LMFDB - Embedded newform 570.2.bi.a.17.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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([18, 9, 20]))

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

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

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (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:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.35
Character	$\chi$	$=$	570.17
Dual form			570.2.bi.a.503.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 + 0.819152i) q^{2} +(1.28946 - 1.15642i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-1.79088 + 1.33893i) q^{5} +(1.68688 + 0.392966i) q^{6} +(-0.768695 + 2.86881i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(0.325391 - 2.98230i) q^{9} +O(q^{10})$	\(q+(0.573576 + 0.819152i) q^{2} +(1.28946 - 1.15642i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-1.79088 + 1.33893i) q^{5} +(1.68688 + 0.392966i) q^{6} +(-0.768695 + 2.86881i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(0.325391 - 2.98230i) q^{9} +(-2.12400 - 0.699027i) q^{10} +(0.0113073 + 0.00652828i) q^{11} +(0.645658 + 1.60721i) q^{12} +(-0.561184 + 6.41436i) q^{13} +(-2.79090 + 1.01580i) q^{14} +(-0.760900 + 3.79750i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(1.36664 + 1.95177i) q^{17} +(2.62959 - 1.44403i) q^{18} +(3.64828 + 2.38539i) q^{19} +(-0.645665 - 2.14082i) q^{20} +(2.32635 + 4.58813i) q^{21} +(0.00113795 + 0.0130069i) q^{22} +(1.98822 + 4.26375i) q^{23} +(-0.946215 + 1.45075i) q^{24} +(1.41453 - 4.79574i) q^{25} +(-5.57622 + 3.21943i) q^{26} +(-3.02921 - 4.22183i) q^{27} +(-2.43289 - 1.70353i) q^{28} +(-0.635081 - 3.60172i) q^{29} +(-3.54717 + 1.55487i) q^{30} +(-4.33765 - 7.51303i) q^{31} +(0.0871557 - 0.996195i) q^{32} +(0.0221297 - 0.00465806i) q^{33} +(-0.814920 + 2.23897i) q^{34} +(-2.46449 - 6.16693i) q^{35} +(2.69116 + 1.32577i) q^{36} +(4.43986 + 4.43986i) q^{37} +(0.138572 + 4.35670i) q^{38} +(6.69406 + 8.91999i) q^{39} +(1.38332 - 1.75682i) q^{40} +(-2.50293 + 2.98287i) q^{41} +(-2.42404 + 4.53728i) q^{42} +(3.15187 - 6.75921i) q^{43} +(-0.0100019 + 0.00839260i) q^{44} +(3.41036 + 5.77663i) q^{45} +(-2.35226 + 4.07424i) q^{46} +(-0.101057 - 0.0707611i) q^{47} +(-1.73111 + 0.0570221i) q^{48} +(-1.57699 - 0.910476i) q^{49} +(4.73978 - 1.59201i) q^{50} +(4.01928 + 0.936306i) q^{51} +(-5.83559 - 2.72118i) q^{52} +(-3.24503 - 6.95899i) q^{53} +(1.72084 - 4.90293i) q^{54} +(-0.0289910 + 0.00344832i) q^{55} -2.97001i q^{56} +(7.46280 - 1.14309i) q^{57} +(2.58609 - 2.58609i) q^{58} +(-0.528090 + 2.99495i) q^{59} +(-3.30824 - 2.01383i) q^{60} +(2.13003 + 0.775267i) q^{61} +(3.66634 - 7.86249i) q^{62} +(8.30552 + 3.22596i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-7.58337 - 12.2388i) q^{65} +(0.0165087 + 0.0154558i) q^{66} +(3.68971 - 5.26945i) q^{67} +(-2.30148 + 0.616680i) q^{68} +(7.49440 + 3.19870i) q^{69} +(3.63808 - 5.55600i) q^{70} +(5.43621 + 14.9359i) q^{71} +(0.457573 + 2.96490i) q^{72} +(-7.57259 + 0.662516i) q^{73} +(-1.09032 + 6.18352i) q^{74} +(-3.72191 - 7.81968i) q^{75} +(-3.48931 + 2.61241i) q^{76} +(-0.0274203 + 0.0274203i) q^{77} +(-3.46727 + 10.5998i) q^{78} +(7.10969 - 8.47300i) q^{79} +(2.23254 + 0.125477i) q^{80} +(-8.78824 - 1.94083i) q^{81} +(-3.87904 - 0.339372i) q^{82} +(1.35195 - 5.04554i) q^{83} +(-5.10709 + 0.616816i) q^{84} +(-5.06078 - 1.66555i) q^{85} +(7.34466 - 1.29506i) q^{86} +(-4.98401 - 3.90984i) q^{87} +(-0.0126117 - 0.00337929i) q^{88} +(-2.01714 + 1.69258i) q^{89} +(-2.77584 + 6.10694i) q^{90} +(-17.9702 - 6.54061i) q^{91} +(-4.68663 + 0.410027i) q^{92} +(-14.2814 - 4.67158i) q^{93} -0.123368i q^{94} +(-9.72751 + 0.612843i) q^{95} +(-1.03963 - 1.38534i) q^{96} +(9.44166 - 6.61112i) q^{97} +(-0.158706 - 1.81402i) q^{98} +(0.0231486 - 0.0315976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.573576	+	0.819152i	0.405580	+	0.579228i
$2$	0.573576	+	0.819152i	0.405580	+	0.579228i
$3$	1.28946	−	1.15642i	0.744468	−	0.667659i
$3$	1.28946	−	1.15642i	0.744468	−	0.667659i
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	−1.79088	+	1.33893i	−0.800908	+	0.598788i
$5$	−1.79088	+	1.33893i	−0.800908	+	0.598788i
$6$	1.68688	+	0.392966i	0.688668	+	0.160428i
$7$	−0.768695	+	2.86881i	−0.290539	+	1.08431i	0.654156	+	0.756359i	$0.273024\pi$
$7$	−0.768695	+	2.86881i	−0.290539	+	1.08431i	−0.944696	+	0.327948i	$0.893643\pi$
$8$	−0.965926	+	0.258819i	−0.341506	+	0.0915064i
$9$	0.325391	−	2.98230i	0.108464	−	0.994100i
$10$	−2.12400	−	0.699027i	−0.671667	−	0.221052i
$11$	0.0113073	+	0.00652828i	0.00340928	+	0.00196835i	0.501704	−	0.865040i	$-0.332707\pi$
$11$	0.0113073	+	0.00652828i	0.00340928	+	0.00196835i	−0.498294	+	0.867008i	$0.666040\pi$
$12$	0.645658	+	1.60721i	0.186386	+	0.463962i
$13$	−0.561184	+	6.41436i	−0.155644	+	1.77902i	0.370701	+	0.928752i	$0.379117\pi$
$13$	−0.561184	+	6.41436i	−0.155644	+	1.77902i	−0.526346	+	0.850271i	$0.676438\pi$
$14$	−2.79090	+	1.01580i	−0.745898	+	0.271485i
$15$	−0.760900	+	3.79750i	−0.196464	+	0.980511i
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	1.36664	+	1.95177i	0.331459	+	0.473373i	0.949942	−	0.312425i	$-0.101141\pi$
$17$	1.36664	+	1.95177i	0.331459	+	0.473373i	−0.618483	+	0.785798i	$0.712252\pi$
$18$	2.62959	−	1.44403i	0.619801	−	0.340362i
$19$	3.64828	+	2.38539i	0.836972	+	0.547245i
$19$	3.64828	+	2.38539i	0.836972	+	0.547245i
$20$	−0.645665	−	2.14082i	−0.144375	−	0.478702i
$21$	2.32635	+	4.58813i	0.507650	+	1.00121i
$22$	0.00113795	+	0.0130069i	0.000242613	+	0.00277308i
$23$	1.98822	+	4.26375i	0.414572	+	0.889053i	0.997090	+	0.0762352i	$0.0242900\pi$
$23$	1.98822	+	4.26375i	0.414572	+	0.889053i	−0.582517	+	0.812818i	$0.697932\pi$
$24$	−0.946215	+	1.45075i	−0.193145	+	0.296133i
$25$	1.41453	−	4.79574i	0.282906	−	0.959148i
$26$	−5.57622	+	3.21943i	−1.09359	+	0.631382i
$27$	−3.02921	−	4.22183i	−0.582972	−	0.812492i
$28$	−2.43289	−	1.70353i	−0.459773	−	0.321936i
$29$	−0.635081	−	3.60172i	−0.117932	−	0.668823i	−0.985257	−	0.171081i	$-0.945274\pi$
$29$	−0.635081	−	3.60172i	−0.117932	−	0.668823i	0.867325	−	0.497742i	$-0.165837\pi$
$30$	−3.54717	+	1.55487i	−0.647621	+	0.283878i
$31$	−4.33765	−	7.51303i	−0.779065	−	1.34938i	−0.932481	−	0.361219i	$-0.882361\pi$
$31$	−4.33765	−	7.51303i	−0.779065	−	1.34938i	0.153416	−	0.988162i	$-0.450973\pi$
$32$	0.0871557	−	0.996195i	0.0154071	−	0.176104i
$33$	0.0221297	−	0.00465806i	0.00385229	−	0.000810865i
$34$	−0.814920	+	2.23897i	−0.139758	+	0.383981i
$35$	−2.46449	−	6.16693i	−0.416575	−	1.04240i
$36$	2.69116	+	1.32577i	0.448526	+	0.220962i
$37$	4.43986	+	4.43986i	0.729909	+	0.729909i	0.970601	−	0.240693i	$-0.0773746\pi$
$37$	4.43986	+	4.43986i	0.729909	+	0.729909i	−0.240693	+	0.970601i	$0.577375\pi$
$38$	0.138572	+	4.35670i	0.0224794	+	0.706749i
$39$	6.69406	+	8.91999i	1.07191	+	1.42834i
$40$	1.38332	−	1.75682i	0.218722	−	0.277778i
$41$	−2.50293	+	2.98287i	−0.390891	+	0.465846i	−0.925220	−	0.379430i	$-0.876120\pi$
$41$	−2.50293	+	2.98287i	−0.390891	+	0.465846i	0.534329	+	0.845277i	$0.320564\pi$
$42$	−2.42404	+	4.53728i	−0.374038	+	0.700117i
$43$	3.15187	−	6.75921i	0.480656	−	1.03077i	−0.505173	−	0.863018i	$-0.668571\pi$
$43$	3.15187	−	6.75921i	0.480656	−	1.03077i	0.985829	−	0.167752i	$-0.0536508\pi$
$44$	−0.0100019	+	0.00839260i	−0.00150784	+	0.00126523i
$45$	3.41036	+	5.77663i	0.508386	+	0.861129i
$46$	−2.35226	+	4.07424i	−0.346822	+	0.600714i
$47$	−0.101057	−	0.0707611i	−0.0147407	−	0.0103216i	0.566183	−	0.824280i	$-0.308420\pi$
$47$	−0.101057	−	0.0707611i	−0.0147407	−	0.0103216i	−0.580924	+	0.813958i	$0.697308\pi$
$48$	−1.73111	+	0.0570221i	−0.249864	+	0.00823043i
$49$	−1.57699	−	0.910476i	−0.225284	−	0.130068i
$50$	4.73978	−	1.59201i	0.670306	−	0.225144i
$51$	4.01928	+	0.936306i	0.562812	+	0.131109i
$52$	−5.83559	−	2.72118i	−0.809251	−	0.377360i
$53$	−3.24503	−	6.95899i	−0.445739	−	0.955891i	−0.992910	−	0.118870i	$-0.962073\pi$
$53$	−3.24503	−	6.95899i	−0.445739	−	0.955891i	0.547171	−	0.837021i	$-0.315705\pi$
$54$	1.72084	−	4.90293i	0.234177	−	0.667204i
$55$	−0.0289910	+	0.00344832i	−0.00390915	+	0.000464972i
$56$		−	2.97001i		−	0.396884i
$57$	7.46280	−	1.14309i	0.988472	−	0.151406i
$58$	2.58609	−	2.58609i	0.339570	−	0.339570i
$59$	−0.528090	+	2.99495i	−0.0687515	+	0.389909i	0.930942	+	0.365166i	$0.118988\pi$
$59$	−0.528090	+	2.99495i	−0.0687515	+	0.389909i	−0.999694	+	0.0247430i	$0.992123\pi$
$60$	−3.30824	−	2.01383i	−0.427092	−	0.259985i
$61$	2.13003	+	0.775267i	0.272722	+	0.0992627i	0.474761	−	0.880115i	$-0.342535\pi$
$61$	2.13003	+	0.775267i	0.272722	+	0.0992627i	−0.202039	+	0.979378i	$0.564757\pi$
$62$	3.66634	−	7.86249i	0.465626	−	0.998538i
$63$	8.30552	+	3.22596i	1.04640	+	0.406433i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−7.58337	−	12.2388i	−0.940601	−	1.51803i
$66$	0.0165087	+	0.0154558i	0.00203209	+	0.00190248i
$67$	3.68971	−	5.26945i	0.450770	−	0.643766i	−0.527875	−	0.849322i	$-0.677011\pi$
$67$	3.68971	−	5.26945i	0.450770	−	0.643766i	0.978645	+	0.205555i	$0.0659001\pi$
$68$	−2.30148	+	0.616680i	−0.279095	+	0.0747834i
$69$	7.49440	+	3.19870i	0.902220	+	0.385079i
$70$	3.63808	−	5.55600i	0.434834	−	0.664069i
$71$	5.43621	+	14.9359i	0.645159	+	1.77256i	0.634877	+	0.772613i	$0.281051\pi$
$71$	5.43621	+	14.9359i	0.645159	+	1.77256i	0.0102820	+	0.999947i	$0.496727\pi$
$72$	0.457573	+	2.96490i	0.0539254	+	0.349417i
$73$	−7.57259	+	0.662516i	−0.886305	+	0.0775416i	−0.521210	−	0.853429i	$-0.674519\pi$
