LMFDB - Embedded newform 975.2.bn.d.407.19

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			407.19
Character	$\chi$	$=$	975.407
Dual form			975.2.bn.d.218.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.65038 - 0.442218i) q^{2} +(0.137150 + 1.72661i) q^{3} +(0.796141 - 0.459652i) q^{4} +(0.989888 + 2.78891i) q^{6} +(-0.109428 - 0.0293212i) q^{7} +(-1.30565 + 1.30565i) q^{8} +(-2.96238 + 0.473611i) q^{9} +(-2.05447 + 3.55845i) q^{11} +(0.902832 + 1.31159i) q^{12} +(-3.24500 - 1.57162i) q^{13} -0.193564 q^{14} +(-2.49674 + 4.32449i) q^{16} +(-5.04353 - 1.35141i) q^{17} +(-4.67961 + 2.09165i) q^{18} +(3.97662 + 6.88771i) q^{19} +(0.0356182 - 0.192962i) q^{21} +(-1.81705 + 6.78132i) q^{22} +(6.69524 - 1.79398i) q^{23} +(-2.43343 - 2.07529i) q^{24} +(-6.05047 - 1.15878i) q^{26} +(-1.22403 - 5.04992i) q^{27} +(-0.100598 + 0.0269551i) q^{28} +(2.00973 - 3.48095i) q^{29} +6.89468i q^{31} +(-1.25240 + 4.67403i) q^{32} +(-6.42584 - 3.05924i) q^{33} -8.92135 q^{34} +(-2.14078 + 1.73873i) q^{36} +(1.09950 + 4.10339i) q^{37} +(9.60880 + 9.60880i) q^{38} +(2.26853 - 5.81840i) q^{39} +(1.73822 - 3.01068i) q^{41} +(-0.0265474 - 0.334211i) q^{42} +(4.88872 + 1.30993i) q^{43} +3.77737i q^{44} +(10.2563 - 5.92150i) q^{46} +(-0.185543 - 0.185543i) q^{47} +(-7.80914 - 3.71780i) q^{48} +(-6.05106 - 3.49358i) q^{49} +(1.64164 - 8.89356i) q^{51} +(-3.30587 + 0.240337i) q^{52} +(-1.94409 - 1.94409i) q^{53} +(-4.25328 - 7.79300i) q^{54} +(0.181159 - 0.104592i) q^{56} +(-11.3470 + 7.81074i) q^{57} +(1.77747 - 6.63362i) q^{58} +(0.619675 - 0.357770i) q^{59} +(2.04160 + 3.53616i) q^{61} +(3.04895 + 11.3788i) q^{62} +(0.338055 + 0.0350341i) q^{63} -1.71922i q^{64} +(-11.9579 - 2.20728i) q^{66} +(0.764792 + 2.85424i) q^{67} +(-4.63654 + 1.24236i) q^{68} +(4.01577 + 11.3140i) q^{69} +(4.25380 + 7.36780i) q^{71} +(3.24947 - 4.48621i) 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} +(1.17093 - 10.6057i) q^{78} +4.84485i q^{79} +(8.55139 - 2.80603i) q^{81} +(1.53734 - 5.73743i) q^{82} +(2.04442 - 2.04442i) q^{83} +(-0.0603381 - 0.169997i) q^{84} +8.64751 q^{86} +(6.28589 + 2.99261i) q^{87} +(-1.96368 - 7.32854i) q^{88} +(-2.79966 - 1.61638i) q^{89} +(0.309013 + 0.267127i) q^{91} +(4.50574 - 4.50574i) q^{92} +(-11.9044 + 0.945607i) q^{93} +(-0.388267 - 0.224166i) q^{94} +(-8.24201 - 1.52137i) q^{96} +(-0.144327 - 0.0386722i) q^{97} +(-11.5315 - 3.08985i) 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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.65038	−	0.442218i	1.16699	−	0.312695i	0.377238	−	0.926116i	$-0.376874\pi$
$2$	1.65038	−	0.442218i	1.16699	−	0.312695i	0.789756	+	0.613421i	$0.210207\pi$
$3$	0.137150	+	1.72661i	0.0791838	+	0.996860i
$3$	0.137150	+	1.72661i	0.0791838	+	0.996860i
$4$	0.796141	−	0.459652i	0.398071	−	0.229826i
$5$		0			0
$5$		0			0
$6$	0.989888	+	2.78891i	0.404120	+	1.13857i
$7$	−0.109428	−	0.0293212i	−0.0413600	−	0.0110824i	0.238080	−	0.971246i	$-0.423482\pi$
$7$	−0.109428	−	0.0293212i	−0.0413600	−	0.0110824i	−0.279440	+	0.960163i	$0.590149\pi$
$8$	−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	$0.954023\pi$
$12$	0.902832	+	1.31159i	0.260625	+	0.378622i
$13$	−3.24500	−	1.57162i	−0.900000	−	0.435890i
$13$	−3.24500	−	1.57162i	−0.900000	−	0.435890i
$14$	−0.193564			−0.0517323
$15$		0			0
$16$	−2.49674	+	4.32449i	−0.624186	+	1.08112i
$17$	−5.04353	−	1.35141i	−1.22324	−	0.327765i	−0.411293	−	0.911503i	$-0.634923\pi$
$17$	−5.04353	−	1.35141i	−1.22324	−	0.327765i	−0.811942	+	0.583738i	$0.801589\pi$
$18$	−4.67961	+	2.09165i	−1.10299	+	0.493007i
$19$	3.97662	+	6.88771i	0.912300	+	1.58015i	0.810807	+	0.585313i	$0.199029\pi$
$19$	3.97662	+	6.88771i	0.912300	+	1.58015i	0.101493	+	0.994836i	$0.467638\pi$
$20$		0			0
$21$	0.0356182	−	0.192962i	0.00777254	−	0.0421077i
$22$	−1.81705	+	6.78132i	−0.387396	+	1.44578i
$23$	6.69524	−	1.79398i	1.39605	−	0.374071i	0.519127	−	0.854697i	$-0.326257\pi$
$23$	6.69524	−	1.79398i	1.39605	−	0.374071i	0.876926	+	0.480625i	$0.159590\pi$
$24$	−2.43343	−	2.07529i	−0.496722	−	0.423616i
$25$		0			0
$26$	−6.05047	−	1.15878i	−1.18659	−	0.227255i
$27$	−1.22403	−	5.04992i	−0.235565	−	0.971858i
$28$	−0.100598	+	0.0269551i	−0.0190112	+	0.00509404i
$29$	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	$0.787473\pi$
$32$	−1.25240	+	4.67403i	−0.221396	+	0.826260i
$33$	−6.42584	−	3.05924i	−1.11860	−	0.532545i
$34$	−8.92135			−1.53000
$35$		0			0
$36$	−2.14078	+	1.73873i	−0.356796	+	0.289788i
$37$	1.09950	+	4.10339i	0.180757	+	0.674593i	0.995499	+	0.0947700i	$0.0302116\pi$
$37$	1.09950	+	4.10339i	0.180757	+	0.674593i	−0.814743	+	0.579823i	$0.803122\pi$
$38$	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	$0.0791589\pi$
$42$	−0.0265474	−	0.334211i	−0.00409636	−	0.0515698i
$43$	4.88872	+	1.30993i	0.745523	+	0.199762i	0.611531	−	0.791220i	$-0.290554\pi$
$43$	4.88872	+	1.30993i	0.745523	+	0.199762i	0.133991	+	0.990982i	$0.457221\pi$
$44$			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	$-0.256092\pi$
$47$	−0.185543	−	0.185543i	−0.0270642	−	0.0270642i	−0.720509	+	0.693445i	$0.756092\pi$
$48$	−7.80914	−	3.71780i	−1.12715	−	0.536619i
$49$	−6.05106	−	3.49358i	−0.864438	−	0.499083i
$50$		0			0
$51$	1.64164	−	8.89356i	0.229875	−	1.24535i
$52$	−3.30587	+	0.240337i	−0.458442	+	0.0333287i
$53$	−1.94409	−	1.94409i	−0.267042	−	0.267042i	0.560865	−	0.827907i	$-0.310469\pi$
$53$	−1.94409	−	1.94409i	−0.267042	−	0.267042i	−0.827907	+	0.560865i	$0.810469\pi$
$54$	−4.25328	−	7.79300i	−0.578799	−	1.06049i
$55$		0			0
$56$	0.181159	−	0.104592i	0.0242084	−	0.0139767i
$57$	−11.3470	+	7.81074i	−1.50295	+	1.03456i
$58$	1.77747	−	6.63362i	0.233394	−	0.871037i
$59$	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	$0.749149\pi$
$62$	3.04895	+	11.3788i	0.387217	+	1.44511i
$63$	0.338055	+	0.0350341i	0.0425909	+	0.00441389i
$64$		−	1.71922i		−	0.214903i
$65$		0			0
$66$	−11.9579	−	2.20728i	−1.47192	−	0.271697i
$67$	0.764792	+	2.85424i	0.0934343	+	0.348701i	0.996777	−	0.0802172i	$-0.0255614\pi$
$67$	0.764792	+	2.85424i	0.0934343	+	0.348701i	−0.903343	+	0.428919i	$0.858895\pi$
