LMFDB - Embedded newform 99.3.k.c.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, degree $4$, 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:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 77x^12 + 88x^11 - 577x^10 + 578x^9 + 1520x^8 + 1868x^7 - 1619x^6 - 16804x^5 + 32427x^4 + 43316x^3 - 71672x^2 + 83521
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			73.2
Root			$-0.797732 + 1.94863i$ of defining polynomial
Character	$\chi$	$=$	99.73
Dual form			99.3.k.c.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30204 + 1.79211i) q^{2} +(-0.280267 - 0.862573i) q^{4} +(7.03442 - 5.11081i) q^{5} +(6.34535 - 2.06173i) q^{7} +(-6.51625 - 2.11726i) q^{8} +O(q^{10})$	\(q+(-1.30204 + 1.79211i) q^{2} +(-0.280267 - 0.862573i) q^{4} +(7.03442 - 5.11081i) q^{5} +(6.34535 - 2.06173i) q^{7} +(-6.51625 - 2.11726i) q^{8} +19.2609i q^{10} +(8.95368 + 6.38997i) q^{11} +(-6.55655 + 9.02432i) q^{13} +(-4.56707 + 14.0560i) q^{14} +(15.2138 - 11.0535i) q^{16} +(4.60052 + 6.33207i) q^{17} +(-8.02898 - 2.60877i) q^{19} +(-6.37996 - 4.63531i) q^{20} +(-23.1096 + 7.72594i) q^{22} -9.30611 q^{23} +(15.6373 - 48.1267i) q^{25} +(-7.63564 - 23.5001i) q^{26} +(-3.55678 - 4.89549i) q^{28} +(-6.82718 + 2.21829i) q^{29} +(22.1867 + 16.1196i) q^{31} +14.2504i q^{32} -17.3378 q^{34} +(34.0987 - 46.9329i) q^{35} +(-16.3598 - 50.3504i) q^{37} +(15.1293 - 10.9921i) q^{38} +(-56.6589 + 18.4096i) q^{40} +(-45.5114 - 14.7876i) q^{41} +45.8381i q^{43} +(3.00240 - 9.51410i) q^{44} +(12.1169 - 16.6775i) q^{46} +(4.96833 - 15.2909i) q^{47} +(-3.62914 + 2.63673i) q^{49} +(65.8878 + 90.6867i) q^{50} +(9.62172 + 3.12629i) q^{52} +(-44.4411 - 32.2883i) q^{53} +(95.6418 - 0.810768i) q^{55} -45.7131 q^{56} +(4.91387 - 15.1233i) q^{58} +(22.0055 + 67.7260i) q^{59} +(-0.764891 - 1.05278i) q^{61} +(-57.7761 + 18.7726i) q^{62} +(35.3168 + 25.6592i) q^{64} +96.9901i q^{65} -28.9406 q^{67} +(4.17250 - 5.74296i) q^{68} +(39.7108 + 122.217i) q^{70} +(17.8405 - 12.9619i) q^{71} +(-119.098 + 38.6972i) q^{73} +(111.535 + 36.2398i) q^{74} +7.65674i q^{76} +(69.9885 + 22.0865i) q^{77} +(25.2021 - 34.6877i) q^{79} +(50.5281 - 155.509i) q^{80} +(85.7587 - 62.3073i) q^{82} +(-78.3011 - 107.772i) q^{83} +(64.7240 + 21.0301i) q^{85} +(-82.1469 - 59.6832i) q^{86} +(-44.8152 - 60.5959i) q^{88} +9.48441 q^{89} +(-22.9979 + 70.7802i) q^{91} +(2.60819 + 8.02720i) q^{92} +(20.9340 + 28.8132i) q^{94} +(-69.8122 + 22.6834i) q^{95} +(-126.223 - 91.7061i) q^{97} -9.93695i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) $ 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8	$ 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) $ 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8 + 10 * q^11 + 30 * q^13 + 2 * q^14 + 16 * q^16 + 10 * q^17 - 42 * q^20 + 42 * q^22 - 132 * q^23 - 2 * q^25 - 46 * q^26 - 50 * q^28 - 160 * q^29 + 10 * q^31 - 368 * q^34 + 320 * q^35 - 126 * q^37 + 130 * q^38 + 30 * q^40 + 120 * q^41 + 206 * q^44 + 50 * q^46 + 150 * q^47 + 210 * q^49 - 330 * q^50 + 110 * q^52 - 342 * q^53 + 244 * q^55 - 524 * q^56 + 150 * q^58 - 110 * q^59 - 90 * q^61 - 40 * q^62 - 168 * q^64 + 36 * q^67 - 80 * q^68 + 340 * q^70 + 236 * q^71 - 350 * q^73 + 730 * q^74 + 390 * q^77 + 210 * q^79 + 806 * q^80 + 114 * q^82 + 190 * q^83 + 110 * q^85 - 736 * q^86 + 144 * q^88 - 76 * q^89 + 306 * q^91 + 150 * q^92 - 350 * q^94 - 430 * q^95 - 354 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−1.30204	+	1.79211i	−0.651021	+	0.896054i	−0.999143	−	0.0413956i	$-0.986820\pi$
$2$	−1.30204	+	1.79211i	−0.651021	+	0.896054i	0.348122	+	0.937449i	$0.386820\pi$
$3$		0			0
$3$		0			0
$4$	−0.280267	−	0.862573i	−0.0700667	−	0.215643i
$5$	7.03442	−	5.11081i	1.40688	−	1.02216i	0.413118	−	0.910678i	$-0.364440\pi$
$5$	7.03442	−	5.11081i	1.40688	−	1.02216i	0.993766	−	0.111484i	$-0.0355602\pi$
$6$		0			0
$7$	6.34535	−	2.06173i	0.906478	−	0.294533i	0.181570	−	0.983378i	$-0.441882\pi$
$7$	6.34535	−	2.06173i	0.906478	−	0.294533i	0.724908	+	0.688846i	$0.241882\pi$
$8$	−6.51625	−	2.11726i	−0.814531	−	0.264657i
$9$		0			0
$10$			19.2609i			1.92609i
$11$	8.95368	+	6.38997i	0.813970	+	0.580906i
$11$	8.95368	+	6.38997i	0.813970	+	0.580906i
$12$		0			0
$13$	−6.55655	+	9.02432i	−0.504350	+	0.694178i	−0.982954	−	0.183853i	$-0.941143\pi$
$13$	−6.55655	+	9.02432i	−0.504350	+	0.694178i	0.478604	+	0.878031i	$0.341143\pi$
$14$	−4.56707	+	14.0560i	−0.326219	+	1.00400i
$15$		0			0
$16$	15.2138	−	11.0535i	0.950861	−	0.690841i
$17$	4.60052	+	6.33207i	0.270619	+	0.372475i	0.922599	−	0.385762i	$-0.126061\pi$
$17$	4.60052	+	6.33207i	0.270619	+	0.372475i	−0.651980	+	0.758236i	$0.726061\pi$
$18$		0			0
$19$	−8.02898	−	2.60877i	−0.422578	−	0.137304i	0.0900055	−	0.995941i	$-0.471312\pi$
$19$	−8.02898	−	2.60877i	−0.422578	−	0.137304i	−0.512584	+	0.858637i	$0.671312\pi$
$20$	−6.37996	−	4.63531i	−0.318998	−	0.231766i
$21$		0			0
$22$	−23.1096	+	7.72594i	−1.05044	+	0.351179i
$23$	−9.30611			−0.404613			−0.202307	−	0.979322i	$-0.564844\pi$
$23$	−9.30611			−0.404613			−0.202307	+	0.979322i	$0.564844\pi$
$24$		0			0
$25$	15.6373	−	48.1267i	0.625492	−	1.92507i
$26$	−7.63564	−	23.5001i	−0.293678	−	0.903849i
$27$		0			0
$28$	−3.55678	−	4.89549i	−0.127028	−	0.174839i
$29$	−6.82718	+	2.21829i	−0.235420	+	0.0764926i	−0.424351	−	0.905498i	$-0.639498\pi$
$29$	−6.82718	+	2.21829i	−0.235420	+	0.0764926i	0.188931	+	0.981990i	$0.439498\pi$
$30$		0			0
$31$	22.1867	+	16.1196i	0.715701	+	0.519987i	0.885008	−	0.465576i	$-0.154153\pi$
$31$	22.1867	+	16.1196i	0.715701	+	0.519987i	−0.169307	+	0.985563i	$0.554153\pi$
$32$			14.2504i			0.445326i
$33$		0			0
$34$	−17.3378			−0.509936
$35$	34.0987	−	46.9329i	0.974250	−	1.34094i
$36$		0			0
$37$	−16.3598	−	50.3504i	−0.442158	−	1.36082i	−0.885571	−	0.464505i	$-0.846232\pi$
$37$	−16.3598	−	50.3504i	−0.442158	−	1.36082i	0.443412	−	0.896318i	$-0.353768\pi$
$38$	15.1293	−	10.9921i	0.398139	−	0.289265i
$39$		0			0
$40$	−56.6589	+	18.4096i	−1.41647	+	0.460240i
$41$	−45.5114	−	14.7876i	−1.11003	−	0.360672i	−0.304078	−	0.952647i	$-0.598348\pi$
$41$	−45.5114	−	14.7876i	−1.11003	−	0.360672i	−0.805956	+	0.591975i	$0.798348\pi$
$42$		0			0
$43$			45.8381i			1.06600i	0.846114	+	0.533002i	$0.178936\pi$
$43$			45.8381i			1.06600i	−0.846114	+	0.533002i	$0.821064\pi$
$44$	3.00240	−	9.51410i	0.0682363	−	0.216229i
$45$		0			0
$46$	12.1169	−	16.6775i	0.263412	−	0.362555i
$47$	4.96833	−	15.2909i	0.105709	−	0.325339i	−0.884187	−	0.467133i	$-0.845287\pi$
$47$	4.96833	−	15.2909i	0.105709	−	0.325339i	0.989896	+	0.141794i	$0.0452870\pi$
$48$		0			0
$49$	−3.62914	+	2.63673i	−0.0740642	+	0.0538108i
$50$	65.8878	+	90.6867i	1.31776	+	1.81373i
$51$		0			0
$52$	9.62172	+	3.12629i	0.185033	+	0.0601209i
$53$	−44.4411	−	32.2883i	−0.838511	−	0.609214i	0.0834437	−	0.996512i	$-0.473408\pi$
$53$	−44.4411	−	32.2883i	−0.838511	−	0.609214i	−0.921954	+	0.387299i	$0.873408\pi$
$54$		0			0
$55$	95.6418	−	0.810768i	1.73894	−	0.0147412i
$56$	−45.7131			−0.816305
$57$		0			0
$58$	4.91387	−	15.1233i	0.0847220	−	0.260747i
$59$	22.0055	+	67.7260i	0.372975	+	1.14790i	0.944835	+	0.327547i	$0.106222\pi$
$59$	22.0055	+	67.7260i	0.372975	+	1.14790i	−0.571860	+	0.820351i	$0.693778\pi$
$60$		0			0
$61$	−0.764891	−	1.05278i	−0.0125392	−	0.0172587i	0.802701	−	0.596381i	$-0.203395\pi$
$61$	−0.764891	−	1.05278i	−0.0125392	−	0.0172587i	−0.815241	+	0.579122i	$0.803395\pi$
$62$	−57.7761	+	18.7726i	−0.931873	+	0.302784i
$63$		0			0
$64$	35.3168	+	25.6592i	0.551825	+	0.400925i
$65$			96.9901i			1.49216i
$66$		0			0
$67$	−28.9406			−0.431949			−0.215975	−	0.976399i	$-0.569293\pi$
