LMFDB - Embedded newform 575.2.p.b.524.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [575,2,Mod(49,575)] 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("575.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(575, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.p (of order $22$, degree $10$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{22})$
Coefficient field:	$\Q(\zeta_{44})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			524.1
Root			$0.540641 - 0.841254i$ of defining polynomial
Character	$\chi$	$=$	575.524
Dual form			575.2.p.b.124.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0666238 + 0.226900i) q^{2} +(-0.361922 - 0.313607i) q^{3} +(1.63546 + 1.05105i) q^{4} +(0.0952700 - 0.0612263i) q^{6} +(-2.31611 + 1.05773i) q^{7} +(-0.704881 + 0.610783i) q^{8} +(-0.394306 - 2.74246i) q^{9} +(3.23616 - 0.950224i) q^{11} +(-0.262294 - 0.893290i) q^{12} +(2.99430 + 1.36745i) q^{13} +(-0.0856910 - 0.595994i) q^{14} +(1.52357 + 3.33616i) q^{16} +(3.39353 + 5.28043i) q^{17} +(0.648534 + 0.0932451i) q^{18} +(3.55928 + 2.28741i) q^{19} +(1.16996 + 0.343532i) q^{21} +0.797593i q^{22} +(0.847210 - 4.72041i) q^{23} +0.446658 q^{24} +(-0.509766 + 0.588302i) q^{26} +(-1.49407 + 2.32482i) q^{27} +(-4.89963 - 0.704460i) q^{28} +(-5.28830 + 3.39858i) q^{29} +(3.10538 + 3.58380i) q^{31} +(-2.70488 + 0.388902i) q^{32} +(-1.46924 - 0.670978i) q^{33} +(-1.42422 + 0.418188i) q^{34} +(2.23758 - 4.89963i) q^{36} +(-0.0375858 + 0.00540403i) q^{37} +(-0.756145 + 0.655203i) q^{38} +(-0.654861 - 1.43394i) q^{39} +(-0.462048 + 3.21361i) q^{41} +(-0.155895 + 0.242577i) q^{42} +(-0.974066 - 0.844033i) q^{43} +(6.29135 + 1.84731i) q^{44} +(1.01462 + 0.506723i) q^{46} -3.41741i q^{47} +(0.494829 - 1.68523i) q^{48} +(-0.338474 + 0.390620i) q^{49} +(0.427789 - 2.97534i) q^{51} +(3.45981 + 5.38357i) q^{52} +(6.11799 - 2.79399i) q^{53} +(-0.427961 - 0.493893i) q^{54} +(0.986535 - 2.16021i) q^{56} +(-0.570833 - 1.94408i) q^{57} +(-0.418811 - 1.42634i) q^{58} +(4.32805 - 9.47711i) q^{59} +(-2.35737 - 2.72055i) q^{61} +(-1.02006 + 0.465844i) q^{62} +(3.81404 + 5.93476i) q^{63} +(-0.951939 + 6.62088i) q^{64} +(0.250131 - 0.288666i) q^{66} +(1.92124 - 6.54316i) q^{67} +12.2027i q^{68} +(-1.78698 + 1.44273i) q^{69} +(-3.92408 - 1.15221i) q^{71} +(1.95299 + 1.69227i) q^{72} +(-2.35800 + 3.66912i) q^{73} +(0.00127794 - 0.00888826i) q^{74} +(3.41689 + 7.48194i) q^{76} +(-6.49022 + 5.62381i) q^{77} +(0.368991 - 0.0530529i) q^{78} +(-0.997820 + 2.18492i) q^{79} +(-6.70548 + 1.96891i) q^{81} +(-0.698384 - 0.318941i) q^{82} +(2.92705 - 0.420847i) q^{83} +(1.55236 + 1.79152i) q^{84} +(0.256407 - 0.164783i) q^{86} +(2.97977 + 0.428426i) q^{87} +(-1.70073 + 2.64639i) q^{88} +(8.09455 - 9.34161i) q^{89} -8.38151 q^{91} +(6.34695 - 6.82959i) q^{92} -2.27092i q^{93} +(0.775410 + 0.227681i) q^{94} +(1.10092 + 0.707516i) q^{96} +(-10.5084 - 1.51088i) q^{97} +(-0.0660811 - 0.102824i) q^{98} +(-3.88199 - 8.50038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{4} + 12 q^{6} + 4 q^{9} + 14 q^{11} - 18 q^{14} + 2 q^{16} - 4 q^{19} - 4 q^{21} + 76 q^{24} + 24 q^{26} - 28 q^{29} + 20 q^{31} - 58 q^{34} + 54 q^{36} - 2 q^{39} + 14 q^{41} + 68 q^{44} - 58 q^{46}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^4 + 12 * q^6 + 4 * q^9 + 14 * q^11 - 18 * q^14 + 2 * q^16 - 4 * q^19 - 4 * q^21 + 76 * q^24 + 24 * q^26 - 28 * q^29 + 20 * q^31 - 58 * q^34 + 54 * q^36 - 2 * q^39 + 14 * q^41 + 68 * q^44 - 58 * q^46 + 36 * q^49 + 14 * q^51 + 12 * q^54 - 4 * q^56 + 42 * q^59 + 6 * q^61 - 48 * q^64 + 4 * q^66 - 52 * q^69 - 28 * q^71 - 20 * q^74 - 32 * q^76 + 30 * q^79 - 88 * q^81 + 34 * q^84 - 22 * q^86 - 50 * q^89 - 8 * q^91 - 34 * q^94 - 102 * q^96 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$-1$

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 $

$2$	−0.0666238	+	0.226900i	−0.0471101	+	0.160442i	−0.979689	−	0.200525i	$-0.935735\pi$
$2$	−0.0666238	+	0.226900i	−0.0471101	+	0.160442i	0.932578	+	0.360967i	$0.117553\pi$
$3$	−0.361922	−	0.313607i	−0.208956	−	0.181061i	0.544095	−	0.839024i	$-0.316873\pi$
$3$	−0.361922	−	0.313607i	−0.208956	−	0.181061i	−0.753051	+	0.657962i	$0.771419\pi$
$4$	1.63546	+	1.05105i	0.817731	+	0.525524i
$5$		0			0
$5$		0			0
$6$	0.0952700	−	0.0612263i	0.0388938	−	0.0249955i
$7$	−2.31611	+	1.05773i	−0.875406	+	0.399784i	−0.801863	−	0.597508i	$-0.796158\pi$
$7$	−2.31611	+	1.05773i	−0.875406	+	0.399784i	−0.0735424	+	0.997292i	$0.523430\pi$
$8$	−0.704881	+	0.610783i	−0.249213	+	0.215944i
$9$	−0.394306	−	2.74246i	−0.131435	−	0.914154i
$10$		0			0
$11$	3.23616	−	0.950224i	0.975740	−	0.286503i	0.245275	−	0.969453i	$-0.421122\pi$
$11$	3.23616	−	0.950224i	0.975740	−	0.286503i	0.730465	+	0.682950i	$0.239303\pi$
$12$	−0.262294	−	0.893290i	−0.0757176	−	0.257871i
$13$	2.99430	+	1.36745i	0.830470	+	0.379263i	0.784842	−	0.619696i	$-0.212744\pi$
$13$	2.99430	+	1.36745i	0.830470	+	0.379263i	0.0456275	+	0.998959i	$0.485471\pi$
$14$	−0.0856910	−	0.595994i	−0.0229019	−	0.159286i
$15$		0			0
$16$	1.52357	+	3.33616i	0.380893	+	0.834040i
$17$	3.39353	+	5.28043i	0.823051	+	1.28069i	0.957112	+	0.289719i	$0.0935619\pi$
$17$	3.39353	+	5.28043i	0.823051	+	1.28069i	−0.134061	+	0.990973i	$0.542802\pi$
$18$	0.648534	+	0.0932451i	0.152861	+	0.0219781i
$19$	3.55928	+	2.28741i	0.816554	+	0.524767i	0.880979	−	0.473155i	$-0.156885\pi$
$19$	3.55928	+	2.28741i	0.816554	+	0.524767i	−0.0644252	+	0.997923i	$0.520521\pi$
$20$		0			0
$21$	1.16996	+	0.343532i	0.255306	+	0.0749647i
$22$			0.797593i			0.170047i
$23$	0.847210	−	4.72041i	0.176655	−	0.984273i
$23$	0.847210	−	4.72041i	0.176655	−	0.984273i
$24$	0.446658			0.0911736
$25$		0			0
$26$	−0.509766	+	0.588302i	−0.0999734	+	0.115375i
$27$	−1.49407	+	2.32482i	−0.287534	+	0.447412i
$28$	−4.89963	−	0.704460i	−0.925943	−	0.133130i
$29$	−5.28830	+	3.39858i	−0.982012	+	0.631101i	−0.930005	−	0.367546i	$-0.880198\pi$
$29$	−5.28830	+	3.39858i	−0.982012	+	0.631101i	−0.0520069	+	0.998647i	$0.516562\pi$
$30$		0			0
$31$	3.10538	+	3.58380i	0.557742	+	0.643669i	0.962669	−	0.270680i	$-0.0872485\pi$
$31$	3.10538	+	3.58380i	0.557742	+	0.643669i	−0.404927	+	0.914349i	$0.632703\pi$
$32$	−2.70488	+	0.388902i	−0.478159	+	0.0687489i
$33$	−1.46924	−	0.670978i	−0.255761	−	0.116802i
$34$	−1.42422	+	0.418188i	−0.244251	+	0.0717187i
$35$		0			0
$36$	2.23758	−	4.89963i	0.372931	−	0.816605i
$37$	−0.0375858	+	0.00540403i	−0.00617907	+	0.000888417i	−0.145404	−	0.989372i	$-0.546448\pi$
$37$	−0.0375858	+	0.00540403i	−0.00617907	+	0.000888417i	0.139225	+	0.990261i	$0.455539\pi$
$38$	−0.756145	+	0.655203i	−0.122663	+	0.106288i
$39$	−0.654861	−	1.43394i	−0.104862	−	0.229615i
$40$		0			0
$41$	−0.462048	+	3.21361i	−0.0721597	+	0.501882i	0.921404	+	0.388606i	$0.127043\pi$
$41$	−0.462048	+	3.21361i	−0.0721597	+	0.501882i	−0.993564	+	0.113275i	$0.963866\pi$
$42$	−0.155895	+	0.242577i	−0.0240550	+	0.0374304i
$43$	−0.974066	−	0.844033i	−0.148544	−	0.128714i	0.577419	−	0.816448i	$-0.304060\pi$
$43$	−0.974066	−	0.844033i	−0.148544	−	0.128714i	−0.725963	+	0.687734i	$0.758605\pi$
$44$	6.29135	+	1.84731i	0.948457	+	0.278492i
$45$		0			0
$46$	1.01462	+	0.506723i	0.149597	+	0.0747123i
$47$		−	3.41741i		−	0.498480i	−0.968442	−	0.249240i	$-0.919819\pi$
$47$		−	3.41741i		−	0.498480i	0.968442	−	0.249240i	$-0.0801809\pi$
$48$	0.494829	−	1.68523i	0.0714224	−	0.243243i
$49$	−0.338474	+	0.390620i	−0.0483534	+	0.0558028i
$50$		0			0
$51$	0.427789	−	2.97534i	0.0599024	−	0.416631i
$52$	3.45981	+	5.38357i	0.479789	+	0.746567i
$53$	6.11799	−	2.79399i	0.840370	−	0.383784i	0.0517465	−	0.998660i	$-0.483521\pi$
$53$	6.11799	−	2.79399i	0.840370	−	0.383784i	0.788624	+	0.614876i	$0.210794\pi$
$54$	−0.427961	−	0.493893i	−0.0582381	−	0.0672104i
$55$		0			0
$56$	0.986535	−	2.16021i	0.131831	−	0.288670i
$57$	−0.570833	−	1.94408i	−0.0756086	−	0.257499i
$58$	−0.418811	−	1.42634i	−0.0549926	−	0.187288i
$59$	4.32805	−	9.47711i	0.563464	−	1.23381i	−0.386741	−	0.922188i	$-0.626399\pi$
$59$	4.32805	−	9.47711i	0.563464	−	1.23381i	0.950205	−	0.311626i	$-0.100874\pi$
$60$		0			0
$61$	−2.35737	−	2.72055i	−0.301830	−	0.348331i	0.584492	−	0.811399i	$-0.301294\pi$
$61$	−2.35737	−	2.72055i	−0.301830	−	0.348331i	−0.886322	+	0.463069i	$0.846748\pi$
$62$	−1.02006	+	0.465844i	−0.129547	+	0.0591622i
$63$	3.81404	+	5.93476i	0.480524	+	0.747710i
$64$	−0.951939	+	6.62088i	−0.118992	+	0.827610i
$65$		0			0
$66$	0.250131	−	0.288666i	0.0307890	−	0.0355324i
$67$	1.92124	−	6.54316i	0.234717	−	0.799374i	−0.754924	−	0.655812i	$-0.772326\pi$
$67$	1.92124	−	6.54316i	0.234717	−	0.799374i	0.989641	−	0.143562i	$-0.0458556\pi$
$68$			12.2027i			1.47979i
$69$	−1.78698	+	1.44273i	−0.215127	+	0.173684i
$70$		0			0
$71$	−3.92408	−	1.15221i	−0.465702	−	0.136742i	0.0404594	−	0.999181i	$-0.487118\pi$
