LMFDB - Embedded newform 99.3.k.c.19.2

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			19.2
Root			$-0.797732 - 1.94863i$ of defining polynomial
Character	$\chi$	$=$	99.19
Dual form			99.3.k.c.73.2

$q$-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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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	0.348122	−	0.937449i	$-0.386820\pi$
$2$	−1.30204	−	1.79211i	−0.651021	−	0.896054i	−0.999143	+	0.0413956i	$0.986820\pi$
$3$		0			0
$3$		0			0
$4$	−0.280267	+	0.862573i	−0.0700667	+	0.215643i
$5$	7.03442	+	5.11081i	1.40688	+	1.02216i	0.993766	+	0.111484i	$0.0355602\pi$
$5$	7.03442	+	5.11081i	1.40688	+	1.02216i	0.413118	+	0.910678i	$0.364440\pi$
$6$		0			0
$7$	6.34535	+	2.06173i	0.906478	+	0.294533i	0.724908	−	0.688846i	$-0.241882\pi$
$7$	6.34535	+	2.06173i	0.906478	+	0.294533i	0.181570	+	0.983378i	$0.441882\pi$
$8$	−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	0.478604	−	0.878031i	$-0.341143\pi$
$13$	−6.55655	−	9.02432i	−0.504350	−	0.694178i	−0.982954	+	0.183853i	$0.941143\pi$
$14$	−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	−0.651980	−	0.758236i	$-0.726061\pi$
$17$	4.60052	−	6.33207i	0.270619	−	0.372475i	0.922599	+	0.385762i	$0.126061\pi$
$18$		0			0
$19$	−8.02898	+	2.60877i	−0.422578	+	0.137304i	−0.512584	−	0.858637i	$-0.671312\pi$
$19$	−8.02898	+	2.60877i	−0.422578	+	0.137304i	0.0900055	+	0.995941i	$0.471312\pi$
$20$	−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	0.188931	−	0.981990i	$-0.439498\pi$
$29$	−6.82718	−	2.21829i	−0.235420	−	0.0764926i	−0.424351	+	0.905498i	$0.639498\pi$
$30$		0			0
$31$	22.1867	−	16.1196i	0.715701	−	0.519987i	−0.169307	−	0.985563i	$-0.554153\pi$
$31$	22.1867	−	16.1196i	0.715701	−	0.519987i	0.885008	+	0.465576i	$0.154153\pi$
$32$		−	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	0.443412	+	0.896318i	$0.353768\pi$
$37$	−16.3598	+	50.3504i	−0.442158	+	1.36082i	−0.885571	+	0.464505i	$0.846232\pi$
$38$	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	−0.805956	−	0.591975i	$-0.798348\pi$
$41$	−45.5114	+	14.7876i	−1.11003	+	0.360672i	−0.304078	+	0.952647i	$0.598348\pi$
$42$		0			0
$43$		−	45.8381i		−	1.06600i	−0.846114	−	0.533002i	$-0.821064\pi$
$43$		−	45.8381i		−	1.06600i	0.846114	−	0.533002i	$-0.178936\pi$
$44$	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	0.989896	−	0.141794i	$-0.0452870\pi$
$47$	4.96833	+	15.2909i	0.105709	+	0.325339i	−0.884187	+	0.467133i	$0.845287\pi$
$48$		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	−0.921954	−	0.387299i	$-0.873408\pi$
$53$	−44.4411	+	32.2883i	−0.838511	+	0.609214i	0.0834437	+	0.996512i	$0.473408\pi$
$54$		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	−0.571860	−	0.820351i	$-0.693778\pi$
$59$	22.0055	−	67.7260i	0.372975	−	1.14790i	0.944835	−	0.327547i	$-0.106222\pi$
$60$		0			0
$61$	−0.764891	+	1.05278i	−0.0125392	+	0.0172587i	−0.815241	−	0.579122i	$-0.803395\pi$
$61$	−0.764891	+	1.05278i	−0.0125392	+	0.0172587i	0.802701	+	0.596381i	$0.203395\pi$
$62$	−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	0.706292	−	0.707921i	$-0.250367\pi$
$71$	17.8405	+	12.9619i	0.251275	+	0.182562i	−0.455017	+	0.890483i	$0.650367\pi$
$72$		0			0
$73$	−119.098	−	38.6972i	−1.63148	−	0.530099i	−0.656867	−	0.754006i	$-0.728119\pi$
$73$	−119.098	−	38.6972i	−1.63148	−	0.530099i	−0.974610	+	0.223907i	$0.928119\pi$
$74$	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	0.938166	−	0.346186i	$-0.112523\pi$
$79$	25.2021	+	34.6877i	0.319014	+	0.439085i	−0.619152	+	0.785271i	$0.712523\pi$
