LMFDB - Embedded newform 975.2.bn.d.407.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			407.6
Character	$\chi$	$=$	975.407
Dual form			975.2.bn.d.218.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.65038 + 0.442218i) q^{2} +(0.744530 + 1.56387i) q^{3} +(0.796141 - 0.459652i) q^{4} +(-1.92033 - 2.25172i) q^{6} +(-0.109428 - 0.0293212i) q^{7} +(1.30565 - 1.30565i) q^{8} +(-1.89135 + 2.32869i) q^{9} +(2.05447 - 3.55845i) q^{11} +(1.31159 + 0.902832i) q^{12} +(-3.24500 - 1.57162i) q^{13} +0.193564 q^{14} +(-2.49674 + 4.32449i) q^{16} +(5.04353 + 1.35141i) q^{17} +(2.09165 - 4.67961i) 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} +(3.01397 + 1.06977i) q^{24} +(6.05047 + 1.15878i) q^{26} +(-5.04992 - 1.22403i) q^{27} +(-0.100598 + 0.0269551i) q^{28} +(-2.00973 + 3.48095i) q^{29} +6.89468i q^{31} +(1.25240 - 4.67403i) q^{32} +(7.09456 + 0.563544i) q^{33} -8.92135 q^{34} +(-0.435393 + 2.72333i) q^{36} +(1.09950 + 4.10339i) q^{37} +(-9.60880 - 9.60880i) q^{38} +(0.0418074 - 6.24486i) q^{39} +(-1.73822 + 3.01068i) q^{41} +(0.144115 + 0.302709i) q^{42} +(4.88872 + 1.30993i) q^{43} -3.77737i q^{44} +(10.2563 - 5.92150i) q^{46} +(0.185543 + 0.185543i) q^{47} +(-8.62182 - 0.684859i) 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} +(8.87558 - 0.213046i) q^{54} +(-0.181159 + 0.104592i) q^{56} +(-7.81074 + 11.3470i) 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} +(0.275247 - 0.199368i) q^{63} -1.71922i q^{64} +(-11.9579 + 2.20728i) q^{66} +(0.764792 + 2.85424i) q^{67} +(4.63654 - 1.24236i) q^{68} +(-7.79036 - 9.13477i) q^{69} +(-4.25380 - 7.36780i) q^{71} +(0.571017 + 5.50991i) 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} +(2.69259 + 10.3249i) q^{78} +4.84485i q^{79} +(-1.84560 - 8.80873i) q^{81} +(1.53734 - 5.73743i) q^{82} +(-2.04442 + 2.04442i) q^{83} +(-0.117052 - 0.137253i) q^{84} -8.64751 q^{86} +(-6.94004 - 0.551270i) 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} +(-10.7823 + 5.13330i) 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	−0.789756	−	0.613421i	$-0.789793\pi$
$2$	−1.65038	+	0.442218i	−1.16699	+	0.312695i	−0.377238	+	0.926116i	$0.623126\pi$
$3$	0.744530	+	1.56387i	0.429855	+	0.902898i
$3$	0.744530	+	1.56387i	0.429855	+	0.902898i
$4$	0.796141	−	0.459652i	0.398071	−	0.229826i
$5$		0			0
$5$		0			0
$6$	−1.92033	−	2.25172i	−0.783970	−	0.919263i
$7$	−0.109428	−	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
$9$	−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	$-0.0459766\pi$
$12$	1.31159	+	0.902832i	0.378622	+	0.260625i
$13$	−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	0.811942	−	0.583738i	$-0.198411\pi$
$17$	5.04353	+	1.35141i	1.22324	+	0.327765i	0.411293	+	0.911503i	$0.365077\pi$
$18$	2.09165	−	4.67961i	0.493007	−	1.10299i
$19$	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	−0.876926	−	0.480625i	$-0.840410\pi$
$23$	−6.69524	+	1.79398i	−1.39605	+	0.374071i	−0.519127	+	0.854697i	$0.673743\pi$
$24$	3.01397	+	1.06977i	0.615223	+	0.218365i
$25$		0			0
$26$	6.05047	+	1.15878i	1.18659	+	0.227255i
$27$	−5.04992	−	1.22403i	−0.971858	−	0.235565i
$28$	−0.100598	+	0.0269551i	−0.0190112	+	0.00509404i
$29$	−2.00973	+	3.48095i	−0.373197	+	0.646396i	−0.990055	−	0.140678i	$-0.955072\pi$
$29$	−2.00973	+	3.48095i	−0.373197	+	0.646396i	0.616858	+	0.787074i	$0.288405\pi$
$30$		0			0
$31$			6.89468i			1.23832i	0.785265	+	0.619160i	$0.212527\pi$
$31$			6.89468i			1.23832i	−0.785265	+	0.619160i	$0.787473\pi$
$32$	1.25240	−	4.67403i	0.221396	−	0.826260i
$33$	7.09456	+	0.563544i	1.23500	+	0.0981004i
$34$	−8.92135			−1.53000
$35$		0			0
$36$	−0.435393	+	2.72333i	−0.0725655	+	0.453888i
$37$	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
$39$	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	$0.254174\pi$
$42$	0.144115	+	0.302709i	0.0222374	+	0.0467090i
$43$	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	0.720509	−	0.693445i	$-0.243908\pi$
$47$	0.185543	+	0.185543i	0.0270642	+	0.0270642i	−0.693445	+	0.720509i	$0.743908\pi$
$48$	−8.62182	−	0.684859i	−1.24445	−	0.0988509i
$49$	−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	0.827907	−	0.560865i	$-0.189531\pi$
$53$	1.94409	+	1.94409i	0.267042	+	0.267042i	−0.560865	+	0.827907i	$0.689531\pi$
$54$	8.87558	−	0.213046i	1.20781	−	0.0289919i
$55$		0			0
$56$	−0.181159	+	0.104592i	−0.0242084	+	0.0139767i
$57$	−7.81074	+	11.3470i	−1.03456	+	1.50295i
$58$	1.77747	−	6.63362i	0.233394	−	0.871037i
$59$	−0.619675	+	0.357770i	−0.0806749	+	0.0465777i	−0.539795	−	0.841797i	$-0.681498\pi$
$59$	−0.619675	+	0.357770i	−0.0806749	+	0.0465777i	0.459120	+	0.888374i	$0.348165\pi$
$60$		0			0
$61$	2.04160	+	3.53616i	0.261400	+	0.452758i	0.966614	−	0.256236i	$-0.0824825\pi$
$61$	2.04160	+	3.53616i	0.261400	+	0.452758i	−0.705214	+	0.708994i	$0.749149\pi$
$62$	−3.04895	−	11.3788i	−0.387217	−	1.44511i
$63$	0.275247	−	0.199368i	0.0346779	−	0.0251180i
$64$		−	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
$69$	−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	$-0.335113\pi$
$72$	0.571017	+	5.50991i	0.0672949	+	0.649349i
$73$	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
$78$	2.69259	+	10.3249i	0.304876	+	1.16906i
$79$			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
$81$	−1.84560	−	8.80873i	−0.205066	−	0.978748i
