LMFDB - Embedded newform 460.2.x.a.433.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			433.11
Character	$\chi$	$=$	460.433
Dual form			460.2.x.a.17.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.20798 + 1.20565i) q^{3} +(1.99649 - 1.00699i) q^{5} +(-0.375619 + 0.501768i) q^{7} +(1.79966 + 2.80032i) q^{9} +O(q^{10})$	\(q+(2.20798 + 1.20565i) q^{3} +(1.99649 - 1.00699i) q^{5} +(-0.375619 + 0.501768i) q^{7} +(1.79966 + 2.80032i) q^{9} +(-0.0603661 - 0.0275683i) q^{11} +(0.355624 - 0.266217i) q^{13} +(5.62228 + 0.183642i) q^{15} +(0.0449704 - 0.628768i) q^{17} +(-0.607236 + 0.700788i) q^{19} +(-1.43431 + 0.655028i) q^{21} +(-3.74968 + 2.98996i) q^{23} +(2.97193 - 4.02090i) q^{25} +(0.0590001 + 0.824930i) q^{27} +(2.43256 - 2.10783i) q^{29} +(-4.49518 - 1.31991i) q^{31} +(-0.100049 - 0.133650i) q^{33} +(-0.244642 + 1.38002i) q^{35} +(-6.71439 - 1.46063i) q^{37} +(1.10617 - 0.159044i) q^{39} +(2.16351 + 1.39041i) q^{41} +(-5.43629 + 9.95581i) q^{43} +(6.41290 + 3.77857i) q^{45} +(2.75870 - 2.75870i) q^{47} +(1.86145 + 6.33950i) q^{49} +(0.857366 - 1.33409i) q^{51} +(-2.18926 - 1.63886i) q^{53} +(-0.148281 + 0.00574849i) q^{55} +(-2.18567 + 0.815211i) q^{57} +(-0.540372 - 0.0776937i) q^{59} +(1.64111 - 5.58909i) q^{61} +(-2.08110 - 0.148843i) q^{63} +(0.441921 - 0.889611i) q^{65} +(2.01402 - 5.39980i) q^{67} +(-11.8841 + 2.08098i) q^{69} +(-2.22873 - 4.88024i) q^{71} +(6.01580 - 0.430258i) q^{73} +(11.4097 - 5.29496i) q^{75} +(0.0365075 - 0.0199346i) q^{77} +(1.20741 - 8.39774i) q^{79} +(3.28414 - 7.19125i) q^{81} +(-3.42936 + 15.7645i) q^{83} +(-0.543382 - 1.30061i) q^{85} +(7.91234 - 1.72122i) q^{87} +(-6.87021 + 2.01727i) q^{89} +0.278437i q^{91} +(-8.33393 - 8.33393i) q^{93} +(-0.506651 + 2.01060i) q^{95} +(-2.64185 - 12.1444i) q^{97} +(-0.0314383 - 0.218658i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{15}{22}\right)$

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			0
$2$		0			0
$3$	2.20798	+	1.20565i	1.27478	+	0.696081i	0.966854	−	0.255331i	$-0.0821844\pi$
$3$	2.20798	+	1.20565i	1.27478	+	0.696081i	0.307923	+	0.951411i	$0.400366\pi$
$4$		0			0
$5$	1.99649	−	1.00699i	0.892857	−	0.450341i
$5$	1.99649	−	1.00699i	0.892857	−	0.450341i
$6$		0			0
$7$	−0.375619	+	0.501768i	−0.141970	+	0.189650i	−0.865891	−	0.500233i	$-0.833248\pi$
$7$	−0.375619	+	0.501768i	−0.141970	+	0.189650i	0.723920	+	0.689884i	$0.242338\pi$
$8$		0			0
$9$	1.79966	+	2.80032i	0.599886	+	0.933441i
$10$		0			0
$11$	−0.0603661	−	0.0275683i	−0.0182010	−	0.00831214i	0.406294	−	0.913743i	$-0.366821\pi$
$11$	−0.0603661	−	0.0275683i	−0.0182010	−	0.00831214i	−0.424495	+	0.905430i	$0.639548\pi$
$12$		0			0
$13$	0.355624	−	0.266217i	0.0986325	−	0.0738353i	−0.548823	−	0.835938i	$-0.684924\pi$
$13$	0.355624	−	0.266217i	0.0986325	−	0.0738353i	0.647456	+	0.762103i	$0.275833\pi$
$14$		0			0
$15$	5.62228	+	0.183642i	1.45167	+	0.0474162i
$16$		0			0
$17$	0.0449704	−	0.628768i	0.0109069	−	0.152499i	−0.989080	−	0.147380i	$-0.952916\pi$
$17$	0.0449704	−	0.628768i	0.0109069	−	0.152499i	0.999987	−	0.00511887i	$-0.00162939\pi$
$18$		0			0
$19$	−0.607236	+	0.700788i	−0.139309	+	0.160772i	−0.821117	−	0.570760i	$-0.806649\pi$
$19$	−0.607236	+	0.700788i	−0.139309	+	0.160772i	0.681808	+	0.731532i	$0.261194\pi$
$20$		0			0
$21$	−1.43431	+	0.655028i	−0.312993	+	0.142939i
$22$		0			0
$23$	−3.74968	+	2.98996i	−0.781863	+	0.623450i
$23$	−3.74968	+	2.98996i	−0.781863	+	0.623450i
$24$		0			0
$25$	2.97193	−	4.02090i	0.594386	−	0.804180i
$26$		0			0
$27$	0.0590001	+	0.824930i	0.0113546	+	0.158758i
$28$		0			0
$29$	2.43256	−	2.10783i	0.451715	−	0.391414i	−0.399075	−	0.916918i	$-0.630669\pi$
$29$	2.43256	−	2.10783i	0.451715	−	0.391414i	0.850791	+	0.525505i	$0.176123\pi$
$30$		0			0
$31$	−4.49518	−	1.31991i	−0.807359	−	0.237062i	−0.148095	−	0.988973i	$-0.547314\pi$
$31$	−4.49518	−	1.31991i	−0.807359	−	0.237062i	−0.659264	+	0.751911i	$0.729132\pi$
$32$		0			0
$33$	−0.100049	−	0.133650i	−0.0174163	−	0.0232655i
$34$		0			0
$35$	−0.244642	+	1.38002i	−0.0413520	+	0.233266i
$36$		0			0
$37$	−6.71439	−	1.46063i	−1.10384	−	0.240126i	−0.376509	−	0.926413i	$-0.622876\pi$
$37$	−6.71439	−	1.46063i	−1.10384	−	0.240126i	−0.727330	+	0.686287i	$0.759239\pi$
$38$		0			0
$39$	1.10617	−	0.159044i	0.177130	−	0.0254674i
$40$		0			0
$41$	2.16351	+	1.39041i	0.337884	+	0.217145i	0.698569	−	0.715543i	$-0.253821\pi$
$41$	2.16351	+	1.39041i	0.337884	+	0.217145i	−0.360685	+	0.932688i	$0.617457\pi$
$42$		0			0
$43$	−5.43629	+	9.95581i	−0.829026	+	1.51825i	0.0259998	+	0.999662i	$0.491723\pi$
$43$	−5.43629	+	9.95581i	−0.829026	+	1.51825i	−0.855026	+	0.518586i	$0.826459\pi$
$44$		0			0
$45$	6.41290	+	3.77857i	0.955979	+	0.563276i
$46$		0			0
$47$	2.75870	−	2.75870i	0.402398	−	0.402398i	−0.476679	−	0.879077i	$-0.658160\pi$
$47$	2.75870	−	2.75870i	0.402398	−	0.402398i	0.879077	+	0.476679i	$0.158160\pi$
$48$		0			0
$49$	1.86145	+	6.33950i	0.265921	+	0.905643i
$50$		0			0
$51$	0.857366	−	1.33409i	0.120055	−	0.186810i
$52$		0			0
$53$	−2.18926	−	1.63886i	−0.300718	−	0.225114i	0.438254	−	0.898851i	$-0.355597\pi$
$53$	−2.18926	−	1.63886i	−0.300718	−	0.225114i	−0.738971	+	0.673737i	$0.764688\pi$
$54$		0			0
$55$	−0.148281	+	0.00574849i	−0.0199942	+	0.000775127i
$56$		0			0
$57$	−2.18567	+	0.815211i	−0.289499	+	0.107977i
$58$		0			0
$59$	−0.540372	−	0.0776937i	−0.0703504	−	0.0101149i	0.107050	−	0.994254i	$-0.465860\pi$
$59$	−0.540372	−	0.0776937i	−0.0703504	−	0.0101149i	−0.177400	+	0.984139i	$0.556769\pi$
$60$		0			0
$61$	1.64111	−	5.58909i	0.210122	−	0.715610i	−0.785221	−	0.619215i	$-0.787451\pi$
$61$	1.64111	−	5.58909i	0.210122	−	0.715610i	0.995343	−	0.0963944i	$-0.0307310\pi$
$62$		0			0
$63$	−2.08110	−	0.148843i	−0.262194	−	0.0187525i
$64$		0			0
$65$	0.441921	−	0.889611i	0.0548136	−	0.110343i
$66$		0			0
$67$	2.01402	−	5.39980i	0.246052	−	0.659691i	−0.753944	−	0.656938i	$-0.771851\pi$
$67$	2.01402	−	5.39980i	0.246052	−	0.659691i	0.999996	−	0.00275241i	$-0.000876121\pi$
$68$		0			0
$69$	−11.8841	+	2.08098i	−1.43067	+	0.250520i
$70$		0			0
$71$	−2.22873	−	4.88024i	−0.264502	−	0.579178i	0.730053	−	0.683390i	$-0.239495\pi$
$71$	−2.22873	−	4.88024i	−0.264502	−	0.579178i	−0.994555	+	0.104212i	$0.966768\pi$
$72$		0			0
$73$	6.01580	−	0.430258i	0.704096	−	0.0503579i	0.285300	−	0.958438i	$-0.407907\pi$
$73$	6.01580	−	0.430258i	0.704096	−	0.0503579i	0.418796	+	0.908080i	$0.362452\pi$
$74$		0			0
$75$	11.4097	−	5.29496i	1.31748	−	0.611409i
$76$		0			0
$77$	0.0365075	−	0.0199346i	0.00416041	−	0.00227176i
$78$		0			0
$79$	1.20741	−	8.39774i	0.135844	−	0.944819i	−0.801891	−	0.597470i	$-0.796173\pi$
$79$	1.20741	−	8.39774i	0.135844	−	0.944819i	0.937736	−	0.347349i	$-0.112918\pi$
$80$		0			0
$81$	3.28414	−	7.19125i	0.364904	−	0.799028i
$82$		0			0
$83$	−3.42936	+	15.7645i	−0.376422	+	1.73038i	0.265948	+	0.963987i	$0.414315\pi$
