LMFDB - Embedded newform 882.2.z.h.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(37,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("882.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.z (of order $21$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.4
Character	$\chi$	$=$	882.109
Dual form			882.2.z.h.793.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.733052 + 0.680173i) q^{2} +(0.0747301 - 0.997204i) q^{4} +(0.253636 - 0.646253i) q^{5} +(-0.581112 + 2.58114i) q^{7} +(0.623490 + 0.781831i) q^{8} +O(q^{10})$	\(q+(-0.733052 + 0.680173i) q^{2} +(0.0747301 - 0.997204i) q^{4} +(0.253636 - 0.646253i) q^{5} +(-0.581112 + 2.58114i) q^{7} +(0.623490 + 0.781831i) q^{8} +(0.253636 + 0.646253i) q^{10} +(-2.19352 - 0.676613i) q^{11} +(-0.439365 - 1.92498i) q^{13} +(-1.32964 - 2.28737i) q^{14} +(-0.988831 - 0.149042i) q^{16} +(-4.80089 + 3.27319i) q^{17} +(1.80759 + 3.13084i) q^{19} +(-0.625492 - 0.301221i) q^{20} +(2.06818 - 0.995983i) q^{22} +(-3.54142 - 2.41450i) q^{23} +(3.31195 + 3.07304i) q^{25} +(1.63140 + 1.11227i) q^{26} +(2.53050 + 0.772376i) q^{28} +(-5.27258 - 2.53914i) q^{29} +(-0.511564 + 0.886055i) q^{31} +(0.826239 - 0.563320i) q^{32} +(1.29297 - 5.66485i) q^{34} +(1.52068 + 1.03022i) q^{35} +(0.0906386 + 1.20949i) q^{37} +(-3.45457 - 1.06559i) q^{38} +(0.663401 - 0.204632i) q^{40} +(-1.61106 - 2.02020i) q^{41} +(-3.88025 + 4.86568i) q^{43} +(-0.838643 + 2.13683i) q^{44} +(4.23832 - 0.638825i) q^{46} +(-4.30004 + 3.98986i) q^{47} +(-6.32462 - 2.99987i) q^{49} -4.51803 q^{50} +(-1.95243 + 0.294282i) q^{52} +(-0.375034 + 5.00447i) q^{53} +(-0.993619 + 1.24596i) q^{55} +(-2.38034 + 1.15499i) q^{56} +(5.59213 - 1.72494i) q^{58} +(3.50526 + 8.93125i) q^{59} +(-0.331877 - 4.42859i) q^{61} +(-0.227668 - 0.997477i) q^{62} +(-0.222521 + 0.974928i) q^{64} +(-1.35547 - 0.204304i) q^{65} +(-6.91733 + 11.9812i) q^{67} +(2.90527 + 5.03207i) q^{68} +(-1.81546 + 0.279125i) q^{70} +(-7.08673 + 3.41279i) q^{71} +(-6.78586 - 6.29636i) q^{73} +(-0.889103 - 0.824967i) q^{74} +(3.25717 - 1.56857i) q^{76} +(3.02112 - 5.26862i) q^{77} +(-3.32182 - 5.75356i) q^{79} +(-0.347122 + 0.601233i) q^{80} +(2.55507 + 0.385115i) q^{82} +(1.37205 - 6.01133i) q^{83} +(0.897633 + 3.93279i) q^{85} +(-0.465078 - 6.20603i) q^{86} +(-0.838643 - 2.13683i) q^{88} +(7.21851 - 2.22662i) q^{89} +(5.22398 - 0.0154332i) q^{91} +(-2.67240 + 3.35108i) q^{92} +(0.438363 - 5.84954i) q^{94} +(2.48179 - 0.374069i) q^{95} -14.6706 q^{97} +(6.67670 - 2.10277i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 5 q^{2} + 5 q^{4} + 3 q^{5} + q^{7} - 10 q^{8}+O(q^{10}) $ 60 * q + 5 * q^2 + 5 * q^4 + 3 * q^5 + q^7 - 10 * q^8	$ 60 q + 5 q^{2} + 5 q^{4} + 3 q^{5} + q^{7} - 10 q^{8} + 3 q^{10} - q^{11} - 4 q^{13} + 4 q^{14} + 5 q^{16} + 6 q^{17} - 12 q^{19} - 6 q^{20} + 9 q^{22} - 2 q^{23} + 6 q^{25} + 2 q^{26} - 5 q^{28} - 6 q^{29} - 7 q^{31} + 5 q^{32} - 12 q^{34} + 40 q^{35} + 6 q^{37} - 26 q^{38} - 11 q^{40} + 12 q^{43} - 15 q^{44} - 2 q^{46} - 44 q^{47} - 43 q^{49} + 86 q^{50} + 2 q^{52} + 13 q^{53} - 45 q^{55} + 8 q^{56} - 18 q^{58} + 53 q^{59} - 32 q^{61} - 14 q^{62} - 10 q^{64} + 2 q^{65} - 4 q^{67} - 36 q^{68} - 8 q^{70} - 42 q^{71} - 40 q^{73} - 8 q^{74} - 4 q^{76} - 55 q^{77} - 3 q^{79} - 11 q^{80} + 17 q^{83} + 16 q^{85} + 64 q^{86} - 15 q^{88} + 50 q^{89} + 72 q^{91} + 4 q^{92} + 26 q^{94} - 26 q^{95} - 2 q^{97} - 53 q^{98}+O(q^{100}) $ 60 * q + 5 * q^2 + 5 * q^4 + 3 * q^5 + q^7 - 10 * q^8 + 3 * q^10 - q^11 - 4 * q^13 + 4 * q^14 + 5 * q^16 + 6 * q^17 - 12 * q^19 - 6 * q^20 + 9 * q^22 - 2 * q^23 + 6 * q^25 + 2 * q^26 - 5 * q^28 - 6 * q^29 - 7 * q^31 + 5 * q^32 - 12 * q^34 + 40 * q^35 + 6 * q^37 - 26 * q^38 - 11 * q^40 + 12 * q^43 - 15 * q^44 - 2 * q^46 - 44 * q^47 - 43 * q^49 + 86 * q^50 + 2 * q^52 + 13 * q^53 - 45 * q^55 + 8 * q^56 - 18 * q^58 + 53 * q^59 - 32 * q^61 - 14 * q^62 - 10 * q^64 + 2 * q^65 - 4 * q^67 - 36 * q^68 - 8 * q^70 - 42 * q^71 - 40 * q^73 - 8 * q^74 - 4 * q^76 - 55 * q^77 - 3 * q^79 - 11 * q^80 + 17 * q^83 + 16 * q^85 + 64 * q^86 - 15 * q^88 + 50 * q^89 + 72 * q^91 + 4 * q^92 + 26 * q^94 - 26 * q^95 - 2 * q^97 - 53 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$1$

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 $

$2$	−0.733052	+	0.680173i	−0.518346	+	0.480955i
$2$	−0.733052	+	0.680173i	−0.518346	+	0.480955i
$3$		0			0
$3$		0			0
$4$	0.0747301	−	0.997204i	0.0373650	−	0.498602i
$5$	0.253636	−	0.646253i	0.113429	−	0.289013i	−0.862874	−	0.505419i	$-0.831338\pi$
$5$	0.253636	−	0.646253i	0.113429	−	0.289013i	0.976304	+	0.216405i	$0.0694333\pi$
$6$		0			0
$7$	−0.581112	+	2.58114i	−0.219640	+	0.975581i
$7$	−0.581112	+	2.58114i	−0.219640	+	0.975581i
$8$	0.623490	+	0.781831i	0.220437	+	0.276419i
$9$		0			0
$10$	0.253636	+	0.646253i	0.0802067	+	0.204363i
$11$	−2.19352	−	0.676613i	−0.661372	−	0.204006i	−0.0541433	−	0.998533i	$-0.517243\pi$
$11$	−2.19352	−	0.676613i	−0.661372	−	0.204006i	−0.607229	+	0.794527i	$0.707719\pi$
$12$		0			0
$13$	−0.439365	−	1.92498i	−0.121858	−	0.533894i	−0.998598	−	0.0529303i	$-0.983144\pi$
$13$	−0.439365	−	1.92498i	−0.121858	−	0.533894i	0.876740	−	0.480964i	$-0.159713\pi$
$14$	−1.32964	−	2.28737i	−0.355361	−	0.611325i
$15$		0			0
$16$	−0.988831	−	0.149042i	−0.247208	−	0.0372606i
$17$	−4.80089	+	3.27319i	−1.16439	+	0.793865i	−0.981911	−	0.189345i	$-0.939363\pi$
$17$	−4.80089	+	3.27319i	−1.16439	+	0.793865i	−0.182476	+	0.983210i	$0.558411\pi$
$18$		0			0
$19$	1.80759	+	3.13084i	0.414690	+	0.718264i	0.995396	−	0.0958492i	$-0.0305566\pi$
$19$	1.80759	+	3.13084i	0.414690	+	0.718264i	−0.580706	+	0.814114i	$0.697223\pi$
$20$	−0.625492	−	0.301221i	−0.139864	−	0.0673551i
$21$		0			0
$22$	2.06818	−	0.995983i	0.440937	−	0.212344i
$23$	−3.54142	−	2.41450i	−0.738438	−	0.503458i	0.134727	−	0.990883i	$-0.456984\pi$
$23$	−3.54142	−	2.41450i	−0.738438	−	0.503458i	−0.873165	+	0.487424i	$0.837936\pi$
$24$		0			0
$25$	3.31195	+	3.07304i	0.662389	+	0.614608i
$26$	1.63140	+	1.11227i	0.319944	+	0.218134i
$27$		0			0
$28$	2.53050	+	0.772376i	0.478220	+	0.145965i
$29$	−5.27258	−	2.53914i	−0.979094	−	0.471507i	−0.125301	−	0.992119i	$-0.539990\pi$
$29$	−5.27258	−	2.53914i	−0.979094	−	0.471507i	−0.853793	+	0.520612i	$0.825704\pi$
$30$		0			0
$31$	−0.511564	+	0.886055i	−0.0918797	+	0.159140i	−0.908302	−	0.418315i	$-0.862621\pi$
$31$	−0.511564	+	0.886055i	−0.0918797	+	0.159140i	0.816422	+	0.577455i	$0.195954\pi$
$32$	0.826239	−	0.563320i	0.146060	−	0.0995819i
$33$		0			0
$34$	1.29297	−	5.66485i	0.221742	−	0.971514i
$35$	1.52068	+	1.03022i	0.257042	+	0.174138i
$36$		0			0
$37$	0.0906386	+	1.20949i	0.0149009	+	0.198839i	0.999686	+	0.0250615i	$0.00797816\pi$
$37$	0.0906386	+	1.20949i	0.0149009	+	0.198839i	−0.984785	+	0.173777i	$0.944403\pi$
$38$	−3.45457	−	1.06559i	−0.560406	−	0.172862i
$39$		0			0
$40$	0.663401	−	0.204632i	0.104893	−	0.0323552i
$41$	−1.61106	−	2.02020i	−0.251605	−	0.315502i	0.639949	−	0.768417i	$-0.278956\pi$
$41$	−1.61106	−	2.02020i	−0.251605	−	0.315502i	−0.891554	+	0.452915i	$0.850384\pi$
$42$		0			0
$43$	−3.88025	+	4.86568i	−0.591732	+	0.742009i	−0.984064	−	0.177815i	$-0.943097\pi$
$43$	−3.88025	+	4.86568i	−0.591732	+	0.742009i	0.392332	+	0.919824i	$0.371669\pi$
$44$	−0.838643	+	2.13683i	−0.126430	+	0.322139i
$45$		0			0
$46$	4.23832	−	0.638825i	0.624907	−	0.0941896i
$47$	−4.30004	+	3.98986i	−0.627226	+	0.581980i	−0.928397	−	0.371590i	$-0.878813\pi$
$47$	−4.30004	+	3.98986i	−0.627226	+	0.581980i	0.301171	+	0.953570i	$0.402622\pi$
$48$		0			0
$49$	−6.32462	−	2.99987i	−0.903517	−	0.428553i
$50$	−4.51803			−0.638945
$51$		0			0
$52$	−1.95243	+	0.294282i	−0.270754	+	0.0408096i
$53$	−0.375034	+	5.00447i	−0.0515148	+	0.687417i	0.910341	+	0.413860i	$0.135820\pi$
$53$	−0.375034	+	5.00447i	−0.0515148	+	0.687417i	−0.961856	+	0.273558i	$0.911800\pi$
$54$		0			0
$55$	−0.993619	+	1.24596i	−0.133980	+	0.168005i
$56$	−2.38034	+	1.15499i	−0.318086	+	0.154341i
$57$		0			0
$58$	5.59213	−	1.72494i	0.734283	−	0.226496i
$59$	3.50526	+	8.93125i	0.456346	+	1.16275i	0.955173	+	0.296048i	$0.0956690\pi$