$80$	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	0.0110157	+	0.999939i	$0.496494\pi$
$83$	−78.3011	+	107.772i	−0.943387	+	1.29846i	−0.954403	+	0.298522i	$0.903506\pi$
$84$		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	−0.999967	−	0.00810612i	$-0.997420\pi$
$97$	−126.223	+	91.7061i	−1.30126	+	0.945424i	−0.301297	+	0.953530i	$0.597420\pi$
$98$			9.93695i			0.101397i
$99$		0			0
$100$	−45.8954			−0.458954
$101$	32.3730	+	44.5576i	0.320525	+	0.441164i	0.938627	−	0.344933i	$-0.112098\pi$
$101$	32.3730	+	44.5576i	0.320525	+	0.441164i	−0.618103	+	0.786097i	$0.712098\pi$
$102$		0			0
$103$	−25.0358	+	77.0524i	−0.243066	+	0.748081i	0.752882	+	0.658155i	$0.228663\pi$
$103$	−25.0358	+	77.0524i	−0.243066	+	0.748081i	−0.995948	+	0.0899260i	$0.971337\pi$
$104$	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	0.0598830	−	0.998205i	$-0.480927\pi$
$107$	74.3714	−	24.1647i	0.695060	−	0.225839i	0.635177	+	0.772367i	$0.280927\pi$
$108$		0			0
$109$			2.67841i			0.0245725i	0.999925	+	0.0122863i	$0.00391094\pi$
$109$			2.67841i			0.0245725i	−0.999925	+	0.0122863i	$0.996089\pi$
$110$	−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	−0.802878	−	0.596143i	$-0.796699\pi$
$113$	−56.9227	−	175.190i	−0.503740	−	1.55035i	0.299138	−	0.954210i	$-0.403301\pi$
$114$		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	−0.438928	−	0.898522i	$-0.644642\pi$
$127$	70.0092	−	96.3594i	0.551254	−	0.758735i	0.990182	+	0.139787i	$0.0446417\pi$
$128$	−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	$-0.978114\pi$
$131$		−	17.9999i		−	0.137403i	0.997637	−	0.0687017i	$-0.0218857\pi$
$132$		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	0.826527	−	0.562896i	$-0.190313\pi$
$137$	74.8831	+	54.4058i	0.546592	+	0.397122i	−0.279935	+	0.960019i	$0.590313\pi$
$138$		0			0
$139$	206.205	+	67.0001i	1.48349	+	0.482015i	0.935153	−	0.354243i	$-0.115261\pi$
$139$	206.205	+	67.0001i	1.48349	+	0.482015i	0.548336	+	0.836258i	$0.315261\pi$
$140$	−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	−0.435570	−	0.900155i	$-0.643453\pi$
$149$	82.7139	−	113.846i	0.555127	−	0.764067i	0.990697	+	0.136088i	$0.0434531\pi$
$150$		0			0
$151$	−10.9455	+	3.55641i	−0.0724869	+	0.0235524i	−0.345036	−	0.938589i	$-0.612133\pi$
$151$	−10.9455	+	3.55641i	−0.0724869	+	0.0235524i	0.272549	+	0.962142i	$0.412133\pi$
$152$	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	−0.983320	−	0.181885i	$-0.941780\pi$
$157$	−46.2689	−	142.401i	−0.294706	−	0.907013i	0.688613	−	0.725129i	$-0.258220\pi$
$158$	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	−0.443379	−	0.896334i	$-0.646220\pi$
$163$	44.3481	−	32.2208i	0.272074	−	0.197673i	0.715453	+	0.698661i	$0.246220\pi$
$164$		−	43.4014i		−	0.264643i
$165$		0			0
$166$	295.091			1.77766
$167$	25.2405	+	34.7406i	0.151141	+	0.208027i	0.877873	−	0.478893i	$-0.158962\pi$
$167$	25.2405	+	34.7406i	0.151141	+	0.208027i	−0.726732	+	0.686921i	$0.758962\pi$
$168$		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	−0.264029	−	0.964515i	$-0.585051\pi$
$173$	15.4481	−	5.01939i	0.0892953	−	0.0290138i	0.353324	+	0.935501i	$0.385051\pi$
$174$		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	−0.998288	−	0.0584889i	$-0.981372\pi$
$179$	−40.2813	−	123.973i	−0.225035	−	0.692586i	0.773253	−	0.634097i	$-0.218628\pi$
$180$		0			0
$181$	82.1481	+	59.6841i	0.453857	+	0.329746i	0.791117	−	0.611665i	$-0.209500\pi$
$181$	82.1481	+	59.6841i	0.453857	+	0.329746i	−0.337260	+	0.941412i	$0.609500\pi$
$182$	−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	−0.730694	−	0.682705i	$-0.760804\pi$