$82$	1.53734	−	5.73743i	0.169771	−	0.633593i
$83$	−2.04442	+	2.04442i	−0.224405	+	0.224405i	−0.810350	−	0.585946i	$-0.800723\pi$
$83$	−2.04442	+	2.04442i	−0.224405	+	0.224405i	0.585946	+	0.810350i	$0.300723\pi$
$84$	−0.117052	−	0.137253i	−0.0127715	−	0.0149755i
$85$		0			0
$86$	−8.64751			−0.932485
$87$	−6.94004	−	0.551270i	−0.744050	−	0.0591023i
$88$	−1.96368	−	7.32854i	−0.209329	−	0.781225i
$89$	2.79966	+	1.61638i	0.296763	+	0.171336i	0.640988	−	0.767551i	$-0.278525\pi$
$89$	2.79966	+	1.61638i	0.296763	+	0.171336i	−0.344225	+	0.938887i	$0.611858\pi$
$90$		0			0
$91$	0.309013	+	0.267127i	0.0323933	+	0.0280025i
$92$	−4.50574	+	4.50574i	−0.469756	+	0.469756i
$93$	−10.7823	+	5.13330i	−1.11808	+	0.532298i
$94$	−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	−0.124339	−	0.992240i	$-0.539681\pi$
$101$	−10.5103	−	6.06812i	−1.04581	−	0.603800i	−0.921474	+	0.388440i	$0.873014\pi$
$102$	−6.64221	−	13.9518i	−0.657677	−	1.38143i
$103$	−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	0.983504	−	0.180884i	$-0.0578958\pi$
$107$	0.427445	+	1.59525i	0.0413227	+	0.154218i	−0.942182	+	0.335102i	$0.891229\pi$
$108$	−4.58308	+	1.34671i	−0.441007	+	0.129587i
$109$	−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
$111$	−5.59853	+	4.77457i	−0.531389	+	0.453182i
$112$	0.400014	−	0.400014i	0.0377977	−	0.0377977i
$113$	2.04834	−	7.64451i	0.192692	−	0.719135i	−0.800161	−	0.599786i	$-0.795253\pi$
$113$	2.04834	−	7.64451i	0.192692	−	0.719135i	0.992852	−	0.119349i	$-0.0380808\pi$
$114$	7.87282	−	22.1809i	0.737357	−	2.07743i
$115$		0			0
$116$			3.69510i			0.343082i
$117$	9.79724	−	4.58411i	0.905755	−	0.423801i
$118$	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
$123$	−6.00245	−	0.476794i	−0.541223	−	0.0429911i
$124$	3.16915	+	5.48913i	0.284598	+	0.492939i
$125$		0			0
$126$	−0.366098	+	0.450752i	−0.0326146	+	0.0401561i
$127$	−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	$0.191519\pi$
$131$			12.9569i			1.13205i	−0.824390	+	0.566023i	$0.808481\pi$
$132$	5.90731	−	2.81237i	0.514165	−	0.244785i
$133$	−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	$0.261993\pi$
$137$	−3.22490	+	12.0355i	−0.275522	+	1.02826i	−0.955491	+	0.295021i	$0.904673\pi$
$138$	16.8966	+	11.6308i	1.43833	+	0.990079i
$139$	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
$141$	−0.152022	+	0.428307i	−0.0128026	+	0.0360699i
$142$	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
$147$	0.958292	−	12.0641i	0.0790386	−	0.995032i
$148$	2.76149	+	2.76149i	0.226993	+	0.226993i
$149$	−10.3032	+	5.94857i	−0.844073	+	0.487326i	−0.858647	−	0.512568i	$-0.828694\pi$
$149$	−10.3032	+	5.94857i	−0.844073	+	0.487326i	0.0145735	+	0.999894i	$0.495361\pi$
$150$		0			0
$151$			11.1014i			0.903416i	0.892166	+	0.451708i	$0.149185\pi$
$151$			11.1014i			0.903416i	−0.892166	+	0.451708i	$0.850815\pi$
$152$	14.1851	+	3.80088i	1.15056	+	0.308292i
$153$	−12.6861	+	9.18883i	−1.02561	+	0.742873i
$154$	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	0.450598	−	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
$159$	−1.59286	+	4.48774i	−0.126322	+	0.355901i
$160$		0			0
$161$	0.785250			0.0618864
$162$	6.94131	+	13.7216i	0.545361	+	1.07807i
$163$	−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	0.0905069	−	0.995896i	$-0.471151\pi$
$167$	8.61742	−	2.30903i	0.666836	−	0.178678i	0.576329	+	0.817218i	$0.304485\pi$
$168$	−0.298446	−	0.205436i	−0.0230256	−	0.0158497i
$169$	8.06000	+	10.1998i	0.620000	+	0.784602i
$170$		0			0
$171$	−23.5605	−	3.76674i	−1.80172	−	0.288050i
$172$	4.49422	−	1.20422i	0.342681	−	0.0918211i
$173$	2.27704	−	8.49801i	0.173120	−	0.646092i	−0.823744	−	0.566961i	$-0.808119\pi$
$173$	2.27704	−	8.49801i	0.173120	−	0.646092i	0.996864	−	0.0791307i	$-0.0252144\pi$
$174$	11.6975	−	2.15920i	0.886783	−	0.163689i
$175$		0			0
$176$	10.2590	+	17.7691i	0.773301	+	1.33940i
$177$	−1.02087	−	0.702718i	−0.0767334	−	0.0528196i
$178$	−5.33529	−	1.42959i	−0.399897	−	0.107152i
$179$	−9.95273	+	17.2386i	−0.743902	+	1.28848i	0.206804	+	0.978382i	$0.433694\pi$
$179$	−9.95273	+	17.2386i	−0.743902	+	1.28848i	−0.950706	+	0.310094i	$0.899640\pi$
$180$		0			0
$181$	7.45086			0.553818			0.276909	−	0.960896i	$-0.410690\pi$
$181$	7.45086			0.553818			0.276909	+	0.960896i	$0.410690\pi$
$182$	−0.628116	−	0.304210i	−0.0465590	−	0.0225496i
$183$	−4.01004	+	5.82556i	−0.296430	+	0.430638i
$184$	−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
$188$	0.233004	+	0.0624332i	0.0169935	+	0.00455341i
$189$	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	$0.0214457\pi$
$192$	2.68863	−	1.28001i	0.194035	−	0.0923770i
$193$	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	−0.545253	−	0.838272i	$-0.683566\pi$
$197$	−8.39781	+	2.25019i	−0.598319	+	0.160319i	−0.0530668	+	0.998591i	$0.516900\pi$
$198$	−12.3549	−	17.0572i	−0.878026	−	1.21220i
$199$	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
$201$	−3.89424	+	3.32110i	−0.274679	+	0.234253i
$202$	20.0294	+	5.36686i	1.40926	+	0.377611i
$203$	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
$207$	8.48540	−	18.9842i	0.589776	−	1.31949i
$208$	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
$213$	8.35516	−	12.1379i	0.572486	−	0.831677i
$214$	−1.41089	−	2.44374i	−0.0964466	−	0.167050i
$215$		0			0
