LMFDB - Embedded newform 975.2.bn.d.368.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			368.6
Character	$\chi$	$=$	975.368
Dual form			975.2.bn.d.257.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.442218 - 1.65038i) q^{2} +(-1.72661 + 0.137150i) q^{3} +(-0.796141 + 0.459652i) q^{4} +(0.989888 + 2.78891i) q^{6} +(-0.0293212 + 0.109428i) q^{7} +(-1.30565 - 1.30565i) q^{8} +(2.96238 - 0.473611i) q^{9} +(-2.05447 + 3.55845i) q^{11} +(1.31159 - 0.902832i) q^{12} +(1.57162 - 3.24500i) q^{13} +0.193564 q^{14} +(-2.49674 + 4.32449i) q^{16} +(-1.35141 + 5.04353i) q^{17} +(-2.09165 - 4.67961i) q^{18} +(-3.97662 - 6.88771i) q^{19} +(0.0356182 - 0.192962i) q^{21} +(6.78132 + 1.81705i) q^{22} +(1.79398 + 6.69524i) q^{23} +(2.43343 + 2.07529i) q^{24} +(-6.05047 - 1.15878i) q^{26} +(-5.04992 + 1.22403i) q^{27} +(-0.0269551 - 0.100598i) q^{28} +(-2.00973 + 3.48095i) q^{29} +6.89468i q^{31} +(4.67403 + 1.25240i) q^{32} +(3.05924 - 6.42584i) q^{33} +8.92135 q^{34} +(-2.14078 + 1.73873i) q^{36} +(4.10339 - 1.09950i) q^{37} +(-9.60880 + 9.60880i) q^{38} +(-2.26853 + 5.81840i) q^{39} +(1.73822 - 3.01068i) q^{41} +(-0.334211 + 0.0265474i) q^{42} +(-1.30993 + 4.88872i) q^{43} -3.77737i q^{44} +(10.2563 - 5.92150i) q^{46} +(-0.185543 + 0.185543i) q^{47} +(3.71780 - 7.80914i) q^{48} +(6.05106 + 3.49358i) q^{49} +(1.64164 - 8.89356i) q^{51} +(0.240337 + 3.30587i) q^{52} +(1.94409 - 1.94409i) q^{53} +(4.25328 + 7.79300i) q^{54} +(0.181159 - 0.104592i) q^{56} +(7.81074 + 11.3470i) q^{57} +(6.63362 + 1.77747i) q^{58} +(-0.619675 + 0.357770i) q^{59} +(2.04160 + 3.53616i) q^{61} +(11.3788 - 3.04895i) q^{62} +(-0.0350341 + 0.338055i) q^{63} +1.71922i q^{64} +(-11.9579 - 2.20728i) q^{66} +(2.85424 - 0.764792i) q^{67} +(-1.24236 - 4.63654i) q^{68} +(-4.01577 - 11.3140i) q^{69} +(4.25380 + 7.36780i) q^{71} +(-4.48621 - 3.24947i) q^{72} +(-3.00868 + 3.00868i) q^{73} +(-3.62918 - 6.28592i) q^{74} +(6.33191 + 3.65573i) q^{76} +(-0.329156 - 0.329156i) q^{77} +(10.6057 + 1.17093i) q^{78} -4.84485i q^{79} +(8.55139 - 2.80603i) q^{81} +(-5.73743 - 1.53734i) q^{82} +(2.04442 + 2.04442i) q^{83} +(0.0603381 + 0.169997i) q^{84} +8.64751 q^{86} +(2.99261 - 6.28589i) q^{87} +(7.32854 - 1.96368i) q^{88} +(2.79966 + 1.61638i) q^{89} +(0.309013 + 0.267127i) q^{91} +(-4.50574 - 4.50574i) q^{92} +(-0.945607 - 11.9044i) q^{93} +(0.388267 + 0.224166i) q^{94} +(-8.24201 - 1.52137i) q^{96} +(-0.0386722 + 0.144327i) q^{97} +(3.08985 - 11.5315i) q^{98} +(-4.40081 + 11.5145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.442218	−	1.65038i	−0.312695	−	1.16699i	−0.926116	−	0.377238i	$-0.876874\pi$
$2$	−0.442218	−	1.65038i	−0.312695	−	1.16699i	0.613421	−	0.789756i	$-0.289793\pi$
$3$	−1.72661	+	0.137150i	−0.996860	+	0.0791838i
$3$	−1.72661	+	0.137150i	−0.996860	+	0.0791838i
$4$	−0.796141	+	0.459652i	−0.398071	+	0.229826i
$5$		0			0
$5$		0			0
$6$	0.989888	+	2.78891i	0.404120	+	1.13857i
$7$	−0.0293212	+	0.109428i	−0.0110824	+	0.0413600i	−0.971246	−	0.238080i	$-0.923482\pi$
$7$	−0.0293212	+	0.109428i	−0.0110824	+	0.0413600i	0.960163	+	0.279440i	$0.0901487\pi$
$8$	−1.30565	−	1.30565i	−0.461618	−	0.461618i
$9$	2.96238	−	0.473611i	0.987460	−	0.157870i
$10$		0			0
$11$	−2.05447	+	3.55845i	−0.619447	+	1.07291i	0.370139	+	0.928976i	$0.379310\pi$
$11$	−2.05447	+	3.55845i	−0.619447	+	1.07291i	−0.989587	+	0.143938i	$0.954023\pi$
$12$	1.31159	−	0.902832i	0.378622	−	0.260625i
$13$	1.57162	−	3.24500i	0.435890	−	0.900000i
$13$	1.57162	−	3.24500i	0.435890	−	0.900000i
$14$	0.193564			0.0517323
$15$		0			0
$16$	−2.49674	+	4.32449i	−0.624186	+	1.08112i
$17$	−1.35141	+	5.04353i	−0.327765	+	1.22324i	0.583738	+	0.811942i	$0.301589\pi$
$17$	−1.35141	+	5.04353i	−0.327765	+	1.22324i	−0.911503	+	0.411293i	$0.865077\pi$
$18$	−2.09165	−	4.67961i	−0.493007	−	1.10299i
$19$	−3.97662	−	6.88771i	−0.912300	−	1.58015i	−0.810807	−	0.585313i	$-0.800971\pi$
$19$	−3.97662	−	6.88771i	−0.912300	−	1.58015i	−0.101493	−	0.994836i	$-0.532362\pi$
$20$		0			0
$21$	0.0356182	−	0.192962i	0.00777254	−	0.0421077i
$22$	6.78132	+	1.81705i	1.44578	+	0.387396i
$23$	1.79398	+	6.69524i	0.374071	+	1.39605i	0.854697	+	0.519127i	$0.173743\pi$
$23$	1.79398	+	6.69524i	0.374071	+	1.39605i	−0.480625	+	0.876926i	$0.659590\pi$
$24$	2.43343	+	2.07529i	0.496722	+	0.423616i
$25$		0			0
$26$	−6.05047	−	1.15878i	−1.18659	−	0.227255i
$27$	−5.04992	+	1.22403i	−0.971858	+	0.235565i
$28$	−0.0269551	−	0.100598i	−0.00509404	−	0.0190112i
$29$	−2.00973	+	3.48095i	−0.373197	+	0.646396i	−0.990055	−	0.140678i	$-0.955072\pi$
$29$	−2.00973	+	3.48095i	−0.373197	+	0.646396i	0.616858	+	0.787074i	$0.288405\pi$
$30$		0			0
$31$			6.89468i			1.23832i	0.785265	+	0.619160i	$0.212527\pi$
$31$			6.89468i			1.23832i	−0.785265	+	0.619160i	$0.787473\pi$
$32$	4.67403	+	1.25240i	0.826260	+	0.221396i
$33$	3.05924	−	6.42584i	0.532545	−	1.11860i
$34$	8.92135			1.53000
$35$		0			0
$36$	−2.14078	+	1.73873i	−0.356796	+	0.289788i
$37$	4.10339	−	1.09950i	0.674593	−	0.180757i	0.0947700	−	0.995499i	$-0.469788\pi$
$37$	4.10339	−	1.09950i	0.674593	−	0.180757i	0.579823	+	0.814743i	$0.303122\pi$
$38$	−9.60880	+	9.60880i	−1.55875	+	1.55875i
$39$	−2.26853	+	5.81840i	−0.363256	+	0.931690i
$40$		0			0
$41$	1.73822	−	3.01068i	0.271464	−	0.470189i	−0.697773	−	0.716319i	$-0.745826\pi$
$41$	1.73822	−	3.01068i	0.271464	−	0.470189i	0.969237	+	0.246130i	$0.0791589\pi$
$42$	−0.334211	+	0.0265474i	−0.0515698	+	0.00409636i
$43$	−1.30993	+	4.88872i	−0.199762	+	0.745523i	0.791220	+	0.611531i	$0.209446\pi$
$43$	−1.30993	+	4.88872i	−0.199762	+	0.745523i	−0.990982	+	0.133991i	$0.957221\pi$
$44$		−	3.77737i		−	0.569461i
$45$		0			0
$46$	10.2563	−	5.92150i	1.51222	−	0.873078i
$47$	−0.185543	+	0.185543i	−0.0270642	+	0.0270642i	−0.720509	−	0.693445i	$-0.756092\pi$
$47$	−0.185543	+	0.185543i	−0.0270642	+	0.0270642i	0.693445	+	0.720509i	$0.256092\pi$
$48$	3.71780	−	7.80914i	0.536619	−	1.12715i
$49$	6.05106	+	3.49358i	0.864438	+	0.499083i
$50$		0			0
$51$	1.64164	−	8.89356i	0.229875	−	1.24535i
$52$	0.240337	+	3.30587i	0.0333287	+	0.458442i
$53$	1.94409	−	1.94409i	0.267042	−	0.267042i	−0.560865	−	0.827907i	$-0.689531\pi$
$53$	1.94409	−	1.94409i	0.267042	−	0.267042i	0.827907	+	0.560865i	$0.189531\pi$
$54$	4.25328	+	7.79300i	0.578799	+	1.06049i
$55$		0			0
$56$	0.181159	−	0.104592i	0.0242084	−	0.0139767i
$57$	7.81074	+	11.3470i	1.03456	+	1.50295i
$58$	6.63362	+	1.77747i	0.871037	+	0.233394i
$59$	−0.619675	+	0.357770i	−0.0806749	+	0.0465777i	−0.539795	−	0.841797i	$-0.681498\pi$
$59$	−0.619675	+	0.357770i	−0.0806749	+	0.0465777i	0.459120	+	0.888374i	$0.348165\pi$
$60$		0			0
$61$	2.04160	+	3.53616i	0.261400	+	0.452758i	0.966614	−	0.256236i	$-0.0824825\pi$
$61$	2.04160	+	3.53616i	0.261400	+	0.452758i	−0.705214	+	0.708994i	$0.749149\pi$
$62$	11.3788	−	3.04895i	1.44511	−	0.387217i
$63$	−0.0350341	+	0.338055i	−0.00441389	+	0.0425909i
$64$			1.71922i			0.214903i
$65$		0			0
$66$	−11.9579	−	2.20728i	−1.47192	−	0.271697i
$67$	2.85424	−	0.764792i	0.348701	−	0.0934343i	−0.0802172	−	0.996777i	$-0.525561\pi$
$67$	2.85424	−	0.764792i	0.348701	−	0.0934343i	0.428919	+	0.903343i	$0.358895\pi$
$68$	−1.24236	−	4.63654i	−0.150658	−	0.562263i
$69$	−4.01577	−	11.3140i	−0.483442	−	1.36205i
$70$		0			0
$71$	4.25380	+	7.36780i	0.504833	+	0.874397i	0.999984	+	0.00558990i	$0.00177933\pi$
$71$	4.25380	+	7.36780i	0.504833	+	0.874397i	−0.495151	+	0.868807i	$0.664887\pi$
$72$	−4.48621	−	3.24947i	−0.528705	−	0.382954i
$73$	−3.00868	+	3.00868i	−0.352139	+	0.352139i	−0.860905	−	0.508766i	$-0.830102\pi$
$73$	−3.00868	+	3.00868i	−0.352139	+	0.352139i	0.508766	+	0.860905i	$0.330102\pi$
$74$	−3.62918	−	6.28592i	−0.421884	−	0.730724i
$75$		0			0
$76$	6.33191	+	3.65573i	0.726319	+	0.419341i
$77$	−0.329156	−	0.329156i	−0.0375108	−	0.0375108i
$78$	10.6057	+	1.17093i	1.20086	+	0.132582i
$79$		−	4.84485i		−	0.545088i	−0.962143	−	0.272544i	$-0.912135\pi$
$79$		−	4.84485i		−	0.545088i	0.962143	−	0.272544i	$-0.0878650\pi$
$80$		0			0
$81$	8.55139	−	2.80603i	0.950154	−	0.311781i
$82$	−5.73743	−	1.53734i	−0.633593	−	0.169771i
$83$	2.04442	+	2.04442i	0.224405	+	0.224405i	0.810350	−	0.585946i	$-0.199277\pi$
$83$	2.04442	+	2.04442i	0.224405	+	0.224405i	−0.585946	+	0.810350i	$0.699277\pi$
