LMFDB - Embedded newform 925.2.y.b.193.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.5
Character	$\chi$	$=$	925.193
Dual form			925.2.y.b.532.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.971183 + 0.560713i) q^{2} +(-0.168506 - 0.628874i) q^{3} +(-0.371203 + 0.642942i) q^{4} +(0.516268 + 0.516268i) q^{6} +(0.377247 + 1.40791i) q^{7} -3.07540i q^{8} +(2.23099 - 1.28806i) q^{9} +0.304712i q^{11} +(0.466879 + 0.125100i) q^{12} +(0.187550 + 0.108282i) q^{13} +(-1.15581 - 1.15581i) q^{14} +(0.982011 + 1.70089i) q^{16} +(-0.836960 - 1.44966i) q^{17} +(-1.44446 + 2.50189i) q^{18} +(-1.91513 - 7.14737i) q^{19} +(0.821827 - 0.474482i) q^{21} +(-0.170856 - 0.295931i) q^{22} +5.69268i q^{23} +(-1.93404 + 0.518224i) q^{24} -0.242860 q^{26} +(-2.56707 - 2.56707i) q^{27} +(-1.04524 - 0.280071i) q^{28} +(-1.05734 - 1.05734i) q^{29} +(2.64214 - 2.64214i) q^{31} +(3.41933 + 1.97415i) q^{32} +(0.191625 - 0.0513459i) q^{33} +(1.62568 + 0.938587i) q^{34} +1.91253i q^{36} +(6.04562 - 0.671196i) q^{37} +(5.86756 + 5.86756i) q^{38} +(0.0364924 - 0.136191i) q^{39} +(2.07096 + 1.19567i) q^{41} +(-0.532096 + 0.921617i) q^{42} -7.13995i q^{43} +(-0.195912 - 0.113110i) q^{44} +(-3.19196 - 5.52863i) q^{46} +(3.92274 - 3.92274i) q^{47} +(0.904172 - 0.904172i) q^{48} +(4.22229 - 2.43774i) q^{49} +(-0.770618 + 0.770618i) q^{51} +(-0.139238 + 0.0803891i) q^{52} +(-2.13924 + 7.98376i) q^{53} +(3.93248 + 1.05370i) q^{54} +(4.32988 - 1.16019i) q^{56} +(-4.17208 + 2.40875i) q^{57} +(1.61973 + 0.434004i) q^{58} +(6.39295 + 1.71299i) q^{59} +(2.09439 + 7.81639i) q^{61} +(-1.08452 + 4.04748i) q^{62} +(2.65511 + 2.65511i) q^{63} -8.35577 q^{64} +(-0.157313 + 0.157313i) q^{66} +(7.56615 - 2.02734i) q^{67} +1.24273 q^{68} +(3.57998 - 0.959252i) q^{69} +(5.55820 - 9.62708i) q^{71} +(-3.96131 - 6.86119i) q^{72} +(8.42960 - 8.42960i) q^{73} +(-5.49505 + 4.04171i) q^{74} +(5.30625 + 1.42180i) q^{76} +(-0.429006 + 0.114952i) q^{77} +(0.0409234 + 0.152728i) q^{78} +(-1.51908 - 5.66927i) q^{79} +(2.68239 - 4.64604i) q^{81} -2.68171 q^{82} +(-1.06045 + 3.95767i) q^{83} +0.704516i q^{84} +(4.00346 + 6.93419i) q^{86} +(-0.486763 + 0.843098i) q^{87} +0.937113 q^{88} +(0.842850 - 3.14556i) q^{89} +(-0.0816982 + 0.304902i) q^{91} +(-3.66007 - 2.11314i) q^{92} +(-2.10679 - 1.21635i) q^{93} +(-1.61017 + 6.00923i) q^{94} +(0.665313 - 2.48298i) q^{96} +4.65513 q^{97} +(-2.73374 + 4.73498i) q^{98} +(0.392488 + 0.679809i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.971183	+	0.560713i	−0.686730	+	0.396484i	−0.802386	−	0.596806i	$-0.796436\pi$
$2$	−0.971183	+	0.560713i	−0.686730	+	0.396484i	0.115656	+	0.993289i	$0.463103\pi$
$3$	−0.168506	−	0.628874i	−0.0972871	−	0.363080i	0.900069	−	0.435747i	$-0.143516\pi$
$3$	−0.168506	−	0.628874i	−0.0972871	−	0.363080i	−0.997356	+	0.0726666i	$0.976849\pi$
$4$	−0.371203	+	0.642942i	−0.185601	+	0.321471i
$5$		0			0
$5$		0			0
$6$	0.516268	+	0.516268i	0.210765	+	0.210765i
$7$	0.377247	+	1.40791i	0.142586	+	0.532139i	0.999851	+	0.0172630i	$0.00549527\pi$
$7$	0.377247	+	1.40791i	0.142586	+	0.532139i	−0.857265	+	0.514876i	$0.827838\pi$
$8$		−	3.07540i		−	1.08732i
$9$	2.23099	−	1.28806i	0.743663	−	0.429354i
$10$		0			0
$11$			0.304712i			0.0918742i	0.998944	+	0.0459371i	$0.0146274\pi$
$11$			0.304712i			0.0918742i	−0.998944	+	0.0459371i	$0.985373\pi$
$12$	0.466879	+	0.125100i	0.134776	+	0.0361132i
$13$	0.187550	+	0.108282i	0.0520170	+	0.0300320i	0.525783	−	0.850619i	$-0.323772\pi$
$13$	0.187550	+	0.108282i	0.0520170	+	0.0300320i	−0.473766	+	0.880651i	$0.657106\pi$
$14$	−1.15581	−	1.15581i	−0.308902	−	0.308902i
$15$		0			0
$16$	0.982011	+	1.70089i	0.245503	+	0.425223i
$17$	−0.836960	−	1.44966i	−0.202993	−	0.351593i	0.746499	−	0.665387i	$-0.231733\pi$
$17$	−0.836960	−	1.44966i	−0.202993	−	0.351593i	−0.949491	+	0.313793i	$0.898400\pi$
$18$	−1.44446	+	2.50189i	−0.340464	+	0.589700i
$19$	−1.91513	−	7.14737i	−0.439361	−	1.63972i	−0.730409	−	0.683010i	$-0.760671\pi$
$19$	−1.91513	−	7.14737i	−0.439361	−	1.63972i	0.291048	−	0.956708i	$-0.405996\pi$
$20$		0			0
$21$	0.821827	−	0.474482i	0.179337	−	0.103540i
$22$	−0.170856	−	0.295931i	−0.0364266	−	0.0630927i
$23$			5.69268i			1.18701i	0.804832	+	0.593503i	$0.202256\pi$
$23$			5.69268i			1.18701i	−0.804832	+	0.593503i	$0.797744\pi$
$24$	−1.93404	+	0.518224i	−0.394784	+	0.105782i
$25$		0			0
$26$	−0.242860			−0.0476288
$27$	−2.56707	−	2.56707i	−0.494032	−	0.494032i
$28$	−1.04524	−	0.280071i	−0.197531	−	0.0529284i
$29$	−1.05734	−	1.05734i	−0.196342	−	0.196342i	0.602088	−	0.798430i	$-0.294336\pi$
$29$	−1.05734	−	1.05734i	−0.196342	−	0.196342i	−0.798430	+	0.602088i	$0.794336\pi$
$30$		0			0
$31$	2.64214	−	2.64214i	0.474542	−	0.474542i	−0.428839	−	0.903381i	$-0.641077\pi$
$31$	2.64214	−	2.64214i	0.474542	−	0.474542i	0.903381	+	0.428839i	$0.141077\pi$
$32$	3.41933	+	1.97415i	0.604458	+	0.348984i
$33$	0.191625	−	0.0513459i	0.0333577	−	0.00893817i
$34$	1.62568	+	0.938587i	0.278802	+	0.160966i
$35$		0			0
$36$			1.91253i			0.318755i
$37$	6.04562	−	0.671196i	0.993893	−	0.110344i
$37$	6.04562	−	0.671196i	0.993893	−	0.110344i
$38$	5.86756	+	5.86756i	0.951844	+	0.951844i
$39$	0.0364924	−	0.136191i	0.00584345	−	0.0218081i
$40$		0			0
$41$	2.07096	+	1.19567i	0.323430	+	0.186732i	0.652920	−	0.757427i	$-0.273544\pi$
$41$	2.07096	+	1.19567i	0.323430	+	0.186732i	−0.329491	+	0.944159i	$0.606877\pi$
$42$	−0.532096	+	0.921617i	−0.0821042	+	0.142209i
$43$		−	7.13995i		−	1.08883i	−0.838815	−	0.544416i	$-0.816751\pi$
$43$		−	7.13995i		−	1.08883i	0.838815	−	0.544416i	$-0.183249\pi$
$44$	−0.195912	−	0.113110i	−0.0295349	−	0.0170520i
$45$		0			0
$46$	−3.19196	−	5.52863i	−0.470629	−	0.815153i
$47$	3.92274	−	3.92274i	0.572191	−	0.572191i	−0.360549	−	0.932740i	$-0.617411\pi$
$47$	3.92274	−	3.92274i	0.572191	−	0.572191i	0.932740	+	0.360549i	$0.117411\pi$
$48$	0.904172	−	0.904172i	0.130506	−	0.130506i
$49$	4.22229	−	2.43774i	0.603185	−	0.348249i
$50$		0			0
$51$	−0.770618	+	0.770618i	−0.107908	+	0.107908i
$52$	−0.139238	+	0.0803891i	−0.0193088	+	0.0111480i
$53$	−2.13924	+	7.98376i	−0.293848	+	1.09665i	0.648281	+	0.761401i	$0.275488\pi$
$53$	−2.13924	+	7.98376i	−0.293848	+	1.09665i	−0.942128	+	0.335253i	$0.891178\pi$
$54$	3.93248	+	1.05370i	0.535142	+	0.143391i
$55$		0			0
$56$	4.32988	−	1.16019i	0.578605	−	0.155037i
$57$	−4.17208	+	2.40875i	−0.552605	+	0.319047i
$58$	1.61973	+	0.434004i	0.212681	+	0.0569876i
$59$	6.39295	+	1.71299i	0.832291	+	0.223012i	0.649713	−	0.760180i	$-0.274889\pi$
$59$	6.39295	+	1.71299i	0.832291	+	0.223012i	0.182578	+	0.983191i	$0.441556\pi$
$60$		0			0
$61$	2.09439	+	7.81639i	0.268160	+	1.00079i	0.960288	+	0.279011i	$0.0900066\pi$
$61$	2.09439	+	7.81639i	0.268160	+	1.00079i	−0.692128	+	0.721775i	$0.743327\pi$
$62$	−1.08452	+	4.04748i	−0.137734	+	0.514030i
$63$	2.65511	+	2.65511i	0.334512	+	0.334512i
$64$	−8.35577			−1.04447
$65$		0			0
$66$	−0.157313	+	0.157313i	−0.0193639	+	0.0193639i
$67$	7.56615	−	2.02734i	0.924353	−	0.247680i	0.234908	−	0.972018i	$-0.424521\pi$
$67$	7.56615	−	2.02734i	0.924353	−	0.247680i	0.689445	+	0.724338i	$0.257855\pi$
$68$	1.24273			0.150703
$69$	3.57998	−	0.959252i	0.430979	−	0.115480i
$70$		0			0
$71$	5.55820	−	9.62708i	0.659637	−	1.14252i	−0.321073	−	0.947054i	$-0.604044\pi$
$71$	5.55820	−	9.62708i	0.659637	−	1.14252i	0.980710	−	0.195470i	$-0.0626231\pi$
$72$	−3.96131	−	6.86119i	−0.466845	−	0.808599i
$73$	8.42960	−	8.42960i	0.986611	−	0.986611i	−0.0133009	−	0.999912i	$-0.504234\pi$
$73$	8.42960	−	8.42960i	0.986611	−	0.986611i	0.999912	+	0.0133009i	$0.00423394\pi$
$74$	−5.49505	+	4.04171i	−0.638787	+	0.469839i
$75$		0			0
$76$	5.30625	+	1.42180i	0.608668	+	0.163092i
$77$	−0.429006	+	0.114952i	−0.0488898	+	0.0131000i
$78$	0.0409234	+	0.152728i	0.00463367	+	0.0172931i
$79$	−1.51908	−	5.66927i	−0.170909	−	0.637843i	−0.997212	−	0.0746166i	$-0.976227\pi$
$79$	−1.51908	−	5.66927i	−0.170909	−	0.637843i	0.826303	−	0.563226i	$-0.190440\pi$
$80$		0			0
$81$	2.68239	−	4.64604i	0.298044	−	0.516227i
