LMFDB - Embedded newform 585.2.bu.c.316.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(316,585)]

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, 1]))

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

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

chi := DirichletCharacter("585.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bu (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.1
Root			$0.665665 - 1.24775i$ of defining polynomial
Character	$\chi$	$=$	585.316
Dual form			585.2.bu.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29515 - 0.747754i) q^{2} +(0.118272 + 0.204852i) q^{4} +1.00000i q^{5} +(-4.18016 + 2.41342i) q^{7} +2.63726i q^{8} +O(q^{10})$	\(q+(-1.29515 - 0.747754i) q^{2} +(0.118272 + 0.204852i) q^{4} +1.00000i q^{5} +(-4.18016 + 2.41342i) q^{7} +2.63726i q^{8} +(0.747754 - 1.29515i) q^{10} +(0.926118 + 0.534695i) q^{11} +(0.331331 - 3.59030i) q^{13} +7.21857 q^{14} +(2.20857 - 3.82535i) q^{16} +(-1.77944 - 3.08209i) q^{17} +(4.96410 - 2.86603i) q^{19} +(-0.204852 + 0.118272i) q^{20} +(-0.799640 - 1.38502i) q^{22} +(3.54290 - 6.13649i) q^{23} -1.00000 q^{25} +(-3.11378 + 4.40221i) q^{26} +(-0.988789 - 0.570878i) q^{28} +(0.736543 - 1.27573i) q^{29} -1.46410i q^{31} +(-1.15297 + 0.665665i) q^{32} +5.32235i q^{34} +(-2.41342 - 4.18016i) q^{35} +(-0.0219955 - 0.0126991i) q^{37} -8.57233 q^{38} -2.63726 q^{40} +(0.232051 + 0.133975i) q^{41} +(1.77944 + 3.08209i) q^{43} +0.252957i q^{44} +(-9.17716 + 5.29844i) q^{46} +6.51793i q^{47} +(8.14918 - 14.1148i) q^{49} +(1.29515 + 0.747754i) q^{50} +(0.774668 - 0.356756i) q^{52} -0.991015 q^{53} +(-0.534695 + 0.926118i) q^{55} +(-6.36482 - 11.0242i) q^{56} +(-1.90786 + 1.10151i) q^{58} +(7.55440 - 4.36153i) q^{59} +(-3.16867 - 5.48830i) q^{61} +(-1.09479 + 1.89623i) q^{62} -6.84325 q^{64} +(3.59030 + 0.331331i) q^{65} +(-4.48009 - 2.58658i) q^{67} +(0.420915 - 0.729047i) q^{68} +7.21857i q^{70} +(6.72458 - 3.88244i) q^{71} -10.1088i q^{73} +(0.0189916 + 0.0328945i) q^{74} +(1.17422 + 0.677939i) q^{76} -5.16177 q^{77} +8.78347 q^{79} +(3.82535 + 2.20857i) q^{80} +(-0.200360 - 0.347034i) q^{82} +0.725474i q^{83} +(3.08209 - 1.77944i) q^{85} -5.32235i q^{86} +(-1.41013 + 2.44242i) q^{88} +(-11.6970 - 6.75327i) q^{89} +(7.27987 + 15.8077i) q^{91} +1.67610 q^{92} +(4.87381 - 8.44168i) q^{94} +(2.86603 + 4.96410i) q^{95} +(-2.97800 + 1.71935i) q^{97} +(-21.1088 + 12.1872i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) $ 8 * q + 2 * q^4 - 6 * q^7	$ 8 q + 2 q^{4} - 6 q^{7} - 2 q^{10} - 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} - 12 q^{20} - 12 q^{22} + 10 q^{23} - 8 q^{25} - 10 q^{26} - 18 q^{28} + 8 q^{29} - 6 q^{32} - 10 q^{35} + 6 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} - 2 q^{43} - 42 q^{46} + 12 q^{49} - 6 q^{52} + 24 q^{53} - 12 q^{56} + 36 q^{58} + 12 q^{59} - 28 q^{61} - 4 q^{62} - 8 q^{64} + 8 q^{65} + 6 q^{67} + 14 q^{68} - 10 q^{74} + 54 q^{76} + 36 q^{77} - 16 q^{79} + 4 q^{82} + 18 q^{85} - 18 q^{88} - 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 16 q^{95} - 30 q^{97} - 72 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 - 6 * q^7 - 2 * q^10 - 4 * q^14 - 2 * q^16 + 2 * q^17 + 12 * q^19 - 12 * q^20 - 12 * q^22 + 10 * q^23 - 8 * q^25 - 10 * q^26 - 18 * q^28 + 8 * q^29 - 6 * q^32 - 10 * q^35 + 6 * q^37 + 16 * q^38 - 12 * q^40 - 12 * q^41 - 2 * q^43 - 42 * q^46 + 12 * q^49 - 6 * q^52 + 24 * q^53 - 12 * q^56 + 36 * q^58 + 12 * q^59 - 28 * q^61 - 4 * q^62 - 8 * q^64 + 8 * q^65 + 6 * q^67 + 14 * q^68 - 10 * q^74 + 54 * q^76 + 36 * q^77 - 16 * q^79 + 4 * q^82 + 18 * q^85 - 18 * q^88 - 24 * q^89 + 28 * q^91 - 44 * q^92 + 32 * q^94 + 16 * q^95 - 30 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.29515	−	0.747754i	−0.915808	−	0.528742i	−0.0335125	−	0.999438i	$-0.510669\pi$
$2$	−1.29515	−	0.747754i	−0.915808	−	0.528742i	−0.882295	+	0.470696i	$0.844003\pi$
$3$		0			0
$3$		0			0
$4$	0.118272	+	0.204852i	0.0591358	+	0.102426i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−4.18016	+	2.41342i	−1.57995	+	0.912187i	−0.585089	+	0.810969i	$0.698941\pi$
$7$	−4.18016	+	2.41342i	−1.57995	+	0.912187i	−0.994864	+	0.101218i	$0.967726\pi$
$8$			2.63726i			0.932413i
$9$		0			0
$10$	0.747754	−	1.29515i	0.236461	−	0.409562i
$11$	0.926118	+	0.534695i	0.279235	+	0.161217i	0.633077	−	0.774089i	$-0.281792\pi$
$11$	0.926118	+	0.534695i	0.279235	+	0.161217i	−0.353842	+	0.935305i	$0.615125\pi$
$12$		0			0
$13$	0.331331	−	3.59030i	0.0918946	−	0.995769i
$13$	0.331331	−	3.59030i	0.0918946	−	0.995769i
$14$	7.21857			1.92924
$15$		0			0
$16$	2.20857	−	3.82535i	0.552142	−	0.956337i
$17$	−1.77944	−	3.08209i	−0.431579	−	0.747516i	0.565431	−	0.824796i	$-0.308710\pi$
$17$	−1.77944	−	3.08209i	−0.431579	−	0.747516i	−0.997009	+	0.0772795i	$0.975377\pi$
$18$		0			0
$19$	4.96410	−	2.86603i	1.13884	−	0.657511i	0.192699	−	0.981258i	$-0.438276\pi$
$19$	4.96410	−	2.86603i	1.13884	−	0.657511i	0.946144	+	0.323747i	$0.104943\pi$
$20$	−0.204852	+	0.118272i	−0.0458064	+	0.0264463i
$21$		0			0
$22$	−0.799640	−	1.38502i	−0.170484	−	0.295287i
$23$	3.54290	−	6.13649i	0.738746	−	1.27955i	−0.214314	−	0.976765i	$-0.568752\pi$
$23$	3.54290	−	6.13649i	0.738746	−	1.27955i	0.953060	−	0.302781i	$-0.0979150\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−3.11378	+	4.40221i	−0.610662	+	0.863344i
$27$		0			0
$28$	−0.988789	−	0.570878i	−0.186864	−	0.107886i
$29$	0.736543	−	1.27573i	0.136773	−	0.236897i	−0.789501	−	0.613750i	$-0.789660\pi$
$29$	0.736543	−	1.27573i	0.136773	−	0.236897i	0.926273	+	0.376853i	$0.122994\pi$
$30$		0			0
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$	−1.15297	+	0.665665i	−0.203818	+	0.117674i
$33$		0			0
$34$			5.32235i			0.912775i
$35$	−2.41342	−	4.18016i	−0.407942	−	0.706577i
$36$		0			0
$37$	−0.0219955	−	0.0126991i	−0.00361604	−	0.00208772i	0.498191	−	0.867067i	$-0.333998\pi$
$37$	−0.0219955	−	0.0126991i	−0.00361604	−	0.00208772i	−0.501807	+	0.864980i	$0.667331\pi$
$38$	−8.57233			−1.39061
$39$		0			0
$40$	−2.63726			−0.416988
$41$	0.232051	+	0.133975i	0.0362402	+	0.0209233i	0.518011	−	0.855374i	$-0.326673\pi$
$41$	0.232051	+	0.133975i	0.0362402	+	0.0209233i	−0.481770	+	0.876297i	$0.660006\pi$
$42$		0			0
$43$	1.77944	+	3.08209i	0.271363	+	0.470014i	0.969211	−	0.246232i	$-0.0791924\pi$
$43$	1.77944	+	3.08209i	0.271363	+	0.470014i	−0.697848	+	0.716246i	$0.745859\pi$
$44$			0.252957i			0.0381347i
$45$		0			0
$46$	−9.17716	+	5.29844i	−1.35310	+	0.781212i
$47$			6.51793i			0.950738i	0.879787	+	0.475369i	$0.157685\pi$
$47$			6.51793i			0.950738i	−0.879787	+	0.475369i	$0.842315\pi$
$48$		0			0
$49$	8.14918	−	14.1148i	1.16417	−	2.01640i
$50$	1.29515	+	0.747754i	0.183162	+	0.105748i
$51$		0			0
$52$	0.774668	−	0.356756i	0.107427	−	0.0494732i
$53$	−0.991015			−0.136126			−0.0680632	−	0.997681i	$-0.521682\pi$
$53$	−0.991015			−0.136126			−0.0680632	+	0.997681i	$0.521682\pi$
$54$		0			0
$55$	−0.534695	+	0.926118i	−0.0720982	+	0.124878i
$56$	−6.36482	−	11.0242i	−0.850535	−	1.47317i
$57$		0			0
$58$	−1.90786	+	1.10151i	−0.250515	+	0.144635i
$59$	7.55440	−	4.36153i	0.983499	−	0.567823i	0.0801741	−	0.996781i	$-0.474452\pi$
$59$	7.55440	−	4.36153i	0.983499	−	0.567823i	0.903325	+	0.428958i	$0.141119\pi$
$60$		0			0
$61$	−3.16867	−	5.48830i	−0.405707	−	0.702704i	0.588697	−	0.808354i	$-0.299641\pi$
$61$	−3.16867	−	5.48830i	−0.405707	−	0.702704i	−0.994403	+	0.105650i	$0.966308\pi$
$62$	−1.09479	+	1.89623i	−0.139038	+	0.240821i
$63$		0			0
$64$	−6.84325			−0.855406
$65$	3.59030	+	0.331331i	0.445321	+	0.0410965i
