LMFDB - Embedded newform 975.2.bn.d.368.19

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			368.19
Character	$\chi$	$=$	975.368
Dual form			975.2.bn.d.257.19

$q$-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} +(-1.56387 + 0.744530i) q^{3} +(-0.796141 + 0.459652i) q^{4} +(-1.92033 - 2.25172i) q^{6} +(-0.0293212 + 0.109428i) q^{7} +(1.30565 + 1.30565i) q^{8} +(1.89135 - 2.32869i) q^{9} +(2.05447 - 3.55845i) q^{11} +(0.902832 - 1.31159i) q^{12} +(1.57162 - 3.24500i) q^{13} -0.193564 q^{14} +(-2.49674 + 4.32449i) q^{16} +(1.35141 - 5.04353i) q^{17} +(4.67961 + 2.09165i) 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} +(-3.01397 - 1.06977i) q^{24} +(6.05047 + 1.15878i) q^{26} +(-1.22403 + 5.04992i) q^{27} +(-0.0269551 - 0.100598i) q^{28} +(2.00973 - 3.48095i) q^{29} +6.89468i q^{31} +(-4.67403 - 1.25240i) q^{32} +(-0.563544 + 7.09456i) q^{33} +8.92135 q^{34} +(-0.435393 + 2.72333i) q^{36} +(4.10339 - 1.09950i) q^{37} +(9.60880 - 9.60880i) q^{38} +(-0.0418074 + 6.24486i) q^{39} +(-1.73822 + 3.01068i) q^{41} +(0.302709 - 0.144115i) q^{42} +(-1.30993 + 4.88872i) q^{43} +3.77737i q^{44} +(10.2563 - 5.92150i) q^{46} +(0.185543 - 0.185543i) q^{47} +(0.684859 - 8.62182i) 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} +(-8.87558 + 0.213046i) q^{54} +(-0.181159 + 0.104592i) q^{56} +(11.3470 + 7.81074i) 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} +(0.199368 + 0.275247i) q^{63} +1.71922i q^{64} +(-11.9579 + 2.20728i) q^{66} +(2.85424 - 0.764792i) q^{67} +(1.24236 + 4.63654i) q^{68} +(7.79036 + 9.13477i) q^{69} +(-4.25380 - 7.36780i) q^{71} +(5.50991 - 0.571017i) 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} +(-10.3249 + 2.69259i) q^{78} -4.84485i q^{79} +(-1.84560 - 8.80873i) q^{81} +(-5.73743 - 1.53734i) q^{82} +(-2.04442 - 2.04442i) q^{83} +(0.117052 + 0.137253i) q^{84} -8.64751 q^{86} +(-0.551270 + 6.94004i) 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} +(-5.13330 - 10.7823i) 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	$0.123126\pi$
$2$	0.442218	+	1.65038i	0.312695	+	1.16699i	−0.613421	+	0.789756i	$0.710207\pi$
$3$	−1.56387	+	0.744530i	−0.902898	+	0.429855i
$3$	−1.56387	+	0.744530i	−0.902898	+	0.429855i
$4$	−0.796141	+	0.459652i	−0.398071	+	0.229826i
$5$		0			0
$5$		0			0
$6$	−1.92033	−	2.25172i	−0.783970	−	0.919263i
$7$	−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
$9$	1.89135	−	2.32869i	0.630450	−	0.776230i
$10$		0			0
$11$	2.05447	−	3.55845i	0.619447	−	1.07291i	−0.370139	−	0.928976i	$-0.620690\pi$
$11$	2.05447	−	3.55845i	0.619447	−	1.07291i	0.989587	−	0.143938i	$-0.0459766\pi$
$12$	0.902832	−	1.31159i	0.260625	−	0.378622i
$13$	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	$-0.698411\pi$
$17$	1.35141	−	5.04353i	0.327765	−	1.22324i	0.911503	−	0.411293i	$-0.134923\pi$
$18$	4.67961	+	2.09165i	1.10299	+	0.493007i
$19$	−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	$-0.826257\pi$
$23$	−1.79398	−	6.69524i	−0.374071	−	1.39605i	0.480625	−	0.876926i	$-0.340410\pi$
$24$	−3.01397	−	1.06977i	−0.615223	−	0.218365i
$25$		0			0
$26$	6.05047	+	1.15878i	1.18659	+	0.227255i
$27$	−1.22403	+	5.04992i	−0.235565	+	0.971858i
$28$	−0.0269551	−	0.100598i	−0.00509404	−	0.0190112i
$29$	2.00973	−	3.48095i	0.373197	−	0.646396i	−0.616858	−	0.787074i	$-0.711595\pi$
$29$	2.00973	−	3.48095i	0.373197	−	0.646396i	0.990055	+	0.140678i	$0.0449282\pi$
$30$		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
$33$	−0.563544	+	7.09456i	−0.0981004	+	1.23500i
$34$	8.92135			1.53000
$35$		0			0
$36$	−0.435393	+	2.72333i	−0.0725655	+	0.453888i
$37$	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
$39$	−0.0418074	+	6.24486i	−0.00669454	+	0.999978i
$40$		0			0
$41$	−1.73822	+	3.01068i	−0.271464	+	0.470189i	−0.969237	−	0.246130i	$-0.920841\pi$
$41$	−1.73822	+	3.01068i	−0.271464	+	0.470189i	0.697773	+	0.716319i	$0.254174\pi$
$42$	0.302709	−	0.144115i	0.0467090	−	0.0222374i
$43$	−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	−0.693445	−	0.720509i	$-0.743908\pi$
$47$	0.185543	−	0.185543i	0.0270642	−	0.0270642i	0.720509	+	0.693445i	$0.243908\pi$
$48$	0.684859	−	8.62182i	0.0988509	−	1.24445i
$49$	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	−0.827907	−	0.560865i	$-0.810469\pi$
$53$	−1.94409	+	1.94409i	−0.267042	+	0.267042i	0.560865	+	0.827907i	$0.310469\pi$
$54$	−8.87558	+	0.213046i	−1.20781	+	0.0289919i
$55$		0			0
$56$	−0.181159	+	0.104592i	−0.0242084	+	0.0139767i
$57$	11.3470	+	7.81074i	1.50295	+	1.03456i
$58$	6.63362	+	1.77747i	0.871037	+	0.233394i
$59$	0.619675	−	0.357770i	0.0806749	−	0.0465777i	−0.459120	−	0.888374i	$-0.651835\pi$
$59$	0.619675	−	0.357770i	0.0806749	−	0.0465777i	0.539795	+	0.841797i	$0.318502\pi$
$60$		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
$63$	0.199368	+	0.275247i	0.0251180	+	0.0346779i
$64$			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
$69$	7.79036	+	9.13477i	0.937849	+	1.09970i
$70$		0			0
$71$	−4.25380	−	7.36780i	−0.504833	−	0.874397i	−0.999984	−	0.00558990i	$-0.998221\pi$
$71$	−4.25380	−	7.36780i	−0.504833	−	0.874397i	0.495151	−	0.868807i	$-0.335113\pi$
$72$	5.50991	−	0.571017i	0.649349	−	0.0672949i
$73$	−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
$78$	−10.3249	+	2.69259i	−1.16906	+	0.304876i
