LMFDB - Embedded newform 570.2.bh.a.67.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			67.6
Character	$\chi$	$=$	570.67
Dual form			570.2.bh.a.553.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.19503 + 0.426412i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.31403 - 0.620043i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})$	\(q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.19503 + 0.426412i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.31403 - 0.620043i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(-2.04265 - 0.909723i) q^{10} +(0.855906 + 1.48247i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(0.379848 + 4.34169i) q^{13} +(2.25119 + 0.819365i) q^{14} +(2.22385 - 0.233479i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-1.68468 + 2.40597i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-4.11443 - 1.43925i) q^{19} +(-1.15144 - 1.91682i) q^{20} +(-2.35927 + 0.416002i) q^{21} +(-0.149194 + 1.70530i) q^{22} +(-2.97582 + 6.38167i) q^{23} +(0.342020 - 0.939693i) q^{24} +(4.63635 - 1.87198i) q^{25} +(-2.17913 + 3.77437i) q^{26} +(-0.965926 - 0.258819i) q^{27} +(1.37410 + 1.96241i) q^{28} +(-1.64793 + 9.34590i) q^{29} +(1.95559 + 1.08429i) q^{30} +(3.34086 + 1.92885i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(-0.723443 - 1.55143i) q^{33} +(-2.76001 + 1.00456i) q^{34} +(-4.81498 + 2.34775i) q^{35} +(0.173648 + 0.984808i) q^{36} +(1.20980 - 1.20980i) q^{37} +(-2.54483 - 3.53891i) q^{38} -4.35827i q^{39} +(0.156234 - 2.23060i) q^{40} +(-5.22904 - 6.23173i) q^{41} +(-2.17121 - 1.01245i) q^{42} +(-0.0702985 + 0.0327807i) q^{43} +(-1.10033 + 1.31132i) q^{44} +(-2.23573 + 0.0387701i) q^{45} +(-6.09803 + 3.52070i) q^{46} +(9.06980 - 6.35074i) q^{47} +(0.819152 - 0.573576i) q^{48} +(-1.09189 + 0.630402i) q^{49} +(4.87159 + 1.12586i) q^{50} +(1.88796 - 2.24998i) q^{51} +(-3.94993 + 1.84188i) q^{52} +(4.55447 + 2.12378i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(-2.51089 - 2.88911i) q^{55} +2.39566i q^{56} +(3.97334 + 1.79237i) q^{57} +(-6.71050 + 6.71050i) q^{58} +(0.147424 + 0.836084i) q^{59} +(0.979999 + 2.00988i) q^{60} +(8.95767 - 3.26033i) q^{61} +(1.63033 + 3.49626i) q^{62} +(2.38655 - 0.208796i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-2.68513 - 9.36817i) q^{65} +(0.297253 - 1.68581i) q^{66} +(4.86921 + 6.95395i) q^{67} +(-2.83706 - 0.760188i) q^{68} +(3.52070 - 6.09803i) q^{69} +(-5.29082 - 0.838601i) q^{70} +(2.56701 - 7.05280i) q^{71} +(-0.422618 + 0.906308i) q^{72} +(0.520564 - 5.95008i) q^{73} +(1.68492 - 0.297098i) q^{74} +(-4.78186 + 1.46077i) q^{75} +(-0.0547650 - 4.35855i) q^{76} +(2.89979 + 2.89979i) q^{77} +(2.49980 - 3.57009i) q^{78} +(5.99318 - 5.02887i) q^{79} +(1.40740 - 1.73759i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-0.709007 - 8.10399i) q^{82} +(2.45543 + 9.16380i) q^{83} +(-1.19783 - 2.07470i) q^{84} +(2.67199 - 5.99954i) q^{85} +(-0.0763874 - 0.0134692i) q^{86} +(2.45621 - 9.16671i) q^{87} +(-1.65348 + 0.443049i) q^{88} +(-9.97257 - 8.36798i) q^{89} +(-1.85364 - 1.25060i) q^{90} +(3.57101 + 9.81128i) q^{91} +(-7.01460 - 0.613698i) q^{92} +(-3.16004 - 2.21268i) q^{93} +11.0722 q^{94} +(9.64503 + 1.40476i) q^{95} +1.00000 q^{96} +(3.43603 + 2.40594i) q^{97} +(-1.25601 - 0.109886i) q^{98} +(0.585474 + 1.60858i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q - 12 * q^5 + 12 * q^7	$ 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$	−0.996195	−	0.0871557i	−0.575153	−	0.0503194i
$3$	−0.996195	−	0.0871557i	−0.575153	−	0.0503194i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−2.19503	+	0.426412i	−0.981649	+	0.190697i
$5$	−2.19503	+	0.426412i	−0.981649	+	0.190697i
$6$	−0.766044	−	0.642788i	−0.312736	−	0.262417i
$7$	2.31403	−	0.620043i	0.874622	−	0.234354i	0.206537	−	0.978439i	$-0.433781\pi$
$7$	2.31403	−	0.620043i	0.874622	−	0.234354i	0.668085	+	0.744085i	$0.267114\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	0.984808	+	0.173648i	0.328269	+	0.0578827i
$10$	−2.04265	−	0.909723i	−0.645941	−	0.287680i
$11$	0.855906	+	1.48247i	0.258065	+	0.446982i	0.965724	−	0.259573i	$-0.0835817\pi$
$11$	0.855906	+	1.48247i	0.258065	+	0.446982i	−0.707658	+	0.706555i	$0.750248\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	0.379848	+	4.34169i	0.105351	+	1.20417i	0.846338	+	0.532647i	$0.178803\pi$
$13$	0.379848	+	4.34169i	0.105351	+	1.20417i	−0.740987	+	0.671520i	$0.765642\pi$
$14$	2.25119	+	0.819365i	0.601655	+	0.218984i
$15$	2.22385	−	0.233479i	0.574194	−	0.0602841i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−1.68468	+	2.40597i	−0.408594	+	0.583533i	−0.969727	−	0.244193i	$-0.921477\pi$
$17$	−1.68468	+	2.40597i	−0.408594	+	0.583533i	0.561133	+	0.827726i	$0.310366\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−4.11443	−	1.43925i	−0.943916	−	0.330187i
$19$	−4.11443	−	1.43925i	−0.943916	−	0.330187i
$20$	−1.15144	−	1.91682i	−0.257470	−	0.428613i
$21$	−2.35927	+	0.416002i	−0.514834	+	0.0907792i
$22$	−0.149194	+	1.70530i	−0.0318083	+	0.363571i
$23$	−2.97582	+	6.38167i	−0.620502	+	1.33067i	0.305153	+	0.952303i	$0.401292\pi$
$23$	−2.97582	+	6.38167i	−0.620502	+	1.33067i	−0.925655	+	0.378368i	$0.876486\pi$
$24$	0.342020	−	0.939693i	0.0698146	−	0.191814i
$25$	4.63635	−	1.87198i	0.927269	−	0.374395i
$26$	−2.17913	+	3.77437i	−0.427364	+	0.740215i
$27$	−0.965926	−	0.258819i	−0.185893	−	0.0498097i
$28$	1.37410	+	1.96241i	0.259680	+	0.370861i
$29$	−1.64793	+	9.34590i	−0.306014	+	1.73549i	0.312681	+	0.949858i	$0.398773\pi$
$29$	−1.64793	+	9.34590i	−0.306014	+	1.73549i	−0.618695	+	0.785632i	$0.712338\pi$
$30$	1.95559	+	1.08429i	0.357039	+	0.197963i
$31$	3.34086	+	1.92885i	0.600036	+	0.346431i	0.769056	−	0.639182i	$-0.220727\pi$
$31$	3.34086	+	1.92885i	0.600036	+	0.346431i	−0.169020	+	0.985613i	$0.554060\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$	−0.723443	−	1.55143i	−0.125935	−	0.270069i
$34$	−2.76001	+	1.00456i	−0.473338	+	0.172281i
$35$	−4.81498	+	2.34775i	−0.813881	+	0.396841i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	1.20980	−	1.20980i	0.198890	−	0.198890i	−0.600634	−	0.799524i	$-0.705085\pi$
$37$	1.20980	−	1.20980i	0.198890	−	0.198890i	0.799524	+	0.600634i	$0.205085\pi$
$38$	−2.54483	−	3.53891i	−0.412825	−	0.574087i
$39$		−	4.35827i		−	0.697882i
$40$	0.156234	−	2.23060i	0.0247028	−	0.352689i
$41$	−5.22904	−	6.23173i	−0.816639	−	0.973233i	0.183312	−	0.983055i	$-0.441318\pi$
$41$	−5.22904	−	6.23173i	−0.816639	−	0.973233i	−0.999952	+	0.00982179i	$0.996874\pi$
$42$	−2.17121	−	1.01245i	−0.335025	−	0.156225i
$43$	−0.0702985	+	0.0327807i	−0.0107204	+	0.00499901i	−0.427971	−	0.903792i	$-0.640771\pi$
$43$	−0.0702985	+	0.0327807i	−0.0107204	+	0.00499901i	0.417251	+	0.908791i	$0.362994\pi$
$44$	−1.10033	+	1.31132i	−0.165881	+	0.197690i
$45$	−2.23573	+	0.0387701i	−0.333283	+	0.00577951i
$46$	−6.09803	+	3.52070i	−0.899105	+	0.519099i
$47$	9.06980	−	6.35074i	1.32297	−	0.926351i	0.323167	−	0.946342i	$-0.395253\pi$
$47$	9.06980	−	6.35074i	1.32297	−	0.926351i	0.999800	+	0.0199908i	$0.00636371\pi$
$48$	0.819152	−	0.573576i	0.118234	−	0.0827886i
$49$	−1.09189	+	0.630402i	−0.155984	+	0.0900574i
$50$	4.87159	+	1.12586i	0.688947	+	0.159221i
$51$	1.88796	−	2.24998i	0.264367	−	0.315060i
$52$	−3.94993	+	1.84188i	−0.547757	+	0.255423i
$53$	4.55447	+	2.12378i	0.625605	+	0.291724i	0.709451	−	0.704754i	$-0.248943\pi$
$53$	4.55447	+	2.12378i	0.625605	+	0.291724i	−0.0838467	+	0.996479i	$0.526721\pi$
$54$	−0.642788	−	0.766044i	−0.0874723	−	0.104245i
$55$	−2.51089	−	2.88911i	−0.338568	−	0.389567i
$56$			2.39566i			0.320134i
$57$	3.97334	+	1.79237i	0.526281	+	0.237405i
$58$	−6.71050	+	6.71050i	−0.881131	+	0.881131i
$59$	0.147424	+	0.836084i	0.0191930	+	0.108849i	0.992899	−	0.118958i	$-0.0379555\pi$
$59$	0.147424	+	0.836084i	0.0191930	+	0.108849i	−0.973706	+	0.227807i	$0.926844\pi$
$60$	0.979999	+	2.00988i	0.126517	+	0.259474i
$61$	8.95767	−	3.26033i	1.14691	−	0.417442i	0.302507	−	0.953147i	$-0.402176\pi$
$61$	8.95767	−	3.26033i	1.14691	−	0.417442i	0.844405	+	0.535705i	$0.179954\pi$
$62$	1.63033	+	3.49626i	0.207052	+	0.444025i
$63$	2.38655	−	0.208796i	0.300677	−	0.0263058i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−2.68513	−	9.36817i	−0.333049	−	1.16198i
$66$	0.297253	−	1.68581i	0.0365893	−	0.207508i
$67$	4.86921	+	6.95395i	0.594868	+	0.849560i	0.997843	−	0.0656511i	$-0.0209124\pi$
$67$	4.86921	+	6.95395i	0.594868	+	0.849560i	−0.402974	+	0.915211i	$0.632024\pi$
$68$	−2.83706	−	0.760188i	−0.344044	−	0.0921864i
$69$	3.52070	−	6.09803i	0.423842	−	0.734116i
$70$	−5.29082	−	0.838601i	−0.632373	−	0.100232i
$71$	2.56701	−	7.05280i	0.304648	−	0.837014i	−0.689029	−	0.724734i	$-0.741963\pi$
$71$	2.56701	−	7.05280i	0.304648	−	0.837014i	0.993677	−	0.112279i	$-0.0358152\pi$
$72$	−0.422618	+	0.906308i	−0.0498060	+	0.106809i
$73$	0.520564	−	5.95008i	0.0609274	−	0.696404i	−0.902895	−	0.429860i	$-0.858563\pi$
$73$	0.520564	−	5.95008i	0.0609274	−	0.696404i	0.963823	−	0.266544i	$-0.0858816\pi$
$74$	1.68492	−	0.297098i	0.195869	−	0.0345369i
$75$	−4.78186	+	1.46077i	−0.552161	+	0.168675i
$76$	−0.0547650	−	4.35855i	−0.00628197	−	0.499961i
$77$	2.89979	+	2.89979i	0.330462	+	0.330462i
$78$	2.49980	−	3.57009i	0.283047	−	0.404233i
$79$	5.99318	−	5.02887i	0.674285	−	0.565793i	−0.240045	−	0.970762i	$-0.577162\pi$