$216$	−8.19162	+	4.99529i	−0.557369	+	0.339886i
$217$	0.202160	−	0.754473i	0.0137235	−	0.0512169i
$218$	1.05438	−	0.282519i	0.0714114	−	0.0191346i
$219$	−2.46511	+	6.94521i	−0.166577	+	0.469314i
$220$		0			0
$221$	−14.2423	−	12.3118i	−0.958043	−	0.828184i
$222$	7.12830	−	10.3556i	0.478420	−	0.695023i
$223$	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	$-0.764440\pi$
$227$	3.58919	−	13.3950i	0.238223	−	0.889061i	0.976669	−	0.214748i	$-0.0688931\pi$
$228$	−1.00277	+	12.6240i	−0.0664100	+	0.836048i
$229$	−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
$231$	−0.759822	−	0.269689i	−0.0499926	−	0.0177442i
$232$	1.92091	+	7.16892i	0.126114	+	0.470663i
$233$	−8.61258	−	8.61258i	−0.564229	−	0.564229i	0.366277	−	0.930506i	$-0.380632\pi$
$233$	−8.61258	−	8.61258i	−0.564229	−	0.564229i	−0.930506	+	0.366277i	$0.880632\pi$
$234$	−14.1420	+	11.8980i	−0.924490	+	0.777798i
$235$		0			0
$236$	−0.328899	+	0.569670i	−0.0214095	+	0.0370824i
$237$	−7.57669	+	3.60714i	−0.492159	+	0.234309i
$238$	0.976248	+	0.261585i	0.0632807	+	0.0169560i
$239$		−	11.5531i		−	0.747310i	−0.927568	−	0.373655i	$-0.878104\pi$
$239$		−	11.5531i		−	0.747310i	0.927568	−	0.373655i	$-0.121896\pi$
$240$		0			0
$241$	12.0934	−	6.98212i	0.779004	−	0.449758i	−0.0570731	−	0.998370i	$-0.518177\pi$
$241$	12.0934	−	6.98212i	0.779004	−	0.449758i	0.836077	+	0.548612i	$0.184843\pi$
$242$	7.10816	+	7.10816i	0.456930	+	0.456930i
$243$	12.4016	−	9.44464i	0.795561	−	0.605874i
$244$	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
$249$	−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	$0.150287\pi$
$252$	0.127496	−	0.285243i	0.00803147	−	0.0179686i
$253$	−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	0.962464	−	0.271409i	$-0.0874895\pi$
$257$	−0.108348	−	0.404361i	−0.00675857	−	0.0252233i	−0.969223	+	0.246185i	$0.920823\pi$
$258$	−6.43833	−	13.5235i	−0.400833	−	0.841939i
$259$		−	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	0.152865	−	0.988247i	$-0.451150\pi$
$263$	12.6393	−	3.38670i	0.779374	−	0.208833i	0.626509	+	0.779414i	$0.284483\pi$
$264$	9.99883	−	8.52725i	0.615386	−	0.524816i
$265$		0			0
$266$	0.769733	+	1.33322i	0.0471953	+	0.0817447i
$267$	−0.443375	+	5.58173i	−0.0271341	+	0.341597i
$268$	1.92084	+	1.92084i	0.117334	+	0.117334i
$269$	−0.403612	−	0.699076i	−0.0246086	−	0.0426234i	0.853459	−	0.521160i	$-0.174501\pi$
$269$	−0.403612	−	0.699076i	−0.0246086	−	0.0426234i	−0.878067	+	0.478537i	$0.841167\pi$
$270$		0			0
$271$	−9.22378	−	5.32535i	−0.560305	−	0.323492i	0.192963	−	0.981206i	$-0.438190\pi$
$271$	−9.22378	−	5.32535i	−0.560305	−	0.323492i	−0.753268	+	0.657714i	$0.771524\pi$
$272$	−18.4366	+	18.4366i	−1.11788	+	1.11788i
$273$	−0.187682	+	0.682138i	−0.0113590	+	0.0412849i
$274$		−	21.2892i		−	1.28613i
$275$		0			0
$276$	−10.4010	−	3.69171i	−0.626069	−	0.222215i
$277$	−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
$279$	−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	$0.368216\pi$
$282$	0.0614889	−	0.774095i	0.00366161	−	0.0460967i
$283$	−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
$288$	8.51564	+	11.7567i	0.501789	+	0.692769i
$289$	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	0.465420	−	0.885090i	$-0.345903\pi$
$293$	7.29093	+	1.95360i	0.425941	+	0.114130i	−0.0394794	+	0.999220i	$0.512570\pi$
$294$	3.75342	+	20.3341i	0.218904	+	1.18591i
$295$		0			0
$296$	6.79317	+	3.92204i	0.394845	+	0.227964i
$297$	−14.7306	+	15.4552i	−0.854757	+	0.896800i
$298$	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
$303$	1.66449	−	20.9546i	0.0956224	−	1.20381i
$304$	−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	$-0.681610\pi$
$307$	5.28300	−	5.28300i	0.301517	−	0.301517i	0.841607	+	0.540090i	$0.181610\pi$
$308$	−0.110757	+	0.413352i	−0.00631098	+	0.0235529i
$309$	−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	$0.978540\pi$
$312$	−8.09904	−	8.20821i	−0.458518	−	0.464698i
$313$	−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	$0.148277\pi$
$317$	23.9045	+	23.9045i	1.34261	+	1.34261i	0.449162	+	0.893450i	$0.351723\pi$
$318$	0.644271	−	8.11085i	0.0361289	−	0.454834i
$319$	8.25787	+	14.3030i	0.462352	+	0.800817i
$320$		0			0
$321$	−2.17651	+	1.85618i	−0.121481	+	0.103602i
$322$	−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
$327$	−0.475658	−	0.999106i	−0.0263039	−	0.0552507i
$328$	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
$333$	−11.6351	−	5.20054i	−0.637597	−	0.284988i
$334$	−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	0.773922	−	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
$342$	40.5495	−	4.20233i	2.19267	−	0.227236i
$343$	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	−0.179877	−	0.983689i	$-0.557570\pi$
$347$	−15.4146	−	4.13034i	−0.827500	−	0.221728i	−0.647623	+	0.761961i	$0.724237\pi$
$348$	−5.77864	+	2.75112i	−0.309768	+	0.147475i
$349$	−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
$351$	14.4633	+	11.9086i	0.771992	+	0.635632i
$352$	−14.0593	−	14.0593i	−0.749363	−	0.749363i
$353$	3.22389	+	12.0317i	0.171590	+	0.640383i	0.997107	+	0.0760061i	$0.0242168\pi$
$353$	3.22389	+	12.0317i	0.171590	+	0.640383i	−0.825517	+	0.564377i	$0.809116\pi$
$354$	1.99558	+	0.708304i	0.106064	+	0.0376459i
$355$		0			0
$356$	2.97190			0.157510
$357$	0.0811285	−	1.02134i	0.00429378	−	0.0540552i