$66$		0			0
$67$	−4.48009	−	2.58658i	−0.547330	−	0.316001i	0.200714	−	0.979650i	$-0.435674\pi$
$67$	−4.48009	−	2.58658i	−0.547330	−	0.316001i	−0.748044	+	0.663649i	$0.769007\pi$
$68$	0.420915	−	0.729047i	0.0510435	−	0.0884099i
$69$		0			0
$70$			7.21857i			0.862785i
$71$	6.72458	−	3.88244i	0.798061	−	0.460761i	−0.0447317	−	0.998999i	$-0.514243\pi$
$71$	6.72458	−	3.88244i	0.798061	−	0.460761i	0.842793	+	0.538238i	$0.180910\pi$
$72$		0			0
$73$		−	10.1088i		−	1.18314i	−0.806252	−	0.591572i	$-0.798507\pi$
$73$		−	10.1088i		−	1.18314i	0.806252	−	0.591572i	$-0.201493\pi$
$74$	0.0189916	+	0.0328945i	0.00220773	+	0.00382391i
$75$		0			0
$76$	1.17422	+	0.677939i	0.134693	+	0.0777649i
$77$	−5.16177			−0.588238
$78$		0			0
$79$	8.78347			0.988218			0.494109	−	0.869400i	$-0.335494\pi$
$79$	8.78347			0.988218			0.494109	+	0.869400i	$0.335494\pi$
$80$	3.82535	+	2.20857i	0.427687	+	0.246925i
$81$		0			0
$82$	−0.200360	−	0.347034i	−0.0221261	−	0.0383235i
$83$			0.725474i			0.0796311i	0.999207	+	0.0398155i	$0.0126770\pi$
$83$			0.725474i			0.0796311i	−0.999207	+	0.0398155i	$0.987323\pi$
$84$		0			0
$85$	3.08209	−	1.77944i	0.334299	−	0.193008i
$86$		−	5.32235i		−	0.573923i
$87$		0			0
$88$	−1.41013	+	2.44242i	−0.150320	+	0.260363i
$89$	−11.6970	−	6.75327i	−1.23988	−	0.715845i	−0.270810	−	0.962633i	$-0.587292\pi$
$89$	−11.6970	−	6.75327i	−1.23988	−	0.715845i	−0.969070	+	0.246788i	$0.920625\pi$
$90$		0			0
$91$	7.27987	+	15.8077i	0.763138	+	1.65709i
$92$	1.67610			0.174745
$93$		0			0
$94$	4.87381	−	8.44168i	0.502695	−	0.870693i
$95$	2.86603	+	4.96410i	0.294048	+	0.509306i
$96$		0			0
$97$	−2.97800	+	1.71935i	−0.302371	+	0.174574i	−0.643507	−	0.765440i	$-0.722521\pi$
$97$	−2.97800	+	1.71935i	−0.302371	+	0.174574i	0.341137	+	0.940014i	$0.389188\pi$
$98$	−21.1088	+	12.1872i	−2.13231	+	1.23109i
$99$		0			0
$100$	−0.118272	−	0.204852i	−0.0118272	−	0.0204852i
$101$	−1.42763	+	2.47273i	−0.142055	+	0.246046i	−0.928270	−	0.371906i	$-0.878704\pi$
$101$	−1.42763	+	2.47273i	−0.142055	+	0.246046i	0.786215	+	0.617953i	$0.212038\pi$
$102$		0			0
$103$	5.54488			0.546354			0.273177	−	0.961964i	$-0.411926\pi$
$103$	5.54488			0.546354			0.273177	+	0.961964i	$0.411926\pi$
$104$	9.46855	+	0.873806i	0.928468	+	0.0856838i
$105$		0			0
$106$	1.28351	+	0.741035i	0.124666	+	0.0719757i
$107$	−2.22056	+	3.84611i	−0.214669	+	0.371818i	−0.953170	−	0.302434i	$-0.902201\pi$
$107$	−2.22056	+	3.84611i	−0.214669	+	0.371818i	0.738501	+	0.674252i	$0.235534\pi$
$108$		0			0
$109$			13.7804i			1.31993i	0.751298	+	0.659963i	$0.229428\pi$
$109$			13.7804i			1.31993i	−0.751298	+	0.659963i	$0.770572\pi$
$110$	1.38502	−	0.799640i	0.132056	−	0.0762427i
$111$		0			0
$112$			21.3208i			2.01463i
$113$	−4.02200	−	6.96630i	−0.378358	−	0.655334i	0.612466	−	0.790497i	$-0.290178\pi$
$113$	−4.02200	−	6.96630i	−0.378358	−	0.655334i	−0.990823	+	0.135163i	$0.956844\pi$
$114$		0			0
$115$	6.13649	+	3.54290i	0.572230	+	0.330377i
$116$	0.348448			0.0323526
$117$		0			0
$118$	−13.0454			−1.20093
$119$	14.8767	+	8.58909i	1.36375	+	0.787361i
$120$		0			0
$121$	−4.92820	−	8.53590i	−0.448018	−	0.775991i
$122$			9.47754i			0.858056i
$123$		0			0
$124$	0.299925	−	0.173162i	0.0269340	−	0.0155504i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	0.353326	−	0.611979i	0.0313526	−	0.0543044i	−0.849923	−	0.526906i	$-0.823352\pi$
$127$	0.353326	−	0.611979i	0.0313526	−	0.0543044i	0.881276	+	0.472602i	$0.156685\pi$
$128$	11.1690	+	6.44840i	0.987205	+	0.569963i
$129$		0			0
$130$	−4.40221	−	3.11378i	−0.386099	−	0.273097i
$131$	−6.26554			−0.547423			−0.273711	−	0.961812i	$-0.588251\pi$
$131$	−6.26554			−0.547423			−0.273711	+	0.961812i	$0.588251\pi$
$132$		0			0
$133$	−13.8338	+	23.9609i	−1.19955	+	2.07767i
$134$	3.86825	+	6.70001i	0.334166	+	0.578793i
$135$		0			0
$136$	8.12828	−	4.69286i	0.696994	−	0.402410i
$137$	14.1212	−	8.15290i	1.20646	−	0.696549i	0.244475	−	0.969656i	$-0.421384\pi$
$137$	14.1212	−	8.15290i	1.20646	−	0.696549i	0.961984	+	0.273107i	$0.0880511\pi$
$138$		0			0
$139$	3.41264	+	5.91087i	0.289456	+	0.501353i	0.973680	−	0.227919i	$-0.0731921\pi$
$139$	3.41264	+	5.91087i	0.289456	+	0.501353i	−0.684224	+	0.729272i	$0.739859\pi$
$140$	0.570878	−	0.988789i	0.0482480	−	0.0835680i
$141$		0			0
$142$	−11.6124			−0.974494
$143$	2.22656	−	3.14788i	0.186195	−	0.263239i
$144$		0			0
$145$	1.27573	+	0.736543i	0.105944	+	0.0611666i
$146$	−7.55889	+	13.0924i	−0.625578	+	1.08353i
$147$		0			0
$148$		−	0.00600778i		−	0.000493837i
$149$	7.30887	−	4.21978i	0.598766	−	0.345698i	−0.169790	−	0.985480i	$-0.554309\pi$
$149$	7.30887	−	4.21978i	0.598766	−	0.345698i	0.768556	+	0.639783i	$0.220976\pi$
$150$		0			0
$151$			1.37017i			0.111503i	0.998445	+	0.0557513i	$0.0177554\pi$
$151$			1.37017i			0.111503i	−0.998445	+	0.0557513i	$0.982245\pi$
$152$	7.55846	+	13.0916i	0.613072	+	1.06187i
$153$		0			0
$154$	6.68525	+	3.85973i	0.538713	+	0.311026i
$155$	1.46410			0.117599
$156$		0			0
$157$	11.9700			0.955311			0.477656	−	0.878547i	$-0.341487\pi$
$157$	11.9700			0.955311			0.477656	+	0.878547i	$0.341487\pi$
$158$	−11.3759	−	6.56787i	−0.905017	−	0.522512i
$159$		0			0
$160$	−0.665665	−	1.15297i	−0.0526255	−	0.0911500i
$161$			34.2020i			2.69550i
$162$		0			0
$163$	19.5474	−	11.2857i	1.53107	−	0.883962i	0.531754	−	0.846899i	$-0.321533\pi$
$163$	19.5474	−	11.2857i	1.53107	−	0.883962i	0.999313	−	0.0370630i	$-0.0118002\pi$
$164$			0.0633815i			0.00494927i
$165$		0			0
$166$	0.542476	−	0.939595i	0.0421043	−	0.0729267i
$167$	−7.09881	−	4.09850i	−0.549323	−	0.317152i	0.199526	−	0.979893i	$-0.436060\pi$
$167$	−7.09881	−	4.09850i	−0.549323	−	0.317152i	−0.748849	+	0.662741i	$0.769393\pi$
$168$		0			0
$169$	−12.7804	−	2.37915i	−0.983111	−	0.183012i
$170$	−5.32235			−0.408205
$171$		0			0
$172$	−0.420915	+	0.729047i	−0.0320945	+	0.0555893i
$173$	4.58386	+	7.93948i	0.348505	+	0.603628i	0.985984	−	0.166840i	$-0.0533563\pi$
$173$	4.58386	+	7.93948i	0.348505	+	0.603628i	−0.637479	+	0.770467i	$0.720023\pi$
$174$		0			0
$175$	4.18016	−	2.41342i	0.315991	−	0.182437i
$176$	4.09079	−	2.36182i	0.308355	−	0.178029i
$177$		0			0
$178$	10.0996	+	17.4930i	0.756994	+	1.31115i
$179$	5.01850	−	8.69229i	0.375100	−	0.649693i	−0.615242	−	0.788338i	$-0.710942\pi$
$179$	5.01850	−	8.69229i	0.375100	−	0.649693i	0.990342	+	0.138646i	$0.0442750\pi$
$180$		0			0
$181$	−17.0238			−1.26537			−0.632686	−	0.774408i	$-0.718048\pi$
$181$	−17.0238			−1.26537			−0.632686	+	0.774408i	$0.718048\pi$
$182$	2.39174	−	25.9168i	0.177287	−	1.92108i
$183$		0			0
$184$	16.1835	+	9.34356i	1.19307	+	0.688817i
$185$	0.0126991	−	0.0219955i	0.000933659	−	0.00161714i
$186$		0			0
$187$		−	3.80584i		−	0.278310i
$188$	−1.33521	+	0.770886i	−0.0973804	+	0.0562226i
$189$		0			0
$190$		−	8.57233i		−	0.621902i
$191$	−1.93870	−	3.35793i	−0.140280	−	0.242971i	0.787322	−	0.616542i	$-0.211467\pi$
$191$	−1.93870	−	3.35793i	−0.140280	−	0.242971i	−0.927602	+	0.373570i	$0.878133\pi$
$192$		0			0
$193$	1.08595	+	0.626972i	0.0781681	+	0.0451304i	0.538575	−	0.842578i	$-0.318963\pi$
$193$	1.08595	+	0.626972i	0.0781681	+	0.0451304i	−0.460406	+	0.887708i	$0.652296\pi$
$194$	5.14261			0.369218
$195$		0			0
$196$	3.85527			0.275376
$197$	−13.2346	−	7.64098i	−0.942923	−	0.544397i	−0.0520479	−	0.998645i	$-0.516575\pi$
$197$	−13.2346	−	7.64098i	−0.942923	−	0.544397i	−0.890876	+	0.454247i	$0.849908\pi$
$198$		0			0
$199$	−6.61480	−	11.4572i	−0.468911	−	0.812177i	0.530458	−	0.847711i	$-0.322020\pi$
$199$	−6.61480	−	11.4572i	−0.468911	−	0.812177i	−0.999368	+	0.0355340i	$0.988687\pi$