$79$	5.99318	−	5.02887i	0.674285	−	0.565793i	0.914330	+	0.404969i	$0.132718\pi$
$80$	1.40740	−	1.73759i	0.157352	−	0.194269i
$81$	0.939693	+	0.342020i	0.104410	+	0.0380022i
$82$	−0.709007	−	8.10399i	−0.0782968	−	0.894936i
$83$	2.45543	+	9.16380i	0.269519	+	1.00586i	0.959426	+	0.281960i	$0.0909846\pi$
$83$	2.45543	+	9.16380i	0.269519	+	1.00586i	−0.689907	+	0.723898i	$0.742349\pi$
$84$	−1.19783	−	2.07470i	−0.130694	−	0.226369i
$85$	2.67199	−	5.99954i	0.289818	−	0.650742i
$86$	−0.0763874	−	0.0134692i	−0.00823706	−	0.00145242i
$87$	2.45621	−	9.16671i	0.263334	−	0.982774i
$88$	−1.65348	+	0.443049i	−0.176262	+	0.0472292i
$89$	−9.97257	−	8.36798i	−1.05709	−	0.887005i	−0.0632695	−	0.997996i	$-0.520153\pi$
$89$	−9.97257	−	8.36798i	−1.05709	−	0.887005i	−0.993821	+	0.110992i	$0.964597\pi$
$90$	−1.85364	−	1.25060i	−0.195391	−	0.131825i
$91$	3.57101	+	9.81128i	0.374344	+	1.02850i
$92$	−7.01460	−	0.613698i	−0.731323	−	0.0639825i
$93$	−3.16004	−	2.21268i	−0.327681	−	0.229444i
$94$	11.0722			1.14201
$95$	9.64503	+	1.40476i	0.989559	+	0.144126i
$96$	1.00000			0.102062
$97$	3.43603	+	2.40594i	0.348876	+	0.244286i	0.734859	−	0.678220i	$-0.237249\pi$
$97$	3.43603	+	2.40594i	0.348876	+	0.244286i	−0.385982	+	0.922506i	$0.626137\pi$
$98$	−1.25601	−	0.109886i	−0.126876	−	0.0111002i
$99$	0.585474	+	1.60858i	0.0588424	+	0.161668i
$100$	3.34481	+	3.71649i	0.334481	+	0.371649i
$101$	−12.2769	−	10.3016i	−1.22160	−	1.02504i	−0.998740	−	0.0501927i	$-0.984016\pi$
$101$	−12.2769	−	10.3016i	−1.22160	−	1.02504i	−0.222859	−	0.974851i	$-0.571539\pi$
$102$	2.83706	−	0.760188i	0.280911	−	0.0752699i
$103$	−1.16729	+	4.35640i	−0.115017	+	0.429249i	−0.999288	−	0.0377245i	$-0.987989\pi$
$103$	−1.16729	+	4.35640i	−0.115017	+	0.429249i	0.884271	+	0.466974i	$0.154656\pi$
$104$	−4.29206	−	0.756806i	−0.420871	−	0.0742109i
$105$	5.00128	−	1.91916i	0.488075	−	0.187291i
$106$	2.51265	+	4.35204i	0.244050	+	0.422707i
$107$	3.29741	+	12.3061i	0.318773	+	1.18968i	0.920426	+	0.390918i	$0.127842\pi$
$107$	3.29741	+	12.3061i	0.318773	+	1.18968i	−0.601653	+	0.798758i	$0.705491\pi$
$108$	−0.0871557	−	0.996195i	−0.00838657	−	0.0958589i
$109$	−11.8150	−	4.30031i	−1.13167	−	0.411895i	−0.292774	−	0.956182i	$-0.594578\pi$
$109$	−11.8150	−	4.30031i	−1.13167	−	0.411895i	−0.838899	+	0.544286i	$0.816800\pi$
$110$	−0.399673	−	3.80680i	−0.0381073	−	0.362965i
$111$	−1.31064	+	1.09976i	−0.124400	+	0.104384i
$112$	−1.37410	+	1.96241i	−0.129840	+	0.185430i
$113$	−0.684236	−	0.684236i	−0.0643675	−	0.0643675i	0.674190	−	0.738558i	$-0.264493\pi$
$113$	−0.684236	−	0.684236i	−0.0643675	−	0.0643675i	−0.738558	+	0.674190i	$0.764493\pi$
$114$	2.22671	+	3.74724i	0.208550	+	0.350961i
$115$	3.81081	−	15.2769i	0.355360	−	1.42458i
$116$	−9.34590	+	1.64793i	−0.867745	+	0.153007i
$117$	−0.379848	+	4.34169i	−0.0351170	+	0.401389i
$118$	−0.358795	+	0.769439i	−0.0330298	+	0.0708326i
$119$	−2.40659	+	6.61205i	−0.220612	+	0.606126i
$120$	−0.350050	+	2.20850i	−0.0319550	+	0.201607i
$121$	4.03485	−	6.98857i	0.366805	−	0.635324i
$122$	9.20774	+	2.46721i	0.833630	+	0.223370i
$123$	4.66601	+	6.66376i	0.420720	+	0.600851i
$124$	−0.669881	+	3.79909i	−0.0601571	+	0.341168i
$125$	−9.37870	+	6.08605i	−0.838857	+	0.544352i
$126$	2.07470	+	1.19783i	0.184829	+	0.106711i
$127$	−1.47390	+	0.128949i	−0.130787	+	0.0114424i	−0.152361	−	0.988325i	$-0.548688\pi$
$127$	−1.47390	+	0.128949i	−0.130787	+	0.0114424i	0.0215742	+	0.999767i	$0.493132\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$	0.0728880	−	0.0265291i	0.00641743	−	0.00233575i
$130$	3.17384	−	9.21408i	0.278364	−	0.808129i
$131$	−0.00149720	−	0.00849106i	−0.000130811	−	0.000741867i	0.984742	−	0.174019i	$-0.0556754\pi$
$131$	−0.00149720	−	0.00849106i	−0.000130811	−	0.000741867i	−0.984873	+	0.173277i	$0.944564\pi$
$132$	1.21043	−	1.21043i	0.105355	−	0.105355i
$133$	−10.4133	−	0.779348i	−0.902950	−	0.0675781i
$134$			8.48921i			0.733356i
$135$	2.23060	+	0.156234i	0.191980	+	0.0134465i
$136$	−1.88796	−	2.24998i	−0.161891	−	0.192934i
$137$	17.3118	+	8.07265i	1.47905	+	0.689693i	0.983835	−	0.179077i	$-0.0573113\pi$
$137$	17.3118	+	8.07265i	1.47905	+	0.689693i	0.495216	+	0.868770i	$0.335089\pi$
$138$	6.38167	−	2.97582i	0.543244	−	0.253319i
$139$	13.9679	−	16.6462i	1.18474	−	1.41192i	0.294967	−	0.955507i	$-0.404691\pi$
$139$	13.9679	−	16.6462i	1.18474	−	1.41192i	0.889771	−	0.456408i	$-0.150864\pi$
$140$	−3.85298	−	3.72163i	−0.325636	−	0.314535i
$141$	−9.58879	+	5.53609i	−0.807522	+	0.466223i
$142$	6.14809	−	4.30494i	0.515936	−	0.361263i
$143$	−6.11131	+	4.27919i	−0.511054	+	0.357844i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	−0.367931	−	21.2173i	−0.0305550	−	1.76200i
$146$	3.83924	−	4.57543i	0.317738	−	0.378666i
$147$	1.14268	−	0.532838i	0.0942463	−	0.0439478i
$148$	1.55062	+	0.723065i	0.127460	+	0.0594356i
$149$	−12.9599	−	15.4451i	−1.06172	−	1.26531i	−0.962801	−	0.270212i	$-0.912906\pi$
$149$	−12.9599	−	15.4451i	−1.06172	−	1.26531i	−0.0989187	−	0.995096i	$-0.531538\pi$
$150$	−4.75493	−	1.54617i	−0.388238	−	0.126244i
$151$			6.25758i			0.509234i	0.967042	+	0.254617i	$0.0819495\pi$
$151$			6.25758i			0.509234i	−0.967042	+	0.254617i	$0.918051\pi$
$152$	2.45510	−	3.60173i	0.199135	−	0.292139i
$153$	−2.07687	+	2.07687i	−0.167905	+	0.167905i
$154$	0.712118	+	4.03862i	0.0573841	+	0.325441i
$155$	−8.15578	−	2.80930i	−0.655088	−	0.225648i
$156$	4.09543	−	1.49062i	0.327897	−	0.119345i
$157$	1.41212	+	3.02830i	0.112699	+	0.241685i	0.954565	−	0.298002i	$-0.0963203\pi$
$157$	1.41212	+	3.02830i	0.112699	+	0.241685i	−0.841866	+	0.539687i	$0.818543\pi$
$158$	7.79377	−	0.681866i	0.620039	−	0.0542464i
$159$	−4.35204	−	2.51265i	−0.345139	−	0.199266i
$160$	2.14952	−	0.616099i	0.169934	−	0.0487069i
$161$	−2.92924	+	16.6125i	−0.230856	+	1.30925i
$162$	0.573576	+	0.819152i	0.0450644	+	0.0643587i
$163$	−2.10710	−	0.564595i	−0.165040	−	0.0442225i	0.175353	−	0.984506i	$-0.443893\pi$
$163$	−2.10710	−	0.564595i	−0.165040	−	0.0442225i	−0.340393	+	0.940283i	$0.610560\pi$
$164$	4.06747	−	7.04507i	0.317616	−	0.550128i
$165$	2.24953	+	3.09695i	0.175126	+	0.241097i
$166$	−3.24477	+	8.91493i	−0.251843	+	0.691933i
$167$	2.67486	−	5.73625i	0.206987	−	0.443884i	−0.775219	−	0.631692i	$-0.782361\pi$
$167$	2.67486	−	5.73625i	0.206987	−	0.443884i	0.982206	+	0.187808i	$0.0601384\pi$
$168$	0.208796	−	2.38655i	0.0161089	−	0.184126i
$169$	−5.90344	+	1.04094i	−0.454111	+	0.0800720i
$170$	5.62996	−	3.38195i	0.431798	−	0.259384i
$171$	−3.80200	−	2.13185i	−0.290746	−	0.163027i
$172$	−0.0548473	−	0.0548473i	−0.00418207	−	0.00418207i
$173$	4.84926	−	6.92546i	0.368682	−	0.526533i	−0.591353	−	0.806413i	$-0.701406\pi$
$173$	4.84926	−	6.92546i	0.368682	−	0.526533i	0.960035	+	0.279880i	$0.0902948\pi$
$174$	7.26982	−	6.10010i	0.551123	−	0.462448i
$175$	9.56795	−	7.20655i	0.723269	−	0.544764i
$176$	−1.60858	−	0.585474i	−0.121251	−	0.0441318i
$177$	−0.0739936	−	0.845751i	−0.00556170	−	0.0635706i
$178$	−3.36938	−	12.5747i	−0.252545	−	0.942512i
$179$	10.9126	+	18.9011i	0.815644	+	1.41274i	0.908864	+	0.417092i	$0.136951\pi$
$179$	10.9126	+	18.9011i	0.815644	+	1.41274i	−0.0932201	+	0.995646i	$0.529716\pi$
$180$	−0.801097	−	2.08764i	−0.0597103	−	0.155604i
$181$	15.0082	+	2.64636i	1.11555	+	0.196702i	0.700888	−	0.713271i	$-0.252787\pi$
$181$	15.0082	+	2.64636i	1.11555	+	0.196702i	0.414666	+	0.909974i	$0.363898\pi$
$182$	−2.70231	+	10.0852i	−0.200309	+	0.747563i
$183$	−9.20774	+	2.46721i	−0.680656	+	0.182381i
$184$	−5.39402	−	4.52612i	−0.397653	−	0.333670i
$185$	−2.13968	+	3.17143i	−0.157312	+	0.233168i
$186$	−1.31941	−	3.62505i	−0.0967437	−	0.265801i
$187$	−5.00870	−	0.438205i	−0.366273	−	0.0320447i
$188$	9.06980	+	6.35074i	0.661483	+	0.463176i
$189$	−2.39566			−0.174259
$190$	7.09501	+	6.68288i	0.514726	+	0.484827i
$191$	17.5242			1.26801			0.634003	−	0.773331i	$-0.281411\pi$
$191$	17.5242			1.26801			0.634003	+	0.773331i	$0.281411\pi$
$192$	0.819152	+	0.573576i	0.0591172	+	0.0413943i
$193$	−21.7247	−	1.90066i	−1.56378	−	0.136813i	−0.727882	−	0.685702i	$-0.759495\pi$
$193$	−21.7247	−	1.90066i	−1.56378	−	0.136813i	−0.835895	+	0.548889i	$0.815051\pi$
$194$	1.43465	+	3.94165i	0.103002	+	0.282994i
$195$	1.85842	+	9.56655i	0.133084	+	0.685075i
$196$	−0.965831	−	0.810429i	−0.0689879	−	0.0578878i
$197$	−12.1093	+	3.24467i	−0.862751	+	0.231173i	−0.662950	−	0.748663i	$-0.730696\pi$
$197$	−12.1093	+	3.24467i	−0.862751	+	0.231173i	−0.199800	+	0.979837i	$0.564029\pi$
$198$	−0.443049	+	1.65348i	−0.0314862	+	0.117508i
$199$	1.02861	+	0.181373i	0.0729166	+	0.0128572i	0.209987	−	0.977704i	$-0.432658\pi$
$199$	1.02861	+	0.181373i	0.0729166	+	0.0128572i	−0.137071	+	0.990561i	$0.543769\pi$
$200$	0.608216	+	4.96287i	0.0430074	+	0.350928i
$201$	−4.24460	−	7.35187i	−0.299391	−	0.518561i
$202$	−4.14793	−	15.4803i	−0.291847	−	1.08919i
$203$	1.98149	+	22.6485i	0.139073	+	1.58961i
$204$	2.76001	+	1.00456i	0.193239	+	0.0703334i
$205$	14.1352	+	11.4491i	0.987246	+	0.799642i
$206$	−3.45492	+	2.89902i	−0.240716	+	0.201985i
$207$	−4.03878	+	5.76797i	−0.280715	+	0.400902i
$208$	−3.08176	−	3.08176i	−0.213682	−	0.213682i
$209$	−1.38792	−	7.33140i	−0.0960042	−	0.507123i
$210$	5.19759	+	1.29653i	0.358668	+	0.0894694i
$211$	9.27697	−	1.63578i	0.638653	−	0.112612i	0.155061	−	0.987905i	$-0.450443\pi$
$211$	9.27697	−	1.63578i	0.638653	−	0.112612i	0.483593	+	0.875293i	$0.339332\pi$
