LMFDB - Embedded newform 833.2.t.d.97.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [833,2,Mod(48,833)] 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("833.48"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.t (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,0,8,0,8,8,0,0,24,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.1
Character	$\chi$	$=$	833.97
Dual form			833.2.t.d.146.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02069 - 2.46415i) q^{2} +(-0.692606 - 1.03656i) q^{3} +(-3.61604 + 3.61604i) q^{4} +(-0.102295 + 0.514273i) q^{5} +(-1.84730 + 2.76469i) q^{6} +(7.67299 + 3.17826i) q^{8} +(0.553301 - 1.33579i) q^{9} +(1.37166 - 0.272840i) q^{10} +(1.40714 - 2.10594i) q^{11} +(6.25272 + 1.24374i) q^{12} +(4.05383 - 4.05383i) q^{13} +(0.603924 - 0.250154i) q^{15} -11.9237i q^{16} +(-3.43012 - 2.28786i) q^{17} -3.85633 q^{18} +(2.11950 - 0.877928i) q^{19} +(-1.48973 - 2.22953i) q^{20} +(-6.62561 - 1.31792i) q^{22} +(5.55766 + 3.71351i) q^{23} +(-2.01991 - 10.1548i) q^{24} +(4.36539 + 1.80820i) q^{25} +(-14.1270 - 5.85158i) q^{26} +(-5.43595 + 1.08128i) q^{27} +(1.43063 - 7.19227i) q^{29} +(-1.23283 - 1.23283i) q^{30} +(-3.99101 + 2.66671i) q^{31} +(-14.0359 + 5.81386i) q^{32} -3.15753 q^{33} +(-2.13656 + 10.7875i) q^{34} +(2.82950 + 6.83101i) q^{36} +(-3.47299 + 2.32058i) q^{37} +(-4.32669 - 4.32669i) q^{38} +(-7.00974 - 1.39432i) q^{39} +(-2.41940 + 3.62089i) q^{40} +(0.585195 + 2.94197i) q^{41} +(0.481907 - 1.16343i) q^{43} +(2.52687 + 12.7034i) q^{44} +(0.630359 + 0.421193i) q^{45} +(3.47803 - 17.4852i) q^{46} +(-4.79985 + 4.79985i) q^{47} +(-12.3596 + 8.25844i) q^{48} -12.6026i q^{50} +(0.00422341 + 5.14010i) q^{51} +29.3176i q^{52} +(-3.83304 - 9.25378i) q^{53} +(8.21283 + 12.2914i) q^{54} +(0.939085 + 0.939085i) q^{55} +(-2.37800 - 1.58893i) q^{57} +(-19.1831 + 3.81575i) q^{58} +(4.43524 - 10.7076i) q^{59} +(-1.27925 + 3.08837i) q^{60} +(-14.9627 + 2.97626i) q^{61} +(10.6447 + 7.11259i) q^{62} +(11.7898 + 11.7898i) q^{64} +(1.67009 + 2.49947i) q^{65} +(3.22284 + 7.78062i) q^{66} +2.63218i q^{67} +(20.6764 - 4.13046i) q^{68} -8.33283i q^{69} +(11.0057 - 7.35375i) q^{71} +(8.49095 - 8.49095i) q^{72} +(-0.581001 + 2.92089i) q^{73} +(9.26308 + 6.18939i) q^{74} +(-1.14919 - 5.77734i) q^{75} +(-4.48959 + 10.8388i) q^{76} +(3.71891 + 18.6962i) q^{78} +(3.51384 - 5.25883i) q^{79} +(6.13205 + 1.21974i) q^{80} +(1.81867 + 1.81867i) q^{81} +(6.65217 - 4.44484i) q^{82} +(-3.82487 - 9.23404i) q^{83} +(1.52747 - 1.52998i) q^{85} -3.35873 q^{86} +(-8.44606 + 3.49847i) q^{87} +(17.4902 - 11.6866i) q^{88} +(-5.73661 - 5.73661i) q^{89} +(0.394484 - 1.98321i) q^{90} +(-33.5249 + 6.66851i) q^{92} +(5.52839 + 2.28993i) q^{93} +(16.7267 + 6.92842i) q^{94} +(0.234679 + 1.17981i) q^{95} +(15.7477 + 10.5223i) q^{96} +(-7.56984 - 1.50573i) q^{97} +(-2.03451 - 3.04487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{3} + 8 q^{5} + 8 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{13} - 40 q^{18} + 24 q^{19} + 24 q^{22} + 8 q^{23} - 24 q^{24} + 8 q^{25} + 8 q^{27} + 80 q^{31} - 40 q^{32} - 80 q^{33} + 120 q^{36} + 48 q^{37}+ \cdots + 40 q^{99}+O(q^{100}) $ 72 * q + 8 * q^3 + 8 * q^5 + 8 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^13 - 40 * q^18 + 24 * q^19 + 24 * q^22 + 8 * q^23 - 24 * q^24 + 8 * q^25 + 8 * q^27 + 80 * q^31 - 40 * q^32 - 80 * q^33 + 120 * q^36 + 48 * q^37 - 56 * q^38 - 16 * q^39 - 32 * q^40 + 24 * q^41 + 24 * q^43 + 32 * q^44 - 48 * q^45 - 40 * q^47 - 40 * q^51 - 24 * q^53 + 200 * q^54 - 48 * q^57 + 32 * q^58 + 8 * q^59 - 80 * q^60 + 128 * q^62 - 24 * q^65 - 8 * q^66 - 40 * q^68 - 48 * q^73 - 32 * q^74 + 128 * q^75 + 72 * q^76 - 48 * q^78 - 32 * q^79 + 256 * q^80 + 16 * q^81 - 152 * q^82 - 32 * q^85 - 80 * q^86 - 64 * q^87 + 56 * q^88 - 64 * q^89 - 376 * q^90 - 216 * q^92 - 32 * q^93 - 128 * q^94 + 32 * q^95 + 32 * q^96 - 8 * q^97 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$-1$	$e\left(\frac{13}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.02069	−	2.46415i	−0.721734	−	1.74242i	−0.668353	−	0.743845i	$-0.733000\pi$
$2$	−1.02069	−	2.46415i	−0.721734	−	1.74242i	−0.0533810	−	0.998574i	$-0.517000\pi$
$3$	−0.692606	−	1.03656i	−0.399876	−	0.598457i	0.575822	−	0.817575i	$-0.304682\pi$
$3$	−0.692606	−	1.03656i	−0.399876	−	0.598457i	−0.975698	+	0.219118i	$0.929682\pi$
$4$	−3.61604	+	3.61604i	−1.80802	+	1.80802i
$5$	−0.102295	+	0.514273i	−0.0457478	+	0.229990i	−0.996894	−	0.0787498i	$-0.974907\pi$
$5$	−0.102295	+	0.514273i	−0.0457478	+	0.229990i	0.951147	+	0.308740i	$0.0999072\pi$
$6$	−1.84730	+	2.76469i	−0.754159	+	1.12868i
$7$		0			0
$7$		0			0
$8$	7.67299	+	3.17826i	2.71281	+	1.12368i
$9$	0.553301	−	1.33579i	0.184434	−	0.445262i
$10$	1.37166	−	0.272840i	0.433757	−	0.0862795i
$11$	1.40714	−	2.10594i	0.424270	−	0.634965i	−0.556335	−	0.830958i	$-0.687793\pi$
$11$	1.40714	−	2.10594i	0.424270	−	0.634965i	0.980605	+	0.195993i	$0.0627929\pi$
$12$	6.25272	+	1.24374i	1.80500	+	0.359037i
$13$	4.05383	−	4.05383i	1.12433	−	1.12433i	0.133249	−	0.991083i	$-0.457459\pi$
$13$	4.05383	−	4.05383i	1.12433	−	1.12433i	0.991083	−	0.133249i	$-0.0425409\pi$
$14$		0			0
$15$	0.603924	−	0.250154i	0.155933	−	0.0645894i
$16$		−	11.9237i		−	2.98093i
$17$	−3.43012	−	2.28786i	−0.831926	−	0.554887i
$17$	−3.43012	−	2.28786i	−0.831926	−	0.554887i
$18$	−3.85633			−0.908946
$19$	2.11950	−	0.877928i	0.486248	−	0.201410i	−0.126071	−	0.992021i	$-0.540237\pi$
$19$	2.11950	−	0.877928i	0.486248	−	0.201410i	0.612319	+	0.790611i	$0.290237\pi$
$20$	−1.48973	−	2.22953i	−0.333113	−	0.498539i
$21$		0			0
$22$	−6.62561	−	1.31792i	−1.41259	−	0.280981i
$23$	5.55766	+	3.71351i	1.15885	+	0.774320i	0.977880	−	0.209168i	$-0.0670755\pi$
$23$	5.55766	+	3.71351i	1.15885	+	0.774320i	0.180972	+	0.983488i	$0.442076\pi$
$24$	−2.01991	−	10.1548i	−0.412313	−	2.07283i
$25$	4.36539	+	1.80820i	0.873077	+	0.361640i
$26$	−14.1270	−	5.85158i	−2.77052	−	1.14759i
$27$	−5.43595	+	1.08128i	−1.04615	+	0.208092i
$28$		0			0
$29$	1.43063	−	7.19227i	0.265661	−	1.33557i	−0.585503	−	0.810671i	$-0.699103\pi$
$29$	1.43063	−	7.19227i	0.265661	−	1.33557i	0.851164	−	0.524900i	$-0.175897\pi$
$30$	−1.23283	−	1.23283i	−0.225083	−	0.225083i
$31$	−3.99101	+	2.66671i	−0.716807	+	0.478955i	−0.859710	−	0.510782i	$-0.829356\pi$
$31$	−3.99101	+	2.66671i	−0.716807	+	0.478955i	0.142904	+	0.989737i	$0.454356\pi$
$32$	−14.0359	+	5.81386i	−2.48122	+	1.02775i
$33$	−3.15753			−0.549655
$34$	−2.13656	+	10.7875i	−0.366417	+	1.85004i
$35$		0			0
$36$	2.82950	+	6.83101i	0.471583	+	1.13850i
$37$	−3.47299	+	2.32058i	−0.570955	+	0.381500i	−0.807275	−	0.590175i	$-0.799059\pi$
$37$	−3.47299	+	2.32058i	−0.570955	+	0.381500i	0.236320	+	0.971675i	$0.424059\pi$
$38$	−4.32669	−	4.32669i	−0.701883	−	0.701883i
$39$	−7.00974	−	1.39432i	−1.12246	−	0.223271i
$40$	−2.41940	+	3.62089i	−0.382541	+	0.572513i
$41$	0.585195	+	2.94197i	0.0913920	+	0.459459i	0.999197	+	0.0400663i	$0.0127569\pi$
$41$	0.585195	+	2.94197i	0.0913920	+	0.459459i	−0.907805	+	0.419393i	$0.862243\pi$
$42$		0			0
$43$	0.481907	−	1.16343i	0.0734901	−	0.177421i	−0.882866	−	0.469626i	$-0.844389\pi$
$43$	0.481907	−	1.16343i	0.0734901	−	0.177421i	0.956356	+	0.292205i	$0.0943889\pi$
$44$	2.52687	+	12.7034i	0.380940	+	1.91512i
$45$	0.630359	+	0.421193i	0.0939684	+	0.0627877i
$46$	3.47803	−	17.4852i	0.512808	−	2.57806i
$47$	−4.79985	+	4.79985i	−0.700130	+	0.700130i	−0.964438	−	0.264308i	$-0.914856\pi$
$47$	−4.79985	+	4.79985i	−0.700130	+	0.700130i	0.264308	+	0.964438i	$0.414856\pi$
$48$	−12.3596	+	8.25844i	−1.78396	+	1.19200i
$49$		0			0
$50$		−	12.6026i		−	1.78227i
$51$	0.00422341	+	5.14010i	0.000591396	+	0.719758i
$52$			29.3176i			4.06562i
$53$	−3.83304	−	9.25378i	−0.526509	−	1.27110i	−0.933796	−	0.357805i	$-0.883525\pi$
$53$	−3.83304	−	9.25378i	−0.526509	−	1.27110i	0.407287	−	0.913300i	$-0.366475\pi$
$54$	8.21283	+	12.2914i	1.11762	+	1.67264i
$55$	0.939085	+	0.939085i	0.126626	+	0.126626i
$56$		0			0
$57$	−2.37800	−	1.58893i	−0.314974	−	0.210459i
$58$	−19.1831	+	3.81575i	−2.51886	+	0.501032i
$59$	4.43524	−	10.7076i	0.577420	−	1.39401i	−0.317701	−	0.948191i	$-0.602911\pi$
$59$	4.43524	−	10.7076i	0.577420	−	1.39401i	0.895121	−	0.445823i	$-0.147089\pi$
$60$	−1.27925	+	3.08837i	−0.165150	+	0.398707i
$61$	−14.9627	+	2.97626i	−1.91577	+	0.381071i	−0.999797	−	0.0201607i	$-0.993582\pi$
$61$	−14.9627	+	2.97626i	−1.91577	+	0.381071i	−0.915977	+	0.401232i	$0.868582\pi$
$62$	10.6447	+	7.11259i	1.35188	+	0.903299i
$63$		0			0
$64$	11.7898	+	11.7898i	1.47372	+	1.47372i
$65$	1.67009	+	2.49947i	0.207149	+	0.310021i
$66$	3.22284	+	7.78062i	0.396704	+	0.957729i