$84$	0.0603381	+	0.169997i	0.00658343	+	0.0185482i
$85$		0			0
$86$	8.64751			0.932485
$87$	2.99261	−	6.28589i	0.320841	−	0.673918i
$88$	7.32854	−	1.96368i	0.781225	−	0.209329i
$89$	2.79966	+	1.61638i	0.296763	+	0.171336i	0.640988	−	0.767551i	$-0.278525\pi$
$89$	2.79966	+	1.61638i	0.296763	+	0.171336i	−0.344225	+	0.938887i	$0.611858\pi$
$90$		0			0
$91$	0.309013	+	0.267127i	0.0323933	+	0.0280025i
$92$	−4.50574	−	4.50574i	−0.469756	−	0.469756i
$93$	−0.945607	−	11.9044i	−0.0980549	−	1.23443i
$94$	0.388267	+	0.224166i	0.0400466	+	0.0231209i
$95$		0			0
$96$	−8.24201	−	1.52137i	−0.841196	−	0.155274i
$97$	−0.0386722	+	0.144327i	−0.00392657	+	0.0146542i	−0.967861	−	0.251485i	$-0.919081\pi$
$97$	−0.0386722	+	0.144327i	−0.00392657	+	0.0146542i	0.963935	+	0.266139i	$0.0857479\pi$
$98$	3.08985	−	11.5315i	0.312122	−	1.16485i
$99$	−4.40081	+	11.5145i	−0.442298	+	1.15725i
$100$		0			0
$101$	10.5103	+	6.06812i	1.04581	+	0.603800i	0.921474	−	0.388440i	$-0.126986\pi$
$101$	10.5103	+	6.06812i	1.04581	+	0.603800i	0.124339	+	0.992240i	$0.460319\pi$
$102$	−15.4037	+	1.22357i	−1.52519	+	0.121151i
$103$	−0.528320	−	0.528320i	−0.0520569	−	0.0520569i	0.680599	−	0.732656i	$-0.261720\pi$
$103$	−0.528320	−	0.528320i	−0.0520569	−	0.0520569i	−0.732656	+	0.680599i	$0.761720\pi$
$104$	−6.28884	+	2.18485i	−0.616671	+	0.214242i
$105$		0			0
$106$	−4.06820	−	2.34878i	−0.395139	−	0.228133i
$107$	−1.59525	+	0.427445i	−0.154218	+	0.0413227i	−0.335102	−	0.942182i	$-0.608771\pi$
$107$	−1.59525	+	0.427445i	−0.154218	+	0.0413227i	0.180884	+	0.983504i	$0.442104\pi$
$108$	3.45782	−	3.29571i	0.332729	−	0.317130i
$109$	0.638870			0.0611926			0.0305963	−	0.999532i	$-0.490259\pi$
$109$	0.638870			0.0611926			0.0305963	+	0.999532i	$0.490259\pi$
$110$		0			0
$111$	−6.93416	+	2.46119i	−0.658162	+	0.233606i
$112$	−0.400014	−	0.400014i	−0.0377977	−	0.0377977i
$113$	−7.64451	−	2.04834i	−0.719135	−	0.192692i	−0.119349	−	0.992852i	$-0.538081\pi$
$113$	−7.64451	−	2.04834i	−0.719135	−	0.192692i	−0.599786	+	0.800161i	$0.704747\pi$
$114$	15.2728	−	17.9085i	1.43043	−	1.67729i
$115$		0			0
$116$		−	3.69510i		−	0.343082i
$117$	3.11888	−	10.3572i	0.288340	−	0.957528i
$118$	0.864487	+	0.864487i	0.0795825	+	0.0795825i
$119$	−0.512280	−	0.295765i	−0.0469606	−	0.0271127i
$120$		0			0
$121$	−2.94173	−	5.09522i	−0.267430	−	0.463202i
$122$	4.93316	−	4.93316i	0.446628	−	0.446628i
$123$	−2.58831	+	5.43667i	−0.233380	+	0.490208i
$124$	−3.16915	−	5.48913i	−0.284598	−	0.492939i
$125$		0			0
$126$	0.573411	−	0.0916742i	0.0510835	−	0.00816699i
$127$	3.29674	+	12.3036i	0.292539	+	1.09177i	0.943152	+	0.332361i	$0.107845\pi$
$127$	3.29674	+	12.3036i	0.292539	+	1.09177i	−0.650614	+	0.759409i	$0.725488\pi$
$128$	12.1854	−	3.26508i	1.07705	−	0.288595i
$129$	1.59125	−	8.62058i	0.140102	−	0.759000i
$130$		0			0
$131$		−	12.9569i		−	1.13205i	−0.824390	−	0.566023i	$-0.808481\pi$
$131$		−	12.9569i		−	1.13205i	0.824390	−	0.566023i	$-0.191519\pi$
$132$	0.518068	+	6.52206i	0.0450921	+	0.567673i
$133$	0.870310	−	0.233199i	0.0754655	−	0.0202209i
$134$	−2.52439	−	4.37238i	−0.218074	−	0.377716i
$135$		0			0
$136$	8.34958	−	4.82063i	0.715970	−	0.413366i
$137$	−12.0355	−	3.22490i	−1.02826	−	0.275522i	−0.295021	−	0.955491i	$-0.595327\pi$
$137$	−12.0355	−	3.22490i	−1.02826	−	0.275522i	−0.733241	+	0.679969i	$0.761993\pi$
$138$	−16.8966	+	11.6308i	−1.43833	+	0.990079i
$139$	−3.31851	+	1.91594i	−0.281472	+	0.162508i	−0.634090	−	0.773260i	$-0.718625\pi$
$139$	−3.31851	+	1.91594i	−0.281472	+	0.162508i	0.352618	+	0.935767i	$0.385292\pi$
$140$		0			0
$141$	0.294914	−	0.345808i	0.0248362	−	0.0291223i
$142$	10.2785	−	10.2785i	0.862557	−	0.862557i
$143$	8.31831	+	12.2593i	0.695612	+	1.02517i
$144$	−5.34818	+	13.9933i	−0.445682	+	1.16610i
$145$		0			0
$146$	6.29594	+	3.63496i	0.521056	+	0.300832i
$147$	−10.9270	−	5.20216i	−0.901243	−	0.429067i
$148$	−2.76149	+	2.76149i	−0.226993	+	0.226993i
$149$	−10.3032	+	5.94857i	−0.844073	+	0.487326i	−0.858647	−	0.512568i	$-0.828694\pi$
$149$	−10.3032	+	5.94857i	−0.844073	+	0.487326i	0.0145735	+	0.999894i	$0.495361\pi$
$150$		0			0
$151$			11.1014i			0.903416i	0.892166	+	0.451708i	$0.149185\pi$
$151$			11.1014i			0.903416i	−0.892166	+	0.451708i	$0.850815\pi$
$152$	−3.80088	+	14.1851i	−0.308292	+	1.15056i
$153$	−1.61472	+	15.5809i	−0.130542	+	1.25964i
$154$	−0.397673	+	0.688790i	−0.0320454	+	0.0555043i
$155$		0			0
$156$	−0.868370	−	5.67500i	−0.0695253	−	0.454364i
$157$	−5.53986	+	5.53986i	−0.442129	+	0.442129i	−0.892727	−	0.450598i	$-0.851211\pi$
$157$	−5.53986	+	5.53986i	−0.442129	+	0.442129i	0.450598	+	0.892727i	$0.351211\pi$
$158$	−7.99583	+	2.14248i	−0.636114	+	0.170446i
$159$	−3.09006	+	3.62333i	−0.245058	+	0.287349i
$160$		0			0
$161$	−0.785250			−0.0618864
$162$	−8.41259	−	12.8721i	−0.660955	−	1.01133i
$163$	−11.8393	−	3.17233i	−0.927326	−	0.248476i	−0.236612	−	0.971604i	$-0.576037\pi$
$163$	−11.8393	−	3.17233i	−0.927326	−	0.248476i	−0.690714	+	0.723128i	$0.742704\pi$
$164$			3.19590i			0.249558i
$165$		0			0
$166$	2.46999	−	4.27815i	0.191708	−	0.332049i
$167$	2.30903	+	8.61742i	0.178678	+	0.666836i	0.995896	+	0.0905069i	$0.0288487\pi$
$167$	2.30903	+	8.61742i	0.178678	+	0.666836i	−0.817218	+	0.576329i	$0.804485\pi$
$168$	−0.298446	+	0.205436i	−0.0230256	+	0.0158497i
$169$	−8.06000	−	10.1998i	−0.620000	−	0.784602i
$170$		0			0
$171$	−15.0424	−	18.5206i	−1.15032	−	1.41631i
$172$	−1.20422	−	4.49422i	−0.0918211	−	0.342681i
$173$	−8.49801	−	2.27704i	−0.646092	−	0.173120i	−0.0791307	−	0.996864i	$-0.525214\pi$
$173$	−8.49801	−	2.27704i	−0.646092	−	0.173120i	−0.566961	+	0.823744i	$0.691881\pi$
$174$	−11.6975	−	2.15920i	−0.886783	−	0.163689i
$175$		0			0
$176$	−10.2590	−	17.7691i	−0.773301	−	1.33940i
$177$	1.02087	−	0.702718i	0.0767334	−	0.0528196i
$178$	1.42959	−	5.33529i	0.107152	−	0.399897i
$179$	−9.95273	+	17.2386i	−0.743902	+	1.28848i	0.206804	+	0.978382i	$0.433694\pi$
$179$	−9.95273	+	17.2386i	−0.743902	+	1.28848i	−0.950706	+	0.310094i	$0.899640\pi$
$180$		0			0
$181$	7.45086			0.553818			0.276909	−	0.960896i	$-0.410690\pi$
$181$	7.45086			0.553818			0.276909	+	0.960896i	$0.410690\pi$
$182$	0.304210	−	0.628116i	0.0225496	−	0.0465590i
$183$	−4.01004	−	5.82556i	−0.296430	−	0.430638i
$184$	6.39934	−	11.0840i	0.471766	−	0.817122i
$185$		0			0
$186$	−19.2287	+	6.82496i	−1.40991	+	0.500430i
$187$	−15.1707	−	15.1707i	−1.10939	−	1.10939i
$188$	0.0624332	−	0.233004i	0.00455341	−	0.0169935i
$189$	0.0141260	−	0.588495i	0.00102752	−	0.0428067i
$190$		0			0
$191$	−19.8776	+	11.4763i	−1.43829	+	0.830399i	−0.997731	−	0.0673227i	$-0.978554\pi$
$191$	−19.8776	+	11.4763i	−1.43829	+	0.830399i	−0.440562	+	0.897722i	$0.645221\pi$
$192$	−0.235792	−	2.96843i	−0.0170168	−	0.214228i
$193$	5.67196	+	21.1680i	0.408276	+	1.52371i	0.797932	+	0.602748i	$0.205928\pi$
$193$	5.67196	+	21.1680i	0.408276	+	1.52371i	−0.389655	+	0.920961i	$0.627406\pi$
$194$	0.255295			0.0183291
$195$		0			0
$196$	−6.42333			−0.458810
$197$	−2.25019	−	8.39781i	−0.160319	−	0.598319i	−0.998591	−	0.0530668i	$-0.983100\pi$
$197$	−2.25019	−	8.39781i	−0.160319	−	0.598319i	0.838272	−	0.545253i	$-0.183566\pi$
$198$	20.9494	+	2.17108i	1.48881	+	0.154292i
$199$	−17.5413	+	10.1275i	−1.24347	+	0.717919i	−0.969799	−	0.243904i	$-0.921572\pi$
$199$	−17.5413	+	10.1275i	−1.24347	+	0.717919i	−0.273673	+	0.961823i	$0.588239\pi$
$200$		0			0
$201$	−4.82328	+	1.71196i	−0.340208	+	0.120752i
$202$	5.36686	−	20.0294i	0.377611	−	1.40926i
$203$	−0.321987	−	0.321987i	−0.0225990	−	0.0225990i
$204$	2.78097	+	7.83511i	0.194707	+	0.548568i
$205$		0			0
$206$	−0.638295	+	1.10556i	−0.0444721	+	0.0770280i
$207$	8.48540	+	18.9842i	0.589776	+	1.31949i
$208$	10.1090	+	14.8984i	0.700934	+	1.03302i
$209$	32.6795			2.26049
$210$		0			0
$211$	3.64767	−	6.31794i	0.251116	−	0.434945i	−0.712718	−	0.701451i	$-0.752536\pi$
$211$	3.64767	−	6.31794i	0.251116	−	0.434945i	0.963833	+	0.266506i	$0.0858692\pi$
$212$	−0.654166	+	2.44138i	−0.0449283	+	0.167675i
$213$	−8.35516	−	12.1379i	−0.572486	−	0.831677i
$214$	1.41089	+	2.44374i	0.0964466	+	0.167050i
$215$		0			0
$216$	8.19162	+	4.99529i	0.557369	+	0.339886i
$217$	−0.754473	−	0.202160i	−0.0512169	−	0.0137235i