$358$	8.80254	−	32.8515i	0.465229	−	1.73626i
$359$		−	29.8863i		−	1.57734i	−0.614816	−	0.788671i	$-0.710770\pi$
$359$		−	29.8863i		−	1.57734i	0.614816	−	0.788671i	$-0.289230\pi$
$360$		0			0
$361$	−22.1271	+	38.3252i	−1.16458	+	2.01712i
$362$	−12.2967	+	3.29490i	−0.646302	+	0.173176i
$363$	5.77804	−	8.39402i	0.303268	−	0.440572i
$364$	0.368803	+	0.0706327i	0.0193305	+	0.00370216i
$365$		0			0
$366$	4.04191	−	11.3877i	0.211274	−	0.595244i
$367$	−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
$372$	−6.22474	+	9.04296i	−0.322738	+	0.468855i
$373$	−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
$378$	−0.977486	−	0.236929i	−0.0502764	−	0.0121863i
$379$	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
$381$	−14.3161	−	16.7867i	−0.733435	−	0.860007i
$382$	−27.7305	+	27.7305i	−1.41882	+	1.41882i
$383$	2.60975	+	0.699279i	0.133352	+	0.0357315i	0.324878	−	0.945756i	$-0.394677\pi$
$383$	2.60975	+	0.699279i	0.133352	+	0.0357315i	−0.191526	+	0.981488i	$0.561344\pi$
$384$	−16.6254	+	14.1786i	−0.848412	+	0.723547i
$385$		0			0
$386$	−32.4270	+	18.7218i	−1.65049	+	0.952912i
$387$	−12.2967	+	8.90678i	−0.625076	+	0.452757i
$388$	−0.132680	+	0.0355516i	−0.00673582	+	0.00180486i
$389$	−38.6182			−1.95802			−0.979011	−	0.203807i	$-0.934668\pi$
$389$	−38.6182			−1.95802			−0.979011	+	0.203807i	$0.934668\pi$
$390$		0			0
$391$	−36.1920			−1.83031
$392$	−12.4620	+	3.33918i	−0.629426	+	0.168654i
$393$	−20.2628	+	9.64677i	−1.02212	+	0.486615i
$394$	12.8645	−	7.42732i	0.648104	−	0.374183i
$395$		0			0
$396$	8.79634	+	7.14433i	0.442033	+	0.359016i
$397$	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
$399$	1.18742	−	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	$0.882746\pi$
$402$	4.95832	−	7.20318i	0.247299	−	0.359262i
$403$	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
$408$	13.7553	+	9.46851i	0.680990	+	0.468761i
$409$	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
$414$	−5.60898	+	35.0835i	−0.275666	+	1.72426i
$415$		0			0
$416$	−11.4099	+	13.1989i	−0.559414	+	0.647130i
$417$	5.46700	+	3.76322i	0.267720	+	0.184286i
$418$	−53.9335	+	14.4514i	−2.63797	+	0.706843i
$419$	10.9200	−	18.9139i	0.533476	−	0.924007i	−0.465760	−	0.884911i	$-0.654219\pi$
$419$	10.9200	−	18.9139i	0.533476	−	0.924007i	0.999235	−	0.0390956i	$-0.0124477\pi$
$420$		0			0
$421$		−	11.3030i		−	0.550876i	−0.961319	−	0.275438i	$-0.911177\pi$
$421$		−	11.3030i		−	0.550876i	0.961319	−	0.275438i	$-0.0888229\pi$
$422$	−3.22612	+	12.0401i	−0.157045	+	0.586101i
$423$	−0.782999	+	0.0811457i	−0.0380707	+	0.00394544i
$424$	5.07663			0.246543
$425$		0			0
$426$	−8.42157	+	23.7270i	−0.408027	+	1.14957i
$427$	−0.119724	−	0.446818i	−0.00579387	−	0.0216230i
$428$	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	$0.187532\pi$
$432$	17.9017	−	18.7822i	0.861295	−	0.903661i
$433$	−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
$438$	0.997073	−	12.5523i	0.0476420	−	0.599774i
$439$	−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	0.830230	−	0.557420i	$-0.188209\pi$
$443$	5.74199	+	5.74199i	0.272810	+	0.272810i	−0.557420	+	0.830230i	$0.688209\pi$
$444$	−2.26258	+	6.37461i	−0.107377	+	0.302525i
$445$		0			0
$446$	−17.9670	+	10.3733i	−0.850763	+	0.491188i
$447$	−16.9738	−	11.6840i	−0.802835	−	0.552633i
$448$	−0.0504097	+	0.188132i	−0.00238163	+	0.00888838i
$449$	23.4891	−	13.5614i	1.10852	−	0.640004i	0.170074	−	0.985431i	$-0.445599\pi$
$449$	23.4891	−	13.5614i	1.10852	−	0.640004i	0.938446	+	0.345427i	$0.112266\pi$
$450$		0			0
$451$	7.14224	+	12.3707i	0.336315	+	0.582515i
$452$	−1.88305	−	7.02763i	−0.0885711	−	0.330552i
$453$	−17.3610	+	8.26530i	−0.815693	+	0.388338i
$454$			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
$459$	−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	$0.538806\pi$
$462$	1.37325	+	0.109082i	0.0638896	+	0.00507496i
$463$	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	−0.0875827	−	0.996157i	$-0.527914\pi$
$467$	19.6345	−	19.6345i	0.908575	−	0.908575i	0.996157	+	0.0875827i	$0.0279142\pi$
$468$	5.69289	−	8.15292i	0.263154	−	0.376869i
$469$		−	0.334760i		−	0.0154578i
$470$		0			0
$471$	4.53900	−	12.7882i	0.209146	−	0.589249i
$472$	−0.341958	+	1.27621i	−0.0157399	+	0.0587421i
$473$	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
$477$	−8.20415	+	0.850233i	−0.375642	+	0.0389295i
$478$	5.10900	+	19.0670i	0.233680	+	0.872107i
$479$	−1.49161	−	0.861181i	−0.0681534	−	0.0393484i	0.465536	−	0.885029i	$-0.345862\pi$
$479$	−1.49161	−	0.861181i	−0.0681534	−	0.0393484i	−0.533689	+	0.845681i	$0.679195\pi$
$480$		0			0
$481$	2.88111	−	15.0435i	0.131367	−	0.685924i
$482$	−16.8711	+	16.8711i	−0.768456	+	0.768456i
$483$	0.584643	+	1.22803i	0.0266022	+	0.0558771i
$484$	−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	−0.0115102	−	0.999934i	$-0.503664\pi$
$491$	−19.5711	−	11.2994i	−0.883233	−	0.509935i	−0.871723	+	0.489999i	$0.836997\pi$
$492$	−4.99796	+	2.37945i	−0.225325	+	0.107274i
$493$	−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
$498$	8.52943	+	0.677520i	0.382213	+	0.0303604i
$499$	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
$501$	10.0269	+	11.7573i	0.447971	+	0.525279i
$502$	−20.8208	+	20.8208i	−0.929276	+	0.929276i
$503$	−8.55700	+	31.9352i	−0.381538	+	1.42392i	0.462015	+	0.886872i	$0.347127\pi$