$67$			2.63218i			0.321571i	0.986989	+	0.160786i	$0.0514028\pi$
$67$			2.63218i			0.321571i	−0.986989	+	0.160786i	$0.948597\pi$
$68$	20.6764	−	4.13046i	2.50738	−	0.500891i
$69$		−	8.33283i		−	1.00316i
$70$		0			0
$71$	11.0057	−	7.35375i	1.30613	−	0.872729i	0.309199	−	0.950997i	$-0.399939\pi$
$71$	11.0057	−	7.35375i	1.30613	−	0.872729i	0.996932	+	0.0782678i	$0.0249389\pi$
$72$	8.49095	−	8.49095i	1.00067	−	1.00067i
$73$	−0.581001	+	2.92089i	−0.0680011	+	0.341864i	−0.999776	−	0.0211724i	$-0.993260\pi$
$73$	−0.581001	+	2.92089i	−0.0680011	+	0.341864i	0.931775	+	0.363037i	$0.118260\pi$
$74$	9.26308	+	6.18939i	1.07681	+	0.719502i
$75$	−1.14919	−	5.77734i	−0.132696	−	0.667110i
$76$	−4.48959	+	10.8388i	−0.514991	+	1.24330i
$77$		0			0
$78$	3.71891	+	18.6962i	0.421084	+	2.11693i
$79$	3.51384	−	5.25883i	0.395338	−	0.591665i	−0.579393	−	0.815048i	$-0.696710\pi$
$79$	3.51384	−	5.25883i	0.395338	−	0.591665i	0.974731	+	0.223384i	$0.0717103\pi$
$80$	6.13205	+	1.21974i	0.685584	+	0.136371i
$81$	1.81867	+	1.81867i	0.202075	+	0.202075i
$82$	6.65217	−	4.44484i	0.734609	−	0.490850i
$83$	−3.82487	−	9.23404i	−0.419834	−	1.01357i	−0.982396	−	0.186813i	$-0.940184\pi$
$83$	−3.82487	−	9.23404i	−0.419834	−	1.01357i	0.562562	−	0.826755i	$-0.309816\pi$
$84$		0			0
$85$	1.52747	−	1.52998i	0.165677	−	0.165950i
$86$	−3.35873			−0.362182
$87$	−8.44606	+	3.49847i	−0.905513	+	0.375076i
$88$	17.4902	−	11.6866i	1.86446	−	1.24580i
$89$	−5.73661	−	5.73661i	−0.608080	−	0.608080i	0.334364	−	0.942444i	$-0.391478\pi$
$89$	−5.73661	−	5.73661i	−0.608080	−	0.608080i	−0.942444	+	0.334364i	$0.891478\pi$
$90$	0.394484	−	1.98321i	0.0415823	−	0.209048i
$91$		0			0
$92$	−33.5249	+	6.66851i	−3.49521	+	0.695240i
$93$	5.52839	+	2.28993i	0.573268	+	0.237455i
$94$	16.7267	+	6.92842i	1.72523	+	0.714612i
$95$	0.234679	+	1.17981i	0.0240776	+	0.121046i
$96$	15.7477	+	10.5223i	1.60725	+	1.07393i
$97$	−7.56984	−	1.50573i	−0.768600	−	0.152884i	−0.204810	−	0.978802i	$-0.565658\pi$
$97$	−7.56984	−	1.50573i	−0.768600	−	0.152884i	−0.563791	+	0.825918i	$0.690658\pi$
$98$		0			0
$99$	−2.03451	−	3.04487i	−0.204476	−	0.306021i
$100$	−22.3239	+	9.24686i	−2.23239	+	0.924686i
$101$	5.70587			0.567755			0.283878	−	0.958861i	$-0.408379\pi$
$101$	5.70587			0.567755			0.283878	+	0.958861i	$0.408379\pi$
$102$	12.6617	−	5.25683i	1.25369	−	0.520504i
$103$			2.22146i			0.218887i	0.993993	+	0.109444i	$0.0349069\pi$
$103$			2.22146i			0.218887i	−0.993993	+	0.109444i	$0.965093\pi$
$104$	43.9892	−	18.2209i	4.31349	−	1.78671i
$105$		0			0
$106$	−18.8904	+	18.8904i	−1.83480	+	1.83480i
$107$	−1.57868	−	0.314019i	−0.152617	−	0.0303574i	0.118191	−	0.992991i	$-0.462291\pi$
$107$	−1.57868	−	0.314019i	−0.152617	−	0.0303574i	−0.270807	+	0.962634i	$0.587291\pi$
$108$	15.7466	−	23.5665i	1.51522	−	2.26769i
$109$	−5.49616	+	1.09325i	−0.526437	+	0.104715i	−0.451152	−	0.892447i	$-0.648987\pi$
$109$	−5.49616	+	1.09325i	−0.526437	+	0.104715i	−0.0752851	+	0.997162i	$0.523987\pi$
$110$	1.35554	−	3.27256i	0.129245	−	0.312026i
$111$	4.81082	+	1.99271i	0.456623	+	0.189139i
$112$		0			0
$113$	−4.96537	+	7.43120i	−0.467103	+	0.699069i	−0.987983	−	0.154561i	$-0.950604\pi$
$113$	−4.96537	+	7.43120i	−0.467103	+	0.699069i	0.520880	+	0.853630i	$0.325604\pi$
$114$	−1.48818	+	7.48156i	−0.139380	+	0.700712i
$115$	−2.47828	+	2.47828i	−0.231101	+	0.231101i
$116$	20.8343	+	31.1807i	1.93441	+	2.89506i
$117$	−3.17207	−	7.65805i	−0.293258	−	0.707987i
$118$	−30.9122			−2.84570
$119$		0			0
$120$	5.42896			0.495594
$121$	1.75459	+	4.23595i	0.159508	+	0.385086i
$122$	22.6061	+	33.8325i	2.04666	+	3.06305i
$123$	2.64421	−	2.64421i	0.238421	−	0.238421i
$124$	4.78872	−	24.0745i	0.430040	−	2.16196i
$125$	−2.83303	+	4.23993i	−0.253394	+	0.379231i
$126$		0			0
$127$	0.610283	+	0.252788i	0.0541539	+	0.0224313i	0.409596	−	0.912267i	$-0.365670\pi$
$127$	0.610283	+	0.252788i	0.0541539	+	0.0224313i	−0.355442	+	0.934698i	$0.615670\pi$
$128$	5.39044	−	13.0137i	0.476452	−	1.15026i
$129$	−1.53973	+	0.306271i	−0.135566	+	0.0269657i
$130$	4.45443	−	6.66652i	0.390679	−	0.584693i
$131$	17.6974	+	3.52023i	1.54623	+	0.307564i	0.893161	−	0.449736i	$-0.148482\pi$
$131$	17.6974	+	3.52023i	1.54623	+	0.307564i	0.653067	+	0.757300i	$0.273482\pi$
$132$	11.4177	−	11.4177i	0.993785	−	0.993785i
$133$		0			0
$134$	6.48608	−	2.68662i	0.560312	−	0.232089i
$135$		−	2.90617i		−	0.250123i
$136$	−19.0479	−	28.4565i	−1.63334	−	2.44012i
$137$	−11.4978			−0.982325			−0.491162	−	0.871068i	$-0.663428\pi$
$137$	−11.4978			−0.982325			−0.491162	+	0.871068i	$0.663428\pi$
$138$	−20.5334	+	8.50520i	−1.74792	+	0.724011i
$139$	9.17849	+	13.7366i	0.778509	+	1.16512i	0.982521	+	0.186153i	$0.0596020\pi$
$139$	9.17849	+	13.7366i	0.778509	+	1.16512i	−0.204011	+	0.978968i	$0.565398\pi$
$140$		0			0
$141$	8.29972	+	1.65092i	0.698963	+	0.139032i
$142$	−29.3541	−	19.6138i	−2.46334	−	1.64595i
$143$	−2.83280	−	14.2415i	−0.236891	−	1.19093i
$144$	−15.9276	−	6.59741i	−1.32730	−	0.549784i
$145$	3.55244	+	1.47147i	0.295014	+	0.122199i
$146$	7.79054	−	1.54963i	0.644750	−	0.128249i
$147$		0			0
$148$	4.16716	−	20.9497i	0.342538	−	1.72206i
$149$	10.0620	+	10.0620i	0.824313	+	0.824313i	0.986723	−	0.162410i	$-0.0519269\pi$
$149$	10.0620	+	10.0620i	0.824313	+	0.824313i	−0.162410	+	0.986723i	$0.551927\pi$
$150$	−13.0633	+	8.72862i	−1.06661	+	0.712689i
$151$	−0.272569	+	0.112902i	−0.0221813	+	0.00918781i	−0.393747	−	0.919219i	$-0.628821\pi$
$151$	−0.272569	+	0.112902i	−0.0221813	+	0.00918781i	0.371565	+	0.928407i	$0.378821\pi$
$152$	19.0532			1.54542
$153$	−4.95398	+	3.31603i	−0.400505	+	0.268085i
$154$		0			0
$155$	−0.963154	−	2.32526i	−0.0773624	−	0.186769i
$156$	30.3894	−	20.3055i	2.43310	−	1.62574i
$157$	−4.29582	−	4.29582i	−0.342844	−	0.342844i	0.514592	−	0.857435i	$-0.327944\pi$
$157$	−4.29582	−	4.29582i	−0.342844	−	0.342844i	−0.857435	+	0.514592i	$0.827944\pi$
$158$	−16.5451	−	3.29102i	−1.31626	−	0.261820i
$159$	−6.93729	+	10.3824i	−0.550163	+	0.823377i
$160$	−1.55411	−	7.81302i	−0.122863	−	0.617673i
$161$		0			0
$162$	2.62520	−	6.33778i	0.206255	−	0.497943i
$163$	−0.866053	−	4.35394i	−0.0678345	−	0.341027i	0.931932	−	0.362633i	$-0.118122\pi$
$163$	−0.866053	−	4.35394i	−0.0678345	−	0.341027i	−0.999767	+	0.0216057i	$0.993122\pi$
$164$	−12.7544	−	8.52219i	−0.995948	−	0.665471i
$165$	0.323000	−	1.62383i	0.0251455	−	0.126415i
$166$	−18.8501	+	18.8501i	−1.46305	+	1.46305i
$167$	4.06684	−	2.71737i	0.314701	−	0.210277i	−0.388180	−	0.921583i	$-0.626896\pi$
$167$	4.06684	−	2.71737i	0.314701	−	0.210277i	0.702882	+	0.711307i	$0.251896\pi$
$168$		0			0
$169$		−	19.8672i		−	1.52824i
$170$	−5.32917	−	2.20229i	−0.408729	−	0.168908i
$171$		−	3.31697i		−	0.253655i
$172$	2.46440	+	5.94958i	0.187909	+	0.453651i
$173$	−12.0740	−	18.0700i	−0.917967	−	1.37383i	−0.927477	−	0.373880i	$-0.878027\pi$
$173$	−12.0740	−	18.0700i	−0.917967	−	1.37383i	0.00951025	−	0.999955i	$-0.496973\pi$
$174$	17.2415	+	17.2415i	1.30708	+	1.30708i
$175$		0			0
$176$	−25.1107	−	16.7784i	−1.89279	−	1.26472i
$177$	−14.1709	+	2.81878i	−1.06515	+	0.211872i
$178$	−8.28061	+	19.9912i	−0.620658	+	1.49840i
$179$	−4.66114	+	11.2530i	−0.348390	+	0.841088i	0.648420	+	0.761283i	$0.275430\pi$
$179$	−4.66114	+	11.2530i	−0.348390	+	0.841088i	−0.996810	+	0.0798057i	$0.974570\pi$
$180$	−3.80245	+	0.756354i	−0.283418	+	0.0563753i
$181$	−8.58766	−	5.73809i	−0.638316	−	0.426509i	0.193854	−	0.981030i	$-0.437901\pi$
$181$	−8.58766	−	5.73809i	−0.638316	−	0.426509i	−0.832169	+	0.554521i	$0.812901\pi$
$182$		0			0
$183$	13.4483	+	13.4483i	0.994126	+	0.994126i
$184$	30.8414	+	46.1574i	2.27366	+	3.40277i
$185$	−0.838139	−	2.02345i	−0.0616212	−	0.148767i
$186$		−	15.9601i		−	1.17025i
$187$	−9.64477	+	4.00428i	−0.705295	+	0.292822i
$188$		−	34.7128i		−	2.53169i
$189$		0			0
$190$	2.66770	−	1.78250i	0.193536	−	0.129316i
$191$	12.1229	−	12.1229i	0.877184	−	0.877184i	−0.116058	−	0.993242i	$-0.537026\pi$
$191$	12.1229	−	12.1229i	0.877184	−	0.877184i	0.993242	+	0.116058i	$0.0370259\pi$
$192$	4.05512	−	20.3865i	0.292653	−	1.47127i
$193$	−2.10219	−	1.40464i	−0.151319	−	0.101108i	0.477606	−	0.878574i	$-0.341505\pi$
$193$	−2.10219	−	1.40464i	−0.151319	−	0.101108i	−0.628925	+	0.777466i	$0.716505\pi$
$194$	4.01606	+	20.1901i	0.288336	+	1.44957i
$195$	1.43413	−	3.46229i	0.102700	−	0.247940i
$196$		0			0
$197$	−0.226605	−	1.13922i	−0.0161450	−	0.0811662i	0.971873	−	0.235506i	$-0.0756748\pi$
$197$	−0.226605	−	1.13922i	−0.0161450	−	0.0811662i	−0.988018	+	0.154340i	$0.950675\pi$
$198$	−5.42641	+	8.12120i	−0.385638	+	0.577149i
$199$	17.1825	+	3.41781i	1.21804	+	0.242282i	0.761940	−	0.647648i	$-0.224247\pi$