$73$	−7.57259	+	0.662516i	−0.886305	+	0.0775416i	−0.365095	+	0.930970i	$0.618963\pi$
$74$	−1.09032	+	6.18352i	−0.126747	+	0.718820i
$75$	−3.72191	−	7.81968i	−0.429769	−	0.902939i
$76$	−3.48931	+	2.61241i	−0.400252	+	0.299664i
$77$	−0.0274203	+	0.0274203i	−0.00312483	+	0.00312483i
$78$	−3.46727	+	10.5998i	−0.392591	+	1.20019i
$79$	7.10969	−	8.47300i	0.799903	−	0.953287i	−0.199744	−	0.979848i	$-0.564011\pi$
$79$	7.10969	−	8.47300i	0.799903	−	0.953287i	0.999647	+	0.0265610i	$0.00845563\pi$
$80$	2.23254	+	0.125477i	0.249606	+	0.0140288i
$81$	−8.78824	−	1.94083i	−0.976471	−	0.215648i
$82$	−3.87904	−	0.339372i	−0.428369	−	0.0374774i
$83$	1.35195	−	5.04554i	0.148396	−	0.553820i	−0.851185	−	0.524866i	$-0.824116\pi$
$83$	1.35195	−	5.04554i	0.148396	−	0.553820i	0.999581	−	0.0289545i	$-0.00921778\pi$
$84$	−5.10709	+	0.616816i	−0.557229	+	0.0673001i
$85$	−5.06078	−	1.66555i	−0.548918	−	0.180654i
$86$	7.34466	−	1.29506i	0.791995	−	0.139650i
$87$	−4.98401	−	3.90984i	−0.534342	−	0.419179i
$88$	−0.0126117	−	0.00337929i	−0.00134441	−	0.000360233i
$89$	−2.01714	+	1.69258i	−0.213816	+	0.179413i	−0.743405	−	0.668841i	$-0.766791\pi$
$89$	−2.01714	+	1.69258i	−0.213816	+	0.179413i	0.529589	+	0.848254i	$0.322346\pi$
$90$	−2.77584	+	6.10694i	−0.292599	+	0.643728i
$91$	−17.9702	−	6.54061i	−1.88379	−	0.685642i
$92$	−4.68663	+	0.410027i	−0.488615	+	0.0427482i
$93$	−14.2814	−	4.67158i	−1.48091	−	0.484420i
$94$		−	0.123368i		−	0.0127245i
$95$	−9.72751	+	0.612843i	−0.998021	+	0.0628763i
$96$	−1.03963	−	1.38534i	−0.106107	−	0.141390i
$97$	9.44166	−	6.61112i	0.958655	−	0.671257i	0.0142002	−	0.999899i	$-0.495480\pi$
$97$	9.44166	−	6.61112i	0.958655	−	0.671257i	0.944455	+	0.328642i	$0.106591\pi$
$98$	−0.158706	−	1.81402i	−0.0160318	−	0.183244i
$99$	0.0231486	−	0.0315976i	0.00232652	−	0.00317568i
$100$	4.02272	+	2.96946i	0.402272	+	0.296946i
$101$	−3.93645	−	4.69127i	−0.391691	−	0.466799i	0.533777	−	0.845625i	$-0.320772\pi$
$101$	−3.93645	−	4.69127i	−0.391691	−	0.466799i	−0.925468	+	0.378826i	$0.876328\pi$
$102$	1.53839	+	3.82945i	0.152323	+	0.379172i
$103$	3.00350	+	11.2092i	0.295944	+	1.10448i	0.940465	+	0.339891i	$0.110390\pi$
$103$	3.00350	+	11.2092i	0.295944	+	1.10448i	−0.644521	+	0.764587i	$0.722943\pi$
$104$	−1.11810	−	6.34104i	−0.109638	−	0.621790i
$105$	−10.3094	−	5.10200i	−1.00610	−	0.497904i
$106$	3.83920	−	6.64969i	0.372896	−	0.645875i
$107$	−1.06973	−	0.286634i	−0.103415	−	0.0277100i	0.206740	−	0.978396i	$-0.433714\pi$
$107$	−1.06973	−	0.286634i	−0.103415	−	0.0277100i	−0.310155	+	0.950686i	$0.600381\pi$
$108$	5.00328	−	1.40258i	0.481441	−	0.134963i
$109$	−1.21855	−	3.34793i	−0.116716	−	0.320673i	0.867555	−	0.497341i	$-0.165690\pi$
$109$	−1.21855	−	3.34793i	−0.116716	−	0.320673i	−0.984271	+	0.176668i	$0.943468\pi$
$110$	−0.0194533	−	0.0217702i	−0.00185480	−	0.00207570i
$111$	10.8593	+	0.590665i	1.03072	+	0.0560634i
$112$	2.43289	−	1.70353i	0.229886	−	0.160968i
$113$	7.56337	+	7.56337i	0.711502	+	0.711502i	0.966849	−	0.255347i	$-0.0821897\pi$
$113$	7.56337	+	7.56337i	0.711502	+	0.711502i	−0.255347	+	0.966849i	$0.582190\pi$
$114$	5.21685	+	5.45752i	0.488603	+	0.511143i
$115$	−9.26954	−	4.97379i	−0.864389	−	0.463809i
$116$	3.60172	+	0.635081i	0.334411	+	0.0589658i
$117$	18.9469	+	3.76079i	1.75165	+	0.347686i
$118$	−2.75622	+	1.28525i	−0.253731	+	0.118317i
$119$	−6.64977	+	2.42032i	−0.609584	+	0.221870i
$120$	−0.247893	−	3.86504i	−0.0226294	−	0.352828i
$121$	−5.49991	−	9.52613i	−0.499992	−	0.866012i
$122$	0.586672	+	2.18949i	0.0531148	+	0.198227i
$123$	0.222036	+	6.74071i	0.0200203	+	0.607789i
$124$	8.54351	−	1.50645i	0.767229	−	0.135283i
$125$	3.88791	+	10.4826i	0.347745	+	0.937589i
$126$	2.12130	+	8.65382i	0.188980	+	0.770944i
$127$	0.856648	+	0.0749470i	0.0760152	+	0.00665047i	0.125100	−	0.992144i	$-0.460075\pi$
$127$	0.856648	+	0.0749470i	0.0760152	+	0.00665047i	−0.0490847	+	0.998795i	$0.515630\pi$
$128$	0.906308	+	0.422618i	0.0801070	+	0.0373545i
$129$	−3.75228	−	12.3606i	−0.330370	−	1.08829i
$130$	5.67576	−	13.2318i	0.497797	−	1.16050i
$131$	18.3121	+	3.22892i	1.59994	+	0.282112i	0.901245	−	0.433311i	$-0.142655\pi$
$131$	18.3121	+	3.22892i	1.59994	+	0.282112i	0.698692	+	0.715423i	$0.253766\pi$
$132$	−0.00319166	+	0.0223883i	−0.000277798	+	0.00194865i
$133$	−9.64763	+	8.63258i	−0.836555	+	0.748539i
$134$	6.43282			0.555711
$135$	11.0777	+	3.50491i	0.953417	+	0.301654i
$136$	−1.82523	−	1.53155i	−0.156512	−	0.131329i
$137$	15.0203	−	7.00408i	1.28327	−	0.598399i	0.343163	−	0.939276i	$-0.388502\pi$
$137$	15.0203	−	7.00408i	1.28327	−	0.598399i	0.940108	+	0.340877i	$0.110724\pi$
$138$	1.67839	+	7.97375i	0.142874	+	0.678771i
$139$	−9.64099	−	11.4897i	−0.817738	−	0.974542i	0.182224	−	0.983257i	$-0.441670\pi$
$139$	−9.64099	−	11.4897i	−0.817738	−	0.974542i	−0.999962	+	0.00871501i	$0.997226\pi$
$140$	6.63793	−	0.206651i	0.561007	−	0.0174652i
$141$	−0.212138	+	0.0256213i	−0.0178653	+	0.00215770i
$142$	−9.11666	+	13.0199i	−0.765053	+	1.09261i
$143$	−0.0482202	+	0.0688656i	−0.00403238	+	0.00575883i
$144$	−2.16625	+	2.07542i	−0.180521	+	0.172951i
$145$	5.95981	+	5.59993i	0.494935	+	0.465049i
$146$	−4.88616	−	5.82310i	−0.404381	−	0.481923i
$147$	−3.08635	+	0.649643i	−0.254558	+	0.0535817i
$148$	−5.69063	+	2.65358i	−0.467767	+	0.218123i
$149$	−3.83904	−	3.22133i	−0.314506	−	0.263902i	0.471845	−	0.881681i	$-0.343588\pi$
$149$	−3.83904	−	3.22133i	−0.314506	−	0.263902i	−0.786352	+	0.617779i	$0.788033\pi$
$150$	4.27071	−	7.53399i	0.348702	−	0.615148i
$151$	2.01893			0.164298			0.0821491	−	0.996620i	$-0.473822\pi$
$151$	2.01893			0.164298			0.0821491	+	0.996620i	$0.473822\pi$
$152$	−4.14135	−	1.35986i	−0.335908	−	0.110299i
$153$	6.26545	−	3.44065i	0.506531	−	0.278160i
$154$	−0.0381890	−	0.00673375i	−0.00307736	−	0.000542621i
$155$	17.8277	+	7.64715i	1.43195	+	0.614234i
$156$	−10.6716	+	3.23954i	−0.854408	+	0.259371i
$157$	−11.0285	−	5.14268i	−0.880170	−	0.410430i	−0.0706357	−	0.997502i	$-0.522503\pi$
$157$	−11.0285	−	5.14268i	−0.880170	−	0.410430i	−0.809535	+	0.587072i	$0.800281\pi$
$158$	11.0186	+	0.964005i	0.876595	+	0.0766921i
$159$	−12.2318	−	5.22069i	−0.970047	−	0.414028i
$160$	1.17775	+	1.90076i	0.0931093	+	0.150269i
$161$	−13.7602	+	2.42630i	−1.08446	+	0.191219i
$162$	−3.45089	−	8.31212i	−0.271128	−	0.653062i
$163$	5.09520	+	19.0156i	0.399087	+	1.48941i	0.814706	+	0.579874i	$0.196898\pi$
$163$	5.09520	+	19.0156i	0.399087	+	1.48941i	−0.415619	+	0.909539i	$0.636435\pi$
$164$	−1.94693	−	3.37218i	−0.152030	−	0.263323i
$165$	−0.0333949	+	0.0379722i	−0.00259979	+	0.00295613i
$166$	4.90851	−	1.78655i	0.380974	−	0.138663i
$167$	17.5645	−	8.19047i	1.35918	−	0.633797i	0.399982	−	0.916523i	$-0.369016\pi$
$167$	17.5645	−	8.19047i	1.35918	−	0.633797i	0.959201	+	0.282726i	$0.0912386\pi$
$168$	−3.43457	−	3.82969i	−0.264983	−	0.295467i
$169$	−28.0266	−	4.94184i	−2.15589	−	0.380141i
$170$	−1.53840	−	5.10086i	−0.117990	−	0.391218i
$171$	8.30106	−	10.1041i	0.634798	−	0.772678i
$172$	5.27358	+	5.27358i	0.402106	+	0.402106i
$173$	12.1063	−	8.47690i	0.920422	−	0.644487i	−0.0142878	−	0.999898i	$-0.504548\pi$
$173$	12.1063	−	8.47690i	0.920422	−	0.644487i	0.934710	+	0.355411i	$0.115659\pi$
$174$	0.344045	−	6.32525i	0.0260820	−	0.479516i
$175$	12.6707	+	7.74447i	0.957816	+	0.585427i
$176$	−0.00446561	−	0.0122692i	−0.000336608	−	0.000924823i
$177$	2.78247	+	4.47255i	0.209143	+	0.336177i
$178$	−2.54346	−	0.681518i	−0.190640	−	0.0510820i
$179$	−1.69181	+	2.93030i	−0.126452	+	0.219021i	−0.922300	−	0.386476i	$-0.873692\pi$
$179$	−1.69181	+	2.93030i	−0.126452	+	0.219021i	0.795848	+	0.605497i	$0.207026\pi$
$180$	−6.59467	+	1.22896i	−0.491538	+	0.0916015i
$181$	0.783468	+	4.44327i	0.0582347	+	0.330266i	0.999982	−	0.00605676i	$-0.00192794\pi$
$181$	0.783468	+	4.44327i	0.0582347	+	0.330266i	−0.941747	+	0.336322i	$0.890817\pi$
$182$	−4.94952	−	18.4719i	−0.366883	−	1.36922i
$183$	3.64311	−	1.46353i	0.269306	−	0.108187i
$184$	−3.02401	−	3.60388i	−0.222933	−	0.265681i
$185$	−13.8959	−	2.00661i	−1.02165	−	0.147529i
$186$	−4.36475	−	14.3782i	−0.320039	−	1.05426i
$187$	0.00271137	+	0.0309911i	0.000198275	+	0.00226629i
$188$	0.101057	−	0.0707611i	0.00737037	−	0.00516079i
$189$	14.4402	−	5.44492i	1.05037	−	0.396060i
$190$	−6.08148	−	7.61680i	−0.441197	−	0.552580i
$191$			22.9198i			1.65842i	0.558941	+	0.829208i	$0.311208\pi$
$191$			22.9198i			1.65842i	−0.558941	+	0.829208i	$0.688792\pi$
$192$	0.538492	−	1.64622i	0.0388623	−	0.118805i
$193$	20.2393	−	1.77071i	1.45686	−	0.127459i	0.668976	−	0.743284i	$-0.266733\pi$
$193$	20.2393	−	1.77071i	1.45686	−	0.127459i	0.787883	+	0.615825i	$0.211177\pi$
$194$	10.8310	+	3.94217i	0.777622	+	0.283031i
$195$	−23.9315	−	7.01178i	−1.71377	−	0.502124i
$196$	1.39493	−	1.17048i	0.0996378	−	0.0836061i
$197$	−1.76851	−	0.473871i	−0.126001	−	0.0337619i	0.195267	−	0.980750i	$-0.437443\pi$
$197$	−1.76851	−	0.473871i	−0.126001	−	0.0337619i	−0.321269	+	0.946988i	$0.604109\pi$
$198$	0.0391607		0.000838602i	0.00278303		5.95969e-5i
$199$	−1.39191	+	0.245432i	−0.0986700	+	0.0173982i	−0.222765	−	0.974872i	$-0.571508\pi$
$199$	−1.39191	+	0.245432i	−0.0986700	+	0.0173982i	0.124095	+	0.992270i	$0.460397\pi$
$200$	−0.125101	+	4.99843i	−0.00884599	+	0.353443i
$201$	−1.33598	−	11.0616i	−0.0942325	−	0.780224i
$202$	1.58501	−	5.91535i	0.111521	−	0.416203i
$203$	10.8208	+	0.946700i	0.759473	+	0.0664453i
$204$	−2.25452	+	3.45665i	−0.157848	+	0.242014i
$205$	0.488591	−	8.69322i	0.0341247	−	0.607161i
$206$	−7.45932	+	8.88967i	−0.519716	+	0.619373i
$207$	13.3627	−	4.54208i	0.928774	−	0.315697i
$208$	4.55296	−	4.55296i	0.315691	−	0.315691i
