LMFDB - Embedded newform 845.2.n.h.484.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(484,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.484"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,16,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			484.12
Character	$\chi$	$=$	845.484
Dual form			845.2.n.h.529.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.768923 - 0.443938i) q^{2} +(1.09905 - 0.634534i) q^{3} +(-0.605838 + 1.04934i) q^{4} +(1.33257 - 1.79562i) q^{5} +(0.563388 - 0.975816i) q^{6} +(1.97564 + 1.14064i) q^{7} +2.85157i q^{8} +(-0.694733 + 1.20331i) q^{9} +(0.227498 - 1.97227i) q^{10} +(1.56914 + 2.71784i) q^{11} +1.53770i q^{12} +2.02549 q^{14} +(0.325171 - 2.81903i) q^{15} +(0.0542440 + 0.0939534i) q^{16} +(1.49323 + 0.862115i) q^{17} +1.23367i q^{18} +(-2.13503 + 3.69799i) q^{19} +(1.07690 + 2.48618i) q^{20} +2.89510 q^{21} +(2.41310 + 1.39321i) q^{22} +(7.47747 - 4.31712i) q^{23} +(1.80942 + 3.13400i) q^{24} +(-1.44852 - 4.78558i) q^{25} +5.57053i q^{27} +(-2.39384 + 1.38208i) q^{28} +(-3.97125 - 6.87840i) q^{29} +(-1.00144 - 2.31197i) q^{30} +4.17039 q^{31} +(-4.85565 - 2.80341i) q^{32} +(3.44912 + 1.99135i) q^{33} +1.53090 q^{34} +(4.68084 - 2.02753i) q^{35} +(-0.841792 - 1.45803i) q^{36} +(-7.62481 + 4.40219i) q^{37} +3.79129i q^{38} +(5.12034 + 3.79991i) q^{40} +(-1.47350 - 2.55217i) q^{41} +(2.22611 - 1.28524i) q^{42} +(0.133162 + 0.0768812i) q^{43} -3.80259 q^{44} +(1.23492 + 2.85098i) q^{45} +(3.83307 - 6.63907i) q^{46} -6.54786i q^{47} +(0.119233 + 0.0688394i) q^{48} +(-0.897887 - 1.55519i) q^{49} +(-3.23830 - 3.03669i) q^{50} +2.18817 q^{51} -1.93126i q^{53} +(2.47297 + 4.28331i) q^{54} +(6.97121 + 0.804117i) q^{55} +(-3.25261 + 5.63369i) q^{56} +5.41901i q^{57} +(-6.10717 - 3.52598i) q^{58} +(2.75557 - 4.77279i) q^{59} +(2.76113 + 2.04909i) q^{60} +(4.95026 - 8.57410i) q^{61} +(3.20671 - 1.85139i) q^{62} +(-2.74509 + 1.58488i) q^{63} -5.19513 q^{64} +3.53615 q^{66} +(5.59042 - 3.22763i) q^{67} +(-1.80931 + 1.04460i) q^{68} +(5.47872 - 9.48942i) q^{69} +(2.69911 - 3.63702i) q^{70} +(2.37216 - 4.10870i) q^{71} +(-3.43133 - 1.98108i) q^{72} +13.1891i q^{73} +(-3.90860 + 6.76989i) q^{74} +(-4.62860 - 4.34044i) q^{75} +(-2.58697 - 4.48076i) q^{76} +7.15931i q^{77} -13.4510 q^{79} +(0.240989 + 0.0277977i) q^{80} +(1.45049 + 2.51233i) q^{81} +(-2.26601 - 1.30828i) q^{82} +6.32511i q^{83} +(-1.75396 + 3.03795i) q^{84} +(3.53786 - 1.53244i) q^{85} +0.136522 q^{86} +(-8.72916 - 5.03978i) q^{87} +(-7.75011 + 4.47453i) q^{88} +(7.86866 + 13.6289i) q^{89} +(2.21521 + 1.64396i) q^{90} +10.4619i q^{92} +(4.58344 - 2.64625i) q^{93} +(-2.90684 - 5.03480i) q^{94} +(3.79511 + 8.76154i) q^{95} -7.11543 q^{96} +(10.4629 + 6.04075i) q^{97} +(-1.38081 - 0.797212i) q^{98} -4.36055 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 16 q^{4} - 16 q^{6} + 18 q^{9} - 13 q^{10} - 22 q^{11} - 8 q^{14} - 8 q^{15} + 12 q^{16} + 28 q^{19} + 10 q^{20} + 52 q^{21} + 34 q^{24} - 16 q^{25} - 20 q^{29} - 31 q^{30} + 64 q^{31} - 36 q^{34}+ \cdots - 152 q^{99}+O(q^{100}) $ 36 * q + 16 * q^4 - 16 * q^6 + 18 * q^9 - 13 * q^10 - 22 * q^11 - 8 * q^14 - 8 * q^15 + 12 * q^16 + 28 * q^19 + 10 * q^20 + 52 * q^21 + 34 * q^24 - 16 * q^25 - 20 * q^29 - 31 * q^30 + 64 * q^31 - 36 * q^34 - 10 * q^35 - 32 * q^36 + 6 * q^40 - 52 * q^41 - 100 * q^44 - 5 * q^45 - 30 * q^46 + 44 * q^49 - 29 * q^50 - 80 * q^51 + 90 * q^54 + 20 * q^55 + 20 * q^56 + 76 * q^59 + 86 * q^60 - 8 * q^61 + 136 * q^64 + 16 * q^66 + 30 * q^69 + 92 * q^70 - 72 * q^71 + 30 * q^74 - 13 * q^75 - 4 * q^76 - 32 * q^79 - 73 * q^80 + 30 * q^81 + 78 * q^84 - 29 * q^85 - 60 * q^86 + 94 * q^89 - 140 * q^90 - 128 * q^94 - 41 * q^95 - 36 * q^96 - 152 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.768923	−	0.443938i	0.543711	−	0.313912i	−0.202871	−	0.979206i	$-0.565027\pi$
$2$	0.768923	−	0.443938i	0.543711	−	0.313912i	0.746581	+	0.665294i	$0.231694\pi$
$3$	1.09905	−	0.634534i	0.634534	−	0.366348i	−0.147972	−	0.988992i	$-0.547275\pi$
$3$	1.09905	−	0.634534i	0.634534	−	0.366348i	0.782506	+	0.622643i	$0.213941\pi$
$4$	−0.605838	+	1.04934i	−0.302919	+	0.524671i
$5$	1.33257	−	1.79562i	0.595943	−	0.803027i
$5$	1.33257	−	1.79562i	0.595943	−	0.803027i
$6$	0.563388	−	0.975816i	0.230002	−	0.398375i
$7$	1.97564	+	1.14064i	0.746723	+	0.431121i	0.824509	−	0.565849i	$-0.191452\pi$
$7$	1.97564	+	1.14064i	0.746723	+	0.431121i	−0.0777855	+	0.996970i	$0.524785\pi$
$8$			2.85157i			1.00818i
$9$	−0.694733	+	1.20331i	−0.231578	+	0.401104i
$10$	0.227498	−	1.97227i	0.0719413	−	0.623688i
$11$	1.56914	+	2.71784i	0.473115	+	0.819459i	0.999526	−	0.0307708i	$-0.00979619\pi$
$11$	1.56914	+	2.71784i	0.473115	+	0.819459i	−0.526412	+	0.850230i	$0.676463\pi$
$12$			1.53770i			0.443896i
$13$		0			0
$13$		0			0
$14$	2.02549			0.541335
$15$	0.325171	−	2.81903i	0.0839587	−	0.727871i
$16$	0.0542440	+	0.0939534i	0.0135610	+	0.0234883i
$17$	1.49323	+	0.862115i	0.362161	+	0.209094i	0.670028	−	0.742336i	$-0.266282\pi$
$17$	1.49323	+	0.862115i	0.362161	+	0.209094i	−0.307867	+	0.951429i	$0.599615\pi$
$18$			1.23367i			0.290780i
$19$	−2.13503	+	3.69799i	−0.489810	+	0.848376i	−0.999931	−	0.0117264i	$-0.996267\pi$
$19$	−2.13503	+	3.69799i	−0.489810	+	0.848376i	0.510121	+	0.860103i	$0.329601\pi$
$20$	1.07690	+	2.48618i	0.240802	+	0.555926i
$21$	2.89510			0.631762
$22$	2.41310	+	1.39321i	0.514475	+	0.297033i
$23$	7.47747	−	4.31712i	1.55916	−	0.900182i	0.561823	−	0.827257i	$-0.310100\pi$
$23$	7.47747	−	4.31712i	1.55916	−	0.900182i	0.997337	−	0.0729246i	$-0.0232333\pi$
$24$	1.80942	+	3.13400i	0.369346	+	0.639726i
$25$	−1.44852	−	4.78558i	−0.289704	−	0.957116i
$26$		0			0
$27$			5.57053i			1.07205i
$28$	−2.39384	+	1.38208i	−0.452393	+	0.261189i
$29$	−3.97125	−	6.87840i	−0.737442	−	1.27729i	−0.953643	−	0.300939i	$-0.902700\pi$
$29$	−3.97125	−	6.87840i	−0.737442	−	1.27729i	0.216201	−	0.976349i	$-0.430633\pi$
$30$	−1.00144	−	2.31197i	−0.182838	−	0.422107i
$31$	4.17039			0.749024			0.374512	−	0.927222i	$-0.377810\pi$
$31$	4.17039			0.749024			0.374512	+	0.927222i	$0.377810\pi$
$32$	−4.85565	−	2.80341i	−0.858365	−	0.495577i
$33$	3.44912	+	1.99135i	0.600415	+	0.346650i
$34$	1.53090			0.262548
$35$	4.68084	−	2.02753i	0.791206	−	0.342715i
$36$	−0.841792	−	1.45803i	−0.140299	−	0.243004i
$37$	−7.62481	+	4.40219i	−1.25351	+	0.723715i	−0.971805	−	0.235786i	$-0.924234\pi$
$37$	−7.62481	+	4.40219i	−1.25351	+	0.723715i	−0.281706	+	0.959501i	$0.590900\pi$
$38$			3.79129i			0.615028i
$39$		0			0
$40$	5.12034	+	3.79991i	0.809597	+	0.600819i
$41$	−1.47350	−	2.55217i	−0.230122	−	0.398583i	0.727722	−	0.685872i	$-0.240579\pi$
$41$	−1.47350	−	2.55217i	−0.230122	−	0.398583i	−0.957844	+	0.287290i	$0.907246\pi$
$42$	2.22611	−	1.28524i	0.343496	−	0.198317i
$43$	0.133162	+	0.0768812i	0.0203070	+	0.0117243i	0.510119	−	0.860104i	$-0.329601\pi$
$43$	0.133162	+	0.0768812i	0.0203070	+	0.0117243i	−0.489812	+	0.871828i	$0.662935\pi$
$44$	−3.80259			−0.573262
$45$	1.23492	+	2.85098i	0.184090	+	0.424998i
$46$	3.83307	−	6.63907i	0.565155	−	0.978877i
$47$		−	6.54786i		−	0.955103i	−0.878604	−	0.477552i	$-0.841524\pi$
$47$		−	6.54786i		−	0.955103i	0.878604	−	0.477552i	$-0.158476\pi$
$48$	0.119233	+	0.0688394i	0.0172098	+	0.00993611i
$49$	−0.897887	−	1.55519i	−0.128270	−	0.222169i
$50$	−3.23830	−	3.03669i	−0.457965	−	0.429453i
$51$	2.18817			0.306404
$52$		0			0
$53$		−	1.93126i		−	0.265279i	−0.991164	−	0.132640i	$-0.957655\pi$
$53$		−	1.93126i		−	0.265279i	0.991164	−	0.132640i	$-0.0423453\pi$
$54$	2.47297	+	4.28331i	0.336529	+	0.582885i
$55$	6.97121	+	0.804117i	0.939997	+	0.108427i
$56$	−3.25261	+	5.63369i	−0.434648	+	0.752833i
$57$			5.41901i			0.717765i
$58$	−6.10717	−	3.52598i	−0.801911	−	0.462983i
$59$	2.75557	−	4.77279i	0.358745	−	0.621365i	−0.629006	−	0.777400i	$-0.716538\pi$
$59$	2.75557	−	4.77279i	0.358745	−	0.621365i	0.987751	+	0.156035i	$0.0498714\pi$
$60$	2.76113	+	2.04909i	0.356460	+	0.264537i
$61$	4.95026	−	8.57410i	0.633816	−	1.09780i	−0.352949	−	0.935642i	$-0.614821\pi$
$61$	4.95026	−	8.57410i	0.633816	−	1.09780i	0.986765	−	0.162158i	$-0.0518455\pi$
$62$	3.20671	−	1.85139i	0.407252	−	0.235127i
$63$	−2.74509	+	1.58488i	−0.345849	+	0.199676i
$64$	−5.19513			−0.649392
$65$		0			0
$66$	3.53615			0.435270
$67$	5.59042	−	3.22763i	0.682978	−	0.394318i	−0.117998	−	0.993014i	$-0.537648\pi$
$67$	5.59042	−	3.22763i	0.682978	−	0.394318i	0.800976	+	0.598696i	$0.204314\pi$
$68$	−1.80931	+	1.04460i	−0.219411	+	0.126677i
$69$	5.47872	−	9.48942i	0.659560	−	1.14239i
$70$	2.69911	−	3.63702i	0.322605	−	0.434707i
$71$	2.37216	−	4.10870i	0.281524	−	0.487613i	−0.690236	−	0.723584i	$-0.742494\pi$