$218$	−0.282519	−	1.05438i	−0.0191346	−	0.0714114i
$219$	4.78218	−	5.60746i	0.323149	−	0.378917i
$220$		0			0
$221$	14.2423	+	12.3118i	0.958043	+	0.828184i
$222$	7.12830	+	10.3556i	0.478420	+	0.695023i
$223$	3.14269	+	11.7287i	0.210450	+	0.785411i	0.987719	+	0.156242i	$0.0499381\pi$
$223$	3.14269	+	11.7287i	0.210450	+	0.785411i	−0.777268	+	0.629169i	$0.783395\pi$
$224$	−0.274097	+	0.474749i	−0.0183139	+	0.0317205i
$225$		0			0
$226$			13.5221i			0.899479i
$227$	13.3950	+	3.58919i	0.889061	+	0.238223i	0.674312	−	0.738446i	$-0.264440\pi$
$227$	13.3950	+	3.58919i	0.889061	+	0.238223i	0.214748	+	0.976669i	$0.431107\pi$
$228$	−11.4341	−	5.44360i	−0.757244	−	0.360511i
$229$	8.51901			0.562952			0.281476	−	0.959568i	$-0.409176\pi$
$229$	8.51901			0.562952			0.281476	+	0.959568i	$0.409176\pi$
$230$		0			0
$231$	0.613468	+	0.523181i	0.0403633	+	0.0344228i
$232$	7.16892	−	1.92091i	0.470663	−	0.126114i
$233$	−8.61258	+	8.61258i	−0.564229	+	0.564229i	−0.930506	−	0.366277i	$-0.880632\pi$
$233$	−8.61258	+	8.61258i	−0.564229	+	0.564229i	0.366277	+	0.930506i	$0.380632\pi$
$234$	−18.4726	−	0.567169i	−1.20759	−	0.0370770i
$235$		0			0
$236$	0.328899	−	0.569670i	0.0214095	−	0.0370824i
$237$	0.664473	+	8.36517i	0.0431621	+	0.543376i
$238$	−0.261585	+	0.976248i	−0.0169560	+	0.0632807i
$239$		−	11.5531i		−	0.747310i	−0.927568	−	0.373655i	$-0.878104\pi$
$239$		−	11.5531i		−	0.747310i	0.927568	−	0.373655i	$-0.121896\pi$
$240$		0			0
$241$	12.0934	−	6.98212i	0.779004	−	0.449758i	−0.0570731	−	0.998370i	$-0.518177\pi$
$241$	12.0934	−	6.98212i	0.779004	−	0.449758i	0.836077	+	0.548612i	$0.184843\pi$
$242$	−7.10816	+	7.10816i	−0.456930	+	0.456930i
$243$	−14.3801	+	6.01775i	−0.922482	+	0.386039i
$244$	−3.25080	−	1.87685i	−0.208111	−	0.120153i
$245$		0			0
$246$	10.1172	+	1.86750i	0.645047	+	0.119067i
$247$	−28.6004	+	2.07924i	−1.81980	+	0.132299i
$248$	9.00206	−	9.00206i	0.571631	−	0.571631i
$249$	−3.81032	−	3.24953i	−0.241469	−	0.205931i
$250$		0			0
$251$	−14.9246	+	8.61672i	−0.942032	+	0.543882i	−0.890597	−	0.454794i	$-0.849713\pi$
$251$	−14.9246	+	8.61672i	−0.942032	+	0.543882i	−0.0514354	+	0.998676i	$0.516380\pi$
$252$	−0.127496	−	0.285243i	−0.00803147	−	0.0179686i
$253$	−27.5104	−	7.37138i	−1.72956	−	0.463435i
$254$	18.8477	−	10.8818i	1.18261	−	0.682782i
$255$		0			0
$256$	−9.05800	−	15.6889i	−0.566125	−	0.980557i
$257$	0.404361	−	0.108348i	0.0252233	−	0.00675857i	−0.246185	−	0.969223i	$-0.579177\pi$
$257$	0.404361	−	0.108348i	0.0252233	−	0.00675857i	0.271409	+	0.962464i	$0.412511\pi$
$258$	−14.9309	+	1.18601i	−0.929557	+	0.0738377i
$259$			0.481265i			0.0299044i
$260$		0			0
$261$	−4.30496	+	11.2637i	−0.266470	+	0.697207i
$262$	−21.3837	+	5.72975i	−1.32109	+	0.353985i
$263$	−3.38670	−	12.6393i	−0.208833	−	0.779374i	−0.988247	−	0.152865i	$-0.951150\pi$
$263$	−3.38670	−	12.6393i	−0.208833	−	0.779374i	0.779414	−	0.626509i	$-0.215517\pi$
$264$	−12.3842	+	4.39562i	−0.762197	+	0.270532i
$265$		0			0
$266$	−0.769733	−	1.33322i	−0.0471953	−	0.0817447i
$267$	−5.05561	−	2.40689i	−0.309398	−	0.147299i
$268$	−1.92084	+	1.92084i	−0.117334	+	0.117334i
$269$	−0.403612	−	0.699076i	−0.0246086	−	0.0426234i	0.853459	−	0.521160i	$-0.174501\pi$
$269$	−0.403612	−	0.699076i	−0.0246086	−	0.0426234i	−0.878067	+	0.478537i	$0.841167\pi$
$270$		0			0
$271$	−9.22378	−	5.32535i	−0.560305	−	0.323492i	0.192963	−	0.981206i	$-0.438190\pi$
$271$	−9.22378	−	5.32535i	−0.560305	−	0.323492i	−0.753268	+	0.657714i	$0.771524\pi$
$272$	−18.4366	−	18.4366i	−1.11788	−	1.11788i
$273$	−0.570181	−	0.418844i	−0.0345089	−	0.0253496i
$274$			21.2892i			1.28613i
$275$		0			0
$276$	8.39764	+	7.16171i	0.505478	+	0.431084i
$277$	27.5691	+	7.38713i	1.65647	+	0.443849i	0.961414	−	0.275107i	$-0.0887134\pi$
$277$	27.5691	+	7.38713i	1.65647	+	0.443849i	0.695055	+	0.718957i	$0.255380\pi$
$278$	4.62953	+	4.62953i	0.277661	+	0.277661i
$279$	3.26539	+	20.4246i	0.195494	+	1.22279i
$280$		0			0
$281$	−13.4870			−0.804568			−0.402284	−	0.915515i	$-0.631784\pi$
$281$	−13.4870			−0.804568			−0.402284	+	0.915515i	$0.631784\pi$
$282$	−0.701130	−	0.333797i	−0.0417517	−	0.0198773i
$283$	1.10046	−	0.294869i	0.0654158	−	0.0175281i	−0.225963	−	0.974136i	$-0.572553\pi$
$283$	1.10046	−	0.294869i	0.0654158	−	0.0175281i	0.291379	+	0.956608i	$0.405886\pi$
$284$	−6.77325	−	3.91054i	−0.401918	−	0.232048i
$285$		0			0
$286$	16.5540	−	19.1496i	0.978858	−	1.13234i
$287$	0.278487	+	0.278487i	0.0164386	+	0.0164386i
$288$	14.4394	+	1.49642i	0.850850	+	0.0881774i
$289$	−8.88844	−	5.13174i	−0.522850	−	0.301867i
$290$		0			0
$291$	0.0469775	−	0.254500i	0.00275387	−	0.0149191i
$292$	1.01239	−	3.77827i	0.0592454	−	0.221107i
$293$	1.95360	−	7.29093i	0.114130	−	0.425941i	−0.885090	−	0.465420i	$-0.845903\pi$
$293$	1.95360	−	7.29093i	0.114130	−	0.425941i	0.999220	+	0.0394794i	$0.0125700\pi$
$294$	−3.75342	+	20.3341i	−0.218904	+	1.18591i
$295$		0			0
$296$	−6.79317	−	3.92204i	−0.394845	−	0.227964i
$297$	6.01927	−	20.4847i	0.349274	−	1.18864i
$298$	14.3737	+	14.3737i	0.832644	+	0.832644i
$299$	24.5455	+	4.70092i	1.41950	+	0.271861i
$300$		0			0
$301$	−0.496555	−	0.286686i	−0.0286210	−	0.0165243i
$302$	18.3214	−	4.90922i	1.05428	−	0.282494i
$303$	−18.9794	−	9.03580i	−1.09034	−	0.519093i
$304$	39.7144			2.27778
$305$		0			0
$306$	26.4284	−	4.22525i	1.51081	−	0.241541i
$307$	−5.28300	−	5.28300i	−0.301517	−	0.301517i	0.540090	−	0.841607i	$-0.318390\pi$
$307$	−5.28300	−	5.28300i	−0.301517	−	0.301517i	−0.841607	+	0.540090i	$0.818390\pi$
$308$	0.413352	+	0.110757i	0.0235529	+	0.00631098i
$309$	0.984663	+	0.839744i	0.0560155	+	0.0477714i
$310$		0			0
$311$		−	2.37607i		−	0.134735i	−0.997728	−	0.0673674i	$-0.978540\pi$
$311$		−	2.37607i		−	0.134735i	0.997728	−	0.0673674i	$-0.0214599\pi$
$312$	10.5587	−	4.63490i	0.597770	−	0.262400i
$313$	−20.5099	−	20.5099i	−1.15929	−	1.15929i	−0.984629	−	0.174659i	$-0.944118\pi$
$313$	−20.5099	−	20.5099i	−1.15929	−	1.15929i	−0.174659	−	0.984629i	$-0.555882\pi$
$314$	11.5927	+	6.69304i	0.654213	+	0.377710i
$315$		0			0
$316$	2.22694	+	3.85718i	0.125275	+	0.216983i
$317$	−23.9045	+	23.9045i	−1.34261	+	1.34261i	−0.449162	+	0.893450i	$0.648277\pi$
$317$	−23.9045	+	23.9045i	−1.34261	+	1.34261i	−0.893450	+	0.449162i	$0.851723\pi$
$318$	7.34634	+	3.49747i	0.411962	+	0.196128i
$319$	−8.25787	−	14.3030i	−0.462352	−	0.800817i
$320$		0			0
$321$	2.69575	−	0.956821i	0.150462	−	0.0534045i
$322$	0.347251	+	1.29596i	0.0193516	+	0.0722210i
$323$	40.1124	−	10.7481i	2.23191	−	0.598040i
$324$	−5.51831	+	6.16466i	−0.306573	+	0.342481i
$325$		0			0
$326$			20.9422i			1.15988i
$327$	−1.10308	+	0.0876212i	−0.0610005	+	0.00484546i
$328$	−6.20041	+	1.66140i	−0.342361	+	0.0917352i
$329$	−0.0148633	−	0.0257440i	−0.000819441	−	0.00141931i
$330$		0			0
$331$	12.0767	−	6.97251i	0.663798	−	0.383244i	−0.129925	−	0.991524i	$-0.541474\pi$
$331$	12.0767	−	6.97251i	0.663798	−	0.383244i	0.793722	+	0.608280i	$0.208140\pi$
$332$	−2.56737	−	0.687925i	−0.140903	−	0.0377548i
$333$	11.6351	−	5.20054i	0.637597	−	0.284988i
$334$	13.2009	−	7.62155i	0.722322	−	0.417033i
$335$		0			0
$336$	0.745531	+	0.635807i	0.0406720	+	0.0346861i
$337$	2.58183	−	2.58183i	0.140641	−	0.140641i	−0.633281	−	0.773922i	$-0.718292\pi$
$337$	2.58183	−	2.58183i	0.140641	−	0.140641i	0.773922	+	0.633281i	$0.218292\pi$
$338$	−13.2693	+	17.8126i	−0.721754	+	0.968877i
$339$	13.4800	+	2.48824i	0.732135	+	0.135143i
$340$		0			0
$341$	−24.5344	−	14.1649i	−1.32861	−	0.767074i
$342$	−23.9141	+	33.0157i	−1.29313	+	1.78529i
$343$	−1.12047	+	1.12047i	−0.0604997	+	0.0604997i
$344$	8.09329	−	4.67266i	0.436361	−	0.251933i
$345$		0			0
$346$			15.0319i			0.808119i
$347$	4.13034	−	15.4146i	0.221728	−	0.827500i	−0.761961	−	0.647623i	$-0.775763\pi$
$347$	4.13034	−	15.4146i	0.221728	−	0.827500i	0.983689	−	0.179877i	$-0.0575701\pi$
$348$	0.506785	+	6.38001i	0.0271665	+	0.342004i
$349$	2.98342	−	5.16743i	0.159699	−	0.276606i	−0.775061	−	0.631886i	$-0.782281\pi$
$349$	2.98342	−	5.16743i	0.159699	−	0.276606i	0.934760	+	0.355280i	$0.115614\pi$
$350$		0			0
$351$	−3.96459	+	18.3107i	−0.211614	+	0.977353i
$352$	−14.0593	+	14.0593i	−0.749363	+	0.749363i
$353$	12.0317	−	3.22389i	0.640383	−	0.171590i	0.0760061	−	0.997107i	$-0.475783\pi$