$67$	−28.9406			−0.431949			−0.215975	+	0.976399i	$0.569293\pi$
$68$	4.17250	−	5.74296i	0.0613603	−	0.0844552i
$69$		0			0
$70$	39.7108	+	122.217i	0.567297	+	1.74596i
$71$	17.8405	−	12.9619i	0.251275	−	0.182562i	−0.455017	−	0.890483i	$-0.650367\pi$
$71$	17.8405	−	12.9619i	0.251275	−	0.182562i	0.706292	+	0.707921i	$0.250367\pi$
$72$		0			0
$73$	−119.098	+	38.6972i	−1.63148	+	0.530099i	−0.974610	−	0.223907i	$-0.928119\pi$
$73$	−119.098	+	38.6972i	−1.63148	+	0.530099i	−0.656867	+	0.754006i	$0.728119\pi$
$74$	111.535	+	36.2398i	1.50722	+	0.489727i
$75$		0			0
$76$			7.65674i			0.100747i
$77$	69.9885	+	22.0865i	0.908942	+	0.286838i
$78$		0			0
$79$	25.2021	−	34.6877i	0.319014	−	0.439085i	−0.619152	−	0.785271i	$-0.712523\pi$
$79$	25.2021	−	34.6877i	0.319014	−	0.439085i	0.938166	+	0.346186i	$0.112523\pi$
$80$	50.5281	−	155.509i	0.631601	−	1.94387i
$81$		0			0
$82$	85.7587	−	62.3073i	1.04584	−	0.759845i
$83$	−78.3011	−	107.772i	−0.943387	−	1.29846i	−0.954403	−	0.298522i	$-0.903506\pi$
$83$	−78.3011	−	107.772i	−0.943387	−	1.29846i	0.0110157	−	0.999939i	$-0.496494\pi$
$84$		0			0
$85$	64.7240	+	21.0301i	0.761459	+	0.247413i
$86$	−82.1469	−	59.6832i	−0.955196	−	0.693991i
$87$		0			0
$88$	−44.8152	−	60.5959i	−0.509263	−	0.688590i
$89$	9.48441			0.106566			0.0532832	−	0.998579i	$-0.483031\pi$
$89$	9.48441			0.106566			0.0532832	+	0.998579i	$0.483031\pi$
$90$		0			0
$91$	−22.9979	+	70.7802i	−0.252724	+	0.777805i
$92$	2.60819	+	8.02720i	0.0283499	+	0.0872522i
$93$		0			0
$94$	20.9340	+	28.8132i	0.222703	+	0.306524i
$95$	−69.8122	+	22.6834i	−0.734865	+	0.238772i
$96$		0			0
$97$	−126.223	−	91.7061i	−1.30126	−	0.945424i	−0.301297	−	0.953530i	$-0.597420\pi$
$97$	−126.223	−	91.7061i	−1.30126	−	0.945424i	−0.999967	+	0.00810612i	$0.997420\pi$
$98$		−	9.93695i		−	0.101397i
$99$		0			0
$100$	−45.8954			−0.458954
$101$	32.3730	−	44.5576i	0.320525	−	0.441164i	−0.618103	−	0.786097i	$-0.712098\pi$
$101$	32.3730	−	44.5576i	0.320525	−	0.441164i	0.938627	+	0.344933i	$0.112098\pi$
$102$		0			0
$103$	−25.0358	−	77.0524i	−0.243066	−	0.748081i	−0.995948	−	0.0899260i	$-0.971337\pi$
$103$	−25.0358	−	77.0524i	−0.243066	−	0.748081i	0.752882	−	0.658155i	$-0.228663\pi$
$104$	61.8309	−	44.9228i	0.594528	−	0.431950i
$105$		0			0
$106$	115.728	−	37.6024i	1.09178	−	0.354740i
$107$	74.3714	+	24.1647i	0.695060	+	0.225839i	0.635177	−	0.772367i	$-0.280927\pi$
$107$	74.3714	+	24.1647i	0.695060	+	0.225839i	0.0598830	+	0.998205i	$0.480927\pi$
$108$		0			0
$109$		−	2.67841i		−	0.0245725i	−0.999925	−	0.0122863i	$-0.996089\pi$
$109$		−	2.67841i		−	0.0245725i	0.999925	−	0.0122863i	$-0.00391094\pi$
$110$	−123.077	+	172.456i	−1.11888	+	1.56778i
$111$		0			0
$112$	73.7475	−	101.505i	0.658460	−	0.906292i
$113$	−56.9227	+	175.190i	−0.503740	+	1.55035i	0.299138	+	0.954210i	$0.403301\pi$
$113$	−56.9227	+	175.190i	−0.503740	+	1.55035i	−0.802878	+	0.596143i	$0.796699\pi$
$114$		0			0
$115$	−65.4631	+	47.5617i	−0.569244	+	0.413580i
$116$	3.82687	+	5.26723i	0.0329902	+	0.0454072i
$117$		0			0
$118$	−150.024	−	48.7459i	−1.27139	−	0.413100i
$119$	42.2469	+	30.6942i	0.355016	+	0.257934i
$120$		0			0
$121$	39.3366	+	114.427i	0.325096	+	0.945681i
$122$	2.88262			0.0236280
$123$		0			0
$124$	7.68613	−	23.6555i	0.0619849	−	0.190770i
$125$	−68.7940	−	211.726i	−0.550352	−	1.69381i
$126$		0			0
$127$	70.0092	+	96.3594i	0.551254	+	0.758735i	0.990182	−	0.139787i	$-0.0446417\pi$
$127$	70.0092	+	96.3594i	0.551254	+	0.758735i	−0.438928	+	0.898522i	$0.644642\pi$
$128$	−146.180	+	47.4967i	−1.14203	+	0.371068i
$129$		0			0
$130$	−173.817	−	126.285i	−1.33705	−	0.971425i
$131$			17.9999i			0.137403i	0.997637	+	0.0687017i	$0.0218857\pi$
$131$			17.9999i			0.137403i	−0.997637	+	0.0687017i	$0.978114\pi$
$132$		0			0
$133$	−56.3253			−0.423498
$134$	37.6819	−	51.8647i	0.281208	−	0.387050i
$135$		0			0
$136$	−16.5715	−	51.0019i	−0.121849	−	0.375014i
$137$	74.8831	−	54.4058i	0.546592	−	0.397122i	−0.279935	−	0.960019i	$-0.590313\pi$
$137$	74.8831	−	54.4058i	0.546592	−	0.397122i	0.826527	+	0.562896i	$0.190313\pi$
$138$		0			0
$139$	206.205	−	67.0001i	1.48349	−	0.482015i	0.548336	−	0.836258i	$-0.315261\pi$
$139$	206.205	−	67.0001i	1.48349	−	0.482015i	0.935153	+	0.354243i	$0.115261\pi$
$140$	−50.0398	−	16.2589i	−0.357427	−	0.116135i
$141$		0			0
$142$			48.8490i			0.344007i
$143$	−116.370	+	38.9047i	−0.813778	+	0.272060i
$144$		0			0
$145$	−36.6880	+	50.4968i	−0.253021	+	0.348254i
$146$	85.7208	−	263.822i	0.587129	−	1.80700i
$147$		0			0
$148$	−38.8458	+	28.2231i	−0.262472	+	0.190697i
$149$	82.7139	+	113.846i	0.555127	+	0.764067i	0.990697	−	0.136088i	$-0.0434531\pi$
$149$	82.7139	+	113.846i	0.555127	+	0.764067i	−0.435570	+	0.900155i	$0.643453\pi$
$150$		0			0
$151$	−10.9455	−	3.55641i	−0.0724869	−	0.0235524i	0.272549	−	0.962142i	$-0.412133\pi$
$151$	−10.9455	−	3.55641i	−0.0724869	−	0.0235524i	−0.345036	+	0.938589i	$0.612133\pi$
$152$	46.7954	+	33.9989i	0.307865	+	0.223677i
$153$		0			0
$154$	−130.709	+	96.6694i	−0.848763	+	0.627723i
$155$	238.455			1.53842
$156$		0			0
$157$	−46.2689	+	142.401i	−0.294706	+	0.907013i	0.688613	+	0.725129i	$0.258220\pi$
$157$	−46.2689	+	142.401i	−0.294706	+	0.907013i	−0.983320	+	0.181885i	$0.941780\pi$
$158$	29.3499	+	90.3298i	0.185759	+	0.571707i
$159$		0			0
$160$	72.8312	+	100.244i	0.455195	+	0.626522i
$161$	−59.0505	+	19.1867i	−0.366773	+	0.119172i
$162$		0			0
$163$	44.3481	+	32.2208i	0.272074	+	0.197673i	0.715453	−	0.698661i	$-0.246220\pi$
$163$	44.3481	+	32.2208i	0.272074	+	0.197673i	−0.443379	+	0.896334i	$0.646220\pi$
$164$			43.4014i			0.264643i
$165$		0			0
$166$	295.091			1.77766
$167$	25.2405	−	34.7406i	0.151141	−	0.208027i	−0.726732	−	0.686921i	$-0.758962\pi$
$167$	25.2405	−	34.7406i	0.151141	−	0.208027i	0.877873	+	0.478893i	$0.158962\pi$
$168$		0			0
$169$	13.7739	+	42.3918i	0.0815026	+	0.250839i
$170$	−121.962	+	88.6103i	−0.717421	+	0.521237i
$171$		0			0
$172$	39.5387	−	12.8469i	0.229876	−	0.0746914i
$173$	15.4481	+	5.01939i	0.0892953	+	0.0290138i	0.353324	−	0.935501i	$-0.385051\pi$
$173$	15.4481	+	5.01939i	0.0892953	+	0.0290138i	−0.264029	+	0.964515i	$0.585051\pi$
$174$		0			0
$175$		−	337.620i		−	1.92926i
$176$	206.851	−	1.75350i	1.17529	−	0.00996306i
$177$		0			0
$178$	−12.3491	+	16.9971i	−0.0693770	+	0.0954892i
$179$	−40.2813	+	123.973i	−0.225035	+	0.692586i	0.773253	+	0.634097i	$0.218628\pi$
$179$	−40.2813	+	123.973i	−0.225035	+	0.692586i	−0.998288	+	0.0584889i	$0.981372\pi$
$180$		0			0
$181$	82.1481	−	59.6841i	0.453857	−	0.329746i	−0.337260	−	0.941412i	$-0.609500\pi$
$181$	82.1481	−	59.6841i	0.453857	−	0.329746i	0.791117	+	0.611665i	$0.209500\pi$
$182$	−96.9015	−	133.374i	−0.532426	−	0.732822i
$183$		0			0
$184$	60.6409	+	19.7034i	0.329570	+	0.107084i
$185$	−372.413	−	270.574i	−2.01305	−	1.46256i
$186$		0			0
$187$	0.729817	+	86.0925i	0.00390277	+	0.460388i
$188$	−14.5820			−0.0775639
$189$		0			0
$190$	50.2474	−	154.646i	0.264460	−	0.813924i
$191$	49.9911	+	153.857i	0.261734	+	0.805533i	0.992428	+	0.122828i	$0.0391964\pi$
$191$	49.9911	+	153.857i	0.261734	+	0.805533i	−0.730694	+	0.682705i	$0.760804\pi$
$192$		0			0
$193$	−20.0973	−	27.6616i	−0.104131	−	0.143324i	0.753771	−	0.657137i	$-0.228233\pi$
$193$	−20.0973	−	27.6616i	−0.104131	−	0.143324i	−0.857902	+	0.513813i	$0.828233\pi$
$194$	328.694	−	106.799i	1.69430	−	0.550512i
$195$		0			0
$196$	3.29150	+	2.39141i	0.0167934	+	0.0122011i
$197$		−	61.8792i		−	0.314107i	−0.987590	−	0.157054i	$-0.949800\pi$
$197$		−	61.8792i		−	0.314107i	0.987590	−	0.157054i	$-0.0501996\pi$
$198$		0			0
$199$	238.301			1.19749			0.598747	−	0.800938i	$-0.295666\pi$