$71$	2.37216	−	4.10870i	0.281524	−	0.487613i	0.971760	+	0.235970i	$0.0758268\pi$
$72$	−3.43133	−	1.98108i	−0.404386	−	0.233473i
$73$			13.1891i			1.54367i	0.635824	+	0.771834i	$0.280660\pi$
$73$			13.1891i			1.54367i	−0.635824	+	0.771834i	$0.719340\pi$
$74$	−3.90860	+	6.76989i	−0.454365	+	0.786983i
$75$	−4.62860	−	4.34044i	−0.534465	−	0.501190i
$76$	−2.58697	−	4.48076i	−0.296746	−	0.513979i
$77$			7.15931i			0.815879i
$78$		0			0
$79$	−13.4510			−1.51335			−0.756676	−	0.653791i	$-0.773178\pi$
$79$	−13.4510			−1.51335			−0.756676	+	0.653791i	$0.773178\pi$
$80$	0.240989	+	0.0277977i	0.0269434	+	0.00310787i
$81$	1.45049	+	2.51233i	0.161166	+	0.279147i
$82$	−2.26601	−	1.30828i	−0.250239	−	0.144476i
$83$			6.32511i			0.694271i	0.937815	+	0.347136i	$0.112846\pi$
$83$			6.32511i			0.694271i	−0.937815	+	0.347136i	$0.887154\pi$
$84$	−1.75396	+	3.03795i	−0.191373	+	0.331467i
$85$	3.53786	−	1.53244i	0.383735	−	0.166217i
$86$	0.136522			0.0147215
$87$	−8.72916	−	5.03978i	−0.935865	−	0.540322i
$88$	−7.75011	+	4.47453i	−0.826164	+	0.476986i
$89$	7.86866	+	13.6289i	0.834077	+	1.44466i	0.894780	+	0.446507i	$0.147332\pi$
$89$	7.86866	+	13.6289i	0.834077	+	1.44466i	−0.0607034	+	0.998156i	$0.519334\pi$
$90$	2.21521	+	1.64396i	0.233504	+	0.173288i
$91$		0			0
$92$			10.4619i			1.09073i
$93$	4.58344	−	2.64625i	0.475281	−	0.274404i
$94$	−2.90684	−	5.03480i	−0.299818	−	0.519300i
$95$	3.79511	+	8.76154i	0.389370	+	0.898915i
$96$	−7.11543			−0.726216
$97$	10.4629	+	6.04075i	1.06235	+	0.613345i	0.926080	−	0.377327i	$-0.123157\pi$
$97$	10.4629	+	6.04075i	1.06235	+	0.613345i	0.136265	+	0.990672i	$0.456490\pi$
$98$	−1.38081	−	0.797212i	−0.139483	−	0.0805306i
$99$	−4.36055			−0.438251
$100$	5.89928	+	1.37930i	0.589928	+	0.137930i
$101$	−1.89550	−	3.28310i	−0.188609	−	0.326681i	0.756178	−	0.654366i	$-0.227065\pi$
$101$	−1.89550	−	3.28310i	−0.188609	−	0.326681i	−0.944787	+	0.327686i	$0.893731\pi$
$102$	1.68253	−	0.971410i	0.166595	−	0.0961839i
$103$		−	14.6259i		−	1.44113i	−0.693388	−	0.720564i	$-0.743883\pi$
$103$		−	14.6259i		−	1.44113i	0.693388	−	0.720564i	$-0.256117\pi$
$104$		0			0
$105$	3.85792	−	5.19850i	0.376494	−	0.507322i
$106$	−0.857360	−	1.48499i	−0.0832742	−	0.144235i
$107$	−3.62951	+	2.09550i	−0.350878	+	0.202580i	−0.665072	−	0.746779i	$-0.731599\pi$
$107$	−3.62951	+	2.09550i	−0.350878	+	0.202580i	0.314194	+	0.949359i	$0.398266\pi$
$108$	−5.84540	−	3.37484i	−0.562473	−	0.324744i
$109$	−16.1460			−1.54650			−0.773252	−	0.634099i	$-0.781371\pi$
$109$	−16.1460			−1.54650			−0.773252	+	0.634099i	$0.781371\pi$
$110$	5.71730	−	2.47648i	0.545123	−	0.236123i
$111$	−5.58667	+	9.67640i	−0.530264	+	0.918444i
$112$			0.247491i			0.0233857i
$113$	−3.04784	−	1.75967i	−0.286717	−	0.165536i	0.349743	−	0.936846i	$-0.386269\pi$
$113$	−3.04784	−	1.75967i	−0.286717	−	0.165536i	−0.636460	+	0.771309i	$0.719602\pi$
$114$	2.40570	+	4.16680i	0.225315	+	0.390256i
$115$	2.21233	−	19.1796i	0.206301	−	1.78850i
$116$	9.62373			0.893541
$117$		0			0
$118$		−	4.89322i		−	0.450457i
$119$	1.96672	+	3.40647i	0.180289	+	0.312270i
$120$	8.03866	+	0.927247i	0.733826	+	0.0846456i
$121$	0.575569	−	0.996915i	0.0523245	−	0.0906286i
$122$		−	8.79043i		−	0.795848i
$123$	−3.23888	−	1.86997i	−0.292040	−	0.168610i
$124$	−2.52658	+	4.37616i	−0.226894	+	0.392991i
$125$	−10.5233	−	3.77613i	−0.941237	−	0.337747i
$126$	−1.40718	+	2.43730i	−0.125361	+	0.217132i
$127$	−2.09788	+	1.21121i	−0.186157	+	0.107478i	−0.590182	−	0.807270i	$-0.700944\pi$
$127$	−2.09788	+	1.21121i	−0.186157	+	0.107478i	0.404025	+	0.914748i	$0.367611\pi$
$128$	5.71663	−	3.30050i	0.505284	−	0.291726i
$129$	0.195135			0.0171807
$130$		0			0
$131$	−5.00647			−0.437418			−0.218709	−	0.975790i	$-0.570184\pi$
$131$	−5.00647			−0.437418			−0.218709	+	0.975790i	$0.570184\pi$
$132$	−4.17922	+	2.41287i	−0.363754	+	0.210014i
$133$	−8.43613	+	4.87060i	−0.731505	+	0.422335i
$134$	2.86573	−	4.96360i	0.247562	−	0.428790i
$135$	10.0026	+	7.42312i	0.860884	+	0.638880i
$136$	−2.45838	+	4.25804i	−0.210805	+	0.365124i
$137$	−11.0985	−	6.40771i	−0.948207	−	0.547447i	−0.0556833	−	0.998448i	$-0.517734\pi$
$137$	−11.0985	−	6.40771i	−0.948207	−	0.547447i	−0.892523	+	0.451001i	$0.851067\pi$
$138$		−	9.72885i		−	0.828175i
$139$	−7.76443	+	13.4484i	−0.658571	+	1.14068i	0.322415	+	0.946598i	$0.395505\pi$
$139$	−7.76443	+	13.4484i	−0.658571	+	1.14068i	−0.980986	+	0.194079i	$0.937828\pi$
$140$	−0.708257	+	6.14016i	−0.0598586	+	0.518938i
$141$	−4.15484	−	7.19639i	−0.349901	−	0.606045i
$142$		−	4.21237i		−	0.353494i
$143$		0			0
$144$	−0.150740			−0.0125617
$145$	−17.6430	−	2.03509i	−1.46517	−	0.169005i
$146$	5.85515	+	10.1414i	0.484575	+	0.839309i
$147$	−1.97364	−	1.13948i	−0.162783	−	0.0939827i
$148$		−	10.6681i		−	0.876908i
$149$	−0.0206906	+	0.0358372i	−0.00169504	+	0.00293590i	−0.866872	−	0.498531i	$-0.833873\pi$
$149$	−0.0206906	+	0.0358372i	−0.00169504	+	0.00293590i	0.865177	+	0.501467i	$0.167206\pi$
$150$	−5.48592	−	1.28265i	−0.447924	−	0.104728i
$151$	−6.01321			−0.489348			−0.244674	−	0.969605i	$-0.578681\pi$
$151$	−6.01321			−0.489348			−0.244674	+	0.969605i	$0.578681\pi$
$152$	−10.5451	−	6.08820i	−0.855318	−	0.493818i
$153$	−2.07479	+	1.19788i	−0.167737	+	0.0968428i
$154$	3.17829	+	5.50496i	0.256114	+	0.443602i
$155$	5.55733	−	7.48844i	0.446375	−	0.601486i
$156$		0			0
$157$		−	22.7846i		−	1.81841i	−0.416348	−	0.909205i	$-0.636690\pi$
$157$		−	22.7846i		−	1.81841i	0.416348	−	0.909205i	$-0.363310\pi$
$158$	−10.3428	+	5.97139i	−0.822825	+	0.475058i
$159$	−1.22545	−	2.12254i	−0.0971845	−	0.168329i
$160$	−11.5043	+	4.98317i	−0.909498	+	0.393954i
$161$	19.6971			1.55235
$162$	2.23063	+	1.28786i	0.175255	+	0.101184i
$163$	1.31745	+	0.760631i	0.103191	+	0.0595772i	0.550707	−	0.834698i	$-0.314358\pi$
$163$	1.31745	+	0.760631i	0.103191	+	0.0595772i	−0.447516	+	0.894276i	$0.647691\pi$
$164$	3.57081			0.278833
$165$	8.17191	−	3.53971i	0.636182	−	0.275566i
$166$	2.80796	+	4.86353i	0.217940	+	0.377483i
$167$	0.0426069	−	0.0245991i	0.00329702	−	0.00190353i	−0.498351	−	0.866976i	$-0.666061\pi$
$167$	0.0426069	−	0.0245991i	0.00329702	−	0.00190353i	0.501648	+	0.865072i	$0.332727\pi$
$168$			8.25557i			0.636931i
$169$		0			0
$170$	2.04003	−	2.74892i	0.156463	−	0.210833i
$171$	−2.96656	−	5.13823i	−0.226858	−	0.392930i
$172$	−0.161350	+	0.0931552i	−0.0123028	+	0.00710302i
$173$	7.79826	+	4.50232i	0.592890	+	0.342305i	0.766240	−	0.642555i	$-0.222126\pi$
$173$	7.79826	+	4.50232i	0.592890	+	0.342305i	−0.173349	+	0.984860i	$0.555459\pi$
$174$	−8.94941			−0.678453
$175$	2.59686	−	11.1068i	0.196304	−	0.839598i
$176$	−0.170233	+	0.294853i	−0.0128318	+	0.0222254i
$177$		−	6.99402i		−	0.525703i
$178$	12.1008	+	6.98640i	0.906993	+	0.523653i
$179$	11.4302	+	19.7977i	0.854332	+	1.47975i	0.877263	+	0.480010i	$0.159367\pi$
$179$	11.4302	+	19.7977i	0.854332	+	1.47975i	−0.0229307	+	0.999737i	$0.507300\pi$
$180$	−3.73981	−	0.431381i	−0.278749	−	0.0321532i
$181$	−17.7138			−1.31666			−0.658328	−	0.752731i	$-0.728736\pi$
$181$	−17.7138			−1.31666			−0.658328	+	0.752731i	$0.728736\pi$
$182$		0			0
$183$		−	12.5644i		−	0.928789i
$184$	12.3106	+	21.3225i	0.907547	+	1.57192i
$185$	−2.25593	+	19.5575i	−0.165859	+	1.43790i
$186$	2.34954	−	4.06953i	0.172277	−	0.298392i
$187$			5.41113i			0.395701i
$188$	6.87094	+	3.96694i	0.501115	+	0.289319i
$189$	−6.35396	+	11.0054i	−0.462183	+	0.800524i
$190$	6.80772	+	5.05216i	0.493884	+	0.366522i
$191$	−4.86758	+	8.43090i	−0.352206	+	0.610038i	−0.986636	−	0.162942i	$-0.947902\pi$
$191$	−4.86758	+	8.43090i	−0.352206	+	0.610038i	0.634430	+	0.772980i	$0.281235\pi$
$192$	−5.70969	+	3.29649i	−0.412061	+	0.237904i
$193$	8.66107	−	5.00047i	0.623437	−	0.359942i	−0.154769	−	0.987951i	$-0.549463\pi$
$193$	8.66107	−	5.00047i	0.623437	−	0.359942i	0.778206	+	0.628009i	$0.216130\pi$
$194$	10.7269			0.770145
$195$		0			0
$196$	2.17590			0.155421
$197$	5.19615	−	3.00000i	0.370210	−	0.213741i	−0.303340	−	0.952882i	$-0.598102\pi$
$197$	5.19615	−	3.00000i	0.370210	−	0.213741i	0.673550	+	0.739141i	$0.264768\pi$
$198$	−3.35293	+	1.93581i	−0.238282	+	0.137572i
$199$	2.90642	−	5.03407i	0.206031	−	0.356856i	−0.744430	−	0.667701i	$-0.767279\pi$
$199$	2.90642	−	5.03407i	0.206031	−	0.356856i	0.950461	+	0.310845i	$0.100612\pi$
$200$	13.6464	−	4.13055i	0.964948	−	0.292074i
$201$	4.09608	−	7.09462i	0.288915	−	0.500416i
$202$	−2.91498	−	1.68297i	−0.205098	−	0.118413i
$203$		−	18.1190i		−	1.27171i
$204$	−1.32567	+	2.29614i	−0.0928158	+	0.160762i
$205$	−6.54628	−	0.755103i	−0.457212	−	0.0527387i
$206$	−6.49297	−	11.2462i	−0.452387	−	0.783557i
$207$			11.9970i			0.833848i
$208$		0			0