$200$		−	2.63726i		−	0.186483i
$201$		0			0
$202$	3.69799	−	2.13504i	0.260190	−	0.150221i
$203$			7.11035i			0.499049i
$204$		0			0
$205$	−0.133975	+	0.232051i	−0.00935719	+	0.0162071i
$206$	−7.18144	−	4.14621i	−0.500355	−	0.288880i
$207$		0			0
$208$	−13.0024	−	9.19686i	−0.901552	−	0.637688i
$209$	6.12979			0.424007
$210$		0			0
$211$	2.40521	−	4.16595i	0.165582	−	0.286796i	−0.771280	−	0.636496i	$-0.780383\pi$
$211$	2.40521	−	4.16595i	0.165582	−	0.286796i	0.936862	+	0.349700i	$0.113717\pi$
$212$	−0.117209	−	0.203012i	−0.00804994	−	0.0139429i
$213$		0			0
$214$	5.75189	−	3.32086i	0.393191	−	0.227009i
$215$	−3.08209	+	1.77944i	−0.210197	+	0.121357i
$216$		0			0
$217$	3.53349	+	6.12019i	0.239869	+	0.415465i
$218$	10.3044	−	17.8477i	0.697900	−	1.20880i
$219$		0			0
$220$	−0.252957			−0.0170543
$221$	−11.6552	+	5.36754i	−0.784013	+	0.361060i
$222$		0			0
$223$	−12.7420	−	7.35661i	−0.853269	−	0.492635i	0.00848317	−	0.999964i	$-0.497300\pi$
$223$	−12.7420	−	7.35661i	−0.853269	−	0.492635i	−0.861753	+	0.507329i	$0.830633\pi$
$224$	3.21306	−	5.56518i	0.214682	−	0.371839i
$225$		0			0
$226$			12.0299i			0.800214i
$227$	−12.9062	+	7.45140i	−0.856615	+	0.494567i	−0.862877	−	0.505413i	$-0.831340\pi$
$227$	−12.9062	+	7.45140i	−0.856615	+	0.494567i	0.00626222	+	0.999980i	$0.498007\pi$
$228$		0			0
$229$			19.3074i			1.27587i	0.770092	+	0.637933i	$0.220210\pi$
$229$			19.3074i			1.27587i	−0.770092	+	0.637933i	$0.779790\pi$
$230$	−5.29844	−	9.17716i	−0.349369	−	0.605124i
$231$		0			0
$232$	3.36444	+	1.94246i	0.220886	+	0.127529i
$233$	−21.1937			−1.38845			−0.694224	−	0.719759i	$-0.744252\pi$
$233$	−21.1937			−1.38845			−0.694224	+	0.719759i	$0.744252\pi$
$234$		0			0
$235$	−6.51793			−0.425183
$236$	1.78694	+	1.03169i	0.116320	+	0.0671573i
$237$		0			0
$238$	−12.8451	−	22.2483i	−0.832621	−	1.44214i
$239$			14.8971i			0.963612i	0.876278	+	0.481806i	$0.160019\pi$
$239$			14.8971i			0.963612i	−0.876278	+	0.481806i	$0.839981\pi$
$240$		0			0
$241$	−8.13343	+	4.69584i	−0.523921	+	0.302486i	−0.738537	−	0.674213i	$-0.764483\pi$
$241$	−8.13343	+	4.69584i	−0.523921	+	0.302486i	0.214617	+	0.976698i	$0.431150\pi$
$242$			14.7403i			0.947544i
$243$		0			0
$244$	0.749527	−	1.29822i	0.0479835	−	0.0831099i
$245$	14.1148	+	8.14918i	0.901762	+	0.520632i
$246$		0			0
$247$	−8.64512	−	18.7722i	−0.550076	−	1.19445i
$248$	3.86122			0.245188
$249$		0			0
$250$	−0.747754	+	1.29515i	−0.0472921	+	0.0819123i
$251$	−5.65817	−	9.80024i	−0.357140	−	0.618585i	0.630341	−	0.776318i	$-0.282915\pi$
$251$	−5.65817	−	9.80024i	−0.357140	−	0.618585i	−0.987482	+	0.157733i	$0.949582\pi$
$252$		0			0
$253$	6.56229	−	3.78874i	0.412568	−	0.238196i
$254$	−0.915219	+	0.528402i	−0.0574260	+	0.0331549i
$255$		0			0
$256$	−2.80038	−	4.85040i	−0.175024	−	0.303150i
$257$	13.2660	−	22.9773i	0.827508	−	1.43329i	−0.0724788	−	0.997370i	$-0.523091\pi$
$257$	13.2660	−	22.9773i	0.827508	−	1.43329i	0.899987	−	0.435917i	$-0.143576\pi$
$258$		0			0
$259$	0.122593			0.00761758
$260$	0.356756	+	0.774668i	0.0221251	+	0.0480428i
$261$		0			0
$262$	8.11480	+	4.68508i	0.501334	+	0.289445i
$263$	−7.07038	+	12.2463i	−0.435979	+	0.755137i	−0.997375	−	0.0724100i	$-0.976931\pi$
$263$	−7.07038	+	12.2463i	−0.435979	+	0.755137i	0.561396	+	0.827547i	$0.310264\pi$
$264$		0			0
$265$		−	0.991015i		−	0.0608776i
$266$	35.8337	−	20.6886i	2.19711	−	1.26850i
$267$		0			0
$268$		−	1.22368i		−	0.0747479i
$269$	12.3872	+	21.4553i	0.755264	+	1.30815i	0.945243	+	0.326367i	$0.105824\pi$
$269$	12.3872	+	21.4553i	0.755264	+	1.30815i	−0.189980	+	0.981788i	$0.560842\pi$
$270$		0			0
$271$	16.2095	+	9.35856i	0.984657	+	0.568492i	0.903673	−	0.428224i	$-0.140860\pi$
$271$	16.2095	+	9.35856i	0.984657	+	0.568492i	0.0809839	+	0.996715i	$0.474194\pi$
$272$	−15.7201			−0.953170
$273$		0			0
$274$	−24.3854			−1.47318
$275$	−0.926118	−	0.534695i	−0.0558470	−	0.0322433i
$276$		0			0
$277$	−11.3323	−	19.6282i	−0.680893	−	1.17934i	−0.974709	−	0.223480i	$-0.928258\pi$
$277$	−11.3323	−	19.6282i	−0.680893	−	1.17934i	0.293815	−	0.955862i	$-0.405075\pi$
$278$		−	10.2073i		−	0.612191i
$279$		0			0
$280$	11.0242	−	6.36482i	0.658822	−	0.380371i
$281$		−	27.8384i		−	1.66070i	−0.557241	−	0.830351i	$-0.688140\pi$
$281$		−	27.8384i		−	1.66070i	0.557241	−	0.830351i	$-0.311860\pi$
$282$		0			0
$283$	3.96004	−	6.85898i	0.235400	−	0.407724i	−0.723989	−	0.689811i	$-0.757693\pi$
$283$	3.96004	−	6.85898i	0.235400	−	0.407724i	0.959389	+	0.282087i	$0.0910268\pi$
$284$	1.59065	+	0.918364i	0.0943879	+	0.0544949i
$285$		0			0
$286$	−5.23757	+	2.41204i	−0.309704	+	0.142627i
$287$	−1.29335			−0.0763439
$288$		0			0
$289$	2.16715	−	3.75362i	0.127480	−	0.220801i
$290$	−1.10151	−	1.90786i	−0.0646827	−	0.112034i
$291$		0			0
$292$	2.07081	−	1.19558i	0.121185	−	0.0699662i
$293$	−0.236400	+	0.136485i	−0.0138106	+	0.00797356i	−0.506889	−	0.862011i	$-0.669205\pi$
$293$	−0.236400	+	0.136485i	−0.0138106	+	0.00797356i	0.493079	+	0.869985i	$0.335871\pi$
$294$		0			0
$295$	4.36153	+	7.55440i	0.253938	+	0.439834i
$296$	0.0334909	−	0.0580080i	0.00194662	−	0.00337165i
$297$		0			0
$298$	−12.6214			−0.731139
$299$	−20.8579	−	14.7533i	−1.20624	−	0.853204i
$300$		0			0
$301$	−14.8767	−	8.58909i	−0.857481	−	0.495067i
$302$	1.02455	−	1.77457i	0.0589560	−	0.102115i
$303$		0			0
$304$		−	25.3192i		−	1.45216i
$305$	5.48830	−	3.16867i	0.314259	−	0.181437i
$306$		0			0
$307$		−	6.85224i		−	0.391078i	−0.980696	−	0.195539i	$-0.937354\pi$
$307$		−	6.85224i		−	0.391078i	0.980696	−	0.195539i	$-0.0626456\pi$
$308$	−0.610491	−	1.05740i	−0.0347859	−	0.0602510i
$309$		0			0
$310$	−1.89623	−	1.09479i	−0.107698	−	0.0621798i
$311$	10.6447			0.603605			0.301803	−	0.953370i	$-0.402412\pi$
$311$	10.6447			0.603605			0.301803	+	0.953370i	$0.402412\pi$
$312$		0			0
$313$	17.8236			1.00745			0.503724	−	0.863865i	$-0.331963\pi$
$313$	17.8236			1.00745			0.503724	+	0.863865i	$0.331963\pi$
$314$	−15.5029	−	8.95062i	−0.874881	−	0.505113i
$315$		0			0
$316$	1.03883	+	1.79931i	0.0584390	+	0.101219i
$317$		−	8.17161i		−	0.458963i	−0.973313	−	0.229482i	$-0.926297\pi$
$317$		−	8.17161i		−	0.458963i	0.973313	−	0.229482i	$-0.0737031\pi$
$318$		0			0
$319$	1.36425	−	0.787651i	0.0763835	−	0.0441000i
$320$		−	6.84325i		−	0.382549i
$321$		0			0
$322$	25.5747	−	44.2967i	1.42522	−	2.46856i
$323$	−17.6667	−	10.1999i	−0.983001	−	0.567536i
$324$		0			0
$325$	−0.331331	+	3.59030i	−0.0183789	+	0.199154i
$326$	−33.7556			−1.86955
$327$		0			0
$328$	−0.353326	+	0.611979i	−0.0195092	+	0.0337909i
$329$	−15.7305	−	27.2460i	−0.867250	−	1.50212i
$330$		0			0
$331$	21.5983	−	12.4698i	1.18715	−	0.685400i	0.229490	−	0.973311i	$-0.426294\pi$
$331$	21.5983	−	12.4698i	1.18715	−	0.685400i	0.957657	+	0.287911i	$0.0929608\pi$
$332$	−0.148615	+	0.0858029i	−0.00815631	+	0.00470905i
$333$		0			0
$334$	6.12934	+	10.6163i	0.335383	+	0.580900i
$335$	2.58658	−	4.48009i	0.141320	−	0.244773i
$336$		0			0
$337$	19.6057			1.06799			0.533996	−	0.845487i	$-0.320690\pi$
$337$	19.6057			1.06799			0.533996	+	0.845487i	$0.320690\pi$
$338$	14.7735	+	12.6380i	0.803575	+	0.687415i
$339$		0			0
$340$	0.729047	+	0.420915i	0.0395381	+	0.0228273i
$341$	0.782847	−	1.35593i	0.0423936	−	0.0734278i
$342$		0			0
$343$			44.8817i			2.42339i
$344$	−8.12828	+	4.69286i	−0.438247	+	0.253022i
$345$		0			0
$346$		−	13.7104i		−	0.737076i
$347$	8.54049	+	14.7926i	0.458478	+	0.794107i	0.998881	−	0.0472996i	$-0.0150615\pi$
$347$	8.54049	+	14.7926i	0.458478	+	0.794107i	−0.540403	+	0.841406i	$0.681728\pi$
$348$		0			0
