LMFDB - Embedded newform 570.2.bi.a.47.7

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			47.7
Character	$\chi$	$=$	570.47
Dual form			570.2.bi.a.473.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(-0.914939 - 1.47068i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.23254 - 0.125477i) q^{5} +(-0.0940712 + 1.72949i) q^{6} +(2.86881 - 0.768695i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-1.32577 + 2.69116i) q^{9} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.914939 - 1.47068i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.23254 - 0.125477i) q^{5} +(-0.0940712 + 1.72949i) q^{6} +(2.86881 - 0.768695i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-1.32577 + 2.69116i) q^{9} +(1.75682 + 1.38332i) q^{10} +(-0.0113073 + 0.00652828i) q^{11} +(1.06906 - 1.36276i) q^{12} +(-6.41436 + 0.561184i) q^{13} +(-2.79090 - 1.01580i) q^{14} +(1.85810 + 3.39815i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-1.95177 - 1.36664i) q^{17} +(2.62959 - 1.44403i) q^{18} +(-3.64828 + 2.38539i) q^{19} +(-0.645665 - 2.14082i) q^{20} +(-3.75528 - 3.51578i) q^{21} +(0.0130069 + 0.00113795i) q^{22} +(4.26375 + 1.98822i) q^{23} +(-1.65737 + 0.503124i) q^{24} +(4.96851 + 0.560267i) q^{25} +(5.57622 + 3.21943i) q^{26} +(5.17082 - 0.512457i) q^{27} +(1.70353 + 2.43289i) q^{28} +(-0.635081 + 3.60172i) q^{29} +(0.427031 - 3.84937i) q^{30} +(-4.33765 + 7.51303i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(0.0199465 + 0.0106564i) q^{33} +(0.814920 + 2.23897i) q^{34} +(-6.50120 + 1.35618i) q^{35} +(-2.98230 - 0.325391i) q^{36} +(4.43986 + 4.43986i) q^{37} +(4.35670 + 0.138572i) q^{38} +(6.69406 + 8.91999i) q^{39} +(-0.699027 + 2.12400i) q^{40} +(2.50293 + 2.98287i) q^{41} +(1.05958 + 5.03390i) q^{42} +(6.75921 - 3.15187i) q^{43} +(-0.0100019 - 0.00839260i) q^{44} +(3.29753 - 5.84177i) q^{45} +(-2.35226 - 4.07424i) q^{46} +(0.0707611 + 0.101057i) q^{47} +(1.64622 + 0.538492i) q^{48} +(1.57699 - 0.910476i) q^{49} +(-3.74861 - 3.30877i) q^{50} +(-0.224140 + 4.12081i) q^{51} +(-2.72118 - 5.83559i) q^{52} +(-6.95899 - 3.24503i) q^{53} +(-4.52962 - 2.54608i) q^{54} +(0.0260632 - 0.0131559i) q^{55} -2.97001i q^{56} +(6.84608 + 3.18295i) q^{57} +(2.58609 - 2.58609i) q^{58} +(-0.528090 - 2.99495i) q^{59} +(-2.55771 + 2.90828i) q^{60} +(2.13003 - 0.775267i) q^{61} +(7.86249 - 3.66634i) q^{62} +(-1.73472 + 8.73953i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(14.3908 - 0.448011i) q^{65} +(-0.0102269 - 0.0201701i) q^{66} +(-5.26945 + 3.68971i) q^{67} +(0.616680 - 2.30148i) q^{68} +(-0.977043 - 8.08969i) q^{69} +(6.10334 + 2.61802i) q^{70} +(-5.43621 + 14.9359i) q^{71} +(2.25632 + 1.97712i) q^{72} +(-0.662516 + 7.57259i) 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} +(-0.367157 - 11.1464i) q^{78} +(-7.10969 - 8.47300i) q^{79} +(1.79088 - 1.33893i) q^{80} +(-5.48464 - 7.13573i) q^{81} +(-0.339372 - 3.87904i) q^{82} +(-5.04554 + 1.35195i) q^{83} +(2.01937 - 4.73128i) q^{84} +(4.18592 + 3.29599i) q^{85} +(-7.34466 - 1.29506i) q^{86} +(5.87802 - 2.36136i) q^{87} +(0.00337929 + 0.0126117i) q^{88} +(-2.01714 - 1.69258i) q^{89} +(-6.05188 + 2.89391i) q^{90} +(-17.9702 + 6.54061i) q^{91} +(-0.410027 + 4.68663i) q^{92} +(15.0179 - 0.494684i) q^{93} -0.123368i q^{94} +(8.44426 - 4.86770i) q^{95} +(-1.03963 - 1.38534i) q^{96} +(-6.61112 + 9.44166i) q^{97} +(-1.81402 - 0.158706i) q^{98} +(-0.00257767 - 0.0390848i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$	−0.914939	−	1.47068i	−0.528240	−	0.849095i
$3$	−0.914939	−	1.47068i	−0.528240	−	0.849095i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−2.23254	−	0.125477i	−0.998424	−	0.0561152i
$5$	−2.23254	−	0.125477i	−0.998424	−	0.0561152i
$6$	−0.0940712	+	1.72949i	−0.0384044	+	0.706063i
$7$	2.86881	−	0.768695i	1.08431	−	0.290539i	0.327948	−	0.944696i	$-0.393643\pi$
$7$	2.86881	−	0.768695i	1.08431	−	0.290539i	0.756359	+	0.654156i	$0.226976\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$	−1.32577	+	2.69116i	−0.441925	+	0.897052i
$10$	1.75682	+	1.38332i	0.555556	+	0.437444i
$11$	−0.0113073	+	0.00652828i	−0.00340928	+	0.00196835i	−0.501704	−	0.865040i	$-0.667293\pi$
$11$	−0.0113073	+	0.00652828i	−0.00340928	+	0.00196835i	0.498294	+	0.867008i	$0.333960\pi$
$12$	1.06906	−	1.36276i	0.308610	−	0.393395i
$13$	−6.41436	+	0.561184i	−1.77902	+	0.155644i	−0.928752	−	0.370701i	$-0.879117\pi$
$13$	−6.41436	+	0.561184i	−1.77902	+	0.155644i	−0.850271	+	0.526346i	$0.823562\pi$
$14$	−2.79090	−	1.01580i	−0.745898	−	0.271485i
$15$	1.85810	+	3.39815i	0.479761	+	0.877399i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−1.95177	−	1.36664i	−0.473373	−	0.331459i	0.312425	−	0.949942i	$-0.398859\pi$
$17$	−1.95177	−	1.36664i	−0.473373	−	0.331459i	−0.785798	+	0.618483i	$0.787748\pi$
$18$	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
$21$	−3.75528	−	3.51578i	−0.819470	−	0.767206i
$22$	0.0130069	+	0.00113795i	0.00277308	+	0.000242613i
$23$	4.26375	+	1.98822i	0.889053	+	0.414572i	0.812818	−	0.582517i	$-0.197932\pi$
$23$	4.26375	+	1.98822i	0.889053	+	0.414572i	0.0762352	+	0.997090i	$0.475710\pi$
$24$	−1.65737	+	0.503124i	−0.338309	+	0.102700i
$25$	4.96851	+	0.560267i	0.993702	+	0.112053i
$26$	5.57622	+	3.21943i	1.09359	+	0.631382i
$27$	5.17082	−	0.512457i	0.995125	−	0.0986225i
$28$	1.70353	+	2.43289i	0.321936	+	0.459773i
$29$	−0.635081	+	3.60172i	−0.117932	+	0.668823i	0.867325	+	0.497742i	$0.165837\pi$
$29$	−0.635081	+	3.60172i	−0.117932	+	0.668823i	−0.985257	+	0.171081i	$0.945274\pi$
$30$	0.427031	−	3.84937i	0.0779647	−	0.702795i