$199$	17.1825	+	3.41781i	1.21804	+	0.242282i	0.456096	+	0.889930i	$0.349247\pi$
$200$	27.7486	+	27.7486i	1.96212	+	1.96212i
$201$	2.72840	−	1.82306i	0.192447	−	0.128589i
$202$	−5.82390	−	14.0601i	−0.409768	−	0.989268i
$203$		0			0
$204$	−18.6020	−	18.5715i	−1.30240	−	1.30027i
$205$	−1.57284			−0.109852
$206$	5.47403	−	2.26742i	0.381393	−	0.157978i
$207$	8.03552	−	5.36916i	0.558507	−	0.373182i
$208$	−48.3368	−	48.3368i	−3.35156	−	3.35156i
$209$	1.13359	−	5.69892i	0.0784118	−	0.394203i
$210$		0			0
$211$	−25.4539	+	5.06309i	−1.75232	+	0.348558i	−0.963835	−	0.266498i	$-0.914133\pi$
$211$	−25.4539	+	5.06309i	−1.75232	+	0.348558i	−0.788483	+	0.615056i	$0.789133\pi$
$212$	47.3224	+	19.6016i	3.25012	+	1.34624i
$213$	−15.2452	−	6.31476i	−1.04458	−	0.432680i
$214$	0.837545	+	4.21062i	0.0572534	+	0.287832i
$215$	0.549022	+	0.366845i	0.0374430	+	0.0250186i
$216$	−45.1466	−	8.98021i	−3.07183	−	0.611026i
$217$		0			0
$218$	8.30380	+	12.4275i	0.562404	+	0.841697i
$219$	3.43008	−	1.42078i	0.231783	−	0.0960077i
$220$	−6.79153			−0.457885
$221$	−23.1797	+	4.63054i	−1.55924	+	0.311484i
$222$		−	13.8885i		−	0.932136i
$223$	−4.08926	+	1.69383i	−0.273837	+	0.113427i	−0.515376	−	0.856964i	$-0.672348\pi$
$223$	−4.08926	+	1.69383i	−0.273837	+	0.113427i	0.241539	+	0.970391i	$0.422348\pi$
$224$		0			0
$225$	4.83075	−	4.83075i	0.322050	−	0.322050i
$226$	23.3797	+	4.65051i	1.55519	+	0.309347i
$227$	8.42280	−	12.6056i	0.559041	−	0.836664i	−0.439048	−	0.898464i	$-0.644684\pi$
$227$	8.42280	−	12.6056i	0.559041	−	0.836664i	0.998089	+	0.0618000i	$0.0196841\pi$
$228$	14.3446	−	2.85331i	0.949993	−	0.188965i
$229$	5.53344	−	13.3589i	0.365660	−	0.882782i	−0.628790	−	0.777575i	$-0.716449\pi$
$229$	5.53344	−	13.3589i	0.365660	−	0.882782i	0.994450	−	0.105207i	$-0.0335505\pi$
$230$	8.63640	+	3.57732i	0.569468	+	0.235881i
$231$		0			0
$232$	33.8361	−	50.6393i	2.22145	−	3.32463i
$233$	2.36356	−	11.8824i	0.154842	−	0.778443i	−0.822827	−	0.568292i	$-0.807604\pi$
$233$	2.36356	−	11.8824i	0.154842	−	0.778443i	0.977669	−	0.210151i	$-0.0673956\pi$
$234$	−15.6329	+	15.6329i	−1.02196	+	1.02196i
$235$	−1.97743	−	2.95943i	−0.128993	−	0.193052i
$236$	22.6812	+	54.7572i	1.47642	+	3.56439i
$237$	−7.88478			−0.512172
$238$		0			0
$239$	1.05884			0.0684908			0.0342454	−	0.999413i	$-0.489097\pi$
$239$	1.05884			0.0684908			0.0342454	+	0.999413i	$0.489097\pi$
$240$	−2.98276	−	7.20102i	−0.192536	−	0.464824i
$241$	−7.51926	−	11.2534i	−0.484358	−	0.724893i	0.506135	−	0.862454i	$-0.331074\pi$
$241$	−7.51926	−	11.2534i	−0.484358	−	0.724893i	−0.990493	+	0.137561i	$0.956074\pi$
$242$	8.64714	−	8.64714i	0.555859	−	0.555859i
$243$	−2.61830	+	13.1631i	−0.167964	+	0.844411i
$244$	43.3433	−	64.8678i	2.77477	−	4.15273i
$245$		0			0
$246$	−9.21466	−	3.81684i	−0.587505	−	0.243353i
$247$	5.03315	−	12.1511i	0.320252	−	0.773156i
$248$	−39.0985	+	7.77717i	−2.48275	+	0.493851i
$249$	−6.92249	+	10.3602i	−0.438695	+	0.656554i
$250$	13.3395	+	2.65338i	0.843662	+	0.167815i
$251$	−0.872746	+	0.872746i	−0.0550873	+	0.0550873i	−0.734114	−	0.679026i	$-0.762402\pi$
$251$	−0.872746	+	0.872746i	−0.0550873	+	0.0550873i	0.679026	+	0.734114i	$0.262402\pi$
$252$		0			0
$253$	15.6409	−	6.47866i	0.983333	−	0.407310i
$254$		−	1.76185i		−	0.110548i
$255$	−2.64385	−	0.523636i	−0.165564	−	0.0327913i
$256$	−4.22307			−0.263942
$257$	1.52849	−	0.633123i	0.0953448	−	0.0394931i	−0.334501	−	0.942395i	$-0.608568\pi$
$257$	1.52849	−	0.633123i	0.0953448	−	0.0394931i	0.429846	+	0.902902i	$0.358568\pi$
$258$	2.32628	+	3.48152i	0.144828	+	0.216750i
$259$		0			0
$260$	−15.0773	−	2.99905i	−0.935052	−	0.185993i
$261$	−8.81577	−	5.89051i	−0.545682	−	0.364613i
$262$	−9.38909	−	47.2021i	−0.580060	−	2.91616i
$263$	5.22916	+	2.16599i	0.322444	+	0.133561i	0.538033	−	0.842923i	$-0.319167\pi$
$263$	5.22916	+	2.16599i	0.322444	+	0.133561i	−0.215590	+	0.976484i	$0.569167\pi$
$264$	−24.2277	−	10.0354i	−1.49111	−	0.617638i
$265$	5.15107	−	1.02461i	0.316428	−	0.0629414i
$266$		0			0
$267$	−1.97312	+	9.91954i	−0.120753	+	0.607066i
$268$	−9.51804	−	9.51804i	−0.581407	−	0.581407i
$269$	−1.77974	+	1.18918i	−0.108513	+	0.0725059i	−0.608642	−	0.793445i	$-0.708286\pi$
$269$	−1.77974	+	1.18918i	−0.108513	+	0.0725059i	0.500130	+	0.865950i	$0.333286\pi$
$270$	−7.16125	+	2.96629i	−0.435820	+	0.180522i
$271$	30.4013			1.84675			0.923374	−	0.383902i	$-0.125420\pi$
$271$	30.4013			1.84675			0.923374	+	0.383902i	$0.125420\pi$
$272$	−27.2798	+	40.8998i	−1.65408	+	2.47991i
$273$		0			0
$274$	11.7357	+	28.3324i	0.708977	+	1.71162i
$275$	9.95070	−	6.64884i	0.600050	−	0.400940i
$276$	30.1318	+	30.1318i	1.81372	+	1.81372i
$277$	21.5768	+	4.29189i	1.29642	+	0.257875i	0.794620	−	0.607107i	$-0.207670\pi$
$277$	21.5768	+	4.29189i	1.29642	+	0.257875i	0.501804	+	0.864982i	$0.332670\pi$
$278$	24.4807	−	36.6379i	1.46825	−	2.19740i
$279$	1.35392	+	6.80663i	0.0810573	+	0.407502i
$280$		0			0
$281$	−6.87792	+	16.6048i	−0.410303	+	0.990558i	0.574754	+	0.818326i	$0.305098\pi$
$281$	−6.87792	+	16.6048i	−0.410303	+	0.990558i	−0.985056	+	0.172232i	$0.944902\pi$
$282$	−4.40329	−	22.1368i	−0.262212	−	1.31823i
$283$	−1.66012	−	1.10925i	−0.0986837	−	0.0659384i	0.505249	−	0.862973i	$-0.331401\pi$
$283$	−1.66012	−	1.10925i	−0.0986837	−	0.0659384i	−0.603933	+	0.797035i	$0.706401\pi$
$284$	−13.2054	+	66.3883i	−0.783599	+	3.93942i
$285$	1.06040	−	1.06040i	0.0628129	−	0.0628129i
$286$	−32.2017	+	21.5165i	−1.90413	+	1.27230i
$287$		0			0
$288$			21.9658i			1.29435i
$289$	6.53142	+	15.6952i	0.384201	+	0.923249i
$290$		−	10.2557i		−	0.602233i
$291$	3.68213	+	8.88945i	0.215850	+	0.521109i
$292$	−8.46112	−	12.6630i	−0.495150	−	0.741044i
$293$	12.2233	+	12.2233i	0.714095	+	0.714095i	0.967389	−	0.253295i	$-0.0815142\pi$
$293$	12.2233	+	12.2233i	0.714095	+	0.714095i	−0.253295	+	0.967389i	$0.581514\pi$
$294$		0			0
$295$	5.05294	+	3.37627i	0.294194	+	0.196574i
$296$	−34.0236	+	6.76771i	−1.97758	+	0.393365i
$297$	−5.37206	+	12.9693i	−0.311719	+	0.752555i
$298$	14.5242	−	35.0645i	0.841364	−	2.03123i
$299$	37.5838	−	7.47588i	2.17353	−	0.432341i
$300$	25.0466	+	16.7356i	1.44606	+	0.966229i
$301$		0			0
$302$	0.556414	+	0.556414i	0.0320180	+	0.0320180i
$303$	−3.95192	−	5.91446i	−0.227032	−	0.339777i
$304$	−10.4682	−	25.2724i	−0.600391	−	1.44947i
$305$		−	7.99935i		−	0.458042i
$306$	13.2277	+	8.82273i	0.756175	+	0.504362i
$307$			12.1777i			0.695018i	0.937677	+	0.347509i	$0.112972\pi$
$307$			12.1777i			0.695018i	−0.937677	+	0.347509i	$0.887028\pi$
$308$		0			0
$309$	2.30268	−	1.53860i	0.130995	−	0.0875278i
$310$	−4.74672	+	4.74672i	−0.269596	+	0.269596i
$311$	−0.751928	+	3.78020i	−0.0426379	+	0.214355i	−0.996231	−	0.0867444i	$-0.972354\pi$
$311$	−0.751928	+	3.78020i	−0.0426379	+	0.214355i	0.953593	+	0.301100i	$0.0973537\pi$
$312$	−49.3542	−	32.9774i	−2.79413	−	1.86698i
$313$	1.25834	+	6.32612i	0.0711258	+	0.357574i	0.999915	−	0.0130348i	$-0.00414921\pi$
$313$	1.25834	+	6.32612i	0.0711258	+	0.357574i	−0.928789	+	0.370608i	$0.879149\pi$
$314$	−6.20088	+	14.9702i	−0.349936	+	0.844820i
$315$		0			0
$316$	6.30995	+	31.7223i	0.354963	+	1.78452i
$317$	−0.579214	+	0.866855i	−0.0325319	+	0.0486874i	−0.847379	−	0.530988i	$-0.821821\pi$
$317$	−0.579214	+	0.866855i	−0.0325319	+	0.0486874i	0.814847	+	0.579676i	$0.196821\pi$
$318$	32.6646	+	6.49739i	1.83174	+	0.364356i
$319$	−13.1334	−	13.1334i	−0.735328	−	0.735328i
$320$	−7.26920	+	4.85713i	−0.406361	+	0.271522i
$321$	0.767904	+	1.85388i	0.0428602	+	0.103474i
$322$		0			0
$323$	−9.27872	−	1.83773i	−0.516282	−	0.102254i
$324$	−13.1528			−0.730710
$325$	25.0267	−	10.3664i	1.38823	−	0.575024i
$326$	−9.84482	+	6.57810i	−0.545254	+	0.364327i
$327$	4.93990	+	4.93990i	0.273177	+	0.273177i
$328$	−4.86015	+	24.4336i	−0.268357	+	1.34912i
$329$		0			0
$330$	−4.33105	+	0.861499i	−0.238416	+	0.0474240i
$331$	−17.3310	−	7.17873i	−0.952597	−	0.394578i	−0.148391	−	0.988929i	$-0.547409\pi$
$331$	−17.3310	−	7.17873i	−0.952597	−	0.394578i	−0.804206	+	0.594350i	$0.797409\pi$
$332$	47.2215	+	19.5598i	2.59161	+	1.07348i
$333$	1.17819	+	5.92315i	0.0645643	+	0.324586i
$334$	−10.8470	−	7.24773i	−0.593521	−	0.396578i
$335$	−1.35366	−	0.269259i	−0.0739582	−	0.0147112i
$336$		0			0
$337$	14.4914	+	21.6879i	0.789396	+	1.18141i	0.979853	+	0.199718i	$0.0640028\pi$
$337$	14.4914	+	21.6879i	0.789396	+	1.18141i	−0.190458	+	0.981695i	$0.560997\pi$
$338$	−48.9557	+	20.2781i	−2.66284	+	1.10298i
$339$	11.1419			0.605146
$340$	0.00908414	+	11.0558i	0.000492657	+	0.599587i
$341$			12.1573i			0.658353i
$342$	−8.17351	+	3.38558i	−0.441973	+	0.183071i
$343$		0			0
$344$	7.39533	−	7.39533i	0.398730	−	0.398730i
$345$	4.28535	+	0.852409i	0.230716	+	0.0458922i
