LMFDB - Embedded newform 370.2.o.d.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			181.3
Character	$\chi$	$=$	370.181
Dual form			370.2.o.d.231.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(0.207212 + 1.17516i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{5} +1.19329 q^{6} +(-2.54999 + 2.13970i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.48102 - 0.539047i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(0.207212 + 1.17516i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{5} +1.19329 q^{6} +(-2.54999 + 2.13970i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.48102 - 0.539047i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-3.17268 + 5.49525i) q^{11} +(0.207212 - 1.17516i) q^{12} +(-6.51288 - 2.37049i) q^{13} +(1.66439 + 2.88281i) q^{14} +(-0.914110 - 0.767030i) q^{15} +(0.766044 + 0.642788i) q^{16} +(4.46459 - 1.62498i) q^{17} +(-0.273681 - 1.55212i) q^{18} +(0.803718 + 4.55811i) q^{19} +(0.939693 - 0.342020i) q^{20} +(-3.04287 - 2.55327i) q^{21} +(4.86083 + 4.07872i) q^{22} +(-0.932323 - 1.61483i) q^{23} +(-1.12132 - 0.408128i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-3.46543 + 6.00230i) q^{26} +(2.73028 + 4.72898i) q^{27} +(3.12803 - 1.13851i) q^{28} +(-1.78944 + 3.09940i) q^{29} +(-0.914110 + 0.767030i) q^{30} +0.0697957 q^{31} +(0.766044 - 0.642788i) q^{32} +(-7.11520 - 2.58972i) q^{33} +(-0.825022 - 4.67893i) q^{34} +(0.578037 - 3.27821i) q^{35} -1.57607 q^{36} +(2.21684 + 5.66442i) q^{37} +4.62843 q^{38} +(1.43616 - 8.14485i) q^{39} +(-0.173648 - 0.984808i) q^{40} +(3.40012 + 1.23754i) q^{41} +(-3.04287 + 2.55327i) q^{42} +7.28570 q^{43} +(4.86083 - 4.07872i) q^{44} +(-0.788034 + 1.36492i) q^{45} +(-1.75219 + 0.637746i) q^{46} +(-4.49490 - 7.78540i) q^{47} +(-0.596643 + 1.03342i) q^{48} +(0.708620 - 4.01878i) q^{49} +(-0.939693 - 0.342020i) q^{50} +(2.83472 + 4.90988i) q^{51} +(5.30934 + 4.45507i) q^{52} +(-7.70559 - 6.46575i) q^{53} +(5.13125 - 1.86762i) q^{54} +(-1.10186 - 6.24896i) q^{55} +(-0.578037 - 3.27821i) q^{56} +(-5.18996 + 1.88899i) q^{57} +(2.74158 + 2.30046i) q^{58} +(0.743052 + 0.623495i) q^{59} +(0.596643 + 1.03342i) q^{60} +(10.1900 + 3.70885i) q^{61} +(0.0121199 - 0.0687354i) q^{62} +(-2.62319 + 4.54350i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(6.51288 - 2.37049i) q^{65} +(-3.78592 + 6.55740i) q^{66} +(-0.628408 + 0.527297i) q^{67} -4.75111 q^{68} +(1.70449 - 1.43024i) q^{69} +(-3.12803 - 1.13851i) q^{70} +(0.750450 + 4.25601i) q^{71} +(-0.273681 + 1.55212i) q^{72} +0.246060 q^{73} +(5.96331 - 1.19955i) q^{74} +1.19329 q^{75} +(0.803718 - 4.55811i) q^{76} +(-3.66785 - 20.8014i) q^{77} +(-7.77172 - 2.82868i) q^{78} +(3.98152 - 3.34089i) q^{79} -1.00000 q^{80} +(-1.36954 + 1.14918i) q^{81} +(1.80916 - 3.13356i) q^{82} +(-3.56146 + 1.29626i) q^{83} +(1.98609 + 3.44002i) q^{84} +(-2.37556 + 4.11458i) q^{85} +(1.26515 - 7.17501i) q^{86} +(-4.01308 - 1.46064i) q^{87} +(-3.17268 - 5.49525i) q^{88} +(-8.68118 - 7.28437i) q^{89} +(1.20734 + 1.01308i) q^{90} +(21.6799 - 7.89085i) q^{91} +(0.323792 + 1.83632i) q^{92} +(0.0144625 + 0.0820210i) q^{93} +(-8.44765 + 3.07469i) q^{94} +(-3.54558 - 2.97510i) q^{95} +(0.914110 + 0.767030i) q^{96} +(5.64365 + 9.77508i) q^{97} +(-3.83468 - 1.39571i) q^{98} +(-1.73661 + 9.84879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{6} - 9 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q + 6 * q^6 - 9 * q^7 - 12 * q^8 + 12 * q^9	$ 24 q + 6 q^{6} - 9 q^{7} - 12 q^{8} + 12 q^{9} + 12 q^{10} - 3 q^{11} - 3 q^{14} + 6 q^{17} - 6 q^{18} - 18 q^{19} + 18 q^{21} + 3 q^{22} + 15 q^{23} - 6 q^{26} - 12 q^{27} + 9 q^{28} - 18 q^{29} - 6 q^{31} - 45 q^{33} - 3 q^{34} + 30 q^{36} - 18 q^{37} - 24 q^{38} + 12 q^{39} + 3 q^{41} + 18 q^{42} + 3 q^{44} + 15 q^{45} + 9 q^{46} - 36 q^{47} - 3 q^{48} - 15 q^{49} + 54 q^{51} - 9 q^{52} - 6 q^{53} + 45 q^{54} - 3 q^{55} + 3 q^{57} - 15 q^{58} - 9 q^{59} + 3 q^{60} - 24 q^{61} + 81 q^{62} - 45 q^{63} - 12 q^{64} - 3 q^{66} + 12 q^{67} + 12 q^{68} + 60 q^{69} - 9 q^{70} + 42 q^{71} - 6 q^{72} - 42 q^{73} + 12 q^{74} + 6 q^{75} - 18 q^{76} + 9 q^{77} + 30 q^{78} - 6 q^{79} - 24 q^{80} - 66 q^{81} - 24 q^{82} - 3 q^{83} - 42 q^{84} + 6 q^{85} - 18 q^{86} - 84 q^{87} - 3 q^{88} + 27 q^{89} + 6 q^{90} + 153 q^{91} - 9 q^{92} - 54 q^{93} - 21 q^{94} - 9 q^{95} - 9 q^{97} - 24 q^{98} + 165 q^{99}+O(q^{100}) $ 24 * q + 6 * q^6 - 9 * q^7 - 12 * q^8 + 12 * q^9 + 12 * q^10 - 3 * q^11 - 3 * q^14 + 6 * q^17 - 6 * q^18 - 18 * q^19 + 18 * q^21 + 3 * q^22 + 15 * q^23 - 6 * q^26 - 12 * q^27 + 9 * q^28 - 18 * q^29 - 6 * q^31 - 45 * q^33 - 3 * q^34 + 30 * q^36 - 18 * q^37 - 24 * q^38 + 12 * q^39 + 3 * q^41 + 18 * q^42 + 3 * q^44 + 15 * q^45 + 9 * q^46 - 36 * q^47 - 3 * q^48 - 15 * q^49 + 54 * q^51 - 9 * q^52 - 6 * q^53 + 45 * q^54 - 3 * q^55 + 3 * q^57 - 15 * q^58 - 9 * q^59 + 3 * q^60 - 24 * q^61 + 81 * q^62 - 45 * q^63 - 12 * q^64 - 3 * q^66 + 12 * q^67 + 12 * q^68 + 60 * q^69 - 9 * q^70 + 42 * q^71 - 6 * q^72 - 42 * q^73 + 12 * q^74 + 6 * q^75 - 18 * q^76 + 9 * q^77 + 30 * q^78 - 6 * q^79 - 24 * q^80 - 66 * q^81 - 24 * q^82 - 3 * q^83 - 42 * q^84 + 6 * q^85 - 18 * q^86 - 84 * q^87 - 3 * q^88 + 27 * q^89 + 6 * q^90 + 153 * q^91 - 9 * q^92 - 54 * q^93 - 21 * q^94 - 9 * q^95 - 9 * q^97 - 24 * q^98 + 165 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	0.207212	+	1.17516i	0.119634	+	0.678477i	0.984351	+	0.176218i	$0.0563865\pi$
$3$	0.207212	+	1.17516i	0.119634	+	0.678477i	−0.864717	+	0.502259i	$0.832502\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	1.19329			0.487157
$7$	−2.54999	+	2.13970i	−0.963807	+	0.808730i	−0.981568	−	0.191112i	$-0.938791\pi$
$7$	−2.54999	+	2.13970i	−0.963807	+	0.808730i	0.0177611	+	0.999842i	$0.494346\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	1.48102	−	0.539047i	0.493673	−	0.179682i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−3.17268	+	5.49525i	−0.956600	+	1.65688i	−0.225935	+	0.974142i	$0.572544\pi$
$11$	−3.17268	+	5.49525i	−0.956600	+	1.65688i	−0.730665	+	0.682737i	$0.760790\pi$
$12$	0.207212	−	1.17516i	0.0598169	−	0.339239i
$13$	−6.51288	−	2.37049i	−1.80635	−	0.657456i	−0.997595	−	0.0693054i	$-0.977922\pi$
$13$	−6.51288	−	2.37049i	−1.80635	−	0.657456i	−0.808751	−	0.588151i	$-0.799856\pi$
$14$	1.66439	+	2.88281i	0.444827	+	0.770463i
$15$	−0.914110	−	0.767030i	−0.236022	−	0.198046i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	4.46459	−	1.62498i	1.08282	−	0.394115i	0.261864	−	0.965105i	$-0.415663\pi$
$17$	4.46459	−	1.62498i	1.08282	−	0.394115i	0.820957	+	0.570990i	$0.193441\pi$
$18$	−0.273681	−	1.55212i	−0.0645073	−	0.365839i
$19$	0.803718	+	4.55811i	0.184386	+	1.04570i	0.926742	+	0.375698i	$0.122597\pi$
$19$	0.803718	+	4.55811i	0.184386	+	1.04570i	−0.742357	+	0.670005i	$0.766292\pi$
$20$	0.939693	−	0.342020i	0.210122	−	0.0764780i
$21$	−3.04287	−	2.55327i	−0.664009	−	0.557170i
$22$	4.86083	+	4.07872i	1.03633	+	0.869586i
$23$	−0.932323	−	1.61483i	−0.194403	−	0.336715i	0.752302	−	0.658819i	$-0.228944\pi$
$23$	−0.932323	−	1.61483i	−0.194403	−	0.336715i	−0.946705	+	0.322103i	$0.895610\pi$
$24$	−1.12132	−	0.408128i	−0.228889	−	0.0833088i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	−3.46543	+	6.00230i	−0.679626	+	1.17715i
$27$	2.73028	+	4.72898i	0.525443	+	0.910093i
$28$	3.12803	−	1.13851i	0.591142	−	0.215158i
$29$	−1.78944	+	3.09940i	−0.332291	+	0.575545i	−0.982961	−	0.183816i	$-0.941155\pi$
$29$	−1.78944	+	3.09940i	−0.332291	+	0.575545i	0.650670	+	0.759361i	$0.274488\pi$
$30$	−0.914110	+	0.767030i	−0.166893	+	0.140040i
$31$	0.0697957			0.0125357			0.00626784	−	0.999980i	$-0.498005\pi$
$31$	0.0697957			0.0125357			0.00626784	+	0.999980i	$0.498005\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−7.11520	−	2.58972i	−1.23860	−	0.450812i
$34$	−0.825022	−	4.67893i	−0.141490	−	0.802430i
$35$	0.578037	−	3.27821i	0.0977060	−	0.554118i
$36$	−1.57607			−0.262678
$37$	2.21684	+	5.66442i	0.364447	+	0.931224i
$37$	2.21684	+	5.66442i	0.364447	+	0.931224i
$38$	4.62843			0.750830
$39$	1.43616	−	8.14485i	0.229969	−	1.30422i
$40$	−0.173648	−	0.984808i	−0.0274562	−	0.155712i
$41$	3.40012	+	1.23754i	0.531009	+	0.193271i	0.593589	−	0.804769i	$-0.297711\pi$
$41$	3.40012	+	1.23754i	0.531009	+	0.193271i	−0.0625799	+	0.998040i	$0.519933\pi$
$42$	−3.04287	+	2.55327i	−0.469525	+	0.393979i
$43$	7.28570			1.11106			0.555529	−	0.831497i	$-0.312516\pi$
$43$	7.28570			1.11106			0.555529	+	0.831497i	$0.312516\pi$
$44$	4.86083	−	4.07872i	0.732798	−	0.614890i
$45$	−0.788034	+	1.36492i	−0.117473	+	0.203470i
$46$	−1.75219	+	0.637746i	−0.258347	+	0.0940305i
$47$	−4.49490	−	7.78540i	−0.655649	−	1.13562i	−0.981731	−	0.190275i	$-0.939062\pi$
$47$	−4.49490	−	7.78540i	−0.655649	−	1.13562i	0.326082	−	0.945341i	$-0.394271\pi$
$48$	−0.596643	+	1.03342i	−0.0861180	+	0.149161i
$49$	0.708620	−	4.01878i	0.101231	−	0.574112i
$50$	−0.939693	−	0.342020i	−0.132893	−	0.0483690i
$51$	2.83472	+	4.90988i	0.396940	+	0.687520i
$52$	5.30934	+	4.45507i	0.736274	+	0.617807i
$53$	−7.70559	−	6.46575i	−1.05844	−	0.888140i	−0.0644876	−	0.997919i	$-0.520541\pi$
$53$	−7.70559	−	6.46575i	−1.05844	−	0.888140i	−0.993956	+	0.109779i	$0.964986\pi$
$54$	5.13125	−	1.86762i	0.698274	−	0.254151i
$55$	−1.10186	−	6.24896i	−0.148575	−	0.842610i
$56$	−0.578037	−	3.27821i	−0.0772434	−	0.438069i
$57$	−5.18996	+	1.88899i	−0.687427	+	0.250203i
$58$	2.74158	+	2.30046i	0.359988	+	0.302065i
$59$	0.743052	+	0.623495i	0.0967372	+	0.0811721i	0.689874	−	0.723930i	$-0.257666\pi$
$59$	0.743052	+	0.623495i	0.0967372	+	0.0811721i	−0.593136	+	0.805102i	$0.702111\pi$
