LMFDB - Embedded newform 585.2.j.e.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.2
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	585.451
Dual form			585.2.j.e.406.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 1.40126i) q^{2} +(-0.309017 - 0.535233i) q^{4} -1.00000 q^{5} +(0.118034 + 0.204441i) q^{7} +2.23607 q^{8} +O(q^{10})$	\(q+(0.809017 - 1.40126i) q^{2} +(-0.309017 - 0.535233i) q^{4} -1.00000 q^{5} +(0.118034 + 0.204441i) q^{7} +2.23607 q^{8} +(-0.809017 + 1.40126i) q^{10} +(2.11803 - 3.66854i) q^{11} +(-1.00000 - 3.46410i) q^{13} +0.381966 q^{14} +(2.42705 - 4.20378i) q^{16} +(2.73607 + 4.73901i) q^{17} +(0.118034 + 0.204441i) q^{19} +(0.309017 + 0.535233i) q^{20} +(-3.42705 - 5.93583i) q^{22} +(4.11803 - 7.13264i) q^{23} +1.00000 q^{25} +(-5.66312 - 1.40126i) q^{26} +(0.0729490 - 0.126351i) q^{28} +(0.736068 - 1.27491i) q^{29} +(-1.69098 - 2.92887i) q^{32} +8.85410 q^{34} +(-0.118034 - 0.204441i) q^{35} +(-1.50000 + 2.59808i) q^{37} +0.381966 q^{38} -2.23607 q^{40} +(-2.97214 + 5.14789i) q^{41} +(0.881966 + 1.52761i) q^{43} -2.61803 q^{44} +(-6.66312 - 11.5409i) q^{46} -12.9443 q^{47} +(3.47214 - 6.01392i) q^{49} +(0.809017 - 1.40126i) q^{50} +(-1.54508 + 1.60570i) q^{52} -6.00000 q^{53} +(-2.11803 + 3.66854i) q^{55} +(0.263932 + 0.457144i) q^{56} +(-1.19098 - 2.06284i) q^{58} +(6.35410 + 11.0056i) q^{59} +(6.20820 + 10.7529i) q^{61} +4.23607 q^{64} +(1.00000 + 3.46410i) q^{65} +(-5.35410 + 9.27358i) q^{67} +(1.69098 - 2.92887i) q^{68} -0.381966 q^{70} +(-0.881966 - 1.52761i) q^{71} -6.00000 q^{73} +(2.42705 + 4.20378i) q^{74} +(0.0729490 - 0.126351i) q^{76} +1.00000 q^{77} +(-2.42705 + 4.20378i) q^{80} +(4.80902 + 8.32946i) q^{82} +8.94427 q^{83} +(-2.73607 - 4.73901i) q^{85} +2.85410 q^{86} +(4.73607 - 8.20311i) q^{88} +(-4.50000 + 7.79423i) q^{89} +(0.590170 - 0.613323i) q^{91} -5.09017 q^{92} +(-10.4721 + 18.1383i) q^{94} +(-0.118034 - 0.204441i) q^{95} +(-2.73607 - 4.73901i) q^{97} +(-5.61803 - 9.73072i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{4} - 4 q^{5} - 4 q^{7}+O(q^{10}) $ 4 * q + q^2 + q^4 - 4 * q^5 - 4 * q^7	$ 4 q + q^{2} + q^{4} - 4 q^{5} - 4 q^{7} - q^{10} + 4 q^{11} - 4 q^{13} + 6 q^{14} + 3 q^{16} + 2 q^{17} - 4 q^{19} - q^{20} - 7 q^{22} + 12 q^{23} + 4 q^{25} - 7 q^{26} + 7 q^{28} - 6 q^{29} - 9 q^{32} + 22 q^{34} + 4 q^{35} - 6 q^{37} + 6 q^{38} + 6 q^{41} + 8 q^{43} - 6 q^{44} - 11 q^{46} - 16 q^{47} - 4 q^{49} + q^{50} + 5 q^{52} - 24 q^{53} - 4 q^{55} + 10 q^{56} - 7 q^{58} + 12 q^{59} - 2 q^{61} + 8 q^{64} + 4 q^{65} - 8 q^{67} + 9 q^{68} - 6 q^{70} - 8 q^{71} - 24 q^{73} + 3 q^{74} + 7 q^{76} + 4 q^{77} - 3 q^{80} + 17 q^{82} - 2 q^{85} - 2 q^{86} + 10 q^{88} - 18 q^{89} - 20 q^{91} + 2 q^{92} - 24 q^{94} + 4 q^{95} - 2 q^{97} - 18 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^4 - 4 * q^5 - 4 * q^7 - q^10 + 4 * q^11 - 4 * q^13 + 6 * q^14 + 3 * q^16 + 2 * q^17 - 4 * q^19 - q^20 - 7 * q^22 + 12 * q^23 + 4 * q^25 - 7 * q^26 + 7 * q^28 - 6 * q^29 - 9 * q^32 + 22 * q^34 + 4 * q^35 - 6 * q^37 + 6 * q^38 + 6 * q^41 + 8 * q^43 - 6 * q^44 - 11 * q^46 - 16 * q^47 - 4 * q^49 + q^50 + 5 * q^52 - 24 * q^53 - 4 * q^55 + 10 * q^56 - 7 * q^58 + 12 * q^59 - 2 * q^61 + 8 * q^64 + 4 * q^65 - 8 * q^67 + 9 * q^68 - 6 * q^70 - 8 * q^71 - 24 * q^73 + 3 * q^74 + 7 * q^76 + 4 * q^77 - 3 * q^80 + 17 * q^82 - 2 * q^85 - 2 * q^86 + 10 * q^88 - 18 * q^89 - 20 * q^91 + 2 * q^92 - 24 * q^94 + 4 * q^95 - 2 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.809017	−	1.40126i	0.572061	−	0.990839i	−0.424293	−	0.905525i	$-0.639477\pi$
$2$	0.809017	−	1.40126i	0.572061	−	0.990839i	0.996354	−	0.0853143i	$-0.0271894\pi$
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.535233i	−0.154508	−	0.267617i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	0.118034	+	0.204441i	0.0446127	+	0.0772714i	0.887469	−	0.460866i	$-0.152461\pi$
$7$	0.118034	+	0.204441i	0.0446127	+	0.0772714i	−0.842857	+	0.538138i	$0.819128\pi$
$8$	2.23607			0.790569
$9$		0			0
$10$	−0.809017	+	1.40126i	−0.255834	+	0.443117i
$11$	2.11803	−	3.66854i	0.638611	−	1.10611i	−0.347126	−	0.937818i	$-0.612843\pi$
$11$	2.11803	−	3.66854i	0.638611	−	1.10611i	0.985738	−	0.168289i	$-0.0538241\pi$
$12$		0			0
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	0.381966			0.102085
$15$		0			0
$16$	2.42705	−	4.20378i	0.606763	−	1.05094i
$17$	2.73607	+	4.73901i	0.663594	+	1.14938i	0.979664	+	0.200643i	$0.0643030\pi$
$17$	2.73607	+	4.73901i	0.663594	+	1.14938i	−0.316071	+	0.948736i	$0.602364\pi$
$18$		0			0
$19$	0.118034	+	0.204441i	0.0270789	+	0.0469020i	0.879247	−	0.476366i	$-0.158046\pi$
$19$	0.118034	+	0.204441i	0.0270789	+	0.0469020i	−0.852168	+	0.523268i	$0.824713\pi$
$20$	0.309017	+	0.535233i	0.0690983	+	0.119682i
$21$		0			0
$22$	−3.42705	−	5.93583i	−0.730650	−	1.26552i
$23$	4.11803	−	7.13264i	0.858669	−	1.48726i	−0.0145291	−	0.999894i	$-0.504625\pi$
$23$	4.11803	−	7.13264i	0.858669	−	1.48726i	0.873199	−	0.487365i	$-0.162042\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−5.66312	−	1.40126i	−1.11063	−	0.274809i
$27$		0			0
$28$	0.0729490	−	0.126351i	0.0137861	−	0.0238782i
$29$	0.736068	−	1.27491i	0.136684	−	0.236744i	−0.789555	−	0.613679i	$-0.789689\pi$
$29$	0.736068	−	1.27491i	0.136684	−	0.236744i	0.926240	+	0.376935i	$0.123022\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−1.69098	−	2.92887i	−0.298926	−	0.517756i
$33$		0			0
$34$	8.85410			1.51847
$35$	−0.118034	−	0.204441i	−0.0199514	−	0.0345568i
$36$		0			0
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$	0.381966			0.0619631
$39$		0			0
$40$	−2.23607			−0.353553
$41$	−2.97214	+	5.14789i	−0.464170	+	0.803965i	−0.999164	−	0.0408904i	$-0.986981\pi$
$41$	−2.97214	+	5.14789i	−0.464170	+	0.803965i	0.534994	+	0.844856i	$0.320314\pi$
$42$		0			0
$43$	0.881966	+	1.52761i	0.134499	+	0.232958i	0.925406	−	0.378978i	$-0.123724\pi$
$43$	0.881966	+	1.52761i	0.134499	+	0.232958i	−0.790907	+	0.611936i	$0.790391\pi$
$44$	−2.61803			−0.394683
$45$		0			0
$46$	−6.66312	−	11.5409i	−0.982423	−	1.70161i
$47$	−12.9443			−1.88812			−0.944058	−	0.329779i	$-0.893026\pi$
$47$	−12.9443			−1.88812			−0.944058	+	0.329779i	$0.893026\pi$
$48$		0			0
$49$	3.47214	−	6.01392i	0.496019	−	0.859131i
$50$	0.809017	−	1.40126i	0.114412	−	0.198168i
$51$		0			0
$52$	−1.54508	+	1.60570i	−0.214265	+	0.222670i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	−2.11803	+	3.66854i	−0.285596	+	0.494666i
$56$	0.263932	+	0.457144i	0.0352694	+	0.0610884i
$57$		0			0
$58$	−1.19098	−	2.06284i	−0.156384	−	0.270865i
$59$	6.35410	+	11.0056i	0.827234	+	1.43281i	0.900200	+	0.435476i	$0.143420\pi$
$59$	6.35410	+	11.0056i	0.827234	+	1.43281i	−0.0729666	+	0.997334i	$0.523247\pi$
$60$		0			0
$61$	6.20820	+	10.7529i	0.794879	+	1.37677i	0.922916	+	0.385002i	$0.125799\pi$
$61$	6.20820	+	10.7529i	0.794879	+	1.37677i	−0.128037	+	0.991769i	$0.540868\pi$
$62$		0			0
$63$		0			0
$64$	4.23607			0.529508
$65$	1.00000	+	3.46410i	0.124035	+	0.429669i
$66$		0			0
$67$	−5.35410	+	9.27358i	−0.654108	+	1.13295i	0.328009	+	0.944675i	$0.393622\pi$
$67$	−5.35410	+	9.27358i	−0.654108	+	1.13295i	−0.982117	+	0.188273i	$0.939711\pi$
$68$	1.69098	−	2.92887i	0.205062	−	0.355177i
