$	6.65774	−	5.76896i	0.242461	−	0.210093i
$755$	−4.18484	−	0.591716i	−0.152302	−	0.0215348i
$756$	−8.18676	+	3.73877i	−0.297749	+	0.135978i
$757$	9.50293	+	12.6944i	0.345390	+	0.461387i	0.939276	−	0.343162i	$-0.111498\pi$
$757$	9.50293	+	12.6944i	0.345390	+	0.461387i	−0.593886	+	0.804549i	$0.702407\pi$
$758$	−27.1553	−	27.1553i	−0.986326	−	0.986326i
$759$	5.23482	−	33.9239i	0.190012	−	1.23136i
$760$	12.0790	−	16.2144i	0.438151	−	0.588159i
$761$	2.43263	−	16.9193i	0.0881826	−	0.613324i	−0.897028	−	0.441974i	$-0.854278\pi$
$761$	2.43263	−	16.9193i	0.0881826	−	0.613324i	0.985210	−	0.171349i	$-0.0548127\pi$
$762$	−11.8561	+	31.7874i	−0.429500	+	1.15153i
$763$	−18.1792	+	9.92661i	−0.658133	+	0.359368i
$764$	1.58175	+	1.82543i	0.0572256	+	0.0660418i
$765$	−0.334536	−	0.123886i	−0.0120952	−	0.00447911i
$766$	−11.6546	+	18.1349i	−0.421098	+	0.655241i
$767$	16.0983	−	6.00436i	0.581276	−	0.216805i
$768$	−1.01708	−	14.2207i	−0.0367008	−	0.513144i
$769$	36.9331	−	23.7355i	1.33184	−	0.855924i	0.335556	−	0.942020i	$-0.391076\pi$
$769$	36.9331	−	23.7355i	1.33184	−	0.855924i	0.996287	+	0.0860967i	$0.0274394\pi$
$770$	−62.4316	+	18.4901i	−2.24988	+	0.666336i
$771$	−2.46890	−	17.1716i	−0.0889153	−	0.618420i
$772$	−1.40625	−	0.305912i	−0.0506121	−	0.0110100i
$773$	29.0209	−	2.07562i	1.04381	−	0.0746548i	0.461111	−	0.887343i	$-0.347451\pi$
$773$	29.0209	−	2.07562i	1.04381	−	0.0746548i	0.582699	+	0.812688i	$0.301997\pi$
$774$	0.480349	−	1.05182i	0.0172658	−	0.0378068i
$775$	−32.1116	−	9.26610i	−1.15348	−	0.332848i
$776$	5.46255	+	18.6037i	0.196094	+	0.667835i
$777$	−1.42813	+	19.9678i	−0.0512338	+	0.716342i
$778$	1.00027	+	1.83185i	0.0358613	+	0.0656751i
$779$	−14.0480	−	30.7608i	−0.503322	−	1.10212i
$780$	−0.0127877	−	5.47499i	−0.000457874	−	0.196036i
$781$		−	17.2285i		−	0.616486i
$782$	2.14125	−	0.442746i	0.0765711	−	0.0158326i
$783$	−5.62802	+	5.62802i	−0.201129	+	0.201129i
$784$	45.8725	+	6.59548i	1.63830	+	0.235553i
$785$	8.38676	+	1.80392i	0.299336	+	0.0643847i
$786$	−3.60521	−	1.05859i	−0.128594	−	0.0377585i
$787$	−25.7117	−	1.83894i	−0.916523	−	0.0655510i	−0.394897	−	0.918725i	$-0.629220\pi$
$787$	−25.7117	−	1.83894i	−0.916523	−	0.0655510i	−0.521626	+	0.853174i	$0.674674\pi$
$788$	−3.81479	+	6.98626i	−0.135896	+	0.248875i
$789$	34.9455	+	22.4581i	1.24409	+	0.799530i
$790$	30.2758	−	16.6238i	1.07717	−	0.591447i
$791$	26.2725	−	30.3201i	0.934144	−	1.07806i
$792$	1.30562	−	6.00185i	0.0463932	−	0.213266i
