LMFDB - Embedded newform 585.2.j.h.406.4

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 50x^{6} - 42x^{5} + 124x^{4} - 12x^{3} + 96x^{2} - 36x + 36 $ x^10 - 2x^9 + 10x^8 - 8x^7 + 50x^6 - 42x^5 + 124x^4 - 12x^3 + 96x^2 - 36*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.4
Root			$-0.473183 + 0.819577i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.h.451.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.473183 + 0.819577i) q^{2} +(0.552196 - 0.956432i) q^{4} +1.00000 q^{5} +(0.781529 - 1.35365i) q^{7} +2.93789 q^{8} +O(q^{10})$	\(q+(0.473183 + 0.819577i) q^{2} +(0.552196 - 0.956432i) q^{4} +1.00000 q^{5} +(0.781529 - 1.35365i) q^{7} +2.93789 q^{8} +(0.473183 + 0.819577i) q^{10} +(0.754712 + 1.30720i) q^{11} +(-3.46327 - 1.00288i) q^{13} +1.47922 q^{14} +(0.285767 + 0.494963i) q^{16} +(1.63121 - 2.82534i) q^{17} +(1.55220 - 2.68848i) q^{19} +(0.552196 - 0.956432i) q^{20} +(-0.714233 + 1.23709i) q^{22} +(1.46894 + 2.54429i) q^{23} +1.00000 q^{25} +(-0.816822 - 3.31296i) q^{26} +(-0.863114 - 1.49496i) q^{28} +(1.30267 + 2.25629i) q^{29} -2.65897 q^{31} +(2.66745 - 4.62016i) q^{32} +3.08744 q^{34} +(0.781529 - 1.35365i) q^{35} +(-0.285767 - 0.494963i) q^{37} +2.93789 q^{38} +2.93789 q^{40} +(2.84400 + 4.92596i) q^{41} +(-0.632648 + 1.09578i) q^{43} +1.66700 q^{44} +(-1.39016 + 2.40783i) q^{46} +5.13459 q^{47} +(2.27843 + 3.94635i) q^{49} +(0.473183 + 0.819577i) q^{50} +(-2.87159 + 2.75859i) q^{52} -2.91733 q^{53} +(0.754712 + 1.30720i) q^{55} +(2.29605 - 3.97687i) q^{56} +(-1.23280 + 2.13528i) q^{58} +(-6.40706 + 11.0974i) q^{59} +(-3.32949 + 5.76684i) q^{61} +(-1.25818 - 2.17923i) q^{62} +6.19183 q^{64} +(-3.46327 - 1.00288i) q^{65} +(-4.74904 - 8.22557i) q^{67} +(-1.80149 - 3.12028i) q^{68} +1.47922 q^{70} +(-0.610068 + 1.05667i) q^{71} -12.8785 q^{73} +(0.270440 - 0.468416i) q^{74} +(-1.71423 - 2.96914i) q^{76} +2.35932 q^{77} +7.76563 q^{79} +(0.285767 + 0.494963i) q^{80} +(-2.69147 + 4.66176i) q^{82} -11.2312 q^{83} +(1.63121 - 2.82534i) q^{85} -1.19743 q^{86} +(2.21726 + 3.84041i) q^{88} +(-0.398407 - 0.690062i) q^{89} +(-4.06419 + 3.90427i) q^{91} +3.24458 q^{92} +(2.42960 + 4.20819i) q^{94} +(1.55220 - 2.68848i) q^{95} +(2.90021 - 5.02331i) q^{97} +(-2.15622 + 3.73469i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8	$ 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8} - 2 q^{10} - 8 q^{11} + q^{13} - 8 q^{14} - 4 q^{16} + 4 q^{19} - 6 q^{20} - 14 q^{22} + 6 q^{23} + 10 q^{25} - 10 q^{26} + 2 q^{28} - 16 q^{29} + 18 q^{31} - 14 q^{32} - q^{35} + 4 q^{37} + 12 q^{38} + 12 q^{40} - 6 q^{41} - 15 q^{43} + 28 q^{44} + 16 q^{46} + 20 q^{47} - 10 q^{49} - 2 q^{50} - 22 q^{52} - 40 q^{53} - 8 q^{55} + 2 q^{56} + 4 q^{58} - 12 q^{59} - 11 q^{61} + 22 q^{62} + 8 q^{64} + q^{65} - 5 q^{67} - 50 q^{68} - 8 q^{70} - 10 q^{71} + 2 q^{73} + 26 q^{74} - 24 q^{76} + 84 q^{77} - 34 q^{79} - 4 q^{80} - 16 q^{82} + 32 q^{83} + 88 q^{86} - 20 q^{88} - 4 q^{89} - q^{91} - 68 q^{92} + 16 q^{94} + 4 q^{95} + 11 q^{97} - 30 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8 - 2 * q^10 - 8 * q^11 + q^13 - 8 * q^14 - 4 * q^16 + 4 * q^19 - 6 * q^20 - 14 * q^22 + 6 * q^23 + 10 * q^25 - 10 * q^26 + 2 * q^28 - 16 * q^29 + 18 * q^31 - 14 * q^32 - q^35 + 4 * q^37 + 12 * q^38 + 12 * q^40 - 6 * q^41 - 15 * q^43 + 28 * q^44 + 16 * q^46 + 20 * q^47 - 10 * q^49 - 2 * q^50 - 22 * q^52 - 40 * q^53 - 8 * q^55 + 2 * q^56 + 4 * q^58 - 12 * q^59 - 11 * q^61 + 22 * q^62 + 8 * q^64 + q^65 - 5 * q^67 - 50 * q^68 - 8 * q^70 - 10 * q^71 + 2 * q^73 + 26 * q^74 - 24 * q^76 + 84 * q^77 - 34 * q^79 - 4 * q^80 - 16 * q^82 + 32 * q^83 + 88 * q^86 - 20 * q^88 - 4 * q^89 - q^91 - 68 * q^92 + 16 * q^94 + 4 * q^95 + 11 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.473183	+	0.819577i	0.334591	+	0.579528i	0.983406	−	0.181418i	$-0.0580686\pi$
$2$	0.473183	+	0.819577i	0.334591	+	0.579528i	−0.648815	+	0.760946i	$0.724735\pi$
$3$		0			0
$3$		0			0
$4$	0.552196	−	0.956432i	0.276098	−	0.478216i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	0.781529	−	1.35365i	0.295390	−	0.511631i	−0.679685	−	0.733504i	$-0.737884\pi$
$7$	0.781529	−	1.35365i	0.295390	−	0.511631i	0.975076	+	0.221873i	$0.0712170\pi$
$8$	2.93789			1.03870
$9$		0			0
$10$	0.473183	+	0.819577i	0.149634	+	0.259173i
$11$	0.754712	+	1.30720i	0.227554	+	0.394135i	0.957083	−	0.289815i	$-0.0935938\pi$
$11$	0.754712	+	1.30720i	0.227554	+	0.394135i	−0.729529	+	0.683950i	$0.760260\pi$
$12$		0			0
$13$	−3.46327	−	1.00288i	−0.960538	−	0.278149i
$13$	−3.46327	−	1.00288i	−0.960538	−	0.278149i
$14$	1.47922			0.395339
$15$		0			0
$16$	0.285767	+	0.494963i	0.0714417	+	0.123741i
$17$	1.63121	−	2.82534i	0.395626	−	0.685245i	−0.597555	−	0.801828i	$-0.703861\pi$
$17$	1.63121	−	2.82534i	0.395626	−	0.685245i	0.993181	+	0.116583i	$0.0371942\pi$
$18$		0			0
$19$	1.55220	−	2.68848i	0.356098	−	0.616780i	−0.631207	−	0.775614i	$-0.717440\pi$
$19$	1.55220	−	2.68848i	0.356098	−	0.616780i	0.987305	+	0.158834i	$0.0507735\pi$
$20$	0.552196	−	0.956432i	0.123475	−	0.213865i
$21$		0			0
$22$	−0.714233	+	1.23709i	−0.152275	+	0.263748i
$23$	1.46894	+	2.54429i	0.306296	+	0.530521i	0.977549	−	0.210708i	$-0.0675769\pi$
$23$	1.46894	+	2.54429i	0.306296	+	0.530521i	−0.671253	+	0.741228i	$0.734244\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−0.816822	−	3.31296i	−0.160192	−	0.649725i
$27$		0			0
$28$	−0.863114	−	1.49496i	−0.163113	−	0.282521i
$29$	1.30267	+	2.25629i	0.241900	+	0.418983i	0.961255	−	0.275659i	$-0.0888962\pi$
$29$	1.30267	+	2.25629i	0.241900	+	0.418983i	−0.719356	+	0.694642i	$0.755563\pi$
$30$		0			0
$31$	−2.65897			−0.477566			−0.238783	−	0.971073i	$-0.576748\pi$
$31$	−2.65897			−0.477566			−0.238783	+	0.971073i	$0.576748\pi$
$32$	2.66745	−	4.62016i	0.471543	−	0.816736i
$33$		0			0
$34$	3.08744			0.529492
$35$	0.781529	−	1.35365i	0.132103	−	0.228808i
$36$		0			0
$37$	−0.285767	−	0.494963i	−0.0469798	−	0.0813713i	0.841579	−	0.540134i	$-0.181626\pi$
$37$	−0.285767	−	0.494963i	−0.0469798	−	0.0813713i	−0.888559	+	0.458762i	$0.848293\pi$
$38$	2.93789			0.476589
$39$		0			0
$40$	2.93789			0.464521
$41$	2.84400	+	4.92596i	0.444159	+	0.769306i	0.997993	−	0.0633212i	$-0.0201693\pi$
$41$	2.84400	+	4.92596i	0.444159	+	0.769306i	−0.553834	+	0.832627i	$0.686836\pi$
$42$		0			0
$43$	−0.632648	+	1.09578i	−0.0964779	+	0.167105i	−0.910224	−	0.414115i	$-0.864091\pi$
$43$	−0.632648	+	1.09578i	−0.0964779	+	0.167105i	0.813747	+	0.581220i	$0.197424\pi$
$44$	1.66700			0.251309
$45$		0			0
$46$	−1.39016	+	2.40783i	−0.204968	+	0.355015i
$47$	5.13459			0.748957			0.374479	−	0.927236i	$-0.377822\pi$
$47$	5.13459			0.748957			0.374479	+	0.927236i	$0.377822\pi$
$48$		0			0
$49$	2.27843	+	3.94635i	0.325489	+	0.563764i
$50$	0.473183	+	0.819577i	0.0669182	+	0.115906i
$51$		0			0
$52$	−2.87159	+	2.75859i	−0.398218	+	0.382548i
$53$	−2.91733			−0.400726			−0.200363	−	0.979722i	$-0.564212\pi$
$53$	−2.91733			−0.400726			−0.200363	+	0.979722i	$0.564212\pi$
$54$		0			0
$55$	0.754712	+	1.30720i	0.101765	+	0.176263i
$56$	2.29605	−	3.97687i	0.306822	−	0.531431i
$57$		0			0
$58$	−1.23280	+	2.13528i	−0.161875	+	0.280375i
$59$	−6.40706	+	11.0974i	−0.834128	+	1.44475i	0.0606096	+	0.998162i	$0.480696\pi$
$59$	−6.40706	+	11.0974i	−0.834128	+	1.44475i	−0.894738	+	0.446591i	$0.852638\pi$
$60$		0			0