$82$	−2.68171			−0.296145
$83$	−1.06045	+	3.95767i	−0.116400	+	0.434410i	−0.999388	−	0.0349854i	$-0.988862\pi$
$83$	−1.06045	+	3.95767i	−0.116400	+	0.434410i	0.882988	+	0.469396i	$0.155528\pi$
$84$			0.704516i			0.0768690i
$85$		0			0
$86$	4.00346	+	6.93419i	0.431704	+	0.747733i
$87$	−0.486763	+	0.843098i	−0.0521864	+	0.0903896i
$88$	0.937113			0.0998966
$89$	0.842850	−	3.14556i	0.0893419	−	0.333429i	−0.906759	−	0.421649i	$-0.861451\pi$
$89$	0.842850	−	3.14556i	0.0893419	−	0.333429i	0.996101	+	0.0882206i	$0.0281181\pi$
$90$		0			0
$91$	−0.0816982	+	0.304902i	−0.00856430	+	0.0319624i
$92$	−3.66007	−	2.11314i	−0.381588	−	0.220310i
$93$	−2.10679	−	1.21635i	−0.218464	−	0.126130i
$94$	−1.61017	+	6.00923i	−0.166076	+	0.619805i
$95$		0			0
$96$	0.665313	−	2.48298i	0.0679032	−	0.253418i
$97$	4.65513			0.472657			0.236328	−	0.971673i	$-0.424056\pi$
$97$	4.65513			0.472657			0.236328	+	0.971673i	$0.424056\pi$
$98$	−2.73374	+	4.73498i	−0.276150	+	0.478306i
$99$	0.392488	+	0.679809i	0.0394465	+	0.0683234i
$100$		0			0
$101$			17.1782i			1.70929i	0.519212	+	0.854646i	$0.326226\pi$
$101$			17.1782i			1.70929i	−0.519212	+	0.854646i	$0.673774\pi$
$102$	0.316316	−	1.18051i	0.0313199	−	0.116887i
$103$	−2.88061			−0.283835			−0.141917	−	0.989879i	$-0.545327\pi$
$103$	−2.88061			−0.283835			−0.141917	+	0.989879i	$0.545327\pi$
$104$	0.333011	−	0.576791i	0.0326544	−	0.0565590i
$105$		0			0
$106$	−2.39900	−	8.95319i	−0.233012	−	0.869611i
$107$	−2.31406	−	8.63621i	−0.223709	−	0.834894i	−0.982918	−	0.184046i	$-0.941080\pi$
$107$	−2.31406	−	8.63621i	−0.223709	−	0.834894i	0.759208	−	0.650848i	$-0.225586\pi$
$108$	2.60338	−	0.697573i	0.250510	−	0.0671240i
$109$	−7.23354	−	1.93822i	−0.692847	−	0.185648i	−0.104823	−	0.994491i	$-0.533427\pi$
$109$	−7.23354	−	1.93822i	−0.692847	−	0.185648i	−0.588024	+	0.808843i	$0.700094\pi$
$110$		0			0
$111$	−1.44082	−	3.68883i	−0.136757	−	0.350128i
$112$	−2.02424	+	2.02424i	−0.191272	+	0.191272i
$113$	−4.73356	−	8.19876i	−0.445296	−	0.771274i	0.552777	−	0.833329i	$-0.313568\pi$
$113$	−4.73356	−	8.19876i	−0.445296	−	0.771274i	−0.998073	+	0.0620546i	$0.980235\pi$
$114$	2.70123	−	4.67867i	0.252994	−	0.438198i
$115$		0			0
$116$	1.07229	−	0.287320i	0.0995597	−	0.0266770i
$117$	0.557895			0.0515774
$118$	−7.16921	+	1.92099i	−0.659980	+	0.176841i
$119$	1.72524	−	1.72524i	0.158153	−	0.158153i
$120$		0			0
$121$	10.9072			0.991559
$122$	−6.41678	−	6.41678i	−0.580948	−	0.580948i
$123$	0.402955	−	1.50385i	0.0363333	−	0.135598i
$124$	0.717973	+	2.67951i	0.0644759	+	0.240627i
$125$		0			0
$126$	−4.06734	−	1.08984i	−0.362348	−	0.0970908i
$127$	13.0380	+	3.49352i	1.15694	+	0.310000i	0.785742	−	0.618555i	$-0.212282\pi$
$127$	13.0380	+	3.49352i	1.15694	+	0.310000i	0.371195	+	0.928555i	$0.378948\pi$
$128$	1.27632	−	0.736883i	0.112812	−	0.0651319i
$129$	−4.49013	+	1.20313i	−0.395334	+	0.105929i
$130$		0			0
$131$	−4.26758	−	1.14350i	−0.372861	−	0.0999077i	0.0675223	−	0.997718i	$-0.478491\pi$
$131$	−4.26758	−	1.14350i	−0.372861	−	0.0999077i	−0.440383	+	0.897810i	$0.645157\pi$
$132$	−0.0381195	+	0.142264i	−0.00331788	+	0.0123825i
$133$	9.34035	−	5.39265i	0.809911	−	0.467602i
$134$	−6.21136	+	6.21136i	−0.536580	+	0.536580i
$135$		0			0
$136$	−4.45828	+	2.57399i	−0.382294	+	0.220718i
$137$	6.35777	−	6.35777i	0.543181	−	0.543181i	−0.381279	−	0.924460i	$-0.624516\pi$
$137$	6.35777	−	6.35777i	0.543181	−	0.543181i	0.924460	+	0.381279i	$0.124516\pi$
$138$	−2.93895	+	2.93895i	−0.250180	+	0.250180i
$139$	11.4157	+	19.7725i	0.968263	+	1.67708i	0.700580	+	0.713574i	$0.252925\pi$
$139$	11.4157	+	19.7725i	0.968263	+	1.67708i	0.267683	+	0.963507i	$0.413742\pi$
$140$		0			0
$141$	−3.12792	−	1.80590i	−0.263418	−	0.152084i
$142$			12.4662i			1.04614i
$143$	−0.0329948	+	0.0571487i	−0.00275917	+	0.00477902i
$144$	4.38171	+	2.52978i	0.365143	+	0.210815i
$145$		0			0
$146$	−3.46010	+	12.9133i	−0.286360	+	1.06871i
$147$	−2.24451	−	2.24451i	−0.185124	−	0.185124i
$148$	−1.81261	+	4.13613i	−0.148996	+	0.339988i
$149$			13.4493i			1.10181i	0.834567	+	0.550906i	$0.185718\pi$
$149$			13.4493i			1.10181i	−0.834567	+	0.550906i	$0.814282\pi$
$150$		0			0
$151$	−14.7480	−	8.51479i	−1.20018	−	0.692924i	−0.239584	−	0.970876i	$-0.577011\pi$
$151$	−14.7480	−	8.51479i	−1.20018	−	0.692924i	−0.960595	+	0.277952i	$0.910344\pi$
$152$	−21.9810	+	5.88980i	−1.78290	+	0.477726i
$153$	−3.73449	−	2.15611i	−0.301916	−	0.174311i
$154$	0.352189	−	0.352189i	0.0283802	−	0.0283802i
$155$		0			0
$156$	0.0740171	+	0.0740171i	0.00592611	+	0.00592611i
$157$	18.1462	+	4.86225i	1.44822	+	0.388050i	0.895404	−	0.445254i	$-0.146887\pi$
$157$	18.1462	+	4.86225i	1.44822	+	0.388050i	0.552816	+	0.833303i	$0.313553\pi$
$158$	4.65413	+	4.65413i	0.370263	+	0.370263i
$159$	5.38125			0.426761
$160$		0			0
$161$	−8.01477	+	2.14755i	−0.631652	+	0.169251i
$162$			6.01620i			0.472678i
$163$	1.48872	+	2.57854i	0.116606	+	0.201967i	0.918421	−	0.395606i	$-0.129465\pi$
$163$	1.48872	+	2.57854i	0.116606	+	0.201967i	−0.801815	+	0.597573i	$0.796132\pi$
$164$	−1.53749	+	0.887672i	−0.120058	+	0.0693155i
$165$		0			0
$166$	−1.18922	−	4.43823i	−0.0923013	−	0.344473i
$167$	−7.96741	+	13.8000i	−0.616536	+	1.06787i	0.373577	+	0.927599i	$0.378131\pi$
$167$	−7.96741	+	13.8000i	−0.616536	+	1.06787i	−0.990113	+	0.140273i	$0.955202\pi$
$168$	−1.45922	−	2.52745i	−0.112582	−	0.194997i
$169$	−6.47655	−	11.2177i	−0.498196	−	0.862901i
$170$		0			0
$171$	−13.4789	−	13.4789i	−1.03076	−	1.03076i
$172$	4.59057	+	2.65037i	0.350028	+	0.202089i
$173$	−4.09940	−	1.09843i	−0.311672	−	0.0835122i	0.0995926	−	0.995028i	$-0.468246\pi$
$173$	−4.09940	−	1.09843i	−0.311672	−	0.0835122i	−0.411264	+	0.911516i	$0.634913\pi$
$174$		−	1.09174i		−	0.0827643i
$175$		0			0
$176$	−0.518283	+	0.299231i	−0.0390670	+	0.0225554i
$177$		−	4.30901i		−	0.323885i
$178$	0.945193	+	3.52751i	0.0708452	+	0.264398i
$179$	−7.33159	−	7.33159i	−0.547989	−	0.547989i	0.377870	−	0.925859i	$-0.376657\pi$
$179$	−7.33159	−	7.33159i	−0.547989	−	0.547989i	−0.925859	+	0.377870i	$0.876657\pi$
$180$		0			0
$181$	−10.6139	+	18.3839i	−0.788929	+	1.36646i	0.137695	+	0.990475i	$0.456031\pi$
$181$	−10.6139	+	18.3839i	−0.788929	+	1.36646i	−0.926624	+	0.375990i	$0.877303\pi$
$182$	−0.0916184	−	0.341925i	−0.00679121	−	0.0253451i
$183$	4.56260	−	2.63422i	0.337277	−	0.194727i
$184$	17.5073			1.29065
$185$		0			0
$186$	2.72810			0.200034
$187$	0.441728	−	0.255032i	0.0323024	−	0.0186498i
$188$	1.06596	+	3.97823i	0.0777434	+	0.290142i
$189$	2.64577	−	4.58261i	0.192451	−	0.333336i
$190$		0			0
$191$	−13.0799	−	13.0799i	−0.946426	−	0.946426i	0.0522100	−	0.998636i	$-0.483373\pi$
$191$	−13.0799	−	13.0799i	−0.946426	−	0.946426i	−0.998636	+	0.0522100i	$0.983373\pi$
$192$	1.40800	+	5.25472i	0.101614	+	0.379227i
$193$		−	10.5415i		−	0.758797i	−0.925233	−	0.379398i	$-0.876131\pi$
$193$		−	10.5415i		−	0.758797i	0.925233	−	0.379398i	$-0.123869\pi$
$194$	−4.52098	+	2.61019i	−0.324587	+	0.187401i
$195$		0			0
$196$			3.61959i			0.258542i
$197$	−12.1424	−	3.25354i	−0.865109	−	0.231805i	−0.201138	−	0.979563i	$-0.564464\pi$
$197$	−12.1424	−	3.25354i	−0.865109	−	0.231805i	−0.663972	+	0.747758i	$0.731131\pi$
$198$	−0.762355	−	0.440146i	−0.0541782	−	0.0312798i
$199$	−4.51277	−	4.51277i	−0.319902	−	0.319902i	0.528828	−	0.848729i	$-0.322632\pi$
$199$	−4.51277	−	4.51277i	−0.319902	−	0.319902i	−0.848729	+	0.528828i	$0.822632\pi$
$200$		0			0
$201$	−2.54989	−	4.41653i	−0.179855	−	0.311518i
$202$	−9.63201	−	16.6831i	−0.677706	−	1.17382i
$203$	1.08975	−	1.88751i	0.0764856	−	0.132477i
$204$	−0.209407	−	0.781518i	−0.0146614	−	0.0547172i
$205$		0			0
$206$	2.79759	−	1.61519i	0.194918	−	0.112536i
$207$	7.33253	+	12.7003i	0.509646	+	0.882732i
$208$			0.425336i			0.0294918i
$209$	2.17789	−	0.583564i	0.150648	−	0.0403660i
$210$		0			0
$211$	−22.3168			−1.53635			−0.768175	−	0.640240i	$-0.778835\pi$
$211$	−22.3168			−1.53635			−0.768175	+	0.640240i	$0.778835\pi$
$212$	−4.33901	−	4.33901i	−0.298004	−	0.298004i
$213$	−6.99081	−	1.87318i	−0.479002	−	0.128348i