$353$	12.0317	−	3.22389i	0.640383	−	0.171590i	0.564377	+	0.825517i	$0.309116\pi$
$354$	−1.61120	−	1.37407i	−0.0856342	−	0.0730309i
$355$		0			0
$356$	−2.97190			−0.157510
$357$	0.925073	+	0.440412i	0.0489600	+	0.0233091i
$358$	32.8515	+	8.80254i	1.73626	+	0.465229i
$359$		−	29.8863i		−	1.57734i	−0.614816	−	0.788671i	$-0.710770\pi$
$359$		−	29.8863i		−	1.57734i	0.614816	−	0.788671i	$-0.289230\pi$
$360$		0			0
$361$	−22.1271	+	38.3252i	−1.16458	+	2.01712i
$362$	−3.29490	−	12.2967i	−0.173176	−	0.646302i
$363$	5.77804	+	8.39402i	0.303268	+	0.440572i
$364$	−0.368803	−	0.0706327i	−0.0193305	−	0.00370216i
$365$		0			0
$366$	−7.84107	+	9.19424i	−0.409860	+	0.480591i
$367$	3.47695	+	12.9762i	0.181496	+	0.677351i	0.995354	+	0.0962869i	$0.0306966\pi$
$367$	3.47695	+	12.9762i	0.181496	+	0.677351i	−0.813858	+	0.581064i	$0.802637\pi$
$368$	−33.4326	−	8.95823i	−1.74279	−	0.466980i
$369$	3.72337	−	9.74201i	0.193831	−	0.507149i
$370$		0			0
$371$	0.155736	+	0.269742i	0.00808539	+	0.0140043i
$372$	6.22474	+	9.04296i	0.322738	+	0.468855i
$373$	5.16696	−	19.2834i	0.267535	−	0.998455i	−0.693145	−	0.720798i	$-0.743776\pi$
$373$	5.16696	−	19.2834i	0.267535	−	0.998455i	0.960680	−	0.277657i	$-0.0895578\pi$
$374$	−18.3287	+	31.7462i	−0.947753	+	1.64156i
$375$		0			0
$376$	0.484510			0.0249867
$377$	8.13714	+	11.9923i	0.419084	+	0.617635i
$378$	−0.977486	+	0.236929i	−0.0502764	+	0.0121863i
$379$	−16.7541	+	29.0190i	−0.860601	+	1.49061i	0.0107483	+	0.999942i	$0.496579\pi$
$379$	−16.7541	+	29.0190i	−0.860601	+	1.49061i	−0.871350	+	0.490663i	$0.836755\pi$
$380$		0			0
$381$	−7.37965	−	20.7914i	−0.378071	−	1.06518i
$382$	27.7305	+	27.7305i	1.41882	+	1.41882i
$383$	0.699279	−	2.60975i	0.0357315	−	0.133352i	−0.945756	−	0.324878i	$-0.894677\pi$
$383$	0.699279	−	2.60975i	0.0357315	−	0.133352i	0.981488	+	0.191526i	$0.0613436\pi$
$384$	−20.5917	+	7.30876i	−1.05082	+	0.372973i
$385$		0			0
$386$	32.4270	−	18.7218i	1.65049	−	0.952912i
$387$	−1.56515	+	15.1026i	−0.0795612	+	0.767710i
$388$	−0.0355516	−	0.132680i	−0.00180486	−	0.00673582i
$389$	−38.6182			−1.95802			−0.979011	−	0.203807i	$-0.934668\pi$
$389$	−38.6182			−1.95802			−0.979011	+	0.203807i	$0.934668\pi$
$390$		0			0
$391$	−36.1920			−1.83031
$392$	−3.33918	−	12.4620i	−0.168654	−	0.629426i
$393$	1.77704	+	22.3715i	0.0896397	+	1.12849i
$394$	−12.8645	+	7.42732i	−0.648104	+	0.374183i
$395$		0			0
$396$	−1.78901	−	11.1900i	−0.0899010	−	0.562320i
$397$	2.93908	−	10.9688i	0.147508	−	0.550509i	−0.852122	−	0.523342i	$-0.824685\pi$
$397$	2.93908	−	10.9688i	0.147508	−	0.550509i	0.999631	−	0.0271666i	$-0.00864845\pi$
$398$	24.4713	+	24.4713i	1.22663	+	1.22663i
$399$	−1.47070	+	0.522007i	−0.0736273	+	0.0261331i
$400$		0			0
$401$	15.5856	−	26.9950i	0.778307	−	1.34807i	−0.154611	−	0.987975i	$-0.549412\pi$
$401$	15.5856	−	26.9950i	0.778307	−	1.34807i	0.932917	−	0.360091i	$-0.117254\pi$
$402$	4.95832	+	7.20318i	0.247299	+	0.359262i
$403$	22.3732	+	10.8358i	1.11449	+	0.539771i
$404$	−11.1569			−0.555076
$405$		0			0
$406$	−0.389012	+	0.673788i	−0.0193063	+	0.0334395i
$407$	−4.51779	+	16.8606i	−0.223938	+	0.835749i
$408$	−13.7553	+	9.46851i	−0.680990	+	0.468761i
$409$	−5.22725	−	9.05386i	−0.258471	−	0.447685i	0.707362	−	0.706852i	$-0.249885\pi$
$409$	−5.22725	−	9.05386i	−0.258471	−	0.447685i	−0.965832	+	0.259167i	$0.916552\pi$
$410$		0			0
$411$	21.2229	+	3.91748i	1.04685	+	0.193235i
$412$	0.663461	+	0.177774i	0.0326864	+	0.00875828i
$413$	−0.0209805	−	0.0783003i	−0.00103238	−	0.00385290i
$414$	27.5787	−	22.3993i	1.35542	−	1.10086i
$415$		0			0
$416$	11.4099	−	13.1989i	0.559414	−	0.647130i
$417$	5.46700	−	3.76322i	0.267720	−	0.184286i
$418$	−14.4514	−	53.9335i	−0.706843	−	2.63797i
$419$	10.9200	−	18.9139i	0.533476	−	0.924007i	−0.465760	−	0.884911i	$-0.654219\pi$
$419$	10.9200	−	18.9139i	0.533476	−	0.924007i	0.999235	−	0.0390956i	$-0.0124477\pi$
$420$		0			0
$421$		−	11.3030i		−	0.550876i	−0.961319	−	0.275438i	$-0.911177\pi$
$421$		−	11.3030i		−	0.550876i	0.961319	−	0.275438i	$-0.0888229\pi$
$422$	−12.0401	−	3.22612i	−0.586101	−	0.157045i
$423$	−0.461774	+	0.637524i	−0.0224522	+	0.0309975i
$424$	−5.07663			−0.246543
$425$		0			0
$426$	−16.3374	+	19.1568i	−0.791548	+	0.928149i
$427$	−0.446818	+	0.119724i	−0.0216230	+	0.00579387i
$428$	1.07357	−	1.07357i	0.0518927	−	0.0518927i
$429$	−16.0439	−	20.0262i	−0.774605	−	0.966875i
$430$		0			0
$431$	1.35987	−	2.35537i	0.0655028	−	0.113454i	−0.831414	−	0.555653i	$-0.812468\pi$
$431$	1.35987	−	2.35537i	0.0655028	−	0.113454i	0.896917	+	0.442199i	$0.145802\pi$
$432$	7.31505	−	24.8944i	0.351945	−	1.19773i
$433$	3.66753	−	13.6874i	0.176250	−	0.657775i	−0.820085	−	0.572242i	$-0.806074\pi$
$433$	3.66753	−	13.6874i	0.176250	−	0.657775i	0.996335	−	0.0855335i	$-0.0272595\pi$
$434$			1.33456i			0.0640611i
$435$		0			0
$436$	−0.508630	+	0.293658i	−0.0243590	+	0.0140637i
$437$	38.9809	−	38.9809i	1.86471	−	1.86471i
$438$	−11.3692	−	5.41268i	−0.543241	−	0.258628i
$439$	8.10140	+	4.67735i	0.386659	+	0.223237i	0.680711	−	0.732552i	$-0.261671\pi$
$439$	8.10140	+	4.67735i	0.386659	+	0.223237i	−0.294053	+	0.955789i	$0.595004\pi$
$440$		0			0
$441$	19.5801	+	7.48347i	0.932388	+	0.356356i
$442$	14.0210	−	28.9497i	0.666910	−	1.37700i
$443$	5.74199	−	5.74199i	0.272810	−	0.272810i	−0.557420	−	0.830230i	$-0.688209\pi$
$443$	5.74199	−	5.74199i	0.272810	−	0.272810i	0.830230	+	0.557420i	$0.188209\pi$
$444$	4.38928	−	5.14676i	0.208306	−	0.244254i
$445$		0			0
$446$	17.9670	−	10.3733i	0.850763	−	0.491188i
$447$	16.9738	−	11.6840i	0.802835	−	0.552633i
$448$	−0.188132	−	0.0504097i	−0.00888838	−	0.00238163i
$449$	23.4891	−	13.5614i	1.10852	−	0.640004i	0.170074	−	0.985431i	$-0.445599\pi$
$449$	23.4891	−	13.5614i	1.10852	−	0.640004i	0.938446	+	0.345427i	$0.112266\pi$
$450$		0			0
$451$	7.14224	+	12.3707i	0.336315	+	0.582515i
$452$	7.02763	−	1.88305i	0.330552	−	0.0885711i
$453$	−1.52256	−	19.1678i	−0.0715359	−	0.900579i
$454$		−	23.6941i		−	1.11202i
$455$		0			0
$456$	4.61715	−	25.0134i	0.216218	−	1.17136i
$457$	−12.9168	+	3.46105i	−0.604224	+	0.161901i	−0.547946	−	0.836514i	$-0.684590\pi$
$457$	−12.9168	+	3.46105i	−0.604224	+	0.161901i	−0.0562781	+	0.998415i	$0.517923\pi$
$458$	−3.76726	−	14.0596i	−0.176032	−	0.656962i
$459$	0.651065	−	27.1236i	0.0303891	−	1.26602i
$460$		0			0
$461$	−17.1508	−	29.7061i	−0.798792	−	1.38355i	−0.920403	−	0.390971i	$-0.872139\pi$
$461$	−17.1508	−	29.7061i	−0.798792	−	1.38355i	0.121611	−	0.992578i	$-0.461194\pi$
$462$	0.592159	−	1.24381i	0.0275498	−	0.0578675i
$463$	−19.4344	+	19.4344i	−0.903191	+	0.903191i	−0.995711	−	0.0925195i	$-0.970508\pi$
$463$	−19.4344	+	19.4344i	−0.903191	+	0.903191i	0.0925195	+	0.995711i	$0.470508\pi$
$464$	−10.0356	−	17.3821i	−0.465889	−	0.806943i
$465$		0			0
$466$	18.0226	+	10.4054i	0.834883	+	0.482020i
$467$	19.6345	+	19.6345i	0.908575	+	0.908575i	0.996157	−	0.0875827i	$-0.0279142\pi$
$467$	19.6345	+	19.6345i	0.908575	+	0.908575i	−0.0875827	+	0.996157i	$0.527914\pi$
$468$	2.27767	+	9.67943i	0.105285	+	0.447432i
$469$			0.334760i			0.0154578i
$470$		0			0
$471$	8.80540	−	10.3250i	0.405731	−	0.475750i
$472$	1.27621	+	0.341958i	0.0587421	+	0.0157399i
$473$	−14.7051	−	14.7051i	−0.676140	−	0.676140i
$474$	13.5119	−	4.79586i	0.620620	−	0.220281i
$475$		0			0
$476$	0.543796			0.0249248
$477$	4.83840	−	6.67989i	0.221535	−	0.305851i
$478$	−19.0670	+	5.10900i	−0.872107	+	0.233680i
$479$	−1.49161	−	0.861181i	−0.0681534	−	0.0393484i	0.465536	−	0.885029i	$-0.345862\pi$
$479$	−1.49161	−	0.861181i	−0.0681534	−	0.0393484i	−0.533689	+	0.845681i	$0.679195\pi$
$480$		0			0
$481$	2.88111	−	15.0435i	0.131367	−	0.685924i
$482$	−16.8711	−	16.8711i	−0.768456	−	0.768456i
$483$	1.35582	−	0.107697i	0.0616921	−	0.00490040i
$484$	4.68406	+	2.70434i	0.212912	+	0.122925i
$485$		0			0
$486$	16.2907	+	21.0714i	0.738961	+	0.955819i
$487$	5.38812	−	20.1087i	0.244159	−	0.911213i	−0.729645	−	0.683826i	$-0.760315\pi$
$487$	5.38812	−	20.1087i	0.244159	−	0.911213i	0.973804	−	0.227388i	$-0.0730184\pi$
$488$	1.95137	−	7.28262i	0.0883344	−	0.329669i
$489$	20.8770	+	3.85362i	0.944089	+	0.174267i
$490$		0			0
$491$	19.5711	+	11.2994i	0.883233	+	0.509935i	0.871723	−	0.489999i	$-0.163003\pi$