$209$	−13.4007			−0.926946
$210$	0.658630	−	5.70992i	0.0454498	−	0.394022i
$211$	−4.35631	−	7.54535i	−0.299901	−	0.519443i	0.676212	−	0.736707i	$-0.263620\pi$
$211$	−4.35631	−	7.54535i	−0.299901	−	0.519443i	−0.976113	+	0.217264i	$0.930287\pi$
$212$	2.02655	+	1.17003i	0.139184	+	0.0803581i
$213$		−	6.02087i		−	0.412543i
$214$	−1.86054	+	3.22256i	−0.127184	+	0.220290i
$215$	0.315498	−	0.136659i	0.0215168	−	0.00932010i
$216$	−15.8848			−1.08082
$217$	8.23920	+	4.75690i	0.559313	+	0.322920i
$218$	−12.4150	+	7.16781i	−0.840850	+	0.485465i
$219$	8.36894	+	14.4954i	0.565520	+	0.979510i
$220$	−5.06722	+	6.82802i	−0.341632	+	0.460345i
$221$		0			0
$222$			9.92055i			0.665824i
$223$	0.0393366	−	0.0227110i	0.00263417	−	0.00152084i	−0.498682	−	0.866785i	$-0.666183\pi$
$223$	0.0393366	−	0.0227110i	0.00263417	−	0.00152084i	0.501317	+	0.865264i	$0.332849\pi$
$224$	−6.39535	−	11.0771i	−0.427307	−	0.740118i
$225$	6.76489	+	1.58168i	0.450992	+	0.105445i
$226$	−3.12474			−0.207855
$227$	−5.56211	−	3.21129i	−0.369170	−	0.213141i	0.303926	−	0.952696i	$-0.401703\pi$
$227$	−5.56211	−	3.21129i	−0.369170	−	0.213141i	−0.673096	+	0.739555i	$0.735036\pi$
$228$	−5.68639	−	3.28304i	−0.376591	−	0.217425i
$229$	7.27972			0.481057			0.240529	−	0.970642i	$-0.422679\pi$
$229$	7.27972			0.481057			0.240529	+	0.970642i	$0.422679\pi$
$230$	−6.81343	−	15.7298i	−0.449264	−	1.03719i
$231$	4.54283	+	7.86840i	0.298896	+	0.517703i
$232$	19.6143	−	11.3243i	1.28774	−	0.743476i
$233$			4.56107i			0.298806i	0.988776	+	0.149403i	$0.0477351\pi$
$233$			4.56107i			0.298806i	−0.988776	+	0.149403i	$0.952265\pi$
$234$		0			0
$235$	−11.7575	−	8.72547i	−0.766973	−	0.569187i
$236$	3.33886	+	5.78308i	0.217341	+	0.376447i
$237$	−14.7832	+	8.53509i	−0.960273	+	0.554414i
$238$	3.02452	+	1.74621i	0.196050	+	0.113190i
$239$	−16.9338			−1.09536			−0.547680	−	0.836688i	$-0.684489\pi$
$239$	−16.9338			−1.09536			−0.547680	+	0.836688i	$0.684489\pi$
$240$	0.282496	−	0.122365i	0.0182350	−	0.00789861i
$241$	−3.06529	+	5.30924i	−0.197453	+	0.341999i	−0.947702	−	0.319157i	$-0.896600\pi$
$241$	−3.06529	+	5.30924i	−0.197453	+	0.341999i	0.750249	+	0.661155i	$0.229934\pi$
$242$		−	1.02207i		−	0.0657010i
$243$	−11.2844	−	6.51502i	−0.723891	−	0.417939i
$244$	5.99811	+	10.3890i	0.383990	+	0.665090i
$245$	−3.98902	−	0.460127i	−0.254849	−	0.0293965i
$246$	−3.32060			−0.211714
$247$		0			0
$248$			11.8922i			0.755152i
$249$	4.01350	+	6.95158i	0.254345	+	0.440539i
$250$	−9.76801	+	1.76816i	−0.617783	+	0.111828i
$251$	−5.79213	+	10.0323i	−0.365596	+	0.633231i	−0.988872	−	0.148772i	$-0.952468\pi$
$251$	−5.79213	+	10.0323i	−0.365596	+	0.633231i	0.623276	+	0.782002i	$0.285801\pi$
$252$		−	3.84072i		−	0.241943i
$253$	23.4665	+	13.5484i	1.47532	+	0.851779i
$254$	−1.07541	+	1.86266i	−0.0674769	+	0.116873i
$255$	2.91588	−	3.92912i	0.182600	−	0.246051i
$256$	8.12557	−	14.0739i	0.507848	−	0.879618i
$257$	−10.7967	+	6.23346i	−0.673477	+	0.388832i	−0.797393	−	0.603460i	$-0.793788\pi$
$257$	−10.7967	+	6.23346i	−0.673477	+	0.388832i	0.123916	+	0.992293i	$0.460455\pi$
$258$	0.150044	−	0.0866279i	0.00934132	−	0.00539322i
$259$	−20.0852			−1.24803
$260$		0			0
$261$	11.0358			0.683101
$262$	−3.84959	+	2.22256i	−0.237829	+	0.137310i
$263$	24.5335	−	14.1644i	1.51280	−	0.873416i	0.512913	−	0.858441i	$-0.328566\pi$
$263$	24.5335	−	14.1644i	1.51280	−	0.873416i	0.999888	−	0.0149750i	$-0.00476687\pi$
$264$	−5.67848	+	9.83541i	−0.349486	+	0.605328i
$265$	−3.46781	−	2.57354i	−0.213026	−	0.158091i
$266$	−4.32449	+	7.49024i	−0.265152	+	0.459256i
$267$	17.2960	+	9.98587i	1.05850	+	0.611125i
$268$			7.82168i			0.477785i
$269$	−6.09431	+	10.5557i	−0.371577	+	0.643590i	−0.989808	−	0.142406i	$-0.954516\pi$
$269$	−6.09431	+	10.5557i	−0.371577	+	0.643590i	0.618231	+	0.785996i	$0.287849\pi$
$270$	10.9866	+	1.26729i	0.668624	+	0.0771247i
$271$	−8.82735	−	15.2894i	−0.536224	−	0.928766i	−0.999103	−	0.0423452i	$-0.986517\pi$
$271$	−8.82735	−	15.2894i	−0.536224	−	0.928766i	0.462880	−	0.886421i	$-0.346816\pi$
$272$			0.187058i			0.0113421i
$273$		0			0
$274$	−11.3785			−0.687400
$275$	10.7335	−	11.4461i	0.647255	−	0.690226i
$276$	6.63844	+	11.4981i	0.399587	+	0.692105i
$277$	10.1542	+	5.86252i	0.610105	+	0.352245i	0.773007	−	0.634398i	$-0.218752\pi$
$277$	10.1542	+	5.86252i	0.610105	+	0.352245i	−0.162901	+	0.986642i	$0.552085\pi$
$278$			13.7877i			0.826932i
$279$	−2.89731	+	5.01828i	−0.173457	+	0.300437i
$280$	5.78164	+	13.3477i	0.345519	+	0.797680i
$281$	20.2642			1.20886			0.604430	−	0.796659i	$-0.293401\pi$
$281$	20.2642			1.20886			0.604430	+	0.796659i	$0.293401\pi$
$282$	−6.38950	−	3.68898i	−0.380489	−	0.219676i
$283$	7.13891	−	4.12165i	0.424364	−	0.245007i	−0.272579	−	0.962133i	$-0.587877\pi$
$283$	7.13891	−	4.12165i	0.424364	−	0.245007i	0.696943	+	0.717127i	$0.254543\pi$
$284$	2.87429	+	4.97842i	0.170558	+	0.295415i
$285$	9.73049	+	7.22120i	0.576384	+	0.427747i
$286$		0			0
$287$		−	6.72292i		−	0.396841i
$288$	6.74675	−	3.89524i	0.397556	−	0.229529i
$289$	−7.01351	−	12.1478i	−0.412560	−	0.714574i
$290$	−14.4695	+	6.26756i	−0.849681	+	0.368044i
$291$	15.3322			0.898792
$292$	−13.8399	−	7.99046i	−0.809918	−	0.467607i
$293$	−18.4650	−	10.6607i	−1.07873	−	0.622808i	−0.148180	−	0.988960i	$-0.547341\pi$
$293$	−18.4650	−	10.6607i	−1.07873	−	0.622808i	−0.930555	+	0.366153i	$0.880675\pi$
$294$	−2.02343			−0.118009
$295$	−4.89814	−	11.3080i	−0.285181	−	0.658380i
$296$	−12.5531	−	21.7427i	−0.729637	−	1.26377i
$297$	−15.1398	+	8.74097i	−0.878501	+	0.507203i
$298$			0.0367414i			0.00212837i
$299$		0			0
$300$	7.35879	−	2.22739i	0.424860	−	0.128598i
$301$	0.175387	+	0.303780i	0.0101092	+	0.0175096i
$302$	−4.62369	+	2.66949i	−0.266064	+	0.153612i
$303$	−4.16648	−	2.40552i	−0.239358	−	0.138193i
$304$	−0.463251			−0.0265693
$305$	−8.79928	−	20.3144i	−0.503845	−	1.16320i
$306$	−1.06357	+	1.84216i	−0.0608002	+	0.105309i
$307$			8.38560i			0.478591i	0.970947	+	0.239296i	$0.0769165\pi$
$307$			8.38560i			0.478591i	−0.970947	+	0.239296i	$0.923083\pi$
$308$	−7.51257	−	4.33738i	−0.428068	−	0.247145i
$309$	−9.28061	−	16.0745i	−0.527955	−	0.914445i
$310$	0.948757	−	8.22514i	0.0538858	−	0.467157i
$311$	−2.82308			−0.160082			−0.0800412	−	0.996792i	$-0.525505\pi$
$311$	−2.82308			−0.160082			−0.0800412	+	0.996792i	$0.525505\pi$
$312$		0			0
$313$			19.1965i			1.08505i	0.840040	+	0.542525i	$0.182532\pi$
$313$			19.1965i			1.08505i	−0.840040	+	0.542525i	$0.817468\pi$
$314$	−10.1150	−	17.5196i	−0.570820	−	0.988689i
$315$	−0.812180	+	7.04111i	−0.0457612	+	0.396721i
$316$	8.14910	−	14.1147i	0.458423	−	0.794012i
$317$			5.76453i			0.323768i	0.986810	+	0.161884i	$0.0517571\pi$
$317$			5.76453i			0.323768i	−0.986810	+	0.161884i	$0.948243\pi$
$318$	−1.88455	−	1.08805i	−0.105681	−	0.0610147i
$319$	12.4629	−	21.5864i	0.697790	−	1.20861i
$320$	−6.92288	+	9.32850i	−0.387001	+	0.521479i
$321$	−2.65933	+	4.60610i	−0.148430	+	0.257087i
$322$	15.1456	−	8.74429i	0.844029	−	0.487300i
$323$	−6.37618	+	3.68129i	−0.354780	+	0.204832i
$324$	−3.51506			−0.195281
$325$		0			0
$326$	1.35069			0.0748079
$327$	−17.7451	+	10.2452i	−0.981309	+	0.566559i
$328$	7.27771	−	4.20179i	0.401844	−	0.232005i
$329$	7.46874	−	12.9362i	0.411765	−	0.713198i
$330$	4.71216	−	6.34958i	0.259396	−	0.349533i
$331$	2.03004	−	3.51614i	0.111581	−	0.193264i	−0.804827	−	0.593510i	$-0.797742\pi$
$331$	2.03004	−	3.51614i	0.111581	−	0.193264i	0.916408	+	0.400245i	$0.131075\pi$
$332$	−6.63721	−	3.83199i	−0.364264	−	0.210308i
$333$		−	12.2334i		−	0.670385i
$334$	0.0218409	−	0.0378296i	0.00119508	−	0.00206994i
$335$	1.65402	−	14.3393i	0.0903686	−	0.783441i
$336$	0.157042	+	0.272004i	0.00856732	+	0.0148390i
$337$		−	24.8339i		−	1.35279i	−0.736539	−	0.676395i	$-0.763541\pi$
$337$		−	24.8339i		−	1.35279i	0.736539	−	0.676395i	$-0.236459\pi$
$338$		0			0
$339$	−4.46629			−0.242576
$340$	−0.535313	+	4.64084i	−0.0290314	+	0.251685i
$341$	6.54394	+	11.3344i	0.354374	+	0.613794i
$342$	−4.56211	−	2.63393i	−0.246691	−	0.142427i
$343$		−	20.0656i		−	1.08344i
$344$	−0.219232	+	0.379721i	−0.0118202	+	0.0204732i
$345$	−9.73864	−	22.4830i	−0.524311	−	1.21045i
$346$	7.99501			0.429815
$347$	25.2532	+	14.5799i	1.35566	+	0.782692i	0.989036	−	0.147675i	$-0.0471791\pi$
$347$	25.2532	+	14.5799i	1.35566	+	0.782692i	0.366627	+	0.930368i	$0.380512\pi$
$348$	10.5769	−	6.10659i	0.566982	−	0.327347i
$349$	3.64520	+	6.31367i	0.195123	+	0.337963i	0.946941	−	0.321408i	$-0.104156\pi$
$349$	3.64520	+	6.31367i	0.195123	+	0.337963i	−0.751818	+	0.659371i	$0.770823\pi$
$350$	−2.93396	−	9.69315i	−0.156827	−	0.518121i
$351$		0			0
$352$		−	17.5958i		−	0.937860i
$353$	12.0840	−	6.97671i	0.643167	−	0.371333i	−0.142667	−	0.989771i	$-0.545568\pi$