$199$	238.301			1.19749			0.598747	+	0.800938i	$0.295666\pi$
$200$	−203.793	+	280.497i	−1.01897	+	1.40249i
$201$		0			0
$202$	37.7010	+	116.032i	0.186639	+	0.574415i
$203$	−38.7473	+	28.1516i	−0.190874	+	0.138678i
$204$		0			0
$205$	−395.723	+	128.578i	−1.93035	+	0.627210i
$206$	170.684	+	55.4586i	0.828562	+	0.269216i
$207$		0			0
$208$			209.767i			1.00849i
$209$	−55.2189	−	74.6631i	−0.264205	−	0.357240i
$210$		0			0
$211$	−110.764	+	152.454i	−0.524948	+	0.722529i	−0.986350	−	0.164662i	$-0.947347\pi$
$211$	−110.764	+	152.454i	−0.524948	+	0.722529i	0.461402	+	0.887191i	$0.347347\pi$
$212$	−15.3957	+	47.3830i	−0.0726211	+	0.223505i
$213$		0			0
$214$	−140.140	+	101.818i	−0.654862	+	0.475785i
$215$	234.270	+	322.445i	1.08963	+	1.49974i
$216$		0			0
$217$	174.017	+	56.5415i	0.801921	+	0.260560i
$218$	4.79999	+	3.48740i	0.0220183	+	0.0159972i
$219$		0			0
$220$	−27.5046	−	82.2708i	−0.125021	−	0.373958i
$221$	−87.3062			−0.395050
$222$		0			0
$223$	−79.8077	+	245.623i	−0.357882	+	1.10145i	0.596437	+	0.802660i	$0.296582\pi$
$223$	−79.8077	+	245.623i	−0.357882	+	1.10145i	−0.954319	+	0.298788i	$0.903418\pi$
$224$	29.3805	+	90.4239i	0.131163	+	0.403678i
$225$		0			0
$226$	−239.843	−	330.116i	−1.06125	−	1.46069i
$227$	42.1402	−	13.6922i	0.185640	−	0.0603180i	−0.214722	−	0.976675i	$-0.568885\pi$
$227$	42.1402	−	13.6922i	0.185640	−	0.0603180i	0.400362	+	0.916357i	$0.368885\pi$
$228$		0			0
$229$	3.10563	+	2.25637i	0.0135617	+	0.00985316i	0.594545	−	0.804062i	$-0.297332\pi$
$229$	3.10563	+	2.25637i	0.0135617	+	0.00985316i	−0.580984	+	0.813915i	$0.697332\pi$
$230$		−	179.244i		−	0.779323i
$231$		0			0
$232$	49.1843			0.212001
$233$	141.858	−	195.250i	0.608831	−	0.837984i	−0.387650	−	0.921807i	$-0.626713\pi$
$233$	141.858	−	195.250i	0.608831	−	0.837984i	0.996481	+	0.0838231i	$0.0267131\pi$
$234$		0			0
$235$	−43.1997	−	132.955i	−0.183829	−	0.565766i
$236$	52.2512	−	37.9627i	0.221403	−	0.160859i
$237$		0			0
$238$	−110.014	+	35.7459i	−0.462246	+	0.150193i
$239$	−440.713	−	143.196i	−1.84399	−	0.599148i	−0.997803	−	0.0662581i	$-0.978894\pi$
$239$	−440.713	−	143.196i	−1.84399	−	0.599148i	−0.846185	−	0.532890i	$-0.821106\pi$
$240$		0			0
$241$		−	447.213i		−	1.85565i	−0.373011	−	0.927827i	$-0.621675\pi$
$241$		−	447.213i		−	1.85565i	0.373011	−	0.927827i	$-0.378325\pi$
$242$	−256.284	−	78.4939i	−1.05903	−	0.324355i
$243$		0			0
$244$	−0.693728	+	0.954835i	−0.00284315	+	0.00391326i
$245$	−12.0531	+	37.0957i	−0.0491964	+	0.151411i
$246$		0			0
$247$	76.1848	−	55.3515i	0.308441	−	0.224095i
$248$	−110.445	−	152.014i	−0.445343	−	0.612962i
$249$		0			0
$250$	469.009	+	152.390i	1.87604	+	0.609561i
$251$	307.937	+	223.730i	1.22684	+	0.891353i	0.996649	−	0.0817922i	$-0.0260644\pi$
$251$	307.937	+	223.730i	1.22684	+	0.891353i	0.230193	+	0.973145i	$0.426064\pi$
$252$		0			0
$253$	−83.3239	−	59.4657i	−0.329343	−	0.235042i
$254$	−263.841			−1.03875
$255$		0			0
$256$	51.2538	−	157.743i	0.200210	−	0.616184i
$257$	−1.02939	−	3.16814i	−0.00400541	−	0.0123274i	0.949034	−	0.315174i	$-0.102063\pi$
$257$	−1.02939	−	3.16814i	−0.00400541	−	0.0123274i	−0.953039	+	0.302847i	$0.902063\pi$
$258$		0			0
$259$	−207.618	−	285.761i	−0.801613	−	1.10333i
$260$	83.6610	−	27.1831i	0.321773	−	0.104550i
$261$		0			0
$262$	−32.2577	−	23.4366i	−0.123121	−	0.0894525i
$263$		−	379.793i		−	1.44408i	−0.691850	−	0.722041i	$-0.743204\pi$
$263$		−	379.793i		−	1.44408i	0.691850	−	0.722041i	$-0.256796\pi$
$264$		0			0
$265$	−477.636			−1.80240
$266$	73.3379	−	100.941i	0.275706	−	0.379477i
$267$		0			0
$268$	8.11110	+	24.9634i	0.0302653	+	0.0931470i
$269$	−151.461	+	110.043i	−0.563053	+	0.409082i	−0.832575	−	0.553912i	$-0.813134\pi$
$269$	−151.461	+	110.043i	−0.563053	+	0.409082i	0.269522	+	0.962994i	$0.413134\pi$
$270$		0			0
$271$	290.222	−	94.2989i	1.07093	−	0.347967i	0.280081	−	0.959976i	$-0.409639\pi$
$271$	290.222	−	94.2989i	1.07093	−	0.347967i	0.790850	+	0.612010i	$0.209639\pi$
$272$	139.983	+	45.4831i	0.514642	+	0.167217i
$273$		0			0
$274$			205.037i			0.748311i
$275$	447.540	−	330.989i	1.62742	−	1.20360i
$276$		0			0
$277$	282.238	−	388.468i	1.01891	−	1.40241i	0.105946	−	0.994372i	$-0.466213\pi$
$277$	282.238	−	388.468i	1.01891	−	1.40241i	0.912965	−	0.408039i	$-0.133787\pi$
$278$	−148.416	+	456.779i	−0.533872	+	1.64309i
$279$		0			0
$280$	−321.565	+	233.631i	−1.14845	+	0.834395i
$281$	5.32429	+	7.32826i	0.0189477	+	0.0260792i	0.818386	−	0.574669i	$-0.194869\pi$
$281$	5.32429	+	7.32826i	0.0189477	+	0.0260792i	−0.799438	+	0.600749i	$0.794869\pi$
$282$		0			0
$283$	−253.650	−	82.4160i	−0.896291	−	0.291223i	−0.175586	−	0.984464i	$-0.556182\pi$
$283$	−253.650	−	82.4160i	−0.896291	−	0.291223i	−0.720705	+	0.693242i	$0.756182\pi$
$284$	−16.1807	−	11.7560i	−0.0569742	−	0.0413942i
$285$		0			0
$286$	81.7977	−	259.204i	0.286006	−	0.906306i
$287$	−319.274			−1.11245
$288$		0			0
$289$	70.3756	−	216.594i	0.243514	−	0.749459i
$290$	−42.7262	−	131.498i	−0.147332	−	0.453441i
$291$		0			0
$292$	66.7584	+	91.8850i	0.228625	+	0.314675i
$293$	161.902	−	52.6053i	0.552568	−	0.179540i	−0.0194065	−	0.999812i	$-0.506178\pi$
$293$	161.902	−	52.6053i	0.552568	−	0.179540i	0.571974	+	0.820271i	$0.306178\pi$
$294$		0			0
$295$	500.930	+	363.947i	1.69807	+	1.23372i
$296$			362.734i			1.22545i
$297$		0			0
$298$	−311.721			−1.04604
$299$	61.0160	−	83.9813i	0.204067	−	0.280874i
$300$		0			0
$301$	94.5058	+	290.859i	0.313973	+	0.966308i
$302$	20.6250	−	14.9849i	0.0682947	−	0.0496190i
$303$		0			0
$304$	−150.987	+	49.0587i	−0.496668	+	0.161377i
$305$	−10.7611	−	3.49650i	−0.0352824	−	0.0114639i
$306$		0			0
$307$			228.869i			0.745501i	0.927932	+	0.372750i	$0.121585\pi$
$307$			228.869i			0.745501i	−0.927932	+	0.372750i	$0.878415\pi$
$308$	−0.564241	−	66.5603i	−0.00183195	−	0.216105i
$309$		0			0
$310$	−310.479	+	427.337i	−1.00154	+	1.37851i
$311$	−87.3160	+	268.731i	−0.280759	+	0.864087i	0.706879	+	0.707334i	$0.250102\pi$
$311$	−87.3160	+	268.731i	−0.280759	+	0.864087i	−0.987638	+	0.156752i	$0.949898\pi$
$312$		0			0
$313$	283.298	−	205.828i	0.905105	−	0.657597i	−0.0346670	−	0.999399i	$-0.511037\pi$
$313$	283.298	−	205.828i	0.905105	−	0.657597i	0.939772	+	0.341801i	$0.111037\pi$
$314$	−194.954	−	268.331i	−0.620872	−	0.854558i
$315$		0			0
$316$	−36.9840	−	12.0168i	−0.117038	−	0.0380280i
$317$	302.908	+	220.075i	0.955545	+	0.694244i	0.952112	−	0.305750i	$-0.0989072\pi$
$317$	302.908	+	220.075i	0.955545	+	0.694244i	0.00343309	+	0.999994i	$0.498907\pi$
$318$		0			0
$319$	−75.3032	−	23.7637i	−0.236060	−	0.0744943i
$320$	379.572			1.18616
$321$		0			0
$322$	42.5017	−	130.807i	0.131993	−	0.406232i
$323$	−20.4185	−	62.8418i	−0.0632153	−	0.194557i
$324$		0			0
$325$	331.784	+	456.661i	1.02087	+	1.40511i
$326$	−115.486	+	37.5237i	−0.354252	+	0.115103i
$327$		0			0
$328$	265.255	+	192.719i	0.808703	+	0.587557i
$329$		−	107.270i		−	0.326048i
$330$		0			0
$331$	262.925			0.794334			0.397167	−	0.917746i	$-0.369993\pi$
$331$	262.925			0.794334			0.397167	+	0.917746i	$0.369993\pi$
$332$	−71.0162	+	97.7455i	−0.213904	+	0.294414i
$333$		0			0
$334$	29.3946	+	90.4674i	0.0880079	+	0.270860i
$335$	−203.580	+	147.910i	−0.607703	+	0.441522i
$336$		0			0
$337$	30.0552	−	9.76554i	0.0891847	−	0.0289779i	−0.264085	−	0.964499i	$-0.585070\pi$
$337$	30.0552	−	9.76554i	0.0891847	−	0.0289779i	0.353269	+	0.935522i	$0.385070\pi$
$338$	−93.9049	−	30.5116i	−0.277825	−	0.0902709i
$339$		0			0
$340$		−	61.7232i		−	0.181539i
$341$	95.6491	+	286.102i	0.280496	+	0.839010i
$342$		0			0
$343$	−209.752	+	288.699i	−0.611523	+	0.841689i
$344$	97.0512	−	298.693i	0.282126	−	0.868293i
$345$		0			0