$346$	−32.2034	+	48.1959i	−1.73127	+	2.59103i
$347$	3.36280	−	0.668902i	0.180524	−	0.0359085i	−0.104000	−	0.994577i	$-0.533164\pi$
$347$	3.36280	−	0.668902i	0.180524	−	0.0359085i	0.284525	+	0.958669i	$0.408164\pi$
$348$	17.8907	−	43.1919i	0.959040	−	2.31533i
$349$	20.9877	+	8.69339i	1.12345	+	0.465346i	0.865548	−	0.500826i	$-0.166970\pi$
$349$	20.9877	+	8.69339i	1.12345	+	0.465346i	0.257897	+	0.966172i	$0.416970\pi$
$350$		0			0
$351$	−17.6531	+	26.4198i	−0.942254	+	1.41018i
$352$	−7.50690	+	37.7397i	−0.400119	+	2.01153i
$353$	4.12105	−	4.12105i	0.219341	−	0.219341i	−0.588880	−	0.808221i	$-0.700431\pi$
$353$	4.12105	−	4.12105i	0.219341	−	0.219341i	0.808221	+	0.588880i	$0.200431\pi$
$354$	21.4100	+	32.0423i	1.13793	+	1.70303i
$355$	2.65601	+	6.41217i	0.140966	+	0.340323i
$356$	41.4876			2.19884
$357$		0			0
$358$	32.4867			1.71697
$359$	−7.30017	−	17.6242i	−0.385288	−	0.930169i	−0.990924	−	0.134426i	$-0.957081\pi$
$359$	−7.30017	−	17.6242i	−0.385288	−	0.930169i	0.605635	−	0.795742i	$-0.292919\pi$
$360$	3.49808	+	5.23525i	0.184365	+	0.275922i
$361$	−9.71349	+	9.71349i	−0.511236	+	0.511236i
$362$	−5.37423	+	27.0181i	−0.282463	+	1.42004i
$363$	3.17557	−	4.75257i	0.166674	−	0.249445i
$364$		0			0
$365$	−1.44270	−	0.597587i	−0.0755145	−	0.0312791i
$366$	19.4122	−	46.8651i	1.01469	−	2.44968i
$367$	−17.1605	+	3.41344i	−0.895773	+	0.178180i	−0.621447	−	0.783456i	$-0.713455\pi$
$367$	−17.1605	+	3.41344i	−0.895773	+	0.178180i	−0.274326	+	0.961637i	$0.588455\pi$
$368$	44.2789	−	66.2680i	2.30820	−	3.45446i
$369$	4.25364	+	0.846101i	0.221436	+	0.0440463i
$370$	−4.13061	+	4.13061i	−0.214740	+	0.214740i
$371$		0			0
$372$	−28.2713	+	11.7104i	−1.46580	+	0.607155i
$373$		−	21.6151i		−	1.11919i	−0.828767	−	0.559594i	$-0.810957\pi$
$373$		−	21.6151i		−	1.11919i	0.828767	−	0.559594i	$-0.189043\pi$
$374$	19.7114	+	19.6791i	1.01925	+	1.01758i
$375$	6.35710			0.328279
$376$	−52.0843	+	21.5740i	−2.68604	+	1.11260i
$377$	−23.3567	−	34.9558i	−1.20293	−	1.80032i
$378$		0			0
$379$	4.13312	+	0.822129i	0.212304	+	0.0422299i	0.300096	−	0.953909i	$-0.402981\pi$
$379$	4.13312	+	0.822129i	0.212304	+	0.0422299i	−0.0877922	+	0.996139i	$0.527981\pi$
$380$	−5.11485	−	3.41763i	−0.262386	−	0.175321i
$381$	−0.160657	−	0.807676i	−0.00823069	−	0.0413785i
$382$	−42.2464	−	17.4990i	−2.16152	−	0.895329i
$383$	−1.92220	−	0.796202i	−0.0982199	−	0.0406840i	0.333032	−	0.942915i	$-0.391928\pi$
$383$	−1.92220	−	0.796202i	−0.0982199	−	0.0406840i	−0.431252	+	0.902231i	$0.641928\pi$
$384$	−17.2229	+	3.42584i	−0.878900	+	0.174824i
$385$		0			0
$386$	−1.31557	+	6.61380i	−0.0669606	+	0.336634i
$387$	−1.28745	−	1.28745i	−0.0654448	−	0.0654448i
$388$	32.8176	−	21.9280i	1.66606	−	1.11323i
$389$	23.8357	−	9.87306i	1.20852	−	0.500584i	0.314776	−	0.949166i	$-0.398071\pi$
$389$	23.8357	−	9.87306i	1.20852	−	0.500584i	0.893742	+	0.448582i	$0.148071\pi$
$390$	−9.99540			−0.506137
$391$	−10.5674	−	25.4529i	−0.534419	−	1.28721i
$392$		0			0
$393$	−8.60839	−	20.7825i	−0.434236	−	1.04834i
$394$	−2.57592	+	1.72118i	−0.129773	+	0.0867116i
$395$	2.34503	+	2.34503i	0.117991	+	0.117991i
$396$	18.3672	+	3.65347i	0.922987	+	0.183594i
$397$	2.60452	−	3.89794i	0.130717	−	0.195632i	−0.760337	−	0.649528i	$-0.774966\pi$
$397$	2.60452	−	3.89794i	0.130717	−	0.195632i	0.891054	+	0.453896i	$0.149966\pi$
$398$	−9.11592	−	45.8288i	−0.456940	−	2.29719i
$399$		0			0
$400$	21.5605	−	52.0517i	1.07803	−	2.60258i
$401$	4.92154	+	24.7422i	0.245770	+	1.23557i	0.884648	+	0.466260i	$0.154399\pi$
$401$	4.92154	+	24.7422i	0.245770	+	1.23557i	−0.638878	+	0.769308i	$0.720601\pi$
$402$	−7.27714	−	4.86243i	−0.362951	−	0.242516i
$403$	−5.36850	+	26.9893i	−0.267424	+	1.34443i
$404$	−20.6326	+	20.6326i	−1.02651	+	1.02651i
$405$	−1.12134	+	0.749253i	−0.0557197	+	0.0372307i
$406$		0			0
$407$			10.5793i			0.524396i
$408$	−16.3041	+	39.4533i	−0.807175	+	1.95323i
$409$		−	5.48856i		−	0.271392i	−0.990751	−	0.135696i	$-0.956673\pi$
$409$		−	5.48856i		−	0.271392i	0.990751	−	0.135696i	$-0.0433270\pi$
$410$	1.60537	+	3.87572i	0.0792838	+	0.191408i
$411$	7.96345	+	11.9181i	0.392808	+	0.587879i
$412$	−8.03289	−	8.03289i	−0.395752	−	0.395752i
$413$		0			0
$414$	−21.4322	−	14.3205i	−1.05333	−	0.703815i
$415$	5.14009	−	1.02243i	0.252317	−	0.0501889i
$416$	−33.3308	+	80.4676i	−1.63418	+	3.94525i
$417$	7.88168	−	19.0281i	0.385968	−	0.931808i
$418$	−15.2001	+	3.02348i	−0.743459	+	0.147883i
$419$	31.1049	+	20.7836i	1.51958	+	1.01535i	0.985455	+	0.169939i	$0.0543572\pi$
$419$	31.1049	+	20.7836i	1.51958	+	1.01535i	0.534121	+	0.845408i	$0.320643\pi$
$420$		0			0
$421$	−22.5977	−	22.5977i	−1.10135	−	1.10135i	−0.994248	−	0.107098i	$-0.965844\pi$
$421$	−22.5977	−	22.5977i	−1.10135	−	1.10135i	−0.107098	−	0.994248i	$-0.534156\pi$
$422$	38.4567	+	57.5545i	1.87204	+	2.80171i
$423$	3.75581	+	9.06734i	0.182614	+	0.440869i
$424$		−	83.1866i		−	4.03990i
$425$	−10.8369	−	16.1897i	−0.525666	−	0.785317i
$426$			44.0118i			2.13238i
$427$		0			0
$428$	6.84407	−	4.57306i	0.330821	−	0.221047i
$429$	−12.8001	+	12.8001i	−0.617994	+	0.617994i
$430$	0.343583	−	1.72731i	0.0165690	−	0.0832981i
$431$	−3.98999	−	2.66603i	−0.192191	−	0.128418i	0.455752	−	0.890107i	$-0.349370\pi$
$431$	−3.98999	−	2.66603i	−0.192191	−	0.128418i	−0.647943	+	0.761689i	$0.724370\pi$
$432$	12.8929	+	64.8168i	0.620308	+	3.11850i
$433$	−8.11597	+	19.5937i	−0.390029	+	0.941613i	0.599904	+	0.800072i	$0.295206\pi$
$433$	−8.11597	+	19.5937i	−0.390029	+	0.941613i	−0.989932	+	0.141541i	$0.954794\pi$
$434$		0			0
$435$	−0.935178	−	4.70146i	−0.0448384	−	0.225418i
$436$	15.9211	−	23.8276i	0.762481	−	1.14113i
$437$	15.0397	+	2.99158i	0.719445	+	0.143107i
$438$	−7.00206	−	7.00206i	−0.334571	−	0.334571i
$439$	22.7989	−	15.2338i	1.08813	−	0.727067i	0.123946	−	0.992289i	$-0.460445\pi$
$439$	22.7989	−	15.2338i	1.08813	−	0.727067i	0.964188	+	0.265222i	$0.0854451\pi$
$440$	4.22094	+	10.1902i	0.201225	+	0.485801i
$441$		0			0
$442$	35.0696	+	52.3921i	1.66809	+	2.49204i
$443$	10.3782			0.493085			0.246543	−	0.969132i	$-0.420705\pi$
$443$	10.3782			0.493085			0.246543	+	0.969132i	$0.420705\pi$
$444$	−24.6018	+	10.1904i	−1.16755	+	0.483615i
$445$	3.53701	−	2.36336i	0.167671	−	0.112034i
$446$	8.34769	+	8.34769i	0.395274	+	0.395274i
$447$	3.46085	−	17.3989i	0.163693	−	0.822939i
$448$		0			0
$449$	18.9429	−	3.76797i	0.893969	−	0.177822i	0.273332	−	0.961920i	$-0.411874\pi$
$449$	18.9429	−	3.76797i	0.893969	−	0.177822i	0.620637	+	0.784098i	$0.286874\pi$
$450$	−16.8344	−	6.97302i	−0.793580	−	0.328711i
$451$	7.01907	+	2.90740i	0.330515	+	0.136904i
$452$	−8.91653	−	44.8264i	−0.419399	−	2.10846i
$453$	0.305812	+	0.204337i	0.0143683	+	0.00960059i
$454$	−39.6592	−	7.88870i	−1.86130	−	0.370235i
$455$		0			0
$456$	−13.1964	−	19.7498i	−0.617977	−	0.924867i
$457$	0.997078	−	0.413003i	0.0466414	−	0.0193195i	−0.359241	−	0.933245i	$-0.616964\pi$
$457$	0.997078	−	0.413003i	0.0466414	−	0.0193195i	0.405882	+	0.913925i	$0.366964\pi$
$458$	−38.5663			−1.80209
$459$	21.1198	+	8.72777i	0.985786	+	0.407377i
$460$		−	17.9231i		−	0.835669i
$461$	10.3807	−	4.29983i	0.483477	−	0.200263i	−0.127613	−	0.991824i	$-0.540731\pi$
$461$	10.3807	−	4.29983i	0.483477	−	0.200263i	0.611090	+	0.791561i	$0.290731\pi$
$462$		0			0
$463$	−17.0641	+	17.0641i	−0.793034	+	0.793034i	−0.981986	−	0.188952i	$-0.939491\pi$
$463$	−17.0641	+	17.0641i	−0.793034	+	0.793034i	0.188952	+	0.981986i	$0.439491\pi$
$464$	−85.7586	−	17.0585i	−3.98124	−	0.791919i
$465$	−1.74318	+	2.60885i	−0.0808381	+	0.120983i
$466$	−31.6925	+	6.30404i	−1.46813	+	0.292029i
$467$	2.94554	−	7.11115i	0.136303	−	0.329065i	−0.840959	−	0.541098i	$-0.818009\pi$
$467$	2.94554	−	7.11115i	0.136303	−	0.329065i	0.977262	+	0.212034i	$0.0680086\pi$
$468$	39.1621	+	16.2215i	1.81027	+	0.749838i
$469$		0			0
$470$	−5.27416	+	7.89334i	−0.243279	+	0.364093i
$471$	−1.47756	+	7.42818i	−0.0680822	+	0.342272i
$472$	68.0632	−	68.0632i	3.13286	−	3.13286i
$473$	−1.77199	−	2.65198i	−0.0814764	−	0.121938i
$474$	8.04788	+	19.4293i	0.369652	+	0.892418i
$475$	10.8399			0.497370
$476$		0			0
$477$	−14.4819			−0.663081
$478$	−1.08074	−	2.60915i	−0.0494321	−	0.119340i
$479$	9.05192	+	13.5472i	0.413593	+	0.618985i	0.978519	−	0.206156i	$-0.0660954\pi$
$479$	9.05192	+	13.5472i	0.413593	+	0.618985i	−0.564926	+	0.825141i	$0.691095\pi$
$480$	−7.02226	+	7.02226i	−0.320521	+	0.320521i
$481$	−4.67168	+	23.4861i	−0.213010	+	1.07088i
$482$	−20.0552	+	30.0147i	−0.913490	+	1.36713i
$483$		0			0
$484$	−21.6620	−	8.97269i	−0.984635	−	0.407849i
$485$	1.54872	−	3.73893i	0.0703236	−	0.169776i
$486$	35.1083	−	6.98347i	1.59254	−	0.316776i