$60$	0.596643	+	1.03342i	0.0770263	+	0.133413i
$61$	10.1900	+	3.70885i	1.30469	+	0.474870i	0.898523	−	0.438927i	$-0.144641\pi$
$61$	10.1900	+	3.70885i	1.30469	+	0.474870i	0.406172	+	0.913797i	$0.366863\pi$
$62$	0.0121199	−	0.0687354i	0.00153923	−	0.00872940i
$63$	−2.62319	+	4.54350i	−0.330491	+	0.572428i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	6.51288	−	2.37049i	0.807823	−	0.294023i
$66$	−3.78592	+	6.55740i	−0.466014	+	0.807160i
$67$	−0.628408	+	0.527297i	−0.0767723	+	0.0644196i	−0.680366	−	0.732872i	$-0.738179\pi$
$67$	−0.628408	+	0.527297i	−0.0767723	+	0.0644196i	0.603594	+	0.797292i	$0.293735\pi$
$68$	−4.75111			−0.576157
$69$	1.70449	−	1.43024i	0.205197	−	0.172180i
$70$	−3.12803	−	1.13851i	−0.373871	−	0.136078i
$71$	0.750450	+	4.25601i	0.0890620	+	0.505096i	0.996406	+	0.0847065i	$0.0269953\pi$
$71$	0.750450	+	4.25601i	0.0890620	+	0.505096i	−0.907344	+	0.420389i	$0.861894\pi$
$72$	−0.273681	+	1.55212i	−0.0322537	+	0.182920i
$73$	0.246060			0.0287991			0.0143995	−	0.999896i	$-0.495416\pi$
$73$	0.246060			0.0287991			0.0143995	+	0.999896i	$0.495416\pi$
$74$	5.96331	−	1.19955i	0.693221	−	0.139445i
$75$	1.19329			0.137789
$76$	0.803718	−	4.55811i	0.0921928	−	0.522851i
$77$	−3.66785	−	20.8014i	−0.417991	−	2.37054i
$78$	−7.77172	−	2.82868i	−0.879974	−	0.320284i
$79$	3.98152	−	3.34089i	0.447956	−	0.375879i	−0.390721	−	0.920509i	$-0.627774\pi$
$79$	3.98152	−	3.34089i	0.447956	−	0.375879i	0.838677	+	0.544630i	$0.183330\pi$
$80$	−1.00000			−0.111803
$81$	−1.36954	+	1.14918i	−0.152171	+	0.127686i
$82$	1.80916	−	3.13356i	0.199789	−	0.346044i
$83$	−3.56146	+	1.29626i	−0.390921	+	0.142284i	−0.530000	−	0.847998i	$-0.677808\pi$
$83$	−3.56146	+	1.29626i	−0.390921	+	0.142284i	0.139079	+	0.990281i	$0.455586\pi$
$84$	1.98609	+	3.44002i	0.216701	+	0.375336i
$85$	−2.37556	+	4.11458i	−0.257665	+	0.446289i
$86$	1.26515	−	7.17501i	0.136424	−	0.773702i
$87$	−4.01308	−	1.46064i	−0.430247	−	0.156597i
$88$	−3.17268	−	5.49525i	−0.338209	−	0.585795i
$89$	−8.68118	−	7.28437i	−0.920203	−	0.772142i	0.0538297	−	0.998550i	$-0.482857\pi$
$89$	−8.68118	−	7.28437i	−0.920203	−	0.772142i	−0.974032	+	0.226408i	$0.927302\pi$
$90$	1.20734	+	1.01308i	0.127265	+	0.106788i
$91$	21.6799	−	7.89085i	2.27267	−	0.827186i
$92$	0.323792	+	1.83632i	0.0337577	+	0.191449i
$93$	0.0144625	+	0.0820210i	0.00149969	+	0.00850518i
$94$	−8.44765	+	3.07469i	−0.871309	+	0.317130i
$95$	−3.54558	−	2.97510i	−0.363769	−	0.305238i
$96$	0.914110	+	0.767030i	0.0932960	+	0.0782846i
$97$	5.64365	+	9.77508i	0.573025	+	0.992509i	0.996253	+	0.0864858i	$0.0275637\pi$
$97$	5.64365	+	9.77508i	0.573025	+	0.992509i	−0.423228	+	0.906023i	$0.639103\pi$
$98$	−3.83468	−	1.39571i	−0.387361	−	0.140988i
$99$	−1.73661	+	9.84879i	−0.174536	+	0.989841i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	3.91753	+	6.78536i	0.389809	+	0.675169i	0.992424	−	0.122864i	$-0.0392077\pi$
$101$	3.91753	+	6.78536i	0.389809	+	0.675169i	−0.602615	+	0.798032i	$0.705874\pi$
$102$	5.32753	−	1.93906i	0.527504	−	0.191996i
$103$	3.82791	−	6.63013i	0.377175	−	0.653286i	−0.613475	−	0.789714i	$-0.710229\pi$
$103$	3.82791	−	6.63013i	0.377175	−	0.653286i	0.990650	+	0.136428i	$0.0435622\pi$
$104$	5.30934	−	4.45507i	0.520624	−	0.436855i
$105$	3.97219			0.387646
$106$	−7.70559	+	6.46575i	−0.748433	+	0.628010i
$107$	−10.6801	−	3.88723i	−1.03248	−	0.375793i	−0.230457	−	0.973082i	$-0.574022\pi$
$107$	−10.6801	−	3.88723i	−1.03248	−	0.375793i	−0.802026	+	0.597289i	$0.796244\pi$
$108$	−0.948216	−	5.37760i	−0.0912421	−	0.517460i
$109$	−0.187043	+	1.06077i	−0.0179155	+	0.101604i	−0.992454	−	0.122615i	$-0.960872\pi$
$109$	−0.187043	+	1.06077i	−0.0179155	+	0.101604i	0.974539	+	0.224219i	$0.0719830\pi$
$110$	−6.34536			−0.605007
$111$	−6.19722	+	3.77887i	−0.588214	+	0.358675i
$112$	−3.32878			−0.314540
$113$	−0.890833	+	5.05217i	−0.0838025	+	0.475268i	0.913806	+	0.406151i	$0.133129\pi$
$113$	−0.890833	+	5.05217i	−0.0838025	+	0.475268i	−0.997609	+	0.0691169i	$0.977982\pi$
$114$	0.959066	+	5.43913i	0.0898247	+	0.509421i
$115$	1.75219	+	0.637746i	0.163393	+	0.0594701i
$116$	2.74158	−	2.30046i	0.254550	−	0.213593i
$117$	−10.9235			−1.00988
$118$	0.743052	−	0.623495i	0.0684035	−	0.0573974i
$119$	−7.90771	+	13.6965i	−0.724898	+	1.25556i
$120$	1.12132	−	0.408128i	0.102362	−	0.0372568i
$121$	−14.6318	−	25.3431i	−1.33017	−	2.30391i
$122$	5.42198	−	9.39115i	0.490883	−	0.850235i
$123$	−0.749761	+	4.25210i	−0.0676036	+	0.383399i
$124$	−0.0655865	−	0.0238715i	−0.00588984	−	0.00214373i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	4.01896	+	3.37231i	0.358038	+	0.300429i
$127$	9.78145	+	8.20761i	0.867963	+	0.728308i	0.963668	−	0.267102i	$-0.0860661\pi$
$127$	9.78145	+	8.20761i	0.867963	+	0.728308i	−0.0957050	+	0.995410i	$0.530511\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	1.50968	+	8.56185i	0.132920	+	0.753828i
$130$	−1.20353	−	6.82556i	−0.105557	−	0.598641i
$131$	−0.631173	+	0.229728i	−0.0551458	+	0.0200714i	−0.369446	−	0.929252i	$-0.620452\pi$
$131$	−0.631173	+	0.229728i	−0.0551458	+	0.0200714i	0.314300	+	0.949324i	$0.398230\pi$
$132$	5.80036	+	4.86708i	0.504857	+	0.423625i
$133$	−11.8025	−	9.90344i	−1.02340	−	0.858737i
$134$	0.410164	+	0.710425i	0.0354328	+	0.0613714i
$135$	−5.13125	−	1.86762i	−0.441627	−	0.160739i
$136$	−0.825022	+	4.67893i	−0.0707451	+	0.401215i
$137$	−3.88198	+	6.72379i	−0.331660	+	0.574452i	−0.982837	−	0.184474i	$-0.940942\pi$
$137$	−3.88198	+	6.72379i	−0.331660	+	0.574452i	0.651178	+	0.758925i	$0.274275\pi$
$138$	−1.11253	−	1.92695i	−0.0947046	−	0.164033i
$139$	−12.8059	+	4.66096i	−1.08618	+	0.395337i	−0.822205	−	0.569192i	$-0.807256\pi$
$139$	−12.8059	+	4.66096i	−1.08618	+	0.395337i	−0.263976	+	0.964529i	$0.585034\pi$
$140$	−1.66439	+	2.88281i	−0.140667	+	0.243642i
$141$	8.21767	−	6.89544i	0.692053	−	0.580701i
$142$	4.32167			0.362666
$143$	33.6897	−	28.2690i	2.81728	−	2.36398i
$144$	1.48102	+	0.539047i	0.123418	+	0.0449206i
$145$	−0.621467	−	3.52451i	−0.0516100	−	0.292695i
$146$	0.0427278	−	0.242321i	0.00353618	−	0.0200547i
$147$	4.86954			0.401633
$148$	−0.145807	−	6.08101i	−0.0119853	−	0.499856i
$149$	4.24531			0.347789			0.173894	−	0.984764i	$-0.444365\pi$
$149$	4.24531			0.347789			0.173894	+	0.984764i	$0.444365\pi$
$150$	0.207212	−	1.17516i	0.0169188	−	0.0959512i
$151$	3.25464	+	18.4580i	0.264859	+	1.50209i	0.769437	+	0.638723i	$0.220537\pi$
$151$	3.25464	+	18.4580i	0.264859	+	1.50209i	−0.504578	+	0.863366i	$0.668352\pi$
$152$	−4.34930	−	1.58302i	−0.352775	−	0.128400i
$153$	5.73620	−	4.81324i	0.463744	−	0.389128i
$154$	−21.1223			−1.70209
$155$	−0.0534666	+	0.0448638i	−0.00429454	+	0.00360355i
$156$	−4.13525	+	7.16246i	−0.331085	+	0.573456i
$157$	−6.88664	+	2.50653i	−0.549613	+	0.200043i	−0.601875	−	0.798591i	$-0.705579\pi$
$157$	−6.88664	+	2.50653i	−0.549613	+	0.200043i	0.0522613	+	0.998633i	$0.483357\pi$
$158$	−2.59875	−	4.50117i	−0.206745	−	0.358094i
$159$	6.00159	−	10.3951i	0.475957	−	0.824382i
$160$	−0.173648	+	0.984808i	−0.0137281	+	0.0778559i
$161$	5.83267	+	2.12292i	0.459679	+	0.167309i
$162$	0.893902	+	1.54828i	0.0702316	+	0.121645i
$163$	3.06634	+	2.57296i	0.240174	+	0.201530i	0.754928	−	0.655808i	$-0.227672\pi$
$163$	3.06634	+	2.57296i	0.240174	+	0.201530i	−0.514753	+	0.857338i	$0.672116\pi$
$164$	−2.77180	−	2.32582i	−0.216441	−	0.181616i
$165$	7.11520	−	2.58972i	0.553917	−	0.201609i
$166$	0.658131	+	3.73245i	0.0510809	+	0.289694i
$167$	4.24355	+	24.0664i	0.328376	+	1.86231i	0.484804	+	0.874623i	$0.338891\pi$
$167$	4.24355	+	24.0664i	0.328376	+	1.86231i	−0.156429	+	0.987689i	$0.549998\pi$
$168$	3.73264	−	1.35857i	0.287979	−	0.104816i
$169$	26.8397	+	22.5212i	2.06459	+	1.73240i
$170$	3.63956	+	3.05396i	0.279142	+	0.234228i
$171$	3.64736	+	6.31741i	0.278921	+	0.483105i
$172$	−6.84632	−	2.49186i	−0.522027	−	0.190002i
$173$	1.25929	−	7.14181i	0.0957424	−	0.542982i	−0.898775	−	0.438410i	$-0.855542\pi$
$173$	1.25929	−	7.14181i	0.0957424	−	0.542982i	0.994517	−	0.104572i	$-0.0333472\pi$
$174$	−2.13532	+	3.69848i	−0.161878	+	0.280381i
$175$	1.66439	+	2.88281i	0.125816	+	0.217920i
$176$	−5.96269	+	2.17024i	−0.449455	+	0.163588i
$177$	−0.578735	+	1.00240i	−0.0435004	+	0.0753449i
$178$	−8.68118	+	7.28437i	−0.650682	+	0.545987i
$179$	3.30235			0.246829			0.123415	−	0.992355i	$-0.460616\pi$
$179$	3.30235			0.246829			0.123415	+	0.992355i	$0.460616\pi$
$180$	1.20734	−	1.01308i	0.0899897	−	0.0755103i
$181$	22.8356	+	8.31147i	1.69736	+	0.617787i	0.995520	−	0.0945517i	$-0.0301418\pi$
$181$	22.8356	+	8.31147i	1.69736	+	0.617787i	0.701836	+	0.712339i	$0.252364\pi$
$182$	−4.00629	−	22.7208i	−0.296966	−	1.68418i
$183$	−2.24700	+	12.7434i	−0.166103	+	0.942017i
$184$	1.86465			0.137463
$185$	−5.33922	−	2.91423i	−0.392547	−	0.214259i
$186$	0.0832863			0.00610684
$187$	−5.23506	+	29.6895i	−0.382826	+	2.17111i
$188$	1.56106	+	8.85323i	0.113852	+	0.645688i
$189$	−17.0808	−	6.21690i	−1.24245	−	0.452213i
$190$	−3.54558	+	2.97510i	−0.257224	+	0.215836i
$191$	18.1773			1.31526			0.657630	−	0.753341i	$-0.271559\pi$
$191$	18.1773			1.31526			0.657630	+	0.753341i	$0.271559\pi$
$192$	0.914110	−	0.767030i	0.0659702	−	0.0553556i
$193$	−7.66203	+	13.2710i	−0.551525	+	0.955269i	0.446640	+	0.894714i	$0.352621\pi$
$193$	−7.66203	+	13.2710i	−0.551525	+	0.955269i	−0.998165	+	0.0605556i	$0.980713\pi$
$194$	10.6066	−	3.86048i	0.761508	−	0.277166i
$195$	4.13525	+	7.16246i	0.296131	+	0.512914i
$196$	−2.04039	+	3.53406i	−0.145742	+	0.252433i
$197$	−0.830377	+	4.70930i	−0.0591619	+	0.335524i	−0.999994	−	0.00334812i	$-0.998934\pi$