$79$		−	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
$81$	−1.84560	−	8.80873i	−0.205066	−	0.978748i
$82$	−5.73743	−	1.53734i	−0.633593	−	0.169771i
$83$	−2.04442	−	2.04442i	−0.224405	−	0.224405i	0.585946	−	0.810350i	$-0.300723\pi$
$83$	−2.04442	−	2.04442i	−0.224405	−	0.224405i	−0.810350	+	0.585946i	$0.800723\pi$
$84$	0.117052	+	0.137253i	0.0127715	+	0.0149755i
$85$		0			0
$86$	−8.64751			−0.932485
$87$	−0.551270	+	6.94004i	−0.0591023	+	0.744050i
$88$	7.32854	−	1.96368i	0.781225	−	0.209329i
$89$	−2.79966	−	1.61638i	−0.296763	−	0.171336i	0.344225	−	0.938887i	$-0.388142\pi$
$89$	−2.79966	−	1.61638i	−0.296763	−	0.171336i	−0.640988	+	0.767551i	$0.721475\pi$
$90$		0			0
$91$	0.309013	+	0.267127i	0.0323933	+	0.0280025i
$92$	4.50574	+	4.50574i	0.469756	+	0.469756i
$93$	−5.13330	−	10.7823i	−0.532298	−	1.11808i
$94$	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	−0.124339	−	0.992240i	$-0.539681\pi$
$101$	−10.5103	−	6.06812i	−1.04581	−	0.603800i	−0.921474	+	0.388440i	$0.873014\pi$
$102$	−13.9518	+	6.64221i	−1.38143	+	0.657677i
$103$	−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	−0.180884	−	0.983504i	$-0.557896\pi$
$107$	1.59525	−	0.427445i	0.154218	−	0.0413227i	0.335102	+	0.942182i	$0.391229\pi$
$108$	−1.34671	−	4.58308i	−0.129587	−	0.441007i
$109$	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
$111$	−5.59853	+	4.77457i	−0.531389	+	0.453182i
$112$	−0.400014	−	0.400014i	−0.0377977	−	0.0377977i
$113$	7.64451	+	2.04834i	0.719135	+	0.192692i	0.599786	−	0.800161i	$-0.295253\pi$
$113$	7.64451	+	2.04834i	0.719135	+	0.192692i	0.119349	+	0.992852i	$0.461919\pi$
$114$	−7.87282	+	22.1809i	−0.737357	+	2.07743i
$115$		0			0
$116$			3.69510i			0.343082i
$117$	−4.58411	−	9.79724i	−0.423801	−	0.905755i
$118$	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
$123$	0.476794	−	6.00245i	0.0429911	−	0.541223i
$124$	−3.16915	−	5.48913i	−0.284598	−	0.492939i
$125$		0			0
$126$	−0.366098	+	0.450752i	−0.0326146	+	0.0401561i
$127$	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	$0.191519\pi$
$131$			12.9569i			1.13205i	−0.824390	+	0.566023i	$0.808481\pi$
$132$	−2.81237	−	5.90731i	−0.244785	−	0.514165i
$133$	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	0.733241	−	0.679969i	$-0.238007\pi$
$137$	12.0355	+	3.22490i	1.02826	+	0.275522i	0.295021	+	0.955491i	$0.404673\pi$
$138$	−11.6308	+	16.8966i	−0.990079	+	1.43833i
$139$	−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
$141$	−0.152022	+	0.428307i	−0.0128026	+	0.0360699i
$142$	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
$147$	−12.0641	−	0.958292i	−0.995032	−	0.0790386i
$148$	−2.76149	+	2.76149i	−0.226993	+	0.226993i
$149$	10.3032	−	5.94857i	0.844073	−	0.487326i	−0.0145735	−	0.999894i	$-0.504639\pi$
$149$	10.3032	−	5.94857i	0.844073	−	0.487326i	0.858647	+	0.512568i	$0.171306\pi$
$150$		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
$153$	−9.18883	−	12.6861i	−0.742873	−	1.02561i
$154$	−0.397673	+	0.688790i	−0.0320454	+	0.0555043i
$155$		0			0
$156$	−2.83718	−	4.99100i	−0.227156	−	0.399600i
$157$	−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
$159$	1.59286	−	4.48774i	0.126322	−	0.355901i
$160$		0			0
$161$	0.785250			0.0618864
$162$	13.7216	−	6.94131i	1.07807	−	0.545361i
$163$	−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	$-0.971151\pi$
$167$	−2.30903	−	8.61742i	−0.178678	−	0.666836i	0.817218	−	0.576329i	$-0.195515\pi$
$168$	0.205436	−	0.298446i	0.0158497	−	0.0230256i
$169$	−8.06000	−	10.1998i	−0.620000	−	0.784602i
$170$		0			0
$171$	−23.5605	−	3.76674i	−1.80172	−	0.288050i
$172$	−1.20422	−	4.49422i	−0.0918211	−	0.342681i
$173$	8.49801	+	2.27704i	0.646092	+	0.173120i	0.566961	−	0.823744i	$-0.308119\pi$
$173$	8.49801	+	2.27704i	0.646092	+	0.173120i	0.0791307	+	0.996864i	$0.474786\pi$
$174$	−11.6975	+	2.15920i	−0.886783	+	0.163689i
$175$		0			0
$176$	10.2590	+	17.7691i	0.773301	+	1.33940i
$177$	−0.702718	+	1.02087i	−0.0528196	+	0.0767334i
$178$	1.42959	−	5.33529i	0.107152	−	0.399897i
$179$	9.95273	−	17.2386i	0.743902	−	1.28848i	−0.206804	−	0.978382i	$-0.566306\pi$
$179$	9.95273	−	17.2386i	0.743902	−	1.28848i	0.950706	−	0.310094i	$-0.100360\pi$
$180$		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
$183$	−5.82556	−	4.01004i	−0.430638	−	0.296430i
$184$	6.39934	−	11.0840i	0.471766	−	0.817122i
$185$		0			0
$186$	15.5249	−	13.2400i	1.13834	−	0.970805i
$187$	−15.1707	−	15.1707i	−1.10939	−	1.10939i
$188$	−0.0624332	+	0.233004i	−0.00455341	+	0.0169935i
$189$	−0.516714	−	0.282014i	−0.0375854	−	0.0205135i
$190$		0			0
$191$	19.8776	−	11.4763i	1.43829	−	0.830399i	0.440562	−	0.897722i	$-0.354779\pi$
$191$	19.8776	−	11.4763i	1.43829	−	0.830399i	0.997731	+	0.0673227i	$0.0214457\pi$
$192$	−1.28001	−	2.68863i	−0.0923770	−	0.194035i
$193$	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	$0.0168996\pi$
$197$	2.25019	+	8.39781i	0.160319	+	0.598319i	−0.838272	+	0.545253i	$0.816434\pi$
$198$	17.0572	−	12.3549i	1.21220	−	0.878026i
$199$	−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
$201$	−3.89424	+	3.32110i	−0.274679	+	0.234253i
$202$	5.36686	−	20.0294i	0.377611	−	1.40926i
$203$	0.321987	+	0.321987i	0.0225990	+	0.0225990i
$204$	−5.39492	−	6.32595i	−0.377720	−	0.442905i
$205$		0			0
$206$	0.638295	−	1.10556i	0.0444721	−	0.0770280i
