LMFDB - Embedded newform 336.2.bo.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

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

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (of order $12$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	336.5
Dual form			336.2.bo.a.269.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14504 - 0.829988i) q^{2} +(0.380888 - 1.68965i) q^{3} +(0.622238 + 1.90074i) q^{4} +(-3.47185 + 0.930279i) q^{5} +(-1.83852 + 1.61859i) q^{6} +(-0.200208 + 2.63817i) q^{7} +(0.865105 - 2.69288i) q^{8} +(-2.70985 - 1.28714i) q^{9} +O(q^{10})$	\(q+(-1.14504 - 0.829988i) q^{2} +(0.380888 - 1.68965i) q^{3} +(0.622238 + 1.90074i) q^{4} +(-3.47185 + 0.930279i) q^{5} +(-1.83852 + 1.61859i) q^{6} +(-0.200208 + 2.63817i) q^{7} +(0.865105 - 2.69288i) q^{8} +(-2.70985 - 1.28714i) q^{9} +(4.74753 + 1.81639i) q^{10} +(4.23921 + 1.13589i) q^{11} +(3.44860 - 0.327397i) q^{12} +(1.18720 + 1.18720i) q^{13} +(2.41889 - 2.85464i) q^{14} +(0.249464 + 6.22055i) q^{15} +(-3.22564 + 2.36543i) q^{16} +(2.65968 + 4.60671i) q^{17} +(2.03458 + 3.72297i) q^{18} +(1.99232 - 0.533840i) q^{19} +(-3.92854 - 6.02023i) q^{20} +(4.38133 + 1.34313i) q^{21} +(-3.91129 - 4.81914i) q^{22} +(-0.573833 + 0.993907i) q^{23} +(-4.22052 - 2.48741i) q^{24} +(6.85819 - 3.95958i) q^{25} +(-0.374031 - 2.34476i) q^{26} +(-3.20696 + 4.08845i) q^{27} +(-5.13905 + 1.26102i) q^{28} +(-0.354471 - 0.354471i) q^{29} +(4.87734 - 7.32984i) q^{30} +(-7.76390 + 4.48249i) q^{31} +(5.65677 - 0.0312713i) q^{32} +(3.53393 - 6.73015i) q^{33} +(0.778067 - 7.48238i) q^{34} +(-1.75914 - 9.34556i) q^{35} +(0.760340 - 5.95163i) q^{36} +(3.94267 - 1.05644i) q^{37} +(-2.72436 - 1.04233i) q^{38} +(2.45815 - 1.55377i) q^{39} +(-0.498386 + 10.1541i) q^{40} +3.75599i q^{41} +(-3.90202 - 5.17438i) q^{42} +(5.87697 + 5.87697i) q^{43} +(0.478761 + 8.76444i) q^{44} +(10.6056 + 1.94782i) q^{45} +(1.48199 - 0.661790i) q^{46} +(-4.63117 + 8.02142i) q^{47} +(2.76815 + 6.35117i) q^{48} +(-6.91983 - 1.05636i) q^{49} +(-11.1393 - 1.15834i) q^{50} +(8.79678 - 2.73930i) q^{51} +(-1.51784 + 2.99528i) q^{52} +(5.91091 + 1.58382i) q^{53} +(7.06547 - 2.01970i) q^{54} -15.7746 q^{55} +(6.93106 + 2.82143i) q^{56} +(-0.143154 - 3.56965i) q^{57} +(0.111677 + 0.700091i) q^{58} +(1.94962 - 7.27607i) q^{59} +(-11.6684 + 4.34483i) q^{60} +(3.15567 - 0.845558i) q^{61} +(12.6104 + 1.31131i) q^{62} +(3.93821 - 6.89134i) q^{63} +(-6.50319 - 4.65924i) q^{64} +(-5.22621 - 3.01736i) q^{65} +(-9.63244 + 4.77317i) q^{66} +(-14.2820 - 3.82686i) q^{67} +(-7.10121 + 7.92185i) q^{68} +(1.46079 + 1.34814i) q^{69} +(-5.74242 + 12.1611i) q^{70} +0.726088 q^{71} +(-5.81040 + 6.18379i) q^{72} +(6.35191 + 11.0018i) q^{73} +(-5.39135 - 2.06271i) q^{74} +(-4.07811 - 13.0961i) q^{75} +(2.25439 + 3.45470i) q^{76} +(-3.84540 + 10.9563i) q^{77} +(-4.10429 - 0.261107i) q^{78} +(2.16393 - 3.74803i) q^{79} +(8.99842 - 11.2132i) q^{80} +(5.68656 + 6.97589i) q^{81} +(3.11743 - 4.30077i) q^{82} +(-6.06782 + 6.06782i) q^{83} +(0.173292 + 9.16351i) q^{84} +(-13.5196 - 13.5196i) q^{85} +(-1.85156 - 11.6072i) q^{86} +(-0.733947 + 0.463919i) q^{87} +(6.72619 - 10.4330i) q^{88} +(-10.0078 - 5.77803i) q^{89} +(-10.5272 - 11.0329i) q^{90} +(-3.36972 + 2.89435i) q^{91} +(-2.24622 - 0.472260i) q^{92} +(4.61668 + 14.8256i) q^{93} +(11.9606 - 5.34104i) q^{94} +(-6.42040 + 3.70682i) q^{95} +(2.10176 - 9.56988i) q^{96} +2.30445i q^{97} +(7.04672 + 6.95296i) q^{98} +(-10.0256 - 8.53454i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.14504	−	0.829988i	−0.809666	−	0.586890i
$2$	−1.14504	−	0.829988i	−0.809666	−	0.586890i
$3$	0.380888	−	1.68965i	0.219906	−	0.975521i
$3$	0.380888	−	1.68965i	0.219906	−	0.975521i
$4$	0.622238	+	1.90074i	0.311119	+	0.950371i
$5$	−3.47185	+	0.930279i	−1.55266	+	0.416034i	−0.930330	−	0.366723i	$-0.880480\pi$
$5$	−3.47185	+	0.930279i	−1.55266	+	0.416034i	−0.622328	+	0.782756i	$0.713813\pi$
$6$	−1.83852	+	1.61859i	−0.750574	+	0.660786i
$7$	−0.200208	+	2.63817i	−0.0756715	+	0.997133i
$7$	−0.200208	+	2.63817i	−0.0756715	+	0.997133i
$8$	0.865105	−	2.69288i	0.305861	−	0.952076i
$9$	−2.70985	−	1.28714i	−0.903283	−	0.429045i
$10$	4.74753	+	1.81639i	1.50130	+	0.574392i
$11$	4.23921	+	1.13589i	1.27817	+	0.342485i	0.833156	−	0.553039i	$-0.186532\pi$
$11$	4.23921	+	1.13589i	1.27817	+	0.342485i	0.445015	+	0.895523i	$0.353198\pi$
$12$	3.44860	−	0.327397i	0.995524	−	0.0945115i
$13$	1.18720	+	1.18720i	0.329270	+	0.329270i	0.852309	−	0.523039i	$-0.175202\pi$
$13$	1.18720	+	1.18720i	0.329270	+	0.329270i	−0.523039	+	0.852309i	$0.675202\pi$
$14$	2.41889	−	2.85464i	0.646476	−	0.762934i
$15$	0.249464	+	6.22055i	0.0644112	+	1.60614i
$16$	−3.22564	+	2.36543i	−0.806410	+	0.591357i
$17$	2.65968	+	4.60671i	0.645068	+	1.11729i	0.984286	+	0.176583i	$0.0565044\pi$
$17$	2.65968	+	4.60671i	0.645068	+	1.11729i	−0.339217	+	0.940708i	$0.610162\pi$
$18$	2.03458	+	3.72297i	0.479555	+	0.877512i
$19$	1.99232	−	0.533840i	0.457069	−	0.122471i	−0.0229363	−	0.999737i	$-0.507302\pi$
$19$	1.99232	−	0.533840i	0.457069	−	0.122471i	0.480005	+	0.877266i	$0.340635\pi$
$20$	−3.92854	−	6.02023i	−0.878448	−	1.34617i
$21$	4.38133	+	1.34313i	0.956084	+	0.293094i
$22$	−3.91129	−	4.81914i	−0.833891	−	1.02744i
$23$	−0.573833	+	0.993907i	−0.119652	+	0.207244i	−0.919630	−	0.392786i	$-0.871511\pi$
$23$	−0.573833	+	0.993907i	−0.119652	+	0.207244i	0.799978	+	0.600030i	$0.204845\pi$
$24$	−4.22052	−	2.48741i	−0.861510	−	0.507741i
$25$	6.85819	−	3.95958i	1.37164	−	0.791916i
$26$	−0.374031	−	2.34476i	−0.0733535	−	0.459845i
$27$	−3.20696	+	4.08845i	−0.617180	+	0.786822i
$28$	−5.13905	+	1.26102i	−0.971189	+	0.238311i
$29$	−0.354471	−	0.354471i	−0.0658237	−	0.0658237i	0.673429	−	0.739252i	$-0.264821\pi$
$29$	−0.354471	−	0.354471i	−0.0658237	−	0.0658237i	−0.739252	+	0.673429i	$0.764821\pi$
$30$	4.87734	−	7.32984i	0.890476	−	1.33824i
$31$	−7.76390	+	4.48249i	−1.39444	+	0.805079i	−0.993803	−	0.111158i	$-0.964544\pi$
$31$	−7.76390	+	4.48249i	−1.39444	+	0.805079i	−0.400636	+	0.916238i	$0.631211\pi$
$32$	5.65677	−	0.0312713i	0.999985	−	0.00552803i
$33$	3.53393	−	6.73015i	0.615178	−	1.17157i
$34$	0.778067	−	7.48238i	0.133437	−	1.28322i
$35$	−1.75914	−	9.34556i	−0.297349	−	1.57969i
$36$	0.760340	−	5.95163i	0.126723	−	0.991938i
$37$	3.94267	−	1.05644i	0.648171	−	0.173677i	0.0802694	−	0.996773i	$-0.474422\pi$
$37$	3.94267	−	1.05644i	0.648171	−	0.173677i	0.567902	+	0.823096i	$0.307755\pi$
$38$	−2.72436	−	1.04233i	−0.441950	−	0.169088i
$39$	2.45815	−	1.55377i	0.393619	−	0.248802i
$40$	−0.498386	+	10.1541i	−0.0788017	+	1.60550i
$41$			3.75599i			0.586588i	0.956022	+	0.293294i	$0.0947514\pi$
$41$			3.75599i			0.586588i	−0.956022	+	0.293294i	$0.905249\pi$
$42$	−3.90202	−	5.17438i	−0.602094	−	0.798425i
$43$	5.87697	+	5.87697i	0.896229	+	0.896229i	0.995100	−	0.0988709i	$-0.0315231\pi$
$43$	5.87697	+	5.87697i	0.896229	+	0.896229i	−0.0988709	+	0.995100i	$0.531523\pi$
$44$	0.478761	+	8.76444i	0.0721759	+	1.32129i
$45$	10.6056	+	1.94782i	1.58099	+	0.290365i
$46$	1.48199	−	0.661790i	0.218508	−	0.0975756i
$47$	−4.63117	+	8.02142i	−0.675525	+	1.17004i	0.300790	+	0.953691i	$0.402750\pi$
$47$	−4.63117	+	8.02142i	−0.675525	+	1.17004i	−0.976315	+	0.216354i	$0.930584\pi$
$48$	2.76815	+	6.35117i	0.399548	+	0.916712i
$49$	−6.91983	−	1.05636i	−0.988548	−	0.150909i
$50$	−11.1393	−	1.15834i	−1.57534	−	0.163814i
$51$	8.79678	−	2.73930i	1.23180	−	0.383579i
$52$	−1.51784	+	2.99528i	−0.210487	+	0.415371i
$53$	5.91091	+	1.58382i	0.811925	+	0.217555i	0.640813	−	0.767697i	$-0.278597\pi$
$53$	5.91091	+	1.58382i	0.811925	+	0.217555i	0.171112	+	0.985252i	$0.445264\pi$
$54$	7.06547	−	2.01970i	0.961488	−	0.274847i
$55$	−15.7746			−2.12705
$56$	6.93106	+	2.82143i	0.926202	+	0.377029i
$57$	−0.143154	−	3.56965i	−0.0189613	−	0.472812i
$58$	0.111677	+	0.700091i	0.0146639	+	0.0919265i
$59$	1.94962	−	7.27607i	0.253819	−	0.947264i	−0.714925	−	0.699201i	$-0.753539\pi$
$59$	1.94962	−	7.27607i	0.253819	−	0.947264i	0.968744	−	0.248063i	$-0.0797940\pi$
$60$	−11.6684	+	4.34483i	−1.50639	+	0.560915i
$61$	3.15567	−	0.845558i	0.404042	−	0.108263i	−0.0510742	−	0.998695i	$-0.516265\pi$
$61$	3.15567	−	0.845558i	0.404042	−	0.108263i	0.455116	+	0.890432i	$0.349598\pi$
$62$	12.6104	+	1.31131i	1.60152	+	0.166537i
$63$	3.93821	−	6.89134i	0.496168	−	0.868227i
$64$	−6.50319	−	4.65924i	−0.812898	−	0.582406i
$65$	−5.22621	−	3.01736i	−0.648232	−	0.374257i
$66$	−9.63244	+	4.77317i	−1.18567	+	0.587537i
$67$	−14.2820	−	3.82686i	−1.74483	−	0.467526i	−0.761319	−	0.648377i	$-0.775448\pi$
$67$	−14.2820	−	3.82686i	−1.74483	−	0.467526i	−0.983510	+	0.180851i	$0.942115\pi$
$68$	−7.10121	+	7.92185i	−0.861148	+	0.960665i
$69$	1.46079	+	1.34814i	0.175859	+	0.162298i
$70$	−5.74242	+	12.1611i	−0.686351	+	1.45353i
$71$	0.726088			0.0861708			0.0430854	−	0.999071i	$-0.486281\pi$
$71$	0.726088			0.0861708			0.0430854	+	0.999071i	$0.486281\pi$
$72$	−5.81040	+	6.18379i	−0.684763	+	0.728766i
$73$	6.35191	+	11.0018i	0.743435	+	1.28767i	0.950922	+	0.309430i	$0.100138\pi$
$73$	6.35191	+	11.0018i	0.743435	+	1.28767i	−0.207487	+	0.978238i	$0.566529\pi$
$74$	−5.39135	−	2.06271i	−0.626732	−	0.239785i
$75$	−4.07811	−	13.0961i	−0.470900	−	1.51221i
$76$	2.25439	+	3.45470i	0.258596	+	0.396282i