$31$	−4.33765	+	7.51303i	−0.779065	+	1.34938i	0.153416	+	0.988162i	$0.450973\pi$
$31$	−4.33765	+	7.51303i	−0.779065	+	1.34938i	−0.932481	+	0.361219i	$0.882361\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$	0.0199465	+	0.0106564i	0.00347224	+	0.00185505i
$34$	0.814920	+	2.23897i	0.139758	+	0.383981i
$35$	−6.50120	+	1.35618i	−1.09890	+	0.229235i
$36$	−2.98230	−	0.325391i	−0.497050	−	0.0542319i
$37$	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	$0.577375\pi$
$38$	4.35670	+	0.138572i	0.706749	+	0.0224794i
$39$	6.69406	+	8.91999i	1.07191	+	1.42834i
$40$	−0.699027	+	2.12400i	−0.110526	+	0.335833i
$41$	2.50293	+	2.98287i	0.390891	+	0.465846i	0.925220	−	0.379430i	$-0.123880\pi$
$41$	2.50293	+	2.98287i	0.390891	+	0.465846i	−0.534329	+	0.845277i	$0.679436\pi$
$42$	1.05958	+	5.03390i	0.163497	+	0.776748i
$43$	6.75921	−	3.15187i	1.03077	−	0.480656i	0.167752	−	0.985829i	$-0.446349\pi$
$43$	6.75921	−	3.15187i	1.03077	−	0.480656i	0.863018	+	0.505173i	$0.168571\pi$
$44$	−0.0100019	−	0.00839260i	−0.00150784	−	0.00126523i
$45$	3.29753	−	5.84177i	0.491567	−	0.870840i
$46$	−2.35226	−	4.07424i	−0.346822	−	0.600714i
$47$	0.0707611	+	0.101057i	0.0103216	+	0.0147407i	0.824280	−	0.566183i	$-0.191580\pi$
$47$	0.0707611	+	0.101057i	0.0103216	+	0.0147407i	−0.813958	+	0.580924i	$0.802692\pi$
$48$	1.64622	+	0.538492i	0.237611	+	0.0777246i
$49$	1.57699	−	0.910476i	0.225284	−	0.130068i
$50$	−3.74861	−	3.30877i	−0.530133	−	0.467930i
$51$	−0.224140	+	4.12081i	−0.0313859	+	0.577029i
$52$	−2.72118	−	5.83559i	−0.377360	−	0.809251i
$53$	−6.95899	−	3.24503i	−0.955891	−	0.445739i	−0.118870	−	0.992910i	$-0.537927\pi$
$53$	−6.95899	−	3.24503i	−0.955891	−	0.445739i	−0.837021	+	0.547171i	$0.815705\pi$
$54$	−4.52962	−	2.54608i	−0.616403	−	0.346478i
$55$	0.0260632	−	0.0131559i	0.00351437	−	0.00177394i
$56$		−	2.97001i		−	0.396884i
$57$	6.84608	+	3.18295i	0.906785	+	0.421592i
$58$	2.58609	−	2.58609i	0.339570	−	0.339570i
$59$	−0.528090	−	2.99495i	−0.0687515	−	0.389909i	−0.999694	−	0.0247430i	$-0.992123\pi$
$59$	−0.528090	−	2.99495i	−0.0687515	−	0.389909i	0.930942	−	0.365166i	$-0.118988\pi$
$60$	−2.55771	+	2.90828i	−0.330199	+	0.375458i
$61$	2.13003	−	0.775267i	0.272722	−	0.0992627i	−0.202039	−	0.979378i	$-0.564757\pi$
$61$	2.13003	−	0.775267i	0.272722	−	0.0992627i	0.474761	+	0.880115i	$0.342535\pi$
$62$	7.86249	−	3.66634i	0.998538	−	0.465626i
$63$	−1.73472	+	8.73953i	−0.218554	+	1.10108i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	14.3908	−	0.448011i	1.78495	−	0.0555689i
$66$	−0.0102269	−	0.0201701i	−0.00125885	−	0.00248276i
$67$	−5.26945	+	3.68971i	−0.643766	+	0.450770i	−0.849322	−	0.527875i	$-0.822989\pi$
$67$	−5.26945	+	3.68971i	−0.643766	+	0.450770i	0.205555	+	0.978645i	$0.434100\pi$
$68$	0.616680	−	2.30148i	0.0747834	−	0.279095i
$69$	−0.977043	−	8.08969i	−0.117622	−	0.973885i
$70$	6.10334	+	2.61802i	0.729488	+	0.312913i
$71$	−5.43621	+	14.9359i	−0.645159	+	1.77256i	−0.0102820	+	0.999947i	$0.503273\pi$
$71$	−5.43621	+	14.9359i	−0.645159	+	1.77256i	−0.634877	+	0.772613i	$0.718949\pi$
$72$	2.25632	+	1.97712i	0.265910	+	0.233006i
$73$	−0.662516	+	7.57259i	−0.0775416	+	0.886305i	0.853429	+	0.521210i	$0.174519\pi$
$73$	−0.662516	+	7.57259i	−0.0775416	+	0.886305i	−0.930970	+	0.365095i	$0.881037\pi$
$74$	−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
$78$	−0.367157	−	11.1464i	−0.0415724	−	1.26208i
$79$	−7.10969	−	8.47300i	−0.799903	−	0.953287i	0.199744	−	0.979848i	$-0.435989\pi$
$79$	−7.10969	−	8.47300i	−0.799903	−	0.953287i	−0.999647	+	0.0265610i	$0.991544\pi$
$80$	1.79088	−	1.33893i	0.200227	−	0.149697i
$81$	−5.48464	−	7.13573i	−0.609405	−	0.792859i
$82$	−0.339372	−	3.87904i	−0.0374774	−	0.428369i
$83$	−5.04554	+	1.35195i	−0.553820	+	0.148396i	−0.524866	−	0.851185i	$-0.675884\pi$
$83$	−5.04554	+	1.35195i	−0.553820	+	0.148396i	−0.0289545	+	0.999581i	$0.509218\pi$
$84$	2.01937	−	4.73128i	0.220331	−	0.516225i
$85$	4.18592	+	3.29599i	0.454027	+	0.357500i
$86$	−7.34466	−	1.29506i	−0.791995	−	0.139650i
$87$	5.87802	−	2.36136i	0.630190	−	0.253164i
$88$	0.00337929	+	0.0126117i	0.000360233	+	0.00134441i
$89$	−2.01714	−	1.69258i	−0.213816	−	0.179413i	0.529589	−	0.848254i	$-0.322346\pi$
$89$	−2.01714	−	1.69258i	−0.213816	−	0.179413i	−0.743405	+	0.668841i	$0.766791\pi$
$90$	−6.05188	+	2.89391i	−0.637924	+	0.305045i
$91$	−17.9702	+	6.54061i	−1.88379	+	0.685642i
$92$	−0.410027	+	4.68663i	−0.0427482	+	0.488615i
$93$	15.0179	−	0.494684i	1.55729	−	0.0512964i
$94$		−	0.123368i		−	0.0127245i
$95$	8.44426	−	4.86770i	0.866362	−	0.499416i
$96$	−1.03963	−	1.38534i	−0.106107	−	0.141390i
$97$	−6.61112	+	9.44166i	−0.671257	+	0.958655i	0.328642	+	0.944455i	$0.393409\pi$
$97$	−6.61112	+	9.44166i	−0.671257	+	0.958655i	−0.999899	+	0.0142002i	$0.995480\pi$
$98$	−1.81402	−	0.158706i	−0.183244	−	0.0160318i
$99$	−0.00257767	−	0.0390848i	−0.000259066	−	0.00392817i
$100$	1.17285	+	4.86050i	0.117285	+	0.486050i
$101$	3.93645	−	4.69127i	0.391691	−	0.466799i	−0.533777	−	0.845625i	$-0.679228\pi$
$101$	3.93645	−	4.69127i	0.391691	−	0.466799i	0.925468	+	0.378826i	$0.123672\pi$
$102$	2.54720	−	3.24701i	0.252211	−	0.321502i
$103$	−11.2092	−	3.00350i	−1.10448	−	0.295944i	−0.339891	−	0.940465i	$-0.610390\pi$
$103$	−11.2092	−	3.00350i	−1.10448	−	0.295944i	−0.764587	+	0.644521i	$0.777057\pi$
$104$	−1.11810	+	6.34104i	−0.109638	+	0.621790i
$105$	7.94269	+	8.32033i	0.775127	+	0.811982i
$106$	3.83920	+	6.64969i	0.372896	+	0.645875i
$107$	0.286634	+	1.06973i	0.0277100	+	0.103415i	0.978396	−	0.206740i	$-0.0662856\pi$