$59$	3.50526	+	8.93125i	0.456346	+	1.16275i	−0.498827	+	0.866701i	$0.666236\pi$
$60$		0			0
$61$	−0.331877	−	4.42859i	−0.0424925	−	0.567023i	−0.977299	−	0.211865i	$-0.932046\pi$
$61$	−0.331877	−	4.42859i	−0.0424925	−	0.567023i	0.934806	−	0.355158i	$-0.115573\pi$
$62$	−0.227668	−	0.997477i	−0.0289138	−	0.126680i
$63$		0			0
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	−1.35547	−	0.204304i	−0.168125	−	0.0253407i
$66$		0			0
$67$	−6.91733	+	11.9812i	−0.845086	+	1.46373i	0.0404608	+	0.999181i	$0.487117\pi$
$67$	−6.91733	+	11.9812i	−0.845086	+	1.46373i	−0.885547	+	0.464550i	$0.846216\pi$
$68$	2.90527	+	5.03207i	0.352315	+	0.610228i
$69$		0			0
$70$	−1.81546	+	0.279125i	−0.216990	+	0.0333618i
$71$	−7.08673	+	3.41279i	−0.841040	+	0.405023i	−0.804244	−	0.594299i	$-0.797429\pi$
$71$	−7.08673	+	3.41279i	−0.841040	+	0.405023i	−0.0367959	+	0.999323i	$0.511715\pi$
$72$		0			0
$73$	−6.78586	−	6.29636i	−0.794225	−	0.736933i	0.174610	−	0.984638i	$-0.444133\pi$
$73$	−6.78586	−	6.29636i	−0.794225	−	0.736933i	−0.968836	+	0.247704i	$0.920324\pi$
$74$	−0.889103	−	0.824967i	−0.103356	−	0.0959005i
$75$		0			0
$76$	3.25717	−	1.56857i	0.373623	−	0.179927i
$77$	3.02112	−	5.26862i	0.344288	−	0.600414i
$78$		0			0
$79$	−3.32182	−	5.75356i	−0.373734	−	0.647327i	0.616403	−	0.787431i	$-0.288589\pi$
$79$	−3.32182	−	5.75356i	−0.373734	−	0.647327i	−0.990137	+	0.140105i	$0.955256\pi$
$80$	−0.347122	+	0.601233i	−0.0388094	+	0.0672199i
$81$		0			0
$82$	2.55507	+	0.385115i	0.282161	+	0.0425289i
$83$	1.37205	−	6.01133i	0.150602	−	0.659829i	−0.842109	−	0.539307i	$-0.818686\pi$
$83$	1.37205	−	6.01133i	0.150602	−	0.659829i	0.992711	−	0.120522i	$-0.0384567\pi$
$84$		0			0
$85$	0.897633	+	3.93279i	0.0973620	+	0.426571i
$86$	−0.465078	−	6.20603i	−0.0501506	−	0.669214i
$87$		0			0
$88$	−0.838643	−	2.13683i	−0.0893996	−	0.227787i
$89$	7.21851	−	2.22662i	0.765161	−	0.236021i	0.112480	−	0.993654i	$-0.464121\pi$
$89$	7.21851	−	2.22662i	0.765161	−	0.236021i	0.652681	+	0.757633i	$0.273644\pi$
$90$		0			0
$91$	5.22398	−	0.0154332i	0.547622	−	0.00161784i
$92$	−2.67240	+	3.35108i	−0.278617	+	0.349375i
$93$		0			0
$94$	0.438363	−	5.84954i	0.0452137	−	0.603334i
$95$	2.48179	−	0.374069i	0.254626	−	0.0383787i
$96$		0			0
$97$	−14.6706			−1.48957			−0.744785	−	0.667304i	$-0.767448\pi$
$97$	−14.6706			−1.48957			−0.744785	+	0.667304i	$0.767448\pi$
$98$	6.67670	−	2.10277i	0.674449	−	0.212412i
$99$		0			0
$100$	3.31195	−	3.07304i	0.331195	−	0.307304i
$101$	−6.72065	+	1.01298i	−0.668730	+	0.100795i	−0.474628	−	0.880187i	$-0.657417\pi$
$101$	−6.72065	+	1.01298i	−0.668730	+	0.100795i	−0.194102	+	0.980981i	$0.562179\pi$
$102$		0			0
$103$	3.52416	−	8.97942i	0.347246	−	0.884768i	−0.645414	−	0.763833i	$-0.723315\pi$
$103$	3.52416	−	8.97942i	0.347246	−	0.884768i	0.992660	−	0.120936i	$-0.0385895\pi$
$104$	1.23107	−	1.54372i	0.120717	−	0.151374i
$105$		0			0
$106$	−3.12899	−	3.92363i	−0.303914	−	0.381096i
$107$	−6.62499	+	2.04354i	−0.640462	+	0.197556i	−0.597942	−	0.801539i	$-0.704015\pi$
$107$	−6.62499	+	2.04354i	−0.640462	+	0.197556i	−0.0425198	+	0.999096i	$0.513539\pi$
$108$		0			0
$109$	−1.12689	−	0.347599i	−0.107936	−	0.0332939i	0.240317	−	0.970695i	$-0.422749\pi$
$109$	−1.12689	−	0.347599i	−0.107936	−	0.0332939i	−0.348253	+	0.937401i	$0.613225\pi$
$110$	−0.119093	−	1.58919i	−0.0113551	−	0.151523i
$111$		0			0
$112$	0.959321	−	2.46571i	0.0906473	−	0.232987i
$113$	3.62276	−	15.8723i	0.340800	−	1.49314i	−0.456588	−	0.889678i	$-0.650929\pi$
$113$	3.62276	−	15.8723i	0.340800	−	1.49314i	0.797389	−	0.603466i	$-0.206214\pi$
$114$		0			0
$115$	−2.45861	+	1.67625i	−0.229267	+	0.156311i
$116$	−2.92606	+	5.06809i	−0.271678	+	0.470560i
$117$		0			0
$118$	−8.64433	−	4.16289i	−0.795775	−	0.383225i
$119$	−5.65872	−	14.2939i	−0.518734	−	1.31032i
$120$		0			0
$121$	−4.73488	−	3.22819i	−0.430444	−	0.293472i
$122$	3.25549	+	3.02065i	0.294738	+	0.273477i
$123$		0			0
$124$	0.845348	+	0.576349i	0.0759145	+	0.0517577i
$125$	5.95345	−	2.86703i	0.532493	−	0.256435i
$126$		0			0
$127$	19.0242	+	9.16156i	1.68812	+	0.812957i	0.995819	+	0.0913520i	$0.0291188\pi$
$127$	19.0242	+	9.16156i	1.68812	+	0.812957i	0.692305	+	0.721605i	$0.256595\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1.13259	−	0.772186i	0.0993346	−	0.0677252i
$131$	14.8824	+	2.24316i	1.30028	+	0.195986i	0.762439	−	0.647060i	$-0.224002\pi$
$131$	14.8824	+	2.24316i	1.30028	+	0.195986i	0.537842	+	0.843046i	$0.319240\pi$
$132$		0			0
$133$	−9.13157	+	2.84629i	−0.791808	+	0.246804i
$134$	−3.07850	−	13.4878i	−0.265942	−	1.16517i
$135$		0			0
$136$	−5.55239	−	1.71268i	−0.476113	−	0.146861i
$137$	6.23389	+	15.8837i	0.532597	+	1.35704i	0.903590	+	0.428399i	$0.140922\pi$
$137$	6.23389	+	15.8837i	0.532597	+	1.35704i	−0.370993	+	0.928636i	$0.620982\pi$
$138$		0			0
$139$	8.33203	+	10.4480i	0.706714	+	0.886191i	0.997505	−	0.0705957i	$-0.0224900\pi$
$139$	8.33203	+	10.4480i	0.706714	+	0.886191i	−0.290791	+	0.956786i	$0.593919\pi$
$140$	1.14098	−	1.43944i	0.0964301	−	0.121655i
$141$		0			0
$142$	2.87365	−	7.32195i	0.241152	−	0.614444i
$143$	−0.338710	+	4.51978i	−0.0283244	+	0.377963i
$144$		0			0
$145$	−2.97825	+	2.76341i	−0.247330	+	0.229489i
$146$	9.25700			0.766115
$147$		0			0
$148$	1.21288			0.0996980
$149$	−6.79746	+	6.30712i	−0.556869	+	0.516699i	−0.907633	−	0.419765i	$-0.862113\pi$
$149$	−6.79746	+	6.30712i	−0.556869	+	0.516699i	0.350763	+	0.936464i	$0.385922\pi$
$150$		0			0
$151$	−0.273031	+	3.64334i	−0.0222189	+	0.296491i	0.975014	+	0.222145i	$0.0713059\pi$
$151$	−0.273031	+	3.64334i	−0.0222189	+	0.296491i	−0.997233	+	0.0743458i	$0.976313\pi$
$152$	−1.32078	+	3.36528i	−0.107129	+	0.272960i
$153$		0			0
$154$	1.36893	+	5.91705i	0.110312	+	0.476810i
$155$	0.442865	+	0.555336i	0.0355718	+	0.0446056i
$156$		0			0
$157$	2.51224	+	6.40109i	0.200499	+	0.510863i	0.995392	−	0.0958864i	$-0.0305685\pi$
$157$	2.51224	+	6.40109i	0.200499	+	0.510863i	−0.794893	+	0.606749i	$0.792473\pi$
$158$	6.34849	+	1.95825i	0.505058	+	0.155790i
$159$		0			0
$160$	−0.154484	−	0.676838i	−0.0122130	−	0.0535087i
$161$	8.29014	−	7.73783i	0.653355	−	0.609826i
$162$		0			0
$163$	−5.11012	−	0.770227i	−0.400256	−	0.0603288i	−0.0541699	−	0.998532i	$-0.517251\pi$
$163$	−5.11012	−	0.770227i	−0.400256	−	0.0603288i	−0.346086	+	0.938203i	$0.612489\pi$
$164$	−2.13495	+	1.45558i	−0.166711	+	0.113662i
$165$		0			0
$166$	3.08296	+	5.33984i	0.239284	+	0.414452i
$167$	10.0767	+	4.85271i	0.779762	+	0.375514i	0.781036	−	0.624486i	$-0.214691\pi$
$167$	10.0767	+	4.85271i	0.779762	+	0.375514i	−0.00127427	+	0.999999i	$0.500406\pi$
$168$		0			0
$169$	8.20008	−	3.94895i	0.630775	−	0.303765i
$170$	−3.33299	−	2.27239i	−0.255628	−	0.174285i
$171$		0			0
$172$	4.56210	+	4.23301i	0.347857	+	0.322764i
$173$	18.6791	+	12.7352i	1.42015	+	0.968240i	0.998097	+	0.0616673i	$0.0196418\pi$
$173$	18.6791	+	12.7352i	1.42015	+	0.968240i	0.422050	+	0.906572i	$0.361311\pi$
$174$		0			0
$175$	−9.85657	+	6.76284i	−0.745086	+	0.511222i
$176$	2.06818	+	0.995983i	0.155895	+	0.0750750i
$177$		0			0
$178$	−3.77706	+	6.54206i	−0.283103	+	0.490348i
$179$	7.66458	−	5.22562i	0.572877	−	0.390581i	−0.241947	−	0.970290i	$-0.577786\pi$
$179$	7.66458	−	5.22562i	0.572877	−	0.390581i	0.814824	+	0.579708i	$0.196833\pi$
$180$		0			0
$181$	2.63638	−	11.5507i	0.195960	−	0.858558i	−0.777350	−	0.629068i	$-0.783437\pi$
$181$	2.63638	−	11.5507i	0.195960	−	0.858558i	0.973311	−	0.229491i	$-0.0737061\pi$
$182$	−3.81895	+	3.56452i	−0.283080	+	0.264220i
$183$		0			0
$184$	−0.320308	−	4.27421i	−0.0236134	−	0.315099i
$185$	0.804625	+	0.248194i	0.0591572	+	0.0182476i
$186$		0			0
$187$	12.7455	−	3.93148i	0.932046	−	0.287498i
$188$	3.65736	+	4.58618i	0.266740	+	0.334482i
$189$		0			0
$190$	−1.56485	+	1.96226i	−0.113526	+	0.142357i
$191$	1.52196	−	3.87789i	0.110125	−	0.280595i	−0.865178	−	0.501465i	$-0.832795\pi$
$191$	1.52196	−	3.87789i	0.110125	−	0.280595i	0.975303	+	0.220871i	$0.0708898\pi$
$192$		0			0
$193$	−15.4304	+	2.32575i	−1.11070	+	0.167412i	−0.678668	−	0.734445i	$-0.737442\pi$