$77$	−3.84540	+	10.9563i	−0.438224	+	1.24859i
$78$	−4.10429	−	0.261107i	−0.464719	−	0.0295646i
$79$	2.16393	−	3.74803i	0.243461	−	0.421686i	−0.718237	−	0.695798i	$-0.755051\pi$
$79$	2.16393	−	3.74803i	0.243461	−	0.421686i	0.961698	+	0.274112i	$0.0883840\pi$
$80$	8.99842	−	11.2132i	1.00605	−	1.25367i
$81$	5.68656	+	6.97589i	0.631840	+	0.775098i
$82$	3.11743	−	4.30077i	0.344263	−	0.474940i
$83$	−6.06782	+	6.06782i	−0.666030	+	0.666030i	−0.956795	−	0.290765i	$-0.906090\pi$
$83$	−6.06782	+	6.06782i	−0.666030	+	0.666030i	0.290765	+	0.956795i	$0.406090\pi$
$84$	0.173292	+	9.16351i	0.0189077	+	0.999821i
$85$	−13.5196	−	13.5196i	−1.46640	−	1.46640i
$86$	−1.85156	−	11.6072i	−0.199658	−	1.25164i
$87$	−0.733947	+	0.463919i	−0.0786874	+	0.0497374i
$88$	6.72619	−	10.4330i	0.717014	−	1.11216i
$89$	−10.0078	−	5.77803i	−1.06083	−	0.612470i	−0.135167	−	0.990823i	$-0.543157\pi$
$89$	−10.0078	−	5.77803i	−1.06083	−	0.612470i	−0.925661	+	0.378353i	$0.876491\pi$
$90$	−10.5272	−	11.0329i	−1.10966	−	1.16296i
$91$	−3.36972	+	2.89435i	−0.353243	+	0.303410i
$92$	−2.24622	−	0.472260i	−0.234185	−	0.0492365i
$93$	4.61668	+	14.8256i	0.478727	+	1.53735i
$94$	11.9606	−	5.34104i	1.23364	−	0.550886i
$95$	−6.42040	+	3.70682i	−0.658719	+	0.380312i
$96$	2.10176	−	9.56988i	0.214510	−	0.976722i
$97$			2.30445i			0.233982i	0.993133	+	0.116991i	$0.0373248\pi$
$97$			2.30445i			0.233982i	−0.993133	+	0.116991i	$0.962675\pi$
$98$	7.04672	+	6.95296i	0.711827	+	0.702355i
$99$	−10.0256	−	8.53454i	−1.00761	−	0.857753i
$100$	11.7936	+	10.5719i	1.17936	+	1.05719i
$101$	3.87010	−	14.4434i	0.385089	−	1.43717i	−0.452936	−	0.891543i	$-0.649624\pi$
$101$	3.87010	−	14.4434i	0.385089	−	1.43717i	0.838026	−	0.545631i	$-0.183710\pi$
$102$	−12.3463	−	4.16461i	−1.22246	−	0.412358i
$103$	−1.05534	+	1.82790i	−0.103986	+	0.180109i	−0.913323	−	0.407235i	$-0.866493\pi$
$103$	−1.05534	+	1.82790i	−0.103986	+	0.180109i	0.809338	+	0.587344i	$0.199826\pi$
$104$	4.22404	−	2.16993i	0.414201	−	0.212780i
$105$	−16.4608	−	0.587278i	−1.60641	−	0.0573125i
$106$	−5.45368	−	6.71953i	−0.529708	−	0.652658i
$107$	0.958024	+	3.57539i	0.0926157	+	0.345646i	0.996647	−	0.0818195i	$-0.0260731\pi$
$107$	0.958024	+	3.57539i	0.0926157	+	0.345646i	−0.904032	+	0.427466i	$0.859406\pi$
$108$	−9.76658	−	3.55161i	−0.939789	−	0.341754i
$109$	1.72218	+	0.461457i	0.164955	+	0.0441996i	0.340351	−	0.940298i	$-0.389454\pi$
$109$	1.72218	+	0.461457i	0.164955	+	0.0441996i	−0.175396	+	0.984498i	$0.556121\pi$
$110$	18.0626	+	13.0927i	1.72220	+	1.24834i
$111$	−0.283294	−	7.06413i	−0.0268890	−	0.670497i
$112$	−5.59460	−	8.98335i	−0.528640	−	0.848846i
$113$		−	0.687876i		−	0.0647099i	−0.999476	−	0.0323549i	$-0.989699\pi$
$113$		−	0.687876i		−	0.0647099i	0.999476	−	0.0323549i	$-0.0103007\pi$
$114$	−2.79885	+	4.20622i	−0.262137	+	0.393948i
$115$	1.06765	−	3.98452i	0.0995588	−	0.371558i
$116$	0.453193	−	0.894324i	0.0420779	−	0.0830359i
$117$	−1.68905	−	4.74522i	−0.156152	−	0.438696i
$118$	−8.27145	+	6.71324i	−0.761448	+	0.618004i
$119$	−12.6858	+	6.09439i	−1.16290	+	0.558672i
$120$	16.9670	+	4.70965i	1.54887	+	0.429931i
$121$	7.15438	+	4.13058i	0.650398	+	0.375508i
$122$	−4.31517	−	1.65097i	−0.390677	−	0.149472i
$123$	6.34632	+	1.43061i	0.572229	+	0.128994i
$124$	−13.3511	−	11.9680i	−1.19896	−	1.07476i
$125$	−7.41925	+	7.41925i	−0.663598	+	0.663598i
$126$	−10.2291	+	4.62219i	−0.911284	+	0.411778i
$127$	8.70170			0.772151			0.386075	−	0.922467i	$-0.373830\pi$
$127$	8.70170			0.772151			0.386075	+	0.922467i	$0.373830\pi$
$128$	3.57930	+	10.7326i	0.316368	+	0.948636i
$129$	12.1685	−	7.69157i	1.07138	−	0.677205i
$130$	3.47986	+	7.79269i	0.305204	+	0.683464i
$131$	1.02679	+	3.83205i	0.0897114	+	0.334807i	0.996165	−	0.0874987i	$-0.0278874\pi$
$131$	1.02679	+	3.83205i	0.0897114	+	0.334807i	−0.906453	+	0.422306i	$0.861221\pi$
$132$	14.9912	+	2.52933i	1.30482	+	0.220150i
$133$	1.00948	+	5.36294i	0.0875330	+	0.465026i
$134$	13.1773	+	16.2358i	1.13834	+	1.40256i
$135$	7.33068	−	17.1778i	0.630925	−	1.47843i
$136$	14.7062	−	3.17692i	1.26105	−	0.272419i
$137$	−0.843369	−	1.46076i	−0.0720538	−	0.124801i	0.827747	−	0.561101i	$-0.189622\pi$
$137$	−0.843369	−	1.46076i	−0.0720538	−	0.124801i	−0.899801	+	0.436300i	$0.856289\pi$
$138$	−0.553722	−	2.75612i	−0.0471360	−	0.234617i
$139$	−4.87417	+	4.87417i	−0.413421	+	0.413421i	−0.882929	−	0.469507i	$-0.844432\pi$
$139$	−4.87417	+	4.87417i	−0.413421	+	0.413421i	0.469507	+	0.882929i	$0.344432\pi$
$140$	16.6689	−	9.15884i	1.40878	−	0.774063i
$141$	11.7895	+	10.8803i	0.992851	+	0.916289i
$142$	−0.831401	−	0.602645i	−0.0697696	−	0.0505728i
$143$	3.68426	+	6.38133i	0.308094	+	0.533634i
$144$	11.7856	−	2.25812i	0.982135	−	0.188177i
$145$	1.56043	+	0.900914i	0.129587	+	0.0748168i
$146$	1.85819	−	17.8696i	0.153785	−	1.47890i
$147$	−4.42057	+	11.2898i	−0.364602	+	0.931163i
$148$	4.46129	+	6.83665i	0.366716	+	0.561969i
$149$	0.179912	+	0.671443i	0.0147390	+	0.0550067i	0.972904	−	0.231211i	$-0.0742687\pi$
$149$	0.179912	+	0.671443i	0.0147390	+	0.0550067i	−0.958165	+	0.286217i	$0.907602\pi$
$150$	−6.20002	+	18.3804i	−0.506230	+	1.50075i
$151$	11.7217	−	6.76750i	0.953895	−	0.550732i	0.0596065	−	0.998222i	$-0.481015\pi$
$151$	11.7217	−	6.76750i	0.953895	−	0.550732i	0.894289	+	0.447490i	$0.147682\pi$
$152$	0.285998	−	5.82689i	0.0231975	−	0.472623i
$153$	−1.27789	−	15.9069i	−0.103311	−	1.28599i
$154$	13.4968	−	9.35381i	1.08760	−	0.753751i
$155$	22.7851	−	22.7851i	1.83015	−	1.83015i
$156$	4.48286	+	3.70549i	0.358916	+	0.296677i
$157$	1.64943	−	6.15575i	0.131639	−	0.491282i	−0.868350	−	0.495951i	$-0.834820\pi$
$157$	1.64943	−	6.15575i	0.131639	−	0.491282i	0.999989	+	0.00466899i	$0.00148619\pi$
$158$	−5.58860	+	2.49561i	−0.444605	+	0.198540i
$159$	4.92750	−	9.38412i	0.390776	−	0.744209i
$160$	−19.6104	+	5.37094i	−1.55033	+	0.424610i
$161$	−2.50721	−	1.71285i	−0.197595	−	0.134992i
$162$	−0.721445	−	12.7075i	−0.0566821	−	0.998392i
$163$	2.68288	+	10.0126i	0.210139	+	0.784250i	0.987821	+	0.155592i	$0.0497287\pi$
$163$	2.68288	+	10.0126i	0.210139	+	0.784250i	−0.777682	+	0.628658i	$0.783605\pi$
$164$	−7.13917	+	2.33712i	−0.557476	+	0.182499i
$165$	−6.00835	+	26.6536i	−0.467750	+	2.07498i
$166$	11.9841	−	1.91168i	0.930148	−	0.148375i
$167$			4.91455i			0.380299i	0.981755	+	0.190150i	$0.0608973\pi$
$167$			4.91455i			0.380299i	−0.981755	+	0.190150i	$0.939103\pi$
$168$	7.40718	−	10.6364i	0.571477	−	0.820618i
$169$		−	10.1811i		−	0.783162i
$170$	4.25937	+	26.7015i	0.326679	+	2.04791i
$171$	−6.08600	−	1.11776i	−0.465408	−	0.0854770i
$172$	−7.51372	+	14.8275i	−0.572916	+	1.13058i
$173$	−4.03480	−	15.0581i	−0.306760	−	1.14484i	−0.931420	−	0.363947i	$-0.881429\pi$
$173$	−4.03480	−	15.0581i	−0.306760	−	1.14484i	0.624660	−	0.780897i	$-0.285238\pi$
$174$	1.22545	+	0.0779606i	0.0929009	+	0.00591018i
$175$	9.07296	+	18.8858i	0.685851	+	1.42763i
$176$	−16.3610	+	6.36357i	−1.23326	+	0.479672i
$177$	−11.5514	−	6.06554i	−0.868260	−	0.455914i
$178$	6.66369	+	14.9225i	0.499465	+	1.11849i
$179$	−2.04444	+	7.62997i	−0.152809	+	0.570290i	0.846474	+	0.532430i	$0.178721\pi$
$179$	−2.04444	+	7.62997i	−0.152809	+	0.570290i	−0.999283	+	0.0378607i	$0.987946\pi$
$180$	2.89689	+	21.3705i	0.215921	+	1.59286i
$181$	15.6426	−	15.6426i	1.16270	−	1.16270i	0.178822	−	0.983881i	$-0.442771\pi$
$181$	15.6426	−	15.6426i	1.16270	−	1.16270i	0.983881	−	0.178822i	$-0.0572287\pi$
$182$	6.26074	−	0.517316i	0.464077	−	0.0383460i
$183$	−0.226745	−	5.65404i	−0.0167614	−	0.417959i
$184$	2.18005	+	2.40510i	0.160715	+	0.177306i
$185$	−12.7056	+	7.33557i	−0.934133	+	0.539322i
$186$	7.01881	−	20.8077i	0.514644	−	1.52570i
$187$	6.04224	+	22.5499i	0.441852	+	1.64901i
$188$	−18.1283	−	3.81142i	−1.32215	−	0.277976i
$189$	−10.1439	−	9.27903i	−0.737863	−	0.674950i
$190$	10.4282	+	1.08440i	0.756544	+	0.0786704i
$191$	−6.19417	−	3.57620i	−0.448194	−	0.258765i	0.258873	−	0.965911i	$-0.416649\pi$
$191$	−6.19417	−	3.57620i	−0.448194	−	0.258765i	−0.707067	+	0.707146i	$0.749982\pi$
$192$	−10.3495	+	9.21347i	−0.746910	+	0.664925i
$193$	−3.95814	−	6.85571i	−0.284913	−	0.493485i	0.687675	−	0.726019i	$-0.258632\pi$
$193$	−3.95814	−	6.85571i	−0.284913	−	0.493485i	−0.972588	+	0.232534i	$0.925298\pi$
$194$	1.91267	−	2.63869i	0.137322	−	0.189447i
$195$	−7.08888	+	7.68121i	−0.507645	+	0.550063i
$196$	−2.29791	−	13.8101i	−0.164137	−	0.986438i
$197$	5.26663	−	5.26663i	0.375232	−	0.375232i	−0.494147	−	0.869379i	$-0.664519\pi$
$197$	5.26663	−	5.26663i	0.375232	−	0.375232i	0.869379	+	0.494147i	$0.164519\pi$
$198$	4.39613	+	18.0935i	0.312419	+	1.28585i
$199$	2.70150	+	4.67914i	0.191505	+	0.331696i	0.945749	−	0.324898i	$-0.105330\pi$
$199$	2.70150	+	4.67914i	0.191505	+	0.331696i	−0.754245	+	0.656594i	$0.771997\pi$
$200$	−4.72961	−	21.8937i	−0.334434	−	1.54812i
$201$	−11.9059	+	22.6741i	−0.839779	+	1.59931i
$202$	−16.4193	+	13.3262i	−1.15526	+	0.937626i
$203$	1.00612	−	0.864186i	0.0706159	−	0.0606540i
$204$	10.6804	+	15.0159i	0.747778	+	1.05132i
$205$	−3.49412	−	13.0402i	−0.244040	−	0.910770i
$206$	2.72555	−	1.21710i	0.189898	−	0.0847996i
$207$	2.83429	−	1.95474i	0.196997	−	0.135864i
$208$	−6.63772	−	1.02124i	−0.460243	−	0.0708103i
$209$	9.05223			0.626156
$210$	18.3608	+	14.3347i	1.26702	+	0.989190i