$107$	0.286634	+	1.06973i	0.0277100	+	0.103415i	−0.950686	+	0.310155i	$0.899619\pi$
$108$	2.25008	+	4.68371i	0.216514	+	0.450690i
$109$	1.21855	−	3.34793i	0.116716	−	0.320673i	−0.867555	−	0.497341i	$-0.834310\pi$
$109$	1.21855	−	3.34793i	0.116716	−	0.320673i	0.984271	+	0.176668i	$0.0565319\pi$
$110$	−0.0288957	−	0.00417260i	−0.00275509	−	0.000397842i
$111$	2.46740	−	10.5918i	0.234195	−	1.00533i
$112$	−1.70353	+	2.43289i	−0.160968	+	0.229886i
$113$	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	$0.582190\pi$
$114$	−3.78231	−	6.53407i	−0.354246	−	0.611972i
$115$	−9.26954	−	4.97379i	−0.864389	−	0.463809i
$116$	−3.60172	+	0.635081i	−0.334411	+	0.0589658i
$117$	6.99376	−	18.0060i	0.646574	−	1.66466i
$118$	−1.28525	+	2.75622i	−0.118317	+	0.253731i
$119$	−6.64977	−	2.42032i	−0.609584	−	0.221870i
$120$	3.76328	−	0.915284i	0.343539	−	0.0835537i
$121$	−5.49991	+	9.52613i	−0.499992	+	0.866012i
$122$	−2.18949	−	0.586672i	−0.198227	−	0.0531148i
$123$	2.09681	−	6.41014i	0.189063	−	0.577983i
$124$	−8.54351	−	1.50645i	−0.767229	−	0.135283i
$125$	−11.0221	−	1.87426i	−0.985849	−	0.167639i
$126$	6.43378	−	6.16401i	0.573167	−	0.549134i
$127$	0.0749470	+	0.856648i	0.00665047	+	0.0760152i	0.998795	−	0.0490847i	$-0.0156304\pi$
$127$	0.0749470	+	0.856648i	0.00665047	+	0.0760152i	−0.992144	+	0.125100i	$0.960075\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$	−10.8196	−	7.05684i	−0.952616	−	0.621320i
$130$	−12.0452	−	7.88721i	−1.05643	−	0.691754i
$131$	−18.3121	+	3.22892i	−1.59994	+	0.282112i	−0.901245	−	0.433311i	$-0.857345\pi$
$131$	−18.3121	+	3.22892i	−1.59994	+	0.282112i	−0.698692	+	0.715423i	$0.746234\pi$
$132$	−0.00319166	+	0.0223883i	−0.000277798	+	0.00194865i
$133$	−8.63258	+	9.64763i	−0.748539	+	0.836555i
$134$	6.43282			0.555711
$135$	−11.6084	+	0.495263i	−0.999091	+	0.0426255i
$136$	−1.82523	+	1.53155i	−0.156512	+	0.131329i
$137$	7.00408	−	15.0203i	0.598399	−	1.28327i	−0.340877	−	0.940108i	$-0.610724\pi$
$137$	7.00408	−	15.0203i	0.598399	−	1.28327i	0.939276	−	0.343163i	$-0.111498\pi$
$138$	−3.83971	+	7.18710i	−0.326858	+	0.611806i
$139$	9.64099	−	11.4897i	0.817738	−	0.974542i	−0.182224	−	0.983257i	$-0.558330\pi$
$139$	9.64099	−	11.4897i	0.817738	−	0.974542i	0.999962	+	0.00871501i	$0.00277411\pi$
$140$	−3.49793	−	5.64529i	−0.295629	−	0.477114i
$141$	0.0838805	−	0.196528i	0.00706402	−	0.0165506i
$142$	13.0199	−	9.11666i	1.09261	−	0.765053i
$143$	0.0688656	−	0.0482202i	0.00575883	−	0.00403238i
$144$	−0.714239	−	2.91374i	−0.0595199	−	0.242811i
$145$	1.86978	−	7.96131i	0.155277	−	0.661151i
$146$	4.88616	−	5.82310i	0.404381	−	0.481923i
$147$	−2.78186	−	1.48621i	−0.229444	−	0.122581i
$148$	−2.65358	+	5.69063i	−0.218123	+	0.467767i
$149$	−3.83904	+	3.22133i	−0.314506	+	0.263902i	−0.786352	−	0.617779i	$-0.788033\pi$
$149$	−3.83904	+	3.22133i	−0.314506	+	0.263902i	0.471845	+	0.881681i	$0.343588\pi$
$150$	−1.43637	+	8.54031i	−0.117279	+	0.697313i
$151$	2.01893			0.164298			0.0821491	−	0.996620i	$-0.473822\pi$
$151$	2.01893			0.164298			0.0821491	+	0.996620i	$0.473822\pi$
$152$	1.35986	+	4.14135i	0.110299	+	0.335908i
$153$	6.26545	−	3.44065i	0.506531	−	0.278160i
$154$	0.0381890	−	0.00673375i	0.00307736	−	0.000542621i
$155$	10.6267	−	16.2289i	0.853558	−	1.30354i
$156$	−6.09255	+	9.34118i	−0.487794	+	0.747893i
$157$	−5.14268	−	11.0285i	−0.410430	−	0.880170i	−0.997502	−	0.0706357i	$-0.977497\pi$
$157$	−5.14268	−	11.0285i	−0.410430	−	0.880170i	0.587072	−	0.809535i	$-0.300281\pi$
$158$	0.964005	+	11.0186i	0.0766921	+	0.876595i
$159$	1.59466	+	13.2034i	0.126465	+	1.04710i
$160$	−2.23499	+	0.0695792i	−0.176691	+	0.00550072i
$161$	13.7602	+	2.42630i	1.08446	+	0.191219i
$162$	0.399867	+	8.99111i	0.0314165	+	0.706409i
$163$	−19.0156	−	5.09520i	−1.48941	−	0.399087i	−0.579874	−	0.814706i	$-0.696898\pi$
$163$	−19.0156	−	5.09520i	−1.48941	−	0.399087i	−0.909539	+	0.415619i	$0.863565\pi$
$164$	−1.94693	+	3.37218i	−0.152030	+	0.263323i
$165$	−0.0431943	−	0.0262938i	−0.00336267	−	0.00204697i
$166$	4.90851	+	1.78655i	0.380974	+	0.138663i
$167$	8.19047	−	17.5645i	0.633797	−	1.35918i	−0.282726	−	0.959201i	$-0.591239\pi$
$167$	8.19047	−	17.5645i	0.633797	−	1.35918i	0.916523	−	0.399982i	$-0.130984\pi$
$168$	−4.36792	+	2.71738i	−0.336992	+	0.209650i
$169$	28.0266	−	4.94184i	2.15589	−	0.380141i
$170$	−1.53840	−	5.10086i	−0.117990	−	0.391218i
$171$	−1.58265	−	12.9806i	−0.121028	−	0.992649i
$172$	5.27358	+	5.27358i	0.402106	+	0.402106i
$173$	−8.47690	+	12.1063i	−0.644487	+	0.920422i	−0.999898	−	0.0142878i	$-0.995452\pi$
$173$	−8.47690	+	12.1063i	−0.644487	+	0.920422i	0.355411	+	0.934710i	$0.384341\pi$
$174$	−6.16941	−	1.43719i	−0.467702	−	0.108953i
$175$	14.6844	−	2.21197i	1.11003	−	0.167209i
$176$	0.00446561	−	0.0122692i	0.000336608	−	0.000924823i
$177$	−3.92143	+	3.51684i	−0.294753	+	0.264342i
$178$	0.681518	+	2.54346i	0.0510820	+	0.190640i
$179$	−1.69181	−	2.93030i	−0.126452	−	0.219021i	0.795848	−	0.605497i	$-0.207026\pi$
$179$	−1.69181	−	2.93030i	−0.126452	−	0.219021i	−0.922300	+	0.386476i	$0.873692\pi$
$180$	6.61729	+	1.10066i	0.493224	+	0.0820385i
$181$	0.783468	−	4.44327i	0.0582347	−	0.330266i	−0.941747	−	0.336322i	$-0.890817\pi$
$181$	0.783468	−	4.44327i	0.0582347	−	0.330266i	0.999982	+	0.00605676i	$0.00192794\pi$
$182$	18.4719	+	4.94952i	1.36922	+	0.366883i
$183$	−3.08901	−	2.42326i	−0.228346	−	0.179132i
$184$	3.02401	−	3.60388i	0.222933	−	0.265681i
$185$	−9.35509	−	10.4693i	−0.687800	−	0.769717i
$186$	−12.5857	−	8.20870i	−0.922828	−	0.601891i
$187$	0.0309911	+	0.00271137i	0.00226629	+	0.000198275i
$188$	−0.0707611	+	0.101057i	−0.00516079	+	0.00737037i