$69$		0			0
$70$	−0.381966			−0.0456537
$71$	−0.881966	−	1.52761i	−0.104670	−	0.181294i	0.808933	−	0.587900i	$-0.200045\pi$
$71$	−0.881966	−	1.52761i	−0.104670	−	0.181294i	−0.913603	+	0.406607i	$0.866712\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	2.42705	+	4.20378i	0.282139	+	0.488679i
$75$		0			0
$76$	0.0729490	−	0.126351i	0.00836783	−	0.0144935i
$77$	1.00000			0.113961
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−2.42705	+	4.20378i	−0.271353	+	0.469996i
$81$		0			0
$82$	4.80902	+	8.32946i	0.531067	+	0.919835i
$83$	8.94427			0.981761			0.490881	−	0.871227i	$-0.336675\pi$
$83$	8.94427			0.981761			0.490881	+	0.871227i	$0.336675\pi$
$84$		0			0
$85$	−2.73607	−	4.73901i	−0.296768	−	0.514018i
$86$	2.85410			0.307766
$87$		0			0
$88$	4.73607	−	8.20311i	0.504867	−	0.874455i
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	−0.999653	−	0.0263586i	$-0.991609\pi$
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	0.522654	+	0.852545i	$0.324942\pi$
$90$		0			0
$91$	0.590170	−	0.613323i	0.0618666	−	0.0642937i
$92$	−5.09017			−0.530687
$93$		0			0
$94$	−10.4721	+	18.1383i	−1.08012	+	1.87082i
$95$	−0.118034	−	0.204441i	−0.0121100	−	0.0209752i
$96$		0			0
$97$	−2.73607	−	4.73901i	−0.277806	−	0.481173i	0.693034	−	0.720905i	$-0.256274\pi$
$97$	−2.73607	−	4.73901i	−0.277806	−	0.481173i	−0.970839	+	0.239732i	$0.922940\pi$
$98$	−5.61803	−	9.73072i	−0.567507	−	0.982951i
$99$		0			0
$100$	−0.309017	−	0.535233i	−0.0309017	−	0.0535233i
$101$	4.73607	−	8.20311i	0.471256	−	0.816240i	−0.528203	−	0.849118i	$-0.677134\pi$
$101$	4.73607	−	8.20311i	0.471256	−	0.816240i	0.999459	+	0.0328781i	$0.0104673\pi$
$102$		0			0
$103$	−4.94427			−0.487174			−0.243587	−	0.969879i	$-0.578324\pi$
$103$	−4.94427			−0.487174			−0.243587	+	0.969879i	$0.578324\pi$
$104$	−2.23607	−	7.74597i	−0.219265	−	0.759555i
$105$		0			0
$106$	−4.85410	+	8.40755i	−0.471472	+	0.816614i
$107$	−5.11803	+	8.86469i	−0.494779	+	0.856982i	−0.999982	−	0.00601821i	$-0.998084\pi$
$107$	−5.11803	+	8.86469i	−0.494779	+	0.856982i	0.505203	+	0.863001i	$0.331418\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	3.42705	+	5.93583i	0.326756	+	0.565959i
$111$		0			0
$112$	1.14590			0.108277
$113$	−3.73607	−	6.47106i	−0.351460	−	0.608746i	0.635046	−	0.772475i	$-0.280981\pi$
$113$	−3.73607	−	6.47106i	−0.351460	−	0.608746i	−0.986505	+	0.163728i	$0.947648\pi$
$114$		0			0
$115$	−4.11803	+	7.13264i	−0.384009	+	0.665122i
$116$	−0.909830			−0.0844756
$117$		0			0
$118$	20.5623			1.89291
$119$	−0.645898	+	1.11873i	−0.0592094	+	0.102554i
$120$		0			0
$121$	−3.47214	−	6.01392i	−0.315649	−	0.546720i
$122$	20.0902			1.81888
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.118034	+	0.204441i	−0.0104738	+	0.0181412i	−0.871215	−	0.490902i	$-0.836667\pi$
$127$	−0.118034	+	0.204441i	−0.0104738	+	0.0181412i	0.860741	+	0.509043i	$0.170001\pi$
$128$	6.80902	−	11.7936i	0.601838	−	1.04241i
$129$		0			0
$130$	5.66312	+	1.40126i	0.496688	+	0.122899i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	−0.0278640	+	0.0482619i	−0.00241612	+	0.00418484i
$134$	8.66312	+	15.0050i	0.748379	+	1.29623i
$135$		0			0
$136$	6.11803	+	10.5967i	0.524617	+	0.908663i
$137$	−3.73607	−	6.47106i	−0.319194	−	0.552860i	0.661126	−	0.750275i	$-0.270079\pi$
$137$	−3.73607	−	6.47106i	−0.319194	−	0.552860i	−0.980320	+	0.197415i	$0.936745\pi$
$138$		0			0
$139$	1.64590	+	2.85078i	0.139603	+	0.241800i	0.927346	−	0.374204i	$-0.122084\pi$
$139$	1.64590	+	2.85078i	0.139603	+	0.241800i	−0.787743	+	0.616004i	$0.788751\pi$
$140$	−0.0729490	+	0.126351i	−0.00616532	+	0.0106786i
$141$		0			0
$142$	−2.85410			−0.239511
$143$	−14.8262	−	3.66854i	−1.23983	−	0.306779i
$144$		0			0
$145$	−0.736068	+	1.27491i	−0.0611271	+	0.105875i
$146$	−4.85410	+	8.40755i	−0.401728	+	0.695814i
$147$		0			0
$148$	1.85410			0.152406
$149$	6.73607	+	11.6672i	0.551840	+	0.955815i	0.998142	+	0.0609327i	$0.0194075\pi$
$149$	6.73607	+	11.6672i	0.551840	+	0.955815i	−0.446302	+	0.894883i	$0.647259\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	0.263932	+	0.457144i	0.0214077	+	0.0370792i
$153$		0			0
$154$	0.809017	−	1.40126i	0.0651924	−	0.112917i
$155$		0			0
$156$		0			0
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$		0			0
$159$		0			0
$160$	1.69098	+	2.92887i	0.133684	+	0.231547i
$161$	1.94427			0.153230
$162$		0			0
$163$	−0.645898	−	1.11873i	−0.0505906	−	0.0876256i	0.839621	−	0.543173i	$-0.182777\pi$
$163$	−0.645898	−	1.11873i	−0.0505906	−	0.0876256i	−0.890212	+	0.455547i	$0.849444\pi$
$164$	3.67376			0.286873
$165$		0			0
$166$	7.23607	−	12.5332i	0.561628	−	0.972768i
$167$	2.59017	−	4.48631i	0.200433	−	0.347161i	−0.748235	−	0.663434i	$-0.769098\pi$
$167$	2.59017	−	4.48631i	0.200433	−	0.347161i	0.948668	+	0.316273i	$0.102432\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	−8.85410			−0.679079
$171$		0			0
$172$	0.545085	−	0.944115i	0.0415623	−	0.0719881i
$173$	8.44427	+	14.6259i	0.642006	+	1.11199i	0.984984	+	0.172644i	$0.0552310\pi$
$173$	8.44427	+	14.6259i	0.642006	+	1.11199i	−0.342978	+	0.939343i	$0.611436\pi$
$174$		0			0
$175$	0.118034	+	0.204441i	0.00892253	+	0.0154543i
$176$	−10.2812	−	17.8075i	−0.774971	−	1.34229i
$177$		0			0
$178$	7.28115	+	12.6113i	0.545745	+	0.945259i
$179$	−1.88197	+	3.25966i	−0.140665	+	0.243638i	−0.927747	−	0.373209i	$-0.878257\pi$
$179$	−1.88197	+	3.25966i	−0.140665	+	0.243638i	0.787082	+	0.616848i	$0.211591\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	−0.381966	−	1.32317i	−0.0283132	−	0.0980798i
$183$		0			0
$184$	9.20820	−	15.9491i	0.678838	−	1.17578i
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$		0			0
$187$	23.1803			1.69511
$188$	4.00000	+	6.92820i	0.291730	+	0.505291i
$189$		0			0
$190$	−0.381966			−0.0277107
$191$	−2.40983	−	4.17395i	−0.174369	−	0.302016i	0.765574	−	0.643348i	$-0.222455\pi$
$191$	−2.40983	−	4.17395i	−0.174369	−	0.302016i	−0.939943	+	0.341332i	$0.889122\pi$
$192$		0			0
$193$	−2.73607	+	4.73901i	−0.196946	+	0.341121i	−0.947537	−	0.319646i	$-0.896436\pi$
$193$	−2.73607	+	4.73901i	−0.196946	+	0.341121i	0.750590	+	0.660768i	$0.229769\pi$
$194$	−8.85410			−0.635687
$195$		0			0
$196$	−4.29180			−0.306557
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	−0.807630	−	0.589689i	$-0.799250\pi$
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	0.914501	+	0.404584i	$0.132584\pi$
$198$		0			0
$199$	7.35410	+	12.7377i	0.521318	+	0.902950i	0.999693	+	0.0247939i	$0.00789296\pi$
$199$	7.35410	+	12.7377i	0.521318	+	0.902950i	−0.478374	+	0.878156i	$0.658774\pi$
$200$	2.23607			0.158114
$201$		0			0
$202$	−7.66312	−	13.2729i	−0.539175	−	0.933879i
$203$	0.347524			0.0243914
$204$		0			0
$205$	2.97214	−	5.14789i	0.207583	−	0.359544i
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$		0			0
$208$	−16.9894	−	4.20378i	−1.17800	−	0.291479i
$209$	1.00000			0.0691714
$210$		0			0
$211$	−4.59017	+	7.95041i	−0.316000	+	0.547329i	−0.979650	−	0.200715i	$-0.935673\pi$
$211$	−4.59017	+	7.95041i	−0.316000	+	0.547329i	0.663649	+	0.748044i	$0.269007\pi$
$212$	1.85410	+	3.21140i	0.127340	+	0.220560i
$213$		0			0
$214$	8.28115	+	14.3434i	0.566088	+	0.980493i
$215$	−0.881966	−	1.52761i	−0.0601496	−	0.104182i