$83$	−3.42936	+	15.7645i	−0.376422	+	1.73038i	−0.642370	+	0.766395i	$0.722049\pi$
$84$		0			0
$85$	−0.543382	−	1.30061i	−0.0589381	−	0.141071i
$86$		0			0
$87$	7.91234	−	1.72122i	0.848292	−	0.184535i
$88$		0			0
$89$	−6.87021	+	2.01727i	−0.728240	+	0.213831i	−0.624778	−	0.780803i	$-0.714810\pi$
$89$	−6.87021	+	2.01727i	−0.728240	+	0.213831i	−0.103463	+	0.994633i	$0.532992\pi$
$90$		0			0
$91$			0.278437i			0.0291881i
$92$		0			0
$93$	−8.33393	−	8.33393i	−0.864188	−	0.864188i
$94$		0			0
$95$	−0.506651	+	2.01060i	−0.0519813	+	0.206283i
$96$		0			0
$97$	−2.64185	−	12.1444i	−0.268239	−	1.23308i	−0.892207	−	0.451626i	$-0.850844\pi$
$97$	−2.64185	−	12.1444i	−0.268239	−	1.23308i	0.623968	−	0.781450i	$-0.285520\pi$
$98$		0			0
$99$	−0.0314383	−	0.218658i	−0.00315966	−	0.0219759i
$100$		0			0
$101$	−2.30151	+	1.47909i	−0.229009	+	0.147175i	−0.650114	−	0.759837i	$-0.725279\pi$
$101$	−2.30151	+	1.47909i	−0.229009	+	0.147175i	0.421105	+	0.907012i	$0.361642\pi$
$102$		0			0
$103$	−0.327369	−	0.877710i	−0.0322566	−	0.0864833i	0.919823	−	0.392333i	$-0.128332\pi$
$103$	−0.327369	−	0.877710i	−0.0322566	−	0.0864833i	−0.952080	+	0.305850i	$0.901059\pi$
$104$		0			0
$105$	−2.20398	+	2.75210i	−0.215086	+	0.268577i
$106$		0			0
$107$	8.54004	+	15.6399i	0.825597	+	1.51197i	0.858678	+	0.512515i	$0.171286\pi$
$107$	8.54004	+	15.6399i	0.825597	+	1.51197i	−0.0330817	+	0.999453i	$0.510532\pi$
$108$		0			0
$109$	−10.8950	−	12.5735i	−1.04355	−	1.20432i	−0.978459	−	0.206441i	$-0.933812\pi$
$109$	−10.8950	−	12.5735i	−1.04355	−	1.20432i	−0.0650903	−	0.997879i	$-0.520734\pi$
$110$		0			0
$111$	−13.0642	−	11.3202i	−1.24000	−	1.07447i
$112$		0			0
$113$	−12.2744	−	4.57810i	−1.15468	−	0.430672i	−0.302100	−	0.953276i	$-0.597688\pi$
$113$	−12.2744	−	4.57810i	−1.15468	−	0.430672i	−0.852575	+	0.522604i	$0.824961\pi$
$114$		0			0
$115$	−4.47533	+	9.74533i	−0.417326	+	0.908757i
$116$		0			0
$117$	1.38550	+	0.516763i	0.128089	+	0.0477748i
$118$		0			0
$119$	0.298604	+	0.258742i	0.0273730	+	0.0237188i
$120$		0			0
$121$	−7.20058	−	8.30992i	−0.654599	−	0.755447i
$122$		0			0
$123$	3.10065	+	5.67842i	0.279576	+	0.512006i
$124$		0			0
$125$	1.88441	−	11.0204i	0.168547	−	0.985694i
$126$		0			0
$127$	4.22789	+	11.3354i	0.375165	+	1.00586i	0.978113	+	0.208075i	$0.0667198\pi$
$127$	4.22789	+	11.3354i	0.375165	+	1.00586i	−0.602948	+	0.797780i	$0.706007\pi$
$128$		0			0
$129$	−24.0064	+	15.4280i	−2.11365	+	1.35836i
$130$		0			0
$131$	1.82067	+	12.6630i	0.159073	+	1.10637i	0.900347	+	0.435173i	$0.143313\pi$
$131$	1.82067	+	12.6630i	0.159073	+	1.10637i	−0.741274	+	0.671202i	$0.765778\pi$
$132$		0			0
$133$	−0.123543	−	0.567920i	−0.0107126	−	0.0492449i
$134$		0			0
$135$	0.948491	+	1.58755i	0.0816331	+	0.136635i
$136$		0			0
$137$	4.36585	+	4.36585i	0.372999	+	0.372999i	0.868569	−	0.495569i	$-0.165040\pi$
$137$	4.36585	+	4.36585i	0.372999	+	0.372999i	−0.495569	+	0.868569i	$0.665040\pi$
$138$		0			0
$139$		−	18.5854i		−	1.57639i	−0.615425	−	0.788196i	$-0.711016\pi$
$139$		−	18.5854i		−	1.57639i	0.615425	−	0.788196i	$-0.288984\pi$
$140$		0			0
$141$	9.41717	−	2.76513i	0.793069	−	0.232866i
$142$		0			0
$143$	−0.0288068	+	0.00626653i	−0.00240894	+	0.000524034i
$144$		0			0
$145$	2.73401	−	6.65782i	0.227048	−	0.552902i
$146$		0			0
$147$	−3.53317	+	16.2417i	−0.291411	+	1.33960i
$148$		0			0
$149$	−1.26806	+	2.77667i	−0.103884	+	0.227474i	−0.954435	−	0.298418i	$-0.903541\pi$
$149$	−1.26806	+	2.77667i	−0.103884	+	0.227474i	0.850551	+	0.525892i	$0.176268\pi$
$150$		0			0
$151$	1.58415	−	11.0180i	0.128916	−	0.896633i	−0.818015	−	0.575197i	$-0.804925\pi$
$151$	1.58415	−	11.0180i	0.128916	−	0.896633i	0.946931	−	0.321436i	$-0.104165\pi$
$152$		0			0
$153$	1.84168	−	1.00564i	0.148891	−	0.0813008i
$154$		0			0
$155$	−10.3037	+	1.89144i	−0.827614	+	0.151924i
$156$		0			0
$157$	3.01861	−	0.215895i	0.240911	−	0.0172303i	0.0496386	−	0.998767i	$-0.484193\pi$
$157$	3.01861	−	0.215895i	0.240911	−	0.0172303i	0.191273	+	0.981537i	$0.438739\pi$
$158$		0			0
$159$	−2.85795	−	6.25803i	−0.226650	−	0.496294i
$160$		0			0
$161$	−0.0918158	−	3.00456i	−0.00723610	−	0.236792i
$162$		0			0
$163$	−3.67174	+	9.84431i	−0.287593	+	0.771066i	0.710159	+	0.704042i	$0.248623\pi$
$163$	−3.67174	+	9.84431i	−0.287593	+	0.771066i	−0.997751	+	0.0670242i	$0.978650\pi$
$164$		0			0
$165$	−0.334332	−	0.166082i	−0.0260277	−	0.0129295i
$166$		0			0
$167$	17.4831	+	1.25042i	1.35289	+	0.0967603i	0.728870	−	0.684652i	$-0.240046\pi$
$167$	17.4831	+	1.25042i	1.35289	+	0.0967603i	0.624015	+	0.781412i	$0.285500\pi$
$168$		0			0
$169$	−3.60693	+	12.2841i	−0.277456	+	0.944928i
$170$		0			0
$171$	−3.05525	−	0.439278i	−0.233641	−	0.0335925i
$172$		0			0
$173$	7.34127	−	2.73815i	0.558147	−	0.208178i	−0.0545294	−	0.998512i	$-0.517366\pi$
$173$	7.34127	−	2.73815i	0.558147	−	0.208178i	0.612676	+	0.790334i	$0.290093\pi$
$174$		0			0
$175$	0.901245	+	3.00154i	0.0681277	+	0.226895i
$176$		0			0
$177$	−1.09946	−	0.823044i	−0.0826403	−	0.0618638i
$178$		0			0
$179$	−0.945877	+	1.47181i	−0.0706981	+	0.110008i	−0.874802	−	0.484480i	$-0.839009\pi$
$179$	−0.945877	+	1.47181i	−0.0706981	+	0.110008i	0.804104	+	0.594488i	$0.202645\pi$
$180$		0			0
$181$	−4.53893	−	15.4582i	−0.337376	−	1.14900i	−0.937179	−	0.348849i	$-0.886572\pi$
$181$	−4.53893	−	15.4582i	−0.337376	−	1.14900i	0.599803	−	0.800148i	$-0.295246\pi$
$182$		0			0
$183$	10.3620	−	10.3620i	0.765981	−	0.765981i
$184$		0			0
$185$	−14.8760	+	3.84522i	−1.09371	+	0.282706i
$186$		0			0
$187$	−0.0200487	+	0.0367165i	−0.00146611	+	0.00268497i
$188$		0			0
$189$	−0.436085	−	0.280255i	−0.0317205	−	0.0203855i
$190$		0			0
$191$	−16.9585	+	2.43827i	−1.22708	+	0.176427i	−0.725216	−	0.688521i	$-0.758260\pi$
$191$	−16.9585	+	2.43827i	−1.22708	+	0.176427i	−0.501861	+	0.864948i	$0.667351\pi$
$192$		0			0
$193$	2.45234	+	0.533474i	0.176523	+	0.0384003i	0.299958	−	0.953952i	$-0.403027\pi$
$193$	2.45234	+	0.533474i	0.176523	+	0.0384003i	−0.123435	+	0.992353i	$0.539391\pi$
$194$		0			0
$195$	2.04831	−	1.43144i	0.146682	−	0.102508i
$196$		0			0
$197$	13.5755	+	18.1348i	0.967216	+	1.29205i	0.956385	+	0.292108i	$0.0943567\pi$
$197$	13.5755	+	18.1348i	0.967216	+	1.29205i	0.0108308	+	0.999941i	$0.496552\pi$
$198$		0			0
$199$	13.2813	+	3.89976i	0.941490	+	0.276446i	0.716239	−	0.697855i	$-0.245862\pi$
$199$	13.2813	+	3.89976i	0.941490	+	0.276446i	0.225250	+	0.974301i	$0.427680\pi$
$200$		0			0
$201$	10.9572	−	9.49444i	0.772859	−	0.669686i
$202$		0			0
$203$	0.143924	+	2.01232i	0.0101015	+	0.141237i
$204$		0			0
$205$	5.71956	+	0.597286i	0.399471	+	0.0417163i
$206$		0			0
$207$	−15.1210	−	5.11941i	−1.05098	−	0.355824i
$208$		0			0
$209$	0.0559759	−	0.0255633i	0.00387194	−	0.00176825i
$210$		0			0
$211$	10.5737	−	12.2027i	0.727921	−	0.840065i	−0.264315	−	0.964436i	$-0.585146\pi$