$212$	−0.437984	+	5.00618i	−0.0300809	+	0.343826i
$213$	−3.17193	+	6.80223i	−0.217337	+	0.466081i
$214$	−4.35741	+	11.9719i	−0.297866	+	0.818381i
$215$	0.140329	−	0.101931i	0.00957039	−	0.00695163i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	8.92682	+	2.39194i	0.605992	+	0.162375i
$218$	−7.21173	−	10.2994i	−0.488440	−	0.697565i
$219$	−1.03717	+	5.88206i	−0.0700852	+	0.397473i
$220$	1.85610	−	3.34759i	0.125138	−	0.225695i
$221$	−11.0859	−	6.40043i	−0.745716	−	0.430539i
$222$	−1.70441	+	0.149116i	−0.114392	+	0.0100080i
$223$	5.10892	+	10.9561i	0.342119	+	0.733676i	0.999808	−	0.0196139i	$-0.00624371\pi$
$223$	5.10892	+	10.9561i	0.342119	+	0.733676i	−0.657689	+	0.753289i	$0.728466\pi$
$224$	−2.25119	+	0.819365i	−0.150414	+	0.0547461i
$225$	4.89097	−	1.03844i	0.326065	−	0.0692296i
$226$	−0.168032	−	0.952954i	−0.0111773	−	0.0633896i
$227$	−6.75173	+	6.75173i	−0.448128	+	0.448128i	−0.894732	−	0.446604i	$-0.852633\pi$
$227$	−6.75173	+	6.75173i	−0.448128	+	0.448128i	0.446604	+	0.894732i	$0.352633\pi$
$228$	−0.325316	+	4.34674i	−0.0215446	+	0.287870i
$229$		−	12.1836i		−	0.805117i	−0.915394	−	0.402558i	$-0.868121\pi$
$229$		−	12.1836i		−	0.805117i	0.915394	−	0.402558i	$-0.131879\pi$
$230$	11.8841	−	10.3283i	0.783615	−	0.681030i
$231$	−2.63602	−	3.14149i	−0.173438	−	0.206695i
$232$	−8.60093	−	4.01068i	−0.564679	−	0.263314i
$233$	14.8472	−	6.92335i	0.972670	−	0.453563i	0.129717	−	0.991551i	$-0.458593\pi$
$233$	14.8472	−	6.92335i	0.972670	−	0.453563i	0.842953	+	0.537988i	$0.180815\pi$
$234$	−2.80144	+	3.33863i	−0.183136	+	0.218253i
$235$	−17.2005	+	17.8076i	−1.12204	+	1.16164i
$236$	−0.735240	+	0.424491i	−0.0478600	+	0.0276320i
$237$	−6.40867	+	4.48740i	−0.416288	+	0.291488i
$238$	−5.76388	+	4.03591i	−0.373617	+	0.261609i
$239$	18.3771	−	10.6100i	1.18872	−	0.686305i	0.230701	−	0.973025i	$-0.425898\pi$
$239$	18.3771	−	10.6100i	1.18872	−	0.686305i	0.958014	+	0.286720i	$0.0925649\pi$
$240$	−1.55349	+	1.60832i	−0.100277	+	0.103816i
$241$	−17.6280	+	21.0082i	−1.13552	+	1.35326i	−0.208594	+	0.978002i	$0.566889\pi$
$241$	−17.6280	+	21.0082i	−1.13552	+	1.35326i	−0.926922	+	0.375254i	$0.877556\pi$
$242$	7.31363	−	3.41040i	0.470138	−	0.219229i
$243$	−0.906308	−	0.422618i	−0.0581397	−	0.0271110i
$244$	6.12741	+	7.30236i	0.392267	+	0.467486i
$245$	2.12792	−	1.84935i	0.135948	−	0.118150i
$246$			8.13495i			0.518665i
$247$	4.68592	−	18.4103i	0.298158	−	1.17142i
$248$	−2.72780	+	2.72780i	−0.173216	+	0.173216i
$249$	−1.64741	−	9.34294i	−0.104400	−	0.592085i
$250$	−11.1734	−	0.394006i	−0.706668	−	0.0249191i
$251$	−20.5769	+	7.48939i	−1.29880	+	0.472726i	−0.896607	−	0.442827i	$-0.853976\pi$
$251$	−20.5769	+	7.48939i	−1.29880	+	0.472726i	−0.402197	+	0.915553i	$0.631753\pi$
$252$	1.01245	+	2.17121i	0.0637784	+	0.136773i
$253$	−12.0077	+	1.05054i	−0.754916	+	0.0660466i
$254$	−1.28131	−	0.739763i	−0.0803963	−	0.0464168i
$255$	−3.18471	+	5.74383i	−0.199435	+	0.359693i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.64469	+	2.34886i	0.102593	+	0.146518i	0.867166	−	0.498019i	$-0.165939\pi$
$257$	1.64469	+	2.34886i	0.102593	+	0.146518i	−0.764573	+	0.644537i	$0.777050\pi$
$258$	0.0749228	+	0.0200755i	0.00466449	+	0.00124985i
$259$	2.04939	−	3.54965i	0.127343	−	0.220564i
$260$	7.88484	−	5.72730i	0.488997	−	0.355192i
$261$	−3.24580	+	8.91775i	−0.200910	+	0.551995i
$262$	0.00364383	−	0.00781423i	0.000225117	−	0.000482765i
$263$	0.748784	−	8.55864i	0.0461720	−	0.527748i	−0.937525	−	0.347917i	$-0.886889\pi$
$263$	0.748784	−	8.55864i	0.0461720	−	0.527748i	0.983697	−	0.179831i	$-0.0575552\pi$
$264$	1.68581	−	0.297253i	0.103754	−	0.0182947i
$265$	−10.9028	−	2.71970i	−0.669755	−	0.167070i
$266$	−8.08308	−	6.61124i	−0.495606	−	0.405361i
$267$	9.20531	+	9.20531i	0.563356	+	0.563356i
$268$	−4.86921	+	6.95395i	−0.297434	+	0.424780i
$269$	−5.25081	+	4.40595i	−0.320148	+	0.268636i	−0.788671	−	0.614815i	$-0.789231\pi$
$269$	−5.25081	+	4.40595i	−0.320148	+	0.268636i	0.468524	+	0.883451i	$0.344786\pi$
$270$	1.73759	+	1.40740i	0.105746	+	0.0856517i
$271$	−5.31048	−	1.93286i	−0.322589	−	0.117413i	0.175650	−	0.984453i	$-0.443797\pi$
$271$	−5.31048	−	1.93286i	−0.322589	−	0.117413i	−0.498239	+	0.867040i	$0.666020\pi$
$272$	−0.255989	−	2.92597i	−0.0155216	−	0.177413i
$273$	−2.70231	−	10.0852i	−0.163552	−	0.610383i
$274$	9.55075	+	16.5424i	0.576982	+	0.999362i
$275$	6.74343	+	5.27102i	0.406644	+	0.317854i
$276$	6.93442	+	1.22273i	0.417403	+	0.0735994i
$277$	−3.88569	+	14.5016i	−0.233468	+	0.871316i	0.745365	+	0.666657i	$0.232275\pi$
$277$	−3.88569	+	14.5016i	−0.233468	+	0.871316i	−0.978833	+	0.204659i	$0.934391\pi$
$278$	20.9897	−	5.62417i	1.25888	−	0.337315i
$279$	2.95516	+	2.47968i	0.176921	+	0.148454i
$280$	−1.02154	−	5.25856i	−0.0610486	−	0.314259i
$281$	−5.69311	−	15.6417i	−0.339622	−	0.933105i	−0.985502	−	0.169665i	$-0.945731\pi$
$281$	−5.69311	−	15.6417i	−0.339622	−	0.933105i	0.645879	−	0.763439i	$-0.276491\pi$
$282$	−11.0301	−	0.965004i	−0.656830	−	0.0574652i
$283$	4.49727	+	3.14902i	0.267335	+	0.187190i	0.699556	−	0.714578i	$-0.253381\pi$
$283$	4.49727	+	3.14902i	0.267335	+	0.187190i	−0.432221	+	0.901768i	$0.642270\pi$
$284$	7.50544			0.445366
$285$	−9.48590	−	2.24004i	−0.561896	−	0.132688i
$286$	−7.46054			−0.441151
$287$	−15.9641	−	11.1782i	−0.942332	−	0.659828i
$288$	−0.996195	−	0.0871557i	−0.0587013	−	0.00513570i
$289$	2.86380	+	7.86823i	0.168459	+	0.462837i
$290$	11.8683	−	17.5912i	0.696932	−	1.03299i
$291$	−3.21327	−	2.69625i	−0.188365	−	0.158057i
$292$	5.76929	−	1.54588i	0.337622	−	0.0904655i
$293$	6.65003	−	24.8183i	0.388499	−	1.44990i	−0.444078	−	0.895988i	$-0.646469\pi$
$293$	6.65003	−	24.8183i	0.388499	−	1.44990i	0.832577	−	0.553910i	$-0.186865\pi$
$294$	1.24165	+	0.218936i	0.0724144	+	0.0127686i
$295$	−0.680117	−	1.77237i	−0.0395980	−	0.103191i
$296$	0.855459	+	1.48170i	0.0497225	+	0.0861219i
$297$	−0.443049	−	1.65348i	−0.0257083	−	0.0959448i
$298$	−1.75724	−	20.0854i	−0.101794	−	1.16351i
$299$	−28.8376	−	10.4960i	−1.66772	−	0.607000i
$300$	−3.00817	−	3.99386i	−0.173677	−	0.230586i
$301$	−0.142347	+	0.119444i	−0.00820477	+	0.00688462i
$302$	−3.58920	+	5.12591i	−0.206535	+	0.294963i
$303$	11.3324	+	11.3324i	0.651027	+	0.651027i
$304$	4.07697	−	1.54218i	0.233830	−	0.0884498i
$305$	−18.2722	+	10.9762i	−1.04626	+	0.628495i
$306$	−2.89252	+	0.510029i	−0.165354	+	0.0291564i
$307$	0.705187	−	8.06032i	0.0402471	−	0.460027i	−0.949153	−	0.314814i	$-0.898058\pi$
$307$	0.705187	−	8.06032i	0.0402471	−	0.460027i	0.989400	−	0.145213i	$-0.0463867\pi$
$308$	−1.73312	+	3.71670i	−0.0987539	+	0.211779i
$309$	1.54254	−	4.23809i	0.0877520	−	0.241097i
$310$	−5.06948	−	6.97921i	−0.287927	−	0.396392i
$311$	−10.8611	+	18.8120i	−0.615879	+	1.06673i	0.374351	+	0.927287i	$0.377866\pi$
$311$	−10.8611	+	18.8120i	−0.615879	+	1.06673i	−0.990230	+	0.139446i	$0.955468\pi$
$312$	4.20977	+	1.12800i	0.238331	+	0.0638606i
$313$	4.48809	+	6.40966i	0.253682	+	0.362295i	0.925712	−	0.378228i	$-0.123467\pi$
$313$	4.48809	+	6.40966i	0.253682	+	0.362295i	−0.672030	+	0.740524i	$0.734578\pi$
$314$	−0.580221	+	3.29060i	−0.0327438	+	0.185699i
$315$	−5.14952	+	1.47597i	−0.290142	+	0.0831612i
$316$	6.77538	+	3.91177i	0.381145	+	0.220054i
$317$	2.35555	−	0.206084i	0.132301	−	0.0115748i	−0.0208128	−	0.999783i	$-0.506625\pi$
$317$	2.35555	−	0.206084i	0.132301	−	0.0115748i	0.153114	+	0.988209i	$0.451070\pi$
$318$	−2.12378	−	4.55447i	−0.119096	−	0.255402i
$319$	−15.2655	+	5.55619i	−0.854705	+	0.311087i
$320$	2.11416	+	0.728233i	0.118185	+	0.0407095i
$321$	−2.21231	−	12.5467i	−0.123479	−	0.700286i
$322$	−11.9280	+	11.9280i	−0.664724	+	0.664724i
$323$	10.3943	−	7.47451i	0.578353	−	0.415893i
$324$			1.00000i			0.0555556i
$325$	9.88864	+	19.4185i	0.548523	+	1.07714i
$326$	−1.40219	−	1.67107i	−0.0776603	−	0.0925520i
$327$	11.3953	+	5.31370i	0.630159	+	0.293848i
$328$	7.37277	−	3.43798i	0.407093	−	0.189831i
$329$	17.0501	−	20.3195i	0.940001	−	1.12025i
$330$	0.0663672	+	3.82715i	0.00365339	+	0.210678i
$331$	−9.49199	+	5.48020i	−0.521727	+	0.301219i	−0.737641	−	0.675193i	$-0.764060\pi$
$331$	−9.49199	+	5.48020i	−0.521727	+	0.301219i	0.215914	+	0.976412i	$0.430727\pi$
$332$	−7.77135	+	5.44156i	−0.426508	+	0.298644i
$333$	1.40150	−	0.981342i	0.0768018	−	0.0537772i
$334$	5.48129	−	3.16462i	0.299923	−	0.173161i
$335$	−13.6533	−	13.1879i	−0.745961	−	0.720530i
$336$	1.53990	−	1.83518i	0.0840085	−	0.100117i
$337$	26.7026	−	12.4516i	1.45458	−	0.678283i	0.475123	−	0.879920i	$-0.342404\pi$
$337$	26.7026	−	12.4516i	1.45458	−	0.678283i	0.979460	+	0.201636i	$0.0646259\pi$
$338$	−5.43288	−	2.53339i	−0.295509	−	0.137798i
$339$	0.621997	+	0.741267i	0.0337822	+	0.0402601i
$340$	6.55160	+	0.458882i	0.355310	+	0.0248864i
$341$			6.60364i			0.357607i
$342$	−1.89164	−	3.92705i	−0.102288	−	0.212350i
$343$	−13.9937	+	13.9937i	−0.755589	+	0.755589i
$344$	−0.0134692	−	0.0763874i	−0.000726208	−	0.00411853i
$345$	−5.12778	+	14.8866i	−0.276070	+	0.801470i
$346$	7.94456	−	2.89158i	0.427102	−	0.155452i
$347$	11.4003	+	24.4480i	0.612000	+	1.31244i	0.931116	+	0.364723i	$0.118836\pi$
$347$	11.4003	+	24.4480i	0.612000	+	1.31244i	−0.319116	+	0.947716i	$0.603386\pi$
$348$	9.45396	−	0.827114i	0.506786	−	0.0443380i
$349$	−1.18924	−	0.686607i	−0.0636584	−	0.0367532i	0.467833	−	0.883817i	$-0.345035\pi$