$349$	−24.5708	−	14.1860i	−1.31525	−	0.759357i	−0.332286	−	0.943179i	$-0.607820\pi$
$349$	−24.5708	−	14.1860i	−1.31525	−	0.759357i	−0.982960	+	0.183822i	$0.941153\pi$
$350$	−7.21857			−0.385849
$351$		0			0
$352$	−1.42371			−0.0758840
$353$	18.4047	+	10.6260i	0.979586	+	0.565564i	0.902145	−	0.431433i	$-0.141992\pi$
$353$	18.4047	+	10.6260i	0.979586	+	0.565564i	0.0774407	+	0.996997i	$0.475325\pi$
$354$		0			0
$355$	3.88244	+	6.72458i	0.206058	+	0.356904i
$356$		−	3.19488i		−	0.169328i
$357$		0			0
$358$	−12.9994	+	7.50520i	−0.687039	+	0.396662i
$359$			32.6519i			1.72330i	0.507502	+	0.861650i	$0.330569\pi$
$359$			32.6519i			1.72330i	−0.507502	+	0.861650i	$0.669431\pi$
$360$		0			0
$361$	6.92820	−	12.0000i	0.364642	−	0.631579i
$362$	22.0484	+	12.7296i	1.15884	+	0.669055i
$363$		0			0
$364$	−2.37724	+	3.36090i	−0.124601	+	0.176159i
$365$	10.1088			0.529118
$366$		0			0
$367$	2.95918	−	5.12546i	0.154468	−	0.267547i	−0.778397	−	0.627772i	$-0.783967\pi$
$367$	2.95918	−	5.12546i	0.154468	−	0.267547i	0.932865	+	0.360226i	$0.117300\pi$
$368$	−15.6495	−	27.1057i	−0.815785	−	1.41298i
$369$		0			0
$370$	−0.0328945	+	0.0189916i	−0.00171010	+	0.000987329i
$371$	4.14261	−	2.39174i	0.215073	−	0.124173i
$372$		0			0
$373$	6.65926	+	11.5342i	0.344803	+	0.597217i	0.985318	−	0.170729i	$-0.0546123\pi$
$373$	6.65926	+	11.5342i	0.344803	+	0.597217i	−0.640515	+	0.767946i	$0.721279\pi$
$374$	−2.84583	+	4.92912i	−0.147154	+	0.254879i
$375$		0			0
$376$	−17.1895			−0.886480
$377$	−4.33621	−	3.06710i	−0.223326	−	0.157963i
$378$		0			0
$379$	−22.0131	−	12.7093i	−1.13074	−	0.652832i	−0.186617	−	0.982433i	$-0.559752\pi$
$379$	−22.0131	−	12.7093i	−1.13074	−	0.652832i	−0.944120	+	0.329601i	$0.893086\pi$
$380$	−0.677939	+	1.17422i	−0.0347775	+	0.0602364i
$381$		0			0
$382$			5.79869i			0.296687i
$383$	9.37632	−	5.41342i	0.479107	−	0.276613i	−0.240937	−	0.970541i	$-0.577455\pi$
$383$	9.37632	−	5.41342i	0.479107	−	0.276613i	0.720044	+	0.693928i	$0.244121\pi$
$384$		0			0
$385$		−	5.16177i		−	0.263068i
$386$	−0.937641	−	1.62404i	−0.0477247	−	0.0826615i
$387$		0			0
$388$	−0.704427	−	0.406701i	−0.0357618	−	0.0206471i
$389$	−23.0370			−1.16802			−0.584011	−	0.811746i	$-0.698518\pi$
$389$	−23.0370			−1.16802			−0.584011	+	0.811746i	$0.698518\pi$
$390$		0			0
$391$	−25.2176			−1.27531
$392$	37.2244	+	21.4915i	1.88012	+	1.08549i
$393$		0			0
$394$	11.4271	+	19.7924i	0.575691	+	0.997126i
$395$			8.78347i			0.441944i
$396$		0			0
$397$	−18.2614	+	10.5432i	−0.916512	+	0.529149i	−0.882521	−	0.470273i	$-0.844155\pi$
$397$	−18.2614	+	10.5432i	−0.916512	+	0.529149i	−0.0339917	+	0.999422i	$0.510822\pi$
$398$			19.7850i			0.991731i
$399$		0			0
$400$	−2.20857	+	3.82535i	−0.110428	+	0.191267i
$401$	17.1273	+	9.88845i	0.855296	+	0.493805i	0.862434	−	0.506169i	$-0.168939\pi$
$401$	17.1273	+	9.88845i	0.855296	+	0.493805i	−0.00713812	+	0.999975i	$0.502272\pi$
$402$		0			0
$403$	−5.25656	−	0.485102i	−0.261848	−	0.0241646i
$404$	−0.675394			−0.0336021
$405$		0			0
$406$	5.31679	−	9.20895i	0.263868	−	0.457033i
$407$	−0.0135803	−	0.0235218i	−0.000673151	−	0.00116593i
$408$		0			0
$409$	−27.6096	+	15.9404i	−1.36521	+	0.788204i	−0.990312	−	0.138862i	$-0.955655\pi$
$409$	−27.6096	+	15.9404i	−1.36521	+	0.788204i	−0.374897	+	0.927066i	$0.622322\pi$
$410$	0.347034	−	0.200360i	0.0171388	−	0.00989508i
$411$		0			0
$412$	0.655802	+	1.13588i	0.0323090	+	0.0559609i
$413$	−21.0524	+	36.4639i	−1.03592	+	1.79427i
$414$		0			0
$415$	−0.725474			−0.0356121
$416$	2.00792	+	4.36004i	0.0984465	+	0.213769i
$417$		0			0
$418$	−7.93899	−	4.58358i	−0.388309	−	0.224190i
$419$	15.3648	−	26.6127i	0.750621	−	1.30011i	−0.196902	−	0.980423i	$-0.563088\pi$
$419$	15.3648	−	26.6127i	0.750621	−	1.30011i	0.947522	−	0.319690i	$-0.103579\pi$
$420$		0			0
$421$			17.9820i			0.876391i	0.898880	+	0.438195i	$0.144382\pi$
$421$			17.9820i			0.876391i	−0.898880	+	0.438195i	$0.855618\pi$
$422$	−6.23021	+	3.59701i	−0.303282	+	0.175100i
$423$		0			0
$424$		−	2.61357i		−	0.126926i
$425$	1.77944	+	3.08209i	0.0863157	+	0.149503i
$426$		0			0
$427$	26.4911	+	15.2947i	1.28200	+	0.740160i
$428$	−1.05051			−0.0507785
$429$		0			0
$430$	5.32235			0.256666
$431$	4.24308	+	2.44974i	0.204382	+	0.118000i	0.598698	−	0.800975i	$-0.295685\pi$
$431$	4.24308	+	2.44974i	0.204382	+	0.118000i	−0.394316	+	0.918975i	$0.629018\pi$
$432$		0			0
$433$	−9.61972	−	16.6618i	−0.462294	−	0.800717i	0.536781	−	0.843722i	$-0.319640\pi$
$433$	−9.61972	−	16.6618i	−0.462294	−	0.800717i	−0.999075	+	0.0430048i	$0.986307\pi$
$434$		−	10.5687i		−	0.507315i
$435$		0			0
$436$	−2.82296	+	1.62983i	−0.135195	+	0.0780549i
$437$		−	40.6162i		−	1.94294i
$438$		0			0
$439$	−4.27987	+	7.41295i	−0.204267	+	0.353801i	−0.949899	−	0.312557i	$-0.898814\pi$
$439$	−4.27987	+	7.41295i	−0.204267	+	0.353801i	0.745632	+	0.666358i	$0.232148\pi$
$440$	−2.44242	−	1.41013i	−0.116438	−	0.0672253i
$441$		0			0
$442$	19.1088	+	1.76346i	0.908913	+	0.0838791i
$443$	37.9652			1.80378			0.901891	−	0.431965i	$-0.142179\pi$
$443$	37.9652			1.80378			0.901891	+	0.431965i	$0.142179\pi$
$444$		0			0
$445$	6.75327	−	11.6970i	0.320136	−	0.554491i
$446$	11.0019	+	19.0558i	0.520954	+	0.902318i
$447$		0			0
$448$	28.6059	−	16.5156i	1.35150	−	0.780290i
$449$	−23.1283	+	13.3531i	−1.09149	+	0.630173i	−0.933973	−	0.357344i	$-0.883683\pi$
$449$	−23.1283	+	13.3531i	−1.09149	+	0.630173i	−0.157518	+	0.987516i	$0.550349\pi$
$450$		0			0
$451$	0.143271	+	0.248153i	0.00674637	+	0.0116851i
$452$	0.951375	−	1.64783i	0.0447489	−	0.0775074i
$453$		0			0
$454$	22.2873			1.04599
$455$	−15.8077	+	7.27987i	−0.741075	+	0.341286i
$456$		0			0
$457$	3.69903	+	2.13563i	0.173033	+	0.0999007i	0.584015	−	0.811743i	$-0.301481\pi$
$457$	3.69903	+	2.13563i	0.173033	+	0.0999007i	−0.410982	+	0.911643i	$0.634814\pi$
$458$	14.4371	−	25.0059i	0.674604	−	1.16845i
$459$		0			0
$460$			1.67610i			0.0781485i
$461$	−17.8767	+	10.3211i	−0.832603	+	0.480704i	−0.854743	−	0.519051i	$-0.826285\pi$
$461$	−17.8767	+	10.3211i	−0.832603	+	0.480704i	0.0221401	+	0.999755i	$0.492952\pi$
$462$		0			0
$463$			32.1040i			1.49200i	0.665947	+	0.745999i	$0.268028\pi$
$463$			32.1040i			1.49200i	−0.665947	+	0.745999i	$0.731972\pi$
$464$	−3.25341	−	5.63507i	−0.151036	−	0.261602i
$465$		0			0
$466$	27.4490	+	15.8477i	1.27155	+	0.734131i
$467$	23.3774			1.08178			0.540888	−	0.841095i	$-0.318088\pi$
$467$	23.3774			1.08178			0.540888	+	0.841095i	$0.318088\pi$
$468$		0			0
$469$	24.9700			1.15301
$470$	8.44168	+	4.87381i	0.389386	+	0.224812i
$471$		0			0
$472$	11.5025	+	19.9229i	0.529446	+	0.917027i
$473$			3.80584i			0.174993i
$474$		0			0
$475$	−4.96410	+	2.86603i	−0.227769	+	0.131502i
$476$			4.06338i			0.186245i
$477$		0			0
$478$	11.1393	−	19.2939i	0.509502	−	0.882483i
$479$	4.48198	+	2.58767i	0.204787	+	0.118234i	0.598886	−	0.800834i	$-0.295610\pi$
$479$	4.48198	+	2.58767i	0.204787	+	0.118234i	−0.394100	+	0.919068i	$0.628943\pi$
$480$		0			0
$481$	−0.0528814	+	0.0747629i	−0.00241119	+	0.00340889i
$482$	14.0453			0.639747
$483$		0			0
$484$	1.16573	−	2.01911i	0.0529879	−	0.0917777i
$485$	−1.71935	−	2.97800i	−0.0780717	−	0.135224i
$486$		0			0
$487$	−26.6501	+	15.3865i	−1.20763	+	0.697227i	−0.962242	−	0.272197i	$-0.912250\pi$
$487$	−26.6501	+	15.3865i	−1.20763	+	0.697227i	−0.245391	+	0.969424i	$0.578917\pi$
$488$	14.4741	−	8.35661i	0.655211	−	0.378286i
$489$		0			0
$490$	−12.1872	−	21.1088i	−0.550560	−	0.953598i
$491$	−17.8992	+	31.0023i	−0.807778	+	1.39911i	0.106622	+	0.994300i	$0.465997\pi$
$491$	−17.8992	+	31.0023i	−0.807778	+	1.39911i	−0.914400	+	0.404813i	$0.867337\pi$