$793$	8.67163	−	11.5839i	0.307939	−	0.411358i
$794$	−9.16993	+	1.31844i	−0.325429	+	0.0467896i
$795$	−2.29395	+	1.99712i	−0.0813581	+	0.0708306i
$796$	−1.83522	−	1.59022i	−0.0650475	−	0.0563640i
$797$	9.98681	+	26.7757i	0.353751	+	0.948443i	0.984953	+	0.172825i	$0.0552894\pi$
$797$	9.98681	+	26.7757i	0.353751	+	0.948443i	−0.631201	+	0.775619i	$0.717438\pi$
$798$	−35.5535	+	7.73420i	−1.25858	+	0.273788i
$799$	3.61551	−	1.06161i	0.127908	−	0.0375571i
$800$	−2.38083	−	10.7036i	−0.0841752	−	0.378428i
$801$	0.730964	−	2.48944i	0.0258273	−	0.0879599i
$802$	−13.5186	−	5.04217i	−0.477358	−	0.178045i
$803$	15.9770	−	11.9602i	0.563816	−	0.422068i
$804$	−0.278365			−0.00981718
$805$	−18.6910	+	40.0793i	−0.658770	+	1.41261i
$806$	41.0822			1.44706
$807$	−30.1737	+	22.5878i	−1.06217	+	0.795127i
$808$	8.30152	+	3.09631i	0.292046	+	0.108928i
$809$	−3.72336	+	12.6806i	−0.130906	+	0.445826i	−0.998693	−	0.0511109i	$-0.983724\pi$
$809$	−3.72336	+	12.6806i	−0.130906	+	0.445826i	0.867787	+	0.496937i	$0.165542\pi$
$810$	1.80494	+	24.4342i	0.0634192	+	0.858532i
$811$	12.9426	−	3.80030i	0.454477	−	0.133447i	−0.0464788	−	0.998919i	$-0.514800\pi$
$811$	12.9426	−	3.80030i	0.454477	−	0.133447i	0.500956	+	0.865473i	$0.332982\pi$
$812$	−2.27010	+	0.493830i	−0.0796649	+	0.0173300i
$813$	−11.6845	−	31.3273i	−0.409792	−	1.09870i
$814$	16.5210	+	14.3155i	0.579060	+	0.501759i
$815$	−3.52245	+	50.9214i	−0.123386	+	1.78370i
$816$	−2.11865	+	0.304616i	−0.0741677	+	0.0106637i
$817$	3.01008	−	4.02100i	0.105310	−	0.140677i
$818$	9.97325	−	45.8463i	0.348707	−	1.60298i
$819$	−5.80785	+	6.70261i	−0.202943	+	0.234208i
$820$	−7.84494	−	2.28359i	−0.273957	−	0.0797466i
$821$	28.1910	+	18.1172i	0.983871	+	0.632296i	0.930505	−	0.366279i	$-0.119369\pi$
$821$	28.1910	+	18.1172i	0.983871	+	0.632296i	0.0533664	+	0.998575i	$0.483005\pi$
$822$	−0.881913	+	1.61510i	−0.0307602	+	0.0563332i
$823$	−13.8351	−	0.989507i	−0.482262	−	0.0344921i	−0.171908	−	0.985113i	$-0.554993\pi$
$823$	−13.8351	−	0.989507i	−0.482262	−	0.0344921i	−0.310354	+	0.950621i	$0.600448\pi$
$824$	−31.8105	−	9.34039i	−1.10817	−	0.325388i
$825$	−2.38622	+	35.7071i	−0.0830776	+	1.24316i
$826$	−27.3073	−	3.92619i	−0.950141	−	0.136610i
$827$	−1.92931	+	1.92931i	−0.0670885	+	0.0670885i	−0.739855	−	0.672766i	$-0.765106\pi$
$827$	−1.92931	+	1.92931i	−0.0670885	+	0.0670885i	0.672766	+	0.739855i	$0.265106\pi$
$828$	0.603005	+	0.823063i	0.0209559	+	0.0286034i