$214$	7.08981	+	7.08981i	0.484649	+	0.484649i
$215$		0			0
$216$	−7.89476	+	7.89476i	−0.537170	+	0.537170i
$217$	4.71662	+	2.72314i	0.320185	+	0.184859i
$218$	8.11187	−	2.17357i	0.549405	−	0.147213i
$219$	−6.72160	−	3.88072i	−0.454203	−	0.262234i
$220$		0			0
$221$		−	0.362510i		−	0.0243851i
$222$	3.46767	+	2.77464i	0.232735	+	0.186222i
$223$	−12.4242	−	12.4242i	−0.831985	−	0.831985i	0.155803	−	0.987788i	$-0.450204\pi$
$223$	−12.4242	−	12.4242i	−0.831985	−	0.831985i	−0.987788	+	0.155803i	$0.950204\pi$
$224$	−1.48949	+	5.55884i	−0.0995205	+	0.371416i
$225$		0			0
$226$	9.19430	+	5.30833i	0.611595	+	0.353105i
$227$	−2.33447	+	4.04343i	−0.154944	+	0.268372i	−0.933039	−	0.359776i	$-0.882853\pi$
$227$	−2.33447	+	4.04343i	−0.154944	+	0.268372i	0.778094	+	0.628147i	$0.216187\pi$
$228$		−	3.57654i		−	0.236862i
$229$	5.96381	+	3.44321i	0.394100	+	0.227534i	0.683935	−	0.729543i	$-0.260267\pi$
$229$	5.96381	+	3.44321i	0.394100	+	0.227534i	−0.289835	+	0.957077i	$0.593601\pi$
$230$		0			0
$231$	0.144580	+	0.250421i	0.00951270	+	0.0164765i
$232$	−3.25173	+	3.25173i	−0.213487	+	0.213487i
$233$	−9.81662	+	9.81662i	−0.643108	+	0.643108i	−0.951318	−	0.308210i	$-0.900270\pi$
$233$	−9.81662	+	9.81662i	−0.643108	+	0.643108i	0.308210	+	0.951318i	$0.400270\pi$
$234$	−0.541818	+	0.312819i	−0.0354198	+	0.0204496i
$235$		0			0
$236$	−3.47443	+	3.47443i	−0.226166	+	0.226166i
$237$	−3.30928	+	1.91061i	−0.214961	+	0.124108i
$238$	−0.708160	+	2.64289i	−0.0459032	+	0.171313i
$239$	−13.0805	−	3.50490i	−0.846105	−	0.226713i	−0.190378	−	0.981711i	$-0.560971\pi$
$239$	−13.0805	−	3.50490i	−0.846105	−	0.226713i	−0.655727	+	0.754998i	$0.727638\pi$
$240$		0			0
$241$	16.2982	−	4.36708i	1.04986	−	0.281308i	0.307664	−	0.951495i	$-0.400453\pi$
$241$	16.2982	−	4.36708i	1.04986	−	0.281308i	0.742192	+	0.670187i	$0.233786\pi$
$242$	−10.5928	+	6.11578i	−0.680933	+	0.393137i
$243$	−13.8938	−	3.72283i	−0.891288	−	0.238820i
$244$	−5.80293	−	1.55489i	−0.371494	−	0.0995416i
$245$		0			0
$246$	0.451884	+	1.68645i	0.0288111	+	0.107524i
$247$	0.414748	−	1.54786i	0.0263898	−	0.0984881i
$248$	−8.12564	−	8.12564i	−0.515978	−	0.515978i
$249$	2.66756			0.169050
$250$		0			0
$251$	15.8893	−	15.8893i	1.00292	−	1.00292i	0.00292894	−	0.999996i	$-0.499068\pi$
$251$	15.8893	−	15.8893i	1.00292	−	1.00292i	0.999996	−	0.00292894i	$-0.000932313\pi$
$252$	−2.69266	+	0.721497i	−0.169622	+	0.0454500i
$253$	−1.73463			−0.109055
$254$	−14.6212	+	3.91773i	−0.917413	+	0.245820i
$255$		0			0
$256$	7.52941	−	13.0413i	0.470588	−	0.815083i
$257$	−9.47446	−	16.4102i	−0.591001	−	1.02364i	−0.994098	−	0.108486i	$-0.965400\pi$
$257$	−9.47446	−	16.4102i	−0.591001	−	1.02364i	0.403097	−	0.915157i	$-0.367934\pi$
$258$	3.68612	−	3.68612i	0.229488	−	0.229488i
$259$	3.22568	+	8.25846i	0.200434	+	0.513156i
$260$		0			0
$261$	−3.72082	−	0.996990i	−0.230313	−	0.0617121i
$262$	4.78578	−	1.28234i	0.295666	−	0.0792235i
$263$	−6.37326	−	23.7853i	−0.392992	−	1.46667i	−0.825174	−	0.564879i	$-0.808923\pi$
$263$	−6.37326	−	23.7853i	−0.392992	−	1.46667i	0.432182	−	0.901786i	$-0.357744\pi$
$264$	−0.157909	−	0.589325i	−0.00971864	−	0.0362705i
$265$		0			0
$266$	−6.04746	+	10.4745i	−0.370793	+	0.642233i
$267$	−2.12018			−0.129753
$268$	−1.50511	+	5.61716i	−0.0919394	+	0.343122i
$269$			0.947483i			0.0577691i	0.999583	+	0.0288845i	$0.00919551\pi$
$269$			0.947483i			0.0577691i	−0.999583	+	0.0288845i	$0.990804\pi$
$270$		0			0
$271$	6.62074	+	11.4675i	0.402181	+	0.696599i	0.993989	−	0.109481i	$-0.0349188\pi$
$271$	6.62074	+	11.4675i	0.402181	+	0.696599i	−0.591807	+	0.806079i	$0.701585\pi$
$272$	1.64381	−	2.84716i	0.0996704	−	0.172634i
$273$	0.205511			0.0124381
$274$	−2.60967	+	9.73943i	−0.157656	+	0.588380i
$275$		0			0
$276$	−0.712154	+	2.65780i	−0.0428667	+	0.159981i
$277$	1.88762	+	1.08982i	0.113416	+	0.0654810i	0.555635	−	0.831426i	$-0.312475\pi$
$277$	1.88762	+	1.08982i	0.113416	+	0.0654810i	−0.442219	+	0.896907i	$0.645809\pi$
$278$	−22.1734	−	12.8018i	−1.32987	−	0.767801i
$279$	2.49134	−	9.29782i	0.149153	−	0.556646i
$280$		0			0
$281$	−4.03027	+	15.0412i	−0.240426	+	0.897280i	0.735202	+	0.677848i	$0.237087\pi$
$281$	−4.03027	+	15.0412i	−0.240426	+	0.897280i	−0.975628	+	0.219432i	$0.929579\pi$
$282$	4.05037			0.241196
$283$	−3.98498	+	6.90219i	−0.236882	+	0.410292i	−0.959818	−	0.280623i	$-0.909459\pi$
$283$	−3.98498	+	6.90219i	−0.236882	+	0.410292i	0.722936	+	0.690915i	$0.242792\pi$
$284$	4.12644	+	7.14720i	0.244859	+	0.424108i
$285$		0			0
$286$		−	0.0740025i		−	0.00437586i
$287$	−0.902127	+	3.36678i	−0.0532508	+	0.198735i
$288$	10.1713			0.599350
$289$	7.09900	−	12.2958i	0.417588	−	0.723284i
$290$		0			0
$291$	−0.784418	−	2.92749i	−0.0459834	−	0.171612i
$292$	2.29066	+	8.54884i	0.134050	+	0.500283i
$293$	−4.80738	+	1.28813i	−0.280850	+	0.0752536i	−0.396494	−	0.918037i	$-0.629773\pi$
$293$	−4.80738	+	1.28813i	−0.280850	+	0.0752536i	0.115644	+	0.993291i	$0.463107\pi$
$294$	3.43836	+	0.921306i	0.200529	+	0.0537316i
$295$		0			0
$296$	−2.06420	−	18.5927i	−0.119979	−	1.08068i
$297$	0.782216	−	0.782216i	0.0453888	−	0.0453888i
$298$	−7.54121	−	13.0618i	−0.436851	−	0.756648i
$299$	−0.616415	+	1.06766i	−0.0356482	+	0.0617445i
$300$		0			0
$301$	10.0524	−	2.69353i	0.579410	−	0.155252i
$302$	19.0974			1.09893
$303$	10.8029	−	2.89463i	0.620610	−	0.166292i
$304$	10.2762	−	10.2762i	0.589382	−	0.589382i
$305$		0			0
$306$	4.83583			0.276446
$307$	−17.8239	−	17.8239i	−1.01726	−	1.01726i	−0.999848	−	0.0174137i	$-0.994457\pi$
$307$	−17.8239	−	17.8239i	−1.01726	−	1.01726i	−0.0174137	−	0.999848i	$-0.505543\pi$
$308$	0.0853410	−	0.318497i	0.00486275	−	0.0181480i
$309$	0.485400	+	1.81154i	0.0276134	+	0.103055i
$310$		0			0
$311$	12.9139	+	3.46026i	0.732278	+	0.196213i	0.605643	−	0.795736i	$-0.292916\pi$
$311$	12.9139	+	3.46026i	0.732278	+	0.196213i	0.126634	+	0.991949i	$0.459582\pi$
$312$	−0.418843	−	0.112229i	−0.0237123	−	0.00635370i
$313$	−4.14421	+	2.39266i	−0.234244	+	0.135241i	−0.612529	−	0.790448i	$-0.709848\pi$
$313$	−4.14421	+	2.39266i	−0.234244	+	0.135241i	0.378284	+	0.925690i	$0.376514\pi$
$314$	−20.3495	+	5.45265i	−1.14839	+	0.307711i
$315$		0			0
$316$	4.20890	+	1.12777i	0.236769	+	0.0634421i
$317$	−8.43852	+	31.4930i	−0.473955	+	1.76882i	0.151390	+	0.988474i	$0.451625\pi$
$317$	−8.43852	+	31.4930i	−0.473955	+	1.76882i	−0.625345	+	0.780349i	$0.715042\pi$
$318$	−5.22618	+	3.01734i	−0.293070	+	0.169204i
$319$	0.322183	−	0.322183i	0.0180388	−	0.0180388i
$320$		0			0
$321$	−5.04115	+	2.91051i	−0.281370	+	0.162449i
$322$	6.57964	−	6.57964i	0.366669	−	0.366669i
$323$	−8.75834	+	8.75834i	−0.487327	+	0.487327i
$324$	1.99142	+	3.44925i	0.110635	+	0.191625i
$325$		0			0
$326$	−2.89164	−	1.66949i	−0.160153	−	0.0924646i
$327$			4.87558i			0.269620i
$328$	3.67716	−	6.36904i	0.203037	−	0.351671i
$329$	7.00270	+	4.04301i	0.386071	+	0.222898i
$330$		0			0
$331$	−2.05282	+	7.66123i	−0.112833	+	0.421099i	−0.999116	−	0.0420458i	$-0.986612\pi$
$331$	−2.05282	+	7.66123i	−0.112833	+	0.421099i	0.886282	+	0.463145i	$0.153279\pi$
$332$	−2.15091	−	2.15091i	−0.118046	−	0.118046i
$333$	12.6232	−	9.28456i	0.691745	−	0.508791i
$334$		−	17.8697i		−	0.977786i
$335$		0			0
$336$	1.61409	+	0.931893i	0.0880556	+	0.0508389i
$337$	−5.86295	+	1.57097i	−0.319375	+	0.0855764i	−0.414945	−	0.909846i	$-0.636199\pi$
$337$	−5.86295	+	1.57097i	−0.319375	+	0.0855764i	0.0955700	+	0.995423i	$0.469533\pi$
$338$	12.5798	+	7.26297i	0.684252	+	0.395053i
$339$	−4.35835	+	4.35835i	−0.236713	+	0.236713i
$340$		0			0
$341$	0.805092	+	0.805092i	0.0435982	+	0.0435982i
$342$	20.6482	+	5.53268i	1.11653	+	0.299173i
$343$	12.2396	+	12.2396i	0.660875	+	0.660875i
$344$	−21.9582			−1.18391
$345$		0			0
$346$	4.59717	−	1.23181i	0.247146	−	0.0662225i
$347$			6.64889i			0.356931i	0.983946	+	0.178466i	$0.0571133\pi$
$347$			6.64889i			0.356931i	−0.983946	+	0.178466i	$0.942887\pi$
$348$	−0.361375	−	0.625921i	−0.0193718	−	0.0335529i
$349$	30.0699	−	17.3608i	1.60960	−	0.929305i	0.620144	−	0.784488i	$-0.287074\pi$