$211$	15.8030	−	15.8030i	1.08793	−	1.08793i	0.0921831	−	0.995742i	$-0.470615\pi$
$211$	15.8030	−	15.8030i	1.08793	−	1.08793i	0.995742	−	0.0921831i	$-0.0293845\pi$
$212$	0.667556	+	12.2206i	0.0458479	+	0.839316i
$213$	0.276558	−	1.22684i	0.0189494	−	0.0840615i
$214$	1.87056	−	4.88912i	0.127869	−	0.334213i
$215$	−25.8712	−	14.9367i	−1.76440	−	1.01868i
$216$	8.23534	+	12.1729i	0.560344	+	0.828260i
$217$	−10.2712	−	21.3799i	−0.697252	−	1.45136i
$218$	−1.58896	−	1.95778i	−0.107618	−	0.132597i
$219$	21.0086	−	6.54206i	1.41963	−	0.442071i
$220$	−9.81557	−	29.9834i	−0.661765	−	2.02148i
$221$	−2.31151	+	8.62667i	−0.155489	+	0.580293i
$222$	−5.53876	+	8.32385i	−0.371737	+	0.558660i
$223$		−	2.66940i		−	0.178756i	−0.995998	−	0.0893780i	$-0.971512\pi$
$223$		−	2.66940i		−	0.178756i	0.995998	−	0.0893780i	$-0.0284879\pi$
$224$	−1.05003	+	14.9297i	−0.0701582	+	0.997536i
$225$	−23.6812	+	1.90244i	−1.57875	+	0.126829i
$226$	−0.570929	+	0.787646i	−0.0379776	+	0.0523934i
$227$	−14.2891	−	3.82875i	−0.948399	−	0.254123i	−0.248716	−	0.968576i	$-0.580009\pi$
$227$	−14.2891	−	3.82875i	−0.948399	−	0.254123i	−0.699683	+	0.714454i	$0.746675\pi$
$228$	6.69592	−	2.49328i	0.443448	−	0.165121i
$229$	0.948247	+	3.53890i	0.0626619	+	0.233857i	0.990153	−	0.139987i	$-0.0447061\pi$
$229$	0.948247	+	3.53890i	0.0626619	+	0.233857i	−0.927491	+	0.373844i	$0.878039\pi$
$230$	−4.52961	+	3.67630i	−0.298674	+	0.242408i
$231$	17.0477	+	10.6705i	1.12166	+	0.702068i
$232$	−1.26120	+	0.647893i	−0.0828020	+	0.0425363i
$233$	9.98697	−	17.2979i	0.654268	−	1.13323i	−0.327809	−	0.944744i	$-0.606310\pi$
$233$	9.98697	−	17.2979i	0.654268	−	1.13323i	0.982077	−	0.188481i	$-0.0603565\pi$
$234$	−2.00445	+	6.83537i	−0.131035	+	0.446842i
$235$	8.61656	−	32.1574i	0.562083	−	2.09772i
$236$	15.0431	−	0.821732i	0.979220	−	0.0534902i
$237$	−5.50865	−	5.08386i	−0.357825	−	0.330232i
$238$	19.5840	+	3.55070i	1.26944	+	0.230158i
$239$			25.3738i			1.64129i	0.571437	+	0.820646i	$0.306386\pi$
$239$			25.3738i			1.64129i	−0.571437	+	0.820646i	$0.693614\pi$
$240$	−15.5190	−	19.4752i	−1.00174	−	1.25712i
$241$	14.5041	−	8.37393i	0.934289	−	0.539412i	0.0461238	−	0.998936i	$-0.485313\pi$
$241$	14.5041	−	8.37393i	0.934289	−	0.539412i	0.888166	+	0.459523i	$0.151980\pi$
$242$	−4.76372	−	10.6677i	−0.306224	−	0.685748i
$243$	13.9528	−	6.95129i	0.895070	−	0.445925i
$244$	3.57076	+	5.47197i	0.228595	+	0.350307i
$245$	25.0073	−	2.76984i	1.59766	−	0.176959i
$246$	−6.07941	−	6.90548i	−0.387609	−	0.440278i
$247$	2.99905	+	1.73151i	0.190825	+	0.110173i
$248$	5.35421	+	24.7851i	0.339993	+	1.57385i
$249$	7.94134	+	12.5637i	0.503262	+	0.796190i
$250$	14.6532	−	2.33746i	0.926752	−	0.147834i
$251$	−14.7477	−	14.7477i	−0.930867	−	0.930867i	0.0668927	−	0.997760i	$-0.478691\pi$
$251$	−14.7477	−	14.7477i	−0.930867	−	0.930867i	−0.997760	+	0.0668927i	$0.978691\pi$
$252$	15.5492	+	3.19747i	0.979505	+	0.201421i
$253$	−3.56157	+	3.56157i	−0.223914	+	0.223914i
$254$	−9.96380	−	7.22231i	−0.625184	−	0.453168i
$255$	−27.9928	+	17.6939i	−1.75298	+	1.10804i
$256$	4.80949	−	15.2600i	0.300593	−	0.953753i
$257$	−2.71449	+	4.70164i	−0.169325	+	0.293280i	−0.938183	−	0.346140i	$-0.887492\pi$
$257$	−2.71449	+	4.70164i	−0.169325	+	0.293280i	0.768857	+	0.639420i	$0.220826\pi$
$258$	−20.3173	−	1.29255i	−1.26490	−	0.0804707i
$259$	1.99770	+	10.6129i	0.124131	+	0.659455i
$260$	2.48326	−	11.8112i	0.154005	−	0.732499i
$261$	0.504311	+	1.41682i	0.0312161	+	0.0876987i
$262$	2.00483	−	5.24008i	0.123859	−	0.323733i
$263$	−2.16667	−	3.75278i	−0.133602	−	0.231406i	0.791460	−	0.611221i	$-0.209321\pi$
$263$	−2.16667	−	3.75278i	−0.133602	−	0.231406i	−0.925063	+	0.379814i	$0.875988\pi$
$264$	−15.0662	−	15.3387i	−0.927263	−	0.944033i
$265$	−21.9952			−1.35115
$266$	3.29528	−	6.97864i	0.202047	−	0.427888i
$267$	−13.5747	+	14.7090i	−0.830759	+	0.900175i
$268$	−1.61296	−	29.5277i	−0.0985273	−	1.80369i
$269$	−1.77193	−	0.474788i	−0.108037	−	0.0289483i	0.204396	−	0.978888i	$-0.434477\pi$
$269$	−1.77193	−	0.474788i	−0.108037	−	0.0289483i	−0.312432	+	0.949940i	$0.601144\pi$
$270$	−22.6513	+	13.5850i	−1.37852	+	0.826754i
$271$	−12.9283	−	7.46415i	−0.785337	−	0.453415i	0.0529812	−	0.998596i	$-0.483128\pi$
$271$	−12.9283	−	7.46415i	−0.785337	−	0.453415i	−0.838319	+	0.545181i	$0.816461\pi$
$272$	−19.4760	−	8.56828i	−1.18091	−	0.519528i
$273$	3.60695	+	6.79608i	0.218303	+	0.411317i
$274$	−0.246720	+	2.37261i	−0.0149049	+	0.143335i
$275$	33.5710	−	8.99532i	2.02441	−	0.542438i
$276$	−1.65351	+	3.61546i	−0.0995298	+	0.217625i
$277$	−3.63115	+	13.5516i	−0.218175	+	0.814239i	0.766850	+	0.641826i	$0.221823\pi$
$277$	−3.63115	+	13.5516i	−0.218175	+	0.814239i	−0.985025	+	0.172413i	$0.944844\pi$
$278$	9.62662	−	1.53562i	0.577367	−	0.0921003i
$279$	26.8086	−	2.15368i	1.60499	−	0.128937i
$280$	−26.6883	−	3.34775i	−1.59493	−	0.200066i
$281$	16.5916			0.989772			0.494886	−	0.868958i	$-0.335210\pi$
$281$	16.5916			0.989772			0.494886	+	0.868958i	$0.335210\pi$
$282$	−4.46887	−	22.2435i	−0.266117	−	1.32458i
$283$	−8.22528	−	2.20396i	−0.488942	−	0.131012i	0.00592132	−	0.999982i	$-0.498115\pi$
$283$	−8.22528	−	2.20396i	−0.488942	−	0.131012i	−0.494863	+	0.868971i	$0.664782\pi$
$284$	0.451800	+	1.38011i	0.0268094	+	0.0818942i
$285$	3.81779	+	12.2601i	0.226146	+	0.726227i
$286$	1.07780	−	10.3648i	0.0637315	−	0.612882i
$287$	−9.90893	−	0.751980i	−0.584906	−	0.0443880i
$288$	−15.3692	−	7.19629i	−0.905641	−	0.424045i
$289$	−5.64785	+	9.78236i	−0.332226	+	0.575433i
$290$	−1.03901	−	2.32672i	−0.0610126	−	0.136630i
$291$	3.89372	+	0.877737i	0.228254	+	0.0514539i
$292$	−16.9592	+	18.9191i	−0.992465	+	1.10716i
$293$	16.3346	+	16.3346i	0.954277	+	0.954277i	0.998999	−	0.0447227i	$-0.0142404\pi$
$293$	16.3346	+	16.3346i	0.954277	+	0.954277i	−0.0447227	+	0.998999i	$0.514240\pi$
$294$	14.4321	−	9.25822i	0.841697	−	0.539950i
$295$			27.0751i			1.57637i
$296$	0.565972	−	11.5311i	0.0328965	−	0.670229i
$297$	−18.2390	+	13.6890i	−1.05834	+	0.794318i
$298$	0.351282	−	0.918155i	0.0203492	−	0.0531873i
$299$	−1.86122	+	0.498713i	−0.107637	+	0.0288413i
$300$	22.3548	−	15.9003i	1.29065	−	0.918007i
$301$	−16.6810	+	14.3278i	−0.961479	+	0.825841i
$302$	−19.0387	−	1.97977i	−1.09556	−	0.113923i
$303$	−22.9303	−	12.0404i	−1.31731	−	0.691705i
$304$	−5.16373	+	6.43466i	−0.296160	+	0.369053i
$305$	−10.1694	+	5.87130i	−0.582298	+	0.336190i
$306$	−11.7393	+	19.2746i	−0.671090	+	1.10186i
$307$	9.20384	+	9.20384i	0.525291	+	0.525291i	0.919165	−	0.393874i	$-0.128865\pi$
$307$	9.20384	+	9.20384i	0.525291	+	0.525291i	−0.393874	+	0.919165i	$0.628865\pi$
$308$	−23.2179	−	0.491662i	−1.32296	−	0.0280150i
$309$	2.68655	+	2.47938i	0.152833	+	0.141047i
$310$	−45.0013	+	7.17852i	−2.55590	+	0.407713i
$311$	1.03956	−	0.600189i	0.0589479	−	0.0340336i	−0.470236	−	0.882540i	$-0.655831\pi$
$311$	1.03956	−	0.600189i	0.0589479	−	0.0340336i	0.529184	+	0.848507i	$0.322498\pi$
$312$	−2.05755	−	7.96366i	−0.116486	−	0.450854i
$313$	10.2740	−	17.7951i	0.580720	−	1.00584i	−0.414674	−	0.909970i	$-0.636104\pi$
$313$	10.2740	−	17.7951i	0.580720	−	1.00584i	0.995394	−	0.0958669i	$-0.0305623\pi$
$314$	−6.99786	+	5.67958i	−0.394912	+	0.320517i
$315$	−7.26201	+	27.5893i	−0.409168	+	1.55448i
$316$	8.47051	+	1.78090i	0.476503	+	0.100183i
$317$	32.1961	−	8.62693i	1.80832	−	0.484537i	0.813090	−	0.582138i	$-0.197784\pi$
$317$	32.1961	−	8.62693i	1.80832	−	0.484537i	0.995226	+	0.0976008i	$0.0311168\pi$
$318$	−13.4309	+	6.65543i	−0.753167	+	0.373218i
$319$	−1.10004	−	1.90532i	−0.0615903	−	0.106677i
$320$	26.9125	+	10.1264i	1.50445	+	0.566084i
$321$	6.40607	−	0.256903i	0.357552	−	0.0143390i
$322$	1.44921	+	4.04224i	0.0807610	+	0.225265i
$323$	7.75818	+	7.75818i	0.431677	+	0.431677i
$324$	−9.72096	+	15.1494i	−0.540053	+	0.841631i
$325$	12.8429	+	3.44124i	0.712394	+	0.190885i
$326$	5.23837	−	13.6916i	0.290126	−	0.758310i
$327$	1.43566	−	2.73412i	0.0793922	−	0.151197i
$328$	10.1144	+	3.24933i	0.558476	+	0.179414i
$329$	−20.2346	−	13.8237i	−1.11557	−	0.762128i
$330$	29.0020	−	25.5326i	1.59651	−	1.40552i
$331$	−24.2392	+	6.49487i	−1.33231	+	0.356990i	−0.853574	−	0.520971i	$-0.825570\pi$
$331$	−24.2392	+	6.49487i	−1.33231	+	0.356990i	−0.478732	+	0.877961i	$0.658903\pi$
$332$	−15.3090	−	7.75773i	−0.840190	−	0.425760i
$333$	−12.0438	−	2.21197i	−0.659997	−	0.121215i
$334$	4.07902	−	5.62736i	0.223194	−	0.307915i
$335$	53.1452			2.90363
$336$	−17.3096	+	6.03127i	−0.944318	+	0.329033i
$337$	−13.5152			−0.736218			−0.368109	−	0.929783i	$-0.619995\pi$
$337$	−13.5152			−0.736218			−0.368109	+	0.929783i	$0.619995\pi$
$338$	−8.45020	+	11.6578i	−0.459630	+	0.634100i
$339$	−1.16227	−	0.262003i	−0.0631259	−	0.0142301i
$340$	17.2848	−	34.1096i	0.937399	−	1.84985i
$341$	−38.0045	+	10.1833i	−2.05806	+	0.551455i
$342$	6.04100	+	6.33119i	0.326660	+	0.342351i
$343$	4.17227	−	18.0442i	0.225281	−	0.974294i
$344$	20.9102	−	10.7418i	1.12740	−	0.579157i
$345$	−6.32580	−	3.32161i	−0.340570	−	0.178830i
$346$	−7.87802	+	20.5910i	−0.423525	+	1.10698i
$347$	21.4731	+	5.75371i	1.15274	+	0.308875i	0.784062	−	0.620683i	$-0.213145\pi$
$347$	21.4731	+	5.75371i	1.15274	+	0.308875i	0.368676	+	0.929558i	$0.379811\pi$
$348$	−1.33848	−	1.10638i	−0.0717501	−	0.0593079i
$349$	9.67470	+	9.67470i	0.517875	+	0.517875i	0.916928	−	0.399053i	$-0.130661\pi$