$209$	0.0256798	+	0.0507893i	0.00177631	+	0.00351317i
$210$	−1.73392	−	11.3714i	−0.119652	−	0.784698i
$211$	0.824143	−	4.67395i	0.0567364	−	0.321768i	−0.943209	−	0.332199i	$-0.892209\pi$
$211$	0.824143	−	4.67395i	0.0567364	−	0.321768i	0.999946	+	0.0104313i	$0.00332046\pi$
$212$	7.64918	−	0.669216i	0.525348	−	0.0459620i
$213$	24.2819	+	12.9726i	1.66377	+	0.888867i
$214$	−0.378777	−	1.04068i	−0.0258926	−	0.0711395i
$215$	3.40548	+	16.3251i	0.232252	+	1.11336i
$216$	4.01868	+	3.29396i	0.273437	+	0.224126i
$217$	24.8878	−	6.66866i	1.68949	−	0.452698i
$218$	2.04353	−	2.91847i	0.138406	−	0.197664i
$219$	−8.99837	+	9.61137i	−0.608054	+	0.649476i
$220$	0.00667515	−	0.0284220i	0.000450038	−	0.00191621i
$221$	−13.2863	+	7.67083i	−0.893731	+	0.515996i
$222$	5.74482	+	9.23424i	0.385567	+	0.619762i
$223$	−4.38394	+	9.40139i	−0.293570	+	0.629564i	−0.996671	−	0.0815266i	$-0.974020\pi$
$223$	−4.38394	+	9.40139i	−0.293570	+	0.629564i	0.703101	+	0.711090i	$0.251798\pi$
$224$	2.79090	+	1.01580i	0.186475	+	0.0678712i
$225$	−13.8421	−	5.77904i	−0.922804	−	0.385269i
$226$	−1.85738	+	10.5337i	−0.123551	+	0.700693i
$227$	−18.4515	+	18.4515i	−1.22467	+	1.22467i	−0.258714	+	0.965954i	$0.583299\pi$
$227$	−18.4515	+	18.4515i	−1.22467	+	1.22467i	−0.965954	+	0.258714i	$0.916701\pi$
$228$	−1.47828	+	7.40369i	−0.0979012	+	0.490322i
$229$			5.63006i			0.372045i	0.982545	+	0.186022i	$0.0595597\pi$
$229$			5.63006i			0.372045i	−0.982545	+	0.186022i	$0.940440\pi$
$230$	−1.24250	−	10.4460i	−0.0819277	−	0.688789i
$231$	−0.00364790	+	0.0670665i	−0.000240015	+	0.00441265i
$232$	1.54563	+	3.31462i	0.101476	+	0.217616i
$233$	−25.7378	−	12.0017i	−1.68614	−	0.786258i	−0.998167	−	0.0605189i	$-0.980724\pi$
$233$	−25.7378	−	12.0017i	−1.68614	−	0.786258i	−0.687970	−	0.725740i	$-0.741498\pi$
$234$	7.78686	+	17.6775i	0.509043	+	1.15562i
$235$	0.275726	−	0.00858387i	0.0179864	−	0.000559950i
$236$	−2.63371	−	1.52058i	−0.171440	−	0.0989811i
$237$	−0.630705	−	19.1473i	−0.0409687	−	1.24375i
$238$	−5.79676	−	4.05894i	−0.375748	−	0.263102i
$239$	6.65461	−	11.5261i	0.430451	−	0.745563i	−0.566461	−	0.824089i	$-0.691688\pi$
$239$	6.65461	−	11.5261i	0.430451	−	0.745563i	0.996912	+	0.0785254i	$0.0250212\pi$
$240$	3.02387	−	2.41996i	0.195190	−	0.156208i
$241$	17.3290	−	14.5408i	1.11626	−	0.936655i	0.117852	−	0.993031i	$-0.462399\pi$
$241$	17.3290	−	14.5408i	1.11626	−	0.936655i	0.998410	+	0.0563764i	$0.0179547\pi$
$242$	4.64873	−	9.96923i	0.298832	−	0.640846i
$243$	−13.5765	+	7.66027i	−0.870930	+	0.491407i
$244$	−1.45702	+	1.73641i	−0.0932765	+	0.111163i
$245$	4.04327	−	0.480925i	0.258315	−	0.0307251i
$246$	−5.39431	+	4.04819i	−0.343929	+	0.258103i
$247$	−17.3481	+	22.0627i	−1.10383	+	1.40382i
$248$	6.13437	+	6.13437i	0.389533	+	0.389533i
$249$	−4.09148	−	8.06942i	−0.259287	−	0.511379i
$250$	−6.35680	+	9.19734i	−0.402040	+	0.581691i
$251$	−9.36305	+	25.7248i	−0.590991	+	1.62373i	0.177680	+	0.984088i	$0.443141\pi$
$251$	−9.36305	+	25.7248i	−0.590991	+	1.62373i	−0.768670	+	0.639645i	$0.779081\pi$
$252$	−5.87207	+	6.70129i	−0.369906	+	0.422142i
$253$	−0.00535354	+	0.0611912i	−0.000336574	+	0.00384706i
$254$	0.429960	+	0.744713i	0.0269781	+	0.0467274i
$255$	−8.45172	+	3.70473i	−0.529267	+	0.231999i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	25.1296	+	17.5959i	1.56754	+	1.09760i	0.950524	+	0.310650i	$0.100547\pi$
$257$	25.1296	+	17.5959i	1.56754	+	1.09760i	0.617014	+	0.786952i	$0.288342\pi$
$258$	7.97298	−	10.1634i	0.496376	−	0.632747i
$259$	−16.1500	+	9.32421i	−1.00351	+	0.579378i
$260$	14.0943	−	2.94013i	0.874093	−	0.182339i
$261$	−10.9481	+	0.722033i	−0.677668	+	0.0446927i
$262$	7.85842	+	16.8524i	0.485495	+	1.04115i
$263$	−0.559369	−	6.39361i	−0.0344921	−	0.394247i	−0.993743	−	0.111691i	$-0.964373\pi$
$263$	−0.559369	−	6.39361i	−0.0344921	−	0.394247i	0.959251	−	0.282556i	$-0.0911823\pi$
$264$	−0.0201701	+	0.0102269i	−0.00124138	+	0.000629424i
$265$	15.1291	+	8.11787i	0.929372	+	0.498677i
$266$	−12.6050	−	2.95143i	−0.772865	−	0.180964i
$267$	−0.643678	+	4.51516i	−0.0393925	+	0.276323i
$268$	3.68971	+	5.26945i	0.225385	+	0.321883i
$269$	−18.5678	−	15.5802i	−1.13210	−	0.949944i	−0.132947	−	0.991123i	$-0.542444\pi$
$269$	−18.5678	−	15.5802i	−1.13210	−	0.949944i	−0.999152	+	0.0411792i	$0.986889\pi$
$270$	3.48286	+	11.0847i	0.211960	+	0.674591i
$271$	7.75631	−	2.82307i	0.471162	−	0.171489i	−0.0955166	−	0.995428i	$-0.530450\pi$
$271$	7.75631	−	2.82307i	0.471162	−	0.171489i	0.566679	+	0.823939i	$0.308228\pi$
$272$	0.207663	−	2.37360i	0.0125914	−	0.143921i
$273$	−30.7354	+	12.3472i	−1.86019	+	0.747288i
$274$	14.3527	+	8.28654i	0.867078	+	0.500608i
$275$	0.0473025	−	0.0449925i	0.00285245	−	0.00271315i
$276$	−5.56903	+	5.94841i	−0.335216	+	0.358052i
$277$	3.01897	−	0.808931i	0.181392	−	0.0486039i	−0.166979	−	0.985960i	$-0.553401\pi$
$277$	3.01897	−	0.808931i	0.181392	−	0.0486039i	0.348372	+	0.937356i	$0.386735\pi$
$278$	3.88195	−	14.4876i	0.232824	−	0.868911i
$279$	−23.8176	+	10.4915i	−1.42592	+	0.628110i
$280$	3.97664	+	5.31894i	0.237649	+	0.317867i
$281$	3.91744	−	10.7631i	0.233695	−	0.642072i	−0.766305	−	0.642477i	$-0.777907\pi$
$281$	3.91744	−	10.7631i	0.233695	−	0.642072i	1.00000		0.000405376i	$0.000129035\pi$
$282$	−0.142665	−	0.159078i	−0.00849560	−	0.00947295i
$283$	−6.31644	−	9.02082i	−0.375474	−	0.536232i	0.586294	−	0.810098i	$-0.300586\pi$
$283$	−6.31644	−	9.02082i	−0.375474	−	0.536232i	−0.961768	+	0.273866i	$0.911697\pi$
$284$	−15.8944			−0.943160
$285$	−11.8345	+	12.0393i	−0.701015	+	0.713147i
$286$	−0.0840694			−0.00497113
$287$	−6.63330	−	9.47333i	−0.391551	−	0.559193i
$288$	−2.94259	−	0.584078i	−0.173394	−	0.0344171i
$289$	3.87266	−	10.6400i	0.227803	−	0.625885i
$290$	−1.16879	+	8.09398i	−0.0686338	+	0.475295i
$291$	4.52937	−	19.4433i	0.265517	−	1.13978i
$292$	1.96742	−	7.34250i	0.115134	−	0.429687i
$293$	−30.5022	+	8.17305i	−1.78196	+	0.477475i	−0.990939	−	0.134314i	$-0.957117\pi$
$293$	−30.5022	+	8.17305i	−1.78196	+	0.477475i	−0.791021	+	0.611789i	$0.790450\pi$
$294$	−2.30241	−	2.15557i	−0.134280	−	0.125715i
$295$	−3.06428	−	6.07068i	−0.178409	−	0.353449i
$296$	−5.43770	−	3.13946i	−0.316060	−	0.182477i
$297$	−0.00669093	−	0.0675132i	−0.000388247	−	0.00391751i
$298$	0.436782	−	4.99244i	0.0253021	−	0.289204i
$299$	−28.4650	+	10.3604i	−1.64617	+	0.599158i
$300$	8.62106	−	0.822964i	0.497737	−	0.0475138i
$301$	16.9680	+	14.2379i	0.978022	+	0.820658i
$302$	1.15801	+	1.65381i	0.0666361	+	0.0951662i
$303$	−10.5010	−	1.49701i	−0.603264	−	0.0860009i
$304$	−1.26145	−	4.17238i	−0.0723489	−	0.239302i
$305$	−4.85266	+	1.46355i	−0.277863	+	0.0838025i
$306$	6.41213	+	3.15888i	0.366557	+	0.180581i
$307$	1.73035	+	19.7780i	0.0987565	+	1.12879i	0.870269	+	0.492577i	$0.163945\pi$
$307$	1.73035	+	19.7780i	0.0987565	+	1.12879i	−0.771512	+	0.636214i	$0.780499\pi$
$308$	−0.0163883	−	0.0351449i	−0.000933812	−	0.00200257i
$309$	16.8354	+	10.9805i	0.957735	+	0.624658i
$310$	3.96135	+	18.9898i	0.224989	+	1.07855i
$311$	−0.0170796	+	0.00986093i	−0.000968497	+	0.000559162i	−0.500484	−	0.865746i	$-0.666845\pi$
$311$	−0.0170796	+	0.00986093i	−0.000968497	+	0.000559162i	0.499516	+	0.866305i	$0.333511\pi$
$312$	−8.77463	−	6.88350i	−0.496766	−	0.389701i
$313$	−7.92925	−	5.55212i	−0.448188	−	0.313824i	0.327602	−	0.944816i	$-0.393759\pi$
$313$	−7.92925	−	5.55212i	−0.448188	−	0.313824i	−0.775790	+	0.630991i	$0.782648\pi$
$314$	−2.11306	−	11.9837i	−0.119247	−	0.676282i
$315$	−19.1936	+	5.34319i	−1.08144	+	0.301055i
$316$	5.53036	+	9.57886i	0.311107	+	0.538853i
$317$	1.43343	−	16.3842i	0.0805093	−	0.920226i	−0.843318	−	0.537415i	$-0.819401\pi$
$317$	1.43343	−	16.3842i	0.0805093	−	0.920226i	0.923827	−	0.382810i	$-0.125044\pi$
$318$	−2.73935	−	13.0142i	−0.153615	−	0.729800i
$319$	0.0163320	−	0.0448718i	0.000914416	−	0.00251234i
$320$	−0.881485	+	2.05499i	−0.0492765	+	0.114877i
$321$	−1.71084	+	0.867457i	−0.0954899	+	0.0484168i
$322$	−9.88004	−	9.88004i	−0.550593	−	0.550593i
$323$	0.330172	+	10.3806i	0.0183712	+	0.577589i
$324$	4.82954	−	7.59444i	0.268308	−	0.421913i
$325$	29.9678	+	11.7646i	1.66231	+	0.652582i
$326$	−12.6541	+	15.0806i	−0.700848	+	0.835238i
$327$	−5.44287	−	2.90786i	−0.300991	−	0.160805i
$328$	1.64562	−	3.52904i	0.0908640	−	0.194859i
$329$	0.280682	−	0.235520i	0.0154745	−	0.0129847i
$330$	−0.0502596	−	0.00557555i	−0.00276670	−	0.000306924i
$331$	−18.0365	+	31.2401i	−0.991373	+	1.71711i	−0.382178	+	0.924089i	$0.624826\pi$
$331$	−18.0365	+	31.2401i	−0.991373	+	1.71711i	−0.609195	+	0.793020i	$0.708507\pi$
$332$	4.27886	+	2.99609i	0.234833	+	0.164432i
$333$	14.6857	−	11.7963i	0.804771	−	0.646434i
$334$	16.7838	+	9.69015i	0.918370	+	0.530221i
$335$	0.447590	+	14.3772i	0.0244545	+	0.785513i
$336$	1.16711	−	5.01006i	0.0636711	−	0.273321i
$337$	7.92261	+	3.69437i	0.431572	+	0.201245i	0.626251	−	0.779622i	$-0.284589\pi$
$337$	7.92261	+	3.69437i	0.431572	+	0.201245i	−0.194679	+	0.980867i	$0.562366\pi$
$338$	−12.0273	−	25.7925i	−0.654197	−	1.40293i
$339$	18.4991	+	1.00621i	1.00473	+	0.0546497i
$340$	3.29599	−	4.18592i	0.178750	−	0.227014i
$341$		−	0.113270i		−	0.00613390i
$342$	13.0381	+	1.00437i	0.705018	+	0.0543099i
$343$	−10.8766	+	10.8766i	−0.587281	+	0.587281i
$344$	−1.29506	+	7.34466i	−0.0698250	+	0.395998i
$345$	−17.7044	+	4.30598i	−0.953175	+	0.231826i
$346$	13.8877	+	5.05472i	0.746609	+	0.271744i
$347$	−7.32202	+	15.7021i	−0.393067	+	0.842934i	0.605813	+	0.795607i	$0.292848\pi$
$347$	−7.32202	+	15.7021i	−0.393067	+	0.842934i	−0.998879	+	0.0473268i	$0.984930\pi$