$61$	−3.32949	+	5.76684i	−0.426297	+	0.738368i	−0.996541	−	0.0831074i	$-0.973516\pi$
$61$	−3.32949	+	5.76684i	−0.426297	+	0.738368i	0.570243	+	0.821476i	$0.306849\pi$
$62$	−1.25818	−	2.17923i	−0.159789	−	0.276763i
$63$		0			0
$64$	6.19183			0.773979
$65$	−3.46327	−	1.00288i	−0.429566	−	0.124392i
$66$		0			0
$67$	−4.74904	−	8.22557i	−0.580187	−	1.00491i	−0.995457	−	0.0952151i	$-0.969646\pi$
$67$	−4.74904	−	8.22557i	−0.580187	−	1.00491i	0.415270	−	0.909698i	$-0.363687\pi$
$68$	−1.80149	−	3.12028i	−0.218463	−	0.378390i
$69$		0			0
$70$	1.47922			0.176801
$71$	−0.610068	+	1.05667i	−0.0724018	+	0.125404i	−0.899953	−	0.435986i	$-0.856400\pi$
$71$	−0.610068	+	1.05667i	−0.0724018	+	0.125404i	0.827552	+	0.561390i	$0.189733\pi$
$72$		0			0
$73$	−12.8785			−1.50731			−0.753657	−	0.657268i	$-0.771712\pi$
$73$	−12.8785			−1.50731			−0.753657	+	0.657268i	$0.771712\pi$
$74$	0.270440	−	0.468416i	0.0314380	−	0.0544522i
$75$		0			0
$76$	−1.71423	−	2.96914i	−0.196636	−	0.340584i
$77$	2.35932			0.268869
$78$		0			0
$79$	7.76563			0.873702			0.436851	−	0.899534i	$-0.356094\pi$
$79$	7.76563			0.873702			0.436851	+	0.899534i	$0.356094\pi$
$80$	0.285767	+	0.494963i	0.0319497	+	0.0553385i
$81$		0			0
$82$	−2.69147	+	4.66176i	−0.297223	+	0.514805i
$83$	−11.2312			−1.23279			−0.616394	−	0.787438i	$-0.711407\pi$
$83$	−11.2312			−1.23279			−0.616394	+	0.787438i	$0.711407\pi$
$84$		0			0
$85$	1.63121	−	2.82534i	0.176929	−	0.306451i
$86$	−1.19743			−0.129122
$87$		0			0
$88$	2.21726	+	3.84041i	0.236361	+	0.409389i
$89$	−0.398407	−	0.690062i	−0.0422311	−	0.0731464i	0.844137	−	0.536127i	$-0.180113\pi$
$89$	−0.398407	−	0.690062i	−0.0422311	−	0.0731464i	−0.886368	+	0.462981i	$0.846780\pi$
$90$		0			0
$91$	−4.06419	+	3.90427i	−0.426043	+	0.409278i
$92$	3.24458			0.338271
$93$		0			0
$94$	2.42960	+	4.20819i	0.250594	+	0.434042i
$95$	1.55220	−	2.68848i	0.159252	−	0.275832i
$96$		0			0
$97$	2.90021	−	5.02331i	0.294472	−	0.510040i	−0.680390	−	0.732850i	$-0.738190\pi$
$97$	2.90021	−	5.02331i	0.294472	−	0.510040i	0.974862	+	0.222810i	$0.0715230\pi$
$98$	−2.15622	+	3.73469i	−0.217811	+	0.377260i
$99$		0			0
$100$	0.552196	−	0.956432i	0.0552196	−	0.0956432i
$101$	3.02001	+	5.23081i	0.300502	+	0.520485i	0.976250	−	0.216648i	$-0.0695125\pi$
$101$	3.02001	+	5.23081i	0.300502	+	0.520485i	−0.675748	+	0.737133i	$0.736179\pi$
$102$		0			0
$103$	−9.34411			−0.920702			−0.460351	−	0.887737i	$-0.652276\pi$
$103$	−9.34411			−0.920702			−0.460351	+	0.887737i	$0.652276\pi$
$104$	−10.1747	−	2.94635i	−0.997712	−	0.288914i
$105$		0			0
$106$	−1.38043	−	2.39098i	−0.134079	−	0.232232i
$107$	−5.50519	−	9.53526i	−0.532206	−	0.921808i	−0.999293	−	0.0375969i	$-0.988030\pi$
$107$	−5.50519	−	9.53526i	−0.532206	−	0.921808i	0.467087	−	0.884212i	$-0.345304\pi$
$108$		0			0
$109$	18.5677			1.77846			0.889230	−	0.457460i	$-0.151241\pi$
$109$	18.5677			1.77846			0.889230	+	0.457460i	$0.151241\pi$
$110$	−0.714233	+	1.23709i	−0.0680995	+	0.117952i
$111$		0			0
$112$	0.893340			0.0844127
$113$	−6.52151	+	11.2956i	−0.613492	+	1.06260i	0.377155	+	0.926150i	$0.376902\pi$
$113$	−6.52151	+	11.2956i	−0.613492	+	1.06260i	−0.990647	+	0.136449i	$0.956431\pi$
$114$		0			0
$115$	1.46894	+	2.54429i	0.136980	+	0.237256i
$116$	2.87732			0.267152
$117$		0			0
$118$	−12.1268			−1.11637
$119$	−2.54967	−	4.41617i	−0.233728	−	0.404829i
$120$		0			0
$121$	4.36082	−	7.55316i	0.396438	−	0.686651i
$122$	−6.30182			−0.570540
$123$		0			0
$124$	−1.46828	+	2.54313i	−0.131855	+	0.228380i
$125$	1.00000			0.0894427
$126$		0			0
$127$	3.80200	+	6.58526i	0.337373	+	0.584347i	0.983938	−	0.178512i	$-0.0571283\pi$
$127$	3.80200	+	6.58526i	0.337373	+	0.584347i	−0.646565	+	0.762859i	$0.723795\pi$
$128$	−2.40503	−	4.16564i	−0.212577	−	0.368194i
$129$		0			0
$130$	−0.816822	−	3.31296i	−0.0716400	−	0.290566i
$131$	−19.0332			−1.66294			−0.831469	−	0.555571i	$-0.812500\pi$
$131$	−19.0332			−1.66294			−0.831469	+	0.555571i	$0.812500\pi$
$132$		0			0
$133$	−2.42617	−	4.20225i	−0.210376	−	0.364382i
$134$	4.49432	−	7.78440i	0.388250	−	0.672469i
$135$		0			0
$136$	4.79231	−	8.30053i	0.410938	−	0.711765i
$137$	−9.53422	+	16.5138i	−0.814563	+	1.41087i	0.0950776	+	0.995470i	$0.469690\pi$
$137$	−9.53422	+	16.5138i	−0.814563	+	1.41087i	−0.909641	+	0.415395i	$0.863643\pi$
$138$		0			0
$139$	7.41454	−	12.8424i	0.628893	−	1.08928i	−0.358881	−	0.933383i	$-0.616842\pi$
$139$	7.41454	−	12.8424i	0.628893	−	1.08928i	0.987774	−	0.155892i	$-0.0498251\pi$
$140$	−0.863114	−	1.49496i	−0.0729465	−	0.126347i
$141$		0			0
$142$	−1.15470			−0.0968999
$143$	−1.30281	−	5.28407i	−0.108946	−	0.441876i
$144$		0			0
$145$	1.30267	+	2.25629i	0.108181	+	0.187375i
$146$	−6.09389	−	10.5549i	−0.504334	−	0.873531i
$147$		0			0
$148$	−0.631197			−0.0518841
$149$	−11.1399	+	19.2949i	−0.912617	+	1.58070i	−0.102265	+	0.994757i	$0.532609\pi$
$149$	−11.1399	+	19.2949i	−0.912617	+	1.58070i	−0.810353	+	0.585942i	$0.800724\pi$
$150$		0			0
$151$	−16.7896			−1.36632			−0.683160	−	0.730269i	$-0.739395\pi$
$151$	−16.7896			−1.36632			−0.683160	+	0.730269i	$0.739395\pi$
$152$	4.56018	−	7.89847i	0.369880	−	0.640650i
$153$		0			0
$154$	1.11639	+	1.93364i	0.0899611	+	0.155817i
$155$	−2.65897			−0.213574
$156$		0			0
$157$	3.26279			0.260399			0.130200	−	0.991488i	$-0.458438\pi$
$157$	3.26279			0.260399			0.130200	+	0.991488i	$0.458438\pi$
$158$	3.67456	+	6.36453i	0.292333	+	0.506335i
$159$		0			0
$160$	2.66745	−	4.62016i	0.210880	−	0.365256i
$161$	4.59209			0.361908
$162$		0			0
$163$	−1.57274	+	2.72407i	−0.123187	+	0.213366i	−0.921023	−	0.389509i	$-0.872645\pi$
$163$	−1.57274	+	2.72407i	−0.123187	+	0.213366i	0.797836	+	0.602875i	$0.205978\pi$
$164$	6.28179			0.490526
$165$		0			0
$166$	−5.31443	−	9.20486i	−0.412480	−	0.714436i
$167$	−5.21393	−	9.03079i	−0.403466	−	0.698823i	0.590676	−	0.806909i	$-0.298861\pi$
$167$	−5.21393	−	9.03079i	−0.403466	−	0.698823i	−0.994142	+	0.108086i	$0.965528\pi$
$168$		0			0
$169$	10.9885	+	6.94649i	0.845266	+	0.534345i
$170$	3.08744			0.236796
$171$		0			0
$172$	0.698691	+	1.21017i	0.0532747	+	0.0922745i
$173$	6.20274	−	10.7435i	0.471586	−	0.816811i	−0.527886	−	0.849315i	$-0.677015\pi$
$173$	6.20274	−	10.7435i	0.471586	−	0.816811i	0.999472	+	0.0325048i	$0.0103484\pi$
$174$		0			0
$175$	0.781529	−	1.35365i	0.0590780	−	0.102326i
$176$	−0.431343	+	0.747108i	−0.0325137	+	0.0563154i
$177$		0			0
$178$	0.377039	−	0.653051i	0.0282603	−	0.0489482i
$179$	−4.58176	−	7.93585i	−0.342457	−	0.593153i	0.642431	−	0.766343i	$-0.277926\pi$
$179$	−4.58176	−	7.93585i	−0.342457	−	0.593153i	−0.984888	+	0.173190i	$0.944592\pi$
$180$		0			0
$181$	−4.71081			−0.350152			−0.175076	−	0.984555i	$-0.556017\pi$
$181$	−4.71081			−0.350152			−0.175076	+	0.984555i	$0.556017\pi$
$182$	−5.12295	−	1.48349i	−0.379738	−	0.109963i
$183$		0			0
$184$	4.31560	+	7.47484i	0.318150	+	0.551052i
$185$	−0.285767	−	0.494963i	−0.0210100	−	0.0363904i
$186$		0			0
$187$	4.92437			0.360106
$188$	2.83530	−	4.91089i	0.206786	−	0.358163i
$189$		0			0
$190$	2.93789			0.213137
$191$	−7.57528	+	13.1208i	−0.548128	+	0.949386i	0.450275	+	0.892890i	$0.351326\pi$
$191$	−7.57528	+	13.1208i	−0.548128	+	0.949386i	−0.998403	+	0.0564956i	$0.982007\pi$
$192$		0			0
$193$	−5.14501	−	8.91142i	−0.370346	−	0.641458i	0.619273	−	0.785176i	$-0.287427\pi$
$193$	−5.14501	−	8.91142i	−0.370346	−	0.641458i	−0.989619	+	0.143718i	$0.954094\pi$
$194$	5.48932			0.394110