$197$	−0.830377	+	4.70930i	−0.0591619	+	0.335524i	0.940832	+	0.338872i	$0.110045\pi$
$198$	9.39761	+	3.42045i	0.667859	+	0.243081i
$199$	8.58946	+	14.8774i	0.608891	+	1.05463i	0.991424	+	0.130688i	$0.0417186\pi$
$199$	8.58946	+	14.8774i	0.608891	+	1.05463i	−0.382533	+	0.923942i	$0.624948\pi$
$200$	0.766044	+	0.642788i	0.0541675	+	0.0454519i
$201$	−0.749871	−	0.629216i	−0.0528918	−	0.0443815i
$202$	7.36255	−	2.67975i	0.518027	−	0.188546i
$203$	−2.06873	−	11.7323i	−0.145196	−	0.823448i
$204$	−0.984487	−	5.58330i	−0.0689279	−	0.390910i
$205$	−3.40012	+	1.23754i	−0.237474	+	0.0864336i
$206$	−5.86470	−	4.92106i	−0.408613	−	0.342867i
$207$	−2.25126	−	1.88903i	−0.156473	−	0.131297i
$208$	−3.46543	−	6.00230i	−0.240284	−	0.416185i
$209$	−27.5979	−	10.0448i	−1.90899	−	0.694814i
$210$	0.689763	−	3.91184i	0.0475982	−	0.269943i
$211$	2.48590	−	4.30570i	0.171136	−	0.296416i	−0.767681	−	0.640832i	$-0.778590\pi$
$211$	2.48590	−	4.30570i	0.171136	−	0.296416i	0.938817	+	0.344415i	$0.111923\pi$
$212$	5.02946	+	8.71129i	0.345425	+	0.598294i
$213$	−4.84598	+	1.76379i	−0.332041	+	0.120853i
$214$	−5.68276	+	9.84282i	−0.388465	+	0.672841i
$215$	−5.58117	+	4.68316i	−0.380633	+	0.319389i
$216$	−5.46056			−0.371544
$217$	−0.177979	+	0.149342i	−0.0120820	+	0.0101380i
$218$	1.01218	+	0.368403i	0.0685534	+	0.0249514i
$219$	0.0509865	+	0.289159i	0.00344535	+	0.0195395i
$220$	−1.10186	+	6.24896i	−0.0742874	+	0.421305i
$221$	−32.9293			−2.21506
$222$	2.64533	+	6.75927i	0.177543	+	0.453652i
$223$	−11.4210			−0.764807			−0.382403	−	0.923995i	$-0.624904\pi$
$223$	−11.4210			−0.764807			−0.382403	+	0.923995i	$0.624904\pi$
$224$	−0.578037	+	3.27821i	−0.0386217	+	0.219035i
$225$	−0.273681	−	1.55212i	−0.0182454	−	0.103475i
$226$	4.82072	+	1.75460i	0.320670	+	0.116714i
$227$	15.0707	−	12.6458i	1.00028	−	0.839331i	0.0132534	−	0.999912i	$-0.495781\pi$
$227$	15.0707	−	12.6458i	1.00028	−	0.839331i	0.987023	+	0.160581i	$0.0513367\pi$
$228$	5.52304			0.365772
$229$	10.6386	−	8.92684i	0.703018	−	0.589902i	−0.219613	−	0.975587i	$-0.570479\pi$
$229$	10.6386	−	8.92684i	0.703018	−	0.589902i	0.922630	+	0.385685i	$0.126035\pi$
$230$	0.932323	−	1.61483i	0.0614755	−	0.106479i
$231$	23.6849	−	8.62061i	1.55835	−	0.567194i
$232$	−1.78944	−	3.09940i	−0.117483	−	0.203486i
$233$	−12.1177	+	20.9884i	−0.793854	+	1.37500i	0.129710	+	0.991552i	$0.458595\pi$
$233$	−12.1177	+	20.9884i	−0.793854	+	1.37500i	−0.923564	+	0.383444i	$0.874738\pi$
$234$	−1.89685	+	10.7576i	−0.124001	+	0.703243i
$235$	8.44765	+	3.07469i	0.551064	+	0.200571i
$236$	−0.484993	−	0.840032i	−0.0315704	−	0.0546815i
$237$	4.75109	+	3.98664i	0.308616	+	0.258960i
$238$	12.1153	+	10.1660i	0.785319	+	0.658961i
$239$	−10.6921	+	3.89159i	−0.691612	+	0.251726i	−0.663825	−	0.747888i	$-0.731068\pi$
$239$	−10.6921	+	3.89159i	−0.691612	+	0.251726i	−0.0277865	+	0.999614i	$0.508846\pi$
$240$	−0.207212	−	1.17516i	−0.0133755	−	0.0758561i
$241$	−4.42946	−	25.1207i	−0.285327	−	1.61817i	−0.704116	−	0.710085i	$-0.748656\pi$
$241$	−4.42946	−	25.1207i	−0.285327	−	1.61817i	0.418789	−	0.908084i	$-0.362455\pi$
$242$	−27.4988	+	10.0088i	−1.76769	+	0.643387i
$243$	10.9148	+	9.15864i	0.700187	+	0.587527i
$244$	−8.30696	−	6.97036i	−0.531798	−	0.446232i
$245$	2.04039	+	3.53406i	0.130356	+	0.225783i
$246$	4.05731	+	1.47674i	0.258685	+	0.0941535i
$247$	5.57046	−	31.5916i	0.354440	−	2.01013i
$248$	−0.0348979	+	0.0604449i	−0.00221602	+	0.00383825i
$249$	−2.26129	−	3.91667i	−0.143304	−	0.248209i
$250$	0.939693	−	0.342020i	0.0594314	−	0.0216313i
$251$	4.10132	−	7.10370i	0.258873	−	0.448382i	−0.707067	−	0.707146i	$-0.749982\pi$
$251$	4.10132	−	7.10370i	0.258873	−	0.448382i	0.965940	+	0.258765i	$0.0833155\pi$
$252$	4.01896	−	3.37231i	0.253171	−	0.212436i
$253$	11.8319			0.743862
$254$	9.78145	−	8.20761i	0.613743	−	0.514991i
$255$	−5.32753	−	1.93906i	−0.333623	−	0.121429i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	3.89683	−	22.1000i	0.243077	−	1.37856i	−0.581838	−	0.813305i	$-0.697666\pi$
$257$	3.89683	−	22.1000i	0.243077	−	1.37856i	0.824916	−	0.565256i	$-0.191223\pi$
$258$	8.69393			0.541260
$259$	−17.7731	−	9.70085i	−1.10437	−	0.602781i
$260$	−6.93086			−0.429834
$261$	−0.979474	+	5.55487i	−0.0606279	+	0.343838i
$262$	0.116636	+	0.661476i	0.00720580	+	0.0408661i
$263$	−8.99471	−	3.27381i	−0.554638	−	0.201872i	0.0494681	−	0.998776i	$-0.484247\pi$
$263$	−8.99471	−	3.27381i	−0.554638	−	0.201872i	−0.604106	+	0.796904i	$0.706470\pi$
$264$	5.80036	−	4.86708i	0.356988	−	0.299548i
$265$	10.0589			0.617915
$266$	−11.8025	+	9.90344i	−0.723656	+	0.607219i
$267$	6.76144	−	11.7112i	0.413793	−	0.716711i
$268$	0.770857	−	0.280569i	0.0470876	−	0.0171385i
$269$	−13.2141	−	22.8874i	−0.805676	−	1.39547i	−0.915834	−	0.401558i	$-0.868469\pi$
$269$	−13.2141	−	22.8874i	−0.805676	−	1.39547i	0.110158	−	0.993914i	$-0.464864\pi$
$270$	−2.73028	+	4.72898i	−0.166160	+	0.287797i
$271$	0.213880	−	1.21297i	0.0129923	−	0.0736829i	−0.977622	−	0.210368i	$-0.932534\pi$
$271$	0.213880	−	1.21297i	0.0129923	−	0.0736829i	0.990615	+	0.136685i	$0.0436449\pi$
$272$	4.46459	+	1.62498i	0.270705	+	0.0985287i
$273$	13.7653	+	23.8423i	0.833116	+	1.44300i
$274$	5.94754	+	4.99058i	0.359304	+	0.301492i
$275$	4.86083	+	4.07872i	0.293119	+	0.245956i
$276$	−2.09087	+	0.761014i	−0.125855	+	0.0458076i
$277$	5.32173	+	30.1810i	0.319752	+	1.81340i	0.544245	+	0.838926i	$0.316816\pi$
$277$	5.32173	+	30.1810i	0.319752	+	1.81340i	−0.224493	+	0.974476i	$0.572073\pi$
$278$	2.36643	+	13.4207i	0.141929	+	0.804920i
$279$	0.103369	−	0.0376232i	0.00618853	−	0.00225244i
$280$	2.54999	+	2.13970i	0.152391	+	0.127871i
$281$	−1.17024	−	0.981947i	−0.0698106	−	0.0585781i	0.607215	−	0.794538i	$-0.292287\pi$
$281$	−1.17024	−	0.981947i	−0.0698106	−	0.0585781i	−0.677025	+	0.735960i	$0.736731\pi$
$282$	−5.36370	−	9.29020i	−0.319404	−	0.553224i
$283$	−20.7969	−	7.56947i	−1.23625	−	0.449958i	−0.360516	−	0.932753i	$-0.617400\pi$
$283$	−20.7969	−	7.56947i	−1.23625	−	0.449958i	−0.875734	+	0.482795i	$0.839622\pi$
$284$	0.750450	−	4.25601i	0.0445310	−	0.252548i
$285$	2.76152	−	4.78309i	0.163578	−	0.283326i
$286$	−21.9894	−	38.0868i	−1.30026	−	2.25212i
$287$	−11.3182	+	4.11950i	−0.668094	+	0.243166i
$288$	0.788034	−	1.36492i	0.0464354	−	0.0804284i
$289$	4.26922	−	3.58230i	0.251131	−	0.210724i
$290$	−3.57888			−0.210159
$291$	−10.3178	+	8.65769i	−0.604842	+	0.507523i
$292$	−0.231220	−	0.0841573i	−0.0135311	−	0.00492494i
$293$	−2.63959	−	14.9698i	−0.154206	−	0.874547i	−0.959508	−	0.281682i	$-0.909108\pi$
$293$	−2.63959	−	14.9698i	−0.154206	−	0.874547i	0.805302	−	0.592865i	$-0.202003\pi$
$294$	0.845587	−	4.79556i	0.0493156	−	0.279683i
$295$	−0.969986			−0.0564748
$296$	−6.01395	−	0.912365i	−0.349554	−	0.0530301i
$297$	−34.6492			−2.01055
$298$	0.737190	−	4.18081i	0.0427042	−	0.242188i
$299$	2.24416	+	12.7273i	0.129783	+	0.736036i
$300$	−1.12132	−	0.408128i	−0.0647396	−	0.0235633i
$301$	−18.5785	+	15.5892i	−1.07085	+	0.898547i
$302$	18.7427			1.07852
$303$	−7.16211	+	6.00972i	−0.411452	+	0.345250i
$304$	−2.31421	+	4.00834i	−0.132729	+	0.229894i
$305$	−10.1900	+	3.70885i	−0.583477	+	0.212368i
$306$	−3.74404	−	6.48487i	−0.214032	−	0.370715i
$307$	8.65201	−	14.9857i	0.493796	−	0.855280i	−0.506178	−	0.862429i	$-0.668942\pi$
$307$	8.65201	−	14.9857i	0.493796	−	0.855280i	0.999974	+	0.00714900i	$0.00227562\pi$
$308$	−3.66785	+	20.8014i	−0.208995	+	1.18527i
$309$	8.58464	+	3.12455i	0.488363	+	0.177750i
$310$	0.0348979	+	0.0604449i	0.00198207	+	0.00343304i
$311$	−21.3671	−	17.9291i	−1.21162	−	1.01667i	−0.999220	−	0.0394842i	$-0.987429\pi$
$311$	−21.3671	−	17.9291i	−1.21162	−	1.01667i	−0.212397	−	0.977183i	$-0.568127\pi$
$312$	6.33557	+	5.31617i	0.358681	+	0.300969i
$313$	−2.13224	+	0.776074i	−0.120522	+	0.0438663i	−0.401577	−	0.915825i	$-0.631538\pi$
$313$	−2.13224	+	0.776074i	−0.120522	+	0.0438663i	0.281055	+	0.959692i	$0.409316\pi$
$314$	1.27260	+	7.21727i	0.0718169	+	0.407294i
$315$	−0.911025	−	5.16668i	−0.0513305	−	0.291110i
$316$	−4.88405	+	1.77765i	−0.274749	+	0.100001i
$317$	−3.31848	−	2.78454i	−0.186385	−	0.156395i	0.544821	−	0.838552i	$-0.316598\pi$
$317$	−3.31848	−	2.78454i	−0.186385	−	0.156395i	−0.731206	+	0.682157i	$0.761042\pi$
$318$	−9.19497	−	7.71549i	−0.515628	−	0.432663i
$319$	−11.3547	−	19.6668i	−0.635739	−	1.10113i
$320$	0.939693	+	0.342020i	0.0525304	+	0.0191195i
$321$	2.35507	−	13.3563i	0.131447	−	0.745474i
$322$	3.10350	−	5.37542i	0.172951	−	0.299560i
$323$	10.9951	+	19.0441i	0.611783	+	1.05964i
$324$	1.67999	−	0.611465i	0.0933326	−	0.0339703i
$325$	−3.46543	+	6.00230i	−0.192227	+	0.332948i
$326$	3.06634	−	2.57296i	0.169829	−	0.142503i
$327$	−1.28533			−0.0710791
$328$	−2.77180	+	2.32582i	−0.153047	+	0.128422i
$329$	28.1204	+	10.2350i	1.55033	+	0.564273i
$330$	−1.31484	−	7.45680i	−0.0723793	−	0.410483i
$331$	−2.33417	+	13.2377i	−0.128298	+	0.727612i	0.850997	+	0.525171i	$0.175999\pi$
$331$	−2.33417	+	13.2377i	−0.128298	+	0.727612i	−0.979294	+	0.202441i	$0.935112\pi$
$332$	3.79002			0.208005
$333$	6.33658	+	7.19413i	0.347242	+	0.394236i
$334$	24.4376			1.33717
$335$	0.142449	−	0.807866i	0.00778279	−	0.0441384i
$336$	−0.689763	−	3.91184i	−0.0376297	−	0.213408i
$337$	17.8559	+	6.49902i	0.972673	+	0.354024i	0.778987	−	0.627040i	$-0.215734\pi$
$337$	17.8559	+	6.49902i	0.972673	+	0.354024i	0.193686	+	0.981064i	$0.437956\pi$
$338$	26.8397	−	22.5212i	1.45989	−	1.22499i
$339$	−6.12168			−0.332484
$340$	3.63956	−	3.05396i	0.197383	−	0.165624i
$341$	−0.221440	+	0.383545i	−0.0119916	+	0.0207701i
$342$	6.85479	−	2.49494i	0.370665	−	0.134911i