$487$	−16.7883	+	25.1254i	−0.760749	+	1.13854i	0.225656	+	0.974207i	$0.427548\pi$
$487$	−16.7883	+	25.1254i	−0.760749	+	1.13854i	−0.986405	+	0.164334i	$0.947452\pi$
$488$	−124.268	−	24.7184i	−5.62534	−	1.11895i
$489$	−3.91328	+	3.91328i	−0.176965	+	0.176965i
$490$		0			0
$491$	32.1947	−	13.3355i	1.45292	−	0.601821i	0.490032	−	0.871705i	$-0.336985\pi$
$491$	32.1947	−	13.3355i	1.45292	−	0.601821i	0.962893	+	0.269883i	$0.0869852\pi$
$492$			19.1231i			0.862138i
$493$	−21.3621	+	21.3972i	−0.962101	+	0.963683i
$494$	−35.0794			−1.57830
$495$	1.77401	−	0.734821i	0.0797360	−	0.0330277i
$496$	31.7971	+	47.5877i	1.42773	+	2.13675i
$497$		0			0
$498$	32.5949	+	6.48353i	1.46061	+	0.290534i
$499$	8.10256	+	5.41396i	0.362720	+	0.242362i	0.723553	−	0.690268i	$-0.242508\pi$
$499$	8.10256	+	5.41396i	0.362720	+	0.242362i	−0.360833	+	0.932630i	$0.617508\pi$
$500$	−5.08739	−	25.5761i	−0.227515	−	1.14380i
$501$	−5.63343	−	2.33344i	−0.251683	−	0.104251i
$502$	3.04138	+	1.25978i	0.135743	+	0.0562268i
$503$	−20.8016	+	4.13770i	−0.927499	+	0.184491i	−0.635654	−	0.771974i	$-0.719269\pi$
$503$	−20.8016	+	4.13770i	−0.927499	+	0.184491i	−0.291846	+	0.956465i	$0.594269\pi$
$504$		0			0
$505$	−0.583684	+	2.93438i	−0.0259736	+	0.130578i
$506$	−31.9288	−	31.9288i	−1.41941	−	1.41941i
$507$	−20.5934	+	13.7601i	−0.914587	+	0.611108i
$508$	−3.12089	+	1.29272i	−0.138467	+	0.0573550i
$509$	−36.3707			−1.61210			−0.806051	−	0.591846i	$-0.798399\pi$
$509$	−36.3707			−1.61210			−0.806051	+	0.591846i	$0.798399\pi$
$510$	1.40822	+	7.04931i	0.0623569	+	0.312149i
$511$		0			0
$512$	−6.47045	−	15.6211i	−0.285956	−	0.690360i
$513$	−10.5722	+	7.06414i	−0.466776	+	0.311890i
$514$	−3.12022	−	3.12022i	−0.137627	−	0.137627i
$515$	−1.14244	−	0.227245i	−0.0503419	−	0.0100136i
$516$	4.46023	−	6.67520i	0.196351	−	0.293859i
$517$	3.35412	+	16.8623i	0.147514	+	0.741602i
$518$		0			0
$519$	−10.3681	+	25.0307i	−0.455108	+	1.09873i
$520$	4.87064	+	24.4864i	0.213592	+	1.07380i
$521$	−5.26308	−	3.51668i	−0.230580	−	0.154068i	0.434914	−	0.900472i	$-0.356779\pi$
$521$	−5.26308	−	3.51668i	−0.230580	−	0.154068i	−0.665493	+	0.746404i	$0.731779\pi$
$522$	−5.51698	+	27.7357i	−0.241472	+	1.21396i
$523$	−5.13336	+	5.13336i	−0.224466	+	0.224466i	−0.810376	−	0.585910i	$-0.800737\pi$
$523$	−5.13336	+	5.13336i	−0.224466	+	0.224466i	0.585910	+	0.810376i	$0.300737\pi$
$524$	−76.7237	+	51.2651i	−3.35169	+	2.23953i
$525$		0			0
$526$		−	15.0962i		−	0.658227i
$527$	19.7907	−	0.0162612i	0.862096	−	0.000708349i
$528$			37.6495i			1.63848i
$529$	8.29571	+	20.0276i	0.360683	+	0.870766i
$530$	−7.78243	−	11.6472i	−0.338047	−	0.505923i
$531$	−11.8491	−	11.8491i	−0.514207	−	0.514207i
$532$		0			0
$533$	14.2986	+	9.55399i	0.619339	+	0.413829i
$534$	26.4572	−	5.26266i	1.14491	−	0.227738i
$535$	0.322983	−	0.779750i	0.0139638	−	0.0337115i
$536$	−8.36573	+	20.1967i	−0.361344	+	0.872363i
$537$	14.8927	−	2.96234i	0.642668	−	0.127835i
$538$	4.74689	+	3.17177i	0.204653	+	0.136745i
$539$		0			0
$540$	10.5088	+	10.5088i	0.452228	+	0.452228i
$541$	−9.69750	−	14.5133i	−0.416928	−	0.623977i	0.562253	−	0.826965i	$-0.309935\pi$
$541$	−9.69750	−	14.5133i	−0.416928	−	0.623977i	−0.979181	+	0.202988i	$0.934935\pi$
$542$	−31.0302	−	74.9134i	−1.33286	−	3.21781i
$543$			12.8758i			0.552555i
$544$	61.4461	+	12.1699i	2.63448	+	0.521780i
$545$		−	2.93836i		−	0.125866i
$546$		0			0
$547$	−22.7183	+	15.1799i	−0.971363	+	0.649044i	−0.936618	−	0.350352i	$-0.886062\pi$
$547$	−22.7183	+	15.1799i	−0.971363	+	0.649044i	−0.0347453	+	0.999396i	$0.511062\pi$
$548$	41.5765	−	41.5765i	1.77606	−	1.77606i
$549$	−4.30321	+	21.6337i	−0.183657	+	0.923304i
$550$	−26.5403	−	17.7337i	−1.13168	−	0.756166i
$551$	−3.28206	−	16.5000i	−0.139820	−	0.702925i
$552$	26.4839	−	63.9377i	1.12723	−	2.72137i
$553$		0			0
$554$	−11.4472	−	57.5492i	−0.486347	−	2.44503i
$555$	−1.51692	+	2.27023i	−0.0643897	+	0.0963659i
$556$	−82.8617	−	16.4822i	−3.51412	−	0.699002i
$557$	−14.5706	−	14.5706i	−0.617378	−	0.617378i	0.327480	−	0.944858i	$-0.393800\pi$
$557$	−14.5706	−	14.5706i	−0.617378	−	0.617378i	−0.944858	+	0.327480i	$0.893800\pi$
$558$	15.3906	−	10.2837i	0.651538	−	0.435344i
$559$	−2.76277	−	6.66991i	−0.116853	−	0.282107i
$560$		0			0
$561$	10.8307	+	7.22397i	0.457272	+	0.304996i
$562$	47.9369			2.02210
$563$	38.2989	−	15.8639i	1.61411	−	0.668585i	0.620788	−	0.783978i	$-0.286813\pi$
$563$	38.2989	−	15.8639i	1.61411	−	0.668585i	0.993320	+	0.115393i	$0.0368127\pi$
$564$	−35.9819	+	24.0423i	−1.51511	+	1.01236i
$565$	−3.31373	−	3.31373i	−0.139410	−	0.139410i
$566$	−1.03892	+	5.22298i	−0.0436689	+	0.219538i
$567$		0			0
$568$	107.818	−	21.4464i	4.52396	−	0.899872i
$569$	−17.8391	−	7.38920i	−0.747854	−	0.309771i	−0.0239883	−	0.999712i	$-0.507636\pi$
$569$	−17.8391	−	7.38920i	−0.747854	−	0.309771i	−0.723866	+	0.689941i	$0.757636\pi$
$570$	−3.69533	−	1.53066i	−0.154780	−	0.0641122i
$571$	2.03586	+	10.2349i	0.0851980	+	0.428319i	0.999717	+	0.0237769i	$0.00756914\pi$
$571$	2.03586	+	10.2349i	0.0851980	+	0.428319i	−0.914519	+	0.404542i	$0.867431\pi$
$572$	61.7412	+	41.2541i	2.58153	+	1.72492i
$573$	−20.9625	−	4.16970i	−0.875722	−	0.174192i
$574$		0			0
$575$	17.5466	+	26.2603i	0.731742	+	1.09513i
$576$	22.2719	−	9.22534i	0.927997	−	0.384389i
$577$	38.4162			1.59929			0.799645	−	0.600473i	$-0.205021\pi$
$577$	38.4162			1.59929			0.799645	+	0.600473i	$0.205021\pi$
$578$	32.0089	−	32.1143i	1.33140	−	1.33578i
$579$			3.15190i			0.130988i
$580$	−18.1666	+	7.52487i	−0.754329	+	0.312453i
$581$		0			0
$582$	18.1467	−	18.1467i	0.752203	−	0.752203i
$583$	−24.8816	−	4.94925i	−1.03049	−	0.204977i
$584$	−13.7414	+	20.5654i	−0.568621	+	0.851002i
$585$	4.26282	−	0.847927i	0.176246	−	0.0350575i
$586$	17.6440	−	42.5963i	0.728866	−	1.75964i
$587$	3.01325	+	1.24813i	0.124370	+	0.0515159i	0.444001	−	0.896026i	$-0.353559\pi$
$587$	3.01325	+	1.24813i	0.124370	+	0.0515159i	−0.319630	+	0.947542i	$0.603559\pi$
$588$		0			0
$589$	−6.11779	+	9.15592i	−0.252079	+	0.377263i
$590$	3.16217	−	15.8973i	0.130185	−	0.654482i
$591$	−1.02392	+	1.02392i	−0.0421185	+	0.0421185i
$592$	27.6699	+	41.4109i	1.13723	+	1.70198i
$593$	2.97392	+	7.17969i	0.122124	+	0.294834i	0.973105	−	0.230363i	$-0.0739914\pi$
$593$	2.97392	+	7.17969i	0.122124	+	0.294834i	−0.850980	+	0.525198i	$0.823991\pi$
$594$	37.4415			1.53624
$595$		0			0
$596$	−72.7692			−2.98074
$597$	−8.35794	−	20.1779i	−0.342068	−	0.825825i
$598$	−56.7829	−	84.9817i	−2.32203	−	3.47516i
$599$	−1.53293	+	1.53293i	−0.0626339	+	0.0626339i	−0.737730	−	0.675096i	$-0.764102\pi$
$599$	−1.53293	+	1.53293i	−0.0626339	+	0.0626339i	0.675096	+	0.737730i	$0.264102\pi$
$600$	9.54420	−	47.9819i	0.389640	−	1.95885i
$601$	20.6572	−	30.9157i	0.842626	−	1.26108i	−0.120684	−	0.992691i	$-0.538509\pi$
$601$	20.6572	−	30.9157i	0.842626	−	1.26108i	0.963311	−	0.268388i	$-0.0864911\pi$
$602$		0			0
$603$	3.51603	+	1.45639i	0.143184	+	0.0593086i
$604$	0.577362	−	1.39388i	0.0234925	−	0.0567160i
$605$	−2.35792	+	0.469019i	−0.0958631	+	0.0190683i
$606$	−10.5405	+	15.7749i	−0.428178	+	0.640813i
$607$	12.9121	+	2.56839i	0.524088	+	0.104248i	0.450042	−	0.893007i	$-0.351409\pi$
$607$	12.9121	+	2.56839i	0.524088	+	0.104248i	0.0740457	+	0.997255i	$0.476409\pi$
$608$	−24.6450	+	24.6450i	−0.999487	+	0.999487i
$609$		0			0
$610$	−19.7116	+	8.16482i	−0.798101	+	0.330584i
$611$			38.9156i			1.57436i
$612$	5.92287	−	29.9047i	0.239418	−	1.20882i
$613$	27.7779			1.12194			0.560970	−	0.827836i	$-0.310428\pi$
$613$	27.7779			1.12194			0.560970	+	0.827836i	$0.310428\pi$
$614$	30.0077	−	12.4296i	1.21101	−	0.501618i
$615$	1.08936	+	1.63034i	0.0439271	+	0.0657416i
$616$		0			0
$617$	5.26805	+	1.04788i	0.212084	+	0.0421861i	0.299989	−	0.953943i	$-0.403017\pi$
$617$	5.26805	+	1.04788i	0.212084	+	0.0421861i	−0.0879048	+	0.996129i	$0.528017\pi$
$618$	−6.14165	−	4.10372i	−0.247053	−	0.165076i
$619$	8.65524	+	43.5128i	0.347884	+	1.74893i	0.618072	+	0.786121i	$0.287914\pi$
$619$	8.65524	+	43.5128i	0.347884	+	1.74893i	−0.270188	+	0.962807i	$0.587086\pi$
$620$	11.8910	+	4.92542i	0.477555	+	0.197810i
$621$	−34.2265	−	14.1771i	−1.37346	−	0.568906i
$622$	10.0825	−	2.00553i	0.404270	−	0.0804143i
$623$		0			0
$624$	−16.6255	+	83.5823i	−0.665554	+	3.34597i
$625$	14.8149	+	14.8149i	0.592597	+	0.592597i
$626$	14.3042	−	9.55773i	0.571709	−	0.382004i
$627$	−6.69239	+	2.77208i	−0.267268	+	0.110706i
$628$	31.0677			1.23974
$629$	17.2219	−	0.0141505i	0.686682	−	0.000564219i
$630$		0			0
$631$	−17.5791	−	42.4398i	−0.699814	−	1.68950i	−0.724006	−	0.689794i	$-0.757701\pi$
$631$	−17.5791	−	42.4398i	−0.699814	−	1.68950i	0.0241917	−	0.999707i	$-0.492299\pi$