$195$		0			0
$196$	5.03255			0.359468
$197$	2.59506	+	4.49478i	0.184890	+	0.320240i	0.943540	−	0.331260i	$-0.107474\pi$
$197$	2.59506	+	4.49478i	0.184890	+	0.320240i	−0.758649	+	0.651499i	$0.774140\pi$
$198$		0			0
$199$	6.30890	−	10.9273i	0.447226	−	0.774618i	−0.550978	−	0.834520i	$-0.685745\pi$
$199$	6.30890	−	10.9273i	0.447226	−	0.774618i	0.998204	+	0.0599015i	$0.0190787\pi$
$200$	2.93789			0.207740
$201$		0			0
$202$	−2.85803	+	4.95025i	−0.201090	+	0.348299i
$203$	4.07230			0.285819
$204$		0			0
$205$	2.84400	+	4.92596i	0.198634	+	0.344044i
$206$	−4.42147	−	7.65821i	−0.308058	−	0.533573i
$207$		0			0
$208$	−0.493299	−	2.00078i	−0.0342041	−	0.138729i
$209$	4.68584			0.324127
$210$		0			0
$211$	3.05458	+	5.29069i	0.210286	+	0.364226i	0.951804	−	0.306707i	$-0.0992271\pi$
$211$	3.05458	+	5.29069i	0.210286	+	0.364226i	−0.741518	+	0.670933i	$0.765894\pi$
$212$	−1.61094	+	2.79023i	−0.110640	+	0.191634i
$213$		0			0
$214$	5.20992	−	9.02384i	0.356143	−	0.616857i
$215$	−0.632648	+	1.09578i	−0.0431462	+	0.0747314i
$216$		0			0
$217$	−2.07807	+	3.59931i	−0.141068	+	0.244337i
$218$	8.78590	+	15.2176i	0.595057	+	1.03067i
$219$		0			0
$220$	1.66700			0.112389
$221$	−8.48279	+	8.14900i	−0.570614	+	0.548161i
$222$		0			0
$223$	3.18831	+	5.52232i	0.213505	+	0.369802i	0.952809	−	0.303570i	$-0.0981786\pi$
$223$	3.18831	+	5.52232i	0.213505	+	0.369802i	−0.739304	+	0.673372i	$0.764845\pi$
$224$	−4.16938	−	7.22158i	−0.278578	−	0.482512i
$225$		0			0
$226$	−12.3435			−0.821075
$227$	−6.72532	+	11.6486i	−0.446375	+	0.773145i	−0.998147	−	0.0608506i	$-0.980619\pi$
$227$	−6.72532	+	11.6486i	−0.446375	+	0.773145i	0.551772	+	0.833995i	$0.313952\pi$
$228$		0			0
$229$	−9.14533			−0.604341			−0.302170	−	0.953254i	$-0.597711\pi$
$229$	−9.14533			−0.604341			−0.302170	+	0.953254i	$0.597711\pi$
$230$	−1.39016	+	2.40783i	−0.0916644	+	0.158767i
$231$		0			0
$232$	3.82710	+	6.62873i	0.251261	+	0.435198i
$233$	22.1655			1.45211			0.726056	−	0.687636i	$-0.241351\pi$
$233$	22.1655			1.45211			0.726056	+	0.687636i	$0.241351\pi$
$234$		0			0
$235$	5.13459			0.334944
$236$	7.07591	+	12.2558i	0.460602	+	0.797787i
$237$		0			0
$238$	2.41292	−	4.17931i	0.156407	−	0.270904i
$239$	17.5940			1.13806			0.569030	−	0.822317i	$-0.307319\pi$
$239$	17.5940			1.13806			0.569030	+	0.822317i	$0.307319\pi$
$240$		0			0
$241$	−14.0692	+	24.3686i	−0.906277	+	1.56972i	−0.0870830	+	0.996201i	$0.527755\pi$
$241$	−14.0692	+	24.3686i	−0.906277	+	1.56972i	−0.819194	+	0.573517i	$0.805579\pi$
$242$	8.25386			0.530578
$243$		0			0
$244$	3.67706	+	6.36885i	0.235400	+	0.407724i
$245$	2.27843	+	3.94635i	0.145563	+	0.252123i
$246$		0			0
$247$	−8.07190	+	7.75427i	−0.513603	+	0.493392i
$248$	−7.81177			−0.496048
$249$		0			0
$250$	0.473183	+	0.819577i	0.0299267	+	0.0518346i
$251$	14.0411	−	24.3199i	0.886268	−	1.53506i	0.0420141	−	0.999117i	$-0.486623\pi$
$251$	14.0411	−	24.3199i	0.886268	−	1.53506i	0.844254	−	0.535944i	$-0.180044\pi$
$252$		0			0
$253$	−2.21726	+	3.84041i	−0.139398	+	0.241444i
$254$	−3.59808	+	6.23206i	−0.225764	+	0.391034i
$255$		0			0
$256$	8.46787	−	14.6668i	0.529242	−	0.916674i
$257$	15.1282	+	26.2028i	0.943672	+	1.63449i	0.758389	+	0.651802i	$0.225987\pi$
$257$	15.1282	+	26.2028i	0.943672	+	1.63449i	0.185282	+	0.982685i	$0.440680\pi$
$258$		0			0
$259$	−0.893340			−0.0555094
$260$	−2.87159	+	2.75859i	−0.178088	+	0.171081i
$261$		0			0
$262$	−9.00618	−	15.5992i	−0.556404	−	0.963720i
$263$	−14.0620	−	24.3561i	−0.867102	−	1.50186i	−0.864945	−	0.501866i	$-0.832647\pi$
$263$	−14.0620	−	24.3561i	−0.867102	−	1.50186i	−0.00215657	−	0.999998i	$-0.500686\pi$
$264$		0			0
$265$	−2.91733			−0.179210
$266$	2.29605	−	3.97687i	0.140780	−	0.243837i
$267$		0			0
$268$	−10.4896			−0.640754
$269$	10.3621	−	17.9477i	0.631787	−	1.09429i	−0.355399	−	0.934715i	$-0.615655\pi$
$269$	10.3621	−	17.9477i	0.631787	−	1.09429i	0.987186	−	0.159573i	$-0.0510117\pi$
$270$		0			0
$271$	3.97408	+	6.88331i	0.241408	+	0.418131i	0.961116	−	0.276146i	$-0.0890574\pi$
$271$	3.97408	+	6.88331i	0.241408	+	0.418131i	−0.719707	+	0.694277i	$0.755724\pi$
$272$	1.86458			0.113057
$273$		0			0
$274$	−18.0457			−1.09018
$275$	0.754712	+	1.30720i	0.0455108	+	0.0788271i
$276$		0			0
$277$	3.08619	−	5.34544i	0.185431	−	0.321176i	−0.758291	−	0.651917i	$-0.773965\pi$
$277$	3.08619	−	5.34544i	0.185431	−	0.321176i	0.943722	+	0.330741i	$0.107299\pi$
$278$	14.0337			0.841687
$279$		0			0
$280$	2.29605	−	3.97687i	0.137215	−	0.237663i
$281$	18.5723			1.10793			0.553967	−	0.832539i	$-0.313114\pi$
$281$	18.5723			1.10793			0.553967	+	0.832539i	$0.313114\pi$
$282$		0			0
$283$	3.63956	+	6.30390i	0.216349	+	0.374728i	0.953689	−	0.300794i	$-0.0972516\pi$
$283$	3.63956	+	6.30390i	0.216349	+	0.374728i	−0.737340	+	0.675522i	$0.763918\pi$
$284$	0.673755	+	1.16698i	0.0399800	+	0.0692474i
$285$		0			0
$286$	3.71423	−	3.56808i	0.219627	−	0.210985i
$287$	8.89069			0.524801
$288$		0			0
$289$	3.17831	+	5.50500i	0.186960	+	0.323823i
$290$	−1.23280	+	2.13528i	−0.0723926	+	0.125388i
$291$		0			0
$292$	−7.11146	+	12.3174i	−0.416167	+	0.720822i
$293$	−3.22104	+	5.57901i	−0.188175	+	0.325929i	−0.944642	−	0.328103i	$-0.893591\pi$
$293$	−3.22104	+	5.57901i	−0.188175	+	0.325929i	0.756467	+	0.654032i	$0.226924\pi$
$294$		0			0
$295$	−6.40706	+	11.0974i	−0.373034	+	0.646113i
$296$	−0.839551	−	1.45415i	−0.0487979	−	0.0845205i
$297$		0			0
$298$	−21.0849			−1.22141
$299$	−2.53574	−	10.2847i	−0.146645	−	0.594781i
$300$		0			0
$301$	0.988865	+	1.71276i	0.0569972	+	0.0987221i
$302$	−7.94456	−	13.7604i	−0.457158	−	0.791821i
$303$		0			0
$304$	1.77426			0.101761
$305$	−3.32949	+	5.76684i	−0.190646	+	0.330208i
$306$		0			0
$307$	4.94599			0.282283			0.141141	−	0.989989i	$-0.454923\pi$
$307$	4.94599			0.282283			0.141141	+	0.989989i	$0.454923\pi$
$308$	1.30281	−	2.25652i	0.0742342	−	0.128577i
$309$		0			0
$310$	−1.25818	−	2.17923i	−0.0714599	−	0.123772i
$311$	30.0486			1.70390			0.851950	−	0.523623i	$-0.175420\pi$
$311$	30.0486			1.70390			0.851950	+	0.523623i	$0.175420\pi$
$312$		0			0
$313$	−4.57620			−0.258662			−0.129331	−	0.991601i	$-0.541283\pi$
$313$	−4.57620			−0.258662			−0.129331	+	0.991601i	$0.541283\pi$
$314$	1.54390	+	2.67411i	0.0871271	+	0.150909i
$315$		0			0
$316$	4.28815	−	7.42730i	0.241227	−	0.417818i
$317$	1.50960			0.0847875			0.0423937	−	0.999101i	$-0.486502\pi$
$317$	1.50960			0.0847875			0.0423937	+	0.999101i	$0.486502\pi$
$318$		0			0
$319$	−1.96628	+	3.40570i	−0.110091	+	0.190682i
$320$	6.19183			0.346134
$321$		0			0
$322$	2.17290	+	3.76357i	0.121091	+	0.209736i
$323$	−5.06391	−	8.77096i	−0.281764	−	0.488029i
$324$		0			0
$325$	−3.46327	−	1.00288i	−0.192108	−	0.0556298i
$326$	−2.97678			−0.164869
$327$		0			0
$328$	8.35537	+	14.4719i	0.461348	+	0.799079i
$329$	4.01283	−	6.95043i	0.221235	−	0.383190i
$330$		0			0
$331$	−4.17945	+	7.23901i	−0.229723	+	0.397892i	−0.957726	−	0.287682i	$-0.907115\pi$
$331$	−4.17945	+	7.23901i	−0.229723	+	0.397892i	0.728003	+	0.685574i	$0.240449\pi$
$332$	−6.20185	+	10.7419i	−0.340371	+	0.589539i
$333$		0			0
$334$	4.93428	−	8.54643i	0.269992	−	0.467640i
$335$	−4.74904	−	8.22557i	−0.259468	−	0.449411i
$336$		0			0
$337$	15.5359			0.846297			0.423148	−	0.906060i	$-0.360925\pi$
$337$	15.5359			0.846297			0.423148	+	0.906060i	$0.360925\pi$
$338$	−0.493629	+	12.2928i	−0.0268499	+	0.668643i
$339$		0			0