$68$	−4.63654	+	1.24236i	−0.562263	+	0.150658i
$69$	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	$0.664887\pi$
$72$	3.24947	−	4.48621i	0.382954	−	0.528705i
$73$	3.00868	+	3.00868i	0.352139	+	0.352139i	0.860905	−	0.508766i	$-0.169898\pi$
$73$	3.00868	+	3.00868i	0.352139	+	0.352139i	−0.508766	+	0.860905i	$0.669898\pi$
$74$	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
$78$	1.17093	−	10.6057i	0.132582	−	1.20086i
$79$			4.84485i			0.545088i	0.962143	+	0.272544i	$0.0878650\pi$
$79$			4.84485i			0.545088i	−0.962143	+	0.272544i	$0.912135\pi$
$80$		0			0
$81$	8.55139	−	2.80603i	0.950154	−	0.311781i
$82$	1.53734	−	5.73743i	0.169771	−	0.633593i
$83$	2.04442	−	2.04442i	0.224405	−	0.224405i	−0.585946	−	0.810350i	$-0.699277\pi$
$83$	2.04442	−	2.04442i	0.224405	−	0.224405i	0.810350	+	0.585946i	$0.199277\pi$
$84$	−0.0603381	−	0.169997i	−0.00658343	−	0.0185482i
$85$		0			0
$86$	8.64751			0.932485
$87$	6.28589	+	2.99261i	0.673918	+	0.320841i
$88$	−1.96368	−	7.32854i	−0.209329	−	0.781225i
$89$	−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
$93$	−11.9044	+	0.945607i	−1.23443	+	0.0980549i
$94$	−0.388267	−	0.224166i	−0.0400466	−	0.0231209i
$95$		0			0
$96$	−8.24201	−	1.52137i	−0.841196	−	0.155274i
$97$	−0.144327	−	0.0386722i	−0.0146542	−	0.00392657i	0.251485	−	0.967861i	$-0.419081\pi$
$97$	−0.144327	−	0.0386722i	−0.0146542	−	0.00392657i	−0.266139	+	0.963935i	$0.585748\pi$
$98$	−11.5315	−	3.08985i	−1.16485	−	0.312122i
$99$	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	$0.460319\pi$
$102$	−1.22357	−	15.4037i	−0.121151	−	1.52519i
$103$	−0.528320	+	0.528320i	−0.0520569	+	0.0520569i	−0.732656	−	0.680599i	$-0.761720\pi$
$103$	−0.528320	+	0.528320i	−0.0520569	+	0.0520569i	0.680599	+	0.732656i	$0.261720\pi$
$104$	6.28884	−	2.18485i	0.616671	−	0.214242i
$105$		0			0
$106$	−4.06820	−	2.34878i	−0.395139	−	0.228133i
$107$	−0.427445	−	1.59525i	−0.0413227	−	0.154218i	0.942182	−	0.335102i	$-0.108771\pi$
$107$	−0.427445	−	1.59525i	−0.0413227	−	0.154218i	−0.983504	+	0.180884i	$0.942104\pi$
$108$	−3.29571	−	3.45782i	−0.317130	−	0.332729i
$109$	−0.638870			−0.0611926			−0.0305963	−	0.999532i	$-0.509741\pi$
$109$	−0.638870			−0.0611926			−0.0305963	+	0.999532i	$0.509741\pi$
$110$		0			0
$111$	−6.93416	+	2.46119i	−0.658162	+	0.233606i
$112$	0.400014	−	0.400014i	0.0377977	−	0.0377977i
$113$	−2.04834	+	7.64451i	−0.192692	+	0.719135i	0.800161	+	0.599786i	$0.204747\pi$
$113$	−2.04834	+	7.64451i	−0.192692	+	0.719135i	−0.992852	+	0.119349i	$0.961919\pi$
$114$	−15.2728	+	17.9085i	−1.43043	+	1.67729i
$115$		0			0
$116$		−	3.69510i		−	0.343082i
$117$	10.3572	+	3.11888i	0.957528	+	0.288340i
$118$	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
$123$	5.43667	+	2.58831i	0.490208	+	0.233380i
$124$	3.16915	+	5.48913i	0.284598	+	0.492939i
$125$		0			0
$126$	0.573411	−	0.0916742i	0.0510835	−	0.00816699i
$127$	−12.3036	+	3.29674i	−1.09177	+	0.292539i	−0.759409	−	0.650614i	$-0.774512\pi$
$127$	−12.3036	+	3.29674i	−1.09177	+	0.292539i	−0.332361	+	0.943152i	$0.607845\pi$
$128$	−3.26508	−	12.1854i	−0.288595	−	1.07705i
$129$	−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	$-0.191519\pi$
$132$	−6.52206	+	0.518068i	−0.567673	+	0.0450921i
$133$	−0.233199	−	0.870310i	−0.0202209	−	0.0754655i
$134$	2.52439	+	4.37238i	0.218074	+	0.377716i
$135$		0			0
$136$	8.34958	−	4.82063i	0.715970	−	0.413366i
$137$	3.22490	−	12.0355i	0.275522	−	1.02826i	−0.679969	−	0.733241i	$-0.738007\pi$
$137$	3.22490	−	12.0355i	0.275522	−	1.02826i	0.955491	−	0.295021i	$-0.0953267\pi$
$138$	11.6308	+	16.8966i	0.990079	+	1.43833i
$139$	3.31851	−	1.91594i	0.281472	−	0.162508i	−0.352618	−	0.935767i	$-0.614708\pi$
$139$	3.31851	−	1.91594i	0.281472	−	0.162508i	0.634090	+	0.773260i	$0.281375\pi$
$140$		0			0
$141$	0.294914	−	0.345808i	0.0248362	−	0.0291223i
$142$	10.2785	+	10.2785i	0.862557	+	0.862557i
$143$	12.2593	−	8.31831i	1.02517	−	0.695612i
$144$	5.34818	−	13.9933i	0.445682	−	1.16610i
$145$		0			0
$146$	6.29594	+	3.63496i	0.521056	+	0.300832i
$147$	5.20216	−	10.9270i	0.429067	−	0.901243i
$148$	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	$0.850815\pi$
$152$	−14.1851	−	3.80088i	−1.15056	−	0.308292i
$153$	15.5809	+	1.61472i	1.25964	+	0.130542i
$154$	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	0.450598	−	0.892727i	$-0.351211\pi$
$157$	−5.53986	−	5.53986i	−0.442129	−	0.442129i	−0.892727	+	0.450598i	$0.851211\pi$
$158$	2.14248	+	7.99583i	0.170446	+	0.636114i
$159$	3.09006	−	3.62333i	0.245058	−	0.287349i
$160$		0			0
$161$	−0.785250			−0.0618864
$162$	12.8721	−	8.41259i	1.01133	−	0.660955i
$163$	−3.17233	+	11.8393i	−0.248476	+	0.927326i	0.723128	+	0.690714i	$0.242704\pi$
$163$	−3.17233	+	11.8393i	−0.248476	+	0.927326i	−0.971604	+	0.236612i	$0.923963\pi$
$164$		−	3.19590i		−	0.249558i
$165$		0			0
$166$	2.46999	−	4.27815i	0.191708	−	0.332049i
$167$	−8.61742	+	2.30903i	−0.666836	+	0.178678i	−0.576329	−	0.817218i	$-0.695515\pi$
$167$	−8.61742	+	2.30903i	−0.666836	+	0.178678i	−0.0905069	+	0.995896i	$0.528849\pi$
$168$	0.205436	+	0.298446i	0.0158497	+	0.0230256i
$169$	8.06000	+	10.1998i	0.620000	+	0.784602i
$170$		0			0
$171$	−15.0424	−	18.5206i	−1.15032	−	1.41631i
$172$	4.49422	−	1.20422i	0.342681	−	0.0918211i
$173$	−2.27704	+	8.49801i	−0.173120	+	0.646092i	0.823744	+	0.566961i	$0.191881\pi$
$173$	−2.27704	+	8.49801i	−0.173120	+	0.646092i	−0.996864	+	0.0791307i	$0.974786\pi$
$174$	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
$178$	−5.33529	−	1.42959i	−0.399897	−	0.107152i
$179$	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	$0.410690\pi$
$182$	0.628116	+	0.304210i	0.0465590	+	0.0225496i
$183$	−5.82556	+	4.01004i	−0.430638	+	0.296430i
$184$	−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
$188$	−0.233004	−	0.0624332i	−0.0169935	−	0.00455341i
$189$	−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	$0.645221\pi$
$192$	2.96843	−	0.235792i	0.214228	−	0.0170168i
$193$	21.1680	−	5.67196i	1.52371	−	0.408276i	0.602748	−	0.797932i	$-0.294072\pi$
$193$	21.1680	−	5.67196i	1.52371	−	0.408276i	0.920961	+	0.389655i	$0.127406\pi$
$194$	−0.255295			−0.0183291
$195$		0			0