$349$	−1.18924	−	0.686607i	−0.0636584	−	0.0367532i	−0.531491	+	0.847064i	$0.678368\pi$
$350$	11.9711	−	0.415310i	0.639883	−	0.0221993i
$351$	0.756806	−	4.29206i	0.0403953	−	0.229093i
$352$	−0.981855	−	1.40223i	−0.0523330	−	0.0747393i
$353$	15.7831	+	4.22908i	0.840051	+	0.225091i	0.653094	−	0.757277i	$-0.273471\pi$
$353$	15.7831	+	4.22908i	0.840051	+	0.225091i	0.186957	+	0.982368i	$0.440137\pi$
$354$	0.424491	−	0.735240i	0.0225614	−	0.0390776i
$355$	−2.62727	+	16.5757i	−0.139441	+	0.879749i
$356$	4.45251	−	12.2332i	0.235983	−	0.648357i
$357$	2.97371	−	6.37714i	0.157386	−	0.337514i
$358$	−1.90219	+	21.7421i	−0.100534	+	1.14911i
$359$	27.7135	−	4.88664i	1.46266	−	0.257907i	0.615035	−	0.788500i	$-0.289142\pi$
$359$	27.7135	−	4.88664i	1.46266	−	0.257907i	0.847627	+	0.530593i	$0.178031\pi$
$360$	0.541201	−	2.16959i	0.0285238	−	0.114347i
$361$	14.8571	+	11.8434i	0.781953	+	0.623337i
$362$	10.7761	+	10.7761i	0.566382	+	0.566382i
$363$	−4.62859	+	6.61031i	−0.242938	+	0.346951i
$364$	−7.99823	+	6.71131i	−0.419221	+	0.351768i
$365$	1.39453	+	13.2826i	0.0729929	+	0.695243i
$366$	−8.95767	−	3.26033i	−0.468225	−	0.170420i
$367$	−1.93291	−	22.0932i	−0.100897	−	1.15326i	−0.862793	−	0.505558i	$-0.831287\pi$
$367$	−1.93291	−	22.0932i	−0.100897	−	1.15326i	0.761896	−	0.647700i	$-0.224269\pi$
$368$	−1.82245	−	6.80147i	−0.0950017	−	0.354551i
$369$	−4.06747	−	7.04507i	−0.211744	−	0.366752i
$370$	−3.57178	+	1.37061i	−0.185688	+	0.0712547i
$371$	11.8560	+	2.09054i	0.615534	+	0.108535i
$372$	0.998444	−	3.72624i	0.0517669	−	0.193197i
$373$	7.69475	−	2.06180i	0.398419	−	0.106756i	−0.0540454	−	0.998538i	$-0.517212\pi$
$373$	7.69475	−	2.06180i	0.398419	−	0.106756i	0.452465	+	0.891782i	$0.350545\pi$
$374$	−3.85154	−	3.23183i	−0.199159	−	0.167114i
$375$	9.87345	−	5.24548i	0.509863	−	0.270875i
$376$	3.78691	+	10.4045i	0.195295	+	0.536569i
$377$	−41.2029	−	3.60479i	−2.12206	−	0.185656i
$378$	−1.96241	−	1.37410i	−0.100936	−	0.0706758i
$379$	−26.6129			−1.36701			−0.683506	−	0.729945i	$-0.739546\pi$
$379$	−26.6129			−1.36701			−0.683506	+	0.729945i	$0.739546\pi$
$380$	1.97875	+	9.54382i	0.101508	+	0.489588i
$381$	1.47953			0.0757984
$382$	14.3550	+	10.0515i	0.734464	+	0.514278i
$383$	3.74822	+	0.327927i	0.191525	+	0.0167563i	0.182515	−	0.983203i	$-0.441576\pi$
$383$	3.74822	+	0.327927i	0.191525	+	0.0167563i	0.00901051	+	0.999959i	$0.497132\pi$
$384$	0.342020	+	0.939693i	0.0174536	+	0.0479535i
$385$	−7.60164	−	5.12863i	−0.387416	−	0.261379i
$386$	−16.7056	−	14.0177i	−0.850295	−	0.713482i
$387$	−0.0749228	+	0.0200755i	−0.00380854	+	0.00102050i
$388$	−1.08565	+	4.05169i	−0.0551154	+	0.205694i
$389$	5.14424	+	0.907069i	0.260823	+	0.0459902i	0.302531	−	0.953140i	$-0.402169\pi$
$389$	5.14424	+	0.907069i	0.260823	+	0.0459902i	−0.0417072	+	0.999130i	$0.513280\pi$
$390$	−3.96482	+	8.90240i	−0.200766	+	0.450791i
$391$	−10.3408	−	17.9108i	−0.522956	−	0.905787i
$392$	−0.326320	−	1.21784i	−0.0164816	−	0.0615103i
$393$	0.000751461		0.00858924i	3.79062e−5		0.000433270i
$394$	−11.7804	−	4.28772i	−0.593489	−	0.216012i
$395$	−11.0109	+	13.5941i	−0.554016	+	0.683994i
$396$	−1.31132	+	1.10033i	−0.0658965	+	0.0552937i
$397$	−12.2805	+	17.5384i	−0.616343	+	0.880229i	−0.999047	−	0.0436418i	$-0.986104\pi$
$397$	−12.2805	+	17.5384i	−0.616343	+	0.880229i	0.382704	+	0.923871i	$0.374993\pi$
$398$	0.738561	+	0.738561i	0.0370207	+	0.0370207i
$399$	10.3058	+	1.68396i	0.515934	+	0.0843036i
$400$	−2.34836	+	4.41420i	−0.117418	+	0.220710i
$401$	−15.2554	+	2.68994i	−0.761820	+	0.134329i	−0.541043	−	0.840995i	$-0.681970\pi$
$401$	−15.2554	+	2.68994i	−0.761820	+	0.134329i	−0.220777	+	0.975324i	$0.570859\pi$
$402$	0.739883	−	8.45690i	0.0369020	−	0.421792i
$403$	−7.10542	+	15.2376i	−0.353946	+	0.759040i
$404$	5.48134	−	15.0599i	0.272707	−	0.749257i
$405$	−2.20850	−	0.350050i	−0.109741	−	0.0173941i
$406$	−11.3675	+	19.6891i	−0.564160	+	0.977153i
$407$	2.82897	+	0.758021i	0.140227	+	0.0375737i
$408$	1.68468	+	2.40597i	0.0834039	+	0.119113i
$409$	−5.88510	+	33.3761i	−0.291000	+	1.65034i	0.392032	+	0.919952i	$0.371772\pi$
$409$	−5.88510	+	33.3761i	−0.291000	+	1.65034i	−0.683032	+	0.730389i	$0.739339\pi$
$410$	5.01193	+	17.4862i	0.247522	+	0.863582i
$411$	−16.5424	−	9.55075i	−0.815976	−	0.471104i
$412$	−4.49292	+	0.393079i	−0.221350	+	0.0193656i
$413$	0.859552	+	1.84332i	0.0422958	+	0.0907036i
$414$	−6.61675	+	2.40830i	−0.325195	+	0.118361i
$415$	−9.29731	−	19.0678i	−0.456387	−	0.936003i
$416$	−0.756806	−	4.29206i	−0.0371054	−	0.210435i
$417$	−15.3655	+	15.3655i	−0.752452	+	0.752452i
$418$	3.06820	−	6.80160i	0.150071	−	0.332677i
$419$		−	8.73152i		−	0.426563i	−0.976991	−	0.213281i	$-0.931585\pi$
$419$		−	8.73152i		−	0.426563i	0.976991	−	0.213281i	$-0.0684151\pi$
$420$	3.51396	+	4.04328i	0.171464	+	0.197292i
$421$	25.7742	+	30.7165i	1.25616	+	1.49703i	0.791016	+	0.611796i	$0.209553\pi$
$421$	25.7742	+	30.7165i	1.25616	+	1.49703i	0.465143	+	0.885236i	$0.346003\pi$
$422$	8.53750	+	3.98110i	0.415599	+	0.193797i
$423$	10.0348	−	4.67931i	0.487909	−	0.227516i
$424$	−3.23020	+	3.84960i	−0.156872	+	0.186953i
$425$	−3.30683	+	14.3086i	−0.160405	+	0.694067i
$426$	−6.49990	+	3.75272i	−0.314921	+	0.181820i
$427$	18.7068	−	13.0986i	0.905285	−	0.633888i
$428$	−10.4362	+	7.30748i	−0.504451	+	0.353221i
$429$	6.46101	−	3.73027i	0.311941	−	0.180099i
$430$	0.173416	−	0.00300724i	0.00836288	−	0.000145022i
$431$	16.1059	−	19.1943i	0.775794	−	0.924555i	−0.222942	−	0.974832i	$-0.571566\pi$
$431$	16.1059	−	19.1943i	0.775794	−	0.924555i	0.998735	+	0.0502770i	$0.0160104\pi$
$432$	0.906308	−	0.422618i	0.0436048	−	0.0203332i
$433$	−9.77731	−	4.55923i	−0.469867	−	0.219103i	0.173239	−	0.984880i	$-0.444577\pi$
$433$	−9.77731	−	4.55923i	−0.469867	−	0.219103i	−0.643106	+	0.765777i	$0.722355\pi$
$434$	5.94047	+	7.07957i	0.285152	+	0.339830i
$435$	−1.48267	+	21.1686i	−0.0710888	+	1.01496i
$436$		−	12.5733i		−	0.602151i
$437$	21.4287	−	21.9740i	1.02507	−	1.05116i
$438$	−4.22341	+	4.22341i	−0.201802	+	0.201802i
$439$	6.16244	+	34.9489i	0.294117	+	1.66802i	0.670769	+	0.741667i	$0.265964\pi$
$439$	6.16244	+	34.9489i	0.294117	+	1.66802i	−0.376651	+	0.926355i	$0.622925\pi$
$440$	3.44053	−	1.67757i	0.164021	−	0.0799752i
$441$	−1.18477	+	0.431220i	−0.0564175	+	0.0205343i
$442$	−5.40988	−	11.6015i	−0.257322	−	0.551828i
$443$	23.4270	−	2.04960i	1.11305	−	0.0973793i	0.484238	−	0.874936i	$-0.339097\pi$
$443$	23.4270	−	2.04960i	1.11305	−	0.0973793i	0.628813	+	0.777557i	$0.283541\pi$
$444$	−1.48170	−	0.855459i	−0.0703183	−	0.0405983i
$445$	25.4583	+	14.1156i	1.20684	+	0.669143i
$446$	−2.09919	+	11.9051i	−0.0993994	+	0.563722i
$447$	11.5645	+	16.5158i	0.546982	+	0.781171i
$448$	−2.31403	−	0.620043i	−0.109328	−	0.0292943i
$449$	−6.75563	+	11.7011i	−0.318818	+	0.552209i	−0.980242	−	0.197803i	$-0.936619\pi$
$449$	−6.75563	+	11.7011i	−0.318818	+	0.552209i	0.661424	+	0.750012i	$0.269953\pi$
$450$	4.60208	+	1.95470i	0.216944	+	0.0921456i
$451$	4.76280	−	13.0857i	0.224272	−	0.616181i
$452$	0.408949	−	0.876993i	0.0192353	−	0.0412503i
$453$	0.545384	−	6.23377i	0.0256244	−	0.292888i
$454$	−9.40333	+	1.65806i	−0.441320	+	0.0778166i
$455$	−12.0221	−	20.0134i	−0.563606	−	0.938241i
$456$	−2.75967	+	3.37405i	−0.129234	+	0.158004i
$457$	−4.29579	−	4.29579i	−0.200949	−	0.200949i	0.599458	−	0.800406i	$-0.295383\pi$
$457$	−4.29579	−	4.29579i	−0.200949	−	0.200949i	−0.800406	+	0.599458i	$0.795383\pi$
$458$	6.98824	−	9.98024i	0.326539	−	0.466346i
$459$	2.24998	−	1.88796i	0.105020	−	0.0881224i
$460$	15.6590	−	1.64402i	0.730104	−	0.0766529i
$461$	16.3108	+	5.93665i	0.759671	+	0.276498i	0.692669	−	0.721255i	$-0.256435\pi$
$461$	16.3108	+	5.93665i	0.759671	+	0.276498i	0.0670015	+	0.997753i	$0.478657\pi$
$462$	−0.357419	−	4.08532i	−0.0166286	−	0.190066i
$463$	−7.84488	−	29.2775i	−0.364582	−	1.36064i	−0.867986	−	0.496589i	$-0.834586\pi$
$463$	−7.84488	−	29.2775i	−0.364582	−	1.36064i	0.503404	−	0.864051i	$-0.332081\pi$
$464$	−4.74504	−	8.21864i	−0.220283	−	0.381541i
$465$	7.87990	+	3.50943i	0.365422	+	0.162746i
$466$	16.1332	+	2.84471i	0.747354	+	0.131779i
$467$	6.37839	−	23.8045i	0.295157	−	1.10154i	−0.645936	−	0.763391i	$-0.723533\pi$
$467$	6.37839	−	23.8045i	0.295157	−	1.10154i	0.941093	−	0.338148i	$-0.109800\pi$
$468$	−4.20977	+	1.12800i	−0.194596	+	0.0521420i
$469$	15.5793	+	13.0725i	0.719383	+	0.603634i
$470$	−24.3038	+	4.72131i	−1.12105	+	0.217778i
$471$	−1.14281	−	3.13985i	−0.0526580	−	0.144677i
$472$	−0.845751	−	0.0739936i	−0.0389289	−	0.00340583i
$473$	−0.108765	−	0.0761583i	−0.00500104	−	0.00350176i
$474$	−7.82354			−0.359347
$475$	−21.7702	+	1.02926i	−0.998884	+	0.0472255i
$476$	−7.03640			−0.322513
$477$	4.11649	+	2.88239i	0.188481	+	0.131976i
$478$	21.1393	+	1.84945i	0.966888	+	0.0845918i
$479$	−9.47955	−	26.0449i	−0.433132	−	1.19002i	−0.943880	−	0.330289i	$-0.892854\pi$
$479$	−9.47955	−	26.0449i	−0.433132	−	1.19002i	0.510748	−	0.859730i	$-0.329369\pi$
$480$	−2.19503	+	0.426412i	−0.100189	+	0.0194630i
$481$	5.71212	+	4.79304i	0.260450	+	0.218544i
$482$	−26.4898	+	7.09791i	−1.20658	+	0.323301i
$483$	4.36597	−	16.2940i	0.198658	−	0.741403i
$484$	7.94710	+	1.40129i	0.361232	+	0.0636949i
$485$	−8.56813	−	3.81595i	−0.389059	−	0.173273i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	0.844459	+	3.15156i	0.0382661	+	0.142811i	0.982416	−	0.186705i	$-0.0597810\pi$