$189$	14.4402	−	5.44492i	1.05037	−	0.396060i
$190$	−9.70913	−	0.856035i	−0.704374	−	0.0621033i
$191$			22.9198i			1.65842i	0.558941	+	0.829208i	$0.311208\pi$
$191$			22.9198i			1.65842i	−0.558941	+	0.829208i	$0.688792\pi$
$192$	0.0570221	+	1.73111i	0.00411522	+	0.124932i
$193$	1.77071	−	20.2393i	0.127459	−	1.45686i	−0.615825	−	0.787883i	$-0.711177\pi$
$193$	1.77071	−	20.2393i	0.127459	−	1.45686i	0.743284	−	0.668976i	$-0.233267\pi$
$194$	10.8310	−	3.94217i	0.777622	−	0.283031i
$195$	−13.8255	−	20.7542i	−0.990067	−	1.48624i
$196$	1.39493	+	1.17048i	0.0996378	+	0.0836061i
$197$	0.473871	+	1.76851i	0.0337619	+	0.126001i	0.980750	−	0.195267i	$-0.0625575\pi$
$197$	0.473871	+	1.76851i	0.0337619	+	0.126001i	−0.946988	+	0.321269i	$0.895891\pi$
$198$	−0.0203066	+	0.0334949i	−0.00144313	+	0.00238038i
$199$	1.39191	+	0.245432i	0.0986700	+	0.0173982i	0.222765	−	0.974872i	$-0.428492\pi$
$199$	1.39191	+	0.245432i	0.0986700	+	0.0173982i	−0.124095	+	0.992270i	$0.539603\pi$
$200$	1.82712	−	4.65421i	0.129197	−	0.329102i
$201$	10.2476	+	4.37380i	0.722810	+	0.308504i
$202$	−5.91535	+	1.58501i	−0.416203	+	0.111521i
$203$	0.946700	+	10.8208i	0.0664453	+	0.759473i
$204$	−3.94895	+	1.19878i	−0.276482	+	0.0839311i
$205$	−5.21361	−	6.97345i	−0.364134	−	0.487047i
$206$	7.45932	+	8.88967i	0.519716	+	0.619373i
$207$	−11.0034	+	8.83849i	−0.764788	+	0.614317i
$208$	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	0.999946	−	0.0104313i	$-0.00332046\pi$
$211$	0.824143	+	4.67395i	0.0567364	+	0.321768i	−0.943209	+	0.332199i	$0.892209\pi$
$212$	0.669216	−	7.64918i	0.0459620	−	0.525348i
$213$	26.9396	−	5.67049i	1.84587	−	0.388536i
$214$	0.378777	−	1.04068i	0.0258926	−	0.0711395i
$215$	−15.4857	+	6.18857i	−1.05612	+	0.422057i
$216$	0.843311	−	5.12726i	0.0573800	−	0.348866i
$217$	−6.66866	+	24.8878i	−0.452698	+	1.68949i
$218$	−2.91847	+	2.04353i	−0.197664	+	0.138406i
$219$	11.7430	−	5.95411i	0.793517	−	0.402341i
$220$	0.0212766	+	0.0199919i	0.00143447	+	0.00134785i
$221$	13.2863	+	7.67083i	0.893731	+	0.515996i
$222$	−8.09638	+	7.26105i	−0.543393	+	0.487330i
$223$	−9.40139	+	4.38394i	−0.629564	+	0.293570i	−0.711090	−	0.703101i	$-0.751798\pi$
$223$	−9.40139	+	4.38394i	−0.629564	+	0.293570i	0.0815266	+	0.996671i	$0.474020\pi$
$224$	2.79090	−	1.01580i	0.186475	−	0.0678712i
$225$	−8.09489	+	12.6282i	−0.539660	+	0.841883i
$226$	−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	$0.916701\pi$
$228$	−0.649500	+	7.52184i	−0.0430142	+	0.498146i
$229$			5.63006i			0.372045i	0.982545	+	0.186022i	$0.0595597\pi$
$229$			5.63006i			0.372045i	−0.982545	+	0.186022i	$0.940440\pi$
$230$	4.74031	+	9.39108i	0.312567	+	0.619229i
$231$	0.0654142	+	0.0152385i	0.00430394	+	0.00100262i
$232$	3.31462	+	1.54563i	0.217616	+	0.101476i
$233$	−12.0017	−	25.7378i	−0.786258	−	1.68614i	−0.725740	−	0.687970i	$-0.758502\pi$
$233$	−12.0017	−	25.7378i	−0.786258	−	1.68614i	−0.0605189	−	0.998167i	$-0.519276\pi$
$234$	−16.0568	+	10.7382i	−1.04967	+	0.701980i
$235$	−0.145297	−	0.234494i	−0.00947813	−	0.0152967i
$236$	2.63371	−	1.52058i	0.171440	−	0.0989811i
$237$	−5.95611	+	18.2083i	−0.386891	+	1.18276i
$238$	4.05894	+	5.79676i	0.263102	+	0.375748i
$239$	6.65461	+	11.5261i	0.430451	+	0.745563i	0.996912	−	0.0785254i	$-0.0250212\pi$
$239$	6.65461	+	11.5261i	0.430451	+	0.745563i	−0.566461	+	0.824089i	$0.691688\pi$
$240$	−3.60768	−	1.40877i	−0.232875	−	0.0909357i
$241$	17.3290	+	14.5408i	1.11626	+	0.936655i	0.998410	−	0.0563764i	$-0.0179547\pi$
$241$	17.3290	+	14.5408i	1.11626	+	0.936655i	0.117852	+	0.993031i	$0.462399\pi$
$242$	9.96923	−	4.64873i	0.640846	−	0.298832i
$243$	−5.47624	+	14.5949i	−0.351301	+	0.936263i
$244$	1.45702	+	1.73641i	0.0932765	+	0.111163i
$245$	−3.63494	+	1.83480i	−0.232228	+	0.117221i
$246$	−5.39431	+	4.04819i	−0.343929	+	0.258103i
$247$	22.0627	−	17.3481i	1.40382	−	1.10383i
$248$	6.13437	+	6.13437i	0.389533	+	0.389533i
$249$	6.60464	+	6.18341i	0.418552	+	0.391857i
$250$	7.95376	+	7.85733i	0.503040	+	0.496941i
$251$	9.36305	+	25.7248i	0.590991	+	1.62373i	0.768670	+	0.639645i	$0.220919\pi$
$251$	9.36305	+	25.7248i	0.590991	+	1.62373i	−0.177680	+	0.984088i	$0.556859\pi$
$252$	−8.80578	+	1.35899i	−0.554712	+	0.0856086i
$253$	−0.0611912	+	0.00535354i	−0.00384706	+	0.000336574i
$254$	0.429960	−	0.744713i	0.0269781	−	0.0467274i
$255$	1.01747	−	9.17176i	0.0637165	−	0.574358i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−17.5959	−	25.1296i	−1.09760	−	1.56754i	−0.786952	−	0.617014i	$-0.788342\pi$
$257$	−17.5959	−	25.1296i	−1.09760	−	1.56754i	−0.310650	−	0.950524i	$-0.600547\pi$
$258$	4.81530	+	11.9865i	0.299787	+	0.746248i
$259$	16.1500	+	9.32421i	1.00351	+	0.579378i
$260$	5.34292	+	13.3697i	0.331354	+	0.829151i
$261$	−8.85082	−	6.48417i	−0.547852	−	0.401360i
$262$	16.8524	+	7.85842i	1.04115	+	0.485495i
$263$	−6.39361	−	0.559369i	−0.394247	−	0.0344921i	−0.111691	−	0.993743i	$-0.535627\pi$
$263$	−6.39361	−	0.559369i	−0.394247	−	0.0344921i	−0.282556	+	0.959251i	$0.591182\pi$
$264$	0.0154558	−	0.0165087i	0.000951242	−	0.00101604i
$265$	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
$268$	−5.26945	−	3.68971i	−0.321883	−	0.225385i
$269$	−18.5678	+	15.5802i	−1.13210	+	0.949944i	−0.999152	−	0.0411792i	$-0.986889\pi$
$269$	−18.5678	+	15.5802i	−1.13210	+	0.949944i	−0.132947	+	0.991123i	$0.542444\pi$
$270$	9.79311	+	6.25260i	0.595990	+	0.380521i
$271$	7.75631	+	2.82307i	0.471162	+	0.171489i	0.566679	−	0.823939i	$-0.308228\pi$
$271$	7.75631	+	2.82307i	0.471162	+	0.171489i	−0.0955166	+	0.995428i	$0.530450\pi$