$196$	−6.42333			−0.458810
$197$	8.39781	−	2.25019i	0.598319	−	0.160319i	0.0530668	−	0.998591i	$-0.483100\pi$
$197$	8.39781	−	2.25019i	0.598319	−	0.160319i	0.545253	+	0.838272i	$0.316434\pi$
$198$	2.17108	−	20.9494i	0.154292	−	1.48881i
$199$	17.5413	−	10.1275i	1.24347	−	0.717919i	0.273673	−	0.961823i	$-0.411761\pi$
$199$	17.5413	−	10.1275i	1.24347	−	0.717919i	0.969799	+	0.243904i	$0.0784282\pi$
$200$		0			0
$201$	−4.82328	+	1.71196i	−0.340208	+	0.120752i
$202$	20.0294	+	5.36686i	1.40926	+	0.377611i
$203$	−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
$207$	−18.9842	+	8.48540i	−1.31949	+	0.589776i
$208$	14.8984	−	10.1090i	1.03302	−	0.700934i
$209$	−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	$0.0858692\pi$
$212$	−2.44138	−	0.654166i	−0.167675	−	0.0449283i
$213$	−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
$217$	0.202160	−	0.754473i	0.0137235	−	0.0512169i
$218$	−1.05438	+	0.282519i	−0.0714114	+	0.0191346i
$219$	−4.78218	+	5.60746i	−0.323149	+	0.378917i
$220$		0			0
$221$	14.2423	+	12.3118i	0.958043	+	0.828184i
$222$	−10.3556	+	7.12830i	−0.695023	+	0.478420i
$223$	11.7287	−	3.14269i	0.785411	−	0.210450i	0.156242	−	0.987719i	$-0.450062\pi$
$223$	11.7287	−	3.14269i	0.785411	−	0.210450i	0.629169	+	0.777268i	$0.283395\pi$
$224$	0.274097	−	0.474749i	0.0183139	−	0.0317205i
$225$		0			0
$226$			13.5221i			0.899479i
$227$	−3.58919	+	13.3950i	−0.238223	+	0.889061i	0.738446	+	0.674312i	$0.235560\pi$
$227$	−3.58919	+	13.3950i	−0.238223	+	0.889061i	−0.976669	+	0.214748i	$0.931107\pi$
$228$	−5.44360	+	11.4341i	−0.360511	+	0.757244i
$229$	−8.51901			−0.562952			−0.281476	−	0.959568i	$-0.590824\pi$
$229$	−8.51901			−0.562952			−0.281476	+	0.959568i	$0.590824\pi$
$230$		0			0
$231$	0.613468	+	0.523181i	0.0403633	+	0.0344228i
$232$	1.92091	+	7.16892i	0.126114	+	0.470663i
$233$	8.61258	+	8.61258i	0.564229	+	0.564229i	0.930506	−	0.366277i	$-0.119368\pi$
$233$	8.61258	+	8.61258i	0.564229	+	0.564229i	−0.366277	+	0.930506i	$0.619368\pi$
$234$	18.4726	+	0.567169i	1.20759	+	0.0370770i
$235$		0			0
$236$	0.328899	−	0.569670i	0.0214095	−	0.0370824i
$237$	−8.36517	+	0.664473i	−0.543376	+	0.0431621i
$238$	0.976248	+	0.261585i	0.0632807	+	0.0169560i
$239$			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
$243$	6.01775	+	14.3801i	0.386039	+	0.922482i
$244$	3.25080	+	1.87685i	0.208111	+	0.120153i
$245$		0			0
$246$	10.1172	+	1.86750i	0.645047	+	0.119067i
$247$	−2.07924	−	28.6004i	−0.132299	−	1.81980i
$248$	−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	$0.516380\pi$
$252$	0.285243	−	0.127496i	0.0179686	−	0.00803147i
$253$	−7.37138	+	27.5104i	−0.463435	+	1.72956i
$254$	−18.8477	+	10.8818i	−1.18261	+	0.682782i
$255$		0			0
$256$	−9.05800	−	15.6889i	−0.566125	−	0.980557i
$257$	0.108348	+	0.404361i	0.00675857	+	0.0252233i	0.969223	−	0.246185i	$-0.0791772\pi$
$257$	0.108348	+	0.404361i	0.00675857	+	0.0252233i	−0.962464	+	0.271409i	$0.912511\pi$
$258$	1.18601	+	14.9309i	0.0738377	+	0.929557i
$259$		−	0.481265i		−	0.0299044i
$260$		0			0
$261$	−4.30496	+	11.2637i	−0.266470	+	0.697207i
$262$	−5.72975	−	21.3837i	−0.353985	−	1.32109i
$263$	−12.6393	+	3.38670i	−0.779374	+	0.208833i	−0.626509	−	0.779414i	$-0.715517\pi$
$263$	−12.6393	+	3.38670i	−0.779374	+	0.208833i	−0.152865	+	0.988247i	$0.548850\pi$
$264$	12.3842	−	4.39562i	0.762197	−	0.270532i
$265$		0			0
$266$	−0.769733	−	1.33322i	−0.0471953	−	0.0817447i
$267$	2.40689	−	5.05561i	0.147299	−	0.309398i
$268$	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
$273$	−0.418844	+	0.570181i	−0.0253496	+	0.0345089i
$274$		−	21.2892i		−	1.28613i
$275$		0			0
$276$	8.39764	+	7.16171i	0.505478	+	0.431084i
$277$	−7.38713	+	27.5691i	−0.443849	+	1.65647i	0.275107	+	0.961414i	$0.411287\pi$
$277$	−7.38713	+	27.5691i	−0.443849	+	1.65647i	−0.718957	+	0.695055i	$0.755380\pi$
$278$	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	$0.631784\pi$
$282$	0.333797	−	0.701130i	0.0198773	−	0.0417517i
$283$	−0.294869	−	1.10046i	−0.0175281	−	0.0654158i	0.956608	−	0.291379i	$-0.0941139\pi$
$283$	−0.294869	−	1.10046i	−0.0175281	−	0.0654158i	−0.974136	+	0.225963i	$0.927447\pi$
$284$	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
$288$	1.49642	−	14.4394i	0.0881774	−	0.850850i
$289$	8.88844	+	5.13174i	0.522850	+	0.301867i
$290$		0			0
$291$	0.0469775	−	0.254500i	0.00275387	−	0.0149191i
$292$	3.77827	+	1.01239i	0.221107	+	0.0592454i
$293$	−7.29093	−	1.95360i	−0.425941	−	0.114130i	0.0394794	−	0.999220i	$-0.487430\pi$
$293$	−7.29093	−	1.95360i	−0.425941	−	0.114130i	−0.465420	+	0.885090i	$0.654097\pi$
$294$	3.75342	−	20.3341i	0.218904	−	1.18591i
$295$		0			0
$296$	−6.79317	−	3.92204i	−0.394845	−	0.227964i
$297$	20.4847	+	6.01927i	1.18864	+	0.349274i
$298$	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
$302$	4.90922	+	18.3214i	0.282494	+	1.05428i
$303$	−9.03580	+	18.9794i	−0.519093	+	1.09034i
$304$	−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	$-0.681610\pi$
$307$	5.28300	−	5.28300i	0.301517	−	0.301517i	0.841607	+	0.540090i	$0.181610\pi$
$308$	0.110757	−	0.413352i	0.00631098	−	0.0235529i
$309$	−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	$-0.0214599\pi$
$312$	4.63490	+	10.5587i	0.262400	+	0.597770i
$313$	−20.5099	+	20.5099i	−1.15929	+	1.15929i	−0.174659	+	0.984629i	$0.555882\pi$
$313$	−20.5099	+	20.5099i	−1.15929	+	1.15929i	−0.984629	+	0.174659i	$0.944118\pi$
$314$	−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	−0.893450	−	0.449162i	$-0.851723\pi$
$317$	−23.9045	−	23.9045i	−1.34261	−	1.34261i	−0.449162	−	0.893450i	$-0.648277\pi$
$318$	3.49747	−	7.34634i	0.196128	−	0.411962i
$319$	8.25787	+	14.3030i	0.462352	+	0.800817i
$320$		0			0
$321$	2.69575	−	0.956821i	0.150462	−	0.0534045i
$322$	−1.29596	+	0.347251i	−0.0722210	+	0.0193516i
$323$	−10.7481	−	40.1124i	−0.598040	−	2.23191i
$324$	5.51831	−	6.16466i	0.306573	−	0.342481i
$325$		0			0
$326$			20.9422i			1.15988i
$327$	−0.0876212	−	1.10308i	−0.00484546	−	0.0610005i
$328$	1.66140	+	6.20041i	0.0917352	+	0.342361i
$329$	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	$0.208140\pi$
$332$	0.687925	−	2.56737i	0.0377548	−	0.140903i