$193$	−15.4304	+	2.32575i	−1.11070	+	0.167412i	−0.432035	+	0.901857i	$0.642204\pi$
$194$	10.7543	−	9.97852i	0.772113	−	0.716416i
$195$		0			0
$196$	−3.46412	+	6.08275i	−0.247437	+	0.434482i
$197$	−7.14953			−0.509383			−0.254691	−	0.967022i	$-0.581974\pi$
$197$	−7.14953			−0.509383			−0.254691	+	0.967022i	$0.581974\pi$
$198$		0			0
$199$	8.77429	−	1.32251i	0.621993	−	0.0937503i	0.169517	−	0.985527i	$-0.445779\pi$
$199$	8.77429	−	1.32251i	0.621993	−	0.0937503i	0.452475	+	0.891777i	$0.350541\pi$
$200$	−0.337632	+	4.50539i	−0.0238742	+	0.318579i
$201$		0			0
$202$	4.23759	−	5.31377i	0.298156	−	0.373875i
$203$	9.61785	−	12.1338i	0.675041	−	0.851624i
$204$		0			0
$205$	−1.71418	+	0.528756i	−0.119724	+	0.0369299i
$206$	3.52416	+	8.97942i	0.245540	+	0.625626i
$207$		0			0
$208$	0.147554	+	1.96897i	0.0102310	+	0.136523i
$209$	−1.84663	−	8.09062i	−0.127734	−	0.559640i
$210$		0			0
$211$	0.162938	−	0.713876i	0.0112171	−	0.0491453i	−0.969010	−	0.247023i	$-0.920548\pi$
$211$	0.162938	−	0.713876i	0.0112171	−	0.0491453i	0.980227	+	0.197878i	$0.0634049\pi$
$212$	4.96245	+	0.747970i	0.340823	+	0.0513708i
$213$		0			0
$214$	3.46650	−	6.00416i	0.236965	−	0.410436i
$215$	2.16029	+	3.74173i	0.147331	+	0.255184i
$216$		0			0
$217$	−1.98976	−	1.83532i	−0.135074	−	0.124590i
$218$	1.06249	−	0.511670i	0.0719612	−	0.0346547i
$219$		0			0
$220$	1.16822	+	1.08395i	0.0787615	+	0.0730800i
$221$	8.41018	+	7.80350i	0.565730	+	0.524920i
$222$		0			0
$223$	7.67736	−	3.69722i	0.514114	−	0.247584i	−0.158792	−	0.987312i	$-0.550760\pi$
$223$	7.67736	−	3.69722i	0.514114	−	0.247584i	0.672906	+	0.739728i	$0.265046\pi$
$224$	0.973873	+	2.45999i	0.0650696	+	0.164365i
$225$		0			0
$226$	8.14026	+	14.0993i	0.541482	+	0.937875i
$227$	−10.6899	+	18.5155i	−0.709514	+	1.22892i	0.255523	+	0.966803i	$0.417752\pi$
$227$	−10.6899	+	18.5155i	−0.709514	+	1.22892i	−0.965037	+	0.262112i	$0.915581\pi$
$228$		0			0
$229$	6.00356	+	0.904891i	0.396727	+	0.0597969i	0.344376	−	0.938832i	$-0.388091\pi$
$229$	6.00356	+	0.904891i	0.396727	+	0.0597969i	0.0523507	+	0.998629i	$0.483329\pi$
$230$	0.662148	−	2.90106i	0.0436608	−	0.191290i
$231$		0			0
$232$	−1.30222	−	5.70540i	−0.0854950	−	0.374578i
$233$	1.34286	+	17.9192i	0.0879734	+	1.17392i	0.850145	+	0.526549i	$0.176514\pi$
$233$	1.34286	+	17.9192i	0.0879734	+	1.17392i	−0.762172	+	0.647375i	$0.775867\pi$
$234$		0			0
$235$	1.48781	+	3.79089i	0.0970543	+	0.247290i
$236$	9.16823	−	2.82802i	0.596801	−	0.184089i
$237$		0			0
$238$	13.8704	+	6.62924i	0.899087	+	0.429710i
$239$	7.37641	−	9.24972i	0.477140	−	0.598315i	−0.483763	−	0.875199i	$-0.660730\pi$
$239$	7.37641	−	9.24972i	0.477140	−	0.598315i	0.960903	+	0.276884i	$0.0893019\pi$
$240$		0			0
$241$	0.696342	−	9.29204i	0.0448553	−	0.598553i	−0.928808	−	0.370562i	$-0.879165\pi$
$241$	0.696342	−	9.29204i	0.0448553	−	0.598553i	0.973663	−	0.227991i	$-0.0732158\pi$
$242$	5.66664	−	0.854109i	0.364266	−	0.0549042i
$243$		0			0
$244$	−4.44101			−0.284307
$245$	−3.54283	+	3.32643i	−0.226343	+	0.212518i
$246$		0			0
$247$	5.23263	−	4.85517i	0.332944	−	0.308927i
$248$	−1.01170	+	0.152489i	−0.0642431	+	0.00968309i
$249$		0			0
$250$	−2.41411	+	6.15106i	−0.152682	+	0.389027i
$251$	17.6609	−	22.1461i	1.11475	−	1.39785i	0.206995	−	0.978342i	$-0.433631\pi$
$251$	17.6609	−	22.1461i	1.11475	−	1.39785i	0.907752	−	0.419507i	$-0.137797\pi$
$252$		0			0
$253$	6.13451	+	7.69244i	0.385674	+	0.483619i
$254$	−20.1772	+	6.22383i	−1.26603	+	0.390518i
$255$		0			0
$256$	0.955573	+	0.294755i	0.0597233	+	0.0184222i
$257$	−0.819909	−	10.9409i	−0.0511445	−	0.682476i	−0.962574	−	0.271020i	$-0.912639\pi$
$257$	−0.819909	−	10.9409i	−0.0511445	−	0.682476i	0.911429	−	0.411457i	$-0.134980\pi$
$258$		0			0
$259$	−3.17453	−	0.468897i	−0.197256	−	0.0291358i
$260$	−0.305026	+	1.33641i	−0.0189169	+	0.0828805i
$261$		0			0
$262$	−12.4353	+	8.47825i	−0.768256	+	0.523788i
$263$	−7.07895	+	12.2611i	−0.436507	+	0.756052i	−0.997417	−	0.0718247i	$-0.977118\pi$
$263$	−7.07895	+	12.2611i	−0.436507	+	0.756052i	0.560911	+	0.827876i	$0.310451\pi$
$264$		0			0
$265$	3.13904	+	1.51168i	0.192830	+	0.0928618i
$266$	4.75795	−	8.29752i	0.291728	−	0.508754i
$267$		0			0
$268$	11.4307	+	7.79334i	0.698243	+	0.476054i
$269$	−11.2875	−	10.4732i	−0.688209	−	0.638564i	0.256474	−	0.966551i	$-0.417439\pi$
$269$	−11.2875	−	10.4732i	−0.688209	−	0.638564i	−0.944682	+	0.327987i	$0.893630\pi$
$270$		0			0
$271$	12.1803	+	8.30436i	0.739898	+	0.504454i	0.873646	−	0.486562i	$-0.161749\pi$
$271$	12.1803	+	8.30436i	0.739898	+	0.504454i	−0.133749	+	0.991015i	$0.542701\pi$
$272$	5.23511	−	2.52110i	0.317425	−	0.152864i
$273$		0			0
$274$	−15.3734	−	7.40345i	−0.928742	−	0.447259i
$275$	−5.18558	−	8.98169i	−0.312702	−	0.541616i
$276$		0			0
$277$	−1.62411	+	1.10730i	−0.0975831	+	0.0665310i	−0.611129	−	0.791531i	$-0.709284\pi$
$277$	−1.62411	+	1.10730i	−0.0975831	+	0.0665310i	0.513545	+	0.858062i	$0.328332\pi$
$278$	−13.2143	−	1.99173i	−0.792540	−	0.119456i
$279$		0			0
$280$	0.142675	+	1.83125i	0.00852644	+	0.109438i
$281$	−0.197562	−	0.865575i	−0.0117856	−	0.0516359i	0.968693	−	0.248261i	$-0.0798590\pi$
$281$	−0.197562	−	0.865575i	−0.0117856	−	0.0516359i	−0.980479	+	0.196625i	$0.937002\pi$
$282$		0			0
$283$	−1.01275	−	0.312391i	−0.0602016	−	0.0185697i	0.264508	−	0.964383i	$-0.414790\pi$
$283$	−1.01275	−	0.312391i	−0.0602016	−	0.0185697i	−0.324710	+	0.945814i	$0.605267\pi$
$284$	2.87365	+	7.32195i	0.170520	+	0.434478i
$285$		0			0
$286$	−2.82594	−	3.54361i	−0.167101	−	0.209538i
$287$	6.15064	−	2.98441i	0.363061	−	0.176164i
$288$		0			0
$289$	6.12395	−	15.6036i	0.360233	−	0.917858i
$290$	0.303614	−	4.05144i	0.0178288	−	0.237909i
$291$		0			0
$292$	−6.78586	+	6.29636i	−0.397113	+	0.368467i
$293$	31.2585			1.82614			0.913069	−	0.407805i	$-0.133706\pi$
$293$	31.2585			1.82614			0.913069	+	0.407805i	$0.133706\pi$
$294$		0			0
$295$	6.66091			0.387813
$296$	−0.889103	+	0.824967i	−0.0516781	+	0.0479502i
$297$		0			0
$298$	0.692959	−	9.24689i	0.0401420	−	0.535658i
$299$	−3.09190	+	7.87803i	−0.178809	+	0.455598i
$300$		0			0
$301$	−10.3042	−	12.8430i	−0.593922	−	0.740257i
$302$	−2.27796	−	2.85647i	−0.131082	−	0.164371i
$303$		0			0
$304$	−1.32078	−	3.36528i	−0.0757517	−	0.193012i
$305$	−2.94617	−	0.908773i	−0.168697	−	0.0520362i
$306$		0			0
$307$	1.62098	+	7.10199i	0.0925144	+	0.405332i	0.999888	−	0.0149939i	$-0.00477290\pi$
$307$	1.62098	+	7.10199i	0.0925144	+	0.405332i	−0.907373	+	0.420326i	$0.861916\pi$
$308$	−5.02811	−	3.40639i	−0.286503	−	0.194097i
$309$		0			0
$310$	−0.702367	−	0.105865i	−0.0398918	−	0.00601272i
$311$	7.39330	−	5.04067i	0.419236	−	0.285830i	−0.335272	−	0.942121i	$-0.608828\pi$
$311$	7.39330	−	5.04067i	0.419236	−	0.285830i	0.754508	+	0.656291i	$0.227876\pi$
$312$		0			0
$313$	−16.0058	−	27.7229i	−0.904704	−	1.56699i	−0.821314	−	0.570476i	$-0.806759\pi$
$313$	−16.0058	−	27.7229i	−0.904704	−	1.56699i	−0.0833899	−	0.996517i	$-0.526575\pi$
$314$	−6.19545	−	2.98357i	−0.349630	−	0.168373i
$315$		0			0
$316$	−5.98572	+	2.88257i	−0.336723	+	0.162157i
$317$	−14.9699	−	10.2063i	−0.840793	−	0.573243i	0.0645547	−	0.997914i	$-0.479437\pi$
$317$	−14.9699	−	10.2063i	−0.840793	−	0.573243i	−0.905348	+	0.424671i	$0.860390\pi$
$318$		0			0
$319$	9.84752	+	9.13716i	0.551355	+	0.511583i
$320$	0.573611	+	0.391082i	0.0320658	+	0.0218621i
$321$		0			0
$322$	−0.814043	+	11.3110i	−0.0453648	+	0.630335i
$323$	−18.9259	−	9.11423i	−1.05306	−	0.507129i
$324$		0			0
$325$	4.46039	−	7.72563i	0.247418	−	0.428541i
$326$	4.26987	−	2.91115i	0.236486	−	0.161234i
$327$		0			0
$328$	0.574979	−	2.51915i	0.0317479	−	0.139097i
$329$	−7.79959	−	13.4176i	−0.430005	−	0.739735i
$330$		0			0
$331$	0.709169	+	9.46320i	0.0389794	+	0.520144i	0.982183	+	0.187928i	$0.0601773\pi$
$331$	0.709169	+	9.46320i	0.0389794	+	0.520144i	−0.943203	+	0.332216i	$0.892204\pi$
$332$	−5.89199	−	1.81744i	−0.323365	−	0.0997448i
$333$		0			0
$334$	−10.6875	+	3.29664i	−0.584792	+	0.180384i
$335$	5.98838	+	7.50920i	0.327180	+	0.410271i
$336$		0			0
$337$	−1.20468	+	1.51062i	−0.0656232	+	0.0822889i	−0.813560	−	0.581481i	$-0.802473\pi$