$492$		0			0
$493$	−5.24255			−0.236113
$494$	−2.84028	+	30.7772i	−0.127790	+	1.38473i
$495$		0			0
$496$	−5.60070	−	3.23357i	−0.251479	−	0.145191i
$497$	−18.7399	+	32.4585i	−0.840600	+	1.45596i
$498$		0			0
$499$			28.8971i			1.29361i	0.762655	+	0.646805i	$0.223895\pi$
$499$			28.8971i			1.29361i	−0.762655	+	0.646805i	$0.776105\pi$
$500$	0.204852	−	0.118272i	0.00916128	−	0.00528927i
$501$		0			0
$502$			16.9237i			0.755340i
$503$	−3.93161	−	6.80974i	−0.175302	−	0.303631i	0.764964	−	0.644073i	$-0.222757\pi$
$503$	−3.93161	−	6.80974i	−0.175302	−	0.303631i	−0.940266	+	0.340442i	$0.889423\pi$
$504$		0			0
$505$	−2.47273	−	1.42763i	−0.110035	−	0.0635289i
$506$	−11.3322			−0.503777
$507$		0			0
$508$	0.167154			0.00741625
$509$	−24.2585	−	14.0057i	−1.07524	−	0.620790i	−0.145631	−	0.989339i	$-0.546521\pi$
$509$	−24.2585	−	14.0057i	−1.07524	−	0.620790i	−0.929608	+	0.368549i	$0.879855\pi$
$510$		0			0
$511$	24.3968	+	42.2564i	1.07925	+	1.86931i
$512$		−	17.4176i		−	0.769757i
$513$		0			0
$514$	−34.3628	+	19.8394i	−1.51568	+	0.875076i
$515$			5.54488i			0.244337i
$516$		0			0
$517$	−3.48510	+	6.03637i	−0.153275	+	0.265479i
$518$	−0.158776	−	0.0916696i	−0.00697623	−	0.00402773i
$519$		0			0
$520$	−0.873806	+	9.46855i	−0.0383189	+	0.415224i
$521$	37.5609			1.64557			0.822786	−	0.568351i	$-0.192419\pi$
$521$	37.5609			1.64557			0.822786	+	0.568351i	$0.192419\pi$
$522$		0			0
$523$	22.6553	−	39.2401i	0.990647	−	1.71585i	0.377154	−	0.926151i	$-0.376903\pi$
$523$	22.6553	−	39.2401i	0.990647	−	1.71585i	0.613493	−	0.789700i	$-0.289764\pi$
$524$	−0.741035	−	1.28351i	−0.0323723	−	0.0560704i
$525$		0			0
$526$	18.3144	−	10.5738i	0.798545	−	0.461040i
$527$	−4.51249	+	2.60529i	−0.196567	+	0.113488i
$528$		0			0
$529$	−13.6043	−	23.5633i	−0.591491	−	1.02449i
$530$	−0.741035	+	1.28351i	−0.0321885	+	0.0557522i
$531$		0			0
$532$	−6.54460			−0.283744
$533$	0.557894	−	0.788741i	0.0241651	−	0.0341642i
$534$		0			0
$535$	−3.84611	−	2.22056i	−0.166282	−	0.0960030i
$536$	6.82149	−	11.8152i	0.294644	−	0.510338i
$537$		0			0
$538$		−	37.0504i		−	1.59736i
$539$	15.0942	−	8.71465i	0.650154	−	0.375367i
$540$		0			0
$541$		−	19.7445i		−	0.848882i	−0.905456	−	0.424441i	$-0.860471\pi$
$541$		−	19.7445i		−	0.848882i	0.905456	−	0.424441i	$-0.139529\pi$
$542$	−13.9958	−	24.2414i	−0.601171	−	1.04126i
$543$		0			0
$544$	4.10328	+	2.36903i	0.175927	+	0.101571i
$545$	−13.7804			−0.590289
$546$		0			0
$547$	−11.8312			−0.505867			−0.252934	−	0.967484i	$-0.581395\pi$
$547$	−11.8312			−0.505867			−0.252934	+	0.967484i	$0.581395\pi$
$548$	3.34028	+	1.92851i	0.142690	+	0.0823820i
$549$		0			0
$550$	0.799640	+	1.38502i	0.0340968	+	0.0590573i
$551$		−	8.44381i		−	0.359718i
$552$		0			0
$553$	−36.7164	+	21.1982i	−1.56134	+	0.901439i
$554$			33.8952i			1.44007i
$555$		0			0
$556$	−0.807237	+	1.39818i	−0.0342345	+	0.0592958i
$557$	3.50412	+	2.02310i	0.148474	+	0.0857217i	0.572397	−	0.819977i	$-0.306014\pi$
$557$	3.50412	+	2.02310i	0.148474	+	0.0857217i	−0.423922	+	0.905699i	$0.639347\pi$
$558$		0			0
$559$	11.6552	−	5.36754i	0.492962	−	0.227023i
$560$	−21.3208			−0.900968
$561$		0			0
$562$	−20.8163	+	36.0549i	−0.878083	+	1.52088i
$563$	−1.94963	−	3.37686i	−0.0821671	−	0.142318i	0.822013	−	0.569468i	$-0.192851\pi$
$563$	−1.94963	−	3.37686i	−0.0821671	−	0.142318i	−0.904181	+	0.427151i	$0.859517\pi$
$564$		0			0
$565$	6.96630	−	4.02200i	0.293074	−	0.169207i
$566$	−10.2577	+	5.92226i	−0.431162	+	0.248931i
$567$		0			0
$568$	10.2390	+	17.7345i	0.429619	+	0.744123i
$569$	8.66778	−	15.0130i	0.363372	−	0.629379i	−0.625141	−	0.780512i	$-0.714959\pi$
$569$	8.66778	−	15.0130i	0.363372	−	0.629379i	0.988514	+	0.151133i	$0.0482920\pi$
$570$		0			0
$571$	−29.5118			−1.23503			−0.617515	−	0.786559i	$-0.711860\pi$
$571$	−29.5118			−1.23503			−0.617515	+	0.786559i	$0.711860\pi$
$572$	0.908189	+	0.0838123i	0.0379733	+	0.00350437i
$573$		0			0
$574$	1.67508	+	0.967106i	0.0699163	+	0.0403662i
$575$	−3.54290	+	6.13649i	−0.147749	+	0.255909i
$576$		0			0
$577$		−	28.3684i		−	1.18099i	−0.807041	−	0.590496i	$-0.798932\pi$
$577$		−	28.3684i		−	1.18099i	0.807041	−	0.590496i	$-0.201068\pi$
$578$	−5.61357	+	3.24100i	−0.233494	+	0.134808i
$579$		0			0
$580$			0.348448i			0.0144685i
$581$	−1.75087	−	3.03260i	−0.0726384	−	0.125813i
$582$		0			0
$583$	−0.917797	−	0.529891i	−0.0380113	−	0.0219458i
$584$	26.6595			1.10318
$585$		0			0
$586$	0.408230			0.0168638
$587$	−29.7806	−	17.1939i	−1.22918	−	0.709667i	−0.262320	−	0.964981i	$-0.584488\pi$
$587$	−29.7806	−	17.1939i	−1.22918	−	0.709667i	−0.966858	+	0.255314i	$0.917821\pi$
$588$		0			0
$589$	−4.19615	−	7.26795i	−0.172899	−	0.299471i
$590$		−	13.0454i		−	0.537071i
$591$		0			0
$592$	−0.0971572	+	0.0560937i	−0.00399314	+	0.00230544i
$593$		−	5.47612i		−	0.224877i	−0.993659	−	0.112439i	$-0.964134\pi$
$593$		−	5.47612i		−	0.224877i	0.993659	−	0.112439i	$-0.0358662\pi$
$594$		0			0
$595$	−8.58909	+	14.8767i	−0.352118	+	0.609887i
$596$	1.72886	+	0.998159i	0.0708170	+	0.0408862i
$597$		0			0
$598$	15.9823	+	34.7043i	0.653564	+	1.41916i
$599$	−38.6039			−1.57731			−0.788657	−	0.614833i	$-0.789223\pi$
$599$	−38.6039			−1.57731			−0.788657	+	0.614833i	$0.789223\pi$
$600$		0			0
$601$	−3.28948	+	5.69754i	−0.134181	+	0.232408i	−0.925284	−	0.379275i	$-0.876174\pi$
$601$	−3.28948	+	5.69754i	−0.134181	+	0.232408i	0.791104	+	0.611682i	$0.209507\pi$
$602$	12.8451	+	22.2483i	0.523525	+	0.906772i
$603$		0			0
$604$	−0.280682	+	0.162052i	−0.0114208	+	0.00659379i
$605$	8.53590	−	4.92820i	0.347034	−	0.200360i
$606$		0			0
$607$	8.38318	+	14.5201i	0.340263	+	0.589352i	0.984481	−	0.175489i	$-0.0561507\pi$
$607$	8.38318	+	14.5201i	0.340263	+	0.589352i	−0.644219	+	0.764841i	$0.722817\pi$
$608$	−3.81563	+	6.60886i	−0.154744	+	0.268025i
$609$		0			0
$610$	−9.47754			−0.383734
$611$	23.4013	+	2.15959i	0.946715	+	0.0873677i
$612$		0			0
$613$	24.9232	+	14.3894i	1.00664	+	0.581184i	0.910206	−	0.414155i	$-0.135923\pi$
$613$	24.9232	+	14.3894i	1.00664	+	0.581184i	0.0964341	+	0.995339i	$0.469256\pi$
$614$	−5.12379	+	8.87466i	−0.206779	+	0.358152i
$615$		0			0
$616$		−	13.6129i		−	0.548481i
$617$	−32.3279	+	18.6645i	−1.30147	+	0.751406i	−0.980657	−	0.195735i	$-0.937291\pi$
$617$	−32.3279	+	18.6645i	−1.30147	+	0.751406i	−0.320817	+	0.947141i	$0.603957\pi$
$618$		0			0
$619$			12.7535i			0.512606i	0.966597	+	0.256303i	$0.0825045\pi$
$619$			12.7535i			0.512606i	−0.966597	+	0.256303i	$0.917496\pi$
$620$	0.173162	+	0.299925i	0.00695434	+	0.0120453i
$621$		0			0
$622$	−13.7864	−	7.95961i	−0.552786	−	0.319151i
$623$	65.1939			2.61194
$624$		0			0
$625$	1.00000			0.0400000
$626$	−23.0842	−	13.3276i	−0.922629	−	0.532680i
$627$		0			0
$628$	1.41571	+	2.45209i	0.0564931	+	0.0978489i
$629$			0.0903896i			0.00360407i
$630$		0			0
$631$	24.8759	−	14.3621i	0.990294	−	0.571746i	0.0849315	−	0.996387i	$-0.472933\pi$
$631$	24.8759	−	14.3621i	0.990294	−	0.571746i	0.905362	+	0.424641i	$0.139600\pi$
$632$			23.1643i			0.921427i
$633$		0			0
$634$	−6.11035	+	10.5834i	−0.242673	+	0.420322i
$635$	0.611979	+	0.353326i	0.0242856	+	0.0140213i
$636$		0			0
$637$	−47.9762	−	33.9346i	−1.90089	−	1.34454i
$638$	−2.35588			−0.0932701
$639$		0			0
$640$	−6.44840	+	11.1690i	−0.254895	+	0.441492i
$641$	11.1985	+	19.3964i	0.442315	+	0.766112i	0.997861	−	0.0653739i	$-0.0208240\pi$
$641$	11.1985	+	19.3964i	0.442315	+	0.766112i	−0.555546	+	0.831486i	$0.687491\pi$
$642$		0			0
$643$	12.2665	−	7.08209i	0.483745	−	0.279290i	−0.238231	−	0.971209i	$-0.576567\pi$