$487$	0.844459	+	3.15156i	0.0382661	+	0.142811i	−0.944150	+	0.329516i	$0.893114\pi$
$488$	0.830817	+	9.49628i	0.0376093	+	0.429877i
$489$	2.04987	+	0.746092i	0.0926983	+	0.0337394i
$490$	2.80383	−	0.294372i	0.126664	−	0.0132984i
$491$	18.3273	−	15.3784i	0.827099	−	0.694019i	−0.127524	−	0.991836i	$-0.540703\pi$
$491$	18.3273	−	15.3784i	0.827099	−	0.694019i	0.954623	+	0.297817i	$0.0962585\pi$
$492$	−4.66601	+	6.66376i	−0.210360	+	0.300425i
$493$	−19.7097	−	19.7097i	−0.887679	−	0.887679i
$494$	14.3982	−	12.3931i	0.647804	−	0.557591i
$495$	−1.97105	−	3.28123i	−0.0885922	−	0.147480i
$496$	−3.79909	+	0.669881i	−0.170584	+	0.0300786i
$497$	1.56710	−	17.9121i	0.0702942	−	0.803466i
$498$	4.00941	−	8.59820i	0.179666	−	0.385295i
$499$	−3.36848	+	9.25483i	−0.150794	+	0.414303i	−0.991972	−	0.126455i	$-0.959640\pi$
$499$	−3.36848	+	9.25483i	−0.150794	+	0.414303i	0.841178	+	0.540758i	$0.181862\pi$
$500$	−8.92672	−	6.73155i	−0.399215	−	0.301044i
$501$	−3.16462	+	5.48129i	−0.141385	+	0.244886i
$502$	−21.1514	−	5.66749i	−0.944032	−	0.252953i
$503$	4.06001	+	5.79829i	0.181027	+	0.258533i	0.899402	−	0.437123i	$-0.144003\pi$
$503$	4.06001	+	5.79829i	0.181027	+	0.258533i	−0.718375	+	0.695656i	$0.755114\pi$
$504$	−0.416002	+	2.35927i	−0.0185302	+	0.105090i
$505$	31.3410	+	17.3772i	1.39465	+	0.773277i
$506$	−10.4387	−	6.02677i	−0.464056	−	0.267923i
$507$	5.97170	−	0.522456i	0.265213	−	0.0232031i
$508$	−0.625274	−	1.34091i	−0.0277421	−	0.0594931i
$509$	−5.81917	+	2.11801i	−0.257930	+	0.0938790i	−0.467749	−	0.883861i	$-0.654935\pi$
$509$	−5.81917	+	2.11801i	−0.257930	+	0.0938790i	0.209819	+	0.977740i	$0.432713\pi$
$510$	−5.90329	+	2.87840i	−0.261402	+	0.127458i
$511$	−2.48470	−	14.0914i	−0.109917	−	0.623369i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	3.60173	+	2.45510i	0.159020	+	0.108395i
$514$			2.86742i			0.126477i
$515$	0.704629	−	10.0602i	0.0310497	−	0.443305i
$516$	0.0498583	+	0.0594188i	0.00219489	+	0.00261577i
$517$	17.1777	+	8.01009i	0.755474	+	0.352283i
$518$	3.71476	−	1.73222i	0.163217	−	0.0761093i
$519$	−5.43440	+	6.47646i	−0.238544	+	0.284285i
$520$	9.74392	−	0.168971i	0.427299	−	0.00740986i
$521$	29.1968	−	16.8568i	1.27914	−	0.738510i	0.302447	−	0.953166i	$-0.402197\pi$
$521$	29.1968	−	16.8568i	1.27914	−	0.738510i	0.976690	+	0.214657i	$0.0688633\pi$
$522$	−7.77381	+	5.44328i	−0.340251	+	0.238246i
$523$	18.5458	−	12.9859i	0.810951	−	0.567834i	−0.0929029	−	0.995675i	$-0.529615\pi$
$523$	18.5458	−	12.9859i	0.810951	−	0.567834i	0.903854	+	0.427841i	$0.140726\pi$
$524$	0.00746691	−	0.00431102i	0.000326194	−	0.000188328i
$525$	−10.1596	+	6.34522i	−0.443403	+	0.276928i
$526$	5.52240	−	6.58134i	0.240788	−	0.286960i
$527$	−10.2690	+	4.78852i	−0.447325	+	0.208591i
$528$	1.55143	+	0.723443i	0.0675172	+	0.0314838i
$529$	−17.0861	−	20.3624i	−0.742874	−	0.885323i
$530$	−7.37111	−	8.48145i	−0.320181	−	0.368411i
$531$			0.848982i			0.0368427i
$532$	−2.82922	−	10.0519i	−0.122662	−	0.435804i
$533$	25.0700	−	25.0700i	1.08590	−	1.08590i
$534$	2.26060	+	12.8205i	0.0978257	+	0.554797i
$535$	−12.4854	−	25.6062i	−0.539791	−	1.10705i
$536$	−7.97724	+	2.90348i	−0.344564	+	0.125411i
$537$	−9.22371	−	19.7803i	−0.398032	−	0.853583i
$538$	−6.82837	+	0.597405i	−0.294392	+	0.0257559i
$539$	−1.86911	−	1.07913i	−0.0805081	−	0.0464814i
$540$	0.616099	+	2.14952i	0.0265127	+	0.0925005i
$541$	6.68676	−	37.9225i	0.287486	−	1.63042i	−0.408780	−	0.912633i	$-0.634046\pi$
$541$	6.68676	−	37.9225i	0.287486	−	1.63042i	0.696266	−	0.717784i	$-0.254843\pi$
$542$	−3.24145	−	4.62927i	−0.139232	−	0.198844i
$543$	−14.7205	−	3.94434i	−0.631716	−	0.169268i
$544$	1.46857	−	2.54364i	0.0629645	−	0.109058i
$545$	27.7681	+	4.40127i	1.18945	+	0.188530i
$546$	3.57101	−	9.81128i	0.152825	−	0.419884i
$547$	−19.0368	+	40.8245i	−0.813955	+	1.74553i	−0.162695	+	0.986676i	$0.552019\pi$
$547$	−19.0368	+	40.8245i	−0.813955	+	1.74553i	−0.651260	+	0.758855i	$0.725759\pi$
$548$	−1.66481	+	19.0288i	−0.0711170	+	0.812871i
$549$	9.38774	−	1.65531i	0.400659	−	0.0706470i
$550$	2.50056	+	8.18564i	0.106624	+	0.349037i
$551$	20.2314	−	36.0813i	0.861887	−	1.53711i
$552$	4.97902	+	4.97902i	0.211921	+	0.211921i
$553$	10.7503	−	15.3530i	0.457149	−	0.652876i
$554$	−11.5007	+	9.65027i	−0.488620	+	0.410001i
$555$	2.40795	−	2.97287i	0.102212	−	0.126191i
$556$	20.4196	+	7.43214i	0.865985	+	0.315193i
$557$	−3.13054	−	35.7822i	−0.132645	−	1.51614i	−0.712645	−	0.701525i	$-0.752503\pi$
$557$	−3.13054	−	35.7822i	−0.132645	−	1.51614i	0.579999	−	0.814617i	$-0.303053\pi$
$558$	0.998444	+	3.72624i	0.0422675	+	0.157745i
$559$	−0.169026	−	0.292762i	−0.00714905	−	0.0123825i
$560$	2.17939	−	4.89349i	0.0920960	−	0.206788i
$561$	4.95145	+	0.873074i	0.209050	+	0.0368612i
$562$	4.30818	−	16.0784i	0.181730	−	0.678224i
$563$	−7.43843	+	1.99312i	−0.313492	+	0.0840000i	−0.412135	−	0.911123i	$-0.635217\pi$
$563$	−7.43843	+	1.99312i	−0.313492	+	0.0840000i	0.0986424	+	0.995123i	$0.468550\pi$
$564$	−8.48179	−	7.11706i	−0.357148	−	0.299682i
$565$	1.79369	+	1.21015i	0.0754609	+	0.0509116i
$566$	1.87774	+	5.15906i	0.0789275	+	0.216851i
$567$	2.38655	+	0.208796i	0.100226	+	0.00876860i
$568$	6.14809	+	4.30494i	0.257968	+	0.180631i
$569$	−20.3387			−0.852643			−0.426322	−	0.904572i	$-0.640191\pi$
$569$	−20.3387			−0.852643			−0.426322	+	0.904572i	$0.640191\pi$
$570$	−6.48556	−	7.27582i	−0.271650	−	0.304750i
$571$	28.1843			1.17948			0.589738	−	0.807594i	$-0.299231\pi$
$571$	28.1843			1.17948			0.589738	+	0.807594i	$0.299231\pi$
$572$	−6.11131	−	4.27919i	−0.255527	−	0.178922i
$573$	−17.4575	−	1.52733i	−0.729298	−	0.0638053i
$574$	−6.66549	−	18.3133i	−0.278212	−	0.764382i
$575$	−1.85060	+	35.1583i	−0.0771753	+	1.46620i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	−1.03800	+	0.278132i	−0.0432127	+	0.0115788i	−0.280361	−	0.959895i	$-0.590454\pi$
$577$	−1.03800	+	0.278132i	−0.0432127	+	0.0115788i	0.237148	+	0.971474i	$0.423787\pi$
$578$	−2.16714	+	8.08788i	−0.0901412	+	0.336412i
$579$	21.4764	+	3.78686i	0.892527	+	0.157377i
$580$	19.8119	−	7.60247i	0.822643	−	0.315676i
$581$	11.3639	+	19.6829i	0.471454	+	0.816583i
$582$	−1.08565	−	4.05169i	−0.0450016	−	0.167948i
$583$	0.749746	+	8.56964i	0.0310513	+	0.354918i
$584$	5.61260	+	2.04282i	0.232251	+	0.0845325i
$585$	−1.01757	−	9.69212i	−0.0420712	−	0.400720i
$586$	19.6826	−	16.5156i	0.813079	−	0.682254i
$587$	18.8229	−	26.8820i	0.776906	−	1.10954i	−0.214243	−	0.976781i	$-0.568728\pi$
$587$	18.8229	−	26.8820i	0.776906	−	1.10954i	0.991149	−	0.132757i	$-0.0423828\pi$
$588$	0.891522	+	0.891522i	0.0367658	+	0.0367658i
$589$	−10.9696	−	12.7444i	−0.451996	−	0.525126i
$590$	0.459470	−	1.84194i	0.0189161	−	0.0758314i
$591$	12.3460	−	2.17693i	0.507846	−	0.0895470i
$592$	−0.149116	+	1.70441i	−0.00612864	+	0.0700507i
$593$	9.62890	−	20.6492i	0.395412	−	0.847963i	−0.603314	−	0.797503i	$-0.706154\pi$
$593$	9.62890	−	20.6492i	0.395412	−	0.847963i	0.998726	−	0.0504596i	$-0.0160686\pi$
$594$	0.585474	−	1.60858i	0.0240223	−	0.0660007i
$595$	2.46309	−	15.5399i	0.100977	−	0.637073i
$596$	10.0810	−	17.4609i	0.412936	−	0.715225i
$597$	−1.00889	−	0.270332i	−0.0412912	−	0.0110640i
$598$	−17.6021	−	25.1384i	−0.719803	−	1.02799i
$599$	−1.30817	+	7.41903i	−0.0534506	+	0.303133i	−0.999800	−	0.0200127i	$-0.993629\pi$
$599$	−1.30817	+	7.41903i	−0.0534506	+	0.303133i	0.946349	+	0.323146i	$0.104740\pi$
$600$	−0.173359	−	4.99699i	−0.00707736	−	0.204001i
$601$	−17.2823	−	9.97794i	−0.704960	−	0.407009i	0.104232	−	0.994553i	$-0.466761\pi$
$601$	−17.2823	−	9.97794i	−0.704960	−	0.407009i	−0.809192	+	0.587544i	$0.800095\pi$
$602$	−0.185114	+	0.0161954i	−0.00754470	+	0.000660075i
$603$	3.58769	+	7.69383i	0.146102	+	0.313317i
$604$	−5.88020	+	2.14022i	−0.239262	+	0.0870842i
$605$	−5.87662	+	17.0606i	−0.238919	+	0.693614i
$606$	2.78295	+	15.7829i	0.113050	+	0.641137i
$607$	−17.0839	+	17.0839i	−0.693415	+	0.693415i	−0.962982	−	0.269567i	$-0.913119\pi$
$607$	−17.0839	+	17.0839i	−0.693415	+	0.693415i	0.269567	+	0.962982i	$0.413119\pi$
$608$	4.22421	+	1.07518i	0.171315	+	0.0436042i
$609$		−	22.7350i		−	0.921269i
$610$	−21.2634	−	1.48931i	−0.860928	−	0.0603005i
$611$	31.0181	+	36.9659i	1.25486	+	1.49548i
$612$	−2.66196	−	1.24129i	−0.107603	−	0.0501762i
$613$	−18.8174	+	8.77468i	−0.760027	+	0.354406i	−0.763687	−	0.645587i	$-0.776613\pi$
$613$	−18.8174	+	8.77468i	−0.760027	+	0.354406i	0.00366013	+	0.999993i	$0.498835\pi$
$614$	5.20087	−	6.19815i	0.209890	−	0.250137i
$615$	−13.0836	−	12.6375i	−0.527580	−	0.509594i
$616$	−3.55150	+	2.05046i	−0.143094	+	0.0826154i
$617$	−7.06806	+	4.94911i	−0.284549	+	0.199244i	−0.707133	−	0.707080i	$-0.750012\pi$
$617$	−7.06806	+	4.94911i	−0.284549	+	0.199244i	0.422584	+	0.906324i	$0.361123\pi$
$618$	3.69444	−	2.58688i	0.148612	−	0.104059i
$619$	−19.5950	+	11.3132i	−0.787592	+	0.454716i	−0.839114	−	0.543956i	$-0.816926\pi$
$619$	−19.5950	+	11.3132i	−0.787592	+	0.454716i	0.0515224	+	0.998672i	$0.483593\pi$
$620$	−0.149563	−	8.62477i	−0.00600661	−	0.346379i
$621$	4.52612	−	5.39402i	0.181627	−	0.216455i
$622$	−19.6871	+	9.18023i	−0.789380	+	0.368094i
$623$	−28.2654	−	13.1804i	−1.13243	−	0.528060i
$624$	2.80144	+	3.33863i	0.112147	+	0.133652i
$625$	17.9914	−	17.3583i	0.719656	−	0.694331i
$626$			7.82475i			0.312740i
$627$	0.743662	+	7.42446i	0.0296990	+	0.296504i
$628$	−2.36270	+	2.36270i	−0.0942820	+	0.0942820i