$349$	9.67470	+	9.67470i	0.517875	+	0.517875i	−0.399053	+	0.916928i	$0.630661\pi$
$350$	5.28607	−	29.1555i	0.282552	−	1.55842i
$351$	−8.66112	+	1.04650i	−0.462296	+	0.0558583i
$352$	24.0158	+	6.29292i	1.28004	+	0.335414i
$353$	10.4529	+	18.1050i	0.556352	+	0.963629i	0.997797	+	0.0663413i	$0.0211326\pi$
$353$	10.4529	+	18.1050i	0.556352	+	0.963629i	−0.441445	+	0.897288i	$0.645534\pi$
$354$	8.19255	+	16.5329i	0.435429	+	0.878711i
$355$	−2.52087	+	0.675465i	−0.133794	+	0.0358500i
$356$	4.75528	−	22.6176i	0.252029	−	1.19873i
$357$	5.46555	+	23.7558i	0.289268	+	1.25729i
$358$	8.67376	−	7.03976i	0.458422	−	0.372063i
$359$	−12.8234	+	22.2109i	−0.676795	+	1.17224i	0.299145	+	0.954208i	$0.403298\pi$
$359$	−12.8234	+	22.2109i	−0.676795	+	1.17224i	−0.975941	+	0.218036i	$0.930035\pi$
$360$	14.4202	−	26.8745i	0.760011	−	1.41641i
$361$	−12.7701	+	7.37285i	−0.672113	+	0.388045i
$362$	−30.8946	+	4.92824i	−1.62378	+	0.259022i
$363$	9.70427	−	10.5151i	0.509342	−	0.551901i
$364$	−7.59817	−	4.60399i	−0.398252	−	0.241315i
$365$	−32.2877	−	32.2877i	−1.69001	−	1.69001i
$366$	−4.43316	+	6.66230i	−0.231725	+	0.348244i
$367$	3.92686	−	2.26718i	0.204981	−	0.118346i	−0.393996	−	0.919112i	$-0.628908\pi$
$367$	3.92686	−	2.26718i	0.204981	−	0.118346i	0.598977	+	0.800767i	$0.295574\pi$
$368$	−0.500041	−	4.56335i	−0.0260664	−	0.237881i
$369$	4.83447	−	10.1782i	0.251673	−	0.529855i
$370$	20.6369	+	2.14596i	1.07286	+	0.111563i
$371$	−5.36180	+	15.2769i	−0.278371	+	0.793135i
$372$	−25.3070	+	18.0002i	−1.31211	+	0.933266i
$373$	−24.1140	+	6.46132i	−1.24857	+	0.334554i	−0.821785	−	0.569797i	$-0.807022\pi$
$373$	−24.1140	+	6.46132i	−1.24857	+	0.334554i	−0.426789	+	0.904351i	$0.640355\pi$
$374$	11.7976	−	30.8356i	0.610038	−	1.59447i
$375$	9.71005	+	15.3619i	0.501425	+	0.793283i
$376$	17.5943	+	19.4105i	0.907355	+	1.00102i
$377$		−	0.841657i		−	0.0433476i
$378$	3.91375	+	19.0442i	0.201301	+	0.979529i
$379$	4.62848	+	4.62848i	0.237749	+	0.237749i	0.815917	−	0.578168i	$-0.196232\pi$
$379$	4.62848	+	4.62848i	0.237749	+	0.237749i	−0.578168	+	0.815917i	$0.696232\pi$
$380$	−11.0407	−	9.89700i	−0.566378	−	0.507705i
$381$	3.31437	−	14.7028i	0.169800	−	0.753249i
$382$	4.12437	+	9.23599i	0.211021	+	0.472554i
$383$	11.9936	−	20.7735i	0.612843	−	1.06148i	−0.377916	−	0.925840i	$-0.623359\pi$
$383$	11.9936	−	20.7735i	0.612843	−	1.06148i	0.990759	−	0.135635i	$-0.0433076\pi$
$384$	19.4977	−	1.95985i	0.994986	−	0.100013i
$385$	3.15820	−	41.6160i	0.160957	−	2.12095i
$386$	−1.15792	+	11.1353i	−0.0589365	+	0.566771i
$387$	−8.36124	−	23.4902i	−0.425026	−	1.19407i
$388$	−4.38017	+	1.43392i	−0.222369	+	0.0727962i
$389$	−32.2238	−	8.63435i	−1.63381	−	0.437779i	−0.678796	−	0.734327i	$-0.737498\pi$
$389$	−32.2238	−	8.63435i	−1.63381	−	0.437779i	−0.955018	+	0.296548i	$0.904164\pi$
$390$	14.4924	−	2.91161i	0.733850	−	0.147435i
$391$	−6.10486			−0.308736
$392$	−8.83104	+	17.7204i	−0.446035	+	0.895016i
$393$	6.86592	−	0.275345i	0.346340	−	0.0138893i
$394$	−10.4018	+	1.65927i	−0.524033	+	0.0835926i
$395$	−4.02611	+	15.0256i	−0.202576	+	0.756022i
$396$	9.98366	−	24.3665i	0.501698	−	1.22447i
$397$	−21.1734	+	5.67340i	−1.06266	+	0.284740i	−0.747476	−	0.664289i	$-0.768734\pi$
$397$	−21.1734	+	5.67340i	−1.06266	+	0.284740i	−0.315188	+	0.949029i	$0.602068\pi$
$398$	0.790301	−	7.60003i	0.0396142	−	0.380955i
$399$	9.44600	+	0.337009i	0.472891	+	0.0168715i
$400$	−12.7559	+	28.9947i	−0.637797	+	1.44974i
$401$	27.0897	+	15.6403i	1.35280	+	0.781037i	0.988640	−	0.150301i	$-0.0480243\pi$
$401$	27.0897	+	15.6403i	1.35280	+	0.781037i	0.364156	+	0.931338i	$0.381358\pi$
$402$	32.4520	−	16.0810i	1.61856	−	0.802047i
$403$	−14.5389	−	3.89570i	−0.724236	−	0.194058i
$404$	29.8613	−	1.63118i	1.48566	−	0.0811545i
$405$	−26.2324	−	18.9291i	−1.30350	−	0.940596i
$406$	−1.86932	+	0.154459i	−0.0927726	+	0.00766567i
$407$	17.9138			0.887955
$408$	0.233526	−	26.0584i	0.0115613	−	1.29008i
$409$	1.88900	+	3.27185i	0.0934052	+	0.161782i	0.908942	−	0.416923i	$-0.136891\pi$
$409$	1.88900	+	3.27185i	0.0934052	+	0.161782i	−0.815537	+	0.578705i	$0.803558\pi$
$410$	−6.82234	+	17.8317i	−0.336931	+	0.880645i
$411$	−2.78940	+	0.868615i	−0.137591	+	0.0428456i
$412$	−4.13104	−	0.868538i	−0.203522	−	0.0427898i
$413$	18.8051	+	6.60014i	0.925341	+	0.324772i
$414$	−4.86779	−	0.114175i	−0.239239	−	0.00561138i
$415$	15.4218	−	26.7113i	0.757026	−	1.31121i
$416$	6.75285	+	6.67860i	0.331086	+	0.327445i
$417$	6.37914	+	10.0922i	0.312388	+	0.494215i
$418$	−10.3652	−	7.51325i	−0.506978	−	0.367485i
$419$	15.4804	−	15.4804i	0.756268	−	0.756268i	−0.219373	−	0.975641i	$-0.570401\pi$
$419$	15.4804	−	15.4804i	0.756268	−	0.756268i	0.975641	+	0.219373i	$0.0704013\pi$
$420$	−9.12627	−	31.6531i	−0.445316	−	1.54451i
$421$	3.12685	+	3.12685i	0.152393	+	0.152393i	0.779186	−	0.626793i	$-0.215633\pi$
$421$	3.12685	+	3.12685i	0.152393	+	0.152393i	−0.626793	+	0.779186i	$0.715633\pi$
$422$	−31.2114	+	4.97879i	−1.51935	+	0.242364i
$423$	22.8744	−	15.7759i	1.11219	−	0.767050i
$424$	9.37859	−	14.5472i	0.455465	−	0.706473i
$425$	36.4813	+	21.0625i	1.76960	+	1.02168i
$426$	−1.33493	+	1.17524i	−0.0646776	+	0.0569405i
$427$	1.59893	+	8.49446i	0.0773778	+	0.411076i
$428$	−6.19978	+	4.04570i	−0.299678	+	0.195556i
$429$	12.1855	−	3.79455i	0.588322	−	0.183203i
$430$	17.2262	+	38.5759i	0.830723	+	1.86030i
$431$	−13.0674	+	7.54448i	−0.629436	+	0.363405i	−0.780534	−	0.625114i	$-0.785053\pi$
$431$	−13.0674	+	7.54448i	−0.629436	+	0.363405i	0.151098	+	0.988519i	$0.451719\pi$
$432$	0.673558	−	20.7737i	0.0324066	−	0.999475i
$433$			23.9322i			1.15011i	0.818116	+	0.575053i	$0.195019\pi$
$433$			23.9322i			1.15011i	−0.818116	+	0.575053i	$0.804981\pi$
$434$	−5.98416	+	33.0058i	−0.287249	+	1.58433i
$435$	2.11658	−	2.29343i	0.101482	−	0.109962i
$436$	0.194497	+	3.56056i	0.00931470	+	0.170520i
$437$	−0.612669	+	2.28651i	−0.0293079	+	0.109379i
$438$	−29.4856	−	9.94600i	−1.40888	−	0.475238i
$439$	9.21861	−	15.9671i	0.439980	−	0.762068i	−0.557707	−	0.830038i	$-0.688319\pi$
$439$	9.21861	−	15.9671i	0.439980	−	0.762068i	0.997687	+	0.0679695i	$0.0216521\pi$
$440$	−13.6467	+	42.4791i	−0.650580	+	2.02511i
$441$	17.3920	+	11.7694i	0.828191	+	0.560445i
$442$	9.80681	−	7.95937i	0.466462	−	0.378588i
$443$	2.76775	+	10.3294i	0.131500	+	0.490765i	0.999988	−	0.00494598i	$-0.00157436\pi$
$443$	2.76775	+	10.3294i	0.131500	+	0.490765i	−0.868488	+	0.495711i	$0.834908\pi$
$444$	13.2508	−	4.93404i	0.628855	−	0.234159i
$445$	40.1209	+	10.7504i	1.90191	+	0.509616i
$446$	−2.21557	+	3.05657i	−0.104910	+	0.144733i
$447$	1.20303	−	0.0482453i	0.0569014	−	0.00228192i
$448$	13.5938	−	16.2237i	0.642249	−	0.766496i
$449$			17.8185i			0.840905i	0.907315	+	0.420453i	$0.138129\pi$
$449$			17.8185i			0.840905i	−0.907315	+	0.420453i	$0.861871\pi$
$450$	28.6949	+	17.4767i	1.35269	+	0.823861i
$451$	−4.26641	+	15.9224i	−0.200897	+	0.749759i
$452$	1.30747	−	0.428023i	0.0614984	−	0.0201325i
$453$	−6.97009	−	22.3832i	−0.327483	−	1.05165i
$454$	13.1838	+	16.2438i	0.618745	+	0.762361i
$455$	9.00661	−	13.1835i	0.422236	−	0.618053i
$456$	−9.73649	−	2.70263i	−0.455953	−	0.126562i
$457$	−11.8432	−	6.83768i	−0.554002	−	0.319853i	0.196732	−	0.980457i	$-0.436967\pi$
$457$	−11.8432	−	6.83768i	−0.554002	−	0.319853i	−0.750735	+	0.660604i	$0.770300\pi$
$458$	1.85147	−	4.83923i	0.0865134	−	0.226122i
$459$	−27.3638	−	3.89955i	−1.27723	−	0.182015i
$460$	8.23788	−	0.449997i	0.384093	−	0.0209812i
$461$	−22.8110	+	22.8110i	−1.06242	+	1.06242i	−0.0644977	+	0.997918i	$0.520545\pi$
$461$	−22.8110	+	22.8110i	−1.06242	+	1.06242i	−0.997918	+	0.0644977i	$0.979455\pi$
$462$	−10.6639	−	26.3676i	−0.496131	−	1.22673i
$463$	38.7273			1.79981			0.899904	−	0.436088i	$-0.143636\pi$
$463$	38.7273			1.79981			0.899904	+	0.436088i	$0.143636\pi$
$464$	1.98187	+	0.304919i	0.0920061	+	0.0141555i
$465$	−29.8204	−	47.1775i	−1.38289	−	2.18781i
$466$	−25.7926	+	11.5178i	−1.19482	+	0.533551i
$467$	−2.31548	−	8.64150i	−0.107148	−	0.399881i	0.891432	−	0.453154i	$-0.149701\pi$
$467$	−2.31548	−	8.64150i	−0.107148	−	0.399881i	−0.998580	+	0.0532732i	$0.983035\pi$
$468$	7.96846	−	6.16310i	0.368342	−	0.284890i
$469$	12.9553	−	36.9122i	0.598219	−	1.70445i
$470$	−36.5566	+	29.6700i	−1.68623	+	1.36857i
$471$	−9.77282	−	5.13161i	−0.450308	−	0.236452i
$472$	−17.9069	−	11.5446i	−0.824234	−	0.531385i
$473$	18.2381	+	31.5893i	0.838589	+	1.45248i
$474$	2.08809	+	10.3933i	0.0959091	+	0.477382i
$475$	11.5499	−	11.5499i	0.529946	−	0.529946i
$476$	−19.4774	−	20.3202i	−0.892746	−	0.931374i
$477$	−13.9791	−	11.9001i	−0.640058	−	0.544866i
$478$	21.0599	−	29.0540i	0.963259	−	1.32890i
$479$	0.344450	+	0.596605i	0.0157383	+	0.0272596i	0.873787	−	0.486308i	$-0.161657\pi$
$479$	0.344450	+	0.596605i	0.0157383	+	0.0272596i	−0.858049	+	0.513568i	$0.828323\pi$
$480$	1.60568	+	35.1804i	0.0732890	+	1.60576i
$481$	5.93495	+	3.42654i	0.270610	+	0.156237i
$482$	−23.5580	−	2.44972i	−1.07304	−	0.111582i
$483$	−3.84909	+	3.58390i	−0.175140	+	0.163073i
$484$	−3.39944	+	16.1688i	−0.154520	+	0.734947i
$485$	−2.14378	−	8.00071i	−0.0973442	−	0.363294i
$486$	−21.7460	−	3.62112i	−0.986417	−	0.164258i
$487$	−21.9107	+	12.6501i	−0.992867	+	0.573232i	−0.906130	−	0.422999i	$-0.860977\pi$