$71$	−3.92408	−	1.15221i	−0.465702	−	0.136742i	−0.506161	+	0.862439i	$0.668936\pi$
$72$	1.95299	+	1.69227i	0.230162	+	0.199436i
$73$	−2.35800	+	3.66912i	−0.275983	+	0.429438i	−0.951381	−	0.308015i	$-0.900335\pi$
$73$	−2.35800	+	3.66912i	−0.275983	+	0.429438i	0.675399	+	0.737453i	$0.263972\pi$
$74$	0.00127794	−	0.00888826i	0.000148557	−	0.00103324i
$75$		0			0
$76$	3.41689	+	7.48194i	0.391944	+	0.858237i
$77$	−6.49022	+	5.62381i	−0.739629	+	0.640892i
$78$	0.368991	−	0.0530529i	0.0417800	−	0.00600706i
$79$	−0.997820	+	2.18492i	−0.112263	+	0.245823i	−0.957421	−	0.288694i	$-0.906779\pi$
$79$	−0.997820	+	2.18492i	−0.112263	+	0.245823i	0.845158	+	0.534517i	$0.179506\pi$
$80$		0			0
$81$	−6.70548	+	1.96891i	−0.745053	+	0.218767i
$82$	−0.698384	−	0.318941i	−0.0771237	−	0.0352212i
$83$	2.92705	−	0.420847i	0.321286	−	0.0461939i	0.0202149	−	0.999796i	$-0.493565\pi$
$83$	2.92705	−	0.420847i	0.321286	−	0.0461939i	0.301071	+	0.953602i	$0.402656\pi$
$84$	1.55236	+	1.79152i	0.169376	+	0.195471i
$85$		0			0
$86$	0.256407	−	0.164783i	0.0276491	−	0.0177690i
$87$	2.97977	+	0.428426i	0.319465	+	0.0459321i
$88$	−1.70073	+	2.64639i	−0.181298	+	0.282106i
$89$	8.09455	−	9.34161i	0.858020	−	0.990208i	−0.141979	−	0.989870i	$-0.545347\pi$
$89$	8.09455	−	9.34161i	0.858020	−	0.990208i	1.00000		0.000338824i	$-0.000107851\pi$
$90$		0			0
$91$	−8.38151			−0.878621
$92$	6.34695	−	6.82959i	0.661716	−	0.712034i
$93$		−	2.27092i		−	0.235484i
$94$	0.775410	+	0.227681i	0.0799774	+	0.0234835i
$95$		0			0
$96$	1.10092	+	0.707516i	0.112362	+	0.0722106i
$97$	−10.5084	−	1.51088i	−1.06697	−	0.153407i	−0.413610	−	0.910454i	$-0.635732\pi$
$97$	−10.5084	−	1.51088i	−1.06697	−	0.153407i	−0.653360	+	0.757047i	$0.726641\pi$
$98$	−0.0660811	−	0.102824i	−0.00667520	−	0.0103868i
$99$	−3.88199	−	8.50038i	−0.390155	−	0.854320i
$100$		0			0
$101$	−1.30916	−	9.10538i	−0.130266	−	0.906019i	−0.945206	−	0.326474i	$-0.894139\pi$
$101$	−1.30916	−	9.10538i	−0.130266	−	0.906019i	0.814940	−	0.579545i	$-0.196770\pi$
$102$	0.646603	+	0.295294i	0.0640232	+	0.0292384i
$103$	−4.16088	−	14.1707i	−0.409984	−	1.39628i	−0.863193	−	0.504873i	$-0.831539\pi$
$103$	−4.16088	−	14.1707i	−0.409984	−	1.39628i	0.453209	−	0.891404i	$-0.350279\pi$
$104$	−2.94584	+	0.864977i	−0.288863	+	0.0848180i
$105$		0			0
$106$	0.226353	+	1.57432i	0.0219853	+	0.152911i
$107$	12.2481	−	10.6131i	1.18407	−	1.02600i	0.185008	−	0.982737i	$-0.440769\pi$
$107$	12.2481	−	10.6131i	1.18407	−	1.02600i	0.999064	−	0.0432669i	$-0.0137766\pi$
$108$	−4.88700	+	2.23182i	−0.470252	+	0.214757i
$109$	−12.6437	+	8.12562i	−1.21105	+	0.778293i	−0.980834	−	0.194847i	$-0.937579\pi$
$109$	−12.6437	+	8.12562i	−1.21105	+	0.778293i	−0.230214	+	0.973140i	$0.573943\pi$
$110$		0			0
$111$	0.0152979	+	0.00983135i	0.00145201	+	0.000933151i
$112$	−7.05751	−	6.11537i	−0.666872	−	0.577848i
$113$	−0.325532	+	1.10866i	−0.0306235	+	0.104294i	−0.973387	−	0.229169i	$-0.926399\pi$
$113$	−0.325532	+	1.10866i	−0.0306235	+	0.104294i	0.942763	+	0.333463i	$0.108217\pi$
$114$	0.479142			0.0448758
$115$		0			0
$116$	−12.2209			−1.13468
$117$	2.56951	−	8.75095i	0.237551	−	0.809026i
$118$	1.86200	+	1.61343i	0.171411	+	0.148529i
$119$	−13.4450	−	8.64060i	−1.23250	−	0.792082i
$120$		0			0
$121$	0.316044	−	0.203109i	0.0287313	−	0.0184645i
$122$	0.774349	−	0.353634i	0.0701063	−	0.0320165i
$123$	1.17504	−	1.01818i	0.105949	−	0.0918058i
$124$	1.31199	+	9.12507i	0.117820	+	0.819455i
$125$		0			0
$126$	−1.60070	+	0.470008i	−0.142602	+	0.0418717i
$127$	2.94228	+	10.0205i	0.261085	+	0.889173i	0.980819	+	0.194923i	$0.0624456\pi$
$127$	2.94228	+	10.0205i	0.261085	+	0.889173i	−0.719734	+	0.694250i	$0.755736\pi$
$128$	−6.41034	−	2.92750i	−0.566599	−	0.258757i
$129$	0.0878411	+	0.610948i	0.00773398	+	0.0537910i
$130$		0			0
$131$	−6.31204	−	13.8214i	−0.551485	−	1.20758i	−0.956085	−	0.293090i	$-0.905316\pi$
$131$	−6.31204	−	13.8214i	−0.551485	−	1.20758i	0.404600	−	0.914494i	$-0.367411\pi$
$132$	−1.69765	−	2.64160i	−0.147762	−	0.229921i
$133$	−10.6631	−	1.53312i	−0.924610	−	0.132939i
$134$	1.35664	+	0.871860i	0.117196	+	0.0753173i
$135$		0			0
$136$	−5.61723	−	1.64937i	−0.481673	−	0.141432i
$137$		−	1.22243i		−	0.104439i	−0.998636	−	0.0522196i	$-0.983370\pi$
$137$		−	1.22243i		−	0.104439i	0.998636	−	0.0522196i	$-0.0166296\pi$
$138$	−0.208299	−	0.501585i	−0.0177316	−	0.0426977i
$139$	−2.18447			−0.185284			−0.0926420	−	0.995699i	$-0.529531\pi$
$139$	−2.18447			−0.185284			−0.0926420	+	0.995699i	$0.529531\pi$
$140$		0			0
$141$	−1.07172	+	1.23684i	−0.0902555	+	0.104160i
$142$	0.522874	−	0.813607i	0.0438786	−	0.0682764i
$143$	10.9894	+	1.58004i	0.918983	+	0.132130i
$144$	8.54854	−	5.49381i	0.712378	−	0.457818i
$145$		0			0
$146$	−0.675423	−	0.779480i	−0.0558984	−	0.0645102i
$147$	0.245002	−	0.0352260i	0.0202074	−	0.00290539i
$148$	−0.0671501	−	0.0306664i	−0.00551970	−	0.00252076i
$149$	−3.97217	+	1.16634i	−0.325413	+	0.0955499i	−0.440359	−	0.897822i	$-0.645149\pi$
$149$	−3.97217	+	1.16634i	−0.325413	+	0.0955499i	0.114946	+	0.993372i	$0.463331\pi$
$150$		0			0
$151$	−2.82316	+	6.18185i	−0.229745	+	0.503072i	−0.989035	−	0.147681i	$-0.952819\pi$
$151$	−2.82316	+	6.18185i	−0.229745	+	0.503072i	0.759290	+	0.650753i	$0.225546\pi$
$152$	−3.90597	+	0.561594i	−0.316816	+	0.0455513i
$153$	13.1433	−	11.3887i	1.06257	−	0.920724i
$154$	−0.843637	−	1.84731i	−0.0679822	−	0.148860i
$155$		0			0
$156$	0.436145	−	3.03345i	0.0349195	−	0.242871i
$157$	5.26441	−	8.19158i	0.420146	−	0.653759i	−0.565077	−	0.825038i	$-0.691154\pi$
$157$	5.26441	−	8.19158i	0.420146	−	0.653759i	0.985223	+	0.171279i	$0.0547899\pi$
$158$	−0.429279	−	0.371973i	−0.0341516	−	0.0295926i
$159$	−3.09045	−	0.907438i	−0.245089	−	0.0719645i
$160$		0			0
$161$	3.03069	+	11.8291i	0.238852	+	0.932262i
$162$		−	1.65265i		−	0.129844i
$163$	−1.69850	+	5.78457i	−0.133037	+	0.453083i	−0.998884	−	0.0472260i	$-0.984962\pi$
$163$	−1.69850	+	5.78457i	−0.133037	+	0.453083i	0.865847	+	0.500309i	$0.166780\pi$
$164$	−4.13332	+	4.77011i	−0.322758	+	0.372483i
$165$		0			0
$166$	−0.0995214	+	0.692186i	−0.00772436	+	0.0537241i
$167$	−0.951323	−	1.48029i	−0.0736155	−	0.114548i	0.802494	−	0.596660i	$-0.203506\pi$
$167$	−0.951323	−	1.48029i	−0.0736155	−	0.114548i	−0.876109	+	0.482112i	$0.839870\pi$
$168$	−1.03451	+	0.472443i	−0.0798139	+	0.0364498i
$169$	−1.41728	−	1.63562i	−0.109021	−	0.125817i
$170$		0			0
$171$	4.86968	−	10.6631i	0.372394	−	0.815429i
$172$	−0.705929	−	2.40417i	−0.0538266	−	0.183317i
$173$	2.87696	+	9.79801i	0.218731	+	0.744929i	0.993615	+	0.112825i	$0.0359901\pi$
$173$	2.87696	+	9.79801i	0.218731	+	0.744929i	−0.774884	+	0.632104i	$0.782192\pi$
$174$	−0.295734	+	0.647566i	−0.0224195	+	0.0490919i
$175$		0			0
$176$	8.10063	+	9.34863i	0.610608	+	0.704679i
$177$	−4.53851	+	2.07267i	−0.341135	+	0.155791i
$178$	1.58032	+	2.45903i	0.118450	+	0.184312i
$179$	−1.46662	+	10.2006i	−0.109620	+	0.762426i	0.858658	+	0.512550i	$0.171299\pi$
$179$	−1.46662	+	10.2006i	−0.109620	+	0.762426i	−0.968278	+	0.249876i	$0.919610\pi$
$180$		0			0
$181$	−6.08462	+	7.02203i	−0.452266	+	0.521943i	−0.935394	−	0.353607i	$-0.884955\pi$
$181$	−6.08462	+	7.02203i	−0.452266	+	0.521943i	0.483128	+	0.875550i	$0.339501\pi$
$182$	0.558408	−	1.90176i	0.0413920	−	0.140968i
$183$			1.72392i			0.127435i
$184$	2.28596	+	3.84479i	0.168523	+	0.283441i
$185$		0			0
$186$	0.515272	+	0.151298i	0.0377816	+	0.0110937i
$187$	15.9996	+	13.8637i	1.17001	+	1.01382i
$188$	3.59186	−	5.58904i	0.261963	−	0.407623i
$189$	1.00140	−	6.96486i	0.0728408	−	0.506619i
$190$		0			0
$191$	−8.52854	−	18.6749i	−0.617104	−	1.35127i	−0.917607	−	0.397488i	$-0.869882\pi$
$191$	−8.52854	−	18.6749i	−0.617104	−	1.35127i	0.300504	−	0.953781i	$-0.402845\pi$
$192$	2.42088	−	2.09771i	0.174712	−	0.151389i
$193$	−13.5967	+	1.95491i	−0.978713	+	0.140718i	−0.613063	−	0.790034i	$-0.710063\pi$
$193$	−13.5967	+	1.95491i	−0.978713	+	0.140718i	−0.365651	+	0.930752i	$0.619154\pi$
$194$	1.04293	−	2.28370i	0.0748781	−	0.163960i
$195$		0			0
$196$	−0.964121	+	0.283091i	−0.0688658	+	0.0202208i
$197$	−2.09164	−	0.955220i	−0.149023	−	0.0680566i	0.339507	−	0.940603i	$-0.389740\pi$
$197$	−2.09164	−	0.955220i	−0.149023	−	0.0680566i	−0.488531	+	0.872547i	$0.662467\pi$
$198$	2.18737	−	0.314496i	0.155449	−	0.0223503i
$199$	1.12023	+	1.29281i	0.0794109	+	0.0916450i	0.794065	−	0.607833i	$-0.207961\pi$
$199$	1.12023	+	1.29281i	0.0794109	+	0.0916450i	−0.714654	+	0.699478i	$0.753416\pi$
$200$		0			0
$201$	−2.74732	+	1.76560i	−0.193781	+	0.124536i
$202$	2.15323	+	0.309588i	0.151501	+	0.0217825i
$203$	8.65347	−	13.4651i	0.607355	−	0.945062i
$204$	3.82685	−	4.41643i	0.267933	−	0.309212i
$205$		0			0
$206$	3.49254			0.243337
$207$	−13.2796	−	0.462154i	−0.922996	−	0.0321219i