$629$	0.872618	+	4.94886i	0.0347936	+	0.197324i
$630$	−5.06482	−	1.74460i	−0.201787	−	0.0695066i
$631$	37.8386	−	13.7721i	1.50633	−	0.548260i	0.548641	−	0.836058i	$-0.315145\pi$
$631$	37.8386	−	13.7721i	1.50633	−	0.548260i	0.957691	+	0.287798i	$0.0929231\pi$
$632$	3.30637	+	7.09053i	0.131520	+	0.282046i
$633$	−9.38424	+	0.821015i	−0.372990	+	0.0326324i
$634$	2.04776	+	1.18228i	0.0813270	+	0.0469542i
$635$	3.18026	−	0.911534i	0.126205	−	0.0361731i
$636$	0.872634	−	4.94896i	0.0346022	−	0.196239i
$637$	−3.15176	−	4.50118i	−0.124877	−	0.178343i
$638$	−15.6917	−	4.20457i	−0.621239	−	0.166461i
$639$	3.75272	−	6.49990i	0.148455	−	0.257132i
$640$	1.31412	+	1.80917i	0.0519452	+	0.0715136i
$641$	−3.89296	+	10.6958i	−0.153763	+	0.422459i	−0.992525	−	0.122038i	$-0.961057\pi$
$641$	−3.89296	+	10.6958i	−0.153763	+	0.422459i	0.838763	+	0.544497i	$0.183279\pi$
$642$	5.38425	−	11.5466i	0.212499	−	0.455706i
$643$	0.0122265	−	0.139749i	0.000482164	−	0.00551116i	−0.995950	−	0.0899110i	$-0.971342\pi$
$643$	0.0122265	−	0.139749i	0.000482164	−	0.00551116i	0.996432	+	0.0843998i	$0.0268973\pi$
$644$	−16.6125	+	2.92924i	−0.654625	+	0.115428i
$645$	−0.148679	+	0.0893125i	−0.00585424	+	0.00351668i
$646$	12.8017	−	0.160853i	0.503676	−	0.00632866i
$647$	5.03919	+	5.03919i	0.198111	+	0.198111i	0.799190	−	0.601079i	$-0.205262\pi$
$647$	5.03919	+	5.03919i	0.198111	+	0.198111i	−0.601079	+	0.799190i	$0.705262\pi$
$648$	−0.573576	+	0.819152i	−0.0225322	+	0.0321793i
$649$	−1.11329	+	0.934161i	−0.0437005	+	0.0366690i
$650$	−3.03768	+	21.5786i	−0.119148	+	0.846382i
$651$	−8.68438	−	3.16086i	−0.340368	−	0.123884i
$652$	−0.190124	−	2.17313i	−0.00744582	−	0.0851061i
$653$	−9.75754	−	36.4156i	−0.381842	−	1.42505i	−0.843085	−	0.537780i	$-0.819263\pi$
$653$	−9.75754	−	36.4156i	−0.381842	−	1.42505i	0.461243	−	0.887274i	$-0.347404\pi$
$654$	6.28664	+	10.8888i	0.245827	+	0.425785i
$655$	0.00690710	+	0.0179997i	0.000269883	+	0.000703308i
$656$	8.01136	+	1.41262i	0.312791	+	0.0551535i
$657$	1.54588	−	5.76929i	0.0603104	−	0.225081i
$658$	25.6214	−	6.86523i	0.998826	−	0.267635i
$659$	−2.95371	−	2.47846i	−0.115060	−	0.0965470i	0.583442	−	0.812155i	$-0.301705\pi$
$659$	−2.95371	−	2.47846i	−0.115060	−	0.0965470i	−0.698502	+	0.715608i	$0.746150\pi$
$660$	−2.14080	+	3.17309i	−0.0833305	+	0.123512i
$661$	−3.10392	−	8.52795i	−0.120729	−	0.331699i	0.864577	−	0.502500i	$-0.167586\pi$
$661$	−3.10392	−	8.52795i	−0.120729	−	0.331699i	−0.985305	+	0.170802i	$0.945364\pi$
$662$	−10.9187	−	0.955262i	−0.424367	−	0.0371273i
$663$	10.4858	+	7.34227i	0.407237	+	0.285150i
$664$	−9.48707			−0.368170
$665$	23.1899	−	2.72967i	0.899267	−	0.105852i
$666$	1.71092			0.0662967
$667$	−54.7385	−	38.3283i	−2.11948	−	1.48408i
$668$	6.30516	+	0.551630i	0.243954	+	0.0213432i
$669$	−4.13459	−	11.3597i	−0.159852	−	0.439191i
$670$	−3.61990	−	18.6341i	−0.139849	−	0.719898i
$671$	12.5003	+	10.4890i	0.482568	+	0.404922i
$672$	2.31403	−	0.620043i	0.0892657	−	0.0239187i
$673$	−11.7624	+	43.8980i	−0.453408	+	1.69214i	0.239317	+	0.970942i	$0.423077\pi$
$673$	−11.7624	+	43.8980i	−0.453408	+	1.69214i	−0.692725	+	0.721202i	$0.743590\pi$
$674$	29.0154	+	5.11621i	1.11763	+	0.197069i
$675$	−4.96287	+	0.608216i	−0.191021	+	0.0234103i
$676$	−2.99726	−	5.19140i	−0.115279	−	0.199669i
$677$	3.64299	+	13.5958i	0.140012	+	0.522530i	0.999927	+	0.0120936i	$0.00384962\pi$
$677$	3.64299	+	13.5958i	0.140012	+	0.522530i	−0.859915	+	0.510437i	$0.829484\pi$
$678$	0.0843367	+	0.963973i	0.00323893	+	0.0370212i
$679$	9.44287	+	3.43692i	0.362384	+	0.131897i
$680$	5.10355	+	4.13374i	0.195712	+	0.158522i
$681$	7.31449	−	6.13759i	0.280292	−	0.235193i
$682$	−3.78769	+	5.40939i	−0.145038	+	0.207136i
$683$	−5.10271	−	5.10271i	−0.195250	−	0.195250i	0.602710	−	0.797960i	$-0.294087\pi$
$683$	−5.10271	−	5.10271i	−0.195250	−	0.195250i	−0.797960	+	0.602710i	$0.794087\pi$
$684$	0.702922	−	4.30185i	0.0268769	−	0.164485i
$685$	−41.4424	−	10.3378i	−1.58343	−	0.394985i
$686$	−19.4894	+	3.43651i	−0.744110	+	0.131207i
$687$	−1.06187	+	12.1373i	−0.0405130	+	0.463066i
$688$	0.0327807	−	0.0702985i	0.00124975	−	0.00268010i
$689$	−7.49080	+	20.5808i	−0.285377	+	0.784066i
$690$	−12.7391	+	9.25325i	−0.484968	+	0.352265i
$691$	−15.0933	+	26.1423i	−0.574175	+	0.994500i	0.421956	+	0.906616i	$0.361344\pi$
$691$	−15.0933	+	26.1423i	−0.574175	+	0.994500i	−0.996131	+	0.0878835i	$0.971990\pi$
$692$	8.16634	+	2.18817i	0.310438	+	0.0831816i
$693$	2.35219	+	3.35928i	0.0893524	+	0.127608i
$694$	−4.68423	+	26.5656i	−0.177811	+	1.00842i
$695$	−23.5617	+	42.4951i	−0.893748	+	1.61193i
$696$	8.21864	+	4.74504i	0.311527	+	0.179860i
$697$	23.8026	−	2.08246i	0.901587	−	0.0788786i
$698$	−0.580345	−	1.24455i	−0.0219664	−	0.0471071i
$699$	−15.3941	+	5.60298i	−0.582257	+	0.211924i
$700$	10.0444	+	6.52614i	0.379642	+	0.246665i
$701$	−1.34289	−	7.61592i	−0.0507204	−	0.287649i	0.948889	−	0.315611i	$-0.102209\pi$
$701$	−1.34289	−	7.61592i	−0.0507204	−	0.287649i	−0.999609	+	0.0279616i	$0.991098\pi$
$702$	3.08176	−	3.08176i	0.116314	−	0.116314i
$703$	−6.71885	+	3.23644i	−0.253406	+	0.122065i
$704$		−	1.71181i		−	0.0645163i
$705$	18.6871	−	16.2407i	0.703796	−	0.611660i
$706$	10.5031	+	12.5171i	0.395289	+	0.471087i
$707$	−34.7966	−	16.2259i	−1.30866	−	0.610238i
$708$	0.769439	−	0.358795i	0.0289173	−	0.0134844i
$709$	25.4571	−	30.3386i	0.956063	−	1.13939i	−0.0340921	−	0.999419i	$-0.510854\pi$
$709$	25.4571	−	30.3386i	0.956063	−	1.13939i	0.990155	−	0.139973i	$-0.0447016\pi$
$710$	−11.6596	+	12.0711i	−0.437577	+	0.453021i
$711$	6.77538	−	3.91177i	0.254097	−	0.146703i
$712$	10.6639	−	7.46697i	0.399648	−	0.279837i
$713$	−22.2511	+	15.5804i	−0.833309	+	0.583489i
$714$	6.09370	−	3.51820i	0.228051	−	0.131665i
$715$	11.5898	−	11.9989i	0.433436	−	0.448733i
$716$	−14.0289	+	16.7190i	−0.524286	+	0.624820i
$717$	−19.2319	+	8.96797i	−0.718228	+	0.334915i
$718$	25.5044	+	11.8929i	0.951817	+	0.443839i
$719$	14.7610	+	17.5914i	0.550492	+	0.656050i	0.967506	−	0.252850i	$-0.0813679\pi$
$719$	14.7610	+	17.5914i	0.550492	+	0.656050i	−0.417014	+	0.908900i	$0.636923\pi$
$720$	1.68775	−	1.46680i	0.0628987	−	0.0546644i
$721$			10.8046i			0.402385i
$722$	5.37714	+	18.2232i	0.200116	+	0.678199i
$723$	19.3919	−	19.3919i	0.721191	−	0.721191i
$724$	2.64636	+	15.0082i	0.0983511	+	0.557777i
$725$	9.85491	+	46.4157i	0.366002	+	1.72384i
$726$	−7.58304	+	2.76000i	−0.281433	+	0.102433i
$727$	−13.2447	−	28.4033i	−0.491217	−	1.05342i	−0.983152	−	0.182787i	$-0.941488\pi$
$727$	−13.2447	−	28.4033i	−0.491217	−	1.05342i	0.491935	−	0.870632i	$-0.336290\pi$
$728$	−10.4012	+	0.909988i	−0.385495	+	0.0337264i
$729$	0.866025	+	0.500000i	0.0320750	+	0.0185185i
$730$	−6.47625	+	11.6803i	−0.239697	+	0.432308i
$731$	0.0395608	−	0.224361i	0.00146321	−	0.00829828i
$732$	−5.46765	−	7.80861i	−0.202090	−	0.288615i
$733$	−3.88632	−	1.04134i	−0.143545	−	0.0384627i	0.186331	−	0.982487i	$-0.440340\pi$
$733$	−3.88632	−	1.04134i	−0.143545	−	0.0384627i	−0.329876	+	0.944024i	$0.607007\pi$
$734$	11.0888	−	19.2064i	0.409296	−	0.708921i
$735$	−2.28100	+	1.65685i	−0.0841361	+	0.0611138i
$736$	2.40830	−	6.61675i	0.0887711	−	0.243897i
$737$	−6.14146	+	13.1704i	−0.226223	+	0.485138i
$738$	0.709007	−	8.10399i	0.0260989	−	0.298312i
$739$	33.8296	−	5.96507i	1.24444	−	0.219429i	0.487623	−	0.873054i	$-0.337864\pi$
$739$	33.8296	−	5.96507i	1.24444	−	0.219429i	0.756818	+	0.653626i	$0.226753\pi$
$740$	−3.71198	−	0.925950i	−0.136455	−	0.0340386i
$741$	−6.27265	+	17.9318i	−0.230431	+	0.658741i
$742$	8.51281	+	8.51281i	0.312515	+	0.312515i
$743$	−9.90428	+	14.1448i	−0.363353	+	0.518922i	−0.958651	−	0.284583i	$-0.908145\pi$
$743$	−9.90428	+	14.1448i	−0.363353	+	0.518922i	0.595298	+	0.803505i	$0.297034\pi$
$744$	2.95516	−	2.47968i	0.108342	−	0.0909094i
$745$	35.0335	+	28.3761i	1.28353	+	1.03962i
$746$	7.48577	+	2.72460i	0.274074	+	0.0997547i
$747$	0.826852	+	9.45097i	0.0302529	+	0.345793i
$748$	−1.30130	−	4.85652i	−0.0475802	−	0.177572i
$749$	15.2606	+	26.4322i	0.557611	+	0.965810i
$750$	11.0965	+	1.36633i	0.405188	+	0.0498914i
$751$	6.97263	+	1.22946i	0.254435	+	0.0448637i	0.299411	−	0.954124i	$-0.403210\pi$
$751$	6.97263	+	1.22946i	0.254435	+	0.0448637i	−0.0449759	+	0.998988i	$0.514321\pi$
$752$	−2.86569	+	10.6949i	−0.104501	+	0.390003i
$753$	21.1514	−	5.66749i	0.770799	−	0.206535i
$754$	−31.6838	−	26.5859i	−1.15386	−	0.968201i
$755$	−2.66831	−	13.7356i	−0.0971096	−	0.499889i
$756$	−0.819365	−	2.25119i	−0.0298000	−	0.0818748i
$757$	−44.9457	−	3.93224i	−1.63358	−	0.142920i	−0.766893	−	0.641775i	$-0.778198\pi$
$757$	−44.9457	−	3.93224i	−1.63358	−	0.142920i	−0.866685	+	0.498855i	$0.833754\pi$
$758$	−21.8000	−	15.2645i	−0.791812	−	0.554432i
$759$	12.0535			0.437516
$760$	−3.85321	+	8.95281i	−0.139771	+	0.324752i
$761$	−6.85682			−0.248560			−0.124280	−	0.992247i	$-0.539662\pi$
$761$	−6.85682			−0.248560			−0.124280	+	0.992247i	$0.539662\pi$
$762$	1.21196	+	0.848621i	0.0439045	+	0.0307423i
$763$	−30.0067	−	2.62525i	−1.08632	−	0.0950403i
$764$	5.99363	+	16.4674i	0.216842	+	0.595768i
$765$	3.67320	−	5.44441i	0.132805	−	0.196843i
$766$	2.88227	+	2.41851i	0.104141	+	0.0873845i
$767$	−3.57401	+	0.957654i	−0.129050	+	0.0345789i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	32.2007	+	5.67786i	1.16119	+	0.204749i	0.720855	−	0.693086i	$-0.243749\pi$