$487$	−21.9107	+	12.6501i	−0.992867	+	0.573232i	−0.0867368	+	0.996231i	$0.527644\pi$
$488$	0.452997	−	9.22932i	0.0205062	−	0.417792i
$489$	17.9397	−	0.719440i	0.811263	−	0.0325342i
$490$	−30.9334	−	17.5842i	−1.39743	−	0.794374i
$491$	20.9262	−	20.9262i	0.944385	−	0.944385i	−0.0541481	−	0.998533i	$-0.517244\pi$
$491$	20.9262	−	20.9262i	0.944385	−	0.944385i	0.998533	+	0.0541481i	$0.0172443\pi$
$492$	1.22970	+	12.9529i	0.0554393	+	0.583962i
$493$	0.690164	−	2.57573i	0.0310834	−	0.116005i
$494$	−1.99691	−	4.47183i	−0.0898453	−	0.201197i
$495$	42.7468	+	20.3041i	1.92133	+	0.912599i
$496$	14.4405	−	32.8239i	0.648399	−	1.47383i
$497$	−0.145369	+	1.91554i	−0.00652068	+	0.0859238i
$498$	1.33453	−	20.9771i	0.0598015	−	0.940008i
$499$	4.35543	+	16.2547i	0.194976	+	0.727660i	0.992273	+	0.124073i	$0.0395958\pi$
$499$	4.35543	+	16.2547i	0.194976	+	0.727660i	−0.797297	+	0.603587i	$0.793738\pi$
$500$	−18.7186	−	9.48554i	−0.837122	−	0.424206i
$501$	8.30388	+	1.87189i	0.370990	+	0.0836299i
$502$	4.64631	+	29.1272i	0.207375	+	1.30001i
$503$			7.13375i			0.318078i	0.987272	+	0.159039i	$0.0508396\pi$
$503$			7.13375i			0.318078i	−0.987272	+	0.159039i	$0.949160\pi$
$504$	−15.1506	−	16.5668i	−0.674860	−	0.737946i
$505$			53.7456i			2.39165i
$506$	7.03421	−	1.12208i	0.312709	−	0.0498826i
$507$	−17.2025	−	3.87786i	−0.763991	−	0.172222i
$508$	5.41453	+	16.5397i	0.240231	+	0.733830i
$509$	−9.34115	−	34.8617i	−0.414039	−	1.54522i	−0.786752	−	0.617269i	$-0.788239\pi$
$509$	−9.34115	−	34.8617i	−0.414039	−	1.54522i	0.372713	−	0.927947i	$-0.378428\pi$
$510$	46.7386	+	2.97342i	2.06962	+	0.131665i
$511$	−30.2964	+	14.5547i	−1.34023	+	0.643864i
$512$	−18.1727	+	13.4816i	−0.803128	+	0.595806i
$513$	−4.20670	+	9.85748i	−0.185730	+	0.435219i
$514$	7.01051	−	3.13057i	0.309220	−	0.138084i
$515$	1.96352	−	7.32797i	0.0865231	−	0.322909i
$516$	22.1914	+	18.3432i	0.976922	+	0.807514i
$517$	−28.7440	+	28.7440i	−1.26416	+	1.26416i
$518$	6.52116	−	13.8103i	0.286523	−	0.606790i
$519$	−26.9797	+	1.08197i	−1.18428	+	0.0474933i
$520$	−12.6466	+	11.4632i	−0.554590	+	0.502696i
$521$	30.7455	−	17.7509i	1.34698	−	0.777682i	0.359163	−	0.933275i	$-0.383062\pi$
$521$	30.7455	−	17.7509i	1.34698	−	0.777682i	0.987821	+	0.155593i	$0.0497289\pi$
$522$	0.598484	−	2.04089i	0.0261949	−	0.0893271i
$523$	−0.273382	−	1.02027i	−0.0119541	−	0.0446135i	0.959691	−	0.281057i	$-0.0906849\pi$
$523$	−0.273382	−	1.02027i	−0.0119541	−	0.0446135i	−0.971645	+	0.236443i	$0.924018\pi$
$524$	−6.64482	+	4.33612i	−0.290280	+	0.189424i
$525$	35.3662	−	8.13678i	1.54351	−	0.355118i
$526$	−0.633839	+	6.09539i	−0.0276367	+	0.265772i
$527$	−41.2991	−	23.8440i	−1.79902	−	1.03866i
$528$	4.52051	+	30.0683i	0.196730	+	1.30855i
$529$	10.8414	+	18.7779i	0.471367	+	0.816431i
$530$	25.1854	+	18.2557i	1.09398	+	0.792979i
$531$	−14.6485	+	17.2076i	−0.635689	+	0.746748i
$532$	−9.56542	+	5.25579i	−0.414714	+	0.227867i
$533$	−4.45912	+	4.45912i	−0.193146	+	0.193146i
$534$	27.7519	−	5.57553i	1.20094	−	0.241277i
$535$	−6.65223	−	11.5220i	−0.287601	−	0.498139i
$536$	−22.6607	+	35.1492i	−0.978795	+	1.51821i
$537$	12.1133	+	6.36056i	0.522727	+	0.274478i
$538$	1.63487	+	2.01434i	0.0704842	+	0.0868442i
$539$	−28.1347	−	12.3383i	−1.21185	−	0.531450i
$540$	37.2121	+	3.24502i	1.60135	+	0.139643i
$541$	−5.11081	−	19.0738i	−0.219731	−	0.820046i	−0.984447	−	0.175680i	$-0.943788\pi$
$541$	−5.11081	−	19.0738i	−0.219731	−	0.820046i	0.764717	−	0.644367i	$-0.222879\pi$
$542$	8.60826	+	19.2771i	0.369756	+	0.828022i
$543$	−20.4724	−	32.3886i	−0.878557	−	1.38993i
$544$	15.1893	+	25.9759i	0.651235	+	1.11371i
$545$	−6.40844			−0.274507
$546$	1.51055	−	10.7755i	0.0646458	−	0.461149i
$547$	−22.5845	+	22.5845i	−0.965643	+	0.965643i	−0.999429	−	0.0337857i	$-0.989244\pi$
$547$	−22.5845	+	22.5845i	−0.965643	+	0.965643i	0.0337857	+	0.999429i	$0.489244\pi$
$548$	2.25175	−	2.51197i	0.0961898	−	0.107306i
$549$	−9.63973	−	1.77043i	−0.411413	−	0.0755603i
$550$	−45.9062	−	17.5635i	−1.95745	−	0.748911i
$551$	−0.895450	−	0.516988i	−0.0381474	−	0.0220244i
$552$	4.89413	−	2.76745i	0.208308	−	0.117790i
$553$	9.45468	+	6.45918i	0.402054	+	0.274672i
$554$	15.4055	−	12.5034i	0.654517	−	0.531217i
$555$	7.55517	+	24.2620i	0.320699	+	1.02987i
$556$	−12.2974	−	6.23164i	−0.521527	−	0.264280i
$557$	10.2480	−	38.2460i	0.434221	−	1.62053i	−0.308704	−	0.951158i	$-0.599895\pi$
$557$	10.2480	−	38.2460i	0.434221	−	1.62053i	0.742924	−	0.669375i	$-0.233438\pi$
$558$	−32.4845	−	19.7848i	−1.37518	−	0.837556i
$559$			13.9543i			0.590203i
$560$	27.7806	+	25.9843i	1.17395	+	1.09804i
$561$	40.4030	−	1.62029i	1.70581	−	0.0684085i
$562$	−18.9981	−	13.7708i	−0.801385	−	0.580888i
$563$	18.0749	+	4.84315i	0.761765	+	0.204114i	0.618730	−	0.785603i	$-0.287647\pi$
$563$	18.0749	+	4.84315i	0.761765	+	0.204114i	0.143035	+	0.989718i	$0.454314\pi$
$564$	−13.3448	+	29.1789i	−0.561919	+	1.22865i
$565$	0.639916	+	2.38820i	0.0269215	+	0.100472i
$566$	7.58902	+	9.35050i	0.318990	+	0.393031i
$567$	−19.5420	+	13.6055i	−0.820688	+	0.571376i
$568$	0.628143	−	1.95527i	0.0263563	−	0.0820412i
$569$	−6.73264	+	11.6613i	−0.282247	+	0.488866i	−0.971938	−	0.235238i	$-0.924413\pi$
$569$	−6.73264	+	11.6613i	−0.282247	+	0.488866i	0.689691	+	0.724104i	$0.257746\pi$
$570$	5.80424	−	17.2071i	0.243113	−	0.720725i
$571$	−0.307963	+	1.14933i	−0.0128879	+	0.0480981i	−0.972070	−	0.234690i	$-0.924593\pi$
$571$	−0.307963	+	1.14933i	−0.0128879	+	0.0480981i	0.959182	+	0.282788i	$0.0912592\pi$
$572$	−9.83677	+	10.9735i	−0.411296	+	0.458827i
$573$	−8.40182	+	9.10386i	−0.350991	+	0.380319i
$574$	10.7220	+	9.08535i	0.447528	+	0.379215i
$575$			9.08854i			0.379018i
$576$	11.6256	+	20.9963i	0.484399	+	0.874847i
$577$	4.52479	−	2.61239i	0.188370	−	0.108755i	−0.402849	−	0.915266i	$-0.631980\pi$
$577$	4.52479	−	2.61239i	0.188370	−	0.108755i	0.591219	+	0.806511i	$0.298647\pi$
$578$	14.5863	−	6.51356i	0.606709	−	0.270928i
$579$	−13.0914	+	4.07663i	−0.544059	+	0.169419i
$580$	−0.741446	+	3.52655i	−0.0307869	+	0.146432i
$581$	−14.7931	−	17.2227i	−0.613720	−	0.714519i
$582$	−3.72996	−	4.23679i	−0.154612	−	0.175621i
$583$	23.2585	+	13.4283i	0.963270	+	0.556144i
$584$	35.1217	−	7.58718i	1.45335	−	0.313960i
$585$	10.2785	+	14.9034i	0.424964	+	0.616181i
$586$	−5.14626	−	32.2613i	−0.212590	−	1.33270i
$587$	−14.4508	−	14.4508i	−0.596449	−	0.596449i	0.342917	−	0.939366i	$-0.388585\pi$
$587$	−14.4508	−	14.4508i	−0.596449	−	0.596449i	−0.939366	+	0.342917i	$0.888585\pi$
$588$	−24.2096	−	1.37744i	−0.998385	−	0.0568045i
$589$	−13.0752	+	13.0752i	−0.538755	+	0.538755i
$590$	22.4720	−	31.0021i	0.925159	−	1.27634i
$591$	−6.89278	−	10.9048i	−0.283531	−	0.448562i
$592$	−10.2187	+	12.7338i	−0.419986	+	0.523356i
$593$	−15.8229	+	27.4061i	−0.649769	+	1.12543i	0.333409	+	0.942782i	$0.391801\pi$
$593$	−15.8229	+	27.4061i	−0.649769	+	1.12543i	−0.983178	+	0.182650i	$0.941532\pi$
$594$	32.2462	−	0.536329i	1.32308	−	0.0220059i
$595$	38.3735	−	32.9601i	1.57316	−	1.35123i
$596$	−1.16429	+	0.759765i	−0.0476912	+	0.0311212i
$597$	8.93509	−	2.78237i	0.365689	−	0.113875i
$598$	2.54510	+	0.973746i	0.104077	+	0.0398194i
$599$	3.13063	+	5.42241i	0.127914	+	0.221554i	0.922868	−	0.385116i	$-0.125839\pi$
$599$	3.13063	+	5.42241i	0.127914	+	0.221554i	−0.794954	+	0.606669i	$0.792505\pi$
$600$	−38.7942	−	0.347660i	−1.58377	−	0.0141931i
$601$	30.7003			1.25229			0.626145	−	0.779706i	$-0.284632\pi$
$601$	30.7003			1.25229			0.626145	+	0.779706i	$0.284632\pi$
$602$	30.9924	−	2.56086i	1.26315	−	0.104373i
$603$	33.7765	+	28.7532i	1.37549	+	1.17092i
$604$	20.1569	+	18.0689i	0.820175	+	0.735211i
$605$	−28.6815	−	7.68519i	−1.16607	−	0.312448i
$606$	16.2627	+	32.8187i	0.660626	+	1.33317i
$607$	−10.6767	−	6.16422i	−0.433356	−	0.250198i	0.267419	−	0.963580i	$-0.413829\pi$
$607$	−10.6767	−	6.16422i	−0.433356	−	0.250198i	−0.700775	+	0.713382i	$0.747162\pi$
$608$	11.2534	−	3.08211i	0.456385	−	0.124996i
$609$	−1.07695	−	2.02915i	−0.0436404	−	0.0822255i
$610$	16.5175	+	1.71760i	0.668773	+	0.0695434i
$611$	−15.0212	+	4.02491i	−0.607691	+	0.162830i
$612$	29.4397	−	12.3268i	1.19003	−	0.498281i
$613$	7.05653	−	26.3353i	0.285010	−	1.06367i	−0.663821	−	0.747891i	$-0.731066\pi$
$613$	7.05653	−	26.3353i	0.285010	−	1.06367i	0.948832	−	0.315782i	$-0.102267\pi$
$614$	−2.89970	−	18.1779i	−0.117022	−	0.733599i
$615$	−23.3643	+	0.936983i	−0.942141	+	0.0377828i
$616$	26.1774	+	19.8336i	1.05472	+	0.799117i
$617$	48.0527			1.93453			0.967264	−	0.253772i	$-0.0816713\pi$
$617$	48.0527			1.93453			0.967264	+	0.253772i	$0.0816713\pi$
$618$	−1.01836	−	5.06880i	−0.0409642	−	0.203897i
$619$	−8.74202	−	2.34242i	−0.351371	−	0.0941497i	0.0788163	−	0.996889i	$-0.474886\pi$
$619$	−8.74202	−	2.34242i	−0.351371	−	0.0941497i	−0.430188	+	0.902739i	$0.641553\pi$
$620$	57.4864	+	29.1309i	2.30871	+	1.16992i
$621$	−2.22328	−	5.53350i	−0.0892172	−	0.222052i
$622$	−1.68849	−	0.175580i	−0.0677021	−	0.00704011i
$623$	17.2470	−	25.2455i	0.690988	−	1.01144i
$624$	−4.25377	+	10.8265i	−0.170287	+	0.433405i
$625$	−0.941352	+	1.63047i	−0.0376541	+	0.0652188i
$626$	−26.5338	+	11.8488i	−1.06051	+	0.473573i
$627$	3.44789	−	15.2951i	0.137695	−	0.610829i
$628$	12.7268	−	0.695207i	0.507856	−	0.0277418i
$629$	15.3530	+	15.3530i	0.612163	+	0.612163i
$630$	31.2141	−	25.5635i	1.24360	−	1.01848i