$216$		0			0
$217$		0			0
$218$	−1.61803	+	2.80252i	−0.109587	+	0.189810i
$219$		0			0
$220$	2.61803			0.176508
$221$	13.6803	−	14.2170i	0.920239	−	0.956341i
$222$		0			0
$223$	6.35410	−	11.0056i	0.425502	−	0.736991i	−0.570965	−	0.820974i	$-0.693431\pi$
$223$	6.35410	−	11.0056i	0.425502	−	0.736991i	0.996467	+	0.0839830i	$0.0267642\pi$
$224$	0.399187	−	0.691412i	0.0266718	−	0.0461969i
$225$		0			0
$226$	−12.0902			−0.804226
$227$	−0.881966	−	1.52761i	−0.0585381	−	0.101391i	0.835271	−	0.549838i	$-0.185311\pi$
$227$	−0.881966	−	1.52761i	−0.0585381	−	0.101391i	−0.893809	+	0.448447i	$0.851977\pi$
$228$		0			0
$229$	−19.8885			−1.31427			−0.657136	−	0.753772i	$-0.728232\pi$
$229$	−19.8885			−1.31427			−0.657136	+	0.753772i	$0.728232\pi$
$230$	6.66312	+	11.5409i	0.439353	+	0.760982i
$231$		0			0
$232$	1.64590	−	2.85078i	0.108058	−	0.187163i
$233$	−19.8885			−1.30294			−0.651471	−	0.758674i	$-0.725848\pi$
$233$	−19.8885			−1.30294			−0.651471	+	0.758674i	$0.725848\pi$
$234$		0			0
$235$	12.9443			0.844391
$236$	3.92705	−	6.80185i	0.255629	−	0.442763i
$237$		0			0
$238$	1.04508	+	1.81014i	0.0677428	+	0.117334i
$239$	−9.88854			−0.639637			−0.319818	−	0.947479i	$-0.603622\pi$
$239$	−9.88854			−0.639637			−0.319818	+	0.947479i	$0.603622\pi$
$240$		0			0
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	0.516695	−	0.856170i	$-0.327162\pi$
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	−0.999812	+	0.0193858i	$0.993829\pi$
$242$	−11.2361			−0.722282
$243$		0			0
$244$	3.83688	−	6.64567i	0.245631	−	0.425446i
$245$	−3.47214	+	6.01392i	−0.221827	+	0.384215i
$246$		0			0
$247$	0.590170	−	0.613323i	0.0375516	−	0.0390248i
$248$		0			0
$249$		0			0
$250$	−0.809017	+	1.40126i	−0.0511667	+	0.0886234i
$251$	7.88197	+	13.6520i	0.497505	+	0.861704i	0.999996	−	0.00287826i	$-0.000916180\pi$
$251$	7.88197	+	13.6520i	0.497505	+	0.861704i	−0.502491	+	0.864583i	$0.667583\pi$
$252$		0			0
$253$	−17.4443	−	30.2144i	−1.09671	−	1.89956i
$254$	0.190983	+	0.330792i	0.0119833	+	0.0207558i
$255$		0			0
$256$	−6.78115	−	11.7453i	−0.423822	−	0.734081i
$257$	4.26393	−	7.38535i	0.265977	−	0.460685i	−0.701842	−	0.712332i	$-0.747639\pi$
$257$	4.26393	−	7.38535i	0.265977	−	0.460685i	0.967819	+	0.251647i	$0.0809722\pi$
$258$		0			0
$259$	−0.708204			−0.0440057
$260$	1.54508	−	1.60570i	0.0958221	−	0.0995812i
$261$		0			0
$262$	9.70820	−	16.8151i	0.599775	−	1.03884i
$263$	4.11803	−	7.13264i	0.253929	−	0.439818i	−0.710675	−	0.703520i	$-0.751610\pi$
$263$	4.11803	−	7.13264i	0.253929	−	0.439818i	0.964604	+	0.263703i	$0.0849438\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$	0.0450850	+	0.0780895i	0.00276434	+	0.00478797i
$267$		0			0
$268$	6.61803			0.404261
$269$	−7.73607	−	13.3993i	−0.471676	−	0.816967i	0.527799	−	0.849370i	$-0.323018\pi$
$269$	−7.73607	−	13.3993i	−0.471676	−	0.816967i	−0.999475	+	0.0324021i	$0.989684\pi$
$270$		0			0
$271$	−7.35410	+	12.7377i	−0.446730	+	0.773759i	−0.998171	−	0.0604550i	$-0.980745\pi$
$271$	−7.35410	+	12.7377i	−0.446730	+	0.773759i	0.551441	+	0.834214i	$0.314078\pi$
$272$	26.5623			1.61058
$273$		0			0
$274$	−12.0902			−0.730394
$275$	2.11803	−	3.66854i	0.127722	−	0.221221i
$276$		0			0
$277$	9.44427	+	16.3580i	0.567451	+	0.982854i	0.996817	+	0.0797238i	$0.0254038\pi$
$277$	9.44427	+	16.3580i	0.567451	+	0.982854i	−0.429366	+	0.903131i	$0.641263\pi$
$278$	5.32624			0.319447
$279$		0			0
$280$	−0.263932	−	0.457144i	−0.0157730	−	0.0273196i
$281$	−19.8885			−1.18645			−0.593226	−	0.805036i	$-0.702146\pi$
$281$	−19.8885			−1.18645			−0.593226	+	0.805036i	$0.702146\pi$
$282$		0			0
$283$	−1.35410	+	2.34537i	−0.0804930	+	0.139418i	−0.903462	−	0.428669i	$-0.858983\pi$
$283$	−1.35410	+	2.34537i	−0.0804930	+	0.139418i	0.822969	+	0.568087i	$0.192316\pi$
$284$	−0.545085	+	0.944115i	−0.0323448	+	0.0560229i
$285$		0			0
$286$	−17.1353	+	17.8075i	−1.01323	+	1.05298i
$287$	−1.40325			−0.0828314
$288$		0			0
$289$	−6.47214	+	11.2101i	−0.380714	+	0.659416i
$290$	1.19098	+	2.06284i	0.0699369	+	0.121134i
$291$		0			0
$292$	1.85410	+	3.21140i	0.108503	+	0.187933i
$293$	−6.02786	−	10.4406i	−0.352152	−	0.609944i	0.634475	−	0.772944i	$-0.281217\pi$
$293$	−6.02786	−	10.4406i	−0.352152	−	0.609944i	−0.986626	+	0.162999i	$0.947883\pi$
$294$		0			0
$295$	−6.35410	−	11.0056i	−0.369950	−	0.640772i
$296$	−3.35410	+	5.80948i	−0.194953	+	0.337669i
$297$		0			0
$298$	21.7984			1.26275
$299$	−28.8262	−	7.13264i	−1.66706	−	0.412491i
$300$		0			0
$301$	−0.208204	+	0.360620i	−0.0120007	+	0.0207858i
$302$	6.47214	−	11.2101i	0.372430	−	0.645067i
$303$		0			0
$304$	1.14590			0.0657218
$305$	−6.20820	−	10.7529i	−0.355481	−	0.615711i
$306$		0			0
$307$	7.05573			0.402692			0.201346	−	0.979520i	$-0.435468\pi$
$307$	7.05573			0.402692			0.201346	+	0.979520i	$0.435468\pi$
$308$	−0.309017	−	0.535233i	−0.0176079	−	0.0304977i
$309$		0			0
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	−31.8885			−1.80245			−0.901224	−	0.433355i	$-0.857330\pi$
$313$	−31.8885			−1.80245			−0.901224	+	0.433355i	$0.857330\pi$
$314$	−14.5623	+	25.2227i	−0.821798	+	1.42340i
$315$		0			0
$316$		0			0
$317$	−23.8885			−1.34171			−0.670857	−	0.741587i	$-0.734074\pi$
$317$	−23.8885			−1.34171			−0.670857	+	0.741587i	$0.734074\pi$
$318$		0			0
$319$	−3.11803	−	5.40059i	−0.174576	−	0.302375i
$320$	−4.23607			−0.236803
$321$		0			0
$322$	1.57295	−	2.72443i	0.0876570	−	0.151826i
$323$	−0.645898	+	1.11873i	−0.0359387	+	0.0622477i
$324$		0			0
$325$	−1.00000	−	3.46410i	−0.0554700	−	0.192154i
$326$	−2.09017			−0.115764
$327$		0			0
$328$	−6.64590	+	11.5110i	−0.366958	+	0.635590i
$329$	−1.52786	−	2.64634i	−0.0842339	−	0.145897i
$330$		0			0
$331$	−12.8262	−	22.2157i	−0.704994	−	1.22109i	−0.966694	−	0.255936i	$-0.917616\pi$
$331$	−12.8262	−	22.2157i	−0.704994	−	1.22109i	0.261700	−	0.965149i	$-0.415717\pi$
$332$	−2.76393	−	4.78727i	−0.151690	−	0.262736i
$333$		0			0
$334$	−4.19098	−	7.25900i	−0.229320	−	0.397195i
$335$	5.35410	−	9.27358i	0.292526	−	0.506670i
$336$		0			0
$337$	27.8885			1.51919			0.759593	−	0.650399i	$-0.225398\pi$
$337$	27.8885			1.51919			0.759593	+	0.650399i	$0.225398\pi$
$338$	0.809017	+	21.0189i	0.0440047	+	1.14328i
$339$		0			0
$340$	−1.69098	+	2.92887i	−0.0917064	+	0.158840i
$341$		0			0
$342$		0			0
$343$	3.29180			0.177740
$344$	1.97214	+	3.41584i	0.106330	+	0.184170i
$345$		0			0
$346$	27.3262			1.46907
$347$	8.64590	+	14.9751i	0.464136	+	0.803907i	0.999162	−	0.0409283i	$-0.0130315\pi$
$347$	8.64590	+	14.9751i	0.464136	+	0.803907i	−0.535026	+	0.844836i	$0.679698\pi$
$348$		0			0
$349$	12.2082	−	21.1452i	0.653490	−	1.13188i	−0.328780	−	0.944407i	$-0.606637\pi$
$349$	12.2082	−	21.1452i	0.653490	−	1.13188i	0.982270	−	0.187472i	$-0.0600293\pi$
$350$	0.381966			0.0204169
$351$		0			0
$352$	−14.3262			−0.763591
$353$	−5.26393	+	9.11740i	−0.280171	+	0.485270i	−0.971427	−	0.237340i	$-0.923724\pi$
$353$	−5.26393	+	9.11740i	−0.280171	+	0.485270i	0.691256	+	0.722610i	$0.257058\pi$
$354$		0			0
$355$	0.881966	+	1.52761i	0.0468099	+	0.0810771i
$356$	5.56231			0.294802
$357$		0			0
$358$	3.04508	+	5.27424i	0.160938	+	0.278752i
$359$	17.8885			0.944121			0.472061	−	0.881566i	$-0.343510\pi$
$359$	17.8885			0.944121			0.472061	+	0.881566i	$0.343510\pi$