$353$	12.0840	−	6.97671i	0.643167	−	0.371333i	0.785833	+	0.618438i	$0.212234\pi$
$354$	−3.10491	−	5.37786i	−0.165024	−	0.285830i
$355$	−4.21661	−	9.73464i	−0.223794	−	0.516661i
$356$	−19.0685			−1.01063
$357$	4.32304	+	2.49591i	0.228799	+	0.132097i
$358$	17.5779	+	10.1486i	0.929019	+	0.536370i
$359$	−16.2637			−0.858366			−0.429183	−	0.903218i	$-0.641198\pi$
$359$	−16.2637			−0.858366			−0.429183	+	0.903218i	$0.641198\pi$
$360$	−8.12976	+	3.52145i	−0.428476	+	0.185597i
$361$	0.383263	+	0.663832i	0.0201718	+	0.0349385i
$362$	−13.6205	+	7.86382i	−0.715880	+	0.413313i
$363$		−	1.46087i		−	0.0766759i
$364$		0			0
$365$	23.6827	+	17.5754i	1.23961	+	0.919939i
$366$	−5.57783	−	9.66108i	−0.291558	−	0.504993i
$367$	29.8328	−	17.2240i	1.55726	−	0.899085i	0.559743	−	0.828666i	$-0.310900\pi$
$367$	29.8328	−	17.2240i	1.55726	−	0.899085i	0.997518	−	0.0704187i	$-0.0224335\pi$
$368$	0.811216	+	0.468356i	0.0422876	+	0.0244147i
$369$	4.09475			0.213164
$370$	6.94768	+	16.0397i	0.361193	+	0.833865i
$371$	2.20287	−	3.81548i	0.114367	−	0.198090i
$372$			6.41280i			0.332488i
$373$	20.1073	+	11.6089i	1.04112	+	0.601088i	0.920149	−	0.391569i	$-0.128067\pi$
$373$	20.1073	+	11.6089i	1.04112	+	0.601088i	0.120966	+	0.992657i	$0.461401\pi$
$374$	2.40221	+	4.16075i	0.124215	+	0.215147i
$375$	−13.9617	+	2.52729i	−0.720980	+	0.130509i
$376$	18.6717			0.962918
$377$		0			0
$378$			11.2831i			0.580338i
$379$	6.13331	+	10.6232i	0.315047	+	0.545678i	0.979448	−	0.201699i	$-0.0646463\pi$
$379$	6.13331	+	10.6232i	0.315047	+	0.545678i	−0.664400	+	0.747377i	$0.731313\pi$
$380$	−11.4931	−	1.32571i	−0.589582	−	0.0680073i
$381$	−1.53711	+	2.66235i	−0.0787485	+	0.136396i
$382$			8.64361i			0.442246i
$383$	−1.63100	−	0.941658i	−0.0833401	−	0.0481165i	0.457751	−	0.889081i	$-0.348655\pi$
$383$	−1.63100	−	0.941658i	−0.0833401	−	0.0481165i	−0.541091	+	0.840964i	$0.681989\pi$
$384$	4.18856	−	7.25480i	0.213746	−	0.370220i
$385$	12.8554	+	9.54027i	0.655173	+	0.486217i
$386$	4.43980	−	7.68995i	0.225980	−	0.391408i
$387$	−0.185024	+	0.106824i	−0.00940532	+	0.00543016i
$388$	−12.6776	+	7.31943i	−0.643609	+	0.371588i
$389$	20.0438			1.01626			0.508131	−	0.861280i	$-0.330337\pi$
$389$	20.0438			1.01626			0.508131	+	0.861280i	$0.330337\pi$
$390$		0			0
$391$	14.8874			0.752889
$392$	4.43472	−	2.56039i	0.223987	−	0.129319i
$393$	−5.50234	+	3.17678i	−0.277556	+	0.160247i
$394$	2.66363	−	4.61353i	0.134191	−	0.232426i
$395$	−17.9243	+	24.1528i	−0.901871	+	1.21526i
$396$	2.64179	−	4.57571i	0.132755	−	0.229938i
$397$	17.8517	+	10.3067i	0.895954	+	0.517279i	0.875885	−	0.482520i	$-0.160278\pi$
$397$	17.8517	+	10.3067i	0.895954	+	0.517279i	0.0200684	+	0.999799i	$0.493612\pi$
$398$		−	5.16108i		−	0.258702i
$399$	−6.18113	+	10.7060i	−0.309443	+	0.535972i
$400$	0.371048	−	0.395682i	0.0185524	−	0.0197841i
$401$	17.9074	+	31.0166i	0.894254	+	1.54889i	0.834725	+	0.550667i	$0.185626\pi$
$401$	17.9074	+	31.0166i	0.894254	+	1.54889i	0.0595288	+	0.998227i	$0.481040\pi$
$402$		−	7.27362i		−	0.362775i
$403$		0			0
$404$	4.59346			0.228533
$405$	6.44407	+	0.743313i	0.320209	+	0.0369355i
$406$	−8.04373	−	13.9321i	−0.399204	−	0.691441i
$407$	−23.9289	−	13.8153i	−1.18611	−	0.684801i
$408$			6.23971i			0.308912i
$409$	−0.110974	+	0.192213i	−0.00548733	+	0.00950434i	−0.868756	−	0.495240i	$-0.835080\pi$
$409$	−0.110974	+	0.192213i	−0.00548733	+	0.00950434i	0.863269	+	0.504745i	$0.168413\pi$
$410$	−5.36881	+	2.32553i	−0.265146	+	0.114850i
$411$	−16.2636			−0.802226
$412$	15.3475	+	8.86090i	0.756119	+	0.436545i
$413$	10.8881	−	6.28623i	0.535767	−	0.309325i
$414$	5.32592	+	9.22476i	0.261755	+	0.453372i
$415$	11.3575	+	8.42865i	0.557518	+	0.413746i
$416$		0			0
$417$			19.7072i			0.965065i
$418$	−10.3041	+	5.94908i	−0.503991	+	0.290979i
$419$	0.340184	+	0.589217i	0.0166191	+	0.0287851i	0.874215	−	0.485538i	$-0.161376\pi$
$419$	0.340184	+	0.589217i	0.0166191	+	0.0287851i	−0.857596	+	0.514324i	$0.828043\pi$
$420$	3.11773	+	7.19772i	0.152130	+	0.351213i
$421$	−2.01932			−0.0984155			−0.0492078	−	0.998789i	$-0.515670\pi$
$421$	−2.01932			−0.0984155			−0.0492078	+	0.998789i	$0.515670\pi$
$422$	−6.69933	−	3.86786i	−0.326118	−	0.188285i
$423$	7.87912	+	4.54901i	0.383096	+	0.221181i
$424$	5.50712			0.267450
$425$	1.96276	−	8.39475i	0.0952077	−	0.407205i
$426$	−2.67289	−	4.62958i	−0.129502	−	0.224304i
$427$	19.5599	−	11.2929i	0.946570	−	0.546502i
$428$		−	5.07814i		−	0.245461i
$429$		0			0
$430$	0.181925	−	0.245142i	0.00877321	−	0.0118218i
$431$	−3.42699	−	5.93571i	−0.165072	−	0.285913i	0.771609	−	0.636097i	$-0.219452\pi$
$431$	−3.42699	−	5.93571i	−0.165072	−	0.285913i	−0.936681	+	0.350184i	$0.886119\pi$
$432$	−0.523370	+	0.302168i	−0.0251807	+	0.0145381i
$433$	−0.451142	−	0.260467i	−0.0216805	−	0.0125172i	0.489121	−	0.872216i	$-0.337318\pi$
$433$	−0.451142	−	0.260467i	−0.0216805	−	0.0125172i	−0.510801	+	0.859699i	$0.670651\pi$
$434$	8.44708			0.405473
$435$	−20.6818	+	8.95842i	−0.991615	+	0.429523i
$436$	9.78184	−	16.9426i	0.468465	−	0.811406i
$437$			36.8688i			1.76367i
$438$	12.8701	+	7.43058i	0.614959	+	0.355047i
$439$	−13.7945	−	23.8927i	−0.658374	−	1.14034i	−0.981036	−	0.193823i	$-0.937911\pi$
$439$	−13.7945	−	23.8927i	−0.658374	−	1.14034i	0.322662	−	0.946514i	$-0.395422\pi$
$440$	−2.29300	+	19.8789i	−0.109314	+	0.947688i
$441$	2.49517			0.118818
$442$		0			0
$443$			7.20684i			0.342408i	0.985236	+	0.171204i	$0.0547656\pi$
$443$			7.20684i			0.342408i	−0.985236	+	0.171204i	$0.945234\pi$
$444$	−6.76924	−	11.7247i	−0.321254	−	0.556428i
$445$	34.9579	+	4.03234i	1.65717	+	0.191151i
$446$	0.0201646	−	0.0349260i	0.000954819	−	0.00165380i
$447$			0.0525156i			0.00248390i
$448$	−10.2637	−	5.92577i	−0.484916	−	0.279966i
$449$	0.0678172	−	0.117463i	0.00320049	−	0.00554341i	−0.864421	−	0.502769i	$-0.832315\pi$
$449$	0.0678172	−	0.117463i	0.00320049	−	0.00554341i	0.867621	+	0.497226i	$0.165648\pi$
$450$	5.90385	−	1.78700i	0.278310	−	0.0842399i
$451$	4.62427	−	8.00946i	0.217748	−	0.377151i
$452$	3.69300	−	2.13215i	0.173704	−	0.100288i
$453$	−6.60879	+	3.81559i	−0.310508	+	0.179272i
$454$	−5.70245			−0.267629
$455$		0			0
$456$	−15.4527			−0.723638
$457$	0.266745	−	0.154005i	0.0124778	−	0.00720406i	−0.493748	−	0.869605i	$-0.664374\pi$
$457$	0.266745	−	0.154005i	0.0124778	−	0.00720406i	0.506226	+	0.862401i	$0.331040\pi$
$458$	5.59754	−	3.23174i	0.261556	−	0.151009i
$459$	−4.80244	+	8.31807i	−0.224159	+	0.388254i
$460$	18.7856	+	13.9412i	0.875884	+	0.650012i
$461$	−14.3360	+	24.8307i	−0.667696	+	1.15648i	0.310851	+	0.950459i	$0.399386\pi$
$461$	−14.3360	+	24.8307i	−0.667696	+	1.15648i	−0.978547	+	0.206024i	$0.933947\pi$
$462$	6.98617	+	4.03347i	0.325026	+	0.187654i
$463$			16.1023i			0.748339i	0.927360	+	0.374169i	$0.122072\pi$
$463$			16.1023i			0.748339i	−0.927360	+	0.374169i	$0.877928\pi$
$464$	0.430833	−	0.746225i	0.0200009	−	0.0346426i
$465$	1.35609	−	11.7564i	0.0628870	−	0.545192i
$466$	2.02483	+	3.50711i	0.0937986	+	0.162464i
$467$			3.47589i			0.160845i	0.996761	+	0.0804224i	$0.0256269\pi$
$467$			3.47589i			0.160845i	−0.996761	+	0.0804224i	$0.974373\pi$
$468$		0			0
$469$	14.7262			0.679994
$470$	−12.9142	−	1.48963i	−0.595686	−	0.0687114i
$471$	−14.4576	−	25.0413i	−0.666172	−	1.15384i
$472$	13.6100	+	7.85771i	0.626449	+	0.361681i
$473$			0.482551i			0.0221877i
$474$	−7.57810	+	13.1257i	−0.348074	+	0.602881i
$475$	20.7897	+	4.86078i	0.953895	+	0.223028i
$476$	−4.76606			−0.218452
$477$	2.32391	+	1.34171i	0.106405	+	0.0614327i
$478$	−13.0208	+	7.51758i	−0.595559	+	0.343846i
$479$	−7.22882	−	12.5207i	−0.330293	−	0.572085i	0.652276	−	0.757982i	$-0.273814\pi$
$479$	−7.22882	−	12.5207i	−0.330293	−	0.572085i	−0.982569	+	0.185897i	$0.940481\pi$
$480$	−9.48181	+	12.7766i	−0.432783	+	0.583171i
$481$		0			0
$482$			5.44320i			0.247931i
$483$	21.6480	−	12.4985i	0.985018	−	0.568701i
$484$	0.697403	+	1.20794i	0.0317002	+	0.0549063i
$485$	24.7894	−	10.7377i	1.12563	−	0.487573i
$486$	−11.5691			−0.524783
$487$	−2.52255	−	1.45639i	−0.114307	−	0.0659954i	0.441756	−	0.897135i	$-0.354356\pi$
$487$	−2.52255	−	1.45639i	−0.114307	−	0.0659954i	−0.556064	+	0.831140i	$0.687689\pi$
$488$	24.4496	+	14.1160i	1.10678	+	0.639002i
$489$	1.93058			0.0873040
$490$	−3.27152	+	1.41708i	−0.147792	+	0.0640170i
$491$	3.80382	+	6.58841i	0.171664	+	0.297331i	0.939002	−	0.343912i	$-0.111752\pi$
$491$	3.80382	+	6.58841i	0.171664	+	0.297331i	−0.767338	+	0.641243i	$0.778419\pi$
$492$	3.92448	−	2.26580i	0.176929	−	0.102150i
$493$		−	13.6947i		−	0.616778i
$494$		0			0
$495$	−5.81073	+	7.82990i	−0.261173	+	0.351928i
$496$	0.226219	+	0.391822i	0.0101575	+	0.0175933i