$208$			12.0729i			0.837104i
$209$	13.6919	+	4.02032i	0.947092	+	0.278091i
$210$		0			0
$211$	−6.73249	−	4.32671i	−0.463484	−	0.297863i	0.287981	−	0.957636i	$-0.407016\pi$
$211$	−6.73249	−	4.32671i	−0.463484	−	0.297863i	−0.751465	+	0.659773i	$0.770652\pi$
$212$	12.9424	+	1.86083i	0.888885	+	0.127802i
$213$	1.05887	+	1.64763i	0.0725524	+	0.112894i
$214$	1.59209	+	3.48618i	0.108833	+	0.238310i
$215$		0			0
$216$	−0.366818	−	2.55128i	−0.0249588	−	0.173592i
$217$	−10.9831	−	5.01580i	−0.745580	−	0.340495i
$218$	−1.00133	−	3.41021i	−0.0678186	−	0.230969i
$219$	2.00407	−	0.588449i	0.135423	−	0.0397637i
$220$		0			0
$221$	2.94051	+	20.4517i	0.197800	+	1.37573i
$222$	−0.00324994	+	0.00281608i	−0.000218121	+	0.000189003i
$223$	−25.9455	+	11.8489i	−1.73744	+	0.793463i	−0.745538	+	0.666463i	$0.767808\pi$
$223$	−25.9455	+	11.8489i	−1.73744	+	0.793463i	−0.991903	+	0.127000i	$0.959465\pi$
$224$	5.85342	−	3.76177i	0.391098	−	0.251344i
$225$		0			0
$226$	−0.229867	−	0.147726i	−0.0152905	−	0.00982661i
$227$	−7.09127	−	6.14462i	−0.470664	−	0.407833i	0.386971	−	0.922092i	$-0.373521\pi$
$227$	−7.09127	−	6.14462i	−0.470664	−	0.407833i	−0.857635	+	0.514259i	$0.828067\pi$
$228$	1.10974	−	3.77944i	0.0734945	−	0.250299i
$229$	6.65292			0.439637			0.219819	−	0.975541i	$-0.429453\pi$
$229$	6.65292			0.439637			0.219819	+	0.975541i	$0.429453\pi$
$230$		0			0
$231$	4.11262			0.270590
$232$	1.65182	−	5.62560i	0.108448	−	0.369339i
$233$	19.3768	+	16.7901i	1.26942	+	1.09996i	0.990189	+	0.139733i	$0.0446244\pi$
$233$	19.3768	+	16.7901i	1.26942	+	1.09996i	0.279229	+	0.960224i	$0.409921\pi$
$234$	1.81440	+	1.16604i	0.118611	+	0.0762266i
$235$		0			0
$236$	17.0393	−	10.9505i	1.10916	−	0.712815i
$237$	1.04634	−	0.477847i	0.0679671	−	0.0310395i
$238$	2.85631	−	2.47501i	0.185147	−	0.160431i
$239$	−0.218040	−	1.51650i	−0.0141038	−	0.0980943i	0.981554	−	0.191187i	$-0.0612337\pi$
$239$	−0.218040	−	1.51650i	−0.0141038	−	0.0980943i	−0.995657	+	0.0930929i	$0.970325\pi$
$240$		0			0
$241$	26.7753	−	7.86194i	1.72475	−	0.506432i	0.738864	−	0.673854i	$-0.235362\pi$
$241$	26.7753	−	7.86194i	1.72475	−	0.506432i	0.985885	+	0.167422i	$0.0535442\pi$
$242$	0.0250294	+	0.0852423i	0.00160895	+	0.00547958i
$243$	10.5857	+	4.83432i	0.679072	+	0.310122i
$244$	−0.995962	−	6.92707i	−0.0637599	−	0.443460i
$245$		0			0
$246$	0.152738	+	0.334450i	0.00973824	+	0.0213238i
$247$	7.52962	+	11.7163i	0.479098	+	0.745492i
$248$	−4.37784	−	0.629439i	−0.277993	−	0.0399694i
$249$	−1.19135	−	0.765631i	−0.0754985	−	0.0485199i
$250$		0			0
$251$	10.8108	+	3.17435i	0.682374	+	0.200363i	0.604506	−	0.796601i	$-0.293371\pi$
$251$	10.8108	+	3.17435i	0.682374	+	0.200363i	0.0778679	+	0.996964i	$0.475189\pi$
$252$			13.7148i			0.863952i
$253$	−1.74373	−	16.0810i	−0.109627	−	1.01101i
$254$	−2.46967			−0.154961
$255$		0			0
$256$	−7.66935	+	8.85090i	−0.479334	+	0.553181i
$257$	−8.88867	+	13.8310i	−0.554460	+	0.862756i	−0.999463	−	0.0327727i	$-0.989566\pi$
$257$	−8.88867	+	13.8310i	−0.554460	+	0.862756i	0.445003	+	0.895529i	$0.353203\pi$
$258$	−0.144476	−	0.0207726i	−0.00899471	−	0.00129324i
$259$	0.0813368	−	0.0522720i	0.00505402	−	0.00324802i
$260$		0			0
$261$	11.4057	+	13.1629i	0.705995	+	0.814761i
$262$	3.55661	−	0.511364i	0.219728	−	0.0315921i
$263$	−21.3747	−	9.76148i	−1.31802	−	0.601919i	−0.372665	−	0.927966i	$-0.621556\pi$
$263$	−21.3747	−	9.76148i	−1.31802	−	0.601919i	−0.945353	+	0.326048i	$0.894283\pi$
$264$	1.44546	−	0.424425i	0.0889618	−	0.0261215i
$265$		0			0
$266$	1.05828	−	2.31732i	0.0648875	−	0.142084i
$267$	−5.85919	+	0.842424i	−0.358577	+	0.0515555i
$268$	10.0193	−	8.68177i	0.612026	−	0.530323i
$269$	−1.84523	−	4.04049i	−0.112506	−	0.246353i	0.845001	−	0.534765i	$-0.179600\pi$
$269$	−1.84523	−	4.04049i	−0.112506	−	0.246353i	−0.957506	+	0.288412i	$0.906873\pi$
$270$		0			0
$271$	2.80373	−	19.5004i	0.170315	−	1.18456i	−0.707905	−	0.706308i	$-0.750360\pi$
$271$	2.80373	−	19.5004i	0.170315	−	1.18456i	0.878220	−	0.478257i	$-0.158731\pi$
$272$	−12.4461	+	19.3665i	−0.754654	+	1.17426i
$273$	3.03345	+	2.62850i	0.183593	+	0.159084i
$274$	0.277369	+	0.0814429i	0.0167565	+	0.00492015i
$275$		0			0
$276$	−4.43891	+	0.481328i	−0.267191	+	0.0289726i
$277$			18.8580i			1.13307i	0.824038	+	0.566535i	$0.191716\pi$
$277$			18.8580i			1.13307i	−0.824038	+	0.566535i	$0.808284\pi$
$278$	0.145537	−	0.495655i	0.00872876	−	0.0297274i
$279$	8.60396	−	9.92950i	0.515105	−	0.594463i
$280$		0			0
$281$	−2.73137	+	18.9971i	−0.162940	+	1.13327i	0.730114	+	0.683325i	$0.239467\pi$
$281$	−2.73137	+	18.9971i	−0.162940	+	1.13327i	−0.893055	+	0.449948i	$0.851442\pi$
$282$	−0.209235	−	0.325577i	−0.0124598	−	0.0193878i
$283$	−0.991551	+	0.452826i	−0.0589416	+	0.0269177i	−0.444668	−	0.895696i	$-0.646678\pi$
$283$	−0.991551	+	0.452826i	−0.0589416	+	0.0269177i	0.385726	+	0.922613i	$0.373951\pi$
$284$	−5.20665	−	6.00879i	−0.308958	−	0.356556i
$285$		0			0
$286$	−1.09067	+	2.38823i	−0.0644926	+	0.141219i
$287$	−2.32898	−	7.93178i	−0.137475	−	0.468198i
$288$	2.13310	+	7.26467i	0.125694	+	0.428075i
$289$	−9.30486	+	20.3748i	−0.547345	+	1.19852i
$290$		0			0
$291$	3.32941	+	3.84234i	0.195173	+	0.225242i
$292$	−7.71283	+	3.52233i	−0.451359	+	0.206129i
$293$	−7.53613	−	11.7264i	−0.440265	−	0.685066i	0.548228	−	0.836329i	$-0.315302\pi$
$293$	−7.53613	−	11.7264i	−0.440265	−	0.685066i	−0.988494	+	0.151262i	$0.951666\pi$
$294$	−0.00833021	+	0.0579379i	−0.000485827	+	0.00337900i
$295$		0			0
$296$	0.0231929	−	0.0267660i	0.00134806	−	0.00155574i
$297$	−2.62596	+	8.94321i	−0.152374	+	0.518938i
$298$		−	0.978991i		−	0.0567114i
$299$	8.99173	−	12.9758i	0.520005	−	0.750410i
$300$		0			0
$301$	3.14880	+	0.924571i	0.181494	+	0.0532914i
$302$	−1.21457	−	1.05243i	−0.0698907	−	0.0605607i
$303$	−2.38170	+	3.70600i	−0.136825	+	0.212904i
$304$	−2.20834	+	15.3593i	−0.126657	+	0.880919i
$305$		0			0
$306$	1.70844	+	3.74097i	0.0976652	+	0.213857i
$307$	19.3701	−	16.7842i	1.10551	−	0.957928i	0.106171	−	0.994348i	$-0.466141\pi$
$307$	19.3701	−	16.7842i	1.10551	−	0.957928i	0.999337	+	0.0364203i	$0.0115955\pi$
$308$	−16.5254	+	2.37599i	−0.941622	+	0.135385i
$309$	−2.93811	+	6.43356i	−0.167143	+	0.365992i
$310$		0			0
$311$	3.56322	−	1.04626i	0.202052	−	0.0593277i	−0.179141	−	0.983823i	$-0.557332\pi$
$311$	3.56322	−	1.04626i	0.202052	−	0.0593277i	0.381192	+	0.924496i	$0.375514\pi$
$312$	1.33743	+	0.610783i	0.0757169	+	0.0345788i
$313$	15.5687	−	2.23843i	0.879992	−	0.126524i	0.312515	−	0.949913i	$-0.398829\pi$
$313$	15.5687	−	2.23843i	0.879992	−	0.126524i	0.567477	+	0.823389i	$0.307919\pi$
$314$	1.50793	+	1.74025i	0.0850976	+	0.0982078i
$315$		0			0
$316$	−3.92835	+	2.52460i	−0.220987	+	0.142020i
$317$	−3.27128	−	0.470339i	−0.183733	−	0.0264169i	0.0498339	−	0.998758i	$-0.484131\pi$
$317$	−3.27128	−	0.470339i	−0.183733	−	0.0264169i	−0.233567	+	0.972341i	$0.575040\pi$
$318$	0.411795	−	0.640766i	0.0230923	−	0.0359324i
$319$	−13.8844	+	16.0234i	−0.777376	+	0.897140i
$320$		0			0
$321$	−7.76120			−0.433188
$322$	−2.88593	−	0.100436i	−0.160827	−	0.00559706i
$323$			26.5569i			1.47766i
$324$	−13.0360	−	3.82771i	−0.724220	−	0.212650i
$325$		0			0
$326$	−1.19936	−	0.770780i	−0.0664263	−	0.0426896i
$327$	7.12429	+	1.02432i	0.393974	+	0.0566449i
$328$	−1.63713	−	2.54742i	−0.0903954	−	0.140658i
$329$	3.61470	+	7.91508i	0.199285	+	0.436373i
$330$		0			0
$331$	−1.13861	−	7.91923i	−0.0625838	−	0.435280i	−0.996890	−	0.0788080i	$-0.974889\pi$
$331$	−1.13861	−	7.91923i	−0.0625838	−	0.435280i	0.934306	−	0.356472i	$-0.116021\pi$
$332$	5.22942	+	2.38819i	0.287001	+	0.131069i
$333$	0.0296407	+	0.100947i	0.00162430	+	0.00553185i
$334$	0.399258	−	0.117233i	0.0218464	−	0.00641468i
$335$		0			0
$336$	0.636445	+	4.42657i	0.0347209	+	0.241489i
$337$	−1.05220	+	0.911733i	−0.0573168	+	0.0496653i	−0.683048	−	0.730373i	$-0.739346\pi$
$337$	−1.05220	+	0.911733i	−0.0573168	+	0.0496653i	0.625731	+	0.780039i	$0.284801\pi$
$338$	0.465547	−	0.212608i	0.0253224	−	0.0115644i
$339$	0.465501	−	0.299159i	0.0252825	−	0.0162481i
$340$		0			0
$341$	13.4549	+	8.64695i	0.728625	+	0.468259i
$342$	2.09502	+	1.81535i	0.113286	+	0.0981627i
$343$	5.39220	−	18.3642i	0.291152	−	0.991571i
$344$	1.20212			0.0648141
$345$		0			0
$346$	−2.41484			−0.129823
$347$	−4.74116	+	16.1469i	−0.254519	+	0.866811i	0.728770	+	0.684758i	$0.240092\pi$
$347$	−4.74116	+	16.1469i	−0.254519	+	0.866811i	−0.983289	+	0.182052i	$0.941726\pi$
$348$	4.42301	+	3.83256i	0.237098	+	0.205447i
$349$	16.0913	+	10.3412i	0.861347	+	0.553554i	0.895095	−	0.445876i	$-0.147108\pi$
$349$	16.0913	+	10.3412i	0.861347	+	0.553554i	−0.0337478	+	0.999430i	$0.510744\pi$
$350$		0			0
$351$	−7.65278	+	4.91814i	−0.408475	+	0.262511i
$352$	−8.38388	+	3.82879i	−0.446862	+	0.204075i