$360$		0			0
$361$	9.47214	−	16.4062i	0.498533	−	0.863485i
$362$	4.85410	−	8.40755i	0.255126	−	0.441891i
$363$		0			0
$364$	−0.510643	−	0.126351i	−0.0267650	−	0.00662261i
$365$	6.00000			0.314054
$366$		0			0
$367$	12.8262	−	22.2157i	0.669524	−	1.15965i	−0.308513	−	0.951220i	$-0.599831\pi$
$367$	12.8262	−	22.2157i	0.669524	−	1.15965i	0.978037	−	0.208430i	$-0.0668353\pi$
$368$	−19.9894	−	34.6226i	−1.04202	−	1.80483i
$369$		0			0
$370$	−2.42705	−	4.20378i	−0.126176	−	0.218544i
$371$	−0.708204	−	1.22665i	−0.0367681	−	0.0636842i
$372$		0			0
$373$	−5.02786	−	8.70852i	−0.260333	−	0.450910i	0.705997	−	0.708214i	$-0.250499\pi$
$373$	−5.02786	−	8.70852i	−0.260333	−	0.450910i	−0.966330	+	0.257305i	$0.917166\pi$
$374$	18.7533	−	32.4816i	0.969709	−	1.67959i
$375$		0			0
$376$	−28.9443			−1.49269
$377$	−5.15248	−	1.27491i	−0.265366	−	0.0656611i
$378$		0			0
$379$	−16.5902	+	28.7350i	−0.852180	+	1.47602i	0.0270571	+	0.999634i	$0.491386\pi$
$379$	−16.5902	+	28.7350i	−0.852180	+	1.47602i	−0.879237	+	0.476385i	$0.841947\pi$
$380$	−0.0729490	+	0.126351i	−0.00374221	+	0.00648169i
$381$		0			0
$382$	−7.79837			−0.399000
$383$	−0.118034	−	0.204441i	−0.00603126	−	0.0104464i	0.862994	−	0.505214i	$-0.168586\pi$
$383$	−0.118034	−	0.204441i	−0.00603126	−	0.0104464i	−0.869025	+	0.494768i	$0.835253\pi$
$384$		0			0
$385$	−1.00000			−0.0509647
$386$	4.42705	+	7.66788i	0.225331	+	0.390285i
$387$		0			0
$388$	−1.69098	+	2.92887i	−0.0858467	+	0.148691i
$389$	35.8885			1.81962			0.909811	−	0.415023i	$-0.136227\pi$
$389$	35.8885			1.81962			0.909811	+	0.415023i	$0.136227\pi$
$390$		0			0
$391$	45.0689			2.27923
$392$	7.76393	−	13.4475i	0.392138	−	0.679203i
$393$		0			0
$394$	−2.42705	−	4.20378i	−0.122273	−	0.211783i
$395$		0			0
$396$		0			0
$397$	−5.02786	−	8.70852i	−0.252341	−	0.437068i	0.711829	−	0.702353i	$-0.247867\pi$
$397$	−5.02786	−	8.70852i	−0.252341	−	0.437068i	−0.964170	+	0.265285i	$0.914534\pi$
$398$	23.7984			1.19290
$399$		0			0
$400$	2.42705	−	4.20378i	0.121353	−	0.210189i
$401$	−13.4443	+	23.2862i	−0.671375	+	1.16286i	0.306139	+	0.951987i	$0.400963\pi$
$401$	−13.4443	+	23.2862i	−0.671375	+	1.16286i	−0.977514	+	0.210869i	$0.932371\pi$
$402$		0			0
$403$		0			0
$404$	−5.85410			−0.291252
$405$		0			0
$406$	0.281153	−	0.486971i	0.0139534	−	0.0241680i
$407$	6.35410	+	11.0056i	0.314961	+	0.545529i
$408$		0			0
$409$	5.44427	+	9.42976i	0.269202	+	0.466271i	0.968656	−	0.248406i	$-0.0799068\pi$
$409$	5.44427	+	9.42976i	0.269202	+	0.466271i	−0.699454	+	0.714678i	$0.746573\pi$
$410$	−4.80902	−	8.32946i	−0.237500	−	0.411363i
$411$		0			0
$412$	1.52786	+	2.64634i	0.0752725	+	0.130376i
$413$	−1.50000	+	2.59808i	−0.0738102	+	0.127843i
$414$		0			0
$415$	−8.94427			−0.439057
$416$	−8.45492	+	8.78661i	−0.414536	+	0.430799i
$417$		0			0
$418$	0.809017	−	1.40126i	0.0395703	−	0.0685378i
$419$	−6.82624	+	11.8234i	−0.333484	+	0.577610i	−0.983192	−	0.182573i	$-0.941557\pi$
$419$	−6.82624	+	11.8234i	−0.333484	+	0.577610i	0.649709	+	0.760183i	$0.274891\pi$
$420$		0			0
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	7.42705	+	12.8640i	0.361543	+	0.626211i
$423$		0			0
$424$	−13.4164			−0.651558
$425$	2.73607	+	4.73901i	0.132719	+	0.229876i
$426$		0			0
$427$	−1.46556	+	2.53842i	−0.0709233	+	0.122843i
$428$	6.32624			0.305790
$429$		0			0
$430$	−2.85410			−0.137637
$431$	2.40983	−	4.17395i	0.116077	−	0.201052i	−0.802133	−	0.597146i	$-0.796301\pi$
$431$	2.40983	−	4.17395i	0.116077	−	0.201052i	0.918210	+	0.396094i	$0.129635\pi$
$432$		0			0
$433$	11.7361	+	20.3275i	0.563999	+	0.976876i	0.997142	+	0.0755503i	$0.0240713\pi$
$433$	11.7361	+	20.3275i	0.563999	+	0.976876i	−0.433143	+	0.901325i	$0.642595\pi$
$434$		0			0
$435$		0			0
$436$	0.618034	+	1.07047i	0.0295985	+	0.0512660i
$437$	1.94427			0.0930071
$438$		0			0
$439$	4.64590	−	8.04693i	0.221737	−	0.384059i	−0.733599	−	0.679583i	$-0.762161\pi$
$439$	4.64590	−	8.04693i	0.221737	−	0.384059i	0.955335	+	0.295524i	$0.0954941\pi$
$440$	−4.73607	+	8.20311i	−0.225783	+	0.391068i
$441$		0			0
$442$	−8.85410	−	30.6715i	−0.421147	−	1.45889i
$443$	16.9443			0.805047			0.402523	−	0.915410i	$-0.368133\pi$
$443$	16.9443			0.805047			0.402523	+	0.915410i	$0.368133\pi$
$444$		0			0
$445$	4.50000	−	7.79423i	0.213320	−	0.369482i
$446$	−10.2812	−	17.8075i	−0.486827	−	0.843209i
$447$		0			0
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−6.97214	−	12.0761i	−0.329035	−	0.569906i	0.653285	−	0.757112i	$-0.273390\pi$
$449$	−6.97214	−	12.0761i	−0.329035	−	0.569906i	−0.982321	+	0.187206i	$0.940057\pi$
$450$		0			0
$451$	12.5902	+	21.8068i	0.592848	+	1.02684i
$452$	−2.30902	+	3.99933i	−0.108607	+	0.188113i
$453$		0			0
$454$	−2.85410			−0.133950
$455$	−0.590170	+	0.613323i	−0.0276676	+	0.0287530i
$456$		0			0
$457$	14.2082	−	24.6093i	0.664632	−	1.15118i	−0.314753	−	0.949174i	$-0.601922\pi$
$457$	14.2082	−	24.6093i	0.664632	−	1.15118i	0.979385	−	0.202002i	$-0.0647449\pi$
$458$	−16.0902	+	27.8690i	−0.751844	+	1.30223i
$459$		0			0
$460$	5.09017			0.237330
$461$	−14.2082	−	24.6093i	−0.661742	−	1.14617i	−0.980158	−	0.198220i	$-0.936484\pi$
$461$	−14.2082	−	24.6093i	−0.661742	−	1.14617i	0.318416	−	0.947951i	$-0.396849\pi$
$462$		0			0
$463$	28.9443			1.34515			0.672577	−	0.740027i	$-0.265187\pi$
$463$	28.9443			1.34515			0.672577	+	0.740027i	$0.265187\pi$
$464$	−3.57295	−	6.18853i	−0.165870	−	0.287295i
$465$		0			0
$466$	−16.0902	+	27.8690i	−0.745363	+	1.29101i
$467$	8.94427			0.413892			0.206946	−	0.978352i	$-0.433648\pi$
$467$	8.94427			0.413892			0.206946	+	0.978352i	$0.433648\pi$
$468$		0			0
$469$	−2.52786			−0.116726
$470$	10.4721	−	18.1383i	0.483044	−	0.836656i
$471$		0			0
$472$	14.2082	+	24.6093i	0.653986	+	1.13274i
$473$	7.47214			0.343569
$474$		0			0
$475$	0.118034	+	0.204441i	0.00541577	+	0.00938039i
$476$	0.798374			0.0365934
$477$		0			0
$478$	−8.00000	+	13.8564i	−0.365911	+	0.633777i
$479$	−4.06231	+	7.03612i	−0.185611	+	0.321489i	−0.943782	−	0.330567i	$-0.892760\pi$
$479$	−4.06231	+	7.03612i	−0.185611	+	0.321489i	0.758171	+	0.652056i	$0.226093\pi$
$480$		0			0
$481$	10.5000	+	2.59808i	0.478759	+	0.118462i
$482$	−24.2705			−1.10549
$483$		0			0
$484$	−2.14590	+	3.71680i	−0.0975408	+	0.168946i
$485$	2.73607	+	4.73901i	0.124238	+	0.215187i
$486$		0			0
$487$	13.0623	+	22.6246i	0.591910	+	1.02522i	0.993975	+	0.109607i	$0.0349591\pi$
$487$	13.0623	+	22.6246i	0.591910	+	1.02522i	−0.402065	+	0.915611i	$0.631708\pi$
$488$	13.8820	+	24.0443i	0.628407	+	1.08843i
$489$		0			0
$490$	5.61803	+	9.73072i	0.253797	+	0.439589i
$491$	2.11803	−	3.66854i	0.0955855	−	0.165559i	−0.814267	−	0.580490i	$-0.802861\pi$
$491$	2.11803	−	3.66854i	0.0955855	−	0.165559i	0.909853	+	0.414931i	$0.136194\pi$
$492$		0			0
$493$	8.05573			0.362812
$494$	−0.381966	−	1.32317i	−0.0171855	−	0.0595322i
$495$		0			0
$496$		0			0
$497$	0.208204	−	0.360620i	0.00933922	−	0.0161760i
$498$		0			0
$499$	13.8885			0.621737			0.310868	−	0.950453i	$-0.399380\pi$
$499$	13.8885			0.621737			0.310868	+	0.950453i	$0.399380\pi$
$500$	0.309017	+	0.535233i	0.0138197	+	0.0239364i
$501$		0			0
$502$	25.5066			1.13841
$503$	−6.59017	−	11.4145i	−0.293841	−	0.508948i	0.680873	−	0.732401i	$-0.261600\pi$