$348$	5.37868	−	3.34619i	0.288327	−	0.179375i
$349$	−13.1227	+	7.57638i	−0.702441	+	0.405554i	−0.808256	−	0.588832i	$-0.799588\pi$
$349$	−13.1227	+	7.57638i	−0.702441	+	0.405554i	0.105815	+	0.994386i	$0.466255\pi$
$350$	0.923724	+	14.8213i	0.0493751	+	0.792231i
$351$	28.7803	−	17.0612i	1.53618	−	0.910661i
$352$	0.00748894	−	0.0106953i	0.000399162	−	0.000570062i
$353$	10.2188	−	2.73813i	0.543894	−	0.145736i	0.0235975	−	0.999722i	$-0.492488\pi$
$353$	10.2188	−	2.73813i	0.543894	−	0.145736i	0.520297	+	0.853986i	$0.325821\pi$
$354$	−2.06774	+	4.84461i	−0.109899	+	0.257488i
$355$	−29.7337	−	19.4697i	−1.57810	−	1.03334i
$356$	−0.900602	−	2.47438i	−0.0477318	−	0.131142i
$357$	−5.77568	+	10.8108i	−0.305682	+	0.572169i
$358$	−3.37075	+	0.294902i	−0.178149	+	0.0155861i
$359$	4.81261	−	27.2936i	0.254000	−	1.44050i	−0.544628	−	0.838678i	$-0.683329\pi$
$359$	4.81261	−	27.2936i	0.254000	−	1.44050i	0.798627	−	0.601826i	$-0.205560\pi$
$360$	−4.78925	−	4.69713i	−0.252416	−	0.247561i
$361$	7.61987	+	17.4051i	0.401046	+	0.916058i
$362$	−3.19033	+	3.19033i	−0.167680	+	0.167680i
$363$	−18.1081	−	5.92332i	−0.950428	−	0.310894i
$364$	12.2923	−	14.6494i	0.644293	−	0.767839i
$365$	12.6746	−	11.3257i	0.663417	−	0.592812i
$366$	3.28846	+	2.14481i	0.171890	+	0.112111i
$367$	10.1359	+	0.886781i	0.529092	+	0.0462896i	0.348573	−	0.937282i	$-0.386666\pi$
$367$	10.1359	+	0.886781i	0.529092	+	0.0462896i	0.180520	+	0.983571i	$0.442222\pi$
$368$	1.21762	−	4.54423i	0.0634729	−	0.236884i
$369$	8.08139	+	8.43508i	0.420700	+	0.439113i
$370$	−6.32667	−	12.5338i	−0.328908	−	0.651603i
$371$	22.4584	−	3.96003i	1.16598	−	0.205594i
$372$	9.27438	−	11.8224i	0.480854	−	0.612961i
$373$	−13.1544	−	3.52470i	−0.681107	−	0.182502i	−0.0983541	−	0.995151i	$-0.531358\pi$
$373$	−13.1544	−	3.52470i	−0.681107	−	0.182502i	−0.582753	+	0.812649i	$0.698024\pi$
$374$	−0.0238312	+	0.0199968i	−0.00123228	+	0.00103401i
$375$	17.1355	+	9.02076i	0.884874	+	0.465830i
$376$	0.115928	+	0.0421944i	0.00597854	+	0.00217601i
$377$	23.4591	−	2.05241i	1.20821	−	0.105704i
$378$	12.7428	+	8.70561i	0.655417	+	0.447768i
$379$		−	0.616566i		−	0.0316709i	−0.999875	−	0.0158354i	$-0.994959\pi$
$379$		−	0.616566i		−	0.0316709i	0.999875	−	0.0158354i	$-0.00504079\pi$
$380$	2.75112	−	9.35047i	0.141129	−	0.479669i
$381$	1.19128	−	0.894003i	0.0610311	−	0.0458011i
$382$	−18.7748	+	13.1462i	−0.960600	+	0.672620i
$383$	0.734884	+	8.39976i	0.0375508	+	0.429208i	0.991580	+	0.129494i	$0.0413355\pi$
$383$	0.734884	+	8.39976i	0.0375508	+	0.429208i	−0.954029	+	0.299713i	$0.903109\pi$
$384$	1.65737	−	0.503124i	0.0845772	−	0.0256749i
$385$	0.0123927	−	0.0858204i	0.000631589	−	0.00437381i
$386$	13.0593	+	15.5635i	0.664700	+	0.792159i
$387$	−19.1324	−	11.5992i	−0.972555	−	0.589621i
$388$	2.98318	+	11.1334i	0.151448	+	0.565212i
$389$	−5.29739	−	30.0430i	−0.268588	−	1.52324i	−0.758619	−	0.651535i	$-0.774125\pi$
$389$	−5.29739	−	30.0430i	−0.268588	−	1.52324i	0.490030	−	0.871705i	$-0.336986\pi$
$390$	−7.98285	−	23.6254i	−0.404227	−	1.19632i
$391$	−5.60466	+	9.70756i	−0.283440	+	0.490932i
$392$	1.75890	+	0.471297i	0.0888381	+	0.0238041i
$393$	27.3466	−	17.0129i	1.37946	−	0.858188i
$394$	−0.626204	−	1.72048i	−0.0315477	−	0.0866766i
$395$	−1.38787	+	24.6935i	−0.0698313	+	1.24247i
$396$	0.0217747	+	0.0325596i	0.00109422	+	0.00163618i
$397$	12.7870	−	8.95353i	0.641760	−	0.449365i	−0.206859	−	0.978371i	$-0.566324\pi$
$397$	12.7870	−	8.95353i	0.641760	−	0.449365i	0.848618	+	0.529006i	$0.177435\pi$
$398$	−0.999414	−	0.999414i	−0.0500961	−	0.0500961i
$399$	−2.45731	+	22.2880i	−0.123020	+	1.11580i
$400$	−4.16623	+	2.76451i	−0.208312	+	0.138225i
$401$	−22.1025	−	3.89727i	−1.10375	−	0.194620i	−0.408053	−	0.912958i	$-0.633792\pi$
$401$	−22.1025	−	3.89727i	−1.10375	−	0.194620i	−0.695694	+	0.718338i	$0.744903\pi$
$402$	8.29483	−	7.43903i	0.413709	−	0.371025i
$403$	50.6255	−	23.6071i	2.52184	−	1.17595i
$404$	5.75470	−	2.09454i	0.286307	−	0.104207i
$405$	18.3374	−	8.29105i	0.911190	−	0.411985i
$406$	5.43108	+	9.40691i	0.269540	+	0.466857i
$407$	0.0212183	+	0.0791876i	0.00105175	+	0.00392518i
$408$	−4.12466	+	0.135865i	−0.204201	+	0.00672630i
$409$	−31.4272	+	5.54147i	−1.55398	+	0.274008i	−0.883682	−	0.468088i	$-0.844943\pi$
$409$	−31.4272	+	5.54147i	−1.55398	+	0.274008i	−0.670294	+	0.742095i	$0.733832\pi$
$410$	7.40131	−	4.58600i	0.365525	−	0.226486i
$411$	11.2684	−	26.4012i	0.555827	−	1.30228i
$412$	−11.5605	−	1.01141i	−0.569544	−	0.0498287i
$413$	−8.18600	−	3.81719i	−0.402806	−	0.187832i
$414$	11.3852	+	8.34088i	0.559552	+	0.409932i
$415$	4.33445	+	10.8461i	0.212770	+	0.532416i
$416$	6.34104	+	1.11810i	0.310895	+	0.0548192i
$417$	−25.7185	−	3.66641i	−1.25944	−	0.179545i
$418$	−0.0268749	+	0.0501672i	−0.00131449	+	0.00245376i
$419$	15.8437			0.774013			0.387007	−	0.922077i	$-0.373509\pi$
$419$	15.8437			0.774013			0.387007	+	0.922077i	$0.373509\pi$
$420$	8.32033	−	7.94269i	0.405991	−	0.387564i
$421$	−2.91058	−	2.44226i	−0.141853	−	0.119029i	0.569100	−	0.822268i	$-0.307292\pi$
$421$	−2.91058	−	2.44226i	−0.141853	−	0.119029i	−0.710953	+	0.703240i	$0.751736\pi$
$422$	4.30138	−	2.00577i	0.209388	−	0.0976393i
$423$	−0.243914	+	0.278358i	−0.0118595	+	0.0135343i
$424$	4.93558	+	5.88199i	0.239693	+	0.285655i
$425$	11.2933	−	3.79323i	0.547806	−	0.183998i
$426$	3.30097	+	27.3313i	0.159933	+	1.32421i
$427$	−3.86143	+	5.51470i	−0.186868	+	0.266875i
$428$	0.635218	−	0.907186i	0.0307044	−	0.0438505i
$429$	0.0174597	+	0.144562i	0.000842960	+	0.00697952i
$430$	−11.4194	+	12.1533i	−0.550694	+	0.586084i
$431$	−11.7945	−	14.0561i	−0.568121	−	0.677060i	0.403123	−	0.915146i	$-0.367925\pi$
$431$	−11.7945	−	14.0561i	−0.568121	−	0.677060i	−0.971244	+	0.238085i	$0.923480\pi$
$432$	−0.393232	+	5.18125i	−0.0189194	+	0.249283i
$433$	19.3673	−	9.03110i	0.930731	−	0.434007i	0.102715	−	0.994711i	$-0.467247\pi$
$433$	19.3673	−	9.03110i	0.930731	−	0.434007i	0.828017	+	0.560704i	$0.189469\pi$
$434$	19.7377	+	16.5619i	0.947439	+	0.794996i
$435$	14.1608	+	0.328830i	0.678957	+	0.0157662i
$436$	3.56279			0.170627
$437$	−2.91711	+	20.2980i	−0.139544	+	0.970986i
$438$	−13.0344	−	1.85818i	−0.622809	−	0.0887873i
$439$	17.9221	+	3.16015i	0.855375	+	0.150826i	0.584106	−	0.811678i	$-0.301445\pi$
$439$	17.9221	+	3.16015i	0.855375	+	0.150826i	0.271270	+	0.962503i	$0.412556\pi$
$440$	0.0271107	−	0.0108342i	0.00129245	−	0.000516503i
$441$	−3.22845	+	4.40680i	−0.153736	+	0.209848i
$442$	−13.9043	−	6.48366i	−0.661358	−	0.308396i
$443$	−15.9443	−	1.39494i	−0.757536	−	0.0662758i	−0.298158	−	0.954517i	$-0.596372\pi$
$443$	−15.9443	−	1.39494i	−0.757536	−	0.0662758i	−0.459378	+	0.888241i	$0.651928\pi$
$444$	−4.26916	+	10.0024i	−0.202605	+	0.474694i
$445$	1.34621	−	5.73202i	0.0638165	−	0.271724i
$446$	−10.2157	+	1.80130i	−0.483727	+	0.0852941i
$447$	−8.67548	+	0.285767i	−0.410336	+	0.0135163i
$448$	0.768695	+	2.86881i	0.0363174	+	0.135538i
$449$	6.43751	+	11.1501i	0.303805	+	0.526205i	0.976995	−	0.213264i	$-0.0684096\pi$
$449$	6.43751	+	11.1501i	0.303805	+	0.526205i	−0.673190	+	0.739470i	$0.735076\pi$
$450$	−3.20557	−	14.6535i	−0.151112	−	0.690771i
$451$	−0.0477744	+	0.0173885i	−0.00224961	+	0.000818791i
$452$	−9.69407	+	4.52042i	−0.455971	+	0.212623i
$453$	2.60332	−	2.33473i	0.122315	−	0.109695i
$454$	−25.6979	−	4.53123i	−1.20606	−	0.212661i
$455$	40.9399	−	12.3474i	1.91929	−	0.578853i
$456$	−6.91266	+	3.03565i	−0.323715	+	0.142157i
$457$	−22.1276	−	22.1276i	−1.03508	−	1.03508i	−0.999362	−	0.0357227i	$-0.988627\pi$
$457$	−22.1276	−	22.1276i	−1.03508	−	1.03508i	−0.0357227	−	0.999362i	$-0.511373\pi$
$458$	−4.61188	+	3.22927i	−0.215499	+	0.150894i
$459$	4.10019	−	11.6820i	0.191380	−	0.545271i
$460$	7.84420	−	7.00938i	0.365738	−	0.326814i
$461$	4.06748	+	11.1753i	0.189441	+	0.520486i	0.997658	−	0.0683995i	$-0.0217893\pi$
$461$	4.06748	+	11.1753i	0.189441	+	0.520486i	−0.808217	+	0.588885i	$0.799567\pi$
$462$	−0.0570300	+	0.0354796i	−0.00265328	+	0.00165066i
$463$	−11.5183	−	3.08632i	−0.535301	−	0.143434i	−0.0189662	−	0.999820i	$-0.506037\pi$
$463$	−11.5183	−	3.08632i	−0.535301	−	0.143434i	−0.516335	+	0.856387i	$0.672704\pi$
$464$	−1.82864	+	3.16730i	−0.0848926	+	0.147038i
$465$	31.8313	−	10.7556i	1.47614	−	0.498778i
$466$	−4.93134	−	27.9670i	−0.228440	−	1.29555i
$467$	0.999809	+	3.73134i	0.0462656	+	0.172666i	0.985193	−	0.171450i	$-0.0548453\pi$
$467$	0.999809	+	3.73134i	0.0462656	+	0.172666i	−0.938927	+	0.344116i	$0.888179\pi$
$468$	−10.0142	+	16.5180i	−0.462908	+	0.763546i
$469$	12.2808	+	14.6357i	0.567074	+	0.675813i
$470$	0.165182	+	0.220938i	0.00761926	+	0.0101911i
$471$	−20.1679	+	6.12232i	−0.929286	+	0.282101i
$472$	−0.265054	−	3.02958i	−0.0122001	−	0.139448i
$473$	0.0797653	−	0.0558522i	0.00366761	−	0.00256809i
$474$	15.3228	−	11.4991i	0.703801	−	0.528171i
$475$	16.6003	−	14.1220i	0.761673	−	0.647961i
$476$		−	7.07654i		−	0.324353i
$477$	−21.8097	+	7.41326i	−0.998598	+	0.339430i
$478$	13.2586	−	1.15998i	0.606433	−	0.0530560i
$479$	32.2060	+	11.7220i	1.47153	+	0.535593i	0.948516	−	0.316730i	$-0.102585\pi$
$479$	32.2060	+	11.7220i	1.47153	+	0.535593i	0.523015	+	0.852324i	$0.324807\pi$
$480$	3.71674	+	1.08898i	0.169645	+	0.0497049i
$481$	−30.9704	+	25.9873i	−1.41213	+	1.18492i
$482$	21.8507	+	5.85486i	0.995270	+	0.266682i
$483$	−14.9374	+	19.0412i	−0.679674	+	0.866403i
$484$	10.8327	−	1.91010i	0.492396	−	0.0868227i
$485$	−8.05708	+	24.4815i	−0.365853	+	1.11165i
$486$	−14.0621	−	6.72743i	−0.637868	−	0.305162i
$487$	1.97848	−	7.38378i	0.0896534	−	0.334591i	−0.906501	−	0.422203i	$-0.861257\pi$