$343$	−4.85872	−	8.41555i	−0.262346	−	0.454397i
$344$	−3.64285	+	6.30960i	−0.196409	+	0.340191i
$345$	−0.386377	+	2.19125i	−0.0208018	+	0.117973i
$346$	−6.81464	−	2.48033i	−0.366357	−	0.133343i
$347$	7.81502	+	13.5360i	0.419532	+	0.726651i	0.995892	−	0.0905445i	$-0.0288607\pi$
$347$	7.81502	+	13.5360i	0.419532	+	0.726651i	−0.576360	+	0.817196i	$0.695527\pi$
$348$	3.27149	+	2.74511i	0.175370	+	0.147153i
$349$	−0.919890	−	0.771879i	−0.0492406	−	0.0413177i	0.617835	−	0.786308i	$-0.288010\pi$
$349$	−0.919890	−	0.771879i	−0.0492406	−	0.0413177i	−0.667076	+	0.744990i	$0.732454\pi$
$350$	3.12803	−	1.13851i	0.167200	−	0.0608559i
$351$	−6.57195	−	37.2714i	−0.350785	−	1.98940i
$352$	1.10186	+	6.24896i	0.0587294	+	0.333071i
$353$	27.8791	−	10.1472i	1.48386	−	0.540080i	0.532033	−	0.846724i	$-0.321428\pi$
$353$	27.8791	−	10.1472i	1.48386	−	0.540080i	0.951824	+	0.306644i	$0.0992060\pi$
$354$	0.886674	+	0.744008i	0.0471262	+	0.0395436i
$355$	−3.31059	−	2.77791i	−0.175708	−	0.147436i
$356$	5.66623	+	9.81421i	0.300310	+	0.520152i
$357$	−17.7342	−	6.45471i	−0.938592	−	0.341619i
$358$	0.573447	−	3.25218i	0.0303076	−	0.171883i
$359$	0.697782	−	1.20859i	0.0368275	−	0.0637871i	−0.847024	−	0.531554i	$-0.821608\pi$
$359$	0.697782	−	1.20859i	0.0368275	−	0.0637871i	0.883852	+	0.467767i	$0.154941\pi$
$360$	−0.788034	−	1.36492i	−0.0415330	−	0.0719373i
$361$	−2.27626	+	0.828493i	−0.119803	+	0.0436049i
$362$	12.1506	−	21.0454i	0.638619	−	1.10612i
$363$	26.7502	−	22.4461i	1.40402	−	1.17811i
$364$	−23.0713			−1.20926
$365$	−0.188493	+	0.158164i	−0.00986615	+	0.00827868i
$366$	12.1596	+	4.42572i	0.635591	+	0.231336i
$367$	−1.07036	−	6.07032i	−0.0558724	−	0.316868i	0.944044	−	0.329820i	$-0.106988\pi$
$367$	−1.07036	−	6.07032i	−0.0558724	−	0.316868i	−0.999916	+	0.0129523i	$0.995877\pi$
$368$	0.323792	−	1.83632i	0.0168788	−	0.0957246i
$369$	5.70273			0.296872
$370$	−3.79711	+	4.75205i	−0.197402	+	0.247047i
$371$	33.4840			1.73840
$372$	0.0144625	−	0.0820210i	0.000749846	−	0.00425259i
$373$	3.66085	+	20.7617i	0.189552	+	1.07500i	0.919967	+	0.391997i	$0.128216\pi$
$373$	3.66085	+	20.7617i	0.189552	+	1.07500i	−0.730415	+	0.683004i	$0.760673\pi$
$374$	28.3294	+	10.3111i	1.46488	+	0.533172i
$375$	−0.914110	+	0.767030i	−0.0472044	+	0.0396092i
$376$	8.98980			0.463614
$377$	19.0015	−	15.9442i	0.978628	−	0.821167i
$378$	−9.08850	+	15.7417i	−0.467462	+	0.809668i
$379$	−27.8918	+	10.1518i	−1.43271	+	0.521463i	−0.937706	−	0.347429i	$-0.887055\pi$
$379$	−27.8918	+	10.1518i	−1.43271	+	0.521463i	−0.495001	+	0.868892i	$0.664832\pi$
$380$	2.31421	+	4.00834i	0.118717	+	0.205623i
$381$	−7.61840	+	13.1955i	−0.390302	+	0.676024i
$382$	3.15645	−	17.9011i	0.161498	−	0.915901i
$383$	−3.02354	−	1.10048i	−0.154496	−	0.0562318i	0.263615	−	0.964628i	$-0.415085\pi$
$383$	−3.02354	−	1.10048i	−0.154496	−	0.0562318i	−0.418110	+	0.908396i	$0.637307\pi$
$384$	−0.596643	−	1.03342i	−0.0304473	−	0.0527363i
$385$	16.1806	+	13.5772i	0.824642	+	0.691957i
$386$	11.7389	+	9.85012i	0.597495	+	0.501358i
$387$	10.7903	−	3.92734i	0.548500	−	0.199638i
$388$	−1.96002	−	11.1158i	−0.0995048	−	0.564320i
$389$	−2.44446	−	13.8632i	−0.123939	−	0.702892i	−0.981932	−	0.189232i	$-0.939400\pi$
$389$	−2.44446	−	13.8632i	−0.123939	−	0.702892i	0.857994	−	0.513660i	$-0.171711\pi$
$390$	7.77172	−	2.82868i	0.393537	−	0.143236i
$391$	−6.78649	−	5.69454i	−0.343208	−	0.287985i
$392$	3.12606	+	2.62308i	0.157890	+	0.132485i
$393$	−0.400753	−	0.694125i	−0.0202153	−	0.0350140i
$394$	4.49356	+	1.63552i	0.226382	+	0.0823965i
$395$	−0.902537	+	5.11854i	−0.0454115	+	0.257542i
$396$	5.00036	−	8.66088i	0.251278	−	0.435226i
$397$	−13.2422	−	22.9361i	−0.664606	−	1.15113i	−0.979392	−	0.201968i	$-0.935266\pi$
$397$	−13.2422	−	22.9361i	−0.664606	−	1.15113i	0.314786	−	0.949163i	$-0.398067\pi$
$398$	16.1429	−	5.87554i	0.809171	−	0.294514i
$399$	9.19249	−	15.9219i	0.460200	−	0.797090i
$400$	0.766044	−	0.642788i	0.0383022	−	0.0321394i
$401$	−10.4623			−0.522463			−0.261232	−	0.965276i	$-0.584129\pi$
$401$	−10.4623			−0.522463			−0.261232	+	0.965276i	$0.584129\pi$
$402$	−0.749871	+	0.629216i	−0.0374001	+	0.0313824i
$403$	−0.454571	−	0.165450i	−0.0226438	−	0.00824166i
$404$	−1.36054	−	7.71603i	−0.0676896	−	0.383887i
$405$	0.310449	−	1.76064i	0.0154263	−	0.0874871i
$406$	−11.9133			−0.591248
$407$	−38.1607	−	5.78929i	−1.89156	−	0.286964i
$408$	−5.66944			−0.280679
$409$	3.46642	−	19.6590i	0.171403	−	0.972077i	−0.770810	−	0.637065i	$-0.780148\pi$
$409$	3.46642	−	19.6590i	0.171403	−	0.972077i	0.942214	−	0.335012i	$-0.108740\pi$
$410$	0.628316	+	3.56336i	0.0310303	+	0.175982i
$411$	−8.70590	−	3.16869i	−0.429430	−	0.156300i
$412$	−5.86470	+	4.92106i	−0.288933	+	0.242443i
$413$	−3.22887			−0.158882
$414$	−2.25126	+	1.88903i	−0.110643	+	0.0928407i
$415$	1.89501	−	3.28226i	0.0930225	−	0.161120i
$416$	−6.51288	+	2.37049i	−0.319320	+	0.116223i
$417$	−8.13089	−	14.0831i	−0.398172	−	0.689653i
$418$	−14.6845	+	25.4344i	−0.718244	+	1.24403i
$419$	1.81578	−	10.2978i	0.0887065	−	0.503079i	−0.907789	−	0.419428i	$-0.862231\pi$
$419$	1.81578	−	10.2978i	0.0887065	−	0.503079i	0.996495	−	0.0836514i	$-0.0266582\pi$
$420$	−3.73264	−	1.35857i	−0.182134	−	0.0662913i
$421$	6.67309	+	11.5581i	0.325227	+	0.563309i	0.981558	−	0.191164i	$-0.0612261\pi$
$421$	6.67309	+	11.5581i	0.325227	+	0.563309i	−0.656332	+	0.754473i	$0.727893\pi$
$422$	−3.80861	−	3.19581i	−0.185400	−	0.155569i
$423$	−10.8537	−	9.10736i	−0.527726	−	0.442815i
$424$	9.45230	−	3.44036i	0.459044	−	0.167078i
$425$	−0.825022	−	4.67893i	−0.0400194	−	0.226962i
$426$	0.895501	+	5.07864i	0.0433872	+	0.246061i
$427$	−33.9202	+	12.3460i	−1.64152	+	0.597463i
$428$	8.70649	+	7.30561i	0.420844	+	0.353130i
$429$	40.2015	+	33.7330i	1.94095	+	1.62865i
$430$	3.64285	+	6.30960i	0.175674	+	0.304276i
$431$	−13.6390	−	4.96419i	−0.656968	−	0.239117i	−0.00804128	−	0.999968i	$-0.502560\pi$
$431$	−13.6390	−	4.96419i	−0.656968	−	0.239117i	−0.648927	+	0.760851i	$0.724782\pi$
$432$	−0.948216	+	5.37760i	−0.0456211	+	0.258730i
$433$	15.5651	−	26.9595i	0.748010	−	1.29559i	−0.200765	−	0.979639i	$-0.564343\pi$
$433$	15.5651	−	26.9595i	0.748010	−	1.29559i	0.948775	−	0.315952i	$-0.102324\pi$
$434$	0.116167	+	0.201208i	0.00557621	+	0.00965828i
$435$	4.01308	−	1.46064i	0.192413	−	0.0700324i
$436$	0.538569	−	0.932829i	0.0257928	−	0.0446744i
$437$	6.61125	−	5.54750i	0.316259	−	0.265373i
$438$	0.293619			0.0140297
$439$	−17.6640	+	14.8218i	−0.843056	+	0.707408i	−0.958249	−	0.285935i	$-0.907696\pi$
$439$	−17.6640	+	14.8218i	−0.843056	+	0.707408i	0.115193	+	0.993343i	$0.463251\pi$
$440$	5.96269	+	2.17024i	0.284260	+	0.103462i
$441$	−1.11683	−	6.33388i	−0.0531826	−	0.301613i
$442$	−5.71811	+	32.4290i	−0.271983	+	1.54249i
$443$	16.7461			0.795629			0.397815	−	0.917466i	$-0.369769\pi$
$443$	16.7461			0.795629			0.397815	+	0.917466i	$0.369769\pi$
$444$	7.11594	−	1.43141i	0.337707	−	0.0679315i
$445$	11.3325			0.537211
$446$	−1.98324	+	11.2475i	−0.0939090	+	0.532584i
$447$	0.879678	+	4.98890i	0.0416073	+	0.235967i
$448$	3.12803	+	1.13851i	0.147786	+	0.0537895i
$449$	−11.8736	+	9.96312i	−0.560349	+	0.470189i	−0.878427	−	0.477876i	$-0.841407\pi$
$449$	−11.8736	+	9.96312i	−0.560349	+	0.470189i	0.318078	+	0.948064i	$0.396963\pi$
$450$	−1.57607			−0.0742966
$451$	−17.5881	+	14.7581i	−0.828190	+	0.694934i
$452$	2.56505	−	4.44280i	0.120650	−	0.208972i
$453$	−21.0166	+	7.64942i	−0.987447	+	0.359401i
$454$	−9.83669	−	17.0376i	−0.461659	−	0.799616i
$455$	−11.5357	+	19.9803i	−0.540800	+	0.936693i
$456$	0.959066	−	5.43913i	0.0449124	−	0.254711i
$457$	6.22910	+	2.26721i	0.291385	+	0.106056i	0.483577	−	0.875302i	$-0.339337\pi$
$457$	6.22910	+	2.26721i	0.291385	+	0.106056i	−0.192192	+	0.981357i	$0.561560\pi$
$458$	−6.94385	−	12.0271i	−0.324465	−	0.561989i
$459$	19.8740	+	16.6763i	0.927641	+	0.778383i
$460$	−1.42840	−	1.19857i	−0.0665995	−	0.0558837i
$461$	20.9107	−	7.61088i	0.973910	−	0.354474i	0.194440	−	0.980914i	$-0.437711\pi$
$461$	20.9107	−	7.61088i	0.973910	−	0.354474i	0.779469	+	0.626440i	$0.215489\pi$
$462$	−4.37680	−	24.8221i	−0.203627	−	1.15483i
$463$	1.03765	+	5.88482i	0.0482238	+	0.273491i	0.999380	−	0.0352205i	$-0.0112134\pi$
$463$	1.03765	+	5.88482i	0.0482238	+	0.273491i	−0.951156	+	0.308711i	$0.900102\pi$
$464$	−3.36305	+	1.22405i	−0.156126	+	0.0568251i
$465$	−0.0638010	−	0.0535354i	−0.00295870	−	0.00248264i
$466$	18.5653	+	15.5782i	0.860023	+	0.721645i
$467$	17.6435	+	30.5594i	0.816444	+	1.41412i	0.908286	+	0.418349i	$0.137391\pi$
$467$	17.6435	+	30.5594i	0.816444	+	1.41412i	−0.0918424	+	0.995774i	$0.529276\pi$
$468$	10.2647	+	3.73606i	0.474488	+	0.172699i
$469$	0.474180	−	2.68921i	0.0218956	−	0.124176i
$470$	4.49490	−	7.78540i	0.207334	−	0.359114i
$471$	−4.37256	−	7.57350i	−0.201477	−	0.348968i
$472$	−0.911489	+	0.331755i	−0.0419547	+	0.0152702i
$473$	−23.1152	+	40.0367i	−1.06284	+	1.84089i
$474$	4.75109	−	3.98664i	0.218225	−	0.183112i
$475$	4.62843			0.212367
$476$	12.1153	−	10.1660i	0.555304	−	0.465956i
$477$	−14.8975	−	5.42224i	−0.682108	−	0.248267i
$478$	1.97581	+	11.2054i	0.0903715	+	0.512522i
$479$	3.45752	−	19.6086i	0.157978	−	0.895938i	−0.798034	−	0.602612i	$-0.794127\pi$
$479$	3.45752	−	19.6086i	0.157978	−	0.895938i	0.956012	−	0.293326i	$-0.0947622\pi$
$480$	−1.19329			−0.0544658
$481$	−1.01057	−	42.1466i	−0.0460779	−	1.92172i
$482$	−25.5083			−1.16187
$483$	−1.28616	+	7.29420i	−0.0585225	+	0.331897i
$484$	5.08158	+	28.8191i	0.230981	+	1.30996i
$485$	−10.6066	−	3.86048i	−0.481620	−	0.175295i
$486$	10.9148	−	9.15864i	0.495107	−	0.415444i
$487$	−4.27038			−0.193509			−0.0967547	−	0.995308i	$-0.530846\pi$