$346$	−29.1094	+	21.1492i	−0.0841311	+	0.0611248i
$347$	−243.062	−	334.546i	−0.700467	−	0.964110i	−0.999950	−	0.0100080i	$-0.996814\pi$
$347$	−243.062	−	334.546i	−0.700467	−	0.964110i	0.299483	−	0.954102i	$-0.403186\pi$
$348$		0			0
$349$	−349.241	−	113.475i	−1.00069	−	0.325144i	−0.237548	−	0.971376i	$-0.576344\pi$
$349$	−349.241	−	113.475i	−1.00069	−	0.325144i	−0.763141	+	0.646232i	$0.776344\pi$
$350$	605.052	+	439.596i	1.72872	+	1.25599i
$351$		0			0
$352$	−91.0598	+	127.594i	−0.258693	+	0.362482i
$353$	415.577			1.17727			0.588636	−	0.808398i	$-0.299665\pi$
$353$	415.577			1.17727			0.588636	+	0.808398i	$0.299665\pi$
$354$		0			0
$355$	59.2519	−	182.359i	0.166907	−	0.513687i
$356$	−2.65817	−	8.18099i	−0.00746676	−	0.0229803i
$357$		0			0
$358$	−169.725	−	233.606i	−0.474092	−	0.652532i
$359$	147.178	−	47.8211i	0.409967	−	0.133206i	−0.0967705	−	0.995307i	$-0.530851\pi$
$359$	147.178	−	47.8211i	0.409967	−	0.133206i	0.506738	+	0.862100i	$0.330851\pi$
$360$		0			0
$361$	−234.396	−	170.299i	−0.649297	−	0.471742i
$362$			224.929i			0.621352i
$363$		0			0
$364$	67.4987			0.185436
$365$	−640.010	+	880.899i	−1.75345	+	2.41342i
$366$		0			0
$367$	−33.6631	−	103.604i	−0.0917251	−	0.282301i	0.894661	−	0.446745i	$-0.147417\pi$
$367$	−33.6631	−	103.604i	−0.0917251	−	0.282301i	−0.986386	+	0.164444i	$0.947417\pi$
$368$	−141.581	+	102.865i	−0.384731	+	0.279524i
$369$		0			0
$370$	969.796	−	315.106i	2.62107	−	0.851637i
$371$	−348.564	−	113.255i	−0.939524	−	0.305270i
$372$		0			0
$373$			721.229i			1.93359i	0.255555	+	0.966795i	$0.417742\pi$
$373$			721.229i			1.93359i	−0.255555	+	0.966795i	$0.582258\pi$
$374$	−155.237	−	110.788i	−0.415073	−	0.296225i
$375$		0			0
$376$	−64.7497	+	89.1204i	−0.172207	+	0.237022i
$377$	24.7442	−	76.1550i	0.0656346	−	0.202003i
$378$		0			0
$379$	10.4666	−	7.60444i	0.0276164	−	0.0200645i	−0.573891	−	0.818931i	$-0.694567\pi$
$379$	10.4666	−	7.60444i	0.0276164	−	0.0200645i	0.601508	+	0.798867i	$0.294567\pi$
$380$	39.1321	+	53.8607i	0.102979	+	0.141739i
$381$		0			0
$382$	−340.818	−	110.739i	−0.892195	−	0.289892i
$383$	−80.5883	−	58.5508i	−0.210413	−	0.152874i	0.477587	−	0.878584i	$-0.341511\pi$
$383$	−80.5883	−	58.5508i	−0.210413	−	0.152874i	−0.688001	+	0.725710i	$0.741511\pi$
$384$		0			0
$385$	605.209	−	202.332i	1.57197	−	0.525538i
$386$	75.7401			0.196218
$387$		0			0
$388$	−43.7272	+	134.578i	−0.112699	+	0.346852i
$389$	−62.4593	−	192.230i	−0.160564	−	0.494164i	0.838118	−	0.545488i	$-0.183656\pi$
$389$	−62.4593	−	192.230i	−0.160564	−	0.494164i	−0.998682	+	0.0513242i	$0.983656\pi$
$390$		0			0
$391$	−42.8129	−	58.9269i	−0.109496	−	0.150708i
$392$	29.2311	−	9.49774i	0.0745690	−	0.0242289i
$393$		0			0
$394$	110.894	+	80.5693i	0.281457	+	0.204491i
$395$		−	372.811i		−	0.943826i
$396$		0			0
$397$	332.729			0.838108			0.419054	−	0.907961i	$-0.362362\pi$
$397$	332.729			0.838108			0.419054	+	0.907961i	$0.362362\pi$
$398$	−310.278	+	427.061i	−0.779594	+	1.07302i
$399$		0			0
$400$	−294.064	−	905.036i	−0.735160	−	2.26259i
$401$	531.427	−	386.105i	1.32526	−	0.962854i	0.325404	−	0.945575i	$-0.394500\pi$
$401$	531.427	−	386.105i	1.32526	−	0.962854i	0.999851	−	0.0172792i	$-0.00550040\pi$
$402$		0			0
$403$	−290.937	+	94.5311i	−0.721928	+	0.234569i
$404$	−47.5073	−	15.4360i	−0.117592	−	0.0382080i
$405$		0			0
$406$		−	106.094i		−	0.261315i
$407$	175.257	−	555.360i	0.430607	−	1.36452i
$408$		0			0
$409$	275.704	−	379.474i	0.674093	−	0.927810i	−0.325751	−	0.945456i	$-0.605617\pi$
$409$	275.704	−	379.474i	0.674093	−	0.927810i	0.999844	+	0.0176458i	$0.00561712\pi$
$410$	284.822	−	876.592i	0.694688	−	2.13803i
$411$		0			0
$412$	−59.4466	+	43.1905i	−0.144288	+	0.104831i
$413$	279.265	+	384.375i	0.676187	+	0.930691i
$414$		0			0
$415$	−1101.61	−	357.934i	−2.65447	−	0.862490i
$416$	−128.600	−	93.4337i	−0.309136	−	0.224600i
$417$		0			0
$418$	205.702	−	1.74376i	0.492109	−	0.00417167i
$419$	−242.229			−0.578112			−0.289056	−	0.957312i	$-0.593341\pi$
$419$	−242.229			−0.578112			−0.289056	+	0.957312i	$0.593341\pi$
$420$		0			0
$421$	−227.921	+	701.470i	−0.541381	+	1.66620i	0.188061	+	0.982157i	$0.439780\pi$
$421$	−227.921	+	701.470i	−0.541381	+	1.66620i	−0.729442	+	0.684042i	$0.760220\pi$
$422$	−128.994	−	397.002i	−0.305673	−	0.940764i
$423$		0			0
$424$	221.226	+	304.492i	0.521760	+	0.718142i
$425$	376.682	−	122.391i	0.886309	−	0.287979i
$426$		0			0
$427$	−7.02405	−	5.10327i	−0.0164498	−	0.0119515i
$428$		−	70.9233i		−	0.165709i
$429$		0			0
$430$	−882.885			−2.05322
$431$	288.861	−	397.583i	0.670212	−	0.922467i	−0.329553	−	0.944137i	$-0.606898\pi$
$431$	288.861	−	397.583i	0.670212	−	0.922467i	0.999765	+	0.0216696i	$0.00689819\pi$
$432$		0			0
$433$	−124.430	−	382.956i	−0.287367	−	0.884425i	−0.985679	−	0.168631i	$-0.946065\pi$
$433$	−124.430	−	382.956i	−0.287367	−	0.884425i	0.698312	−	0.715793i	$-0.253935\pi$
$434$	−327.906	+	238.237i	−0.755543	+	0.548934i
$435$		0			0
$436$	−2.31032	+	0.750668i	−0.00529890	+	0.00172172i
$437$	74.7186	+	24.2775i	0.170981	+	0.0555550i
$438$		0			0
$439$			68.4030i			0.155815i	0.996961	+	0.0779077i	$0.0248240\pi$
$439$			68.4030i			0.155815i	−0.996961	+	0.0779077i	$0.975176\pi$
$440$	−624.943	−	197.215i	−1.42032	−	0.448216i
$441$		0			0
$442$	113.676	−	156.462i	0.257186	−	0.353986i
$443$	−96.8586	+	298.100i	−0.218642	+	0.672912i	0.780233	+	0.625490i	$0.215101\pi$
$443$	−96.8586	+	298.100i	−0.218642	+	0.672912i	−0.998875	+	0.0474225i	$0.984899\pi$
$444$		0			0
$445$	66.7173	−	48.4730i	0.149927	−	0.108928i
$446$	−336.270	−	462.835i	−0.753968	−	1.03775i
$447$		0			0
$448$	277.000	+	90.0026i	0.618303	+	0.200899i
$449$	266.257	+	193.447i	0.592999	+	0.430839i	0.843387	−	0.537306i	$-0.180558\pi$
$449$	266.257	+	193.447i	0.592999	+	0.430839i	−0.250388	+	0.968146i	$0.580558\pi$
$450$		0			0
$451$	−313.002	−	423.219i	−0.694019	−	0.938402i
$452$	167.068			0.369619
$453$		0			0
$454$	−30.3305	+	93.3475i	−0.0668072	+	0.205611i
$455$	199.967	+	615.436i	0.439488	+	1.35261i
$456$		0			0
$457$	52.0476	+	71.6374i	0.113890	+	0.156756i	0.862156	−	0.506642i	$-0.169114\pi$
$457$	52.0476	+	71.6374i	0.113890	+	0.156756i	−0.748267	+	0.663398i	$0.769114\pi$
$458$	−8.08733	+	2.62773i	−0.0176579	+	0.00573741i
$459$		0			0
$460$	59.3726	+	43.1367i	0.129071	+	0.0937755i
$461$			607.310i			1.31737i	0.752417	+	0.658687i	$0.228888\pi$
$461$			607.310i			1.31737i	−0.752417	+	0.658687i	$0.771112\pi$
$462$		0			0
$463$	−40.7126			−0.0879321			−0.0439660	−	0.999033i	$-0.513999\pi$
$463$	−40.7126			−0.0879321			−0.0439660	+	0.999033i	$0.513999\pi$
$464$	−79.3475	+	109.213i	−0.171008	+	0.235372i
$465$		0			0
$466$	165.205	+	508.448i	0.354517	+	1.09109i
$467$	−362.278	+	263.210i	−0.775756	+	0.563620i	−0.903702	−	0.428162i	$-0.859161\pi$
$467$	−362.278	+	263.210i	−0.775756	+	0.563620i	0.127946	+	0.991781i	$0.459161\pi$
$468$		0			0
$469$	−183.638	+	59.6677i	−0.391553	+	0.127223i
$470$	294.518	+	95.6946i	0.626633	+	0.203605i
$471$		0			0
$472$		−	487.911i		−	1.03371i
$473$	−292.904	+	410.420i	−0.619248	+	0.867695i
$474$		0			0
$475$	−251.103	+	345.614i	−0.528639	+	0.727609i
$476$	14.6356	−	45.0436i	0.0307470	−	0.0946294i
$477$		0			0
$478$	830.450	−	603.357i	1.73734	−	1.26225i
$479$	−34.3810	−	47.3214i	−0.0717766	−	0.0987920i	0.771619	−	0.636085i	$-0.219447\pi$
$479$	−34.3810	−	47.3214i	−0.0717766	−	0.0987920i	−0.843396	+	0.537293i	$0.819447\pi$
$480$		0			0
$481$	561.642	+	182.489i	1.16766	+	0.379394i
$482$	801.453	+	582.290i	1.66277	+	1.20807i
$483$		0			0
$484$	87.6772	−	66.0009i	0.181151	−	0.136366i
$485$	−1356.60			−2.79710
$486$		0			0
$487$	−201.875	+	621.309i	−0.414529	+	1.27579i	0.498143	+	0.867095i	$0.334015\pi$