$829$			13.4993i			0.468849i	0.972134	+	0.234424i	$0.0753205\pi$
$829$			13.4993i			0.468849i	−0.972134	+	0.234424i	$0.924679\pi$
$830$	−3.25860	+	0.00761098i	−0.113108	+	0.000264181i
$831$	−8.25155	−	18.0684i	−0.286243	−	0.626785i
$832$	−11.1782	−	20.4713i	−0.387533	−	0.709713i
$833$	0.210385	−	2.94157i	0.00728941	−	0.101919i
$834$	−1.04715	−	3.56627i	−0.0362599	−	0.123490i
$835$	2.24446	+	5.97496i	0.0776726	+	0.206772i
$836$	−2.71084	+	5.93591i	−0.0937563	+	0.205298i
$837$	−37.0226	+	2.64791i	−1.27969	+	0.0915251i
$838$	3.95746	+	0.860892i	0.136708	+	0.0297390i
$839$	−5.83579	−	40.5888i	−0.201474	−	1.40128i	−0.799914	−	0.600114i	$-0.795122\pi$
$839$	−5.83579	−	40.5888i	−0.201474	−	1.40128i	0.598441	−	0.801167i	$-0.295787\pi$
$840$	17.1522	−	31.5871i	0.591807	−	1.08986i
$841$	22.6680	−	14.5678i	0.781655	−	0.502339i
$842$	2.28774	+	31.9867i	0.0788406	+	1.10234i
$843$	35.6572	−	13.2994i	1.22810	−	0.458057i
$844$	3.55722	−	5.53514i	0.122444	−	0.190527i
$845$	−2.60002	−	5.65825i	−0.0894435	−	0.194650i
$846$	7.01090	+	8.09101i	0.241040	+	0.278175i
$847$	−35.5980	+	19.4380i	−1.22316	+	0.667897i
$848$	1.40405	−	3.76441i	0.0482154	−	0.129270i
$849$	0.303167	−	2.10857i	0.0104047	−	0.0723661i
$850$	−2.18427	+	0.652457i	−0.0749198	+	0.0223791i
$851$	14.7172	−	1.96146i	0.504499	−	0.0672381i
$852$	−1.64480	−	1.64480i	−0.0563500	−	0.0563500i
$853$	16.9825	+	22.6859i	0.581469	+	0.776751i	0.990756	−	0.135654i	$-0.0433137\pi$
$853$	16.9825	+	22.6859i	0.581469	+	0.776751i	−0.409288	+	0.912405i	$0.634223\pi$
$854$	−21.1347	+	9.65189i	−0.723214	+	0.330281i
$855$	0.616394	−	4.35937i	0.0210802	−	0.149087i
$856$	−28.1206	+	24.3666i	−0.961141	+	0.832833i
$857$	−0.670306	−	0.366015i	−0.0228972	−	0.0125028i	0.467760	−	0.883856i	$-0.345061\pi$
$857$	−0.670306	−	0.366015i	−0.0228972	−	0.0125028i	−0.490657	+	0.871353i	$0.663243\pi$
$858$	−9.35057	−	42.9839i	−0.319223	−	1.46745i
$859$	−4.96348	−	2.26675i	−0.169352	−	0.0773404i	0.328935	−	0.944352i	$-0.393310\pi$
$859$	−4.96348	−	2.26675i	−0.169352	−	0.0773404i	−0.498287	+	0.867012i	$0.666037\pi$
$860$	−0.260735	−	1.18524i	−0.00889098	−	0.0404165i
$861$	−32.5014	−	50.5732i	−1.10765	−	1.72353i
$862$	43.9883	+	32.9292i	1.49825	+	1.12157i
$863$	−28.2172	−	21.1231i	−0.960524	−	0.719039i	−0.000804477	−	1.00000i	$-0.500256\pi$
$863$	−28.2172	−	21.1231i	−0.960524	−	0.719039i	−0.959719	+	0.280961i	$0.909347\pi$
$864$	−6.58368	−	10.2444i	−0.223981	−	0.348522i
$865$	6.37958	+	29.0002i	0.216912	+	0.986035i