$632$	43.6756	−	29.1831i	1.73732	−	1.16084i
$633$	22.8777	+	22.8777i	0.909307	+	0.909307i
$634$	2.72726	+	0.542485i	0.108313	+	0.0215448i
$635$	−0.192431	+	0.287993i	−0.00763639	+	0.0114287i
$636$	−12.4576	−	62.6286i	−0.493976	−	2.48339i
$637$		0			0
$638$	−18.9576	+	45.7677i	−0.750539	+	1.81196i
$639$	−3.73360	−	18.7701i	−0.147699	−	0.742532i
$640$	6.14116	+	4.10339i	0.242751	+	0.162201i
$641$	6.94648	−	34.9223i	0.274370	−	1.37935i	−0.560159	−	0.828385i	$-0.689260\pi$
$641$	6.94648	−	34.9223i	0.274370	−	1.37935i	0.834529	−	0.550964i	$-0.185740\pi$
$642$	3.78447	−	3.78447i	0.149361	−	0.149361i
$643$	30.6620	−	20.4877i	1.20919	−	0.807956i	0.223203	−	0.974772i	$-0.428349\pi$
$643$	30.6620	−	20.4877i	1.20919	−	0.807956i	0.985988	+	0.166816i	$0.0533486\pi$
$644$		0			0
$645$		−	0.823172i		−	0.0324124i
$646$	4.94221	+	24.7399i	0.194449	+	0.973380i
$647$		−	26.0587i		−	1.02447i	−0.858845	−	0.512236i	$-0.828817\pi$
$647$		−	26.0587i		−	1.02447i	0.858845	−	0.512236i	$-0.171183\pi$
$648$	8.17446	+	19.7349i	0.321123	+	0.775259i
$649$	−16.3086	−	24.4075i	−0.640169	−	0.958080i
$650$	−51.0888	−	51.0888i	−2.00387	−	2.00387i
$651$		0			0
$652$	18.8757	+	12.6123i	0.739229	+	0.493937i
$653$	−15.7695	+	3.13675i	−0.617108	+	0.122750i	−0.493739	−	0.869610i	$-0.664370\pi$
$653$	−15.7695	+	3.13675i	−0.617108	+	0.122750i	−0.123370	+	0.992361i	$0.539370\pi$
$654$	7.13058	−	17.2147i	0.278828	−	0.673149i
$655$	−3.62072	+	8.74119i	−0.141473	+	0.341547i
$656$	35.0793	−	6.97770i	1.36962	−	0.272433i
$657$	3.58022	+	2.39223i	0.139678	+	0.0933296i
$658$		0			0
$659$	6.26306	+	6.26306i	0.243974	+	0.243974i	0.818492	−	0.574518i	$-0.194810\pi$
$659$	6.26306	+	6.26306i	0.243974	+	0.243974i	−0.574518	+	0.818492i	$0.694810\pi$
$660$	4.70385	+	7.03981i	0.183097	+	0.274024i
$661$	4.77553	+	11.5292i	0.185747	+	0.448432i	0.989133	−	0.147027i	$-0.0469703\pi$
$661$	4.77553	+	11.5292i	0.185747	+	0.448432i	−0.803386	+	0.595459i	$0.796970\pi$
$662$			50.0334i			1.94460i
$663$	20.8542	+	20.8200i	0.809911	+	0.808581i
$664$		−	83.0091i		−	3.22138i
$665$		0			0
$666$	13.3930	−	8.94890i	0.518967	−	0.346763i
$667$	34.6595	−	34.6595i	1.34202	−	1.34202i
$668$	−4.87971	+	24.5320i	−0.188802	+	0.949170i
$669$	4.58799	+	3.06560i	0.177382	+	0.118523i
$670$	0.718162	+	3.61045i	0.0277450	+	0.139484i
$671$	−14.7868	+	35.6985i	−0.570839	+	1.37813i
$672$		0			0
$673$	−6.95731	−	34.9768i	−0.268185	−	1.34826i	−0.846477	−	0.532426i	$-0.821281\pi$
$673$	−6.95731	−	34.9768i	−0.268185	−	1.34826i	0.578292	−	0.815830i	$-0.303719\pi$
$674$	38.6511	−	57.8455i	1.48878	−	2.22812i
$675$	−25.6852	−	5.10910i	−0.988623	−	0.196649i
$676$	71.8403	+	71.8403i	2.76309	+	2.76309i
$677$	−24.8340	+	16.5935i	−0.954447	+	0.637741i	−0.932174	−	0.362011i	$-0.882090\pi$
$677$	−24.8340	+	16.5935i	−0.954447	+	0.637741i	−0.0222734	+	0.999752i	$0.507090\pi$
$678$	−11.3724	−	27.4554i	−0.436754	−	1.05442i
$679$		0			0
$680$	16.5829	−	6.88484i	0.635926	−	0.264022i
$681$	−18.9001			−0.724254
$682$	29.9574	−	12.4088i	1.14713	−	0.475156i
$683$	−5.57478	+	3.72495i	−0.213313	+	0.142531i	−0.657637	−	0.753335i	$-0.728444\pi$
$683$	−5.57478	+	3.72495i	−0.213313	+	0.142531i	0.444324	+	0.895866i	$0.353444\pi$
$684$	11.9943	+	11.9943i	0.458612	+	0.458612i
$685$	1.17617	−	5.91302i	0.0449392	−	0.225925i
$686$		0			0
$687$	−17.6798	+	3.51673i	−0.674526	+	0.134172i
$688$	−13.8724	−	5.74613i	−0.528879	−	0.219069i
$689$	−53.0518	−	21.9748i	−2.02111	−	0.837173i
$690$	−2.27353	−	11.4298i	−0.0865518	−	0.435125i
$691$	8.05335	+	5.38107i	0.306364	+	0.204706i	0.699242	−	0.714885i	$-0.253521\pi$
$691$	8.05335	+	5.38107i	0.306364	+	0.204706i	−0.392879	+	0.919590i	$0.628521\pi$
$692$	109.002	+	21.6818i	4.14362	+	0.824217i
$693$		0			0
$694$	−5.08063	−	7.60371i	−0.192858	−	0.288633i
$695$	−8.00327	+	3.31506i	−0.303581	+	0.125747i
$696$	−75.9256			−2.87795
$697$	4.72353	−	11.4302i	0.178916	−	0.432948i
$698$		−	60.5901i		−	2.29337i
$699$	−13.9538	+	5.77986i	−0.527782	+	0.218614i
$700$		0			0
$701$	8.61342	−	8.61342i	0.325324	−	0.325324i	−0.525481	−	0.850805i	$-0.676115\pi$
$701$	8.61342	−	8.61342i	0.325324	−	0.325324i	0.850805	+	0.525481i	$0.176115\pi$
$702$	83.1206	+	16.5337i	3.13718	+	0.624025i
$703$	−5.32371	+	7.96750i	−0.200788	+	0.300500i
$704$	41.4185	−	8.23865i	1.56102	−	0.310506i
$705$	−1.69804	+	4.09944i	−0.0639521	+	0.154394i
$706$	−14.3612	−	5.94860i	−0.540490	−	0.223878i
$707$		0			0
$708$	41.0499	−	61.4354i	1.54275	−	2.30889i
$709$	−4.03236	+	20.2721i	−0.151439	+	0.761333i	0.828179	+	0.560463i	$0.189377\pi$
$709$	−4.03236	+	20.2721i	−0.151439	+	0.761333i	−0.979618	+	0.200870i	$0.935623\pi$
$710$	13.0896	−	13.0896i	0.491245	−	0.491245i
$711$	−5.08047	−	7.60346i	−0.190532	−	0.285152i
$712$	−25.7846	−	62.2494i	−0.966317	−	2.33290i
$713$	−32.0835			−1.20154
$714$		0			0
$715$	7.61379			0.284739
$716$	−23.8364	−	57.5461i	−0.890807	−	2.15060i
$717$	−0.733360	−	1.09755i	−0.0273878	−	0.0409888i
$718$	−35.9775	+	35.9775i	−1.34267	+	1.34267i
$719$	−8.40274	+	42.2434i	−0.313369	+	1.57541i	0.427659	+	0.903940i	$0.359339\pi$
$719$	−8.40274	+	42.2434i	−0.313369	+	1.57541i	−0.741028	+	0.671474i	$0.765661\pi$
$720$	5.02219	−	7.51623i	0.187166	−	0.280113i
$721$		0			0
$722$	33.8499	+	14.0211i	1.25976	+	0.521811i
$723$	−6.45688	+	15.5883i	−0.240134	+	0.579735i
$724$	51.8024	−	10.3041i	1.92522	−	0.382950i
$725$	19.2503	−	28.8101i	0.714939	−	1.06998i
$726$	−14.9523	−	2.97420i	−0.554932	−	0.110383i
$727$	−30.4945	+	30.4945i	−1.13098	+	1.13098i	−0.140964	+	0.990015i	$0.545020\pi$
$727$	−30.4945	+	30.4945i	−1.13098	+	1.13098i	−0.990015	+	0.140964i	$0.954980\pi$
$728$		0			0
$729$	22.5864	−	9.35558i	0.836532	−	0.346503i
$730$			4.16499i			0.154153i
$731$	−4.31475	+	2.88815i	−0.159587	+	0.106822i
$732$	−97.2590			−3.59480
$733$	11.6338	−	4.81889i	0.429705	−	0.177990i	−0.157339	−	0.987545i	$-0.550292\pi$
$733$	11.6338	−	4.81889i	0.429705	−	0.177990i	0.587044	+	0.809555i	$0.300292\pi$
$734$	25.9268	+	38.8021i	0.956974	+	1.43221i
$735$		0			0
$736$	−99.5966	−	19.8110i	−3.67118	−	0.730243i
$737$	5.54321	+	3.70385i	0.204187	+	0.136433i
$738$	−2.25670	−	11.3452i	−0.0830704	−	0.417623i
$739$	16.2864	+	6.74604i	0.599104	+	0.248157i	0.661562	−	0.749891i	$-0.269894\pi$
$739$	16.2864	+	6.74604i	0.599104	+	0.248157i	−0.0624578	+	0.998048i	$0.519894\pi$
$740$	10.3476	+	4.28612i	0.380385	+	0.157561i
$741$	−16.0813	+	3.19877i	−0.590761	+	0.117510i
$742$		0			0
$743$	2.00037	−	10.0565i	0.0733865	−	0.368939i	−0.926588	−	0.376078i	$-0.877272\pi$
$743$	2.00037	−	10.0565i	0.0733865	−	0.368939i	0.999975	+	0.00713909i	$0.00227246\pi$
$744$	35.1413	+	35.1413i	1.28834	+	1.28834i
$745$	−6.20392	+	4.14533i	−0.227294	+	0.151873i
$746$	−53.2630	+	22.0622i	−1.95010	+	0.807756i
$747$	−14.4510			−0.528735
$748$	20.3962	−	49.3554i	0.745759	−	1.80461i
$749$		0			0
$750$	−6.48860	−	15.6649i	−0.236930	−	0.572000i
$751$	−8.27749	+	5.53084i	−0.302050	+	0.201823i	−0.697354	−	0.716727i	$-0.745639\pi$
$751$	−8.27749	+	5.53084i	−0.302050	+	0.201823i	0.395304	+	0.918550i	$0.370639\pi$
$752$	57.2321	+	57.2321i	2.08704	+	2.08704i
$753$	1.50912	+	0.300183i	0.0549954	+	0.0109393i
$754$	−62.2966	+	93.2334i	−2.26871	+	3.39536i
$755$	−0.0301798	−	0.151724i	−0.00109836	−	0.00552181i
$756$		0			0
$757$	12.8788	−	31.0921i	0.468087	−	1.13006i	−0.496910	−	0.867802i	$-0.665532\pi$
$757$	12.8788	−	31.0921i	0.468087	−	1.13006i	0.964997	−	0.262260i	$-0.0844680\pi$
$758$	−2.19277	−	11.0238i	−0.0796448	−	0.400402i
$759$	−17.5485	−	11.7255i	−0.636969	−	0.425609i
$760$	−1.94905	+	9.79856i	−0.0706996	+	0.355431i
$761$	13.1216	−	13.1216i	0.475658	−	0.475658i	−0.428082	−	0.903740i	$-0.640811\pi$
$761$	13.1216	−	13.1216i	0.475658	−	0.475658i	0.903740	+	0.428082i	$0.140811\pi$
$762$	−1.82626	+	1.22027i	−0.0661583	+	0.0442055i
$763$		0			0
$764$			87.6738i			3.17193i
$765$	−1.19858	−	2.88691i	−0.0433347	−	0.104377i
$766$			5.54927i			0.200503i
$767$	−25.4272	−	61.3867i	−0.918123	−	2.21655i
$768$	2.92492	+	4.37745i	0.105544	+	0.157958i
$769$	33.9055	+	33.9055i	1.22266	+	1.22266i	0.966682	+	0.255981i	$0.0823986\pi$
$769$	33.9055	+	33.9055i	1.22266	+	1.22266i	0.255981	+	0.966682i	$0.417601\pi$
$770$		0			0
$771$	−1.71491	−	1.14587i	−0.0617610	−	0.0412674i
$772$	12.6808	−	2.52237i	0.456392	−	0.0907820i
$773$	5.14945	−	12.4319i	0.185213	−	0.447143i	−0.803814	−	0.594881i	$-0.797199\pi$
$773$	5.14945	−	12.4319i	0.185213	−	0.447143i	0.989027	+	0.147738i	$0.0471992\pi$
$774$	−1.85839	+	4.48655i	−0.0667985	+	0.161266i
$775$	−22.2442	+	4.42465i	−0.799037	+	0.158938i
$776$	−53.2977	−	35.6124i	−1.91327	−	1.27841i
$777$		0			0
$778$	−48.6575	−	48.6575i	−1.74445	−	1.74445i