$497$	9.37309	−	5.41156i	0.420441	−	0.242742i
$498$	6.17214	+	3.56349i	0.276580	+	0.159684i
$499$	4.07246			0.182309			0.0911543	−	0.995837i	$-0.470944\pi$
$499$	4.07246			0.182309			0.0911543	+	0.995837i	$0.470944\pi$
$500$	10.3379	−	8.75487i	0.462325	−	0.391530i
$501$	0.0312179	−	0.0540710i	0.00139471	−	0.00241571i
$502$			10.2854i			0.459059i
$503$	−29.5160	−	17.0410i	−1.31605	−	0.759823i	−0.332961	−	0.942941i	$-0.608048\pi$
$503$	−29.5160	−	17.0410i	−1.31605	−	0.759823i	−0.983091	+	0.183118i	$0.941381\pi$
$504$	−4.51939	−	7.82782i	−0.201310	−	0.348679i
$505$	−8.42109	−	0.971359i	−0.374733	−	0.0432249i
$506$	24.0586			1.06953
$507$		0			0
$508$		−	2.93519i		−	0.130228i
$509$	0.653321	+	1.13159i	0.0289579	+	0.0501566i	0.880141	−	0.474712i	$-0.157448\pi$
$509$	0.653321	+	1.13159i	0.0289579	+	0.0501566i	−0.851183	+	0.524869i	$0.824114\pi$
$510$	0.497804	−	4.31566i	0.0220431	−	0.191101i
$511$	−15.0440	+	26.0570i	−0.665508	+	1.15269i
$512$		−	1.22700i		−	0.0542260i
$513$	−20.5998	−	11.8933i	−0.909501	−	0.525101i
$514$	−5.53454	+	9.58610i	−0.244118	+	0.422825i
$515$	−26.2625	−	19.4900i	−1.15726	−	0.858831i
$516$	−0.118220	+	0.204764i	−0.00520436	+	0.00901421i
$517$	17.7960	−	10.2745i	0.782668	−	0.451874i
$518$	−15.4440	+	8.91659i	−0.678570	+	0.391773i
$519$	11.4275			0.501612
$520$		0			0
$521$	−0.550102			−0.0241004			−0.0120502	−	0.999927i	$-0.503836\pi$
$521$	−0.550102			−0.0241004			−0.0120502	+	0.999927i	$0.503836\pi$
$522$	8.48571	−	4.89922i	0.371409	−	0.214433i
$523$	−14.7684	+	8.52654i	−0.645777	+	0.372840i	−0.786837	−	0.617161i	$-0.788283\pi$
$523$	−14.7684	+	8.52654i	−0.645777	+	0.372840i	0.141059	+	0.990001i	$0.454949\pi$
$524$	3.03311	−	5.25350i	0.132502	−	0.229500i
$525$	−4.19360	−	13.8547i	−0.183024	−	0.604670i
$526$	12.5763	−	21.7827i	0.548351	−	0.949771i
$527$	6.22734	+	3.59535i	0.271267	+	0.156616i
$528$			0.432076i			0.0188037i
$529$	25.7751	−	44.6437i	1.12065	−	1.94103i
$530$	−3.80897	−	0.439359i	−0.165451	−	0.0190845i
$531$	3.82878	+	6.63164i	0.166155	+	0.287788i
$532$		−	11.8032i		−	0.511733i
$533$		0			0
$534$	17.7324			0.767357
$535$	−1.07385	+	9.30964i	−0.0464266	+	0.402491i
$536$	9.20381	+	15.9415i	0.397544	+	0.688567i
$537$	25.1246	+	14.5057i	1.08421	+	0.625967i
$538$			10.8220i			0.466569i
$539$	2.81783	−	4.88062i	0.121373	−	0.210223i
$540$	−13.8493	+	5.99891i	−0.595980	+	0.258152i
$541$	30.1330			1.29552			0.647759	−	0.761845i	$-0.275706\pi$
$541$	30.1330			1.29552			0.647759	+	0.761845i	$0.275706\pi$
$542$	−13.5751	−	7.83759i	−0.583101	−	0.336654i
$543$	−19.4683	+	11.2400i	−0.835463	+	0.482355i
$544$	−4.83372	−	8.37225i	−0.207244	−	0.358957i
$545$	−21.5156	+	28.9921i	−0.921628	+	1.24188i
$546$		0			0
$547$		−	5.36791i		−	0.229515i	−0.993394	−	0.114758i	$-0.963391\pi$
$547$		−	5.36791i		−	0.229515i	0.993394	−	0.114758i	$-0.0366091\pi$
$548$	13.4478	−	7.76407i	0.574460	−	0.331665i
$549$	6.87822	+	11.9134i	0.293555	+	0.508452i
$550$	3.17188	−	13.5662i	0.135249	−	0.578464i
$551$	33.9150			1.44483
$552$	27.0598	+	15.6230i	1.15174	+	0.664957i
$553$	−26.5743	−	15.3427i	−1.13005	−	0.652437i
$554$	10.4104			0.442294
$555$	9.93054	+	22.9260i	0.421528	+	0.973156i
$556$	−9.40798	−	16.2951i	−0.398987	−	0.691066i
$557$	6.11007	−	3.52765i	0.258892	−	0.149471i	−0.364937	−	0.931032i	$-0.618909\pi$
$557$	6.11007	−	3.52765i	0.258892	−	0.149471i	0.623829	+	0.781561i	$0.285576\pi$
$558$			5.14490i			0.217801i
$559$		0			0
$560$	0.444401	+	0.329799i	0.0187794	+	0.0139366i
$561$	3.43355	+	5.94708i	0.144965	+	0.251086i
$562$	15.5816	−	8.99604i	0.657270	−	0.379475i
$563$	−27.4232	−	15.8328i	−1.15575	−	0.667273i	−0.205468	−	0.978664i	$-0.565872\pi$
$563$	−27.4232	−	15.8328i	−1.15575	−	0.667273i	−0.950282	+	0.311391i	$0.899205\pi$
$564$	10.0686			0.423966
$565$	−7.22117	+	3.12789i	−0.303797	+	0.131591i
$566$	3.65951	−	6.33846i	0.153821	−	0.266426i
$567$			6.61795i			0.277928i
$568$	11.7163	+	6.76438i	0.491603	+	0.283827i
$569$	6.79091	+	11.7622i	0.284690	+	0.493097i	0.972534	−	0.232761i	$-0.0747761\pi$
$569$	6.79091	+	11.7622i	0.284690	+	0.493097i	−0.687844	+	0.725858i	$0.741443\pi$
$570$	10.6878	+	1.23282i	0.447661	+	0.0516370i
$571$	−34.7338			−1.45356			−0.726782	−	0.686868i	$-0.758985\pi$
$571$	−34.7338			−1.45356			−0.726782	+	0.686868i	$0.758985\pi$
$572$		0			0
$573$			12.3546i			0.516120i
$574$	−2.98456	−	5.16941i	−0.124573	−	0.215767i
$575$	−31.4912	−	29.5306i	−1.31327	−	1.23151i
$576$	3.60923	−	6.25137i	0.150385	−	0.260474i
$577$		−	43.8511i		−	1.82555i	−0.408467	−	0.912773i	$-0.633937\pi$
$577$		−	43.8511i		−	1.82555i	0.408467	−	0.912773i	$-0.366063\pi$
$578$	−10.7857	−	6.22713i	−0.448626	−	0.259015i
$579$	6.34594	−	10.9915i	0.263728	−	0.456791i
$580$	12.8243	−	17.2806i	0.532500	−	0.717538i
$581$	−7.21467	+	12.4962i	−0.299315	+	0.518429i
$582$	11.7893	−	6.80657i	0.488683	−	0.282141i
$583$	5.24885	−	3.03043i	0.217385	−	0.125507i
$584$	−37.6097			−1.55630
$585$		0			0
$586$	−18.9308			−0.782026
$587$	3.56795	−	2.05996i	0.147265	−	0.0850235i	−0.424557	−	0.905401i	$-0.639570\pi$
$587$	3.56795	−	2.05996i	0.147265	−	0.0850235i	0.571822	+	0.820378i	$0.306237\pi$
$588$	2.39141	−	1.38068i	0.0986201	−	0.0569383i
$589$	−8.90392	+	15.4220i	−0.366879	+	0.635454i
$590$	−8.78637	−	6.52055i	−0.361729	−	0.268447i
$591$	3.80720	−	6.59426i	0.156607	−	0.271252i
$592$	−0.827201	−	0.477585i	−0.0339977	−	0.0196286i
$593$			2.16800i			0.0890292i	0.999009	+	0.0445146i	$0.0141741\pi$
$593$			2.16800i			0.0890292i	−0.999009	+	0.0445146i	$0.985826\pi$
$594$	−7.76090	+	13.4423i	−0.318433	+	0.551543i
$595$	8.73752	+	1.00786i	0.358203	+	0.0413182i
$596$	−0.0250703	−	0.0434231i	−0.00102692	−	0.00177868i
$597$		−	7.37689i		−	0.301916i
$598$		0			0
$599$	37.1445			1.51768			0.758841	−	0.651276i	$-0.225766\pi$
$599$	37.1445			1.51768			0.758841	+	0.651276i	$0.225766\pi$
$600$	12.3771	−	13.1988i	0.505291	−	0.538838i
$601$	0.556602	+	0.964062i	0.0227043	+	0.0393249i	0.877154	−	0.480209i	$-0.159439\pi$
$601$	0.556602	+	0.964062i	0.0227043	+	0.0393249i	−0.854450	+	0.519534i	$0.826106\pi$
$602$	0.269719	+	0.155722i	0.0109929	+	0.00634677i
$603$			8.96936i			0.365261i
$604$	3.64303	−	6.30991i	0.148233	−	0.256747i
$605$	−1.02310	−	2.36196i	−0.0415948	−	0.0960274i
$606$	−4.27160			−0.173522
$607$	−7.11683	−	4.10890i	−0.288863	−	0.166775i	0.348566	−	0.937284i	$-0.386669\pi$
$607$	−7.11683	−	4.10890i	−0.288863	−	0.166775i	−0.637429	+	0.770509i	$0.720002\pi$
$608$	20.7339	−	11.9707i	0.840872	−	0.485478i
$609$	−11.4971	−	19.9136i	−0.465888	−	0.806941i
$610$	−15.7843	−	11.7139i	−0.639087	−	0.474280i
$611$		0			0
$612$		−	2.90289i		−	0.117342i
$613$	−24.7777	+	14.3054i	−1.00076	+	0.577790i	−0.908474	−	0.417942i	$-0.862752\pi$
$613$	−24.7777	+	14.3054i	−1.00076	+	0.577790i	−0.0922886	+	0.995732i	$0.529418\pi$
$614$	3.72269	+	6.44788i	0.150235	+	0.260215i
$615$	−7.67380	+	3.32395i	−0.309437	+	0.134034i
$616$	−20.4153			−0.822555
$617$	0.731464	+	0.422311i	0.0294476	+	0.0170016i	0.514652	−	0.857399i	$-0.327921\pi$
$617$	0.731464	+	0.422311i	0.0294476	+	0.0170016i	−0.485204	+	0.874401i	$0.661255\pi$
$618$	−14.2721	−	8.24003i	−0.574110	−	0.331462i
$619$	9.06143			0.364210			0.182105	−	0.983279i	$-0.441709\pi$
$619$	9.06143			0.364210			0.182105	+	0.983279i	$0.441709\pi$
$620$	4.49109	+	10.3683i	0.180367	+	0.416402i
$621$	24.0487	+	41.6535i	0.965039	+	1.67150i
$622$	−2.17073	+	1.25327i	−0.0870385	+	0.0502517i
$623$			35.9012i			1.43835i
$624$		0			0
$625$	−20.8036	+	13.8640i	−0.832144	+	0.554560i
$626$	8.52205	+	14.7606i	0.340610	+	0.589953i
$627$	−14.7280	+	8.50321i	−0.588179	+	0.339585i
$628$	23.9089	+	13.8038i	0.954068	+	0.550831i
$629$	−15.1808			−0.605297
$630$	2.50131	+	5.77463i	0.0996546	+	0.230067i
$631$	−7.05868	+	12.2260i	−0.281002	+	0.486709i	−0.971632	−	0.236499i	$-0.924000\pi$
$631$	−7.05868	+	12.2260i	−0.281002	+	0.486709i	0.690630	+	0.723208i	$0.257333\pi$
$632$		−	38.3564i		−	1.52573i
$633$	−9.57556	−	5.52845i	−0.380594	−	0.219736i
$634$	2.55910	+	4.43248i	0.101635	+	0.176036i
$635$	−0.620692	+	5.38102i	−0.0246314	+	0.213539i
$636$	2.96970			0.117756
$637$		0			0
$638$		−	22.1311i		−	0.876177i
$639$	3.29604	+	5.70890i	0.130389	+	0.225841i
$640$	1.69136	−	14.6631i	0.0668568	−	0.579608i
$641$	4.59506	−	7.95887i	0.181494	−	0.314356i	−0.760896	−	0.648874i	$-0.775240\pi$
$641$	4.59506	−	7.95887i	0.181494	−	0.314356i	0.942389	+	0.334518i	$0.108573\pi$
$642$			4.72232i			0.186375i
$643$	3.58664	+	2.07075i	0.141443	+	0.0816624i	0.569052	−	0.822302i	$-0.307310\pi$
$643$	3.58664	+	2.07075i	0.141443	+	0.0816624i	−0.427608	+	0.903964i	$0.640644\pi$
$644$	−11.9333	+	20.6690i	−0.470236	+	0.814473i