$487$	−201.875	+	621.309i	−0.414529	+	1.27579i	−0.912672	+	0.408693i	$0.865985\pi$
$488$	2.75521	+	8.47967i	0.00564592	+	0.0173764i
$489$		0			0
$490$	−50.7858	−	69.9007i	−0.103645	−	0.142654i
$491$	−280.340	+	91.0879i	−0.570957	+	0.185515i	−0.580245	−	0.814442i	$-0.697043\pi$
$491$	−280.340	+	91.0879i	−0.570957	+	0.185515i	0.00928858	+	0.999957i	$0.497043\pi$
$492$		0			0
$493$	−45.4549	−	33.0249i	−0.0922007	−	0.0669877i
$494$			208.601i			0.422270i
$495$		0			0
$496$	515.722			1.03976
$497$	86.4803	−	119.030i	0.174005	−	0.239497i
$498$		0			0
$499$	12.7690	+	39.2989i	0.0255892	+	0.0787554i	0.963036	−	0.269374i	$-0.0868169\pi$
$499$	12.7690	+	39.2989i	0.0255892	+	0.0787554i	−0.937446	+	0.348130i	$0.886817\pi$
$500$	−163.349	+	118.680i	−0.326697	+	0.237360i
$501$		0			0
$502$	−801.895	+	260.551i	−1.59740	+	0.519027i
$503$	582.346	+	189.216i	1.15774	+	0.376174i	0.824056	−	0.566509i	$-0.191706\pi$
$503$	582.346	+	189.216i	1.15774	+	0.376174i	0.333689	+	0.942683i	$0.391706\pi$
$504$		0			0
$505$		−	478.889i		−	0.948295i
$506$	215.060	−	71.8984i	0.425020	−	0.142092i
$507$		0			0
$508$	63.4957	−	87.3944i	0.124992	−	0.172036i
$509$	92.7000	−	285.301i	0.182122	−	0.560513i	−0.817765	−	0.575552i	$-0.804787\pi$
$509$	92.7000	−	285.301i	0.182122	−	0.560513i	0.999887	+	0.0150389i	$0.00478721\pi$
$510$		0			0
$511$	−675.934	+	491.095i	−1.32277	+	0.961046i
$512$	−145.419	−	200.151i	−0.284021	−	0.390921i
$513$		0			0
$514$	7.01795	+	2.28027i	0.0136536	+	0.00443632i
$515$	−569.912	−	414.066i	−1.10663	−	0.804011i
$516$		0			0
$517$	142.193	−	105.163i	0.275036	−	0.203409i
$518$	782.442			1.51051
$519$		0			0
$520$	205.353	−	632.012i	0.394910	−	1.21541i
$521$	−196.473	−	604.683i	−0.377108	−	1.16062i	−0.942045	−	0.335485i	$-0.891100\pi$
$521$	−196.473	−	604.683i	−0.377108	−	1.16062i	0.564937	−	0.825134i	$-0.308900\pi$
$522$		0			0
$523$	4.83865	+	6.65983i	0.00925172	+	0.0127339i	0.813618	−	0.581400i	$-0.197495\pi$
$523$	4.83865	+	6.65983i	0.00925172	+	0.0127339i	−0.804366	+	0.594134i	$0.797495\pi$
$524$	15.5262	−	5.04476i	0.0296301	−	0.00962741i
$525$		0			0
$526$	680.631	+	494.507i	1.29397	+	0.940128i
$527$			214.647i			0.407299i
$528$		0			0
$529$	−442.396			−0.836288
$530$	621.903	−	855.976i	1.17340	−	1.61505i
$531$		0			0
$532$	15.7861	+	48.5846i	0.0296731	+	0.0913245i
$533$	431.845	−	313.754i	0.810216	−	0.588657i
$534$		0			0
$535$	646.661	−	210.113i	1.20871	−	0.392734i
$536$	188.584	+	61.2747i	0.351836	+	0.114319i
$537$		0			0
$538$		−	414.716i		−	0.770847i
$539$	−49.3428	+	0.418285i	−0.0915451	+	0.000776039i
$540$		0			0
$541$	−121.004	+	166.548i	−0.223667	+	0.307852i	−0.906073	−	0.423122i	$-0.860934\pi$
$541$	−121.004	+	166.548i	−0.223667	+	0.307852i	0.682405	+	0.730974i	$0.260934\pi$
$542$	−208.888	+	642.891i	−0.385402	+	1.18615i
$543$		0			0
$544$	−90.2348	+	65.5594i	−0.165873	+	0.120514i
$545$	−13.6888	−	18.8410i	−0.0251171	−	0.0345707i
$546$		0			0
$547$	886.431	+	288.019i	1.62053	+	0.526543i	0.972067	−	0.234702i	$-0.0754114\pi$
$547$	886.431	+	288.019i	1.62053	+	0.526543i	0.648465	+	0.761245i	$0.275411\pi$
$548$	−67.9162	−	49.3440i	−0.123935	−	0.0900438i
$549$		0			0
$550$	10.4523	+	1233.00i	0.0190042	+	2.24182i
$551$	60.6023			0.109986
$552$		0			0
$553$	88.3994	−	272.065i	0.159854	−	0.491981i
$554$	328.690	+	1011.60i	0.593303	+	1.82600i
$555$		0			0
$556$	−115.585	−	159.089i	−0.207887	−	0.286131i
$557$	709.178	−	230.426i	1.27321	−	0.413691i	0.407026	−	0.913417i	$-0.366566\pi$
$557$	709.178	−	230.426i	1.27321	−	0.413691i	0.866184	+	0.499726i	$0.166566\pi$
$558$		0			0
$559$	−413.658	−	300.540i	−0.739996	−	0.537639i
$560$		−	1090.94i		−	1.94810i
$561$		0			0
$562$	−20.0655			−0.0357037
$563$	−450.422	+	619.953i	−0.800040	+	1.10116i	0.192745	+	0.981249i	$0.438261\pi$
$563$	−450.422	+	619.953i	−0.800040	+	1.10116i	−0.992785	+	0.119911i	$0.961739\pi$
$564$		0			0
$565$	494.944	+	1523.28i	0.876007	+	2.69607i
$566$	477.962	−	347.259i	0.844455	−	0.613533i
$567$		0			0
$568$	−143.697	+	46.6900i	−0.252988	+	0.0822006i
$569$	−842.875	−	273.867i	−1.48133	−	0.481312i	−0.546818	−	0.837251i	$-0.684161\pi$
$569$	−842.875	−	273.867i	−1.48133	−	0.481312i	−0.934509	+	0.355939i	$0.884161\pi$
$570$		0			0
$571$			504.852i			0.884154i	0.896977	+	0.442077i	$0.145758\pi$
$571$			504.852i			0.884154i	−0.896977	+	0.442077i	$0.854242\pi$
$572$	66.1729	+	89.4742i	0.115687	+	0.156423i
$573$		0			0
$574$	415.708	−	572.172i	0.724229	−	0.996816i
$575$	−145.523	+	447.872i	−0.253083	+	0.778908i
$576$		0			0
$577$	−699.892	+	508.501i	−1.21298	+	0.881285i	−0.995498	−	0.0947786i	$-0.969786\pi$
$577$	−699.892	+	508.501i	−1.21298	+	0.881285i	−0.217486	+	0.976063i	$0.569786\pi$
$578$	296.527	+	408.135i	0.513023	+	0.706115i
$579$		0			0
$580$	53.8396	+	17.4935i	0.0928269	+	0.0301613i
$581$	−719.045	−	522.417i	−1.23760	−	0.899168i
$582$		0			0
$583$	−191.589	−	573.076i	−0.328627	−	0.982978i
$584$	858.004			1.46918
$585$		0			0
$586$	−116.529	+	358.641i	−0.198856	+	0.612015i
$587$	226.704	+	697.722i	0.386207	+	1.18862i	0.935601	+	0.353060i	$0.114859\pi$
$587$	226.704	+	697.722i	0.386207	+	1.18862i	−0.549393	+	0.835564i	$0.685141\pi$
$588$		0			0
$589$	−136.085	−	187.304i	−0.231043	−	0.318004i
$590$	−1304.46	+	423.846i	−2.21096	+	0.718384i
$591$		0			0
$592$	−805.442	−	585.188i	−1.36054	−	0.988493i
$593$		−	1126.19i		−	1.89915i	−0.313544	−	0.949574i	$-0.601516\pi$
$593$		−	1126.19i		−	1.89915i	0.313544	−	0.949574i	$-0.398484\pi$
$594$		0			0
$595$	454.054			0.763117
$596$	75.0184	−	103.254i	0.125870	−	0.173245i
$597$		0			0
$598$	71.0581	+	218.694i	0.118826	+	0.365710i
$599$	−29.7104	+	21.5858i	−0.0496000	+	0.0360365i	−0.612309	−	0.790619i	$-0.709759\pi$
$599$	−29.7104	+	21.5858i	−0.0496000	+	0.0360365i	0.562709	+	0.826655i	$0.309759\pi$
$600$		0			0
$601$	610.772	−	198.452i	1.01626	−	0.330203i	0.246915	−	0.969037i	$-0.420583\pi$
$601$	610.772	−	198.452i	1.01626	−	0.330203i	0.769344	+	0.638834i	$0.220583\pi$
$602$	−644.301	−	209.346i	−1.07027	−	0.347751i
$603$		0			0
$604$			10.4381i			0.0172815i
$605$	861.526	+	603.889i	1.42401	+	0.998163i
$606$		0			0
$607$	388.522	−	534.754i	0.640069	−	0.880979i	−0.358551	−	0.933510i	$-0.616729\pi$
$607$	388.522	−	534.754i	0.640069	−	0.880979i	0.998619	+	0.0525314i	$0.0167289\pi$
$608$	37.1762	−	114.417i	0.0611450	−	0.188185i
$609$		0			0
$610$	20.2776	−	14.7325i	0.0332419	−	0.0241517i
$611$	105.415	+	145.092i	0.172529	+	0.237466i
$612$		0			0
$613$	694.004	+	225.496i	1.13214	+	0.367856i	0.814390	−	0.580318i	$-0.197072\pi$
$613$	694.004	+	225.496i	1.13214	+	0.367856i	0.317753	+	0.948173i	$0.397072\pi$
$614$	−410.157	−	297.997i	−0.668009	−	0.485337i
$615$		0			0
$616$	−409.300	−	292.105i	−0.664448	−	0.474197i
$617$	329.848			0.534600			0.267300	−	0.963613i	$-0.413868\pi$
$617$	329.848			0.534600			0.267300	+	0.963613i	$0.413868\pi$
$618$		0			0
$619$	319.295	−	982.689i	0.515824	−	1.58754i	−0.265954	−	0.963986i	$-0.585687\pi$
$619$	319.295	−	982.689i	0.515824	−	1.58754i	0.781778	−	0.623557i	$-0.214313\pi$
$620$	−66.8311	−	205.685i	−0.107792	−	0.331750i
$621$		0			0
$622$	−367.906	−	506.379i	−0.591488	−	0.814114i
$623$	60.1818	−	19.5543i	0.0966001	−	0.0313873i
$624$		0			0
$625$	−542.543	−	394.180i	−0.868068	−	0.630688i
$626$			775.697i			1.23913i
$627$		0			0
$628$	135.799			0.216240
$629$	243.559	−	335.230i	0.387216	−	0.532957i
$630$		0			0
$631$	−264.132	−	812.915i	−0.418593	−	1.28830i	−0.908998	−	0.416801i	$-0.863151\pi$
$631$	−264.132	−	812.915i	−0.418593	−	1.28830i	0.490405	−	0.871495i	$-0.336849\pi$