$487$	−4.27038			−0.193509			−0.0967547	+	0.995308i	$0.530846\pi$
$488$	−8.30696	+	6.97036i	−0.376038	+	0.315534i
$489$	−2.38826	+	4.13658i	−0.108001	+	0.187063i
$490$	3.83468	−	1.39571i	0.173233	−	0.0630517i
$491$	−10.6686	−	18.4786i	−0.481467	−	0.833926i	0.518306	−	0.855195i	$-0.326563\pi$
$491$	−10.6686	−	18.4786i	−0.481467	−	0.833926i	−0.999774	+	0.0212691i	$0.993229\pi$
$492$	2.15885	−	3.73924i	0.0973285	−	0.168578i
$493$	−2.95266	+	16.7454i	−0.132981	+	0.754173i
$494$	−30.1444	−	10.9717i	−1.35626	−	0.493638i
$495$	−5.00036	−	8.66088i	−0.224750	−	0.389278i
$496$	0.0534666	+	0.0448638i	0.00240072	+	0.00201445i
$497$	−11.0202	−	9.24707i	−0.494325	−	0.414788i
$498$	−4.24984	+	1.54681i	−0.190440	+	0.0693144i
$499$	−4.64266	−	26.3298i	−0.207834	−	1.17869i	−0.892917	−	0.450221i	$-0.851345\pi$
$499$	−4.64266	−	26.3298i	−0.207834	−	1.17869i	0.685083	−	0.728465i	$-0.259766\pi$
$500$	−0.173648	−	0.984808i	−0.00776578	−	0.0440419i
$501$	−27.4025	+	9.97368i	−1.22425	+	0.445591i
$502$	−6.28359	−	5.27256i	−0.280450	−	0.235326i
$503$	33.8915	+	28.4384i	1.51115	+	1.26800i	0.861486	+	0.507781i	$0.169534\pi$
$503$	33.8915	+	28.4384i	1.51115	+	1.26800i	0.649662	+	0.760223i	$0.274910\pi$
$504$	−2.62319	−	4.54350i	−0.116846	−	0.202384i
$505$	−7.36255	−	2.67975i	−0.327629	−	0.119247i
$506$	2.05458	−	11.6521i	0.0913372	−	0.517999i
$507$	−20.9045	+	36.2076i	−0.928399	+	1.60803i
$508$	−6.38439	−	11.0581i	−0.283261	−	0.490623i
$509$	10.7290	−	3.90505i	0.475556	−	0.173088i	−0.0931117	−	0.995656i	$-0.529681\pi$
$509$	10.7290	−	3.90505i	0.475556	−	0.173088i	0.568667	+	0.822568i	$0.307459\pi$
$510$	−2.83472	+	4.90988i	−0.125523	+	0.217413i
$511$	−0.627450	+	0.526493i	−0.0277568	+	0.0232907i
$512$	1.00000			0.0441942
$513$	−19.3609	+	16.2457i	−0.854803	+	0.717265i
$514$	−21.0876	−	7.67525i	−0.930133	−	0.338541i
$515$	1.32942	+	7.53951i	0.0585812	+	0.332230i
$516$	1.50968	−	8.56185i	0.0664601	−	0.376914i
$517$	57.0436			2.50877
$518$	−12.6397	+	15.8185i	−0.555358	+	0.695026i
$519$	8.65370			0.379855
$520$	−1.20353	+	6.82556i	−0.0527783	+	0.299321i
$521$	−0.0977574	−	0.554410i	−0.00428283	−	0.0242891i	0.982591	−	0.185780i	$-0.0594810\pi$
$521$	−0.0977574	−	0.554410i	−0.00428283	−	0.0242891i	−0.986874	+	0.161490i	$0.948370\pi$
$522$	5.30040	+	1.92919i	0.231992	+	0.0844382i
$523$	−12.3048	+	10.3249i	−0.538050	+	0.451478i	−0.870871	−	0.491512i	$-0.836444\pi$
$523$	−12.3048	+	10.3249i	−0.538050	+	0.451478i	0.332820	+	0.942990i	$0.392000\pi$
$524$	0.671680			0.0293425
$525$	−3.04287	+	2.55327i	−0.132802	+	0.111434i
$526$	−4.78599	+	8.28957i	−0.208679	+	0.361443i
$527$	0.311609	−	0.113416i	0.0135739	−	0.00494049i
$528$	−3.78592	−	6.55740i	−0.164761	−	0.285374i
$529$	9.76155	−	16.9075i	0.424415	−	0.735109i
$530$	1.74671	−	9.90611i	0.0758724	−	0.430294i
$531$	1.43657	+	0.522868i	0.0623418	+	0.0226905i
$532$	7.70351	+	13.3429i	0.333990	+	0.578487i
$533$	−19.2109	−	16.1199i	−0.832118	−	0.698230i
$534$	−10.3591	−	8.69234i	−0.448283	−	0.376154i
$535$	10.6801	−	3.88723i	0.461740	−	0.168060i
$536$	−0.142449	−	0.807866i	−0.00615284	−	0.0348945i
$537$	0.684286	+	3.88078i	0.0295291	+	0.167468i
$538$	−24.8343	+	9.03896i	−1.07068	+	0.389697i
$539$	19.8360	+	16.6444i	0.854396	+	0.716924i
$540$	4.18303	+	3.50998i	0.180009	+	0.151045i
$541$	12.2468	+	21.2120i	0.526530	+	0.911976i	0.999522	+	0.0309096i	$0.00984041\pi$
$541$	12.2468	+	21.2120i	0.526530	+	0.911976i	−0.472993	+	0.881066i	$0.656826\pi$
$542$	−1.15741	−	0.421262i	−0.0497149	−	0.0180947i
$543$	−5.03548	+	28.5576i	−0.216093	+	1.22553i
$544$	2.37556	−	4.11458i	0.101851	−	0.176411i
$545$	−0.538569	−	0.932829i	−0.0230698	−	0.0399580i
$546$	25.8704	−	9.41604i	1.10715	−	0.402969i
$547$	13.1188	−	22.7225i	0.560920	−	0.971542i	−0.436496	−	0.899706i	$-0.643781\pi$
$547$	13.1188	−	22.7225i	0.560920	−	0.971542i	0.997416	−	0.0718363i	$-0.0228859\pi$
$548$	5.94754	−	4.99058i	0.254066	−	0.213187i
$549$	17.0908			0.729419
$550$	4.86083	−	4.07872i	0.207266	−	0.173917i
$551$	−15.5656	−	5.66543i	−0.663118	−	0.241355i
$552$	0.386377	+	2.19125i	0.0164453	+	0.0932659i
$553$	−3.00435	+	17.0385i	−0.127758	+	0.724550i
$554$	30.6466			1.30205
$555$	2.31833	−	6.87828i	0.0984078	−	0.291967i
$556$	13.6277			0.577945
$557$	−1.28766	+	7.30268i	−0.0545599	+	0.309424i	−0.999859	−	0.0167798i	$-0.994659\pi$
$557$	−1.28766	+	7.30268i	−0.0545599	+	0.309424i	0.945299	+	0.326204i	$0.105770\pi$
$558$	−0.0191018	−	0.108332i	−0.000808643	−	0.00458604i
$559$	−47.4509	−	17.2707i	−2.00696	−	0.730473i
$560$	2.54999	−	2.13970i	0.107757	−	0.0904188i
$561$	−35.9746			−1.51885
$562$	−1.17024	+	0.981947i	−0.0493636	+	0.0414209i
$563$	−15.5514	+	26.9357i	−0.655411	+	1.13521i	0.326379	+	0.945239i	$0.394171\pi$
$563$	−15.5514	+	26.9357i	−0.655411	+	1.13521i	−0.981791	+	0.189967i	$0.939162\pi$
$564$	−10.0805	+	3.66899i	−0.424464	+	0.154492i
$565$	−2.56505	−	4.44280i	−0.107913	−	0.186910i
$566$	−11.0658	+	19.1666i	−0.465131	+	0.805631i
$567$	1.03342	−	5.86079i	0.0433994	−	0.246130i
$568$	−4.06104	−	1.47810i	−0.170397	−	0.0620196i
$569$	18.3108	+	31.7152i	0.767628	+	1.32957i	0.938846	+	0.344338i	$0.111897\pi$
$569$	18.3108	+	31.7152i	0.767628	+	1.32957i	−0.171218	+	0.985233i	$0.554770\pi$
$570$	−4.23089	−	3.55014i	−0.177213	−	0.148699i
$571$	2.67082	+	2.24108i	0.111770	+	0.0937863i	0.696960	−	0.717110i	$-0.254536\pi$
$571$	2.67082	+	2.24108i	0.111770	+	0.0937863i	−0.585190	+	0.810896i	$0.698980\pi$
$572$	−41.3266	+	15.0416i	−1.72795	+	0.628922i
$573$	3.76655	+	21.3611i	0.157350	+	0.892375i
$574$	2.09153	+	11.8616i	0.0872986	+	0.495095i
$575$	−1.75219	+	0.637746i	−0.0730715	+	0.0265959i
$576$	−1.20734	−	1.01308i	−0.0503058	−	0.0422115i
$577$	12.4447	+	10.4424i	0.518080	+	0.434721i	0.863962	−	0.503557i	$-0.167976\pi$
$577$	12.4447	+	10.4424i	0.518080	+	0.434721i	−0.345882	+	0.938278i	$0.612420\pi$
$578$	−2.78653	−	4.82642i	−0.115905	−	0.200753i
$579$	−17.1832	−	6.25418i	−0.714110	−	0.259915i
$580$	−0.621467	+	3.52451i	−0.0258050	+	0.146347i
$581$	6.30808	−	10.9259i	0.261703	−	0.453283i
$582$	6.73448	+	11.6645i	0.279153	+	0.483508i
$583$	59.9783	−	21.8303i	2.48405	−	0.904119i
$584$	−0.123030	+	0.213094i	−0.00509101	+	0.00881789i
$585$	8.36789	−	7.02149i	0.345970	−	0.290303i
$586$	−15.2008			−0.627938
$587$	20.3822	−	17.1027i	0.841265	−	0.705905i	−0.116583	−	0.993181i	$-0.537194\pi$
$587$	20.3822	−	17.1027i	0.841265	−	0.705905i	0.957848	+	0.287276i	$0.0927496\pi$
$588$	−4.57587	−	1.66548i	−0.188706	−	0.0686833i
$589$	0.0560961	+	0.318137i	0.00231140	+	0.0131086i
$590$	−0.168436	+	0.955250i	−0.00693441	+	0.0393270i
$591$	−5.70624			−0.234723
$592$	−1.94282	+	5.76415i	−0.0798492	+	0.236905i
$593$	−18.0393			−0.740785			−0.370392	−	0.928875i	$-0.620777\pi$
$593$	−18.0393			−0.740785			−0.370392	+	0.928875i	$0.620777\pi$
$594$	−6.01678	+	34.1228i	−0.246871	+	1.40008i
$595$	−2.74632	−	15.5751i	−0.112588	−	0.638518i
$596$	−3.98928	−	1.45198i	−0.163407	−	0.0594754i
$597$	−15.7034	+	13.1767i	−0.642699	+	0.539288i
$598$	12.9236			0.528485
$599$	−8.55716	+	7.18031i	−0.349636	+	0.293379i	−0.800644	−	0.599141i	$-0.795509\pi$
$599$	−8.55716	+	7.18031i	−0.349636	+	0.293379i	0.451008	+	0.892520i	$0.351065\pi$
$600$	−0.596643	+	1.03342i	−0.0243579	+	0.0421890i
$601$	13.2023	−	4.80526i	0.538535	−	0.196011i	−0.0584104	−	0.998293i	$-0.518603\pi$
$601$	13.2023	−	4.80526i	0.538535	−	0.196011i	0.596945	+	0.802282i	$0.296381\pi$
$602$	12.1263	+	21.0033i	0.494229	+	0.856030i
$603$	−0.646447	+	1.11968i	−0.0263253	+	0.0455968i
$604$	3.25464	−	18.4580i	0.132429	−	0.751044i
$605$	27.4988	+	10.0088i	1.11799	+	0.406914i
$606$	4.67473	+	8.09688i	0.189898	+	0.328913i
$607$	−5.17649	−	4.34359i	−0.210107	−	0.176301i	0.531661	−	0.846957i	$-0.321568\pi$
$607$	−5.17649	−	4.34359i	−0.210107	−	0.176301i	−0.741768	+	0.670656i	$0.766013\pi$
$608$	3.54558	+	2.97510i	0.143792	+	0.120656i
$609$	13.3587	−	4.86216i	0.541321	−	0.197025i
$610$	1.88303	+	10.6792i	0.0762418	+	0.432389i
$611$	10.8195	+	61.3604i	0.437710	+	2.48238i
$612$	−7.03649	+	2.56107i	−0.284433	+	0.103525i
$613$	0.268541	+	0.225333i	0.0108463	+	0.00910109i	0.648195	−	0.761475i	$-0.275524\pi$
$613$	0.268541	+	0.225333i	0.0108463	+	0.00910109i	−0.637348	+	0.770576i	$0.719969\pi$
$614$	−13.2556	−	11.1228i	−0.534954	−	0.448880i
$615$	−2.15885	−	3.73924i	−0.0870532	−	0.150781i
$616$	19.8485	+	7.22426i	0.799718	+	0.291074i
$617$	5.75078	−	32.6143i	0.231518	−	1.31300i	−0.618307	−	0.785937i	$-0.712181\pi$
$617$	5.75078	−	32.6143i	0.231518	−	1.31300i	0.849824	−	0.527066i	$-0.176708\pi$
$618$	4.56779	−	7.91164i	0.183743	−	0.318253i
$619$	−14.9398	−	25.8766i	−0.600483	−	1.04007i	−0.992748	−	0.120215i	$-0.961642\pi$
$619$	−14.9398	−	25.8766i	−0.600483	−	1.04007i	0.392265	−	0.919852i	$-0.371692\pi$
$620$	0.0655865	−	0.0238715i	0.00263402	−	0.000958704i
$621$	5.09100	−	8.81787i	0.204295	−	0.353849i
$622$	−21.3671	+	17.9291i	−0.856743	+	0.718893i
$623$	37.7233			1.51135
$624$	6.33557	−	5.31617i	0.253626	−	0.212817i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	0.394023	+	2.23461i	0.0157483	+	0.0893132i
$627$	6.08562	−	34.5133i	0.243036	−	1.37833i
$628$	7.32861			0.292443
$629$	19.1018	+	21.6869i	0.761640	+	0.864715i
$630$	−5.24639			−0.209021
$631$	−1.85767	+	10.5354i	−0.0739528	+	0.419407i	0.925245	+	0.379369i	$0.123859\pi$
$631$	−1.85767	+	10.5354i	−0.0739528	+	0.419407i	−0.999198	+	0.0400381i	$0.987252\pi$
$632$	0.902537	+	5.11854i	0.0359010	+	0.203605i
$633$	5.57498	+	2.02913i	0.221586	+	0.0806505i
$634$	−3.31848	+	2.78454i	−0.131794	+	0.110588i