$866$	49.9511	+	22.8119i	1.69741	+	0.775180i
$867$	−5.63727	−	25.9141i	−0.191452	−	0.880089i
$868$	−9.50879	−	5.19219i	−0.322750	−	0.176235i
$869$	34.4456	−	29.8473i	1.16849	−	1.01250i
$870$	−1.08843	+	7.69782i	−0.0369014	+	0.260981i
$871$	−1.63238	+	0.745482i	−0.0553110	+	0.0252597i
$872$	−7.48250	−	9.99545i	−0.253389	−	0.338489i
$873$	2.98542	+	2.98542i	0.101041	+	0.101041i
$874$	10.9567	+	24.6612i	0.370616	+	0.834176i
$875$	15.8093	−	43.3109i	0.534452	−	1.46417i
$876$	0.383479	−	2.66716i	0.0129566	−	0.0901149i
$877$	−15.5240	+	41.6214i	−0.524208	+	1.40545i	0.357613	+	0.933870i	$0.383591\pi$
$877$	−15.5240	+	41.6214i	−0.524208	+	1.40545i	−0.881821	+	0.471585i	$0.843682\pi$
$878$	−36.3208	+	19.8326i	−1.22577	+	0.669319i
$879$	1.96605	+	2.26894i	0.0663133	+	0.0765296i
$880$	−19.7384	−	42.9552i	−0.665380	−	1.44802i
$881$	7.42462	−	11.5529i	0.250142	−	0.389228i	−0.693362	−	0.720589i	$-0.743871\pi$
$881$	7.42462	−	11.5529i	0.250142	−	0.389228i	0.943504	+	0.331361i	$0.107508\pi$
$882$	7.85055	−	2.92810i	0.264342	−	0.0985944i
$883$	−2.94868	−	41.2280i	−0.0992310	−	1.38743i	−0.766323	−	0.642456i	$-0.777916\pi$
$883$	−2.94868	−	41.2280i	−0.0992310	−	1.38743i	0.667092	−	0.744976i	$-0.267539\pi$
$884$	0.387164	−	0.248815i	0.0130217	−	0.00836856i
$885$	−7.23569	+	13.3251i	−0.243225	+	0.447917i
$886$	−3.36654	−	23.4148i	−0.113101	−	0.786635i
$887$	−45.2295	−	9.83907i	−1.51866	−	0.330364i	−0.625542	−	0.780191i	$-0.715122\pi$
$887$	−45.2295	−	9.83907i	−1.51866	−	0.330364i	−0.893116	+	0.449827i	$0.851486\pi$
$888$	−12.0368	+	0.860886i	−0.403927	+	0.0288895i
$889$	23.9605	−	52.4663i	0.803611	−	1.75966i
$890$	−5.83025	−	15.5207i	−0.195430	−	0.520255i
$891$	9.10873	+	31.0215i	0.305154	+	1.03926i
$892$	−0.310284	+	4.33833i	−0.0103891	+	0.145258i
$893$	22.2875	+	40.8166i	0.745824	+	1.36587i
$894$	7.65853	+	16.7699i	0.256140	+	0.560868i
$895$	−3.87443	+	0.00904935i	−0.129508	+	0.000302486i
$896$			55.5387i			1.85542i
$897$	−26.0734	−	14.5879i	−0.870566	−	0.487076i
$898$	−14.1032	+	14.1032i	−0.470631	+	0.470631i
$899$	−9.48355	−	1.36353i	−0.316294	−	0.0454762i
$900$	−0.700359	−	0.800669i	−0.0233453	−	0.0266890i
$901$	−0.245309	−	0.0720292i	−0.00817242	−	0.00239964i
$902$	−65.4794	−	4.68318i	−2.18023	−	0.155933i
$903$	4.27930	−	7.83695i	0.142406	−	0.260797i
$904$	20.3451	+	13.0750i	0.676667	+	0.434867i
$905$	52.8500	+	15.3842i	1.75679	+	0.511387i
$906$	−3.00239	+	3.46495i	−0.0997479	+	0.115115i