$632$	−237.666	+	172.675i	−0.376054	+	0.273219i
$633$		0			0
$634$	−788.797	+	256.296i	−1.24416	+	0.404252i
$635$	984.948	+	320.029i	1.55110	+	0.503983i
$636$		0			0
$637$		−	50.0384i		−	0.0785532i
$638$	140.635	−	104.010i	0.220431	−	0.163025i
$639$		0			0
$640$	−785.544	+	1081.21i	−1.22741	+	1.68939i
$641$	−139.978	+	430.809i	−0.218375	+	0.672089i	0.780522	+	0.625128i	$0.214953\pi$
$641$	−139.978	+	430.809i	−0.218375	+	0.672089i	−0.998897	+	0.0469602i	$0.985047\pi$
$642$		0			0
$643$	214.596	−	155.913i	0.333742	−	0.242477i	−0.408275	−	0.912859i	$-0.633870\pi$
$643$	214.596	−	155.913i	0.333742	−	0.242477i	0.742017	+	0.670382i	$0.233870\pi$
$644$	33.0998	+	45.5580i	0.0513972	+	0.0707422i
$645$		0			0
$646$	139.205	+	45.2305i	0.215488	+	0.0700162i
$647$	−277.346	−	201.504i	−0.428665	−	0.311443i	0.352450	−	0.935831i	$-0.385349\pi$
$647$	−277.346	−	201.504i	−0.428665	−	0.311443i	−0.781115	+	0.624388i	$0.785349\pi$
$648$		0			0
$649$	−235.737	+	747.011i	−0.363231	+	1.15102i
$650$	−1250.38			−1.92366
$651$		0			0
$652$	15.3635	−	47.2839i	0.0235636	−	0.0725213i
$653$	−167.848	−	516.582i	−0.257041	−	0.791091i	−0.993421	−	0.114522i	$-0.963466\pi$
$653$	−167.848	−	516.582i	−0.257041	−	0.791091i	0.736380	−	0.676569i	$-0.236534\pi$
$654$		0			0
$655$	91.9937	+	126.619i	0.140448	+	0.193311i
$656$	−855.854	+	278.084i	−1.30466	+	0.423908i
$657$		0			0
$658$	192.239	+	139.670i	0.292156	+	0.212264i
$659$			309.878i			0.470224i	0.971968	+	0.235112i	$0.0755457\pi$
$659$			309.878i			0.470224i	−0.971968	+	0.235112i	$0.924454\pi$
$660$		0			0
$661$	389.483			0.589234			0.294617	−	0.955615i	$-0.404808\pi$
$661$	389.483			0.589234			0.294617	+	0.955615i	$0.404808\pi$
$662$	−342.339	+	471.189i	−0.517128	+	0.711766i
$663$		0			0
$664$	282.048	+	868.055i	0.424771	+	1.30731i
$665$	−396.216	+	287.867i	−0.595813	+	0.432883i
$666$		0			0
$667$	63.5345	−	20.6436i	0.0952541	−	0.0309499i
$668$	−37.0404	−	12.0351i	−0.0554496	−	0.0180167i
$669$		0			0
$670$		−	557.423i		−	0.831974i
$671$	−0.121341	−	14.3139i	−0.000180836	−	0.0213322i
$672$		0			0
$673$	424.350	−	584.068i	0.630535	−	0.867857i	−0.367531	−	0.930011i	$-0.619797\pi$
$673$	424.350	−	584.068i	0.630535	−	0.867857i	0.998067	+	0.0621539i	$0.0197970\pi$
$674$	−21.6323	+	66.5773i	−0.0320954	+	0.0987794i
$675$		0			0
$676$	32.7056	−	23.7620i	0.0483811	−	0.0351510i
$677$	497.292	+	684.464i	0.734553	+	1.01103i	0.998914	+	0.0466016i	$0.0148391\pi$
$677$	497.292	+	684.464i	0.734553	+	1.01103i	−0.264360	+	0.964424i	$0.585161\pi$
$678$		0			0
$679$	−990.000	−	321.670i	−1.45803	−	0.473741i
$680$	−377.232	−	274.075i	−0.554752	−	0.403051i
$681$		0			0
$682$	−637.265	−	201.104i	−0.934406	−	0.294874i
$683$	−49.2192			−0.0720632			−0.0360316	−	0.999351i	$-0.511472\pi$
$683$	−49.2192			−0.0720632			−0.0360316	+	0.999351i	$0.511472\pi$
$684$		0			0
$685$	248.702	−	765.426i	0.363069	−	1.11741i
$686$	−244.274	−	751.797i	−0.356084	−	1.09591i
$687$		0			0
$688$	506.670	+	697.372i	0.736439	+	1.01362i
$689$	582.760	−	189.350i	0.845805	−	0.274819i
$690$		0			0
$691$	−570.918	−	414.796i	−0.826220	−	0.600284i	0.0922674	−	0.995734i	$-0.470589\pi$
$691$	−570.918	−	414.796i	−0.826220	−	0.600284i	−0.918487	+	0.395450i	$0.870589\pi$
$692$		−	14.7319i		−	0.0212888i
$693$		0			0
$694$	916.019			1.31991
$695$	1108.11	−	1525.18i	1.59440	−	2.19450i
$696$		0			0
$697$	−115.740	−	356.212i	−0.166055	−	0.511065i
$698$	658.086	−	478.127i	0.942816	−	0.684996i
$699$		0			0
$700$	−291.222	+	94.6239i	−0.416032	+	0.135177i
$701$	54.1902	+	17.6075i	0.0773041	+	0.0251176i	0.347414	−	0.937712i	$-0.387060\pi$
$701$	54.1902	+	17.6075i	0.0773041	+	0.0251176i	−0.270110	+	0.962830i	$0.587060\pi$
$702$		0			0
$703$			446.942i			0.635764i
$704$	152.254	+	455.417i	0.216270	+	0.646900i
$705$		0			0
$706$	−541.099	+	744.759i	−0.766429	+	1.05490i
$707$	113.552	−	349.478i	0.160611	−	0.494311i
$708$		0			0
$709$	−389.569	+	283.038i	−0.549462	+	0.399207i	−0.827587	−	0.561337i	$-0.810287\pi$
$709$	−389.569	+	283.038i	−0.549462	+	0.399207i	0.278125	+	0.960545i	$0.410287\pi$
$710$	249.658	+	343.625i	0.351631	+	0.483978i
$711$		0			0
$712$	−61.8028	−	20.0809i	−0.0868017	−	0.0282036i
$713$	−206.472	−	150.011i	−0.289582	−	0.210394i
$714$		0			0
$715$	−619.764	+	868.418i	−0.866802	+	1.21457i
$716$	118.225			0.165119
$717$		0			0
$718$	−105.932	+	326.024i	−0.147537	+	0.454073i
$719$	−305.211	−	939.343i	−0.424494	−	1.30646i	−0.903478	−	0.428634i	$-0.858995\pi$
$719$	−305.211	−	939.343i	−0.424494	−	1.30646i	0.478985	−	0.877823i	$-0.341005\pi$
$720$		0			0
$721$	−317.722	−	437.307i	−0.440669	−	0.606528i
$722$	610.388	−	198.327i	0.845412	−	0.274691i
$723$		0			0
$724$	−74.5053	−	54.1313i	−0.102908	−	0.0747670i
$725$			363.258i			0.501045i
$726$		0			0
$727$	−146.472			−0.201474			−0.100737	−	0.994913i	$-0.532120\pi$
$727$	−146.472			−0.201474			−0.100737	+	0.994913i	$0.532120\pi$
$728$	299.720	−	412.529i	0.411703	−	0.566661i
$729$		0			0
$730$	−745.344	−	2293.93i	−1.02102	−	3.14238i
$731$	−290.250	+	210.879i	−0.397059	+	0.288481i
$732$		0			0
$733$	133.580	−	43.4026i	0.182237	−	0.0592123i	−0.216477	−	0.976288i	$-0.569457\pi$
$733$	133.580	−	43.4026i	0.182237	−	0.0592123i	0.398714	+	0.917075i	$0.369457\pi$
$734$	229.501	+	74.5694i	0.312672	+	0.101593i
$735$		0			0
$736$		−	132.616i		−	0.180185i
$737$	−259.125	−	184.930i	−0.351594	−	0.250922i
$738$		0			0
$739$	389.245	−	535.750i	0.526718	−	0.724966i	−0.459907	−	0.887967i	$-0.652117\pi$
$739$	389.245	−	535.750i	0.526718	−	0.724966i	0.986626	+	0.163001i	$0.0521174\pi$
$740$	−129.015	+	397.067i	−0.174344	+	0.536577i
$741$		0			0
$742$	656.810	−	477.200i	0.885189	−	0.643127i
$743$	−112.831	−	155.299i	−0.151859	−	0.209016i	0.726309	−	0.687368i	$-0.241234\pi$
$743$	−112.831	−	155.299i	−0.151859	−	0.209016i	−0.878168	+	0.478353i	$0.841234\pi$
$744$		0			0
$745$	1163.69	+	378.105i	1.56200	+	0.507524i
$746$	−1292.52	−	939.070i	−1.73260	−	1.25881i
$747$		0			0
$748$	74.0565	−	24.7584i	0.0990060	−	0.0330995i
$749$	521.733			0.696573
$750$		0			0
$751$	−370.773	+	1141.12i	−0.493706	+	1.51947i	0.325257	+	0.945626i	$0.394549\pi$
$751$	−370.773	+	1141.12i	−0.493706	+	1.51947i	−0.818963	+	0.573846i	$0.805451\pi$
$752$	−93.4307	−	287.550i	−0.124243	−	0.382381i
$753$		0			0
$754$	104.260	+	143.501i	0.138276	+	0.190320i
$755$	−95.1715	+	30.9231i	−0.126055	+	0.0409578i
$756$		0			0
$757$	462.848	+	336.279i	0.611425	+	0.444226i	0.849916	−	0.526919i	$-0.176653\pi$
$757$	462.848	+	336.279i	0.611425	+	0.444226i	−0.238491	+	0.971145i	$0.576653\pi$
$758$			28.6586i			0.0378082i
$759$		0			0
$760$	502.940			0.661764
$761$	42.2940	−	58.2127i	0.0555769	−	0.0764950i	−0.780324	−	0.625376i	$-0.784946\pi$
$761$	42.2940	−	58.2127i	0.0555769	−	0.0764950i	0.835901	+	0.548881i	$0.184946\pi$
$762$		0			0
$763$	−5.52214	−	16.9954i	−0.00723741	−	0.0222745i
$764$	118.702	−	86.2420i	0.155369	−	0.112882i
$765$		0			0
$766$	209.859	−	68.1872i	0.273967	−	0.0890173i
$767$	−755.461	−	245.464i	−0.984955	−	0.320031i
$768$		0			0
$769$			87.6070i			0.113923i	0.998376	+	0.0569616i	$0.0181413\pi$
$769$			87.6070i			0.113923i	−0.998376	+	0.0569616i	$0.981859\pi$
$770$	−425.407	+	1348.04i	−0.552476	+	1.75071i
$771$		0			0
$772$	−18.2275	+	25.0880i	−0.0236108	+	0.0324975i
$773$	237.268	−	730.235i	0.306944	−	0.944676i	−0.672001	−	0.740550i	$-0.734565\pi$
$773$	237.268	−	730.235i	0.306944	−	0.944676i	0.978945	−	0.204126i	$-0.0654351\pi$
$774$		0			0
$775$	1122.72	−	815.707i	1.44868	−	1.05253i
$776$	628.333	+	864.826i	0.809708	+	1.11447i
$777$		0			0
$778$	425.821	+	138.358i	0.547328	+	0.177838i
$779$	326.833	+	237.458i	0.419554	+	0.304824i