$635$	−12.7688			−0.506713
$636$	−9.19497	+	7.71549i	−0.364604	+	0.305939i
$637$	−14.1417	+	24.4941i	−0.560313	+	0.970490i
$638$	−21.3398	+	7.76704i	−0.844850	+	0.307500i
$639$	3.40562	+	5.89871i	0.134724	+	0.233349i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	0.754439	−	4.27864i	0.0297986	−	0.168996i	−0.966277	−	0.257506i	$-0.917099\pi$
$641$	0.754439	−	4.27864i	0.0297986	−	0.168996i	0.996075	+	0.0885098i	$0.0282105\pi$
$642$	−12.7444	−	4.63858i	−0.502981	−	0.183070i
$643$	−0.643888	−	1.11525i	−0.0253925	−	0.0439810i	0.853050	−	0.521829i	$-0.174750\pi$
$643$	−0.643888	−	1.11525i	−0.0253925	−	0.0439810i	−0.878442	+	0.477848i	$0.841417\pi$
$644$	−4.75483	−	3.98978i	−0.187367	−	0.157219i
$645$	−6.65993	−	5.58835i	−0.262235	−	0.220041i
$646$	20.6640	−	7.52109i	0.813015	−	0.295913i
$647$	0.0845244	+	0.479362i	0.00332300	+	0.0188457i	0.986424	−	0.164217i	$-0.0525099\pi$
$647$	0.0845244	+	0.479362i	0.00332300	+	0.0188457i	−0.983101	+	0.183063i	$0.941399\pi$
$648$	−0.310449	−	1.76064i	−0.0121956	−	0.0691646i
$649$	−5.78373	+	2.10510i	−0.227031	+	0.0826326i
$650$	5.30934	+	4.45507i	0.208250	+	0.174742i
$651$	−0.212379	−	0.178208i	−0.00832381	−	0.00698450i
$652$	−2.00141	−	3.46655i	−0.0783813	−	0.135760i
$653$	−9.51929	−	3.46474i	−0.372519	−	0.135586i	0.148975	−	0.988841i	$-0.452403\pi$
$653$	−9.51929	−	3.46474i	−0.372519	−	0.135586i	−0.521493	+	0.853255i	$0.674625\pi$
$654$	−0.223196	+	1.26581i	−0.00872765	+	0.0494970i
$655$	0.335840	−	0.581692i	0.0131224	−	0.0227286i
$656$	1.80916	+	3.13356i	0.0706360	+	0.122345i
$657$	0.364419	−	0.132638i	0.0142173	−	0.00517469i
$658$	14.9625	−	25.9159i	0.583300	−	1.01031i
$659$	−24.2937	+	20.3848i	−0.946349	+	0.794081i	−0.978679	−	0.205396i	$-0.934152\pi$
$659$	−24.2937	+	20.3848i	−0.946349	+	0.794081i	0.0323302	+	0.999477i	$0.489707\pi$
$660$	−7.57183			−0.294733
$661$	1.36712	−	1.14715i	0.0531750	−	0.0446191i	−0.615813	−	0.787892i	$-0.711172\pi$
$661$	1.36712	−	1.14715i	0.0531750	−	0.0446191i	0.668988	+	0.743273i	$0.266728\pi$
$662$	12.6313	+	4.59742i	0.490930	+	0.178684i
$663$	−6.82334	−	38.6971i	−0.264997	−	1.50287i
$664$	0.658131	−	3.73245i	0.0255404	−	0.144847i
$665$	15.4070			0.597459
$666$	8.18517	−	4.99106i	0.317169	−	0.193400i
$667$	6.67335			0.258393
$668$	4.24355	−	24.0664i	0.164188	−	0.931156i
$669$	−2.36657	−	13.4215i	−0.0914968	−	0.518904i
$670$	−0.770857	−	0.280569i	−0.0297808	−	0.0108393i
$671$	−52.7107	+	44.2295i	−2.03487	+	1.70746i
$672$	−3.97219			−0.153230
$673$	11.7606	−	9.86829i	0.453337	−	0.380395i	−0.387336	−	0.921939i	$-0.626604\pi$
$673$	11.7606	−	9.86829i	0.453337	−	0.380395i	0.840672	+	0.541544i	$0.182160\pi$
$674$	9.50093	−	16.4561i	0.365962	−	0.633865i
$675$	5.13125	−	1.86762i	0.197502	−	0.0718848i
$676$	−17.5184	−	30.3427i	−0.673784	−	1.16703i
$677$	−10.1792	+	17.6309i	−0.391219	+	0.677611i	−0.992611	−	0.121343i	$-0.961280\pi$
$677$	−10.1792	+	17.6309i	−0.391219	+	0.677611i	0.601391	+	0.798955i	$0.294613\pi$
$678$	−1.06302	+	6.02868i	−0.0408250	+	0.231530i
$679$	−35.3070	−	12.8507i	−1.35496	−	0.493164i
$680$	−2.37556	−	4.11458i	−0.0910984	−	0.157787i
$681$	17.9836	+	15.0901i	0.689134	+	0.578252i
$682$	0.339265	+	0.284677i	0.0129911	+	0.0109009i
$683$	17.2726	−	6.28671i	0.660917	−	0.240554i	0.0102849	−	0.999947i	$-0.496726\pi$
$683$	17.2726	−	6.28671i	0.660917	−	0.240554i	0.650632	+	0.759393i	$0.274504\pi$
$684$	−1.26671	−	7.18390i	−0.0484340	−	0.274683i
$685$	−1.34820	−	7.64601i	−0.0515120	−	0.292139i
$686$	−9.13141	+	3.32356i	−0.348639	+	0.126894i
$687$	12.6949	+	10.6523i	0.484340	+	0.406409i
$688$	5.58117	+	4.68316i	0.212780	+	0.178544i
$689$	34.8585	+	60.3767i	1.32800	+	2.30017i
$690$	2.09087	+	0.761014i	0.0795980	+	0.0289713i
$691$	2.54899	−	14.4561i	0.0969683	−	0.549935i	−0.897158	−	0.441710i	$-0.854372\pi$
$691$	2.54899	−	14.4561i	0.0969683	−	0.549935i	0.994126	−	0.108225i	$-0.0345167\pi$
$692$	−3.62599	+	6.28041i	−0.137840	+	0.238745i
$693$	−16.6451	−	28.8302i	−0.632296	−	1.09517i
$694$	14.6874	−	5.34579i	0.557528	−	0.202923i
$695$	6.81387	−	11.8020i	0.258465	−	0.447674i
$696$	3.27149	−	2.74511i	0.124006	−	0.104053i
$697$	17.1911			0.651159
$698$	−0.919890	+	0.771879i	−0.0348183	+	0.0292161i
$699$	−27.1756	−	9.89111i	−1.02788	−	0.374116i
$700$	−0.578037	−	3.27821i	−0.0218477	−	0.123905i
$701$	−3.20968	+	18.2030i	−0.121228	+	0.687519i	0.862249	+	0.506485i	$0.169055\pi$
$701$	−3.20968	+	18.2030i	−0.121228	+	0.687519i	−0.983477	+	0.181034i	$0.942056\pi$
$702$	−37.8464			−1.42842
$703$	−24.0373	+	14.6572i	−0.906585	+	0.552807i
$704$	6.34536			0.239150
$705$	−1.86279	+	10.5644i	−0.0701569	+	0.397879i
$706$	−5.15186	−	29.2176i	−0.193893	−	1.09962i
$707$	−24.5083	−	8.92030i	−0.921730	−	0.335482i
$708$	0.886674	−	0.744008i	0.0333233	−	0.0279615i
$709$	48.5567			1.82358			0.911792	−	0.410652i	$-0.134699\pi$
$709$	48.5567			1.82358			0.911792	+	0.410652i	$0.134699\pi$
$710$	−3.31059	+	2.77791i	−0.124244	+	0.104253i
$711$	4.09581	−	7.09415i	0.153605	−	0.266051i
$712$	10.6490	−	3.87593i	0.399090	−	0.145257i
$713$	−0.0650721	−	0.112708i	−0.00243697	−	0.00422096i
$714$	−9.43616	+	16.3439i	−0.353139	+	0.611655i
$715$	−7.63684	+	43.3107i	−0.285602	+	1.61973i
$716$	−3.10319	−	1.12947i	−0.115972	−	0.0422102i
$717$	−6.78875	−	11.7585i	−0.253531	−	0.439128i
$718$	−1.06906	−	0.897051i	−0.0398971	−	0.0334777i
$719$	−7.88504	−	6.61633i	−0.294062	−	0.246748i	0.483805	−	0.875176i	$-0.339254\pi$
$719$	−7.88504	−	6.61633i	−0.294062	−	0.246748i	−0.777868	+	0.628428i	$0.783699\pi$
$720$	−1.48102	+	0.539047i	−0.0551943	+	0.0200891i
$721$	4.42534	+	25.0974i	0.164808	+	0.934675i
$722$	0.420637	+	2.38555i	0.0156545	+	0.0887810i
$723$	28.6030	−	10.4106i	1.06376	−	0.387176i
$724$	−18.6157	−	15.6205i	−0.691849	−	0.580530i
$725$	2.74158	+	2.30046i	0.101820	+	0.0854370i
$726$	−17.4599	−	30.2415i	−0.647999	−	1.12237i
$727$	8.34786	+	3.03837i	0.309605	+	0.112687i	0.492150	−	0.870511i	$-0.336211\pi$
$727$	8.34786	+	3.03837i	0.309605	+	0.112687i	−0.182545	+	0.983198i	$0.558433\pi$
$728$	−4.00629	+	22.7208i	−0.148483	+	0.842089i
$729$	−11.1829	+	19.3693i	−0.414180	+	0.717381i
$730$	0.123030	+	0.213094i	0.00455354	+	0.00788696i
$731$	32.5276	−	11.8391i	1.20308	−	0.437885i
$732$	6.46997	−	11.2063i	0.239137	−	0.414198i
$733$	27.9210	−	23.4285i	1.03129	−	0.865352i	0.0402833	−	0.999188i	$-0.487174\pi$
$733$	27.9210	−	23.4285i	1.03129	−	0.865352i	0.991003	+	0.133836i	$0.0427295\pi$
$734$	−6.16396			−0.227516
$735$	−3.73028	+	3.13008i	−0.137594	+	0.115455i
$736$	−1.75219	−	0.637746i	−0.0645867	−	0.0235076i
$737$	−0.903888	−	5.12620i	−0.0332951	−	0.188826i
$738$	0.990269	−	5.61609i	0.0364523	−	0.206731i
$739$	22.4150			0.824550			0.412275	−	0.911059i	$-0.364734\pi$
$739$	22.4150			0.824550			0.412275	+	0.911059i	$0.364734\pi$
$740$	4.02050	+	4.56460i	0.147796	+	0.167798i
$741$	38.2794			1.40623
$742$	5.81443	−	32.9753i	0.213454	−	1.21056i
$743$	−7.20936	−	40.8863i	−0.264486	−	1.49997i	−0.770495	−	0.637446i	$-0.779991\pi$
$743$	−7.20936	−	40.8863i	−0.264486	−	1.49997i	0.506009	−	0.862528i	$-0.331120\pi$
$744$	−0.0782635	−	0.0284856i	−0.00286928	−	0.00104433i
$745$	−3.25209	+	2.72883i	−0.119147	+	0.0999766i
$746$	21.0820			0.771866
$747$	−4.57584	+	3.83959i	−0.167421	+	0.140483i
$748$	15.0738	−	26.1085i	0.551152	−	0.954622i
$749$	35.5517	−	12.9397i	1.29903	−	0.472808i
$750$	0.596643	+	1.03342i	0.0217863	+	0.0377350i
$751$	22.7053	−	39.3268i	0.828530	−	1.43506i	−0.0706614	−	0.997500i	$-0.522511\pi$
$751$	22.7053	−	39.3268i	0.828530	−	1.43506i	0.899191	−	0.437556i	$-0.144156\pi$
$752$	1.56106	−	8.85323i	0.0569261	−	0.322844i
$753$	9.19781	+	3.34773i	0.335187	+	0.121998i
$754$	−12.4024	−	21.4815i	−0.451667	−	0.782311i
$755$	−14.3578	−	12.0476i	−0.522532	−	0.438457i
$756$	13.9244	+	11.6840i	0.506425	+	0.424941i
$757$	45.4426	−	16.5398i	1.65164	−	0.601148i	0.662623	−	0.748953i	$-0.269443\pi$
$757$	45.4426	−	16.5398i	1.65164	−	0.601148i	0.989016	+	0.147806i	$0.0472210\pi$
$758$	5.15420	+	29.2309i	0.187209	+	1.06172i
$759$	2.45170	+	13.9043i	0.0889911	+	0.504694i
$760$	4.34930	−	1.58302i	0.157766	−	0.0574220i
$761$	24.6233	+	20.6614i	0.892593	+	0.748975i	0.968729	−	0.248123i	$-0.0798136\pi$
$761$	24.6233	+	20.6614i	0.892593	+	0.748975i	−0.0761352	+	0.997098i	$0.524258\pi$
$762$	11.6721	+	9.79403i	0.422834	+	0.354800i
$763$	−1.79278	−	3.10518i	−0.0649029	−	0.112415i
$764$	−17.0810	−	6.21699i	−0.617970	−	0.224923i
$765$	−1.30029	+	7.37432i	−0.0470121	+	0.266619i
$766$	−1.60879	+	2.78651i	−0.0581280	+	0.100681i
$767$	−3.36142	−	5.82215i	−0.121374	−	0.210225i
$768$	−1.12132	+	0.408128i	−0.0404622	+	0.0147270i
$769$	12.6680	−	21.9416i	0.456818	−	0.791233i	−0.541972	−	0.840396i	$-0.682322\pi$
$769$	12.6680	−	21.9416i	0.456818	−	0.791233i	0.998791	+	0.0491637i	$0.0156556\pi$
$770$	16.1806	−	13.5772i	0.583110	−	0.489287i
$771$	26.7785			0.964403
$772$	11.7389	−	9.85012i	0.422493	−	0.354514i
$773$	−31.2224	−	11.3640i	−1.12299	−	0.408735i	−0.287248	−	0.957856i	$-0.592740\pi$
$773$	−31.2224	−	11.3640i	−1.12299	−	0.408735i	−0.835743	+	0.549121i	$0.814962\pi$
$774$	−1.99396	−	11.3083i	−0.0716714	−	0.406469i
$775$	0.0121199	−	0.0687354i	0.000435360	−	0.00246905i
$776$	−11.2873			−0.405190
$777$	7.71723	−	22.8963i	0.276854	−	0.821400i
$778$	−14.0771			−0.504687
$779$	−2.90812	+	16.4927i	−0.104194	+	0.590914i
$780$	−1.43616	−	8.14485i	−0.0514227	−	0.291632i
$781$	−25.7688	−	9.37906i	−0.922079	−	0.335609i
$782$	−6.78649	+	5.69454i	−0.242685	+	0.203636i
$783$	−19.5427			−0.698399
$784$	3.12606	−	2.62308i	0.111645	−	0.0936813i