$503$	−8.55700	+	31.9352i	−0.381538	+	1.42392i	−0.843553	+	0.537047i	$0.819540\pi$
$504$	0.0990719	−	0.619683i	0.00441302	−	0.0276029i
$505$		0			0
$506$		−	48.6623i		−	2.16330i
$507$	−9.95022	+	20.1988i	−0.441905	+	0.897062i
$508$	−8.28006	+	8.28006i	−0.367368	+	0.367368i
$509$	−5.25012	−	3.03116i	−0.232707	−	0.134354i	0.379113	−	0.925350i	$-0.376229\pi$
$509$	−5.25012	−	3.03116i	−0.232707	−	0.134354i	−0.611820	+	0.790997i	$0.709562\pi$
$510$		0			0
$511$	−0.241016	−	0.417452i	−0.0106619	−	0.0184670i
$512$	4.04633	+	4.04633i	0.178824	+	0.178824i
$513$	−11.6509	−	39.6500i	−0.514398	−	1.75059i
$514$	0.357631	+	0.619435i	0.0157744	+	0.0273221i
$515$		0			0
$516$	5.22933	+	6.13178i	0.230208	+	0.269936i
$517$	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	$-0.827554\pi$
$521$		−	23.5394i		−	1.03128i	0.856805	−	0.515640i	$-0.172446\pi$
$522$	12.0858	+	16.6857i	0.528982	+	0.730312i
$523$	−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
$528$	−20.1503	+	29.2733i	−0.876931	+	1.27396i
$529$	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
$533$	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
$537$	−34.3690	−	2.73004i	−1.48313	−	0.117810i
$538$	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
$543$	5.54739	+	11.6521i	0.238061	+	0.500041i
$544$	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	0.553993	−	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
$549$	−12.0960	−	1.93385i	−0.516244	−	0.0825347i
$550$		0			0
$551$	−31.9677			−1.36187
$552$	−22.0984	−	1.75534i	−0.940569	−	0.0747124i
$553$	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	0.256531	−	0.966536i	$-0.417420\pi$
$557$	22.7031	−	6.08328i	0.961962	−	0.257757i	0.705431	+	0.708779i	$0.250754\pi$
$558$	32.2644	+	14.4213i	1.36586	+	0.610501i
$559$	−13.8052	−	11.9339i	−0.583896	−	0.504752i
$560$		0			0
$561$	35.0200	+	12.4299i	1.47855	+	0.524791i
$562$	−22.2587	+	5.96419i	−0.938926	+	0.251584i
$563$	9.60782	−	35.8569i	0.404921	−	1.51119i	−0.399279	−	0.916829i	$-0.630740\pi$
$563$	9.60782	−	35.8569i	0.404921	−	1.51119i	0.804201	−	0.594358i	$-0.202594\pi$
$564$	0.0758413	+	0.410870i	0.00319350	+	0.0173007i
$565$		0			0
$566$	0.973289	+	1.68579i	0.0409104	+	0.0708589i
$567$	−0.0563221	+	1.01804i	−0.00236531	+	0.0427537i
$568$	−15.1738	−	4.06580i	−0.636678	−	0.170597i
$569$	−6.61515	+	11.4578i	−0.277322	+	0.480335i	−0.970718	−	0.240221i	$-0.922780\pi$
$569$	−6.61515	+	11.4578i	−0.277322	+	0.480335i	0.693397	+	0.720556i	$0.256113\pi$
$570$		0			0
$571$	16.3611			0.684690			0.342345	−	0.939574i	$-0.388779\pi$
$571$	16.3611			0.684690			0.342345	+	0.939574i	$0.388779\pi$
$572$	−5.93661	+	12.2576i	−0.248222	+	0.512515i
$573$	32.7469	+	22.5414i	1.36802	+	0.941681i
$574$	−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	$-0.764535\pi$
$577$	−1.55067	+	1.55067i	−0.0645553	+	0.0645553i	0.674092	+	0.738647i	$0.264535\pi$
$578$	−16.9386	−	4.53869i	−0.704554	−	0.188785i
$579$	24.6304	+	28.8810i	1.02361	+	1.20025i
$580$		0			0
$581$	0.283663	−	0.163773i	0.0117683	−	0.00679444i
$582$	0.190075	+	0.399247i	0.00787886	+	0.0165493i
$583$	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	−0.638061	−	0.769986i	$-0.720263\pi$
$587$	−19.5193	+	5.23017i	−0.805646	+	0.215872i	−0.167585	+	0.985858i	$0.553597\pi$
$588$	−4.78237	−	10.0452i	−0.197221	−	0.414258i
$589$	−47.4885	+	27.4175i	−1.95673	+	1.12972i
$590$		0			0
$591$	−9.77142	−	11.4577i	−0.401942	−	0.471307i
$592$	−20.4902	−	5.49034i	−0.842143	−	0.225651i
$593$	−3.08282	+	3.08282i	−0.126596	+	0.126596i	−0.767566	−	0.640970i	$-0.778532\pi$
$593$	−3.08282	+	3.08282i	−0.126596	+	0.126596i	0.640970	+	0.767566i	$0.278532\pi$
$594$	17.4765	−	32.0210i	0.717071	−	1.31384i
$595$		0			0
$596$	−5.46855	+	9.47180i	−0.224000	+	0.387980i
$597$	28.8981	+	19.8921i	1.18272	+	0.814128i
$598$	−42.5882	+	3.09615i	−1.74156	+	0.126611i
$599$	−17.9813			−0.734698			−0.367349	−	0.930083i	$-0.619734\pi$
$599$	−17.9813			−0.734698			−0.367349	+	0.930083i	$0.619734\pi$
$600$		0			0
$601$	−4.18909	+	7.25572i	−0.170877	+	0.295967i	−0.938727	−	0.344663i	$-0.887993\pi$
$601$	−4.18909	+	7.25572i	−0.170877	+	0.295967i	0.767850	+	0.640630i	$0.221327\pi$
$602$	0.946282	+	0.253555i	0.0385676	+	0.0103341i
$603$	−8.09314	−	3.61741i	−0.329578	−	0.147312i
$604$	5.10277	+	8.83825i	0.207629	+	0.359623i
$605$		0			0
$606$	6.51944	+	35.3190i	0.264834	+	1.43474i
$607$	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
$609$	0.743273	+	0.263815i	0.0301189	+	0.0106903i
$610$		0			0
$611$	−0.310483	−	0.893690i	−0.0125608	−	0.0361548i
$612$	−5.87625	+	13.1468i	−0.237533	+	0.531428i
$613$	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	$-0.725178\pi$
$617$	7.27686	−	27.1576i	0.292955	−	1.09332i	0.942828	−	0.333281i	$-0.108156\pi$
$618$	2.20418	+	0.175085i	0.0886650	+	0.00704295i
$619$	−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
$621$	36.0063	−	0.864283i	1.44488	−	0.0346825i
$622$	−1.05074	−	3.92142i	−0.0421309	−	0.157235i
$623$	−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
$627$	24.3309	+	51.1063i	0.971681	+	2.04099i
$628$	−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
$633$	12.5962	+	1.00056i	0.500654	+	0.0397686i
$634$	−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
$639$	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	$0.359116\pi$