$631$		−	23.0668i		−	0.918275i	−0.888365	−	0.459138i	$-0.848158\pi$
$631$		−	23.0668i		−	0.918275i	0.888365	−	0.459138i	$-0.151842\pi$
$632$	−8.22096	−	9.06963i	−0.327012	−	0.360770i
$633$	−20.6824	−	32.7208i	−0.822053	−	1.30053i
$634$	−44.0262	−	16.8442i	−1.74850	−	0.668970i
$635$	−30.2110	+	8.09501i	−1.19889	+	0.321241i
$636$	20.9029	+	3.52675i	0.828852	+	0.139845i
$637$	−6.96112	−	9.46935i	−0.275810	−	0.375189i
$638$	−0.321806	+	3.09469i	−0.0127404	+	0.122520i
$639$	−1.96759	−	0.934574i	−0.0778366	−	0.0369712i
$640$	−22.4111	−	33.9322i	−0.885876	−	1.34129i
$641$	34.2865	−	19.7953i	1.35424	−	0.781868i	0.365396	−	0.930852i	$-0.380934\pi$
$641$	34.2865	−	19.7953i	1.35424	−	0.781868i	0.988840	+	0.148984i	$0.0476002\pi$
$642$	−7.54844	−	5.02280i	−0.297913	−	0.198234i
$643$	−23.6231	−	23.6231i	−0.931604	−	0.931604i	0.0662026	−	0.997806i	$-0.478912\pi$
$643$	−23.6231	−	23.6231i	−0.931604	−	0.931604i	−0.997806	+	0.0662026i	$0.978912\pi$
$644$	1.69561	−	5.83135i	0.0668165	−	0.229788i
$645$	−35.0919	+	38.0241i	−1.38174	+	1.49720i
$646$	−2.44423	−	15.3226i	−0.0961671	−	0.602861i
$647$	4.05749	−	2.34259i	0.159516	−	0.0920968i	−0.418117	−	0.908393i	$-0.637310\pi$
$647$	4.05749	−	2.34259i	0.159516	−	0.0920968i	0.577633	+	0.816296i	$0.303976\pi$
$648$	23.7047	−	9.27835i	0.931208	−	0.364488i
$649$	16.5297	−	28.6302i	0.648847	−	1.12384i
$650$	−11.8494	−	14.5998i	−0.464773	−	0.572651i
$651$	−40.0367	+	9.21135i	−1.56916	+	0.361021i
$652$	−17.3620	+	11.3297i	−0.679950	+	0.443705i
$653$	−20.9177	+	5.60487i	−0.818571	+	0.219335i	−0.643722	−	0.765260i	$-0.722611\pi$
$653$	−20.9177	+	5.60487i	−0.818571	+	0.219335i	−0.174849	+	0.984595i	$0.555944\pi$
$654$	−3.91318	+	1.93910i	−0.153017	+	0.0758250i
$655$	−7.12975	−	12.3491i	−0.278582	−	0.482519i
$656$	−8.88454	−	12.1155i	−0.346883	−	0.473030i
$657$	−3.05187	−	37.9891i	−0.119065	−	1.48210i
$658$	11.6959	+	32.6233i	0.455955	+	1.27179i
$659$	−22.1458	−	22.1458i	−0.862677	−	0.862677i	0.128971	−	0.991648i	$-0.458833\pi$
$659$	−22.1458	−	22.1458i	−0.862677	−	0.862677i	−0.991648	+	0.128971i	$0.958833\pi$
$660$	−54.4002	+	5.16456i	−2.11753	+	0.201030i
$661$	34.8139	+	9.32835i	1.35410	+	0.362831i	0.861648	−	0.507507i	$-0.169433\pi$
$661$	34.8139	+	9.32835i	1.35410	+	0.362831i	0.492455	+	0.870338i	$0.336099\pi$
$662$	33.1455	+	12.6813i	1.28824	+	0.492875i
$663$	13.6956	+	7.19144i	0.531895	+	0.279292i
$664$	11.0906	+	21.5892i	0.430399	+	0.837823i
$665$	−8.49379	−	17.6802i	−0.329375	−	0.685609i
$666$	11.9548	+	12.5290i	0.463238	+	0.485490i
$667$	0.555719	−	0.148904i	0.0215175	−	0.00576560i
$668$	−9.34129	+	3.05802i	−0.361425	+	0.118318i
$669$	−4.51035	−	1.01674i	−0.174380	−	0.0393095i
$670$	−60.8534	−	44.1099i	−2.35097	−	1.70411i
$671$	14.3380			0.553512
$672$	24.8261	+	7.46075i	0.957689	+	0.287805i
$673$	−24.5092			−0.944762			−0.472381	−	0.881394i	$-0.656605\pi$
$673$	−24.5092			−0.944762			−0.472381	+	0.881394i	$0.656605\pi$
$674$	15.4754	+	11.2174i	0.596091	+	0.432079i
$675$	−5.80541	+	40.7376i	−0.223450	+	1.56799i
$676$	19.3517	−	6.33508i	0.744294	−	0.243657i
$677$	25.2585	−	6.76799i	0.970763	−	0.260115i	0.261613	−	0.965173i	$-0.415746\pi$
$677$	25.2585	−	6.76799i	0.970763	−	0.260115i	0.709150	+	0.705058i	$0.249079\pi$
$678$	1.11339	+	1.26468i	0.0427594	+	0.0485696i
$679$	−6.07952	−	0.461370i	−0.233311	−	0.0177057i
$680$	−48.1023	+	24.7107i	−1.84464	+	0.947611i
$681$	−11.9118	+	22.6852i	−0.456460	+	0.869300i
$682$	51.9687	+	19.8830i	1.98998	+	0.761360i
$683$	1.16459	+	0.312051i	0.0445618	+	0.0119403i	0.281031	−	0.959699i	$-0.409324\pi$
$683$	1.16459	+	0.312051i	0.0445618	+	0.0119403i	−0.236469	+	0.971639i	$0.575990\pi$
$684$	−1.66238	−	12.2634i	−0.0635626	−	0.468904i
$685$	4.28696	+	4.28696i	0.163796	+	0.163796i
$686$	−19.7539	+	17.1984i	−0.754206	+	0.656637i
$687$	6.34069	−	0.254282i	0.241913	−	0.00970145i
$688$	−32.8585	−	5.05542i	−1.25272	−	0.192736i
$689$	5.13712	+	8.89775i	0.195709	+	0.338977i
$690$	4.48640	+	9.05372i	0.170794	+	0.344669i
$691$	−20.9494	+	5.61338i	−0.796953	+	0.213543i	−0.634246	−	0.773131i	$-0.718689\pi$
$691$	−20.9494	+	5.61338i	−0.796953	+	0.213543i	−0.162707	+	0.986674i	$0.552023\pi$
$692$	26.1109	−	17.0388i	0.992588	−	0.647719i
$693$	24.5227	−	24.7404i	0.931541	−	0.939812i
$694$	−19.8121	−	24.4107i	−0.752057	−	0.926616i
$695$	12.3880	−	21.4567i	0.469905	−	0.813899i
$696$	0.614337	+	2.37777i	0.0232864	+	0.0901291i
$697$	−17.3028	+	9.98976i	−0.655389	+	0.378389i
$698$	−3.04804	−	19.1078i	−0.115370	−	0.723242i
$699$	−25.4236	−	23.4631i	−0.961608	−	0.887455i
$700$	−30.2515	+	28.9968i	−1.14340	+	1.09598i
$701$	−25.7800	−	25.7800i	−0.973695	−	0.973695i	0.0259675	−	0.999663i	$-0.491733\pi$
$701$	−25.7800	−	25.7800i	−0.973695	−	0.973695i	−0.999663	+	0.0259675i	$0.991733\pi$
$702$	10.7859	+	5.99034i	0.407088	+	0.226091i
$703$	7.29108	−	4.20951i	0.274988	−	0.158765i
$704$	−22.2760	−	27.1385i	−0.839558	−	1.02282i
$705$	−51.0530	−	26.8074i	−1.92277	−	1.00962i
$706$	3.05790	−	29.4067i	0.115086	−	1.10674i
$707$	37.3293	+	13.1017i	1.40391	+	0.492738i
$708$	4.34127	−	25.7305i	0.163155	−	0.967012i
$709$	−1.78977	+	0.479566i	−0.0672161	+	0.0180105i	−0.292270	−	0.956336i	$-0.594411\pi$
$709$	−1.78977	+	0.479566i	−0.0672161	+	0.0180105i	0.225054	+	0.974346i	$0.427744\pi$
$710$	3.44713	+	1.31886i	0.129368	+	0.0494958i
$711$	−10.6881	+	7.37133i	−0.400836	+	0.276446i
$712$	−24.2174	+	21.9513i	−0.907584	+	0.822659i
$713$		−	10.2888i		−	0.385319i
$714$	13.4587	−	31.7377i	0.503681	−	1.18775i
$715$	−18.7276	−	18.7276i	−0.700373	−	0.700373i
$716$	−15.7747	+	0.861700i	−0.589529	+	0.0322032i
$717$	42.8728	+	9.66455i	1.60112	+	0.360929i
$718$	33.1181	−	14.7890i	1.23596	−	0.551922i
$719$	1.10491	−	1.91376i	0.0412061	−	0.0713711i	−0.844687	−	0.535261i	$-0.820213\pi$
$719$	1.10491	−	1.91376i	0.0412061	−	0.0713711i	0.885893	+	0.463890i	$0.153547\pi$
$720$	−38.8172	+	18.8038i	−1.44663	+	0.700776i
$721$	−4.61102	−	3.15012i	−0.171723	−	0.117317i
$722$	20.7417	+	2.15686i	0.771927	+	0.0802700i
$723$	−8.62461	−	27.6964i	−0.320753	−	1.03004i
$724$	39.4659	+	19.9991i	1.46674	+	0.743260i
$725$	−3.83459	−	1.02748i	−0.142413	−	0.0381595i
$726$	−19.8392	+	3.98582i	−0.736302	+	0.147928i
$727$	39.3777			1.46044			0.730220	−	0.683212i	$-0.239418\pi$
$727$	39.3777			1.46044			0.730220	+	0.683212i	$0.239418\pi$
$728$	4.87896	+	11.5782i	0.180826	+	0.429115i
$729$	−6.43082	−	26.2230i	−0.238178	−	0.971221i
$730$	10.1723	+	63.7691i	0.376494	+	2.36020i
$731$	−11.4426	+	42.7044i	−0.423220	+	1.57948i
$732$	10.6058	−	3.94914i	0.392001	−	0.145965i
$733$	12.0233	−	3.22163i	0.444090	−	0.118994i	−0.0298428	−	0.999555i	$-0.509501\pi$
$733$	12.0233	−	3.22163i	0.444090	−	0.118994i	0.473933	+	0.880561i	$0.342834\pi$
$734$	−6.37815	−	0.663242i	−0.235422	−	0.0244807i
$735$	4.84492	−	43.3087i	0.178707	−	1.59747i
$736$	−3.21496	+	5.64025i	−0.118505	+	0.207902i
$737$	−56.1977	−	32.4458i	−2.07007	−	1.19516i
$738$	−13.9834	+	7.64187i	−0.514737	+	0.281301i
$739$	4.88989	+	1.31024i	0.179878	+	0.0481981i	0.347633	−	0.937631i	$-0.386985\pi$
$739$	4.88989	+	1.31024i	0.179878	+	0.0481981i	−0.167756	+	0.985829i	$0.553652\pi$
$740$	−21.8489	−	19.5856i	−0.803183	−	0.719979i
$741$	4.06794	−	4.40785i	0.149440	−	0.161926i
$742$	18.8191	−	13.0424i	0.690870	−	0.478801i
$743$	−33.6542			−1.23465			−0.617327	−	0.786707i	$-0.711785\pi$
$743$	−33.6542			−1.23465			−0.617327	+	0.786707i	$0.711785\pi$
$744$	43.9175	+	0.393573i	1.61009	+	0.0144291i
$745$	−1.24926	−	2.16378i	−0.0457693	−	0.0792747i
$746$	32.9743	+	12.6158i	1.20728	+	0.461899i
$747$	24.2530	−	8.63277i	0.887370	−	0.315856i
$748$	−39.1019	+	25.5162i	−1.42971	+	0.932963i
$749$	−9.62428	+	1.81160i	−0.351664	+	0.0661945i
$750$	1.63175	−	25.6492i	0.0595832	−	0.936576i
$751$	−17.8556	+	30.9268i	−0.651559	+	1.12853i	0.331186	+	0.943566i	$0.392551\pi$
$751$	−17.8556	+	30.9268i	−0.651559	+	1.12853i	−0.982745	+	0.184968i	$0.940782\pi$
$752$	−4.03562	−	36.8289i	−0.147164	−	1.34301i
$753$	−30.5357	+	19.3013i	−1.11278	+	0.703378i
$754$	−0.698566	+	0.963732i	−0.0254403	+	0.0350971i
$755$	−34.4002	+	34.4002i	−1.25195	+	1.25195i
$756$	11.3251	−	25.0548i	0.411889	−	0.911234i
$757$	−1.46026	−	1.46026i	−0.0530740	−	0.0530740i	0.680072	−	0.733146i	$-0.261949\pi$
$757$	−1.46026	−	1.46026i	−0.0530740	−	0.0530740i	−0.733146	+	0.680072i	$0.761949\pi$
$758$	−1.45821	−	9.14138i	−0.0529647	−	0.332030i
$759$	4.66126	+	7.37437i	0.169193	+	0.267673i
$760$	4.42770	+	20.4962i	0.160609	+	0.743474i
$761$	0.655244	+	0.378306i	0.0237526	+	0.0137136i	0.511829	−	0.859087i	$-0.328968\pi$
$761$	0.655244	+	0.378306i	0.0237526	+	0.0137136i	−0.488077	+	0.872801i	$0.662301\pi$
$762$	−15.9983	+	14.0845i	−0.579556	+	0.510226i
$763$	−1.56219	+	4.45101i	−0.0565552	+	0.161137i
$764$	2.94319	−	13.9988i	0.106481	−	0.506458i
$765$	19.2344	+	54.0374i	0.695423	+	1.95373i
$766$	−30.9749	+	13.8320i	−1.11917	+	0.499769i
$767$	10.9527	−	6.32357i	0.395481	−	0.228331i
$768$	−23.9523	−	13.9387i	−0.864304	−	0.502970i
$769$			1.88931i			0.0681304i	0.999420	+	0.0340652i	$0.0108454\pi$
$769$			1.88931i			0.0681304i	−0.999420	+	0.0340652i	$0.989155\pi$
$770$	−38.1571	+	45.0308i	−1.37509	+	1.62280i
$771$	6.91022	+	6.37735i	0.248865	+	0.229675i
$772$	10.5680	−	11.7893i	0.380351	−	0.424306i