$487$	1.97848	−	7.38378i	0.0896534	−	0.334591i	0.996155	+	0.0876121i	$0.0279236\pi$
$488$	−2.25810	−	0.197558i	−0.102220	−	0.00894305i
$489$	28.5600	+	18.6275i	1.29153	+	0.842366i
$490$	2.71307	+	3.03621i	0.122564	+	0.137162i
$491$	16.5625	−	19.7385i	0.747457	−	0.890784i	−0.249529	−	0.968367i	$-0.580276\pi$
$491$	16.5625	−	19.7385i	0.747457	−	0.890784i	0.996986	+	0.0775831i	$0.0247203\pi$
$492$	−6.41014	−	2.09681i	−0.288991	−	0.0945316i
$493$	6.16179	−	6.16179i	0.277513	−	0.277513i
$494$	−28.0232	−	1.55605i	−1.26082	−	0.0700102i
$495$	0.000850510		0.0875820i	3.82276e−5		0.00393652i
$496$	−1.50645	+	8.54351i	−0.0676416	+	0.383615i
$497$	−47.0269	+	4.11432i	−2.10944	+	0.184552i
$498$	4.26331	−	7.97997i	0.191043	−	0.357591i
$499$	1.02094	+	2.80501i	0.0457036	+	0.125570i	0.960445	−	0.278471i	$-0.0898276\pi$
$499$	1.02094	+	2.80501i	0.0457036	+	0.125570i	−0.914741	+	0.404041i	$0.867605\pi$
$500$	−11.1801	+	0.0681879i	−0.499991	+	0.00304945i
$501$	13.1770	−	30.8732i	0.588707	−	1.37931i
$502$	−26.4429	+	7.08536i	−1.18021	+	0.316235i
$503$	13.1989	−	18.8500i	0.588509	−	0.840478i	−0.408888	−	0.912585i	$-0.634083\pi$
$503$	13.1989	−	18.8500i	0.588509	−	0.840478i	0.997397	+	0.0721063i	$0.0229721\pi$
$504$	−8.85746	−	0.966415i	−0.394543	−	0.0430475i
$505$	13.3310	+	3.13090i	0.593222	+	0.139323i
$506$	−0.0531956	+	0.0307125i	−0.00236483	+	0.00136534i
$507$	−41.8538	+	26.0382i	−1.85879	+	1.15640i
$508$	−0.363418	+	0.779352i	−0.0161241	+	0.0345782i
$509$	−4.17522	−	1.51966i	−0.185064	−	0.0673576i	0.247826	−	0.968805i	$-0.420284\pi$
$509$	−4.17522	−	1.51966i	−0.185064	−	0.0673576i	−0.432890	+	0.901447i	$0.642506\pi$
$510$	−7.88244	−	4.79830i	−0.349040	−	0.212472i
$511$	3.92038	−	22.2336i	0.173427	−	0.983556i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.980702	−	22.6283i	−0.0432991	−	0.999062i
$514$			30.6775i			1.35313i
$515$	−20.3873	−	16.0529i	−0.898372	−	0.707377i
$516$	12.8985	+	0.701580i	0.567825	+	0.0308853i
$517$	−0.000680739	−	0.00145985i	−2.99389e−5	−	6.42041e-5i
$518$	−16.9012	−	7.88116i	−0.742597	−	0.346278i
$519$	5.80765	−	24.9305i	0.254927	−	1.09433i
$520$	10.4926	+	9.85901i	0.460131	+	0.432346i
$521$	−26.6388	−	15.3799i	−1.16707	−	0.673807i	−0.214081	−	0.976816i	$-0.568676\pi$
$521$	−26.6388	−	15.3799i	−1.16707	−	0.673807i	−0.952988	+	0.303009i	$0.902009\pi$
$522$	−6.87101	−	8.55399i	−0.300736	−	0.374398i
$523$	8.22569	+	5.75969i	0.359684	+	0.251854i	0.739424	−	0.673240i	$-0.235098\pi$
$523$	8.22569	+	5.75969i	0.359684	+	0.251854i	−0.379740	+	0.925093i	$0.623987\pi$
$524$	−9.29730	+	16.1034i	−0.406155	+	0.703480i
$525$	25.2942	−	4.66650i	1.10393	−	0.203663i
$526$	4.91650	−	4.12543i	0.214370	−	0.179877i
$527$	8.73567	−	18.7337i	0.380532	−	0.816053i
$528$	−0.0199465	−	0.0106564i	−0.000868060	−	0.000463761i
$529$	0.557565	−	0.664480i	0.0242419	−	0.0288904i
$530$	2.02791	+	17.0492i	0.0880869	+	0.740571i
$531$	8.76001	+	2.54946i	0.380152	+	0.110637i
$532$	−4.81228	−	12.0183i	−0.208639	−	0.521060i
$533$	−17.7286	−	17.7286i	−0.767911	−	0.767911i
$534$	−4.06780	+	2.06252i	−0.176031	+	0.0892539i
$535$	2.29955	−	0.918970i	0.0994182	−	0.0397305i
$536$	−2.20015	+	6.04487i	−0.0950321	+	0.261099i
$537$	1.20714	+	5.73494i	0.0520920	+	0.247481i
$538$	2.11253	−	24.1463i	0.0910776	−	1.04102i
$539$	−0.0118877	−	0.0205901i	−0.000512039	−	0.000886877i
$540$	−7.08234	+	9.21089i	−0.304775	+	0.396374i
$541$	−4.47302	−	25.3677i	−0.192310	−	1.09064i	−0.916198	−	0.400726i	$-0.868758\pi$
$541$	−4.47302	−	25.3677i	−0.192310	−	1.09064i	0.723888	−	0.689918i	$-0.242353\pi$
$542$	6.76135	+	4.73435i	0.290425	+	0.203358i
$543$	6.14853	+	4.82338i	0.263859	+	0.206991i
$544$	2.06345	−	1.19133i	0.0884697	−	0.0510780i
$545$	6.66492	+	4.36420i	0.285494	+	0.186942i
$546$	−27.7434	−	18.0949i	−1.18731	−	0.774391i
$547$	−1.74350	−	3.73894i	−0.0745465	−	0.159865i	0.865503	−	0.500904i	$-0.166999\pi$
$547$	−1.74350	−	3.73894i	−0.0745465	−	0.159865i	−0.940049	+	0.341039i	$0.889221\pi$
$548$	1.44444	+	16.5100i	0.0617034	+	0.705273i
$549$	3.00517	−	6.10012i	0.128258	−	0.260347i
$550$	0.0639873	+	0.0129413i	0.00272843	+	0.000551818i
$551$	6.27455	−	14.6550i	0.267305	−	0.624324i
$552$	−8.06692	−	1.15002i	−0.343351	−	0.0489479i
$553$	18.8422	+	26.9095i	0.801253	+	1.14431i
$554$	2.39425	+	2.00901i	0.101722	+	0.0853547i
$555$	−20.2387	+	13.4821i	−0.859084	+	0.572283i
$556$	14.0942	−	5.12986i	0.597726	−	0.217555i
$557$	0.555233	−	6.34634i	0.0235260	−	0.268903i	−0.975317	−	0.220810i	$-0.929130\pi$
$557$	0.555233	−	6.34634i	0.0235260	−	0.268903i	0.998843	−	0.0480933i	$-0.0153145\pi$
$558$	−22.2553	−	13.4925i	−0.942143	−	0.571184i
$559$	41.5872	+	24.0104i	1.75895	+	1.01553i
$560$	−2.07612	+	6.30829i	−0.0877319	+	0.266574i
$561$	0.0393348	+	0.0368261i	0.00166072	+	0.00155480i
$562$	11.0636	−	2.96447i	0.466688	−	0.125049i
$563$	3.44082	−	12.8413i	0.145013	−	0.541198i	−0.854741	−	0.519054i	$-0.826284\pi$
$563$	3.44082	−	12.8413i	0.145013	−	0.541198i	0.999755	−	0.0221434i	$-0.00704903\pi$
$564$	0.0484795	−	0.208108i	0.00204135	−	0.00876293i
$565$	−23.6720	−	3.41829i	−0.995887	−	0.143808i
$566$	3.76646	−	10.3483i	0.158316	−	0.434970i
$567$	12.3233	−	23.7199i	0.517532	−	0.996141i
$568$	−9.11666	−	13.0199i	−0.382526	−	0.546304i
$569$	−32.9924			−1.38311			−0.691557	−	0.722322i	$-0.743075\pi$
$569$	−32.9924			−1.38311			−0.691557	+	0.722322i	$0.743075\pi$
$570$	−16.6500	−	2.78878i	−0.697392	−	0.116809i
$571$	27.9412			1.16930			0.584651	−	0.811285i	$-0.301232\pi$
$571$	27.9412			1.16930			0.584651	+	0.811285i	$0.301232\pi$
$572$	−0.0482202	−	0.0688656i	−0.00201619	−	0.00287942i
$573$	26.5048	+	29.5540i	1.10726	+	1.23464i
$574$	3.95540	−	10.8674i	0.165095	−	0.453595i
$575$	23.2602	−	3.50378i	0.970018	−	0.146118i
$576$	−1.20935	−	2.74544i	−0.0503897	−	0.114394i
$577$	3.16294	−	11.8042i	0.131675	−	0.491417i	−0.868315	−	0.496014i	$-0.834797\pi$
$577$	3.16294	−	11.8042i	0.131675	−	0.491417i	0.999989	+	0.00459688i	$0.00146324\pi$
$578$	10.9371	−	2.93058i	0.454923	−	0.121896i
$579$	24.0500	−	25.6884i	0.999485	−	1.06757i
$580$	−7.30059	+	3.68510i	−0.303141	+	0.153015i
$581$	13.4355	+	7.75696i	0.557397	+	0.321813i
$582$	18.5249	−	7.44194i	0.767883	−	0.308479i
$583$	0.00873767	−	0.0998720i	0.000361877	−	0.00413628i
$584$	7.14309	−	2.59987i	0.295583	−	0.107583i
$585$	−38.9672	+	18.6335i	−1.61110	+	0.770400i
$586$	−24.1903	−	20.2981i	−0.999294	−	0.838507i
$587$	−5.34832	−	7.63819i	−0.220749	−	0.315262i	0.693468	−	0.720487i	$-0.256082\pi$
$587$	−5.34832	−	7.63819i	−0.220749	−	0.315262i	−0.914217	+	0.405225i	$0.867193\pi$
$588$	0.445129	−	3.12241i	0.0183568	−	0.128766i
$589$	2.09653	−	37.7566i	0.0863859	−	1.55573i
$590$	3.21521	−	5.99211i	0.132368	−	0.246691i
$591$	−2.82841	+	1.43410i	−0.116345	+	0.0589912i
$592$	−0.547243	−	6.25502i	−0.0224916	−	0.257080i
$593$	0.417073	+	0.894416i	0.0171271	+	0.0367293i	0.914685	−	0.404167i	$-0.132438\pi$
$593$	0.417073	+	0.894416i	0.0171271	+	0.0367293i	−0.897558	+	0.440896i	$0.854661\pi$
$594$	0.0514658	−	0.0442049i	0.00211167	−	0.00181375i
$595$	8.66833	−	13.2381i	0.355367	−	0.542709i
$596$	4.34009	−	2.50575i	0.177777	−	0.102640i
$597$	−1.51099	+	1.92611i	−0.0618406	+	0.0788303i
$598$	−24.8136	−	17.3747i	−1.01470	−	0.710503i
$599$	−2.80787	−	15.9242i	−0.114726	−	0.650646i	−0.986885	−	0.161423i	$-0.948392\pi$
$599$	−2.80787	−	15.9242i	−0.114726	−	0.650646i	0.872159	−	0.489223i	$-0.162719\pi$
$600$	5.61897	+	6.58993i	0.229394	+	0.269033i
$601$	19.1563	+	33.1796i	0.781400	+	1.35342i	0.931126	+	0.364697i	$0.118828\pi$
$601$	19.1563	+	33.1796i	0.781400	+	1.35342i	−0.149726	+	0.988728i	$0.547839\pi$
$602$	−1.93052	+	22.0659i	−0.0786821	+	0.899340i
$603$	−14.5145	−	12.7185i	−0.591076	−	0.517936i
$604$	−0.690515	+	1.89717i	−0.0280967	+	0.0771949i
$605$	22.6045	+	9.69619i	0.919005	+	0.394206i
$606$	−4.79682	−	9.46052i	−0.194857	−	0.384308i
$607$	−2.87539	−	2.87539i	−0.116709	−	0.116709i	0.646341	−	0.763049i	$-0.276299\pi$
$607$	−2.87539	−	2.87539i	−0.116709	−	0.116709i	−0.763049	+	0.646341i	$0.776299\pi$
$608$	2.69428	−	3.42650i	0.109267	−	0.138963i
$609$	15.0478	−	11.2927i	0.609766	−	0.457603i
$610$	−3.98224	−	3.13561i	−0.161236	−	0.126957i
$611$	0.510599	−	0.608508i	0.0206566	−	0.0246176i
$612$	1.09024	+	7.06437i	0.0440705	+	0.285560i
$613$	−17.9096	+	38.4073i	−0.723363	+	1.55126i	0.107140	+	0.994244i	$0.465831\pi$
$613$	−17.9096	+	38.4073i	−0.723363	+	1.55126i	−0.830503	+	0.557014i	$0.811947\pi$
$614$	−15.2087	+	12.7616i	−0.613774	+	0.515017i
$615$	−9.42299	−	11.7745i	−0.379972	−	0.474795i
$616$	0.0193891	−	0.0335828i	0.000781207	−	0.00135309i
$617$	17.8602	+	12.5058i	0.719024	+	0.503466i	0.874896	−	0.484311i	$-0.160930\pi$
$617$	17.8602	+	12.5058i	0.719024	+	0.503466i	−0.155872	+	0.987777i	$0.549819\pi$
$618$	0.661721	+	20.0889i	0.0266183	+	0.808096i
$619$	−25.1365	−	14.5125i	−1.01032	−	0.583309i	−0.0990347	−	0.995084i	$-0.531575\pi$
$619$	−25.1365	−	14.5125i	−1.01032	−	0.583309i	−0.911285	+	0.411775i	$0.864909\pi$
$620$	−13.2834	+	14.1370i	−0.533474	+	0.567757i
$621$	11.9781	−	21.3097i	0.480665	−	0.855130i
$622$	−0.0178741	−	0.00833482i	−0.000716685	−	0.000334196i
$623$	−3.30512	−	7.08785i	−0.132417	−	0.283969i
$624$	0.605711	−	11.1360i	0.0242479	−	0.445796i
$625$	−20.9982	−	13.5674i	−0.839929	−	0.542697i
$626$		−	9.67983i		−	0.386884i
$627$	0.0918466	+	0.0357940i	0.00366800	+	0.00142947i
$628$	8.60450	−	8.60450i	0.343357	−	0.343357i
$629$	−2.59787	+	14.7333i	−0.103584	+	0.587454i
$630$	−15.3859	−	12.6577i	−0.612988	−	0.504296i
$631$	−6.70570	−	2.44067i	−0.266950	−	0.0971617i	0.205078	−	0.978746i	$-0.434255\pi$