$353$	25.4309	−	22.0360i	1.35355	−	1.17286i	0.385324	−	0.922781i	$-0.374090\pi$
$353$	25.4309	−	22.0360i	1.35355	−	1.17286i	0.968226	−	0.250076i	$-0.0804557\pi$
$354$	−0.167915	−	1.16788i	−0.00892459	−	0.0620719i
$355$		0			0
$356$	23.0568	−	6.77009i	1.22201	−	0.358814i
$357$	2.15630	+	7.34368i	0.114123	+	0.388669i
$358$	−2.21679	−	1.01238i	−0.117161	−	0.0535057i
$359$	−2.79386	−	19.4317i	−0.147454	−	1.02557i	−0.920368	−	0.391054i	$-0.872110\pi$
$359$	−2.79386	−	19.4317i	−0.147454	−	1.02557i	0.772914	−	0.634511i	$-0.218799\pi$
$360$		0			0
$361$	−0.456674	−	0.999978i	−0.0240355	−	0.0526304i
$362$	−1.18792	−	1.84843i	−0.0624355	−	0.0971515i
$363$	−0.178080	−	0.0256040i	−0.00934678	−	0.00134386i
$364$	−13.7076	−	8.80937i	−0.718476	−	0.461736i
$365$		0			0
$366$	−0.391156	−	0.114854i	−0.0204461	−	0.00600350i
$367$		−	6.73062i		−	0.351336i	−0.984449	−	0.175668i	$-0.943792\pi$
$367$		−	6.73062i		−	0.351336i	0.984449	−	0.175668i	$-0.0562085\pi$
$368$	17.0388	−	4.36546i	0.888210	−	0.227565i
$369$	8.99539			0.468281
$370$		0			0
$371$	−11.2146	+	12.9424i	−0.582234	+	0.671934i
$372$	2.38685	−	3.71401i	0.123752	−	0.192563i
$373$	−25.0702	−	3.60455i	−1.29809	−	0.186637i	−0.541595	−	0.840640i	$-0.682179\pi$
$373$	−25.0702	−	3.60455i	−1.29809	−	0.186637i	−0.756492	+	0.654003i	$0.773088\pi$
$374$	−4.21163	+	2.70665i	−0.217778	+	0.139958i
$375$		0			0
$376$	2.08729	+	2.40887i	0.107644	+	0.124228i
$377$	−20.4822	+	2.94489i	−1.05488	+	0.151669i
$378$	1.51361	+	0.691242i	0.0778516	+	0.0355536i
$379$	27.6884	−	8.13003i	1.42226	−	0.417612i	0.521989	−	0.852952i	$-0.325190\pi$
$379$	27.6884	−	8.13003i	1.42226	−	0.417612i	0.900266	+	0.435340i	$0.143372\pi$
$380$		0			0
$381$	2.07762	−	4.54935i	0.106440	−	0.233070i
$382$	4.80554	−	0.690932i	0.245873	−	0.0353512i
$383$	−9.74573	+	8.44472i	−0.497983	+	0.431505i	−0.867290	−	0.497802i	$-0.834140\pi$
$383$	−9.74573	+	8.44472i	−0.497983	+	0.431505i	0.369307	+	0.929307i	$0.379595\pi$
$384$	1.40196	+	3.06986i	0.0715433	+	0.156658i
$385$		0			0
$386$	0.462296	−	3.21534i	0.0235302	−	0.163656i
$387$	−1.93065	+	3.00415i	−0.0981404	+	0.152709i
$388$	−15.5981	−	13.5159i	−0.791875	−	0.686164i
$389$	2.01154	+	0.590642i	0.101989	+	0.0299467i	0.332329	−	0.943164i	$-0.392166\pi$
$389$	2.01154	+	0.590642i	0.101989	+	0.0299467i	−0.230340	+	0.973110i	$0.573984\pi$
$390$		0			0
$391$	27.8008	−	11.5452i	1.40595	−	0.583865i
$392$		−	0.482074i		−	0.0243484i
$393$	−2.05004	+	6.98178i	−0.103411	+	0.352184i
$394$	0.356092	−	0.410953i	0.0179397	−	0.0207035i
$395$		0			0
$396$	2.58545	−	17.9822i	0.129924	−	0.903640i
$397$	−1.01587	−	1.58072i	−0.0509849	−	0.0793341i	0.814825	−	0.579707i	$-0.196833\pi$
$397$	−1.01587	−	1.58072i	−0.0509849	−	0.0793341i	−0.865810	+	0.500372i	$0.833196\pi$
$398$	−0.367973	+	0.168047i	−0.0184448	+	0.00842346i
$399$	3.37842	+	3.89890i	0.169132	+	0.195189i
$400$		0			0
$401$	7.00168	−	15.3315i	0.349647	−	0.765620i	−0.650335	−	0.759647i	$-0.725372\pi$
$401$	7.00168	−	15.3315i	0.349647	−	0.765620i	0.999982	−	0.00597275i	$-0.00190120\pi$
$402$	−0.217577	−	0.740998i	−0.0108517	−	0.0369576i
$403$	4.39777	+	14.9774i	0.219068	+	0.746079i
$404$	7.42911	−	16.2675i	0.369612	−	0.809338i
$405$		0			0
$406$	2.47869	+	2.86057i	0.123016	+	0.141967i
$407$	−0.116499	+	0.0532033i	−0.00577464	+	0.00263719i
$408$	1.51574	+	2.35854i	0.0750405	+	0.116765i
$409$	1.85146	−	12.8772i	0.0915489	−	0.636736i	−0.891449	−	0.453121i	$-0.850311\pi$
$409$	1.85146	−	12.8772i	0.0915489	−	0.636736i	0.982998	−	0.183616i	$-0.0587802\pi$
$410$		0			0
$411$	−0.383363	+	0.442424i	−0.0189099	+	0.0218232i
$412$	8.08908	−	27.5489i	0.398520	−	1.35724i
$413$			26.5279i			1.30535i
$414$	0.989600	−	2.98235i	0.0486362	−	0.146574i
$415$		0			0
$416$	−8.63102	−	2.53430i	−0.423170	−	0.124254i
$417$	0.790607	+	0.685065i	0.0387162	+	0.0335478i
$418$	−1.82442	+	2.83885i	−0.0892353	+	0.138853i
$419$	−4.18557	+	29.1113i	−0.204479	+	1.42218i	0.586308	+	0.810088i	$0.300581\pi$
$419$	−4.18557	+	29.1113i	−0.204479	+	1.42218i	−0.790787	+	0.612092i	$0.790328\pi$
$420$		0			0
$421$	9.26262	+	20.2823i	0.451432	+	0.988499i	0.989357	+	0.145506i	$0.0464811\pi$
$421$	9.26262	+	20.2823i	0.451432	+	0.988499i	−0.537925	+	0.842993i	$0.680792\pi$
$422$	1.43027	−	1.23934i	0.0696247	−	0.0603301i
$423$	−9.37211	+	1.34751i	−0.455688	+	0.0655180i
$424$	−2.60593	+	5.70619i	−0.126555	+	0.277117i
$425$		0			0
$426$	−0.444393	+	0.130485i	−0.0215309	+	0.00632204i
$427$	8.33753	+	3.80762i	0.403481	+	0.184264i
$428$	31.1862	−	4.48390i	1.50744	−	0.216737i
$429$	−3.48181	−	4.01822i	−0.168103	−	0.194001i
$430$		0			0
$431$	−1.48190	+	0.952360i	−0.0713807	+	0.0458736i	−0.575844	−	0.817559i	$-0.695327\pi$
$431$	−1.48190	+	0.952360i	−0.0713807	+	0.0458736i	0.504464	+	0.863433i	$0.331690\pi$
$432$	−10.0323	−	1.44243i	−0.482680	−	0.0693989i
$433$	−7.46017	+	11.6083i	−0.358513	+	0.557857i	−0.972923	−	0.231130i	$-0.925758\pi$
$433$	−7.46017	+	11.6083i	−0.358513	+	0.557857i	0.614410	+	0.788987i	$0.289394\pi$
$434$	1.86982	−	2.15789i	0.0897542	−	0.103582i
$435$		0			0
$436$	−29.2187			−1.39932
$437$	13.8129	−	14.8633i	0.660763	−	0.711009i
$438$			0.493928i			0.0236008i
$439$	6.89730	+	2.02523i	0.329190	+	0.0966590i	0.442151	−	0.896940i	$-0.354215\pi$
$439$	6.89730	+	2.02523i	0.329190	+	0.0966590i	−0.112961	+	0.993599i	$0.536034\pi$
$440$		0			0
$441$	1.20472	+	0.774228i	0.0573677	+	0.0368680i
$442$	−4.83639	−	0.695368i	−0.230044	−	0.0330753i
$443$	−12.6464	−	19.6782i	−0.600849	−	0.934939i	−0.999838	−	0.0179838i	$-0.994275\pi$
$443$	−12.6464	−	19.6782i	−0.600849	−	0.934939i	0.398989	−	0.916956i	$-0.369361\pi$
$444$	0.0146859	+	0.0321576i	0.000696961	+	0.00152613i
$445$		0			0
$446$	−0.959929	−	6.67646i	−0.0454540	−	0.316139i
$447$	1.80339	+	0.823580i	0.0852973	+	0.0389540i
$448$	−4.79831	−	16.3415i	−0.226699	−	0.772066i
$449$	6.47903	−	1.90241i	0.305764	−	0.0897804i	−0.125251	−	0.992125i	$-0.539974\pi$
$449$	6.47903	−	1.90241i	0.305764	−	0.0897804i	0.431015	+	0.902345i	$0.358155\pi$
$450$		0			0
$451$	1.55839	+	10.8388i	0.0733816	+	0.510380i
$452$	−1.69765	+	1.47102i	−0.0798508	+	0.0691911i
$453$	2.96043	−	1.35199i	0.139093	−	0.0635218i
$454$	1.86666	−	1.19963i	0.0876067	−	0.0563014i
$455$		0			0
$456$	1.58978	+	1.02169i	0.0744482	+	0.0478449i
$457$	5.46019	+	4.73128i	0.255417	+	0.221320i	0.773152	−	0.634221i	$-0.218679\pi$
$457$	5.46019	+	4.73128i	0.255417	+	0.221320i	−0.517735	+	0.855541i	$0.673225\pi$
$458$	−0.443242	+	1.50955i	−0.0207114	+	0.0705364i
$459$	−17.3462			−0.809653
$460$		0			0
$461$	−32.1800			−1.49877			−0.749385	−	0.662134i	$-0.769651\pi$
$461$	−32.1800			−1.49877			−0.749385	+	0.662134i	$0.769651\pi$
$462$	−0.273998	+	0.933152i	−0.0127476	+	0.0434142i
$463$	14.1886	+	12.2945i	0.659399	+	0.571373i	0.918958	−	0.394355i	$-0.129032\pi$
$463$	14.1886	+	12.2945i	0.659399	+	0.571373i	−0.259559	+	0.965727i	$0.583577\pi$
$464$	−19.3953	−	12.4646i	−0.900406	−	0.578656i
$465$		0			0
$466$	−5.10063	+	3.27798i	−0.236282	+	0.151849i
$467$	25.9018	−	11.8290i	1.19859	−	0.547379i	0.286784	−	0.957995i	$-0.407414\pi$
$467$	25.9018	−	11.8290i	1.19859	−	0.547379i	0.911808	+	0.410617i	$0.134687\pi$
$468$	13.4000	−	11.6112i	0.619415	−	0.536727i
$469$	2.47109	+	17.1868i	0.114104	+	0.793613i
$470$		0			0
$471$	−4.47424	+	1.31376i	−0.206162	+	0.0605347i
$472$	2.73769	+	9.32373i	0.126013	+	0.429160i
$473$	−3.95426	−	1.80585i	−0.181817	−	0.0830330i
$474$	0.0387123	+	0.269250i	0.00177812	+	0.0123671i
$475$		0			0
$476$	−12.9072	−	28.2627i	−0.591599	−	1.29542i
$477$	−10.0748	−	15.6767i	−0.461292	−	0.717785i
$478$	0.358621	+	0.0515618i	0.0164029	+	0.00235838i
$479$	−3.97699	−	2.55585i	−0.181713	−	0.116780i	0.446622	−	0.894723i	$-0.352627\pi$
$479$	−3.97699	−	2.55585i	−0.181713	−	0.116780i	−0.628335	+	0.777943i	$0.716263\pi$
$480$		0			0
$481$	−0.119933	−	0.0352155i	−0.00546848	−	0.00160569i
$482$			6.59911i			0.300581i
$483$	2.61281	−	5.23165i	0.118887	−	0.238048i
$484$	0.730356			0.0331980
$485$		0			0
$486$	−1.80216	+	2.07981i	−0.0817479	+	0.0943421i
$487$	17.1256	−	26.6479i	0.776034	−	1.20753i	−0.197794	−	0.980244i	$-0.563378\pi$
$487$	17.1256	−	26.6479i	0.776034	−	1.20753i	0.973827	−	0.227288i	$-0.0729860\pi$
$488$	3.32333	+	0.477823i	0.150440	+	0.0216300i
$489$	2.42881	−	1.56090i	0.109835	−	0.0705864i
$490$		0			0
$491$	4.71421	+	5.44049i	0.212749	+	0.245526i	0.852087	−	0.523400i	$-0.175337\pi$
$491$	4.71421	+	5.44049i	0.212749	+	0.245526i	−0.639338	+	0.768926i	$0.720791\pi$
$492$	2.99188	−	0.430167i	0.134884	−	0.0193934i
$493$	−35.8920	−	16.3913i	−1.61649	−	0.738227i
$494$	−3.16008	+	0.927884i	−0.142179	+	0.0417475i
$495$		0			0
$496$	−7.22485	+	15.8202i	−0.324405	+	0.710349i
$497$	10.3073	−	1.48197i	0.462346	−	0.0664753i
$498$	0.253094	−	0.219307i	0.0113414	−	0.00982738i