$491$	19.5711	+	11.2994i	0.883233	+	0.509935i	0.0115102	+	0.999934i	$0.496336\pi$
$492$	−0.438319	−	5.51808i	−0.0197609	−	0.248774i
$493$	−14.8403	−	14.8403i	−0.668374	−	0.668374i
$494$	16.0791	+	46.2819i	0.723434	+	2.08232i
$495$		0			0
$496$	−29.8159	−	17.2142i	−1.33878	−	0.772942i
$497$	−0.930972	+	0.249453i	−0.0417598	+	0.0111895i
$498$	−3.67797	+	7.72547i	−0.164814	+	0.346186i
$499$	−35.8828			−1.60634			−0.803168	−	0.595753i	$-0.796854\pi$
$499$	−35.8828			−1.60634			−0.803168	+	0.595753i	$0.796854\pi$
$500$		0			0
$501$	−5.16868	−	14.5623i	−0.230920	−	0.650594i
$502$	20.8208	+	20.8208i	0.929276	+	0.929276i
$503$	31.9352	+	8.55700i	1.42392	+	0.381538i	0.886872	−	0.462015i	$-0.152873\pi$
$503$	31.9352	+	8.55700i	1.42392	+	0.381538i	0.537047	+	0.843553i	$0.319540\pi$
$504$	0.487125	−	0.395640i	0.0216983	−	0.0176232i
$505$		0			0
$506$			48.6623i			2.16330i
$507$	15.3154	+	16.5057i	0.680181	+	0.733044i
$508$	−8.28006	−	8.28006i	−0.367368	−	0.367368i
$509$	−5.25012	−	3.03116i	−0.232707	−	0.134354i	0.379113	−	0.925350i	$-0.376229\pi$
$509$	−5.25012	−	3.03116i	−0.232707	−	0.134354i	−0.611820	+	0.790997i	$0.709562\pi$
$510$		0			0
$511$	−0.241016	−	0.417452i	−0.0106619	−	0.0184670i
$512$	−4.04633	+	4.04633i	−0.178824	+	0.178824i
$513$	28.5124	+	29.9149i	1.25886	+	1.32078i
$514$	−0.357631	−	0.619435i	−0.0157744	−	0.0273221i
$515$		0			0
$516$	2.69561	+	7.59462i	0.118668	+	0.334334i
$517$	−0.279053	−	1.04144i	−0.0122727	−	0.0458025i
$518$	0.794270	−	0.212824i	0.0348982	−	0.00935095i
$519$	14.9851	+	2.76605i	0.657772	+	0.121416i
$520$		0			0
$521$			23.5394i			1.03128i	0.856805	+	0.515640i	$0.172446\pi$
$521$			23.5394i			1.03128i	−0.856805	+	0.515640i	$0.827554\pi$
$522$	20.4931	+	2.12379i	0.896960	+	0.0929560i
$523$	30.6087	−	8.20158i	1.33843	−	0.358630i	0.482575	−	0.875854i	$-0.339701\pi$
$523$	30.6087	−	8.20158i	1.33843	−	0.358630i	0.855850	+	0.517225i	$0.173035\pi$
$524$	5.95565	+	10.3155i	0.260174	+	0.450634i
$525$		0			0
$526$	−19.3620	+	11.1787i	−0.844224	+	0.487413i
$527$	−34.7735	−	9.31753i	−1.51476	−	0.405878i
$528$	20.1503	+	29.2733i	0.876931	+	1.27396i
$529$	−21.6892	+	12.5223i	−0.943010	+	0.544447i
$530$		0			0
$531$	−1.66627	+	1.35334i	−0.0723100	+	0.0587297i
$532$	−0.585699	+	0.585699i	−0.0253933	+	0.0253933i
$533$	−7.03782	−	10.3722i	−0.304842	−	0.449268i
$534$	−1.73660	+	9.40804i	−0.0751502	+	0.407126i
$535$		0			0
$536$	−4.72521	−	2.72810i	−0.204098	−	0.117836i
$537$	14.8202	−	31.1295i	0.639540	−	1.34334i
$538$	−0.975256	+	0.975256i	−0.0420463	+	0.0420463i
$539$	−24.8635	+	14.3550i	−1.07095	+	0.618312i
$540$		0			0
$541$			26.7974i			1.15211i	0.817411	+	0.576055i	$0.195409\pi$
$541$			26.7974i			1.15211i	−0.817411	+	0.576055i	$0.804591\pi$
$542$	−4.70993	+	17.5777i	−0.202309	+	0.755027i
$543$	−12.8647	+	1.02189i	−0.552079	+	0.0438534i
$544$	−12.6331	+	21.8811i	−0.541638	+	0.938145i
$545$		0			0
$546$	−0.439107	+	1.12624i	−0.0187920	+	0.0481984i
$547$	−6.51421	+	6.51421i	−0.278528	+	0.278528i	−0.832521	−	0.553993i	$-0.813103\pi$
$547$	−6.51421	+	6.51421i	−0.278528	+	0.278528i	0.553993	+	0.832521i	$0.313103\pi$
$548$	11.0643	−	2.96467i	0.472643	−	0.126644i
$549$	7.72276	+	9.50851i	0.329599	+	0.405813i
$550$		0			0
$551$	31.9677			1.36187
$552$	−9.52901	+	20.0154i	−0.405581	+	0.851912i
$553$	0.530163	+	0.142057i	0.0225448	+	0.00604087i
$554$		−	48.7662i		−	2.07188i
$555$		0			0
$556$	1.76133	−	3.05072i	0.0746971	−	0.129379i
$557$	6.08328	+	22.7031i	0.257757	+	0.961962i	0.966536	+	0.256531i	$0.0825797\pi$
$557$	6.08328	+	22.7031i	0.257757	+	0.961962i	−0.708779	+	0.705431i	$0.750754\pi$
$558$	32.2644	−	14.4213i	1.36586	−	0.610501i
$559$	13.8052	+	11.9339i	0.583896	+	0.504752i
$560$		0			0
$561$	28.2746	+	24.1133i	1.19376	+	1.01806i
$562$	5.96419	+	22.2587i	0.251584	+	0.938926i
$563$	−35.8569	−	9.60782i	−1.51119	−	0.404921i	−0.594358	−	0.804201i	$-0.702594\pi$
$563$	−35.8569	−	9.60782i	−1.51119	−	0.404921i	−0.916829	+	0.399279i	$0.869260\pi$
$564$	−0.0758413	+	0.410870i	−0.00319350	+	0.0173007i
$565$		0			0
$566$	−0.973289	−	1.68579i	−0.0409104	−	0.0708589i
$567$	0.0563221	+	1.01804i	0.00236531	+	0.0427537i
$568$	4.06580	−	15.1738i	0.170597	−	0.636678i
$569$	−6.61515	+	11.4578i	−0.277322	+	0.480335i	−0.970718	−	0.240221i	$-0.922780\pi$
$569$	−6.61515	+	11.4578i	−0.277322	+	0.480335i	0.693397	+	0.720556i	$0.256113\pi$
$570$		0			0
$571$	16.3611			0.684690			0.342345	−	0.939574i	$-0.388779\pi$
$571$	16.3611			0.684690			0.342345	+	0.939574i	$0.388779\pi$
$572$	−12.2576	−	5.93661i	−0.512515	−	0.248222i
$573$	32.7469	−	22.5414i	1.36802	−	0.941681i
$574$	0.336457	−	0.582760i	0.0140434	−	0.0243240i
$575$		0			0
$576$	0.814243	+	5.09299i	0.0339268	+	0.212208i
$577$	1.55067	+	1.55067i	0.0645553	+	0.0645553i	0.738647	−	0.674092i	$-0.235465\pi$
$577$	1.55067	+	1.55067i	0.0645553	+	0.0645553i	−0.674092	+	0.738647i	$0.735465\pi$
$578$	−4.53869	+	16.9386i	−0.188785	+	0.704554i
$579$	−12.6965	−	35.7711i	−0.527648	−	1.48660i
$580$		0			0
$581$	−0.283663	+	0.163773i	−0.0117683	+	0.00679444i
$582$	−0.440796	+	0.0350138i	−0.0182716	+	0.00145137i
$583$	2.92388	+	10.9121i	0.121095	+	0.451931i
$584$	7.85658			0.325107
$585$		0			0
$586$	−12.8967			−0.532758
$587$	−5.23017	−	19.5193i	−0.215872	−	0.805646i	−0.985858	−	0.167585i	$-0.946403\pi$
$587$	−5.23017	−	19.5193i	−0.215872	−	0.805646i	0.769986	−	0.638061i	$-0.220263\pi$
$588$	11.0906	−	0.880963i	0.457369	−	0.0363303i
$589$	47.4885	−	27.4175i	1.95673	−	1.12972i
$590$		0			0
$591$	5.03696	+	14.1912i	0.207193	+	0.583746i
$592$	−5.49034	+	20.4902i	−0.225651	+	0.842143i
$593$	3.08282	+	3.08282i	0.126596	+	0.126596i	0.767566	−	0.640970i	$-0.221468\pi$
$593$	3.08282	+	3.08282i	0.126596	+	0.126596i	−0.640970	+	0.767566i	$0.721468\pi$
$594$	−36.4693	−	0.875395i	−1.49635	−	0.0359179i
$595$		0			0
$596$	5.46855	−	9.47180i	0.224000	−	0.387980i
$597$	28.8981	−	19.8921i	1.18272	−	0.814128i
$598$	−3.09615	−	42.5882i	−0.126611	−	1.74156i
$599$	−17.9813			−0.734698			−0.367349	−	0.930083i	$-0.619734\pi$
$599$	−17.9813			−0.734698			−0.367349	+	0.930083i	$0.619734\pi$
$600$		0			0
$601$	−4.18909	+	7.25572i	−0.170877	+	0.295967i	−0.938727	−	0.344663i	$-0.887993\pi$
$601$	−4.18909	+	7.25572i	−0.170877	+	0.295967i	0.767850	+	0.640630i	$0.221327\pi$
$602$	−0.253555	+	0.946282i	−0.0103341	+	0.0385676i
$603$	8.09314	−	3.61741i	0.329578	−	0.147312i
$604$	−5.10277	−	8.83825i	−0.207629	−	0.359623i
$605$		0			0
$606$	−6.51944	+	35.3190i	−0.264834	+	1.43474i
$607$	−17.1283	−	4.58950i	−0.695214	−	0.186282i	−0.106128	−	0.994352i	$-0.533845\pi$
$607$	−17.1283	−	4.58950i	−0.695214	−	0.186282i	−0.589086	+	0.808070i	$0.700512\pi$
$608$	−9.96067	−	37.1737i	−0.403958	−	1.50759i
$609$	0.600107	+	0.511786i	0.0243176	+	0.0207386i
$610$		0			0
$611$	0.310483	+	0.893690i	0.0125608	+	0.0361548i
$612$	−5.87625	−	13.1468i	−0.237533	−	0.531428i
$613$	9.88511	+	36.8917i	0.399256	+	1.49004i	0.814409	+	0.580291i	$0.197061\pi$
$613$	9.88511	+	36.8917i	0.399256	+	1.49004i	−0.415153	+	0.909752i	$0.636272\pi$
$614$	−6.38272	+	11.0552i	−0.257585	+	0.446151i
$615$		0			0
$616$			0.859527i			0.0346313i
$617$	27.1576	+	7.27686i	1.09332	+	0.292955i	0.760043	−	0.649872i	$-0.225178\pi$
$617$	27.1576	+	7.27686i	1.09332	+	0.292955i	0.333281	+	0.942828i	$0.391844\pi$
$618$	0.950461	−	1.99642i	0.0382331	−	0.0803076i
$619$	34.9871			1.40625			0.703125	−	0.711066i	$-0.251787\pi$
$619$	34.9871			1.40625			0.703125	+	0.711066i	$0.251787\pi$
$620$		0			0
$621$	−17.2547	−	31.6145i	−0.692406	−	1.26865i
$622$	−3.92142	+	1.05074i	−0.157235	+	0.0421309i
$623$	−0.258967	+	0.258967i	−0.0103753	+	0.0103753i
$624$	−19.4977	−	24.3373i	−0.780531	−	0.974271i
$625$		0			0
$626$	−24.7792	+	42.9189i	−0.990378	+	1.71538i
$627$	−56.4248	+	4.48200i	−2.25339	+	0.178994i
$628$	1.86410	−	6.95692i	0.0743857	−	0.277611i
$629$			22.1814i			0.884431i
$630$		0			0
$631$	−10.8292	+	6.25222i	−0.431102	+	0.248897i	−0.699816	−	0.714323i	$-0.746735\pi$
$631$	−10.8292	+	6.25222i	−0.431102	+	0.248897i	0.268714	+	0.963220i	$0.413401\pi$
$632$	−6.32569	+	6.32569i	−0.251623	+	0.251623i
$633$	−5.43160	+	11.4089i	−0.215887	+	0.453464i
$634$	50.0225	+	28.8805i	1.98665	+	1.14699i