$643$	12.2665	−	7.08209i	0.483745	−	0.279290i	0.721976	+	0.691918i	$0.243234\pi$
$644$	−7.00637	+	4.04513i	−0.276090	+	0.159400i
$645$		0			0
$646$	15.2540	+	26.4207i	0.600160	+	1.03951i
$647$	11.8048	−	20.4466i	0.464096	−	0.803838i	−0.535064	−	0.844812i	$-0.679713\pi$
$647$	11.8048	−	20.4466i	0.464096	−	0.803838i	0.999160	+	0.0409732i	$0.0130458\pi$
$648$		0			0
$649$	9.32835			0.366170
$650$	3.11378	−	4.40221i	0.122132	−	0.172669i
$651$		0			0
$652$	4.62379	+	2.66955i	0.181082	+	0.104548i
$653$	16.6383	−	28.8183i	0.651105	−	1.12775i	−0.331750	−	0.943367i	$-0.607639\pi$
$653$	16.6383	−	28.8183i	0.651105	−	1.12775i	0.982855	−	0.184380i	$-0.0590277\pi$
$654$		0			0
$655$		−	6.26554i		−	0.244815i
$656$	1.02500	−	0.591784i	0.0400195	−	0.0231053i
$657$		0			0
$658$			47.0502i			1.83421i
$659$	11.5454	+	19.9972i	0.449745	+	0.778982i	0.998369	−	0.0570875i	$-0.0181814\pi$
$659$	11.5454	+	19.9972i	0.449745	+	0.778982i	−0.548624	+	0.836069i	$0.684848\pi$
$660$		0			0
$661$	11.6364	+	6.71826i	0.452602	+	0.261310i	0.708929	−	0.705280i	$-0.249179\pi$
$661$	11.6364	+	6.71826i	0.452602	+	0.261310i	−0.256326	+	0.966590i	$0.582512\pi$
$662$	−37.2972			−1.44960
$663$		0			0
$664$	−1.91326			−0.0742491
$665$	−23.9609	−	13.8338i	−0.929164	−	0.536453i
$666$		0			0
$667$	−5.21900	−	9.03957i	−0.202080	−	0.350014i
$668$		−	1.93895i		−	0.0750200i
$669$		0			0
$670$	−6.70001	+	3.86825i	−0.258844	+	0.149444i
$671$		−	6.77708i		−	0.261626i
$672$		0			0
$673$	−0.972620	+	1.68463i	−0.0374918	+	0.0649376i	−0.884162	−	0.467180i	$-0.845270\pi$
$673$	−0.972620	+	1.68463i	−0.0374918	+	0.0649376i	0.846671	+	0.532117i	$0.178603\pi$
$674$	−25.3923	−	14.6603i	−0.978075	−	0.564692i
$675$		0			0
$676$	−1.02419	−	2.89949i	−0.0393919	−	0.111519i
$677$	−24.8683			−0.955768			−0.477884	−	0.878423i	$-0.658596\pi$
$677$	−24.8683			−0.955768			−0.477884	+	0.878423i	$0.658596\pi$
$678$		0			0
$679$	8.29903	−	14.3743i	0.318488	−	0.551637i
$680$	4.69286	+	8.12828i	0.179963	+	0.311705i
$681$		0			0
$682$	−2.02781	+	1.17075i	−0.0776487	+	0.0448305i
$683$	12.6631	−	7.31107i	0.484542	−	0.279750i	−0.237766	−	0.971323i	$-0.576415\pi$
$683$	12.6631	−	7.31107i	0.484542	−	0.279750i	0.722307	+	0.691572i	$0.243082\pi$
$684$		0			0
$685$	8.15290	+	14.1212i	0.311506	+	0.539545i
$686$	33.5605	−	58.1285i	1.28135	−	2.21935i
$687$		0			0
$688$	15.7201			0.599323
$689$	−0.328354	+	3.55804i	−0.0125093	+	0.135550i
$690$		0			0
$691$	−3.05231	−	1.76225i	−0.116115	−	0.0670393i	0.440817	−	0.897597i	$-0.354689\pi$
$691$	−3.05231	−	1.76225i	−0.116115	−	0.0670393i	−0.556933	+	0.830558i	$0.688022\pi$
$692$	−1.08428	+	1.87803i	−0.0412182	+	0.0713920i
$693$		0			0
$694$		−	25.5447i		−	0.969665i
$695$	−5.91087	+	3.41264i	−0.224212	+	0.129449i
$696$		0			0
$697$		−	0.953601i		−	0.0361202i
$698$	21.2152	+	36.7458i	0.803008	+	1.39085i
$699$		0			0
$700$	0.988789	+	0.570878i	0.0373727	+	0.0215772i
$701$	−1.53457			−0.0579599			−0.0289800	−	0.999580i	$-0.509226\pi$
$701$	−1.53457			−0.0579599			−0.0289800	+	0.999580i	$0.509226\pi$
$702$		0			0
$703$	−0.145584			−0.00549081
$704$	−6.33766	−	3.65905i	−0.238860	−	0.137906i
$705$		0			0
$706$	−15.8912	−	27.5244i	−0.598075	−	1.03590i
$707$		−	13.7819i		−	0.518322i
$708$		0			0
$709$	12.1289	−	7.00262i	0.455510	−	0.262989i	−0.254644	−	0.967035i	$-0.581958\pi$
$709$	12.1289	−	7.00262i	0.455510	−	0.262989i	0.710155	+	0.704046i	$0.248625\pi$
$710$		−	11.6124i		−	0.435807i
$711$		0			0
$712$	17.8101	−	30.8481i	0.667463	−	1.15608i
$713$	−8.98444	−	5.18717i	−0.336470	−	0.194261i
$714$		0			0
$715$	3.14788	+	2.22656i	0.117724	+	0.0832687i
$716$	2.37418			0.0887274
$717$		0			0
$718$	24.4156	−	42.2890i	0.911181	−	1.57821i
$719$	−11.2381	−	19.4649i	−0.419109	−	0.725918i	0.576741	−	0.816927i	$-0.304324\pi$
$719$	−11.2381	−	19.4649i	−0.419109	−	0.725918i	−0.995850	+	0.0910091i	$0.970991\pi$
$720$		0			0
$721$	−23.1785	+	13.3821i	−0.863213	+	0.498376i
$722$	−17.9461	+	10.3612i	−0.667884	+	0.385603i
$723$		0			0
$724$	−2.01344	−	3.48737i	−0.0748288	−	0.129607i
$725$	−0.736543	+	1.27573i	−0.0273545	+	0.0473794i
$726$		0			0
$727$	10.3421			0.383566			0.191783	−	0.981437i	$-0.438573\pi$
$727$	10.3421			0.383566			0.191783	+	0.981437i	$0.438573\pi$
$728$	−41.6890	+	19.1989i	−1.54510	+	0.711560i
$729$		0			0
$730$	−13.0924	−	7.55889i	−0.484571	−	0.279767i
$731$	6.33285	−	10.9688i	0.234229	−	0.405696i
$732$		0			0
$733$		−	27.3533i		−	1.01032i	−0.863026	−	0.505159i	$-0.831434\pi$
$733$		−	27.3533i		−	1.01032i	0.863026	−	0.505159i	$-0.168566\pi$
$734$	−7.66516	+	4.42548i	−0.282926	+	0.163348i
$735$		0			0
$736$			9.43355i			0.347725i
$737$	−2.76606	−	4.79096i	−0.101889	−	0.176477i
$738$		0			0
$739$	11.6495	+	6.72583i	0.428533	+	0.247413i	0.698721	−	0.715394i	$-0.253753\pi$
$739$	11.6495	+	6.72583i	0.428533	+	0.247413i	−0.270189	+	0.962807i	$0.587086\pi$
$740$	0.00600778			0.000220851
$741$		0			0
$742$	−7.15372			−0.262621
$743$	−14.1964	−	8.19632i	−0.520817	−	0.300694i	0.216452	−	0.976293i	$-0.430552\pi$
$743$	−14.1964	−	8.19632i	−0.520817	−	0.300694i	−0.737269	+	0.675599i	$0.763885\pi$
$744$		0			0
$745$	4.21978	+	7.30887i	0.154601	+	0.267776i
$746$		−	19.9179i		−	0.729248i
$747$		0			0
$748$	0.779635	−	0.450122i	0.0285063	−	0.0164581i
$749$		−	21.4365i		−	0.783274i
$750$		0			0
$751$	−13.8328	+	23.9590i	−0.504764	+	0.874277i	0.495221	+	0.868767i	$0.335087\pi$
$751$	−13.8328	+	23.9590i	−0.504764	+	0.874277i	−0.999985	+	0.00551009i	$0.998246\pi$
$752$	24.9334	+	14.3953i	0.909226	+	0.524942i
$753$		0			0
$754$	3.32260	+	7.21476i	0.121002	+	0.262746i
$755$	−1.37017			−0.0498654
$756$		0			0
$757$	−11.4989	+	19.9167i	−0.417935	+	0.723885i	−0.995732	−	0.0922961i	$-0.970579\pi$
$757$	−11.4989	+	19.9167i	−0.417935	+	0.723885i	0.577797	+	0.816181i	$0.303913\pi$
$758$	19.0068	+	32.9208i	0.690359	+	1.19574i
$759$		0			0
$760$	−13.0916	+	7.55846i	−0.474884	+	0.274174i
$761$	−6.63759	+	3.83221i	−0.240612	+	0.138918i	−0.615458	−	0.788170i	$-0.711029\pi$
$761$	−6.63759	+	3.83221i	−0.240612	+	0.138918i	0.374846	+	0.927087i	$0.377696\pi$
$762$		0			0
$763$	−33.2580	−	57.6045i	−1.20402	−	2.08542i
$764$	0.458587	−	0.794296i	0.0165911	−	0.0287366i
$765$		0			0
$766$	−16.1916			−0.585027
$767$	−13.1562	−	28.5676i	−0.475042	−	1.03152i
$768$		0			0
$769$	6.26219	+	3.61548i	0.225820	+	0.130377i	0.608642	−	0.793445i	$-0.291714\pi$
$769$	6.26219	+	3.61548i	0.225820	+	0.130377i	−0.382822	+	0.923822i	$0.625048\pi$
$770$	−3.85973	+	6.68525i	−0.139095	+	0.240920i
$771$		0			0
$772$			0.296612i			0.0106753i
$773$	29.0981	−	16.7998i	1.04658	−	0.604246i	0.124893	−	0.992170i	$-0.460141\pi$
$773$	29.0981	−	16.7998i	1.04658	−	0.604246i	0.921691	+	0.387924i	$0.126808\pi$
$774$		0			0
$775$			1.46410i			0.0525921i
$776$	−4.53438	−	7.85378i	−0.162775	−	0.281934i
$777$		0			0
$778$	29.8363	+	17.2260i	1.06968	+	0.617582i
$779$	1.53590			0.0550293
$780$		0			0
$781$	8.30368			0.297129
$782$	32.6605	+	18.8565i	1.16794	+	0.674309i
$783$		0			0
$784$	−35.9960	−	62.3470i	−1.28557	−	2.22668i
$785$			11.9700i			0.427228i
$786$		0			0
$787$	2.57355	−	1.48584i	0.0917371	−	0.0529645i	−0.453430	−	0.891292i	$-0.649800\pi$
$787$	2.57355	−	1.48584i	0.0917371	−	0.0529645i	0.545167	+	0.838328i	$0.316466\pi$
$788$		−	3.61484i		−	0.128773i
$789$		0			0
$790$	6.56787	−	11.3759i	0.233674	−	0.404736i
$791$	33.6252	+	19.4135i	1.19557	+	0.690265i
$792$		0			0
$793$	−20.7545	+	9.55802i	−0.737013	+	0.339415i
$794$	31.5349			1.11913
$795$		0			0
$796$	1.56469	−	2.71012i	0.0554588	−	0.0960575i
$797$	11.2875	+	19.5506i	0.399825	+	0.692517i	0.993704	−	0.112037i	$-0.0357375\pi$