$207$	−18.9842	−	8.48540i	−1.31949	−	0.589776i
$208$	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
$213$	12.1379	+	8.35516i	0.831677	+	0.572486i
$214$	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
$219$	2.46511	−	6.94521i	0.166577	−	0.469314i
$220$		0			0
$221$	−14.2423	−	12.3118i	−0.958043	−	0.828184i
$222$	−10.3556	−	7.12830i	−0.695023	−	0.478420i
$223$	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	−0.214748	−	0.976669i	$-0.568893\pi$
$227$	−13.3950	−	3.58919i	−0.889061	−	0.238223i	−0.674312	+	0.738446i	$0.735560\pi$
$228$	−12.6240	−	1.00277i	−0.836048	−	0.0664100i
$229$	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
$231$	−0.759822	−	0.269689i	−0.0499926	−	0.0177442i
$232$	7.16892	−	1.92091i	0.470663	−	0.126114i
$233$	8.61258	−	8.61258i	0.564229	−	0.564229i	−0.366277	−	0.930506i	$-0.619368\pi$
$233$	8.61258	−	8.61258i	0.564229	−	0.564229i	0.930506	+	0.366277i	$0.119368\pi$
$234$	14.1420	−	11.8980i	0.924490	−	0.777798i
$235$		0			0
$236$	−0.328899	+	0.569670i	−0.0214095	+	0.0370824i
$237$	3.60714	+	7.57669i	0.234309	+	0.492159i
$238$	−0.261585	+	0.976248i	−0.0169560	+	0.0632807i
$239$			11.5531i			0.747310i	0.927568	+	0.373655i	$0.121896\pi$
$239$			11.5531i			0.747310i	−0.927568	+	0.373655i	$0.878104\pi$
$240$		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
$243$	9.44464	+	12.4016i	0.605874	+	0.795561i
$244$	−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
$249$	4.71934	+	1.67507i	0.299076	+	0.106153i
$250$		0			0
$251$	14.9246	−	8.61672i	0.942032	−	0.543882i	0.0514354	−	0.998676i	$-0.483620\pi$
$251$	14.9246	−	8.61672i	0.942032	−	0.543882i	0.890597	+	0.454794i	$0.150287\pi$
$252$	−0.285243	−	0.127496i	−0.0179686	−	0.00803147i
$253$	−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	−0.271409	−	0.962464i	$-0.587489\pi$
$257$	−0.404361	+	0.108348i	−0.0252233	+	0.00675857i	0.246185	+	0.969223i	$0.420823\pi$
$258$	13.5235	−	6.43833i	0.841939	−	0.400833i
$259$			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	$0.0488501\pi$
$263$	3.38670	+	12.6393i	0.208833	+	0.779374i	−0.779414	+	0.626509i	$0.784483\pi$
$264$	−9.99883	+	8.52725i	−0.615386	+	0.524816i
$265$		0			0
$266$	0.769733	+	1.33322i	0.0471953	+	0.0817447i
$267$	5.58173	+	0.443375i	0.341597	+	0.0271341i
$268$	−1.92084	+	1.92084i	−0.117334	+	0.117334i
$269$	0.403612	+	0.699076i	0.0246086	+	0.0426234i	0.878067	−	0.478537i	$-0.158833\pi$
$269$	0.403612	+	0.699076i	0.0246086	+	0.0426234i	−0.853459	+	0.521160i	$0.825499\pi$
$270$		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
$273$	−0.682138	−	0.187682i	−0.0412849	−	0.0113590i
$274$			21.2892i			1.28613i
$275$		0			0
$276$	−10.4010	−	3.69171i	−0.626069	−	0.222215i
$277$	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
$279$	16.0556	+	13.0402i	0.961222	+	0.780699i
$280$		0			0
$281$	13.4870			0.804568			0.402284	−	0.915515i	$-0.368216\pi$
$281$	13.4870			0.804568			0.402284	+	0.915515i	$0.368216\pi$
$282$	−0.774095	−	0.0614889i	−0.0460967	−	0.00366161i
$283$	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
$288$	−11.7567	+	8.51564i	−0.692769	+	0.501789i
$289$	−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	−0.999220	−	0.0394794i	$-0.987430\pi$
$293$	−1.95360	+	7.29093i	−0.114130	+	0.425941i	0.885090	+	0.465420i	$0.154097\pi$
$294$	−3.75342	−	20.3341i	−0.218904	−	1.18591i
$295$		0			0
$296$	6.79317	+	3.92204i	0.394845	+	0.227964i
$297$	15.4552	+	14.7306i	0.896800	+	0.854757i
$298$	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
$303$	20.9546	+	1.66449i	1.20381	+	0.0956224i
$304$	39.7144			2.27778
$305$		0			0
$306$	16.8734	−	20.7751i	0.964587	−	1.18763i
$307$	−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
$309$	1.21957	+	0.432871i	0.0693790	+	0.0246252i
$310$		0			0
$311$			2.37607i			0.134735i	0.997728	+	0.0673674i	$0.0214599\pi$
$311$			2.37607i			0.134735i	−0.997728	+	0.0673674i	$0.978540\pi$
$312$	−8.20821	+	8.09904i	−0.464698	+	0.458518i
$313$	−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	$-0.351723\pi$
$317$	23.9045	−	23.9045i	1.34261	−	1.34261i	0.893450	−	0.449162i	$-0.148277\pi$
$318$	8.11085	+	0.644271i	0.454834	+	0.0361289i
$319$	−8.25787	−	14.3030i	−0.462352	−	0.800817i
$320$		0			0
$321$	−2.17651	+	1.85618i	−0.121481	+	0.103602i
$322$	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
$327$	−0.999106	+	0.475658i	−0.0552507	+	0.0263039i
$328$	−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
$333$	5.20054	−	11.6351i	0.284988	−	0.637597i
$334$	13.2009	−	7.62155i	0.722322	−	0.417033i
$335$		0			0
$336$	0.923390	+	0.327745i	0.0503750	+	0.0178800i
$337$	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
$342$	−4.20233	−	40.5495i	−0.227236	−	2.19267i
$343$	−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	$0.224237\pi$
$347$	−4.13034	+	15.4146i	−0.221728	+	0.827500i	−0.983689	+	0.179877i	$0.942430\pi$
$348$	−2.75112	−	5.77864i	−0.147475	−	0.309768i
$349$	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
$351$	14.4633	+	11.9086i	0.771992	+	0.635632i
$352$	−14.0593	+	14.0593i	−0.749363	+	0.749363i
$353$	−12.0317	+	3.22389i	−0.640383	+	0.171590i	−0.564377	−	0.825517i	$-0.690884\pi$
$353$	−12.0317	+	3.22389i	−0.640383	+	0.171590i	−0.0760061	+	0.997107i	$0.524217\pi$
$354$	−1.99558	−	0.708304i	−0.106064	−	0.0376459i