$191$	49.9911	−	153.857i	0.261734	−	0.805533i	0.992428	−	0.122828i	$-0.0391964\pi$
$192$		0			0
$193$	−20.0973	+	27.6616i	−0.104131	+	0.143324i	−0.857902	−	0.513813i	$-0.828233\pi$
$193$	−20.0973	+	27.6616i	−0.104131	+	0.143324i	0.753771	+	0.657137i	$0.228233\pi$
$194$	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	$0.0501996\pi$
$197$			61.8792i			0.314107i	−0.987590	+	0.157054i	$0.949800\pi$
$198$		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	0.461402	−	0.887191i	$-0.347347\pi$
$211$	−110.764	−	152.454i	−0.524948	−	0.722529i	−0.986350	+	0.164662i	$0.947347\pi$
$212$	−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	−0.954319	−	0.298788i	$-0.903418\pi$
$223$	−79.8077	−	245.623i	−0.357882	−	1.10145i	0.596437	−	0.802660i	$-0.296582\pi$
$224$	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	0.400362	−	0.916357i	$-0.368885\pi$
$227$	42.1402	+	13.6922i	0.185640	+	0.0603180i	−0.214722	+	0.976675i	$0.568885\pi$
$228$		0			0
$229$	3.10563	−	2.25637i	0.0135617	−	0.00985316i	−0.580984	−	0.813915i	$-0.697332\pi$
$229$	3.10563	−	2.25637i	0.0135617	−	0.00985316i	0.594545	+	0.804062i	$0.297332\pi$
$230$			179.244i			0.779323i
$231$		0			0
$232$	49.1843			0.212001
$233$	141.858	+	195.250i	0.608831	+	0.837984i	0.996481	−	0.0838231i	$-0.0267131\pi$
$233$	141.858	+	195.250i	0.608831	+	0.837984i	−0.387650	+	0.921807i	$0.626713\pi$
$234$		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	−0.846185	+	0.532890i	$0.821106\pi$
$239$	−440.713	+	143.196i	−1.84399	+	0.599148i	−0.997803	+	0.0662581i	$0.978894\pi$
$240$		0			0
$241$			447.213i			1.85565i	0.373011	+	0.927827i	$0.378325\pi$
$241$			447.213i			1.85565i	−0.373011	+	0.927827i	$0.621675\pi$
$242$	−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	0.230193	−	0.973145i	$-0.426064\pi$
$251$	307.937	−	223.730i	1.22684	−	0.891353i	0.996649	+	0.0817922i	$0.0260644\pi$
$252$		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	−0.953039	−	0.302847i	$-0.902063\pi$
$257$	−1.02939	+	3.16814i	−0.00400541	+	0.0123274i	0.949034	+	0.315174i	$0.102063\pi$
$258$		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	$0.256796\pi$
$263$			379.793i			1.44408i	−0.691850	+	0.722041i	$0.743204\pi$
$264$		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	0.269522	−	0.962994i	$-0.413134\pi$
$269$	−151.461	−	110.043i	−0.563053	−	0.409082i	−0.832575	+	0.553912i	$0.813134\pi$
$270$		0			0
$271$	290.222	+	94.2989i	1.07093	+	0.347967i	0.790850	−	0.612010i	$-0.209639\pi$
$271$	290.222	+	94.2989i	1.07093	+	0.347967i	0.280081	+	0.959976i	$0.409639\pi$
$272$	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	0.912965	+	0.408039i	$0.133787\pi$
$277$	282.238	+	388.468i	1.01891	+	1.40241i	0.105946	+	0.994372i	$0.466213\pi$
$278$	−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	−0.799438	−	0.600749i	$-0.794869\pi$
$281$	5.32429	−	7.32826i	0.0189477	−	0.0260792i	0.818386	+	0.574669i	$0.194869\pi$
$282$		0			0
$283$	−253.650	+	82.4160i	−0.896291	+	0.291223i	−0.720705	−	0.693242i	$-0.756182\pi$
$283$	−253.650	+	82.4160i	−0.896291	+	0.291223i	−0.175586	+	0.984464i	$0.556182\pi$
$284$	−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	0.571974	−	0.820271i	$-0.306178\pi$
$293$	161.902	+	52.6053i	0.552568	+	0.179540i	−0.0194065	+	0.999812i	$0.506178\pi$
$294$		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	$-0.878415\pi$
$307$		−	228.869i		−	0.745501i	0.927932	−	0.372750i	$-0.121585\pi$
$308$	−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	−0.987638	−	0.156752i	$-0.949898\pi$