$797$	11.2875	+	19.5506i	0.399825	+	0.692517i	−0.593879	+	0.804554i	$0.702404\pi$
$798$		0			0
$799$	20.0888	−	11.5983i	0.710692	−	0.410318i
$800$	1.15297	−	0.665665i	0.0407635	−	0.0235348i
$801$		0			0
$802$	−14.7882	−	25.6140i	−0.522191	−	0.904462i
$803$	5.40512	−	9.36194i	0.190742	−	0.330376i
$804$		0			0
$805$	−34.2020			−1.20546
$806$	6.44528	+	4.55889i	0.227025	+	0.160580i
$807$		0			0
$808$	−6.52125	−	3.76505i	−0.229417	−	0.132454i
$809$	6.82921	−	11.8285i	0.240102	−	0.415869i	−0.720641	−	0.693308i	$-0.756152\pi$
$809$	6.82921	−	11.8285i	0.240102	−	0.415869i	0.960743	+	0.277439i	$0.0894857\pi$
$810$		0			0
$811$			14.1147i			0.495636i	0.968807	+	0.247818i	$0.0797135\pi$
$811$			14.1147i			0.495636i	−0.968807	+	0.247818i	$0.920287\pi$
$812$	−1.45657	+	0.840952i	−0.0511157	+	0.0295116i
$813$		0			0
$814$			0.0406189i			0.00142369i
$815$	11.2857	+	19.5474i	0.395320	+	0.684714i
$816$		0			0
$817$	17.6667	+	10.1999i	0.618079	+	0.356848i
$818$	47.6781			1.66703
$819$		0			0
$820$	−0.0633815			−0.00221338
$821$	1.37318	+	0.792808i	0.0479244	+	0.0276692i	0.523771	−	0.851859i	$-0.324525\pi$
$821$	1.37318	+	0.792808i	0.0479244	+	0.0276692i	−0.475846	+	0.879528i	$0.657858\pi$
$822$		0			0
$823$	9.28238	+	16.0776i	0.323563	+	0.560428i	0.981221	−	0.192889i	$-0.0617857\pi$
$823$	9.28238	+	16.0776i	0.323563	+	0.560428i	−0.657657	+	0.753317i	$0.728452\pi$
$824$			14.6233i			0.509427i
$825$		0			0
$826$	54.5320	−	31.4840i	1.89741	−	1.09547i
$827$			9.01023i			0.313316i	0.987653	+	0.156658i	$0.0500721\pi$
$827$			9.01023i			0.313316i	−0.987653	+	0.156658i	$0.949928\pi$
$828$		0			0
$829$	23.5588	−	40.8051i	0.818233	−	1.41722i	−0.0887506	−	0.996054i	$-0.528287\pi$
$829$	23.5588	−	40.8051i	0.818233	−	1.41722i	0.906983	−	0.421167i	$-0.138379\pi$
$830$	0.939595	+	0.542476i	0.0326138	+	0.0188296i
$831$		0			0
$832$	−2.26738	+	24.5693i	−0.0786072	+	0.851787i
$833$	−58.0041			−2.00972
$834$		0			0
$835$	4.09850	−	7.09881i	0.141835	−	0.245665i
$836$	0.724980	+	1.25570i	0.0250740	+	0.0434294i
$837$		0			0
$838$	−39.7994	+	22.9782i	−1.37485	+	0.793769i
$839$	−46.3121	+	26.7383i	−1.59887	+	0.923108i	−0.607164	+	0.794576i	$0.707693\pi$
$839$	−46.3121	+	26.7383i	−1.59887	+	0.923108i	−0.991705	+	0.128531i	$0.958974\pi$
$840$		0			0
$841$	13.4150	+	23.2355i	0.462586	+	0.801223i
$842$	13.4461	−	23.2894i	0.463384	−	0.802605i
$843$		0			0
$844$	1.13787			0.0391672
$845$	2.37915	−	12.7804i	0.0818453	−	0.439660i
$846$		0			0
$847$	41.2014	+	23.7876i	1.41570	+	0.817353i
$848$	−2.18872	+	3.79098i	−0.0751611	+	0.130183i
$849$		0			0
$850$		−	5.32235i		−	0.182555i
$851$	−0.155856	+	0.0899835i	−0.00534268	+	0.00308460i
$852$		0			0
$853$		−	27.7756i		−	0.951019i	−0.879711	−	0.475510i	$-0.842264\pi$
$853$		−	27.7756i		−	0.951019i	0.879711	−	0.475510i	$-0.157736\pi$
$854$	−22.8733	−	39.6177i	−0.782707	−	1.35569i
$855$		0			0
$856$	−10.1432	−	5.85619i	−0.346688	−	0.200160i
$857$	53.6917			1.83407			0.917037	−	0.398801i	$-0.130574\pi$
$857$	53.6917			1.83407			0.917037	+	0.398801i	$0.130574\pi$
$858$		0			0
$859$	2.08958			0.0712955			0.0356477	−	0.999364i	$-0.488651\pi$
$859$	2.08958			0.0712955			0.0356477	+	0.999364i	$0.488651\pi$
$860$	−0.729047	−	0.420915i	−0.0248603	−	0.0143531i
$861$		0			0
$862$	−3.66361	−	6.34556i	−0.124783	−	0.216131i
$863$		−	1.75413i		−	0.0597113i	−0.999554	−	0.0298557i	$-0.990495\pi$
$863$		−	1.75413i		−	0.0597113i	0.999554	−	0.0298557i	$-0.00950476\pi$
$864$		0			0
$865$	−7.93948	+	4.58386i	−0.269950	+	0.155856i
$866$			28.7727i			0.977737i
$867$		0			0
$868$	−0.835823	+	1.44769i	−0.0283697	+	0.0491377i
$869$	8.13453	+	4.69647i	0.275945	+	0.159317i
$870$		0			0
$871$	−10.7710	+	15.2278i	−0.364961	+	0.515975i
$872$	−36.3426			−1.23072
$873$		0			0
$874$	−30.3709	+	52.6040i	−1.02731	+	1.77936i
$875$	2.41342	+	4.18016i	0.0815885	+	0.141315i
$876$		0			0
$877$	−18.6777	+	10.7836i	−0.630702	+	0.364136i	−0.781024	−	0.624501i	$-0.785302\pi$
$877$	−18.6777	+	10.7836i	−0.630702	+	0.364136i	0.150322	+	0.988637i	$0.451969\pi$
$878$	11.0861	−	6.40058i	0.374139	−	0.216009i
$879$		0			0
$880$	2.36182	+	4.09079i	0.0796169	+	0.137900i
$881$	−12.5132	+	21.6734i	−0.421579	+	0.730196i	−0.996094	−	0.0882978i	$-0.971857\pi$
$881$	−12.5132	+	21.6734i	−0.421579	+	0.730196i	0.574515	+	0.818494i	$0.305191\pi$
$882$		0			0
$883$	48.7832			1.64169			0.820843	−	0.571154i	$-0.193504\pi$
$883$	48.7832			1.64169			0.820843	+	0.571154i	$0.193504\pi$
$884$	−2.47803	−	1.75277i	−0.0833452	−	0.0589519i
$885$		0			0
$886$	−49.1705	−	28.3886i	−1.65192	−	0.953734i
$887$	−16.8967	+	29.2659i	−0.567334	+	0.982651i	0.429494	+	0.903070i	$0.358692\pi$
$887$	−16.8967	+	29.2659i	−0.567334	+	0.982651i	−0.996828	+	0.0795819i	$0.974641\pi$
$888$		0			0
$889$			3.41090i			0.114398i
$890$	−17.4930	+	10.0996i	−0.586365	+	0.338538i
$891$		0			0
$892$		−	3.48031i		−	0.116530i
$893$	18.6806	+	32.3557i	0.625121	+	1.08274i
$894$		0			0
$895$	8.69229	+	5.01850i	0.290551	+	0.167750i
$896$	−62.2508			−2.07965
$897$		0			0
$898$	39.9394			1.33279
$899$	−1.86780	−	1.07837i	−0.0622946	−	0.0359658i
$900$		0			0
$901$	1.76346	+	3.05440i	0.0587493	+	0.101757i
$902$		−	0.428526i		−	0.0142683i
$903$		0			0
$904$	18.3720	−	10.6071i	0.611043	−	0.352786i
$905$		−	17.0238i		−	0.565892i
$906$		0			0
$907$	−17.3135	+	29.9879i	−0.574885	+	0.995731i	0.421169	+	0.906982i	$0.361620\pi$
$907$	−17.3135	+	29.9879i	−0.574885	+	0.995731i	−0.996054	+	0.0887485i	$0.971713\pi$
$908$	−3.05288	−	1.76258i	−0.101313	−	0.0584932i
$909$		0			0
$910$	25.9168	+	2.39174i	0.859134	+	0.0792853i
$911$	−31.1865			−1.03326			−0.516628	−	0.856210i	$-0.672813\pi$
$911$	−31.1865			−1.03326			−0.516628	+	0.856210i	$0.672813\pi$
$912$		0			0
$913$	−0.387907	+	0.671874i	−0.0128378	+	0.0222358i
$914$	−3.19386	−	5.53192i	−0.105643	−	0.182980i
$915$		0			0
$916$	−3.95516	+	2.28351i	−0.130682	+	0.0754493i
$917$	26.1910	−	15.1214i	0.864903	−	0.499352i
$918$		0			0
$919$	25.9610	+	44.9658i	0.856374	+	1.48328i	0.875364	+	0.483464i	$0.160621\pi$
$919$	25.9610	+	44.9658i	0.856374	+	1.48328i	−0.0189904	+	0.999820i	$0.506045\pi$
$920$	−9.34356	+	16.1835i	−0.308048	+	0.533555i
$921$		0			0
$922$	30.8707			1.01667
$923$	−11.7110	−	25.4296i	−0.385474	−	0.837026i
$924$		0			0
$925$	0.0219955	+	0.0126991i	0.000723209	+	0.000417545i
$926$	24.0059	−	41.5794i	0.788882	−	1.36638i
$927$		0			0
$928$			1.96117i			0.0643784i
$929$	17.7462	−	10.2457i	0.582232	−	0.336152i	−0.179788	−	0.983705i	$-0.557541\pi$
$929$	17.7462	−	10.2457i	0.582232	−	0.336152i	0.762020	+	0.647553i	$0.224208\pi$
$930$		0			0
$931$		−	93.4231i		−	3.06182i
$932$	−2.50662	−	4.34159i	−0.0821070	−	0.142213i
$933$		0			0
$934$	−30.2771	−	17.4805i	−0.990698	−	0.571980i
$935$	3.80584			0.124464
$936$		0			0
$937$	−39.6806			−1.29631			−0.648154	−	0.761510i	$-0.724459\pi$
$937$	−39.6806			−1.29631			−0.648154	+	0.761510i	$0.724459\pi$
$938$	−32.3399	−	18.6714i	−1.05593	−	0.609644i
$939$		0			0
$940$	−0.770886	−	1.33521i	−0.0251435	−	0.0435499i
$941$		−	19.6189i		−	0.639557i	−0.947492	−	0.319779i	$-0.896391\pi$
$941$		−	19.6189i		−	0.639557i	0.947492	−	0.319779i	$-0.103609\pi$
$942$		0			0
$943$	1.64427	−	0.949318i	0.0535447	−	0.0309140i
$944$		−	38.5309i		−	1.25408i
$945$		0			0
$946$	2.84583	−	4.92912i	0.0925259	−	0.160260i
$947$	49.5474	+	28.6062i	1.61007	+	0.929576i	0.989352	+	0.145544i	$0.0464933\pi$
$947$	49.5474	+	28.6062i	1.61007	+	0.929576i	0.620721	+	0.784032i	$0.286840\pi$
$948$		0			0
$949$	−36.2936	−	3.34935i	−1.17814	−	0.108725i