$635$		0			0
$636$	0.794654	−	4.30503i	0.0315101	−	0.170706i
$637$	20.8467	−	14.1451i	0.825974	−	0.560449i
$638$	−19.9537	+	19.9537i	−0.789973	+	0.789973i
$639$	16.0908	+	19.8116i	0.636544	+	0.783733i
$640$		0			0
$641$	3.54806	−	2.04848i	0.140140	−	0.0809099i	−0.428291	−	0.903641i	$-0.640884\pi$
$641$	3.54806	−	2.04848i	0.140140	−	0.0809099i	0.568431	+	0.822731i	$0.307551\pi$
$642$	−2.77122	−	4.02588i	−0.109371	−	0.158889i
$643$	40.3600	+	10.8144i	1.59164	+	0.426479i	0.942505	−	0.334192i	$-0.108464\pi$
$643$	40.3600	+	10.8144i	1.59164	+	0.426479i	0.649137	+	0.760672i	$0.275130\pi$
$644$	0.625170	−	0.360942i	0.0246351	−	0.0142231i
$645$		0			0
$646$	−35.4768	−	61.4477i	−1.39582	−	2.41763i
$647$	−6.30036	+	1.68818i	−0.247693	+	0.0663691i	−0.380529	−	0.924769i	$-0.624258\pi$
$647$	−6.30036	+	1.68818i	−0.247693	+	0.0663691i	0.132836	+	0.991138i	$0.457591\pi$
$648$	−14.8289	−	7.50144i	−0.582532	−	0.294685i
$649$		−	2.94012i		−	0.115410i
$650$		0			0
$651$	1.33041	+	0.245576i	0.0521428	+	0.00962489i
$652$	10.8839	−	2.91634i	0.426247	−	0.114213i
$653$	11.9894	+	44.7451i	0.469182	+	1.75101i	0.642637	+	0.766171i	$0.277840\pi$
$653$	11.9894	+	44.7451i	0.469182	+	1.75101i	−0.173454	+	0.984842i	$0.555493\pi$
$654$	0.632409	+	1.78175i	0.0247292	+	0.0696720i
$655$		0			0
$656$	8.67976	+	15.0338i	0.338888	+	0.586971i
$657$	−7.48790	+	10.3378i	−0.292131	+	0.403315i
$658$	−0.0359145	+	0.0359145i	−0.00140009	+	0.00140009i
$659$	12.0799	+	20.9230i	0.470566	+	0.815045i	0.999433	−	0.0336601i	$-0.0107164\pi$
$659$	12.0799	+	20.9230i	0.470566	+	0.815045i	−0.528867	+	0.848705i	$0.677383\pi$
$660$		0			0
$661$	35.3712	+	20.4215i	1.37578	+	0.794306i	0.991648	−	0.128973i	$-0.0411680\pi$
$661$	35.3712	+	20.4215i	1.37578	+	0.794306i	0.384130	+	0.923279i	$0.374501\pi$
$662$	−16.8478	−	16.8478i	−0.654809	−	0.654809i
$663$	−26.2796	−	19.3044i	−1.02061	−	0.749722i
$664$		−	5.33862i		−	0.207178i
$665$		0			0
$666$	−13.7281	−	16.9025i	−0.531953	−	0.654958i
$667$	−26.9112	−	7.21084i	−1.04201	−	0.279205i
$668$	−5.79933	−	5.79933i	−0.224383	−	0.224383i
$669$	−7.03481	−	19.8199i	−0.271981	−	0.766281i
$670$		0			0
$671$	−16.7777			−0.647694
$672$	0.408147	−	0.857300i	0.0157446	−	0.0330711i
$673$	−11.9542	+	3.20311i	−0.460799	+	0.123471i	−0.481748	−	0.876310i	$-0.659998\pi$
$673$	−11.9542	+	3.20311i	−0.460799	+	0.123471i	0.0209488	+	0.999781i	$0.493331\pi$
$674$	−5.40272	−	3.11926i	−0.208105	−	0.120150i
$675$		0			0
$676$	11.1053	+	4.41570i	0.427126	+	0.169834i
$677$	17.7462	+	17.7462i	0.682043	+	0.682043i	0.960460	−	0.278418i	$-0.0898099\pi$
$677$	17.7462	+	17.7462i	0.682043	+	0.682043i	−0.278418	+	0.960460i	$0.589810\pi$
$678$	−1.85457	−	23.3475i	−0.0712242	−	0.896655i
$679$	−0.0146595	−	0.00846367i	−0.000562580	−	0.000324806i
$680$		0			0
$681$	−23.6203	−	4.36001i	−0.905132	−	0.167076i
$682$	−12.5280	+	46.7550i	−0.479721	+	1.79034i
$683$	−5.71276	+	21.3203i	−0.218593	+	0.815798i	0.766278	+	0.642509i	$0.222106\pi$
$683$	−5.71276	+	21.3203i	−0.218593	+	0.815798i	−0.984871	+	0.173290i	$0.944560\pi$
$684$	20.4889	+	7.83079i	0.783413	+	0.299418i
$685$		0			0
$686$	2.34469	+	1.35371i	0.0895208	+	0.0516848i
$687$	−14.7090	+	1.16839i	−0.561185	+	0.0445767i
$688$	−17.8706	−	17.8706i	−0.681312	−	0.681312i
$689$	−3.25319	−	9.36396i	−0.123937	−	0.356738i
$690$		0			0
$691$	−7.86173	−	4.53897i	−0.299074	−	0.172671i	0.342953	−	0.939353i	$-0.388573\pi$
$691$	−7.86173	−	4.53897i	−0.299074	−	0.172671i	−0.642027	+	0.766682i	$0.721906\pi$
$692$	7.81226	−	2.09329i	0.296978	−	0.0795749i
$693$	−1.13098	−	0.819193i	−0.0429622	−	0.0311186i
$694$	−27.2665			−1.03502
$695$		0			0
$696$	−12.1145	+	4.29988i	−0.459199	+	0.162987i
$697$	12.8354	+	12.8354i	0.486176	+	0.486176i
$698$	−9.84754	−	2.63864i	−0.372735	−	0.0998740i
$699$	13.6894	−	16.0518i	0.517779	−	0.607135i
$700$		0			0
$701$			31.3445i			1.18386i	0.805988	+	0.591932i	$0.201635\pi$
$701$			31.3445i			1.18386i	−0.805988	+	0.591932i	$0.798365\pi$
$702$	31.9728	−	1.55424i	1.20674	−	0.0586611i
$703$	−23.8907	−	23.8907i	−0.901053	−	0.901053i
$704$	−6.11777	−	3.53210i	−0.230572	−	0.133121i
$705$		0			0
$706$	−10.6413	−	18.4312i	−0.400489	−	0.693667i
$707$	−0.972198	+	0.972198i	−0.0365633	+	0.0365633i
$708$	−0.489751	+	1.02871i	−0.0184060	+	0.0386612i
$709$	16.2682	+	28.1774i	0.610967	+	1.05823i	0.991078	+	0.133285i	$0.0425524\pi$
$709$	16.2682	+	28.1774i	0.610967	+	1.05823i	−0.380111	+	0.924941i	$0.624114\pi$
$710$		0			0
$711$	−2.29457	−	14.3523i	−0.0860532	−	0.538252i
$712$	−1.54495	−	5.76582i	−0.0578993	−	0.216083i
$713$	−46.1615	+	12.3689i	−1.72876	+	0.463220i
$714$	0.317763	−	1.72148i	0.0118920	−	0.0644247i
$715$		0			0
$716$		−	18.2992i		−	0.683873i
$717$	1.58452	+	19.9478i	0.0591749	+	0.744964i
$718$	−49.3238	+	13.2163i	−1.84075	+	0.493227i
$719$	14.5548	+	25.2096i	0.542802	+	0.940160i	0.998742	+	0.0501495i	$0.0159698\pi$
$719$	14.5548	+	25.2096i	0.542802	+	0.940160i	−0.455940	+	0.890010i	$0.650697\pi$
$720$		0			0
$721$	0.0733041	−	0.0423222i	0.00272999	−	0.00157616i
$722$	73.0360	+	19.5699i	2.71812	+	0.728318i
$723$	−19.9230	+	13.7140i	−0.740944	+	0.510030i
$724$	−5.93194	+	3.42480i	−0.220459	+	0.127282i
$725$		0			0
$726$	11.2982	−	13.2479i	0.419314	−	0.491677i
$727$	−12.8617	+	12.8617i	−0.477014	+	0.477014i	−0.904175	−	0.427161i	$-0.859514\pi$
$727$	−12.8617	+	12.8617i	−0.477014	+	0.477014i	0.427161	+	0.904175i	$0.359514\pi$
$728$	−0.0546877	−	0.752239i	−0.00202686	−	0.0278798i
$729$	24.0035	−	12.3626i	0.889018	−	0.457873i
$730$		0			0
$731$	−22.8861	−	13.2133i	−0.846475	−	0.488712i
$732$	5.87029	+	2.79475i	0.216972	+	0.103297i
$733$	9.86693	−	9.86693i	0.364443	−	0.364443i	−0.501003	−	0.865446i	$-0.667035\pi$
$733$	9.86693	−	9.86693i	0.364443	−	0.364443i	0.865446	+	0.501003i	$0.167035\pi$
$734$	19.8780	−	11.4766i	0.733711	−	0.423608i
$735$		0			0
$736$			33.5405i			1.23632i
$737$	−3.14249	+	11.7279i	−0.115755	+	0.432004i
$738$	−17.7245	−	1.83687i	−0.652450	−	0.0676162i
$739$	−12.6022	+	21.8276i	−0.463578	+	0.802941i	−0.999136	−	0.0415576i	$-0.986768\pi$
$739$	−12.6022	+	21.8276i	−0.463578	+	0.802941i	0.535558	+	0.844498i	$0.320101\pi$
$740$		0			0
$741$	49.0966	−	7.51259i	1.80361	−	0.275982i
$742$	0.376307	−	0.376307i	0.0138147	−	0.0138147i
$743$	−36.3190	+	9.73165i	−1.33242	+	0.357020i	−0.853615	−	0.520904i	$-0.825595\pi$
$743$	−36.3190	+	9.73165i	−1.33242	+	0.357020i	−0.478801	+	0.877924i	$0.658928\pi$
$744$	−14.3084	+	16.7777i	−0.524573	+	0.615100i
$745$		0			0
$746$	−34.1098			−1.24885
$747$	7.02462	+	5.08809i	0.257017	+	0.186164i
$748$	19.0513	+	5.10478i	0.696584	+	0.186649i
$749$		−	0.187098i		−	0.00683642i
$750$		0			0
$751$	14.1002	−	24.4223i	0.514524	−	0.891182i	−0.485334	−	0.874329i	$-0.661302\pi$
$751$	14.1002	−	24.4223i	0.514524	−	0.891182i	0.999858	−	0.0168530i	$-0.00536474\pi$
$752$	−0.339125	−	1.26563i	−0.0123666	−	0.0461529i
$753$	24.5872	−	16.9246i	0.896007	−	0.616768i
$754$	16.1934	−	18.7326i	0.589730	−	0.682200i
$755$		0			0
$756$	0.259257	+	0.475018i	0.00942907	+	0.0172762i
$757$	−7.80797	−	29.1397i	−0.283785	−	1.05910i	−0.949722	−	0.313093i	$-0.898635\pi$
$757$	−7.80797	−	29.1397i	−0.283785	−	1.05910i	0.665937	−	0.746008i	$-0.268032\pi$
$758$	55.3013	+	14.8179i	2.00863	+	0.538211i
$759$	48.5108	+	8.95446i	1.76083	+	0.325026i
$760$		0			0
$761$	−14.3226	−	24.8075i	−0.519195	−	0.899272i	−0.999751	−	0.0223082i	$-0.992898\pi$
$761$	−14.3226	−	24.8075i	−0.519195	−	0.899272i	0.480556	−	0.876964i	$-0.340435\pi$
$762$	−31.0503	+	21.3735i	−1.12483	+	0.774282i
$763$	−0.0187324	+	0.0699104i	−0.000678160	+	0.00253093i
$764$	10.5503	−	18.2736i	0.381695	−	0.661115i
$765$		0			0
$766$	−4.61630			−0.166794
$767$	0.187066	+	2.57312i	0.00675455	+	0.0929101i
$768$	17.7914	+	25.8464i	0.641992	+	0.932650i
$769$	−26.5529	+	45.9910i	−0.957522	+	1.65848i	−0.229035	+	0.973418i	$0.573557\pi$
$769$	−26.5529	+	45.9910i	−0.957522	+	1.65848i	−0.728488	+	0.685059i	$0.759776\pi$
$770$		0			0
$771$	−0.683314	+	0.242533i	−0.0246090	+	0.00873463i
$772$	−14.2456	−	14.2456i	−0.512711	−	0.512711i
$773$	9.14659	−	34.1355i	0.328980	−	1.22777i	−0.581270	−	0.813711i	$-0.697444\pi$
$773$	9.14659	−	34.1355i	0.328980	−	1.22777i	0.910250	−	0.414059i	$-0.135889\pi$