$780$		0			0
$781$	242.564	−	2.05625i	0.310582	−	0.00263284i
$782$	161.348			0.206327
$783$		0			0
$784$	−26.0681	+	80.2292i	−0.0332501	+	0.102333i
$785$	402.309	+	1238.18i	0.512496	+	1.57730i
$786$		0			0
$787$	184.277	+	253.635i	0.234151	+	0.322281i	0.909882	−	0.414867i	$-0.136172\pi$
$787$	184.277	+	253.635i	0.234151	+	0.322281i	−0.675731	+	0.737148i	$0.736172\pi$
$788$	−53.3753	+	17.3427i	−0.0677352	+	0.0220085i
$789$		0			0
$790$	668.118	+	485.416i	0.845718	+	0.614450i
$791$			1229.00i			1.55373i
$792$		0			0
$793$	14.5157			0.0183048
$794$	−433.227	+	596.286i	−0.545626	+	0.750990i
$795$		0			0
$796$	−66.7880	−	205.552i	−0.0839045	−	0.258231i
$797$	−543.195	+	394.654i	−0.681550	+	0.495175i	−0.873871	−	0.486157i	$-0.838398\pi$
$797$	−543.195	+	394.654i	−0.681550	+	0.495175i	0.192322	+	0.981332i	$0.438398\pi$
$798$		0			0
$799$	119.680	−	38.8865i	0.149788	−	0.0486689i
$800$	685.826	+	222.839i	0.857283	+	0.278548i
$801$		0			0
$802$			1455.10i			1.81434i
$803$	−1313.64	−	414.549i	−1.63591	−	0.516250i
$804$		0			0
$805$	−317.327	+	436.763i	−0.394194	+	0.542562i
$806$	209.402	−	644.474i	0.259804	−	0.799595i
$807$		0			0
$808$	−305.290	+	221.807i	−0.377835	+	0.274513i
$809$	623.003	+	857.490i	0.770090	+	1.05994i	0.996307	+	0.0858610i	$0.0273641\pi$
$809$	623.003	+	857.490i	0.770090	+	1.05994i	−0.226217	+	0.974077i	$0.572636\pi$
$810$		0			0
$811$	−826.402	−	268.514i	−1.01899	−	0.331090i	−0.248562	−	0.968616i	$-0.579958\pi$
$811$	−826.402	−	268.514i	−1.01899	−	0.331090i	−0.770429	+	0.637525i	$0.779958\pi$
$812$	35.1424	+	25.5324i	0.0432788	+	0.0314439i
$813$		0			0
$814$	767.073	+	1037.18i	0.942351	+	1.27418i
$815$	476.637			0.584831
$816$		0			0
$817$	119.581	−	368.034i	0.146366	−	0.450470i
$818$	321.080	+	988.183i	0.392518	+	1.20805i
$819$		0			0
$820$	221.816	+	305.304i	0.270507	+	0.372321i
$821$	−712.961	+	231.655i	−0.868406	+	0.282162i	−0.709135	−	0.705073i	$-0.750914\pi$
$821$	−712.961	+	231.655i	−0.868406	+	0.282162i	−0.159271	+	0.987235i	$0.550914\pi$
$822$		0			0
$823$	−958.515	−	696.402i	−1.16466	−	0.846175i	−0.174300	−	0.984693i	$-0.555766\pi$
$823$	−958.515	−	696.402i	−1.16466	−	0.846175i	−0.990360	+	0.138517i	$0.955766\pi$
$824$			555.100i			0.673665i
$825$		0			0
$826$	−1052.46			−1.27416
$827$	−58.9806	+	81.1798i	−0.0713188	+	0.0981618i	−0.843186	−	0.537622i	$-0.819323\pi$
$827$	−58.9806	+	81.1798i	−0.0713188	+	0.0981618i	0.771867	+	0.635783i	$0.219323\pi$
$828$		0			0
$829$	76.9895	+	236.949i	0.0928704	+	0.285826i	0.986693	−	0.162595i	$-0.0519865\pi$
$829$	76.9895	+	236.949i	0.0928704	+	0.285826i	−0.893822	+	0.448421i	$0.851987\pi$
$830$	2075.79	−	1508.15i	2.50096	−	1.81705i
$831$		0			0
$832$	−463.113	+	150.475i	−0.556626	+	0.180859i
$833$	−33.3919	−	10.8497i	−0.0400863	−	0.0130248i
$834$		0			0
$835$		−	373.379i		−	0.447161i
$836$	−48.9263	+	68.5559i	−0.0585243	+	0.0820047i
$837$		0			0
$838$	315.392	−	434.100i	0.376363	−	0.518019i
$839$	37.6013	−	115.725i	0.0448169	−	0.137932i	−0.926144	−	0.377170i	$-0.876897\pi$
$839$	37.6013	−	115.725i	0.0448169	−	0.137932i	0.970961	+	0.239237i	$0.0768974\pi$
$840$		0			0
$841$	−638.694	+	464.038i	−0.759445	+	0.551769i
$842$	−960.346	−	1321.80i	−1.14055	−	1.56984i
$843$		0			0
$844$	162.546	+	52.8144i	0.192590	+	0.0625763i
$845$	313.548	+	227.806i	0.371063	+	0.269593i
$846$		0			0
$847$	485.522	+	644.980i	0.573226	+	0.761488i
$848$	−1033.01			−1.21818
$849$		0			0
$850$	−271.117	+	834.412i	−0.318961	+	0.981662i
$851$	152.247	+	468.567i	0.178903	+	0.550607i
$852$		0			0
$853$	84.7128	+	116.597i	0.0993116	+	0.136691i	0.855781	−	0.517339i	$-0.173077\pi$
$853$	84.7128	+	116.597i	0.0993116	+	0.136691i	−0.756469	+	0.654029i	$0.773077\pi$
$854$	18.2912	−	5.94318i	0.0214183	−	0.00695922i
$855$		0			0
$856$	−433.460	−	314.927i	−0.506378	−	0.367905i
$857$		−	527.163i		−	0.615126i	−0.951528	−	0.307563i	$-0.900487\pi$
$857$		−	527.163i		−	0.615126i	0.951528	−	0.307563i	$-0.0995134\pi$
$858$		0			0
$859$	122.027			0.142057			0.0710284	−	0.997474i	$-0.477372\pi$
$859$	122.027			0.142057			0.0710284	+	0.997474i	$0.477372\pi$
$860$	212.474	−	292.445i	0.247063	−	0.340053i
$861$		0			0
$862$	336.403	+	1035.34i	0.390258	+	1.20109i
$863$	683.821	−	496.825i	0.792377	−	0.575696i	−0.116291	−	0.993215i	$-0.537100\pi$
$863$	683.821	−	496.825i	0.792377	−	0.575696i	0.908668	+	0.417520i	$0.137100\pi$
$864$		0			0
$865$	134.322	−	43.6437i	0.155285	−	0.0504552i
$866$	848.311	+	275.633i	0.979574	+	0.318283i
$867$		0			0
$868$		−	165.949i		−	0.191185i
$869$	447.305	−	149.542i	0.514735	−	0.172085i
$870$		0			0
$871$	189.751	−	261.169i	0.217854	−	0.299850i
$872$	−5.67088	+	17.4532i	−0.00650330	+	0.0200151i
$873$		0			0
$874$	−140.795	+	102.293i	−0.161092	+	0.117040i
$875$	−873.044	−	1201.64i	−0.997764	−	1.37330i
$876$		0			0
$877$	−869.851	−	282.632i	−0.991848	−	0.322271i	−0.232245	−	0.972657i	$-0.574607\pi$
$877$	−869.851	−	282.632i	−0.991848	−	0.322271i	−0.759604	+	0.650386i	$0.774607\pi$
$878$	−122.586	−	89.0636i	−0.139619	−	0.101439i
$879$		0			0
$880$	1446.11	−	1069.51i	1.64331	−	1.21535i
$881$	−618.978			−0.702586			−0.351293	−	0.936266i	$-0.614258\pi$
$881$	−618.978			−0.702586			−0.351293	+	0.936266i	$0.614258\pi$
$882$		0			0
$883$	−18.1024	+	55.7133i	−0.0205010	+	0.0630955i	−0.960784	−	0.277299i	$-0.910561\pi$
$883$	−18.1024	+	55.7133i	−0.0205010	+	0.0630955i	0.940283	+	0.340395i	$0.110561\pi$
$884$	24.4690	+	75.3079i	0.0276799	+	0.0851900i
$885$		0			0
$886$	−408.113	−	561.720i	−0.460625	−	0.633995i
$887$	−1008.67	+	327.736i	−1.13717	+	0.369489i	−0.816296	−	0.577634i	$-0.803976\pi$
$887$	−1008.67	+	327.736i	−1.13717	+	0.369489i	−0.320873	+	0.947122i	$0.603976\pi$
$888$		0			0
$889$	642.899	+	467.094i	0.723171	+	0.525415i
$890$			182.678i			0.205257i
$891$		0			0
$892$	234.235			0.262595
$893$	−79.7812	+	109.809i	−0.0893407	+	0.122967i
$894$		0			0
$895$	350.246	+	1077.95i	0.391337	+	1.20441i
$896$	−829.636	+	602.766i	−0.925934	+	0.672730i
$897$		0			0
$898$	−693.355	+	225.285i	−0.772110	+	0.250874i
$899$	−187.231	−	60.8350i	−0.208266	−	0.0676696i
$900$		0			0
$901$		−	429.947i		−	0.477189i
$902$	1166.00	−	9.88431i	1.29268	−	0.0109582i
$903$		0			0
$904$	741.845	−	1021.06i	0.820625	−	1.12949i
$905$	272.831	−	839.686i	0.301470	−	0.927830i
$906$		0			0
$907$	1009.83	−	733.687i	1.11338	−	0.808916i	0.130186	−	0.991490i	$-0.458443\pi$
$907$	1009.83	−	733.687i	1.11338	−	0.808916i	0.983192	+	0.182573i	$0.0584427\pi$
$908$	−23.6210	−	32.5115i	−0.0260143	−	0.0358056i
$909$		0			0
$910$	−1363.29	−	442.961i	−1.49812	−	0.486770i
$911$	−501.049	−	364.034i	−0.549999	−	0.399598i	0.277786	−	0.960643i	$-0.410399\pi$
$911$	−501.049	−	364.034i	−0.549999	−	0.399598i	−0.827785	+	0.561045i	$0.810399\pi$
$912$		0			0
$913$	−12.4215	−	1465.30i	−0.0136052	−	1.60493i
$914$	−196.150			−0.214606
$915$		0			0
$916$	1.07588	−	3.31122i	0.00117454	−	0.00361487i
$917$	37.1108	+	114.215i	0.0404698	+	0.124553i
$918$		0			0
$919$	1001.70	+	1378.73i	1.08999	+	1.50025i	0.848020	+	0.529964i	$0.177795\pi$
$919$	1001.70	+	1378.73i	1.08999	+	1.50025i	0.241973	+	0.970283i	$0.422205\pi$
$920$	527.274	−	171.322i	0.573124	−	0.186219i
$921$		0			0
$922$	−1088.36	−	790.743i	−1.18044	−	0.857639i
$923$			245.984i			0.266504i
$924$		0			0
$925$	−2679.02			−2.89624
$926$	53.0095	−	72.9613i	0.0572456	−	0.0787919i
$927$		0			0
$928$	−31.6115	−	97.2903i	−0.0340642	−	0.104839i
$929$	−408.628	+	296.886i	−0.439858	+	0.319575i	−0.785578	−	0.618762i	$-0.787635\pi$
$929$	−408.628	+	296.886i	−0.439858	+	0.319575i	0.345721	+	0.938338i	$0.387635\pi$
$930$		0			0