$499$	9.46867	+	20.7335i	0.423876	+	0.928159i	0.994281	+	0.106795i	$0.0340590\pi$
$499$	9.46867	+	20.7335i	0.423876	+	0.928159i	−0.570405	+	0.821364i	$0.693214\pi$
$500$		0			0
$501$	−0.119924	+	0.834090i	−0.00535781	+	0.0372644i
$502$	−1.44052	+	2.24149i	−0.0642935	+	0.100043i
$503$	18.4625	+	15.9978i	0.823201	+	0.713308i	0.960819	−	0.277177i	$-0.0893990\pi$
$503$	18.4625	+	15.9978i	0.823201	+	0.713308i	−0.137617	+	0.990485i	$0.543944\pi$
$504$	−6.31329	−	1.85375i	−0.281216	−	0.0825726i
$505$		0			0
$506$	3.76496	+	0.675728i	0.167373	+	0.0300398i
$507$			1.03644i			0.0460297i
$508$	−5.72001	+	19.4806i	−0.253785	+	0.864311i
$509$	−5.12772	+	5.91771i	−0.227282	+	0.262298i	−0.857924	−	0.513776i	$-0.828246\pi$
$509$	−5.12772	+	5.91771i	−0.227282	+	0.262298i	0.630642	+	0.776074i	$0.282792\pi$
$510$		0			0
$511$	1.58044	−	10.9922i	0.0699144	−	0.486266i
$512$	−9.11729	−	14.1868i	−0.402931	−	0.626973i
$513$	−10.6356	+	4.85713i	−0.469575	+	0.214448i
$514$	−2.54606	−	2.93831i	−0.112302	−	0.129603i
$515$		0			0
$516$	−0.498475	+	1.09151i	−0.0219441	+	0.0480510i
$517$	−3.24730	−	11.0593i	−0.142816	−	0.486387i
$518$	0.00644153	+	0.0219379i	0.000283025	+	0.000963894i
$519$	2.03149	−	4.44835i	0.0891727	−	0.195261i
$520$		0			0
$521$	−1.98664	−	2.29270i	−0.0870361	−	0.100445i	0.710561	−	0.703636i	$-0.248441\pi$
$521$	−1.98664	−	2.29270i	−0.0870361	−	0.100445i	−0.797597	+	0.603191i	$0.793896\pi$
$522$	−3.74654	+	1.71099i	−0.163982	+	0.0748880i
$523$	16.0293	+	24.9421i	0.700913	+	1.09064i	0.991029	+	0.133650i	$0.0426699\pi$
$523$	16.0293	+	24.9421i	0.700913	+	1.09064i	−0.290115	+	0.956992i	$0.593694\pi$
$524$	4.20389	−	29.2387i	0.183648	−	1.27730i
$525$		0			0
$526$	3.63894	−	4.19956i	0.158665	−	0.183109i
$527$	−8.38581	+	28.5594i	−0.365292	+	1.24407i
$528$		−	5.92389i		−	0.257804i
$529$	−21.5645	−	7.99835i	−0.937586	−	0.347754i
$530$		0			0
$531$	−27.6972	−	8.13263i	−1.20196	−	0.352926i
$532$	−15.8277	−	13.7148i	−0.686219	−	0.594613i
$533$	−5.77797	+	8.99069i	−0.250271	+	0.389430i
$534$	0.199216	−	1.38557i	0.00862090	−	0.0599597i
$535$		0			0
$536$	2.64220	+	5.78561i	0.114126	+	0.249900i
$537$	3.72977	−	3.23187i	0.160952	−	0.139465i
$538$	1.03972	−	0.149489i	0.0448256	−	0.00644494i
$539$	−0.724181	+	1.58573i	−0.0311927	+	0.0683024i
$540$		0			0
$541$	−22.8021	+	6.69531i	−0.980341	+	0.287854i	−0.732365	−	0.680912i	$-0.761584\pi$
$541$	−22.8021	+	6.69531i	−0.980341	+	0.287854i	−0.247976	+	0.968766i	$0.579765\pi$
$542$	4.23784	+	1.93536i	0.182031	+	0.0831307i
$543$	4.40432	−	0.633245i	0.189007	−	0.0271752i
$544$	−11.2326	−	12.9632i	−0.481595	−	0.555791i
$545$		0			0
$546$	−0.798507	+	0.513169i	−0.0341729	+	0.0219616i
$547$	−18.9185	−	2.72007i	−0.808896	−	0.116302i	−0.274556	−	0.961571i	$-0.588531\pi$
$547$	−18.9185	−	2.72007i	−0.808896	−	0.116302i	−0.534340	+	0.845269i	$0.679440\pi$
$548$	1.28483	−	1.99924i	0.0548853	−	0.0854032i
$549$	−6.53148	+	7.53773i	−0.278757	+	0.321702i
$550$		0			0
$551$	−26.5965			−1.13305
$552$	0.378413	−	2.10841i	0.0161063	−	0.0897397i
$553$		−	6.11593i		−	0.260076i
$554$	−4.27888	−	1.25639i	−0.181792	−	0.0533790i
$555$		0			0
$556$	−3.57261	−	2.29598i	−0.151513	−	0.0973712i
$557$	−19.4260	−	2.79304i	−0.823106	−	0.118345i	−0.282123	−	0.959378i	$-0.591039\pi$
$557$	−19.4260	−	2.79304i	−0.823106	−	0.118345i	−0.540983	+	0.841033i	$0.681948\pi$
$558$	1.67977	+	2.61378i	0.0711104	+	0.110650i
$559$	−1.76247	−	3.85928i	−0.0745447	−	0.163230i
$560$		0			0
$561$	−1.44284	−	10.0352i	−0.0609168	−	0.423685i
$562$	−4.12847	−	1.88541i	−0.174149	−	0.0795312i
$563$	−12.5877	−	42.8697i	−0.530507	−	1.80674i	−0.588592	−	0.808430i	$-0.700318\pi$
$563$	−12.5877	−	42.8697i	−0.530507	−	1.80674i	0.0580848	−	0.998312i	$-0.481501\pi$
$564$	−3.05274	+	0.896365i	−0.128543	+	0.0377438i
$565$		0			0
$566$	−0.0366853	−	0.255152i	−0.00154200	−	0.0107248i
$567$	13.4480	−	11.6528i	0.564764	−	0.489371i
$568$	3.46976	−	1.58458i	0.145588	−	0.0664877i
$569$	−3.48719	+	2.24108i	−0.146191	+	0.0939510i	−0.611691	−	0.791096i	$-0.709511\pi$
$569$	−3.48719	+	2.24108i	−0.146191	+	0.0939510i	0.465501	+	0.885047i	$0.345874\pi$
$570$		0			0
$571$	−11.2629	−	7.23824i	−0.471339	−	0.302911i	0.283324	−	0.959024i	$-0.408563\pi$
$571$	−11.2629	−	7.23824i	−0.471339	−	0.302911i	−0.754662	+	0.656113i	$0.772199\pi$
$572$	16.3121	+	14.1345i	0.682043	+	0.590994i
$573$	−2.76992	+	9.43347i	−0.115715	+	0.394089i
$574$	1.95489			0.0815954
$575$		0			0
$576$	18.5329			0.772203
$577$	−6.60044	+	22.4790i	−0.274780	+	0.935814i	0.700279	+	0.713869i	$0.253059\pi$
$577$	−6.60044	+	22.4790i	−0.274780	+	0.935814i	−0.975059	+	0.221945i	$0.928759\pi$
$578$	−4.00311	−	3.46872i	−0.166508	−	0.144280i
$579$	5.53403	+	3.55650i	0.229986	+	0.147803i
$580$		0			0
$581$	−6.33422	+	4.07076i	−0.262788	+	0.168883i
$582$	−1.09364	+	0.499451i	−0.0453330	+	0.0207029i
$583$	17.1439	−	14.8553i	0.710028	−	0.615242i
$584$	−0.578925	−	4.02651i	−0.0239561	−	0.166618i
$585$		0			0
$586$	3.16281	−	0.928686i	0.130655	−	0.0383637i
$587$	−11.2879	−	38.4429i	−0.465899	−	1.58671i	−0.772594	−	0.634900i	$-0.781041\pi$
$587$	−11.2879	−	38.4429i	−0.465899	−	1.58671i	0.306695	−	0.951808i	$-0.400777\pi$
$588$	0.437716	+	0.199898i	0.0180511	+	0.00824366i
$589$	2.85529	+	19.8590i	0.117650	+	0.818276i
$590$		0			0
$591$	0.457447	+	1.00167i	0.0188169	+	0.0412032i
$592$	−0.0752935	−	0.117159i	−0.00309454	−	0.00481520i
$593$	−5.78174	−	0.831288i	−0.237427	−	0.0341369i	0.0225738	−	0.999745i	$-0.492814\pi$
$593$	−5.78174	−	0.831288i	−0.237427	−	0.0341369i	−0.260001	+	0.965608i	$0.583723\pi$
$594$	−1.85426	−	1.19166i	−0.0760812	−	0.0488944i
$595$		0			0
$596$	−7.72221	−	2.26745i	−0.316314	−	0.0928782i
$597$		−	0.819209i		−	0.0335280i
$598$	2.34514	+	2.90472i	0.0959000	+	0.118783i
$599$	5.01179			0.204776			0.102388	−	0.994745i	$-0.467352\pi$
$599$	5.01179			0.204776			0.102388	+	0.994745i	$0.467352\pi$
$600$		0			0
$601$	−8.34466	+	9.63025i	−0.340386	+	0.392826i	−0.899973	−	0.435945i	$-0.856414\pi$
$601$	−8.34466	+	9.63025i	−0.340386	+	0.392826i	0.559587	+	0.828771i	$0.310960\pi$
$602$	−0.419570	+	0.652864i	−0.0171004	+	0.0266087i
$603$	−18.7019	−	2.68893i	−0.761601	−	0.109502i
$604$	−11.1146	+	7.14291i	−0.452246	+	0.290641i
$605$		0			0
$606$	−0.682212	−	0.787315i	−0.0277130	−	0.0319825i
$607$	0.611774	−	0.0879598i	0.0248311	−	0.00357018i	−0.129888	−	0.991529i	$-0.541462\pi$
$607$	0.611774	−	0.0879598i	0.0248311	−	0.00357018i	0.154719	+	0.987958i	$0.450553\pi$
$608$	−10.5170	−	4.80294i	−0.426520	−	0.194785i
$609$	−7.35462	+	2.15951i	−0.298024	+	0.0875079i
$610$		0			0
$611$	4.67314	−	10.2328i	0.189055	−	0.413973i
$612$	33.4654	−	4.81160i	1.35276	−	0.194498i
$613$	24.0381	−	20.8291i	0.970890	−	0.841281i	−0.0164557	−	0.999865i	$-0.505238\pi$
$613$	24.0381	−	20.8291i	0.970890	−	0.841281i	0.987346	+	0.158584i	$0.0506928\pi$
$614$	2.51784	+	5.51329i	0.101612	+	0.222498i
$615$		0			0
$616$	1.13991	−	7.92823i	0.0459282	−	0.319437i
$617$	21.6123	−	33.6295i	0.870080	−	1.35387i	−0.0644251	−	0.997923i	$-0.520521\pi$
$617$	21.6123	−	33.6295i	0.870080	−	1.35387i	0.934505	−	0.355949i	$-0.115842\pi$
$618$	−1.26403	−	1.09528i	−0.0508466	−	0.0440588i
$619$	−33.7104	−	9.89827i	−1.35494	−	0.397845i	−0.477961	−	0.878381i	$-0.658624\pi$
$619$	−33.7104	−	9.89827i	−1.35494	−	0.397845i	−0.876975	+	0.480536i	$0.840442\pi$
$620$		0			0
$621$	9.70831	+	9.02224i	0.389581	+	0.362050i
$622$			0.878199i			0.0352126i
$623$	−8.86693	+	30.1980i	−0.355246	+	1.20986i
$624$	3.78614	−	4.36944i	0.151567	−	0.174918i
$625$		0			0
$626$	−0.529342	+	3.68166i	−0.0211568	+	0.147149i
$627$	−3.69462	−	5.74894i	−0.147549	−	0.229590i
$628$	17.2195	−	7.86387i	0.687132	−	0.313803i
$629$	−0.156084	−	0.180131i	−0.00622348	−	0.00718228i
$630$		0			0
$631$	19.6170	−	42.9552i	0.780941	−	1.71002i	0.0800078	−	0.996794i	$-0.474505\pi$
$631$	19.6170	−	42.9552i	0.780941	−	1.71002i	0.700933	−	0.713227i	$-0.252767\pi$
$632$	−0.631168	−	2.14956i	−0.0251065	−	0.0855049i
$633$	1.07975	+	3.67729i	0.0429162	+	0.146159i
$634$	0.324665	−	0.710917i	0.0128941	−	0.0282341i
$635$		0			0
$636$	−4.10055	−	4.73229i	−0.162598	−	0.187648i
$637$	−1.54765	+	0.706786i	−0.0613200	+	0.0280039i
$638$	−2.71068	−	4.21791i	−0.107317	−	0.166989i
$639$	−1.61261	+	11.2160i	−0.0637939	+	0.443696i
$640$		0			0
$641$	−4.52524	+	5.22241i	−0.178736	+	0.206273i	−0.838047	−	0.545598i	$-0.816303\pi$
$641$	−4.52524	+	5.22241i	−0.178736	+	0.206273i	0.659311	+	0.751870i	$0.270848\pi$
$642$	0.517081	−	1.76102i	0.0204076	−	0.0695017i
$643$			38.9219i			1.53493i	0.641091	+	0.767465i	$0.278482\pi$
$643$			38.9219i			1.53493i	−0.641091	+	0.767465i	$0.721518\pi$
$644$	−7.47635	+	22.5314i	−0.294609	+	0.887862i
$645$		0			0
$646$	−6.02575	−	1.76932i	−0.237080	−	0.0696130i