$337$	−1.20468	+	1.51062i	−0.0656232	+	0.0822889i	0.747937	+	0.663770i	$0.231045\pi$
$338$	−3.32511	+	8.47225i	−0.180862	+	0.460830i
$339$		0			0
$340$	3.98887	−	0.601226i	0.216327	−	0.0326060i
$341$	1.72164	−	1.59745i	0.0932323	−	0.0865069i
$342$		0			0
$343$	11.4184	−	14.5815i	0.616536	−	0.787327i
$344$	−6.22343			−0.335545
$345$		0			0
$346$	−22.3549	+	3.36946i	−1.20181	+	0.181143i
$347$	−2.09851	+	28.0027i	−0.112654	+	1.50326i	0.599009	+	0.800742i	$0.295561\pi$
$347$	−2.09851	+	28.0027i	−0.112654	+	1.50326i	−0.711663	+	0.702521i	$0.752058\pi$
$348$		0			0
$349$	−20.5993	+	25.8307i	−1.10265	+	1.38268i	−0.186215	+	0.982509i	$0.559622\pi$
$349$	−20.5993	+	25.8307i	−1.10265	+	1.38268i	−0.916439	+	0.400175i	$0.868949\pi$
$350$	2.62548	−	11.6617i	0.140338	−	0.623343i
$351$		0			0
$352$	−2.19352	+	0.676613i	−0.116915	+	0.0360636i
$353$	9.24128	+	23.5464i	0.491863	+	1.25325i	0.934313	+	0.356454i	$0.116014\pi$
$353$	9.24128	+	23.5464i	0.491863	+	1.25325i	−0.442449	+	0.896793i	$0.645890\pi$
$354$		0			0
$355$	0.408078	+	5.44543i	0.0216586	+	0.289013i
$356$	−1.68095	−	7.36472i	−0.0890902	−	0.390330i
$357$		0			0
$358$	−2.06421	+	9.04389i	−0.109097	+	0.477984i
$359$	−27.0043	−	4.07025i	−1.42523	−	0.214820i	−0.609289	−	0.792948i	$-0.708545\pi$
$359$	−27.0043	−	4.07025i	−1.42523	−	0.214820i	−0.815945	+	0.578129i	$0.803783\pi$
$360$		0			0
$361$	2.96522	−	5.13591i	0.156064	−	0.270311i
$362$	5.92389	+	10.2605i	0.311353	+	0.539278i
$363$		0			0
$364$	0.374998	−	5.21053i	0.0196553	−	0.273106i
$365$	−5.79018	+	2.78841i	−0.303072	+	0.145952i
$366$		0			0
$367$	0.610566	+	0.566523i	0.0318713	+	0.0295722i	0.695948	−	0.718093i	$-0.254985\pi$
$367$	0.610566	+	0.566523i	0.0318713	+	0.0295722i	−0.664076	+	0.747665i	$0.731175\pi$
$368$	3.14201	+	2.91536i	0.163788	+	0.151973i
$369$		0			0
$370$	−0.758646	+	0.365345i	−0.0394401	+	0.0189934i
$371$	−12.6993	−	3.87618i	−0.659317	−	0.201241i
$372$		0			0
$373$	6.11965	+	10.5996i	0.316864	+	0.548824i	0.979832	−	0.199824i	$-0.0640369\pi$
$373$	6.11965	+	10.5996i	0.316864	+	0.548824i	−0.662968	+	0.748648i	$0.730704\pi$
$374$	−6.66906	+	11.5511i	−0.344849	+	0.597296i
$375$		0			0
$376$	−5.80043	−	0.874274i	−0.299134	−	0.0450872i
$377$	−2.57122	+	11.2652i	−0.132424	+	0.580190i
$378$		0			0
$379$	−4.57273	−	20.0345i	−0.234886	−	1.02910i	−0.945526	−	0.325546i	$-0.894452\pi$
$379$	−4.57273	−	20.0345i	−0.234886	−	1.02910i	0.710641	−	0.703555i	$-0.248405\pi$
$380$	−0.187559	−	2.50280i	−0.00962158	−	0.128391i
$381$		0			0
$382$	1.52196	+	3.87789i	0.0778703	+	0.198410i
$383$	24.1781	−	7.45797i	1.23545	−	0.381084i	0.392835	−	0.919609i	$-0.371494\pi$
$383$	24.1781	−	7.45797i	1.23545	−	0.381084i	0.842610	+	0.538525i	$0.181018\pi$
$384$		0			0
$385$	−2.63860	−	3.28872i	−0.134475	−	0.167609i
$386$	9.72935	−	12.2002i	0.495211	−	0.620975i
$387$		0			0
$388$	−1.09633	+	14.6295i	−0.0556579	+	0.742703i
$389$	−13.1064	+	1.97547i	−0.664521	+	0.100160i	−0.472637	−	0.881257i	$-0.656698\pi$
$389$	−13.1064	+	1.97547i	−0.664521	+	0.100160i	−0.191884	+	0.981418i	$0.561460\pi$
$390$		0			0
$391$	24.9051			1.25950
$392$	−1.59794	−	6.81517i	−0.0807083	−	0.344218i
$393$		0			0
$394$	5.24098	−	4.86291i	0.264037	−	0.244990i
$395$	−4.56079	+	0.687429i	−0.229478	+	0.0345883i
$396$		0			0
$397$	12.9985	−	33.1196i	0.652374	−	1.66222i	−0.0930736	−	0.995659i	$-0.529669\pi$
$397$	12.9985	−	33.1196i	0.652374	−	1.66222i	0.745448	−	0.666564i	$-0.232236\pi$
$398$	−5.53247	+	6.93750i	−0.277318	+	0.347746i
$399$		0			0
$400$	−2.81694	−	3.53233i	−0.140847	−	0.176617i
$401$	−2.79000	+	0.860600i	−0.139326	+	0.0429763i	−0.363634	−	0.931542i	$-0.618464\pi$
$401$	−2.79000	+	0.860600i	−0.139326	+	0.0429763i	0.224308	+	0.974518i	$0.427988\pi$
$402$		0			0
$403$	1.93040	+	0.595451i	0.0961603	+	0.0296615i
$404$	0.507908	+	6.77756i	0.0252694	+	0.337196i
$405$		0			0
$406$	1.20268	+	15.4365i	0.0596878	+	0.766100i
$407$	0.619537	−	2.71437i	0.0307093	−	0.134546i
$408$		0			0
$409$	13.6335	−	9.29514i	0.674132	−	0.459615i	−0.177247	−	0.984166i	$-0.556719\pi$
$409$	13.6335	−	9.29514i	0.674132	−	0.459615i	0.851379	+	0.524551i	$0.175767\pi$
$410$	0.896940	−	1.55355i	0.0442967	−	0.0767242i
$411$		0			0
$412$	−8.69095	−	4.18534i	−0.428172	−	0.206197i
$413$	−25.0898	+	3.85752i	−1.23459	+	0.189816i
$414$		0			0
$415$	−3.53684	−	2.41138i	−0.173617	−	0.118370i
$416$	−1.44740	−	1.34299i	−0.0709647	−	0.0658456i
$417$		0			0
$418$	6.85669	+	4.67481i	0.335372	+	0.228653i
$419$	−5.10398	+	2.45795i	−0.249346	+	0.120079i	−0.554382	−	0.832262i	$-0.687046\pi$
$419$	−5.10398	+	2.45795i	−0.249346	+	0.120079i	0.305037	+	0.952341i	$0.401331\pi$
$420$		0			0
$421$	−8.35610	−	4.02409i	−0.407252	−	0.196122i	0.219031	−	0.975718i	$-0.429710\pi$
$421$	−8.35610	−	4.02409i	−0.407252	−	0.196122i	−0.626283	+	0.779596i	$0.715425\pi$
$422$	0.366118	+	0.634134i	0.0178223	+	0.0308692i
$423$		0			0
$424$	−4.14649	+	2.82703i	−0.201371	+	0.137293i
$425$	−25.9589	−	3.91268i	−1.25919	−	0.189793i
$426$		0			0
$427$	11.6237	+	1.71689i	0.562510	+	0.0830859i
$428$	1.54274	+	6.75918i	0.0745711	+	0.326717i
$429$		0			0
$430$	−4.12863	−	1.27351i	−0.199100	−	0.0614143i
$431$	12.2589	+	31.2353i	0.590492	+	1.50455i	0.843524	+	0.537091i	$0.180477\pi$
$431$	12.2589	+	31.2353i	0.590492	+	1.50455i	−0.253032	+	0.967458i	$0.581428\pi$
$432$		0			0
$433$	−5.54508	−	6.95331i	−0.266480	−	0.334155i	0.630531	−	0.776164i	$-0.282837\pi$
$433$	−5.54508	−	6.95331i	−0.266480	−	0.334155i	−0.897010	+	0.442009i	$0.854266\pi$
$434$	2.70693	−	0.00799711i	0.129937	−	0.000383873i
$435$		0			0
$436$	−0.430839	+	1.09776i	−0.0206334	+	0.0525732i
$437$	1.15797	−	15.4521i	0.0553933	−	0.739173i
$438$		0			0
$439$	−0.537597	+	0.498818i	−0.0256581	+	0.0238073i	−0.692898	−	0.721036i	$-0.743666\pi$
$439$	−0.537597	+	0.498818i	−0.0256581	+	0.0238073i	0.667240	+	0.744843i	$0.267476\pi$
$440$	−1.59364			−0.0759739
$441$		0			0
$442$	−11.4728			−0.545707
$443$	−13.1347	+	12.1872i	−0.624047	+	0.579031i	−0.927504	−	0.373814i	$-0.878050\pi$
$443$	−13.1347	+	12.1872i	−0.624047	+	0.579031i	0.303457	+	0.952845i	$0.401859\pi$
$444$		0			0
$445$	0.391915	−	5.22974i	0.0185785	−	0.247913i
$446$	−3.11315	+	7.93218i	−0.147412	+	0.375600i
$447$		0			0
$448$	−2.38712	−	1.14090i	−0.112781	−	0.0539025i
$449$	−17.6253	−	22.1015i	−0.831792	−	1.04303i	−0.998374	−	0.0570062i	$-0.981845\pi$
$449$	−17.6253	−	22.1015i	−0.831792	−	1.04303i	0.166582	−	0.986028i	$-0.446727\pi$
$450$		0			0
$451$	2.16700	+	5.52142i	0.102040	+	0.259994i
$452$	−15.5572	−	4.79877i	−0.731750	−	0.225715i
$453$		0			0
$454$	−4.75746	−	20.8438i	−0.223279	−	0.978248i
$455$	1.31501	−	3.37993i	0.0616488	−	0.158454i
$456$		0			0
$457$	−37.8814	−	5.70971i	−1.77202	−	0.267089i	−0.819831	−	0.572605i	$-0.805933\pi$
$457$	−37.8814	−	5.70971i	−1.77202	−	0.267089i	−0.952187	+	0.305516i	$0.901171\pi$
$458$	−5.01641	+	3.42013i	−0.234401	+	0.159812i
$459$		0			0
$460$	1.48783	+	2.57700i	0.0693706	+	0.120153i
$461$	−2.93793	−	1.41483i	−0.136833	−	0.0658952i	0.364215	−	0.931315i	$-0.381337\pi$
$461$	−2.93793	−	1.41483i	−0.136833	−	0.0658952i	−0.501047	+	0.865420i	$0.667052\pi$
$462$		0			0
$463$	6.73583	−	3.24381i	0.313041	−	0.150752i	−0.270766	−	0.962645i	$-0.587277\pi$
$463$	6.73583	−	3.24381i	0.313041	−	0.150752i	0.583807	+	0.811893i	$0.301563\pi$
$464$	4.83525	+	3.29662i	0.224471	+	0.153042i
$465$		0			0
$466$	−13.1725	−	12.2223i	−0.610205	−	0.566187i
$467$	5.98968	+	4.08369i	0.277169	+	0.188971i	0.693924	−	0.720048i	$-0.255880\pi$
$467$	5.98968	+	4.08369i	0.277169	+	0.188971i	−0.416755	+	0.909019i	$0.636833\pi$
$468$		0			0
$469$	−26.9054	−	24.8170i	−1.24237	−	1.14594i
$470$	−3.66910	−	1.76695i	−0.169243	−	0.0815032i
$471$		0			0
$472$	−4.79724	+	8.30907i	−0.220811	+	0.382456i
$473$	11.8036	−	8.04755i	0.542730	−	0.370027i
$474$		0			0
$475$	−3.63454	+	15.9240i	−0.166764	+	0.730642i
$476$	−14.6768	+	4.57472i	−0.672709	+	0.209682i
$477$		0			0
$478$	0.884119	+	11.7978i	0.0404387	+	0.539617i
$479$	−17.8912	−	5.51872i	−0.817472	−	0.252157i	−0.142306	−	0.989823i	$-0.545452\pi$