$333$	−5.20054	−	11.6351i	−0.284988	−	0.637597i
$334$	−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	0.773922	−	0.633281i	$-0.218292\pi$
$337$	2.58183	+	2.58183i	0.140641	+	0.140641i	−0.633281	+	0.773922i	$0.718292\pi$
$338$	17.8126	+	13.2693i	0.968877	+	0.721754i
$339$	−13.4800	−	2.48824i	−0.732135	−	0.135143i
$340$		0			0
$341$	−24.5344	−	14.1649i	−1.32861	−	0.767074i
$342$	−33.0157	−	23.9141i	−1.78529	−	1.29313i
$343$	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
$347$	15.4146	+	4.13034i	0.827500	+	0.221728i	0.647623	−	0.761961i	$-0.275763\pi$
$347$	15.4146	+	4.13034i	0.827500	+	0.221728i	0.179877	+	0.983689i	$0.442430\pi$
$348$	6.38001	−	0.506785i	0.342004	−	0.0271665i
$349$	−2.98342	+	5.16743i	−0.159699	+	0.276606i	−0.934760	−	0.355280i	$-0.884386\pi$
$349$	−2.98342	+	5.16743i	−0.159699	+	0.276606i	0.775061	+	0.631886i	$0.217719\pi$
$350$		0			0
$351$	−3.96459	+	18.3107i	−0.211614	+	0.977353i
$352$	−14.0593	−	14.0593i	−0.749363	−	0.749363i
$353$	−3.22389	−	12.0317i	−0.171590	−	0.640383i	−0.997107	−	0.0760061i	$-0.975783\pi$
$353$	−3.22389	−	12.0317i	−0.171590	−	0.640383i	0.825517	−	0.564377i	$-0.190884\pi$
$354$	1.61120	+	1.37407i	0.0856342	+	0.0730309i
$355$		0			0
$356$	−2.97190			−0.157510
$357$	−0.440412	+	0.925073i	−0.0233091	+	0.0489600i
$358$	8.80254	−	32.8515i	0.465229	−	1.73626i
$359$			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
$362$	12.2967	−	3.29490i	0.646302	−	0.173176i
$363$	8.39402	−	5.77804i	0.440572	−	0.303268i
$364$	0.368803	+	0.0706327i	0.0193305	+	0.00370216i
$365$		0			0
$366$	−7.84107	+	9.19424i	−0.409860	+	0.480591i
$367$	−12.9762	+	3.47695i	−0.677351	+	0.181496i	−0.581064	−	0.813858i	$-0.697363\pi$
$367$	−12.9762	+	3.47695i	−0.677351	+	0.181496i	−0.0962869	+	0.995354i	$0.530697\pi$
$368$	−8.95823	+	33.4326i	−0.466980	+	1.74279i
$369$	−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
$373$	−19.2834	−	5.16696i	−0.998455	−	0.267535i	−0.277657	−	0.960680i	$-0.589558\pi$
$373$	−19.2834	−	5.16696i	−0.998455	−	0.267535i	−0.720798	+	0.693145i	$0.756224\pi$
$374$	18.3287	−	31.7462i	0.947753	−	1.64156i
$375$		0			0
$376$	0.484510			0.0249867
$377$	−11.9923	+	8.13714i	−0.617635	+	0.419084i
$378$	0.236929	+	0.977486i	0.0121863	+	0.0502764i
$379$	16.7541	−	29.0190i	0.860601	−	1.49061i	−0.0107483	−	0.999942i	$-0.503421\pi$
$379$	16.7541	−	29.0190i	0.860601	−	1.49061i	0.871350	−	0.490663i	$-0.163245\pi$
$380$		0			0
$381$	−7.37965	−	20.7914i	−0.378071	−	1.06518i
$382$	−27.7305	+	27.7305i	−1.41882	+	1.41882i
$383$	−2.60975	−	0.699279i	−0.133352	−	0.0357315i	0.191526	−	0.981488i	$-0.438656\pi$
$383$	−2.60975	−	0.699279i	−0.133352	−	0.0357315i	−0.324878	+	0.945756i	$0.605323\pi$
$384$	20.5917	−	7.30876i	1.05082	−	0.372973i
$385$		0			0
$386$	32.4270	−	18.7218i	1.65049	−	0.952912i
$387$	−15.1026	−	1.56515i	−0.767710	−	0.0795612i
$388$	−0.132680	+	0.0355516i	−0.00673582	+	0.00180486i
$389$	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
$392$	12.4620	−	3.33918i	0.629426	−	0.168654i
$393$	22.3715	−	1.77704i	1.12849	−	0.0896397i
$394$	12.8645	−	7.42732i	0.648104	−	0.374183i
$395$		0			0
$396$	−1.78901	−	11.1900i	−0.0899010	−	0.562320i
$397$	10.9688	+	2.93908i	0.550509	+	0.147508i	0.523342	−	0.852122i	$-0.324685\pi$
$397$	10.9688	+	2.93908i	0.550509	+	0.147508i	0.0271666	+	0.999631i	$0.491352\pi$
$398$	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	$-0.117254\pi$
$402$	−7.20318	+	4.95832i	−0.359262	+	0.247299i
$403$	10.8358	−	22.3732i	0.539771	−	1.11449i
$404$	11.1569			0.555076
$405$		0			0
$406$	−0.389012	+	0.673788i	−0.0193063	+	0.0334395i
$407$	−16.8606	−	4.51779i	−0.835749	−	0.223938i
$408$	9.46851	+	13.7553i	0.468761	+	0.680990i
$409$	5.22725	+	9.05386i	0.258471	+	0.447685i	0.965832	−	0.259167i	$-0.0834481\pi$
$409$	5.22725	+	9.05386i	0.258471	+	0.447685i	−0.707362	+	0.706852i	$0.750115\pi$
$410$		0			0
$411$	21.2229	+	3.91748i	1.04685	+	0.193235i
$412$	−0.177774	+	0.663461i	−0.00875828	+	0.0326864i
$413$	−0.0783003	+	0.0209805i	−0.00385290	+	0.00103238i
$414$	−27.5787	+	22.3993i	−1.35542	+	1.10086i
$415$		0			0
$416$	11.4099	−	13.1989i	0.559414	−	0.647130i
$417$	3.76322	+	5.46700i	0.184286	+	0.267720i
$418$	−53.9335	+	14.4514i	−2.63797	+	0.706843i
$419$	−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	$-0.0888229\pi$
$422$	3.22612	−	12.0401i	0.157045	−	0.586101i
$423$	0.637524	+	0.461774i	0.0309975	+	0.0224522i
$424$	5.07663			0.246543
$425$		0			0
$426$	−16.3374	+	19.1568i	−0.791548	+	0.928149i
$427$	−0.119724	−	0.446818i	−0.00579387	−	0.0216230i
$428$	−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	$0.145802\pi$
$432$	24.8944	+	7.31505i	1.19773	+	0.351945i
$433$	−13.6874	−	3.66753i	−0.657775	−	0.176250i	−0.0855335	−	0.996335i	$-0.527259\pi$
$433$	−13.6874	−	3.66753i	−0.657775	−	0.176250i	−0.572242	+	0.820085i	$0.693926\pi$
$434$		−	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
$438$	−5.41268	+	11.3692i	−0.258628	+	0.543241i
$439$	−8.10140	−	4.67735i	−0.386659	−	0.223237i	0.294053	−	0.955789i	$-0.404996\pi$
$439$	−8.10140	−	4.67735i	−0.386659	−	0.223237i	−0.680711	+	0.732552i	$0.738329\pi$
$440$		0			0
$441$	19.5801	+	7.48347i	0.932388	+	0.356356i
$442$	28.9497	+	14.0210i	1.37700	+	0.666910i
$443$	−5.74199	−	5.74199i	−0.272810	−	0.272810i	0.557420	−	0.830230i	$-0.311791\pi$
$443$	−5.74199	−	5.74199i	−0.272810	−	0.272810i	−0.830230	+	0.557420i	$0.811791\pi$
$444$	−4.38928	+	5.14676i	−0.208306	+	0.244254i
$445$		0			0
$446$	17.9670	−	10.3733i	0.850763	−	0.491188i
$447$	11.6840	+	16.9738i	0.552633	+	0.802835i
$448$	−0.0504097	+	0.188132i	−0.00238163	+	0.00888838i
$449$	−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
$452$	1.88305	+	7.02763i	0.0885711	+	0.330552i
$453$	−19.1678	+	1.52256i	−0.900579	+	0.0715359i
$454$			23.6941i			1.11202i
$455$		0			0
$456$	4.61715	−	25.0134i	0.216218	−	1.17136i
$457$	−3.46105	−	12.9168i	−0.161901	−	0.604224i	−0.998415	−	0.0562781i	$-0.982077\pi$
$457$	−3.46105	−	12.9168i	−0.161901	−	0.604224i	0.836514	−	0.547946i	$-0.184590\pi$
$458$	−14.0596	+	3.76726i	−0.656962	+	0.176032i