$211$	10.5737	−	12.2027i	0.727921	−	0.840065i	0.992236	+	0.124371i	$0.0396913\pi$
$212$		0			0
$213$	0.962859	−	13.4625i	0.0659740	−	0.922437i
$214$		0			0
$215$	−0.828047	+	25.3510i	−0.0564723	+	1.72892i
$216$		0			0
$217$	2.35076	−	1.75976i	0.159580	−	0.119460i
$218$		0			0
$219$	13.8015	+	6.30293i	0.932618	+	0.425912i
$220$		0			0
$221$	−0.151396	−	0.235577i	−0.0101840	−	0.0158466i
$222$		0			0
$223$	−4.07424	+	5.44255i	−0.272832	+	0.364460i	−0.915940	−	0.401315i	$-0.868553\pi$
$223$	−4.07424	+	5.44255i	−0.272832	+	0.364460i	0.643109	+	0.765775i	$0.277644\pi$
$224$		0			0
$225$	16.6083	+	1.08612i	1.10722	+	0.0724081i
$226$		0			0
$227$	−2.18768	−	1.19456i	−0.145201	−	0.0792860i	0.405006	−	0.914314i	$-0.367269\pi$
$227$	−2.18768	−	1.19456i	−0.145201	−	0.0792860i	−0.550207	+	0.835028i	$0.685451\pi$
$228$		0			0
$229$	20.4130			1.34893			0.674466	−	0.738306i	$-0.264374\pi$
$229$	20.4130			1.34893			0.674466	+	0.738306i	$0.264374\pi$
$230$		0			0
$231$	0.104642			0.00688492
$232$		0			0
$233$	21.9341	+	11.9769i	1.43695	+	0.784634i	0.993733	−	0.111781i	$-0.0356554\pi$
$233$	21.9341	+	11.9769i	1.43695	+	0.784634i	0.443217	+	0.896415i	$0.353837\pi$
$234$		0			0
$235$	2.72972	−	8.28571i	0.178067	−	0.540500i
$236$		0			0
$237$	12.7906	−	17.0863i	0.830842	−	1.10987i
$238$		0			0
$239$	5.54892	+	8.63428i	0.358930	+	0.558505i	0.973017	−	0.230732i	$-0.0741122\pi$
$239$	5.54892	+	8.63428i	0.358930	+	0.558505i	−0.614088	+	0.789238i	$0.710476\pi$
$240$		0			0
$241$	10.2180	+	4.66642i	0.658201	+	0.300590i	0.716374	−	0.697716i	$-0.245800\pi$
$241$	10.2180	+	4.66642i	0.658201	+	0.300590i	−0.0581732	+	0.998307i	$0.518528\pi$
$242$		0			0
$243$	17.9076	−	13.4055i	1.14878	−	0.859963i
$244$		0			0
$245$	10.1002	+	10.7823i	0.645278	+	0.688855i
$246$		0			0
$247$	−0.0293863	+	0.410874i	−0.00186980	+	0.0261433i
$248$		0			0
$249$	−26.5784	+	30.6731i	−1.68434	+	1.94383i
$250$		0			0
$251$	16.9727	−	7.75119i	1.07131	−	0.489251i	0.199905	−	0.979815i	$-0.435937\pi$
$251$	16.9727	−	7.75119i	1.07131	−	0.489251i	0.871405	+	0.490565i	$0.163210\pi$
$252$		0			0
$253$	0.308782	−	0.0771200i	0.0194129	−	0.00484849i
$254$		0			0
$255$	0.368304	−	3.52685i	0.0230641	−	0.220860i
$256$		0			0
$257$	0.484145	+	6.76923i	0.0302001	+	0.422253i	0.989952	+	0.141404i	$0.0451616\pi$
$257$	0.484145	+	6.76923i	0.0302001	+	0.422253i	−0.959752	+	0.280849i	$0.909384\pi$
$258$		0			0
$259$	3.25495	−	2.82043i	0.202253	−	0.175253i
$260$		0			0
$261$	10.2804	+	3.01859i	0.636339	+	0.186846i
$262$		0			0
$263$	8.44180	+	11.2769i	0.520544	+	0.695365i	0.981370	−	0.192125i	$-0.0615380\pi$
$263$	8.44180	+	11.2769i	0.520544	+	0.695365i	−0.460827	+	0.887490i	$0.652447\pi$
$264$		0			0
$265$	−6.02115	−	1.06739i	−0.369876	−	0.0655695i
$266$		0			0
$267$	−17.6014	−	3.82895i	−1.07719	−	0.234328i
$268$		0			0
$269$	24.8992	−	3.57996i	1.51813	−	0.218274i	0.667727	−	0.744407i	$-0.267267\pi$
$269$	24.8992	−	3.57996i	1.51813	−	0.218274i	0.850403	+	0.526132i	$0.176358\pi$
$270$		0			0
$271$	−2.52309	−	1.62149i	−0.153267	−	0.0984986i	0.461760	−	0.887005i	$-0.347218\pi$
$271$	−2.52309	−	1.62149i	−0.153267	−	0.0984986i	−0.615026	+	0.788507i	$0.710855\pi$
$272$		0			0
$273$	−0.335697	+	0.614783i	−0.0203173	+	0.0372083i
$274$		0			0
$275$	−0.290253	+	0.160795i	−0.0175029	+	0.00969629i
$276$		0			0
$277$	−14.8274	+	14.8274i	−0.890894	+	0.890894i	−0.994607	−	0.103714i	$-0.966927\pi$
$277$	−14.8274	+	14.8274i	−0.890894	+	0.890894i	0.103714	+	0.994607i	$0.466927\pi$
$278$		0			0
$279$	−4.39363	−	14.9633i	−0.263040	−	0.895832i
$280$		0			0
$281$	−13.0016	+	20.2309i	−0.775611	+	1.20687i	0.198344	+	0.980132i	$0.436444\pi$
$281$	−13.0016	+	20.2309i	−0.775611	+	1.20687i	−0.973955	+	0.226741i	$0.927193\pi$
$282$		0			0
$283$	9.91550	+	7.42265i	0.589415	+	0.441231i	0.851899	−	0.523706i	$-0.175451\pi$
$283$	9.91550	+	7.42265i	0.589415	+	0.441231i	−0.262484	+	0.964936i	$0.584542\pi$
$284$		0			0
$285$	−3.54274	+	3.82851i	−0.209854	+	0.226781i
$286$		0			0
$287$	−1.51032	+	0.563319i	−0.0891512	+	0.0332517i
$288$		0			0
$289$	16.4336	+	2.36280i	0.966685	+	0.138988i
$290$		0			0
$291$	8.80870	−	29.9997i	0.516375	−	1.75861i
$292$		0			0
$293$	−22.9457	−	1.64111i	−1.34050	−	0.0958748i	−0.617420	−	0.786634i	$-0.711822\pi$
$293$	−22.9457	−	1.64111i	−1.34050	−	0.0958748i	−0.723085	+	0.690759i	$0.757276\pi$
$294$		0			0
$295$	−1.15708	+	0.389036i	−0.0673680	+	0.0226505i
$296$		0			0
$297$	0.0191803	−	0.0514243i	0.00111295	−	0.00298394i
$298$		0			0
$299$	−0.537500	+	2.06153i	−0.0310844	+	0.119222i
$300$		0			0
$301$	−2.95354	−	6.46734i	−0.170239	−	0.372771i
$302$		0			0
$303$	−6.86495	+	0.490991i	−0.394381	+	0.0282067i
$304$		0			0
$305$	−2.35173	−	12.8111i	−0.134660	−	0.733563i
$306$		0			0
$307$	−5.34440	+	2.91826i	−0.305021	+	0.166554i	−0.624469	−	0.781050i	$-0.714684\pi$
$307$	−5.34440	+	2.91826i	−0.305021	+	0.166554i	0.319448	+	0.947604i	$0.396503\pi$
$308$		0			0
$309$	0.335385	−	2.33265i	0.0190794	−	0.132700i
$310$		0			0
$311$	−13.1657	+	28.8289i	−0.746558	+	1.63473i	0.0258965	+	0.999665i	$0.491756\pi$
$311$	−13.1657	+	28.8289i	−0.746558	+	1.63473i	−0.772455	+	0.635070i	$0.780971\pi$
$312$		0			0
$313$	−1.97651	+	9.08588i	−0.111719	+	0.513564i	0.886944	+	0.461877i	$0.152824\pi$
$313$	−1.97651	+	9.08588i	−0.111719	+	0.513564i	−0.998663	+	0.0516878i	$0.983540\pi$
$314$		0			0
$315$	−4.30477	+	1.79849i	−0.242546	+	0.101333i
$316$		0			0
$317$	13.8144	−	3.00514i	0.775895	−	0.168786i	0.192853	−	0.981228i	$-0.438226\pi$
$317$	13.8144	−	3.00514i	0.775895	−	0.168786i	0.583042	+	0.812442i	$0.301862\pi$
$318$		0			0
$319$	−0.204953	+	0.0601797i	−0.0114752	+	0.00336942i
$320$		0			0
$321$			44.8289i			2.50210i
$322$		0			0
$323$	0.413325	+	0.413325i	0.0229980	+	0.0229980i
$324$		0			0
$325$	−0.0135409	−	2.22111i	−0.000751116	−	0.123205i
$326$		0			0
$327$	−8.89669	−	40.8974i	−0.491988	−	2.26163i
$328$		0			0
$329$	0.348008	+	2.42045i	0.0191863	+	0.133444i
$330$		0			0
$331$	−25.3702	+	16.3045i	−1.39447	+	0.896174i	−0.999744	−	0.0226235i	$-0.992798\pi$
$331$	−25.3702	+	16.3045i	−1.39447	+	0.896174i	−0.394730	+	0.918797i	$0.629162\pi$
$332$		0			0
$333$	−7.99339	−	21.4311i	−0.438035	−	1.17442i
$334$		0			0
$335$	−1.41659	−	12.8087i	−0.0773966	−	0.699817i
$336$		0			0
$337$	9.29950	+	17.0308i	0.506576	+	0.927725i	0.998373	+	0.0570153i	$0.0181584\pi$
$337$	9.29950	+	17.0308i	0.506576	+	0.927725i	−0.491797	+	0.870710i	$0.663660\pi$
$338$		0			0
$339$	−21.5820	−	24.9069i	−1.17217	−	1.35276i
$340$		0			0
$341$	0.234969	+	0.203602i	0.0127243	+	0.0110257i
$342$		0			0
$343$	−7.99102	−	2.98050i	−0.431474	−	0.160932i
$344$		0			0
$345$	−21.6309	+	16.1218i	−1.16457	+	0.867969i
$346$		0			0
$347$	−10.9819	−	4.09604i	−0.589539	−	0.219887i	0.0369497	−	0.999317i	$-0.488236\pi$