$907$	−0.593994	+	2.73055i	−0.0197233	+	0.0906664i	−0.985956	−	0.167003i	$-0.946591\pi$
$907$	−0.593994	+	2.73055i	−0.0197233	+	0.0906664i	0.966233	+	0.257670i	$0.0829546\pi$
$908$	−3.49372	+	4.66706i	−0.115943	+	0.154882i
$909$	1.90968	−	0.274570i	0.0633400	−	0.00910692i
$910$	−3.91101	+	56.5386i	−0.129649	+	1.87424i
$911$	−35.2034	−	30.5039i	−1.16634	−	1.01064i	−0.999697	−	0.0246230i	$-0.992161\pi$
$911$	−35.2034	−	30.5039i	−1.16634	−	1.01064i	−0.166644	−	0.986017i	$-0.553293\pi$
$912$	−9.23164	−	24.7510i	−0.305690	−	0.819587i
$913$	−4.20177	+	0.914039i	−0.139058	+	0.0302503i
$914$	−50.6109	+	14.8607i	−1.67406	+	0.491549i
$915$	0.940748	+	12.7353i	0.0311002	+	0.421015i
$916$	0.618607	−	2.10678i	0.0204394	−	0.0696101i
$917$	5.98524	+	2.23238i	0.197650	+	0.0737196i
$918$	−2.02672	+	1.51719i	−0.0668918	+	0.0500746i
$919$	−48.5619			−1.60191			−0.800955	−	0.598725i	$-0.795674\pi$
$919$	−48.5619			−1.60191			−0.800955	+	0.598725i	$0.795674\pi$
$920$	−25.5177	−	7.71404i	−0.841293	−	0.254324i
$921$	12.6583			0.417105
$922$	0.129897	−	0.0972393i	0.00427791	−	0.00320241i
$923$	−14.0503	−	5.24048i	−0.462470	−	0.172492i
$924$	−3.26828	+	11.1307i	−0.107519	+	0.366175i
$925$	−15.1101	+	3.36100i	−0.496817	+	0.110509i
$926$	−53.5740	+	15.7307i	−1.76055	+	0.516944i
$927$	−7.05424	+	1.53456i	−0.231692	+	0.0504014i
$928$	−1.09850	−	2.94520i	−0.0360602	−	0.0966811i
$929$	15.1725	+	13.1470i	0.497793	+	0.431340i	0.867224	−	0.497918i	$-0.165902\pi$
$929$	15.1725	+	13.1470i	0.497793	+	0.431340i	−0.369431	+	0.929258i	$0.620447\pi$
$930$	−27.3443	+	23.8061i	−0.896656	+	0.780631i
$931$	36.0260	−	5.17976i	1.18071	−	0.169760i
$932$	3.19383	−	4.26646i	0.104617	−	0.139752i
$933$	−1.38878	+	6.38413i	−0.0454667	+	0.209007i
$934$	31.1251	−	35.9202i	1.01844	−	1.17535i
$935$	−2.63685	+	1.44784i	−0.0862343	+	0.0473493i
$936$	−4.49751	−	2.89037i	−0.147006	−	0.0944748i
$937$	22.8241	−	41.7992i	0.745631	−	1.36552i	−0.178691	−	0.983905i	$-0.557186\pi$
$937$	22.8241	−	41.7992i	0.745631	−	1.36552i	0.924321	−	0.381615i	$-0.124632\pi$
$938$	2.87411	+	0.205561i	0.0938431	+	0.00671179i
$939$	28.3485	+	8.32388i	0.925119	+	0.271639i
$940$	10.9850	+	2.36278i	0.358290	+	0.0770653i
$941$	15.8119	+	2.27341i	0.515453	+	0.0741110i	0.395133	−	0.918624i	$-0.370699\pi$
$941$	15.8119	+	2.27341i	0.515453	+	0.0741110i	0.120321	+	0.992735i	$0.461608\pi$
$942$	6.58023	−	6.58023i	0.214396	−	0.214396i
$943$	−31.8505	+	31.2008i	−1.03720	+	1.01604i
$944$		−	20.0297i		−	0.651911i