$459$	−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	$-0.461194\pi$
$462$	1.24381	+	0.592159i	0.0578675	+	0.0275498i
$463$	19.4344	+	19.4344i	0.903191	+	0.903191i	0.995711	−	0.0925195i	$-0.0294920\pi$
$463$	19.4344	+	19.4344i	0.903191	+	0.903191i	−0.0925195	+	0.995711i	$0.529492\pi$
$464$	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	$-0.972086\pi$
$467$	−19.6345	+	19.6345i	−0.908575	+	0.908575i	0.0875827	+	0.996157i	$0.472086\pi$
$468$	9.67943	−	2.27767i	0.447432	−	0.105285i
$469$		−	0.334760i		−	0.0154578i
$470$		0			0
$471$	8.80540	−	10.3250i	0.405731	−	0.475750i
$472$	−0.341958	+	1.27621i	−0.0157399	+	0.0587421i
$473$	−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
$477$	6.67989	+	4.83840i	0.305851	+	0.221535i
$478$	5.10900	+	19.0670i	0.233680	+	0.872107i
$479$	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
$483$	−0.107697	−	1.35582i	−0.00490040	−	0.0616921i
$484$	−4.68406	−	2.70434i	−0.212912	−	0.122925i
$485$		0			0
$486$	16.2907	+	21.0714i	0.738961	+	0.955819i
$487$	20.1087	+	5.38812i	0.911213	+	0.244159i	0.683826	−	0.729645i	$-0.260315\pi$
$487$	20.1087	+	5.38812i	0.911213	+	0.244159i	0.227388	+	0.973804i	$0.426982\pi$
$488$	−7.28262	−	1.95137i	−0.329669	−	0.0883344i
$489$	−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	$0.496336\pi$
$492$	5.51808	−	0.438319i	0.248774	−	0.0197609i
$493$	−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
$497$	−0.249453	−	0.930972i	−0.0111895	−	0.0417598i
$498$	7.72547	+	3.67797i	0.346186	+	0.164814i
$499$	35.8828			1.60634			0.803168	−	0.595753i	$-0.203146\pi$
$499$	35.8828			1.60634			0.803168	+	0.595753i	$0.203146\pi$
$500$		0			0
$501$	−5.16868	−	14.5623i	−0.230920	−	0.650594i
$502$	−20.8208	+	20.8208i	−0.929276	+	0.929276i
$503$	8.55700	−	31.9352i	0.381538	−	1.42392i	−0.462015	−	0.886872i	$-0.652873\pi$
$503$	8.55700	−	31.9352i	0.381538	−	1.42392i	0.843553	−	0.537047i	$-0.180460\pi$
$504$	−0.487125	+	0.395640i	−0.0216983	+	0.0176232i
$505$		0			0
$506$			48.6623i			2.16330i
$507$	−16.5057	+	15.3154i	−0.733044	+	0.680181i
$508$	−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
$513$	29.9149	−	28.5124i	1.32078	−	1.25886i
$514$	0.357631	+	0.619435i	0.0157744	+	0.0273221i
$515$		0			0
$516$	2.69561	+	7.59462i	0.118668	+	0.334334i
$517$	1.04144	−	0.279053i	0.0458025	−	0.0122727i
$518$	−0.212824	−	0.794270i	−0.00935095	−	0.0348982i
$519$	−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	$0.827554\pi$
$522$	−2.12379	+	20.4931i	−0.0929560	+	0.896960i
$523$	−8.20158	−	30.6087i	−0.358630	−	1.33843i	−0.875854	−	0.482575i	$-0.839701\pi$
$523$	−8.20158	−	30.6087i	−0.358630	−	1.33843i	0.517225	−	0.855850i	$-0.326965\pi$
$524$	−5.95565	−	10.3155i	−0.260174	−	0.450634i
$525$		0			0
$526$	−19.3620	+	11.1787i	−0.844224	+	0.487413i
$527$	9.31753	−	34.7735i	0.405878	−	1.51476i
$528$	29.2733	−	20.1503i	1.27396	−	0.876931i
$529$	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
$533$	−10.3722	+	7.03782i	−0.449268	+	0.304842i
$534$	1.73660	−	9.40804i	0.0751502	−	0.407126i
$535$		0			0
$536$	−4.72521	−	2.72810i	−0.204098	−	0.117836i
$537$	31.1295	+	14.8202i	1.34334	+	0.639540i
$538$	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	$0.804591\pi$
$542$	−17.5777	−	4.70993i	−0.755027	−	0.202309i
$543$	1.02189	+	12.8647i	0.0438534	+	0.552079i
$544$	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	0.553993	−	0.832521i	$-0.313103\pi$
$547$	−6.51421	−	6.51421i	−0.278528	−	0.278528i	−0.832521	+	0.553993i	$0.813103\pi$
$548$	−2.96467	−	11.0643i	−0.126644	−	0.472643i
$549$	−7.72276	−	9.50851i	−0.329599	−	0.405813i
$550$		0			0
$551$	31.9677			1.36187
$552$	−20.0154	−	9.52901i	−0.851912	−	0.405581i
$553$	0.142057	−	0.530163i	0.00604087	−	0.0225448i
$554$			48.7662i			2.07188i
$555$		0			0
$556$	1.76133	−	3.05072i	0.0746971	−	0.129379i
$557$	−22.7031	+	6.08328i	−0.961962	+	0.257757i	−0.705431	−	0.708779i	$-0.749246\pi$
$557$	−22.7031	+	6.08328i	−0.961962	+	0.257757i	−0.256531	+	0.966536i	$0.582580\pi$
$558$	−14.4213	−	32.2644i	−0.610501	−	1.36586i
$559$	−13.8052	−	11.9339i	−0.583896	−	0.504752i
$560$		0			0
$561$	28.2746	+	24.1133i	1.19376	+	1.01806i
$562$	−22.2587	+	5.96419i	−0.938926	+	0.251584i
$563$	−9.60782	+	35.8569i	−0.404921	+	1.51119i	0.399279	+	0.916829i	$0.369260\pi$
$563$	−9.60782	+	35.8569i	−0.404921	+	1.51119i	−0.804201	+	0.594358i	$0.797406\pi$
$564$	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
$568$	−15.1738	−	4.06580i	−0.636678	−	0.170597i
$569$	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	$0.388779\pi$
$572$	5.93661	−	12.2576i	0.248222	−	0.512515i
$573$	−22.5414	−	32.7469i	−0.941681	−	1.36802i
$574$	−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	$-0.764535\pi$
$577$	−1.55067	+	1.55067i	−0.0645553	+	0.0645553i	0.674092	+	0.738647i	$0.264535\pi$
$578$	16.9386	+	4.53869i	0.704554	+	0.188785i
$579$	12.6965	+	35.7711i	0.527648	+	1.48660i
$580$		0			0
$581$	−0.283663	+	0.163773i	−0.0117683	+	0.00679444i
$582$	−0.0350138	−	0.440796i	−0.00145137	−	0.0182716i
$583$	10.9121	−	2.92388i	0.451931	−	0.121095i
$584$	−7.85658			−0.325107
$585$		0			0
$586$	−12.8967			−0.532758
$587$	19.5193	−	5.23017i	0.805646	−	0.215872i	0.167585	−	0.985858i	$-0.446403\pi$
$587$	19.5193	−	5.23017i	0.805646	−	0.215872i	0.638061	+	0.769986i	$0.279737\pi$
$588$	−0.880963	−	11.0906i	−0.0363303	−	0.457369i
$589$	−47.4885	+	27.4175i	−1.95673	+	1.12972i
$590$		0			0
$591$	5.03696	+	14.1912i	0.207193	+	0.583746i
$592$	−20.4902	−	5.49034i	−0.842143	−	0.225651i
$593$	3.08282	−	3.08282i	0.126596	−	0.126596i	−0.640970	−	0.767566i	$-0.721468\pi$
$593$	3.08282	−	3.08282i	0.126596	−	0.126596i	0.767566	+	0.640970i	$0.221468\pi$
$594$	36.4693	+	0.875395i	1.49635	+	0.0359179i
$595$		0			0
$596$	5.46855	−	9.47180i	0.224000	−	0.387980i
$597$	19.8921	+	28.8981i	0.814128	+	1.18272i
$598$	−42.5882	+	3.09615i	−1.74156	+	0.126611i
$599$	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	$0.221327\pi$
$602$	−0.946282	−	0.253555i	−0.0385676	−	0.0103341i
$603$	−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
$607$	4.58950	−	17.1283i	0.186282	−	0.695214i	−0.808070	−	0.589086i	$-0.799488\pi$