$347$	−10.9819	−	4.09604i	−0.589539	−	0.219887i	−0.626489	+	0.779430i	$0.715509\pi$
$348$		0			0
$349$	−3.14419	−	2.72446i	−0.168305	−	0.145837i	0.566636	−	0.823968i	$-0.308245\pi$
$349$	−3.14419	−	2.72446i	−0.168305	−	0.145837i	−0.734941	+	0.678131i	$0.762790\pi$
$350$		0			0
$351$	0.240592	+	0.277658i	0.0128419	+	0.0148203i
$352$		0			0
$353$	−12.5382	−	22.9620i	−0.667340	−	1.22214i	−0.963680	−	0.267059i	$-0.913948\pi$
$353$	−12.5382	−	22.9620i	−0.667340	−	1.22214i	0.296340	−	0.955082i	$-0.404234\pi$
$354$		0			0
$355$	−9.36400	−	7.49903i	−0.496990	−	0.398007i
$356$		0			0
$357$	0.347359	+	0.931306i	0.0183842	+	0.0492900i
$358$		0			0
$359$	6.36390	−	4.08983i	0.335874	−	0.215853i	−0.361822	−	0.932247i	$-0.617845\pi$
$359$	6.36390	−	4.08983i	0.335874	−	0.215853i	0.697696	+	0.716394i	$0.254209\pi$
$360$		0			0
$361$	2.58161	+	17.9555i	0.135874	+	0.945027i
$362$		0			0
$363$	−5.87990	−	27.0295i	−0.308615	−	1.41868i
$364$		0			0
$365$	11.5772	−	6.91687i	0.605978	−	0.362045i
$366$		0			0
$367$	−18.7614	−	18.7614i	−0.979339	−	0.979339i	0.0204514	−	0.999791i	$-0.493490\pi$
$367$	−18.7614	−	18.7614i	−0.979339	−	0.979339i	−0.999791	+	0.0204514i	$0.993490\pi$
$368$		0			0
$369$			8.56079i			0.445657i
$370$		0			0
$371$	1.64465	−	0.482913i	0.0853861	−	0.0250716i
$372$		0			0
$373$	11.7344	−	2.55265i	0.607582	−	0.132171i	0.101760	−	0.994809i	$-0.467553\pi$
$373$	11.7344	−	2.55265i	0.607582	−	0.132171i	0.505823	+	0.862638i	$0.331189\pi$
$374$		0			0
$375$	17.4474	−	22.0608i	0.900982	−	1.13922i
$376$		0			0
$377$	0.303939	−	1.39718i	0.0156536	−	0.0719586i
$378$		0			0
$379$	8.74596	−	19.1510i	0.449250	−	0.983720i	−0.540558	−	0.841307i	$-0.681787\pi$
$379$	8.74596	−	19.1510i	0.449250	−	0.983720i	0.989807	−	0.142413i	$-0.0454860\pi$
$380$		0			0
$381$	−4.33142	+	30.1257i	−0.221905	+	1.54339i
$382$		0			0
$383$	−14.7924	+	8.07728i	−0.755858	+	0.412730i	−0.810472	−	0.585778i	$-0.800789\pi$
$383$	−14.7924	+	8.07728i	−0.755858	+	0.412730i	0.0546135	+	0.998508i	$0.482607\pi$
$384$		0			0
$385$	0.0528127	−	0.0765619i	0.00269159	−	0.00390196i
$386$		0			0
$387$	−37.6630	+	2.69371i	−1.91452	+	0.136929i
$388$		0			0
$389$	−1.66613	−	3.64832i	−0.0844762	−	0.184977i	0.862680	−	0.505751i	$-0.168784\pi$
$389$	−1.66613	−	3.64832i	−0.0844762	−	0.184977i	−0.947156	+	0.320774i	$0.896057\pi$
$390$		0			0
$391$	1.71137	+	2.49214i	0.0865476	+	0.126033i
$392$		0			0
$393$	−11.2472	+	30.1548i	−0.567344	+	1.52111i
$394$		0			0
$395$	−6.04588	−	17.9818i	−0.304201	−	0.904764i
$396$		0			0
$397$	−5.79219	−	0.414266i	−0.290702	−	0.0207914i	−0.0747732	−	0.997201i	$-0.523823\pi$
$397$	−5.79219	−	0.414266i	−0.290702	−	0.0207914i	−0.215929	+	0.976409i	$0.569278\pi$
$398$		0			0
$399$	0.411930	−	1.40291i	0.0206223	−	0.0702331i
$400$		0			0
$401$	25.1757	+	3.61972i	1.25722	+	0.180760i	0.738539	−	0.674210i	$-0.235516\pi$
$401$	25.1757	+	3.61972i	1.25722	+	0.180760i	0.518676	+	0.854971i	$0.326425\pi$
$402$		0			0
$403$	−1.94998	+	0.727304i	−0.0971353	+	0.0362296i
$404$		0			0
$405$	−0.684803	−	17.6644i	−0.0340281	−	0.877749i
$406$		0			0
$407$	0.365054	+	0.273276i	0.0180951	+	0.0135458i
$408$		0			0
$409$	7.07719	−	11.0123i	0.349944	−	0.544524i	−0.621006	−	0.783806i	$-0.713276\pi$
$409$	7.07719	−	11.0123i	0.349944	−	0.544524i	0.970950	+	0.239282i	$0.0769120\pi$
$410$		0			0
$411$	4.37602	+	14.9034i	0.215853	+	0.735129i
$412$		0			0
$413$	0.241958	−	0.241958i	0.0119060	−	0.0119060i
$414$		0			0
$415$	9.02809	+	34.9271i	0.443171	+	1.71450i
$416$		0			0
$417$	22.4074	−	41.0361i	1.09730	−	2.00955i
$418$		0			0
$419$	−7.82261	−	5.02729i	−0.382160	−	0.245599i	0.335430	−	0.942065i	$-0.391118\pi$
$419$	−7.82261	−	5.02729i	−0.382160	−	0.245599i	−0.717590	+	0.696466i	$0.754755\pi$
$420$		0			0
$421$	−18.1246	+	2.60592i	−0.883338	+	0.127005i	−0.569031	−	0.822316i	$-0.692681\pi$
$421$	−18.1246	+	2.60592i	−0.883338	+	0.127005i	−0.314308	+	0.949321i	$0.601772\pi$
$422$		0			0
$423$	12.6900	+	2.76054i	0.617008	+	0.134222i
$424$		0			0
$425$	−2.39456	−	2.04948i	−0.116153	−	0.0994142i
$426$		0			0
$427$	2.18800	+	2.92282i	0.105885	+	0.141445i
$428$		0			0
$429$	−0.0711600	−	0.0208945i	−0.00343564	−	0.00100879i
$430$		0			0
$431$	8.96570	−	7.76882i	0.431862	−	0.374211i	−0.411631	−	0.911351i	$-0.635041\pi$
$431$	8.96570	−	7.76882i	0.431862	−	0.374211i	0.843493	+	0.537140i	$0.180495\pi$
$432$		0			0
$433$	1.73635	+	24.2774i	0.0834438	+	1.16670i	0.850805	+	0.525482i	$0.176115\pi$
$433$	1.73635	+	24.2774i	0.0834438	+	1.16670i	−0.767361	+	0.641215i	$0.778431\pi$
$434$		0			0
$435$	14.0636	−	11.4041i	0.674299	−	0.546783i
$436$		0			0
$437$	0.181614	−	4.44334i	0.00868776	−	0.212554i
$438$		0			0
$439$	0.292086	−	0.133391i	0.0139405	−	0.00636641i	−0.408433	−	0.912788i	$-0.633924\pi$
$439$	0.292086	−	0.133391i	0.0139405	−	0.00636641i	0.422373	+	0.906422i	$0.361197\pi$
$440$		0			0
$441$	−14.4027	+	16.6216i	−0.685842	+	0.791504i
$442$		0			0
$443$	−0.618405	+	8.64643i	−0.0293813	+	0.410804i	0.961383	+	0.275212i	$0.0887481\pi$
$443$	−0.618405	+	8.64643i	−0.0293813	+	0.410804i	−0.990765	+	0.135592i	$0.956706\pi$
$444$		0			0
$445$	−11.6849	+	10.9457i	−0.553918	+	0.518877i
$446$		0			0
$447$	−6.14755	+	4.60200i	−0.290769	+	0.217667i
$448$		0			0
$449$	23.3864	+	10.6802i	1.10367	+	0.504031i	0.882076	−	0.471107i	$-0.156145\pi$
$449$	23.3864	+	10.6802i	1.10367	+	0.504031i	0.221598	+	0.975138i	$0.428873\pi$
$450$		0			0
$451$	−0.0922717	−	0.143578i	−0.00434490	−	0.00676080i
$452$		0			0
$453$	16.7816	−	22.4176i	0.788468	−	1.05327i
$454$		0			0
$455$	0.280384	+	0.555896i	0.0131446	+	0.0260608i
$456$		0			0
$457$	−11.0496	−	6.03353i	−0.516878	−	0.282237i	0.199562	−	0.979885i	$-0.436048\pi$
$457$	−11.0496	−	6.03353i	−0.516878	−	0.282237i	−0.716440	+	0.697648i	$0.754230\pi$
$458$		0			0
$459$	0.521343			0.0243342
$460$		0			0
$461$	26.5054			1.23448			0.617241	−	0.786774i	$-0.288251\pi$
$461$	26.5054			1.23448			0.617241	+	0.786774i	$0.288251\pi$
$462$		0			0
$463$	−14.1938	−	7.75038i	−0.659640	−	0.360191i	0.114303	−	0.993446i	$-0.463537\pi$
$463$	−14.1938	−	7.75038i	−0.659640	−	0.360191i	−0.773943	+	0.633255i	$0.781718\pi$
$464$		0			0
$465$	−25.0308	−	8.24638i	−1.16078	−	0.382417i
$466$		0			0
$467$	0.655124	−	0.875143i	0.0303155	−	0.0404968i	−0.785127	−	0.619334i	$-0.787403\pi$
$467$	0.655124	−	0.875143i	0.0303155	−	0.0404968i	0.815443	+	0.578838i	$0.196493\pi$
$468$		0			0
$469$	1.95294	+	3.03884i	0.0901785	+	0.140320i
$470$		0			0
$471$	6.92532	+	3.16269i	0.319102	+	0.145729i
$472$		0			0
$473$	0.602632	−	0.451124i	0.0277090	−	0.0207427i
$474$		0			0
$475$	1.01313	+	4.52433i	0.0464857	+	0.207590i
$476$		0			0
$477$	0.649415	−	9.08001i	0.0297347	−	0.415745i
$478$		0			0
$479$	−14.6334	+	16.8878i	−0.668616	+	0.771624i	−0.984159	−	0.177287i	$-0.943268\pi$
$479$	−14.6334	+	16.8878i	−0.668616	+	0.771624i	0.315543	+	0.948911i	$0.397813\pi$