$785$	3.66430	−	6.34676i	0.130785	−	0.226526i
$786$	−0.753169	+	0.274131i	−0.0268647	+	0.00977794i
$787$	1.71526	+	2.97092i	0.0611425	+	0.105902i	0.894976	−	0.446114i	$-0.147192\pi$
$787$	1.71526	+	2.97092i	0.0611425	+	0.105902i	−0.833834	+	0.552015i	$0.813859\pi$
$788$	2.39098	−	4.14129i	0.0851750	−	0.147527i
$789$	1.98343	−	11.2486i	0.0706119	−	0.400460i
$790$	4.88405	+	1.77765i	0.173767	+	0.0632459i
$791$	−8.53849	−	14.7891i	−0.303594	−	0.525840i
$792$	−7.66100	−	6.42834i	−0.272222	−	0.228421i
$793$	−57.5743	−	48.3106i	−2.04452	−	1.71556i
$794$	−24.8871	+	9.05818i	−0.883212	+	0.321463i
$795$	2.08433	+	11.8208i	0.0739236	+	0.419241i
$796$	−2.98309	−	16.9179i	−0.105733	−	0.599641i
$797$	−1.60488	+	0.584127i	−0.0568476	+	0.0206908i	−0.370287	−	0.928917i	$-0.620741\pi$
$797$	−1.60488	+	0.584127i	−0.0568476	+	0.0206908i	0.313440	+	0.949608i	$0.398519\pi$
$798$	−14.0837	−	11.8176i	−0.498558	−	0.418340i
$799$	−32.7189	−	27.4545i	−1.15751	−	0.971269i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−16.7836	−	6.10873i	−0.593020	−	0.215842i
$802$	−1.81676	+	10.3034i	−0.0641521	+	0.363825i
$803$	−0.780669	+	1.35216i	−0.0275492	+	0.0477166i
$804$	0.489443	+	0.847741i	0.0172613	+	0.0298975i
$805$	−5.83267	+	2.12292i	−0.205575	+	0.0748230i
$806$	−0.241872	+	0.418935i	−0.00851958	+	0.0147563i
$807$	24.1582	−	20.2712i	0.850410	−	0.713579i
$808$	−7.83506			−0.275636
$809$	−16.2838	+	13.6637i	−0.572508	+	0.480392i	−0.882477	−	0.470355i	$-0.844126\pi$
$809$	−16.2838	+	13.6637i	−0.572508	+	0.480392i	0.309969	+	0.950747i	$0.399681\pi$
$810$	−1.67999	−	0.611465i	−0.0590287	−	0.0214847i
$811$	8.79903	+	49.9018i	0.308976	+	1.75229i	0.604173	+	0.796853i	$0.293503\pi$
$811$	8.79903	+	49.9018i	0.308976	+	1.75229i	−0.295198	+	0.955436i	$0.595385\pi$
$812$	−2.06873	+	11.7323i	−0.0725980	+	0.411724i
$813$	1.46975			0.0515465
$814$	−12.3279	+	36.5756i	−0.432092	+	1.28198i
$815$	−4.00282			−0.140213
$816$	−0.984487	+	5.58330i	−0.0344639	+	0.195455i
$817$	5.85565	+	33.2090i	0.204863	+	1.16184i
$818$	−18.7584	−	6.82751i	−0.655873	−	0.238718i
$819$	27.8549	−	23.3730i	0.973328	−	0.816719i
$820$	3.61833			0.126357
$821$	26.8431	−	22.5241i	0.936831	−	0.786095i	−0.0401997	−	0.999192i	$-0.512799\pi$
$821$	26.8431	−	22.5241i	0.936831	−	0.786095i	0.977031	+	0.213097i	$0.0683550\pi$
$822$	−4.63231	+	8.02340i	−0.161570	+	0.279848i
$823$	3.17650	−	1.15615i	0.110726	−	0.0403008i	−0.286063	−	0.958211i	$-0.592347\pi$
$823$	3.17650	−	1.15615i	0.110726	−	0.0403008i	0.396789	+	0.917910i	$0.370125\pi$
$824$	3.82791	+	6.63013i	0.133352	+	0.230972i
$825$	−3.78592	+	6.55740i	−0.131809	+	0.228299i
$826$	−0.560687	+	3.17982i	−0.0195088	+	0.110640i
$827$	−13.4730	−	4.90377i	−0.468502	−	0.170521i	0.0969718	−	0.995287i	$-0.469084\pi$
$827$	−13.4730	−	4.90377i	−0.468502	−	0.170521i	−0.565474	+	0.824766i	$0.691307\pi$
$828$	1.46940	+	2.54508i	0.0510653	+	0.0884477i
$829$	−17.8164	−	14.9498i	−0.618791	−	0.519227i	0.278632	−	0.960398i	$-0.410119\pi$
$829$	−17.8164	−	14.9498i	−0.618791	−	0.519227i	−0.897423	+	0.441171i	$0.854563\pi$
$830$	−2.90333	−	2.43618i	−0.100776	−	0.0845611i
$831$	−34.3647	+	12.5077i	−1.19210	+	0.433889i
$832$	1.20353	+	6.82556i	0.0417249	+	0.236634i
$833$	−3.36673	−	19.0937i	−0.116650	−	0.661557i
$834$	−15.2811	+	5.56186i	−0.529140	+	0.192591i
$835$	−18.7203	−	15.7082i	−0.647843	−	0.543605i
$836$	22.4980	+	18.8781i	0.778110	+	0.652912i
$837$	0.190562	+	0.330063i	0.00658678	+	0.0114086i
$838$	−9.82603	−	3.57638i	−0.339434	−	0.123544i
$839$	−3.81602	+	21.6417i	−0.131743	+	0.747154i	0.845329	+	0.534246i	$0.179405\pi$
$839$	−3.81602	+	21.6417i	−0.131743	+	0.747154i	−0.977072	+	0.212908i	$0.931707\pi$
$840$	−1.98609	+	3.44002i	−0.0685267	+	0.118692i
$841$	8.09580	+	14.0223i	0.279165	+	0.483529i
$842$	12.5413	−	4.56466i	0.432202	−	0.157309i
$843$	0.911455	−	1.57869i	0.0313922	−	0.0543728i
$844$	−3.80861	+	3.19581i	−0.131098	+	0.110004i
$845$	−35.0368			−1.20530
$846$	−10.8537	+	9.10736i	−0.373159	+	0.313118i
$847$	91.5375	+	33.3169i	3.14527	+	1.14478i
$848$	−1.74671	−	9.90611i	−0.0599824	−	0.340177i
$849$	4.58594	−	26.0082i	0.157389	−	0.892598i
$850$	−4.75111			−0.162962
$851$	7.08026	−	8.86089i	0.242708	−	0.303747i
$852$	5.15698			0.176675
$853$	−4.55001	+	25.8044i	−0.155790	+	0.883526i	0.802271	+	0.596960i	$0.203625\pi$
$853$	−4.55001	+	25.8044i	−0.155790	+	0.883526i	−0.958060	+	0.286566i	$0.907486\pi$
$854$	6.26821	+	35.5488i	0.214494	+	1.21645i
$855$	−6.85479	−	2.49494i	−0.234429	−	0.0853252i
$856$	8.70649	−	7.30561i	0.297582	−	0.249701i
$857$	0.0425422			0.00145321			0.000726607	−	1.00000i	$-0.499769\pi$
$857$	0.0425422			0.00145321			0.000726607		1.00000i	$0.499769\pi$
$858$	40.2015	−	33.7330i	1.37246	−	1.15163i
$859$	−12.5296	+	21.7020i	−0.427506	+	0.740461i	−0.996651	−	0.0817757i	$-0.973941\pi$
$859$	−12.5296	+	21.7020i	−0.427506	+	0.740461i	0.569145	+	0.822237i	$0.307274\pi$
$860$	6.84632	−	2.49186i	0.233458	−	0.0849716i
$861$	−7.18634	−	12.4471i	−0.244910	−	0.424196i
$862$	−7.25717	+	12.5698i	−0.247180	+	0.428128i
$863$	−6.19408	+	35.1284i	−0.210849	+	1.19578i	0.677118	+	0.735875i	$0.263229\pi$
$863$	−6.19408	+	35.1284i	−0.210849	+	1.19578i	−0.887966	+	0.459908i	$0.847882\pi$
$864$	5.13125	+	1.86762i	0.174569	+	0.0635378i
$865$	3.62599	+	6.28041i	0.123288	+	0.213540i
$866$	−23.8471	−	20.0101i	−0.810357	−	0.679970i
$867$	5.09440	+	4.27471i	0.173015	+	0.145177i
$868$	0.218323	−	0.0794631i	0.00741037	−	0.00269715i
$869$	5.72692	+	32.4790i	0.194273	+	1.10177i
$870$	−0.741587	−	4.20575i	−0.0251422	−	0.142588i
$871$	5.34270	−	1.94458i	0.181030	−	0.0658897i
$872$	−0.825136	−	0.692371i	−0.0279426	−	0.0234466i
$873$	13.6276	+	11.4349i	0.461224	+	0.387013i
$874$	−4.31519	−	7.47413i	−0.145963	−	0.252816i
$875$	−3.12803	−	1.13851i	−0.105747	−	0.0384887i
$876$	0.0509865	−	0.289159i	0.00172267	−	0.00976977i
$877$	−18.2031	+	31.5287i	−0.614676	+	1.06465i	0.375765	+	0.926715i	$0.377380\pi$
$877$	−18.2031	+	31.5287i	−0.614676	+	1.06465i	−0.990441	+	0.137935i	$0.955953\pi$
$878$	11.5293	+	19.9694i	0.389097	+	0.673935i
$879$	17.0450	−	6.20386i	0.574912	−	0.209251i
$880$	3.17268	−	5.49525i	0.106951	−	0.185245i
$881$	−36.0834	+	30.2776i	−1.21568	+	1.02008i	−0.216641	+	0.976251i	$0.569510\pi$
$881$	−36.0834	+	30.2776i	−1.21568	+	1.02008i	−0.999039	+	0.0438257i	$0.986045\pi$
$882$	−6.43159			−0.216563
$883$	−1.72881	+	1.45065i	−0.0581792	+	0.0488181i	−0.671414	−	0.741083i	$-0.734313\pi$
$883$	−1.72881	+	1.45065i	−0.0581792	+	0.0488181i	0.613234	+	0.789901i	$0.289868\pi$
$884$	30.9434	+	11.2625i	1.04074	+	0.378798i
$885$	−0.200993	−	1.13989i	−0.00675630	−	0.0383169i
$886$	2.90792	−	16.4917i	0.0976936	−	0.554048i
$887$	40.1531			1.34821			0.674105	−	0.738636i	$-0.264530\pi$
$887$	40.1531			1.34821			0.674105	+	0.738636i	$0.264530\pi$
$888$	−0.173990	−	7.25639i	−0.00583871	−	0.243509i
$889$	−42.5044			−1.42555
$890$	1.96786	−	11.1603i	0.0659629	−	0.374094i
$891$	−1.96991	−	11.1719i	−0.0659945	−	0.374273i
$892$	10.7322	+	3.90621i	0.359342	+	0.130790i
$893$	31.8741	−	26.7455i	1.06663	−	0.895005i
$894$	5.06586			0.169428
$895$	−2.52974	+	2.12271i	−0.0845600	+	0.0709543i
$896$	1.66439	−	2.88281i	0.0556034	−	0.0963079i
$897$	−14.4915	+	5.27448i	−0.483857	+	0.176110i
$898$	7.74993	+	13.4233i	0.258619	+	0.447941i
$899$	−0.124895	+	0.216325i	−0.00416549	+	0.00721485i
$900$	−0.273681	+	1.55212i	−0.00912271	+	0.0517375i
$901$	−44.9089	−	16.3455i	−1.49613	−	0.544548i
$902$	11.4798	+	19.8836i	0.382236	+	0.662051i
$903$	−22.1695	−	18.6024i	−0.737753	−	0.619049i
$904$	−3.92989	−	3.29757i	−0.130706	−	0.109675i
$905$	−22.8356	+	8.31147i	−0.759081	+	0.276283i
$906$	3.88371	+	22.0256i	0.129028	+	0.731753i
$907$	−6.38176	−	36.1928i	−0.211903	−	1.20176i	−0.886201	−	0.463301i	$-0.846665\pi$
$907$	−6.38176	−	36.1928i	−0.211903	−	1.20176i	0.674298	−	0.738459i	$-0.264446\pi$
$908$	−18.4869	+	6.72869i	−0.613510	+	0.223299i
$909$	9.45957	+	7.93752i	0.313754	+	0.263271i
$910$	17.6736	+	14.8299i	0.585876	+	0.491608i
$911$	−16.6256	−	28.7964i	−0.550831	−	0.954068i	−0.998215	−	0.0597254i	$-0.980977\pi$
$911$	−16.6256	−	28.7964i	−0.550831	−	0.954068i	0.447384	−	0.894342i	$-0.352356\pi$
$912$	−5.18996	−	1.88899i	−0.171857	−	0.0625507i
$913$	4.17608	−	23.6837i	0.138208	−	0.783817i
$914$	3.31444	−	5.74077i	0.109632	−	0.189888i
$915$	−6.46997	−	11.2063i	−0.213891	−	0.370470i
$916$	−13.0502	+	4.74987i	−0.431189	+	0.156940i
$917$	1.11794	−	1.93632i	0.0369175	−	0.0639431i
$918$	19.8740	−	16.6763i	0.655941	−	0.550400i
$919$	12.6944			0.418751			0.209375	−	0.977835i	$-0.432857\pi$
$919$	12.6944			0.418751			0.209375	+	0.977835i	$0.432857\pi$
$920$	−1.42840	+	1.19857i	−0.0470930	+	0.0395157i
$921$	19.4034	+	7.06225i	0.639363	+	0.232709i
$922$	−3.86415	−	21.9147i	−0.127259	−	0.721721i
$923$	5.20126	−	29.4978i	0.171202	−	0.970932i
$924$	−25.2050			−0.829183
$925$	5.96331	−	1.19955i	0.196072	−	0.0394409i
$926$	5.97561			0.196371
$927$	2.09525	−	11.8828i	0.0688172	−	0.390282i
$928$	0.621467	+	3.52451i	0.0204006	+	0.115698i
$929$	−0.255948	−	0.0931575i	−0.00839739	−	0.00305640i	0.337818	−	0.941211i	$-0.390311\pi$
$929$	−0.255948	−	0.0931575i	−0.00839739	−	0.00305640i	−0.346215	+	0.938155i	$0.612533\pi$
$930$	−0.0638010	+	0.0535354i	−0.00209212	+	0.00175549i
$931$	18.8876			0.619016
$932$	18.5653	−	15.5782i	0.608128	−	0.510280i
$933$	16.6420	−	28.8248i	0.544836	−	0.943683i
$934$	33.1589	−	12.0689i	1.08499	−	0.394905i
$935$	−15.0738	−	26.1085i	−0.492965	−	0.853840i
$936$	5.46175	−	9.46003i	0.178523	−	0.309211i
$937$	−8.30648	+	47.1084i	−0.271361	+	1.53896i	0.478928	+	0.877854i	$0.341026\pi$