$607$	4.58950	−	17.1283i	0.186282	−	0.695214i	0.994352	−	0.106128i	$-0.0338454\pi$
$608$	−37.1737	+	9.96067i	−1.50759	+	0.403958i
$609$	−0.600107	−	0.511786i	−0.0243176	−	0.0207386i
$610$		0			0
$611$	0.310483	+	0.893690i	0.0125608	+	0.0361548i
$612$	13.1468	−	5.87625i	0.531428	−	0.237533i
$613$	36.8917	−	9.88511i	1.49004	−	0.399256i	0.580291	−	0.814409i	$-0.302939\pi$
$613$	36.8917	−	9.88511i	1.49004	−	0.399256i	0.909752	+	0.415153i	$0.136272\pi$
$614$	6.38272	−	11.0552i	0.257585	−	0.446151i
$615$		0			0
$616$			0.859527i			0.0346313i
$617$	−7.27686	+	27.1576i	−0.292955	+	1.09332i	0.649872	+	0.760043i	$0.274822\pi$
$617$	−7.27686	+	27.1576i	−0.292955	+	1.09332i	−0.942828	+	0.333281i	$0.891844\pi$
$618$	−1.99642	−	0.950461i	−0.0803076	−	0.0382331i
$619$	−34.9871			−1.40625			−0.703125	−	0.711066i	$-0.748213\pi$
$619$	−34.9871			−1.40625			−0.703125	+	0.711066i	$0.748213\pi$
$620$		0			0
$621$	−17.2547	−	31.6145i	−0.692406	−	1.26865i
$622$	−1.05074	−	3.92142i	−0.0421309	−	0.157235i
$623$	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
$627$	−4.48200	−	56.4248i	−0.178994	−	2.25339i
$628$	−6.95692	−	1.86410i	−0.277611	−	0.0743857i
$629$		−	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
$633$	11.4089	+	5.43160i	0.453464	+	0.215887i
$634$	−50.0225	−	28.8805i	−1.98665	−	1.14699i
$635$		0			0
$636$	0.794654	−	4.30503i	0.0315101	−	0.170706i
$637$	14.1451	+	20.8467i	0.560449	+	0.825974i
$638$	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	$0.307551\pi$
$642$	4.02588	−	2.77122i	0.158889	−	0.109371i
$643$	10.8144	−	40.3600i	0.426479	−	1.59164i	−0.334192	−	0.942505i	$-0.608464\pi$
$643$	10.8144	−	40.3600i	0.426479	−	1.59164i	0.760672	−	0.649137i	$-0.224870\pi$
$644$	−0.625170	+	0.360942i	−0.0246351	+	0.0142231i
$645$		0			0
$646$	−35.4768	−	61.4477i	−1.39582	−	2.41763i
$647$	−1.68818	−	6.30036i	−0.0663691	−	0.247693i	0.924769	−	0.380529i	$-0.124258\pi$
$647$	−1.68818	−	6.30036i	−0.0663691	−	0.247693i	−0.991138	+	0.132836i	$0.957591\pi$
$648$	−7.50144	+	14.8289i	−0.294685	+	0.582532i
$649$			2.94012i			0.115410i
$650$		0			0
$651$	1.33041	+	0.245576i	0.0521428	+	0.00962489i
$652$	2.91634	+	10.8839i	0.114213	+	0.426247i
$653$	44.7451	−	11.9894i	1.75101	−	0.469182i	0.766171	−	0.642637i	$-0.222160\pi$
$653$	44.7451	−	11.9894i	1.75101	−	0.469182i	0.984842	+	0.173454i	$0.0554929\pi$
$654$	−0.632409	−	1.78175i	−0.0247292	−	0.0696720i
$655$		0			0
$656$	8.67976	+	15.0338i	0.338888	+	0.586971i
$657$	−10.3378	−	7.48790i	−0.403315	−	0.292131i
$658$	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
$663$	−19.3044	+	26.2796i	−0.749722	+	1.02061i
$664$			5.33862i			0.207178i
$665$		0			0
$666$	−13.7281	−	16.9025i	−0.531953	−	0.654958i
$667$	7.21084	−	26.9112i	0.279205	−	1.04201i
$668$	−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
$672$	0.857300	+	0.408147i	0.0330711	+	0.0157446i
$673$	3.20311	+	11.9542i	0.123471	+	0.460799i	0.999781	−	0.0209488i	$-0.00666871\pi$
$673$	3.20311	+	11.9542i	0.123471	+	0.460799i	−0.876310	+	0.481748i	$0.840002\pi$
$674$	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	$-0.910190\pi$
$677$	−17.7462	+	17.7462i	−0.682043	+	0.682043i	0.278418	+	0.960460i	$0.410190\pi$
$678$	−23.3475	+	1.85457i	−0.896655	+	0.0712242i
$679$	0.0146595	+	0.00846367i	0.000562580	+	0.000324806i
$680$		0			0
$681$	−23.6203	−	4.36001i	−0.905132	−	0.167076i
$682$	−46.7550	−	12.5280i	−1.79034	−	0.479721i
$683$	21.3203	+	5.71276i	0.815798	+	0.218593i	0.642509	−	0.766278i	$-0.277894\pi$
$683$	21.3203	+	5.71276i	0.815798	+	0.218593i	0.173290	+	0.984871i	$0.444560\pi$
$684$	−20.4889	−	7.83079i	−0.783413	−	0.299418i
$685$		0			0
$686$	2.34469	+	1.35371i	0.0895208	+	0.0516848i
$687$	−1.16839	−	14.7090i	−0.0445767	−	0.561185i
$688$	−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	$0.721906\pi$
$692$	2.09329	+	7.81226i	0.0795749	+	0.296978i
$693$	−0.819193	+	1.13098i	−0.0311186	+	0.0429622i
$694$	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
$698$	−2.63864	+	9.84754i	−0.0998740	+	0.372735i
$699$	−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	$0.798365\pi$
$702$	1.55424	+	31.9728i	0.0586611	+	1.20674i
$703$	−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
$708$	1.02871	+	0.489751i	0.0386612	+	0.0184060i
$709$	−16.2682	−	28.1774i	−0.610967	−	1.05823i	−0.991078	−	0.133285i	$-0.957448\pi$
$709$	−16.2682	−	28.1774i	−0.610967	−	1.05823i	0.380111	−	0.924941i	$-0.375886\pi$
$710$		0			0
$711$	−2.29457	−	14.3523i	−0.0860532	−	0.538252i
$712$	5.76582	−	1.54495i	0.216083	−	0.0578993i
$713$	12.3689	+	46.1615i	0.463220	+	1.72876i
$714$	−0.317763	+	1.72148i	−0.0118920	+	0.0644247i
$715$		0			0
$716$		−	18.2992i		−	0.683873i
$717$	−19.9478	+	1.58452i	−0.744964	+	0.0591749i
$718$	13.2163	+	49.3238i	0.493227	+	1.84075i
$719$	−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
$722$	−19.5699	+	73.0360i	−0.728318	+	2.71812i
$723$	13.7140	+	19.9230i	0.510030	+	0.740944i
$724$	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	0.427161	−	0.904175i	$-0.359514\pi$
$727$	−12.8617	−	12.8617i	−0.477014	−	0.477014i	−0.904175	+	0.427161i	$0.859514\pi$
$728$	−0.752239	+	0.0546877i	−0.0278798	+	0.00202686i
$729$	−24.0035	+	12.3626i	−0.889018	+	0.457873i
$730$		0			0
$731$	−22.8861	−	13.2133i	−0.846475	−	0.488712i
$732$	−2.79475	+	5.87029i	−0.103297	+	0.216972i
$733$	−9.86693	−	9.86693i	−0.364443	−	0.364443i	0.501003	−	0.865446i	$-0.332965\pi$
$733$	−9.86693	−	9.86693i	−0.364443	−	0.364443i	−0.865446	+	0.501003i	$0.832965\pi$
$734$	−19.8780	+	11.4766i	−0.733711	+	0.423608i
$735$		0			0
$736$			33.5405i			1.23632i
$737$	−11.7279	−	3.14249i	−0.432004	−	0.115755i
$738$	−1.83687	+	17.7245i	−0.0676162	+	0.652450i
$739$	12.6022	−	21.8276i	0.463578	−	0.802941i	−0.535558	−	0.844498i	$-0.679899\pi$
$739$	12.6022	−	21.8276i	0.463578	−	0.802941i	0.999136	+	0.0415576i	$0.0132320\pi$
$740$		0			0
$741$	49.0966	−	7.51259i	1.80361	−	0.275982i
$742$	0.376307	+	0.376307i	0.0138147	+	0.0138147i
$743$	9.73165	+	36.3190i	0.357020	+	1.33242i	0.877924	+	0.478801i	$0.158928\pi$