$479$	−17.8912	−	5.51872i	−0.817472	−	0.252157i	−0.675166	+	0.737666i	$0.735928\pi$
$480$		0			0
$481$	2.28842	−	0.705884i	0.104343	−	0.0321855i
$482$	5.80974	+	7.28518i	0.264626	+	0.331831i
$483$		0			0
$484$	−3.57300	+	4.48040i	−0.162409	+	0.203655i
$485$	−3.72098	+	9.48091i	−0.168961	+	0.430506i
$486$		0			0
$487$	−3.62075	+	0.545741i	−0.164072	+	0.0247299i	−0.230564	−	0.973057i	$-0.574057\pi$
$487$	−3.62075	+	0.545741i	−0.164072	+	0.0247299i	0.0664924	+	0.997787i	$0.478819\pi$
$488$	3.25549	−	3.02065i	0.147369	−	0.136739i
$489$		0			0
$490$	0.334526	−	4.84818i	0.0151124	−	0.219018i
$491$	−14.4058			−0.650123			−0.325061	−	0.945693i	$-0.605385\pi$
$491$	−14.4058			−0.650123			−0.325061	+	0.945693i	$0.605385\pi$
$492$		0			0
$493$	33.6242	−	5.06803i	1.51436	−	0.228253i
$494$	−0.533434	+	7.11818i	−0.0240003	+	0.320262i
$495$		0			0
$496$	0.637910	−	0.799914i	0.0286430	−	0.0359172i
$497$	−4.69072	−	20.2751i	−0.210407	−	0.909462i
$498$		0			0
$499$	−35.3878	+	10.9157i	−1.58417	+	0.488653i	−0.956966	−	0.290199i	$-0.906279\pi$
$499$	−35.3878	+	10.9157i	−1.58417	+	0.488653i	−0.627208	+	0.778852i	$0.715802\pi$
$500$	−2.41411	−	6.15106i	−0.107962	−	0.275084i
$501$		0			0
$502$	2.11680	+	28.2467i	0.0944773	+	1.26071i
$503$	−2.85948	−	12.5282i	−0.127498	−	0.558605i	−0.997812	−	0.0661085i	$-0.978942\pi$
$503$	−2.85948	−	12.5282i	−0.127498	−	0.558605i	0.870315	−	0.492496i	$-0.163915\pi$
$504$		0			0
$505$	−1.04996	+	4.60017i	−0.0467226	+	0.204705i
$506$	−9.72910	−	1.46643i	−0.432511	−	0.0651906i
$507$		0			0
$508$	10.5576	−	18.2863i	0.468419	−	0.811325i
$509$	8.57858	+	14.8585i	0.380239	+	0.658593i	0.991096	−	0.133148i	$-0.0425084\pi$
$509$	8.57858	+	14.8585i	0.380239	+	0.658593i	−0.610857	+	0.791741i	$0.709175\pi$
$510$		0			0
$511$	20.1952	−	13.8564i	0.893382	−	0.612971i
$512$	−0.900969	+	0.433884i	−0.0398176	+	0.0191751i
$513$		0			0
$514$	8.04276	+	7.46259i	0.354751	+	0.329161i
$515$	−4.90913	−	4.55500i	−0.216322	−	0.200717i
$516$		0			0
$517$	12.1318	−	5.84238i	0.533557	−	0.256948i
$518$	2.64603	−	1.81551i	0.116260	−	0.0797687i
$519$		0			0
$520$	−0.685388	−	1.18713i	−0.0300563	−	0.0520590i
$521$	−19.6228	+	33.9877i	−0.859692	+	1.48903i	0.0125309	+	0.999921i	$0.496011\pi$
$521$	−19.6228	+	33.9877i	−0.859692	+	1.48903i	−0.872223	+	0.489109i	$0.837322\pi$
$522$		0			0
$523$	−19.5713	−	2.94990i	−0.855794	−	0.128990i	−0.293532	−	0.955949i	$-0.594831\pi$
$523$	−19.5713	−	2.94990i	−0.855794	−	0.128990i	−0.562262	+	0.826959i	$0.690069\pi$
$524$	3.34905	−	14.6732i	0.146304	−	0.641000i
$525$		0			0
$526$	−3.15043	−	13.8029i	−0.137365	−	0.601836i
$527$	−0.444265	−	5.92830i	−0.0193525	−	0.258241i
$528$		0			0
$529$	−1.69098	−	4.30856i	−0.0735210	−	0.187328i
$530$	−3.32928	+	1.02695i	−0.144615	+	0.0446077i
$531$		0			0
$532$	2.15593	+	9.31874i	0.0934712	+	0.404019i
$533$	−3.18101	+	3.98886i	−0.137785	+	0.172777i
$534$		0			0
$535$	−0.359691	+	4.79974i	−0.0155508	+	0.207511i
$536$	−13.6801	+	2.06195i	−0.590892	+	0.0890626i
$537$		0			0
$538$	15.3979			0.663851
$539$	11.8435	+	10.8596i	0.510134	+	0.467756i
$540$		0			0
$541$	−1.51361	+	1.40443i	−0.0650753	+	0.0603810i	−0.712040	−	0.702139i	$-0.752229\pi$
$541$	−1.51361	+	1.40443i	−0.0650753	+	0.0603810i	0.646965	+	0.762520i	$0.276038\pi$
$542$	−14.5772	+	2.19715i	−0.626142	+	0.0943758i
$543$		0			0
$544$	−2.12283	+	5.40887i	−0.0910154	+	0.231903i
$545$	−0.510456	+	0.640091i	−0.0218655	+	0.0274185i
$546$		0			0
$547$	19.1367	+	23.9967i	0.818227	+	1.02602i	0.999096	+	0.0425171i	$0.0135377\pi$
$547$	19.1367	+	23.9967i	0.818227	+	1.02602i	−0.180869	+	0.983507i	$0.557891\pi$
$548$	16.3051	−	5.02947i	0.696521	−	0.214848i
$549$		0			0
$550$	9.91040	+	3.05695i	0.422581	+	0.130349i
$551$	−1.58103	−	21.0974i	−0.0673541	−	0.898778i
$552$		0			0
$553$	16.7811	−	5.23064i	0.713606	−	0.222429i
$554$	0.437401	−	1.91638i	0.0185834	−	0.0814191i
$555$		0			0
$556$	11.0415	−	7.52795i	0.468263	−	0.319256i
$557$	20.0790	−	34.7778i	0.850773	−	1.47358i	−0.0297388	−	0.999558i	$-0.509468\pi$
$557$	20.0790	−	34.7778i	0.850773	−	1.47358i	0.880512	−	0.474024i	$-0.157199\pi$
$558$		0			0
$559$	11.0712	+	5.33160i	0.468261	+	0.225503i
$560$	−1.35015	−	1.24536i	−0.0570544	−	0.0526259i
$561$		0			0
$562$	0.733564	+	0.500135i	0.0309435	+	0.0210969i
$563$	6.94016	+	6.43952i	0.292493	+	0.271394i	0.812746	−	0.582619i	$-0.197972\pi$
$563$	6.94016	+	6.43952i	0.292493	+	0.271394i	−0.520253	+	0.854012i	$0.674162\pi$
$564$		0			0
$565$	−9.33869	−	6.36701i	−0.392882	−	0.267862i
$566$	0.954876	−	0.459844i	0.0401364	−	0.0193287i
$567$		0			0
$568$	−7.08673	−	3.41279i	−0.297352	−	0.143197i
$569$	−0.992289	−	1.71869i	−0.0415989	−	0.0720514i	0.844476	−	0.535593i	$-0.179912\pi$
$569$	−0.992289	−	1.71869i	−0.0415989	−	0.0720514i	−0.886075	+	0.463541i	$0.846578\pi$
$570$		0			0
$571$	−28.6818	+	19.5549i	−1.20030	+	0.818349i	−0.987325	−	0.158709i	$-0.949267\pi$
$571$	−28.6818	+	19.5549i	−1.20030	+	0.818349i	−0.212972	+	0.977058i	$0.568314\pi$
$572$	4.48183	+	0.675527i	0.187395	+	0.0282452i
$573$		0			0
$574$	−2.47882	+	6.37122i	−0.103464	+	0.265930i
$575$	−4.30915	−	18.8796i	−0.179704	−	0.787335i
$576$		0			0
$577$	29.2940	+	9.03602i	1.21953	+	0.376174i	0.836708	−	0.547649i	$-0.184477\pi$
$577$	29.2940	+	9.03602i	1.21953	+	0.376174i	0.382819	+	0.923823i	$0.374953\pi$
$578$	6.12395	+	15.6036i	0.254723	+	0.649023i
$579$		0			0
$580$	2.53312	+	3.17643i	0.105182	+	0.131894i
$581$	14.7188	+	7.03471i	0.610639	+	0.291849i
$582$		0			0
$583$	4.20873	−	10.7237i	0.174308	−	0.444130i
$584$	0.691777	−	9.23112i	0.0286259	−	0.381986i
$585$		0			0
$586$	−22.9141	+	21.2611i	−0.946571	+	0.878290i
$587$	−26.0343			−1.07455			−0.537275	−	0.843407i	$-0.680546\pi$
$587$	−26.0343			−1.07455			−0.537275	+	0.843407i	$0.680546\pi$
$588$		0			0
$589$	−3.69880			−0.152406
$590$	−4.88279	+	4.53057i	−0.201021	+	0.186521i
$591$		0			0
$592$	0.0906386	−	1.20949i	0.00372522	−	0.0497096i
$593$	−12.3085	+	31.3616i	−0.505450	+	1.28787i	0.419493	+	0.907759i	$0.362208\pi$
$593$	−12.3085	+	31.3616i	−0.505450	+	1.28787i	−0.924943	+	0.380107i	$0.875887\pi$
$594$		0			0
$595$	−10.6727	+	0.0315305i	−0.437539	+	0.00129262i
$596$	5.78151	+	7.24978i	0.236820	+	0.296963i
$597$		0			0
$598$	−3.09190	−	7.87803i	−0.126437	−	0.322156i
$599$	−36.0263	−	11.1127i	−1.47200	−	0.454051i	−0.548009	−	0.836473i	$-0.684614\pi$
$599$	−36.0263	−	11.1127i	−1.47200	−	0.454051i	−0.923988	+	0.382422i	$0.875090\pi$
$600$		0			0
$601$	1.68159	+	7.36752i	0.0685934	+	0.300527i	0.997575	−	0.0695984i	$-0.0221718\pi$
$601$	1.68159	+	7.36752i	0.0685934	+	0.300527i	−0.928982	+	0.370126i	$0.879315\pi$
$602$	16.2889	+	2.40597i	0.663887	+	0.0980599i
$603$		0			0
$604$	3.61275	+	0.544535i	0.147001	+	0.0221568i
$605$	−3.28716	+	2.24115i	−0.133642	+	0.0911157i
$606$		0			0
$607$	8.25530	+	14.2986i	0.335072	+	0.580362i	0.983499	−	0.180915i	$-0.0579060\pi$
$607$	8.25530	+	14.2986i	0.335072	+	0.580362i	−0.648427	+	0.761277i	$0.724573\pi$
$608$	3.25717	+	1.56857i	0.132096	+	0.0636139i
$609$		0			0
$610$	2.77782	−	1.33773i	0.112471	−	0.0541630i
$611$	9.56969	+	6.52451i	0.387148	+	0.263953i
$612$		0			0
$613$	−29.9820	−	27.8192i	−1.21096	−	1.12361i	−0.988901	−	0.148573i	$-0.952532\pi$
$613$	−29.9820	−	27.8192i	−1.21096	−	1.12361i	−0.222059	−	0.975033i	$-0.571278\pi$
$614$	−6.01884	−	4.10358i	−0.242901	−	0.165607i
$615$		0			0
$616$	6.00281	−	0.922922i	0.241860	−	0.0371856i
$617$	34.9474	+	16.8298i	1.40693	+	0.677542i	0.974554	−	0.224151i	$-0.0719610\pi$
$617$	34.9474	+	16.8298i	1.40693	+	0.677542i	0.432376	+	0.901693i	$0.357675\pi$
$618$		0			0
$619$	16.8517	−	29.1880i	0.677326	−	1.17316i	−0.298457	−	0.954423i	$-0.596472\pi$
$619$	16.8517	−	29.1880i	0.677326	−	1.17316i	0.975783	−	0.218740i	$-0.0701947\pi$
$620$	0.586878	−	0.400127i	0.0235696	−	0.0160695i
$621$		0			0
$622$	−1.99115	+	8.72379i	−0.0798378	+	0.349792i
$623$	1.55245	+	19.9259i	0.0621978	+	0.798316i
$624$		0			0
$625$	1.34534	+	17.9523i	0.0538137	+	0.718094i
$626$	30.5895	+	9.43561i	1.22260	+	0.377123i
$627$		0			0