$645$	0.260031	−	0.350389i	0.0102387	−	0.0137965i
$646$	−3.26853	+	5.66126i	−0.128599	+	0.222739i
$647$	4.20955	−	2.43038i	0.165494	−	0.0955483i	−0.414965	−	0.909837i	$-0.636206\pi$
$647$	4.20955	−	2.43038i	0.165494	−	0.0955483i	0.580460	+	0.814289i	$0.302873\pi$
$648$	−7.16408	+	4.13618i	−0.281432	+	0.162485i
$649$	17.2956			0.678911
$650$		0			0
$651$	12.0737			0.473204
$652$	−1.59632	+	0.921638i	−0.0625169	+	0.0360941i
$653$	−37.1054	+	21.4228i	−1.45205	+	0.838340i	−0.998598	−	0.0529423i	$-0.983140\pi$
$653$	−37.1054	+	21.4228i	−1.45205	+	0.838340i	−0.453449	+	0.891282i	$0.649807\pi$
$654$	−9.09644	+	15.7555i	−0.355699	+	0.616088i
$655$	−6.67147	+	8.98973i	−0.260676	+	0.351258i
$656$	0.159857	−	0.276880i	0.00624137	−	0.0108104i
$657$	−15.8706	−	9.16291i	−0.619172	−	0.357479i
$658$		−	13.2626i		−	0.517031i
$659$	0.177817	−	0.307989i	0.00692678	−	0.0119975i	−0.862541	−	0.505987i	$-0.831128\pi$
$659$	0.177817	−	0.307989i	0.00692678	−	0.0119975i	0.869468	+	0.493989i	$0.164462\pi$
$660$	−1.23649	+	10.7196i	−0.0481303	+	0.417261i
$661$	6.46993	+	11.2063i	0.251651	+	0.435873i	0.963981	−	0.265973i	$-0.0856931\pi$
$661$	6.46993	+	11.2063i	0.251651	+	0.435873i	−0.712329	+	0.701845i	$0.752360\pi$
$662$		−	3.60485i		−	0.140107i
$663$		0			0
$664$	−18.0365			−0.699952
$665$	−2.49597	+	21.6385i	−0.0967895	+	0.839106i
$666$	−5.43086	−	9.40653i	−0.210442	−	0.364496i
$667$	−59.3898	−	34.2887i	−2.29958	−	1.32766i
$668$			0.0596123i			0.00230647i
$669$	0.0288218	−	0.0499208i	0.00111432	−	0.00193005i
$670$	−5.09396	−	11.7601i	−0.196797	−	0.454333i
$671$	31.0707			1.19947
$672$	−14.0576	−	8.11614i	−0.542282	−	0.313087i
$673$	23.8167	−	13.7506i	0.918065	−	0.530045i	0.0350476	−	0.999386i	$-0.488842\pi$
$673$	23.8167	−	13.7506i	0.918065	−	0.530045i	0.883017	+	0.469341i	$0.155508\pi$
$674$	−11.0247	−	19.0954i	−0.424656	−	0.735526i
$675$	26.6582	−	8.06902i	1.02608	−	0.310577i
$676$		0			0
$677$		−	12.6270i		−	0.485297i	−0.970114	−	0.242648i	$-0.921984\pi$
$677$		−	12.6270i		−	0.485297i	0.970114	−	0.242648i	$-0.0780161\pi$
$678$	−3.43423	+	1.98276i	−0.131891	+	0.0761473i
$679$	13.7806	+	23.8687i	0.528852	+	0.915998i
$680$	4.36987	+	10.0885i	0.167577	+	0.386875i
$681$	−8.15069			−0.312335
$682$	10.0636	+	5.81021i	0.385354	+	0.222484i
$683$	25.1530	+	14.5221i	0.962453	+	0.555673i	0.896927	−	0.442178i	$-0.145794\pi$
$683$	25.1530	+	14.5221i	0.962453	+	0.555673i	0.0655262	+	0.997851i	$0.479127\pi$
$684$	7.18901			0.274879
$685$	−26.2953	+	11.3900i	−1.00469	+	0.435188i
$686$	−8.90788	−	15.4289i	−0.340105	−	0.589078i
$687$	8.00074	−	4.61923i	0.305247	−	0.176235i
$688$			0.0166814i			0.000635972i
$689$		0			0
$690$	−17.4693	−	12.9644i	−0.665046	−	0.493545i
$691$	−2.77180	−	4.80090i	−0.105444	−	0.182635i	0.808475	−	0.588530i	$-0.200293\pi$
$691$	−2.77180	−	4.80090i	−0.105444	−	0.182635i	−0.913920	+	0.405895i	$0.866960\pi$
$692$	−9.44896	+	5.45536i	−0.359196	+	0.207382i
$693$	−8.61489	−	4.97381i	−0.327253	−	0.188939i
$694$	25.8904			0.982785
$695$	13.8016	+	31.8629i	0.523524	+	1.20863i
$696$	14.3713	−	24.8918i	0.544743	−	0.943522i
$697$		−	5.08130i		−	0.192468i
$698$	5.60576	+	3.23649i	0.212181	+	0.122503i
$699$	2.89416	+	5.01283i	0.109467	+	0.189602i
$700$	10.0816	+	9.45395i	0.381049	+	0.357326i
$701$	−7.14386			−0.269820			−0.134910	−	0.990858i	$-0.543075\pi$
$701$	−7.14386			−0.269820			−0.134910	+	0.990858i	$0.543075\pi$
$702$		0			0
$703$		−	37.5953i		−	1.41793i
$704$	−8.15192	−	14.1195i	−0.307237	−	0.532150i
$705$	−18.4586	−	2.12917i	−0.695191	−	0.0801892i
$706$	6.19445	−	10.7291i	0.233131	−	0.403795i
$707$		−	8.64831i		−	0.325253i
$708$	7.33912	+	4.23725i	0.275821	+	0.159245i
$709$	−16.6348	+	28.8123i	−0.624733	+	1.08207i	0.363859	+	0.931454i	$0.381459\pi$
$709$	−16.6348	+	28.8123i	−0.624733	+	1.08207i	−0.988592	+	0.150616i	$0.951874\pi$
$710$	−7.56382	−	5.61327i	−0.283865	−	0.210662i
$711$	9.34483	−	16.1857i	0.350458	−	0.607012i
$712$	−38.8638	+	22.4380i	−1.45648	+	0.840901i
$713$	31.1840	−	18.0041i	1.16785	−	0.674257i
$714$	4.43211			0.165868
$715$		0			0
$716$	−27.6994			−1.03517
$717$	−18.6111	+	10.7451i	−0.695043	+	0.401283i
$718$	−12.5055	+	7.22008i	−0.466703	+	0.269451i
$719$	1.46562	−	2.53852i	0.0546583	−	0.0946710i	−0.837402	−	0.546588i	$-0.815926\pi$
$719$	1.46562	−	2.53852i	0.0546583	−	0.0946710i	0.892060	+	0.451917i	$0.149260\pi$
$720$	−0.200872	+	0.270673i	−0.00748606	+	0.0100874i
$721$	16.6828	−	28.8955i	0.621301	−	1.07612i
$722$	0.589400	+	0.340290i	0.0219352	+	0.0126643i
$723$			7.78013i			0.289346i
$724$	10.7317	−	18.5878i	0.398840	−	0.690811i
$725$	−27.1647	+	28.9682i	−1.00887	+	1.07585i
$726$	−0.648537	−	1.12330i	−0.0240695	−	0.0416895i
$727$			14.9385i			0.554039i	0.960864	+	0.277019i	$0.0893466\pi$
$727$			14.9385i			0.554039i	−0.960864	+	0.277019i	$0.910653\pi$
$728$		0			0
$729$	−25.2390			−0.934777
$730$	26.0125	+	3.00050i	0.962767	+	0.111054i
$731$	0.132561	+	0.229602i	0.00490294	+	0.00849215i
$732$	13.1844	+	7.61201i	0.487309	+	0.281348i
$733$		−	9.64485i		−	0.356241i	−0.984009	−	0.178120i	$-0.942998\pi$
$733$		−	9.64485i		−	0.356241i	0.984009	−	0.178120i	$-0.0570016\pi$
$734$	15.2928	−	26.4878i	0.564466	−	0.977684i
$735$	−4.67608	+	2.02547i	−0.172480	+	0.0747106i
$736$	−48.4106			−1.78444
$737$	17.5444	+	10.1292i	0.646254	+	0.373115i
$738$	3.14855	−	1.81782i	0.115900	−	0.0669148i
$739$	−19.3003	−	33.4291i	−0.709973	−	1.22971i	−0.964867	−	0.262740i	$-0.915374\pi$
$739$	−19.3003	−	33.4291i	−0.709973	−	1.22971i	0.254894	−	0.966969i	$-0.417960\pi$
$740$	−19.1558	−	14.2159i	−0.704181	−	0.522588i
$741$		0			0
$742$		−	3.91175i		−	0.143605i
$743$	−37.5776	+	21.6954i	−1.37859	+	0.795928i	−0.991990	−	0.126320i	$-0.959683\pi$
$743$	−37.5776	+	21.6954i	−1.37859	+	0.795928i	−0.386599	+	0.922248i	$0.626350\pi$
$744$	7.54597	+	13.0700i	0.276649	+	0.479170i
$745$	0.0367784	+	0.0849081i	0.00134746	+	0.00311079i
$746$	20.6146			0.754754
$747$	−7.61109	−	4.39426i	−0.278475	−	0.160778i
$748$	−5.67813	−	3.27827i	−0.207613	−	0.119865i
$749$	−9.56084			−0.349345
$750$	−9.61353	+	8.14143i	−0.351036	+	0.297283i
$751$	17.4385	+	30.2044i	0.636341	+	1.10217i	0.986229	+	0.165383i	$0.0528860\pi$
$751$	17.4385	+	30.2044i	0.636341	+	1.10217i	−0.349889	+	0.936791i	$0.613781\pi$
$752$	0.615193	−	0.355182i	0.0224338	−	0.0129522i
$753$			14.7012i			0.535742i
$754$		0			0
$755$	−8.01302	+	10.7974i	−0.291624	+	0.392959i
$756$	−7.69895	−	13.3350i	−0.280008	−	0.484988i
$757$	−10.0908	+	5.82591i	−0.366755	+	0.211746i	−0.672040	−	0.740515i	$-0.734582\pi$
$757$	−10.0908	+	5.82591i	−0.366755	+	0.211746i	0.305285	+	0.952261i	$0.401248\pi$
$758$	9.43209	+	5.44562i	0.342589	+	0.197794i
$759$	34.3876			1.24819
$760$	−24.9841	+	10.8220i	−0.906270	+	0.392556i
$761$	−24.5342	+	42.4945i	−0.889364	+	1.54042i	−0.0487353	+	0.998812i	$0.515519\pi$
$761$	−24.5342	+	42.4945i	−0.889364	+	1.54042i	−0.840629	+	0.541612i	$0.817814\pi$
$762$			2.72952i			0.0988803i
$763$	−31.8987	−	18.4167i	−1.15481	−	0.666730i
$764$	−5.89793	−	10.2155i	−0.213380	−	0.369584i
$765$	−0.613860	+	5.32179i	−0.0221942	+	0.192410i
$766$	−1.67215			−0.0604172
$767$		0			0
$768$		−	20.6238i		−	0.744197i
$769$	−20.0601	−	34.7451i	−0.723386	−	1.25294i	−0.959635	−	0.281248i	$-0.909252\pi$
$769$	−20.0601	−	34.7451i	−0.723386	−	1.25294i	0.236249	−	0.971692i	$-0.424082\pi$
$770$	14.1201	+	1.62873i	0.508854	+	0.0586954i
$771$	−7.91068	+	13.7017i	−0.284896	+	0.493455i
$772$			12.1179i			0.436133i
$773$	10.0859	+	5.82307i	0.362763	+	0.209441i	0.670292	−	0.742097i	$-0.266169\pi$
$773$	10.0859	+	5.82307i	0.362763	+	0.209441i	−0.307529	+	0.951539i	$0.599502\pi$
$774$	−0.0948464	+	0.164279i	−0.00340918	+	0.00590488i
$775$	−6.04088	−	19.9577i	−0.216995	−	0.716903i
$776$	−17.2256	+	29.8357i	−0.618364	+	1.07104i
$777$	−22.0746	+	12.7448i	−0.791920	+	0.457216i
$778$	15.4121	−	8.89821i	0.552552	−	0.319016i
$779$	12.5839			0.450864
$780$		0			0
$781$	14.8891			0.532772
$782$	11.4473	−	6.60909i	0.409354	−	0.236341i
$783$	38.3164	−	22.1220i	1.36932	−	0.790575i
$784$	0.0974100	−	0.168719i	0.00347893	−	0.00602568i
$785$	−40.9126	−	30.3621i	−1.46023	−	1.08367i
$786$	−2.82058	+	4.88540i	−0.100607	+	0.174256i
$787$	−22.1392	−	12.7821i	−0.789176	−	0.455631i	0.0504961	−	0.998724i	$-0.483920\pi$
$787$	−22.1392	−	12.7821i	−0.789176	−	0.455631i	−0.839673	+	0.543093i	$0.817253\pi$
$788$			7.27005i			0.258985i
$789$	17.9756	−	31.1347i	0.639949	−	1.10842i
$790$	−3.06007	+	26.5290i	−0.108873	+	0.943858i
$791$	−4.01430	−	6.95298i	−0.142732	−	0.247219i
$792$		−	12.4344i		−	0.441837i
$793$		0			0
$794$	18.3022			0.649519
$795$	−5.44428	−	0.627989i	−0.193089	−	0.0222725i