$945$	−0.119595	−	51.2038i	−0.00389042	−	1.66566i
$946$	−4.05054	−	8.86944i	−0.131694	−	0.288371i
$947$	−5.42750	−	9.93973i	−0.176370	−	0.322998i	0.774508	−	0.632565i	$-0.217998\pi$
$947$	−5.42750	−	9.93973i	−0.176370	−	0.322998i	−0.950878	+	0.309567i	$0.899816\pi$
$948$	0.439000	−	6.13802i	0.0142581	−	0.199354i
$949$	−4.89405	−	16.6676i	−0.158868	−	0.541054i
$950$	−13.5986	−	24.6297i	−0.441197	−	0.799094i
$951$	13.4177	−	29.3806i	0.435098	−	0.952731i
$952$	3.01368	−	0.215543i	0.0976739	−	0.00698577i
$953$	36.2222	+	7.87966i	1.17335	+	0.255247i	0.756665	−	0.653802i	$-0.226827\pi$
$953$	36.2222	+	7.87966i	1.17335	+	0.255247i	0.416688	+	0.909050i	$0.363191\pi$
$954$	−0.103376	−	0.718994i	−0.00334691	−	0.0232783i
$955$	−13.1761	+	3.90231i	−0.426369	+	0.126276i
$956$	7.85856	−	5.05039i	0.254164	−	0.163341i
$957$	0.731872	+	10.2329i	0.0236581	+	0.330783i
$958$	−30.6352	+	11.4264i	−0.989780	+	0.369169i
$959$	1.69141	−	2.63189i	0.0546186	−	0.0849881i
$960$	19.3028	+	7.14825i	0.622994	+	0.230709i
$961$	−8.95886	−	10.3391i	−0.288996	−	0.333519i
$962$	16.6999	−	9.11883i	0.538426	−	0.294003i
$963$	−2.83146	+	7.59145i	−0.0912426	+	0.244631i
$964$	−1.35948	+	9.45542i	−0.0437860	+	0.304538i
$965$	4.89137	−	6.56602i	0.157459	−	0.211368i
$966$	25.5187	+	40.6222i	0.821052	+	1.30700i
$967$	18.9542	+	18.9542i	0.609525	+	0.609525i	0.942822	−	0.333297i	$-0.108161\pi$
$967$	18.9542	+	18.9542i	0.609525	+	0.609525i	−0.333297	+	0.942822i	$0.608161\pi$
$968$	−14.6520	−	19.5728i	−0.470933	−	0.629093i
$969$	−1.52909	+	0.698311i	−0.0491214	+	0.0224330i
$970$	26.7139	+	3.77722i	0.857732	+	0.121279i
$971$	40.0798	−	34.7294i	1.28622	−	1.11452i	0.299158	−	0.954204i	$-0.403294\pi$
$971$	40.0798	−	34.7294i	1.28622	−	1.11452i	0.987066	−	0.160315i	$-0.0512511\pi$
$972$	−1.91524	−	1.04580i	−0.0614314	−	0.0335441i
$973$	1.34320	+	6.17460i	0.0430611	+	0.197949i
$974$	11.6800	+	5.33409i	0.374252	+	0.170915i
$975$	28.3941	+	12.8072i	0.909339	+	0.410159i
$976$	−9.11994	−	14.1909i	−0.291922	−	0.454240i
$977$	26.9507	+	20.1751i	0.862230	+	0.645457i	0.936070	−	0.351813i	$-0.114435\pi$
$977$	26.9507	+	20.1751i	0.862230	+	0.645457i	−0.0738405	+	0.997270i	$0.523526\pi$
$978$	44.3264	+	33.1823i	1.41740	+	1.06105i
$979$	−11.8283	−	18.4053i	−0.378035	−	0.588235i
$980$	4.73702	−	7.40893i	0.151318	−	0.236670i
$981$	−2.47313	−	1.12944i	−0.0789609	−	0.0360602i
$982$	−8.39611	−	38.5963i	−0.267931	−	1.23166i