$340$	−1.80149	−	3.12028i	−0.0976998	−	0.169221i
$341$	−2.00676	−	3.47581i	−0.108672	−	0.188226i
$342$		0			0
$343$	18.0640			0.975366
$344$	−1.85865	+	3.21928i	−0.100212	+	0.173572i
$345$		0			0
$346$	11.7401			0.631153
$347$	−2.89046	+	5.00643i	−0.155168	+	0.268759i	−0.933120	−	0.359564i	$-0.882925\pi$
$347$	−2.89046	+	5.00643i	−0.155168	+	0.268759i	0.777952	+	0.628324i	$0.216259\pi$
$348$		0			0
$349$	−2.72812	−	4.72525i	−0.146033	−	0.252937i	0.783725	−	0.621108i	$-0.213317\pi$
$349$	−2.72812	−	4.72525i	−0.146033	−	0.252937i	−0.929758	+	0.368172i	$0.879984\pi$
$350$	1.47922			0.0790679
$351$		0			0
$352$	8.05262			0.429206
$353$	−6.13125	−	10.6196i	−0.326334	−	0.565226i	0.655448	−	0.755240i	$-0.272480\pi$
$353$	−6.13125	−	10.6196i	−0.326334	−	0.565226i	−0.981781	+	0.190014i	$0.939147\pi$
$354$		0			0
$355$	−0.610068	+	1.05667i	−0.0323791	+	0.0560822i
$356$	−0.879996			−0.0466397
$357$		0			0
$358$	4.33602	−	7.51021i	0.229166	−	0.396927i
$359$	27.4508			1.44880			0.724398	−	0.689382i	$-0.242118\pi$
$359$	27.4508			1.44880			0.724398	+	0.689382i	$0.242118\pi$
$360$		0			0
$361$	4.68137	+	8.10838i	0.246388	+	0.426757i
$362$	−2.22908	−	3.86087i	−0.117158	−	0.202923i
$363$		0			0
$364$	1.48993	+	6.04304i	0.0780937	+	0.316741i
$365$	−12.8785			−0.674092
$366$		0			0
$367$	−16.9110	−	29.2908i	−0.882749	−	1.52897i	−0.848272	−	0.529561i	$-0.822357\pi$
$367$	−16.9110	−	29.2908i	−0.882749	−	1.52897i	−0.0344768	−	0.999405i	$-0.510976\pi$
$368$	−0.839551	+	1.45415i	−0.0437646	+	0.0758026i
$369$		0			0
$370$	0.270440	−	0.468416i	0.0140595	−	0.0243518i
$371$	−2.27998	+	3.94904i	−0.118371	+	0.205024i
$372$		0			0
$373$	1.52596	−	2.64304i	0.0790113	−	0.136852i	−0.823812	−	0.566863i	$-0.808157\pi$
$373$	1.52596	−	2.64304i	0.0790113	−	0.136852i	0.902824	+	0.430011i	$0.141490\pi$
$374$	2.33013	+	4.03590i	0.120488	+	0.208691i
$375$		0			0
$376$	15.0849			0.777942
$377$	−2.24871	−	9.12056i	−0.115814	−	0.469733i
$378$		0			0
$379$	1.50609	+	2.60862i	0.0773626	+	0.133996i	0.902111	−	0.431504i	$-0.142017\pi$
$379$	1.50609	+	2.60862i	0.0773626	+	0.133996i	−0.824749	+	0.565500i	$0.808683\pi$
$380$	−1.71423	−	2.96914i	−0.0879383	−	0.152314i
$381$		0			0
$382$	−14.3380			−0.733594
$383$	1.60958	−	2.78787i	0.0822456	−	0.142454i	−0.821969	−	0.569533i	$-0.807124\pi$
$383$	1.60958	−	2.78787i	0.0822456	−	0.142454i	0.904214	+	0.427079i	$0.140457\pi$
$384$		0			0
$385$	2.35932			0.120242
$386$	4.86906	−	8.43346i	0.247829	−	0.429252i
$387$		0			0
$388$	−3.20297	−	5.54771i	−0.162606	−	0.281642i
$389$	12.8066			0.649322			0.324661	−	0.945830i	$-0.394750\pi$
$389$	12.8066			0.649322			0.324661	+	0.945830i	$0.394750\pi$
$390$		0			0
$391$	9.58463			0.484715
$392$	6.69376	+	11.5939i	0.338086	+	0.585582i
$393$		0			0
$394$	−2.45588	+	4.25370i	−0.123725	+	0.214298i
$395$	7.76563			0.390731
$396$		0			0
$397$	17.1125	−	29.6397i	0.858853	−	1.48758i	−0.0141718	−	0.999900i	$-0.504511\pi$
$397$	17.1125	−	29.6397i	0.858853	−	1.48758i	0.873024	−	0.487677i	$-0.162155\pi$
$398$	11.9410			0.598551
$399$		0			0
$400$	0.285767	+	0.494963i	0.0142883	+	0.0247481i
$401$	13.0953	+	22.6817i	0.653948	+	1.13267i	0.982156	+	0.188066i	$0.0602220\pi$
$401$	13.0953	+	22.6817i	0.653948	+	1.13267i	−0.328208	+	0.944606i	$0.606445\pi$
$402$		0			0
$403$	9.20874	+	2.66663i	0.458720	+	0.132834i
$404$	6.67054			0.331872
$405$		0			0
$406$	1.92694	+	3.33756i	0.0956325	+	0.165640i
$407$	0.431343	−	0.747108i	0.0213809	−	0.0370328i
$408$		0			0
$409$	−7.14686	+	12.3787i	−0.353390	+	0.612089i	−0.986841	−	0.161694i	$-0.948304\pi$
$409$	−7.14686	+	12.3787i	−0.353390	+	0.612089i	0.633451	+	0.773782i	$0.281638\pi$
$410$	−2.69147	+	4.66176i	−0.132922	+	0.230228i
$411$		0			0
$412$	−5.15978	+	8.93700i	−0.254204	+	0.440294i
$413$	10.0146	+	17.3458i	0.492787	+	0.853532i
$414$		0			0
$415$	−11.2312			−0.551320
$416$	−13.8716	+	13.3257i	−0.680109	+	0.653347i
$417$		0			0
$418$	2.21726	+	3.84041i	0.108450	+	0.187840i
$419$	−11.7425	−	20.3386i	−0.573659	−	0.993607i	−0.996186	−	0.0872566i	$-0.972190\pi$
$419$	−11.7425	−	20.3386i	−0.573659	−	0.993607i	0.422527	−	0.906351i	$-0.361143\pi$
$420$		0			0
$421$	−12.7618			−0.621971			−0.310985	−	0.950415i	$-0.600659\pi$
$421$	−12.7618			−0.621971			−0.310985	+	0.950415i	$0.600659\pi$
$422$	−2.89075	+	5.00693i	−0.140720	+	0.243733i
$423$		0			0
$424$	−8.57080			−0.416235
$425$	1.63121	−	2.82534i	0.0791253	−	0.137049i
$426$		0			0
$427$	5.20418	+	9.01391i	0.251848	+	0.436214i
$428$	−12.1598			−0.587765
$429$		0			0
$430$	−1.19743			−0.0577453
$431$	−7.34814	−	12.7274i	−0.353948	−	0.613055i	0.632990	−	0.774160i	$-0.281828\pi$
$431$	−7.34814	−	12.7274i	−0.353948	−	0.613055i	−0.986937	+	0.161105i	$0.948494\pi$
$432$		0			0
$433$	9.76216	−	16.9085i	0.469139	−	0.812573i	−0.530238	−	0.847849i	$-0.677898\pi$
$433$	9.76216	−	16.9085i	0.469139	−	0.812573i	0.999378	+	0.0352756i	$0.0112309\pi$
$434$	−3.93322			−0.188801
$435$		0			0
$436$	10.2530	−	17.7587i	0.491030	−	0.850488i
$437$	9.12036			0.436286
$438$		0			0
$439$	−15.2080	−	26.3410i	−0.725838	−	1.25719i	−0.958628	−	0.284661i	$-0.908119\pi$
$439$	−15.2080	−	26.3410i	−0.725838	−	1.25719i	0.232791	−	0.972527i	$-0.425214\pi$
$440$	2.21726	+	3.84041i	0.105704	+	0.183084i
$441$		0			0
$442$	−10.6926	−	3.09633i	−0.508597	−	0.147278i
$443$	−8.83602			−0.419812			−0.209906	−	0.977722i	$-0.567316\pi$
$443$	−8.83602			−0.419812			−0.209906	+	0.977722i	$0.567316\pi$
$444$		0			0
$445$	−0.398407	−	0.690062i	−0.0188863	−	0.0327121i
$446$	−3.01731	+	5.22613i	−0.142874	+	0.247465i
$447$		0			0
$448$	4.83910	−	8.38156i	0.228626	−	0.395992i
$449$	−10.5602	+	18.2908i	−0.498366	+	0.863195i	−0.999998	−	0.00188602i	$-0.999400\pi$
$449$	−10.5602	+	18.2908i	−0.498366	+	0.863195i	0.501632	+	0.865081i	$0.332733\pi$
$450$		0			0
$451$	−4.29281	+	7.43536i	−0.202140	+	0.350117i
$452$	7.20230	+	12.4748i	0.338768	+	0.586763i
$453$		0			0
$454$	−12.7292			−0.597412
$455$	−4.06419	+	3.90427i	−0.190532	+	0.183035i
$456$		0			0
$457$	−19.7092	−	34.1373i	−0.921957	−	1.59688i	−0.796383	−	0.604792i	$-0.793256\pi$
$457$	−19.7092	−	34.1373i	−0.921957	−	1.59688i	−0.125574	−	0.992084i	$-0.540077\pi$
$458$	−4.32742	−	7.49530i	−0.202207	−	0.350233i
$459$		0			0
$460$	3.24458			0.151279
$461$	0.212077	−	0.367328i	0.00987742	−	0.0171082i	−0.861044	−	0.508530i	$-0.830189\pi$
$461$	0.212077	−	0.367328i	0.00987742	−	0.0171082i	0.870922	+	0.491422i	$0.163523\pi$
$462$		0			0
$463$	30.1509			1.40123			0.700616	−	0.713538i	$-0.252909\pi$
$463$	30.1509			1.40123			0.700616	+	0.713538i	$0.252909\pi$
$464$	−0.744520	+	1.28955i	−0.0345635	+	0.0598657i
$465$		0			0
$466$	10.4883	+	18.1663i	0.485863	+	0.841540i
$467$	−8.07034			−0.373451			−0.186725	−	0.982412i	$-0.559787\pi$
$467$	−8.07034			−0.373451			−0.186725	+	0.982412i	$0.559787\pi$
$468$		0			0
$469$	−14.8460			−0.685526
$470$	2.42960	+	4.20819i	0.112069	+	0.194109i
$471$		0			0
$472$	−18.8232	+	32.6028i	−0.866410	+	1.50067i
$473$	−1.90987			−0.0878158
$474$		0			0
$475$	1.55220	−	2.68848i	0.0712196	−	0.123356i
$476$	−5.63168			−0.258128
$477$		0			0
$478$	8.32517	+	14.4196i	0.380785	+	0.659538i
$479$	−18.6079	−	32.2299i	−0.850218	−	1.47262i	−0.881012	−	0.473094i	$-0.843137\pi$
$479$	−18.6079	−	32.2299i	−0.850218	−	1.47262i	0.0307941	−	0.999526i	$-0.490196\pi$
$480$		0			0
$481$	0.493299	+	2.00078i	0.0224925	+	0.0912276i