$480$		0			0
$481$	−2.77665	+	1.26805i	−0.126604	+	0.0578182i
$482$		0			0
$483$	3.41971	−	6.74469i	0.155602	−	0.306894i
$484$		0			0
$485$	−17.5037	−	21.5858i	−0.794804	−	0.980161i
$486$		0			0
$487$	−2.46915	−	34.5233i	−0.111888	−	1.56440i	−0.674874	−	0.737933i	$-0.735802\pi$
$487$	−2.46915	−	34.5233i	−0.111888	−	1.56440i	0.562986	−	0.826467i	$-0.309653\pi$
$488$		0			0
$489$	−19.9759	+	17.3092i	−0.903340	+	0.782749i
$490$		0			0
$491$	−12.5216	−	3.67666i	−0.565090	−	0.165925i	−0.0133046	−	0.999911i	$-0.504235\pi$
$491$	−12.5216	−	3.67666i	−0.565090	−	0.165925i	−0.551785	+	0.833986i	$0.686053\pi$
$492$		0			0
$493$	−1.21594	−	1.62431i	−0.0547632	−	0.0731551i
$494$		0			0
$495$	−0.282953	−	0.404890i	−0.0127178	−	0.0181984i
$496$		0			0
$497$	3.28590	+	0.714804i	0.147393	+	0.0320633i
$498$		0			0
$499$	40.5651	−	5.83238i	1.81594	−	0.261093i	0.851304	−	0.524672i	$-0.175812\pi$
$499$	40.5651	−	5.83238i	1.81594	−	0.261093i	0.964638	+	0.263579i	$0.0849030\pi$
$500$		0			0
$501$	37.0948	+	23.8394i	1.65727	+	1.06507i
$502$		0			0
$503$	−9.70407	+	17.7717i	−0.432683	+	0.792400i	−0.999506	−	0.0314399i	$-0.989991\pi$
$503$	−9.70407	+	17.7717i	−0.432683	+	0.792400i	0.566822	+	0.823840i	$0.308173\pi$
$504$		0			0
$505$	−3.10551	+	5.27060i	−0.138193	+	0.234538i
$506$		0			0
$507$	−22.7743	+	22.7743i	−1.01144	+	1.01144i
$508$		0			0
$509$	−12.4509	−	42.4037i	−0.551874	−	1.87951i	−0.469550	−	0.882906i	$-0.655584\pi$
$509$	−12.4509	−	42.4037i	−0.551874	−	1.87951i	−0.0823239	−	0.996606i	$-0.526234\pi$
$510$		0			0
$511$	−2.04376	+	3.18015i	−0.0904104	+	0.140681i
$512$		0			0
$513$	−0.613927	−	0.459580i	−0.0271056	−	0.0202910i
$514$		0			0
$515$	−1.53744	−	1.42268i	−0.0677475	−	0.0626907i
$516$		0			0
$517$	−0.242585	+	0.0904793i	−0.0106689	+	0.00397928i
$518$		0			0
$519$	19.5106	+	2.80520i	0.856421	+	0.123135i
$520$		0			0
$521$	−3.21246	+	10.9406i	−0.140740	+	0.479317i	−0.999451	−	0.0331439i	$-0.989448\pi$
$521$	−3.21246	+	10.9406i	−0.140740	+	0.479317i	0.858710	+	0.512461i	$0.171266\pi$
$522$		0			0
$523$	14.9697	+	1.07066i	0.654581	+	0.0468165i	0.394680	−	0.918819i	$-0.370856\pi$
$523$	14.9697	+	1.07066i	0.654581	+	0.0468165i	0.259901	+	0.965635i	$0.416310\pi$
$524$		0			0
$525$	−1.62887	+	7.71392i	−0.0710899	+	0.336663i
$526$		0			0
$527$	−1.03206	+	2.76707i	−0.0449574	+	0.120535i
$528$		0			0
$529$	5.12025	−	22.4228i	0.222620	−	0.974905i
$530$		0			0
$531$	−0.754917	−	1.65304i	−0.0327606	−	0.0717357i
$532$		0			0
$533$	1.13955	−	0.0815021i	0.0493593	−	0.00353025i
$534$		0			0
$535$	32.7994	+	22.6251i	1.41804	+	0.978170i
$536$		0			0
$537$	−3.86296	+	2.10934i	−0.166699	+	0.0910246i
$538$		0			0
$539$	0.0624009	−	0.434008i	0.00268780	−	0.0186940i
$540$		0			0
$541$	2.75542	−	6.03353i	0.118465	−	0.259402i	−0.841105	−	0.540871i	$-0.818095\pi$
$541$	2.75542	−	6.03353i	0.118465	−	0.259402i	0.959570	+	0.281470i	$0.0908218\pi$
$542$		0			0
$543$	8.61525	−	39.6037i	0.369716	−	1.69956i
$544$		0			0
$545$	−34.4131	−	14.1316i	−1.47409	−	0.605332i
$546$		0			0
$547$	2.89385	−	0.629519i	0.123732	−	0.0269163i	−0.150273	−	0.988645i	$-0.548015\pi$
$547$	2.89385	−	0.629519i	0.123732	−	0.0269163i	0.274005	+	0.961728i	$0.411652\pi$
$548$		0			0
$549$	18.6047	−	5.46283i	0.794029	−	0.233148i
$550$		0			0
$551$			2.98466i			0.127151i
$552$		0			0
$553$	3.76019	+	3.76019i	0.159899	+	0.159899i
$554$		0			0
$555$	−37.4820	−	9.44510i	−1.59102	−	0.400922i
$556$		0			0
$557$	−5.88830	−	27.0681i	−0.249495	−	1.14691i	−0.915927	−	0.401345i	$-0.868543\pi$
$557$	−5.88830	−	27.0681i	−0.249495	−	1.14691i	0.666432	−	0.745566i	$-0.267821\pi$
$558$		0			0
$559$	0.717132	+	4.98776i	0.0303315	+	0.210960i
$560$		0			0
$561$	−0.0885342	+	0.0568975i	−0.00373792	+	0.00240221i
$562$		0			0
$563$	−5.69270	−	15.2627i	−0.239919	−	0.643247i	0.760060	−	0.649853i	$-0.225170\pi$
$563$	−5.69270	−	15.2627i	−0.239919	−	0.643247i	−0.999978	+	0.00660664i	$0.997897\pi$
$564$		0			0
$565$	−29.1158	+	3.22007i	−1.22491	+	0.135470i
$566$		0			0
$567$	2.37476	+	4.34904i	0.0997304	+	0.182643i
$568$		0			0
$569$	20.3645	+	23.5018i	0.853722	+	0.985248i	0.999992	−	0.00399652i	$-0.00127213\pi$
$569$	20.3645	+	23.5018i	0.853722	+	0.985248i	−0.146270	+	0.989245i	$0.546727\pi$
$570$		0			0
$571$	−24.2033	−	20.9723i	−1.01288	−	0.877663i	−0.0203625	−	0.999793i	$-0.506482\pi$
$571$	−24.2033	−	20.9723i	−1.01288	−	0.877663i	−0.992514	+	0.122130i	$0.961027\pi$
$572$		0			0
$573$	−40.3838	−	15.0624i	−1.68706	−	0.629240i
$574$		0			0
$575$	0.878538	+	23.9631i	0.0366376	+	0.999329i
$576$		0			0
$577$	−7.44290	−	2.77606i	−0.309852	−	0.115569i	0.189728	−	0.981837i	$-0.439239\pi$
$577$	−7.44290	−	2.77606i	−0.309852	−	0.115569i	−0.499580	+	0.866268i	$0.666512\pi$
$578$		0			0
$579$	4.77153	+	4.13455i	0.198298	+	0.171826i
$580$		0			0
$581$	−6.62200	−	7.64220i	−0.274727	−	0.317052i
$582$		0			0
$583$	0.0869764	+	0.159285i	0.00360219	+	0.00659693i
$584$		0			0
$585$	3.28650	−	0.363473i	0.135880	−	0.0150278i
$586$		0			0
$587$	2.85130	+	7.64463i	0.117686	+	0.315528i	0.982415	−	0.186711i	$-0.0597827\pi$
$587$	2.85130	+	7.64463i	0.117686	+	0.315528i	−0.864729	+	0.502238i	$0.832510\pi$
$588$		0			0
$589$	3.65461	−	2.34868i	0.150586	−	0.0967755i
$590$		0			0
$591$	8.11031	+	56.4085i	0.333614	+	2.32033i
$592$		0			0
$593$	−2.23157	−	10.2584i	−0.0916398	−	0.421261i	−0.999995	−	0.00306243i	$-0.999025\pi$
$593$	−2.23157	−	10.2584i	−0.0916398	−	0.421261i	0.908356	−	0.418199i	$-0.137338\pi$
$594$		0			0
$595$	0.856710	+	0.215883i	0.0351217	+	0.00885033i
$596$		0			0
$597$	24.6232	+	24.6232i	1.00776	+	1.00776i
$598$		0			0
$599$			11.0925i			0.453227i	0.973985	+	0.226614i	$0.0727654\pi$
$599$			11.0925i			0.453227i	−0.973985	+	0.226614i	$0.927235\pi$
$600$		0			0
$601$	−6.06702	+	1.78144i	−0.247479	+	0.0726664i	−0.403119	−	0.915147i	$-0.632074\pi$
$601$	−6.06702	+	1.78144i	−0.247479	+	0.0726664i	0.155640	+	0.987814i	$0.450256\pi$
$602$		0			0
$603$	18.7457	−	4.07789i	0.763386	−	0.166064i
$604$		0			0
$605$	−22.7439	−	9.33971i	−0.924671	−	0.379713i
$606$		0			0
$607$	−6.87335	+	31.5963i	−0.278981	+	1.28245i	0.597832	+	0.801621i	$0.296029\pi$
$607$	−6.87335	+	31.5963i	−0.278981	+	1.28245i	−0.876813	+	0.480832i	$0.840335\pi$
$608$		0			0
$609$	−2.10837	+	4.61668i	−0.0854353	+	0.187077i
$610$		0			0
$611$	0.246648	−	1.71548i	0.00997832	−	0.0694007i
$612$		0			0
$613$	−33.4827	+	18.2829i	−1.35235	+	0.738440i	−0.981718	−	0.190339i	$-0.939041\pi$
$613$	−33.4827	+	18.2829i	−1.35235	+	0.738440i	−0.370633	+	0.928779i	$0.620859\pi$
$614$		0			0
$615$	11.9085	+	8.21456i	0.480199	+	0.331243i
$616$		0			0
$617$	−15.0077	+	1.07337i	−0.604188	+	0.0432124i	−0.370083	−	0.928999i	$-0.620671\pi$
$617$	−15.0077	+	1.07337i	−0.604188	+	0.0432124i	−0.234105	+	0.972211i	$0.575216\pi$
$618$		0			0