$355$		0			0
$356$	2.97190			0.157510
$357$	−1.02134	−	0.0811285i	−0.0540552	−	0.00429378i
$358$	32.8515	+	8.80254i	1.73626	+	0.465229i
$359$			29.8863i			1.57734i	0.614816	+	0.788671i	$0.289230\pi$
$359$			29.8863i			1.57734i	−0.614816	+	0.788671i	$0.710770\pi$
$360$		0			0
$361$	−22.1271	+	38.3252i	−1.16458	+	2.01712i
$362$	3.29490	+	12.2967i	0.173176	+	0.646302i
$363$	8.39402	+	5.77804i	0.440572	+	0.303268i
$364$	−0.368803	−	0.0706327i	−0.0193305	−	0.00370216i
$365$		0			0
$366$	4.04191	−	11.3877i	0.211274	−	0.595244i
$367$	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
$372$	9.04296	+	6.22474i	0.468855	+	0.322738i
$373$	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
$378$	0.236929	−	0.977486i	0.0121863	−	0.0502764i
$379$	−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
$381$	−14.3161	−	16.7867i	−0.733435	−	0.860007i
$382$	27.7305	+	27.7305i	1.41882	+	1.41882i
$383$	−0.699279	+	2.60975i	−0.0357315	+	0.133352i	−0.981488	−	0.191526i	$-0.938656\pi$
$383$	−0.699279	+	2.60975i	−0.0357315	+	0.133352i	0.945756	+	0.324878i	$0.105323\pi$
$384$	16.6254	−	14.1786i	0.848412	−	0.723547i
$385$		0			0
$386$	−32.4270	+	18.7218i	−1.65049	+	0.952912i
$387$	8.90678	+	12.2967i	0.452757	+	0.625076i
$388$	−0.0355516	−	0.132680i	−0.00180486	−	0.00673582i
$389$	38.6182			1.95802			0.979011	−	0.203807i	$-0.0653316\pi$
$389$	38.6182			1.95802			0.979011	+	0.203807i	$0.0653316\pi$
$390$		0			0
$391$	−36.1920			−1.83031
$392$	3.33918	+	12.4620i	0.168654	+	0.629426i
$393$	−9.64677	−	20.2628i	−0.486615	−	1.02212i
$394$	−12.8645	+	7.42732i	−0.648104	+	0.374183i
$395$		0			0
$396$	8.79634	+	7.14433i	0.442033	+	0.359016i
$397$	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
$399$	−1.18742	+	1.01266i	−0.0594456	+	0.0506966i
$400$		0			0
$401$	−15.5856	+	26.9950i	−0.778307	+	1.34807i	0.154611	+	0.987975i	$0.450588\pi$
$401$	−15.5856	+	26.9950i	−0.778307	+	1.34807i	−0.932917	+	0.360091i	$0.882746\pi$
$402$	−7.20318	−	4.95832i	−0.359262	−	0.247299i
$403$	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
$408$	−9.46851	+	13.7553i	−0.468761	+	0.680990i
$409$	−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
$414$	5.60898	−	35.0835i	0.275666	−	1.72426i
$415$		0			0
$416$	−11.4099	+	13.1989i	−0.559414	+	0.647130i
$417$	3.76322	−	5.46700i	0.184286	−	0.267720i
$418$	−14.4514	−	53.9335i	−0.706843	−	2.63797i
$419$	−10.9200	+	18.9139i	−0.533476	+	0.924007i	0.465760	+	0.884911i	$0.345781\pi$
$419$	−10.9200	+	18.9139i	−0.533476	+	0.924007i	−0.999235	+	0.0390956i	$0.987552\pi$
$420$		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
$423$	−0.0811457	−	0.782999i	−0.00394544	−	0.0380707i
$424$	−5.07663			−0.246543
$425$		0			0
$426$	−8.42157	+	23.7270i	−0.408027	+	1.14957i
$427$	−0.446818	+	0.119724i	−0.0216230	+	0.00579387i
$428$	−1.07357	+	1.07357i	−0.0518927	+	0.0518927i
$429$	22.1361	+	12.9787i	1.06874	+	0.626616i
$430$		0			0
$431$	−1.35987	+	2.35537i	−0.0655028	+	0.113454i	−0.896917	−	0.442199i	$-0.854198\pi$
$431$	−1.35987	+	2.35537i	−0.0655028	+	0.113454i	0.831414	+	0.555653i	$0.187532\pi$
$432$	−18.7822	−	17.9017i	−0.903661	−	0.861295i
$433$	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
$438$	12.5523	+	0.997073i	0.599774	+	0.0476420i
$439$	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	−0.830230	−	0.557420i	$-0.811791\pi$
$443$	−5.74199	+	5.74199i	−0.272810	+	0.272810i	0.557420	+	0.830230i	$0.311791\pi$
$444$	2.26258	−	6.37461i	0.107377	−	0.302525i
$445$		0			0
$446$	−17.9670	+	10.3733i	−0.850763	+	0.491188i
$447$	−11.6840	+	16.9738i	−0.552633	+	0.802835i
$448$	−0.188132	−	0.0504097i	−0.00888838	−	0.00238163i
$449$	−23.4891	+	13.5614i	−1.10852	+	0.640004i	−0.938446	−	0.345427i	$-0.887734\pi$
$449$	−23.4891	+	13.5614i	−1.10852	+	0.640004i	−0.170074	+	0.985431i	$0.554401\pi$
$450$		0			0
$451$	7.14224	+	12.3707i	0.336315	+	0.582515i
$452$	−7.02763	+	1.88305i	−0.330552	+	0.0885711i
$453$	−8.26530	−	17.3610i	−0.388338	−	0.815693i
$454$		−	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
$459$	23.8153	+	12.9980i	1.11160	+	0.606693i
$460$		0			0
$461$	17.1508	+	29.7061i	0.798792	+	1.38355i	0.920403	+	0.390971i	$0.127861\pi$
$461$	17.1508	+	29.7061i	0.798792	+	1.38355i	−0.121611	+	0.992578i	$0.538806\pi$
$462$	0.109082	−	1.37325i	0.00507496	−	0.0638896i
$463$	−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	0.0875827	−	0.996157i	$-0.472086\pi$
$467$	−19.6345	−	19.6345i	−0.908575	−	0.908575i	−0.996157	+	0.0875827i	$0.972086\pi$
$468$	8.15292	+	5.69289i	0.376869	+	0.263154i
$469$			0.334760i			0.0154578i
$470$		0			0
$471$	4.53900	−	12.7882i	0.209146	−	0.589249i
$472$	1.27621	+	0.341958i	0.0587421	+	0.0157399i
$473$	14.7051	+	14.7051i	0.676140	+	0.676140i
$474$	−10.9093	+	9.30368i	−0.501079	+	0.427332i
$475$		0			0
$476$	−0.543796			−0.0249248
$477$	0.850233	+	8.20415i	0.0389295	+	0.375642i
$478$	−19.0670	+	5.10900i	−0.872107	+	0.233680i
$479$	1.49161	+	0.861181i	0.0681534	+	0.0393484i	0.533689	−	0.845681i	$-0.320805\pi$
$479$	1.49161	+	0.861181i	0.0681534	+	0.0393484i	−0.465536	+	0.885029i	$0.654138\pi$
$480$		0			0
$481$	2.88111	−	15.0435i	0.131367	−	0.685924i
$482$	16.8711	+	16.8711i	0.768456	+	0.768456i
$483$	−1.22803	+	0.584643i	−0.0558771	+	0.0266022i