$628$	6.57093	−	2.02686i	0.262209	−	0.0808807i
$629$	−4.39403	−	5.50994i	−0.175201	−	0.219696i
$630$		0			0
$631$	14.0589	−	17.6293i	0.559676	−	0.701811i	−0.418822	−	0.908068i	$-0.637557\pi$
$631$	14.0589	−	17.6293i	0.559676	−	0.701811i	0.978498	+	0.206257i	$0.0661284\pi$
$632$	2.42720	−	6.18439i	0.0965487	−	0.246002i
$633$		0			0
$634$	17.9158	−	2.70037i	0.711525	−	0.107245i
$635$	10.7459	−	9.97074i	0.426438	−	0.395677i
$636$		0			0
$637$	−2.99588	+	13.4928i	−0.118701	+	0.534605i
$638$	−13.4336			−0.531841
$639$		0			0
$640$	−0.686490	+	0.103472i	−0.0271359	+	0.00409008i
$641$	−2.33536	+	31.1633i	−0.0922413	+	1.23087i	0.738515	+	0.674238i	$0.235528\pi$
$641$	−2.33536	+	31.1633i	−0.0922413	+	1.23087i	−0.830756	+	0.556637i	$0.812091\pi$
$642$		0			0
$643$	−24.7182	+	30.9956i	−0.974790	+	1.22235i	0.000177625		1.00000i	$0.499943\pi$
$643$	−24.7182	+	30.9956i	−0.974790	+	1.22235i	−0.974967	+	0.222348i	$0.928628\pi$
$644$	−7.09667	−	8.84521i	−0.279648	−	0.348550i
$645$		0			0
$646$	20.0729	−	6.19167i	0.789758	−	0.243608i
$647$	−2.31194	−	5.89074i	−0.0908919	−	0.231589i	0.878198	−	0.478298i	$-0.158746\pi$
$647$	−2.31194	−	5.89074i	−0.0908919	−	0.231589i	−0.969090	+	0.246709i	$0.920651\pi$
$648$		0			0
$649$	−1.64587	−	21.9626i	−0.0646061	−	0.862108i
$650$	1.98506	+	8.69712i	0.0778605	+	0.341129i
$651$		0			0
$652$	−1.14995	+	5.03827i	−0.0450356	+	0.197314i
$653$	−12.5500	−	1.89161i	−0.491120	−	0.0740245i	−0.101187	−	0.994867i	$-0.532264\pi$
$653$	−12.5500	−	1.89161i	−0.491120	−	0.0740245i	−0.389934	+	0.920843i	$0.627502\pi$
$654$		0			0
$655$	5.22436	−	9.04886i	0.204133	−	0.353568i
$656$	1.29197	+	2.23775i	0.0504428	+	0.0873696i
$657$		0			0
$658$	14.8438	+	4.53072i	0.578671	+	0.176626i
$659$	−21.1039	+	10.1631i	−0.822092	+	0.395899i	−0.797143	−	0.603790i	$-0.793657\pi$
$659$	−21.1039	+	10.1631i	−0.822092	+	0.395899i	−0.0249486	+	0.999689i	$0.507942\pi$
$660$		0			0
$661$	4.73573	+	4.39411i	0.184198	+	0.170911i	0.766882	−	0.641788i	$-0.221807\pi$
$661$	4.73573	+	4.39411i	0.184198	+	0.170911i	−0.582684	+	0.812699i	$0.697997\pi$
$662$	−6.95647	−	6.45466i	−0.270371	−	0.250867i
$663$		0			0
$664$	5.55530	−	2.67529i	0.215588	−	0.103821i
$665$	−0.476670	+	6.62323i	−0.0184845	+	0.256838i
$666$		0			0
$667$	12.5417	+	21.7228i	0.485616	+	0.841111i
$668$	5.59217	−	9.68593i	0.216368	−	0.374760i
$669$		0			0
$670$	−9.49735	−	1.43149i	−0.366915	−	0.0553035i
$671$	−2.26846	+	9.93877i	−0.0875729	+	0.383682i
$672$		0			0
$673$	6.60730	+	28.9485i	0.254693	+	1.11588i	0.926838	+	0.375463i	$0.122516\pi$
$673$	6.60730	+	28.9485i	0.254693	+	1.11588i	−0.672145	+	0.740420i	$0.734627\pi$
$674$	−0.144390	−	1.92676i	−0.00556171	−	0.0742159i
$675$		0			0
$676$	−3.32511	−	8.47225i	−0.127889	−	0.325856i
$677$	38.4845	−	11.8709i	1.47908	−	0.456236i	0.552878	−	0.833262i	$-0.313529\pi$
$677$	38.4845	−	11.8709i	1.47908	−	0.456236i	0.926203	+	0.377026i	$0.123053\pi$
$678$		0			0
$679$	8.52525	−	37.8669i	0.327169	−	1.45320i
$680$	−2.51511	+	3.15385i	−0.0964502	+	0.120945i
$681$		0			0
$682$	−0.175511	+	2.34203i	−0.00672066	+	0.0896810i
$683$	46.6275	−	7.02797i	1.78415	−	0.268918i	0.827776	−	0.561058i	$-0.189606\pi$
$683$	46.6275	−	7.02797i	1.78415	−	0.268918i	0.956375	+	0.292141i	$0.0943675\pi$
$684$		0			0
$685$	11.8460			0.452613
$686$	1.54765	+	18.4555i	0.0590895	+	0.704634i
$687$		0			0
$688$	4.56210	−	4.23301i	0.173928	−	0.161382i
$689$	9.79831	−	1.47686i	0.373286	−	0.0562638i
$690$		0			0
$691$	−6.02453	+	15.3503i	−0.229184	+	0.583951i	−0.998490	−	0.0549288i	$-0.982507\pi$
$691$	−6.02453	+	15.3503i	−0.229184	+	0.583951i	0.769306	+	0.638880i	$0.220602\pi$
$692$	14.0955	−	17.6752i	0.535830	−	0.671910i
$693$		0			0
$694$	−17.5084	−	21.9548i	−0.664608	−	0.833392i
$695$	8.86538	−	2.73461i	0.336283	−	0.103730i
$696$		0			0
$697$	14.3470	+	4.42546i	0.543432	+	0.167626i
$698$	−2.46898	−	32.9463i	−0.0934524	−	1.24704i
$699$		0			0
$700$	6.00734	+	10.3344i	0.227056	+	0.390603i
$701$	1.34456	−	5.89088i	0.0507831	−	0.222495i	−0.943168	−	0.332315i	$-0.892170\pi$
$701$	1.34456	−	5.89088i	0.0507831	−	0.222495i	0.993952	+	0.109820i	$0.0350274\pi$
$702$		0			0
$703$	−3.62288	+	2.47004i	−0.136639	+	0.0931591i
$704$	1.14775	−	1.98797i	0.0432576	−	0.0749243i
$705$		0			0
$706$	−22.7899	−	10.9751i	−0.857711	−	0.413052i
$707$	1.29082	−	17.9356i	0.0485461	−	0.674539i
$708$		0			0
$709$	15.4474	+	10.5319i	0.580140	+	0.395533i	0.817534	−	0.575881i	$-0.195341\pi$
$709$	15.4474	+	10.5319i	0.580140	+	0.395533i	−0.237394	+	0.971414i	$0.576293\pi$
$710$	−4.00297	−	3.71422i	−0.150229	−	0.139392i
$711$		0			0
$712$	6.24151	+	4.25539i	0.233910	+	0.159477i
$713$	3.95105	−	1.90272i	0.147968	−	0.0712576i
$714$		0			0
$715$	2.83501	+	1.36527i	0.106023	+	0.0510582i
$716$	−4.63823	−	8.03366i	−0.173339	−	0.300232i
$717$		0			0
$718$	22.5641	−	15.3839i	0.842083	−	0.574122i
$719$	−40.6817	−	6.13178i	−1.51717	−	0.228677i	−0.662981	−	0.748636i	$-0.730709\pi$
$719$	−40.6817	−	6.13178i	−1.51717	−	0.228677i	−0.854191	+	0.519959i	$0.825947\pi$
$720$		0			0
$721$	21.1292	+	14.3144i	0.786894	+	0.533097i
$722$	1.31965	+	5.78175i	0.0491122	+	0.215175i
$723$		0			0
$724$	−11.3214	−	3.49219i	−0.420757	−	0.129786i
$725$	−9.65963	−	24.6123i	−0.358750	−	0.914080i
$726$		0			0
$727$	29.8273	+	37.4023i	1.10623	+	1.38717i	0.913946	+	0.405836i	$0.133019\pi$
$727$	29.8273	+	37.4023i	1.10623	+	1.38717i	0.192288	+	0.981338i	$0.438409\pi$
$728$	3.26916	+	4.07465i	0.121163	+	0.151017i
$729$		0			0
$730$	2.34791	−	5.98237i	0.0869000	−	0.221417i
$731$	2.70235	−	36.0604i	0.0999500	−	1.33374i
$732$		0			0
$733$	−11.7341	+	10.8876i	−0.433408	+	0.402144i	−0.866477	−	0.499217i	$-0.833621\pi$
$733$	−11.7341	+	10.8876i	−0.433408	+	0.402144i	0.433069	+	0.901361i	$0.357431\pi$
$734$	−0.832910			−0.0307433
$735$		0			0
$736$	−4.28620			−0.157991
$737$	23.2799	−	21.6006i	0.857527	−	0.795669i
$738$		0			0
$739$	−2.74556	+	36.6369i	−0.100997	+	1.34771i	0.684575	+	0.728942i	$0.259988\pi$
$739$	−2.74556	+	36.6369i	−0.100997	+	1.34771i	−0.785572	+	0.618770i	$0.787631\pi$
$740$	0.307630	−	0.783827i	0.0113087	−	0.0288141i
$741$		0			0
$742$	11.9457	−	5.79630i	0.438542	−	0.212789i
$743$	25.3752	+	31.8195i	0.930925	+	1.16734i	0.985643	+	0.168841i	$0.0540025\pi$
$743$	25.3752	+	31.8195i	0.930925	+	1.16734i	−0.0547182	+	0.998502i	$0.517426\pi$
$744$		0			0
$745$	2.35192	+	5.99259i	0.0861677	+	0.219552i
$746$	−11.6956	−	3.60760i	−0.428205	−	0.132084i
$747$		0			0
$748$	−2.96801	−	13.0037i	−0.108521	−	0.475462i
$749$	−1.42481	−	18.2876i	−0.0520613	−	0.668214i
$750$		0			0
$751$	−44.8263	−	6.75647i	−1.63573	−	0.246547i	−0.734098	−	0.679044i	$-0.762395\pi$
$751$	−44.8263	−	6.75647i	−1.63573	−	0.246547i	−0.901635	+	0.432497i	$0.857633\pi$
$752$	4.84667	−	3.30440i	0.176740	−	0.120499i
$753$		0			0
$754$	−5.77747	−	10.0069i	−0.210403	−	0.364429i
$755$	2.28527	+	1.10053i	0.0831696	+	0.0400524i
$756$		0			0
$757$	−32.8920	+	15.8400i	−1.19548	+	0.575713i	−0.922384	−	0.386274i	$-0.873762\pi$
$757$	−32.8920	+	15.8400i	−1.19548	+	0.575713i	−0.273096	+	0.961987i	$0.588048\pi$
$758$	16.9789	+	11.5760i	0.616703	+	0.420461i
$759$		0			0
$760$	1.83983	+	1.70711i	0.0667376	+	0.0619234i
$761$	11.3967	+	7.77014i	0.413130	+	0.281667i	0.751996	−	0.659167i	$-0.229091\pi$
$761$	11.3967	+	7.77014i	0.413130	+	0.281667i	−0.338866	+	0.940835i	$0.610043\pi$
$762$		0			0
$763$	1.55205	−	2.70667i	0.0561880	−	0.0979879i
$764$	−3.75331	−	1.80750i	−0.135790	−	0.0653931i
$765$		0			0
$766$	−12.6511	+	21.9124i	−0.457104	+	0.791727i
$767$	15.6524	−	10.6716i	0.565176	−	0.385331i
$768$		0			0
$769$	−2.37980	+	10.4266i	−0.0858178	+	0.375992i	−0.999539	−	0.0303486i	$-0.990338\pi$
$769$	−2.37980	+	10.4266i	−0.0858178	+	0.375992i	0.913722	+	0.406341i	$0.133195\pi$
$770$	4.17112	+	0.616099i	0.150317	+	0.0222027i
$771$		0			0
$772$	1.16614	+	15.5610i	0.0419702	+	0.560054i
$773$	36.7416	+	11.3333i	1.32150	+	0.407630i	0.873684	−	0.486493i	$-0.161724\pi$
$773$	36.7416	+	11.3333i	1.32150	+	0.407630i	0.447820	+	0.894124i	$0.352200\pi$
$774$		0			0
$775$	−4.41716	+	1.36251i	−0.158669	+	0.0489429i