$773$	0.725893	−	2.70907i	0.0261086	−	0.0974385i	−0.951642	−	0.307209i	$-0.900605\pi$
$773$	0.725893	−	2.70907i	0.0261086	−	0.0974385i	0.977751	+	0.209770i	$0.0672717\pi$
$774$	−9.92259	+	33.8369i	−0.356660	+	1.21624i
$775$	−35.4976	+	61.4836i	−1.27511	+	2.20856i
$776$	6.20561	+	1.99359i	0.222768	+	0.0715658i
$777$	18.6931	+	0.666919i	0.670610	+	0.0239256i
$778$	29.7312	+	36.6321i	1.06592	+	1.31332i
$779$	2.00510	+	7.48313i	0.0718401	+	0.268111i
$780$	−19.0110	−	8.69459i	−0.680702	−	0.311316i
$781$	3.07804	+	0.824759i	0.110141	+	0.0295122i
$782$	6.99031	+	5.06696i	0.249973	+	0.181194i
$783$	2.58601	−	0.312462i	0.0924166	−	0.0111665i
$784$	24.8196	−	12.9609i	0.886416	−	0.462890i
$785$			22.9063i			0.817559i
$786$	−8.09029	−	5.38335i	−0.288571	−	0.192018i
$787$	7.85594	−	29.3188i	0.280034	−	1.04510i	−0.672358	−	0.740226i	$-0.734719\pi$
$787$	7.85594	−	29.3188i	0.280034	−	1.04510i	0.952392	−	0.304875i	$-0.0986147\pi$
$788$	13.2876	+	6.73341i	0.473351	+	0.239868i
$789$	−7.16614	+	2.23153i	−0.255121	+	0.0794444i
$790$	17.0812	−	13.8634i	0.607721	−	0.493236i
$791$	1.81473	+	0.137718i	0.0645244	+	0.00489670i
$792$	−31.6557	+	19.6144i	−1.12483	+	0.696967i
$793$	4.75026	+	2.74256i	0.168687	+	0.0973912i
$794$	28.9533	+	11.0774i	1.02751	+	0.393123i
$795$	−8.37769	+	37.1642i	−0.297126	+	1.31808i
$796$	−7.21286	+	8.04640i	−0.255653	+	0.285197i
$797$	21.9677	−	21.9677i	0.778135	−	0.778135i	−0.201378	−	0.979514i	$-0.564542\pi$
$797$	21.9677	−	21.9677i	0.778135	−	0.778135i	0.979514	+	0.201378i	$0.0645420\pi$
$798$	−10.5363	−	8.22596i	−0.372983	−	0.291196i
$799$	−49.2698			−1.74304
$800$	38.6714	−	22.6129i	1.36724	−	0.799486i
$801$	19.6826	+	28.5390i	0.695451	+	1.00838i
$802$	−18.0376	−	40.3929i	−0.636930	−	1.42632i
$803$	14.4302	+	53.8542i	0.509230	+	1.90047i
$804$	−50.5059	−	8.52140i	−1.78121	−	0.300527i
$805$	10.2981	+	3.61437i	0.362959	+	0.127390i
$806$	13.4143	+	16.5279i	0.472498	+	0.582170i
$807$	−1.47713	+	2.81311i	−0.0519976	+	0.0990262i
$808$	−35.5463	−	22.9168i	−1.25051	−	0.806209i
$809$	−24.0495	−	41.6549i	−0.845535	−	1.46451i	−0.885156	−	0.465295i	$-0.845948\pi$
$809$	−24.0495	−	41.6549i	−0.845535	−	1.46451i	0.0396205	−	0.999215i	$-0.487385\pi$
$810$	14.3262	+	43.4472i	0.503373	+	1.52658i
$811$	26.9083	−	26.9083i	0.944877	−	0.944877i	−0.0536814	−	0.998558i	$-0.517096\pi$
$811$	26.9083	−	26.9083i	0.944877	−	0.944877i	0.998558	+	0.0536814i	$0.0170955\pi$
$812$	2.26864	+	1.37465i	0.0796137	+	0.0482407i
$813$	−17.5360	+	19.0013i	−0.615016	+	0.666405i
$814$	−20.5121	−	14.8683i	−0.718947	−	0.521132i
$815$	−18.6291	−	32.2665i	−0.652549	−	1.13025i
$816$	−21.8956	+	29.6442i	−0.766499	+	1.03775i
$817$	14.8461	+	8.57142i	0.519401	+	0.299876i
$818$	0.552611	−	5.31425i	0.0193216	−	0.185808i
$819$	12.8568	−	3.50595i	0.449255	−	0.122508i
$820$	22.6120	−	14.7556i	0.789644	−	0.515287i
$821$	0.905449	+	3.37918i	0.0316004	+	0.117934i	0.979924	−	0.199369i	$-0.0638893\pi$
$821$	0.905449	+	3.37918i	0.0316004	+	0.117934i	−0.948324	+	0.317303i	$0.897223\pi$
$822$	3.91492	+	1.32057i	0.136548	+	0.0460602i
$823$	1.48518	−	0.857471i	0.0517702	−	0.0298896i	−0.473891	−	0.880583i	$-0.657151\pi$
$823$	1.48518	−	0.857471i	0.0517702	−	0.0298896i	0.525662	+	0.850694i	$0.323818\pi$
$824$	4.00934	+	4.42323i	0.139672	+	0.154091i
$825$	−2.41218	−	60.1495i	−0.0839815	−	2.09414i
$826$	−16.0546	−	23.1655i	−0.558612	−	0.806030i
$827$	−5.87450	+	5.87450i	−0.204276	+	0.204276i	−0.801829	−	0.597553i	$-0.796140\pi$
$827$	−5.87450	+	5.87450i	−0.204276	+	0.204276i	0.597553	+	0.801829i	$0.296140\pi$
$828$	5.47906	+	4.17095i	0.190410	+	0.144950i
$829$	0.587294	−	2.19181i	0.0203976	−	0.0761247i	−0.954977	−	0.296680i	$-0.904120\pi$
$829$	0.587294	−	2.19181i	0.0203976	−	0.0761247i	0.975374	+	0.220556i	$0.0707871\pi$
$830$	−39.8287	+	17.7857i	−1.38247	+	0.617349i
$831$	21.5145	+	11.2970i	0.746329	+	0.391890i
$832$	−2.18913	−	13.2521i	−0.0758944	−	0.459432i
$833$	−13.5382	−	34.6873i	−0.469071	−	1.20184i
$834$	1.07200	−	16.8505i	0.0371203	−	0.583487i
$835$	−4.57190	−	17.0626i	−0.158217	−	0.590475i
$836$	5.63265	+	17.2060i	0.194809	+	0.595081i
$837$	6.57209	−	46.1175i	0.227165	−	1.59405i
$838$	−30.5743	+	4.87715i	−1.05617	+	0.168478i
$839$			45.0323i			1.55469i	0.629076	+	0.777344i	$0.283433\pi$
$839$			45.0323i			1.55469i	−0.629076	+	0.777344i	$0.716567\pi$
$840$	−15.8218	+	43.8188i	−0.545903	+	1.51189i
$841$		−	28.7487i		−	0.991334i
$842$	−0.985122	−	6.17562i	−0.0339495	−	0.212826i
$843$	6.31954	−	28.0340i	0.217656	−	0.965544i
$844$	39.8707	+	20.2042i	1.37241	+	0.695458i
$845$	9.47127	+	35.3473i	0.325822	+	1.21598i
$846$	−39.2860	−	0.921458i	−1.35068	−	0.0316804i
$847$	−12.3295	+	18.0475i	−0.423648	+	0.620118i
$848$	−22.8129	+	8.87299i	−0.783397	+	0.304700i
$849$	−6.85683	+	13.0584i	−0.235326	+	0.448163i
$850$	−24.2909	−	54.3964i	−0.833173	−	1.86578i
$851$	−1.21243	+	4.52487i	−0.0415617	+	0.155110i
$852$	2.50398	−	0.237719i	0.0857851	−	0.00814413i
$853$	−19.3306	+	19.3306i	−0.661867	+	0.661867i	−0.955820	−	0.293953i	$-0.905029\pi$
$853$	−19.3306	+	19.3306i	−0.661867	+	0.661867i	0.293953	+	0.955820i	$0.405029\pi$
$854$	5.21946	−	11.0536i	0.178606	−	0.378246i
$855$	22.1695	−	1.78100i	0.758181	−	0.0609088i
$856$	10.4569	+	0.513249i	0.357409	+	0.0175425i
$857$	−22.6727	+	13.0901i	−0.774484	+	0.447148i	−0.834472	−	0.551051i	$-0.814227\pi$
$857$	−22.6727	+	13.0901i	−0.774484	+	0.447148i	0.0599880	+	0.998199i	$0.480894\pi$
$858$	−17.1024	−	5.76892i	−0.583865	−	0.196948i
$859$	7.46406	+	27.8562i	0.254670	+	0.950443i	0.968274	+	0.249893i	$0.0803953\pi$
$859$	7.46406	+	27.8562i	0.254670	+	0.950443i	−0.713603	+	0.700550i	$0.752938\pi$
$860$	12.2928	−	58.4686i	0.419182	−	1.99376i
$861$	−5.04477	+	16.4562i	−0.171925	+	0.560827i
$862$	21.2246	+	2.20707i	0.722912	+	0.0751731i
$863$	32.4823	+	18.7537i	1.10571	+	0.638383i	0.937715	−	0.347405i	$-0.112937\pi$
$863$	32.4823	+	18.7537i	1.10571	+	0.638383i	0.167996	+	0.985788i	$0.446270\pi$
$864$	−18.0132	+	23.2277i	−0.612821	+	0.790222i
$865$	28.0164	+	48.5259i	0.952587	+	1.64993i
$866$	19.8634	−	27.4033i	0.674987	−	0.931203i
$867$	14.3776	+	13.2689i	0.488288	+	0.450635i
$868$	34.2465	−	32.8262i	1.16240	−	1.11419i
$869$	13.4307	−	13.4307i	0.455605	−	0.455605i
$870$	−4.32709	+	0.869341i	−0.146702	+	0.0294734i
$871$	−12.4124	−	21.4989i	−0.420578	−	0.728463i
$872$	2.73252	−	4.23842i	0.0925346	−	0.143531i
$873$	2.96614	−	6.24472i	0.100389	−	0.211352i
$874$	2.59931	−	2.10964i	0.0879230	−	0.0713597i
$875$	−18.0878	−	21.0586i	−0.611480	−	0.711911i
$876$	25.5071	+	35.8613i	0.861807	+	1.21164i
$877$	−0.706320	−	2.63602i	−0.0238507	−	0.0890121i	0.952975	−	0.303050i	$-0.0980050\pi$
$877$	−0.706320	−	2.63602i	−0.0238507	−	0.0890121i	−0.976825	+	0.214038i	$0.931338\pi$
$878$	−23.8082	+	10.6317i	−0.803488	+	0.358801i
$879$	33.8214	−	21.3781i	1.14077	−	0.721066i
$880$	50.8832	−	37.3137i	1.71527	−	1.25784i
$881$	37.3777			1.25929			0.629643	−	0.776884i	$-0.283201\pi$
$881$	37.3777			1.25929			0.629643	+	0.776884i	$0.283201\pi$
$882$	−10.1462	−	27.9116i	−0.341639	−	0.939831i
$883$	22.9358	−	22.9358i	0.771851	−	0.771851i	−0.206579	−	0.978430i	$-0.566233\pi$
$883$	22.9358	−	22.9358i	0.771851	−	0.771851i	0.978430	+	0.206579i	$0.0662329\pi$
$884$	−17.8354	+	0.974264i	−0.599869	+	0.0327680i
$885$	45.7475	+	10.3126i	1.53779	+	0.346654i
$886$	5.40409	−	14.1248i	0.181554	−	0.474532i
$887$	30.3724	+	17.5355i	1.01981	+	0.588786i	0.914048	−	0.405606i	$-0.132940\pi$
$887$	30.3724	+	17.5355i	1.01981	+	0.588786i	0.105759	+	0.994392i	$0.466273\pi$
$888$	−19.2679	−	5.34834i	−0.646589	−	0.179478i
$889$	−1.74215	+	22.9565i	−0.0584298	+	0.769937i
$890$	−37.0174	−	45.6095i	−1.24083	−	1.52883i
$891$	16.1827	+	36.0316i	0.542140	+	1.20710i
$892$	5.07383	−	1.66100i	0.169884	−	0.0556144i
$893$	−4.94460	+	18.4535i	−0.165465	+	0.617523i
$894$	−1.41756	−	0.943259i	−0.0474104	−	0.0315473i
$895$		−	28.3920i		−	0.949040i
$896$	−29.0310	+	7.29403i	−0.969857	+	0.243676i
$897$	0.133735	+	3.33477i	0.00446527	+	0.111345i
$898$	14.7891	−	20.4029i	0.493519	−	0.680853i
$899$	4.34100	+	1.16317i	0.144780	+	0.0387938i
$900$	−18.3514	−	43.8280i	−0.611713	−	1.46093i
$901$	8.42494	+	31.4423i	0.280675	+	1.04749i
$902$	18.1007	−	14.6908i	0.602686	−	0.489150i
$903$	17.8554	+	33.6424i	0.594190	+	1.11955i
$904$	−1.85237	−	0.595085i	−0.0616088	−	0.0197922i
$905$	−39.7567	+	68.8606i	−1.32156	+	2.28901i
$906$	−10.5967	+	31.4148i	−0.352053	+	1.04369i
$907$	2.39707	−	8.94598i	0.0795934	−	0.297047i	−0.914642	−	0.404264i	$-0.867528\pi$
$907$	2.39707	−	8.94598i	0.0795934	−	0.297047i	0.994236	+	0.107218i	$0.0341942\pi$
$908$	−1.61375	−	29.5422i	−0.0535543	−	0.980393i
$909$	−29.0780	+	34.1581i	−0.964457	+	1.13295i
$910$	−21.2551	+	7.62028i	−0.704600	+	0.252610i
$911$		−	9.81518i		−	0.325191i	−0.986693	−	0.162596i	$-0.948013\pi$
$911$		−	9.81518i		−	0.325191i	0.986693	−	0.162596i	$-0.0519866\pi$
$912$	8.90553	+	11.1758i	0.294892	+	0.370068i
$913$	−32.6152	+	18.8304i	−1.07940	+	0.623194i
$914$	7.88577	+	17.6592i	0.260838	+	0.584113i
$915$	6.04706	+	19.4190i	0.199910	+	0.641974i
$916$	−6.13651	+	4.00441i	−0.202756	+	0.132310i
$917$	−10.3151	+	1.94165i	−0.340636	+	0.0641188i
$918$	28.0961	+	27.1768i	0.927309	+	0.896967i