$774$	25.6172	−	4.09555i	0.920791	−	0.147212i
$775$		0			0
$776$	0.238933	−	0.137948i	0.00857720	−	0.00495205i
$777$	−0.0660057	−	0.830959i	−0.00236794	−	0.0298105i
$778$	17.0777	+	63.7347i	0.612264	+	2.28500i
$779$	−27.6489			−0.990626
$780$		0			0
$781$	−34.9573			−1.25087
$782$	16.0047	+	59.7305i	0.572329	+	2.13596i
$783$	5.88817	−	20.0385i	0.210426	−	0.716118i
$784$	−30.2159	+	17.4452i	−1.07914	+	0.623042i
$785$		0			0
$786$	36.1355	−	12.8258i	1.28891	−	0.457482i
$787$	−4.96521	+	18.5304i	−0.176991	+	0.660539i	0.819213	+	0.573489i	$0.194410\pi$
$787$	−4.96521	+	18.5304i	−0.176991	+	0.660539i	−0.996204	+	0.0870495i	$0.972256\pi$
$788$	5.65154	+	5.65154i	0.201328	+	0.201328i
$789$	7.58100	+	21.3587i	0.269891	+	0.760391i
$790$		0			0
$791$	0.448293	−	0.776465i	0.0159394	−	0.0276079i
$792$	20.7799	−	9.28803i	0.738382	−	0.330036i
$793$	14.6834	−	1.06748i	0.521424	−	0.0379075i
$794$	−19.4024			−0.688566
$795$		0			0
$796$	9.31025	−	16.1258i	0.329993	−	0.571565i
$797$	4.06620	−	15.1753i	0.144032	−	0.537535i	−0.855764	−	0.517366i	$-0.826913\pi$
$797$	4.06620	−	15.1753i	0.144032	−	0.537535i	0.999797	−	0.0201695i	$-0.00642060\pi$
$798$	1.51188	+	2.19638i	0.0535200	+	0.0777509i
$799$	−0.685047	−	1.18654i	−0.0242352	−	0.0419766i
$800$		0			0
$801$	9.05919	+	3.46239i	0.320091	+	0.122338i
$802$	−51.4442	−	13.7844i	−1.81656	−	0.486745i
$803$	−4.52499	−	16.8875i	−0.159683	−	0.595946i
$804$	3.05311	−	3.57999i	0.107675	−	0.126257i
$805$		0			0
$806$	7.98939	−	41.7160i	0.281414	−	1.46938i
$807$	0.792760	+	1.15168i	0.0279065	+	0.0405410i
$808$	−5.79994	−	21.6457i	−0.204041	−	0.761492i
$809$	9.50547	−	16.4640i	0.334195	−	0.578842i	−0.649135	−	0.760673i	$-0.724869\pi$
$809$	9.50547	−	16.4640i	0.334195	−	0.578842i	0.983330	+	0.181831i	$0.0582024\pi$
$810$		0			0
$811$		−	18.8816i		−	0.663023i	−0.943451	−	0.331512i	$-0.892441\pi$
$811$		−	18.8816i		−	0.663023i	0.943451	−	0.331512i	$-0.107559\pi$
$812$	0.404349	+	0.108345i	0.0141899	+	0.00380216i
$813$	16.6563	+	7.92978i	0.584161	+	0.278109i
$814$	29.8242			1.04534
$815$		0			0
$816$	34.3614	+	29.3042i	1.20289	+	1.02585i
$817$	38.8812	−	10.4182i	1.36028	−	0.364486i
$818$	−12.6307	+	12.6307i	−0.441623	+	0.441623i
$819$	1.04193	+	0.644981i	0.0364079	+	0.0225374i
$820$		0			0
$821$	0.931007	−	1.61255i	0.0324924	−	0.0562784i	−0.849322	−	0.527875i	$-0.822989\pi$
$821$	0.931007	−	1.61255i	0.0324924	−	0.0562784i	0.881814	+	0.471597i	$0.156322\pi$
$822$	−2.91983	−	36.7583i	−0.101841	−	1.28209i
$823$	−5.74475	+	21.4397i	−0.200249	+	0.747341i	0.790596	+	0.612338i	$0.209771\pi$
$823$	−5.74475	+	21.4397i	−0.200249	+	0.747341i	−0.990845	+	0.135003i	$0.956896\pi$
$824$			1.37961i			0.0480608i
$825$		0			0
$826$	−0.119947	+	0.0692515i	−0.00417349	+	0.00240957i
$827$	5.90430	−	5.90430i	0.205313	−	0.205313i	−0.596959	−	0.802272i	$-0.703625\pi$
$827$	5.90430	−	5.90430i	0.205313	−	0.205313i	0.802272	+	0.596959i	$0.203625\pi$
$828$	−15.4817	−	11.2138i	−0.538026	−	0.389705i
$829$	−27.7895	−	16.0443i	−0.965168	−	0.557240i	−0.0674084	−	0.997725i	$-0.521473\pi$
$829$	−27.7895	−	16.0443i	−0.965168	−	0.557240i	−0.897760	+	0.440485i	$0.854806\pi$
$830$		0			0
$831$	−48.6143	−	8.97358i	−1.68641	−	0.311290i
$832$	5.57887	+	2.70197i	0.193412	+	0.0936739i
$833$	−25.7974	+	25.7974i	−0.893829	+	0.893829i
$834$	−8.62834	−	7.35846i	−0.298775	−	0.254802i
$835$		0			0
$836$	−26.0175	+	15.0212i	−0.899833	+	0.519519i
$837$	−8.43932	−	34.8176i	−0.291706	−	1.20347i
$838$	−36.0442	−	9.65801i	−1.24513	−	0.333630i
$839$	−6.21211	+	3.58656i	−0.214466	+	0.123822i	−0.603385	−	0.797450i	$-0.706182\pi$
$839$	−6.21211	+	3.58656i	−0.214466	+	0.123822i	0.388919	+	0.921272i	$0.372848\pi$
$840$		0			0
$841$	6.42199	+	11.1232i	0.221448	+	0.383559i
$842$	−18.6543	+	4.99840i	−0.642869	+	0.172256i
$843$	23.2868	−	1.84975i	0.802042	−	0.0637088i
$844$			6.70663i			0.230852i
$845$		0			0
$846$	1.25636	+	0.480177i	0.0431946	+	0.0165088i
$847$	0.643817	−	0.172510i	0.0221218	−	0.00592752i
$848$	3.55330	+	13.2611i	0.122021	+	0.455388i
$849$	−1.85963	+	0.660053i	−0.0638225	+	0.0226530i
$850$		0			0
$851$	14.7228	+	25.5007i	0.504692	+	0.874152i
$852$	12.2311	+	5.82303i	0.419031	+	0.199494i
$853$	26.8806	−	26.8806i	0.920373	−	0.920373i	−0.0766825	−	0.997056i	$-0.524433\pi$
$853$	26.8806	−	26.8806i	0.920373	−	0.920373i	0.997056	+	0.0766825i	$0.0244328\pi$
$854$	0.395181	+	0.684474i	0.0135228	+	0.0234222i
$855$		0			0
$856$	2.64094	+	1.52474i	0.0902653	+	0.0521147i
$857$	−31.5042	−	31.5042i	−1.07616	−	1.07616i	−0.996850	−	0.0793118i	$-0.974728\pi$
$857$	−31.5042	−	31.5042i	−1.07616	−	1.07616i	−0.0793118	−	0.996850i	$-0.525272\pi$
$858$	−25.9559	+	35.3344i	−0.886121	+	1.20630i
$859$		−	29.9066i		−	1.02040i	−0.860055	−	0.510201i	$-0.829571\pi$
$859$		−	29.9066i		−	1.02040i	0.860055	−	0.510201i	$-0.170429\pi$
$860$		0			0
$861$	−0.519033	−	0.442644i	−0.0176886	−	0.0150853i
$862$	−4.48861	−	1.20272i	−0.152883	−	0.0409648i
$863$	9.69182	+	9.69182i	0.329913	+	0.329913i	0.852553	−	0.522640i	$-0.175053\pi$
$863$	9.69182	+	9.69182i	0.329913	+	0.329913i	−0.522640	+	0.852553i	$0.675053\pi$
$864$	−25.1365	−	0.603367i	−0.855161	−	0.0205270i
$865$		0			0
$866$	−24.2113			−0.822732
$867$	16.0507	+	7.64148i	0.545111	+	0.259518i
$868$	0.693590	−	0.185847i	0.0235420	−	0.00630806i
$869$	17.2402	+	9.95361i	0.584832	+	0.337653i
$870$		0			0
$871$	2.00405	−	10.4640i	0.0679045	−	0.354558i
$872$	−0.834142	−	0.834142i	−0.0282476	−	0.0282476i
$873$	−0.0462071	+	0.445866i	−0.00156387	+	0.0150903i
$874$	−81.5712	−	47.0952i	−2.75919	−	1.59302i
$875$		0			0
$876$	−1.22981	+	6.66246i	−0.0415513	+	0.225104i
$877$	9.13551	−	34.0942i	0.308484	−	1.15128i	−0.621420	−	0.783478i	$-0.713444\pi$
$877$	9.13551	−	34.0942i	0.308484	−	1.15128i	0.929904	−	0.367801i	$-0.119889\pi$
$878$	4.13681	−	15.4388i	0.139610	−	0.521033i
$879$	−2.37315	+	12.8565i	−0.0800445	+	0.433640i
$880$		0			0
$881$	−0.0237715	−	0.0137245i	−0.000800881	−	0.000462389i	0.499600	−	0.866257i	$-0.333481\pi$
$881$	−0.0237715	−	0.0137245i	−0.000800881	−	0.000462389i	−0.500400	+	0.865794i	$0.666814\pi$
$882$	3.69187	−	35.6240i	0.124312	−	1.19952i
$883$	12.5285	+	12.5285i	0.421617	+	0.421617i	0.885760	−	0.464143i	$-0.153638\pi$
$883$	12.5285	+	12.5285i	0.421617	+	0.421617i	−0.464143	+	0.885760i	$0.653638\pi$
$884$	−16.9981	−	3.25545i	−0.571707	−	0.109492i
$885$		0			0
$886$	−12.0157	−	6.93725i	−0.403674	−	0.233061i
$887$	−2.92906	+	0.784839i	−0.0983482	+	0.0263523i	−0.307658	−	0.951497i	$-0.599545\pi$
$887$	−2.92906	+	0.784839i	−0.0983482	+	0.0263523i	0.209309	+	0.977849i	$0.432878\pi$
$888$	12.2671	+	5.84015i	0.411656	+	0.195983i
$889$	−1.44303			−0.0483976
$890$		0			0
$891$	−7.58347	+	36.1946i	−0.254056	+	1.21257i
$892$	−7.89315	−	7.89315i	−0.264282	−	0.264282i
$893$	2.01580	+	0.540132i	0.0674562	+	0.0180748i
$894$	−26.7891	−	22.8464i	−0.895961	−	0.764097i
$895$		0			0
$896$			1.42917i			0.0477451i
$897$	−43.0253	−	4.75024i	−1.43657	−	0.158606i
$898$	−32.7688	−	32.7688i	−1.09351	−	1.09351i
$899$	−24.0000	−	13.8564i	−0.800446	−	0.462138i
$900$		0			0
$901$	7.17782	+	12.4324i	0.239128	+	0.414182i
$902$	17.2580	−	17.2580i	0.574627	−	0.574627i
$903$	0.896678	+	0.426893i	0.0298396	+	0.0142061i
$904$	7.30666	+	12.6555i	0.243016	+	0.420916i
$905$		0			0
$906$	−30.9607	+	10.9891i	−1.02860	+	0.365089i
$907$	−4.50525	−	16.8138i	−0.149594	−	0.558294i	−0.999508	−	0.0313715i	$-0.990012\pi$
$907$	−4.50525	−	16.8138i	−0.149594	−	0.558294i	0.849913	−	0.526922i	$-0.176654\pi$
$908$	−12.3141	+	3.29956i	−0.408659	+	0.109500i
$909$	34.0094	+	12.9983i	1.12802	+	0.431126i
$910$		0			0
$911$		−	4.78351i		−	0.158485i	−0.996855	−	0.0792423i	$-0.974750\pi$
$911$		−	4.78351i		−	0.158485i	0.996855	−	0.0792423i	$-0.0252501\pi$
$912$	−68.5714	+	5.44685i	−2.27063	+	0.180363i
$913$	−11.4752	+	3.07477i	−0.379774	+	0.101760i
$914$	11.4241	+	19.7871i	0.377876	+	0.654500i
$915$		0			0
$916$	−6.78234	+	3.91578i	−0.224095	+	0.129381i
$917$	1.41785	+	0.379911i	0.0468214	+	0.0125458i
$918$	−45.0521	+	10.9200i	−1.48694	+	0.360415i
$919$	−20.5581	+	11.8693i	−0.678151	+	0.391530i	−0.799158	−	0.601121i	$-0.794721\pi$