$631$	−6.70570	−	2.44067i	−0.266950	−	0.0971617i	−0.472027	+	0.881584i	$0.656478\pi$
$632$	−4.67446	+	10.0244i	−0.185940	+	0.398750i
$633$	−4.34235	−	6.97990i	−0.172593	−	0.277426i
$634$	14.2433	−	8.22337i	0.565673	−	0.326592i
$635$	−1.63451	+	1.01277i	−0.0648634	+	0.0401906i
$636$	9.08938	−	9.70858i	0.360417	−	0.384970i
$637$	6.72510	−	9.60443i	0.266458	−	0.380542i
$638$	0.0461245	−	0.0123590i	0.00182609	−	0.000489298i
$639$	46.3121	−	11.3524i	1.83208	−	0.449094i
$640$	−2.18895	+	0.456623i	−0.0865258	+	0.0180496i
$641$	−4.30425	−	11.8258i	−0.170008	−	0.467093i	0.825204	−	0.564835i	$-0.191060\pi$
$641$	−4.30425	−	11.8258i	−0.170008	−	0.467093i	−0.995212	+	0.0977423i	$0.968838\pi$
$642$	−1.69188	−	0.903887i	−0.0667731	−	0.0356736i
$643$	−25.9040	+	2.26631i	−1.02155	+	0.0893745i	−0.585605	−	0.810596i	$-0.699143\pi$
$643$	−25.9040	+	2.26631i	−1.02155	+	0.0893745i	−0.435950	+	0.899971i	$0.643588\pi$
$644$	2.42630	−	13.7602i	0.0956095	−	0.542228i
$645$	23.2699	+	17.1123i	0.916250	+	0.673797i
$646$	−8.31387	+	6.22450i	−0.327105	+	0.244900i
$647$	7.38551	−	7.38551i	0.290354	−	0.290354i	−0.546866	−	0.837220i	$-0.684179\pi$
$647$	7.38551	−	7.38551i	0.290354	−	0.290354i	0.837220	+	0.546866i	$0.184179\pi$
$648$	8.99111	−	0.399867i	0.353204	−	0.0157082i
$649$	−0.0255232	+	0.0304173i	−0.00100187	+	0.00119398i
$650$	7.55183	+	31.2961i	0.296207	+	1.22753i
$651$	24.3799	−	37.3796i	0.955524	−	1.46502i
$652$	−19.6114	−	1.71578i	−0.768043	−	0.0671951i
$653$	−6.18538	+	23.0841i	−0.242053	+	0.903353i	0.732789	+	0.680455i	$0.238218\pi$
$653$	−6.18538	+	23.0841i	−0.242053	+	0.903353i	−0.974842	+	0.222897i	$0.928449\pi$
$654$	−0.739926	−	6.12641i	−0.0289334	−	0.239562i
$655$	−37.1182	+	18.7360i	−1.45033	+	0.732077i
$656$	3.83471	−	0.676162i	0.149720	−	0.0263997i
$657$	−0.488233	+	22.7993i	−0.0190478	+	0.889486i
$658$	0.353920	+	0.0948326i	0.0137972	+	0.00369696i
$659$	−2.36293	+	1.98274i	−0.0920468	+	0.0772365i	−0.687650	−	0.726042i	$-0.741358\pi$
$659$	−2.36293	+	1.98274i	−0.0920468	+	0.0772365i	0.595603	+	0.803279i	$0.296913\pi$
$660$	−0.0242605	−	0.0443682i	−0.000944337	−	0.00172703i
$661$	−16.0212	−	5.83125i	−0.623154	−	0.226809i	0.0110951	−	0.999938i	$-0.496468\pi$
$661$	−16.0212	−	5.83125i	−0.623154	−	0.226809i	−0.634249	+	0.773129i	$0.718690\pi$
$662$	−35.9356	+	3.14396i	−1.39668	+	0.122194i
$663$	−8.26136	+	25.2557i	−0.320845	+	0.980849i
$664$			5.22353i			0.202712i
$665$	5.71936	−	28.3774i	0.221787	−	1.10043i
$666$	18.0863	+	5.26373i	0.700831	+	0.203965i
$667$	14.0942	−	9.86884i	0.545728	−	0.382123i
$668$	1.68910	+	19.3065i	0.0653534	+	0.746993i
$669$	5.21905	+	17.1923i	0.201780	+	0.664694i
$670$	−11.5204	+	8.61310i	−0.445073	+	0.332753i
$671$	0.0190237	+	0.0226716i	0.000734403	+	0.000875228i
$672$	4.77343	−	1.91761i	0.184139	−	0.0739735i
$673$	−9.71856	−	36.2702i	−0.374623	−	1.39811i	−0.853895	−	0.520446i	$-0.825766\pi$
$673$	−9.71856	−	36.2702i	−0.374623	−	1.39811i	0.479272	−	0.877667i	$-0.340901\pi$
$674$	1.51797	+	8.60883i	0.0584700	+	0.331600i
$675$	−24.5317	+	8.55540i	−0.944226	+	0.329298i
$676$	14.2295	−	24.6461i	0.547287	−	0.947929i
$677$	−29.7006	−	7.95825i	−1.14149	−	0.305860i	−0.361938	−	0.932202i	$-0.617885\pi$
$677$	−29.7006	−	7.95825i	−1.14149	−	0.305860i	−0.779548	+	0.626342i	$0.784551\pi$
$678$	9.78639	+	15.7307i	0.375844	+	0.604133i
$679$	11.7083	+	32.1682i	0.449322	+	1.23450i
$680$	5.31941	+	0.298971i	0.203990	+	0.0114650i
$681$	−2.45473	+	45.1300i	−0.0940653	+	1.72939i
$682$	0.0927851	−	0.0649688i	0.00355292	−	0.00248778i
$683$	25.6939	+	25.6939i	0.983151	+	0.983151i	0.999860	−	0.0167097i	$-0.00531911\pi$
$683$	25.6939	+	25.6939i	0.983151	+	0.983151i	−0.0167097	+	0.999860i	$0.505319\pi$
$684$	6.65560	+	11.2562i	0.254483	+	0.430393i
$685$	−17.5216	+	32.6546i	−0.669467	+	1.24767i
$686$	−15.1481	−	2.67102i	−0.578358	−	0.101980i
$687$	6.51071	+	7.25971i	0.248399	+	0.276975i
$688$	−6.75921	+	3.15187i	−0.257692	+	0.120164i
$689$	46.4585	−	16.9095i	1.76993	−	0.644201i
$690$	−13.6821	−	12.0328i	−0.520869	−	0.458082i
$691$	6.08746	+	10.5438i	0.231578	+	0.401105i	0.958273	−	0.285856i	$-0.0922778\pi$
$691$	6.08746	+	10.5438i	0.231578	+	0.401105i	−0.726695	+	0.686961i	$0.758944\pi$
$692$	3.82509	+	14.2754i	0.145408	+	0.542671i
$693$	0.0728532	+	0.0906978i	0.00276746	+	0.00344533i
$694$	−17.0622	+	3.00852i	−0.647671	+	0.114202i
$695$	32.6498	+	7.66807i	1.23848	+	0.290866i
$696$	5.82612	+	2.48666i	0.220839	+	0.0942566i
$697$	−9.24247	−	0.808611i	−0.350084	−	0.0306283i
$698$	−13.7331	−	6.40383i	−0.519804	−	0.242389i
$699$	−47.0667	+	14.2880i	−1.78023	+	0.540420i
$700$	−11.6111	+	9.25781i	−0.438857	+	0.349912i
$701$	−24.1534	−	4.25889i	−0.912261	−	0.160856i	−0.302231	−	0.953235i	$-0.597731\pi$
$701$	−24.1534	−	4.25889i	−0.912261	−	0.160856i	−0.610030	+	0.792379i	$0.708842\pi$
$702$	30.4834	+	13.7895i	1.15052	+	0.520452i
$703$	5.60706	+	26.7886i	0.211474	+	1.01035i
$704$	0.0130566			0.000492088
$705$	0.345610	−	0.329924i	0.0130164	−	0.0124256i
$706$	8.10423	+	6.80026i	0.305007	+	0.255931i
$707$	16.4843	−	7.68675i	0.619956	−	0.289090i
$708$	−5.15448	+	1.08496i	−0.193717	+	0.0407754i
$709$	−16.2328	−	19.3455i	−0.609636	−	0.726536i	0.369615	−	0.929185i	$-0.379490\pi$
$709$	−16.2328	−	19.3455i	−0.609636	−	0.726536i	−0.979252	+	0.202649i	$0.935045\pi$
$710$	−1.10592	−	35.5238i	−0.0415045	−	1.33318i
$711$	−22.9556	−	23.9603i	−0.860903	−	0.898581i
$712$	1.51033	−	2.15698i	0.0566021	−	0.0808362i
$713$	23.4095	−	33.4322i	0.876692	−	1.25205i
$714$	−12.1685	+	1.46967i	−0.455395	+	0.0550009i
$715$	−0.00584948	−	0.187894i	−0.000218758	−	0.00702683i
$716$	−2.17495	−	2.59200i	−0.0812817	−	0.0968678i
$717$	−4.74820	−	22.5579i	−0.177325	−	0.842442i
$718$	25.1180	−	11.7127i	0.937397	−	0.437115i
$719$	−14.6836	−	12.3210i	−0.547606	−	0.459496i	0.326524	−	0.945189i	$-0.394123\pi$
$719$	−14.6836	−	12.3210i	−0.547606	−	0.459496i	−0.874129	+	0.485693i	$0.838567\pi$
$720$	1.10066	−	6.61729i	0.0410192	−	0.246612i
$721$	−34.4659			−1.28358
$722$	−9.88685	+	16.2250i	−0.367951	+	0.603831i
$723$	5.52978	−	38.7893i	0.205655	−	1.44259i
$724$	−4.44327	−	0.783468i	−0.165133	−	0.0291174i
$725$	−18.1713	−	2.04906i	−0.674863	−	0.0761001i
$726$	−5.53428	−	18.2308i	−0.205396	−	0.676607i
$727$	−29.4267	−	13.7219i	−1.09138	−	0.508917i	−0.208261	−	0.978073i	$-0.566780\pi$
$727$	−29.4267	−	13.7219i	−1.09138	−	0.508917i	−0.883115	+	0.469156i	$0.844558\pi$
$728$	19.0507	+	1.66672i	0.706066	+	0.0617728i
$729$	−8.64776	+	25.5777i	−0.320287	+	0.947320i
$730$	16.5473	+	3.88626i	0.612442	+	0.143837i
$731$	17.4999	−	3.08570i	0.647256	−	0.114129i
$732$	0.129254	+	3.92396i	0.00477735	+	0.145034i
$733$	−1.63221	−	6.09148i	−0.0602869	−	0.224994i	0.929209	−	0.369555i	$-0.120490\pi$
$733$	−1.63221	−	6.09148i	−0.0602869	−	0.224994i	−0.989496	+	0.144561i	$0.953823\pi$
$734$	5.08733	+	8.81152i	0.187777	+	0.325239i
$735$	4.65747	−	5.29584i	0.171793	−	0.195340i
$736$	4.42081	−	1.60904i	0.162953	−	0.0593101i
$737$	0.0761212	−	0.0354959i	0.00280396	−	0.00130751i
$738$	−2.27432	+	11.4581i	−0.0837188	+	0.421777i
$739$	23.1972	+	4.09030i	0.853324	+	0.150464i	0.583167	−	0.812352i	$-0.301813\pi$
$739$	23.1972	+	4.09030i	0.853324	+	0.150464i	0.270157	+	0.962816i	$0.412924\pi$
$740$	6.63829	−	12.3716i	0.244028	−	0.454790i
$741$	3.14417	+	48.5105i	0.115504	+	1.78208i
$742$	16.1255	+	16.1255i	0.591986	+	0.591986i
$743$	23.8951	−	16.7315i	0.876625	−	0.613820i	−0.0462451	−	0.998930i	$-0.514726\pi$
$743$	23.8951	−	16.7315i	0.876625	−	0.613820i	0.922871	+	0.385110i	$0.125837\pi$
$744$	15.0039	+	0.816096i	0.550069	+	0.0299195i
$745$	11.1884	+	0.628831i	0.409912	+	0.0230386i
$746$	−4.65777	−	12.7971i	−0.170533	−	0.468535i
$747$	−14.6074	−	5.67369i	−0.534457	−	0.207590i
$748$	−0.0300494	−	0.00805172i	−0.00109872	−	0.000294400i
$749$	1.64460	−	2.84852i	0.0600922	−	0.104083i
$750$	2.43916	+	19.2107i	0.0890655	+	0.701475i
$751$	−6.24535	−	35.4191i	−0.227896	−	1.29246i	−0.857071	−	0.515199i	$-0.827718\pi$
$751$	−6.24535	−	35.4191i	−0.227896	−	1.29246i	0.629175	−	0.777264i	$-0.283393\pi$
$752$	0.0319301	+	0.119165i	0.00116437	+	0.00434549i
$753$	17.6754	+	43.9986i	0.644126	+	1.60340i
$754$	15.1368	+	18.0394i	0.551251	+	0.656955i
$755$	−3.61567	+	2.70321i	−0.131588	+	0.0983799i
$756$	0.177727	+	15.4316i	0.00646387	+	0.561242i
$757$	2.01560	+	23.0384i	0.0732582	+	0.837345i	0.940574	+	0.339588i	$0.110287\pi$
$757$	2.01560	+	23.0384i	0.0732582	+	0.837345i	−0.867316	+	0.497757i	$0.834157\pi$
$758$	0.505062	−	0.353648i	0.0183447	−	0.0128451i
$759$	0.0638596	+	0.0850943i	0.00231795	+	0.00308873i
$760$	9.23744	−	3.10962i	0.335077	−	0.112798i
$761$			11.4937i			0.416648i	0.978060	+	0.208324i	$0.0668008\pi$
$761$			11.4937i			0.416648i	−0.978060	+	0.208324i	$0.933199\pi$
$762$	1.41561	+	0.463060i	0.0512823	+	0.0167749i
$763$	10.5413	−	0.922240i	0.381619	−	0.0333873i
$764$	−21.5375	−	7.83902i	−0.779200	−	0.283606i
$765$	−6.61390	+	14.5508i	−0.239126	+	0.526085i
$766$	−6.45917	+	5.41989i	−0.233379	+	0.195828i
$767$	−18.9143	−	5.06808i	−0.682957	−	0.182998i
$768$	1.36276	+	1.06906i	0.0491744	+	0.0385762i
$769$	16.9086	−	2.98143i	0.609738	−	0.107513i	0.139751	−	0.990187i	$-0.455370\pi$
$769$	16.9086	−	2.98143i	0.609738	−	0.107513i	0.469987	+	0.882673i	$0.344259\pi$
$770$	0.0774081	−	0.0390731i	0.00278959	−	0.00140810i
$771$	52.7517	−	6.37115i	1.89981	−	0.229451i
$772$	−5.25834	+	19.6244i	−0.189252	+	0.706297i
$773$	37.1845	+	3.25322i	1.33743	+	0.117010i	0.733318	−	0.679886i	$-0.237971\pi$