$796$	3.52164	+	6.09966i	0.124821	+	0.216197i
$797$	39.6074	+	22.8674i	1.40297	+	0.810003i	0.994696	−	0.102858i	$-0.0327986\pi$
$797$	39.6074	+	22.8674i	1.40297	+	0.810003i	0.408271	+	0.912861i	$0.366132\pi$
$798$			10.9761i			0.388551i
$799$	5.64501	−	9.77744i	0.199706	−	0.345901i
$800$	−6.38245	+	27.2979i	−0.225654	+	0.965126i
$801$	−21.8665			−0.772614
$802$	27.5389	+	15.8996i	0.972431	+	0.561433i
$803$	−35.8459	+	20.6956i	−1.26497	+	0.730333i
$804$	4.96312	+	8.59638i	0.175036	+	0.303171i
$805$	26.2477	−	35.3685i	0.925112	−	1.24658i
$806$		0			0
$807$			15.4682i			0.544506i
$808$	9.36199	−	5.40515i	0.329354	−	0.190152i
$809$	15.7281	+	27.2418i	0.552970	+	0.957772i	0.998058	+	0.0622856i	$0.0198390\pi$
$809$	15.7281	+	27.2418i	0.552970	+	0.957772i	−0.445088	+	0.895487i	$0.646828\pi$
$810$	5.28498	−	2.28922i	0.185695	−	0.0804349i
$811$	−38.0128			−1.33481			−0.667406	−	0.744694i	$-0.732595\pi$
$811$	−38.0128			−1.33481			−0.667406	+	0.744694i	$0.732595\pi$
$812$	19.0131	+	10.9772i	0.667228	+	0.385224i
$813$	−19.4033	−	11.2025i	−0.680504	−	0.392889i
$814$	−24.5326			−0.859868
$815$	3.12140	−	1.35205i	0.109338	−	0.0473603i
$816$	0.118695	+	0.205586i	0.00415515	+	0.00719694i
$817$	−0.568612	+	0.328288i	−0.0198932	+	0.0114853i
$818$			0.197063i			0.00689015i
$819$		0			0
$820$	4.75835	−	6.41182i	0.166169	−	0.223910i
$821$	27.8796	+	48.2890i	0.973006	+	1.68530i	0.686363	+	0.727259i	$0.259206\pi$
$821$	27.8796	+	48.2890i	0.973006	+	1.68530i	0.286643	+	0.958037i	$0.407461\pi$
$822$	−12.5055	+	7.22005i	−0.436179	+	0.251828i
$823$	26.6045	+	15.3601i	0.927375	+	0.535420i	0.885980	−	0.463723i	$-0.153487\pi$
$823$	26.6045	+	15.3601i	0.927375	+	0.535420i	0.0413947	+	0.999143i	$0.486820\pi$
$824$	41.7067			1.45292
$825$	4.53366	−	19.3906i	0.157842	−	0.675093i
$826$	5.58139	−	9.66725i	0.194201	−	0.336367i
$827$		−	37.7024i		−	1.31104i	−0.755177	−	0.655520i	$-0.772449\pi$
$827$		−	37.7024i		−	1.31104i	0.755177	−	0.655520i	$-0.227551\pi$
$828$	−12.5889	−	7.26823i	−0.437496	−	0.252589i
$829$	−6.91039	−	11.9691i	−0.240008	−	0.415705i	0.720709	−	0.693238i	$-0.243817\pi$
$829$	−6.91039	−	11.9691i	−0.240008	−	0.415705i	−0.960716	+	0.277533i	$0.910483\pi$
$830$	12.4749	+	1.43895i	0.433008	+	0.0499468i
$831$	14.8799			0.516177
$832$		0			0
$833$		−	3.09633i		−	0.107281i
$834$	8.74877	+	15.1533i	0.302945	+	0.524716i
$835$	0.0126059	−	0.109286i	0.000436247	−	0.00378199i
$836$	8.11866	−	14.0619i	0.280790	−	0.486342i
$837$			23.2313i			0.802990i
$838$	0.523151	+	0.302042i	0.0180720	+	0.0104339i
$839$	8.04509	−	13.9345i	0.277747	−	0.481073i	−0.693077	−	0.720863i	$-0.743745\pi$
$839$	8.04509	−	13.9345i	0.277747	−	0.481073i	0.970825	+	0.239791i	$0.0770788\pi$
$840$	14.8239	+	11.0011i	0.511473	+	0.379575i
$841$	−17.0416	+	29.5170i	−0.587642	+	1.01783i
$842$	−1.55270	+	0.896452i	−0.0535096	+	0.0308938i
$843$	22.2712	−	12.8583i	0.767062	−	0.442864i
$844$	10.5569			0.363382
$845$		0			0
$846$	8.07792			0.277725
$847$	2.27424	−	1.31303i	0.0781438	−	0.0451163i
$848$	0.181448	−	0.104759i	0.00623097	−	0.00359745i
$849$	5.23065	−	9.05976i	0.179516	−	0.310930i
$850$	−2.21754	−	7.32626i	−0.0760610	−	0.251289i
$851$	−38.0095	+	65.8345i	−1.30295	+	2.25678i
$852$	6.31795	+	3.64767i	0.216449	+	0.124967i
$853$			48.9861i			1.67725i	0.544709	+	0.838625i	$0.316640\pi$
$853$			48.9861i			1.67725i	−0.544709	+	0.838625i	$0.683360\pi$
$854$	10.0267	−	17.3668i	0.343107	−	0.594278i
$855$	−13.1795	−	1.52023i	−0.450728	−	0.0519907i
$856$	−5.97547	−	10.3498i	−0.204237	−	0.353749i
$857$			8.57696i			0.292983i	0.989212	+	0.146492i	$0.0467982\pi$
$857$			8.57696i			0.292983i	−0.989212	+	0.146492i	$0.953202\pi$
$858$		0			0
$859$	17.9983			0.614095			0.307048	−	0.951694i	$-0.400659\pi$
$859$	17.9983			0.614095			0.307048	+	0.951694i	$0.400659\pi$
$860$	−0.0477379	+	0.413859i	−0.00162785	+	0.0141125i
$861$	−4.26592	−	7.38879i	−0.145382	−	0.251809i
$862$	−5.27018	−	3.04274i	−0.179503	−	0.103636i
$863$			2.18400i			0.0743444i	0.999309	+	0.0371722i	$0.0118350\pi$
$863$			2.18400i			0.0743444i	−0.999309	+	0.0371722i	$0.988165\pi$
$864$	15.6165	−	27.0485i	0.531283	−	0.920210i
$865$	18.4762	−	8.00306i	0.628209	−	0.272112i
$866$	−0.462525			−0.0157172
$867$	−15.4163	−	8.90063i	−0.523566	−	0.302281i
$868$	−9.98324	+	5.76383i	−0.338853	+	0.195637i
$869$	−21.1065	−	36.5575i	−0.715989	−	1.24013i
$870$	−11.9257	+	16.0698i	−0.404319	+	0.544816i
$871$		0			0
$872$		−	46.0414i		−	1.55916i
$873$	−14.5378	+	8.39342i	−0.492031	+	0.284074i
$874$	16.3675	+	28.3493i	0.553637	+	0.958928i
$875$	−16.4832	−	19.4636i	−0.557234	−	0.657991i
$876$	−20.2809			−0.685228
$877$	−24.2145	−	13.9802i	−0.817665	−	0.472079i	0.0319457	−	0.999490i	$-0.489830\pi$
$877$	−24.2145	−	13.9802i	−0.817665	−	0.472079i	−0.849611	+	0.527411i	$0.823163\pi$
$878$	−21.2138	−	12.2478i	−0.715930	−	0.413343i
$879$	−27.0584			−0.912658
$880$	0.302597	+	0.698587i	0.0102005	+	0.0235494i
$881$	1.69272	+	2.93188i	0.0570292	+	0.0987775i	0.893131	−	0.449798i	$-0.148504\pi$
$881$	1.69272	+	2.93188i	0.0570292	+	0.0987775i	−0.836101	+	0.548575i	$0.815171\pi$
$882$	1.91859	−	1.10770i	0.0646024	−	0.0372982i
$883$		−	9.67005i		−	0.325423i	−0.986674	−	0.162712i	$-0.947976\pi$
$883$		−	9.67005i		−	0.325423i	0.986674	−	0.162712i	$-0.0520240\pi$
$884$		0			0
$885$	−12.5586	−	9.32002i	−0.422153	−	0.313289i
$886$	3.19939	+	5.54151i	0.107486	+	0.186171i
$887$	8.78091	−	5.06966i	0.294834	−	0.170223i	−0.345286	−	0.938498i	$-0.612218\pi$
$887$	8.78091	−	5.06966i	0.294834	−	0.170223i	0.640120	+	0.768275i	$0.278885\pi$
$888$	−27.5929	−	15.9308i	−0.925959	−	0.534602i
$889$	−5.52622			−0.185343
$890$	28.6701	−	12.4186i	0.961023	−	0.416272i
$891$	−4.55207	+	7.88441i	−0.152500	+	0.264138i
$892$			0.0550368i			0.00184277i
$893$	24.2139	+	13.9799i	0.810287	+	0.467819i
$894$	0.0233137	+	0.0403805i	0.000779726	+	0.00135052i
$895$	50.7806	+	5.85746i	1.69741	+	0.195793i
$896$	15.0587			0.503076
$897$		0			0
$898$		−	0.120427i		−	0.00401869i
$899$	−16.5616	−	28.6856i	−0.552362	−	0.956718i
$900$	−5.75815	+	6.14044i	−0.191938	+	0.204681i
$901$	1.66497	−	2.88381i	0.0554682	−	0.0960737i
$902$		−	8.21155i		−	0.273415i
$903$	0.385517	+	0.222579i	0.0128292	+	0.00740695i
$904$	5.01783	−	8.69114i	0.166891	−	0.289063i
$905$	−23.6048	+	31.8073i	−0.784652	+	1.05731i
$906$	−3.38777	+	5.86778i	−0.112551	+	0.194944i
$907$	−42.2301	+	24.3816i	−1.40223	+	0.809577i	−0.994621	−	0.103581i	$-0.966970\pi$
$907$	−42.2301	+	24.3816i	−1.40223	+	0.809577i	−0.407607	+	0.913157i	$0.633637\pi$
$908$	6.73948	−	3.89104i	0.223658	−	0.129129i
$909$	5.26746			0.174711
$910$		0			0
$911$	−53.5943			−1.77566			−0.887829	−	0.460174i	$-0.847787\pi$
$911$	−53.5943			−1.77566			−0.887829	+	0.460174i	$0.847787\pi$
$912$	−0.509134	+	0.293949i	−0.0168591	+	0.00973361i
$913$	−17.1906	+	9.92502i	−0.568927	+	0.328470i
$914$	0.136738	−	0.236836i	0.00452288	−	0.00783385i
$915$	−22.5610	−	16.7430i	−0.745843	−	0.553506i
$916$	−4.41033	+	7.63892i	−0.145721	+	0.252397i
$917$	−9.89101	−	5.71058i	−0.326630	−	0.188580i
$918$			8.52794i			0.281464i
$919$	−14.1071	+	24.4342i	−0.465350	+	0.806010i	−0.999217	−	0.0395582i	$-0.987405\pi$
$919$	−14.1071	+	24.4342i	−0.465350	+	0.806010i	0.533867	+	0.845568i	$0.320738\pi$
$920$	54.6919	+	6.30862i	1.80314	+	0.207989i
$921$	5.32095	+	9.21615i	0.175331	+	0.303683i
$922$			25.4572i			0.838390i
$923$		0			0
$924$	−11.0089			−0.362165
$925$	32.1117	+	30.1125i	1.05583	+	0.990093i
$926$	7.14843	+	12.3815i	0.234912	+	0.406880i
$927$	17.5995	+	10.1611i	0.578043	+	0.333733i
$928$			44.5321i			1.46184i
$929$	−1.45288	+	2.51645i	−0.0476673	+	0.0825622i	−0.888875	−	0.458151i	$-0.848512\pi$
$929$	−1.45288	+	2.51645i	−0.0476673	+	0.0825622i	0.841207	+	0.540713i	$0.181845\pi$
$930$	−4.17641	−	9.64182i	−0.136950	−	0.316168i
$931$	7.66808			0.251311
$932$	−4.78613	−	2.76327i	−0.156775	−	0.0905140i
$933$	−3.10270	+	1.79134i	−0.101578	+	0.0586459i
$934$	1.54308	+	2.67269i	0.0504911	+	0.0874531i
$935$	9.71635	+	7.21071i	0.317759	+	0.235815i
$936$		0			0
$937$			44.6821i			1.45970i	0.683607	+	0.729850i	$0.260410\pi$
$937$			44.6821i			1.45970i	−0.683607	+	0.729850i	$0.739590\pi$
$938$	11.3233	−	6.53753i	0.369720	−	0.213458i
$939$	12.1808	+	21.0978i	0.397506	+	0.688501i
$940$	16.2791	−	7.05140i	0.530967	−	0.229991i
$941$	5.09938			0.166235			0.0831175	−	0.996540i	$-0.473512\pi$
$941$	5.09938			0.166235			0.0831175	+	0.996540i	$0.473512\pi$
$942$	−22.2336	−	12.8366i	−0.724410	−	0.418238i
$943$	−22.0361	−	12.7225i	−0.717594	−	0.414303i
$944$	0.597894			0.0194598
$945$	11.2944	+	26.0748i	0.367408	+	0.848212i