$349$	30.0699	−	17.3608i	1.60960	−	0.929305i	0.989458	−	0.144817i	$-0.0462594\pi$
$350$		0			0
$351$	−0.203486	−	0.759420i	−0.0108613	−	0.0405348i
$352$	−0.601548	+	1.04191i	−0.0320626	+	0.0555341i
$353$	16.1620	+	27.9934i	0.860217	+	1.48994i	0.871719	+	0.490006i	$0.163005\pi$
$353$	16.1620	+	27.9934i	0.860217	+	1.48994i	−0.0115020	+	0.999934i	$0.503661\pi$
$354$	2.41611	+	4.18483i	0.128415	+	0.222421i
$355$		0			0
$356$	1.70954	+	1.70954i	0.0906057	+	0.0906057i
$357$	−1.37567	−	0.794244i	−0.0728083	−	0.0420359i
$358$	11.2312	+	3.00940i	0.593589	+	0.159052i
$359$			27.1360i			1.43218i	0.698007	+	0.716091i	$0.254071\pi$
$359$			27.1360i			1.43218i	−0.698007	+	0.716091i	$0.745929\pi$
$360$		0			0
$361$	−30.9626	+	17.8763i	−1.62961	+	0.940857i
$362$		−	23.8055i		−	1.25119i
$363$	−1.83792	−	6.85922i	−0.0964659	−	0.360016i
$364$	−0.165708	−	0.165708i	−0.00868544	−	0.00868544i
$365$		0			0
$366$	−2.95408	+	5.11661i	−0.154412	+	0.267450i
$367$	0.861087	+	3.21362i	0.0449484	+	0.167750i	0.984752	−	0.173967i	$-0.0556585\pi$
$367$	0.861087	+	3.21362i	0.0449484	+	0.167750i	−0.939803	+	0.341716i	$0.888992\pi$
$368$	−9.68264	+	5.59028i	−0.504743	+	0.291413i
$369$	6.16038			0.320697
$370$		0			0
$371$	−12.0474			−0.625471
$372$	1.56409	−	0.903028i	0.0810943	−	0.0468198i
$373$	1.71380	+	6.39597i	0.0887370	+	0.331171i	0.995996	−	0.0894022i	$-0.0284957\pi$
$373$	1.71380	+	6.39597i	0.0887370	+	0.331171i	−0.907259	+	0.420573i	$0.861829\pi$
$374$	−0.285999	+	0.495365i	−0.0147887	+	0.0256147i
$375$		0			0
$376$	−12.0640	−	12.0640i	−0.622154	−	0.622154i
$377$	−0.0838127	−	0.312793i	−0.00431658	−	0.0161097i
$378$			5.93407i			0.305215i
$379$	−4.32757	+	2.49852i	−0.222292	+	0.128340i	−0.607011	−	0.794693i	$-0.707632\pi$
$379$	−4.32757	+	2.49852i	−0.222292	+	0.128340i	0.384719	+	0.923034i	$0.374298\pi$
$380$		0			0
$381$		−	8.78794i		−	0.450220i
$382$	20.0370	+	5.36889i	1.02518	+	0.274697i
$383$	26.9406	+	15.5541i	1.37660	+	0.794779i	0.991748	−	0.128200i	$-0.0409200\pi$
$383$	26.9406	+	15.5541i	1.37660	+	0.794779i	0.384850	+	0.922979i	$0.374253\pi$
$384$	−0.678474	−	0.678474i	−0.0346232	−	0.0346232i
$385$		0			0
$386$	5.91077	+	10.2378i	0.300850	+	0.521088i
$387$	−9.19670	−	15.9291i	−0.467494	−	0.809724i
$388$	−1.72800	+	2.99298i	−0.0877257	+	0.151945i
$389$	−7.78268	−	29.0453i	−0.394597	−	1.47266i	−0.822465	−	0.568816i	$-0.807402\pi$
$389$	−7.78268	−	29.0453i	−0.394597	−	1.47266i	0.427867	−	0.903842i	$-0.359265\pi$
$390$		0			0
$391$	8.25243	−	4.76454i	0.417344	−	0.240953i
$392$	−7.49704	−	12.9852i	−0.378658	−	0.655854i
$393$			2.87646i			0.145098i
$394$	13.6168	−	3.64861i	0.686003	−	0.183814i
$395$		0			0
$396$	−0.582771			−0.0292853
$397$	−14.9255	−	14.9255i	−0.749091	−	0.749091i	0.225218	−	0.974308i	$-0.427691\pi$
$397$	−14.9255	−	14.9255i	−0.749091	−	0.749091i	−0.974308	+	0.225218i	$0.927691\pi$
$398$	6.91309	+	1.85236i	0.346522	+	0.0928502i
$399$	−4.96520	−	4.96520i	−0.248571	−	0.248571i
$400$		0			0
$401$	13.4254	−	13.4254i	0.670431	−	0.670431i	−0.287385	−	0.957815i	$-0.592786\pi$
$401$	13.4254	−	13.4254i	0.670431	−	0.670431i	0.957815	+	0.287385i	$0.0927858\pi$
$402$	4.95281	+	2.85951i	0.247024	+	0.142619i
$403$	0.781628	−	0.209437i	0.0389357	−	0.0104328i
$404$	−11.0446	−	6.37658i	−0.549488	−	0.317247i
$405$		0			0
$406$			2.44415i			0.121301i
$407$	0.204522	+	1.84217i	0.0101378	+	0.0913132i
$408$	2.36996	+	2.36996i	0.117331	+	0.117331i
$409$	4.92570	−	18.3829i	0.243560	−	0.908978i	−0.730542	−	0.682868i	$-0.760732\pi$
$409$	4.92570	−	18.3829i	0.243560	−	0.908978i	0.974102	−	0.226110i	$-0.0726010\pi$
$410$		0			0
$411$	−5.06955	−	2.92691i	−0.250063	−	0.144374i
$412$	1.06929	−	1.85206i	0.0526801	−	0.0912446i
$413$			9.64690i			0.474693i
$414$	−14.2424	−	8.22288i	−0.699978	−	0.404132i
$415$		0			0
$416$	0.427530	+	0.740503i	0.0209614	+	0.0363062i
$417$	10.5108	−	10.5108i	0.514716	−	0.514716i
$418$	−1.78792	+	1.78792i	−0.0874499	+	0.0874499i
$419$	5.69651	−	3.28888i	0.278293	−	0.160672i	−0.354358	−	0.935110i	$-0.615300\pi$
$419$	5.69651	−	3.28888i	0.278293	−	0.160672i	0.632650	+	0.774438i	$0.281967\pi$
$420$		0			0
$421$	20.7180	−	20.7180i	1.00973	−	1.00973i	0.00978057	−	0.999952i	$-0.496887\pi$
$421$	20.7180	−	20.7180i	1.00973	−	1.00973i	0.999952	−	0.00978057i	$-0.00311330\pi$
$422$	21.6737	−	12.5133i	1.05506	−	0.609138i
$423$	3.69886	−	13.8043i	0.179845	−	0.671190i
$424$	24.5533	+	6.57903i	1.19241	+	0.319506i
$425$		0			0
$426$	7.83967	−	2.10063i	0.379833	−	0.101776i
$427$	−10.2146	+	5.89742i	−0.494321	+	0.285396i
$428$	6.41157	+	1.71798i	0.309915	+	0.0830415i
$429$	0.0414992	+	0.0111197i	0.00200360	+	0.000536863i
$430$		0			0
$431$	0.999182	+	3.72900i	0.0481289	+	0.179620i	0.985806	−	0.167888i	$-0.0536947\pi$
$431$	0.999182	+	3.72900i	0.0481289	+	0.179620i	−0.937677	+	0.347508i	$0.887028\pi$
$432$	1.84542	−	6.88719i	0.0887877	−	0.331360i
$433$	3.44115	+	3.44115i	0.165371	+	0.165371i	0.784941	−	0.619570i	$-0.212693\pi$
$433$	3.44115	+	3.44115i	0.165371	+	0.165371i	−0.619570	+	0.784941i	$0.712693\pi$
$434$	−6.10760			−0.293174
$435$		0			0
$436$	3.93127	−	3.93127i	0.188274	−	0.188274i
$437$	40.6877	−	10.9022i	1.94636	−	0.521525i
$438$	8.70386			0.415887
$439$	−16.0618	+	4.30375i	−0.766589	+	0.205407i	−0.620864	−	0.783918i	$-0.713218\pi$
$439$	−16.0618	+	4.30375i	−0.766589	+	0.205407i	−0.145725	+	0.989325i	$0.546551\pi$
$440$		0			0
$441$	6.27992	−	10.8771i	0.299044	−	0.517959i
$442$	0.203264	+	0.352064i	0.00966829	+	0.0167460i
$443$	−10.2533	+	10.2533i	−0.487148	+	0.487148i	−0.907405	−	0.420257i	$-0.861940\pi$
$443$	−10.2533	+	10.2533i	−0.487148	+	0.487148i	0.420257	+	0.907405i	$0.361940\pi$
$444$	2.90654	+	0.442939i	0.137938	+	0.0210210i
$445$		0			0
$446$	19.0326	+	5.09976i	0.901218	+	0.241481i
$447$	8.45794	−	2.26630i	0.400047	−	0.107192i
$448$	−3.15219	−	11.7641i	−0.148927	−	0.555804i
$449$	9.86280	+	36.8085i	0.465454	+	1.73710i	0.655379	+	0.755301i	$0.272509\pi$
$449$	9.86280	+	36.8085i	0.465454	+	1.73710i	−0.189924	+	0.981799i	$0.560824\pi$
$450$		0			0
$451$	−0.364335	+	0.631047i	−0.0171559	+	0.0297148i
$452$	7.02844			0.330590
$453$	−2.86959	+	10.7095i	−0.134825	+	0.503174i
$454$		−	5.23587i		−	0.245732i
$455$		0			0
$456$	7.40788	+	12.8308i	0.346906	+	0.600858i
$457$	1.69499	−	2.93581i	0.0792884	−	0.137332i	−0.823655	−	0.567092i	$-0.808069\pi$
$457$	1.69499	−	2.93581i	0.0792884	−	0.137332i	0.902943	+	0.429760i	$0.141402\pi$
$458$	−7.72260			−0.360853
$459$	−1.57283	+	5.86989i	−0.0734136	+	0.273983i
$460$		0			0
$461$	−7.45792	+	27.8333i	−0.347350	+	1.29633i	0.542493	+	0.840061i	$0.317481\pi$
$461$	−7.45792	+	27.8333i	−0.347350	+	1.29633i	−0.889843	+	0.456267i	$0.849186\pi$
$462$	−0.280828	−	0.162136i	−0.0130653	−	0.00754326i
$463$	16.2095	+	9.35855i	0.753319	+	0.434929i	0.826892	−	0.562361i	$-0.190107\pi$
$463$	16.2095	+	9.35855i	0.753319	+	0.434929i	−0.0735730	+	0.997290i	$0.523440\pi$
$464$	0.760099	−	2.83673i	0.0352867	−	0.131692i
$465$		0			0
$466$	4.02943	−	15.0380i	0.186660	−	0.696623i
$467$	−29.5406			−1.36698			−0.683488	−	0.729962i	$-0.739538\pi$
$467$	−29.5406			−1.36698			−0.683488	+	0.729962i	$0.739538\pi$
$468$	−0.207092	+	0.358695i	−0.00957285	+	0.0165807i
$469$	5.70862	+	9.88763i	0.263600	+	0.456568i
$470$		0			0
$471$		−	12.2310i		−	0.563573i
$472$	5.26812	−	19.6609i	0.242485	−	0.904966i
$473$	2.17563			0.100036
$474$	2.14261	−	3.71111i	0.0984133	−	0.170457i
$475$		0			0
$476$	0.468816	+	1.74964i	0.0214881	+	0.0801948i
$477$	5.51095	+	20.5672i	0.252329	+	0.941706i
$478$	14.6688	−	3.93048i	0.670934	−	0.179776i
$479$	−24.6241	−	6.59800i	−1.12510	−	0.301470i	−0.352156	−	0.935941i	$-0.614551\pi$
$479$	−24.6241	−	6.59800i	−1.12510	−	0.301470i	−0.772947	+	0.634471i	$0.781218\pi$
$480$		0			0
$481$	1.20653	+	0.528749i	0.0550132	+	0.0241089i
$482$	−13.3798	+	13.3798i	−0.609433	+	0.609433i
$483$	2.70108	+	4.67840i	0.122903	+	0.212875i
$484$	−4.04877	+	7.01267i	−0.184035	+	0.318758i
$485$		0			0
$486$	15.5809	−	4.17488i	0.706762	−	0.189376i