$769$	32.2007	+	5.67786i	1.16119	+	0.204749i	0.440333	+	0.897835i	$0.354860\pi$
$770$	−3.28524	−	8.56125i	−0.118392	−	0.308526i
$771$	−1.43371	−	2.48326i	−0.0516339	−	0.0894325i
$772$	−5.64424	−	21.0646i	−0.203141	−	0.758131i
$773$	1.85022	+	21.1482i	0.0665479	+	0.760646i	0.954012	+	0.299769i	$0.0969096\pi$
$773$	1.85022	+	21.1482i	0.0665479	+	0.760646i	−0.887464	+	0.460877i	$0.847535\pi$
$774$	−0.0728880	−	0.0265291i	−0.00261990	−	0.000953567i
$775$	19.1001	+	2.68879i	0.686097	+	0.0965840i
$776$	−3.21327	+	2.69625i	−0.115350	+	0.0967898i
$777$	−2.35096	+	3.35752i	−0.0843403	+	0.120450i
$778$	3.69364	+	3.69364i	0.132424	+	0.132424i
$779$	12.5455	+	33.1659i	0.449490	+	1.18829i
$780$	−8.35400	+	5.01829i	−0.299121	+	0.179684i
$781$	12.6527	−	2.23101i	0.452749	−	0.0798319i
$782$	1.80252	−	20.6029i	0.0644579	−	0.736758i
$783$	4.01068	−	8.60093i	0.143330	−	0.307372i
$784$	0.431220	−	1.18477i	0.0154007	−	0.0423131i
$785$	−4.39096	−	6.04508i	−0.156720	−	0.215758i
$786$	−0.00431102	+	0.00746691i	−0.000153769	+	0.000266336i
$787$	6.91692	+	1.85338i	0.246562	+	0.0660660i	0.379983	−	0.924993i	$-0.375930\pi$
$787$	6.91692	+	1.85338i	0.246562	+	0.0660660i	−0.133422	+	0.991059i	$0.542596\pi$
$788$	−7.19061	−	10.2693i	−0.256155	−	0.365827i
$789$	−1.49187	+	8.46081i	−0.0531119	+	0.301213i
$790$	−16.8168	+	4.82008i	−0.598316	+	0.171491i
$791$	−2.00760	−	1.15909i	−0.0713820	−	0.0412124i
$792$	−1.70530	+	0.149194i	−0.0605951	+	0.00530139i
$793$	17.5579	+	37.6530i	0.623498	+	1.33710i
$794$	−20.1193	+	7.32282i	−0.714006	+	0.259877i
$795$	10.6243	+	3.65959i	0.376805	+	0.129792i
$796$	0.181373	+	1.02861i	0.00642858	+	0.0364583i
$797$	16.8065	−	16.8065i	0.595317	−	0.595317i	−0.343746	−	0.939063i	$-0.611696\pi$
$797$	16.8065	−	16.8065i	0.595317	−	0.595317i	0.939063	+	0.343746i	$0.111696\pi$
$798$	7.47611	+	7.29057i	0.264652	+	0.258083i
$799$			32.5206i			1.15050i
$800$	−4.45555	+	2.26894i	−0.157527	+	0.0802191i
$801$	−8.36798	−	9.97257i	−0.295668	−	0.352364i
$802$	−14.0394	−	6.54668i	−0.495748	−	0.231171i
$803$	9.26638	−	4.32098i	0.327003	−	0.152484i
$804$	5.45676	−	6.50311i	0.192445	−	0.229347i
$805$	−0.654006	−	37.7141i	−0.0230507	−	1.32925i
$806$	−14.5604	+	8.40643i	−0.512867	+	0.296104i
$807$	5.61484	−	3.93155i	0.197652	−	0.138397i
$808$	13.1280	−	9.19235i	0.461843	−	0.323386i
$809$	−8.76271	+	5.05915i	−0.308080	+	0.177870i	−0.646067	−	0.763281i	$-0.723587\pi$
$809$	−8.76271	+	5.05915i	−0.308080	+	0.177870i	0.337987	+	0.941151i	$0.390254\pi$
$810$	−1.60832	−	1.55349i	−0.0565105	−	0.0545840i
$811$	7.37090	−	8.78429i	0.258827	−	0.308458i	−0.620945	−	0.783854i	$-0.713251\pi$
$811$	7.37090	−	8.78429i	0.258827	−	0.308458i	0.879772	+	0.475396i	$0.157695\pi$
$812$	−20.6049	+	9.60823i	−0.723091	+	0.337183i
$813$	5.12182	+	2.38834i	0.179630	+	0.0837628i
$814$	1.88258	+	2.24357i	0.0659843	+	0.0786370i
$815$	4.86590	+	0.340813i	0.170445	+	0.0119382i
$816$			2.93714i			0.102821i
$817$	0.336418	−	0.0336969i	0.0117698	−	0.00117890i
$818$	−23.9645	+	23.9645i	−0.837900	+	0.837900i
$819$	1.81305	+	10.2823i	0.0633531	+	0.359293i
$820$	−5.92414	+	17.1986i	−0.206880	+	0.600601i
$821$	−7.07506	+	2.57511i	−0.246921	+	0.0898720i	−0.462516	−	0.886611i	$-0.653053\pi$
$821$	−7.07506	+	2.57511i	−0.246921	+	0.0898720i	0.215595	+	0.976483i	$0.430831\pi$
$822$	−8.07265	−	17.3118i	−0.281566	−	0.603820i
$823$	1.20127	−	0.105098i	0.0418738	−	0.00366348i	−0.0661996	−	0.997806i	$-0.521087\pi$
$823$	1.20127	−	0.105098i	0.0418738	−	0.00366348i	0.108073	+	0.994143i	$0.465532\pi$
$824$	−3.90584	−	2.25504i	−0.136067	−	0.0785581i
$825$	−6.25837	−	5.83869i	−0.217888	−	0.203277i
$826$	−0.353178	+	2.00297i	−0.0122887	+	0.0696924i
$827$	−3.10904	−	4.44016i	−0.108112	−	0.154400i	0.761450	−	0.648223i	$-0.224488\pi$
$827$	−3.10904	−	4.44016i	−0.108112	−	0.154400i	−0.869562	+	0.493824i	$0.835599\pi$
$828$	−6.80147	−	1.82245i	−0.236367	−	0.0633344i
$829$	−27.3630	+	47.3940i	−0.950355	+	1.64606i	−0.205698	+	0.978615i	$0.565947\pi$
$829$	−27.3630	+	47.3940i	−0.950355	+	1.64606i	−0.744657	+	0.667448i	$0.767387\pi$
$830$	3.32094	−	20.9522i	0.115272	−	0.727261i
$831$	5.13480	−	14.1077i	0.178124	−	0.489392i
$832$	1.84188	−	3.94993i	0.0638559	−	0.136939i
$833$	0.322752	−	3.68907i	0.0111827	−	0.127819i
$834$	−21.4000	+	3.77340i	−0.741021	+	0.130662i
$835$	−3.42540	+	13.7318i	−0.118541	+	0.475210i
$836$	6.41456	−	3.81170i	0.221852	−	0.131830i
$837$	−2.72780	−	2.72780i	−0.0942866	−	0.0942866i
$838$	5.00819	−	7.15244i	0.173005	−	0.247077i
$839$	16.1084	−	13.5165i	0.556123	−	0.466642i	−0.320885	−	0.947118i	$-0.603980\pi$
$839$	16.1084	−	13.5165i	0.556123	−	0.466642i	0.877008	+	0.480476i	$0.159536\pi$
$840$	0.559338	+	5.32758i	0.0192990	+	0.183819i
$841$	−57.3790	−	20.8843i	−1.97859	−	0.720147i
$842$	3.49473	+	39.9450i	0.120436	+	1.37659i
$843$	4.30818	+	16.0784i	0.148382	+	0.553768i
$844$	4.71004	+	8.15803i	0.162126	+	0.280811i
$845$	12.5144	−	4.80219i	0.430508	−	0.165200i
$846$	10.9040	+	1.92266i	0.374886	+	0.0661026i
$847$	5.00356	−	18.6735i	0.171924	−	0.641631i
$848$	−4.85407	+	1.30064i	−0.166689	+	0.0446643i
$849$	−4.20570	−	3.52900i	−0.144339	−	0.121115i
$850$	−10.9158	+	9.82417i	−0.374411	+	0.336966i
$851$	4.12040	+	11.3207i	0.141246	+	0.388069i
$852$	−7.47687	−	0.654142i	−0.256154	−	0.0224105i
$853$	17.3356	+	12.1385i	0.593558	+	0.415614i	0.831387	−	0.555693i	$-0.187547\pi$
$853$	17.3356	+	12.1385i	0.593558	+	0.415614i	−0.237829	+	0.971307i	$0.576436\pi$
$854$	22.8368			0.781459
$855$	9.25457	+	3.05826i	0.316500	+	0.104590i
$856$	−12.7402			−0.435451
$857$	1.93198	+	1.35279i	0.0659951	+	0.0462103i	0.606108	−	0.795382i	$-0.292730\pi$
$857$	1.93198	+	1.35279i	0.0659951	+	0.0462103i	−0.540113	+	0.841592i	$0.681619\pi$
$858$	7.43215	+	0.650229i	0.253729	+	0.0221984i
$859$	−12.5873	−	34.5833i	−0.429473	−	1.17997i	−0.946133	−	0.323778i	$-0.895047\pi$
$859$	−12.5873	−	34.5833i	−0.429473	−	1.17997i	0.516660	−	0.856191i	$-0.327175\pi$
$860$	0.143779	+	0.0970041i	0.00490283	+	0.00330781i
$861$	14.9291	+	12.5270i	0.508783	+	0.426920i
$862$	24.2025	−	6.48505i	0.824342	−	0.220882i
$863$	−1.91706	+	7.15456i	−0.0652575	+	0.243544i	−0.990848	−	0.134982i	$-0.956902\pi$
$863$	−1.91706	+	7.15456i	−0.0652575	+	0.243544i	0.925591	+	0.378526i	$0.123569\pi$
$864$	0.984808	+	0.173648i	0.0335038	+	0.00590763i
$865$	−7.69118	+	17.2694i	−0.261508	+	0.587177i
$866$	−5.39403	−	9.34274i	−0.183297	−	0.317479i
$867$	−2.16714	−	8.08788i	−0.0736000	−	0.274679i
$868$	0.805470	+	9.20656i	0.0273394	+	0.312491i
$869$	12.5848	+	4.58048i	0.426909	+	0.155382i
$870$	−13.3563	+	16.4899i	−0.452822	+	0.559059i
$871$	−28.3423	+	23.7820i	−0.960342	+	0.805823i
$872$	7.21173	−	10.2994i	0.244220	−	0.348783i
$873$	2.96605	+	2.96605i	0.100385	+	0.100385i
$874$	30.1571	−	5.70908i	1.02008	−	0.193113i
$875$	−17.9290	+	19.8985i	−0.606111	+	0.672692i
$876$	−5.88206	+	1.03717i	−0.198737	+	0.0350426i
$877$	3.49502	−	39.9482i	0.118018	−	1.34896i	−0.674124	−	0.738619i	$-0.735479\pi$
$877$	3.49502	−	39.9482i	0.118018	−	1.34896i	0.792142	−	0.610337i	$-0.208966\pi$
$878$	−14.9979	+	32.1631i	−0.506155	+	1.08545i
$879$	−8.78778	+	24.1442i	−0.296404	+	0.814364i
$880$	3.78053	+	0.599219i	0.127442	+	0.0201997i
$881$	−11.6288	+	20.1416i	−0.391784	+	0.678589i	−0.992685	−	0.120734i	$-0.961475\pi$
$881$	−11.6288	+	20.1416i	−0.391784	+	0.678589i	0.600901	+	0.799323i	$0.294808\pi$
$882$	−1.21784	−	0.326320i	−0.0410069	−	0.0109878i
$883$	13.5329	+	19.3270i	0.455419	+	0.650406i	0.979543	−	0.201236i	$-0.0644959\pi$
$883$	13.5329	+	19.3270i	0.455419	+	0.650406i	−0.524124	+	0.851642i	$0.675607\pi$
$884$	2.22285	−	12.6064i	0.0747624	−	0.423999i
$885$	0.523057	+	1.82490i	0.0175824	+	0.0613434i
$886$	20.3659	+	11.7582i	0.684205	+	0.395026i
$887$	−20.5806	+	1.80057i	−0.691029	+	0.0604572i	−0.427260	−	0.904129i	$-0.640521\pi$
$887$	−20.5806	+	1.80057i	−0.691029	+	0.0604572i	−0.263769	+	0.964586i	$0.584966\pi$
$888$	−0.723065	−	1.55062i	−0.0242645	−	0.0520353i
$889$	−3.33069	+	1.21227i	−0.111708	+	0.0406583i
$890$	12.7579	+	26.1651i	0.427645	+	0.877057i
$891$	0.297253	+	1.68581i	0.00995835	+	0.0564766i
$892$	−8.54802	+	8.54802i	−0.286209	+	0.286209i
$893$	−46.4574	+	13.0760i	−1.55464	+	0.437571i
$894$			20.1621i			0.674321i
$895$	−32.0131	−	36.8354i	−1.07008	−	1.23127i
$896$	−1.53990	−	1.83518i	−0.0514445	−	0.0613092i
$897$	27.8131	+	12.9694i	0.928651	+	0.433037i
$898$	−12.2454	+	5.71011i	−0.408633	+	0.190549i
$899$	−23.5323	+	28.0447i	−0.784847	+	0.935344i
$900$	2.64863	+	4.24084i	0.0882877	+	0.141361i
$901$	−12.7826	+	7.38001i	−0.425849	+	0.245864i
$902$	11.4071	−	7.98734i	0.379815	−	0.265949i
$903$	0.152216	−	0.106583i	0.00506543	−	0.00354685i
$904$	0.838014	−	0.483828i	0.0278719	−	0.0160919i
$905$	−34.0720	+	0.590848i	−1.13259	+	0.0196404i
$906$	4.02229	−	4.79358i	0.133632	−	0.159256i
$907$	−44.2960	+	20.6556i	−1.47082	+	0.685856i	−0.982407	−	0.186754i	$-0.940203\pi$
$907$	−44.2960	+	20.6556i	−1.47082	+	0.685856i	−0.488417	+	0.872610i	$0.662425\pi$
$908$	−8.65378	−	4.03532i	−0.287186	−	0.133917i
$909$	−10.3016	−	12.2769i	−0.341681	−	0.407200i
$910$	1.63123	−	23.2896i	0.0540748	−	0.772043i
$911$		−	50.6764i		−	1.67899i	−0.543371	−	0.839493i	$-0.682852\pi$
$911$		−	50.6764i		−	1.67899i	0.543371	−	0.839493i	$-0.317148\pi$
$912$	−4.19587	+	1.18098i	−0.138939	+	0.0391060i
$913$	−11.4835	+	11.4835i	−0.380047	+	0.380047i