$503$	−6.59017	−	11.4145i	−0.293841	−	0.508948i	−0.974715	+	0.223453i	$0.928267\pi$
$504$		0			0
$505$	−4.73607	+	8.20311i	−0.210752	+	0.365034i
$506$	−56.4508			−2.50955
$507$		0			0
$508$	0.145898			0.00647318
$509$	5.68034	−	9.83864i	0.251777	−	0.436090i	−0.712238	−	0.701938i	$-0.752319\pi$
$509$	5.68034	−	9.83864i	0.251777	−	0.436090i	0.964015	+	0.265848i	$0.0856518\pi$
$510$		0			0
$511$	−0.708204	−	1.22665i	−0.0313291	−	0.0542636i
$512$	5.29180			0.233867
$513$		0			0
$514$	−6.89919	−	11.9497i	−0.304310	−	0.527081i
$515$	4.94427			0.217871
$516$		0			0
$517$	−27.4164	+	47.4866i	−1.20577	+	2.08846i
$518$	−0.572949	+	0.992377i	−0.0251739	+	0.0436025i
$519$		0			0
$520$	2.23607	+	7.74597i	0.0980581	+	0.339683i
$521$	41.7771			1.83029			0.915144	−	0.403128i	$-0.132077\pi$
$521$	41.7771			1.83029			0.915144	+	0.403128i	$0.132077\pi$
$522$		0			0
$523$	−9.35410	+	16.2018i	−0.409026	+	0.708454i	−0.994781	−	0.102034i	$-0.967465\pi$
$523$	−9.35410	+	16.2018i	−0.409026	+	0.708454i	0.585755	+	0.810488i	$0.300798\pi$
$524$	−3.70820	−	6.42280i	−0.161994	−	0.280581i
$525$		0			0
$526$	−6.66312	−	11.5409i	−0.290526	−	0.503205i
$527$		0			0
$528$		0			0
$529$	−22.4164	−	38.8264i	−0.974626	−	1.68810i
$530$	4.85410	−	8.40755i	0.210849	−	0.365201i
$531$		0			0
$532$	0.0344419			0.00149324
$533$	20.8050	+	5.14789i	0.901162	+	0.222980i
$534$		0			0
$535$	5.11803	−	8.86469i	0.221272	−	0.383254i
$536$	−11.9721	+	20.7363i	−0.517118	+	0.895674i
$537$		0			0
$538$	−25.0344			−1.07931
$539$	−14.7082	−	25.4754i	−0.633527	−	1.09730i
$540$		0			0
$541$	7.88854			0.339155			0.169577	−	0.985517i	$-0.445760\pi$
$541$	7.88854			0.339155			0.169577	+	0.985517i	$0.445760\pi$
$542$	11.8992	+	20.6100i	0.511114	+	0.885275i
$543$		0			0
$544$	9.25329	−	16.0272i	0.396731	−	0.687159i
$545$	2.00000			0.0856706
$546$		0			0
$547$	−34.8328			−1.48934			−0.744672	−	0.667431i	$-0.767394\pi$
$547$	−34.8328			−1.48934			−0.744672	+	0.667431i	$0.767394\pi$
$548$	−2.30902	+	3.99933i	−0.0986363	+	0.170843i
$549$		0			0
$550$	−3.42705	−	5.93583i	−0.146130	−	0.253104i
$551$	0.347524			0.0148050
$552$		0			0
$553$		0			0
$554$	30.5623			1.29847
$555$		0			0
$556$	1.01722	−	1.76188i	0.0431398	−	0.0747203i
$557$	3.97214	−	6.87994i	0.168305	−	0.291512i	−0.769519	−	0.638624i	$-0.779504\pi$
$557$	3.97214	−	6.87994i	0.168305	−	0.291512i	0.937824	+	0.347111i	$0.112837\pi$
$558$		0			0
$559$	4.40983	−	4.58283i	0.186516	−	0.193833i
$560$	−1.14590			−0.0484230
$561$		0			0
$562$	−16.0902	+	27.8690i	−0.678723	+	1.17558i
$563$	8.64590	+	14.9751i	0.364381	+	0.631127i	0.988677	−	0.150062i	$-0.0479472\pi$
$563$	8.64590	+	14.9751i	0.364381	+	0.631127i	−0.624295	+	0.781188i	$0.714614\pi$
$564$		0			0
$565$	3.73607	+	6.47106i	0.157178	+	0.272240i
$566$	2.19098	+	3.79489i	0.0920939	+	0.159511i
$567$		0			0
$568$	−1.97214	−	3.41584i	−0.0827490	−	0.143325i
$569$	−9.44427	+	16.3580i	−0.395924	+	0.685761i	−0.993219	−	0.116261i	$-0.962909\pi$
$569$	−9.44427	+	16.3580i	−0.395924	+	0.685761i	0.597294	+	0.802022i	$0.296242\pi$
$570$		0			0
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$	2.61803	+	9.06914i	0.109466	+	0.379200i
$573$		0			0
$574$	−1.13525	+	1.96632i	−0.0473846	+	0.0820726i
$575$	4.11803	−	7.13264i	0.171734	−	0.297452i
$576$		0			0
$577$	−7.88854			−0.328404			−0.164202	−	0.986427i	$-0.552505\pi$
$577$	−7.88854			−0.328404			−0.164202	+	0.986427i	$0.552505\pi$
$578$	10.4721	+	18.1383i	0.435583	+	0.754453i
$579$		0			0
$580$	0.909830			0.0377786
$581$	1.05573	+	1.82857i	0.0437990	+	0.0758621i
$582$		0			0
$583$	−12.7082	+	22.0113i	−0.526320	+	0.911613i
$584$	−13.4164			−0.555175
$585$		0			0
$586$	−19.5066			−0.805809
$587$	2.88197	−	4.99171i	0.118951	−	0.206030i	−0.800401	−	0.599465i	$-0.795380\pi$
$587$	2.88197	−	4.99171i	0.118951	−	0.206030i	0.919352	+	0.393435i	$0.128713\pi$
$588$		0			0
$589$		0			0
$590$	−20.5623			−0.846537
$591$		0			0
$592$	7.28115	+	12.6113i	0.299254	+	0.518322i
$593$	−27.8885			−1.14525			−0.572623	−	0.819819i	$-0.694074\pi$
$593$	−27.8885			−1.14525			−0.572623	+	0.819819i	$0.694074\pi$
$594$		0			0
$595$	0.645898	−	1.11873i	0.0264792	−	0.0458634i
$596$	4.16312	−	7.21073i	0.170528	−	0.295363i
$597$		0			0
$598$	−33.3156	+	34.6226i	−1.36238	+	1.41582i
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$		0			0
$601$	−13.0279	+	22.5649i	−0.531418	+	0.920442i	0.467910	+	0.883776i	$0.345007\pi$
$601$	−13.0279	+	22.5649i	−0.531418	+	0.920442i	−0.999328	+	0.0366662i	$0.988326\pi$
$602$	0.336881	+	0.583495i	0.0137302	+	0.0237815i
$603$		0			0
$604$	−2.47214	−	4.28187i	−0.100590	−	0.174227i
$605$	3.47214	+	6.01392i	0.141162	+	0.244500i
$606$		0			0
$607$	−6.35410	−	11.0056i	−0.257905	−	0.446705i	0.707775	−	0.706437i	$-0.249699\pi$
$607$	−6.35410	−	11.0056i	−0.257905	−	0.446705i	−0.965681	+	0.259733i	$0.916366\pi$
$608$	0.399187	−	0.691412i	0.0161892	−	0.0280405i
$609$		0			0
$610$	−20.0902			−0.813427
$611$	12.9443	+	44.8403i	0.523669	+	1.81404i
$612$		0			0
$613$	−11.0279	+	19.1008i	−0.445411	+	0.771475i	−0.998081	−	0.0619256i	$-0.980276\pi$
$613$	−11.0279	+	19.1008i	−0.445411	+	0.771475i	0.552670	+	0.833400i	$0.313609\pi$
$614$	5.70820	−	9.88690i	0.230364	−	0.399003i
$615$		0			0
$616$	2.23607			0.0900937
$617$	−6.79180	−	11.7637i	−0.273427	−	0.473590i	0.696310	−	0.717741i	$-0.254824\pi$
$617$	−6.79180	−	11.7637i	−0.273427	−	0.473590i	−0.969737	+	0.244151i	$0.921491\pi$
$618$		0			0
$619$	12.0000			0.482321			0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000			0.482321			0.241160	+	0.970485i	$0.422472\pi$
$620$		0			0
$621$		0			0
$622$	19.4164	−	33.6302i	0.778527	−	1.34845i
$623$	−2.12461			−0.0851208
$624$		0			0
$625$	1.00000			0.0400000
$626$	−25.7984	+	44.6841i	−1.03111	+	1.78594i
$627$		0			0
$628$	5.56231	+	9.63420i	0.221960	+	0.384446i
$629$	−16.4164			−0.654565
$630$		0			0
$631$	−12.0623	−	20.8925i	−0.480193	−	0.831718i	0.519549	−	0.854441i	$-0.326100\pi$
$631$	−12.0623	−	20.8925i	−0.480193	−	0.831718i	−0.999742	+	0.0227223i	$0.992767\pi$
$632$		0			0
$633$		0			0
$634$	−19.3262	+	33.4740i	−0.767543	+	1.32942i
$635$	0.118034	−	0.204441i	0.00468404	−	0.00811299i
$636$		0			0
$637$	−24.3050	−	6.01392i	−0.962997	−	0.238280i
$638$	−10.0902			−0.399474
$639$		0			0
$640$	−6.80902	+	11.7936i	−0.269150	+	0.466182i
$641$	−13.4443	−	23.2862i	−0.531017	−	0.919748i	−0.999345	−	0.0361934i	$-0.988477\pi$
$641$	−13.4443	−	23.2862i	−0.531017	−	0.919748i	0.468328	−	0.883555i	$-0.344857\pi$
$642$		0			0
$643$	15.3541	+	26.5941i	0.605507	+	1.04877i	0.991971	+	0.126464i	$0.0403628\pi$
$643$	15.3541	+	26.5941i	0.605507	+	1.04877i	−0.386465	+	0.922304i	$0.626304\pi$
$644$	−0.600813	−	1.04064i	−0.0236754	−	0.0410069i
$645$		0			0
$646$	1.04508	+	1.81014i	0.0411183	+	0.0712190i
$647$	−23.2984	+	40.3540i	−0.915954	+	1.58648i	−0.110454	+	0.993881i	$0.535231\pi$
$647$	−23.2984	+	40.3540i	−0.915954	+	1.58648i	−0.805499	+	0.592597i	$0.798103\pi$
$648$		0			0
$649$	53.8328			2.11312
$650$	−5.66312	−	1.40126i	−0.222126	−	0.0549619i
$651$		0			0
$652$	−0.399187	+	0.691412i	−0.0156334	+	0.0270778i
$653$	−10.5000	+	18.1865i	−0.410897	+	0.711694i	−0.994988	−	0.0999939i	$-0.968118\pi$