$950$	8.57233			0.278123
$951$		0			0
$952$	−22.6517	+	39.2339i	−0.734146	+	1.27158i
$953$	−13.7385	−	23.7958i	−0.445033	−	0.770820i	0.553021	−	0.833167i	$-0.313475\pi$
$953$	−13.7385	−	23.7958i	−0.445033	−	0.770820i	−0.998055	+	0.0623470i	$0.980141\pi$
$954$		0			0
$955$	3.35793	−	1.93870i	0.108660	−	0.0627350i
$956$	−3.05170	+	1.76190i	−0.0986991	+	0.0569840i
$957$		0			0
$958$	−3.86988	−	6.70283i	−0.125030	−	0.216559i
$959$	−39.3527	+	68.1609i	−1.27077	+	2.20103i
$960$		0			0
$961$	28.8564			0.930852
$962$	0.124393	−	0.0572867i	0.00401061	−	0.00184700i
$963$		0			0
$964$	−1.92391	−	1.11077i	−0.0619649	−	0.0357755i
$965$	−0.626972	+	1.08595i	−0.0201829	+	0.0349579i
$966$		0			0
$967$			10.3643i			0.333293i	0.986017	+	0.166647i	$0.0532939\pi$
$967$			10.3643i			0.333293i	−0.986017	+	0.166647i	$0.946706\pi$
$968$	22.5114	−	12.9970i	0.723544	−	0.417738i
$969$		0			0
$970$			5.14261i			0.165119i
$971$	20.8758	+	36.1579i	0.669935	+	1.16036i	0.977922	+	0.208971i	$0.0670113\pi$
$971$	20.8758	+	36.1579i	0.669935	+	1.16036i	−0.307987	+	0.951391i	$0.599655\pi$
$972$		0			0
$973$	−28.5308	−	16.4723i	−0.914656	−	0.528077i
$974$	46.0212			1.47461
$975$		0			0
$976$	−27.9929			−0.896030
$977$	11.9458	+	6.89691i	0.382180	+	0.220652i	0.678766	−	0.734354i	$-0.262515\pi$
$977$	11.9458	+	6.89691i	0.382180	+	0.220652i	−0.296586	+	0.955006i	$0.595848\pi$
$978$		0			0
$979$	−7.22187	−	12.5087i	−0.230812	−	0.399778i
$980$			3.85527i			0.123152i
$981$		0			0
$982$	46.3641	−	26.7683i	1.47954	−	0.854212i
$983$		−	37.9997i		−	1.21200i	−0.795463	−	0.606002i	$-0.792773\pi$
$983$		−	37.9997i		−	1.21200i	0.795463	−	0.606002i	$-0.207227\pi$
$984$		0			0
$985$	7.64098	−	13.2346i	0.243462	−	0.421688i
$986$	6.78988	+	3.92014i	0.216234	+	0.124843i
$987$		0			0
$988$	2.82306	−	3.99119i	0.0898134	−	0.126977i
$989$	25.2176			0.801873
$990$		0			0
$991$	26.2765	−	45.5122i	0.834700	−	1.44574i	−0.0595748	−	0.998224i	$-0.518974\pi$
$991$	26.2765	−	45.5122i	0.834700	−	1.44574i	0.894275	−	0.447519i	$-0.147692\pi$
$992$	0.974602	+	1.68806i	0.0309436	+	0.0535960i
$993$		0			0
$994$	48.5419	−	28.0257i	1.53966	−	0.888920i
$995$	11.4572	−	6.61480i	0.363217	−	0.209703i
$996$		0			0
$997$	−9.29497	−	16.0994i	−0.294375	−	0.509872i	0.680465	−	0.732781i	$-0.261778\pi$
$997$	−9.29497	−	16.0994i	−0.294375	−	0.509872i	−0.974839	+	0.222909i	$0.928445\pi$
$998$	21.6079	−	37.4260i	0.683986	−	1.18470i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bu.c.316.1		8
3.2	odd	2		65.2.m.a.56.4	yes	8
12.11	even	2		1040.2.da.b.641.3		8
13.6	odd	12		7605.2.a.cf.1.4		4
13.7	odd	12		7605.2.a.cj.1.1		4
13.10	even	6	inner	585.2.bu.c.361.1		8
15.2	even	4		325.2.m.c.199.1		8
15.8	even	4		325.2.m.b.199.4		8
15.14	odd	2		325.2.n.d.251.1		8
39.2	even	12		845.2.e.m.146.4		8
39.5	even	4		845.2.e.m.191.4		8
39.8	even	4		845.2.e.n.191.1		8
39.11	even	12		845.2.e.n.146.1		8
39.17	odd	6		845.2.c.g.506.7		8
39.20	even	12		845.2.a.l.1.4		4
39.23	odd	6		65.2.m.a.36.4	✓	8
39.29	odd	6		845.2.m.g.361.1		8
39.32	even	12		845.2.a.m.1.1		4
39.35	odd	6		845.2.c.g.506.2		8
39.38	odd	2		845.2.m.g.316.1		8
156.23	even	6		1040.2.da.b.881.3		8
195.23	even	12		325.2.m.c.49.1		8
195.59	even	12		4225.2.a.bl.1.1		4
195.62	even	12		325.2.m.b.49.4		8
195.149	even	12		4225.2.a.bi.1.4		4
195.179	odd	6		325.2.n.d.101.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.4	✓	8	39.23	odd	6
65.2.m.a.56.4	yes	8	3.2	odd	2
325.2.m.b.49.4		8	195.62	even	12
325.2.m.b.199.4		8	15.8	even	4
325.2.m.c.49.1		8	195.23	even	12
325.2.m.c.199.1		8	15.2	even	4
325.2.n.d.101.1		8	195.179	odd	6
325.2.n.d.251.1		8	15.14	odd	2
585.2.bu.c.316.1		8	1.1	even	1	trivial
585.2.bu.c.361.1		8	13.10	even	6	inner
845.2.a.l.1.4		4	39.20	even	12
845.2.a.m.1.1		4	39.32	even	12
845.2.c.g.506.2		8	39.35	odd	6
845.2.c.g.506.7		8	39.17	odd	6
845.2.e.m.146.4		8	39.2	even	12
845.2.e.m.191.4		8	39.5	even	4
845.2.e.n.146.1		8	39.11	even	12
845.2.e.n.191.1		8	39.8	even	4
845.2.m.g.316.1		8	39.38	odd	2
845.2.m.g.361.1		8	39.29	odd	6
1040.2.da.b.641.3		8	12.11	even	2
1040.2.da.b.881.3		8	156.23	even	6
4225.2.a.bi.1.4		4	195.149	even	12
4225.2.a.bl.1.1		4	195.59	even	12
7605.2.a.cf.1.4		4	13.6	odd	12
7605.2.a.cj.1.1		4	13.7	odd	12

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.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29515 - 0.747754i) q^{2} +(0.118272 + 0.204852i) q^{4} +1.00000i q^{5} +(-4.18016 + 2.41342i) q^{7} +2.63726i q^{8} +O(q^{10})\)	\(q+(-1.29515 - 0.747754i) q^{2} +(0.118272 + 0.204852i) q^{4} +1.00000i q^{5} +(-4.18016 + 2.41342i) q^{7} +2.63726i q^{8} +(0.747754 - 1.29515i) q^{10} +(0.926118 + 0.534695i) q^{11} +(0.331331 - 3.59030i) q^{13} +7.21857 q^{14} +(2.20857 - 3.82535i) q^{16} +(-1.77944 - 3.08209i) q^{17} +(4.96410 - 2.86603i) q^{19} +(-0.204852 + 0.118272i) q^{20} +(-0.799640 - 1.38502i) q^{22} +(3.54290 - 6.13649i) q^{23} -1.00000 q^{25} +(-3.11378 + 4.40221i) q^{26} +(-0.988789 - 0.570878i) q^{28} +(0.736543 - 1.27573i) q^{29} -1.46410i q^{31} +(-1.15297 + 0.665665i) q^{32} +5.32235i q^{34} +(-2.41342 - 4.18016i) q^{35} +(-0.0219955 - 0.0126991i) q^{37} -8.57233 q^{38} -2.63726 q^{40} +(0.232051 + 0.133975i) q^{41} +(1.77944 + 3.08209i) q^{43} +0.252957i q^{44} +(-9.17716 + 5.29844i) q^{46} +6.51793i q^{47} +(8.14918 - 14.1148i) q^{49} +(1.29515 + 0.747754i) q^{50} +(0.774668 - 0.356756i) q^{52} -0.991015 q^{53} +(-0.534695 + 0.926118i) q^{55} +(-6.36482 - 11.0242i) q^{56} +(-1.90786 + 1.10151i) q^{58} +(7.55440 - 4.36153i) q^{59} +(-3.16867 - 5.48830i) q^{61} +(-1.09479 + 1.89623i) q^{62} -6.84325 q^{64} +(3.59030 + 0.331331i) q^{65} +(-4.48009 - 2.58658i) q^{67} +(0.420915 - 0.729047i) q^{68} +7.21857i q^{70} +(6.72458 - 3.88244i) q^{71} -10.1088i q^{73} +(0.0189916 + 0.0328945i) q^{74} +(1.17422 + 0.677939i) q^{76} -5.16177 q^{77} +8.78347 q^{79} +(3.82535 + 2.20857i) q^{80} +(-0.200360 - 0.347034i) q^{82} +0.725474i q^{83} +(3.08209 - 1.77944i) q^{85} -5.32235i q^{86} +(-1.41013 + 2.44242i) q^{88} +(-11.6970 - 6.75327i) q^{89} +(7.27987 + 15.8077i) q^{91} +1.67610 q^{92} +(4.87381 - 8.44168i) q^{94} +(2.86603 + 4.96410i) q^{95} +(-2.97800 + 1.71935i) q^{97} +(-21.1088 + 12.1872i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) \) 8 * q + 2 * q^4 - 6 * q^7	\( 8 q + 2 q^{4} - 6 q^{7} - 2 q^{10} - 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} - 12 q^{20} - 12 q^{22} + 10 q^{23} - 8 q^{25} - 10 q^{26} - 18 q^{28} + 8 q^{29} - 6 q^{32} - 10 q^{35} + 6 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} - 2 q^{43} - 42 q^{46} + 12 q^{49} - 6 q^{52} + 24 q^{53} - 12 q^{56} + 36 q^{58} + 12 q^{59} - 28 q^{61} - 4 q^{62} - 8 q^{64} + 8 q^{65} + 6 q^{67} + 14 q^{68} - 10 q^{74} + 54 q^{76} + 36 q^{77} - 16 q^{79} + 4 q^{82} + 18 q^{85} - 18 q^{88} - 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 16 q^{95} - 30 q^{97} - 72 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 - 6 * q^7 - 2 * q^10 - 4 * q^14 - 2 * q^16 + 2 * q^17 + 12 * q^19 - 12 * q^20 - 12 * q^22 + 10 * q^23 - 8 * q^25 - 10 * q^26 - 18 * q^28 + 8 * q^29 - 6 * q^32 - 10 * q^35 + 6 * q^37 + 16 * q^38 - 12 * q^40 - 12 * q^41 - 2 * q^43 - 42 * q^46 + 12 * q^49 - 6 * q^52 + 24 * q^53 - 12 * q^56 + 36 * q^58 + 12 * q^59 - 28 * q^61 - 4 * q^62 - 8 * q^64 + 8 * q^65 + 6 * q^67 + 14 * q^68 - 10 * q^74 + 54 * q^76 + 36 * q^77 - 16 * q^79 + 4 * q^82 + 18 * q^85 - 18 * q^88 - 24 * q^89 + 28 * q^91 - 44 * q^92 + 32 * q^94 + 16 * q^95 - 30 * q^97 - 72 * q^98

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