$311$	−87.3160	−	268.731i	−0.280759	−	0.864087i	0.706879	−	0.707334i	$-0.250102\pi$
$312$		0			0
$313$	283.298	+	205.828i	0.905105	+	0.657597i	0.939772	−	0.341801i	$-0.111037\pi$
$313$	283.298	+	205.828i	0.905105	+	0.657597i	−0.0346670	+	0.999399i	$0.511037\pi$
$314$	−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	0.00343309	−	0.999994i	$-0.498907\pi$
$317$	302.908	−	220.075i	0.955545	−	0.694244i	0.952112	+	0.305750i	$0.0989072\pi$
$318$		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	0.353269	−	0.935522i	$-0.385070\pi$
$337$	30.0552	+	9.76554i	0.0891847	+	0.0289779i	−0.264085	+	0.964499i	$0.585070\pi$
$338$	−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	0.299483	+	0.954102i	$0.403186\pi$
$347$	−243.062	+	334.546i	−0.700467	+	0.964110i	−0.999950	+	0.0100080i	$0.996814\pi$
$348$		0			0
$349$	−349.241	+	113.475i	−1.00069	+	0.325144i	−0.763141	−	0.646232i	$-0.776344\pi$
$349$	−349.241	+	113.475i	−1.00069	+	0.325144i	−0.237548	+	0.971376i	$0.576344\pi$
$350$	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	0.506738	−	0.862100i	$-0.330851\pi$
$359$	147.178	+	47.8211i	0.409967	+	0.133206i	−0.0967705	+	0.995307i	$0.530851\pi$
$360$		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	−0.986386	−	0.164444i	$-0.947417\pi$
$367$	−33.6631	+	103.604i	−0.0917251	+	0.282301i	0.894661	+	0.446745i	$0.147417\pi$
$368$	−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	$-0.582258\pi$
$373$		−	721.229i		−	1.93359i	0.255555	−	0.966795i	$-0.417742\pi$
$374$	−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	0.601508	−	0.798867i	$-0.294567\pi$
$379$	10.4666	+	7.60444i	0.0276164	+	0.0200645i	−0.573891	+	0.818931i	$0.694567\pi$
$380$	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	−0.688001	−	0.725710i	$-0.741511\pi$
$383$	−80.5883	+	58.5508i	−0.210413	+	0.152874i	0.477587	+	0.878584i	$0.341511\pi$
$384$		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	−0.998682	−	0.0513242i	$-0.983656\pi$
$389$	−62.4593	+	192.230i	−0.160564	+	0.494164i	0.838118	+	0.545488i	$0.183656\pi$
$390$		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	0.999851	+	0.0172792i	$0.00550040\pi$
$401$	531.427	+	386.105i	1.32526	+	0.962854i	0.325404	+	0.945575i	$0.394500\pi$
$402$		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	0.999844	−	0.0176458i	$-0.00561712\pi$
$409$	275.704	+	379.474i	0.674093	+	0.927810i	−0.325751	+	0.945456i	$0.605617\pi$
$410$	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	−0.729442	−	0.684042i	$-0.760220\pi$
$421$	−227.921	−	701.470i	−0.541381	−	1.66620i	0.188061	−	0.982157i	$-0.439780\pi$
$422$	−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	0.999765	−	0.0216696i	$-0.00689819\pi$
$431$	288.861	+	397.583i	0.670212	+	0.922467i	−0.329553	+	0.944137i	$0.606898\pi$
$432$		0			0
$433$	−124.430	+	382.956i	−0.287367	+	0.884425i	0.698312	+	0.715793i	$0.253935\pi$
$433$	−124.430	+	382.956i	−0.287367	+	0.884425i	−0.985679	+	0.168631i	$0.946065\pi$
$434$	−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	$-0.975176\pi$
$439$		−	68.4030i		−	0.155815i	0.996961	−	0.0779077i	$-0.0248240\pi$
$440$	−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	−0.998875	−	0.0474225i	$-0.984899\pi$
$443$	−96.8586	−	298.100i	−0.218642	−	0.672912i	0.780233	−	0.625490i	$-0.215101\pi$
$444$		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	−0.250388	−	0.968146i	$-0.580558\pi$
$449$	266.257	−	193.447i	0.592999	−	0.430839i	0.843387	+	0.537306i	$0.180558\pi$