$653$	−10.5000	+	18.1865i	−0.410897	+	0.711694i	0.584091	+	0.811688i	$0.301451\pi$
$654$		0			0
$655$	−12.0000			−0.468879
$656$	14.4271	+	24.9884i	0.563282	+	0.975633i
$657$		0			0
$658$	−4.94427			−0.192748
$659$	−24.1180	−	41.7737i	−0.939505	−	1.62727i	−0.766396	−	0.642368i	$-0.777952\pi$
$659$	−24.1180	−	41.7737i	−0.939505	−	1.62727i	−0.173109	−	0.984903i	$-0.555381\pi$
$660$		0			0
$661$	−1.68034	+	2.91043i	−0.0653576	+	0.113203i	−0.896853	−	0.442330i	$-0.854152\pi$
$661$	−1.68034	+	2.91043i	−0.0653576	+	0.113203i	0.831495	+	0.555532i	$0.187485\pi$
$662$	−41.5066			−1.61320
$663$		0			0
$664$	20.0000			0.776151
$665$	0.0278640	−	0.0482619i	0.00108052	−	0.00187152i
$666$		0			0
$667$	−6.06231	−	10.5002i	−0.234733	−	0.406570i
$668$	−3.20163			−0.123875
$669$		0			0
$670$	−8.66312	−	15.0050i	−0.334685	−	0.579692i
$671$	52.5967			2.03047
$672$		0			0
$673$	18.2082	−	31.5375i	0.701875	−	1.21568i	−0.265933	−	0.963992i	$-0.585680\pi$
$673$	18.2082	−	31.5375i	0.701875	−	1.21568i	0.967808	−	0.251691i	$-0.0809867\pi$
$674$	22.5623	−	39.0791i	0.869068	−	1.50527i
$675$		0			0
$676$	7.10739	+	3.74663i	0.273361	+	0.144101i
$677$	−47.8885			−1.84051			−0.920253	−	0.391324i	$-0.872017\pi$
$677$	−47.8885			−1.84051			−0.920253	+	0.391324i	$0.872017\pi$
$678$		0			0
$679$	0.645898	−	1.11873i	0.0247873	−	0.0429328i
$680$	−6.11803	−	10.5967i	−0.234616	−	0.406367i
$681$		0			0
$682$		0			0
$683$	15.1180	+	26.1852i	0.578475	+	1.00195i	0.995654	+	0.0931246i	$0.0296855\pi$
$683$	15.1180	+	26.1852i	0.578475	+	1.00195i	−0.417179	+	0.908824i	$0.636981\pi$
$684$		0			0
$685$	3.73607	+	6.47106i	0.142748	+	0.247246i
$686$	2.66312	−	4.61266i	0.101678	−	0.176112i
$687$		0			0
$688$	8.56231			0.326435
$689$	6.00000	+	20.7846i	0.228582	+	0.791831i
$690$		0			0
$691$	5.29837	−	9.17705i	0.201560	−	0.349112i	−0.747471	−	0.664294i	$-0.768732\pi$
$691$	5.29837	−	9.17705i	0.201560	−	0.349112i	0.949031	+	0.315182i	$0.102066\pi$
$692$	5.21885	−	9.03931i	0.198391	−	0.343623i
$693$		0			0
$694$	27.9787			1.06206
$695$	−1.64590	−	2.85078i	−0.0624325	−	0.108136i
$696$		0			0
$697$	−32.5279			−1.23208
$698$	−19.7533	−	34.2137i	−0.747673	−	1.29501i
$699$		0			0
$700$	0.0729490	−	0.126351i	0.00275721	−	0.00477563i
$701$	27.8885			1.05334			0.526668	−	0.850071i	$-0.323441\pi$
$701$	27.8885			1.05334			0.526668	+	0.850071i	$0.323441\pi$
$702$		0			0
$703$	−0.708204			−0.0267104
$704$	8.97214	−	15.5402i	0.338150	−	0.585693i
$705$		0			0
$706$	8.51722	+	14.7523i	0.320550	+	0.555209i
$707$	2.23607			0.0840960
$708$		0			0
$709$	19.1525	+	33.1731i	0.719286	+	1.24584i	0.961283	+	0.275563i	$0.0888644\pi$
$709$	19.1525	+	33.1731i	0.719286	+	1.24584i	−0.241997	+	0.970277i	$0.577802\pi$
$710$	2.85410			0.107113
$711$		0			0
$712$	−10.0623	+	17.4284i	−0.377101	+	0.653158i
$713$		0			0
$714$		0			0
$715$	14.8262	+	3.66854i	0.554470	+	0.137196i
$716$	2.32624			0.0869356
$717$		0			0
$718$	14.4721	−	25.0665i	0.540095	−	0.935473i
$719$	4.06231	+	7.03612i	0.151498	+	0.262403i	0.931779	−	0.363027i	$-0.118257\pi$
$719$	4.06231	+	7.03612i	0.151498	+	0.262403i	−0.780280	+	0.625430i	$0.784923\pi$
$720$		0			0
$721$	−0.583592	−	1.01081i	−0.0217341	−	0.0376446i
$722$	−15.3262	−	26.5458i	−0.570384	−	0.987933i
$723$		0			0
$724$	−1.85410	−	3.21140i	−0.0689072	−	0.119351i
$725$	0.736068	−	1.27491i	0.0273369	−	0.0473489i
$726$		0			0
$727$	11.0557			0.410034			0.205017	−	0.978758i	$-0.434275\pi$
$727$	11.0557			0.410034			0.205017	+	0.978758i	$0.434275\pi$
$728$	1.31966	−	1.37143i	0.0489099	−	0.0508286i
$729$		0			0
$730$	4.85410	−	8.40755i	0.179658	−	0.311177i
$731$	−4.82624	+	8.35929i	−0.178505	+	0.309179i
$732$		0			0
$733$	−8.11146			−0.299603			−0.149802	−	0.988716i	$-0.547864\pi$
$733$	−8.11146			−0.299603			−0.149802	+	0.988716i	$0.547864\pi$
$734$	−20.7533	−	35.9458i	−0.766018	−	1.32678i
$735$		0			0
$736$	−27.8541			−1.02672
$737$	22.6803	+	39.2835i	0.835441	+	1.44703i
$738$		0			0
$739$	19.7705	−	34.2435i	0.727270	−	1.25967i	−0.230763	−	0.973010i	$-0.574122\pi$
$739$	19.7705	−	34.2435i	0.727270	−	1.25967i	0.958033	−	0.286659i	$-0.0925445\pi$
$740$	−1.85410			−0.0681581
$741$		0			0
$742$	−2.29180			−0.0841345
$743$	1.06231	−	1.83997i	0.0389722	−	0.0675019i	−0.845881	−	0.533371i	$-0.820925\pi$
$743$	1.06231	−	1.83997i	0.0389722	−	0.0675019i	0.884854	+	0.465869i	$0.154258\pi$
$744$		0			0
$745$	−6.73607	−	11.6672i	−0.246790	−	0.427454i
$746$	−16.2705			−0.595706
$747$		0			0
$748$	−7.16312	−	12.4069i	−0.261910	−	0.453641i
$749$	−2.41641			−0.0882936
$750$		0			0
$751$	8.64590	−	14.9751i	0.315493	−	0.546450i	−0.664049	−	0.747689i	$-0.731163\pi$
$751$	8.64590	−	14.9751i	0.315493	−	0.546450i	0.979542	+	0.201239i	$0.0644967\pi$
$752$	−31.4164	+	54.4148i	−1.14564	+	1.98430i
$753$		0			0
$754$	−5.95492	+	6.18853i	−0.216865	+	0.225373i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−14.4443	+	25.0182i	−0.524986	+	0.909302i	0.474591	+	0.880207i	$0.342596\pi$
$757$	−14.4443	+	25.0182i	−0.524986	+	0.909302i	−0.999577	+	0.0290958i	$0.990737\pi$
$758$	26.8435	+	46.4942i	0.974998	+	1.68875i
$759$		0			0
$760$	−0.263932	−	0.457144i	−0.00957382	−	0.0165823i
$761$	−10.0279	−	17.3688i	−0.363510	−	0.629617i	0.625026	−	0.780604i	$-0.285088\pi$
$761$	−10.0279	−	17.3688i	−0.363510	−	0.629617i	−0.988536	+	0.150986i	$0.951755\pi$
$762$		0			0
$763$	−0.236068	−	0.408882i	−0.00854623	−	0.0148025i
$764$	−1.48936	+	2.57964i	−0.0538830	+	0.0933282i
$765$		0			0
$766$	−0.381966			−0.0138010
$767$	31.7705	−	33.0169i	1.14717	−	1.19217i
$768$		0			0
$769$	11.9164	−	20.6398i	0.429717	−	0.744291i	−0.567131	−	0.823627i	$-0.691947\pi$
$769$	11.9164	−	20.6398i	0.429717	−	0.744291i	0.996848	+	0.0793363i	$0.0252801\pi$
$770$	−0.809017	+	1.40126i	−0.0291549	+	0.0504979i
$771$		0			0
$772$	3.38197			0.121720
$773$	−18.9721	−	32.8607i	−0.682380	−	1.18192i	−0.974252	−	0.225460i	$-0.927612\pi$
$773$	−18.9721	−	32.8607i	−0.682380	−	1.18192i	0.291872	−	0.956457i	$-0.405722\pi$
$774$		0			0
$775$		0			0
$776$	−6.11803	−	10.5967i	−0.219625	−	0.380401i
$777$		0			0
$778$	29.0344	−	50.2891i	1.04094	−	1.80295i
$779$	−1.40325			−0.0502767
$780$		0			0
$781$	−7.47214			−0.267374
$782$	36.4615	−	63.1532i	1.30386	−	2.25835i
$783$		0			0
$784$	−16.8541	−	29.1922i	−0.601932	−	1.04258i
$785$	18.0000			0.642448
$786$		0			0
$787$	18.7705	+	32.5115i	0.669096	+	1.15891i	0.978157	+	0.207867i	$0.0666520\pi$
$787$	18.7705	+	32.5115i	0.669096	+	1.15891i	−0.309061	+	0.951042i	$0.600015\pi$
$788$	−1.85410			−0.0660496
$789$		0			0
$790$		0			0
$791$	0.881966	−	1.52761i	0.0313591	−	0.0543156i
$792$		0			0
$793$	31.0410	−	32.2588i	1.10230	−	1.14554i
$794$	−16.2705			−0.577419
$795$		0			0
$796$	4.54508	−	7.87232i	0.161096	−	0.279027i
$797$	0.0835921	+	0.144786i	0.00296099	+	0.00512858i	0.867502	−	0.497434i	$-0.165724\pi$
$797$	0.0835921	+	0.144786i	0.00296099	+	0.00512858i	−0.864541	+	0.502562i	$0.832391\pi$
$798$		0			0
$799$	−35.4164	−	61.3430i	−1.25294	−	2.17016i
$800$	−1.69098	−	2.92887i	−0.0597853	−	0.103551i
$801$		0			0
$802$	21.7533	+	37.6778i	0.768135	+	1.33045i
$803$	−12.7082	+	22.0113i	−0.448463	+	0.776760i
$804$		0			0
$805$	−1.94427			−0.0685266
$806$		0			0
$807$		0			0