$487$	−20.4907			−0.928523			−0.464262	−	0.885698i	$-0.653680\pi$
$487$	−20.4907			−0.928523			−0.464262	+	0.885698i	$0.653680\pi$
$488$	24.0385	−	6.44111i	1.08817	−	0.291575i
$489$	1.37072	−	1.37072i	0.0619861	−	0.0619861i
$490$		0			0
$491$	10.9509			0.494205			0.247103	−	0.968989i	$-0.420522\pi$
$491$	10.9509			0.494205			0.247103	+	0.968989i	$0.420522\pi$
$492$	0.817310	+	0.817310i	0.0368472	+	0.0368472i
$493$	−0.647826	+	2.41772i	−0.0291766	+	0.108889i
$494$	0.465109	+	1.73581i	0.0209262	+	0.0780978i
$495$		0			0
$496$	7.08860	+	1.89939i	0.318288	+	0.0852849i
$497$	15.6508	+	4.19363i	0.702036	+	0.188110i
$498$	−2.59069	+	1.49574i	−0.116092	+	0.0670256i
$499$	10.0040	−	2.68057i	0.447842	−	0.119999i	−0.0278474	−	0.999612i	$-0.508865\pi$
$499$	10.0040	−	2.68057i	0.447842	−	0.119999i	0.475690	+	0.879613i	$0.342199\pi$
$500$		0			0
$501$	10.0210	+	2.68511i	0.447704	+	0.119962i
$502$	−6.52209	+	24.3408i	−0.291095	+	1.08638i
$503$	9.95261	−	5.74614i	0.443765	−	0.256208i	−0.261428	−	0.965223i	$-0.584194\pi$
$503$	9.95261	−	5.74614i	0.443765	−	0.256208i	0.705193	+	0.709015i	$0.250860\pi$
$504$	8.16552	−	8.16552i	0.363721	−	0.363721i
$505$		0			0
$506$	1.68464	−	0.972629i	0.0748915	−	0.0432386i
$507$	−5.96319	+	5.96319i	−0.264834	+	0.264834i
$508$	−7.08588	+	7.08588i	−0.314385	+	0.314385i
$509$	−1.18398	−	2.05071i	−0.0524789	−	0.0908962i	0.838593	−	0.544759i	$-0.183379\pi$
$509$	−1.18398	−	2.05071i	−0.0524789	−	0.0908962i	−0.891072	+	0.453863i	$0.850046\pi$
$510$		0			0
$511$	15.0481	+	8.68805i	0.665691	+	0.384337i
$512$			19.8349i			0.876586i
$513$	−13.4315	+	23.2640i	−0.593015	+	1.02713i
$514$	18.4029	+	10.6249i	0.811716	+	0.468644i
$515$		0			0
$516$	0.893207	−	3.33350i	0.0393213	−	0.146749i
$517$	1.19531	+	1.19531i	0.0525696	+	0.0525696i
$518$	−7.76334	−	6.21180i	−0.341102	−	0.272931i
$519$			2.76310i			0.121287i
$520$		0			0
$521$	20.3329	+	11.7392i	0.890800	+	0.514303i	0.874204	−	0.485559i	$-0.161384\pi$
$521$	20.3329	+	11.7392i	0.890800	+	0.514303i	0.0165956	+	0.999862i	$0.494717\pi$
$522$	4.17262	−	1.11805i	0.182630	−	0.0489357i
$523$	5.78356	+	3.33914i	0.252898	+	0.146010i	0.621090	−	0.783739i	$-0.286690\pi$
$523$	5.78356	+	3.33914i	0.252898	+	0.146010i	−0.368193	+	0.929749i	$0.620023\pi$
$524$	2.31934	−	2.31934i	0.101321	−	0.101321i
$525$		0			0
$526$	19.5263	+	19.5263i	0.851388	+	0.851388i
$527$	−6.04155	−	1.61883i	−0.263174	−	0.0705173i
$528$	0.275512	+	0.275512i	0.0119901	+	0.0119901i
$529$	−9.40663			−0.408984
$530$		0			0
$531$	16.4690	−	4.41286i	0.714695	−	0.191502i
$532$			8.00707i			0.347151i
$533$	0.258939	+	0.448495i	0.0112159	+	0.0194265i
$534$	2.05909	−	1.18881i	0.0891054	−	0.0514450i
$535$		0			0
$536$	−6.23490	−	23.2690i	−0.269307	−	1.00507i
$537$	−3.37523	+	5.84606i	−0.145652	+	0.252276i
$538$	−0.531266	−	0.920179i	−0.0229045	−	0.0396718i
$539$	0.742810	+	1.28658i	0.0319951	+	0.0554171i
$540$		0			0
$541$	−0.605374	−	0.605374i	−0.0260271	−	0.0260271i	0.693973	−	0.720001i	$-0.255858\pi$
$541$	−0.605374	−	0.605374i	−0.0260271	−	0.0260271i	−0.720001	+	0.693973i	$0.755858\pi$
$542$	−12.8599	−	7.42467i	−0.552380	−	0.318917i
$543$	13.3497	+	3.57703i	0.572889	+	0.153505i
$544$		−	6.60914i		−	0.283364i
$545$		0			0
$546$	−0.199589	+	0.115233i	−0.00854162	+	0.00493151i
$547$		−	41.1854i		−	1.76096i	−0.474084	−	0.880479i	$-0.657221\pi$
$547$		−	41.1854i		−	1.76096i	0.474084	−	0.880479i	$-0.342779\pi$
$548$	1.72766	+	6.44770i	0.0738018	+	0.275432i
$549$	14.7406	+	14.7406i	0.629112	+	0.629112i
$550$		0			0
$551$	−5.53223	+	9.58210i	−0.235681	+	0.408211i
$552$	−2.95009	−	11.0099i	−0.125564	−	0.468611i
$553$	7.40873	−	4.27743i	0.315051	−	0.181895i
$554$	−2.44430			−0.103849
$555$		0			0
$556$	−16.9501			−0.718844
$557$	21.6691	−	12.5106i	0.918148	−	0.530093i	0.0351044	−	0.999384i	$-0.488824\pi$
$557$	21.6691	−	12.5106i	0.918148	−	0.530093i	0.883044	+	0.469291i	$0.155490\pi$
$558$	2.79385	+	10.4268i	0.118273	+	0.441402i
$559$	0.773128	−	1.33910i	0.0326998	−	0.0566377i
$560$		0			0
$561$	−0.234817	−	0.234817i	−0.00991397	−	0.00991397i
$562$	−4.51964	−	16.8675i	−0.190650	−	0.711514i
$563$		−	27.0919i		−	1.14179i	−0.821024	−	0.570894i	$-0.806597\pi$
$563$		−	27.0919i		−	1.14179i	0.821024	−	0.570894i	$-0.193403\pi$
$564$	2.32218	−	1.34071i	0.0977815	−	0.0564542i
$565$		0			0
$566$		−	8.93771i		−	0.375680i
$567$	7.55312	+	2.02385i	0.317201	+	0.0849938i
$568$	−29.6071	−	17.0937i	−1.24229	−	0.717235i
$569$	0.342231	+	0.342231i	0.0143471	+	0.0143471i	0.714244	−	0.699897i	$-0.246771\pi$
$569$	0.342231	+	0.342231i	0.0143471	+	0.0143471i	−0.699897	+	0.714244i	$0.746771\pi$
$570$		0			0
$571$	10.4604	+	18.1179i	0.437754	+	0.758212i	0.997516	−	0.0704415i	$-0.0224408\pi$
$571$	10.4604	+	18.1179i	0.437754	+	0.758212i	−0.559762	+	0.828653i	$0.689107\pi$
$572$	−0.0244956	−	0.0424275i	−0.00102421	−	0.00177398i
$573$	−6.02155	+	10.4296i	−0.251554	+	0.435704i
$574$	−1.01167	−	3.77559i	−0.0422262	−	0.157590i
$575$		0			0
$576$	−18.6416	+	10.7627i	−0.776734	+	0.448448i
$577$	21.7763	+	37.7177i	0.906561	+	1.57021i	0.818808	+	0.574067i	$0.194635\pi$
$577$	21.7763	+	37.7177i	0.906561	+	1.57021i	0.0877527	+	0.996142i	$0.472031\pi$
$578$			15.9220i			0.662267i
$579$	−6.62930	+	1.77631i	−0.275504	+	0.0738211i
$580$		0			0
$581$	−5.97208			−0.247764
$582$	2.40329	+	2.40329i	0.0996196	+	0.0996196i
$583$	−2.43275	−	0.651853i	−0.100754	−	0.0269970i
$584$	−25.9244	−	25.9244i	−1.07276	−	1.07276i
$585$		0			0
$586$	3.94657	−	3.94657i	0.163031	−	0.163031i
$587$	−5.95996	−	3.44098i	−0.245994	−	0.142025i	0.371935	−	0.928259i	$-0.378695\pi$
$587$	−5.95996	−	3.44098i	−0.245994	−	0.142025i	−0.617929	+	0.786234i	$0.712028\pi$
$588$	2.27626	−	0.609923i	0.0938715	−	0.0251528i
$589$	−23.9444	−	13.8243i	−0.986610	−	0.569620i
$590$		0			0
$591$			8.18427i			0.336656i
$592$	7.07850	+	9.62383i	0.290924	+	0.395537i
$593$	−20.5768	−	20.5768i	−0.844989	−	0.844989i	0.144514	−	0.989503i	$-0.453838\pi$
$593$	−20.5768	−	20.5768i	−0.844989	−	0.844989i	−0.989503	+	0.144514i	$0.953838\pi$
$594$	−0.321076	+	1.19827i	−0.0131739	+	0.0491658i
$595$		0			0
$596$	−8.64715	−	4.99243i	−0.354201	−	0.204498i
$597$	−2.07753	+	3.59839i	−0.0850277	+	0.147272i
$598$		−	1.38253i		−	0.0565357i
$599$	8.65201	+	4.99524i	0.353511	+	0.204100i	0.666231	−	0.745746i	$-0.267907\pi$
$599$	8.65201	+	4.99524i	0.353511	+	0.204100i	−0.312719	+	0.949846i	$0.601240\pi$
$600$		0			0
$601$	−4.37991	−	7.58622i	−0.178660	−	0.309448i	0.762762	−	0.646680i	$-0.223843\pi$
$601$	−4.37991	−	7.58622i	−0.178660	−	0.309448i	−0.941422	+	0.337231i	$0.890510\pi$
$602$	−8.25240	+	8.25240i	−0.336343	+	0.336343i
$603$	14.2687	−	14.2687i	0.581064	−	0.581064i
$604$	10.9490	−	6.32143i	0.445510	−	0.257215i
$605$		0			0
$606$	−8.86853	+	8.86853i	−0.360259	+	0.360259i
$607$	−7.78561	+	4.49502i	−0.316008	+	0.182447i	−0.649612	−	0.760266i	$-0.725069\pi$
$607$	−7.78561	+	4.49502i	−0.316008	+	0.182447i	0.333604	+	0.942713i	$0.391735\pi$
$608$	7.56152	−	28.2200i	0.306660	−	1.14447i
$609$	−1.37063	−	0.367260i	−0.0555409	−	0.0148821i
$610$		0			0
$611$	1.16047	−	0.310948i	0.0469477	−	0.0125796i
$612$	2.77251	−	1.60071i	0.112072	−	0.0647048i
$613$	31.2871	+	8.38336i	1.26368	+	0.338601i	0.827605	−	0.561311i	$-0.189703\pi$
$613$	31.2871	+	8.38336i	1.26368	+	0.338601i	0.436071	+	0.899912i	$0.356370\pi$
$614$	27.3043	+	7.31617i	1.10191	+	0.295256i
$615$		0			0
$616$	0.353523	+	1.31937i	0.0142439	+	0.0531588i
$617$	−6.50389	+	24.2728i	−0.261837	+	0.977188i	0.702321	+	0.711860i	$0.252147\pi$
$617$	−6.50389	+	24.2728i	−0.261837	+	0.977188i	−0.964158	+	0.265328i	$0.914520\pi$
$618$	−1.48716	−	1.48716i	−0.0598225	−	0.0598225i
$619$	2.68730			0.108012			0.0540058	−	0.998541i	$-0.482801\pi$
$619$	2.68730			0.108012			0.0540058	+	0.998541i	$0.482801\pi$
$620$		0			0
$621$	14.6135	−	14.6135i	0.586419	−	0.586419i
$622$	−14.4819	+	3.88042i	−0.580672	+	0.155591i
$623$	4.74662			0.190169
$624$	0.267483	−	0.0716718i	0.0107079	−	0.00286917i
$625$		0			0
$626$	2.68319	−	4.64742i	0.107242	−	0.185748i