$484$	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	−0.0115102	−	0.999934i	$-0.503664\pi$
$491$	−19.5711	−	11.2994i	−0.883233	−	0.509935i	−0.871723	+	0.489999i	$0.836997\pi$
$492$	2.37945	+	4.99796i	0.107274	+	0.225325i
$493$	−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
$498$	−0.677520	+	8.52943i	−0.0303604	+	0.382213i
$499$	−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
$501$	10.0269	+	11.7573i	0.447971	+	0.525279i
$502$	20.8208	+	20.8208i	0.929276	+	0.929276i
$503$	−31.9352	−	8.55700i	−1.42392	−	0.381538i	−0.537047	−	0.843553i	$-0.680460\pi$
$503$	−31.9352	−	8.55700i	−1.42392	−	0.381538i	−0.886872	+	0.462015i	$0.847127\pi$
$504$	−0.0990719	+	0.619683i	−0.00441302	+	0.0276029i
$505$		0			0
$506$		−	48.6623i		−	2.16330i
$507$	20.1988	+	9.95022i	0.897062	+	0.441905i
$508$	−8.28006	−	8.28006i	−0.367368	−	0.367368i
$509$	5.25012	+	3.03116i	0.232707	+	0.134354i	0.611820	−	0.790997i	$-0.290438\pi$
$509$	5.25012	+	3.03116i	0.232707	+	0.134354i	−0.379113	+	0.925350i	$0.623771\pi$
$510$		0			0
$511$	−0.241016	−	0.417452i	−0.0106619	−	0.0184670i
$512$	4.04633	−	4.04633i	0.178824	−	0.178824i
$513$	39.6500	−	11.6509i	1.75059	−	0.514398i
$514$	−0.357631	−	0.619435i	−0.0157744	−	0.0273221i
$515$		0			0
$516$	5.22933	+	6.13178i	0.230208	+	0.269936i
$517$	−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	$-0.827554\pi$
$521$		−	23.5394i		−	1.03128i	0.856805	−	0.515640i	$-0.172446\pi$
$522$	16.6857	−	12.0858i	0.730312	−	0.528982i
$523$	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
$528$	−29.2733	−	20.1503i	−1.27396	−	0.876931i
$529$	−21.6892	+	12.5223i	−0.943010	+	0.544447i
$530$		0			0
$531$	0.338887	−	2.11970i	0.0147065	−	0.0919871i
$532$	−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
$537$	−2.73004	+	34.3690i	−0.117810	+	1.48313i
$538$	−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
$543$	−11.6521	+	5.54739i	−0.500041	+	0.238061i
$544$	−12.6331	+	21.8811i	−0.541638	+	0.938145i
$545$		0			0
$546$	0.00809242	−	1.20878i	0.000346324	−	0.0517311i
$547$	−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
$549$	12.0960	+	1.93385i	0.516244	+	0.0825347i
$550$		0			0
$551$	−31.9677			−1.36187
$552$	−1.75534	+	22.0984i	−0.0747124	+	0.940569i
$553$	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	$-0.917420\pi$
$557$	−6.08328	−	22.7031i	−0.257757	−	0.961962i	0.708779	−	0.705431i	$-0.249246\pi$
$558$	−14.4213	+	32.2644i	−0.610501	+	1.36586i
$559$	13.8052	+	11.9339i	0.583896	+	0.504752i
$560$		0			0
$561$	35.0200	+	12.4299i	1.47855	+	0.524791i
$562$	5.96419	+	22.2587i	0.251584	+	0.938926i
$563$	35.8569	+	9.60782i	1.51119	+	0.404921i	0.916829	−	0.399279i	$-0.130740\pi$
$563$	35.8569	+	9.60782i	1.51119	+	0.404921i	0.594358	+	0.804201i	$0.297406\pi$
$564$	−0.0758413	−	0.410870i	−0.00319350	−	0.0173007i
$565$		0			0
$566$	0.973289	+	1.68579i	0.0409104	+	0.0708589i
$567$	1.01804	+	0.0563221i	0.0427537	+	0.00236531i
$568$	4.06580	−	15.1738i	0.170597	−	0.636678i
$569$	6.61515	−	11.4578i	0.277322	−	0.480335i	−0.693397	−	0.720556i	$-0.743887\pi$
$569$	6.61515	−	11.4578i	0.277322	−	0.480335i	0.970718	+	0.240221i	$0.0772199\pi$
$570$		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
$573$	−22.5414	+	32.7469i	−0.941681	+	1.36802i
$574$	0.336457	−	0.582760i	0.0140434	−	0.0243240i
$575$		0			0
$576$	4.00354	+	3.25165i	0.166814	+	0.135485i
$577$	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
$579$	−24.6304	−	28.8810i	−1.02361	−	1.20025i
$580$		0			0
$581$	0.283663	−	0.163773i	0.0117683	−	0.00679444i
$582$	0.399247	−	0.190075i	0.0165493	−	0.00787886i
$583$	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	$0.0535967\pi$
$587$	5.23017	+	19.5193i	0.215872	+	0.805646i	−0.769986	+	0.638061i	$0.779737\pi$
$588$	10.0452	−	4.78237i	0.414258	−	0.197221i
$589$	47.4885	−	27.4175i	1.95673	−	1.12972i
$590$		0			0
$591$	−9.77142	−	11.4577i	−0.401942	−	0.471307i
$592$	−5.49034	+	20.4902i	−0.225651	+	0.842143i
$593$	−3.08282	−	3.08282i	−0.126596	−	0.126596i	0.640970	−	0.767566i	$-0.278532\pi$
$593$	−3.08282	−	3.08282i	−0.126596	−	0.126596i	−0.767566	+	0.640970i	$0.778532\pi$
$594$	−17.4765	+	32.0210i	−0.717071	+	1.31384i
$595$		0			0
$596$	−5.46855	+	9.47180i	−0.224000	+	0.387980i
$597$	19.8921	−	28.8981i	0.814128	−	1.18272i
$598$	−3.09615	−	42.5882i	−0.126611	−	1.74156i
$599$	17.9813			0.734698			0.367349	−	0.930083i	$-0.380266\pi$
$599$	17.9813			0.734698			0.367349	+	0.930083i	$0.380266\pi$
$600$		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
$603$	3.61741	−	8.09314i	0.147312	−	0.329578i
$604$	−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
$609$	−0.743273	−	0.263815i	−0.0301189	−	0.0106903i
$610$		0			0
$611$	−0.310483	−	0.893690i	−0.0125608	−	0.0361548i
$612$	13.1468	+	5.87625i	0.531428	+	0.237533i
$613$	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	−0.333281	−	0.942828i	$-0.608156\pi$
$617$	−27.1576	−	7.27686i	−1.09332	−	0.292955i	−0.760043	+	0.649872i	$0.774822\pi$
$618$	−0.175085	+	2.20418i	−0.00704295	+	0.0886650i
$619$	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
$621$	36.0063	−	0.864283i	1.44488	−	0.0346825i
$622$	−3.92142	+	1.05074i	−0.157235	+	0.0421309i
$623$	0.258967	−	0.258967i	0.0103753	−	0.0103753i
$624$	−26.9014	−	15.7726i	−1.07692	−	0.631410i
$625$		0			0
$626$	24.7792	−	42.9189i	0.990378	−	1.71538i