$619$	−0.577910	−	1.26545i	−0.0232282	−	0.0508626i	0.897662	−	0.440684i	$-0.145264\pi$
$619$	−0.577910	−	1.26545i	−0.0232282	−	0.0508626i	−0.920891	+	0.389821i	$0.872537\pi$
$620$		0			0
$621$	−2.68774	−	2.91682i	−0.107855	−	0.117048i
$622$		0			0
$623$	1.56837	−	4.20497i	0.0628356	−	0.168469i
$624$		0			0
$625$	−7.33526	−	23.8997i	−0.293410	−	0.955987i
$626$		0			0
$627$	0.154414	+	0.0110439i	0.00616670	+	0.000441051i
$628$		0			0
$629$	−1.22034	+	4.15611i	−0.0486583	+	0.165715i
$630$		0			0
$631$	−40.4216	−	5.81176i	−1.60916	−	0.231362i	−0.721686	−	0.692220i	$-0.756633\pi$
$631$	−40.4216	−	5.81176i	−1.60916	−	0.231362i	−0.887474	+	0.460858i	$0.847542\pi$
$632$		0			0
$633$	38.0585	−	14.1951i	1.51269	−	0.564204i
$634$		0			0
$635$	19.8556	+	18.3736i	0.787946	+	0.729133i
$636$		0			0
$637$	2.34966	+	1.75893i	0.0930969	+	0.0696915i
$638$		0			0
$639$	9.65529	−	15.0239i	0.381958	−	0.594338i
$640$		0			0
$641$	−9.59468	−	32.6765i	−0.378967	−	1.29064i	−0.899544	−	0.436829i	$-0.856101\pi$
$641$	−9.59468	−	32.6765i	−0.378967	−	1.29064i	0.520577	−	0.853815i	$-0.325717\pi$
$642$		0			0
$643$	23.4585	−	23.4585i	0.925112	−	0.925112i	−0.0722733	−	0.997385i	$-0.523025\pi$
$643$	23.4585	−	23.4585i	0.925112	−	0.925112i	0.997385	+	0.0722733i	$0.0230254\pi$
$644$		0			0
$645$	−32.3926	+	54.9760i	−1.27546	+	2.16468i
$646$		0			0
$647$	6.45768	−	11.8264i	0.253878	−	0.464942i	−0.719393	−	0.694603i	$-0.755580\pi$
$647$	6.45768	−	11.8264i	0.253878	−	0.464942i	0.973271	+	0.229661i	$0.0737618\pi$
$648$		0			0
$649$	0.0304782	+	0.0195872i	0.00119638	+	0.000768864i
$650$		0			0
$651$	7.31207	−	1.05132i	0.286583	−	0.0412044i
$652$		0			0
$653$	37.1674	+	8.08527i	1.45447	+	0.316401i	0.869210	−	0.494443i	$-0.164628\pi$
$653$	37.1674	+	8.08527i	1.45447	+	0.316401i	0.585262	+	0.810844i	$0.300992\pi$
$654$		0			0
$655$	16.3865	+	23.4482i	0.640275	+	0.916197i
$656$		0			0
$657$	12.0312	+	16.0719i	0.469383	+	0.627023i
$658$		0			0
$659$	−27.8366	−	8.17355i	−1.08436	−	0.318396i	−0.309738	−	0.950822i	$-0.600241\pi$
$659$	−27.8366	−	8.17355i	−1.08436	−	0.318396i	−0.774621	+	0.632426i	$0.782059\pi$
$660$		0			0
$661$	13.6495	−	11.8273i	0.530902	−	0.460030i	−0.347685	−	0.937611i	$-0.613032\pi$
$661$	13.6495	−	11.8273i	0.530902	−	0.460030i	0.878587	+	0.477582i	$0.158487\pi$
$662$		0			0
$663$	−0.0502566	−	0.702679i	−0.00195181	−	0.0272898i
$664$		0			0
$665$	−0.818545	−	1.00944i	−0.0317418	−	0.0391444i
$666$		0			0
$667$	−2.81901	+	15.1769i	−0.109153	+	0.587654i
$668$		0			0
$669$	−15.5576	+	7.10493i	−0.601493	+	0.274693i
$670$		0			0
$671$	−0.253149	+	0.292149i	−0.00977269	+	0.0112783i
$672$		0			0
$673$	−3.21307	+	44.9246i	−0.123855	+	1.73171i	0.433251	+	0.901273i	$0.357366\pi$
$673$	−3.21307	+	44.9246i	−0.123855	+	1.73171i	−0.557106	+	0.830442i	$0.688088\pi$
$674$		0			0
$675$	3.49230	+	2.21440i	0.134419	+	0.0852323i
$676$		0			0
$677$	23.2096	−	17.3745i	0.892018	−	0.667756i	−0.0516449	−	0.998666i	$-0.516446\pi$
$677$	23.2096	−	17.3745i	0.892018	−	0.667756i	0.943663	+	0.330909i	$0.107355\pi$
$678$		0			0
$679$	7.08599	+	3.23606i	0.271935	+	0.124189i
$680$		0			0
$681$	−3.39013	−	5.27514i	−0.129910	−	0.202144i
$682$		0			0
$683$	26.6171	−	35.5563i	1.01848	−	1.36053i	0.0872093	−	0.996190i	$-0.472205\pi$
$683$	26.6171	−	35.5563i	1.01848	−	1.36053i	0.931268	−	0.364336i	$-0.118704\pi$
$684$		0			0
$685$	13.1127	+	4.31999i	0.501012	+	0.165058i
$686$		0			0
$687$	45.0715	+	24.6109i	1.71959	+	0.938965i
$688$		0			0
$689$	−1.21485			−0.0462819
$690$		0			0
$691$	49.5944			1.88666			0.943330	−	0.331856i	$-0.107675\pi$
$691$	49.5944			1.88666			0.943330	+	0.331856i	$0.107675\pi$
$692$		0			0
$693$	0.121524	+	0.0663573i	0.00461632	+	0.00252070i
$694$		0			0
$695$	−18.7153	−	37.1055i	−0.709913	−	1.40749i
$696$		0			0
$697$	0.971536	−	1.29782i	0.0367996	−	0.0491585i
$698$		0			0
$699$	33.9900	+	52.8895i	1.28562	+	2.00047i
$700$		0			0
$701$	35.3225	+	16.1312i	1.33411	+	0.609268i	0.949487	−	0.313805i	$-0.101604\pi$
$701$	35.3225	+	16.1312i	1.33411	+	0.609268i	0.384624	+	0.923073i	$0.374331\pi$
$702$		0			0
$703$	5.10081	−	3.81842i	0.192381	−	0.144014i
$704$		0			0
$705$	16.0168	−	15.0036i	0.603228	−	0.565067i
$706$		0			0
$707$	0.122330	−	1.71040i	0.00460070	−	0.0643262i
$708$		0			0
$709$	−9.20810	+	10.6267i	−0.345817	+	0.399094i	−0.901838	−	0.432074i	$-0.857782\pi$
$709$	−9.20810	+	10.6267i	−0.345817	+	0.399094i	0.556021	+	0.831168i	$0.312327\pi$
$710$		0			0
$711$	25.6893	−	11.7319i	0.963424	−	0.439981i
$712$		0			0
$713$	20.8020	−	8.49120i	0.779040	−	0.317998i
$714$		0			0
$715$	−0.0512021	+	0.0415193i	−0.00191485	+	0.00155273i
$716$		0			0
$717$	1.84199	+	25.7543i	0.0687903	+	0.961813i
$718$		0			0
$719$	−32.6514	+	28.2926i	−1.21769	+	1.05514i	−0.220885	+	0.975300i	$0.570895\pi$
$719$	−32.6514	+	28.2926i	−1.21769	+	1.05514i	−0.996808	+	0.0798375i	$0.974560\pi$
$720$		0			0
$721$	0.563372	+	0.165421i	0.0209811	+	0.00616060i
$722$		0			0
$723$	16.9351	+	22.6227i	0.629824	+	0.841347i
$724$		0			0
$725$	−1.24595	−	16.0454i	−0.0462735	−	0.595911i
$726$		0			0
$727$	−5.04338	−	1.09712i	−0.187049	−	0.0406900i	0.118065	−	0.993006i	$-0.462331\pi$
$727$	−5.04338	−	1.09712i	−0.187049	−	0.0406900i	−0.305114	+	0.952316i	$0.598695\pi$
$728$		0			0
$729$	32.2264	−	4.63345i	1.19357	−	0.171609i
$730$		0			0
$731$	6.01542	+	3.86588i	0.222489	+	0.142985i
$732$		0			0
$733$	10.7627	−	19.7104i	0.397529	−	0.728019i	−0.599870	−	0.800097i	$-0.704781\pi$
$733$	10.7627	−	19.7104i	0.397529	−	0.728019i	0.997399	+	0.0720780i	$0.0229631\pi$
$734$		0			0
$735$	9.30137	+	35.9843i	0.343086	+	1.32730i
$736$		0			0
$737$	−0.270442	+	0.270442i	−0.00996185	+	0.00996185i
$738$		0			0
$739$	−12.2377	−	41.6776i	−0.450170	−	1.53314i	−0.802146	−	0.597128i	$-0.796308\pi$
$739$	−12.2377	−	41.6776i	−0.450170	−	1.53314i	0.351977	−	0.936009i	$-0.385510\pi$
$740$		0			0
$741$	−0.560253	+	0.871771i	−0.0205814	+	0.0320253i
$742$		0			0
$743$	12.4131	+	9.29232i	0.455392	+	0.340902i	0.802222	−	0.597026i	$-0.203651\pi$
$743$	12.4131	+	9.29232i	0.455392	+	0.340902i	−0.346830	+	0.937928i	$0.612742\pi$
$744$		0			0
$745$	0.264415	+	6.82053i	0.00968742	+	0.249885i
$746$		0			0
$747$	−50.3175	+	18.7674i	−1.84102	+	0.686665i
$748$		0			0
$749$	−11.0554	−	1.58953i	−0.403956	−	0.0580800i
$750$		0			0
$751$	7.01304	−	23.8842i	0.255909	−	0.871547i	−0.726872	−	0.686773i	$-0.759026\pi$
$751$	7.01304	−	23.8842i	0.255909	−	0.871547i	0.982781	−	0.184774i	$-0.0591553\pi$
$752$		0			0
$753$	46.8206	+	3.34868i	1.70624	+	0.122033i
$754$		0			0
$755$	−7.93232	−	23.5925i	−0.288687	−	0.858621i
$756$		0			0
$757$	−6.46470	+	17.3325i	−0.234964	+	0.629962i	−0.999900	−	0.0141442i	$-0.995498\pi$
$757$	−6.46470	+	17.3325i	−0.234964	+	0.629962i	0.764936	+	0.644106i	$0.222770\pi$
$758$		0			0