$627$	−0.733976	−	1.27128i	−0.0293122	−	0.0507702i
$628$	−9.86205	+	9.86205i	−0.393539	+	0.393539i
$629$	−6.03294	−	8.20231i	−0.240549	−	0.327047i
$630$		0			0
$631$	−28.7677	−	7.70828i	−1.14522	−	0.306862i	−0.364174	−	0.931331i	$-0.618649\pi$
$631$	−28.7677	−	7.70828i	−1.14522	−	0.306862i	−0.781049	+	0.624469i	$0.785315\pi$
$632$	−17.4353	+	4.67177i	−0.693538	+	0.185833i
$633$	3.76052	+	14.0344i	0.149467	+	0.557819i
$634$	−9.46317	−	35.3170i	−0.375831	−	1.40262i
$635$		0			0
$636$	−1.99754	+	3.45984i	−0.0792075	+	0.137191i
$637$	1.05585			0.0418344
$638$	−0.132246	+	0.493550i	−0.00523569	+	0.0195399i
$639$		−	28.6372i		−	1.13287i
$640$		0			0
$641$	17.3530	+	30.0563i	0.685403	+	1.18715i	0.973310	+	0.229494i	$0.0737071\pi$
$641$	17.3530	+	30.0563i	0.685403	+	1.18715i	−0.287908	+	0.957658i	$0.592960\pi$
$642$	3.26392	−	5.65327i	0.128817	−	0.223117i
$643$	−36.7811			−1.45050			−0.725252	−	0.688484i	$-0.758277\pi$
$643$	−36.7811			−1.45050			−0.725252	+	0.688484i	$0.758277\pi$
$644$	1.59435	−	5.95021i	0.0628263	−	0.234471i
$645$		0			0
$646$	3.59504	−	13.4169i	0.141445	−	0.527879i
$647$	11.1099	+	6.41429i	0.436775	+	0.252172i	0.702229	−	0.711952i	$-0.252188\pi$
$647$	11.1099	+	6.41429i	0.436775	+	0.252172i	−0.265454	+	0.964124i	$0.585522\pi$
$648$	−14.2884	−	8.24944i	−0.561303	−	0.324068i
$649$	−0.521968	+	1.94801i	−0.0204890	+	0.0764661i
$650$		0			0
$651$	0.917733	−	3.42503i	0.0359688	−	0.134237i
$652$	−2.21047			−0.0865688
$653$	−2.16024	+	3.74165i	−0.0845368	+	0.146422i	−0.905194	−	0.424999i	$-0.860274\pi$
$653$	−2.16024	+	3.74165i	−0.0845368	+	0.146422i	0.820657	+	0.571421i	$0.193608\pi$
$654$	−2.73380	−	4.73508i	−0.106900	−	0.185156i
$655$		0			0
$656$			4.69664i			0.183373i
$657$	7.94850	−	29.6642i	0.310100	−	1.15731i
$658$	−9.06787			−0.353502
$659$	−21.0003	+	36.3737i	−0.818057	+	1.41692i	0.0890543	+	0.996027i	$0.471616\pi$
$659$	−21.0003	+	36.3737i	−0.818057	+	1.41692i	−0.907112	+	0.420890i	$0.861718\pi$
$660$		0			0
$661$	−0.968343	−	3.61391i	−0.0376642	−	0.140565i	0.944533	−	0.328415i	$-0.106515\pi$
$661$	−0.968343	−	3.61391i	−0.0376642	−	0.140565i	−0.982198	+	0.187851i	$0.939848\pi$
$662$	−2.30208	−	8.59150i	−0.0894731	−	0.333918i
$663$	−0.227973	+	0.0610853i	−0.00885375	+	0.00237235i
$664$	12.1714	+	3.26132i	0.472342	+	0.126564i
$665$		0			0
$666$	−7.05343	+	16.0950i	−0.273315	+	0.623667i
$667$	6.01907	−	6.01907i	0.233059	−	0.233059i
$668$	−5.91505	−	10.2452i	−0.228860	−	0.396397i
$669$	−5.71969	+	9.90680i	−0.221136	+	0.383019i
$670$		0			0
$671$	−2.38175	+	0.638187i	−0.0919464	+	0.0246370i
$672$	3.74680			0.144536
$673$	−31.2551	+	8.37477i	−1.20479	+	0.322824i	−0.804717	−	0.593658i	$-0.797683\pi$
$673$	−31.2551	+	8.37477i	−1.20479	+	0.322824i	−0.400077	+	0.916482i	$0.631017\pi$
$674$	4.81313	−	4.81313i	0.185395	−	0.185395i
$675$		0			0
$676$	9.61646			0.369864
$677$	−29.3319	−	29.3319i	−1.12732	−	1.12732i	−0.990612	−	0.136704i	$-0.956349\pi$
$677$	−29.3319	−	29.3319i	−1.12732	−	1.12732i	−0.136704	−	0.990612i	$-0.543651\pi$
$678$	1.78897	−	6.67654i	0.0687051	−	0.256411i
$679$	1.75614	+	6.55399i	0.0673943	+	0.251519i
$680$		0			0
$681$	2.93618	+	0.786746i	0.112515	+	0.0301482i
$682$	−1.23332	−	0.330466i	−0.0472261	−	0.0126542i
$683$	8.59531	−	4.96250i	0.328890	−	0.189885i	−0.326458	−	0.945212i	$-0.605855\pi$
$683$	8.59531	−	4.96250i	0.328890	−	0.189885i	0.655348	+	0.755327i	$0.272522\pi$
$684$	13.6695	−	3.66274i	0.522668	−	0.140049i
$685$		0			0
$686$	−18.7497	−	5.02398i	−0.715869	−	0.191816i
$687$	1.16040	−	4.33069i	0.0442722	−	0.165226i
$688$	12.1443	−	7.01151i	0.462997	−	0.267311i
$689$	−1.26571	+	1.26571i	−0.0482198	+	0.0482198i
$690$		0			0
$691$	−18.1286	+	10.4665i	−0.689643	+	0.398165i	−0.803478	−	0.595334i	$-0.797020\pi$
$691$	−18.1286	+	10.4665i	−0.689643	+	0.398165i	0.113836	+	0.993500i	$0.463686\pi$
$692$	2.22794	−	2.22794i	0.0846935	−	0.0846935i
$693$	−0.809043	+	0.809043i	−0.0307330	+	0.0307330i
$694$	−3.72811	−	6.45728i	−0.141517	−	0.245115i
$695$		0			0
$696$	2.59286	+	1.49699i	0.0982823	+	0.0567433i
$697$		−	4.00291i		−	0.151621i
$698$	−19.4689	+	33.7211i	−0.736908	+	1.27636i
$699$	7.82757	+	4.51925i	0.296066	+	0.170934i
$700$		0			0
$701$	10.8748	−	40.5851i	0.410734	−	1.53288i	−0.382496	−	0.923957i	$-0.624935\pi$
$701$	10.8748	−	40.5851i	0.410734	−	1.53288i	0.793230	−	0.608922i	$-0.208398\pi$
$702$	0.623438	+	0.623438i	0.0235302	+	0.0235302i
$703$	−16.3754	−	41.9248i	−0.617611	−	1.58122i
$704$		−	2.54610i		−	0.0959599i
$705$		0			0
$706$	−31.3925	−	18.1245i	−1.18147	−	0.682124i
$707$	−24.1853	+	6.48042i	−0.909580	+	0.243721i
$708$	2.77044	+	1.59952i	0.104120	+	0.0601135i
$709$	−26.6934	+	26.6934i	−1.00249	+	1.00249i	−0.00249582	+	0.999997i	$0.500794\pi$
$709$	−26.6934	+	26.6934i	−1.00249	+	1.00249i	−0.999997	+	0.00249582i	$0.999206\pi$
$710$		0			0
$711$	−10.6914	−	10.6914i	−0.400959	−	0.400959i
$712$	−9.67386	−	2.59210i	−0.362543	−	0.0971431i
$713$	15.0409	+	15.0409i	0.563284	+	0.563284i
$714$	1.78137			0.0666661
$715$		0			0
$716$	7.43530	−	1.99228i	0.277870	−	0.0744551i
$717$			8.81656i			0.329260i
$718$	−15.2155	−	26.3540i	−0.567837	−	0.983522i
$719$	−9.07260	+	5.23807i	−0.338351	+	0.195347i	−0.659542	−	0.751667i	$-0.729250\pi$
$719$	−9.07260	+	5.23807i	−0.338351	+	0.195347i	0.321192	+	0.947014i	$0.395917\pi$
$720$		0			0
$721$	−1.08670	−	4.05562i	−0.0404709	−	0.151039i
$722$	20.0469	−	34.7223i	0.746069	−	1.29223i
$723$	−5.49268	−	9.51360i	−0.204275	−	0.353815i
$724$	−7.87986	−	13.6483i	−0.292853	−	0.507236i
$725$		0			0
$726$	5.63101	+	5.63101i	0.208986	+	0.208986i
$727$	29.1355	+	16.8214i	1.08058	+	0.623871i	0.931052	−	0.364887i	$-0.118892\pi$
$727$	29.1355	+	16.8214i	1.08058	+	0.623871i	0.149524	+	0.988758i	$0.452226\pi$
$728$	0.937696	+	0.251255i	0.0347533	+	0.00931212i
$729$		−	6.72958i		−	0.249244i
$730$		0			0
$731$	−10.3505	+	5.97585i	−0.382826	+	0.221025i
$732$			3.91132i			0.144566i
$733$	6.28732	+	23.4646i	0.232227	+	0.866685i	0.979379	+	0.202031i	$0.0647542\pi$
$733$	6.28732	+	23.4646i	0.232227	+	0.866685i	−0.747152	+	0.664654i	$0.768579\pi$
$734$	−2.63819	−	2.63819i	−0.0973774	−	0.0973774i
$735$		0			0
$736$	−11.2382	+	19.4652i	−0.414246	+	0.717495i
$737$	0.617757	+	2.30550i	0.0227554	+	0.0849241i
$738$	−5.98286	+	3.45420i	−0.220232	+	0.127151i
$739$	−19.6504			−0.722850			−0.361425	−	0.932401i	$-0.617710\pi$
$739$	−19.6504			−0.722850			−0.361425	+	0.932401i	$0.617710\pi$
$740$		0			0
$741$	−1.04330			−0.0383265
$742$	11.7002	−	6.75514i	0.429529	−	0.247989i
$743$	0.143337	+	0.534940i	0.00525852	+	0.0196250i	0.968505	−	0.248993i	$-0.0800997\pi$
$743$	0.143337	+	0.534940i	0.00525852	+	0.0196250i	−0.963247	+	0.268618i	$0.913433\pi$
$744$	−3.74078	+	6.47922i	−0.137144	+	0.237540i
$745$		0			0
$746$	−5.25071	−	5.25071i	−0.192242	−	0.192242i
$747$	2.73186	+	10.1954i	0.0999535	+	0.373031i
$748$			0.378674i			0.0138457i
$749$	11.2860	−	6.51598i	0.412381	−	0.238089i
$750$		0			0
$751$		−	35.5149i		−	1.29596i	−0.761658	−	0.647979i	$-0.775614\pi$
$751$		−	35.5149i		−	1.29596i	0.761658	−	0.647979i	$-0.224386\pi$
$752$	10.5243	+	2.81999i	0.383783	+	0.102834i
$753$	−12.6698	−	7.31492i	−0.461714	−	0.266571i
$754$	0.256785	+	0.256785i	0.00935154	+	0.00935154i
$755$		0			0
$756$	1.96424	+	3.40216i	0.0714385	+	0.123735i
$757$	−0.838715	−	1.45270i	−0.0304836	−	0.0527992i	0.850381	−	0.526167i	$-0.176371\pi$
$757$	−0.838715	−	1.45270i	−0.0304836	−	0.0527992i	−0.880865	+	0.473368i	$0.843038\pi$
$758$	2.80191	−	4.85304i	0.101770	−	0.176270i
$759$	0.292296	+	1.09086i	0.0106097	+	0.0395958i
$760$		0			0
$761$	−36.9267	+	21.3196i	−1.33859	+	0.772836i	−0.986598	−	0.163167i	$-0.947829\pi$
$761$	−36.9267	+	21.3196i	−1.33859	+	0.772836i	−0.351992	+	0.936003i	$0.614496\pi$
$762$	4.92751	+	8.53470i	0.178505	+	0.309179i
$763$		−	10.9153i		−	0.395162i
$764$	13.2649	−	3.55432i	0.479907	−	0.128591i
$765$		0			0
$766$	−34.8856			−1.26047
$767$	1.01351	+	1.01351i	0.0365958	+	0.0365958i
$768$	−9.47009	−	2.53750i	−0.341723	−	0.0915643i