$743$	9.73165	+	36.3190i	0.357020	+	1.33242i	−0.520904	+	0.853615i	$0.674405\pi$
$744$	14.3084	−	16.7777i	0.524573	−	0.615100i
$745$		0			0
$746$	−34.1098			−1.24885
$747$	−5.08809	+	7.02462i	−0.186164	+	0.257017i
$748$	5.10478	−	19.0513i	0.186649	−	0.696584i
$749$			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	$-0.00536474\pi$
$752$	1.26563	−	0.339125i	0.0461529	−	0.0123666i
$753$	−16.9246	−	24.5872i	−0.616768	−	0.896007i
$754$	−16.1934	+	18.7326i	−0.589730	+	0.682200i
$755$		0			0
$756$	0.259257	+	0.475018i	0.00942907	+	0.0172762i
$757$	29.1397	−	7.80797i	1.05910	−	0.283785i	0.313093	−	0.949722i	$-0.398635\pi$
$757$	29.1397	−	7.80797i	1.05910	−	0.283785i	0.746008	+	0.665937i	$0.231968\pi$
$758$	14.8179	−	55.3013i	0.538211	−	2.00863i
$759$	−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	$-0.340435\pi$
$762$	−21.3735	−	31.0503i	−0.774282	−	1.12483i
$763$	0.0699104	+	0.0187324i	0.00253093	+	0.000678160i
$764$	−10.5503	+	18.2736i	−0.381695	+	0.661115i
$765$		0			0
$766$	−4.61630			−0.166794
$767$	−2.57312	+	0.187066i	−0.0929101	+	0.00675455i
$768$	25.8464	−	17.7914i	0.932650	−	0.641992i
$769$	26.5529	−	45.9910i	0.957522	−	1.65848i	0.229035	−	0.973418i	$-0.426443\pi$
$769$	26.5529	−	45.9910i	0.957522	−	1.65848i	0.728488	−	0.685059i	$-0.240224\pi$
$770$		0			0
$771$	−0.683314	+	0.242533i	−0.0246090	+	0.00873463i
$772$	14.2456	−	14.2456i	0.512711	−	0.512711i
$773$	−34.1355	−	9.14659i	−1.22777	−	0.328980i	−0.414059	−	0.910250i	$-0.635889\pi$
$773$	−34.1355	−	9.14659i	−1.22777	−	0.328980i	−0.813711	+	0.581270i	$0.802556\pi$
$774$	−25.6172	+	4.09555i	−0.920791	+	0.147212i
$775$		0			0
$776$	0.238933	−	0.137948i	0.00857720	−	0.00495205i
$777$	0.830959	−	0.0660057i	0.0298105	−	0.00236794i
$778$	63.7347	−	17.0777i	2.28500	−	0.612264i
$779$	27.6489			0.990626
$780$		0			0
$781$	−34.9573			−1.25087
$782$	−59.7305	+	16.0047i	−2.13596	+	0.572329i
$783$	−20.0385	−	5.88817i	−0.716118	−	0.210426i
$784$	30.2159	−	17.4452i	1.07914	−	0.623042i
$785$		0			0
$786$	36.1355	−	12.8258i	1.28891	−	0.457482i
$787$	−18.5304	−	4.96521i	−0.660539	−	0.176991i	−0.0870495	−	0.996204i	$-0.527744\pi$
$787$	−18.5304	−	4.96521i	−0.660539	−	0.176991i	−0.573489	+	0.819213i	$0.694410\pi$
$788$	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
$792$	9.28803	+	20.7799i	0.330036	+	0.738382i
$793$	−1.06748	−	14.6834i	−0.0379075	−	0.521424i
$794$	19.4024			0.688566
$795$		0			0
$796$	9.31025	−	16.1258i	0.329993	−	0.571565i
$797$	15.1753	+	4.06620i	0.537535	+	0.144032i	0.517366	−	0.855764i	$-0.326913\pi$
$797$	15.1753	+	4.06620i	0.537535	+	0.144032i	0.0201695	+	0.999797i	$0.493579\pi$
$798$	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
$802$	13.7844	−	51.4442i	0.486745	−	1.81656i
$803$	−16.8875	+	4.52499i	−0.595946	+	0.159683i
$804$	−3.05311	+	3.57999i	−0.107675	+	0.126257i
$805$		0			0
$806$	7.98939	−	41.7160i	0.281414	−	1.46938i
$807$	−1.15168	+	0.792760i	−0.0405410	+	0.0279065i
$808$	−21.6457	+	5.79994i	−0.761492	+	0.204041i
$809$	−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	$-0.107559\pi$
$812$	−0.108345	+	0.404349i	−0.00380216	+	0.0141899i
$813$	7.92978	−	16.6563i	0.278109	−	0.584161i
$814$	−29.8242			−1.04534
$815$		0			0
$816$	34.3614	+	29.3042i	1.20289	+	1.02585i
$817$	10.4182	+	38.8812i	0.364486	+	1.36028i
$818$	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	$0.156322\pi$
$822$	36.7583	−	2.91983i	1.28209	−	0.101841i
$823$	21.4397	+	5.74475i	0.747341	+	0.200249i	0.612338	−	0.790596i	$-0.290229\pi$
$823$	21.4397	+	5.74475i	0.747341	+	0.200249i	0.135003	+	0.990845i	$0.456896\pi$
$824$		−	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	$-0.203625\pi$
$827$	5.90430	+	5.90430i	0.205313	+	0.205313i	−0.596959	+	0.802272i	$0.703625\pi$
$828$	−11.2138	+	15.4817i	−0.389705	+	0.538026i
$829$	27.7895	+	16.0443i	0.965168	+	0.557240i	0.897760	−	0.440485i	$-0.145194\pi$
$829$	27.7895	+	16.0443i	0.965168	+	0.557240i	0.0674084	+	0.997725i	$0.478527\pi$
$830$		0			0
$831$	−48.6143	−	8.97358i	−1.68641	−	0.311290i
$832$	−2.70197	+	5.57887i	−0.0936739	+	0.193412i
$833$	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
$837$	34.8176	−	8.43932i	1.20347	−	0.291706i
$838$	−9.65801	+	36.0442i	−0.333630	+	1.24513i
$839$	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
$842$	−4.99840	−	18.6543i	−0.172256	−	0.642869i
$843$	−1.84975	−	23.2868i	−0.0637088	−	0.802042i
$844$		−	6.70663i		−	0.230852i
$845$		0			0
$846$	1.25636	+	0.480177i	0.0431946	+	0.0165088i
$847$	0.172510	+	0.643817i	0.00592752	+	0.0221218i
$848$	13.2611	−	3.55330i	0.455388	−	0.122021i
$849$	1.85963	−	0.660053i	0.0638225	−	0.0226530i
$850$		0			0
$851$	14.7228	+	25.5007i	0.504692	+	0.874152i
$852$	−5.82303	+	12.2311i	−0.199494	+	0.419031i
$853$	−26.8806	−	26.8806i	−0.920373	−	0.920373i	0.0766825	−	0.997056i	$-0.475567\pi$
$853$	−26.8806	−	26.8806i	−0.920373	−	0.920373i	−0.997056	+	0.0766825i	$0.975567\pi$
$854$	−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	0.0793118	−	0.996850i	$-0.474728\pi$
$857$	31.5042	−	31.5042i	1.07616	−	1.07616i	0.996850	−	0.0793118i	$-0.0252723\pi$
$858$	35.3344	+	25.9559i	1.20630	+	0.886121i
$859$			29.9066i			1.02040i	0.860055	+	0.510201i	$0.170429\pi$
$859$			29.9066i			1.02040i	−0.860055	+	0.510201i	$0.829571\pi$
$860$		0			0
$861$	−0.519033	−	0.442644i	−0.0176886	−	0.0150853i
$862$	1.20272	−	4.48861i	0.0409648	−	0.152883i
$863$	9.69182	−	9.69182i	0.329913	−	0.329913i	−0.522640	−	0.852553i	$-0.675053\pi$
$863$	9.69182	−	9.69182i	0.329913	−	0.329913i	0.852553	+	0.522640i	$0.175053\pi$
$864$	25.1365	+	0.603367i	0.855161	+	0.0205270i
$865$		0			0
$866$	−24.2113			−0.822732
$867$	−7.64148	+	16.0507i	−0.259518	+	0.545111i
$868$	−0.185847	−	0.693590i	−0.00630806	−	0.0235420i
$869$	−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
$873$	0.445866	+	0.0462071i	0.0150903	+	0.00156387i
$874$	81.5712	+	47.0952i	2.75919	+	1.59302i
$875$		0			0
$876$	−1.22981	+	6.66246i	−0.0415513	+	0.225104i
$877$	34.0942	+	9.13551i	1.15128	+	0.308484i	0.783478	−	0.621420i	$-0.213444\pi$
$877$	34.0942	+	9.13551i	1.15128	+	0.308484i	0.367801	+	0.929904i	$0.380111\pi$