$450$		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	−0.748267	−	0.663398i	$-0.769114\pi$
$457$	52.0476	−	71.6374i	0.113890	−	0.156756i	0.862156	+	0.506642i	$0.169114\pi$
$458$	−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	$-0.771112\pi$
$461$		−	607.310i		−	1.31737i	0.752417	−	0.658687i	$-0.228888\pi$
$462$		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	0.127946	−	0.991781i	$-0.459161\pi$
$467$	−362.278	−	263.210i	−0.775756	−	0.563620i	−0.903702	+	0.428162i	$0.859161\pi$
$468$		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	−0.843396	−	0.537293i	$-0.819447\pi$
$479$	−34.3810	+	47.3214i	−0.0717766	+	0.0987920i	0.771619	+	0.636085i	$0.219447\pi$
$480$		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	−0.912672	−	0.408693i	$-0.865985\pi$
$487$	−201.875	−	621.309i	−0.414529	−	1.27579i	0.498143	−	0.867095i	$-0.334015\pi$
$488$	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	0.00928858	−	0.999957i	$-0.497043\pi$
$491$	−280.340	−	91.0879i	−0.570957	−	0.185515i	−0.580245	+	0.814442i	$0.697043\pi$
$492$		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	−0.937446	−	0.348130i	$-0.886817\pi$
$499$	12.7690	−	39.2989i	0.0255892	−	0.0787554i	0.963036	+	0.269374i	$0.0868169\pi$
$500$	−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	0.333689	−	0.942683i	$-0.391706\pi$
$503$	582.346	−	189.216i	1.15774	−	0.376174i	0.824056	+	0.566509i	$0.191706\pi$
$504$		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	0.999887	−	0.0150389i	$-0.00478721\pi$
$509$	92.7000	+	285.301i	0.182122	+	0.560513i	−0.817765	+	0.575552i	$0.804787\pi$
$510$		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	0.564937	+	0.825134i	$0.308900\pi$
$521$	−196.473	+	604.683i	−0.377108	+	1.16062i	−0.942045	+	0.335485i	$0.891100\pi$
$522$		0			0
$523$	4.83865	−	6.65983i	0.00925172	−	0.0127339i	−0.804366	−	0.594134i	$-0.797495\pi$
$523$	4.83865	−	6.65983i	0.00925172	−	0.0127339i	0.813618	+	0.581400i	$0.197495\pi$
$524$	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	0.682405	−	0.730974i	$-0.260934\pi$
$541$	−121.004	−	166.548i	−0.223667	−	0.307852i	−0.906073	+	0.423122i	$0.860934\pi$
$542$	−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	0.648465	−	0.761245i	$-0.275411\pi$
$547$	886.431	−	288.019i	1.62053	−	0.526543i	0.972067	+	0.234702i	$0.0754114\pi$
$548$	−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	0.866184	−	0.499726i	$-0.166566\pi$
$557$	709.178	+	230.426i	1.27321	+	0.413691i	0.407026	+	0.913417i	$0.366566\pi$
$558$		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	−0.992785	−	0.119911i	$-0.961739\pi$
$563$	−450.422	−	619.953i	−0.800040	−	1.10116i	0.192745	−	0.981249i	$-0.438261\pi$
$564$		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	−0.934509	−	0.355939i	$-0.884161\pi$
$569$	−842.875	+	273.867i	−1.48133	+	0.481312i	−0.546818	+	0.837251i	$0.684161\pi$
$570$		0			0
$571$		−	504.852i		−	0.884154i	−0.896977	−	0.442077i	$-0.854242\pi$
$571$		−	504.852i		−	0.884154i	0.896977	−	0.442077i	$-0.145758\pi$
$572$	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	−0.217486	−	0.976063i	$-0.569786\pi$
$577$	−699.892	−	508.501i	−1.21298	−	0.881285i	−0.995498	+	0.0947786i	$0.969786\pi$
$578$	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	−0.549393	−	0.835564i	$-0.685141\pi$
$587$	226.704	−	697.722i	0.386207	−	1.18862i	0.935601	−	0.353060i	$-0.114859\pi$
$588$		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	$0.398484\pi$
$593$			1126.19i			1.89915i	−0.313544	+	0.949574i	$0.601516\pi$
$594$		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	0.562709	−	0.826655i	$-0.309759\pi$