$272$	2.37360	−	0.207663i	0.143921	−	0.0125914i
$273$	26.0607	+	20.4441i	1.57727	+	1.23733i
$274$	−14.3527	+	8.28654i	−0.867078	+	0.500608i
$275$	−0.0598381	+	0.0261007i	−0.00360837	+	0.00157393i
$276$	7.26766	−	3.68496i	0.437462	−	0.221808i
$277$	−0.808931	+	3.01897i	−0.0486039	+	0.181392i	−0.985960	−	0.166979i	$-0.946599\pi$
$277$	−0.808931	+	3.01897i	−0.0486039	+	0.181392i	0.937356	+	0.348372i	$0.113265\pi$
$278$	−14.4876	+	3.88195i	−0.868911	+	0.232824i
$279$	−14.4680	−	21.6339i	−0.866176	−	1.29519i
$280$	−0.372669	+	6.63068i	−0.0222712	+	0.396259i
$281$	−3.91744	−	10.7631i	−0.233695	−	0.642072i	0.766305	−	0.642477i	$-0.222093\pi$
$281$	−3.91744	−	10.7631i	−0.233695	−	0.642072i	−1.00000		0.000405376i	$0.999871\pi$
$282$	−0.181435	+	0.112874i	−0.0108043	+	0.00672157i
$283$	9.02082	+	6.31644i	0.536232	+	0.375474i	0.810098	−	0.586294i	$-0.199414\pi$
$283$	9.02082	+	6.31644i	0.536232	+	0.375474i	−0.273866	+	0.961768i	$0.588303\pi$
$284$	−15.8944			−0.943160
$285$	−14.8848	−	7.96511i	−0.881699	−	0.471812i
$286$	−0.0840694			−0.00497113
$287$	9.47333	+	6.63330i	0.559193	+	0.391551i
$288$	−1.08618	+	2.79646i	−0.0640038	+	0.164783i
$289$	−3.87266	−	10.6400i	−0.227803	−	0.625885i
$290$	−6.09806	+	5.44907i	−0.358090	+	0.319980i
$291$	19.9344	+	1.08428i	1.16857	+	0.0635615i
$292$	−7.34250	+	1.96742i	−0.429687	+	0.115134i
$293$	8.17305	−	30.5022i	0.477475	−	1.78196i	−0.134314	−	0.990939i	$-0.542883\pi$
$293$	8.17305	−	30.5022i	0.477475	−	1.78196i	0.611789	−	0.791021i	$-0.290450\pi$
$294$	1.42631	+	2.81304i	0.0831843	+	0.164060i
$295$	0.803187	+	6.75262i	0.0467634	+	0.393153i
$296$	5.43770	−	3.13946i	0.316060	−	0.182477i
$297$	−0.0551227	+	0.0395511i	−0.00319854	+	0.00229499i
$298$	4.99244	−	0.436782i	0.289204	−	0.0253021i
$299$	−28.4650	−	10.3604i	−1.64617	−	0.599158i
$300$	6.07513	−	6.17194i	0.350748	−	0.356337i
$301$	16.9680	−	14.2379i	0.978022	−	0.820658i
$302$	−1.65381	−	1.15801i	−0.0951662	−	0.0666361i
$303$	−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
$306$	−7.10583	−	0.775299i	−0.406213	−	0.0443209i
$307$	19.7780	+	1.73035i	1.12879	+	0.0987565i	0.636214	−	0.771512i	$-0.280499\pi$
$307$	19.7780	+	1.73035i	1.12879	+	0.0987565i	0.492577	+	0.870269i	$0.336055\pi$
$308$	−0.0351449	−	0.0163883i	−0.00200257	−	0.000933812i
$309$	5.83857	+	19.2332i	0.332145	+	1.09414i
$310$	−18.0134	+	7.19871i	−1.02309	+	0.408859i
$311$	0.0170796	+	0.00986093i	0.000968497	+	0.000559162i	0.500484	−	0.865746i	$-0.333155\pi$
$311$	0.0170796	+	0.00986093i	0.000968497	+	0.000559162i	−0.499516	+	0.866305i	$0.666489\pi$
$312$	10.3486	−	4.15730i	0.585874	−	0.235361i
$313$	5.55212	+	7.92925i	0.313824	+	0.448188i	0.944816	−	0.327602i	$-0.106241\pi$
$313$	5.55212	+	7.92925i	0.313824	+	0.448188i	−0.630991	+	0.775790i	$0.717352\pi$
$314$	−2.11306	+	11.9837i	−0.119247	+	0.676282i
$315$	4.96944	−	19.2937i	0.279996	−	1.08708i
$316$	5.53036	−	9.57886i	0.311107	−	0.538853i
$317$	16.3842	−	1.43343i	0.920226	−	0.0805093i	0.382810	−	0.923827i	$-0.374956\pi$
$317$	16.3842	−	1.43343i	0.920226	−	0.0805093i	0.537415	+	0.843318i	$0.319401\pi$
$318$	6.26690	−	11.7303i	0.351430	−	0.657801i
$319$	−0.0163320	−	0.0448718i	−0.000914416	−	0.00251234i
$320$	1.87070	+	1.22494i	0.104575	+	0.0684762i
$321$	1.31098	−	1.40029i	0.0731717	−	0.0781563i
$322$	−9.88004	−	9.88004i	−0.550593	−	0.550593i
$323$	10.3806	+	0.330172i	0.577589	+	0.0183712i
$324$	4.82954	−	7.59444i	0.268308	−	0.421913i
$325$	−32.1842	−	0.805509i	−1.78526	−	0.0446816i
$326$	12.6541	+	15.0806i	0.700848	+	0.835238i
$327$	−6.03861	+	1.27106i	−0.333936	+	0.0702899i
$328$	3.52904	−	1.64562i	0.194859	−	0.0908640i
$329$	0.280682	+	0.235520i	0.0154745	+	0.0129847i
$330$	0.0203012	+	0.0463138i	0.00111754	+	0.00254949i
$331$	−18.0365	−	31.2401i	−0.991373	−	1.71711i	−0.609195	−	0.793020i	$-0.708507\pi$
$331$	−18.0365	−	31.2401i	−0.991373	−	1.71711i	−0.382178	−	0.924089i	$-0.624826\pi$
$332$	−2.99609	−	4.27886i	−0.164432	−	0.234833i
$333$	−17.8346	+	6.06210i	−0.977331	+	0.332201i
$334$	−16.7838	+	9.69015i	−0.918370	+	0.530221i
$335$	12.2273	−	7.57625i	0.668047	−	0.413935i
$336$	5.13661	+	0.279392i	0.280225	+	0.0152421i
$337$	3.69437	+	7.92261i	0.201245	+	0.431572i	0.980867	−	0.194679i	$-0.0623664\pi$
$337$	3.69437	+	7.92261i	0.201245	+	0.431572i	−0.779622	+	0.626251i	$0.784589\pi$
$338$	−25.7925	−	12.0273i	−1.40293	−	0.654197i
$339$	4.20325	−	18.0433i	0.228289	−	0.979977i
$340$	−1.66555	+	5.06078i	−0.0903270	+	0.274459i
$341$		−	0.113270i		−	0.00613390i
$342$	−6.14892	+	11.5408i	−0.332495	+	0.624057i
$343$	−10.8766	+	10.8766i	−0.587281	+	0.587281i
$344$	−1.29506	−	7.34466i	−0.0698250	−	0.395998i
$345$	1.16622	+	18.1832i	0.0627872	+	0.978950i
$346$	13.8877	−	5.05472i	0.746609	−	0.271744i
$347$	−15.7021	+	7.32202i	−0.842934	+	0.393067i	−0.795607	−	0.605813i	$-0.792848\pi$
$347$	−15.7021	+	7.32202i	−0.842934	+	0.393067i	−0.0473268	+	0.998879i	$0.515070\pi$
$348$	4.22935	+	4.71590i	0.226717	+	0.252799i
$349$	13.1227	+	7.57638i	0.702441	+	0.405554i	0.808256	−	0.588832i	$-0.200412\pi$
$349$	13.1227	+	7.57638i	0.702441	+	0.405554i	−0.105815	+	0.994386i	$0.533745\pi$
$350$	−13.2975	−	6.61067i	−0.710780	−	0.353355i
$351$	−32.8799	+	6.18887i	−1.75500	+	0.330337i
$352$	−0.0106953	+	0.00748894i	−0.000570062	+	0.000399162i
$353$	−2.73813	+	10.2188i	−0.145736	+	0.543894i	0.853986	+	0.520297i	$0.174179\pi$
$353$	−2.73813	+	10.2188i	−0.145736	+	0.543894i	−0.999722	+	0.0235975i	$0.992488\pi$
$354$	5.22943	−	0.631591i	0.277941	−	0.0335687i
$355$	14.0107	−	32.6628i	0.743610	−	1.73356i
$356$	0.900602	−	2.47438i	0.0477318	−	0.131142i