$482$	−26.6292			−1.21293
$483$		0			0
$484$	−4.81606	−	8.34165i	−0.218912	−	0.379166i
$485$	2.90021	−	5.02331i	0.131692	−	0.228097i
$486$		0			0
$487$	5.72861	−	9.92224i	0.259588	−	0.449619i	−0.706544	−	0.707669i	$-0.749747\pi$
$487$	5.72861	−	9.92224i	0.259588	−	0.449619i	0.966132	+	0.258050i	$0.0830799\pi$
$488$	−9.78167	+	16.9423i	−0.442795	+	0.766944i
$489$		0			0
$490$	−2.15622	+	3.73469i	−0.0974082	+	0.168716i
$491$	−10.5519	−	18.2765i	−0.476202	−	0.824807i	0.523426	−	0.852071i	$-0.324654\pi$
$491$	−10.5519	−	18.2765i	−0.476202	−	0.824807i	−0.999628	+	0.0272644i	$0.991320\pi$
$492$		0			0
$493$	8.49971			0.382808
$494$	−10.1747	−	2.94635i	−0.457782	−	0.132563i
$495$		0			0
$496$	−0.759847	−	1.31609i	−0.0341181	−	0.0590943i
$497$	0.953572	+	1.65164i	0.0427736	+	0.0740860i
$498$		0			0
$499$	−19.9900			−0.894876			−0.447438	−	0.894315i	$-0.647663\pi$
$499$	−19.9900			−0.894876			−0.447438	+	0.894315i	$0.647663\pi$
$500$	0.552196	−	0.956432i	0.0246950	−	0.0427729i
$501$		0			0
$502$	26.5761			1.18615
$503$	5.37097	−	9.30280i	0.239480	−	0.414791i	−0.721085	−	0.692846i	$-0.756356\pi$
$503$	5.37097	−	9.30280i	0.239480	−	0.414791i	0.960565	+	0.278055i	$0.0896897\pi$
$504$		0			0
$505$	3.02001	+	5.23081i	0.134389	+	0.232768i
$506$	−4.19668			−0.186565
$507$		0			0
$508$	8.39780			0.372592
$509$	1.11592	+	1.93284i	0.0494624	+	0.0856715i	0.889697	−	0.456552i	$-0.150916\pi$
$509$	1.11592	+	1.93284i	0.0494624	+	0.0856715i	−0.840234	+	0.542224i	$0.817583\pi$
$510$		0			0
$511$	−10.0649	+	17.4330i	−0.445246	+	0.771189i
$512$	6.40728			0.283164
$513$		0			0
$514$	−14.3168	+	24.7975i	−0.631488	+	1.09377i
$515$	−9.34411			−0.411751
$516$		0			0
$517$	3.87514	+	6.71193i	0.170428	+	0.295190i
$518$	−0.422713	−	0.732161i	−0.0185729	−	0.0321693i
$519$		0			0
$520$	−10.1747	−	2.94635i	−0.446190	−	0.129206i
$521$	−33.9482			−1.48730			−0.743649	−	0.668570i	$-0.766907\pi$
$521$	−33.9482			−1.48730			−0.743649	+	0.668570i	$0.766907\pi$
$522$		0			0
$523$	−2.60173	−	4.50633i	−0.113766	−	0.197048i	0.803520	−	0.595278i	$-0.202958\pi$
$523$	−2.60173	−	4.50633i	−0.113766	−	0.197048i	−0.917286	+	0.398230i	$0.869625\pi$
$524$	−10.5101	+	18.2040i	−0.459134	+	0.795243i
$525$		0			0
$526$	13.3078	−	23.0498i	0.580248	−	1.00502i
$527$	−4.33734	+	7.51250i	−0.188938	+	0.327250i
$528$		0			0
$529$	7.18440	−	12.4437i	0.312365	−	0.541033i
$530$	−1.38043	−	2.39098i	−0.0599621	−	0.103857i
$531$		0			0
$532$	−5.35889			−0.232337
$533$	−4.90940	−	19.9121i	−0.212650	−	0.862490i
$534$		0			0
$535$	−5.50519	−	9.53526i	−0.238010	−	0.412245i
$536$	−13.9521	−	24.1658i	−0.602641	−	1.04380i
$537$		0			0
$538$	19.6126			0.845561
$539$	−3.43911	+	5.95671i	−0.148133	+	0.256574i
$540$		0			0
$541$	−5.87388			−0.252538			−0.126269	−	0.991996i	$-0.540300\pi$
$541$	−5.87388			−0.252538			−0.126269	+	0.991996i	$0.540300\pi$
$542$	−3.76093	+	6.51413i	−0.161546	+	0.279806i
$543$		0			0
$544$	−8.70234	−	15.0729i	−0.373110	−	0.646245i
$545$	18.5677			0.795352
$546$		0			0
$547$	43.6009			1.86424			0.932119	−	0.362151i	$-0.117958\pi$
$547$	43.6009			1.86424			0.932119	+	0.362151i	$0.117958\pi$
$548$	10.5295	+	18.2377i	0.449799	+	0.779074i
$549$		0			0
$550$	−0.714233	+	1.23709i	−0.0304550	+	0.0527496i
$551$	8.08800			0.344560
$552$		0			0
$553$	6.06907	−	10.5119i	0.258083	−	0.447013i
$554$	5.84133			0.248174
$555$		0			0
$556$	−8.18856	−	14.1830i	−0.347272	−	0.601493i
$557$	−17.8250	−	30.8737i	−0.755268	−	1.30816i	−0.945241	−	0.326373i	$-0.894173\pi$
$557$	−17.8250	−	30.8737i	−0.755268	−	1.30816i	0.189973	−	0.981789i	$-0.439160\pi$
$558$		0			0
$559$	3.28996	−	3.16050i	0.139151	−	0.133675i
$560$	0.893340			0.0377505
$561$		0			0
$562$	8.78811	+	15.2215i	0.370704	+	0.642079i
$563$	9.10954	−	15.7782i	0.383921	−	0.664971i	−0.607698	−	0.794168i	$-0.707907\pi$
$563$	9.10954	−	15.7782i	0.383921	−	0.664971i	0.991619	+	0.129197i	$0.0412401\pi$
$564$		0			0
$565$	−6.52151	+	11.2956i	−0.274362	+	0.475209i
$566$	−3.44435	+	5.96580i	−0.144777	+	0.250761i
$567$		0			0
$568$	−1.79231	+	3.10438i	−0.0752038	+	0.130257i
$569$	13.2713	+	22.9866i	0.556362	+	0.963648i	0.997796	+	0.0663539i	$0.0211366\pi$
$569$	13.2713	+	22.9866i	0.556362	+	0.963648i	−0.441434	+	0.897294i	$0.645530\pi$
$570$		0			0
$571$	26.7099			1.11778			0.558888	−	0.829243i	$-0.311228\pi$
$571$	26.7099			1.11778			0.558888	+	0.829243i	$0.311228\pi$
$572$	−5.77325	−	1.67180i	−0.241392	−	0.0699014i
$573$		0			0
$574$	4.20692	+	7.28660i	0.175593	+	0.304137i
$575$	1.46894	+	2.54429i	0.0612592	+	0.106104i
$576$		0			0
$577$	−12.0139			−0.500144			−0.250072	−	0.968227i	$-0.580454\pi$
$577$	−12.0139			−0.500144			−0.250072	+	0.968227i	$0.580454\pi$
$578$	−3.00784	+	5.20974i	−0.125110	+	0.216697i
$579$		0			0
$580$	2.87732			0.119474
$581$	−8.77754	+	15.2031i	−0.364154	+	0.630733i
$582$		0			0
$583$	−2.20174	−	3.81353i	−0.0911869	−	0.157940i
$584$	−37.8356			−1.56565
$585$		0			0
$586$	−6.09657			−0.251847
$587$	−21.6560	−	37.5093i	−0.893840	−	1.54818i	−0.835234	−	0.549895i	$-0.814668\pi$
$587$	−21.6560	−	37.5093i	−0.893840	−	1.54818i	−0.0586057	−	0.998281i	$-0.518665\pi$
$588$		0			0
$589$	−4.12725	+	7.14861i	−0.170060	+	0.294553i
$590$	−12.1268			−0.499254
$591$		0			0
$592$	0.163325	−	0.282888i	0.00671263	−	0.0116266i
$593$	1.84854			0.0759104			0.0379552	−	0.999279i	$-0.487916\pi$
$593$	1.84854			0.0759104			0.0379552	+	0.999279i	$0.487916\pi$
$594$		0			0
$595$	−2.54967	−	4.41617i	−0.104526	−	0.181045i
$596$	12.3028	+	21.3091i	0.503944	+	0.872856i
$597$		0			0
$598$	7.22926	−	6.94479i	0.295626	−	0.283993i
$599$	−25.2041			−1.02981			−0.514906	−	0.857247i	$-0.672173\pi$
$599$	−25.2041			−1.02981			−0.514906	+	0.857247i	$0.672173\pi$
$600$		0			0
$601$	−4.04333	−	7.00325i	−0.164931	−	0.285669i	0.771700	−	0.635987i	$-0.219407\pi$
$601$	−4.04333	−	7.00325i	−0.164931	−	0.285669i	−0.936631	+	0.350318i	$0.886073\pi$
$602$	−0.935828	+	1.62090i	−0.0381415	+	0.0660630i
$603$		0			0
$604$	−9.27117	+	16.0581i	−0.377238	+	0.653396i
$605$	4.36082	−	7.55316i	0.177293	−	0.307080i
$606$		0			0
$607$	−22.5197	+	39.0052i	−0.914045	+	1.58317i	−0.105752	+	0.994393i	$0.533725\pi$
$607$	−22.5197	+	39.0052i	−0.914045	+	1.58317i	−0.808293	+	0.588780i	$0.799608\pi$
$608$	−8.28081	−	14.3428i	−0.335831	−	0.581677i
$609$		0			0
$610$	−6.30182			−0.255153
$611$	−17.7825	−	5.14938i	−0.719402	−	0.208322i
$612$		0			0
$613$	20.6480	+	35.7634i	0.833965	+	1.44447i	0.894870	+	0.446327i	$0.147268\pi$
$613$	20.6480	+	35.7634i	0.833965	+	1.44447i	−0.0609049	+	0.998144i	$0.519399\pi$
$614$	2.34036	+	4.05362i	0.0944492	+	0.163591i
$615$		0			0
$616$	6.93141			0.279275
$617$	−3.43181	+	5.94406i	−0.138159	+	0.239299i	−0.926800	−	0.375555i	$-0.877452\pi$
$617$	−3.43181	+	5.94406i	−0.138159	+	0.239299i	0.788641	+	0.614855i	$0.210785\pi$
$618$		0			0
$619$	−37.3813			−1.50248			−0.751241	−	0.660028i	$-0.770544\pi$
$619$	−37.3813			−1.50248			−0.751241	+	0.660028i	$0.770544\pi$
$620$	−1.46828	+	2.54313i	−0.0589674	+	0.102134i
$621$		0			0
$622$	14.2185	+	24.6271i	0.570109	+	0.987458i
$623$	−1.24547			−0.0498986
$624$		0			0
$625$	1.00000			0.0400000
$626$	−2.16538	−	3.75055i	−0.0865460	−	0.149902i
$627$		0			0
$628$	1.80170	−	3.12064i	0.0718957	−	0.124527i
$629$	−1.86458			−0.0743457
$630$		0			0
$631$	−4.40493	+	7.62957i	−0.175358	+	0.303728i	−0.940285	−	0.340388i	$-0.889441\pi$