$919$	−20.5581	+	11.8693i	−0.678151	+	0.391530i	0.121007	+	0.992652i	$0.461388\pi$
$920$		0			0
$921$	9.84626	+	8.39713i	0.324445	+	0.276695i
$922$	−41.4418	+	41.4418i	−1.36481	+	1.36481i
$923$	30.5938	−	2.22417i	1.00701	−	0.0732094i
$924$	−0.728888	−	0.134543i	−0.0239787	−	0.00442616i
$925$		0			0
$926$	40.6683	+	23.4798i	1.33644	+	0.771595i
$927$	−1.81530	−	1.31487i	−0.0596223	−	0.0431859i
$928$	−13.7531	+	13.7531i	−0.451467	+	0.451467i
$929$	27.3742	−	15.8045i	0.898117	−	0.518528i	0.0215282	−	0.999768i	$-0.493147\pi$
$929$	27.3742	−	15.8045i	0.898117	−	0.518528i	0.876589	+	0.481240i	$0.159814\pi$
$930$		0			0
$931$		−	55.5706i		−	1.82125i
$932$	2.89804	−	10.8156i	0.0949283	−	0.354277i
$933$	0.325879	+	4.10256i	0.0106688	+	0.134312i
$934$	23.7216	−	41.0870i	0.776194	−	1.34441i
$935$		0			0
$936$	−17.5952	+	9.45081i	−0.575116	+	0.308909i
$937$	12.6526	−	12.6526i	0.413344	−	0.413344i	−0.469558	−	0.882902i	$-0.655587\pi$
$937$	12.6526	−	12.6526i	0.413344	−	0.413344i	0.882902	+	0.469558i	$0.155587\pi$
$938$	0.552480	−	0.148037i	0.0180391	−	0.00483357i
$939$	38.2256	+	32.5997i	1.24744	+	1.06385i
$940$		0			0
$941$	49.4334			1.61148			0.805741	−	0.592268i	$-0.201767\pi$
$941$	49.4334			1.61148			0.805741	+	0.592268i	$0.201767\pi$
$942$	−20.9340	−	9.96635i	−0.682068	−	0.324721i
$943$	23.2755	+	6.23666i	0.757956	+	0.203094i
$944$		−	3.57304i		−	0.116293i
$945$		0			0
$946$	−17.7661	+	30.7718i	−0.577625	+	1.00048i
$947$	6.33163	+	23.6300i	0.205750	+	0.767871i	0.989220	+	0.146440i	$0.0467815\pi$
$947$	6.33163	+	23.6300i	0.205750	+	0.767871i	−0.783469	+	0.621431i	$0.786552\pi$
$948$	−4.37408	−	6.35443i	−0.142064	−	0.206382i
$949$	5.03464	+	14.4916i	0.163431	+	0.470419i
$950$		0			0
$951$	37.9953	−	44.5524i	1.23208	−	1.44471i
$952$	0.282693	+	1.05503i	0.00916215	+	0.0341936i
$953$	41.7321	+	11.1821i	1.35184	+	0.362223i	0.860812	−	0.508923i	$-0.169956\pi$
$953$	41.7321	+	11.1821i	1.35184	+	0.362223i	0.491024	+	0.871146i	$0.336623\pi$
$954$	−13.1640	−	5.03122i	−0.426199	−	0.162892i
$955$		0			0
$956$	5.31043	+	9.19793i	0.171751	+	0.297482i
$957$	16.2198	+	23.5632i	0.524312	+	0.761691i
$958$	−0.761659	+	2.84255i	−0.0246081	+	0.0918386i
$959$	0.705791	−	1.22247i	0.0227912	−	0.0394755i
$960$		0			0
$961$	−16.5366			−0.533437
$962$	−26.1015	+	1.89758i	−0.841546	+	0.0611803i
$963$	−4.52328	+	2.02178i	−0.145761	+	0.0651510i
$964$	−6.41870	+	11.1175i	−0.206732	+	0.358071i
$965$		0			0
$966$	−0.777310	−	2.18999i	−0.0250095	−	0.0704619i
$967$	−4.55251	−	4.55251i	−0.146399	−	0.146399i	0.630108	−	0.776507i	$-0.283010\pi$
$967$	−4.55251	−	4.55251i	−0.146399	−	0.146399i	−0.776507	+	0.630108i	$0.783010\pi$
$968$	−2.81172	+	10.4935i	−0.0903721	+	0.337273i
$969$	−67.7845	+	24.0592i	−2.17755	+	0.772893i
$970$		0			0
$971$	−51.2257	+	29.5752i	−1.64391	+	0.949113i	−0.664488	+	0.747299i	$0.731350\pi$
$971$	−51.2257	+	29.5752i	−1.64391	+	0.949113i	−0.979424	+	0.201814i	$0.935316\pi$
$972$	8.68250	−	11.4008i	0.278491	−	0.365681i
$973$	−0.112355	−	0.419316i	−0.00360195	−	0.0134427i
$974$	−35.5697			−1.13973
$975$		0			0
$976$	−20.3894			−0.652649
$977$	−14.9944	−	55.9598i	−0.479713	−	1.79031i	−0.602772	−	0.797914i	$-0.705937\pi$
$977$	−14.9944	−	55.9598i	−0.479713	−	1.79031i	0.123059	−	0.992399i	$-0.460730\pi$
$978$	−2.87223	−	36.1590i	−0.0918437	−	1.15624i
$979$	−11.5036	+	6.64164i	−0.367658	+	0.212268i
$980$		0			0
$981$	1.89257	−	0.302576i	0.0604252	−	0.00966050i
$982$	9.99359	−	37.2966i	0.318908	−	1.19018i
$983$	−17.2893	−	17.2893i	−0.551443	−	0.551443i	0.375414	−	0.926857i	$-0.377500\pi$
$983$	−17.2893	−	17.2893i	−0.551443	−	0.551443i	−0.926857	+	0.375414i	$0.877500\pi$
$984$	10.4778	−	3.71898i	0.334022	−	0.118557i
$985$		0			0
$986$	−17.9295	+	31.0548i	−0.570991	+	0.988985i
$987$	0.0291940	+	0.0424114i	0.000929254	+	0.00134997i
$988$	21.8142	−	14.8016i	0.694002	−	0.470901i
$989$	−35.0811			−1.11551
$990$		0			0
$991$	6.95908	−	12.0535i	0.221063	−	0.382892i	−0.734068	−	0.679076i	$-0.762381\pi$
$991$	6.95908	−	12.0535i	0.221063	−	0.382892i	0.955131	+	0.296184i	$0.0957142\pi$
$992$	−8.63491	+	32.2259i	−0.274159	+	1.02317i
$993$	−19.8956	+	13.6952i	−0.631367	+	0.434602i
$994$	0.823384	+	1.42614i	0.0261162	+	0.0452345i
$995$		0			0
$996$	4.52721	+	0.835664i	0.143450	+	0.0264790i
$997$	−46.6520	−	12.5004i	−1.47748	−	0.395891i	−0.571994	−	0.820258i	$-0.693830\pi$
$997$	−46.6520	−	12.5004i	−1.47748	−	0.395891i	−0.905490	+	0.424367i	$0.860497\pi$
$998$	15.8680	+	59.2202i	0.502293	+	1.87458i
$999$	−19.3760	+	10.5751i	−0.613029	+	0.334581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.368.6		96
3.2	odd	2	inner	975.2.bn.d.368.19		96
5.2	odd	4	inner	975.2.bn.d.407.19		96
5.3	odd	4		195.2.bf.a.17.6	✓	96
5.4	even	2		195.2.bf.a.173.19	yes	96
13.10	even	6	inner	975.2.bn.d.218.6		96
15.2	even	4	inner	975.2.bn.d.407.6		96
15.8	even	4		195.2.bf.a.17.19	yes	96
15.14	odd	2		195.2.bf.a.173.6	yes	96
39.23	odd	6	inner	975.2.bn.d.218.19		96
65.23	odd	12		195.2.bf.a.62.6	yes	96
65.49	even	6		195.2.bf.a.23.19	yes	96
65.62	odd	12	inner	975.2.bn.d.257.19		96
195.23	even	12		195.2.bf.a.62.19	yes	96
195.62	even	12	inner	975.2.bn.d.257.6		96
195.179	odd	6		195.2.bf.a.23.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.6	✓	96	5.3	odd	4
195.2.bf.a.17.19	yes	96	15.8	even	4
195.2.bf.a.23.6	yes	96	195.179	odd	6
195.2.bf.a.23.19	yes	96	65.49	even	6
195.2.bf.a.62.6	yes	96	65.23	odd	12
195.2.bf.a.62.19	yes	96	195.23	even	12
195.2.bf.a.173.6	yes	96	15.14	odd	2
195.2.bf.a.173.19	yes	96	5.4	even	2
975.2.bn.d.218.6		96	13.10	even	6	inner
975.2.bn.d.218.19		96	39.23	odd	6	inner
975.2.bn.d.257.6		96	195.62	even	12	inner
975.2.bn.d.257.19		96	65.62	odd	12	inner
975.2.bn.d.368.6		96	1.1	even	1	trivial
975.2.bn.d.368.19		96	3.2	odd	2	inner
975.2.bn.d.407.6		96	15.2	even	4	inner
975.2.bn.d.407.19		96	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.442218 - 1.65038i) q^{2} +(-1.72661 + 0.137150i) q^{3} +(-0.796141 + 0.459652i) q^{4} +(0.989888 + 2.78891i) q^{6} +(-0.0293212 + 0.109428i) q^{7} +(-1.30565 - 1.30565i) q^{8} +(2.96238 - 0.473611i) q^{9} +(-2.05447 + 3.55845i) q^{11} +(1.31159 - 0.902832i) q^{12} +(1.57162 - 3.24500i) q^{13} +0.193564 q^{14} +(-2.49674 + 4.32449i) q^{16} +(-1.35141 + 5.04353i) q^{17} +(-2.09165 - 4.67961i) q^{18} +(-3.97662 - 6.88771i) q^{19} +(0.0356182 - 0.192962i) q^{21} +(6.78132 + 1.81705i) q^{22} +(1.79398 + 6.69524i) q^{23} +(2.43343 + 2.07529i) q^{24} +(-6.05047 - 1.15878i) q^{26} +(-5.04992 + 1.22403i) q^{27} +(-0.0269551 - 0.100598i) q^{28} +(-2.00973 + 3.48095i) q^{29} +6.89468i q^{31} +(4.67403 + 1.25240i) q^{32} +(3.05924 - 6.42584i) q^{33} +8.92135 q^{34} +(-2.14078 + 1.73873i) q^{36} +(4.10339 - 1.09950i) q^{37} +(-9.60880 + 9.60880i) q^{38} +(-2.26853 + 5.81840i) q^{39} +(1.73822 - 3.01068i) q^{41} +(-0.334211 + 0.0265474i) q^{42} +(-1.30993 + 4.88872i) q^{43} -3.77737i q^{44} +(10.2563 - 5.92150i) q^{46} +(-0.185543 + 0.185543i) q^{47} +(3.71780 - 7.80914i) q^{48} +(6.05106 + 3.49358i) q^{49} +(1.64164 - 8.89356i) q^{51} +(0.240337 + 3.30587i) q^{52} +(1.94409 - 1.94409i) q^{53} +(4.25328 + 7.79300i) q^{54} +(0.181159 - 0.104592i) q^{56} +(7.81074 + 11.3470i) q^{57} +(6.63362 + 1.77747i) q^{58} +(-0.619675 + 0.357770i) q^{59} +(2.04160 + 3.53616i) q^{61} +(11.3788 - 3.04895i) q^{62} +(-0.0350341 + 0.338055i) q^{63} +1.71922i q^{64} +(-11.9579 - 2.20728i) q^{66} +(2.85424 - 0.764792i) q^{67} +(-1.24236 - 4.63654i) q^{68} +(-4.01577 - 11.3140i) q^{69} +(4.25380 + 7.36780i) q^{71} +(-4.48621 - 3.24947i) q^{72} +(-3.00868 + 3.00868i) q^{73} +(-3.62918 - 6.28592i) q^{74} +(6.33191 + 3.65573i) q^{76} +(-0.329156 - 0.329156i) q^{77} +(10.6057 + 1.17093i) q^{78} -4.84485i q^{79} +(8.55139 - 2.80603i) q^{81} +(-5.73743 - 1.53734i) q^{82} +(2.04442 + 2.04442i) q^{83} +(0.0603381 + 0.169997i) q^{84} +8.64751 q^{86} +(2.99261 - 6.28589i) q^{87} +(7.32854 - 1.96368i) q^{88} +(2.79966 + 1.61638i) q^{89} +(0.309013 + 0.267127i) q^{91} +(-4.50574 - 4.50574i) q^{92} +(-0.945607 - 11.9044i) q^{93} +(0.388267 + 0.224166i) q^{94} +(-8.24201 - 1.52137i) q^{96} +(-0.0386722 + 0.144327i) q^{97} +(3.08985 - 11.5315i) q^{98} +(-4.40081 + 11.5145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more