$919$	−34.2959	−	19.8007i	−1.13132	−	0.653166i	−0.187051	−	0.982350i	$-0.559893\pi$
$919$	−34.2959	−	19.8007i	−1.13132	−	0.653166i	−0.944266	+	0.329184i	$0.893226\pi$
$920$	−9.80620	−	6.32208i	−0.323301	−	0.208433i
$921$	19.0569	−	12.0457i	0.627947	−	0.396918i
$922$	45.0525	−	7.18668i	1.48372	−	0.236681i
$923$	0.862013	+	0.862013i	0.0283735	+	0.0283735i
$924$	−9.67415	+	39.0429i	−0.318256	+	1.28442i
$925$	22.8566	−	22.8566i	0.751519	−	0.751519i
$926$	−44.3443	−	32.1432i	−1.45724	−	1.05629i
$927$	5.21257	−	3.59497i	0.171203	−	0.118074i
$928$	−2.01625	−	1.99408i	−0.0661865	−	0.0654588i
$929$	4.36606	−	7.56224i	0.143246	−	0.248109i	−0.785471	−	0.618898i	$-0.787579\pi$
$929$	4.36606	−	7.56224i	0.143246	−	0.248109i	0.928717	+	0.370789i	$0.120913\pi$
$930$	−5.01125	+	78.7708i	−0.164325	+	2.58300i
$931$	−14.3504	+	1.58947i	−0.470316	+	0.0520928i
$932$	39.0932	+	8.21921i	1.28054	+	0.269229i
$933$	−0.618155	−	1.98509i	−0.0202375	−	0.0649891i
$934$	−4.52102	+	11.8167i	−0.147932	+	0.386654i
$935$	−41.9555	−	72.6690i	−1.37209	−	2.37653i
$936$	−14.2395	+	0.443280i	−0.465433	+	0.0144891i
$937$	17.9874			0.587623			0.293811	−	0.955863i	$-0.405076\pi$
$937$	17.9874			0.587623			0.293811	+	0.955863i	$0.405076\pi$
$938$	−45.4711	+	31.5133i	−1.48468	+	1.02895i
$939$	−26.1542	−	24.1374i	−0.853512	−	0.787694i
$940$	66.4846	−	3.63174i	2.16849	−	0.118454i
$941$	23.0907	+	6.18713i	0.752735	+	0.201695i	0.614731	−	0.788737i	$-0.289265\pi$
$941$	23.0907	+	6.18713i	0.752735	+	0.201695i	0.138004	+	0.990432i	$0.455931\pi$
$942$	6.93111	+	13.9872i	0.225828	+	0.455729i
$943$	−3.73311	−	2.15531i	−0.121567	−	0.0701866i
$944$	10.9223	+	28.0817i	0.355490	+	0.913980i
$945$	43.8503	+	22.7787i	1.42645	+	0.740991i
$946$	5.33539	−	51.3085i	0.173469	−	1.66818i
$947$	7.49923	−	2.00941i	0.243692	−	0.0652971i	−0.134905	−	0.990858i	$-0.543073\pi$
$947$	7.49923	−	2.00941i	0.243692	−	0.0652971i	0.378598	+	0.925561i	$0.376406\pi$
$948$	6.23541	−	13.6339i	0.202517	−	0.442808i
$949$	−5.52039	+	20.6024i	−0.179200	+	0.668782i
$950$	−22.8114	+	3.63883i	−0.740100	+	0.118059i
$951$	−2.31340	−	57.6862i	−0.0750170	−	1.87060i
$952$	5.43694	+	39.4335i	0.176212	+	1.27805i
$953$	40.5352			1.31306			0.656531	−	0.754299i	$-0.272023\pi$
$953$	40.5352			1.31306			0.656531	+	0.754299i	$0.272023\pi$
$954$	6.12970	+	25.2285i	0.198456	+	0.816803i
$955$	24.8321	+	6.65374i	0.803548	+	0.215310i
$956$	−48.2290	+	15.7885i	−1.55984	+	0.510638i
$957$	−3.63832	+	1.13297i	−0.117610	+	0.0366236i
$958$	0.100766	−	0.969027i	0.00325559	−	0.0313078i
$959$	4.02257	−	1.93249i	0.129896	−	0.0624034i
$960$	27.3608	−	41.6157i	0.883065	−	1.34314i
$961$	24.6855	−	42.7565i	0.796305	−	1.37924i
$962$	−3.95177	−	8.84947i	−0.127410	−	0.285318i
$963$	2.00592	−	10.9219i	0.0646397	−	0.351953i
$964$	24.9417	+	22.3579i	0.803317	+	0.720100i
$965$	20.1198	+	20.1198i	0.647679	+	0.647679i
$966$	7.38196	−	0.909013i	0.237511	−	0.0292470i
$967$		−	54.5781i		−	1.75511i	−0.479474	−	0.877556i	$-0.659172\pi$
$967$		−	54.5781i		−	1.75511i	0.479474	−	0.877556i	$-0.340828\pi$
$968$	17.3125	−	15.6925i	0.556443	−	0.504376i
$969$	16.0636	−	10.1536i	0.516038	−	0.326181i
$970$	−4.18578	+	10.9405i	−0.134397	+	0.351277i
$971$	28.0159	−	7.50683i	0.899072	−	0.240906i	0.220454	−	0.975397i	$-0.429246\pi$
$971$	28.0159	−	7.50683i	0.899072	−	0.240906i	0.678618	+	0.734492i	$0.262579\pi$
$972$	21.8945	+	22.1952i	0.702268	+	0.711913i
$973$	−11.8830	−	13.8347i	−0.380952	−	0.443520i
$974$	35.5881	+	3.70068i	1.14032	+	0.118577i
$975$	10.7062	−	20.3893i	0.342872	−	0.652979i
$976$	−8.17893	+	10.1920i	−0.261801	+	0.326237i
$977$	−20.1250	+	11.6191i	−0.643854	+	0.371729i	−0.786098	−	0.618102i	$-0.787902\pi$
$977$	−20.1250	+	11.6191i	−0.643854	+	0.371729i	0.142243	+	0.989832i	$0.454568\pi$
$978$	−21.1389	−	14.0660i	−0.675947	−	0.449781i
$979$	−35.8621	−	35.8621i	−1.14616	−	1.14616i
$980$	20.8253	+	45.8090i	0.665239	+	1.46331i
$981$	−4.07289	−	3.46716i	−0.130037	−	0.110698i
$982$	−41.3298	+	6.59285i	−1.31889	+	0.210386i
$983$	2.87845	−	1.66187i	0.0918082	−	0.0530055i	−0.453393	−	0.891311i	$-0.649787\pi$
$983$	2.87845	−	1.66187i	0.0918082	−	0.0530055i	0.545201	+	0.838305i	$0.316453\pi$
$984$	9.34270	−	15.8522i	0.297834	−	0.505351i
$985$	−13.3855	+	23.1844i	−0.426498	+	0.738716i
$986$	−2.92809	+	2.37649i	−0.0932494	+	0.0756827i
$987$	−31.0644	+	28.9242i	−0.988792	+	0.920668i
$988$	−1.42502	+	6.77784i	−0.0453358	+	0.215632i
$989$	−9.21356	+	2.46877i	−0.292974	+	0.0785022i
$990$	−32.0947	−	58.7283i	−1.02004	−	1.86651i
$991$	−10.2091	−	17.6827i	−0.324303	−	0.561710i	0.657068	−	0.753831i	$-0.271796\pi$
$991$	−10.2091	−	17.6827i	−0.324303	−	0.561710i	−0.981371	+	0.192122i	$0.938463\pi$
$992$	−43.7784	+	25.5992i	−1.38997	+	0.812775i
$993$	1.74166	+	43.4296i	0.0552700	+	1.37820i
$994$	1.75633	−	2.07272i	0.0557074	−	0.0657427i
$995$	−13.7321	−	13.7321i	−0.435338	−	0.435338i
$996$	−18.9389	+	22.9120i	−0.600101	+	0.725996i
$997$	−8.68030	−	2.32588i	−0.274908	−	0.0736613i	0.118731	−	0.992926i	$-0.462117\pi$
$997$	−8.68030	−	2.32588i	−0.274908	−	0.0736613i	−0.393639	+	0.919265i	$0.628784\pi$
$998$	8.50406	−	22.2273i	0.269191	−	0.703592i
$999$	−8.32481	+	19.5074i	−0.263385	+	0.617185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.5.13	✓	240
3.2	odd	2	inner	336.2.bo.a.5.48	yes	240
7.3	odd	6	inner	336.2.bo.a.101.53	yes	240
16.13	even	4	inner	336.2.bo.a.173.8	yes	240
21.17	even	6	inner	336.2.bo.a.101.8	yes	240
48.29	odd	4	inner	336.2.bo.a.173.53	yes	240
112.45	odd	12	inner	336.2.bo.a.269.48	yes	240
336.269	even	12	inner	336.2.bo.a.269.13	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.13	✓	240	1.1	even	1	trivial
336.2.bo.a.5.48	yes	240	3.2	odd	2	inner
336.2.bo.a.101.8	yes	240	21.17	even	6	inner
336.2.bo.a.101.53	yes	240	7.3	odd	6	inner
336.2.bo.a.173.8	yes	240	16.13	even	4	inner
336.2.bo.a.173.53	yes	240	48.29	odd	4	inner
336.2.bo.a.269.13	yes	240	336.269	even	12	inner
336.2.bo.a.269.48	yes	240	112.45	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14504 - 0.829988i) q^{2} +(0.380888 - 1.68965i) q^{3} +(0.622238 + 1.90074i) q^{4} +(-3.47185 + 0.930279i) q^{5} +(-1.83852 + 1.61859i) q^{6} +(-0.200208 + 2.63817i) q^{7} +(0.865105 - 2.69288i) q^{8} +(-2.70985 - 1.28714i) q^{9} +O(q^{10})\)	\(q+(-1.14504 - 0.829988i) q^{2} +(0.380888 - 1.68965i) q^{3} +(0.622238 + 1.90074i) q^{4} +(-3.47185 + 0.930279i) q^{5} +(-1.83852 + 1.61859i) q^{6} +(-0.200208 + 2.63817i) q^{7} +(0.865105 - 2.69288i) q^{8} +(-2.70985 - 1.28714i) q^{9} +(4.74753 + 1.81639i) q^{10} +(4.23921 + 1.13589i) q^{11} +(3.44860 - 0.327397i) q^{12} +(1.18720 + 1.18720i) q^{13} +(2.41889 - 2.85464i) q^{14} +(0.249464 + 6.22055i) q^{15} +(-3.22564 + 2.36543i) q^{16} +(2.65968 + 4.60671i) q^{17} +(2.03458 + 3.72297i) q^{18} +(1.99232 - 0.533840i) q^{19} +(-3.92854 - 6.02023i) q^{20} +(4.38133 + 1.34313i) q^{21} +(-3.91129 - 4.81914i) q^{22} +(-0.573833 + 0.993907i) q^{23} +(-4.22052 - 2.48741i) q^{24} +(6.85819 - 3.95958i) q^{25} +(-0.374031 - 2.34476i) q^{26} +(-3.20696 + 4.08845i) q^{27} +(-5.13905 + 1.26102i) q^{28} +(-0.354471 - 0.354471i) q^{29} +(4.87734 - 7.32984i) q^{30} +(-7.76390 + 4.48249i) q^{31} +(5.65677 - 0.0312713i) q^{32} +(3.53393 - 6.73015i) q^{33} +(0.778067 - 7.48238i) q^{34} +(-1.75914 - 9.34556i) q^{35} +(0.760340 - 5.95163i) q^{36} +(3.94267 - 1.05644i) q^{37} +(-2.72436 - 1.04233i) q^{38} +(2.45815 - 1.55377i) q^{39} +(-0.498386 + 10.1541i) q^{40} +3.75599i q^{41} +(-3.90202 - 5.17438i) q^{42} +(5.87697 + 5.87697i) q^{43} +(0.478761 + 8.76444i) q^{44} +(10.6056 + 1.94782i) q^{45} +(1.48199 - 0.661790i) q^{46} +(-4.63117 + 8.02142i) q^{47} +(2.76815 + 6.35117i) q^{48} +(-6.91983 - 1.05636i) q^{49} +(-11.1393 - 1.15834i) q^{50} +(8.79678 - 2.73930i) q^{51} +(-1.51784 + 2.99528i) q^{52} +(5.91091 + 1.58382i) q^{53} +(7.06547 - 2.01970i) q^{54} -15.7746 q^{55} +(6.93106 + 2.82143i) q^{56} +(-0.143154 - 3.56965i) q^{57} +(0.111677 + 0.700091i) q^{58} +(1.94962 - 7.27607i) q^{59} +(-11.6684 + 4.34483i) q^{60} +(3.15567 - 0.845558i) q^{61} +(12.6104 + 1.31131i) q^{62} +(3.93821 - 6.89134i) q^{63} +(-6.50319 - 4.65924i) q^{64} +(-5.22621 - 3.01736i) q^{65} +(-9.63244 + 4.77317i) q^{66} +(-14.2820 - 3.82686i) q^{67} +(-7.10121 + 7.92185i) q^{68} +(1.46079 + 1.34814i) q^{69} +(-5.74242 + 12.1611i) q^{70} +0.726088 q^{71} +(-5.81040 + 6.18379i) q^{72} +(6.35191 + 11.0018i) q^{73} +(-5.39135 - 2.06271i) q^{74} +(-4.07811 - 13.0961i) q^{75} +(2.25439 + 3.45470i) q^{76} +(-3.84540 + 10.9563i) q^{77} +(-4.10429 - 0.261107i) q^{78} +(2.16393 - 3.74803i) q^{79} +(8.99842 - 11.2132i) q^{80} +(5.68656 + 6.97589i) q^{81} +(3.11743 - 4.30077i) q^{82} +(-6.06782 + 6.06782i) q^{83} +(0.173292 + 9.16351i) q^{84} +(-13.5196 - 13.5196i) q^{85} +(-1.85156 - 11.6072i) q^{86} +(-0.733947 + 0.463919i) q^{87} +(6.72619 - 10.4330i) q^{88} +(-10.0078 - 5.77803i) q^{89} +(-10.5272 - 11.0329i) q^{90} +(-3.36972 + 2.89435i) q^{91} +(-2.24622 - 0.472260i) q^{92} +(4.61668 + 14.8256i) q^{93} +(11.9606 - 5.34104i) q^{94} +(-6.42040 + 3.70682i) q^{95} +(2.10176 - 9.56988i) q^{96} +2.30445i q^{97} +(7.04672 + 6.95296i) q^{98} +(-10.0256 - 8.53454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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