$773$	37.1845	+	3.25322i	1.33743	+	0.117010i	0.604116	+	0.796897i	$0.293526\pi$
$774$	−1.47238	−	22.3254i	−0.0529235	−	0.802470i
$775$	−42.1663	+	10.1748i	−1.51466	+	0.365491i
$776$	−7.40886	+	8.82953i	−0.265962	+	0.316962i
$777$	−10.0420	+	30.6993i	−0.360256	+	1.10133i
$778$	21.5713	−	21.5713i	0.773369	−	0.773369i
$779$	−16.2467	+	4.91190i	−0.582097	+	0.175987i
$780$	14.7740	−	20.0901i	0.528994	−	0.719342i
$781$	−0.0360366	+	0.204374i	−0.00128949	+	0.00731306i
$782$	−11.1667	+	0.976957i	−0.399319	+	0.0349359i
$783$	−13.2821	+	13.5916i	−0.474663	+	0.485723i
$784$	0.622802	+	1.71113i	0.0222429	+	0.0611119i
$785$	26.6365	−	5.55647i	0.950696	−	0.198319i
$786$	29.6216	+	12.6428i	1.05657	+	0.450955i
$787$	28.9664	−	7.76152i	1.03254	−	0.276668i	0.297521	−	0.954715i	$-0.403840\pi$
$787$	28.9664	−	7.76152i	1.03254	−	0.276668i	0.735019	+	0.678047i	$0.237173\pi$
$788$	1.05016	−	1.49978i	0.0374104	−	0.0534276i
$789$	−8.11497	−	7.59741i	−0.288901	−	0.270475i
$790$	−21.0238	+	13.0268i	−0.747994	+	0.463471i
$791$	−27.5118	+	15.8839i	−0.978207	+	0.564768i
$792$	−0.0141818	+	0.0365122i	−0.000503928	+	0.00129741i
$793$	−6.16818	+	13.2277i	−0.219038	+	0.469729i
$794$	14.6686	+	5.33894i	0.520569	+	0.189472i
$795$	28.8959	−	7.02792i	1.02483	−	0.249255i
$796$	0.245432	−	1.39191i	0.00869909	−	0.0493350i
$797$	6.78737	−	6.78737i	0.240421	−	0.240421i	−0.576603	−	0.817024i	$-0.695622\pi$
$797$	6.78737	−	6.78737i	0.240421	−	0.240421i	0.817024	+	0.576603i	$0.195622\pi$
$798$	−19.6667	+	10.7710i	−0.696195	+	0.381288i
$799$		−	0.293945i		−	0.0103990i
$800$	−4.65421	−	1.82712i	−0.164551	−	0.0645985i
$801$	4.39142	+	6.56646i	0.155163	+	0.232014i
$802$	−9.48502	−	20.3407i	−0.334928	−	0.718255i
$803$	−0.0899508	−	0.0419447i	−0.00317429	−	0.00148020i
$804$	10.8514	+	2.52788i	0.382700	+	0.0891513i
$805$	21.3943	−	22.7692i	0.754050	−	0.802509i
$806$	48.3754	+	27.9295i	1.70395	+	0.983776i
$807$	−41.9596	+	1.38213i	−1.47705	+	0.0486534i
$808$	5.01651	+	3.51260i	0.176480	+	0.123573i
$809$	1.84919	−	3.20290i	0.0650142	−	0.112608i	−0.831686	−	0.555246i	$-0.812624\pi$
$809$	1.84919	−	3.20290i	0.0650142	−	0.112608i	0.896700	+	0.442638i	$0.145957\pi$
$810$	17.3095	+	10.2655i	0.608194	+	0.360694i
$811$	29.8059	−	25.0101i	1.04663	−	0.878224i	0.0538922	−	0.998547i	$-0.482837\pi$
$811$	29.8059	−	25.0101i	1.04663	−	0.878224i	0.992735	+	0.120322i	$0.0383928\pi$
$812$	−4.59055	+	9.84446i	−0.161097	+	0.345473i
$813$	6.73677	−	12.6098i	0.236269	−	0.442243i
$814$	−0.0526964	+	0.0628011i	−0.00184701	+	0.00220118i
$815$	−34.5854	−	27.2325i	−1.21147	−	0.953914i
$816$	−2.47710	−	3.30080i	−0.0867160	−	0.115551i
$817$	27.6222	−	17.1410i	0.966380	−	0.599689i
$818$	−22.5652	−	22.5652i	−0.788974	−	0.788974i
$819$	−25.3534	+	51.4642i	−0.885920	+	1.79831i
$820$	8.00185	+	3.43238i	0.279437	+	0.119864i
$821$	10.1863	−	27.9865i	0.355503	−	0.976736i	−0.625068	−	0.780570i	$-0.714929\pi$
$821$	10.1863	−	27.9865i	0.355503	−	0.976736i	0.980571	−	0.196165i	$-0.0628489\pi$
$822$	28.0899	−	5.91261i	0.979747	−	0.206226i
$823$	2.14831	−	24.5553i	0.0748855	−	0.855946i	−0.862137	−	0.506676i	$-0.830874\pi$
$823$	2.14831	−	24.5553i	0.0748855	−	0.855946i	0.937022	−	0.349270i	$-0.113570\pi$
$824$	−5.80232	−	10.0499i	−0.202133	−	0.350105i
$825$	0.00896426	−	0.112717i	0.000312095	−	0.00392431i
$826$	−1.56843	−	8.89503i	−0.0545728	−	0.309498i
$827$	−24.9241	−	17.4521i	−0.866696	−	0.606867i	0.0533939	−	0.998574i	$-0.482996\pi$
$827$	−24.9241	−	17.4521i	−0.866696	−	0.606867i	−0.920090	+	0.391706i	$0.871885\pi$
$828$	−0.302164	+	14.1103i	−0.0105009	+	0.490369i
$829$	−25.6487	+	14.8083i	−0.890816	+	0.514313i	−0.874209	−	0.485549i	$-0.838620\pi$
$829$	−25.6487	+	14.8083i	−0.890816	+	0.514313i	−0.0166068	+	0.999862i	$0.505286\pi$
$830$	−6.39850	+	9.77166i	−0.222095	+	0.339179i
$831$	2.95737	−	4.53427i	0.102590	−	0.157292i
$832$	2.72118	+	5.83559i	0.0943399	+	0.202313i
$833$	−0.378144	−	4.32221i	−0.0131019	−	0.149756i
$834$	−11.7482	−	23.1703i	−0.406806	−	0.802323i
$835$	−20.4895	+	38.1858i	−0.709069	+	1.32148i
$836$	−0.0565093	+	0.00676012i	−0.00195442	+	0.000233804i
$837$	−18.5791	+	41.0714i	−0.642188	+	1.41964i
$838$	9.08755	+	12.9784i	0.313924	+	0.448330i
$839$	41.3668	+	34.7108i	1.42814	+	1.19835i	0.946803	+	0.321815i	$0.104293\pi$
$839$	41.3668	+	34.7108i	1.42814	+	1.19835i	0.481337	+	0.876536i	$0.340152\pi$
$840$	11.2786	+	2.25988i	0.389149	+	0.0779733i
$841$	14.6820	−	5.34382i	0.506277	−	0.184270i
$842$	0.331147	−	3.78503i	0.0114121	−	0.130441i
$843$	−7.39526	−	18.4087i	−0.254706	−	0.634030i
$844$	4.11020	+	2.37303i	0.141479	+	0.0816829i
$845$	56.8091	−	28.6754i	1.95429	−	0.986463i
$846$	−0.367921	−	0.0401430i	−0.0126494	−	0.00138014i
$847$	31.5564	−	8.45551i	1.08429	−	0.290535i
$848$	−1.98732	+	7.41676i	−0.0682447	+	0.254693i
$849$	−18.5766	−	4.32749i	−0.637548	−	0.148519i
$850$	9.58481	+	7.07524i	0.328756	+	0.242679i
$851$	−10.1030	+	27.7579i	−0.346328	+	0.951528i
$852$	−20.4951	+	18.3806i	−0.702152	+	0.629709i
$853$	−5.84543	−	8.34814i	−0.200144	−	0.285835i	0.706516	−	0.707697i	$-0.250266\pi$
$853$	−5.84543	−	8.34814i	−0.200144	−	0.285835i	−0.906660	+	0.421862i	$0.861377\pi$
$854$	−6.73220			−0.230371
$855$	−1.33757	+	29.2098i	−0.0457438	+	0.998953i
$856$	1.10747			0.0378525
$857$	28.6610	+	40.9322i	0.979043	+	1.39822i	0.916437	+	0.400179i	$0.131052\pi$
$857$	28.6610	+	40.9322i	0.979043	+	1.39822i	0.0626057	+	0.998038i	$0.480059\pi$
$858$	−0.108404	+	0.0972194i	−0.00370084	+	0.00331902i
$859$	1.80928	−	4.97097i	0.0617320	−	0.169607i	−0.904992	−	0.425428i	$-0.860124\pi$
$859$	1.80928	−	4.97097i	0.0617320	−	0.169607i	0.966724	+	0.255821i	$0.0823457\pi$
$860$	−16.5053	−	2.38341i	−0.562827	−	0.0812735i
$861$	−19.5085	−	4.54457i	−0.664847	−	0.154879i
$862$	4.74907	−	17.7238i	0.161754	−	0.603674i
$863$	−9.80064	+	2.62607i	−0.333618	+	0.0893926i	−0.421739	−	0.906717i	$-0.638580\pi$
$863$	−9.80064	+	2.62607i	−0.333618	+	0.0893926i	0.0881215	+	0.996110i	$0.471914\pi$
$864$	−4.46978	+	2.64973i	−0.152065	+	0.0901456i
$865$	−10.3309	+	31.3906i	−0.351262	+	1.06731i
$866$	18.5065	+	10.6847i	0.628875	+	0.363081i
$867$	−7.31072	−	18.1983i	−0.248285	−	0.618046i
$868$	−2.24563	+	25.6677i	−0.0762217	+	0.871218i
$869$	0.135706	−	0.0493928i	0.00460350	−	0.00167554i
$870$	7.85293	+	11.7884i	0.266239	+	0.399666i
$871$	31.7296	+	26.6243i	1.07512	+	0.902129i
$872$	2.04353	+	2.91847i	0.0692028	+	0.0988318i
$873$	−16.6441	−	30.3091i	−0.563318	−	1.02581i
$874$	−18.3004	+	9.25290i	−0.619019	+	0.312984i
$875$	−33.0611	+	3.09576i	−1.11767	+	0.104656i
$876$	−5.95411	−	11.7430i	−0.201171	−	0.396759i
$877$	3.17086	+	36.2431i	0.107072	+	1.22384i	0.839638	+	0.543147i	$0.182767\pi$
$877$	3.17086	+	36.2431i	0.107072	+	1.22384i	−0.732565	+	0.680697i	$0.761677\pi$
$878$	7.69105	+	16.4935i	0.259560	+	0.556629i
$879$	−29.8798	+	45.8122i	−1.00782	+	1.54521i
$880$	0.0244249	+	0.0159935i	0.000823365	+	0.000539141i
$881$	43.8420	−	25.3122i	1.47707	−	0.852790i	0.477410	−	0.878681i	$-0.341576\pi$
$881$	43.8420	−	25.3122i	1.47707	−	0.852790i	0.999665	+	0.0258910i	$0.00824227\pi$
$882$	−5.46160	−	0.116957i	−0.183902	−	0.00393814i
$883$	−40.0931	−	28.0735i	−1.34924	−	0.944748i	−0.999970	−	0.00772593i	$-0.997541\pi$
$883$	−40.0931	−	28.0735i	−1.34924	−	0.944748i	−0.349270	−	0.937022i	$-0.613570\pi$
$884$	−2.66405	−	15.1086i	−0.0896017	−	0.508157i
$885$	−10.9715	−	4.28428i	−0.368803	−	0.144015i
$886$	−8.00259	−	13.8609i	−0.268852	−	0.465666i
$887$	0.0594329	−	0.679322i	0.00199556	−	0.0228094i	−0.995132	−	0.0985547i	$-0.968578\pi$
$887$	0.0594329	−	0.679322i	0.00199556	−	0.0228094i	0.997127	+	0.0757453i	$0.0241336\pi$
$888$	−10.6422	+	2.24007i	−0.357129	+	0.0751717i
$889$	−0.873509	+	2.39995i	−0.0292966	+	0.0804916i
$890$	5.46755	−	2.18500i	0.183273	−	0.0732413i
$891$	−0.0867012	−	0.0793177i	−0.00290460	−	0.00265724i
$892$	−7.33502	−	7.33502i	−0.245595	−	0.245595i
$893$	−0.199893	−	0.499217i	−0.00668916	−	0.0167057i
$894$	−5.21014	−	6.94263i	−0.174253	−	0.232196i
$895$	−0.893636	−	7.51305i	−0.0298709	−	0.251134i
$896$	−1.90908	+	2.27516i	−0.0637780	+	0.0760077i
$897$	−24.7234	+	46.2767i	−0.825489	+	1.54513i
$898$	−5.44122	+	11.6687i	−0.181576	+	0.389390i
$899$	−24.3051	+	20.3944i	−0.810620	+	0.680191i
$900$	10.1648	−	11.0307i	0.338826	−	0.367691i
$901$	9.14753	−	15.8440i	0.304748	−	0.527840i
$902$	−0.0416461	−	0.0291609i	−0.00138666	−	0.000970952i
$903$	38.3445	−	1.26305i	1.27603	−	0.0420317i
$904$	−9.26320	−	5.34811i	−0.308090	−	0.177876i
$905$	−7.35233	−	6.90837i	−0.244400	−	0.229642i
$906$	3.40570	+	0.793371i	0.113147	+	0.0263580i
$907$	−20.9733	−	9.78002i	−0.696408	−	0.324740i	0.0419782	−	0.999119i	$-0.486634\pi$
$907$	−20.9733	−	9.78002i	−0.696408	−	0.324740i	−0.738386	+	0.674378i	$0.764412\pi$
$908$	−11.0279	−	23.6495i	−0.365975	−	0.784836i
$909$	−15.2717	+	10.2132i	−0.506530	+	0.338749i
$910$	33.5965	+	26.4539i	1.11371	+	0.876938i
$911$			25.0000i			0.828286i	0.910212	+	0.414143i	$0.135919\pi$
$911$			25.0000i			0.828286i	−0.910212	+	0.414143i	$0.864081\pi$
$912$	−6.45160	−	3.92134i	−0.213634	−	0.129848i
$913$	0.0482256	−	0.0482256i	0.00159604	−	0.00159604i
$914$	5.43399	−	30.8177i	0.179741	−	1.01936i
$915$	−4.56482	+	7.49889i	−0.150908	+	0.247906i
$916$	−5.29053	−	1.92559i	−0.174804	−	0.0636234i
$917$	−23.3396	+	50.0519i	−0.770741	+	1.65286i
$918$	11.9211	−	3.34187i	0.393456	−	0.110298i
$919$	14.0895	−	8.13460i	0.464771	−	0.268336i	−0.249277	−	0.968432i	$-0.580193\pi$
$919$	14.0895	−	8.13460i	0.464771	−	0.268336i	0.714048	+	0.700097i	$0.246860\pi$