$599$	−29.7104	−	21.5858i	−0.0496000	−	0.0360365i	−0.612309	+	0.790619i	$0.709759\pi$
$600$		0			0
$601$	610.772	+	198.452i	1.01626	+	0.330203i	0.769344	−	0.638834i	$-0.220583\pi$
$601$	610.772	+	198.452i	1.01626	+	0.330203i	0.246915	+	0.969037i	$0.420583\pi$
$602$	−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	0.998619	−	0.0525314i	$-0.0167289\pi$
$607$	388.522	+	534.754i	0.640069	+	0.880979i	−0.358551	+	0.933510i	$0.616729\pi$
$608$	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	0.317753	−	0.948173i	$-0.397072\pi$
$613$	694.004	−	225.496i	1.13214	−	0.367856i	0.814390	+	0.580318i	$0.197072\pi$
$614$	−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	0.781778	+	0.623557i	$0.214313\pi$
$619$	319.295	+	982.689i	0.515824	+	1.58754i	−0.265954	+	0.963986i	$0.585687\pi$
$620$	−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	0.490405	+	0.871495i	$0.336849\pi$
$631$	−264.132	+	812.915i	−0.418593	+	1.28830i	−0.908998	+	0.416801i	$0.863151\pi$
$632$	−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	−0.998897	−	0.0469602i	$-0.985047\pi$
$641$	−139.978	−	430.809i	−0.218375	−	0.672089i	0.780522	−	0.625128i	$-0.214953\pi$
$642$		0			0
$643$	214.596	+	155.913i	0.333742	+	0.242477i	0.742017	−	0.670382i	$-0.233870\pi$
$643$	214.596	+	155.913i	0.333742	+	0.242477i	−0.408275	+	0.912859i	$0.633870\pi$
$644$	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	−0.781115	−	0.624388i	$-0.785349\pi$
$647$	−277.346	+	201.504i	−0.428665	+	0.311443i	0.352450	+	0.935831i	$0.385349\pi$
$648$		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	0.736380	+	0.676569i	$0.236534\pi$
$653$	−167.848	+	516.582i	−0.257041	+	0.791091i	−0.993421	+	0.114522i	$0.963466\pi$
$654$		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	$-0.924454\pi$
$659$		−	309.878i		−	0.470224i	0.971968	−	0.235112i	$-0.0755457\pi$
$660$		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	0.998067	−	0.0621539i	$-0.0197970\pi$
$673$	424.350	+	584.068i	0.630535	+	0.867857i	−0.367531	+	0.930011i	$0.619797\pi$
$674$	−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	−0.264360	−	0.964424i	$-0.585161\pi$
$677$	497.292	−	684.464i	0.734553	−	1.01103i	0.998914	−	0.0466016i	$-0.0148391\pi$
$678$		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	−0.918487	−	0.395450i	$-0.870589\pi$
$691$	−570.918	+	414.796i	−0.826220	+	0.600284i	0.0922674	+	0.995734i	$0.470589\pi$
$692$			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	−0.270110	−	0.962830i	$-0.587060\pi$
$701$	54.1902	−	17.6075i	0.0773041	−	0.0251176i	0.347414	+	0.937712i	$0.387060\pi$
$702$		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	0.278125	−	0.960545i	$-0.410287\pi$
$709$	−389.569	−	283.038i	−0.549462	−	0.399207i	−0.827587	+	0.561337i	$0.810287\pi$
$710$	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	0.478985	+	0.877823i	$0.341005\pi$
$719$	−305.211	+	939.343i	−0.424494	+	1.30646i	−0.903478	+	0.428634i	$0.858995\pi$
$720$		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	0.398714	−	0.917075i	$-0.369457\pi$
$733$	133.580	+	43.4026i	0.182237	+	0.0592123i	−0.216477	+	0.976288i	$0.569457\pi$
$734$	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	0.986626	−	0.163001i	$-0.0521174\pi$
$739$	389.245	+	535.750i	0.526718	+	0.724966i	−0.459907	+	0.887967i	$0.652117\pi$
$740$	−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	−0.878168	−	0.478353i	$-0.841234\pi$
$743$	−112.831	+	155.299i	−0.151859	+	0.209016i	0.726309	+	0.687368i	$0.241234\pi$