$642$	2.77122	−	4.02588i	0.109371	−	0.158889i
$643$	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	0.991138	−	0.132836i	$-0.0424085\pi$
$647$	1.68818	+	6.30036i	0.0663691	+	0.247693i	−0.924769	+	0.380529i	$0.875742\pi$
$648$	−13.9109	−	9.09144i	−0.546470	−	0.357146i
$649$			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	−0.984842	−	0.173454i	$-0.944507\pi$
$653$	−44.7451	+	11.9894i	−1.75101	+	0.469182i	−0.766171	+	0.642637i	$0.777840\pi$
$654$	1.22684	+	1.43856i	0.0479731	+	0.0562521i
$655$		0			0
$656$	−8.67976	−	15.0338i	−0.338888	−	0.586971i
$657$	−12.6967	+	1.31582i	−0.495347	+	0.0513350i
$658$	0.0359145	+	0.0359145i	0.00140009	+	0.00140009i
$659$	12.0799	+	20.9230i	0.470566	+	0.815045i	0.999433	−	0.0336601i	$-0.0107164\pi$
$659$	12.0799	+	20.9230i	0.470566	+	0.815045i	−0.528867	+	0.848705i	$0.677383\pi$
$660$		0			0
$661$	35.3712	+	20.4215i	1.37578	+	0.794306i	0.991648	−	0.128973i	$-0.0411680\pi$
$661$	35.3712	+	20.4215i	1.37578	+	0.794306i	0.384130	+	0.923279i	$0.374501\pi$
$662$	−16.8478	+	16.8478i	−0.654809	+	0.654809i
$663$	8.65022	−	31.4396i	0.335947	−	1.22101i
$664$			5.33862i			0.207178i
$665$		0			0
$666$	21.5020	+	3.43764i	0.833186	+	0.133206i
$667$	7.21084	−	26.9112i	0.279205	−	1.04201i
$668$	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
$672$	−0.946517	−	0.0751849i	−0.0365127	−	0.00290032i
$673$	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	−0.278418	−	0.960460i	$-0.589810\pi$
$677$	17.7462	−	17.7462i	0.682043	−	0.682043i	0.960460	+	0.278418i	$0.0898099\pi$
$678$	−21.1468	+	10.0676i	−0.812138	+	0.386645i
$679$	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	−0.173290	−	0.984871i	$-0.555440\pi$
$683$	−21.3203	−	5.71276i	−0.815798	−	0.218593i	−0.642509	+	0.766278i	$0.722106\pi$
$684$	−20.4889	+	7.83079i	−0.783413	+	0.299418i
$685$		0			0
$686$	−2.34469	−	1.35371i	−0.0895208	−	0.0516848i
$687$	−6.34267	−	13.3226i	−0.241988	−	0.508289i
$688$	−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
$693$	−0.143953	−	1.38905i	−0.00546834	−	0.0527657i
$694$	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
$698$	2.63864	−	9.84754i	0.0998740	−	0.372735i
$699$	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	$-0.201635\pi$
$702$	−29.1360	−	13.2577i	−1.09967	−	0.500380i
$703$	−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
$708$	−1.13576	−	0.0902174i	−0.0426846	−	0.00339058i
$709$	−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
$711$	−11.2821	−	9.16330i	−0.423114	−	0.343650i
$712$	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
$717$	18.0676	−	8.60166i	0.674745	−	0.321235i
$718$	13.2163	+	49.3238i	0.493227	+	1.84075i
$719$	14.5548	+	25.2096i	0.542802	+	0.940160i	0.998742	+	0.0501495i	$0.0159698\pi$
$719$	14.5548	+	25.2096i	0.542802	+	0.940160i	−0.455940	+	0.890010i	$0.650697\pi$
$720$		0			0
$721$	0.0733041	−	0.0423222i	0.00272999	−	0.00157616i
$722$	19.5699	−	73.0360i	0.728318	−	2.71812i
$723$	19.9230	+	13.7140i	0.740944	+	0.510030i
$724$	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	0.427161	−	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
$732$	−0.514822	+	6.48119i	−0.0190284	+	0.239552i
$733$	−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
$738$	10.4531	+	14.4315i	0.384782	+	0.531230i
$739$	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
$741$	43.1790	−	24.5455i	1.58622	−	0.901701i
$742$	0.376307	+	0.376307i	0.0138147	+	0.0138147i
$743$	−9.73165	−	36.3190i	−0.357020	−	1.33242i	−0.877924	−	0.478801i	$-0.841072\pi$
$743$	−9.73165	−	36.3190i	−0.357020	−	1.33242i	0.520904	−	0.853615i	$-0.325595\pi$
$744$	−7.37570	+	20.7803i	−0.270406	+	0.761843i
$745$		0			0
$746$	34.1098			1.24885
$747$	−0.894111	−	8.62754i	−0.0327138	−	0.315665i
$748$	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
$753$	24.5872	+	16.9246i	0.896007	+	0.616768i
$754$	−16.1934	+	18.7326i	−0.589730	+	0.682200i
$755$		0			0
$756$	0.541006	−	0.0129861i	0.0196762	−	0.000472300i
$757$	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	$0.00710150\pi$
$761$	14.3226	+	24.8075i	0.519195	+	0.899272i	−0.480556	+	0.876964i	$0.659565\pi$
$762$	31.0503	+	21.3735i	1.12483	+	0.774282i
$763$	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
$768$	17.7914	−	25.8464i	0.641992	−	0.932650i
$769$	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
$771$	0.551697	−	0.470501i	0.0198689	−	0.0169447i
$772$	14.2456	−	14.2456i	0.512711	−	0.512711i
$773$	34.1355	+	9.14659i	1.22777	+	0.328980i	0.813711	−	0.581270i	$-0.197444\pi$
$773$	34.1355	+	9.14659i	1.22777	+	0.328980i	0.414059	+	0.910250i	$0.364111\pi$
$774$	16.3555	−	20.1374i	0.587885	−	0.723823i
$775$		0			0
$776$	−0.238933	+	0.137948i	−0.00857720	+	0.00495205i
$777$	0.752634	−	0.358317i	0.0270006	−	0.0128545i
$778$	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
$783$	14.4098	−	15.1186i	0.514963	−	0.540293i
$784$	30.2159	−	17.4452i	1.07914	−	0.623042i
$785$		0			0
$786$	29.1753	−	24.8814i	1.04065	−	0.887489i
$787$	−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
$789$	14.7067	+	17.2447i	0.523572	+	0.613928i
$790$		0			0
$791$	−0.448293	+	0.776465i	−0.0159394	+	0.0276079i
$792$	20.7799	+	9.28803i	0.738382	+	0.330036i
$793$	−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	−0.0201695	−	0.999797i	$-0.506421\pi$