$779$	3.82316	+	5.72177i	0.136979	+	0.205004i
$780$	7.33390	+	17.7056i	0.262596	+	0.633963i
$781$		−	33.5251i		−	1.19962i
$782$	−51.9338	+	52.0192i	−1.85715	+	1.86020i
$783$			40.6437i			1.45249i
$784$		0			0
$785$	2.64867	−	1.76978i	0.0945350	−	0.0631663i
$786$	−42.4248	+	42.4248i	−1.51324	+	1.51324i
$787$	−8.03399	+	40.3896i	−0.286381	+	1.43973i	0.522941	+	0.852369i	$0.324835\pi$
$787$	−8.03399	+	40.3896i	−0.286381	+	1.43973i	−0.809322	+	0.587365i	$0.800165\pi$
$788$	4.93888	+	3.30005i	0.175940	+	0.117560i
$789$	−1.37657	−	6.92050i	−0.0490073	−	0.246376i
$790$	3.38497	−	8.17203i	0.120432	−	0.290748i
$791$		0			0
$792$	−5.93344	−	29.8294i	−0.210836	−	1.05994i
$793$	−48.5909	+	72.7214i	−1.72551	+	2.58241i
$794$	−12.2635	−	2.43936i	−0.435216	−	0.0865698i
$795$	−4.62973	−	4.62973i	−0.164200	−	0.164200i
$796$	−74.4915	+	49.7736i	−2.64028	+	1.76418i
$797$	−9.18481	−	22.1741i	−0.325343	−	0.785446i	−0.998926	−	0.0463352i	$-0.985246\pi$
$797$	−9.18481	−	22.1741i	−0.325343	−	0.785446i	0.673583	−	0.739111i	$-0.264754\pi$
$798$		0			0
$799$	27.4454	−	5.48268i	0.970949	−	0.193963i
$800$	−71.7847			−2.53797
$801$	−10.8370	+	4.48882i	−0.382906	+	0.158605i
$802$	55.9453	−	37.3815i	1.97550	−	1.31998i
$803$	5.33367	+	5.33367i	0.188221	+	0.188221i
$804$	−3.27375	+	16.4582i	−0.115456	+	0.580437i
$805$		0			0
$806$	71.9853	−	14.3188i	2.53557	−	0.504357i
$807$	2.46532	+	1.02117i	0.0867832	+	0.0359468i
$808$	43.7811	+	18.1347i	1.54021	+	0.637977i
$809$	1.81221	+	9.11061i	0.0637140	+	0.320312i	0.999478	−	0.0323158i	$-0.0102882\pi$
$809$	1.81221	+	9.11061i	0.0637140	+	0.320312i	−0.935764	+	0.352628i	$0.885288\pi$
$810$	2.99081	+	1.99839i	0.105086	+	0.0702164i
$811$	37.7137	+	7.50173i	1.32431	+	0.263421i	0.806073	−	0.591817i	$-0.201589\pi$
$811$	37.7137	+	7.50173i	1.32431	+	0.263421i	0.518235	+	0.855238i	$0.326589\pi$
$812$		0			0
$813$	−21.0561	−	31.5127i	−0.738470	−	1.10520i
$814$	26.0690	−	10.7981i	0.913717	−	0.378474i
$815$	2.32771			0.0815361
$816$	61.2891	−	0.0503588i	2.14555	−	0.00176291i
$817$		−	2.88897i		−	0.101072i
$818$	−13.5246	+	5.60209i	−0.472878	+	0.195873i
$819$		0			0
$820$	5.68744	−	5.68744i	0.198614	−	0.198614i
$821$	28.0760	+	5.58467i	0.979861	+	0.194906i	0.658937	−	0.752198i	$-0.271007\pi$
$821$	28.0760	+	5.58467i	0.979861	+	0.194906i	0.320924	+	0.947105i	$0.396007\pi$
$822$	21.2400	−	31.7878i	0.740828	−	1.10873i
$823$	19.6162	−	3.90190i	0.683777	−	0.136012i	0.159035	−	0.987273i	$-0.449162\pi$
$823$	19.6162	−	3.90190i	0.683777	−	0.136012i	0.524742	+	0.851261i	$0.324162\pi$
$824$	−7.06038	+	17.0453i	−0.245960	+	0.593800i
$825$	−13.7838	−	5.70944i	−0.479891	−	0.198777i
$826$		0			0
$827$	−31.4011	+	46.9950i	−1.09192	+	1.63418i	−0.391987	+	0.919971i	$0.628212\pi$
$827$	−31.4011	+	46.9950i	−1.09192	+	1.63418i	−0.699935	+	0.714206i	$0.746788\pi$
$828$	−9.64164	+	48.4718i	−0.335070	+	1.68451i
$829$	−0.0194933	+	0.0194933i	−0.000677029	+	0.000677029i	−0.707445	−	0.706768i	$-0.750152\pi$
$829$	−0.0194933	+	0.0194933i	−0.000677029	+	0.000677029i	0.706768	+	0.707445i	$0.250152\pi$
$830$	−7.76582	−	11.6224i	−0.269556	−	0.403419i
$831$	−10.4954	−	25.3382i	−0.364082	−	0.878972i
$832$	95.5876			3.31390
$833$		0			0
$834$	−54.9328			−1.90217
$835$	0.981454	+	2.36944i	0.0339646	+	0.0819979i
$836$	16.5084	+	24.7066i	0.570956	+	0.854495i
$837$	18.8115	−	18.8115i	0.650220	−	0.650220i
$838$	19.4657	−	97.8608i	0.672433	−	3.38055i
$839$	−2.23886	+	3.35069i	−0.0772941	+	0.115679i	−0.868102	−	0.496385i	$-0.834660\pi$
$839$	−2.23886	+	3.35069i	−0.0772941	+	0.115679i	0.790808	+	0.612064i	$0.209660\pi$
$840$		0			0
$841$	−22.8895	−	9.48113i	−0.789293	−	0.326936i
$842$	−32.6191	+	78.7494i	−1.12413	+	2.71389i
$843$	21.9755	−	4.37120i	0.756876	−	0.150552i
$844$	73.7339	−	110.351i	2.53802	−	3.79842i
$845$	10.2171	+	2.03232i	0.351480	+	0.0699138i
$846$	18.5098	−	18.5098i	0.636380	−	0.636380i
$847$		0			0
$848$	−110.340	+	45.7042i	−3.78908	+	1.56949i
$849$			2.48908i			0.0854251i
$850$	−28.8329	+	43.2283i	−0.988960	+	1.48272i
$851$	−27.9192			−0.957056
$852$	77.9614	−	32.2927i	2.67091	−	1.10633i
$853$	23.1252	+	34.6093i	0.791792	+	1.18500i	0.979236	+	0.202725i	$0.0649799\pi$
$853$	23.1252	+	34.6093i	0.791792	+	1.18500i	−0.187443	+	0.982275i	$0.560020\pi$
$854$		0			0
$855$	1.70583	+	0.339310i	0.0583380	+	0.0116042i
$856$	−11.1152	−	7.42692i	−0.379909	−	0.253847i
$857$	−1.76013	−	8.84878i	−0.0601249	−	0.302268i	0.939008	−	0.343894i	$-0.111746\pi$
$857$	−1.76013	−	8.84878i	−0.0601249	−	0.302268i	−0.999133	+	0.0416259i	$0.986746\pi$
$858$	44.6062	+	18.4765i	1.52283	+	0.630777i
$859$	−21.0846	−	8.73354i	−0.719398	−	0.297985i	−0.00721099	−	0.999974i	$-0.502295\pi$
$859$	−21.0846	−	8.73354i	−0.719398	−	0.297985i	−0.712187	+	0.701989i	$0.752295\pi$
$860$	−3.31181	+	0.658759i	−0.112932	+	0.0224635i
$861$		0			0
$862$	−2.49697	+	12.5531i	−0.0850472	+	0.427561i
$863$	12.6091	+	12.6091i	0.429220	+	0.429220i	0.888362	−	0.459143i	$-0.151843\pi$
$863$	12.6091	+	12.6091i	0.429220	+	0.429220i	−0.459143	+	0.888362i	$0.651843\pi$
$864$	70.0120	−	46.7806i	2.38186	−	1.59151i
$865$	10.5280	−	4.36084i	0.357963	−	0.148273i
$866$	56.5657			1.92218
$867$	11.7453	−	17.6408i	0.398892	−	0.599113i
$868$		0			0
$869$	−6.13031	−	14.7999i	−0.207956	−	0.502051i
$870$	−10.6306	+	7.10313i	−0.360411	+	0.240819i
$871$	10.6704	+	10.6704i	0.361553	+	0.361553i
$872$	−45.6467	−	9.07968i	−1.54579	−	0.307477i
$873$	−6.19974	+	9.27857i	−0.209829	+	0.314032i
$874$	−7.97907	−	40.1135i	−0.269896	−	1.35686i
$875$		0			0
$876$	−7.26567	+	17.5409i	−0.245484	+	0.592652i
$877$	4.81231	+	24.1931i	0.162500	+	0.816943i	0.972929	+	0.231105i	$0.0742342\pi$
$877$	4.81231	+	24.1931i	0.162500	+	0.816943i	−0.810429	+	0.585837i	$0.800766\pi$
$878$	−60.8088	−	40.6312i	−2.05220	−	1.37124i
$879$	4.20424	−	21.1361i	0.141805	−	0.712904i
$880$	11.1974	−	11.1974i	0.377464	−	0.377464i
$881$	4.63851	−	3.09936i	0.156275	−	0.104420i	−0.474974	−	0.880000i	$-0.657542\pi$
$881$	4.63851	−	3.09936i	0.156275	−	0.104420i	0.631249	+	0.775580i	$0.282542\pi$
$882$		0			0
$883$		−	44.5704i		−	1.49991i	−0.661488	−	0.749956i	$-0.730075\pi$
$883$		−	44.5704i		−	1.49991i	0.661488	−	0.749956i	$-0.269925\pi$
$884$	67.0745	−	100.563i	2.25596	−	3.38230i
$885$		−	7.57609i		−	0.254667i
$886$	−10.5929	−	25.5736i	−0.355876	−	0.859161i
$887$	2.73518	+	4.09348i	0.0918383	+	0.137446i	0.874544	−	0.484946i	$-0.161161\pi$
$887$	2.73518	+	4.09348i	0.0918383	+	0.137446i	−0.782706	+	0.622392i	$0.786161\pi$
$888$	30.5800	+	30.5800i	1.02620	+	1.02620i
$889$		0			0
$890$	−9.43385	−	6.30350i	−0.316223	−	0.211294i
$891$	6.38916	−	1.27088i	0.214045	−	0.0425762i
$892$	8.66196	−	20.9118i	0.290024	−	0.700180i
$893$	−5.95938	+	14.3872i	−0.199423	+	0.481450i
$894$	−46.4059	+	9.23071i	−1.55205	+	0.308721i
$895$	−5.31030	−	3.54823i	−0.177504	−	0.118604i
$896$		0			0
$897$	−33.7799	−	33.7799i	−1.12788	−	1.12788i
$898$	−28.6196	−	42.8322i	−0.955047	−	1.42933i
$899$	13.4700	+	32.5195i	0.449250	+	1.08459i
$900$			34.9363i			1.16454i
$901$	−8.02355	+	40.5110i	−0.267303	+	1.34962i
$902$		−	20.2636i		−	0.674704i
$903$		0			0
$904$	−61.7175	+	41.2383i	−2.05269	+	1.37157i
$905$	3.82942	−	3.82942i	0.127294	−	0.127294i
$906$	0.191380	−	0.962131i	0.00635817	−	0.0319647i
$907$	29.0963	+	19.4415i	0.966126	+	0.645545i	0.935253	−	0.353979i	$-0.115172\pi$
$907$	29.0963	+	19.4415i	0.966126	+	0.645545i	0.0308722	+	0.999523i	$0.490172\pi$
$908$	15.1252	+	76.0395i	0.501947	+	2.52346i
$909$	3.15706	−	7.62183i	0.104713	−	0.252800i
$910$		0			0
$911$	6.88434	+	34.6099i	0.228088	+	1.14668i	0.909797	+	0.415053i	$0.136237\pi$
$911$	6.88434	+	34.6099i	0.228088	+	1.14668i	−0.681709	+	0.731624i	$0.738763\pi$
$912$	−18.9460	+	28.3547i	−0.627364	+	0.938917i
$913$	−24.8285	−	4.93869i	−0.821703	−	0.163447i
$914$	−2.03541	−	2.03541i	−0.0673253	−	0.0673253i
$915$	−8.29179	+	5.54040i	−0.274118	+	0.183160i
$916$	28.2972	+	68.3154i	0.934965	+	2.25721i
$917$		0			0
$918$	−0.0500807	−	60.9506i	−0.00165291	−	2.01167i
$919$	−55.0834			−1.81703			−0.908517	−	0.417849i	$-0.862784\pi$
$919$	−55.0834			−1.81703			−0.908517	+	0.417849i	$0.862784\pi$
$920$	−26.8924	+	11.1392i	−0.886617	+	0.367249i
$921$	12.6229	−	8.43434i	0.415938	−	0.277921i
$922$	−21.1909	−	21.1909i	−0.697883	−	0.697883i
$923$	14.8043	−	74.4260i	0.487288	−	2.44976i
$924$		0			0
$925$	−19.3570	+	3.85034i	−0.636454	+	0.126599i
$926$	59.4655	+	24.6314i	1.95416	+	0.809438i
$927$	2.96740	+	1.22914i	0.0974623	+	0.0403702i
$928$	21.7346	+	109.267i	0.713475	+	3.58688i
$929$	−46.9447	−	31.3674i	−1.54020	−	1.02913i	−0.979579	−	0.201062i	$-0.935561\pi$