$627$	51.1063	−	24.3309i	2.04099	−	0.971681i
$628$	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
$633$	−1.00056	+	12.5962i	−0.0397686	+	0.500654i
$634$	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
$639$	−25.2027	−	4.02929i	−0.997005	−	0.159396i
$640$		0			0
$641$	−3.54806	+	2.04848i	−0.140140	+	0.0809099i	−0.568431	−	0.822731i	$-0.692449\pi$
$641$	−3.54806	+	2.04848i	−0.140140	+	0.0809099i	0.428291	+	0.903641i	$0.359116\pi$
$642$	−4.02588	−	2.77122i	−0.158889	−	0.109371i
$643$	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	−0.132836	−	0.991138i	$-0.542409\pi$
$647$	6.30036	−	1.68818i	0.247693	−	0.0663691i	0.380529	+	0.924769i	$0.375742\pi$
$648$	9.09144	−	13.9109i	0.357146	−	0.546470i
$649$		−	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	$-0.722160\pi$
$653$	−11.9894	−	44.7451i	−0.469182	−	1.75101i	0.173454	−	0.984842i	$-0.444507\pi$
$654$	−1.22684	−	1.43856i	−0.0479731	−	0.0562521i
$655$		0			0
$656$	−8.67976	−	15.0338i	−0.338888	−	0.586971i
$657$	1.31582	+	12.6967i	0.0513350	+	0.495347i
$658$	−0.0359145	+	0.0359145i	−0.00140009	+	0.00140009i
$659$	−12.0799	−	20.9230i	−0.470566	−	0.815045i	0.528867	−	0.848705i	$-0.322617\pi$
$659$	−12.0799	−	20.9230i	−0.470566	−	0.815045i	−0.999433	+	0.0336601i	$0.989284\pi$
$660$		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
$663$	31.4396	+	8.65022i	1.22101	+	0.335947i
$664$		−	5.33862i		−	0.207178i
$665$		0			0
$666$	21.5020	+	3.43764i	0.833186	+	0.133206i
$667$	−26.9112	−	7.21084i	−1.04201	−	0.279205i
$668$	5.79933	+	5.79933i	0.224383	+	0.224383i
$669$	−13.6471	−	16.0023i	−0.527628	−	0.618683i
$670$		0			0
$671$	16.7777			0.647694
$672$	−0.0751849	+	0.946517i	−0.00290032	+	0.0365127i
$673$	−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	0.278418	−	0.960460i	$-0.410190\pi$
$677$	−17.7462	−	17.7462i	−0.682043	−	0.682043i	−0.960460	+	0.278418i	$0.910190\pi$
$678$	−10.0676	−	21.1468i	−0.386645	−	0.812138i
$679$	−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	$-0.777894\pi$
$683$	5.71276	−	21.3203i	0.218593	−	0.815798i	0.984871	−	0.173290i	$-0.0554397\pi$
$684$	20.4889	−	7.83079i	0.783413	−	0.299418i
$685$		0			0
$686$	−2.34469	−	1.35371i	−0.0895208	−	0.0516848i
$687$	−13.3226	+	6.34267i	−0.508289	+	0.241988i
$688$	−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
$693$	1.38905	−	0.143953i	0.0527657	−	0.00546834i
$694$	−27.2665			−1.03502
$695$		0			0
$696$	−9.78106	+	8.34152i	−0.370750	+	0.316185i
$697$	12.8354	+	12.8354i	0.486176	+	0.486176i
$698$	9.84754	+	2.63864i	0.372735	+	0.0998740i
$699$	−7.05659	+	19.8812i	−0.266905	+	0.751977i
$700$		0			0
$701$		−	31.3445i		−	1.18386i	−0.805988	−	0.591932i	$-0.798365\pi$
$701$		−	31.3445i		−	1.18386i	0.805988	−	0.591932i	$-0.201635\pi$
$702$	−13.2577	+	29.1360i	−0.500380	+	1.09967i
$703$	−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
$708$	0.0902174	−	1.13576i	0.00339058	−	0.0426846i
$709$	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
$711$	−11.2821	−	9.16330i	−0.423114	−	0.343650i
$712$	−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
$717$	−8.60166	−	18.0676i	−0.321235	−	0.674745i
$718$	−49.3238	+	13.2163i	−1.84075	+	0.493227i
$719$	−14.5548	−	25.2096i	−0.542802	−	0.940160i	−0.998742	−	0.0501495i	$-0.984030\pi$
$719$	−14.5548	−	25.2096i	−0.542802	−	0.940160i	0.455940	−	0.890010i	$-0.349303\pi$
$720$		0			0
$721$	0.0733041	−	0.0423222i	0.00272999	−	0.00157616i
$722$	−73.0360	−	19.5699i	−2.71812	−	0.728318i
$723$	−13.7140	+	19.9230i	−0.510030	+	0.740944i
$724$	−5.93194	+	3.42480i	−0.220459	+	0.127282i
$725$		0			0
$726$	−5.82396	+	16.4084i	−0.216148	+	0.608975i
$727$	−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
$732$	6.48119	+	0.514822i	0.239552	+	0.0190284i
$733$	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
$738$	−14.4315	+	10.4531i	−0.531230	+	0.384782i
$739$	−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
$741$	43.1790	−	24.5455i	1.58622	−	0.901701i
$742$	0.376307	−	0.376307i	0.0138147	−	0.0138147i
$743$	36.3190	−	9.73165i	1.33242	−	0.357020i	0.478801	−	0.877924i	$-0.341072\pi$
$743$	36.3190	−	9.73165i	1.33242	−	0.357020i	0.853615	+	0.520904i	$0.174405\pi$
$744$	7.37570	−	20.7803i	0.270406	−	0.761843i
$745$		0			0
$746$	34.1098			1.24885
$747$	−8.62754	+	0.894111i	−0.315665	+	0.0327138i
$748$	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
$753$	−16.9246	+	24.5872i	−0.616768	+	0.896007i
$754$	16.1934	−	18.7326i	0.589730	−	0.682200i
$755$		0			0
$756$	0.541006	−	0.0129861i	0.0196762	−	0.000472300i
$757$	−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	$0.00710150\pi$
$761$	14.3226	+	24.8075i	0.519195	+	0.899272i	−0.480556	+	0.876964i	$0.659565\pi$
$762$	21.3735	−	31.0503i	0.774282	−	1.12483i
$763$	−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
$768$	25.8464	+	17.7914i	0.932650	+	0.641992i
$769$	−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
$771$	0.551697	−	0.470501i	0.0198689	−	0.0169447i
$772$	−14.2456	−	14.2456i	−0.512711	−	0.512711i
$773$	−9.14659	+	34.1355i	−0.328980	+	1.22777i	0.581270	+	0.813711i	$0.302556\pi$
$773$	−9.14659	+	34.1355i	−0.328980	+	1.22777i	−0.910250	+	0.414059i	$0.864111\pi$
$774$	−16.3555	+	20.1374i	−0.587885	+	0.723823i
$775$		0			0
$776$	−0.238933	+	0.137948i	−0.00857720	+	0.00495205i