$931$	36.0170	−	11.7026i	0.0386863	−	0.0125699i
$932$	−208.176	−	67.6403i	−0.223364	−	0.0725755i
$933$		0			0
$934$		−	991.952i		−	1.06205i
$935$	445.136	+	601.881i	0.476081	+	0.643723i
$936$		0			0
$937$	−767.618	+	1056.54i	−0.819230	+	1.12757i	0.170604	+	0.985340i	$0.445428\pi$
$937$	−767.618	+	1056.54i	−0.819230	+	1.12757i	−0.989833	+	0.142233i	$0.954572\pi$
$938$	132.174	−	406.789i	0.140910	−	0.433677i
$939$		0			0
$940$	−102.576	+	74.5258i	−0.109123	+	0.0792828i
$941$	18.7120	+	25.7548i	0.0198852	+	0.0273696i	0.818844	−	0.574016i	$-0.194615\pi$
$941$	18.7120	+	25.7548i	0.0198852	+	0.0273696i	−0.798959	+	0.601386i	$0.794615\pi$
$942$		0			0
$943$	423.534	+	137.615i	0.449135	+	0.145933i
$944$	1083.39	+	787.131i	1.14766	+	0.833826i
$945$		0			0
$946$	−354.143	−	1059.30i	−0.374358	−	1.11977i
$947$	749.175			0.791103			0.395552	−	0.918444i	$-0.370553\pi$
$947$	749.175			0.791103			0.395552	+	0.918444i	$0.370553\pi$
$948$		0			0
$949$	431.655	−	1328.50i	0.454852	−	1.39989i
$950$	−292.431	−	900.009i	−0.307822	−	0.947378i
$951$		0			0
$952$	−210.304	−	289.459i	−0.220907	−	0.304053i
$953$	−1381.62	+	448.916i	−1.44976	+	0.471055i	−0.924925	−	0.380149i	$-0.875873\pi$
$953$	−1381.62	+	448.916i	−1.44976	+	0.471055i	−0.524834	+	0.851205i	$0.675873\pi$
$954$		0			0
$955$	1137.99	+	826.799i	1.19161	+	0.865758i
$956$			420.280i			0.439624i
$957$		0			0
$958$	129.571			0.135251
$959$	362.989	−	499.612i	0.378508	−	0.520972i
$960$		0			0
$961$	−64.5558	−	198.682i	−0.0671756	−	0.206745i
$962$	−1058.32	+	768.916i	−1.10013	+	0.799288i
$963$		0			0
$964$	−385.754	+	125.339i	−0.400159	+	0.130020i
$965$	−282.746	−	91.8697i	−0.293001	−	0.0952018i
$966$		0			0
$967$			950.193i			0.982619i	0.870985	+	0.491310i	$0.163482\pi$
$967$			950.193i			0.982619i	−0.870985	+	0.491310i	$0.836518\pi$
$968$	−14.0548	−	828.924i	−0.0145194	−	0.856326i
$969$		0			0
$970$	1766.34	−	2431.16i	1.82097	−	2.50636i
$971$	203.659	−	626.798i	0.209742	−	0.645519i	−0.789744	−	0.613437i	$-0.789786\pi$
$971$	203.659	−	626.798i	0.209742	−	0.645519i	0.999485	−	0.0320814i	$-0.0102136\pi$
$972$		0			0
$973$	1170.31	−	850.277i	1.20278	−	0.873872i
$974$	−850.602	−	1170.75i	−0.873308	−	1.20200i
$975$		0			0
$976$	−23.2738	−	7.56211i	−0.0238461	−	0.00774806i
$977$	167.165	+	121.452i	0.171100	+	0.124312i	0.670040	−	0.742325i	$-0.266277\pi$
$977$	167.165	+	121.452i	0.171100	+	0.124312i	−0.498940	+	0.866637i	$0.666277\pi$
$978$		0			0
$979$	84.9203	+	60.6051i	0.0867419	+	0.0619051i
$980$	35.3758			0.0360978
$981$		0			0
$982$	201.775	−	620.999i	0.205473	−	0.632382i
$983$	−70.5920	−	217.260i	−0.0718129	−	0.221017i	0.908708	−	0.417432i	$-0.137070\pi$
$983$	−70.5920	−	217.260i	−0.0718129	−	0.221017i	−0.980521	+	0.196415i	$0.937070\pi$
$984$		0			0
$985$	−316.252	−	435.284i	−0.321068	−	0.441913i
$986$	118.369	−	38.4603i	0.120049	−	0.0390063i
$987$		0			0
$988$	−69.0968	−	50.2018i	−0.0699361	−	0.0508115i
$989$		−	426.575i		−	0.431319i
$990$		0			0
$991$	−1872.78			−1.88979			−0.944895	−	0.327373i	$-0.893837\pi$
$991$	−1872.78			−1.88979			−0.944895	+	0.327373i	$0.893837\pi$
$992$	−229.711	+	316.171i	−0.231564	+	0.318720i
$993$		0			0
$994$	100.713	+	309.964i	0.101321	+	0.311835i
$995$	1676.31	−	1217.91i	1.68473	−	1.22403i
$996$		0			0
$997$	−1461.15	+	474.757i	−1.46555	+	0.476185i	−0.929760	−	0.368167i	$-0.879985\pi$
$997$	−1461.15	+	474.757i	−1.46555	+	0.476185i	−0.535788	+	0.844352i	$0.679985\pi$
$998$	−87.0537	−	28.2855i	−0.0872281	−	0.0283421i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.c.73.2		16
3.2	odd	2		33.3.g.a.7.3	✓	16
11.5	even	5		1089.3.c.m.604.5		16
11.6	odd	10		1089.3.c.m.604.12		16
11.8	odd	10	inner	99.3.k.c.19.2		16
12.11	even	2		528.3.bf.b.337.1		16
33.2	even	10		363.3.g.g.94.3		16
33.5	odd	10		363.3.c.e.241.12		16
33.8	even	10		33.3.g.a.19.3	yes	16
33.14	odd	10		363.3.g.f.118.2		16
33.17	even	10		363.3.c.e.241.5		16
33.20	odd	10		363.3.g.a.94.2		16
33.26	odd	10		363.3.g.g.112.3		16
33.29	even	10		363.3.g.a.112.2		16
33.32	even	2		363.3.g.f.40.2		16
132.107	odd	10		528.3.bf.b.481.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.g.a.7.3	✓	16	3.2	odd	2
33.3.g.a.19.3	yes	16	33.8	even	10
99.3.k.c.19.2		16	11.8	odd	10	inner
99.3.k.c.73.2		16	1.1	even	1	trivial
363.3.c.e.241.5		16	33.17	even	10
363.3.c.e.241.12		16	33.5	odd	10
363.3.g.a.94.2		16	33.20	odd	10
363.3.g.a.112.2		16	33.29	even	10
363.3.g.f.40.2		16	33.32	even	2
363.3.g.f.118.2		16	33.14	odd	10
363.3.g.g.94.3		16	33.2	even	10
363.3.g.g.112.3		16	33.26	odd	10
528.3.bf.b.337.1		16	12.11	even	2
528.3.bf.b.481.1		16	132.107	odd	10
1089.3.c.m.604.5		16	11.5	even	5
1089.3.c.m.604.12		16	11.6	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30204 + 1.79211i) q^{2} +(-0.280267 - 0.862573i) q^{4} +(7.03442 - 5.11081i) q^{5} +(6.34535 - 2.06173i) q^{7} +(-6.51625 - 2.11726i) q^{8} +O(q^{10})\)	\(q+(-1.30204 + 1.79211i) q^{2} +(-0.280267 - 0.862573i) q^{4} +(7.03442 - 5.11081i) q^{5} +(6.34535 - 2.06173i) q^{7} +(-6.51625 - 2.11726i) q^{8} +19.2609i q^{10} +(8.95368 + 6.38997i) q^{11} +(-6.55655 + 9.02432i) q^{13} +(-4.56707 + 14.0560i) q^{14} +(15.2138 - 11.0535i) q^{16} +(4.60052 + 6.33207i) q^{17} +(-8.02898 - 2.60877i) q^{19} +(-6.37996 - 4.63531i) q^{20} +(-23.1096 + 7.72594i) q^{22} -9.30611 q^{23} +(15.6373 - 48.1267i) q^{25} +(-7.63564 - 23.5001i) q^{26} +(-3.55678 - 4.89549i) q^{28} +(-6.82718 + 2.21829i) q^{29} +(22.1867 + 16.1196i) q^{31} +14.2504i q^{32} -17.3378 q^{34} +(34.0987 - 46.9329i) q^{35} +(-16.3598 - 50.3504i) q^{37} +(15.1293 - 10.9921i) q^{38} +(-56.6589 + 18.4096i) q^{40} +(-45.5114 - 14.7876i) q^{41} +45.8381i q^{43} +(3.00240 - 9.51410i) q^{44} +(12.1169 - 16.6775i) q^{46} +(4.96833 - 15.2909i) q^{47} +(-3.62914 + 2.63673i) q^{49} +(65.8878 + 90.6867i) q^{50} +(9.62172 + 3.12629i) q^{52} +(-44.4411 - 32.2883i) q^{53} +(95.6418 - 0.810768i) q^{55} -45.7131 q^{56} +(4.91387 - 15.1233i) q^{58} +(22.0055 + 67.7260i) q^{59} +(-0.764891 - 1.05278i) q^{61} +(-57.7761 + 18.7726i) q^{62} +(35.3168 + 25.6592i) q^{64} +96.9901i q^{65} -28.9406 q^{67} +(4.17250 - 5.74296i) q^{68} +(39.7108 + 122.217i) q^{70} +(17.8405 - 12.9619i) q^{71} +(-119.098 + 38.6972i) q^{73} +(111.535 + 36.2398i) q^{74} +7.65674i q^{76} +(69.9885 + 22.0865i) q^{77} +(25.2021 - 34.6877i) q^{79} +(50.5281 - 155.509i) q^{80} +(85.7587 - 62.3073i) q^{82} +(-78.3011 - 107.772i) q^{83} +(64.7240 + 21.0301i) q^{85} +(-82.1469 - 59.6832i) q^{86} +(-44.8152 - 60.5959i) q^{88} +9.48441 q^{89} +(-22.9979 + 70.7802i) q^{91} +(2.60819 + 8.02720i) q^{92} +(20.9340 + 28.8132i) q^{94} +(-69.8122 + 22.6834i) q^{95} +(-126.223 - 91.7061i) q^{97} -9.93695i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) \) 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8	\( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) \) 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8 + 10 * q^11 + 30 * q^13 + 2 * q^14 + 16 * q^16 + 10 * q^17 - 42 * q^20 + 42 * q^22 - 132 * q^23 - 2 * q^25 - 46 * q^26 - 50 * q^28 - 160 * q^29 + 10 * q^31 - 368 * q^34 + 320 * q^35 - 126 * q^37 + 130 * q^38 + 30 * q^40 + 120 * q^41 + 206 * q^44 + 50 * q^46 + 150 * q^47 + 210 * q^49 - 330 * q^50 + 110 * q^52 - 342 * q^53 + 244 * q^55 - 524 * q^56 + 150 * q^58 - 110 * q^59 - 90 * q^61 - 40 * q^62 - 168 * q^64 + 36 * q^67 - 80 * q^68 + 340 * q^70 + 236 * q^71 - 350 * q^73 + 730 * q^74 + 390 * q^77 + 210 * q^79 + 806 * q^80 + 114 * q^82 + 190 * q^83 + 110 * q^85 - 736 * q^86 + 144 * q^88 - 76 * q^89 + 306 * q^91 + 150 * q^92 - 350 * q^94 - 430 * q^95 - 354 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more