$647$	8.80704	+	7.63135i	0.346241	+	0.300019i	0.810568	−	0.585644i	$-0.199158\pi$
$647$	8.80704	+	7.63135i	0.346241	+	0.300019i	−0.464328	+	0.885664i	$0.653704\pi$
$648$	3.52399	−	5.48343i	0.138435	−	0.215410i
$649$	5.00091	−	34.7821i	0.196303	−	1.36532i
$650$		0			0
$651$	2.40202	+	5.25970i	0.0941428	+	0.206144i
$652$	−8.85770	+	7.67524i	−0.346894	+	0.300586i
$653$	−39.0509	+	5.61467i	−1.52818	+	0.219719i	−0.854557	−	0.519357i	$-0.826171\pi$
$653$	−39.0509	+	5.61467i	−1.52818	+	0.219719i	−0.673622	+	0.739076i	$0.735262\pi$
$654$	−0.707065	+	1.54826i	−0.0276484	+	0.0605416i
$655$		0			0
$656$	−11.4251	+	3.35471i	−0.446075	+	0.130979i
$657$	10.9922	+	5.01996i	0.428846	+	0.195847i
$658$	−2.03676	+	0.292841i	−0.0794010	+	0.0114161i
$659$	−0.488601	−	0.563876i	−0.0190332	−	0.0219655i	0.746153	−	0.665774i	$-0.231899\pi$
$659$	−0.488601	−	0.563876i	−0.0190332	−	0.0219655i	−0.765186	+	0.643809i	$0.777353\pi$
$660$		0			0
$661$	−24.5667	+	15.7881i	−0.955534	+	0.614085i	−0.922759	−	0.385378i	$-0.874071\pi$
$661$	−24.5667	+	15.7881i	−0.955534	+	0.614085i	−0.0327757	+	0.999463i	$0.510435\pi$
$662$	1.87273	+	0.269258i	0.0727857	+	0.0104650i
$663$	5.34956	−	8.32407i	0.207760	−	0.323280i
$664$	−1.80618	+	2.08444i	−0.0700933	+	0.0808920i
$665$		0			0
$666$	−0.0248796			−0.000964065
$667$	11.5624	+	27.8422i	0.447698	+	1.07806i
$668$		−	3.42084i		−	0.132356i
$669$	13.1062	+	3.84832i	0.506714	+	0.148785i
$670$		0			0
$671$	−10.2140	−	6.56412i	−0.394306	−	0.253405i
$672$	−3.29820	−	0.474210i	−0.127231	−	0.0182930i
$673$	9.04766	+	14.0784i	0.348762	+	0.542683i	0.970673	−	0.240404i	$-0.0772800\pi$
$673$	9.04766	+	14.0784i	0.348762	+	0.542683i	−0.621911	+	0.783088i	$0.713644\pi$
$674$	−0.136771	−	0.299486i	−0.00526821	−	0.0115358i
$675$		0			0
$676$	−0.598783	−	4.16463i	−0.0230301	−	0.160178i
$677$	−41.1418	−	18.7888i	−1.58121	−	0.722113i	−0.585159	−	0.810919i	$-0.698968\pi$
$677$	−41.1418	−	18.7888i	−1.58121	−	0.722113i	−0.996049	+	0.0888053i	$0.971695\pi$
$678$	0.0368658	+	0.125553i	0.00141582	+	0.00482184i
$679$	25.9367	−	7.61572i	0.995361	−	0.292264i
$680$		0			0
$681$	0.639489	+	4.44775i	0.0245053	+	0.170438i
$682$	−2.85841	+	2.47683i	−0.109454	+	0.0948426i
$683$	−31.6589	+	14.4581i	−1.21139	+	0.553225i	−0.915625	−	0.402034i	$-0.868303\pi$
$683$	−31.6589	+	14.4581i	−1.21139	+	0.553225i	−0.295769	+	0.955259i	$0.595576\pi$
$684$	19.1716	−	12.3209i	0.733046	−	0.471100i
$685$		0			0
$686$	3.80758	+	2.44698i	0.145374	+	0.0934261i
$687$	−2.40784	−	2.08640i	−0.0918647	−	0.0796012i
$688$	1.33177	−	4.53559i	0.0507732	−	0.172918i
$689$	22.1397			0.843457
$690$		0			0
$691$	10.7550			0.409140			0.204570	−	0.978852i	$-0.434420\pi$
$691$	10.7550			0.409140			0.204570	+	0.978852i	$0.434420\pi$
$692$	−5.59303	+	19.0481i	−0.212615	+	0.724100i
$693$	17.9822	+	15.5817i	0.683087	+	0.591899i
$694$	−3.34785	−	2.15153i	−0.127083	−	0.0816711i
$695$		0			0
$696$	−2.36206	+	1.51800i	−0.0895336	+	0.0575398i
$697$	−18.5372	+	8.46566i	−0.702147	+	0.320660i
$698$	−3.41849	+	2.96214i	−0.129392	+	0.112119i
$699$	−1.74740	−	12.1534i	−0.0660927	−	0.459685i
$700$		0			0
$701$	19.4393	−	5.70790i	0.734214	−	0.215585i	0.106811	−	0.994279i	$-0.465936\pi$
$701$	19.4393	−	5.70790i	0.734214	−	0.215585i	0.627403	+	0.778695i	$0.284118\pi$
$702$	−0.606069	−	2.06408i	−0.0228746	−	0.0779037i
$703$	−0.146140	−	0.0667397i	−0.00551176	−	0.00251714i
$704$	3.21069	+	22.3308i	0.121007	+	0.841624i
$705$		0			0
$706$	3.30566	+	7.23839i	0.124410	+	0.272420i
$707$	12.6632	+	19.7043i	0.476248	+	0.741056i
$708$	−9.60103	−	1.38042i	−0.360829	−	0.0518793i
$709$	11.0641	+	7.11045i	0.415520	+	0.267038i	0.731654	−	0.681676i	$-0.238749\pi$
$709$	11.0641	+	7.11045i	0.415520	+	0.267038i	−0.316134	+	0.948714i	$0.602385\pi$
$710$		0			0
$711$	6.38551	+	1.87495i	0.239475	+	0.0703163i
$712$			11.5287i			0.432057i
$713$	19.5479	−	11.6224i	0.732074	−	0.435263i
$714$	−1.80994			−0.0677353
$715$		0			0
$716$	−13.1199	+	15.1412i	−0.490313	+	0.565851i
$717$	−0.396672	+	0.617234i	−0.0148140	+	0.0230510i
$718$	4.59519	+	0.660688i	0.171491	+	0.0246567i
$719$	24.1781	−	15.5383i	0.901692	−	0.579482i	−0.00559955	−	0.999984i	$-0.501782\pi$
$719$	24.1781	−	15.5383i	0.901692	−	0.579482i	0.907292	+	0.420502i	$0.138146\pi$
$720$		0			0
$721$	24.6258	+	28.4197i	0.917112	+	1.05840i
$722$	0.257320	−	0.0369970i	0.00957646	−	0.00137689i
$723$	−12.1561	−	5.55152i	−0.452092	−	0.206463i
$724$	−17.3317	+	5.08903i	−0.644126	+	0.189132i
$725$		0			0
$726$	0.0176739	−	0.0387005i	0.000655941	−	0.00143631i
$727$	27.5653	−	3.96330i	1.02234	−	0.146991i	0.389302	−	0.921110i	$-0.372716\pi$
$727$	27.5653	−	3.96330i	1.02234	−	0.146991i	0.633039	+	0.774120i	$0.281807\pi$
$728$	5.90797	−	5.11928i	0.218964	−	0.189733i
$729$	6.39435	+	14.0017i	0.236828	+	0.518580i
$730$		0			0
$731$	1.15134	−	8.00774i	0.0425838	−	0.296177i
$732$	−1.81192	+	2.81940i	−0.0669704	+	0.104208i
$733$	18.9049	+	16.3812i	0.698267	+	0.605052i	0.929927	−	0.367745i	$-0.119870\pi$
$733$	18.9049	+	16.3812i	0.698267	+	0.605052i	−0.231660	+	0.972797i	$0.574416\pi$
$734$	1.52718	+	0.448420i	0.0563691	+	0.0165515i
$735$		0			0
$736$	−0.455820	+	13.0976i	−0.0168017	+	0.482784i
$737$		−	23.0003i		−	0.847229i
$738$	−0.599307	+	2.04105i	−0.0220608	+	0.0751322i
$739$	4.18350	−	4.82801i	0.153892	−	0.177601i	−0.673568	−	0.739125i	$-0.735239\pi$
$739$	4.18350	−	4.82801i	0.153892	−	0.177601i	0.827461	+	0.561524i	$0.189785\pi$
$740$		0			0
$741$	0.949187	−	6.60174i	0.0348692	−	0.242521i
$742$	−2.18946	−	3.40686i	−0.0803775	−	0.125070i
$743$	26.3062	−	12.0136i	0.965081	−	0.440738i	0.130394	−	0.991462i	$-0.458376\pi$
$743$	26.3062	−	12.0136i	0.965081	−	0.440738i	0.834687	+	0.550725i	$0.185649\pi$
$744$	1.38704	+	1.60073i	0.0508514	+	0.0586857i
$745$		0			0
$746$	2.48815	−	5.44828i	0.0910975	−	0.199476i
$747$	−2.30831	−	7.86139i	−0.0844567	−	0.287633i
$748$	11.5953	+	39.4899i	0.423966	+	1.44390i
$749$	−17.1422	+	37.5362i	−0.626363	+	1.37154i
$750$		0			0
$751$	32.9193	+	37.9909i	1.20124	+	1.38631i	0.901778	+	0.432200i	$0.142263\pi$
$751$	32.9193	+	37.9909i	1.20124	+	1.38631i	0.299465	+	0.954107i	$0.403192\pi$
$752$	11.4010	−	5.20667i	0.415753	−	0.189868i
$753$	−2.91718	−	4.53922i	−0.106308	−	0.165418i
$754$	0.696404	−	4.84360i	0.0253615	−	0.176393i
$755$		0			0
$756$	8.95814	−	10.3382i	0.325804	−	0.375998i
$757$	−9.90983	+	33.7498i	−0.360179	+	1.22666i	0.557782	+	0.829987i	$0.311652\pi$
$757$	−9.90983	+	33.7498i	−0.360179	+	1.22666i	−0.917961	+	0.396670i	$0.870166\pi$
$758$			6.82414i			0.247864i
$759$	−4.41204	+	6.36693i	−0.160147	+	0.231105i
$760$		0			0
$761$	33.8907	+	9.95120i	1.22854	+	0.360731i	0.830697	−	0.556725i	$-0.187942\pi$
$761$	33.8907	+	9.95120i	1.22854	+	0.360731i	0.397839	+	0.917455i	$0.369760\pi$
$762$	0.893827	+	0.774506i	0.0323799	+	0.0280574i
$763$	20.6895	−	32.1934i	0.749008	−	1.16548i
$764$	5.68011	−	39.5060i	0.205499	−	1.42928i
$765$		0			0
$766$	−1.26681	−	2.77392i	−0.0457716	−	0.100226i
$767$	25.9190	−	22.4589i	0.935880	−	0.810944i
$768$	5.55141	−	0.798172i	0.200319	−	0.0288016i
$769$	20.4810	−	44.8471i	0.738563	−	1.61723i	−0.0473404	−	0.998879i	$-0.515075\pi$
$769$	20.4810	−	44.8471i	0.738563	−	1.61723i	0.785904	−	0.618349i	$-0.212198\pi$
$770$		0			0
$771$	7.55452	−	2.21821i	0.272069	−	0.0798868i
$772$	−24.2916	−	11.0936i	−0.874275	−	0.399268i
$773$	3.70661	−	0.532931i	0.133318	−	0.0191682i	−0.0753329	−	0.997158i	$-0.524002\pi$
$773$	3.70661	−	0.532931i	0.133318	−	0.0191682i	0.208651	+	0.977990i	$0.433093\pi$
$774$	−0.553013	−	0.638211i	−0.0198777	−	0.0229400i
$775$		0			0
$776$	8.33002	−	5.35338i	0.299030	−	0.192175i
$777$	−0.0458304	−	0.00658942i	−0.00164416	−	0.000236394i
$778$	−0.268033	+	0.417068i	−0.00960945	+	0.0149526i
$779$	−8.99539	+	10.3812i	−0.322293	+	0.371946i
$780$		0			0
$781$	−13.7938			−0.493581
$782$	0.767407	+	7.07718i	0.0274424	+	0.253079i
$783$		−	17.3721i		−	0.620827i
$784$	−1.81886	−	0.534065i	−0.0649593	−	0.0190738i
$785$		0			0
$786$	−1.44758	−	0.930305i	−0.0516336	−	0.0331829i
$787$	11.5183	+	1.65608i	0.410584	+	0.0590330i	0.344512	−	0.938782i	$-0.388044\pi$
$787$	11.5183	+	1.65608i	0.410584	+	0.0590330i	0.0660715	+	0.997815i	$0.478953\pi$
$788$	−2.41682	−	3.76064i	−0.0860956	−	0.133967i
$789$	4.67469	+	10.2361i	0.166423	+	0.364416i
$790$		0			0
$791$	−0.418697	−	2.91210i	−0.0148871	−	0.103542i
$792$	7.92823	+	3.62070i	0.281717	+	0.128656i
$793$	−3.33846	−	11.3697i	−0.118552	−	0.403751i
$794$	0.426346	−	0.125187i	0.0151305	−	0.00444270i
$795$		0			0
$796$	0.473283	+	3.29176i	0.0167751	+	0.116673i
$797$	−37.8299	+	32.7798i	−1.34000	+	1.16112i	−0.367029	+	0.930210i	$0.619625\pi$
$797$	−37.8299	+	32.7798i	−1.34000	+	1.16112i	−0.972975	+	0.230910i	$0.925830\pi$
$798$	−1.10974	+	0.506803i	−0.0392845	+	0.0179406i