$937$	−8.30648	+	47.1084i	−0.271361	+	1.53896i	−0.750289	+	0.661110i	$0.770086\pi$
$938$	−2.56601	−	0.933952i	−0.0837833	−	0.0304946i
$939$	−1.35384	−	2.34491i	−0.0441807	−	0.0765233i
$940$	−6.88659	−	5.77853i	−0.224616	−	0.188475i
$941$	−10.3733	−	8.70423i	−0.338160	−	0.283750i	0.457855	−	0.889027i	$-0.348618\pi$
$941$	−10.3733	−	8.70423i	−0.338160	−	0.283750i	−0.796015	+	0.605277i	$0.793062\pi$
$942$	−8.21773	+	2.99101i	−0.267748	+	0.0974523i
$943$	−1.17159	−	6.64440i	−0.0381521	−	0.216371i
$944$	0.168436	+	0.955250i	0.00548213	+	0.0310907i
$945$	17.0808	−	6.21690i	0.555638	−	0.202236i
$946$	35.4146	+	29.7163i	1.15143	+	0.966162i
$947$	−36.6496	−	30.7527i	−1.19095	−	0.999327i	−0.999842	−	0.0177581i	$-0.994347\pi$
$947$	−36.6496	−	30.7527i	−1.19095	−	0.999327i	−0.191109	−	0.981569i	$-0.561208\pi$
$948$	−3.10105	−	5.37118i	−0.100718	−	0.174448i
$949$	−1.60256	−	0.583282i	−0.0520211	−	0.0189341i
$950$	0.803718	−	4.55811i	0.0260761	−	0.147885i
$951$	2.58464	−	4.47673i	0.0838127	−	0.145168i
$952$	−7.90771	−	13.6965i	−0.256290	−	0.443908i
$953$	0.510090	−	0.185658i	0.0165235	−	0.00601404i	−0.333745	−	0.942663i	$-0.608313\pi$
$953$	0.510090	−	0.185658i	0.0165235	−	0.00601404i	0.350269	+	0.936649i	$0.386090\pi$
$954$	−7.92678	+	13.7296i	−0.256639	+	0.444512i
$955$	−13.9246	+	11.6841i	−0.450589	+	0.378089i
$956$	11.3782			0.367999
$957$	20.7588	−	17.4187i	0.671037	−	0.563067i
$958$	−18.7103	−	6.80998i	−0.604502	−	0.220021i
$959$	−4.48785	−	25.4519i	−0.144920	−	0.821884i
$960$	−0.207212	+	1.17516i	−0.00668774	+	0.0379280i
$961$	−30.9951			−0.999843
$962$	−41.6818	−	6.32347i	−1.34388	−	0.203877i
$963$	−17.9128			−0.577233
$964$	−4.42946	+	25.1207i	−0.142663	+	0.809085i
$965$	−2.66100	−	15.0913i	−0.0856605	−	0.485805i
$966$	6.96004	+	2.53325i	0.223936	+	0.0815059i
$967$	25.8080	−	21.6555i	0.829930	−	0.696394i	−0.125345	−	0.992113i	$-0.540004\pi$
$967$	25.8080	−	21.6555i	0.829930	−	0.696394i	0.955275	+	0.295719i	$0.0955593\pi$
$968$	29.2636			0.940569
$969$	−20.1015	+	16.8671i	−0.645752	+	0.541850i
$970$	−5.64365	+	9.77508i	−0.181207	+	0.313859i
$971$	34.6395	−	12.6077i	1.11163	−	0.404602i	0.280042	−	0.959988i	$-0.409652\pi$
$971$	34.6395	−	12.6077i	1.11163	−	0.404602i	0.831593	+	0.555386i	$0.187429\pi$
$972$	−7.12416	−	12.3394i	−0.228507	−	0.395787i
$973$	22.6819	−	39.2861i	0.727147	−	1.25946i
$974$	−0.741544	+	4.20550i	−0.0237606	+	0.134753i
$975$	−7.77172	−	2.82868i	−0.248894	−	0.0905901i
$976$	5.42198	+	9.39115i	0.173553	+	0.300603i
$977$	−8.90859	−	7.47519i	−0.285011	−	0.239153i	0.489062	−	0.872249i	$-0.337339\pi$
$977$	−8.90859	−	7.47519i	−0.285011	−	0.239153i	−0.774073	+	0.633096i	$0.781784\pi$
$978$	3.65902	+	3.07028i	0.117003	+	0.0981768i
$979$	67.5720	−	24.5942i	2.15961	−	0.786034i
$980$	−0.708620	−	4.01878i	−0.0226360	−	0.128375i
$981$	0.294793	+	1.67185i	0.00941200	+	0.0533781i
$982$	−20.0504	+	7.29775i	−0.639834	+	0.232881i
$983$	18.5368	+	15.5542i	0.591232	+	0.496103i	0.888614	−	0.458656i	$-0.151669\pi$
$983$	18.5368	+	15.5542i	0.591232	+	0.496103i	−0.297382	+	0.954759i	$0.596113\pi$
$984$	−3.30755	−	2.77536i	−0.105441	−	0.0884754i
$985$	−2.39098	−	4.14129i	−0.0761828	−	0.131953i
$986$	15.9782	+	5.81560i	0.508851	+	0.185206i
$987$	−6.20083	+	35.1667i	−0.197375	+	1.11937i
$988$	−16.0395	+	27.7812i	−0.510284	+	0.883838i
$989$	−6.79262	−	11.7652i	−0.215993	−	0.374111i
$990$	−9.39761	+	3.42045i	−0.298676	+	0.108709i
$991$	−19.4722	+	33.7269i	−0.618556	+	1.07137i	0.371193	+	0.928556i	$0.378949\pi$
$991$	−19.4722	+	33.7269i	−0.618556	+	1.07137i	−0.989749	+	0.142815i	$0.954385\pi$
$992$	0.0534666	−	0.0448638i	0.00169757	−	0.00142443i
$993$	−16.0401			−0.509017
$994$	−11.0202	+	9.24707i	−0.349540	+	0.293299i
$995$	−16.1429	−	5.87554i	−0.511765	−	0.186267i
$996$	0.785338	+	4.45388i	0.0248844	+	0.141126i
$997$	−9.78255	+	55.4796i	−0.309816	+	1.75706i	0.290103	+	0.956995i	$0.406310\pi$
$997$	−9.78255	+	55.4796i	−0.309816	+	1.75706i	−0.599919	+	0.800061i	$0.704801\pi$
$998$	−26.7360			−0.846314
$999$	−20.7343	+	25.9489i	−0.656005	+	0.820985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.d.181.3	✓	24
37.9	even	9	inner	370.2.o.d.231.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.d.181.3	✓	24	1.1	even	1	trivial
370.2.o.d.231.3	yes	24	37.9	even	9	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(0.207212 + 1.17516i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{5} +1.19329 q^{6} +(-2.54999 + 2.13970i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.48102 - 0.539047i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(0.207212 + 1.17516i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{5} +1.19329 q^{6} +(-2.54999 + 2.13970i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.48102 - 0.539047i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-3.17268 + 5.49525i) q^{11} +(0.207212 - 1.17516i) q^{12} +(-6.51288 - 2.37049i) q^{13} +(1.66439 + 2.88281i) q^{14} +(-0.914110 - 0.767030i) q^{15} +(0.766044 + 0.642788i) q^{16} +(4.46459 - 1.62498i) q^{17} +(-0.273681 - 1.55212i) q^{18} +(0.803718 + 4.55811i) q^{19} +(0.939693 - 0.342020i) q^{20} +(-3.04287 - 2.55327i) q^{21} +(4.86083 + 4.07872i) q^{22} +(-0.932323 - 1.61483i) q^{23} +(-1.12132 - 0.408128i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-3.46543 + 6.00230i) q^{26} +(2.73028 + 4.72898i) q^{27} +(3.12803 - 1.13851i) q^{28} +(-1.78944 + 3.09940i) q^{29} +(-0.914110 + 0.767030i) q^{30} +0.0697957 q^{31} +(0.766044 - 0.642788i) q^{32} +(-7.11520 - 2.58972i) q^{33} +(-0.825022 - 4.67893i) q^{34} +(0.578037 - 3.27821i) q^{35} -1.57607 q^{36} +(2.21684 + 5.66442i) q^{37} +4.62843 q^{38} +(1.43616 - 8.14485i) q^{39} +(-0.173648 - 0.984808i) q^{40} +(3.40012 + 1.23754i) q^{41} +(-3.04287 + 2.55327i) q^{42} +7.28570 q^{43} +(4.86083 - 4.07872i) q^{44} +(-0.788034 + 1.36492i) q^{45} +(-1.75219 + 0.637746i) q^{46} +(-4.49490 - 7.78540i) q^{47} +(-0.596643 + 1.03342i) q^{48} +(0.708620 - 4.01878i) q^{49} +(-0.939693 - 0.342020i) q^{50} +(2.83472 + 4.90988i) q^{51} +(5.30934 + 4.45507i) q^{52} +(-7.70559 - 6.46575i) q^{53} +(5.13125 - 1.86762i) q^{54} +(-1.10186 - 6.24896i) q^{55} +(-0.578037 - 3.27821i) q^{56} +(-5.18996 + 1.88899i) q^{57} +(2.74158 + 2.30046i) q^{58} +(0.743052 + 0.623495i) q^{59} +(0.596643 + 1.03342i) q^{60} +(10.1900 + 3.70885i) q^{61} +(0.0121199 - 0.0687354i) q^{62} +(-2.62319 + 4.54350i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(6.51288 - 2.37049i) q^{65} +(-3.78592 + 6.55740i) q^{66} +(-0.628408 + 0.527297i) q^{67} -4.75111 q^{68} +(1.70449 - 1.43024i) q^{69} +(-3.12803 - 1.13851i) q^{70} +(0.750450 + 4.25601i) q^{71} +(-0.273681 + 1.55212i) q^{72} +0.246060 q^{73} +(5.96331 - 1.19955i) q^{74} +1.19329 q^{75} +(0.803718 - 4.55811i) q^{76} +(-3.66785 - 20.8014i) q^{77} +(-7.77172 - 2.82868i) q^{78} +(3.98152 - 3.34089i) q^{79} -1.00000 q^{80} +(-1.36954 + 1.14918i) q^{81} +(1.80916 - 3.13356i) q^{82} +(-3.56146 + 1.29626i) q^{83} +(1.98609 + 3.44002i) q^{84} +(-2.37556 + 4.11458i) q^{85} +(1.26515 - 7.17501i) q^{86} +(-4.01308 - 1.46064i) q^{87} +(-3.17268 - 5.49525i) q^{88} +(-8.68118 - 7.28437i) q^{89} +(1.20734 + 1.01308i) q^{90} +(21.6799 - 7.89085i) q^{91} +(0.323792 + 1.83632i) q^{92} +(0.0144625 + 0.0820210i) q^{93} +(-8.44765 + 3.07469i) q^{94} +(-3.54558 - 2.97510i) q^{95} +(0.914110 + 0.767030i) q^{96} +(5.64365 + 9.77508i) q^{97} +(-3.83468 - 1.39571i) q^{98} +(-1.73661 + 9.84879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{6} - 9 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q + 6 * q^6 - 9 * q^7 - 12 * q^8 + 12 * q^9	\( 24 q + 6 q^{6} - 9 q^{7} - 12 q^{8} + 12 q^{9} + 12 q^{10} - 3 q^{11} - 3 q^{14} + 6 q^{17} - 6 q^{18} - 18 q^{19} + 18 q^{21} + 3 q^{22} + 15 q^{23} - 6 q^{26} - 12 q^{27} + 9 q^{28} - 18 q^{29} - 6 q^{31} - 45 q^{33} - 3 q^{34} + 30 q^{36} - 18 q^{37} - 24 q^{38} + 12 q^{39} + 3 q^{41} + 18 q^{42} + 3 q^{44} + 15 q^{45} + 9 q^{46} - 36 q^{47} - 3 q^{48} - 15 q^{49} + 54 q^{51} - 9 q^{52} - 6 q^{53} + 45 q^{54} - 3 q^{55} + 3 q^{57} - 15 q^{58} - 9 q^{59} + 3 q^{60} - 24 q^{61} + 81 q^{62} - 45 q^{63} - 12 q^{64} - 3 q^{66} + 12 q^{67} + 12 q^{68} + 60 q^{69} - 9 q^{70} + 42 q^{71} - 6 q^{72} - 42 q^{73} + 12 q^{74} + 6 q^{75} - 18 q^{76} + 9 q^{77} + 30 q^{78} - 6 q^{79} - 24 q^{80} - 66 q^{81} - 24 q^{82} - 3 q^{83} - 42 q^{84} + 6 q^{85} - 18 q^{86} - 84 q^{87} - 3 q^{88} + 27 q^{89} + 6 q^{90} + 153 q^{91} - 9 q^{92} - 54 q^{93} - 21 q^{94} - 9 q^{95} - 9 q^{97} - 24 q^{98} + 165 q^{99}+O(q^{100}) \) 24 * q + 6 * q^6 - 9 * q^7 - 12 * q^8 + 12 * q^9 + 12 * q^10 - 3 * q^11 - 3 * q^14 + 6 * q^17 - 6 * q^18 - 18 * q^19 + 18 * q^21 + 3 * q^22 + 15 * q^23 - 6 * q^26 - 12 * q^27 + 9 * q^28 - 18 * q^29 - 6 * q^31 - 45 * q^33 - 3 * q^34 + 30 * q^36 - 18 * q^37 - 24 * q^38 + 12 * q^39 + 3 * q^41 + 18 * q^42 + 3 * q^44 + 15 * q^45 + 9 * q^46 - 36 * q^47 - 3 * q^48 - 15 * q^49 + 54 * q^51 - 9 * q^52 - 6 * q^53 + 45 * q^54 - 3 * q^55 + 3 * q^57 - 15 * q^58 - 9 * q^59 + 3 * q^60 - 24 * q^61 + 81 * q^62 - 45 * q^63 - 12 * q^64 - 3 * q^66 + 12 * q^67 + 12 * q^68 + 60 * q^69 - 9 * q^70 + 42 * q^71 - 6 * q^72 - 42 * q^73 + 12 * q^74 + 6 * q^75 - 18 * q^76 + 9 * q^77 + 30 * q^78 - 6 * q^79 - 24 * q^80 - 66 * q^81 - 24 * q^82 - 3 * q^83 - 42 * q^84 + 6 * q^85 - 18 * q^86 - 84 * q^87 - 3 * q^88 + 27 * q^89 + 6 * q^90 + 153 * q^91 - 9 * q^92 - 54 * q^93 - 21 * q^94 - 9 * q^95 - 9 * q^97 - 24 * q^98 + 165 * q^99

Introduction

L-functions

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