$797$	−15.1753	−	4.06620i	−0.537535	−	0.144032i	−0.517366	+	0.855764i	$0.673087\pi$
$798$	−1.51188	+	2.19638i	−0.0535200	+	0.0777509i
$799$	0.685047	+	1.18654i	0.0242352	+	0.0419766i
$800$		0			0
$801$	−9.05919	+	3.46239i	−0.320091	+	0.122338i
$802$	13.7844	−	51.4442i	0.486745	−	1.81656i
$803$	16.8875	−	4.52499i	0.595946	−	0.159683i
$804$	−1.57381	+	4.43406i	−0.0555041	+	0.156377i
$805$		0			0
$806$	−7.98939	+	41.7160i	−0.281414	+	1.46938i
$807$	0.792760	−	1.15168i	0.0279065	−	0.0405410i
$808$	−21.6457	+	5.79994i	−0.761492	+	0.204041i
$809$	9.50547	−	16.4640i	0.334195	−	0.578842i	−0.649135	−	0.760673i	$-0.724869\pi$
$809$	9.50547	−	16.4640i	0.334195	−	0.578842i	0.983330	+	0.181831i	$0.0582024\pi$
$810$		0			0
$811$		−	18.8816i		−	0.663023i	−0.943451	−	0.331512i	$-0.892441\pi$
$811$		−	18.8816i		−	0.663023i	0.943451	−	0.331512i	$-0.107559\pi$
$812$	0.108345	−	0.404349i	0.00380216	−	0.0141899i
$813$	1.46075	−	18.3896i	0.0512307	−	0.644953i
$814$	−29.8242			−1.04534
$815$		0			0
$816$	−42.5589	−	15.1057i	−1.48986	−	0.528806i
$817$	10.4182	+	38.8812i	0.364486	+	1.36028i
$818$	−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	$0.177011\pi$
$822$	33.2935	−	15.8505i	1.16124	−	0.552849i
$823$	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	0.596959	−	0.802272i	$-0.296375\pi$
$827$	−5.90430	−	5.90430i	−0.205313	−	0.205313i	−0.802272	+	0.596959i	$0.796375\pi$
$828$	−1.97055	−	19.0144i	−0.0684813	−	0.660797i
$829$	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
$834$	−10.6868	−	3.79313i	−0.370053	−	0.131345i
$835$		0			0
$836$	26.0175	−	15.0212i	0.899833	−	0.519519i
$837$	8.43932	−	34.8176i	0.291706	−	1.20347i
$838$	−9.65801	+	36.0442i	−0.333630	+	1.24513i
$839$	−6.21211	+	3.58656i	−0.214466	+	0.123822i	−0.603385	−	0.797450i	$-0.706182\pi$
$839$	−6.21211	+	3.58656i	−0.214466	+	0.123822i	0.388919	+	0.921272i	$0.372848\pi$
$840$		0			0
$841$	6.42199	+	11.1232i	0.221448	+	0.383559i
$842$	4.99840	+	18.6543i	0.172256	+	0.642869i
$843$	10.0415	+	21.0919i	0.345847	+	0.726443i
$844$		−	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
$849$	1.50144	−	1.28046i	0.0515293	−	0.0439454i
$850$		0			0
$851$	−14.7228	−	25.5007i	−0.504692	−	0.874152i
$852$	1.07266	−	13.5040i	0.0367488	−	0.462638i
$853$	−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	$0.525272\pi$
$857$	−31.5042	+	31.5042i	−1.07616	+	1.07616i	−0.996850	+	0.0793118i	$0.974728\pi$
$858$	42.2724	+	11.6307i	1.44316	+	0.397066i
$859$			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
$861$	0.642858	+	0.228174i	0.0219085	+	0.00777615i
$862$	1.20272	−	4.48861i	0.0409648	−	0.152883i
$863$	−9.69182	+	9.69182i	−0.329913	+	0.329913i	−0.852553	−	0.522640i	$-0.824947\pi$
$863$	−9.69182	+	9.69182i	−0.329913	+	0.329913i	0.522640	+	0.852553i	$0.324947\pi$
$864$	−12.0457	+	22.0705i	−0.409804	+	0.750854i
$865$		0			0
$866$	24.2113			0.822732
$867$	−1.40764	+	17.7211i	−0.0478060	+	0.601839i
$868$	−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
$873$	0.363028	−	0.262950i	0.0122866	−	0.00889949i
$874$	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	0.500400	−	0.865794i	$-0.333186\pi$
$881$	0.0237715	+	0.0137245i	0.000800881	+	0.000462389i	−0.499600	+	0.866257i	$0.666519\pi$
$882$	−29.0053	+	21.0092i	−0.976660	+	0.707418i
$883$	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	0.977849	−	0.209309i	$-0.0671216\pi$
$887$	0.784839	+	2.92906i	0.0263523	+	0.0983482i	−0.951497	+	0.307658i	$0.900455\pi$
$888$	−1.07582	+	13.5437i	−0.0361021	+	0.454496i
$889$	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
$893$	−0.540132	+	2.01580i	−0.0180748	+	0.0674562i
$894$	33.1801	+	11.7768i	1.10971	+	0.393876i
$895$		0			0
$896$		−	1.42917i		−	0.0477451i
$897$	10.9233	+	41.8858i	0.364717	+	1.39853i
$898$	−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
$903$	0.0786383	−	0.989992i	0.00261692	−	0.0329449i
$904$	−7.30666	−	12.6555i	−0.243016	−	0.420916i
$905$		0			0
$906$	24.9972	−	21.3182i	0.830477	−	0.708251i
$907$	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	$0.0252501\pi$
$911$			4.78351i			0.158485i	−0.996855	+	0.0792423i	$0.974750\pi$
$912$	−29.5686	−	62.1080i	−0.979114	−	2.05660i
$913$	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
$918$	45.0521	+	10.9200i	1.48694	+	0.360415i
$919$	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
$921$	12.1953	+	4.32855i	0.401848	+	0.142631i
$922$	−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
$927$	−0.231056	−	2.22953i	−0.00758888	−	0.0732274i
$928$	13.7531	+	13.7531i	0.451467	+	0.451467i
$929$	27.3742	−	15.8045i	0.898117	−	0.518528i	0.0215282	−	0.999768i	$-0.493147\pi$
$929$	27.3742	−	15.8045i	0.898117	−	0.518528i	0.876589	+	0.481240i	$0.159814\pi$
$930$		0			0
$931$		−	55.5706i		−	1.82125i
$932$	−10.8156	−	2.89804i	−0.354277	−	0.0949283i
$933$	−3.71586	+	1.76906i	−0.121652	+	0.0579164i
$934$	−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	0.882902	−	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
$939$	−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	$0.798233\pi$
$942$	−1.83591	+	23.1126i	−0.0598171	+	0.753048i
$943$	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	0.146440	−	0.989220i	$-0.453218\pi$
$947$	23.6300	−	6.33163i	0.767871	−	0.205750i	0.621431	+	0.783469i	$0.286552\pi$