$808$	10.5902	−	18.3427i	0.372561	−	0.645294i
$809$	16.4443	−	28.4823i	0.578150	−	1.00138i	−0.417542	−	0.908658i	$-0.637108\pi$
$809$	16.4443	−	28.4823i	0.578150	−	1.00138i	0.995692	−	0.0927271i	$-0.0295584\pi$
$810$		0			0
$811$	−39.7771			−1.39676			−0.698381	−	0.715726i	$-0.746096\pi$
$811$	−39.7771			−1.39676			−0.698381	+	0.715726i	$0.746096\pi$
$812$	−0.107391	−	0.186006i	−0.00376868	−	0.00652755i
$813$		0			0
$814$	20.5623			0.720708
$815$	0.645898	+	1.11873i	0.0226248	+	0.0391873i
$816$		0			0
$817$	−0.208204	+	0.360620i	−0.00728413	+	0.0126165i
$818$	17.6180			0.616000
$819$		0			0
$820$	−3.67376			−0.128293
$821$	9.68034	−	16.7668i	0.337846	−	0.585167i	−0.646181	−	0.763184i	$-0.723635\pi$
$821$	9.68034	−	16.7668i	0.337846	−	0.585167i	0.984027	+	0.178017i	$0.0569683\pi$
$822$		0			0
$823$	−11.2984	−	19.5694i	−0.393837	−	0.682145i	0.599115	−	0.800663i	$-0.295519\pi$
$823$	−11.2984	−	19.5694i	−0.393837	−	0.682145i	−0.992952	+	0.118518i	$0.962186\pi$
$824$	−11.0557			−0.385145
$825$		0			0
$826$	2.42705	+	4.20378i	0.0844479	+	0.146268i
$827$	−8.94427			−0.311023			−0.155511	−	0.987834i	$-0.549703\pi$
$827$	−8.94427			−0.311023			−0.155511	+	0.987834i	$0.549703\pi$
$828$		0			0
$829$	−18.6246	+	32.2588i	−0.646860	+	1.12039i	0.337009	+	0.941501i	$0.390585\pi$
$829$	−18.6246	+	32.2588i	−0.646860	+	1.12039i	−0.983869	+	0.178892i	$0.942749\pi$
$830$	−7.23607	+	12.5332i	−0.251168	+	0.435035i
$831$		0			0
$832$	−4.23607	−	14.6742i	−0.146859	−	0.508735i
$833$	38.0000			1.31662
$834$		0			0
$835$	−2.59017	+	4.48631i	−0.0896365	+	0.155255i
$836$	−0.309017	−	0.535233i	−0.0106876	−	0.0185114i
$837$		0			0
$838$	11.0451	+	19.1306i	0.381546	+	0.660857i
$839$	8.64590	+	14.9751i	0.298490	+	0.516999i	0.975791	−	0.218707i	$-0.0701839\pi$
$839$	8.64590	+	14.9751i	0.298490	+	0.516999i	−0.677301	+	0.735706i	$0.736851\pi$
$840$		0			0
$841$	13.4164	+	23.2379i	0.462635	+	0.801307i
$842$	4.85410	−	8.40755i	0.167283	−	0.289743i
$843$		0			0
$844$	5.67376			0.195299
$845$	11.0000	−	6.92820i	0.378412	−	0.238337i
$846$		0			0
$847$	0.819660	−	1.41969i	0.0281639	−	0.0487812i
$848$	−14.5623	+	25.2227i	−0.500072	+	0.866149i
$849$		0			0
$850$	8.85410			0.303693
$851$	12.3541	+	21.3979i	0.423493	+	0.733512i
$852$		0			0
$853$	6.00000			0.205436			0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000			0.205436			0.102718	+	0.994711i	$0.467246\pi$
$854$	2.37132	+	4.10725i	0.0811450	+	0.140547i
$855$		0			0
$856$	−11.4443	+	19.8221i	−0.391157	+	0.677504i
$857$	−0.111456			−0.00380727			−0.00190364	−	0.999998i	$-0.500606\pi$
$857$	−0.111456			−0.00380727			−0.00190364	+	0.999998i	$0.500606\pi$
$858$		0			0
$859$	−13.8885			−0.473871			−0.236935	−	0.971525i	$-0.576143\pi$
$859$	−13.8885			−0.473871			−0.236935	+	0.971525i	$0.576143\pi$
$860$	−0.545085	+	0.944115i	−0.0185872	+	0.0321940i
$861$		0			0
$862$	−3.89919	−	6.75359i	−0.132807	−	0.230028i
$863$	38.8328			1.32188			0.660942	−	0.750437i	$-0.270157\pi$
$863$	38.8328			1.32188			0.660942	+	0.750437i	$0.270157\pi$
$864$		0			0
$865$	−8.44427	−	14.6259i	−0.287114	−	0.497296i
$866$	37.9787			1.29057
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	37.4787	+	9.27358i	1.26992	+	0.314223i
$872$	−4.47214			−0.151446
$873$		0			0
$874$	1.57295	−	2.72443i	0.0532058	−	0.0921551i
$875$	−0.118034	−	0.204441i	−0.00399028	−	0.00691136i
$876$		0			0
$877$	−27.8607	−	48.2561i	−0.940788	−	1.62949i	−0.763972	−	0.645249i	$-0.776754\pi$
$877$	−27.8607	−	48.2561i	−0.940788	−	1.62949i	−0.176816	−	0.984244i	$-0.556580\pi$
$878$	−7.51722	−	13.0202i	−0.253694	−	0.439411i
$879$		0			0
$880$	10.2812	+	17.8075i	0.346578	+	0.600290i
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	−0.711582	−	0.702603i	$-0.752021\pi$
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	0.964263	+	0.264946i	$0.0853542\pi$
$882$		0			0
$883$	10.8328			0.364553			0.182277	−	0.983247i	$-0.441653\pi$
$883$	10.8328			0.364553			0.182277	+	0.983247i	$0.441653\pi$
$884$	−11.8369	−	2.92887i	−0.398117	−	0.0985085i
$885$		0			0
$886$	13.7082	−	23.7433i	0.460536	−	0.797672i
$887$	−20.2426	+	35.0613i	−0.679682	+	1.17724i	0.295395	+	0.955375i	$0.404549\pi$
$887$	−20.2426	+	35.0613i	−0.679682	+	1.17724i	−0.975077	+	0.221868i	$0.928785\pi$
$888$		0			0
$889$	−0.0557281			−0.00186906
$890$	−7.28115	−	12.6113i	−0.244065	−	0.422733i
$891$		0			0
$892$	−7.85410			−0.262975
$893$	−1.52786	−	2.64634i	−0.0511280	−	0.0885563i
$894$		0			0
$895$	1.88197	−	3.25966i	0.0629072	−	0.108958i
$896$	3.21478			0.107398
$897$		0			0
$898$	−22.5623			−0.752914
$899$		0			0
$900$		0			0
$901$	−16.4164	−	28.4341i	−0.546910	−	0.947276i
$902$	40.7426			1.35658
$903$		0			0
$904$	−8.35410	−	14.4697i	−0.277853	−	0.481256i
$905$	−6.00000			−0.199447
$906$		0			0
$907$	10.0623	−	17.4284i	0.334113	−	0.578701i	−0.649201	−	0.760617i	$-0.724896\pi$
$907$	10.0623	−	17.4284i	0.334113	−	0.578701i	0.983314	+	0.181916i	$0.0582298\pi$
$908$	−0.545085	+	0.944115i	−0.0180893	+	0.0313316i
$909$		0			0
$910$	0.381966	+	1.32317i	0.0126620	+	0.0438626i
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$	18.9443	−	32.8124i	0.626964	−	1.08593i
$914$	−22.9894	−	39.8187i	−0.760420	−	1.31709i
$915$		0			0
$916$	6.14590	+	10.6450i	0.203066	+	0.351721i
$917$	1.41641	+	2.45329i	0.0467739	+	0.0810148i
$918$		0			0
$919$	−16.6459	−	28.8315i	−0.549098	−	0.951065i	−0.998337	−	0.0576532i	$-0.981638\pi$
$919$	−16.6459	−	28.8315i	−0.549098	−	0.951065i	0.449239	−	0.893412i	$-0.351695\pi$
$920$	−9.20820	+	15.9491i	−0.303585	+	0.525825i
$921$		0			0
$922$	−45.9787			−1.51423
$923$	−4.40983	+	4.58283i	−0.145151	+	0.150846i
$924$		0			0
$925$	−1.50000	+	2.59808i	−0.0493197	+	0.0854242i
$926$	23.4164	−	40.5584i	0.769511	−	1.33283i
$927$		0			0
$928$	−4.97871			−0.163434
$929$	1.02786	+	1.78031i	0.0337231	+	0.0584102i	0.882394	−	0.470511i	$-0.155930\pi$
$929$	1.02786	+	1.78031i	0.0337231	+	0.0584102i	−0.848671	+	0.528921i	$0.822597\pi$
$930$		0			0
$931$	1.63932			0.0537266
$932$	6.14590	+	10.6450i	0.201316	+	0.348689i
$933$		0			0
$934$	7.23607	−	12.5332i	0.236771	−	0.410100i
$935$	−23.1803			−0.758078
$936$		0			0
$937$	−6.00000			−0.196011			−0.0980057	−	0.995186i	$-0.531246\pi$
$937$	−6.00000			−0.196011			−0.0980057	+	0.995186i	$0.531246\pi$
$938$	−2.04508	+	3.54219i	−0.0667744	+	0.115657i
$939$		0			0
$940$	−4.00000	−	6.92820i	−0.130466	−	0.225973i
$941$	−23.8885			−0.778744			−0.389372	−	0.921081i	$-0.627308\pi$
$941$	−23.8885			−0.778744			−0.389372	+	0.921081i	$0.627308\pi$
$942$		0			0
$943$	24.4787	+	42.3984i	0.797137	+	1.38068i
$944$	61.6869			2.00774
$945$		0			0
$946$	6.04508	−	10.4704i	0.196543	−	0.340422i
$947$	8.40983	−	14.5663i	0.273283	−	0.473340i	−0.696418	−	0.717637i	$-0.745224\pi$
$947$	8.40983	−	14.5663i	0.273283	−	0.473340i	0.969700	+	0.244297i	$0.0785572\pi$
$948$		0			0
$949$	6.00000	+	20.7846i	0.194768	+	0.674697i
$950$	0.381966			0.0123926
$951$		0			0
$952$	−1.44427	+	2.50155i	−0.0468091	+	0.0810758i
$953$	−28.0967	−	48.6650i	−0.910143	−	1.57641i	−0.813861	−	0.581060i	$-0.802638\pi$
$953$	−28.0967	−	48.6650i	−0.910143	−	1.57641i	−0.0962820	−	0.995354i	$-0.530695\pi$
$954$		0			0
$955$	2.40983	+	4.17395i	0.0779803	+	0.135066i