$631$	−4.40493	+	7.62957i	−0.175358	+	0.303728i	0.764927	+	0.644117i	$0.222775\pi$
$632$	22.8146			0.907515
$633$		0			0
$634$	0.714316	+	1.23723i	0.0283691	+	0.0491367i
$635$	3.80200	+	6.58526i	0.150878	+	0.261328i
$636$		0			0
$637$	−3.93308	−	15.9523i	−0.155834	−	0.632051i
$638$	−3.72164			−0.147341
$639$		0			0
$640$	−2.40503	−	4.16564i	−0.0950672	−	0.164661i
$641$	4.08665	−	7.07829i	0.161413	−	0.279576i	−0.773963	−	0.633231i	$-0.781728\pi$
$641$	4.08665	−	7.07829i	0.161413	−	0.279576i	0.935376	+	0.353656i	$0.115062\pi$
$642$		0			0
$643$	−12.6636	+	21.9339i	−0.499402	+	0.864989i	−1.00000		0.000690710i	$-0.999780\pi$
$643$	−12.6636	+	21.9339i	−0.499402	+	0.864989i	0.500598	+	0.865680i	$0.333113\pi$
$644$	2.53574	−	4.39202i	0.0999220	−	0.173070i
$645$		0			0
$646$	4.79231	−	8.30053i	0.188551	−	0.326580i
$647$	0.573255	+	0.992906i	0.0225370	+	0.0390352i	0.877074	−	0.480355i	$-0.159492\pi$
$647$	0.573255	+	0.992906i	0.0225370	+	0.0390352i	−0.854537	+	0.519391i	$0.826159\pi$
$648$		0			0
$649$	−19.3419			−0.759238
$650$	−0.816822	−	3.31296i	−0.0320384	−	0.129945i
$651$		0			0
$652$	1.73693	+	3.00845i	0.0680233	+	0.117820i
$653$	11.4214	+	19.7825i	0.446956	+	0.774150i	0.998186	−	0.0602031i	$-0.0191748\pi$
$653$	11.4214	+	19.7825i	0.446956	+	0.774150i	−0.551231	+	0.834353i	$0.685842\pi$
$654$		0			0
$655$	−19.0332			−0.743689
$656$	−1.62544	+	2.81535i	−0.0634629	+	0.109921i
$657$		0			0
$658$	7.59521			0.296092
$659$	−9.54096	+	16.5254i	−0.371663	+	0.643739i	−0.989822	−	0.142314i	$-0.954546\pi$
$659$	−9.54096	+	16.5254i	−0.371663	+	0.643739i	0.618158	+	0.786054i	$0.287879\pi$
$660$		0			0
$661$	−5.79424	−	10.0359i	−0.225370	−	0.390352i	0.731060	−	0.682313i	$-0.239026\pi$
$661$	−5.79424	−	10.0359i	−0.225370	−	0.390352i	−0.956430	+	0.291961i	$0.905692\pi$
$662$	−7.91057			−0.307453
$663$		0			0
$664$	−32.9961			−1.28050
$665$	−2.42617	−	4.20225i	−0.0940829	−	0.162956i
$666$		0			0
$667$	−3.82710	+	6.62873i	−0.148186	+	0.256666i
$668$	−11.5164			−0.445585
$669$		0			0
$670$	4.49432	−	7.78440i	0.173631	−	0.300738i
$671$	−10.0512			−0.388023
$672$		0			0
$673$	−17.7188	−	30.6899i	−0.683010	−	1.18301i	−0.974058	−	0.226299i	$-0.927337\pi$
$673$	−17.7188	−	30.6899i	−0.683010	−	1.18301i	0.291048	−	0.956708i	$-0.405996\pi$
$674$	7.35134	+	12.7329i	0.283163	+	0.490453i
$675$		0			0
$676$	12.7116	−	6.67389i	0.488909	−	0.256688i
$677$	30.5442			1.17391			0.586954	−	0.809620i	$-0.300327\pi$
$677$	30.5442			1.17391			0.586954	+	0.809620i	$0.300327\pi$
$678$		0			0
$679$	−4.53320	−	7.85173i	−0.173968	−	0.301322i
$680$	4.79231	−	8.30053i	0.183777	−	0.318311i
$681$		0			0
$682$	1.89913	−	3.28939i	0.0727214	−	0.125957i
$683$	−9.78636	+	16.9505i	−0.374465	+	0.648592i	−0.990247	−	0.139325i	$-0.955507\pi$
$683$	−9.78636	+	16.9505i	−0.374465	+	0.648592i	0.615782	+	0.787916i	$0.288840\pi$
$684$		0			0
$685$	−9.53422	+	16.5138i	−0.364284	+	0.630958i
$686$	8.54759	+	14.8049i	0.326348	+	0.565252i
$687$		0			0
$688$	−0.723159			−0.0275702
$689$	10.1035	+	2.92573i	0.384913	+	0.111462i
$690$		0			0
$691$	8.38548	+	14.5241i	0.318999	+	0.552522i	0.980279	−	0.197617i	$-0.0633202\pi$
$691$	8.38548	+	14.5241i	0.318999	+	0.552522i	−0.661281	+	0.750138i	$0.729987\pi$
$692$	−6.85026	−	11.8650i	−0.260408	−	0.451040i
$693$		0			0
$694$	−5.47087			−0.207671
$695$	7.41454	−	12.8424i	0.281250	−	0.487139i
$696$		0			0
$697$	18.5567			0.702884
$698$	2.58180	−	4.47181i	0.0977226	−	0.169260i
$699$		0			0
$700$	−0.863114	−	1.49496i	−0.0326227	−	0.0565041i
$701$	40.4052			1.52608			0.763041	−	0.646350i	$-0.223706\pi$
$701$	40.4052			1.52608			0.763041	+	0.646350i	$0.223706\pi$
$702$		0			0
$703$	−1.77426			−0.0669176
$704$	4.67305	+	8.09396i	0.176122	+	0.305053i
$705$		0			0
$706$	5.80240	−	10.0501i	0.218376	−	0.378239i
$707$	9.44089			0.355061
$708$		0			0
$709$	−8.69058	+	15.0525i	−0.326382	+	0.565310i	−0.981791	−	0.189964i	$-0.939163\pi$
$709$	−8.69058	+	15.0525i	−0.326382	+	0.565310i	0.655409	+	0.755274i	$0.272496\pi$
$710$	−1.15470			−0.0433349
$711$		0			0
$712$	−1.17048	−	2.02733i	−0.0438655	−	0.0759772i
$713$	−3.90589	−	6.76519i	−0.146277	−	0.253359i
$714$		0			0
$715$	−1.30281	−	5.28407i	−0.0487222	−	0.197613i
$716$	−10.1201			−0.378207
$717$		0			0
$718$	12.9892	+	22.4980i	0.484754	+	0.839618i
$719$	−1.23074	+	2.13171i	−0.0458990	+	0.0794995i	−0.888062	−	0.459723i	$-0.847949\pi$
$719$	−1.23074	+	2.13171i	−0.0458990	+	0.0794995i	0.842163	+	0.539223i	$0.181282\pi$
$720$		0			0
$721$	−7.30269	+	12.6486i	−0.271966	+	0.471060i
$722$	−4.43029	+	7.67349i	−0.164878	+	0.285578i
$723$		0			0
$724$	−2.60129	+	4.50557i	−0.0966763	+	0.167448i
$725$	1.30267	+	2.25629i	0.0483799	+	0.0837965i
$726$		0			0
$727$	30.0547			1.11467			0.557333	−	0.830289i	$-0.311825\pi$
$727$	30.0547			1.11467			0.557333	+	0.830289i	$0.311825\pi$
$728$	−11.9401	+	11.4703i	−0.442531	+	0.425118i
$729$		0			0
$730$	−6.09389	−	10.5549i	−0.225545	−	0.390655i
$731$	2.06396	+	3.57489i	0.0763384	+	0.132222i
$732$		0			0
$733$	18.4533			0.681587			0.340794	−	0.940138i	$-0.389304\pi$
$733$	18.4533			0.681587			0.340794	+	0.940138i	$0.389304\pi$
$734$	16.0040	−	27.7198i	0.590719	−	1.02316i
$735$		0			0
$736$	15.6733			0.577727
$737$	7.16831	−	12.4159i	0.264048	−	0.457344i
$738$		0			0
$739$	−17.8603	−	30.9349i	−0.657002	−	1.13796i	−0.981388	−	0.192036i	$-0.938491\pi$
$739$	−17.8603	−	30.9349i	−0.657002	−	1.13796i	0.324386	−	0.945925i	$-0.394842\pi$
$740$	−0.631197			−0.0232033
$741$		0			0
$742$	−4.31539			−0.158423
$743$	5.57372	+	9.65396i	0.204480	+	0.354170i	0.949967	−	0.312351i	$-0.101116\pi$
$743$	5.57372	+	9.65396i	0.204480	+	0.354170i	−0.745487	+	0.666520i	$0.767783\pi$
$744$		0			0
$745$	−11.1399	+	19.2949i	−0.408135	+	0.706910i
$746$	2.88823			0.105746
$747$		0			0
$748$	2.71922	−	4.70982i	0.0994245	−	0.172208i
$749$	−17.2098			−0.628834
$750$		0			0
$751$	−6.32279	−	10.9514i	−0.230722	−	0.399622i	0.727299	−	0.686321i	$-0.240775\pi$
$751$	−6.32279	−	10.9514i	−0.230722	−	0.399622i	−0.958021	+	0.286699i	$0.907442\pi$
$752$	1.46730	+	2.54143i	0.0535068	+	0.0926764i
$753$		0			0
$754$	6.41095	−	6.15868i	0.233473	−	0.224286i
$755$	−16.7896			−0.611037
$756$		0			0
$757$	−2.77640	−	4.80887i	−0.100910	−	0.174781i	0.811150	−	0.584839i	$-0.198842\pi$
$757$	−2.77640	−	4.80887i	−0.100910	−	0.174781i	−0.912060	+	0.410057i	$0.865509\pi$
$758$	−1.42531	+	2.46871i	−0.0517696	+	0.0896676i
$759$		0			0
$760$	4.56018	−	7.89847i	0.165415	−	0.286507i
$761$	15.1323	−	26.2099i	0.548544	−	0.950106i	−0.449830	−	0.893114i	$-0.648516\pi$
$761$	15.1323	−	26.2099i	0.548544	−	0.950106i	0.998375	−	0.0569925i	$-0.0181511\pi$
$762$		0			0
$763$	14.5112	−	25.1341i	0.525340	−	0.909915i
$764$	8.36608	+	14.4905i	0.302674	+	0.524247i
$765$		0			0
$766$	3.04650			0.110074
$767$	33.3187	−	32.0076i	1.20307	−	1.15573i
$768$		0			0
$769$	26.1245	+	45.2489i	0.942072	+	1.63172i	0.761510	+	0.648153i	$0.224458\pi$
$769$	26.1245	+	45.2489i	0.942072	+	1.63172i	0.180562	+	0.983564i	$0.442208\pi$
$770$	1.11639	+	1.93364i	0.0402318	+	0.0696836i
$771$		0			0
$772$	−11.3642			−0.409007
$773$	−19.7389	+	34.1887i	−0.709957	+	1.22968i	0.254915	+	0.966963i	$0.417952\pi$
$773$	−19.7389	+	34.1887i	−0.709957	+	1.22968i	−0.964872	+	0.262719i	$0.915381\pi$
$774$		0			0
$775$	−2.65897			−0.0955132
$776$	8.52050	−	14.7579i	0.305868	−	0.529779i