$920$	10.2410	+	2.40518i	0.337636	+	0.0792965i
$921$	25.1029	+	23.5019i	0.827168	+	0.774413i
$922$	−6.82126	+	9.74177i	−0.224646	+	0.320828i
$923$	−98.8547	+	26.4880i	−3.25384	+	0.871864i
$924$	−0.0617743	−	0.0263660i	−0.00203222	−	0.000867378i
$925$	27.5727	−	15.0121i	0.906586	−	0.493595i
$926$	−4.07847	−	11.2055i	−0.134027	−	0.368235i
$927$	34.4066	−	5.30997i	1.13006	−	0.174402i
$928$	−3.64337	+	0.318753i	−0.119599	+	0.0104636i
$929$	−0.604747	+	3.42969i	−0.0198411	+	0.112524i	−0.993120	−	0.117102i	$-0.962639\pi$
$929$	−0.604747	+	3.42969i	−0.0198411	+	0.112524i	0.973279	+	0.229627i	$0.0737506\pi$
$930$	27.0681	+	19.9055i	0.887599	+	0.652728i
$931$	−3.58146	−	7.08340i	−0.117378	−	0.232149i
$932$	20.0808	−	20.0808i	0.657767	−	0.657767i
$933$	−0.0106201	+	0.0324664i	−0.000347685	+	0.00106290i
$934$	−2.48307	+	2.95920i	−0.0812484	+	0.0968281i
$935$	−0.0463506	−	0.0518711i	−0.00151583	−	0.00169637i
$936$	−19.2747	+	1.27118i	−0.630014	+	0.0415499i
$937$	−6.14337	−	0.537476i	−0.200695	−	0.0175586i	−0.0136352	−	0.999907i	$-0.504340\pi$
$937$	−6.14337	−	0.537476i	−0.200695	−	0.0175586i	−0.187060	+	0.982348i	$0.559896\pi$
$938$	−4.94487	+	18.4545i	−0.161456	+	0.602561i
$939$	−16.6450	+	2.01032i	−0.543189	+	0.0656043i
$940$	−0.0862377	+	0.262034i	−0.00281276	+	0.00854660i
$941$	−3.79454	+	0.669080i	−0.123699	+	0.0218114i	−0.235155	−	0.971958i	$-0.575560\pi$
$941$	−3.79454	+	0.669080i	−0.123699	+	0.0218114i	0.111456	+	0.993769i	$0.464449\pi$
$942$	−16.5829	−	13.0089i	−0.540300	−	0.423854i
$943$	−17.6946	−	4.74125i	−0.576215	−	0.154396i
$944$	2.32966	−	1.95481i	0.0758239	−	0.0636238i
$945$	−18.5703	+	29.0856i	−0.604091	+	0.946155i
$946$	0.0915029	+	0.0333043i	0.00297502	+	0.00108282i
$947$	10.3917	−	0.909155i	0.337684	−	0.0295436i	0.0829474	−	0.996554i	$-0.473567\pi$
$947$	10.3917	−	0.909155i	0.337684	−	0.0295436i	0.254737	+	0.967010i	$0.418011\pi$
$948$	18.2083	+	5.95611i	0.591379	+	0.193445i
$949$		−	48.9451i		−	1.58883i
$950$	21.0896	+	5.49811i	0.684237	+	0.178382i
$951$	−17.0986	−	22.7843i	−0.554460	−	0.738831i
$952$	5.79676	−	4.05894i	0.187874	−	0.131551i
$953$	−0.0280694	−	0.320834i	−0.000909256	−	0.0103928i	0.995727	−	0.0923510i	$-0.0294382\pi$
$953$	−0.0280694	−	0.320834i	−0.000909256	−	0.0103928i	−0.996636	+	0.0819581i	$0.973883\pi$
$954$	−18.5821	−	13.6134i	−0.601619	−	0.440750i
$955$	−30.6880	−	41.0466i	−0.993039	−	1.32824i
$956$	8.55500	+	10.1955i	0.276689	+	0.329745i
$957$	−0.0308312	−	0.0767468i	−0.000996631	−	0.00248087i
$958$	8.87049	+	33.1051i	0.286592	+	1.06958i
$959$	8.54734	+	48.4744i	0.276008	+	1.56532i
$960$	1.23979	+	3.66918i	0.0400141	+	0.118422i
$961$	−22.1304	+	38.3310i	−0.713885	+	1.23649i
$962$	−39.0514	−	10.4638i	−1.25907	−	0.337367i
$963$	−1.20291	+	3.09700i	−0.0387633	+	0.0997994i
$964$	7.73699	+	21.2572i	0.249192	+	0.684649i
$965$	−33.8754	+	30.2702i	−1.09049	+	0.974433i
$966$	−24.1653	−	1.31441i	−0.777507	−	0.0422904i
$967$	12.8404	−	8.99097i	0.412920	−	0.289130i	−0.348599	−	0.937272i	$-0.613343\pi$
$967$	12.8404	−	8.99097i	0.412920	−	0.289130i	0.761520	+	0.648142i	$0.224454\pi$
$968$	7.77805	+	7.77805i	0.249996	+	0.249996i
$969$	12.4300	+	13.0034i	0.399309	+	0.417731i
$970$	−24.6754	+	7.44202i	−0.792279	+	0.238949i
$971$	−31.1862	−	5.49897i	−1.00081	−	0.176470i	−0.350846	−	0.936433i	$-0.614106\pi$
$971$	−31.1862	−	5.49897i	−1.00081	−	0.176470i	−0.649966	+	0.759963i	$0.725217\pi$
$972$	−2.55488	−	15.3777i	−0.0819478	−	0.493239i
$973$	40.3727	−	18.8261i	1.29429	−	0.603537i
$974$	7.18324	−	2.61449i	0.230166	−	0.0837736i
$975$	52.2469	−	19.4854i	1.67324	−	0.624032i
$976$	−1.13336	−	1.96304i	−0.0362781	−	0.0628355i
$977$	0.472655	+	1.76397i	0.0151216	+	0.0564345i	0.973074	−	0.230491i	$-0.0740333\pi$
$977$	0.472655	+	1.76397i	0.0151216	+	0.0564345i	−0.957953	+	0.286926i	$0.907367\pi$
$978$	1.12256	+	34.0793i	0.0358954	+	1.08974i
$979$	−0.0338580	+	0.00597009i	−0.00108211	+	0.000190805i
$980$	−0.930958	+	3.96392i	−0.0297384	+	0.126623i
$981$	−10.3810	+	2.54469i	−0.331441	+	0.0812456i
$982$	25.6687	+	2.24572i	0.819120	+	0.0716638i
$983$	6.34214	+	2.95739i	0.202283	+	0.0943261i	0.521120	−	0.853484i	$-0.325514\pi$
$983$	6.34214	+	2.95739i	0.202283	+	0.0943261i	−0.318837	+	0.947810i	$0.603292\pi$
$984$	−1.95909	−	6.45356i	−0.0624537	−	0.205732i
$985$	3.80168	−	1.51927i	0.121132	−	0.0484078i
$986$	8.58170	+	1.51319i	0.273297	+	0.0481896i
$987$	0.0895672	−	0.628280i	0.00285095	−	0.0199984i
$988$	−14.7988	−	23.8478i	−0.470812	−	0.758698i
$989$	35.0862			1.11568
$990$	−0.0712551	+	0.0509317i	−0.00226464	+	0.00161871i
$991$	6.19973	+	5.20219i	0.196941	+	0.165253i	0.735925	−	0.677063i	$-0.236747\pi$
$991$	6.19973	+	5.20219i	0.196941	+	0.165253i	−0.538985	+	0.842316i	$0.681192\pi$
$992$	−7.86249	+	3.66634i	−0.249634	+	0.116406i
$993$	12.8694	+	61.1404i	0.408397	+	1.94023i
$994$	−30.3438	−	36.1623i	−0.962446	−	1.14700i
$995$	2.16414	−	2.30321i	0.0686077	−	0.0730168i
$996$	8.98214	−	1.08483i	0.284610	−	0.0343742i
$997$	−13.8623	+	19.7974i	−0.439022	+	0.626989i	−0.976301	−	0.216416i	$-0.930563\pi$
$997$	−13.8623	+	19.7974i	−0.439022	+	0.626989i	0.537279	+	0.843405i	$0.319452\pi$
$998$	−1.71214	+	2.44519i	−0.0541970	+	0.0774013i
$999$	5.29508	−	32.1936i	0.167529	−	1.01856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.17.35	yes	480
3.2	odd	2	inner	570.2.bi.a.17.17	✓	480
5.3	odd	4	inner	570.2.bi.a.473.35	yes	480
15.8	even	4	inner	570.2.bi.a.473.7	yes	480
19.9	even	9	inner	570.2.bi.a.47.7	yes	480
57.47	odd	18	inner	570.2.bi.a.47.35	yes	480
95.28	odd	36	inner	570.2.bi.a.503.17	yes	480
285.218	even	36	inner	570.2.bi.a.503.35	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.17	✓	480	3.2	odd	2	inner
570.2.bi.a.17.35	yes	480	1.1	even	1	trivial
570.2.bi.a.47.7	yes	480	19.9	even	9	inner
570.2.bi.a.47.35	yes	480	57.47	odd	18	inner
570.2.bi.a.473.7	yes	480	15.8	even	4	inner
570.2.bi.a.473.35	yes	480	5.3	odd	4	inner
570.2.bi.a.503.17	yes	480	95.28	odd	36	inner
570.2.bi.a.503.35	yes	480	285.218	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.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573576 + 0.819152i) q^{2} +(1.28946 - 1.15642i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-1.79088 + 1.33893i) q^{5} +(1.68688 + 0.392966i) q^{6} +(-0.768695 + 2.86881i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(0.325391 - 2.98230i) q^{9} +O(q^{10})\)	\(q+(0.573576 + 0.819152i) q^{2} +(1.28946 - 1.15642i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-1.79088 + 1.33893i) q^{5} +(1.68688 + 0.392966i) q^{6} +(-0.768695 + 2.86881i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(0.325391 - 2.98230i) q^{9} +(-2.12400 - 0.699027i) q^{10} +(0.0113073 + 0.00652828i) q^{11} +(0.645658 + 1.60721i) q^{12} +(-0.561184 + 6.41436i) q^{13} +(-2.79090 + 1.01580i) q^{14} +(-0.760900 + 3.79750i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(1.36664 + 1.95177i) q^{17} +(2.62959 - 1.44403i) q^{18} +(3.64828 + 2.38539i) q^{19} +(-0.645665 - 2.14082i) q^{20} +(2.32635 + 4.58813i) q^{21} +(0.00113795 + 0.0130069i) q^{22} +(1.98822 + 4.26375i) q^{23} +(-0.946215 + 1.45075i) q^{24} +(1.41453 - 4.79574i) q^{25} +(-5.57622 + 3.21943i) q^{26} +(-3.02921 - 4.22183i) q^{27} +(-2.43289 - 1.70353i) q^{28} +(-0.635081 - 3.60172i) q^{29} +(-3.54717 + 1.55487i) q^{30} +(-4.33765 - 7.51303i) q^{31} +(0.0871557 - 0.996195i) q^{32} +(0.0221297 - 0.00465806i) q^{33} +(-0.814920 + 2.23897i) q^{34} +(-2.46449 - 6.16693i) q^{35} +(2.69116 + 1.32577i) q^{36} +(4.43986 + 4.43986i) q^{37} +(0.138572 + 4.35670i) q^{38} +(6.69406 + 8.91999i) q^{39} +(1.38332 - 1.75682i) q^{40} +(-2.50293 + 2.98287i) q^{41} +(-2.42404 + 4.53728i) q^{42} +(3.15187 - 6.75921i) q^{43} +(-0.0100019 + 0.00839260i) q^{44} +(3.41036 + 5.77663i) q^{45} +(-2.35226 + 4.07424i) q^{46} +(-0.101057 - 0.0707611i) q^{47} +(-1.73111 + 0.0570221i) q^{48} +(-1.57699 - 0.910476i) q^{49} +(4.73978 - 1.59201i) q^{50} +(4.01928 + 0.936306i) q^{51} +(-5.83559 - 2.72118i) q^{52} +(-3.24503 - 6.95899i) q^{53} +(1.72084 - 4.90293i) q^{54} +(-0.0289910 + 0.00344832i) q^{55} -2.97001i q^{56} +(7.46280 - 1.14309i) q^{57} +(2.58609 - 2.58609i) q^{58} +(-0.528090 + 2.99495i) q^{59} +(-3.30824 - 2.01383i) q^{60} +(2.13003 + 0.775267i) q^{61} +(3.66634 - 7.86249i) q^{62} +(8.30552 + 3.22596i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-7.58337 - 12.2388i) q^{65} +(0.0165087 + 0.0154558i) q^{66} +(3.68971 - 5.26945i) q^{67} +(-2.30148 + 0.616680i) q^{68} +(7.49440 + 3.19870i) q^{69} +(3.63808 - 5.55600i) q^{70} +(5.43621 + 14.9359i) q^{71} +(0.457573 + 2.96490i) q^{72} +(-7.57259 + 0.662516i) q^{73} +(-1.09032 + 6.18352i) q^{74} +(-3.72191 - 7.81968i) q^{75} +(-3.48931 + 2.61241i) q^{76} +(-0.0274203 + 0.0274203i) q^{77} +(-3.46727 + 10.5998i) q^{78} +(7.10969 - 8.47300i) q^{79} +(2.23254 + 0.125477i) q^{80} +(-8.78824 - 1.94083i) q^{81} +(-3.87904 - 0.339372i) q^{82} +(1.35195 - 5.04554i) q^{83} +(-5.10709 + 0.616816i) q^{84} +(-5.06078 - 1.66555i) q^{85} +(7.34466 - 1.29506i) q^{86} +(-4.98401 - 3.90984i) q^{87} +(-0.0126117 - 0.00337929i) q^{88} +(-2.01714 + 1.69258i) q^{89} +(-2.77584 + 6.10694i) q^{90} +(-17.9702 - 6.54061i) q^{91} +(-4.68663 + 0.410027i) q^{92} +(-14.2814 - 4.67158i) q^{93} -0.123368i q^{94} +(-9.72751 + 0.612843i) q^{95} +(-1.03963 - 1.38534i) q^{96} +(9.44166 - 6.61112i) q^{97} +(-0.158706 - 1.81402i) q^{98} +(0.0231486 - 0.0315976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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