$776$	−9.14695	−	11.4699i	−0.328356	−	0.411746i
$777$		0			0
$778$	8.26402	−	10.3627i	0.296279	−	0.371522i
$779$	3.41280	−	8.69566i	0.122276	−	0.311554i
$780$		0			0
$781$	17.8540	−	2.69106i	0.638868	−	0.0962938i
$782$	−18.2567	+	16.9398i	−0.652859	+	0.605765i
$783$		0			0
$784$	5.80687	+	3.90900i	0.207388	+	0.139607i
$785$	4.77392			0.170389
$786$		0			0
$787$	−34.9943	+	5.27454i	−1.24741	+	0.188017i	−0.739360	−	0.673310i	$-0.764872\pi$
$787$	−34.9943	+	5.27454i	−1.24741	+	0.188017i	−0.508051	+	0.861327i	$0.669634\pi$
$788$	−0.534285	+	7.12954i	−0.0190331	+	0.253979i
$789$		0			0
$790$	2.87573	−	3.60605i	0.102314	−	0.128297i
$791$	38.8636	+	18.5745i	1.38183	+	0.660432i
$792$		0			0
$793$	−8.37915	+	2.58463i	−0.297552	+	0.0917827i
$794$	12.9985	+	33.1196i	0.461298	+	1.17537i
$795$		0			0
$796$	−0.663110	−	8.84859i	−0.0235033	−	0.313630i
$797$	1.96064	+	8.59010i	0.0694493	+	0.304277i	0.997709	−	0.0676563i	$-0.0215521\pi$
$797$	1.96064	+	8.59010i	0.0694493	+	0.304277i	−0.928259	+	0.371933i	$0.878695\pi$
$798$		0			0
$799$	7.58446	−	33.2297i	0.268319	−	1.17558i
$800$	4.46756	+	0.673377i	0.157952	+	0.0238075i
$801$		0			0
$802$	1.45986	−	2.52854i	0.0515493	−	0.0892860i
$803$	10.6248	+	18.4026i	0.374940	+	0.649414i
$804$		0			0
$805$	−2.89792	−	7.32012i	−0.102138	−	0.258000i
$806$	−1.82010	+	0.876512i	−0.0641102	+	0.0308738i
$807$		0			0
$808$	−4.98223	−	4.62284i	−0.175274	−	0.162631i
$809$	−14.5438	−	13.4947i	−0.511333	−	0.474448i	0.381797	−	0.924246i	$-0.375305\pi$
$809$	−14.5438	−	13.4947i	−0.511333	−	0.474448i	−0.893130	+	0.449799i	$0.851496\pi$
$810$		0			0
$811$	16.0320	−	7.72060i	0.562960	−	0.271107i	−0.130686	−	0.991424i	$-0.541718\pi$
$811$	16.0320	−	7.72060i	0.562960	−	0.271107i	0.693645	+	0.720317i	$0.256004\pi$
$812$	−11.3811	−	10.4977i	−0.399398	−	0.368398i
$813$		0			0
$814$	1.39209	+	2.41116i	0.0487926	+	0.0845112i
$815$	−1.79387	+	3.10708i	−0.0628366	+	0.108836i
$816$		0			0
$817$	−22.2476	−	3.35328i	−0.778344	−	0.117316i
$818$	−3.67174	+	16.0869i	−0.128379	+	0.562466i
$819$		0			0
$820$	0.399176	+	1.74890i	0.0139398	+	0.0610744i
$821$	−1.08732	−	14.5093i	−0.0379477	−	0.506377i	−0.983500	−	0.180907i	$-0.942097\pi$
$821$	−1.08732	−	14.5093i	−0.0379477	−	0.506377i	0.945552	−	0.325470i	$-0.105522\pi$
$822$		0			0
$823$	2.50071	+	6.37170i	0.0871692	+	0.222103i	0.967810	−	0.251680i	$-0.0809831\pi$
$823$	2.50071	+	6.37170i	0.0871692	+	0.222103i	−0.880641	+	0.473784i	$0.842888\pi$
$824$	9.21767	−	2.84327i	0.321113	−	0.0990502i
$825$		0			0
$826$	15.7683	−	19.8932i	0.548651	−	0.692172i
$827$	5.94790	−	7.45843i	0.206829	−	0.259355i	−0.667588	−	0.744531i	$-0.732673\pi$
$827$	5.94790	−	7.45843i	0.206829	−	0.259355i	0.874416	+	0.485176i	$0.161244\pi$
$828$		0			0
$829$	1.64698	−	21.9774i	0.0572020	−	0.763308i	−0.892678	−	0.450694i	$-0.851176\pi$
$829$	1.64698	−	21.9774i	0.0572020	−	0.763308i	0.949880	−	0.312614i	$-0.101204\pi$
$830$	4.23284	−	0.637998i	0.146924	−	0.0221452i
$831$		0			0
$832$	1.97449			0.0684530
$833$	40.1829	−	6.29964i	1.39226	−	0.218270i
$834$		0			0
$835$	5.69190	−	5.28131i	0.196976	−	0.182767i
$836$	−8.20599	+	1.23685i	−0.283810	+	0.0427775i
$837$		0			0
$838$	2.06965	−	5.27339i	0.0714950	−	0.182166i
$839$	1.33073	−	1.66868i	0.0459419	−	0.0576093i	−0.758330	−	0.651871i	$-0.773984\pi$
$839$	1.33073	−	1.66868i	0.0459419	−	0.0576093i	0.804272	+	0.594262i	$0.202556\pi$
$840$		0			0
$841$	3.27168	+	4.10256i	0.112817	+	0.141467i
$842$	8.86253	−	2.73373i	0.305423	−	0.0942105i
$843$		0			0
$844$	−0.699704	−	0.215830i	−0.0240848	−	0.00742918i
$845$	−0.472189	−	6.30092i	−0.0162438	−	0.216758i
$846$		0			0
$847$	11.0839	−	10.3455i	0.380848	−	0.355475i
$848$	1.11672	−	4.89268i	0.0383484	−	0.168015i
$849$		0			0
$850$	21.6905	−	14.7884i	0.743979	−	0.507236i
$851$	2.59932	−	4.50215i	0.0891035	−	0.154332i
$852$		0			0
$853$	−36.7989	−	17.7214i	−1.25997	−	0.606771i	−0.319805	−	0.947483i	$-0.603617\pi$
$853$	−36.7989	−	17.7214i	−1.25997	−	0.606771i	−0.940167	+	0.340713i	$0.889332\pi$
$854$	−9.68855	+	6.64755i	−0.331535	+	0.227475i
$855$		0			0
$856$	−5.72832	−	3.90550i	−0.195790	−	0.133487i
$857$	−28.1880	−	26.1546i	−0.962883	−	0.893425i	0.0314745	−	0.999505i	$-0.489980\pi$
$857$	−28.1880	−	26.1546i	−0.962883	−	0.893425i	−0.994358	+	0.106080i	$0.966170\pi$
$858$		0			0
$859$	6.34024	+	4.32271i	0.216326	+	0.147489i	0.666635	−	0.745384i	$-0.267734\pi$
$859$	6.34024	+	4.32271i	0.216326	+	0.147489i	−0.450309	+	0.892873i	$0.648686\pi$
$860$	3.89271	−	1.87463i	0.132740	−	0.0639244i
$861$		0			0
$862$	−30.2318	−	14.5589i	−1.02970	−	0.495877i
$863$	21.6491	+	37.4974i	0.736945	+	1.27643i	0.953865	+	0.300237i	$0.0970657\pi$
$863$	21.6491	+	37.4974i	0.736945	+	1.27643i	−0.216920	+	0.976189i	$0.569601\pi$
$864$		0			0
$865$	12.9679	−	8.84134i	0.440921	−	0.300615i
$866$	8.79429	+	1.32553i	0.298842	+	0.0450432i
$867$		0			0
$868$	−1.97888	+	1.84704i	−0.0671676	+	0.0626927i
$869$	3.39356	+	14.8682i	0.115119	+	0.504368i
$870$		0			0
$871$	26.1028	+	8.05164i	0.884458	+	0.272819i
$872$	−0.430839	−	1.09776i	−0.0145901	−	0.0371748i
$873$		0			0
$874$	9.66122	+	12.1148i	0.326796	+	0.409789i
$875$	3.94060	+	17.0328i	0.133217	+	0.575813i
$876$		0			0
$877$	−4.77280	+	12.1609i	−0.161166	+	0.410644i	−0.988531	−	0.151021i	$-0.951744\pi$
$877$	−4.77280	+	12.1609i	−0.161166	+	0.410644i	0.827365	+	0.561665i	$0.189839\pi$
$878$	0.0548047	−	0.731318i	0.00184957	−	0.0246808i
$879$		0			0
$880$	1.16822	−	1.08395i	0.0393808	−	0.0365400i
$881$	8.59025			0.289413			0.144706	−	0.989475i	$-0.453776\pi$
$881$	8.59025			0.289413			0.144706	+	0.989475i	$0.453776\pi$
$882$		0			0
$883$	−31.6523			−1.06519			−0.532593	−	0.846372i	$-0.678782\pi$
$883$	−31.6523			−1.06519			−0.532593	+	0.846372i	$0.678782\pi$
$884$	8.41018	−	7.80350i	0.282865	−	0.262460i
$885$		0			0
$886$	1.33900	−	17.8677i	0.0449845	−	0.600277i
$887$	−7.59866	+	19.3611i	−0.255138	+	0.650081i	−0.999850	−	0.0173046i	$-0.994492\pi$
$887$	−7.59866	+	19.3611i	−0.255138	+	0.650081i	0.744712	+	0.667386i	$0.232587\pi$
$888$		0			0
$889$	−34.7025	+	43.7803i	−1.16388	+	1.46834i
$890$	3.26983	+	4.10024i	0.109605	+	0.137440i
$891$		0			0
$892$	−3.11315	−	7.93218i	−0.104236	−	0.265589i
$893$	−20.2643	−	6.25072i	−0.678120	−	0.209172i
$894$		0			0
$895$	−1.43306	−	6.27867i	−0.0479021	−	0.209873i
$896$	2.52589	−	0.787315i	0.0843842	−	0.0263023i
$897$		0			0
$898$	27.9531	+	4.21326i	0.932808	+	0.140598i
$899$	4.94708	−	3.37287i	0.164995	−	0.112491i
$900$		0			0
$901$	−14.5801	−	25.2535i	−0.485734	−	0.841315i
$902$	−5.34404	−	2.57355i	−0.177937	−	0.0856900i
$903$		0			0
$904$	14.6682	−	7.06386i	0.487859	−	0.234940i
$905$	−6.79602	−	4.63344i	−0.225907	−	0.154021i
$906$		0			0
$907$	−6.63505	−	6.15643i	−0.220313	−	0.204421i	0.562293	−	0.826938i	$-0.309919\pi$
$907$	−6.63505	−	6.15643i	−0.220313	−	0.204421i	−0.782606	+	0.622517i	$0.786110\pi$
$908$	17.6648	+	12.0437i	0.586228	+	0.399684i
$909$		0			0
$910$	1.33496	+	3.37210i	0.0442536	+	0.111784i
$911$	13.6406	+	6.56898i	0.451934	+	0.217640i	0.645983	−	0.763352i	$-0.276448\pi$
$911$	13.6406	+	6.56898i	0.451934	+	0.217640i	−0.194049	+	0.980992i	$0.562162\pi$
$912$		0			0
$913$	−7.07696	+	12.2576i	−0.234213	+	0.405669i
$914$	31.6526	−	21.5804i	1.04698	−	0.713816i
$915$		0			0
$916$	1.35101	−	5.91915i	0.0446386	−	0.195574i
$917$	−14.4383	+	37.1101i	−0.476794	+	1.22548i
$918$		0			0
$919$	−0.605897	−	8.08514i	−0.0199867	−	0.266704i	−0.998241	−	0.0592931i	$-0.981115\pi$
$919$	−0.605897	−	8.08514i	−0.0199867	−	0.266704i	0.978254	−	0.207411i	$-0.0665037\pi$
$920$	−2.84347	−	0.877093i	−0.0937463	−	0.0289169i
$921$		0			0
$922$	3.11598	−	0.961153i	0.102619	−	0.0316539i
$923$	9.68322	+	12.1424i	0.318727	+	0.399671i
$924$		0			0
$925$	−3.41661	+	4.28429i	−0.112337	+	0.140867i
$926$	−2.73137	+	6.95941i	−0.0897582	+	0.228700i
$927$		0			0
$928$	−5.78676	+	0.872214i	−0.189960	+	0.0286318i
$929$	13.0223	−	12.0829i	0.427248	−	0.396428i	−0.437026	−	0.899449i	$-0.643968\pi$
$929$	13.0223	−	12.0829i	0.427248	−	0.396428i	0.864275	+	0.503020i	$0.167778\pi$