$983$	2.56624	+	1.40127i	0.0818503	+	0.0446936i	0.519653	−	0.854378i	$-0.326061\pi$
$983$	2.56624	+	1.40127i	0.0818503	+	0.0446936i	−0.437803	+	0.899071i	$0.644243\pi$
$984$	27.3874	−	23.7313i	0.873077	−	0.756526i
$985$	−27.2236	−	36.1900i	−0.867417	−	1.15311i
$986$	−0.594450	+	0.271476i	−0.0189312	+	0.00864557i
$987$	49.5439	+	66.1829i	1.57700	+	2.10662i
$988$	4.01630	+	4.01630i	0.127776	+	0.127776i
$989$	−6.33466	−	1.93114i	−0.201431	−	0.0614066i
$990$	−6.85400	−	5.10590i	−0.217834	−	0.162276i
$991$	−5.16058	+	35.8926i	−0.163931	+	1.14017i	0.727202	+	0.686424i	$0.240820\pi$
$991$	−5.16058	+	35.8926i	−0.163931	+	1.14017i	−0.891133	+	0.453742i	$0.850089\pi$
$992$	5.12279	−	13.7347i	0.162649	−	0.436078i
$993$	−2.93148	+	1.60071i	−0.0930276	+	0.0507969i
$994$	15.7679	+	18.1972i	0.500128	+	0.577179i
$995$	12.5536	−	5.76850i	0.397975	−	0.182874i
$996$	−0.313878	+	0.488404i	−0.00994561	+	0.0154757i
$997$	28.6935	−	10.7021i	0.908733	−	0.338940i	0.148744	−	0.988876i	$-0.452477\pi$
$997$	28.6935	−	10.7021i	0.908733	−	0.338940i	0.759989	+	0.649936i	$0.225204\pi$
$998$	3.10840	+	43.4611i	0.0983946	+	1.37574i
$999$	−14.4619	+	9.29413i	−0.457556	+	0.294053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.107.3	yes	200
5.2	odd	4		575.2.r.b.268.3		200
5.3	odd	4	inner	115.2.l.a.38.8	✓	200
5.4	even	2		575.2.r.b.107.8		200
23.20	odd	22	inner	115.2.l.a.112.8	yes	200
115.43	even	44	inner	115.2.l.a.43.3	yes	200
115.89	odd	22		575.2.r.b.457.3		200
115.112	even	44		575.2.r.b.43.8		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.38.8	✓	200	5.3	odd	4	inner
115.2.l.a.43.3	yes	200	115.43	even	44	inner
115.2.l.a.107.3	yes	200	1.1	even	1	trivial
115.2.l.a.112.8	yes	200	23.20	odd	22	inner
575.2.r.b.43.8		200	115.112	even	44
575.2.r.b.107.8		200	5.4	even	2
575.2.r.b.268.3		200	5.2	odd	4
575.2.r.b.457.3		200	115.89	odd	22

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23839 + 0.927048i) q^{2} +(-1.46916 - 0.547968i) q^{3} +(0.110730 - 0.377111i) q^{4} +(1.69332 + 1.46036i) q^{5} +(2.32738 - 0.683382i) q^{6} +(-4.02961 + 0.876587i) q^{7} +(-0.868729 - 2.32915i) q^{8} +(-0.409093 - 0.354481i) q^{9} +(-3.45082 - 0.238708i) q^{10} +(-4.51811 + 0.649606i) q^{11} +(-0.369324 + 0.493360i) q^{12} +(-0.844524 + 3.88221i) q^{13} +(4.17759 - 4.82120i) q^{14} +(-1.68753 - 3.07339i) q^{15} +(3.89634 + 2.50403i) q^{16} +(0.141248 - 0.258676i) q^{17} +(0.835238 + 0.0597374i) q^{18} +(3.49008 + 1.02478i) q^{19} +(0.738221 - 0.476866i) q^{20} +(6.40047 + 0.920248i) q^{21} +(4.99297 - 4.99297i) q^{22} +(-0.292826 - 4.78688i) q^{23} +3.89793i q^{24} +(0.734685 + 4.94573i) q^{25} +(-2.55315 - 5.59062i) q^{26} +(2.66120 + 4.87362i) q^{27} +(-0.115627 + 1.61667i) q^{28} +(0.403824 + 1.37530i) q^{29} +(4.93900 + 2.24164i) q^{30} +(-2.77678 + 6.08030i) q^{31} +(-2.18744 + 0.156449i) q^{32} +(6.99378 + 1.52140i) q^{33} +(0.0648851 + 0.451286i) q^{34} +(-8.10356 - 4.40034i) q^{35} +(-0.178977 + 0.115022i) q^{36} +(0.220858 + 3.08799i) q^{37} +(-5.27211 + 1.96640i) q^{38} +(3.36807 - 5.24081i) q^{39} +(1.93037 - 5.21266i) q^{40} +(-6.08818 - 7.02614i) q^{41} +(-8.77940 + 4.79391i) q^{42} +(0.482569 - 1.29382i) q^{43} +(-0.255316 + 1.77576i) q^{44} +(-0.175056 - 1.19767i) q^{45} +(4.80030 + 5.65657i) q^{46} +(9.04049 + 9.04049i) q^{47} +(-4.35221 - 5.81388i) q^{48} +(9.10189 - 4.15669i) q^{49} +(-5.49476 - 5.44366i) q^{50} +(-0.349262 + 0.302637i) q^{51} +(1.37051 + 0.748357i) q^{52} +(-0.184392 - 0.847638i) q^{53} +(-7.81368 - 3.56839i) q^{54} +(-8.59928 - 5.49808i) q^{55} +(5.54234 + 8.62405i) q^{56} +(-4.56593 - 3.41802i) q^{57} +(-1.77506 - 1.32879i) q^{58} +(-2.33805 - 3.63807i) q^{59} +(-1.34587 + 0.296070i) q^{60} +(-3.31298 - 1.51299i) q^{61} +(-2.19799 - 10.1040i) q^{62} +(1.95921 + 1.06981i) q^{63} +(-4.43677 + 3.84448i) q^{64} +(-7.09949 + 5.34053i) q^{65} +(-10.0714 + 4.59948i) q^{66} +(0.270684 + 0.361592i) q^{67} +(-0.0819094 - 0.0819094i) q^{68} +(-2.19285 + 7.19315i) q^{69} +(14.1147 - 2.06305i) q^{70} +(-0.537154 + 3.73599i) q^{71} +(-0.470249 + 1.26079i) q^{72} +(-3.83749 + 2.09543i) q^{73} +(-3.13623 - 3.61940i) q^{74} +(1.63073 - 7.66864i) q^{75} +(0.772913 - 1.20268i) q^{76} +(17.6368 - 6.57817i) q^{77} +(0.687502 + 9.61254i) q^{78} +(-8.40008 + 5.39840i) q^{79} +(2.94098 + 9.93019i) q^{80} +(-1.00803 - 7.01097i) q^{81} +(14.0531 + 3.05707i) q^{82} +(0.939647 - 0.0672048i) q^{83} +(1.05576 - 2.31179i) q^{84} +(0.616939 - 0.231749i) q^{85} +(0.601822 + 2.04962i) q^{86} +(0.160338 - 2.24181i) q^{87} +(5.43804 + 9.95903i) q^{88} +(1.99112 + 4.35995i) q^{89} +(1.32709 + 1.32090i) q^{90} -16.3841i q^{91} +(-1.83761 - 0.419623i) q^{92} +(7.41134 - 7.41134i) q^{93} +(-19.5766 - 2.81470i) q^{94} +(4.41329 + 6.83207i) q^{95} +(3.29943 + 0.968799i) q^{96} +(-7.77981 - 0.556423i) q^{97} +(-7.41825 + 13.5855i) q^{98} +(2.07860 + 1.33583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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