$914$	−1.05494	−	5.98287i	−0.0348944	−	0.197896i
$915$	19.1593	−	9.34189i	0.633386	−	0.308833i
$916$	11.4489	−	4.16705i	0.378281	−	0.137683i
$917$	−0.00872939	−	0.0187202i	−0.000288270	−	0.000618197i
$918$	2.92597	−	0.255989i	0.0965713	−	0.00844889i
$919$	11.5546	+	6.67104i	0.381151	+	0.220057i	0.678319	−	0.734768i	$-0.262709\pi$
$919$	11.5546	+	6.67104i	0.381151	+	0.220057i	−0.297168	+	0.954825i	$0.596042\pi$
$920$	13.7701	+	7.63492i	0.453985	+	0.251716i
$921$	−1.40501	+	7.96819i	−0.0462966	+	0.262561i
$922$	9.95592	+	14.2185i	0.327881	+	0.468262i
$923$	31.5961	+	8.46616i	1.04000	+	0.278667i
$924$	2.05046	−	3.55150i	0.0674552	−	0.116836i
$925$	3.34434	−	7.87378i	0.109961	−	0.258888i
$926$	10.3667	−	28.4823i	0.340672	−	0.935988i
$927$	−1.90604	+	4.08752i	−0.0626027	+	0.134252i
$928$	0.827114	−	9.45396i	0.0271514	−	0.310341i
$929$	12.5223	−	2.20802i	0.410843	−	0.0724428i	0.0355933	−	0.999366i	$-0.488668\pi$
$929$	12.5223	−	2.20802i	0.410843	−	0.0724428i	0.375250	+	0.926924i	$0.377557\pi$
$930$	4.44191	+	7.39448i	0.145656	+	0.242475i
$931$	5.39980	−	1.02224i	0.176971	−	0.0335027i
$932$	11.5838	+	11.5838i	0.379441	+	0.379441i
$933$	12.4594	−	17.7938i	0.407902	−	0.582544i
$934$	18.8785	−	15.8410i	0.617725	−	0.518333i
$935$	11.1811	−	1.17390i	0.365662	−	0.0383905i
$936$	−4.09543	−	1.49062i	−0.133863	−	0.0487223i
$937$	4.31988	+	49.3764i	0.141124	+	1.61306i	0.655298	+	0.755371i	$0.272543\pi$
$937$	4.31988	+	49.3764i	0.141124	+	1.61306i	−0.514173	+	0.857686i	$0.671901\pi$
$938$	5.26367	+	19.6443i	0.171865	+	0.641409i
$939$	−3.91238	−	6.77643i	−0.127676	−	0.221141i
$940$	−22.6166	−	10.0726i	−0.737671	−	0.328533i
$941$	−18.2583	−	3.21943i	−0.595203	−	0.104950i	−0.132072	−	0.991240i	$-0.542163\pi$
$941$	−18.2583	−	3.21943i	−0.595203	−	0.104950i	−0.463131	+	0.886290i	$0.653274\pi$
$942$	0.864808	−	3.22751i	0.0281770	−	0.105158i
$943$	55.3296	−	14.8255i	1.80178	−	0.482785i
$944$	−0.650358	−	0.545715i	−0.0211673	−	0.0177615i
$945$	5.25856	−	1.02154i	0.171061	−	0.0332307i
$946$	−0.0454128	−	0.124771i	−0.00147650	−	0.00405664i
$947$	−46.3472	−	4.05485i	−1.50608	−	0.131765i	−0.695983	−	0.718058i	$-0.745031\pi$
$947$	−46.3472	−	4.05485i	−1.50608	−	0.131765i	−0.810099	+	0.586293i	$0.800587\pi$
$948$	−6.40867	−	4.48740i	−0.208144	−	0.145744i
$949$	26.0311			0.845005
$950$	−18.4234	−	11.6437i	−0.597735	−	0.377773i
$951$	−2.36455			−0.0766758
$952$	−5.76388	−	4.03591i	−0.186808	−	0.130805i
$953$	−1.33671	−	0.116947i	−0.0433003	−	0.00378829i	0.0654850	−	0.997854i	$-0.479141\pi$
$953$	−1.33671	−	0.116947i	−0.0433003	−	0.00378829i	−0.108785	+	0.994065i	$0.534696\pi$
$954$	1.71875	+	4.72224i	0.0556467	+	0.152888i
$955$	−38.4662	+	7.47252i	−1.24474	+	0.241805i
$956$	16.2555	+	13.6400i	0.525740	+	0.441148i
$957$	15.6917	−	4.20457i	0.507240	−	0.135915i
$958$	7.17352	−	26.7719i	0.231766	−	0.864962i
$959$	45.0655	+	7.94627i	1.45524	+	0.256598i
$960$	−2.04265	−	0.909723i	−0.0659261	−	0.0293612i
$961$	−8.05910	−	13.9588i	−0.259971	−	0.450283i
$962$	1.92992	+	7.20256i	0.0622231	+	0.232220i
$963$	1.11038	+	12.6917i	0.0357816	+	0.408985i
$964$	−25.7703	−	9.37964i	−0.830007	−	0.302098i
$965$	48.4969	−	5.09164i	1.56117	−	0.163906i
$966$	12.9223	−	10.8431i	0.415767	−	0.348870i
$967$	−23.5063	+	33.5705i	−0.755913	+	1.07956i	0.238201	+	0.971216i	$0.423442\pi$
$967$	−23.5063	+	33.5705i	−0.755913	+	1.07956i	−0.994114	+	0.108340i	$0.965447\pi$
$968$	5.70614	+	5.70614i	0.183402	+	0.183402i
$969$	−11.0062	+	6.54015i	−0.353569	+	0.210100i
$970$	−4.82986	−	8.04032i	−0.155078	−	0.258159i
$971$	−20.3306	+	3.58483i	−0.652440	+	0.115043i	−0.490065	−	0.871686i	$-0.663027\pi$
$971$	−20.3306	+	3.58483i	−0.652440	+	0.115043i	−0.162376	+	0.986729i	$0.551916\pi$
$972$	0.0871557	−	0.996195i	0.00279552	−	0.0319530i
$973$	22.0007	−	47.1806i	0.705309	−	1.51254i
$974$	−1.11592	+	3.06597i	−0.0357564	+	0.0982400i
$975$	−8.15858	−	20.2064i	−0.261284	−	0.647124i
$976$	−4.76628	+	8.25544i	−0.152565	+	0.264250i
$977$	43.8189	+	11.7412i	1.40189	+	0.375636i	0.879024	−	0.476778i	$-0.158195\pi$
$977$	43.8189	+	11.7412i	1.40189	+	0.375636i	0.522868	+	0.852414i	$0.324862\pi$
$978$	1.25121	+	1.78692i	0.0400094	+	0.0571394i
$979$	3.86972	−	21.9463i	0.123677	−	0.701406i
$980$	2.46561	+	1.36708i	0.0787610	+	0.0436697i
$981$	−10.8888	−	6.28664i	−0.347652	−	0.200717i
$982$	23.8335	−	2.08516i	0.760559	−	0.0665403i
$983$	13.0649	+	28.0177i	0.416705	+	0.893626i	0.996865	+	0.0791234i	$0.0252121\pi$
$983$	13.0649	+	28.0177i	0.416705	+	0.893626i	−0.580160	+	0.814502i	$0.697010\pi$
$984$	−7.64435	+	2.78232i	−0.243693	+	0.0886970i
$985$	25.1967	−	12.2857i	0.802834	−	0.391455i
$986$	−4.84022	−	27.4502i	−0.154144	−	0.874194i
$987$	−18.7562	+	18.7562i	−0.597015	+	0.597015i
$988$	18.9027	−	1.89336i	0.601374	−	0.0602359i
$989$		−	0.546171i		−	0.0173672i
$990$	0.267444	−	3.81837i	0.00849992	−	0.121356i
$991$	−4.52891	−	5.39735i	−0.143866	−	0.171452i	0.689300	−	0.724476i	$-0.257918\pi$
$991$	−4.52891	−	5.39735i	−0.143866	−	0.171452i	−0.833165	+	0.553024i	$0.813474\pi$
$992$	−3.49626	−	1.63033i	−0.111006	−	0.0517631i
$993$	9.93350	−	4.63207i	0.315230	−	0.146994i
$994$	11.5576	−	13.7739i	0.366586	−	0.436880i
$995$	−2.33518	+	0.0404947i	−0.0740303	+	0.00128377i
$996$	8.21604	−	4.74353i	0.260335	−	0.150305i
$997$	23.9820	−	16.7924i	0.759519	−	0.531821i	−0.128455	−	0.991715i	$-0.541002\pi$
$997$	23.9820	−	16.7924i	0.759519	−	0.531821i	0.887974	+	0.459895i	$0.152113\pi$
$998$	−8.06765	+	5.64903i	−0.255377	+	0.178817i
$999$	−1.48170	+	0.855459i	−0.0468788	+	0.0270655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.a.67.6	✓	120
5.3	odd	4	inner	570.2.bh.a.523.8	yes	120
19.2	odd	18	inner	570.2.bh.a.97.8	yes	120
95.78	even	36	inner	570.2.bh.a.553.6	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.a.67.6	✓	120	1.1	even	1	trivial
570.2.bh.a.97.8	yes	120	19.2	odd	18	inner
570.2.bh.a.523.8	yes	120	5.3	odd	4	inner
570.2.bh.a.553.6	yes	120	95.78	even	36	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.19503 + 0.426412i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.31403 - 0.620043i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})\)	\(q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.19503 + 0.426412i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.31403 - 0.620043i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(-2.04265 - 0.909723i) q^{10} +(0.855906 + 1.48247i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(0.379848 + 4.34169i) q^{13} +(2.25119 + 0.819365i) q^{14} +(2.22385 - 0.233479i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-1.68468 + 2.40597i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-4.11443 - 1.43925i) q^{19} +(-1.15144 - 1.91682i) q^{20} +(-2.35927 + 0.416002i) q^{21} +(-0.149194 + 1.70530i) q^{22} +(-2.97582 + 6.38167i) q^{23} +(0.342020 - 0.939693i) q^{24} +(4.63635 - 1.87198i) q^{25} +(-2.17913 + 3.77437i) q^{26} +(-0.965926 - 0.258819i) q^{27} +(1.37410 + 1.96241i) q^{28} +(-1.64793 + 9.34590i) q^{29} +(1.95559 + 1.08429i) q^{30} +(3.34086 + 1.92885i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(-0.723443 - 1.55143i) q^{33} +(-2.76001 + 1.00456i) q^{34} +(-4.81498 + 2.34775i) q^{35} +(0.173648 + 0.984808i) q^{36} +(1.20980 - 1.20980i) q^{37} +(-2.54483 - 3.53891i) q^{38} -4.35827i q^{39} +(0.156234 - 2.23060i) q^{40} +(-5.22904 - 6.23173i) q^{41} +(-2.17121 - 1.01245i) q^{42} +(-0.0702985 + 0.0327807i) q^{43} +(-1.10033 + 1.31132i) q^{44} +(-2.23573 + 0.0387701i) q^{45} +(-6.09803 + 3.52070i) q^{46} +(9.06980 - 6.35074i) q^{47} +(0.819152 - 0.573576i) q^{48} +(-1.09189 + 0.630402i) q^{49} +(4.87159 + 1.12586i) q^{50} +(1.88796 - 2.24998i) q^{51} +(-3.94993 + 1.84188i) q^{52} +(4.55447 + 2.12378i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(-2.51089 - 2.88911i) q^{55} +2.39566i q^{56} +(3.97334 + 1.79237i) q^{57} +(-6.71050 + 6.71050i) q^{58} +(0.147424 + 0.836084i) q^{59} +(0.979999 + 2.00988i) q^{60} +(8.95767 - 3.26033i) q^{61} +(1.63033 + 3.49626i) q^{62} +(2.38655 - 0.208796i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-2.68513 - 9.36817i) q^{65} +(0.297253 - 1.68581i) q^{66} +(4.86921 + 6.95395i) q^{67} +(-2.83706 - 0.760188i) q^{68} +(3.52070 - 6.09803i) q^{69} +(-5.29082 - 0.838601i) q^{70} +(2.56701 - 7.05280i) q^{71} +(-0.422618 + 0.906308i) q^{72} +(0.520564 - 5.95008i) q^{73} +(1.68492 - 0.297098i) q^{74} +(-4.78186 + 1.46077i) q^{75} +(-0.0547650 - 4.35855i) q^{76} +(2.89979 + 2.89979i) q^{77} +(2.49980 - 3.57009i) q^{78} +(5.99318 - 5.02887i) q^{79} +(1.40740 - 1.73759i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-0.709007 - 8.10399i) q^{82} +(2.45543 + 9.16380i) q^{83} +(-1.19783 - 2.07470i) q^{84} +(2.67199 - 5.99954i) q^{85} +(-0.0763874 - 0.0134692i) q^{86} +(2.45621 - 9.16671i) q^{87} +(-1.65348 + 0.443049i) q^{88} +(-9.97257 - 8.36798i) q^{89} +(-1.85364 - 1.25060i) q^{90} +(3.57101 + 9.81128i) q^{91} +(-7.01460 - 0.613698i) q^{92} +(-3.16004 - 2.21268i) q^{93} +11.0722 q^{94} +(9.64503 + 1.40476i) q^{95} +1.00000 q^{96} +(3.43603 + 2.40594i) q^{97} +(-1.25601 - 0.109886i) q^{98} +(0.585474 + 1.60858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q - 12 * q^5 + 12 * q^7	\( 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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