$357$	2.52463	+	11.9941i	0.133618	+	0.634795i
$358$	−0.294902	+	3.37075i	−0.0155861	+	0.178149i
$359$	4.81261	+	27.2936i	0.254000	+	1.44050i	0.798627	+	0.601826i	$0.205560\pi$
$359$	4.81261	+	27.2936i	0.254000	+	1.44050i	−0.544628	+	0.838678i	$0.683329\pi$
$360$	−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
$363$	19.0419	−	0.627234i	0.999442	−	0.0329212i
$364$	−12.2923	−	14.6494i	−0.644293	−	0.767839i
$365$	2.42928	−	16.8230i	0.127155	−	0.880557i
$366$	1.14045	+	3.75680i	0.0596120	+	0.196371i
$367$	0.886781	+	10.1359i	0.0462896	+	0.529092i	0.983571	+	0.180520i	$0.0577779\pi$
$367$	0.886781	+	10.1359i	0.0462896	+	0.529092i	−0.937282	+	0.348573i	$0.886666\pi$
$368$	−4.54423	+	1.21762i	−0.236884	+	0.0634729i
$369$	−11.3457	+	2.78115i	−0.590633	+	0.144781i
$370$	1.65830	+	13.9418i	0.0862109	+	0.724800i
$371$	−22.4584	−	3.96003i	−1.16598	−	0.205594i
$372$	5.60128	+	13.9430i	0.290413	+	0.722913i
$373$	3.52470	+	13.1544i	0.182502	+	0.681107i	0.995151	+	0.0983541i	$0.0313578\pi$
$373$	3.52470	+	13.1544i	0.182502	+	0.681107i	−0.812649	+	0.582753i	$0.801976\pi$
$374$	−0.0238312	−	0.0199968i	−0.00123228	−	0.00103401i
$375$	7.32814	+	17.9248i	0.378423	+	0.925633i
$376$	0.115928	−	0.0421944i	0.00597854	−	0.00217601i
$377$	2.05241	−	23.4591i	0.105704	−	1.20821i
$378$	−14.9518	−	3.82232i	−0.769036	−	0.196599i
$379$		−	0.616566i		−	0.0316709i	−0.999875	−	0.0158354i	$-0.994959\pi$
$379$		−	0.616566i		−	0.0316709i	0.999875	−	0.0158354i	$-0.00504079\pi$
$380$	7.46225	+	6.27015i	0.382805	+	0.321652i
$381$	1.19128	−	0.894003i	0.0610311	−	0.0458011i
$382$	13.1462	−	18.7748i	0.672620	−	0.960600i
$383$	8.39976	+	0.734884i	0.429208	+	0.0375508i	0.299713	−	0.954029i	$-0.403109\pi$
$383$	8.39976	+	0.734884i	0.429208	+	0.0375508i	0.129494	+	0.991580i	$0.458665\pi$
$384$	0.946215	−	1.45075i	0.0482863	−	0.0740333i
$385$	0.0646576	−	0.0577764i	0.00329526	−	0.00294456i
$386$	−13.0593	+	15.5635i	−0.664700	+	0.792159i
$387$	−0.479013	+	22.3688i	−0.0243496	+	1.13707i
$388$	−11.1334	−	2.98318i	−0.565212	−	0.151448i
$389$	−5.29739	+	30.0430i	−0.268588	+	1.52324i	0.490030	+	0.871705i	$0.336986\pi$
$389$	−5.29739	+	30.0430i	−0.268588	+	1.52324i	−0.758619	+	0.651535i	$0.774125\pi$
$390$	−0.578924	+	24.9309i	−0.0293149	+	1.26242i
$391$	−5.60466	−	9.70756i	−0.283440	−	0.490932i
$392$	−0.471297	−	1.75890i	−0.0238041	−	0.0888381i
$393$	21.5032	+	23.9769i	1.08469	+	1.20948i
$394$	0.626204	−	1.72048i	0.0315477	−	0.0866766i
$395$	14.8095	+	19.8085i	0.745149	+	0.996672i
$396$	0.0358461	−	0.0157900i	0.00180133	−	0.000793478i
$397$	−8.95353	+	12.7870i	−0.449365	+	0.641760i	−0.978371	−	0.206859i	$-0.933676\pi$
$397$	−8.95353	+	12.7870i	−0.449365	+	0.641760i	0.529006	+	0.848618i	$0.322565\pi$
$398$	−0.999414	−	0.999414i	−0.0500961	−	0.0500961i
$399$	22.0868	+	3.86873i	1.10572	+	0.193679i
$400$	−4.16623	+	2.76451i	−0.208312	+	0.138225i
$401$	22.1025	−	3.89727i	1.10375	−	0.194620i	0.408053	−	0.912958i	$-0.366208\pi$
$401$	22.1025	−	3.89727i	1.10375	−	0.194620i	0.695694	+	0.718338i	$0.255097\pi$
$402$	−5.88563	−	9.46059i	−0.293549	−	0.471851i
$403$	23.6071	−	50.6255i	1.17595	−	2.52184i
$404$	5.75470	+	2.09454i	0.286307	+	0.104207i
$405$	11.3493	+	16.6190i	0.563953	+	0.825807i
$406$	5.43108	−	9.40691i	0.269540	−	0.466857i
$407$	−0.0791876	−	0.0212183i	−0.00392518	−	0.00105175i
$408$	3.92238	+	1.28305i	0.194187	+	0.0635203i
$409$	31.4272	+	5.54147i	1.55398	+	0.274008i	0.883682	−	0.468088i	$-0.155057\pi$
$409$	31.4272	+	5.54147i	1.55398	+	0.274008i	0.670294	+	0.742095i	$0.266168\pi$
$410$	0.270932	+	8.70272i	0.0133804	+	0.429797i
$411$	−28.4983	+	3.44192i	−1.40572	+	0.169777i
$412$	−1.01141	−	11.5605i	−0.0498287	−	0.569544i
$413$	−3.81719	−	8.18600i	−0.187832	−	0.402806i
$414$	14.0830	−	0.928784i	0.692141	−	0.0456472i
$415$	11.4340	−	2.38518i	0.561275	−	0.117084i
$416$	−6.34104	+	1.11810i	−0.310895	+	0.0548192i
$417$	−25.7185	−	3.66641i	−1.25944	−	0.179545i
$418$	−0.0501672	+	0.0268749i	−0.00245376	+	0.00131449i
$419$	15.8437			0.774013			0.387007	−	0.922077i	$-0.373509\pi$
$419$	15.8437			0.774013			0.387007	+	0.922077i	$0.373509\pi$
$420$	−5.10200	+	10.3094i	−0.248952	+	0.503048i
$421$	−2.91058	+	2.44226i	−0.141853	+	0.119029i	−0.710953	−	0.703240i	$-0.751736\pi$
$421$	−2.91058	+	2.44226i	−0.141853	+	0.119029i	0.569100	+	0.822268i	$0.307292\pi$
$422$	2.00577	−	4.30138i	0.0976393	−	0.209388i
$423$	−0.365775	+	0.0564499i	−0.0177846	+	0.00274469i
$424$	−4.93558	+	5.88199i	−0.239693	+	0.285655i
$425$	−8.93169	−	7.88368i	−0.433250	−	0.382415i
$426$	−25.3201	−	10.8069i	−1.22676	−	0.523597i
$427$	5.51470	−	3.86143i	0.266875	−	0.186868i
$428$	−0.907186	+	0.635218i	−0.0438505	+	0.0307044i
$429$	−0.133924	−	0.0571605i	−0.00646592	−	0.00275973i
$430$	16.2348	+	3.81287i	0.782911	+	0.183873i
$431$	11.7945	−	14.0561i	0.568121	−	0.677060i	−0.403123	−	0.915146i	$-0.632075\pi$
$431$	11.7945	−	14.0561i	0.568121	−	0.677060i	0.971244	+	0.238085i	$0.0765198\pi$
$432$	−3.63168	+	3.71630i	−0.174729	+	0.178801i
$433$	9.03110	−	19.3673i	0.434007	−	0.930731i	−0.560704	−	0.828017i	$-0.689469\pi$
$433$	9.03110	−	19.3673i	0.434007	−	0.930731i	0.994711	−	0.102715i	$-0.0327529\pi$
$434$	19.7377	−	16.5619i	0.947439	−	0.794996i
$435$	−13.4192	+	4.53427i	−0.643404	+	0.217402i
$436$	3.56279			0.170627
$437$	−20.2980	+	2.91711i	−0.970986	+	0.139544i
$438$	−13.0344	−	1.85818i	−0.622809	−	0.0887873i
$439$	−17.9221	+	3.16015i	−0.855375	+	0.150826i	−0.584106	−	0.811678i	$-0.698555\pi$
$439$	−17.9221	+	3.16015i	−0.855375	+	0.150826i	−0.271270	+	0.962503i	$0.587444\pi$