$777$		0			0
$778$	6.05988	+	10.4960i	0.217257	+	0.376300i
$779$	17.6578			0.632657
$780$		0			0
$781$	−1.84170			−0.0659013
$782$	4.53528	+	7.85534i	0.162181	+	0.280906i
$783$		0			0
$784$	−1.30220	+	2.25547i	−0.0465070	+	0.0805525i
$785$	3.26279			0.116454
$786$		0			0
$787$	15.6650	−	27.1326i	0.558396	−	0.967171i	−0.439234	−	0.898373i	$-0.644750\pi$
$787$	15.6650	−	27.1326i	0.558396	−	0.967171i	0.997631	−	0.0687984i	$-0.0219165\pi$
$788$	5.73193			0.204192
$789$		0			0
$790$	3.67456	+	6.36453i	0.130735	+	0.226440i
$791$	10.1935	+	17.6556i	0.362439	+	0.627762i
$792$		0			0
$793$	17.3144	−	16.6330i	0.614851	−	0.590657i
$794$	32.3894			1.14946
$795$		0			0
$796$	−6.96750	−	12.0681i	−0.246956	−	0.427741i
$797$	7.46182	−	12.9243i	0.264311	−	0.457801i	−0.703072	−	0.711119i	$-0.748189\pi$
$797$	7.46182	−	12.9243i	0.264311	−	0.457801i	0.967383	+	0.253318i	$0.0815220\pi$
$798$		0			0
$799$	8.37559	−	14.5070i	0.296307	−	0.513219i
$800$	2.66745	−	4.62016i	0.0943086	−	0.163347i
$801$		0			0
$802$	−12.3929	+	21.4652i	−0.437610	+	0.757963i
$803$	−9.71956	−	16.8348i	−0.342996	−	0.594086i
$804$		0			0
$805$	4.59209			0.161850
$806$	2.17191	+	8.80908i	0.0765022	+	0.310286i
$807$		0			0
$808$	8.87245	+	15.3675i	0.312132	+	0.540628i
$809$	2.64058	+	4.57362i	0.0928379	+	0.160800i	0.908704	−	0.417441i	$-0.137073\pi$
$809$	2.64058	+	4.57362i	0.0928379	+	0.160800i	−0.815866	+	0.578241i	$0.803739\pi$
$810$		0			0
$811$	18.5871			0.652682			0.326341	−	0.945252i	$-0.394184\pi$
$811$	18.5871			0.652682			0.326341	+	0.945252i	$0.394184\pi$
$812$	2.24871	−	3.89487i	0.0789141	−	0.136683i
$813$		0			0
$814$	0.816417			0.0286154
$815$	−1.57274	+	2.72407i	−0.0550908	+	0.0954201i
$816$		0			0
$817$	1.96399	+	3.40172i	0.0687112	+	0.119011i
$818$	−13.5271			−0.472963
$819$		0			0
$820$	6.28179			0.219370
$821$	16.6136	+	28.7755i	0.579817	+	1.00427i	0.995500	+	0.0947634i	$0.0302095\pi$
$821$	16.6136	+	28.7755i	0.579817	+	1.00427i	−0.415682	+	0.909510i	$0.636457\pi$
$822$		0			0
$823$	−7.88588	+	13.6587i	−0.274884	+	0.476114i	−0.970106	−	0.242682i	$-0.921973\pi$
$823$	−7.88588	+	13.6587i	−0.274884	+	0.476114i	0.695221	+	0.718796i	$0.255306\pi$
$824$	−27.4520			−0.956334
$825$		0			0
$826$	−9.47748	+	16.4155i	−0.329764	+	0.571168i
$827$	1.81664			0.0631709			0.0315854	−	0.999501i	$-0.489944\pi$
$827$	1.81664			0.0631709			0.0315854	+	0.999501i	$0.489944\pi$
$828$		0			0
$829$	−14.8025	−	25.6387i	−0.514112	−	0.890468i	−0.999866	−	0.0163726i	$-0.994788\pi$
$829$	−14.8025	−	25.6387i	−0.514112	−	0.890468i	0.485754	−	0.874096i	$-0.338545\pi$
$830$	−5.31443	−	9.20486i	−0.184467	−	0.319505i
$831$		0			0
$832$	−21.4440	−	6.20967i	−0.743436	−	0.215282i
$833$	14.8664			0.515089
$834$		0			0
$835$	−5.21393	−	9.03079i	−0.180435	−	0.312523i
$836$	2.58750	−	4.48169i	0.0894907	−	0.155002i
$837$		0			0
$838$	11.1127	−	19.2478i	0.383882	−	0.664904i
$839$	−3.46542	+	6.00229i	−0.119640	+	0.207222i	−0.919625	−	0.392798i	$-0.871507\pi$
$839$	−3.46542	+	6.00229i	−0.119640	+	0.207222i	0.799985	+	0.600020i	$0.204841\pi$
$840$		0			0
$841$	11.1061	−	19.2363i	0.382969	−	0.663322i
$842$	−6.03865	−	10.4593i	−0.208106	−	0.360450i
$843$		0			0
$844$	6.74691			0.232238
$845$	10.9885	+	6.94649i	0.378015	+	0.238966i
$846$		0			0
$847$	−6.81621	−	11.8060i	−0.234208	−	0.405660i
$848$	−0.833676	−	1.44397i	−0.0286286	−	0.0495861i
$849$		0			0
$850$	3.08744			0.105898
$851$	0.839551	−	1.45415i	0.0287794	−	0.0498475i
$852$		0			0
$853$	6.90807			0.236528			0.118264	−	0.992982i	$-0.462267\pi$
$853$	6.90807			0.236528			0.118264	+	0.992982i	$0.462267\pi$
$854$	−4.92506	+	8.53045i	−0.168532	+	0.291906i
$855$		0			0
$856$	−16.1736	−	28.0135i	−0.552803	−	0.957483i
$857$	29.6052			1.01129			0.505646	−	0.862741i	$-0.331254\pi$
$857$	29.6052			1.01129			0.505646	+	0.862741i	$0.331254\pi$
$858$		0			0
$859$	−51.0371			−1.74136			−0.870681	−	0.491848i	$-0.836322\pi$
$859$	−51.0371			−1.74136			−0.870681	+	0.491848i	$0.836322\pi$
$860$	0.698691	+	1.21017i	0.0238252	+	0.0412664i
$861$		0			0
$862$	6.95403	−	12.0447i	0.236855	−	0.410245i
$863$	22.2757			0.758272			0.379136	−	0.925341i	$-0.376221\pi$
$863$	22.2757			0.758272			0.379136	+	0.925341i	$0.376221\pi$
$864$		0			0
$865$	6.20274	−	10.7435i	0.210900	−	0.365289i
$866$	18.4771			0.627879
$867$		0			0
$868$	2.29500	+	3.97506i	0.0778974	+	0.134922i
$869$	5.86082	+	10.1512i	0.198815	+	0.344357i
$870$		0			0
$871$	8.19792	+	33.2501i	0.277776	+	1.12664i
$872$	54.5498			1.84729
$873$		0			0
$874$	4.31560	+	7.47484i	0.145977	+	0.252840i
$875$	0.781529	−	1.35365i	0.0264205	−	0.0457616i
$876$		0			0
$877$	−6.99768	+	12.1203i	−0.236295	+	0.409275i	−0.959648	−	0.281203i	$-0.909266\pi$
$877$	−6.99768	+	12.1203i	−0.236295	+	0.409275i	0.723353	+	0.690478i	$0.242600\pi$
$878$	14.3923	−	24.9282i	0.485717	−	0.841287i
$879$		0			0
$880$	−0.431343	+	0.747108i	−0.0145406	+	0.0251850i
$881$	−27.8497	−	48.2370i	−0.938279	−	1.62515i	−0.768679	−	0.639634i	$-0.779086\pi$
$881$	−27.8497	−	48.2370i	−0.938279	−	1.62515i	−0.169600	−	0.985513i	$-0.554248\pi$
$882$		0			0
$883$	35.1425			1.18264			0.591320	−	0.806437i	$-0.298607\pi$
$883$	35.1425			1.18264			0.591320	+	0.806437i	$0.298607\pi$
$884$	3.10979	+	12.6131i	0.104594	+	0.424223i
$885$		0			0
$886$	−4.18105	−	7.24180i	−0.140465	−	0.243293i
$887$	18.2086	+	31.5383i	0.611386	+	1.05895i	0.991007	+	0.133809i	$0.0427209\pi$
$887$	18.2086	+	31.5383i	0.611386	+	1.05895i	−0.379622	+	0.925142i	$0.623946\pi$
$888$		0			0
$889$	11.8855			0.398627
$890$	0.377039	−	0.653051i	0.0126384	−	0.0218903i
$891$		0			0
$892$	7.04230			0.235794
$893$	7.96989	−	13.8043i	0.266702	−	0.461942i
$894$		0			0
$895$	−4.58176	−	7.93585i	−0.153152	−	0.265266i
$896$	−7.51841			−0.251172
$897$		0			0
$898$	−19.9876			−0.666994
$899$	−3.46377	−	5.99942i	−0.115523	−	0.200092i
$900$		0			0
$901$	−4.75878	+	8.24245i	−0.158538	+	0.274596i
$902$	−8.12513			−0.270537
$903$		0			0
$904$	−19.1595	+	33.1852i	−0.637234	+	1.10372i
$905$	−4.71081			−0.156593
$906$		0			0
$907$	−10.9265	−	18.9253i	−0.362809	−	0.628403i	0.625613	−	0.780133i	$-0.284849\pi$
$907$	−10.9265	−	18.9253i	−0.362809	−	0.628403i	−0.988422	+	0.151730i	$0.951516\pi$
$908$	7.42739	+	12.8646i	0.246487	+	0.426927i
$909$		0			0
$910$	−5.12295	−	1.48349i	−0.169824	−	0.0491770i
$911$	10.6483			0.352794			0.176397	−	0.984319i	$-0.443556\pi$
$911$	10.6483			0.352794			0.176397	+	0.984319i	$0.443556\pi$
$912$		0			0
$913$	−8.47635	−	14.6815i	−0.280526	−	0.485886i
$914$	18.6521	−	32.3064i	0.616957	−	1.06860i
$915$		0			0
$916$	−5.05002	+	8.74689i	−0.166857	+	0.289005i
$917$	−14.8750	+	25.7642i	−0.491216	+	0.850810i
$918$		0			0
$919$	23.9865	−	41.5459i	0.791243	−	1.37047i	−0.133955	−	0.990987i	$-0.542768\pi$
$919$	23.9865	−	41.5459i	0.791243	−	1.37047i	0.925198	−	0.379485i	$-0.123899\pi$
$920$	4.31560	+	7.47484i	0.142281	+	0.246438i
$921$		0			0
$922$	0.401405			0.0132196
$923$	3.17254	−	3.04770i	0.104426	−	0.100316i
$924$		0			0
$925$	−0.285767	−	0.494963i	−0.00939595	−	0.0162743i
$926$	14.2669	+	24.7110i	0.468839	+	0.812054i
$927$		0			0
$928$	13.8992			0.456265
$929$	6.61228	−	11.4528i	0.216942	−	0.375754i	−0.736930	−	0.675969i	$-0.763725\pi$
$929$	6.61228	−	11.4528i	0.216942	−	0.375754i	0.953872	+	0.300215i	$0.0970585\pi$
$930$		0			0
$931$	14.1462			0.463625
$932$	12.2397	−	21.1998i	0.400925	−	0.694423i