$769$	−10.2716	−	10.2716i	−0.370402	−	0.370402i	0.497222	−	0.867623i	$-0.334354\pi$
$769$	−10.2716	−	10.2716i	−0.370402	−	0.370402i	−0.867623	+	0.497222i	$0.834354\pi$
$770$		0			0
$771$	−8.72347	+	8.72347i	−0.314168	+	0.314168i
$772$	6.77760	+	3.91305i	0.243931	+	0.140834i
$773$	−43.3603	+	11.6184i	−1.55956	+	0.417883i	−0.932525	−	0.361107i	$-0.882399\pi$
$773$	−43.3603	+	11.6184i	−1.55956	+	0.417883i	−0.627037	+	0.778990i	$0.715732\pi$
$774$	17.8633	+	10.3134i	0.642085	+	0.370708i
$775$		0			0
$776$		−	14.3164i		−	0.513928i
$777$	4.64998	−	3.42014i	0.166817	−	0.122697i
$778$	23.8445	+	23.8445i	0.854866	+	0.854866i
$779$	4.57973	−	17.0918i	0.164086	−	0.612376i
$780$		0			0
$781$	2.93349	+	1.69365i	0.104968	+	0.0606036i
$782$	−5.34308	+	9.25449i	−0.191068	+	0.330940i
$783$			5.42850i			0.193999i
$784$	8.29267	+	4.78778i	0.296167	+	0.170992i
$785$		0			0
$786$	−1.61287	−	2.79357i	−0.0575290	−	0.0996432i
$787$	8.11887	−	8.11887i	0.289407	−	0.289407i	−0.547439	−	0.836846i	$-0.684397\pi$
$787$	8.11887	−	8.11887i	0.289407	−	0.289407i	0.836846	+	0.547439i	$0.184397\pi$
$788$	6.59913	−	6.59913i	0.235084	−	0.235084i
$789$	−13.8840	+	8.01594i	−0.494284	+	0.285375i
$790$		0			0
$791$	9.75737	−	9.75737i	0.346932	−	0.346932i
$792$	2.09069	−	1.20706i	0.0742894	−	0.0428910i
$793$	−0.453570	+	1.69275i	−0.0161067	+	0.0601112i
$794$	22.8643	+	6.12648i	0.811425	+	0.217421i
$795$		0			0
$796$	4.57660	−	1.22630i	0.162213	−	0.0434649i
$797$	11.1254	−	6.42328i	0.394083	−	0.227524i	−0.289845	−	0.957074i	$-0.593604\pi$
$797$	11.1254	−	6.42328i	0.394083	−	0.227524i	0.683928	+	0.729550i	$0.260270\pi$
$798$	7.60617	+	2.03807i	0.269256	+	0.0721468i
$799$	−8.96981	−	2.40345i	−0.317329	−	0.0850280i
$800$		0			0
$801$	−2.17129	−	8.10335i	−0.0767186	−	0.286318i
$802$	−5.51071	+	20.5662i	−0.194590	+	0.726219i
$803$	2.56860	+	2.56860i	0.0906440	+	0.0906440i
$804$	3.78610			0.133526
$805$		0			0
$806$	−0.641670	+	0.641670i	−0.0226019	+	0.0226019i
$807$	0.595847	−	0.159657i	0.0209748	−	0.00562019i
$808$	52.8298			1.85855
$809$	38.4820	−	10.3112i	1.35296	−	0.362523i	0.491730	−	0.870747i	$-0.336365\pi$
$809$	38.4820	−	10.3112i	1.35296	−	0.362523i	0.861225	+	0.508224i	$0.169698\pi$
$810$		0			0
$811$	3.73404	−	6.46755i	0.131120	−	0.227106i	−0.792989	−	0.609236i	$-0.791476\pi$
$811$	3.73404	−	6.46755i	0.131120	−	0.227106i	0.924109	+	0.382130i	$0.124809\pi$
$812$	0.809038	+	1.40130i	0.0283917	+	0.0491758i
$813$	6.09595	−	6.09595i	0.213794	−	0.213794i
$814$	−1.23156	−	1.67441i	−0.0431661	−	0.0586880i
$815$		0			0
$816$	−2.06749	−	0.553983i	−0.0723768	−	0.0193933i
$817$	−51.0318	+	13.6739i	−1.78538	+	0.478391i
$818$	5.52380	+	20.6151i	0.193135	+	0.720790i
$819$	0.210465	+	0.785465i	0.00735423	+	0.0274464i
$820$		0			0
$821$	−27.5640	+	47.7422i	−0.961990	+	1.66622i	−0.244496	+	0.969650i	$0.578622\pi$
$821$	−27.5640	+	47.7422i	−0.961990	+	1.66622i	−0.717494	+	0.696565i	$0.754711\pi$
$822$	6.56462			0.228967
$823$	13.5807	−	50.6839i	0.473393	−	1.76673i	−0.154046	−	0.988064i	$-0.549231\pi$
$823$	13.5807	−	50.6839i	0.473393	−	1.76673i	0.627440	−	0.778665i	$-0.284103\pi$
$824$			8.85902i			0.308619i
$825$		0			0
$826$	−5.40914	−	9.36890i	−0.188208	−	0.325986i
$827$	−14.6165	+	25.3166i	−0.508267	+	0.880344i	0.491687	+	0.870772i	$0.336380\pi$
$827$	−14.6165	+	25.3166i	−0.508267	+	0.880344i	−0.999954	+	0.00957215i	$0.996953\pi$
$828$	−10.8874			−0.378364
$829$	−4.99822	+	18.6536i	−0.173595	+	0.647867i	0.823191	+	0.567764i	$0.192192\pi$
$829$	−4.99822	+	18.6536i	−0.173595	+	0.647867i	−0.996787	+	0.0801028i	$0.974475\pi$
$830$		0			0
$831$	0.367283	−	1.37072i	0.0127409	−	0.0475497i
$832$	−1.56712	−	0.904779i	−0.0543302	−	0.0313676i
$833$	−7.06778	−	4.08058i	−0.244884	−	0.141384i
$834$	−4.31436	+	16.1014i	−0.149394	+	0.557547i
$835$		0			0
$836$	−0.433241	+	1.61688i	−0.0149840	+	0.0559209i
$837$	−13.5651			−0.468878
$838$	−3.68823	+	6.38821i	−0.127408	+	0.220677i
$839$	−2.06406	−	3.57506i	−0.0712593	−	0.123425i	0.828194	−	0.560441i	$-0.189368\pi$
$839$	−2.06406	−	3.57506i	−0.0712593	−	0.123425i	−0.899453	+	0.437017i	$0.856035\pi$
$840$		0			0
$841$		−	26.7641i		−	0.922899i
$842$	−8.50411	+	31.7378i	−0.293071	+	1.09376i
$843$	10.1381			0.349175
$844$	8.28405	−	14.3484i	0.285149	−	0.493892i
$845$		0			0
$846$	4.14799	+	15.4805i	0.142611	+	0.532231i
$847$	4.11470	+	15.3563i	0.141383	+	0.527647i
$848$	−15.6803	+	4.20152i	−0.538463	+	0.144281i
$849$	5.01210	+	1.34299i	0.172015	+	0.0460912i
$850$		0			0
$851$	3.82090	+	34.4158i	0.130979	+	1.17976i
$852$	3.79935	−	3.79935i	0.130164	−	0.130164i
$853$	14.1534	+	24.5144i	0.484604	+	0.839359i	0.999844	−	0.0176876i	$-0.00563042\pi$
$853$	14.1534	+	24.5144i	0.484604	+	0.839359i	−0.515240	+	0.857046i	$0.672297\pi$
$854$	6.61352	−	11.4550i	0.226310	−	0.391980i
$855$		0			0
$856$	−26.5598	+	7.11668i	−0.907796	+	0.243243i
$857$	−12.8826			−0.440060			−0.220030	−	0.975493i	$-0.570615\pi$
$857$	−12.8826			−0.440060			−0.220030	+	0.975493i	$0.570615\pi$
$858$	−0.0465382	+	0.0124699i	−0.00158879	+	0.000425714i
$859$	−33.1013	+	33.1013i	−1.12940	+	1.12940i	−0.139127	+	0.990275i	$0.544429\pi$
$859$	−33.1013	+	33.1013i	−1.12940	+	1.12940i	−0.990275	+	0.139127i	$0.955571\pi$
$860$		0			0
$861$	2.26929			0.0773373
$862$	−3.06128	−	3.06128i	−0.104268	−	0.104268i
$863$	4.47233	−	16.6909i	0.152240	−	0.568166i	−0.847086	−	0.531456i	$-0.821645\pi$
$863$	4.47233	−	16.6909i	0.152240	−	0.568166i	0.999326	−	0.0367109i	$-0.0116881\pi$
$864$	−3.70987	−	13.8454i	−0.126212	−	0.471031i
$865$		0			0
$866$	−5.27147	−	1.41249i	−0.179132	−	0.0479983i
$867$	−8.92874	−	2.39245i	−0.303236	−	0.0812519i
$868$	−3.50165	+	2.02168i	−0.118854	+	0.0686202i
$869$	1.72750	−	0.462881i	0.0586013	−	0.0157022i
$870$		0			0
$871$	1.63856	+	0.439050i	0.0555203	+	0.0148766i
$872$	−5.96081	+	22.2460i	−0.201858	+	0.753346i
$873$	10.3855	−	5.99609i	0.351497	−	0.202937i
$874$	−33.4022	+	33.4022i	−1.12984	+	1.12984i
$875$		0			0
$876$	4.99015	−	2.88107i	0.168602	−	0.0973422i
$877$	−41.3950	+	41.3950i	−1.39781	+	1.39781i	−0.591523	+	0.806288i	$0.701473\pi$
$877$	−41.3950	+	41.3950i	−1.39781	+	1.39781i	−0.806288	+	0.591523i	$0.798527\pi$
$878$	13.1858	−	13.1858i	0.444999	−	0.444999i
$879$	1.62015	+	2.80618i	0.0546462	+	0.0946500i
$880$		0			0
$881$	47.1023	+	27.1945i	1.58692	+	0.916206i	0.993811	+	0.111080i	$0.0354311\pi$
$881$	47.1023	+	27.1945i	1.58692	+	0.916206i	0.593104	+	0.805126i	$0.297902\pi$
$882$			14.0849i			0.474264i
$883$	−10.2127	+	17.6889i	−0.343684	+	0.595278i	−0.985114	−	0.171904i	$-0.945008\pi$
$883$	−10.2127	+	17.6889i	−0.343684	+	0.595278i	0.641430	+	0.767182i	$0.278342\pi$
$884$	0.233073	+	0.134565i	0.00783910	+	0.00452591i
$885$		0			0
$886$	4.20866	−	15.7069i	0.141393	−	0.527685i
$887$	−10.3419	−	10.3419i	−0.347246	−	0.347246i	0.511837	−	0.859083i	$-0.328965\pi$
$887$	−10.3419	−	10.3419i	−0.347246	−	0.347246i	−0.859083	+	0.511837i	$0.828965\pi$
$888$	−11.3446	+	4.43111i	−0.380701	+	0.148698i
$889$			19.6742i			0.659852i
$890$		0			0
$891$	1.41570	+	0.817358i	0.0474279	+	0.0273825i
$892$	12.5999	−	3.37614i	0.421877	−	0.113042i
$893$	−35.5499	−	20.5247i	−1.18963	−	0.686833i
$894$	−6.94346	+	6.94346i	−0.232224	+	0.232224i
$895$		0			0
$896$	1.51895	+	1.51895i	0.0507446	+	0.0507446i
$897$	0.775294	+	0.207739i	0.0258863	+	0.00693622i
$898$	−30.2176	−	30.2176i	−1.00837	−	1.00837i
$899$	−5.58725			−0.186345
$900$		0			0
$901$	13.3642	−	3.58092i	0.445225	−	0.119298i
$902$		−	0.817149i		−	0.0272081i
$903$	−3.38778	−	5.86780i	−0.112738	−	0.195268i
$904$	−25.2145	+	14.5576i	−0.838621	+	0.484178i
$905$		0			0
$906$	−3.21803	−	12.0098i	−0.106912	−	0.399000i
$907$	22.9241	−	39.7058i	0.761184	−	1.31841i	−0.181057	−	0.983473i	$-0.557952\pi$
$907$	22.9241	−	39.7058i	0.761184	−	1.31841i	0.942241	−	0.334936i	$-0.108715\pi$
$908$	−1.73313	−	3.00186i	−0.0575158	−	0.0996203i
$909$	22.1265	+	38.3243i	0.733891	+	1.27114i
$910$		0			0
$911$	−9.77449	−	9.77449i	−0.323843	−	0.323843i	0.526396	−	0.850239i	$-0.323543\pi$