$440$	−0.00596193	−	0.0285802i	−0.000284224	−	0.00136251i
$441$	0.359498	+	5.45101i	0.0171190	+	0.259572i
$442$	−6.48366	−	13.9043i	−0.308396	−	0.661358i
$443$	−1.39494	−	15.9443i	−0.0662758	−	0.757536i	−0.954517	−	0.298158i	$-0.903628\pi$
$443$	−1.39494	−	15.9443i	−0.0662758	−	0.757536i	0.888241	−	0.459378i	$-0.151928\pi$
$444$	10.7969	−	1.30401i	0.512400	−	0.0618857i
$445$	4.29097	+	4.03186i	0.203411	+	0.191129i
$446$	10.2157	+	1.80130i	0.483727	+	0.0852941i
$447$	8.25002	+	2.69866i	0.390213	+	0.127642i
$448$	−2.86881	−	0.768695i	−0.135538	−	0.0363174i
$449$	6.43751	−	11.1501i	0.303805	−	0.526205i	−0.673190	−	0.739470i	$-0.735076\pi$
$449$	6.43751	−	11.1501i	0.303805	−	0.526205i	0.976995	+	0.213264i	$0.0684096\pi$
$450$	13.8742	−	5.70142i	0.654037	−	0.268767i
$451$	−0.0477744	−	0.0173885i	−0.00224961	−	0.000818791i
$452$	−4.52042	+	9.69407i	−0.212623	+	0.455971i
$453$	−1.84720	−	2.96919i	−0.0867889	−	0.139505i
$454$	25.6979	−	4.53123i	1.20606	−	0.212661i
$455$	40.9399	−	12.3474i	1.91929	−	0.578853i
$456$	4.84639	−	5.78900i	0.226953	−	0.271095i
$457$	−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	$-0.511373\pi$
$458$	3.22927	−	4.61188i	0.150894	−	0.215499i
$459$	−10.7926	−	6.06646i	−0.503754	−	0.283158i
$460$	1.50347	−	10.4117i	0.0700996	−	0.485446i
$461$	−4.06748	+	11.1753i	−0.189441	+	0.520486i	−0.997658	−	0.0683995i	$-0.978211\pi$
$461$	−4.06748	+	11.1753i	−0.189441	+	0.520486i	0.808217	+	0.588885i	$0.200433\pi$
$462$	−0.0448437	−	0.0500027i	−0.00208632	−	0.00232633i
$463$	3.08632	+	11.5183i	0.143434	+	0.535301i	0.999820	+	0.0189662i	$0.00603749\pi$
$463$	3.08632	+	11.5183i	0.143434	+	0.535301i	−0.856387	+	0.516335i	$0.827296\pi$
$464$	−1.82864	−	3.16730i	−0.0848926	−	0.147038i
$465$	−33.5902	−	0.780004i	−1.55771	−	0.0361718i
$466$	−4.93134	+	27.9670i	−0.228440	+	1.29555i
$467$	−3.73134	−	0.999809i	−0.172666	−	0.0462656i	0.171450	−	0.985193i	$-0.445155\pi$
$467$	−3.73134	−	0.999809i	−0.172666	−	0.0462656i	−0.344116	+	0.938927i	$0.611821\pi$
$468$	19.3122	+	0.413558i	0.892705	+	0.0191167i
$469$	−12.2808	+	14.6357i	−0.567074	+	0.675813i
$470$	−0.0154799	+	0.275425i	−0.000714036	+	0.0127044i
$471$	−11.5141	+	17.6536i	−0.530543	+	0.813436i
$472$	−3.02958	−	0.265054i	−0.139448	−	0.0122001i
$473$	−0.0558522	+	0.0797653i	−0.00256809	+	0.00366761i
$474$	15.3228	−	11.4991i	0.703801	−	0.528171i
$475$	−19.4630	+	9.80781i	−0.893022	+	0.450013i
$476$		−	7.07654i		−	0.324353i
$477$	17.9589	−	14.4255i	0.822283	−	0.660500i
$478$	1.15998	−	13.2586i	0.0530560	−	0.606433i
$479$	32.2060	−	11.7220i	1.47153	−	0.535593i	0.523015	−	0.852324i	$-0.324807\pi$
$479$	32.2060	−	11.7220i	1.47153	−	0.535593i	0.948516	+	0.316730i	$0.102585\pi$
$480$	2.14720	+	3.22328i	0.0980059	+	0.147122i
$481$	−30.9704	−	25.9873i	−1.41213	−	1.18492i
$482$	−5.85486	−	21.8507i	−0.266682	−	0.995270i
$483$	−9.02145	−	22.4567i	−0.410490	−	1.02182i
$484$	−10.8327	−	1.91010i	−0.492396	−	0.0868227i
$485$	15.9443	−	20.2494i	0.723995	−	0.919477i
$486$	12.8572	−	8.81439i	0.583213	−	0.399829i
$487$	−7.38378	+	1.97848i	−0.334591	+	0.0896534i	−0.422203	−	0.906501i	$-0.638743\pi$
$487$	−7.38378	+	1.97848i	−0.334591	+	0.0896534i	0.0876121	+	0.996155i	$0.472076\pi$
$488$	−0.197558	−	2.25810i	−0.00894305	−	0.102220i
$489$	9.90467	+	32.6275i	0.447905	+	1.47547i
$490$	4.02997	+	0.581938i	0.182056	+	0.0262893i
$491$	−16.5625	−	19.7385i	−0.747457	−	0.890784i	0.249529	−	0.968367i	$-0.419724\pi$
$491$	−16.5625	−	19.7385i	−0.747457	−	0.890784i	−0.996986	+	0.0775831i	$0.975280\pi$
$492$	6.74071	−	0.222036i	0.303895	−	0.0100102i
$493$	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
$497$	−4.11432	+	47.0269i	−0.184552	+	2.10944i
$498$	−1.86355	−	8.85342i	−0.0835076	−	0.396731i
$499$	−1.02094	+	2.80501i	−0.0457036	+	0.125570i	−0.960445	−	0.278471i	$-0.910172\pi$
$499$	−1.02094	+	2.80501i	−0.0457036	+	0.125570i	0.914741	+	0.404041i	$0.132395\pi$
$500$	−2.00856	−	10.9984i	−0.0898256	−	0.491865i
$501$	−33.3255	+	4.02493i	−1.48887	+	0.179821i
$502$	7.08536	−	26.4429i	0.316235	−	1.18021i
$503$	−18.8500	+	13.1989i	−0.840478	+	0.588509i	−0.912585	−	0.408888i	$-0.865917\pi$
$503$	−18.8500	+	13.1989i	−0.840478	+	0.588509i	0.0721063	+	0.997397i	$0.477028\pi$
$504$	7.99276	+	3.93756i	0.356026	+	0.175393i
$505$	−9.37694	+	9.97954i	−0.417268	+	0.444084i
$506$	0.0531956	+	0.0307125i	0.00236483	+	0.00136534i
$507$	−32.9104	−	36.6965i	−1.46160	−	1.62975i
$508$	−0.779352	+	0.363418i	−0.0345782	+	0.0161241i
$509$	−4.17522	+	1.51966i	−0.185064	+	0.0673576i	−0.432890	−	0.901447i	$-0.642506\pi$
$509$	−4.17522	+	1.51966i	−0.185064	+	0.0673576i	0.247826	+	0.968805i	$0.420284\pi$
$510$	−6.09417	+	6.92947i	−0.269854	+	0.306842i
$511$	3.92038	+	22.2336i	0.173427	+	0.983556i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−17.6422	+	14.2040i	−0.778921	+	0.627122i
$514$			30.6775i			1.35313i
$515$	24.6482	+	8.11196i	1.08613	+	0.357456i
$516$	2.93072	−	12.5807i	0.129018	−	0.553835i
$517$	−0.00145985		0.000680739i	−6.42041e−5		2.99389e-5i
$518$	−7.88116	−	16.9012i	−0.346278	−	0.742597i
$519$	25.5602	+	1.39028i	1.12197	+	0.0610265i
$520$	3.29186	−	14.0164i	0.144357	−	0.614658i
$521$	26.6388	−	15.3799i	1.16707	−	0.673807i	0.214081	−	0.976816i	$-0.431324\pi$
$521$	26.6388	−	15.3799i	1.16707	−	0.673807i	0.952988	+	0.303009i	$0.0979911\pi$
$522$	3.53100	+	10.3881i	0.154548	+	0.454677i
$523$	−5.75969	−	8.22569i	−0.251854	−	0.359684i	0.673240	−	0.739424i	$-0.264902\pi$
$523$	−5.75969	−	8.22569i	−0.251854	−	0.359684i	−0.925093	+	0.379740i	$0.876013\pi$