$946$	0.214223	+	0.371045i	0.00696498	+	0.0120637i
$947$	5.93410	−	3.42605i	0.192832	−	0.111332i	−0.400476	−	0.916307i	$-0.631155\pi$
$947$	5.93410	−	3.42605i	0.192832	−	0.111332i	0.593308	+	0.804976i	$0.297822\pi$
$948$		−	20.6835i		−	0.671770i
$949$		0			0
$950$	18.1435	−	5.49175i	0.588654	−	0.178176i
$951$	3.65779	+	6.33548i	0.118612	+	0.205442i
$952$	−9.71377	+	5.60825i	−0.314825	+	0.181764i
$953$	−27.6397	−	15.9578i	−0.895337	−	0.516923i	−0.0196525	−	0.999807i	$-0.506256\pi$
$953$	−27.6397	−	15.9578i	−0.895337	−	0.516923i	−0.875684	+	0.482884i	$0.839589\pi$
$954$	2.38254			0.0771377
$955$	8.65232	+	19.9751i	0.279982	+	0.646379i
$956$	10.2592	−	17.7694i	0.331805	−	0.574704i
$957$		−	31.6326i		−	1.02254i
$958$	−11.1168	−	6.41830i	−0.359168	−	0.207366i
$959$	−14.6178	−	25.3187i	−0.472032	−	0.817583i
$960$	−1.68930	+	14.6452i	−0.0545221	+	0.472673i
$961$	−13.6079			−0.438964
$962$		0			0
$963$		−	5.82325i		−	0.187652i
$964$	−3.71414	−	6.43309i	−0.119625	−	0.207196i
$965$	2.56252	−	22.2155i	0.0824904	−	0.715142i
$966$	11.0971	−	19.2207i	0.357043	−	0.618417i
$967$			15.8568i			0.509920i	0.966952	+	0.254960i	$0.0820623\pi$
$967$			15.8568i			0.509920i	−0.966952	+	0.254960i	$0.917938\pi$
$968$	2.84277	+	1.64128i	0.0913702	+	0.0527526i
$969$	−4.67181	+	8.09181i	−0.150080	+	0.259946i
$970$	14.2943	−	19.2614i	0.458962	−	0.618447i
$971$	−9.15839	+	15.8628i	−0.293907	+	0.509061i	−0.974730	−	0.223386i	$-0.928289\pi$
$971$	−9.15839	+	15.8628i	−0.293907	+	0.509061i	0.680823	+	0.732448i	$0.261622\pi$
$972$	13.6730	−	7.89410i	0.438561	−	0.253203i
$973$	−30.6795	+	17.7128i	−0.983540	+	0.567847i
$974$	−2.58619			−0.0828669
$975$		0			0
$976$	1.07409			0.0343807
$977$	−11.7245	+	6.76912i	−0.375099	+	0.216563i	−0.675684	−	0.737192i	$-0.736151\pi$
$977$	−11.7245	+	6.76912i	−0.375099	+	0.216563i	0.300585	+	0.953755i	$0.402818\pi$
$978$	1.48447	−	0.857060i	0.0474681	−	0.0274057i
$979$	−24.6941	+	42.7715i	−0.789228	+	1.36698i
$980$	2.89953	−	3.90709i	0.0926222	−	0.124807i
$981$	11.2171	−	19.4287i	0.358136	−	0.620309i
$982$	5.84969	+	3.37732i	0.186671	+	0.107775i
$983$		−	34.5313i		−	1.10138i	−0.834711	−	0.550688i	$-0.814365\pi$
$983$		−	34.5313i		−	1.10138i	0.834711	−	0.550688i	$-0.185635\pi$
$984$	5.33235	−	9.23590i	0.169989	−	0.294430i
$985$	1.53737	−	13.3280i	0.0489845	−	0.424666i
$986$	−6.07959	−	10.5302i	−0.193614	−	0.335349i
$987$		−	18.9567i		−	0.603398i
$988$		0			0
$989$	1.32762			0.0422159
$990$	−0.992018	+	8.60019i	−0.0315284	+	0.273332i
$991$	−21.7636	−	37.6957i	−0.691343	−	1.19744i	−0.971398	−	0.237458i	$-0.923686\pi$
$991$	−21.7636	−	37.6957i	−0.691343	−	1.19744i	0.280055	−	0.959984i	$-0.409647\pi$
$992$	−20.2499	−	11.6913i	−0.642936	−	0.371199i
$993$		−	5.15253i		−	0.163510i
$994$	4.80479	−	8.32214i	0.152399	−	0.263962i
$995$	−5.16628	−	11.9271i	−0.163782	−	0.378114i
$996$	−9.72612			−0.308184
$997$	−39.3004	−	22.6901i	−1.24466	−	0.718602i	−0.274617	−	0.961554i	$-0.588551\pi$
$997$	−39.3004	−	22.6901i	−1.24466	−	0.718602i	−0.970038	+	0.242952i	$0.921884\pi$
$998$	3.13141	−	1.80792i	0.0991231	−	0.0572287i
$999$	−24.5225	−	42.4743i	−0.775858	−	1.34383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.n.h.484.12		36
5.4	even	2	inner	845.2.n.h.484.7		36
13.2	odd	12		845.2.d.e.844.24		36
13.3	even	3		845.2.b.h.339.12	yes	18
13.4	even	6		845.2.n.i.529.12		36
13.5	odd	4		845.2.l.g.699.14		72
13.6	odd	12		845.2.l.g.654.13		72
13.7	odd	12		845.2.l.g.654.23		72
13.8	odd	4		845.2.l.g.699.24		72
13.9	even	3	inner	845.2.n.h.529.7		36
13.10	even	6		845.2.b.g.339.7	✓	18
13.11	odd	12		845.2.d.e.844.14		36
13.12	even	2		845.2.n.i.484.7		36
65.3	odd	12		4225.2.a.cb.1.12		18
65.4	even	6		845.2.n.i.529.7		36
65.9	even	6	inner	845.2.n.h.529.12		36
65.19	odd	12		845.2.l.g.654.24		72
65.23	odd	12		4225.2.a.ca.1.7		18
65.24	odd	12		845.2.d.e.844.23		36
65.29	even	6		845.2.b.h.339.7	yes	18
65.34	odd	4		845.2.l.g.699.13		72
65.42	odd	12		4225.2.a.cb.1.7		18
65.44	odd	4		845.2.l.g.699.23		72
65.49	even	6		845.2.b.g.339.12	yes	18
65.54	odd	12		845.2.d.e.844.13		36
65.59	odd	12		845.2.l.g.654.14		72
65.62	odd	12		4225.2.a.ca.1.12		18
65.64	even	2		845.2.n.i.484.12		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.b.g.339.7	✓	18	13.10	even	6
845.2.b.g.339.12	yes	18	65.49	even	6
845.2.b.h.339.7	yes	18	65.29	even	6
845.2.b.h.339.12	yes	18	13.3	even	3
845.2.d.e.844.13		36	65.54	odd	12
845.2.d.e.844.14		36	13.11	odd	12
845.2.d.e.844.23		36	65.24	odd	12
845.2.d.e.844.24		36	13.2	odd	12
845.2.l.g.654.13		72	13.6	odd	12
845.2.l.g.654.14		72	65.59	odd	12
845.2.l.g.654.23		72	13.7	odd	12
845.2.l.g.654.24		72	65.19	odd	12
845.2.l.g.699.13		72	65.34	odd	4
845.2.l.g.699.14		72	13.5	odd	4
845.2.l.g.699.23		72	65.44	odd	4
845.2.l.g.699.24		72	13.8	odd	4
845.2.n.h.484.7		36	5.4	even	2	inner
845.2.n.h.484.12		36	1.1	even	1	trivial
845.2.n.h.529.7		36	13.9	even	3	inner
845.2.n.h.529.12		36	65.9	even	6	inner
845.2.n.i.484.7		36	13.12	even	2
845.2.n.i.484.12		36	65.64	even	2
845.2.n.i.529.7		36	65.4	even	6
845.2.n.i.529.12		36	13.4	even	6
4225.2.a.ca.1.7		18	65.23	odd	12
4225.2.a.ca.1.12		18	65.62	odd	12
4225.2.a.cb.1.7		18	65.42	odd	12
4225.2.a.cb.1.12		18	65.3	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.768923 - 0.443938i) q^{2} +(1.09905 - 0.634534i) q^{3} +(-0.605838 + 1.04934i) q^{4} +(1.33257 - 1.79562i) q^{5} +(0.563388 - 0.975816i) q^{6} +(1.97564 + 1.14064i) q^{7} +2.85157i q^{8} +(-0.694733 + 1.20331i) q^{9} +(0.227498 - 1.97227i) q^{10} +(1.56914 + 2.71784i) q^{11} +1.53770i q^{12} +2.02549 q^{14} +(0.325171 - 2.81903i) q^{15} +(0.0542440 + 0.0939534i) q^{16} +(1.49323 + 0.862115i) q^{17} +1.23367i q^{18} +(-2.13503 + 3.69799i) q^{19} +(1.07690 + 2.48618i) q^{20} +2.89510 q^{21} +(2.41310 + 1.39321i) q^{22} +(7.47747 - 4.31712i) q^{23} +(1.80942 + 3.13400i) q^{24} +(-1.44852 - 4.78558i) q^{25} +5.57053i q^{27} +(-2.39384 + 1.38208i) q^{28} +(-3.97125 - 6.87840i) q^{29} +(-1.00144 - 2.31197i) q^{30} +4.17039 q^{31} +(-4.85565 - 2.80341i) q^{32} +(3.44912 + 1.99135i) q^{33} +1.53090 q^{34} +(4.68084 - 2.02753i) q^{35} +(-0.841792 - 1.45803i) q^{36} +(-7.62481 + 4.40219i) q^{37} +3.79129i q^{38} +(5.12034 + 3.79991i) q^{40} +(-1.47350 - 2.55217i) q^{41} +(2.22611 - 1.28524i) q^{42} +(0.133162 + 0.0768812i) q^{43} -3.80259 q^{44} +(1.23492 + 2.85098i) q^{45} +(3.83307 - 6.63907i) q^{46} -6.54786i q^{47} +(0.119233 + 0.0688394i) q^{48} +(-0.897887 - 1.55519i) q^{49} +(-3.23830 - 3.03669i) q^{50} +2.18817 q^{51} -1.93126i q^{53} +(2.47297 + 4.28331i) q^{54} +(6.97121 + 0.804117i) q^{55} +(-3.25261 + 5.63369i) q^{56} +5.41901i q^{57} +(-6.10717 - 3.52598i) q^{58} +(2.75557 - 4.77279i) q^{59} +(2.76113 + 2.04909i) q^{60} +(4.95026 - 8.57410i) q^{61} +(3.20671 - 1.85139i) q^{62} +(-2.74509 + 1.58488i) q^{63} -5.19513 q^{64} +3.53615 q^{66} +(5.59042 - 3.22763i) q^{67} +(-1.80931 + 1.04460i) q^{68} +(5.47872 - 9.48942i) q^{69} +(2.69911 - 3.63702i) q^{70} +(2.37216 - 4.10870i) q^{71} +(-3.43133 - 1.98108i) q^{72} +13.1891i q^{73} +(-3.90860 + 6.76989i) q^{74} +(-4.62860 - 4.34044i) q^{75} +(-2.58697 - 4.48076i) q^{76} +7.15931i q^{77} -13.4510 q^{79} +(0.240989 + 0.0277977i) q^{80} +(1.45049 + 2.51233i) q^{81} +(-2.26601 - 1.30828i) q^{82} +6.32511i q^{83} +(-1.75396 + 3.03795i) q^{84} +(3.53786 - 1.53244i) q^{85} +0.136522 q^{86} +(-8.72916 - 5.03978i) q^{87} +(-7.75011 + 4.47453i) q^{88} +(7.86866 + 13.6289i) q^{89} +(2.21521 + 1.64396i) q^{90} +10.4619i q^{92} +(4.58344 - 2.64625i) q^{93} +(-2.90684 - 5.03480i) q^{94} +(3.79511 + 8.76154i) q^{95} -7.11543 q^{96} +(10.4629 + 6.04075i) q^{97} +(-1.38081 - 0.797212i) q^{98} -4.36055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 16 q^{4} - 16 q^{6} + 18 q^{9} - 13 q^{10} - 22 q^{11} - 8 q^{14} - 8 q^{15} + 12 q^{16} + 28 q^{19} + 10 q^{20} + 52 q^{21} + 34 q^{24} - 16 q^{25} - 20 q^{29} - 31 q^{30} + 64 q^{31} - 36 q^{34}+ \cdots - 152 q^{99}+O(q^{100}) \) 36 * q + 16 * q^4 - 16 * q^6 + 18 * q^9 - 13 * q^10 - 22 * q^11 - 8 * q^14 - 8 * q^15 + 12 * q^16 + 28 * q^19 + 10 * q^20 + 52 * q^21 + 34 * q^24 - 16 * q^25 - 20 * q^29 - 31 * q^30 + 64 * q^31 - 36 * q^34 - 10 * q^35 - 32 * q^36 + 6 * q^40 - 52 * q^41 - 100 * q^44 - 5 * q^45 - 30 * q^46 + 44 * q^49 - 29 * q^50 - 80 * q^51 + 90 * q^54 + 20 * q^55 + 20 * q^56 + 76 * q^59 + 86 * q^60 - 8 * q^61 + 136 * q^64 + 16 * q^66 + 30 * q^69 + 92 * q^70 - 72 * q^71 + 30 * q^74 - 13 * q^75 - 4 * q^76 - 32 * q^79 - 73 * q^80 + 30 * q^81 + 78 * q^84 - 29 * q^85 - 60 * q^86 + 94 * q^89 - 140 * q^90 - 128 * q^94 - 41 * q^95 - 36 * q^96 - 152 * q^99

Introduction

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