$911$	−9.77449	−	9.77449i	−0.323843	−	0.323843i	−0.850239	+	0.526396i	$0.823543\pi$
$912$	−8.19406	−	4.73084i	−0.271332	−	0.156654i
$913$	−1.20595	−	0.323133i	−0.0399111	−	0.0106941i
$914$			3.80161i			0.125746i
$915$		0			0
$916$	−4.42757	+	2.55626i	−0.146291	+	0.0844611i
$917$		−	6.43974i		−	0.212659i
$918$	−1.76381	−	6.58265i	−0.0582146	−	0.217260i
$919$	15.6733	+	15.6733i	0.517015	+	0.517015i	0.916667	−	0.399652i	$-0.130869\pi$
$919$	15.6733	+	15.6733i	0.517015	+	0.517015i	−0.399652	+	0.916667i	$0.630869\pi$
$920$		0			0
$921$	−8.20553	+	14.2124i	−0.270381	+	0.468314i
$922$	−8.36350	−	31.2130i	−0.275437	−	1.02795i
$923$	2.08488	−	1.20370i	0.0686246	−	0.0396204i
$924$	−0.214675			−0.00706228
$925$		0			0
$926$	−20.9898			−0.689769
$927$	−6.42660	+	3.71040i	−0.211077	+	0.121865i
$928$	−1.52804	−	5.70272i	−0.0501603	−	0.187201i
$929$	−17.3589	+	30.0664i	−0.569526	+	0.986447i	0.427087	+	0.904210i	$0.359540\pi$
$929$	−17.3589	+	30.0664i	−0.569526	+	0.986447i	−0.996613	+	0.0822368i	$0.973794\pi$
$930$		0			0
$931$	−25.5097	−	25.5097i	−0.836046	−	0.836046i
$932$	−2.66756	−	9.95547i	−0.0873789	−	0.326102i
$933$		−	8.70426i		−	0.284965i
$934$	28.6893	−	16.5638i	0.938743	−	0.541983i
$935$		0			0
$936$		−	1.71575i		−	0.0560811i
$937$	55.8758	+	14.9719i	1.82538	+	0.489110i	0.997427	−	0.0716843i	$-0.0228374\pi$
$937$	55.8758	+	14.9719i	1.82538	+	0.489110i	0.827955	+	0.560794i	$0.189504\pi$
$938$	−11.0882	−	6.40179i	−0.362044	−	0.209026i
$939$	2.20300	+	2.20300i	0.0718923	+	0.0718923i
$940$		0			0
$941$	8.50292	+	14.7275i	0.277187	+	0.480102i	0.970685	−	0.240357i	$-0.0772644\pi$
$941$	8.50292	+	14.7275i	0.277187	+	0.480102i	−0.693497	+	0.720459i	$0.743931\pi$
$942$	6.85805	+	11.8785i	0.223447	+	0.387022i
$943$	−6.80657	+	11.7893i	−0.221652	+	0.383913i
$944$	3.36434	+	12.5559i	0.109500	+	0.408660i
$945$		0			0
$946$	−2.11293	+	1.21990i	−0.0686974	+	0.0396625i
$947$	−19.8712	−	34.4179i	−0.645727	−	1.11843i	−0.984133	−	0.177432i	$-0.943221\pi$
$947$	−19.8712	−	34.4179i	−0.645727	−	1.11843i	0.338406	−	0.941000i	$-0.390112\pi$
$948$		−	2.83690i		−	0.0921383i
$949$	2.49375	−	0.668197i	0.0809504	−	0.0216906i
$950$		0			0
$951$	21.2271			0.688334
$952$	−5.30581	−	5.30581i	−0.171962	−	0.171962i
$953$	−7.54213	−	2.02091i	−0.244314	−	0.0654636i	0.134584	−	0.990902i	$-0.457030\pi$
$953$	−7.54213	−	2.02091i	−0.244314	−	0.0654636i	−0.378898	+	0.925439i	$0.623697\pi$
$954$	−16.8844	−	16.8844i	−0.546653	−	0.546653i
$955$		0			0
$956$	7.10896	−	7.10896i	0.229920	−	0.229920i
$957$	−0.256902	−	0.148323i	−0.00830447	−	0.00479459i
$958$	27.6141	−	7.39917i	0.892170	−	0.239056i
$959$	11.3496	+	6.55269i	0.366497	+	0.211597i
$960$		0			0
$961$			17.0382i			0.549620i
$962$	−1.46824	+	0.163007i	−0.0473380	+	0.00525555i
$963$	−16.2866	−	16.2866i	−0.524829	−	0.524829i
$964$	−3.24214	+	12.0998i	−0.104422	+	0.389710i
$965$		0			0
$966$	−5.24647	−	3.02905i	−0.168803	−	0.0974582i
$967$	−16.7585	+	29.0265i	−0.538916	+	0.933429i	0.460047	+	0.887895i	$0.347833\pi$
$967$	−16.7585	+	29.0265i	−0.538916	+	0.933429i	−0.998963	+	0.0455348i	$0.985501\pi$
$968$		−	33.5439i		−	1.07814i
$969$	6.98372	+	4.03205i	0.224350	+	0.129528i
$970$		0			0
$971$	25.5539	+	44.2607i	0.820064	+	1.42039i	0.905634	+	0.424061i	$0.139396\pi$
$971$	25.5539	+	44.2607i	0.820064	+	1.42039i	−0.0855692	+	0.996332i	$0.527271\pi$
$972$	7.55099	−	7.55099i	0.242198	−	0.242198i
$973$	−23.5313	+	23.5313i	−0.754379	+	0.754379i
$974$	19.9002	−	11.4894i	0.637645	−	0.368144i
$975$		0			0
$976$	−11.2381	+	11.2381i	−0.359723	+	0.359723i
$977$	−11.6861	+	6.74695i	−0.373870	+	0.215854i	−0.675148	−	0.737682i	$-0.735920\pi$
$977$	−11.6861	+	6.74695i	−0.373870	+	0.215854i	0.301278	+	0.953536i	$0.402587\pi$
$978$	−0.562639	+	2.09980i	−0.0179912	+	0.0671442i
$979$	0.958490	+	0.256827i	0.0306335	+	0.00820821i
$980$		0			0
$981$	−18.6345	+	4.99309i	−0.594953	+	0.159417i
$982$	−10.6353	+	6.14028i	−0.339385	+	0.195944i
$983$	33.9029	+	9.08426i	1.08134	+	0.289743i	0.755143	−	0.655560i	$-0.227567\pi$
$983$	33.9029	+	9.08426i	1.08134	+	0.289743i	0.326193	+	0.945303i	$0.394234\pi$
$984$	−4.62494	−	1.23925i	−0.147438	−	0.0395058i
$985$		0			0
$986$	−0.726488	−	2.71129i	−0.0231361	−	0.0863451i
$987$	1.36254	−	5.08509i	0.0433703	−	0.161860i
$988$	0.841230	+	0.841230i	0.0267631	+	0.0267631i
$989$	40.6455			1.29245
$990$		0			0
$991$	17.5135	−	17.5135i	0.556333	−	0.556333i	−0.371928	−	0.928262i	$-0.621303\pi$
$991$	17.5135	−	17.5135i	0.556333	−	0.556333i	0.928262	+	0.371928i	$0.121303\pi$
$992$	14.2503	−	3.81836i	0.452448	−	0.121233i
$993$	5.16386			0.163870
$994$	−17.5513	+	4.70284i	−0.556692	+	0.149165i
$995$		0			0
$996$	−0.990208	+	1.71509i	−0.0313759	+	0.0543447i
$997$	5.20395	+	9.01350i	0.164811	+	0.285461i	0.936588	−	0.350432i	$-0.113965\pi$
$997$	5.20395	+	9.01350i	0.164811	+	0.285461i	−0.771777	+	0.635893i	$0.780632\pi$
$998$	−8.21271	+	8.21271i	−0.259969	+	0.259969i
$999$	−17.2425	−	13.7965i	−0.545529	−	0.436502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.193.5		68
5.2	odd	4		925.2.t.b.82.5		68
5.3	odd	4		185.2.p.a.82.13	✓	68
5.4	even	2		185.2.u.a.8.13	yes	68
37.14	odd	12		925.2.t.b.643.5		68
185.14	odd	12		185.2.p.a.88.13	yes	68
185.88	even	12		185.2.u.a.162.13	yes	68
185.162	even	12	inner	925.2.y.b.532.5		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.13	✓	68	5.3	odd	4
185.2.p.a.88.13	yes	68	185.14	odd	12
185.2.u.a.8.13	yes	68	5.4	even	2
185.2.u.a.162.13	yes	68	185.88	even	12
925.2.t.b.82.5		68	5.2	odd	4
925.2.t.b.643.5		68	37.14	odd	12
925.2.y.b.193.5		68	1.1	even	1	trivial
925.2.y.b.532.5		68	185.162	even	12	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.971183 + 0.560713i) q^{2} +(-0.168506 - 0.628874i) q^{3} +(-0.371203 + 0.642942i) q^{4} +(0.516268 + 0.516268i) q^{6} +(0.377247 + 1.40791i) q^{7} -3.07540i q^{8} +(2.23099 - 1.28806i) q^{9} +0.304712i q^{11} +(0.466879 + 0.125100i) q^{12} +(0.187550 + 0.108282i) q^{13} +(-1.15581 - 1.15581i) q^{14} +(0.982011 + 1.70089i) q^{16} +(-0.836960 - 1.44966i) q^{17} +(-1.44446 + 2.50189i) q^{18} +(-1.91513 - 7.14737i) q^{19} +(0.821827 - 0.474482i) q^{21} +(-0.170856 - 0.295931i) q^{22} +5.69268i q^{23} +(-1.93404 + 0.518224i) q^{24} -0.242860 q^{26} +(-2.56707 - 2.56707i) q^{27} +(-1.04524 - 0.280071i) q^{28} +(-1.05734 - 1.05734i) q^{29} +(2.64214 - 2.64214i) q^{31} +(3.41933 + 1.97415i) q^{32} +(0.191625 - 0.0513459i) q^{33} +(1.62568 + 0.938587i) q^{34} +1.91253i q^{36} +(6.04562 - 0.671196i) q^{37} +(5.86756 + 5.86756i) q^{38} +(0.0364924 - 0.136191i) q^{39} +(2.07096 + 1.19567i) q^{41} +(-0.532096 + 0.921617i) q^{42} -7.13995i q^{43} +(-0.195912 - 0.113110i) q^{44} +(-3.19196 - 5.52863i) q^{46} +(3.92274 - 3.92274i) q^{47} +(0.904172 - 0.904172i) q^{48} +(4.22229 - 2.43774i) q^{49} +(-0.770618 + 0.770618i) q^{51} +(-0.139238 + 0.0803891i) q^{52} +(-2.13924 + 7.98376i) q^{53} +(3.93248 + 1.05370i) q^{54} +(4.32988 - 1.16019i) q^{56} +(-4.17208 + 2.40875i) q^{57} +(1.61973 + 0.434004i) q^{58} +(6.39295 + 1.71299i) q^{59} +(2.09439 + 7.81639i) q^{61} +(-1.08452 + 4.04748i) q^{62} +(2.65511 + 2.65511i) q^{63} -8.35577 q^{64} +(-0.157313 + 0.157313i) q^{66} +(7.56615 - 2.02734i) q^{67} +1.24273 q^{68} +(3.57998 - 0.959252i) q^{69} +(5.55820 - 9.62708i) q^{71} +(-3.96131 - 6.86119i) q^{72} +(8.42960 - 8.42960i) q^{73} +(-5.49505 + 4.04171i) q^{74} +(5.30625 + 1.42180i) q^{76} +(-0.429006 + 0.114952i) q^{77} +(0.0409234 + 0.152728i) q^{78} +(-1.51908 - 5.66927i) q^{79} +(2.68239 - 4.64604i) q^{81} -2.68171 q^{82} +(-1.06045 + 3.95767i) q^{83} +0.704516i q^{84} +(4.00346 + 6.93419i) q^{86} +(-0.486763 + 0.843098i) q^{87} +0.937113 q^{88} +(0.842850 - 3.14556i) q^{89} +(-0.0816982 + 0.304902i) q^{91} +(-3.66007 - 2.11314i) q^{92} +(-2.10679 - 1.21635i) q^{93} +(-1.61017 + 6.00923i) q^{94} +(0.665313 - 2.48298i) q^{96} +4.65513 q^{97} +(-2.73374 + 4.73498i) q^{98} +(0.392488 + 0.679809i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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