$799$	18.0454	−	11.5971i	0.638400	−	0.410275i
$800$		0			0
$801$	−28.8107	−	18.5155i	−1.01798	−	0.654214i
$802$	3.01224	+	2.61012i	0.106366	+	0.0921667i
$803$	−4.14439	+	14.1145i	−0.146252	+	0.498090i
$804$	−6.34887			−0.223907
$805$		0			0
$806$	−3.69137			−0.130023
$807$	−0.599297	+	2.04102i	−0.0210962	+	0.0718472i
$808$	6.48421	+	5.61860i	0.228114	+	0.197662i
$809$	26.9667	+	17.3305i	0.948100	+	0.609307i	0.920681	−	0.390317i	$-0.127635\pi$
$809$	26.9667	+	17.3305i	0.948100	+	0.609307i	0.0274196	+	0.999624i	$0.491271\pi$
$810$		0			0
$811$	40.6899	−	26.1498i	1.42882	−	0.918244i	0.428926	−	0.903339i	$-0.358892\pi$
$811$	40.6899	−	26.1498i	1.42882	−	0.918244i	0.999889	−	0.0149043i	$-0.00474437\pi$
$812$	28.3049	−	12.9264i	0.993306	−	0.453628i
$813$	−7.13020	+	6.17835i	−0.250067	+	0.216684i
$814$	−0.00431021	−	0.0299782i	−0.000151073	−	0.00105073i
$815$		0			0
$816$	10.5780	−	3.10597i	0.370303	−	0.108731i
$817$	−1.53632	−	5.23223i	−0.0537491	−	0.183053i
$818$	2.79848	+	1.27802i	0.0978466	+	0.0446851i
$819$	3.30488	+	22.9860i	0.115482	+	0.803195i
$820$		0			0
$821$	−4.37202	−	9.57340i	−0.152585	−	0.334114i	0.817868	−	0.575406i	$-0.195156\pi$
$821$	−4.37202	−	9.57340i	−0.152585	−	0.334114i	−0.970452	+	0.241292i	$0.922429\pi$
$822$	−0.0748449	−	0.116461i	−0.00261052	−	0.00406204i
$823$	−47.0790	−	6.76894i	−1.64107	−	0.235950i	−0.740940	−	0.671571i	$-0.765620\pi$
$823$	−47.0790	−	6.76894i	−1.64107	−	0.235950i	−0.900131	+	0.435620i	$0.856529\pi$
$824$	11.5881	+	7.44724i	0.403692	+	0.259437i
$825$		0			0
$826$	−6.01917	−	1.76739i	−0.209434	−	0.0614953i
$827$			52.9294i			1.84053i	0.391291	+	0.920267i	$0.372029\pi$
$827$			52.9294i			1.84053i	−0.391291	+	0.920267i	$0.627971\pi$
$828$	−21.2325	−	14.7133i	−0.737881	−	0.511323i
$829$	−12.4245			−0.431522			−0.215761	−	0.976446i	$-0.569223\pi$
$829$	−12.4245			−0.431522			−0.215761	+	0.976446i	$0.569223\pi$
$830$		0			0
$831$	5.91401	−	6.82514i	0.205155	−	0.236761i
$832$	−11.9041	+	18.5232i	−0.412701	+	0.642176i
$833$	−3.21126	−	0.461709i	−0.111264	−	0.0159973i
$834$	−0.208114	+	0.133747i	−0.00720641	+	0.00463128i
$835$		0			0
$836$	18.1671	+	20.9660i	0.628323	+	0.725123i
$837$	−12.9714	+	1.86500i	−0.448356	+	0.0644638i
$838$	−6.32649	−	2.88921i	−0.218545	−	0.0998061i
$839$	−41.9145	+	12.3072i	−1.44705	+	0.424892i	−0.908565	−	0.417744i	$-0.862821\pi$
$839$	−41.9145	+	12.3072i	−1.44705	+	0.424892i	−0.538484	+	0.842636i	$0.681003\pi$
$840$		0			0
$841$	4.36870	−	9.56611i	0.150645	−	0.329866i
$842$	−5.21916	+	0.750402i	−0.179864	+	0.0258606i
$843$	6.94618	−	6.01890i	0.239239	−	0.207302i
$844$	−6.46316	−	14.1523i	−0.222471	−	0.487144i
$845$		0			0
$846$	0.318657	−	2.21631i	0.0109556	−	0.0761982i
$847$	−0.517157	+	0.804712i	−0.0177697	+	0.0276502i
$848$	18.6424	+	16.1537i	0.640183	+	0.554722i
$849$	0.500874	+	0.147070i	0.0171899	+	0.00504742i
$850$		0			0
$851$	−0.00633388	+	0.181999i	−0.000217123	+	0.00623884i
$852$			3.80756i			0.130445i
$853$	8.40397	−	28.6213i	0.287746	−	0.979975i	−0.681075	−	0.732214i	$-0.738487\pi$
$853$	8.40397	−	28.6213i	0.287746	−	0.979975i	0.968821	−	0.247761i	$-0.0796947\pi$
$854$	−1.41943	+	1.63810i	−0.0485718	+	0.0560548i
$855$		0			0
$856$	−2.15120	+	14.9619i	−0.0735264	+	0.511387i
$857$	3.55559	+	5.53260i	0.121457	+	0.188990i	0.896658	−	0.442724i	$-0.145988\pi$
$857$	3.55559	+	5.53260i	0.121457	+	0.188990i	−0.775201	+	0.631714i	$0.782352\pi$
$858$	1.14370	−	0.522312i	0.0390454	−	0.0178314i
$859$	12.0994	+	13.9634i	0.412825	+	0.476425i	0.923638	−	0.383267i	$-0.125201\pi$
$859$	12.0994	+	13.9634i	0.412825	+	0.476425i	−0.510813	+	0.859692i	$0.670656\pi$
$860$		0			0
$861$	−1.64455	+	3.60107i	−0.0560463	+	0.122724i
$862$	−0.117360	−	0.399693i	−0.00399731	−	0.0136136i
$863$	−8.32088	−	28.3383i	−0.283246	−	0.964648i	−0.971075	−	0.238775i	$-0.923254\pi$
$863$	−8.32088	−	28.3383i	−0.283246	−	0.964648i	0.687829	−	0.725873i	$-0.258564\pi$
$864$	3.13715	−	6.86940i	0.106728	−	0.233702i
$865$		0			0
$866$	−2.13689	−	2.46610i	−0.0726144	−	0.0838014i
$867$	9.75732	−	4.45602i	0.331376	−	0.151334i
$868$	−12.6906	−	19.7469i	−0.430746	−	0.670253i
$869$	−1.15295	+	8.01891i	−0.0391110	+	0.272023i
$870$		0			0
$871$	14.7002	−	16.9650i	0.498099	−	0.574836i
$872$	3.94932	−	13.4502i	0.133741	−	0.455480i
$873$			29.4147i			0.995538i
$874$	2.45221	+	4.12441i	0.0829473	+	0.139510i
$875$		0			0
$876$	3.89607	+	1.14399i	0.131636	+	0.0386519i
$877$	6.50563	+	5.63716i	0.219680	+	0.190353i	0.757747	−	0.652548i	$-0.226300\pi$
$877$	6.50563	+	5.63716i	0.219680	+	0.190353i	−0.538068	+	0.842902i	$0.680845\pi$
$878$	−0.919049	+	1.43007i	−0.0310164	+	0.0482625i
$879$	−0.950007	+	6.60744i	−0.0320429	+	0.222864i
$880$		0			0
$881$	−2.08959	−	4.57555i	−0.0703999	−	0.154154i	0.871161	−	0.490998i	$-0.163368\pi$
$881$	−2.08959	−	4.57555i	−0.0703999	−	0.154154i	−0.941561	+	0.336844i	$0.890641\pi$
$882$	−0.255935	+	0.221769i	−0.00861779	+	0.00746736i
$883$	−21.4157	+	3.07912i	−0.720696	+	0.103621i	−0.492897	−	0.870088i	$-0.664062\pi$
$883$	−21.4157	+	3.07912i	−0.720696	+	0.103621i	−0.227799	+	0.973708i	$0.573153\pi$
$884$	−16.6866	+	36.5386i	−0.561231	+	1.22892i
$885$		0			0
$886$	5.30753	−	1.55843i	0.178310	−	0.0523565i
$887$	−25.0277	−	11.4298i	−0.840349	−	0.383774i	−0.0517330	−	0.998661i	$-0.516474\pi$
$887$	−25.0277	−	11.4298i	−0.840349	−	0.383774i	−0.788616	+	0.614887i	$0.789202\pi$
$888$	−0.0167880	+	0.00241375i	−0.000563369	+	8.10002e-5i
$889$	−17.4136	−	20.0963i	−0.584032	−	0.674009i
$890$		0			0
$891$	−19.8291	+	12.7434i	−0.664301	+	0.426920i
$892$	−54.8867	−	7.89152i	−1.83774	−	0.264228i
$893$	7.81701	−	12.1635i	0.261586	−	0.407036i
$894$	−0.307019	+	0.354318i	−0.0102682	+	0.0118502i
$895$		0			0
$896$	17.9435			0.599451
$897$	−7.32361	+	1.87636i	−0.244528	+	0.0626497i
$898$			1.59684i			0.0532871i
$899$	−28.6020	−	8.39831i	−0.953930	−	0.280099i
$900$		0			0
$901$	35.5150	+	22.8241i	1.18318	+	0.760382i
$902$	−2.56315	−	0.368526i	−0.0853436	−	0.0122706i
$903$	−0.849668	−	1.32211i	−0.0282752	−	0.0439970i
$904$	−0.447689	−	0.980303i	−0.0148899	−	0.0326044i
$905$		0			0
$906$	0.109530	+	0.761797i	0.00363888	+	0.0253090i
$907$	−1.73410	−	0.791937i	−0.0575799	−	0.0262959i	0.386417	−	0.922324i	$-0.373713\pi$
$907$	−1.73410	−	0.791937i	−0.0575799	−	0.0262959i	−0.443997	+	0.896028i	$0.646440\pi$
$908$	−5.13922	−	17.5026i	−0.170551	−	0.580843i
$909$	−24.4549	+	7.18062i	−0.811119	+	0.238166i
$910$		0			0
$911$	5.36602	+	37.3215i	0.177784	+	1.23652i	0.861875	+	0.507120i	$0.169290\pi$
$911$	5.36602	+	37.3215i	0.177784	+	1.23652i	−0.684091	+	0.729397i	$0.739801\pi$
$912$	5.61605	−	4.86633i	0.185966	−	0.161140i
$913$	9.07253	−	4.14328i	0.300257	−	0.137123i
$914$	−1.43731	+	0.923700i	−0.0475418	+	0.0305533i
$915$		0			0
$916$	10.8806	+	6.99253i	0.359505	+	0.231040i
$917$	29.2387	+	25.3355i	0.965546	+	0.836651i
$918$	1.15567	−	3.93586i	0.0381429	−	0.129903i
$919$	1.89744			0.0625909			0.0312955	−	0.999510i	$-0.490037\pi$
$919$	1.89744			0.0625909			0.0312955	+	0.999510i	$0.490037\pi$
$920$		0			0
$921$	−12.2741			−0.404446
$922$	2.14395	−	7.30163i	0.0706073	−	0.240466i
$923$	−10.1743	−	8.81605i	−0.334890	−	0.290184i
$924$	6.72603	+	4.32256i	0.221270	+	0.142202i
$925$		0			0
$926$	−3.73491	+	2.40028i	−0.122737	+	0.0788781i
$927$	−37.2219	+	16.9987i	−1.22253	+	0.558309i
$928$	12.9825	−	11.2494i	0.426171	−	0.369279i
$929$	−3.96319	−	27.5646i	−0.130028	−	0.904366i	−0.945512	−	0.325586i	$-0.894438\pi$
$929$	−3.96319	−	27.5646i	−0.130028	−	0.904366i	0.815484	−	0.578779i	$-0.196471\pi$
$930$		0			0
$931$	−2.09823	+	0.616095i	−0.0687666	+	0.0201917i
$932$	14.0429	+	47.8256i	0.459989	+	1.56658i
$933$	−1.61772	−	0.738788i	−0.0529618	−	0.0241868i
$934$	0.958311	+	6.66520i	0.0313569	+	0.218092i
$935$		0			0
$936$	3.53373	+	7.73779i	0.115504	+	0.252918i
$937$	−7.74624	−	12.0534i	−0.253059	−	0.393767i	0.691361	−	0.722510i	$-0.257011\pi$
$937$	−7.74624	−	12.0534i	−0.253059	−	0.393767i	−0.944420	+	0.328743i	$0.893375\pi$
$938$	−4.06432	−	0.584360i	−0.132705	−	0.0190800i
$939$	−6.33663	−	4.07230i	−0.206788	−	0.132895i
$940$		0			0
$941$	33.6359	+	9.87638i	1.09650	+	0.321961i	0.779460	−	0.626452i	$-0.215494\pi$
$941$	33.6359	+	9.87638i	1.09650	+	0.321961i	0.317038	+	0.948413i	$0.397312\pi$
$942$		−	1.10273i		−	0.0359290i
$943$	14.7781	+	4.90365i	0.481241	+	0.159685i
$944$	38.2113			1.24367
$945$		0			0
$946$	0.673195	−	0.776908i	0.0218874	−	0.0252595i
$947$	−4.27924	+	6.65862i	−0.139057	+	0.216376i	−0.903796	−	0.427963i	$-0.859231\pi$
$947$	−4.27924	+	6.65862i	−0.139057	+	0.216376i	0.764740	+	0.644339i	$0.222868\pi$
$948$	2.21349	+	0.318252i	0.0718908	+	0.0103363i
$949$	−12.0779	+	7.76199i	−0.392065	+	0.251965i
$950$		0			0
$951$	1.03645	+	1.19612i	0.0336091	+	0.0387870i