$956$	3.05573	+	5.29268i	0.0988293	+	0.171177i
$957$		0			0
$958$	6.57295	+	11.3847i	0.212362	+	0.367822i
$959$	0.881966	−	1.52761i	0.0284802	−	0.0493291i
$960$		0			0
$961$	−31.0000			−1.00000
$962$	12.1353	−	12.6113i	0.391256	−	0.406605i
$963$		0			0
$964$	−4.63525	+	8.02850i	−0.149292	+	0.258580i
$965$	2.73607	−	4.73901i	0.0880771	−	0.152554i
$966$		0			0
$967$	−1.16718			−0.0375341			−0.0187671	−	0.999824i	$-0.505974\pi$
$967$	−1.16718			−0.0375341			−0.0187671	+	0.999824i	$0.505974\pi$
$968$	−7.76393	−	13.4475i	−0.249542	−	0.432220i
$969$		0			0
$970$	8.85410			0.284288
$971$	−8.11803	−	14.0608i	−0.260520	−	0.451234i	0.705860	−	0.708351i	$-0.250561\pi$
$971$	−8.11803	−	14.0608i	−0.260520	−	0.451234i	−0.966380	+	0.257117i	$0.917227\pi$
$972$		0			0
$973$	−0.388544	+	0.672978i	−0.0124561	+	0.0215747i
$974$	42.2705			1.35443
$975$		0			0
$976$	60.2705			1.92921
$977$	17.2082	−	29.8055i	0.550539	−	0.953562i	−0.447696	−	0.894186i	$-0.647755\pi$
$977$	17.2082	−	29.8055i	0.550539	−	0.953562i	0.998236	−	0.0593763i	$-0.0189112\pi$
$978$		0			0
$979$	19.0623	+	33.0169i	0.609234	+	1.05522i
$980$	4.29180			0.137096
$981$		0			0
$982$	−3.42705	−	5.93583i	−0.109362	−	0.189420i
$983$	14.8328			0.473093			0.236547	−	0.971620i	$-0.423984\pi$
$983$	14.8328			0.473093			0.236547	+	0.971620i	$0.423984\pi$
$984$		0			0
$985$	−1.50000	+	2.59808i	−0.0477940	+	0.0827816i
$986$	6.51722	−	11.2882i	0.207551	−	0.359488i
$987$		0			0
$988$	−0.510643	−	0.126351i	−0.0162457	−	0.00401977i
$989$	14.5279			0.461959
$990$		0			0
$991$	16.6459	−	28.8315i	0.528774	−	0.915864i	−0.470663	−	0.882313i	$-0.655985\pi$
$991$	16.6459	−	28.8315i	0.528774	−	0.915864i	0.999437	−	0.0335508i	$-0.0106816\pi$
$992$		0			0
$993$		0			0
$994$	−0.336881	−	0.583495i	−0.0106852	−	0.0185073i
$995$	−7.35410	−	12.7377i	−0.233141	−	0.403812i
$996$		0			0
$997$	−8.44427	−	14.6259i	−0.267433	−	0.463207i	0.700765	−	0.713392i	$-0.252842\pi$
$997$	−8.44427	−	14.6259i	−0.267433	−	0.463207i	−0.968198	+	0.250185i	$0.919509\pi$
$998$	11.2361	−	19.4614i	0.355672	−	0.616041i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.e.451.2		4
3.2	odd	2		65.2.e.a.61.1	yes	4
12.11	even	2		1040.2.q.n.321.1		4
13.3	even	3	inner	585.2.j.e.406.2		4
13.4	even	6		7605.2.a.bf.1.2		2
13.9	even	3		7605.2.a.ba.1.1		2
15.2	even	4		325.2.o.a.74.1		8
15.8	even	4		325.2.o.a.74.4		8
15.14	odd	2		325.2.e.b.126.2		4
39.2	even	12		845.2.m.e.361.1		8
39.5	even	4		845.2.m.e.316.4		8
39.8	even	4		845.2.m.e.316.1		8
39.11	even	12		845.2.m.e.361.4		8
39.17	odd	6		845.2.a.b.1.1		2
39.20	even	12		845.2.c.c.506.4		4
39.23	odd	6		845.2.e.g.146.2		4
39.29	odd	6		65.2.e.a.16.1	✓	4
39.32	even	12		845.2.c.c.506.1		4
39.35	odd	6		845.2.a.e.1.2		2
39.38	odd	2		845.2.e.g.191.2		4
156.107	even	6		1040.2.q.n.81.1		4
195.29	odd	6		325.2.e.b.276.2		4
195.68	even	12		325.2.o.a.224.1		8
195.74	odd	6		4225.2.a.u.1.1		2
195.107	even	12		325.2.o.a.224.4		8
195.134	odd	6		4225.2.a.y.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.a.16.1	✓	4	39.29	odd	6
65.2.e.a.61.1	yes	4	3.2	odd	2
325.2.e.b.126.2		4	15.14	odd	2
325.2.e.b.276.2		4	195.29	odd	6
325.2.o.a.74.1		8	15.2	even	4
325.2.o.a.74.4		8	15.8	even	4
325.2.o.a.224.1		8	195.68	even	12
325.2.o.a.224.4		8	195.107	even	12
585.2.j.e.406.2		4	13.3	even	3	inner
585.2.j.e.451.2		4	1.1	even	1	trivial
845.2.a.b.1.1		2	39.17	odd	6
845.2.a.e.1.2		2	39.35	odd	6
845.2.c.c.506.1		4	39.32	even	12
845.2.c.c.506.4		4	39.20	even	12
845.2.e.g.146.2		4	39.23	odd	6
845.2.e.g.191.2		4	39.38	odd	2
845.2.m.e.316.1		8	39.8	even	4
845.2.m.e.316.4		8	39.5	even	4
845.2.m.e.361.1		8	39.2	even	12
845.2.m.e.361.4		8	39.11	even	12
1040.2.q.n.81.1		4	156.107	even	6
1040.2.q.n.321.1		4	12.11	even	2
4225.2.a.u.1.1		2	195.74	odd	6
4225.2.a.y.1.2		2	195.134	odd	6
7605.2.a.ba.1.1		2	13.9	even	3
7605.2.a.bf.1.2		2	13.4	even	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 1.40126i) q^{2} +(-0.309017 - 0.535233i) q^{4} -1.00000 q^{5} +(0.118034 + 0.204441i) q^{7} +2.23607 q^{8} +O(q^{10})\)	\(q+(0.809017 - 1.40126i) q^{2} +(-0.309017 - 0.535233i) q^{4} -1.00000 q^{5} +(0.118034 + 0.204441i) q^{7} +2.23607 q^{8} +(-0.809017 + 1.40126i) q^{10} +(2.11803 - 3.66854i) q^{11} +(-1.00000 - 3.46410i) q^{13} +0.381966 q^{14} +(2.42705 - 4.20378i) q^{16} +(2.73607 + 4.73901i) q^{17} +(0.118034 + 0.204441i) q^{19} +(0.309017 + 0.535233i) q^{20} +(-3.42705 - 5.93583i) q^{22} +(4.11803 - 7.13264i) q^{23} +1.00000 q^{25} +(-5.66312 - 1.40126i) q^{26} +(0.0729490 - 0.126351i) q^{28} +(0.736068 - 1.27491i) q^{29} +(-1.69098 - 2.92887i) q^{32} +8.85410 q^{34} +(-0.118034 - 0.204441i) q^{35} +(-1.50000 + 2.59808i) q^{37} +0.381966 q^{38} -2.23607 q^{40} +(-2.97214 + 5.14789i) q^{41} +(0.881966 + 1.52761i) q^{43} -2.61803 q^{44} +(-6.66312 - 11.5409i) q^{46} -12.9443 q^{47} +(3.47214 - 6.01392i) q^{49} +(0.809017 - 1.40126i) q^{50} +(-1.54508 + 1.60570i) q^{52} -6.00000 q^{53} +(-2.11803 + 3.66854i) q^{55} +(0.263932 + 0.457144i) q^{56} +(-1.19098 - 2.06284i) q^{58} +(6.35410 + 11.0056i) q^{59} +(6.20820 + 10.7529i) q^{61} +4.23607 q^{64} +(1.00000 + 3.46410i) q^{65} +(-5.35410 + 9.27358i) q^{67} +(1.69098 - 2.92887i) q^{68} -0.381966 q^{70} +(-0.881966 - 1.52761i) q^{71} -6.00000 q^{73} +(2.42705 + 4.20378i) q^{74} +(0.0729490 - 0.126351i) q^{76} +1.00000 q^{77} +(-2.42705 + 4.20378i) q^{80} +(4.80902 + 8.32946i) q^{82} +8.94427 q^{83} +(-2.73607 - 4.73901i) q^{85} +2.85410 q^{86} +(4.73607 - 8.20311i) q^{88} +(-4.50000 + 7.79423i) q^{89} +(0.590170 - 0.613323i) q^{91} -5.09017 q^{92} +(-10.4721 + 18.1383i) q^{94} +(-0.118034 - 0.204441i) q^{95} +(-2.73607 - 4.73901i) q^{97} +(-5.61803 - 9.73072i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} - 4 q^{5} - 4 q^{7}+O(q^{10}) \) 4 * q + q^2 + q^4 - 4 * q^5 - 4 * q^7	\( 4 q + q^{2} + q^{4} - 4 q^{5} - 4 q^{7} - q^{10} + 4 q^{11} - 4 q^{13} + 6 q^{14} + 3 q^{16} + 2 q^{17} - 4 q^{19} - q^{20} - 7 q^{22} + 12 q^{23} + 4 q^{25} - 7 q^{26} + 7 q^{28} - 6 q^{29} - 9 q^{32} + 22 q^{34} + 4 q^{35} - 6 q^{37} + 6 q^{38} + 6 q^{41} + 8 q^{43} - 6 q^{44} - 11 q^{46} - 16 q^{47} - 4 q^{49} + q^{50} + 5 q^{52} - 24 q^{53} - 4 q^{55} + 10 q^{56} - 7 q^{58} + 12 q^{59} - 2 q^{61} + 8 q^{64} + 4 q^{65} - 8 q^{67} + 9 q^{68} - 6 q^{70} - 8 q^{71} - 24 q^{73} + 3 q^{74} + 7 q^{76} + 4 q^{77} - 3 q^{80} + 17 q^{82} - 2 q^{85} - 2 q^{86} + 10 q^{88} - 18 q^{89} - 20 q^{91} + 2 q^{92} - 24 q^{94} + 4 q^{95} - 2 q^{97} - 18 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^4 - 4 * q^5 - 4 * q^7 - q^10 + 4 * q^11 - 4 * q^13 + 6 * q^14 + 3 * q^16 + 2 * q^17 - 4 * q^19 - q^20 - 7 * q^22 + 12 * q^23 + 4 * q^25 - 7 * q^26 + 7 * q^28 - 6 * q^29 - 9 * q^32 + 22 * q^34 + 4 * q^35 - 6 * q^37 + 6 * q^38 + 6 * q^41 + 8 * q^43 - 6 * q^44 - 11 * q^46 - 16 * q^47 - 4 * q^49 + q^50 + 5 * q^52 - 24 * q^53 - 4 * q^55 + 10 * q^56 - 7 * q^58 + 12 * q^59 - 2 * q^61 + 8 * q^64 + 4 * q^65 - 8 * q^67 + 9 * q^68 - 6 * q^70 - 8 * q^71 - 24 * q^73 + 3 * q^74 + 7 * q^76 + 4 * q^77 - 3 * q^80 + 17 * q^82 - 2 * q^85 - 2 * q^86 + 10 * q^88 - 18 * q^89 - 20 * q^91 + 2 * q^92 - 24 * q^94 + 4 * q^95 - 2 * q^97 - 18 * q^98

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