$878$	−15.4388	−	4.13681i	−0.521033	−	0.139610i
$879$	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	$0.666814\pi$
$882$	35.6240	+	3.69187i	1.19952	+	0.124312i
$883$	12.5285	−	12.5285i	0.421617	−	0.421617i	−0.464143	−	0.885760i	$-0.653638\pi$
$883$	12.5285	−	12.5285i	0.421617	−	0.421617i	0.885760	+	0.464143i	$0.153638\pi$
$884$	16.9981	+	3.25545i	0.571707	+	0.109492i
$885$		0			0
$886$	−12.0157	−	6.93725i	−0.403674	−	0.233061i
$887$	−0.784839	−	2.92906i	−0.0263523	−	0.0983482i	0.951497	−	0.307658i	$-0.0995451\pi$
$887$	−0.784839	−	2.92906i	−0.0263523	−	0.0983482i	−0.977849	+	0.209309i	$0.932878\pi$
$888$	5.84015	−	12.2671i	0.195983	−	0.411656i
$889$	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
$893$	0.540132	−	2.01580i	0.0180748	−	0.0674562i
$894$	26.7891	+	22.8464i	0.895961	+	0.764097i
$895$		0			0
$896$			1.42917i			0.0477451i
$897$	4.75024	−	43.0253i	0.158606	−	1.43657i
$898$	−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
$903$	0.426893	−	0.896678i	0.0142061	−	0.0298396i
$904$	−7.30666	−	12.6555i	−0.243016	−	0.420916i
$905$		0			0
$906$	−30.9607	+	10.9891i	−1.02860	+	0.365089i
$907$	16.8138	−	4.50525i	0.558294	−	0.149594i	0.0313715	−	0.999508i	$-0.490012\pi$
$907$	16.8138	−	4.50525i	0.558294	−	0.149594i	0.526922	+	0.849913i	$0.323346\pi$
$908$	3.29956	+	12.3141i	0.109500	+	0.408659i
$909$	−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	$-0.0252501\pi$
$912$	−5.44685	−	68.5714i	−0.180363	−	2.27063i
$913$	3.07477	+	11.4752i	0.101760	+	0.379774i
$914$	−11.4241	−	19.7871i	−0.377876	−	0.654500i
$915$		0			0
$916$	−6.78234	+	3.91578i	−0.224095	+	0.129381i
$917$	−0.379911	+	1.41785i	−0.0125458	+	0.0468214i
$918$	10.9200	+	45.0521i	0.360415	+	1.48694i
$919$	20.5581	−	11.8693i	0.678151	−	0.391530i	−0.121007	−	0.992652i	$-0.538612\pi$
$919$	20.5581	−	11.8693i	0.678151	−	0.391530i	0.799158	+	0.601121i	$0.205279\pi$
$920$		0			0
$921$	9.84626	+	8.39713i	0.324445	+	0.276695i
$922$	−41.4418	−	41.4418i	−1.36481	−	1.36481i
$923$	−2.22417	−	30.5938i	−0.0732094	−	1.00701i
$924$	0.728888	+	0.134543i	0.0239787	+	0.00442616i
$925$		0			0
$926$	40.6683	+	23.4798i	1.33644	+	0.771595i
$927$	1.31487	−	1.81530i	0.0431859	−	0.0596223i
$928$	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
$932$	10.8156	+	2.89804i	0.354277	+	0.0949283i
$933$	4.10256	−	0.325879i	0.134312	−	0.0106688i
$934$	−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	0.882902	−	0.469558i	$-0.155587\pi$
$937$	12.6526	+	12.6526i	0.413344	+	0.413344i	−0.469558	+	0.882902i	$0.655587\pi$
$938$	−0.148037	−	0.552480i	−0.00483357	−	0.0180391i
$939$	−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	$0.201767\pi$
$942$	9.96635	−	20.9340i	0.324721	−	0.682068i
$943$	6.23666	−	23.2755i	0.203094	−	0.757956i
$944$			3.57304i			0.116293i
$945$		0			0
$946$	−17.7661	+	30.7718i	−0.577625	+	1.00048i
$947$	−23.6300	+	6.33163i	−0.767871	+	0.205750i	−0.621431	−	0.783469i	$-0.713448\pi$
$947$	−23.6300	+	6.33163i	−0.767871	+	0.205750i	−0.146440	+	0.989220i	$0.546782\pi$
$948$	−6.35443	+	4.37408i	−0.206382	+	0.142064i
$949$	−5.03464	−	14.4916i	−0.163431	−	0.470419i
$950$		0			0
$951$	37.9953	−	44.5524i	1.23208	−	1.44471i
$952$	−1.05503	+	0.282693i	−0.0341936	+	0.00916215i
$953$	11.1821	−	41.7321i	0.362223	−	1.35184i	−0.508923	−	0.860812i	$-0.669956\pi$
$953$	11.1821	−	41.7321i	0.362223	−	1.35184i	0.871146	−	0.491024i	$-0.163377\pi$
$954$	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
$958$	2.84255	+	0.761659i	0.0918386	+	0.0246081i
$959$	−0.705791	+	1.22247i	−0.0227912	+	0.0394755i
$960$		0			0
$961$	−16.5366			−0.533437
$962$	−1.89758	−	26.1015i	−0.0611803	−	0.841546i
$963$	2.02178	+	4.52328i	0.0651510	+	0.145761i
$964$	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	$-0.716990\pi$
$967$	4.55251	−	4.55251i	0.146399	−	0.146399i	0.776507	+	0.630108i	$0.216990\pi$
$968$	10.4935	+	2.81172i	0.337273	+	0.0903721i
$969$	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	$0.935316\pi$
$972$	11.4008	+	8.68250i	0.365681	+	0.278491i
$973$	−0.419316	+	0.112355i	−0.0134427	+	0.00360195i
$974$	35.5697			1.13973
$975$		0			0
$976$	−20.3894			−0.652649
$977$	55.9598	−	14.9944i	1.79031	−	0.479713i	0.797914	−	0.602772i	$-0.205937\pi$
$977$	55.9598	−	14.9944i	1.79031	−	0.479713i	0.992399	+	0.123059i	$0.0392703\pi$
$978$	−36.1590	+	2.87223i	−1.15624	+	0.0918437i
$979$	11.5036	−	6.64164i	0.367658	−	0.212268i
$980$		0			0
$981$	1.89257	−	0.302576i	0.0604252	−	0.00966050i
$982$	37.2966	+	9.99359i	1.19018	+	0.318908i
$983$	−17.2893	+	17.2893i	−0.551443	+	0.551443i	−0.926857	−	0.375414i	$-0.877500\pi$
$983$	−17.2893	+	17.2893i	−0.551443	+	0.551443i	0.375414	+	0.926857i	$0.377500\pi$
$984$	−10.4778	+	3.71898i	−0.334022	+	0.118557i
$985$		0			0
$986$	−17.9295	+	31.0548i	−0.570991	+	0.988985i
$987$	−0.0424114	+	0.0291940i	−0.00134997	+	0.000929254i
$988$	−14.8016	−	21.8142i	−0.470901	−	0.694002i
$989$	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	$0.0957142\pi$
$992$	−32.2259	−	8.63491i	−1.02317	−	0.274159i
$993$	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
$997$	12.5004	−	46.6520i	0.395891	−	1.47748i	−0.424367	−	0.905490i	$-0.639503\pi$
$997$	12.5004	−	46.6520i	0.395891	−	1.47748i	0.820258	−	0.571994i	$-0.193830\pi$
$998$	59.2202	−	15.8680i	1.87458	−	0.502293i
$999$	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.407.19		96
3.2	odd	2	inner	975.2.bn.d.407.6		96
5.2	odd	4		195.2.bf.a.173.19	yes	96
5.3	odd	4	inner	975.2.bn.d.368.6		96
5.4	even	2		195.2.bf.a.17.6	✓	96
13.10	even	6	inner	975.2.bn.d.257.19		96
15.2	even	4		195.2.bf.a.173.6	yes	96
15.8	even	4	inner	975.2.bn.d.368.19		96
15.14	odd	2		195.2.bf.a.17.19	yes	96
39.23	odd	6	inner	975.2.bn.d.257.6		96
65.23	odd	12	inner	975.2.bn.d.218.6		96
65.49	even	6		195.2.bf.a.62.6	yes	96
65.62	odd	12		195.2.bf.a.23.19	yes	96
195.23	even	12	inner	975.2.bn.d.218.19		96
195.62	even	12		195.2.bf.a.23.6	yes	96
195.179	odd	6		195.2.bf.a.62.19	yes	96

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

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

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