$744$		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	−0.818963	−	0.573846i	$-0.805451\pi$
$751$	−370.773	−	1141.12i	−0.493706	−	1.51947i	0.325257	−	0.945626i	$-0.394549\pi$
$752$	−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	−0.238491	−	0.971145i	$-0.576653\pi$
$757$	462.848	−	336.279i	0.611425	−	0.444226i	0.849916	+	0.526919i	$0.176653\pi$
$758$		−	28.6586i		−	0.0378082i
$759$		0			0
$760$	502.940			0.661764
$761$	42.2940	+	58.2127i	0.0555769	+	0.0764950i	0.835901	−	0.548881i	$-0.184946\pi$
$761$	42.2940	+	58.2127i	0.0555769	+	0.0764950i	−0.780324	+	0.625376i	$0.784946\pi$
$762$		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	$-0.981859\pi$
$769$		−	87.6070i		−	0.113923i	0.998376	−	0.0569616i	$-0.0181413\pi$
$770$	−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	0.978945	+	0.204126i	$0.0654351\pi$
$773$	237.268	+	730.235i	0.306944	+	0.944676i	−0.672001	+	0.740550i	$0.734565\pi$
$774$		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	−0.675731	−	0.737148i	$-0.736172\pi$
$787$	184.277	−	253.635i	0.234151	−	0.322281i	0.909882	+	0.414867i	$0.136172\pi$
$788$	−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	0.192322	−	0.981332i	$-0.438398\pi$
$797$	−543.195	−	394.654i	−0.681550	−	0.495175i	−0.873871	+	0.486157i	$0.838398\pi$
$798$		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	−0.226217	−	0.974077i	$-0.572636\pi$
$809$	623.003	−	857.490i	0.770090	−	1.05994i	0.996307	−	0.0858610i	$-0.0273641\pi$
$810$		0			0
$811$	−826.402	+	268.514i	−1.01899	+	0.331090i	−0.770429	−	0.637525i	$-0.779958\pi$
$811$	−826.402	+	268.514i	−1.01899	+	0.331090i	−0.248562	+	0.968616i	$0.579958\pi$
$812$	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	−0.159271	−	0.987235i	$-0.550914\pi$
$821$	−712.961	−	231.655i	−0.868406	−	0.282162i	−0.709135	+	0.705073i	$0.750914\pi$
$822$		0			0
$823$	−958.515	+	696.402i	−1.16466	+	0.846175i	−0.990360	−	0.138517i	$-0.955766\pi$
$823$	−958.515	+	696.402i	−1.16466	+	0.846175i	−0.174300	+	0.984693i	$0.555766\pi$
$824$		−	555.100i		−	0.673665i
$825$		0			0
$826$	−1052.46			−1.27416
$827$	−58.9806	−	81.1798i	−0.0713188	−	0.0981618i	0.771867	−	0.635783i	$-0.219323\pi$
$827$	−58.9806	−	81.1798i	−0.0713188	−	0.0981618i	−0.843186	+	0.537622i	$0.819323\pi$
$828$		0			0
$829$	76.9895	−	236.949i	0.0928704	−	0.285826i	−0.893822	−	0.448421i	$-0.851987\pi$
$829$	76.9895	−	236.949i	0.0928704	−	0.285826i	0.986693	+	0.162595i	$0.0519865\pi$
$830$	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	0.970961	−	0.239237i	$-0.0768974\pi$
$839$	37.6013	+	115.725i	0.0448169	+	0.137932i	−0.926144	+	0.377170i	$0.876897\pi$
$840$		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	−0.756469	−	0.654029i	$-0.773077\pi$
$853$	84.7128	−	116.597i	0.0993116	−	0.136691i	0.855781	+	0.517339i	$0.173077\pi$
$854$	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	$0.0995134\pi$
$857$			527.163i			0.615126i	−0.951528	+	0.307563i	$0.900487\pi$
$858$		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	0.908668	−	0.417520i	$-0.137100\pi$
$863$	683.821	+	496.825i	0.792377	+	0.575696i	−0.116291	+	0.993215i	$0.537100\pi$
$864$		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	−0.759604	−	0.650386i	$-0.774607\pi$
$877$	−869.851	+	282.632i	−0.991848	+	0.322271i	−0.232245	+	0.972657i	$0.574607\pi$
$878$	−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	0.940283	−	0.340395i	$-0.110561\pi$
$883$	−18.1024	−	55.7133i	−0.0205010	−	0.0630955i	−0.960784	+	0.277299i	$0.910561\pi$
$884$	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	−0.320873	−	0.947122i	$-0.603976\pi$