$933$		0			0
$934$	−3.81874	−	6.61426i	−0.124953	−	0.216425i
$935$	4.92437			0.161044
$936$		0			0
$937$	46.3689			1.51481			0.757403	−	0.652948i	$-0.226468\pi$
$937$	46.3689			1.51481			0.757403	+	0.652948i	$0.226468\pi$
$938$	−7.02489	−	12.1675i	−0.229371	−	0.397282i
$939$		0			0
$940$	2.83530	−	4.91089i	0.0924773	−	0.160175i
$941$	13.3676			0.435772			0.217886	−	0.975974i	$-0.430084\pi$
$941$	13.3676			0.435772			0.217886	+	0.975974i	$0.430084\pi$
$942$		0			0
$943$	−8.35537	+	14.4719i	−0.272088	+	0.471271i
$944$	−7.32370			−0.238366
$945$		0			0
$946$	−0.903716	−	1.56528i	−0.0293823	−	0.0508917i
$947$	−20.3814	−	35.3017i	−0.662307	−	1.14715i	−0.980008	−	0.198959i	$-0.936244\pi$
$947$	−20.3814	−	35.3017i	−0.662307	−	1.14715i	0.317700	−	0.948191i	$-0.397089\pi$
$948$		0			0
$949$	44.6017	+	12.9156i	1.44783	+	0.419258i
$950$	2.93789			0.0953177
$951$		0			0
$952$	−7.49066	−	12.9742i	−0.242774	−	0.420497i
$953$	−24.3152	+	42.1151i	−0.787645	+	1.36424i	0.139760	+	0.990185i	$0.455367\pi$
$953$	−24.3152	+	42.1151i	−0.787645	+	1.36424i	−0.927406	+	0.374057i	$0.877967\pi$
$954$		0			0
$955$	−7.57528	+	13.1208i	−0.245130	+	0.424578i
$956$	9.71533	−	16.8274i	0.314216	−	0.544239i
$957$		0			0
$958$	17.6099	−	30.5012i	0.568950	−	0.985450i
$959$	14.9025	+	25.8120i	0.481228	+	0.833511i
$960$		0			0
$961$	−23.9299			−0.771931
$962$	−1.40637	+	1.35103i	−0.0453432	+	0.0435590i
$963$		0			0
$964$	15.5379	+	26.9125i	0.500443	+	0.866792i
$965$	−5.14501	−	8.91142i	−0.165624	−	0.286869i
$966$		0			0
$967$	−36.5694			−1.17599			−0.587996	−	0.808864i	$-0.700083\pi$
$967$	−36.5694			−1.17599			−0.587996	+	0.808864i	$0.700083\pi$
$968$	12.8116	−	22.1904i	0.411781	−	0.713225i
$969$		0			0
$970$	5.48932			0.176251
$971$	−24.8685	+	43.0735i	−0.798068	+	1.38229i	0.122805	+	0.992431i	$0.460811\pi$
$971$	−24.8685	+	43.0735i	−0.798068	+	1.38229i	−0.920873	+	0.389863i	$0.872522\pi$
$972$		0			0
$973$	−11.5894	−	20.0734i	−0.371538	−	0.643522i
$974$	10.8427			0.347423
$975$		0			0
$976$	−3.80583			−0.121822
$977$	−9.50095	−	16.4561i	−0.303962	−	0.526478i	0.673067	−	0.739581i	$-0.264976\pi$
$977$	−9.50095	−	16.4561i	−0.303962	−	0.526478i	−0.977030	+	0.213103i	$0.931643\pi$
$978$		0			0
$979$	0.601365	−	1.04160i	0.0192197	−	0.0332895i
$980$	5.03255			0.160759
$981$		0			0
$982$	9.98600	−	17.2963i	0.318666	−	0.551946i
$983$	−3.16020			−0.100795			−0.0503974	−	0.998729i	$-0.516049\pi$
$983$	−3.16020			−0.100795			−0.0503974	+	0.998729i	$0.516049\pi$
$984$		0			0
$985$	2.59506	+	4.49478i	0.0826855	+	0.143216i
$986$	4.02192	+	6.96616i	0.128084	+	0.221848i
$987$		0			0
$988$	2.95916	+	12.0021i	0.0941434	+	0.381838i
$989$	−3.71730			−0.118203
$990$		0			0
$991$	7.75746	+	13.4363i	0.246424	+	0.426819i	0.962531	−	0.271172i	$-0.0874111\pi$
$991$	7.75746	+	13.4363i	0.246424	+	0.426819i	−0.716107	+	0.697990i	$0.754078\pi$
$992$	−7.09268	+	12.2849i	−0.225193	+	0.390045i
$993$		0			0
$994$	−0.902428	+	1.56305i	−0.0286233	+	0.0495770i
$995$	6.30890	−	10.9273i	0.200005	−	0.346420i
$996$		0			0
$997$	−8.40480	+	14.5575i	−0.266183	+	0.461042i	−0.967873	−	0.251440i	$-0.919096\pi$
$997$	−8.40480	+	14.5575i	−0.266183	+	0.461042i	0.701690	+	0.712482i	$0.252429\pi$
$998$	−9.45893	−	16.3834i	−0.299417	−	0.518606i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.h.406.4	✓	10
3.2	odd	2		585.2.j.i.406.2	yes	10
13.3	even	3		7605.2.a.co.1.2		5
13.9	even	3	inner	585.2.j.h.451.4	yes	10
13.10	even	6		7605.2.a.cl.1.4		5
39.23	odd	6		7605.2.a.cn.1.2		5
39.29	odd	6		7605.2.a.cm.1.4		5
39.35	odd	6		585.2.j.i.451.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.j.h.406.4	✓	10	1.1	even	1	trivial
585.2.j.h.451.4	yes	10	13.9	even	3	inner
585.2.j.i.406.2	yes	10	3.2	odd	2
585.2.j.i.451.2	yes	10	39.35	odd	6
7605.2.a.cl.1.4		5	13.10	even	6
7605.2.a.cm.1.4		5	39.29	odd	6
7605.2.a.cn.1.2		5	39.23	odd	6
7605.2.a.co.1.2		5	13.3	even	3

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)

\(f(q)\)	\(=\)	\(q+(0.473183 + 0.819577i) q^{2} +(0.552196 - 0.956432i) q^{4} +1.00000 q^{5} +(0.781529 - 1.35365i) q^{7} +2.93789 q^{8} +O(q^{10})\)	\(q+(0.473183 + 0.819577i) q^{2} +(0.552196 - 0.956432i) q^{4} +1.00000 q^{5} +(0.781529 - 1.35365i) q^{7} +2.93789 q^{8} +(0.473183 + 0.819577i) q^{10} +(0.754712 + 1.30720i) q^{11} +(-3.46327 - 1.00288i) q^{13} +1.47922 q^{14} +(0.285767 + 0.494963i) q^{16} +(1.63121 - 2.82534i) q^{17} +(1.55220 - 2.68848i) q^{19} +(0.552196 - 0.956432i) q^{20} +(-0.714233 + 1.23709i) q^{22} +(1.46894 + 2.54429i) q^{23} +1.00000 q^{25} +(-0.816822 - 3.31296i) q^{26} +(-0.863114 - 1.49496i) q^{28} +(1.30267 + 2.25629i) q^{29} -2.65897 q^{31} +(2.66745 - 4.62016i) q^{32} +3.08744 q^{34} +(0.781529 - 1.35365i) q^{35} +(-0.285767 - 0.494963i) q^{37} +2.93789 q^{38} +2.93789 q^{40} +(2.84400 + 4.92596i) q^{41} +(-0.632648 + 1.09578i) q^{43} +1.66700 q^{44} +(-1.39016 + 2.40783i) q^{46} +5.13459 q^{47} +(2.27843 + 3.94635i) q^{49} +(0.473183 + 0.819577i) q^{50} +(-2.87159 + 2.75859i) q^{52} -2.91733 q^{53} +(0.754712 + 1.30720i) q^{55} +(2.29605 - 3.97687i) q^{56} +(-1.23280 + 2.13528i) q^{58} +(-6.40706 + 11.0974i) q^{59} +(-3.32949 + 5.76684i) q^{61} +(-1.25818 - 2.17923i) q^{62} +6.19183 q^{64} +(-3.46327 - 1.00288i) q^{65} +(-4.74904 - 8.22557i) q^{67} +(-1.80149 - 3.12028i) q^{68} +1.47922 q^{70} +(-0.610068 + 1.05667i) q^{71} -12.8785 q^{73} +(0.270440 - 0.468416i) q^{74} +(-1.71423 - 2.96914i) q^{76} +2.35932 q^{77} +7.76563 q^{79} +(0.285767 + 0.494963i) q^{80} +(-2.69147 + 4.66176i) q^{82} -11.2312 q^{83} +(1.63121 - 2.82534i) q^{85} -1.19743 q^{86} +(2.21726 + 3.84041i) q^{88} +(-0.398407 - 0.690062i) q^{89} +(-4.06419 + 3.90427i) q^{91} +3.24458 q^{92} +(2.42960 + 4.20819i) q^{94} +(1.55220 - 2.68848i) q^{95} +(2.90021 - 5.02331i) q^{97} +(-2.15622 + 3.73469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8	\( 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8} - 2 q^{10} - 8 q^{11} + q^{13} - 8 q^{14} - 4 q^{16} + 4 q^{19} - 6 q^{20} - 14 q^{22} + 6 q^{23} + 10 q^{25} - 10 q^{26} + 2 q^{28} - 16 q^{29} + 18 q^{31} - 14 q^{32} - q^{35} + 4 q^{37} + 12 q^{38} + 12 q^{40} - 6 q^{41} - 15 q^{43} + 28 q^{44} + 16 q^{46} + 20 q^{47} - 10 q^{49} - 2 q^{50} - 22 q^{52} - 40 q^{53} - 8 q^{55} + 2 q^{56} + 4 q^{58} - 12 q^{59} - 11 q^{61} + 22 q^{62} + 8 q^{64} + q^{65} - 5 q^{67} - 50 q^{68} - 8 q^{70} - 10 q^{71} + 2 q^{73} + 26 q^{74} - 24 q^{76} + 84 q^{77} - 34 q^{79} - 4 q^{80} - 16 q^{82} + 32 q^{83} + 88 q^{86} - 20 q^{88} - 4 q^{89} - q^{91} - 68 q^{92} + 16 q^{94} + 4 q^{95} + 11 q^{97} - 30 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8 - 2 * q^10 - 8 * q^11 + q^13 - 8 * q^14 - 4 * q^16 + 4 * q^19 - 6 * q^20 - 14 * q^22 + 6 * q^23 + 10 * q^25 - 10 * q^26 + 2 * q^28 - 16 * q^29 + 18 * q^31 - 14 * q^32 - q^35 + 4 * q^37 + 12 * q^38 + 12 * q^40 - 6 * q^41 - 15 * q^43 + 28 * q^44 + 16 * q^46 + 20 * q^47 - 10 * q^49 - 2 * q^50 - 22 * q^52 - 40 * q^53 - 8 * q^55 + 2 * q^56 + 4 * q^58 - 12 * q^59 - 11 * q^61 + 22 * q^62 + 8 * q^64 + q^65 - 5 * q^67 - 50 * q^68 - 8 * q^70 - 10 * q^71 + 2 * q^73 + 26 * q^74 - 24 * q^76 + 84 * q^77 - 34 * q^79 - 4 * q^80 - 16 * q^82 + 32 * q^83 + 88 * q^86 - 20 * q^88 - 4 * q^89 - q^91 - 68 * q^92 + 16 * q^94 + 4 * q^95 + 11 * q^97 - 30 * q^98

Introduction

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