$759$	0.774762	+	0.202002i	0.0281221	+	0.00733222i
$760$		0			0
$761$	−18.8886	−	41.3602i	−0.684710	−	1.49930i	−0.857575	−	0.514359i	$-0.828030\pi$
$761$	−18.8886	−	41.3602i	−0.684710	−	1.49930i	0.172865	−	0.984945i	$-0.444697\pi$
$762$		0			0
$763$	10.4013	−	0.743917i	0.376553	−	0.0269316i
$764$		0			0
$765$	2.66423	−	3.86230i	0.0963256	−	0.139642i
$766$		0			0
$767$	−0.212853	+	0.116226i	−0.00768567	+	0.00419669i
$768$		0			0
$769$	3.29776	−	22.9364i	0.118920	−	0.827109i	−0.839828	−	0.542853i	$-0.817344\pi$
$769$	3.29776	−	22.9364i	0.118920	−	0.827109i	0.958748	−	0.284256i	$-0.0917467\pi$
$770$		0			0
$771$	−7.09232	+	15.5300i	−0.255424	+	0.559300i
$772$		0			0
$773$	6.57341	−	30.2175i	0.236429	−	1.08685i	−0.693885	−	0.720085i	$-0.744103\pi$
$773$	6.57341	−	30.2175i	0.236429	−	1.08685i	0.930315	−	0.366762i	$-0.119534\pi$
$774$		0			0
$775$	−18.6666	+	14.1520i	−0.670523	+	0.508355i
$776$		0			0
$777$	10.5873	−	2.30312i	0.379817	−	0.0826241i
$778$		0			0
$779$	−2.28814	+	0.671859i	−0.0819812	+	0.0240719i
$780$		0			0
$781$			0.356043i			0.0127402i
$782$		0			0
$783$	1.88233	+	1.88233i	0.0672690	+	0.0672690i
$784$		0			0
$785$	5.80922	−	3.47075i	0.207340	−	0.123876i
$786$		0			0
$787$	0.601648	+	2.76573i	0.0214464	+	0.0985877i	0.986626	−	0.163001i	$-0.0521173\pi$
$787$	0.601648	+	2.76573i	0.0214464	+	0.0985877i	−0.965179	+	0.261589i	$0.915754\pi$
$788$		0			0
$789$	5.04332	+	35.0770i	0.179547	+	1.24878i
$790$		0			0
$791$	6.90763	−	4.43926i	0.245607	−	0.157842i
$792$		0			0
$793$	−0.904295	−	2.42451i	−0.0321124	−	0.0860968i
$794$		0			0
$795$	−12.0077	−	9.61616i	−0.425868	−	0.341050i
$796$		0			0
$797$	20.6727	+	37.8593i	0.732265	+	1.34104i	0.932455	+	0.361286i	$0.117662\pi$
$797$	20.6727	+	37.8593i	0.732265	+	1.34104i	−0.200190	+	0.979757i	$0.564156\pi$
$798$		0			0
$799$	−1.61052	−	1.85864i	−0.0569762	−	0.0657541i
$800$		0			0
$801$	−18.0130	−	15.6084i	−0.636460	−	0.551495i
$802$		0			0
$803$	−0.375011	−	0.139872i	−0.0132339	−	0.00493598i
$804$		0			0
$805$	−3.20888	−	5.90610i	−0.113098	−	0.208163i
$806$		0			0
$807$	59.2930	+	22.1151i	2.08721	+	0.778490i
$808$		0			0
$809$	−26.6523	−	23.0943i	−0.937043	−	0.811953i	0.0453128	−	0.998973i	$-0.485572\pi$
$809$	−26.6523	−	23.0943i	−0.937043	−	0.811953i	−0.982356	+	0.187020i	$0.940117\pi$
$810$		0			0
$811$	5.30963	+	6.12764i	0.186446	+	0.215170i	0.841276	−	0.540606i	$-0.181805\pi$
$811$	5.30963	+	6.12764i	0.186446	+	0.215170i	−0.654830	+	0.755777i	$0.727260\pi$
$812$		0			0
$813$	−3.61598	−	6.62218i	−0.126818	−	0.232250i
$814$		0			0
$815$	2.58257	+	23.3515i	0.0904634	+	0.817966i
$816$		0			0
$817$	−3.67580	−	9.85521i	−0.128600	−	0.344790i
$818$		0			0
$819$	−0.779713	+	0.501091i	−0.0272454	+	0.0175095i
$820$		0			0
$821$	−2.05382	−	14.2846i	−0.0716788	−	0.498537i	−0.993760	−	0.111540i	$-0.964422\pi$
$821$	−2.05382	−	14.2846i	−0.0716788	−	0.498537i	0.922081	−	0.386997i	$-0.126487\pi$
$822$		0			0
$823$	−7.69710	−	35.3830i	−0.268304	−	1.23337i	−0.892119	−	0.451801i	$-0.850782\pi$
$823$	−7.69710	−	35.3830i	−0.268304	−	1.23337i	0.623815	−	0.781572i	$-0.285582\pi$
$824$		0			0
$825$	−0.834734	+	0.00508894i	−0.0290617	+	0.000177174i
$826$		0			0
$827$	−25.2641	−	25.2641i	−0.878519	−	0.878519i	0.114862	−	0.993381i	$-0.463357\pi$
$827$	−25.2641	−	25.2641i	−0.878519	−	0.878519i	−0.993381	+	0.114862i	$0.963357\pi$
$828$		0			0
$829$			5.69858i			0.197920i	0.995091	+	0.0989600i	$0.0315516\pi$
$829$			5.69858i			0.197920i	−0.995091	+	0.0989600i	$0.968448\pi$
$830$		0			0
$831$	−50.6153	+	14.8620i	−1.75582	+	0.515556i
$832$		0			0
$833$	4.06979	−	0.885328i	0.141010	−	0.0306748i
$834$		0			0
$835$	36.1640	−	15.1089i	1.25151	−	0.522867i
$836$		0			0
$837$	0.823612	−	3.78608i	0.0284682	−	0.130866i
$838$		0			0
$839$	−3.85614	+	8.44376i	−0.133129	+	0.291511i	−0.964443	−	0.264292i	$-0.914862\pi$
$839$	−3.85614	+	8.44376i	−0.133129	+	0.291511i	0.831314	+	0.555803i	$0.187589\pi$
$840$		0			0
$841$	−2.65271	+	18.4500i	−0.0914727	+	0.636206i
$842$		0			0
$843$	−53.0986	+	28.9940i	−1.82881	+	0.998607i
$844$		0			0
$845$	5.16878	+	28.1571i	0.177811	+	0.968635i
$846$		0			0
$847$	6.87432	−	0.491661i	0.236204	−	0.0168937i
$848$		0			0
$849$	12.9441	+	28.3436i	0.444240	+	0.972751i
$850$		0			0
$851$	29.5441	−	14.5989i	1.01276	−	0.500444i
$852$		0			0
$853$	−17.8462	+	47.8474i	−0.611041	+	1.63826i	0.149339	+	0.988786i	$0.452285\pi$
$853$	−17.8462	+	47.8474i	−0.611041	+	1.63826i	−0.760380	+	0.649478i	$0.774987\pi$
$854$		0			0
$855$	−6.54212	+	2.19960i	−0.223736	+	0.0752247i
$856$		0			0
$857$	−4.57022	−	0.326869i	−0.156116	−	0.0111656i	−0.00693755	−	0.999976i	$-0.502208\pi$
$857$	−4.57022	−	0.326869i	−0.156116	−	0.0111656i	−0.149178	+	0.988810i	$0.547663\pi$
$858$		0			0
$859$	12.7831	−	43.5352i	0.436153	−	1.48540i	−0.389396	−	0.921071i	$-0.627316\pi$
$859$	12.7831	−	43.5352i	0.436153	−	1.48540i	0.825549	−	0.564331i	$-0.190866\pi$
$860$		0			0
$861$	−4.01391	−	0.577113i	−0.136794	−	0.0196680i
$862$		0			0
$863$	−32.2387	+	12.0244i	−1.09742	+	0.409316i	−0.831977	−	0.554811i	$-0.812791\pi$
$863$	−32.2387	+	12.0244i	−1.09742	+	0.409316i	−0.265442	+	0.964127i	$0.585518\pi$
$864$		0			0
$865$	11.8995	−	12.8593i	0.404594	−	0.437229i
$866$		0			0
$867$	33.4364	+	25.0302i	1.13556	+	0.850069i
$868$		0			0
$869$	−0.304398	+	0.473652i	−0.0103260	+	0.0160675i
$870$		0			0
$871$	−0.721284	−	2.45647i	−0.0244398	−	0.0832343i
$872$		0			0
$873$	29.2538	−	29.2538i	0.990091	−	0.990091i
$874$		0			0
$875$	4.82186	+	5.08500i	0.163009	+	0.171904i
$876$		0			0
$877$	22.0748	−	40.4271i	0.745414	−	1.36512i	−0.179044	−	0.983841i	$-0.557300\pi$
$877$	22.0748	−	40.4271i	0.745414	−	1.36512i	0.924458	−	0.381283i	$-0.124518\pi$
$878$		0			0
$879$	−48.6851	−	31.2880i	−1.64211	−	1.05532i
$880$		0			0
$881$	−37.4715	+	5.38759i	−1.26245	+	0.181512i	−0.740844	−	0.671677i	$-0.765574\pi$
$881$	−37.4715	+	5.38759i	−1.26245	+	0.181512i	−0.521602	+	0.853189i	$0.674665\pi$
$882$		0			0
$883$	−28.3370	−	6.16433i	−0.953615	−	0.207446i	−0.291266	−	0.956642i	$-0.594077\pi$
$883$	−28.3370	−	6.16433i	−0.953615	−	0.207446i	−0.662349	+	0.749196i	$0.730440\pi$
$884$		0			0
$885$	−3.02385	−	0.536051i	−0.101646	−	0.0180192i
$886$		0			0
$887$	−31.9121	−	42.6295i	−1.07150	−	1.43136i	−0.894456	−	0.447157i	$-0.852437\pi$
$887$	−31.9121	−	42.6295i	−1.07150	−	1.43136i	−0.177046	−	0.984203i	$-0.556654\pi$
$888$		0			0
$889$	−7.27582	−	2.13637i	−0.244023	−	0.0716517i
$890$		0			0
$891$	−0.396501	+	0.343570i	−0.0132833	+	0.0115100i
$892$		0			0
$893$	0.258081	+	3.60845i	0.00863636	+	0.120752i
$894$		0			0
$895$	−0.406327	+	3.89095i	−0.0135820	+	0.130060i
$896$		0			0
$897$	−3.67227	+	3.90379i	−0.122614	+	0.130344i
$898$		0			0
$899$	−13.7169	+	6.26432i	−0.457486	+	0.208927i
$900$		0			0
$901$	−1.12891	+	1.30283i	−0.0376095	+	0.0434037i
$902$		0			0