$777$	−0.358317	−	0.752634i	−0.0128545	−	0.0270006i
$778$	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
$783$	15.1186	+	14.4098i	0.540293	+	0.514963i
$784$	−30.2159	+	17.4452i	−1.07914	+	0.623042i
$785$		0			0
$786$	29.1753	−	24.8814i	1.04065	−	0.887489i
$787$	−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
$789$	−14.7067	−	17.2447i	−0.523572	−	0.613928i
$790$		0			0
$791$	−0.448293	+	0.776465i	−0.0159394	+	0.0276079i
$792$	9.28803	−	20.7799i	0.330036	−	0.738382i
$793$	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	$0.173087\pi$
$797$	−4.06620	+	15.1753i	−0.144032	+	0.537535i	−0.999797	+	0.0201695i	$0.993579\pi$
$798$	−2.19638	−	1.51188i	−0.0777509	−	0.0535200i
$799$	−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
$804$	1.57381	−	4.43406i	0.0555041	−	0.156377i
$805$		0			0
$806$	−7.98939	+	41.7160i	−0.281414	+	1.46938i
$807$	−1.15168	−	0.792760i	−0.0405410	−	0.0279065i
$808$	−5.79994	−	21.6457i	−0.204041	−	0.761492i
$809$	−9.50547	+	16.4640i	−0.334195	+	0.578842i	−0.983330	−	0.181831i	$-0.941798\pi$
$809$	−9.50547	+	16.4640i	−0.334195	+	0.578842i	0.649135	+	0.760673i	$0.275131\pi$
$810$		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
$813$	18.3896	+	1.46075i	0.644953	+	0.0512307i
$814$	29.8242			1.04534
$815$		0			0
$816$	−42.5589	−	15.1057i	−1.48986	−	0.528806i
$817$	38.8812	−	10.4182i	1.36028	−	0.364486i
$818$	12.6307	−	12.6307i	0.441623	−	0.441623i
$819$	1.20651	−	0.214364i	0.0421588	−	0.00749047i
$820$		0			0
$821$	−0.931007	+	1.61255i	−0.0324924	+	0.0562784i	−0.881814	−	0.471597i	$-0.843678\pi$
$821$	−0.931007	+	1.61255i	−0.0324924	+	0.0562784i	0.849322	+	0.527875i	$0.177011\pi$
$822$	−15.8505	−	33.2935i	−0.552849	−	1.16124i
$823$	−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	−0.802272	−	0.596959i	$-0.796375\pi$
$827$	−5.90430	+	5.90430i	−0.205313	+	0.205313i	0.596959	+	0.802272i	$0.296375\pi$
$828$	19.0144	−	1.97055i	0.660797	−	0.0684813i
$829$	−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
$834$	10.6868	+	3.79313i	0.370053	+	0.131345i
$835$		0			0
$836$	26.0175	−	15.0212i	0.899833	−	0.519519i
$837$	−34.8176	−	8.43932i	−1.20347	−	0.291706i
$838$	−36.0442	−	9.65801i	−1.24513	−	0.333630i
$839$	6.21211	−	3.58656i	0.214466	−	0.123822i	−0.388919	−	0.921272i	$-0.627152\pi$
$839$	6.21211	−	3.58656i	0.214466	−	0.123822i	0.603385	+	0.797450i	$0.293818\pi$
$840$		0			0
$841$	6.42199	+	11.1232i	0.221448	+	0.383559i
$842$	18.6543	−	4.99840i	0.642869	−	0.172256i
$843$	−21.0919	+	10.0415i	−0.726443	+	0.345847i
$844$			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
$849$	−1.50144	+	1.28046i	−0.0515293	+	0.0439454i
$850$		0			0
$851$	−14.7228	−	25.5007i	−0.504692	−	0.874152i
$852$	−13.5040	−	1.07266i	−0.462638	−	0.0367488i
$853$	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	$0.0252723\pi$
$857$	31.5042	+	31.5042i	1.07616	+	1.07616i	0.0793118	+	0.996850i	$0.474728\pi$
$858$	−11.6307	+	42.2724i	−0.397066	+	1.44316i
$859$		−	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
$861$	0.642858	+	0.228174i	0.0219085	+	0.00777615i
$862$	−4.48861	−	1.20272i	−0.152883	−	0.0409648i
$863$	−9.69182	−	9.69182i	−0.329913	−	0.329913i	0.522640	−	0.852553i	$-0.324947\pi$
$863$	−9.69182	−	9.69182i	−0.329913	−	0.329913i	−0.852553	+	0.522640i	$0.824947\pi$
$864$	12.0457	−	22.0705i	0.409804	−	0.750854i
$865$		0			0
$866$	24.2113			0.822732
$867$	17.7211	+	1.40764i	0.601839	+	0.0478060i
$868$	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
$873$	0.262950	+	0.363028i	0.00889949	+	0.0122866i
$874$	−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	0.500400	−	0.865794i	$-0.333186\pi$
$881$	0.0237715	+	0.0137245i	0.000800881	+	0.000462389i	−0.499600	+	0.866257i	$0.666519\pi$
$882$	21.0092	+	29.0053i	0.707418	+	0.976660i
$883$	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	−0.209309	−	0.977849i	$-0.567122\pi$
$887$	2.92906	−	0.784839i	0.0983482	−	0.0263523i	0.307658	+	0.951497i	$0.400455\pi$
$888$	−13.5437	−	1.07582i	−0.454496	−	0.0361021i
$889$	−1.44303			−0.0483976
$890$		0			0
$891$	−35.1372	−	11.5298i	−1.17714	−	0.386264i
$892$	−7.89315	−	7.89315i	−0.264282	−	0.264282i
$893$	−2.01580	−	0.540132i	−0.0674562	−	0.0180748i
$894$	−33.1801	−	11.7768i	−1.10971	−	0.393876i
$895$		0			0
$896$		−	1.42917i		−	0.0477451i
$897$	41.8858	−	10.9233i	1.39853	−	0.364717i
$898$	−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
$903$	0.989992	+	0.0786383i	0.0329449	+	0.00261692i
$904$	7.30666	+	12.6555i	0.243016	+	0.420916i
$905$		0			0
$906$	24.9972	−	21.3182i	0.830477	−	0.708251i
$907$	−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	$0.0252501\pi$
$911$			4.78351i			0.158485i	−0.996855	+	0.0792423i	$0.974750\pi$
$912$	−62.1080	+	29.5686i	−2.05660	+	0.979114i
$913$	−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
$918$	−10.9200	+	45.0521i	−0.360415	+	1.48694i
$919$	−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
$921$	12.1953	+	4.32855i	0.401848	+	0.142631i
$922$	−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
$927$	−2.22953	+	0.231056i	−0.0732274	+	0.00758888i
$928$	−13.7531	+	13.7531i	−0.451467	+	0.451467i
$929$	−27.3742	+	15.8045i	−0.898117	+	0.518528i	−0.876589	−	0.481240i	$-0.840186\pi$
$929$	−27.3742	+	15.8045i	−0.898117	+	0.518528i	−0.0215282	+	0.999768i	$0.506853\pi$