$948$	−4.37408	+	6.35443i	−0.142064	+	0.206382i
$949$	−5.03464	−	14.4916i	−0.163431	−	0.470419i
$950$		0			0
$951$	−19.5858	+	55.1811i	−0.635114	+	1.78937i
$952$	−1.05503	+	0.282693i	−0.0341936	+	0.00916215i
$953$	−11.1821	+	41.7321i	−0.362223	+	1.35184i	0.508923	+	0.860812i	$0.330044\pi$
$953$	−11.1821	+	41.7321i	−0.362223	+	1.35184i	−0.871146	+	0.491024i	$0.836623\pi$
$954$	13.1640	−	5.03122i	0.426199	−	0.162892i
$955$		0			0
$956$	−5.31043	−	9.19793i	−0.171751	−	0.297482i
$957$	−16.2198	+	23.5632i	−0.524312	+	0.761691i
$958$	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
$963$	−4.52328	−	2.02178i	−0.145761	−	0.0651510i
$964$	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	$-0.716990\pi$
$967$	4.55251	−	4.55251i	0.146399	−	0.146399i	0.776507	+	0.630108i	$0.216990\pi$
$968$	−10.4935	−	2.81172i	−0.337273	−	0.0903721i
$969$	−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	$-0.0646838\pi$
$972$	5.53215	−	13.2197i	0.177444	−	0.424021i
$973$	−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	−0.992399	−	0.123059i	$-0.960730\pi$
$977$	−55.9598	+	14.9944i	−1.79031	+	0.479713i	−0.797914	+	0.602772i	$0.794063\pi$
$978$	32.7508	−	15.5921i	1.04725	−	0.498580i
$979$	11.5036	−	6.64164i	0.367658	−	0.212268i
$980$		0			0
$981$	1.20833	−	1.48773i	0.0385789	−	0.0474995i
$982$	37.2966	+	9.99359i	1.19018	+	0.318908i
$983$	17.2893	−	17.2893i	0.551443	−	0.551443i	−0.375414	−	0.926857i	$-0.622500\pi$
$983$	17.2893	−	17.2893i	0.551443	−	0.551443i	0.926857	+	0.375414i	$0.122500\pi$
$984$	−8.45965	+	7.21460i	−0.269684	+	0.229993i
$985$		0			0
$986$	17.9295	−	31.0548i	0.570991	−	0.988985i
$987$	0.0291940	−	0.0424114i	0.000929254	−	0.00134997i
$988$	−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
$993$	19.8956	+	13.6952i	0.631367	+	0.434602i
$994$	−0.823384	−	1.42614i	−0.0261162	−	0.0452345i
$995$		0			0
$996$	−4.52721	+	0.835664i	−0.143450	+	0.0264790i
$997$	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
$999$	−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.407.6		96
3.2	odd	2	inner	975.2.bn.d.407.19		96
5.2	odd	4		195.2.bf.a.173.6	yes	96
5.3	odd	4	inner	975.2.bn.d.368.19		96
5.4	even	2		195.2.bf.a.17.19	yes	96
13.10	even	6	inner	975.2.bn.d.257.6		96
15.2	even	4		195.2.bf.a.173.19	yes	96
15.8	even	4	inner	975.2.bn.d.368.6		96
15.14	odd	2		195.2.bf.a.17.6	✓	96
39.23	odd	6	inner	975.2.bn.d.257.19		96
65.23	odd	12	inner	975.2.bn.d.218.19		96
65.49	even	6		195.2.bf.a.62.19	yes	96
65.62	odd	12		195.2.bf.a.23.6	yes	96
195.23	even	12	inner	975.2.bn.d.218.6		96
195.62	even	12		195.2.bf.a.23.19	yes	96
195.179	odd	6		195.2.bf.a.62.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.6	✓	96	15.14	odd	2
195.2.bf.a.17.19	yes	96	5.4	even	2
195.2.bf.a.23.6	yes	96	65.62	odd	12
195.2.bf.a.23.19	yes	96	195.62	even	12
195.2.bf.a.62.6	yes	96	195.179	odd	6
195.2.bf.a.62.19	yes	96	65.49	even	6
195.2.bf.a.173.6	yes	96	5.2	odd	4
195.2.bf.a.173.19	yes	96	15.2	even	4
975.2.bn.d.218.6		96	195.23	even	12	inner
975.2.bn.d.218.19		96	65.23	odd	12	inner
975.2.bn.d.257.6		96	13.10	even	6	inner
975.2.bn.d.257.19		96	39.23	odd	6	inner
975.2.bn.d.368.6		96	15.8	even	4	inner
975.2.bn.d.368.19		96	5.3	odd	4	inner
975.2.bn.d.407.6		96	1.1	even	1	trivial
975.2.bn.d.407.19		96	3.2	odd	2	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+(-1.65038 + 0.442218i) q^{2} +(0.744530 + 1.56387i) q^{3} +(0.796141 - 0.459652i) q^{4} +(-1.92033 - 2.25172i) q^{6} +(-0.109428 - 0.0293212i) q^{7} +(1.30565 - 1.30565i) q^{8} +(-1.89135 + 2.32869i) q^{9} +(2.05447 - 3.55845i) q^{11} +(1.31159 + 0.902832i) q^{12} +(-3.24500 - 1.57162i) q^{13} +0.193564 q^{14} +(-2.49674 + 4.32449i) q^{16} +(5.04353 + 1.35141i) q^{17} +(2.09165 - 4.67961i) 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} +(3.01397 + 1.06977i) q^{24} +(6.05047 + 1.15878i) q^{26} +(-5.04992 - 1.22403i) q^{27} +(-0.100598 + 0.0269551i) q^{28} +(-2.00973 + 3.48095i) q^{29} +6.89468i q^{31} +(1.25240 - 4.67403i) q^{32} +(7.09456 + 0.563544i) q^{33} -8.92135 q^{34} +(-0.435393 + 2.72333i) q^{36} +(1.09950 + 4.10339i) q^{37} +(-9.60880 - 9.60880i) q^{38} +(0.0418074 - 6.24486i) q^{39} +(-1.73822 + 3.01068i) q^{41} +(0.144115 + 0.302709i) q^{42} +(4.88872 + 1.30993i) q^{43} -3.77737i q^{44} +(10.2563 - 5.92150i) q^{46} +(0.185543 + 0.185543i) q^{47} +(-8.62182 - 0.684859i) 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} +(8.87558 - 0.213046i) q^{54} +(-0.181159 + 0.104592i) q^{56} +(-7.81074 + 11.3470i) 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} +(0.275247 - 0.199368i) q^{63} -1.71922i q^{64} +(-11.9579 + 2.20728i) q^{66} +(0.764792 + 2.85424i) q^{67} +(4.63654 - 1.24236i) q^{68} +(-7.79036 - 9.13477i) q^{69} +(-4.25380 - 7.36780i) q^{71} +(0.571017 + 5.50991i) 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} +(2.69259 + 10.3249i) q^{78} +4.84485i q^{79} +(-1.84560 - 8.80873i) q^{81} +(1.53734 - 5.73743i) q^{82} +(-2.04442 + 2.04442i) q^{83} +(-0.117052 - 0.137253i) q^{84} -8.64751 q^{86} +(-6.94004 - 0.551270i) 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} +(-10.7823 + 5.13330i) 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

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Database

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