$903$	1.27599	−	17.8407i	0.0424623	−	0.593700i
$904$		0			0
$905$	−24.6282	−	26.2914i	−0.818669	−	0.873956i
$906$		0			0
$907$	−1.48982	+	1.11527i	−0.0494688	+	0.0370319i	−0.623726	−	0.781643i	$-0.714382\pi$
$907$	−1.48982	+	1.11527i	−0.0494688	+	0.0370319i	0.574257	+	0.818675i	$0.305291\pi$
$908$		0			0
$909$	−8.28387	−	3.78312i	−0.274759	−	0.125478i
$910$		0			0
$911$	−13.8084	−	21.4863i	−0.457492	−	0.711871i	0.533499	−	0.845801i	$-0.320877\pi$
$911$	−13.8084	−	21.4863i	−0.457492	−	0.711871i	−0.990991	+	0.133929i	$0.957240\pi$
$912$		0			0
$913$	0.641618	−	0.857101i	0.0212345	−	0.0283659i
$914$		0			0
$915$	10.2531	−	31.1221i	0.338959	−	1.02886i
$916$		0			0
$917$	−7.03778	−	3.84292i	−0.232408	−	0.126904i
$918$		0			0
$919$	11.6605			0.384644			0.192322	−	0.981332i	$-0.438398\pi$
$919$	11.6605			0.384644			0.192322	+	0.981332i	$0.438398\pi$
$920$		0			0
$921$	−15.3187			−0.504769
$922$		0			0
$923$	−2.09179	−	1.14221i	−0.0688523	−	0.0375962i
$924$		0			0
$925$	−25.8277	+	22.6570i	−0.849211	+	0.744958i
$926$		0			0
$927$	1.86872	−	2.49632i	0.0613768	−	0.0819898i
$928$		0			0
$929$	5.14718	+	8.00916i	0.168873	+	0.262772i	0.915367	−	0.402620i	$-0.131901\pi$
$929$	5.14718	+	8.00916i	0.168873	+	0.262772i	−0.746494	+	0.665393i	$0.768264\pi$
$930$		0			0
$931$	−5.57298	−	2.54510i	−0.182647	−	0.0834122i
$932$		0			0
$933$	−63.8270	+	47.7803i	−2.08960	+	1.56426i
$934$		0			0
$935$	−0.00305379	+	0.0934929i	−9.98696e−5	+	0.00305755i
$936$		0			0
$937$	−1.18848	+	16.6172i	−0.0388260	+	0.542859i	0.940398	+	0.340076i	$0.110453\pi$
$937$	−1.18848	+	16.6172i	−0.0388260	+	0.542859i	−0.979224	+	0.202782i	$0.935002\pi$
$938$		0			0
$939$	−15.3185	+	17.6785i	−0.499899	+	0.576914i
$940$		0			0
$941$	37.4588	−	17.1069i	1.22112	−	0.557668i	0.302631	−	0.953108i	$-0.402135\pi$
$941$	37.4588	−	17.1069i	1.22112	−	0.557668i	0.918492	+	0.395439i	$0.129408\pi$
$942$		0			0
$943$	−12.2698	+	1.25524i	−0.399558	+	0.0408763i
$944$		0			0
$945$	−1.15285	−	0.120391i	−0.0375023	−	0.00391631i
$946$		0			0
$947$	−1.80278	−	25.2061i	−0.0585824	−	0.819090i	−0.938788	−	0.344496i	$-0.888050\pi$
$947$	−1.80278	−	25.2061i	−0.0585824	−	0.819090i	0.880205	−	0.474593i	$-0.157405\pi$
$948$		0			0
$949$	2.02482	−	1.75452i	0.0657285	−	0.0569541i
$950$		0			0
$951$	34.1251	+	10.0200i	1.10658	+	0.324922i
$952$		0			0
$953$	−0.508094	−	0.678733i	−0.0164588	−	0.0219863i	0.792236	−	0.610214i	$-0.208917\pi$
$953$	−0.508094	−	0.678733i	−0.0164588	−	0.0219863i	−0.808695	+	0.588228i	$0.799826\pi$
$954$		0			0
$955$	−31.4022	+	21.9451i	−1.01615	+	0.710127i
$956$		0			0
$957$	−0.525088	−	0.114226i	−0.0169737	−	0.00369240i
$958$		0			0
$959$	−3.83053	+	0.550748i	−0.123694	+	0.0177846i
$960$		0			0
$961$	−7.61433	−	4.89343i	−0.245624	−	0.157853i
$962$		0			0
$963$	−28.4277	+	52.0614i	−0.916068	+	1.67765i
$964$		0			0
$965$	5.43327	−	1.40441i	0.174903	−	0.0452097i
$966$		0			0
$967$	−5.19326	+	5.19326i	−0.167004	+	0.167004i	−0.785661	−	0.618657i	$-0.787677\pi$
$967$	−5.19326	+	5.19326i	−0.167004	+	0.167004i	0.618657	+	0.785661i	$0.287677\pi$
$968$		0			0
$969$	0.414288	+	1.41094i	0.0133089	+	0.0453258i
$970$		0			0
$971$	−24.5163	+	38.1481i	−0.786765	+	1.22423i	0.183699	+	0.982983i	$0.441193\pi$
$971$	−24.5163	+	38.1481i	−0.786765	+	1.22423i	−0.970464	+	0.241247i	$0.922444\pi$
$972$		0			0
$973$	9.32554	+	6.98101i	0.298963	+	0.223801i
$974$		0			0
$975$	2.64798	−	4.92048i	0.0848031	−	0.157582i
$976$		0			0
$977$	23.9432	−	8.93037i	0.766012	−	0.285708i	0.0640736	−	0.997945i	$-0.479591\pi$
$977$	23.9432	−	8.93037i	0.766012	−	0.285708i	0.701939	+	0.712237i	$0.252318\pi$
$978$		0			0
$979$	0.470340	+	0.0676247i	0.0150321	+	0.00216129i
$980$		0			0
$981$	15.6025	−	53.1374i	0.498151	−	1.69655i
$982$		0			0
$983$	−7.65470	−	0.547475i	−0.244147	−	0.0174617i	−0.0512706	−	0.998685i	$-0.516327\pi$
$983$	−7.65470	−	0.547475i	−0.244147	−	0.0174617i	−0.192876	+	0.981223i	$0.561782\pi$
$984$		0			0
$985$	45.3650	+	22.5354i	1.44545	+	0.718038i
$986$		0			0
$987$	−2.14981	+	5.76387i	−0.0684293	+	0.183466i
$988$		0			0
$989$	−9.38316	−	53.5854i	−0.298367	−	1.70392i
$990$		0			0
$991$	−11.2360	−	24.6034i	−0.356923	−	0.781551i	−0.999878	−	0.0156474i	$-0.995019\pi$
$991$	−11.2360	−	24.6034i	−0.356923	−	0.781551i	0.642955	−	0.765904i	$-0.277708\pi$
$992$		0			0
$993$	−75.6743	+	5.41233i	−2.40145	+	0.171755i
$994$		0			0
$995$	30.4431	−	5.58841i	0.965111	−	0.177164i
$996$		0			0
$997$	−45.4417	+	24.8131i	−1.43915	+	0.785837i	−0.993975	−	0.109605i	$-0.965042\pi$
$997$	−45.4417	+	24.8131i	−1.43915	+	0.785837i	−0.445178	+	0.895442i	$0.646860\pi$
$998$		0			0
$999$	0.808764	−	5.62508i	0.0255882	−	0.177970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.433.11	yes	240
5.2	odd	4	inner	460.2.x.a.157.11	yes	240
23.17	odd	22	inner	460.2.x.a.293.11	yes	240
115.17	even	44	inner	460.2.x.a.17.11	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.17.11	✓	240	115.17	even	44	inner
460.2.x.a.157.11	yes	240	5.2	odd	4	inner
460.2.x.a.293.11	yes	240	23.17	odd	22	inner
460.2.x.a.433.11	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.20798 + 1.20565i) q^{3} +(1.99649 - 1.00699i) q^{5} +(-0.375619 + 0.501768i) q^{7} +(1.79966 + 2.80032i) q^{9} +O(q^{10})\)	\(q+(2.20798 + 1.20565i) q^{3} +(1.99649 - 1.00699i) q^{5} +(-0.375619 + 0.501768i) q^{7} +(1.79966 + 2.80032i) q^{9} +(-0.0603661 - 0.0275683i) q^{11} +(0.355624 - 0.266217i) q^{13} +(5.62228 + 0.183642i) q^{15} +(0.0449704 - 0.628768i) q^{17} +(-0.607236 + 0.700788i) q^{19} +(-1.43431 + 0.655028i) q^{21} +(-3.74968 + 2.98996i) q^{23} +(2.97193 - 4.02090i) q^{25} +(0.0590001 + 0.824930i) q^{27} +(2.43256 - 2.10783i) q^{29} +(-4.49518 - 1.31991i) q^{31} +(-0.100049 - 0.133650i) q^{33} +(-0.244642 + 1.38002i) q^{35} +(-6.71439 - 1.46063i) q^{37} +(1.10617 - 0.159044i) q^{39} +(2.16351 + 1.39041i) q^{41} +(-5.43629 + 9.95581i) q^{43} +(6.41290 + 3.77857i) q^{45} +(2.75870 - 2.75870i) q^{47} +(1.86145 + 6.33950i) q^{49} +(0.857366 - 1.33409i) q^{51} +(-2.18926 - 1.63886i) q^{53} +(-0.148281 + 0.00574849i) q^{55} +(-2.18567 + 0.815211i) q^{57} +(-0.540372 - 0.0776937i) q^{59} +(1.64111 - 5.58909i) q^{61} +(-2.08110 - 0.148843i) q^{63} +(0.441921 - 0.889611i) q^{65} +(2.01402 - 5.39980i) q^{67} +(-11.8841 + 2.08098i) q^{69} +(-2.22873 - 4.88024i) q^{71} +(6.01580 - 0.430258i) q^{73} +(11.4097 - 5.29496i) q^{75} +(0.0365075 - 0.0199346i) q^{77} +(1.20741 - 8.39774i) q^{79} +(3.28414 - 7.19125i) q^{81} +(-3.42936 + 15.7645i) q^{83} +(-0.543382 - 1.30061i) q^{85} +(7.91234 - 1.72122i) q^{87} +(-6.87021 + 2.01727i) q^{89} +0.278437i q^{91} +(-8.33393 - 8.33393i) q^{93} +(-0.506651 + 2.01060i) q^{95} +(-2.64185 - 12.1444i) q^{97} +(-0.0314383 - 0.218658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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