$930$		0			0
$931$		−	55.5706i		−	1.82125i
$932$	−2.89804	+	10.8156i	−0.0949283	+	0.354277i
$933$	−1.76906	−	3.71586i	−0.0579164	−	0.121652i
$934$	23.7216	−	41.0870i	0.776194	−	1.34441i
$935$		0			0
$936$	6.80655	−	18.7771i	0.222479	−	0.613747i
$937$	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
$939$	47.3449	+	16.8045i	1.54504	+	0.548393i
$940$		0			0
$941$	−49.4334			−1.61148			−0.805741	−	0.592268i	$-0.798233\pi$
$941$	−49.4334			−1.61148			−0.805741	+	0.592268i	$0.798233\pi$
$942$	23.1126	+	1.83591i	0.753048	+	0.0598171i
$943$	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	$-0.953218\pi$
$947$	−6.33163	−	23.6300i	−0.205750	−	0.767871i	0.783469	−	0.621431i	$-0.213448\pi$
$948$	−6.35443	−	4.37408i	−0.206382	−	0.142064i
$949$	5.03464	+	14.4916i	0.163431	+	0.470419i
$950$		0			0
$951$	−19.5858	+	55.1811i	−0.635114	+	1.78937i
$952$	0.282693	+	1.05503i	0.00916215	+	0.0341936i
$953$	−41.7321	−	11.1821i	−1.35184	−	0.362223i	−0.491024	−	0.871146i	$-0.663377\pi$
$953$	−41.7321	−	11.1821i	−1.35184	−	0.362223i	−0.860812	+	0.508923i	$0.830044\pi$
$954$	−13.1640	+	5.03122i	−0.426199	+	0.162892i
$955$		0			0
$956$	−5.31043	−	9.19793i	−0.171751	−	0.297482i
$957$	23.5632	+	16.2198i	0.761691	+	0.524312i
$958$	−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
$963$	2.02178	−	4.52328i	0.0651510	−	0.145761i
$964$	−6.41870	+	11.1175i	−0.206732	+	0.358071i
$965$		0			0
$966$	−1.50794	−	1.76817i	−0.0485170	−	0.0568898i
$967$	−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
$969$	54.7281	−	46.6735i	1.75812	−	1.49937i
$970$		0			0
$971$	51.2257	−	29.5752i	1.64391	−	0.949113i	0.664488	−	0.747299i	$-0.268650\pi$
$971$	51.2257	−	29.5752i	1.64391	−	0.949113i	0.979424	−	0.201814i	$-0.0646838\pi$
$972$	−13.2197	−	5.53215i	−0.424021	−	0.177444i
$973$	−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	$0.294063\pi$
$977$	14.9944	+	55.9598i	0.479713	+	1.79031i	−0.123059	+	0.992399i	$0.539270\pi$
$978$	15.5921	+	32.7508i	0.498580	+	1.04725i
$979$	−11.5036	+	6.64164i	−0.367658	+	0.212268i
$980$		0			0
$981$	1.20833	−	1.48773i	0.0385789	−	0.0474995i
$982$	9.99359	−	37.2966i	0.318908	−	1.19018i
$983$	17.2893	+	17.2893i	0.551443	+	0.551443i	0.926857	−	0.375414i	$-0.122500\pi$
$983$	17.2893	+	17.2893i	0.551443	+	0.551443i	−0.375414	+	0.926857i	$0.622500\pi$
$984$	8.45965	−	7.21460i	0.269684	−	0.229993i
$985$		0			0
$986$	17.9295	−	31.0548i	0.570991	−	0.988985i
$987$	−0.0424114	−	0.0291940i	−0.00134997	−	0.000929254i
$988$	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
$993$	−13.6952	+	19.8956i	−0.434602	+	0.631367i
$994$	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
$999$	0.529703	+	22.0676i	0.0167591	+	0.698189i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.6	✓	96	15.8	even	4
195.2.bf.a.17.19	yes	96	5.3	odd	4
195.2.bf.a.23.6	yes	96	65.49	even	6
195.2.bf.a.23.19	yes	96	195.179	odd	6
195.2.bf.a.62.6	yes	96	195.23	even	12
195.2.bf.a.62.19	yes	96	65.23	odd	12
195.2.bf.a.173.6	yes	96	5.4	even	2
195.2.bf.a.173.19	yes	96	15.14	odd	2
975.2.bn.d.218.6		96	39.23	odd	6	inner
975.2.bn.d.218.19		96	13.10	even	6	inner
975.2.bn.d.257.6		96	65.62	odd	12	inner
975.2.bn.d.257.19		96	195.62	even	12	inner
975.2.bn.d.368.6		96	3.2	odd	2	inner
975.2.bn.d.368.19		96	1.1	even	1	trivial
975.2.bn.d.407.6		96	5.2	odd	4	inner
975.2.bn.d.407.19		96	15.2	even	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} +(-1.56387 + 0.744530i) q^{3} +(-0.796141 + 0.459652i) q^{4} +(-1.92033 - 2.25172i) q^{6} +(-0.0293212 + 0.109428i) q^{7} +(1.30565 + 1.30565i) q^{8} +(1.89135 - 2.32869i) q^{9} +(2.05447 - 3.55845i) q^{11} +(0.902832 - 1.31159i) q^{12} +(1.57162 - 3.24500i) q^{13} -0.193564 q^{14} +(-2.49674 + 4.32449i) q^{16} +(1.35141 - 5.04353i) q^{17} +(4.67961 + 2.09165i) 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} +(-3.01397 - 1.06977i) q^{24} +(6.05047 + 1.15878i) q^{26} +(-1.22403 + 5.04992i) q^{27} +(-0.0269551 - 0.100598i) q^{28} +(2.00973 - 3.48095i) q^{29} +6.89468i q^{31} +(-4.67403 - 1.25240i) q^{32} +(-0.563544 + 7.09456i) q^{33} +8.92135 q^{34} +(-0.435393 + 2.72333i) q^{36} +(4.10339 - 1.09950i) q^{37} +(9.60880 - 9.60880i) q^{38} +(-0.0418074 + 6.24486i) q^{39} +(-1.73822 + 3.01068i) q^{41} +(0.302709 - 0.144115i) q^{42} +(-1.30993 + 4.88872i) q^{43} +3.77737i q^{44} +(10.2563 - 5.92150i) q^{46} +(0.185543 - 0.185543i) q^{47} +(0.684859 - 8.62182i) 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} +(-8.87558 + 0.213046i) q^{54} +(-0.181159 + 0.104592i) q^{56} +(11.3470 + 7.81074i) 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} +(0.199368 + 0.275247i) q^{63} +1.71922i q^{64} +(-11.9579 + 2.20728i) q^{66} +(2.85424 - 0.764792i) q^{67} +(1.24236 + 4.63654i) q^{68} +(7.79036 + 9.13477i) q^{69} +(-4.25380 - 7.36780i) q^{71} +(5.50991 - 0.571017i) 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} +(-10.3249 + 2.69259i) q^{78} -4.84485i q^{79} +(-1.84560 - 8.80873i) q^{81} +(-5.73743 - 1.53734i) q^{82} +(-2.04442 - 2.04442i) q^{83} +(0.117052 + 0.137253i) q^{84} -8.64751 q^{86} +(-0.551270 + 6.94004i) 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} +(-5.13330 - 10.7823i) 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

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