$930$		0			0
$931$	−2.04021	−	25.2239i	−0.0668653	−	0.826680i
$932$	17.9694			0.588608
$933$		0			0
$934$	−7.16836	+	1.08046i	−0.234556	+	0.0353536i
$935$	0.691994	−	9.23402i	0.0226306	−	0.301985i
$936$		0			0
$937$	−15.0021	+	18.8121i	−0.490099	+	0.614564i	−0.963964	−	0.266033i	$-0.914287\pi$
$937$	−15.0021	+	18.8121i	−0.490099	+	0.614564i	0.473865	+	0.880597i	$0.342858\pi$
$938$	36.6029	−	0.108136i	1.19513	−	0.00353077i
$939$		0			0
$940$	3.89147	−	1.20036i	0.126926	−	0.0391514i
$941$	8.37215	+	21.3319i	0.272924	+	0.695400i	0.999961	+	0.00880166i	$0.00280169\pi$
$941$	8.37215	+	21.3319i	0.272924	+	0.695400i	−0.727037	+	0.686598i	$0.759103\pi$
$942$		0			0
$943$	0.827655	+	11.0443i	0.0269521	+	0.359651i
$944$	−2.13497	−	9.35393i	−0.0694875	−	0.304444i
$945$		0			0
$946$	−3.17892	+	13.9278i	−0.103356	+	0.452830i
$947$	57.3598	+	8.64559i	1.86394	+	0.280944i	0.981783	−	0.190008i	$-0.0608514\pi$
$947$	57.3598	+	8.64559i	1.86394	+	0.280944i	0.882159	+	0.470952i	$0.156089\pi$
$948$		0			0
$949$	−9.13892	+	15.8291i	−0.296662	+	0.513833i
$950$	−8.16675	−	14.1452i	−0.264964	−	0.458932i
$951$		0			0
$952$	7.64725	−	13.3363i	0.247849	−	0.432230i
$953$	14.7851	−	7.12013i	0.478936	−	0.230644i	−0.178809	−	0.983884i	$-0.557224\pi$
$953$	14.7851	−	7.12013i	0.478936	−	0.230644i	0.657746	+	0.753240i	$0.271510\pi$
$954$		0			0
$955$	−2.12008	−	1.96715i	−0.0686041	−	0.0636553i
$956$	−8.67262	−	8.04701i	−0.280492	−	0.260259i
$957$		0			0
$958$	16.8689	−	8.12363i	0.545009	−	0.262463i
$959$	−44.6207	+	6.86036i	−1.44088	+	0.221533i
$960$		0			0
$961$	14.9766	+	25.9402i	0.483116	+	0.836782i
$962$	−1.19741	+	2.07397i	−0.0386060	+	0.0668675i
$963$		0			0
$964$	−9.21402	−	1.38879i	−0.296764	−	0.0447299i
$965$	−2.41067	+	10.5618i	−0.0776022	+	0.339997i
$966$		0			0
$967$	−7.01637	−	30.7407i	−0.225631	−	0.988555i	−0.953157	−	0.302475i	$-0.902187\pi$
$967$	−7.01637	−	30.7407i	−0.225631	−	0.988555i	0.727526	−	0.686080i	$-0.240670\pi$
$968$	−0.428252	−	5.71462i	−0.0137645	−	0.183675i
$969$		0			0
$970$	−3.72098	−	9.48091i	−0.119474	−	0.304414i
$971$	−13.8738	+	4.27949i	−0.445230	+	0.137335i	−0.509260	−	0.860613i	$-0.670081\pi$
$971$	−13.8738	+	4.27949i	−0.445230	+	0.137335i	0.0640298	+	0.997948i	$0.479605\pi$
$972$		0			0
$973$	−31.8097	+	15.4347i	−1.01977	+	0.494814i
$974$	2.28300	−	2.86280i	0.0731521	−	0.0917299i
$975$		0			0
$976$	−0.331877	+	4.42859i	−0.0106231	+	0.141756i
$977$	−21.7428	+	3.27719i	−0.695612	+	0.104847i	−0.487325	−	0.873221i	$-0.662027\pi$
$977$	−21.7428	+	3.27719i	−0.695612	+	0.104847i	−0.208288	+	0.978068i	$0.566789\pi$
$978$		0			0
$979$	−17.3405			−0.554206
$980$	3.05237	+	3.78150i	0.0975045	+	0.120796i
$981$		0			0
$982$	10.5602	−	9.79840i	0.336988	−	0.312680i
$983$	29.6300	−	4.46601i	0.945051	−	0.142444i	0.341602	−	0.939845i	$-0.389031\pi$
$983$	29.6300	−	4.46601i	0.945051	−	0.142444i	0.603449	+	0.797401i	$0.293793\pi$
$984$		0			0
$985$	−1.81338	+	4.62041i	−0.0577790	+	0.147218i
$986$	−21.2011	+	26.5854i	−0.675181	+	0.846651i
$987$		0			0
$988$	−4.45056	−	5.58082i	−0.141591	−	0.177550i
$989$	25.4898	−	7.86256i	0.810528	−	0.250015i
$990$		0			0
$991$	−43.5126	−	13.4219i	−1.38222	−	0.426359i	−0.487556	−	0.873092i	$-0.662111\pi$
$991$	−43.5126	−	13.4219i	−1.38222	−	0.426359i	−0.894668	+	0.446732i	$0.852588\pi$
$992$	0.0764585	+	1.02027i	0.00242756	+	0.0323935i
$993$		0			0
$994$	17.2291	+	11.6722i	0.546474	+	0.370219i
$995$	1.37080	−	6.00585i	0.0434572	−	0.190398i
$996$		0			0
$997$	0.854312	−	0.582460i	0.0270563	−	0.0184467i	−0.549716	−	0.835351i	$-0.685264\pi$
$997$	0.854312	−	0.582460i	0.0270563	−	0.0184467i	0.576773	+	0.816905i	$0.304312\pi$
$998$	18.5165	−	32.0716i	0.586130	−	1.01521i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.z.h.109.4	yes	60
3.2	odd	2		882.2.z.g.109.2	✓	60
49.9	even	21	inner	882.2.z.h.793.4	yes	60
147.107	odd	42		882.2.z.g.793.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.z.g.109.2	✓	60	3.2	odd	2
882.2.z.g.793.2	yes	60	147.107	odd	42
882.2.z.h.109.4	yes	60	1.1	even	1	trivial
882.2.z.h.793.4	yes	60	49.9	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.z (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.733052 + 0.680173i) q^{2} +(0.0747301 - 0.997204i) q^{4} +(0.253636 - 0.646253i) q^{5} +(-0.581112 + 2.58114i) q^{7} +(0.623490 + 0.781831i) q^{8} +O(q^{10})\)	\(q+(-0.733052 + 0.680173i) q^{2} +(0.0747301 - 0.997204i) q^{4} +(0.253636 - 0.646253i) q^{5} +(-0.581112 + 2.58114i) q^{7} +(0.623490 + 0.781831i) q^{8} +(0.253636 + 0.646253i) q^{10} +(-2.19352 - 0.676613i) q^{11} +(-0.439365 - 1.92498i) q^{13} +(-1.32964 - 2.28737i) q^{14} +(-0.988831 - 0.149042i) q^{16} +(-4.80089 + 3.27319i) q^{17} +(1.80759 + 3.13084i) q^{19} +(-0.625492 - 0.301221i) q^{20} +(2.06818 - 0.995983i) q^{22} +(-3.54142 - 2.41450i) q^{23} +(3.31195 + 3.07304i) q^{25} +(1.63140 + 1.11227i) q^{26} +(2.53050 + 0.772376i) q^{28} +(-5.27258 - 2.53914i) q^{29} +(-0.511564 + 0.886055i) q^{31} +(0.826239 - 0.563320i) q^{32} +(1.29297 - 5.66485i) q^{34} +(1.52068 + 1.03022i) q^{35} +(0.0906386 + 1.20949i) q^{37} +(-3.45457 - 1.06559i) q^{38} +(0.663401 - 0.204632i) q^{40} +(-1.61106 - 2.02020i) q^{41} +(-3.88025 + 4.86568i) q^{43} +(-0.838643 + 2.13683i) q^{44} +(4.23832 - 0.638825i) q^{46} +(-4.30004 + 3.98986i) q^{47} +(-6.32462 - 2.99987i) q^{49} -4.51803 q^{50} +(-1.95243 + 0.294282i) q^{52} +(-0.375034 + 5.00447i) q^{53} +(-0.993619 + 1.24596i) q^{55} +(-2.38034 + 1.15499i) q^{56} +(5.59213 - 1.72494i) q^{58} +(3.50526 + 8.93125i) q^{59} +(-0.331877 - 4.42859i) q^{61} +(-0.227668 - 0.997477i) q^{62} +(-0.222521 + 0.974928i) q^{64} +(-1.35547 - 0.204304i) q^{65} +(-6.91733 + 11.9812i) q^{67} +(2.90527 + 5.03207i) q^{68} +(-1.81546 + 0.279125i) q^{70} +(-7.08673 + 3.41279i) q^{71} +(-6.78586 - 6.29636i) q^{73} +(-0.889103 - 0.824967i) q^{74} +(3.25717 - 1.56857i) q^{76} +(3.02112 - 5.26862i) q^{77} +(-3.32182 - 5.75356i) q^{79} +(-0.347122 + 0.601233i) q^{80} +(2.55507 + 0.385115i) q^{82} +(1.37205 - 6.01133i) q^{83} +(0.897633 + 3.93279i) q^{85} +(-0.465078 - 6.20603i) q^{86} +(-0.838643 - 2.13683i) q^{88} +(7.21851 - 2.22662i) q^{89} +(5.22398 - 0.0154332i) q^{91} +(-2.67240 + 3.35108i) q^{92} +(0.438363 - 5.84954i) q^{94} +(2.48179 - 0.374069i) q^{95} -14.6706 q^{97} +(6.67670 - 2.10277i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 5 q^{4} + 3 q^{5} + q^{7} - 10 q^{8}+O(q^{10}) \) 60 * q + 5 * q^2 + 5 * q^4 + 3 * q^5 + q^7 - 10 * q^8	\( 60 q + 5 q^{2} + 5 q^{4} + 3 q^{5} + q^{7} - 10 q^{8} + 3 q^{10} - q^{11} - 4 q^{13} + 4 q^{14} + 5 q^{16} + 6 q^{17} - 12 q^{19} - 6 q^{20} + 9 q^{22} - 2 q^{23} + 6 q^{25} + 2 q^{26} - 5 q^{28} - 6 q^{29} - 7 q^{31} + 5 q^{32} - 12 q^{34} + 40 q^{35} + 6 q^{37} - 26 q^{38} - 11 q^{40} + 12 q^{43} - 15 q^{44} - 2 q^{46} - 44 q^{47} - 43 q^{49} + 86 q^{50} + 2 q^{52} + 13 q^{53} - 45 q^{55} + 8 q^{56} - 18 q^{58} + 53 q^{59} - 32 q^{61} - 14 q^{62} - 10 q^{64} + 2 q^{65} - 4 q^{67} - 36 q^{68} - 8 q^{70} - 42 q^{71} - 40 q^{73} - 8 q^{74} - 4 q^{76} - 55 q^{77} - 3 q^{79} - 11 q^{80} + 17 q^{83} + 16 q^{85} + 64 q^{86} - 15 q^{88} + 50 q^{89} + 72 q^{91} + 4 q^{92} + 26 q^{94} - 26 q^{95} - 2 q^{97} - 53 q^{98}+O(q^{100}) \) 60 * q + 5 * q^2 + 5 * q^4 + 3 * q^5 + q^7 - 10 * q^8 + 3 * q^10 - q^11 - 4 * q^13 + 4 * q^14 + 5 * q^16 + 6 * q^17 - 12 * q^19 - 6 * q^20 + 9 * q^22 - 2 * q^23 + 6 * q^25 + 2 * q^26 - 5 * q^28 - 6 * q^29 - 7 * q^31 + 5 * q^32 - 12 * q^34 + 40 * q^35 + 6 * q^37 - 26 * q^38 - 11 * q^40 + 12 * q^43 - 15 * q^44 - 2 * q^46 - 44 * q^47 - 43 * q^49 + 86 * q^50 + 2 * q^52 + 13 * q^53 - 45 * q^55 + 8 * q^56 - 18 * q^58 + 53 * q^59 - 32 * q^61 - 14 * q^62 - 10 * q^64 + 2 * q^65 - 4 * q^67 - 36 * q^68 - 8 * q^70 - 42 * q^71 - 40 * q^73 - 8 * q^74 - 4 * q^76 - 55 * q^77 - 3 * q^79 - 11 * q^80 + 17 * q^83 + 16 * q^85 + 64 * q^86 - 15 * q^88 + 50 * q^89 + 72 * q^91 + 4 * q^92 + 26 * q^94 - 26 * q^95 - 2 * q^97 - 53 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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