$887$	−1008.67	−	327.736i	−1.13717	−	0.369489i	−0.816296	+	0.577634i	$0.803976\pi$
$888$		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	0.983192	−	0.182573i	$-0.0584427\pi$
$907$	1009.83	+	733.687i	1.11338	+	0.808916i	0.130186	+	0.991490i	$0.458443\pi$
$908$	−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	−0.827785	−	0.561045i	$-0.810399\pi$
$911$	−501.049	+	364.034i	−0.549999	+	0.399598i	0.277786	+	0.960643i	$0.410399\pi$
$912$		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	0.241973	−	0.970283i	$-0.422205\pi$
$919$	1001.70	−	1378.73i	1.08999	−	1.50025i	0.848020	−	0.529964i	$-0.177795\pi$
$920$	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	0.345721	−	0.938338i	$-0.387635\pi$
$929$	−408.628	−	296.886i	−0.439858	−	0.319575i	−0.785578	+	0.618762i	$0.787635\pi$
$930$		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	−0.989833	−	0.142233i	$-0.954572\pi$
$937$	−767.618	−	1056.54i	−0.819230	−	1.12757i	0.170604	−	0.985340i	$-0.445428\pi$
$938$	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	−0.798959	−	0.601386i	$-0.794615\pi$
$941$	18.7120	−	25.7548i	0.0198852	−	0.0273696i	0.818844	+	0.574016i	$0.194615\pi$
$942$		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	−0.524834	−	0.851205i	$-0.675873\pi$
$953$	−1381.62	−	448.916i	−1.44976	−	0.471055i	−0.924925	+	0.380149i	$0.875873\pi$
$954$		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	$-0.836518\pi$
$967$		−	950.193i		−	0.982619i	0.870985	−	0.491310i	$-0.163482\pi$
$968$	−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	0.999485	+	0.0320814i	$0.0102136\pi$
$971$	203.659	+	626.798i	0.209742	+	0.645519i	−0.789744	+	0.613437i	$0.789786\pi$
$972$		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	−0.498940	−	0.866637i	$-0.666277\pi$
$977$	167.165	−	121.452i	0.171100	−	0.124312i	0.670040	+	0.742325i	$0.266277\pi$
$978$		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	−0.980521	−	0.196415i	$-0.937070\pi$
$983$	−70.5920	+	217.260i	−0.0718129	+	0.221017i	0.908708	+	0.417432i	$0.137070\pi$
$984$		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	−0.535788	−	0.844352i	$-0.679985\pi$
$997$	−1461.15	−	474.757i	−1.46555	−	0.476185i	−0.929760	+	0.368167i	$0.879985\pi$
$998$	−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.19.2		16
3.2	odd	2		33.3.g.a.19.3	yes	16
11.2	odd	10		1089.3.c.m.604.5		16
11.7	odd	10	inner	99.3.k.c.73.2		16
11.9	even	5		1089.3.c.m.604.12		16
12.11	even	2		528.3.bf.b.481.1		16
33.2	even	10		363.3.c.e.241.12		16
33.5	odd	10		363.3.g.a.112.2		16
33.8	even	10		363.3.g.a.94.2		16
33.14	odd	10		363.3.g.g.94.3		16
33.17	even	10		363.3.g.g.112.3		16
33.20	odd	10		363.3.c.e.241.5		16
33.26	odd	10		363.3.g.f.40.2		16
33.29	even	10		33.3.g.a.7.3	✓	16
33.32	even	2		363.3.g.f.118.2		16
132.95	odd	10		528.3.bf.b.337.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.g.a.7.3	✓	16	33.29	even	10
33.3.g.a.19.3	yes	16	3.2	odd	2
99.3.k.c.19.2		16	1.1	even	1	trivial
99.3.k.c.73.2		16	11.7	odd	10	inner
363.3.c.e.241.5		16	33.20	odd	10
363.3.c.e.241.12		16	33.2	even	10
363.3.g.a.94.2		16	33.8	even	10
363.3.g.a.112.2		16	33.5	odd	10
363.3.g.f.40.2		16	33.26	odd	10
363.3.g.f.118.2		16	33.32	even	2
363.3.g.g.94.3		16	33.14	odd	10
363.3.g.g.112.3		16	33.17	even	10
528.3.bf.b.337.1		16	132.95	odd	10
528.3.bf.b.481.1		16	12.11	even	2
1089.3.c.m.604.5		16	11.2	odd	10
1089.3.c.m.604.12		16	11.9	even	5

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

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