$929$	−46.9447	−	31.3674i	−1.54020	−	1.02913i	−0.560626	−	0.828069i	$-0.689439\pi$
$930$	8.20785	+	1.63264i	0.269146	+	0.0535365i
$931$		0			0
$932$	34.4205	+	51.5139i	1.12748	+	1.68740i
$933$	4.43918	−	1.83877i	0.145332	−	0.0601986i
$934$	−20.5294			−0.671743
$935$	−1.07268	−	5.36966i	−0.0350804	−	0.175607i
$936$		−	68.8418i		−	2.25016i
$937$	−36.5459	+	15.1378i	−1.19390	+	0.494531i	−0.889025	−	0.457860i	$-0.848616\pi$
$937$	−36.5459	+	15.1378i	−1.19390	+	0.494531i	−0.304880	+	0.952391i	$0.598616\pi$
$938$		0			0
$939$	5.68585	−	5.68585i	0.185551	−	0.185551i
$940$	17.8519	+	3.55096i	0.582264	+	0.115820i
$941$	1.07774	−	1.61295i	0.0351332	−	0.0525806i	−0.813487	−	0.581583i	$-0.802434\pi$
$941$	1.07774	−	1.61295i	0.0351332	−	0.0525806i	0.848620	+	0.529002i	$0.177434\pi$
$942$	19.8123	−	3.94091i	0.645519	−	0.128402i
$943$	−7.67273	+	18.5236i	−0.249858	+	0.603212i
$944$	−127.675	−	52.8846i	−4.15546	−	1.72125i
$945$		0			0
$946$	−4.72623	+	7.07330i	−0.153663	+	0.229973i
$947$	6.91198	−	34.7489i	0.224609	−	1.12919i	−0.689677	−	0.724117i	$-0.742247\pi$
$947$	6.91198	−	34.7489i	0.224609	−	1.12919i	0.914286	−	0.405069i	$-0.132753\pi$
$948$	28.5117	−	28.5117i	0.926016	−	0.926016i
$949$	9.48553	+	14.1961i	0.307913	+	0.460825i
$950$	−11.0642	−	26.7112i	−0.358969	−	0.866627i
$951$	1.29971			0.0421460
$952$		0			0
$953$	−29.7422			−0.963445			−0.481722	−	0.876324i	$-0.659989\pi$
$953$	−29.7422			−0.963445			−0.481722	+	0.876324i	$0.659989\pi$
$954$	14.7815	+	35.6856i	0.478568	+	1.15537i
$955$	4.99438	+	7.47461i	0.161614	+	0.241873i
$956$	−3.82881	+	3.82881i	−0.123833	+	0.123833i
$957$	−4.51725	+	22.7098i	−0.146022	+	0.734103i
$958$	24.1431	−	36.1327i	0.780028	−	1.16739i
$959$		0			0
$960$	10.0694	+	4.17088i	0.324988	+	0.134614i
$961$	−3.04636	+	7.35455i	−0.0982696	+	0.237244i
$962$	62.6417	−	12.4602i	2.01965	−	0.401734i
$963$	−1.29295	+	1.93503i	−0.0416647	+	0.0623556i
$964$	67.8824	+	13.5027i	2.18635	+	0.434891i
$965$	0.937411	−	0.937411i	0.0301763	−	0.0301763i
$966$		0			0
$967$	−33.3628	+	13.8193i	−1.07288	+	0.444400i	−0.848004	−	0.529989i	$-0.822196\pi$
$967$	−33.3628	+	13.8193i	−1.07288	+	0.444400i	−0.224871	+	0.974389i	$0.572196\pi$
$968$			38.0789i			1.22390i
$969$	4.52159	+	10.8908i	0.145254	+	0.349861i
$970$	−10.7941			−0.346576
$971$	−5.43698	+	2.25207i	−0.174481	+	0.0722723i	−0.468214	−	0.883615i	$-0.655102\pi$
$971$	−5.43698	+	2.25207i	−0.174481	+	0.0722723i	0.293733	+	0.955887i	$0.405102\pi$
$972$	−38.1302	−	57.0659i	−1.22303	−	1.83039i
$973$		0			0
$974$	79.0484	+	15.7237i	2.53287	+	0.503820i
$975$	−28.0790	−	18.7618i	−0.899248	−	0.600858i
$976$	35.4881	+	178.411i	1.13595	+	5.71079i
$977$	14.1270	+	5.85161i	0.451964	+	0.187210i	0.597041	−	0.802211i	$-0.296343\pi$
$977$	14.1270	+	5.85161i	0.451964	+	0.187210i	−0.145077	+	0.989420i	$0.546343\pi$
$978$	13.6372	+	5.64869i	0.436068	+	0.180625i
$979$	−20.1532	+	4.00872i	−0.644100	+	0.128119i
$980$		0			0
$981$	−1.58068	+	7.94660i	−0.0504672	+	0.253716i
$982$	−65.7212	−	65.7212i	−2.09725	−	2.09725i
$983$	30.7786	−	20.5656i	0.981686	−	0.655941i	0.0424083	−	0.999100i	$-0.486497\pi$
$983$	30.7786	−	20.5656i	0.981686	−	0.655941i	0.939277	+	0.343159i	$0.111497\pi$
$984$	28.6930	−	11.8850i	0.914700	−	0.378881i
$985$	0.609052			0.0194060
$986$	74.5301	+	30.7996i	2.37352	+	0.980860i
$987$		0			0
$988$	25.7387	+	62.1388i	0.818859	+	1.97690i
$989$	6.99867	−	4.67636i	0.222545	−	0.148700i
$990$	−3.62142	−	3.62142i	−0.115096	−	0.115096i
$991$	5.89240	+	1.17207i	0.187178	+	0.0372321i	0.287789	−	0.957694i	$-0.407080\pi$
$991$	5.89240	+	1.17207i	0.187178	+	0.0372321i	−0.100611	+	0.994926i	$0.532080\pi$
$992$	40.5135	−	60.6328i	1.28631	−	1.92509i
$993$	4.56237	+	22.9366i	0.144782	+	0.727871i
$994$		0			0
$995$	−3.51538	+	8.48688i	−0.111445	+	0.269052i
$996$	−12.4310	−	62.4950i	−0.393892	−	1.98023i
$997$	−8.33672	−	5.57042i	−0.264027	−	0.176417i	0.416510	−	0.909131i	$-0.363253\pi$
$997$	−8.33672	−	5.57042i	−0.264027	−	0.176417i	−0.680536	+	0.732714i	$0.738253\pi$
$998$	5.07065	−	25.4919i	0.160509	−	0.806931i
$999$	16.3698	−	16.3698i	0.517917	−	0.517917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.t.d.97.1	yes	72
7.2	even	3		833.2.bc.a.80.1		144
7.3	odd	6		833.2.bc.d.607.9		144
7.4	even	3		833.2.bc.a.607.9		144
7.5	odd	6		833.2.bc.d.80.1		144
7.6	odd	2		833.2.t.a.97.1	✓	72
17.10	odd	16		833.2.t.a.146.1	yes	72
119.10	even	48		833.2.bc.a.656.1		144
119.27	even	16	inner	833.2.t.d.146.1	yes	72
119.44	odd	48		833.2.bc.d.129.9		144
119.61	even	48		833.2.bc.a.129.9		144
119.95	odd	48		833.2.bc.d.656.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.t.a.97.1	✓	72	7.6	odd	2
833.2.t.a.146.1	yes	72	17.10	odd	16
833.2.t.d.97.1	yes	72	1.1	even	1	trivial
833.2.t.d.146.1	yes	72	119.27	even	16	inner
833.2.bc.a.80.1		144	7.2	even	3
833.2.bc.a.129.9		144	119.61	even	48
833.2.bc.a.607.9		144	7.4	even	3
833.2.bc.a.656.1		144	119.10	even	48
833.2.bc.d.80.1		144	7.5	odd	6
833.2.bc.d.129.9		144	119.44	odd	48
833.2.bc.d.607.9		144	7.3	odd	6
833.2.bc.d.656.1		144	119.95	odd	48

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02069 - 2.46415i) q^{2} +(-0.692606 - 1.03656i) q^{3} +(-3.61604 + 3.61604i) q^{4} +(-0.102295 + 0.514273i) q^{5} +(-1.84730 + 2.76469i) q^{6} +(7.67299 + 3.17826i) q^{8} +(0.553301 - 1.33579i) q^{9} +(1.37166 - 0.272840i) q^{10} +(1.40714 - 2.10594i) q^{11} +(6.25272 + 1.24374i) q^{12} +(4.05383 - 4.05383i) q^{13} +(0.603924 - 0.250154i) q^{15} -11.9237i q^{16} +(-3.43012 - 2.28786i) q^{17} -3.85633 q^{18} +(2.11950 - 0.877928i) q^{19} +(-1.48973 - 2.22953i) q^{20} +(-6.62561 - 1.31792i) q^{22} +(5.55766 + 3.71351i) q^{23} +(-2.01991 - 10.1548i) q^{24} +(4.36539 + 1.80820i) q^{25} +(-14.1270 - 5.85158i) q^{26} +(-5.43595 + 1.08128i) q^{27} +(1.43063 - 7.19227i) q^{29} +(-1.23283 - 1.23283i) q^{30} +(-3.99101 + 2.66671i) q^{31} +(-14.0359 + 5.81386i) q^{32} -3.15753 q^{33} +(-2.13656 + 10.7875i) q^{34} +(2.82950 + 6.83101i) q^{36} +(-3.47299 + 2.32058i) q^{37} +(-4.32669 - 4.32669i) q^{38} +(-7.00974 - 1.39432i) q^{39} +(-2.41940 + 3.62089i) q^{40} +(0.585195 + 2.94197i) q^{41} +(0.481907 - 1.16343i) q^{43} +(2.52687 + 12.7034i) q^{44} +(0.630359 + 0.421193i) q^{45} +(3.47803 - 17.4852i) q^{46} +(-4.79985 + 4.79985i) q^{47} +(-12.3596 + 8.25844i) q^{48} -12.6026i q^{50} +(0.00422341 + 5.14010i) q^{51} +29.3176i q^{52} +(-3.83304 - 9.25378i) q^{53} +(8.21283 + 12.2914i) q^{54} +(0.939085 + 0.939085i) q^{55} +(-2.37800 - 1.58893i) q^{57} +(-19.1831 + 3.81575i) q^{58} +(4.43524 - 10.7076i) q^{59} +(-1.27925 + 3.08837i) q^{60} +(-14.9627 + 2.97626i) q^{61} +(10.6447 + 7.11259i) q^{62} +(11.7898 + 11.7898i) q^{64} +(1.67009 + 2.49947i) q^{65} +(3.22284 + 7.78062i) q^{66} +2.63218i q^{67} +(20.6764 - 4.13046i) q^{68} -8.33283i q^{69} +(11.0057 - 7.35375i) q^{71} +(8.49095 - 8.49095i) q^{72} +(-0.581001 + 2.92089i) q^{73} +(9.26308 + 6.18939i) q^{74} +(-1.14919 - 5.77734i) q^{75} +(-4.48959 + 10.8388i) q^{76} +(3.71891 + 18.6962i) q^{78} +(3.51384 - 5.25883i) q^{79} +(6.13205 + 1.21974i) q^{80} +(1.81867 + 1.81867i) q^{81} +(6.65217 - 4.44484i) q^{82} +(-3.82487 - 9.23404i) q^{83} +(1.52747 - 1.52998i) q^{85} -3.35873 q^{86} +(-8.44606 + 3.49847i) q^{87} +(17.4902 - 11.6866i) q^{88} +(-5.73661 - 5.73661i) q^{89} +(0.394484 - 1.98321i) q^{90} +(-33.5249 + 6.66851i) q^{92} +(5.52839 + 2.28993i) q^{93} +(16.7267 + 6.92842i) q^{94} +(0.234679 + 1.17981i) q^{95} +(15.7477 + 10.5223i) q^{96} +(-7.56984 - 1.50573i) q^{97} +(-2.03451 - 3.04487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{3} + 8 q^{5} + 8 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{13} - 40 q^{18} + 24 q^{19} + 24 q^{22} + 8 q^{23} - 24 q^{24} + 8 q^{25} + 8 q^{27} + 80 q^{31} - 40 q^{32} - 80 q^{33} + 120 q^{36} + 48 q^{37}+ \cdots + 40 q^{99}+O(q^{100}) \) 72 * q + 8 * q^3 + 8 * q^5 + 8 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^13 - 40 * q^18 + 24 * q^19 + 24 * q^22 + 8 * q^23 - 24 * q^24 + 8 * q^25 + 8 * q^27 + 80 * q^31 - 40 * q^32 - 80 * q^33 + 120 * q^36 + 48 * q^37 - 56 * q^38 - 16 * q^39 - 32 * q^40 + 24 * q^41 + 24 * q^43 + 32 * q^44 - 48 * q^45 - 40 * q^47 - 40 * q^51 - 24 * q^53 + 200 * q^54 - 48 * q^57 + 32 * q^58 + 8 * q^59 - 80 * q^60 + 128 * q^62 - 24 * q^65 - 8 * q^66 - 40 * q^68 - 48 * q^73 - 32 * q^74 + 128 * q^75 + 72 * q^76 - 48 * q^78 - 32 * q^79 + 256 * q^80 + 16 * q^81 - 152 * q^82 - 32 * q^85 - 80 * q^86 - 64 * q^87 + 56 * q^88 - 64 * q^89 - 376 * q^90 - 216 * q^92 - 32 * q^93 - 128 * q^94 + 32 * q^95 + 32 * q^96 - 8 * q^97 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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