$952$	14.7547	−	2.12140i	0.478202	−	0.0687550i
$953$	16.0497	+	7.32967i	0.519902	+	0.237431i	0.658042	−	0.752982i	$-0.271385\pi$
$953$	16.0497	+	7.32967i	0.519902	+	0.237431i	−0.138140	+	0.990413i	$0.544112\pi$
$954$	4.22825	−	1.24153i	0.136895	−	0.0401959i
$955$		0			0
$956$	1.23732	−	2.70935i	0.0400178	−	0.0876267i
$957$	10.0501	−	1.44499i	0.324875	−	0.0467099i
$958$	0.844885	−	0.732097i	0.0272970	−	0.0236530i
$959$	1.29300	+	2.83128i	0.0417532	+	0.0914267i
$960$		0			0
$961$	1.21153	−	8.42636i	0.0390816	−	0.271818i
$962$	0.0159808	−	0.0248666i	0.000515241	−	0.000801731i
$963$	−33.9354	−	29.4052i	−1.09355	−	0.947570i
$964$	52.0533	+	15.2842i	1.67652	+	0.492272i
$965$		0			0
$966$	1.01298	+	0.941399i	0.0325923	+	0.0302890i
$967$			18.1226i			0.582785i	0.956604	+	0.291392i	$0.0941185\pi$
$967$			18.1226i			0.582785i	−0.956604	+	0.291392i	$0.905881\pi$
$968$	−0.0987179	+	0.336202i	−0.00317291	+	0.0108060i
$969$	8.32843	−	9.61152i	0.267548	−	0.308766i
$970$		0			0
$971$	1.50925	−	10.4971i	0.0484342	−	0.336867i	−0.951168	−	0.308673i	$-0.900115\pi$
$971$	1.50925	−	10.4971i	0.0484342	−	0.336867i	0.999602	−	0.0281944i	$-0.00897575\pi$
$972$	12.2314	+	19.0324i	0.392322	+	0.610465i
$973$	5.05946	−	2.31058i	0.162199	−	0.0740737i
$974$	4.90544	+	5.66117i	0.157180	+	0.181396i
$975$		0			0
$976$	5.48457	−	12.0095i	0.175557	−	0.384416i
$977$	1.85240	+	6.30869i	0.0592635	+	0.201833i	0.983803	−	0.179253i	$-0.0573682\pi$
$977$	1.85240	+	6.30869i	0.0592635	+	0.201833i	−0.924539	+	0.381086i	$0.875550\pi$
$978$	0.192352	+	0.655090i	0.00615073	+	0.0209475i
$979$	17.3187	−	37.9226i	0.553507	−	1.21201i
$980$		0			0
$981$	27.2697	+	31.4709i	0.870654	+	1.00479i
$982$	−1.54852	+	0.707187i	−0.0494154	+	0.0225672i
$983$	23.6323	+	36.7725i	0.753752	+	1.17286i	0.980040	+	0.198800i	$0.0637045\pi$
$983$	23.6323	+	36.7725i	0.753752	+	1.17286i	−0.226288	+	0.974060i	$0.572659\pi$
$984$	−0.206377	+	1.43538i	−0.00657906	+	0.0457584i
$985$		0			0
$986$	6.11044	−	7.05183i	0.194596	−	0.224576i
$987$	1.17399	−	3.99824i	0.0373685	−	0.127265i
$988$			27.0756i			0.861390i
$989$	−4.80942	+	3.88292i	−0.152931	+	0.123470i
$990$		0			0
$991$	−52.0340	−	15.2786i	−1.65291	−	0.485339i	−0.683333	−	0.730107i	$-0.739470\pi$
$991$	−52.0340	−	15.2786i	−1.65291	−	0.485339i	−0.969582	+	0.244768i	$0.921288\pi$
$992$	−9.79341	−	8.48604i	−0.310941	−	0.269432i
$993$	−2.07144	+	3.22322i	−0.0657351	+	0.102286i
$994$	−0.350454	+	2.43746i	−0.0111157	+	0.0773115i
$995$		0			0
$996$	−1.14369	−	2.50432i	−0.0362391	−	0.0793525i
$997$	−0.519758	+	0.450373i	−0.0164609	+	0.0142635i	−0.663052	−	0.748573i	$-0.730739\pi$
$997$	−0.519758	+	0.450373i	−0.0164609	+	0.0142635i	0.646591	+	0.762836i	$0.276194\pi$
$998$	−5.33527	+	0.767096i	−0.168885	+	0.0242820i
$999$	0.0435926	−	0.0954544i	0.00137921	−	0.00302004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.p.b.524.1		20
5.2	odd	4		23.2.c.a.18.1	yes	10
5.3	odd	4		575.2.k.b.501.1		10
5.4	even	2	inner	575.2.p.b.524.2		20
15.2	even	4		207.2.i.c.64.1		10
20.7	even	4		368.2.m.c.225.1		10
23.9	even	11	inner	575.2.p.b.124.2		20
115.2	odd	44		529.2.c.d.118.1		10
115.7	even	44		529.2.c.e.399.1		10
115.9	even	22	inner	575.2.p.b.124.1		20
115.12	odd	44		529.2.c.g.177.1		10
115.17	even	44		529.2.c.h.487.1		10
115.22	even	4		529.2.c.a.501.1		10
115.27	odd	44		529.2.c.b.334.1		10
115.32	odd	44		23.2.c.a.9.1	✓	10
115.37	even	44		529.2.c.a.170.1		10
115.42	even	44		529.2.c.c.334.1		10
115.52	odd	44		529.2.c.i.487.1		10
115.57	even	44		529.2.c.f.177.1		10
115.62	odd	44		529.2.c.d.399.1		10
115.67	even	44		529.2.c.e.118.1		10
115.72	odd	44		529.2.a.i.1.2		5
115.77	odd	44		529.2.c.b.255.1		10
115.78	odd	44		575.2.k.b.101.1		10
115.82	odd	44		529.2.c.i.466.1		10
115.87	odd	44		529.2.c.g.266.1		10
115.97	even	44		529.2.c.f.266.1		10
115.102	even	44		529.2.c.h.466.1		10
115.107	even	44		529.2.c.c.255.1		10
115.112	even	44		529.2.a.j.1.2		5
345.32	even	44		207.2.i.c.55.1		10
345.227	odd	44		4761.2.a.bn.1.4		5
345.302	even	44		4761.2.a.bo.1.4		5
460.147	even	44		368.2.m.c.193.1		10
460.187	even	44		8464.2.a.bs.1.3		5
460.227	odd	44		8464.2.a.bt.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.9.1	✓	10	115.32	odd	44
23.2.c.a.18.1	yes	10	5.2	odd	4
207.2.i.c.55.1		10	345.32	even	44
207.2.i.c.64.1		10	15.2	even	4
368.2.m.c.193.1		10	460.147	even	44
368.2.m.c.225.1		10	20.7	even	4
529.2.a.i.1.2		5	115.72	odd	44
529.2.a.j.1.2		5	115.112	even	44
529.2.c.a.170.1		10	115.37	even	44
529.2.c.a.501.1		10	115.22	even	4
529.2.c.b.255.1		10	115.77	odd	44
529.2.c.b.334.1		10	115.27	odd	44
529.2.c.c.255.1		10	115.107	even	44
529.2.c.c.334.1		10	115.42	even	44
529.2.c.d.118.1		10	115.2	odd	44
529.2.c.d.399.1		10	115.62	odd	44
529.2.c.e.118.1		10	115.67	even	44
529.2.c.e.399.1		10	115.7	even	44
529.2.c.f.177.1		10	115.57	even	44
529.2.c.f.266.1		10	115.97	even	44
529.2.c.g.177.1		10	115.12	odd	44
529.2.c.g.266.1		10	115.87	odd	44
529.2.c.h.466.1		10	115.102	even	44
529.2.c.h.487.1		10	115.17	even	44
529.2.c.i.466.1		10	115.82	odd	44
529.2.c.i.487.1		10	115.52	odd	44
575.2.k.b.101.1		10	115.78	odd	44
575.2.k.b.501.1		10	5.3	odd	4
575.2.p.b.124.1		20	115.9	even	22	inner
575.2.p.b.124.2		20	23.9	even	11	inner
575.2.p.b.524.1		20	1.1	even	1	trivial
575.2.p.b.524.2		20	5.4	even	2	inner
4761.2.a.bn.1.4		5	345.227	odd	44
4761.2.a.bo.1.4		5	345.302	even	44
8464.2.a.bs.1.3		5	460.187	even	44
8464.2.a.bt.1.3		5	460.227	odd	44

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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.p (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0666238 + 0.226900i) q^{2} +(-0.361922 - 0.313607i) q^{3} +(1.63546 + 1.05105i) q^{4} +(0.0952700 - 0.0612263i) q^{6} +(-2.31611 + 1.05773i) q^{7} +(-0.704881 + 0.610783i) q^{8} +(-0.394306 - 2.74246i) q^{9} +(3.23616 - 0.950224i) q^{11} +(-0.262294 - 0.893290i) q^{12} +(2.99430 + 1.36745i) q^{13} +(-0.0856910 - 0.595994i) q^{14} +(1.52357 + 3.33616i) q^{16} +(3.39353 + 5.28043i) q^{17} +(0.648534 + 0.0932451i) q^{18} +(3.55928 + 2.28741i) q^{19} +(1.16996 + 0.343532i) q^{21} +0.797593i q^{22} +(0.847210 - 4.72041i) q^{23} +0.446658 q^{24} +(-0.509766 + 0.588302i) q^{26} +(-1.49407 + 2.32482i) q^{27} +(-4.89963 - 0.704460i) q^{28} +(-5.28830 + 3.39858i) q^{29} +(3.10538 + 3.58380i) q^{31} +(-2.70488 + 0.388902i) q^{32} +(-1.46924 - 0.670978i) q^{33} +(-1.42422 + 0.418188i) q^{34} +(2.23758 - 4.89963i) q^{36} +(-0.0375858 + 0.00540403i) q^{37} +(-0.756145 + 0.655203i) q^{38} +(-0.654861 - 1.43394i) q^{39} +(-0.462048 + 3.21361i) q^{41} +(-0.155895 + 0.242577i) q^{42} +(-0.974066 - 0.844033i) q^{43} +(6.29135 + 1.84731i) q^{44} +(1.01462 + 0.506723i) q^{46} -3.41741i q^{47} +(0.494829 - 1.68523i) q^{48} +(-0.338474 + 0.390620i) q^{49} +(0.427789 - 2.97534i) q^{51} +(3.45981 + 5.38357i) q^{52} +(6.11799 - 2.79399i) q^{53} +(-0.427961 - 0.493893i) q^{54} +(0.986535 - 2.16021i) q^{56} +(-0.570833 - 1.94408i) q^{57} +(-0.418811 - 1.42634i) q^{58} +(4.32805 - 9.47711i) q^{59} +(-2.35737 - 2.72055i) q^{61} +(-1.02006 + 0.465844i) q^{62} +(3.81404 + 5.93476i) q^{63} +(-0.951939 + 6.62088i) q^{64} +(0.250131 - 0.288666i) q^{66} +(1.92124 - 6.54316i) q^{67} +12.2027i q^{68} +(-1.78698 + 1.44273i) q^{69} +(-3.92408 - 1.15221i) q^{71} +(1.95299 + 1.69227i) q^{72} +(-2.35800 + 3.66912i) q^{73} +(0.00127794 - 0.00888826i) q^{74} +(3.41689 + 7.48194i) q^{76} +(-6.49022 + 5.62381i) q^{77} +(0.368991 - 0.0530529i) q^{78} +(-0.997820 + 2.18492i) q^{79} +(-6.70548 + 1.96891i) q^{81} +(-0.698384 - 0.318941i) q^{82} +(2.92705 - 0.420847i) q^{83} +(1.55236 + 1.79152i) q^{84} +(0.256407 - 0.164783i) q^{86} +(2.97977 + 0.428426i) q^{87} +(-1.70073 + 2.64639i) q^{88} +(8.09455 - 9.34161i) q^{89} -8.38151 q^{91} +(6.34695 - 6.82959i) q^{92} -2.27092i q^{93} +(0.775410 + 0.227681i) q^{94} +(1.10092 + 0.707516i) q^{96} +(-10.5084 - 1.51088i) q^{97} +(-0.0660811 - 0.102824i) q^{98} +(-3.88199 - 8.50038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{4} + 12 q^{6} + 4 q^{9} + 14 q^{11} - 18 q^{14} + 2 q^{16} - 4 q^{19} - 4 q^{21} + 76 q^{24} + 24 q^{26} - 28 q^{29} + 20 q^{31} - 58 q^{34} + 54 q^{36} - 2 q^{39} + 14 q^{41} + 68 q^{44} - 58 q^{46}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^4 + 12 * q^6 + 4 * q^9 + 14 * q^11 - 18 * q^14 + 2 * q^16 - 4 * q^19 - 4 * q^21 + 76 * q^24 + 24 * q^26 - 28 * q^29 + 20 * q^31 - 58 * q^34 + 54 * q^36 - 2 * q^39 + 14 * q^41 + 68 * q^44 - 58 * q^46 + 36 * q^49 + 14 * q^51 + 12 * q^54 - 4 * q^56 + 42 * q^59 + 6 * q^61 - 48 * q^64 + 4 * q^66 - 52 * q^69 - 28 * q^71 - 20 * q^74 - 32 * q^76 + 30 * q^79 - 88 * q^81 + 34 * q^84 - 22 * q^86 - 50 * q^89 - 8 * q^91 - 34 * q^94 - 102 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more