$524$	−9.29730	−	16.1034i	−0.406155	−	0.703480i
$525$	−16.6884	−	19.5721i	−0.728341	−	0.854198i
$526$	4.91650	+	4.12543i	0.214370	+	0.179877i
$527$	18.7337	−	8.73567i	0.816053	−	0.380532i
$528$	−0.0221297	+	0.00465806i	−0.000963072	+	0.000202716i
$529$	−0.557565	−	0.664480i	−0.0242419	−	0.0288904i
$530$	−7.73680	−	15.3275i	−0.336065	−	0.665782i
$531$	8.76001	+	2.54946i	0.380152	+	0.110637i
$532$	−12.0183	−	4.81228i	−0.521060	−	0.208639i
$533$	−17.7286	−	17.7286i	−0.767911	−	0.767911i
$534$	3.11706	−	3.32940i	0.134888	−	0.144077i
$535$	−0.505696	−	2.42419i	−0.0218632	−	0.104807i
$536$	2.20015	+	6.04487i	0.0950321	+	0.261099i
$537$	−2.76162	+	5.16915i	−0.119173	+	0.223065i
$538$	24.1463	−	2.11253i	1.04102	−	0.0910776i
$539$	−0.0118877	+	0.0205901i	−0.000512039	+	0.000886877i
$540$	−4.43570	−	10.7389i	−0.190882	−	0.462130i
$541$	−4.47302	+	25.3677i	−0.192310	+	1.09064i	0.723888	+	0.689918i	$0.242353\pi$
$541$	−4.47302	+	25.3677i	−0.192310	+	1.09064i	−0.916198	+	0.400726i	$0.868758\pi$
$542$	−4.73435	−	6.76135i	−0.203358	−	0.290425i
$543$	−7.25143	+	2.91309i	−0.311189	+	0.125013i
$544$	−2.06345	−	1.19133i	−0.0884697	−	0.0510780i
$545$	−3.14055	+	7.32150i	−0.134526	+	0.313619i
$546$	−9.62147	−	31.6946i	−0.411761	−	1.35640i
$547$	−3.73894	−	1.74350i	−0.159865	−	0.0745465i	0.341039	−	0.940049i	$-0.389221\pi$
$547$	−3.73894	−	1.74350i	−0.159865	−	0.0745465i	−0.500904	+	0.865503i	$0.666999\pi$
$548$	16.5100	+	1.44444i	0.705273	+	0.0617034i
$549$	−0.737574	+	6.76007i	−0.0314789	+	0.288513i
$550$	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
$553$	−26.9095	−	18.8422i	−1.14431	−	0.801253i
$554$	2.39425	−	2.00901i	0.101722	−	0.0853547i
$555$	−6.83760	+	23.3371i	−0.290240	+	0.990603i
$556$	14.0942	+	5.12986i	0.597726	+	0.217555i
$557$	6.34634	−	0.555233i	0.268903	−	0.0235260i	0.0480933	−	0.998843i	$-0.484686\pi$
$557$	6.34634	−	0.555233i	0.268903	−	0.0235260i	0.220810	+	0.975317i	$0.429130\pi$
$558$	−0.557201	+	26.0199i	−0.0235882	+	1.10151i
$559$	−41.5872	+	24.0104i	−1.75895	+	1.01553i
$560$	4.10847	−	5.21778i	0.173615	−	0.220491i
$561$	−0.0243674	−	0.0480585i	−0.00102879	−	0.00202903i
$562$	−2.96447	+	11.0636i	−0.125049	+	0.466688i
$563$	−12.8413	+	3.44082i	−0.541198	+	0.145013i	−0.519054	−	0.854741i	$-0.673716\pi$
$563$	−12.8413	+	3.44082i	−0.541198	+	0.145013i	−0.0221434	+	0.999755i	$0.507049\pi$
$564$	0.213365	+	0.0116054i	0.00898428	+	0.000488676i
$565$	−15.9365	−	17.8346i	−0.670455	−	0.750307i
$566$	−3.76646	−	10.3483i	−0.158316	−	0.434970i
$567$	−21.2196	−	16.2550i	−0.891139	−	0.682647i
$568$	13.0199	+	9.11666i	0.546304	+	0.382526i
$569$	−32.9924			−1.38311			−0.691557	−	0.722322i	$-0.743075\pi$
$569$	−32.9924			−1.38311			−0.691557	+	0.722322i	$0.743075\pi$
$570$	7.62431	+	15.0622i	0.319347	+	0.630886i
$571$	27.9412			1.16930			0.584651	−	0.811285i	$-0.301232\pi$
$571$	27.9412			1.16930			0.584651	+	0.811285i	$0.301232\pi$
$572$	0.0688656	+	0.0482202i	0.00287942	+	0.00201619i
$573$	33.7075	−	20.9702i	1.40815	−	0.876041i
$574$	−3.95540	−	10.8674i	−0.165095	−	0.453595i
$575$	20.0706	+	12.2673i	0.837000	+	0.511583i
$576$	2.49373	−	1.66772i	0.103906	−	0.0694884i
$577$	−11.8042	+	3.16294i	−0.491417	+	0.131675i	−0.496014	−	0.868315i	$-0.665203\pi$
$577$	−11.8042	+	3.16294i	−0.491417	+	0.131675i	0.00459688	+	0.999989i	$0.498537\pi$
$578$	−2.93058	+	10.9371i	−0.121896	+	0.454923i
$579$	−31.3856	+	15.9136i	−1.30434	+	0.661347i
$580$	8.12069	−	0.965911i	0.337193	−	0.0401073i
$581$	−13.4355	+	7.75696i	−0.557397	+	0.321813i
$582$	−15.7074	−	12.3221i	−0.651092	−	0.510767i
$583$	0.0998720	−	0.00873767i	0.00413628	−	0.000361877i
$584$	7.14309	+	2.59987i	0.295583	+	0.107583i
$585$	−17.8732	+	39.3217i	−0.738967	+	1.62575i
$586$	−24.1903	+	20.2981i	−0.999294	+	0.838507i
$587$	7.63819	+	5.34832i	0.315262	+	0.220749i	0.720487	−	0.693468i	$-0.243918\pi$
$587$	7.63819	+	5.34832i	0.315262	+	0.220749i	−0.405225	+	0.914217i	$0.632807\pi$
$588$	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
$591$	2.16734	−	2.31499i	0.0891526	−	0.0952260i
$592$	−6.25502	−	0.547243i	−0.257080	−	0.0224916i
$593$	0.894416	+	0.417073i	0.0367293	+	0.0171271i	0.440896	−	0.897558i	$-0.354661\pi$
$593$	0.894416	+	0.417073i	0.0367293	+	0.0171271i	−0.404167	+	0.914685i	$0.632438\pi$
$594$	0.0678394		0.000781313i	0.00278348		3.20577e-5i
$595$	14.5422	+	6.23787i	0.596173	+	0.255728i
$596$	−4.34009	−	2.50575i	−0.177777	−	0.102640i
$597$	−0.912564	−	2.27161i	−0.0373487	−	0.0929707i
$598$	17.3747	+	24.8136i	0.710503	+	1.01470i
$599$	−2.80787	+	15.9242i	−0.114726	+	0.650646i	0.872159	+	0.489223i	$0.162719\pi$
$599$	−2.80787	+	15.9242i	−0.114726	+	0.650646i	−0.986885	+	0.161423i	$0.948392\pi$
$600$	−8.51653	+	1.57121i	−0.347686	+	0.0641443i
$601$	19.1563	−	33.1796i	0.781400	−	1.35342i	−0.149726	−	0.988728i	$-0.547839\pi$
$601$	19.1563	−	33.1796i	0.781400	−	1.35342i	0.931126	−	0.364697i	$-0.118828\pi$
$602$	−22.0659	+	1.93052i	−0.899340	+	0.0786821i
$603$	−2.94348	−	19.0727i	−0.119868	−	0.776698i
$604$	0.690515	+	1.89717i	0.0280967	+	0.0771949i
$605$	13.4741	−	20.5774i	0.547801	−	0.836590i
$606$	7.74323	+	7.24938i	0.314547	+	0.294486i
$607$	−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	$0.776299\pi$
$608$	−3.42650	+	2.69428i	−0.138963	+	0.109267i
$609$	15.0478	−	11.2927i	0.609766	−	0.457603i
$610$	4.81452	+	1.58450i	0.194934	+	0.0641547i
$611$	−0.510599	−	0.608508i	−0.0206566	−	0.0246176i
$612$	5.37606	+	4.71082i	0.217314	+	0.190424i
$613$	−38.4073	+	17.9096i	−1.55126	+	0.723363i	−0.994244	−	0.107140i	$-0.965831\pi$
$613$	−38.4073	+	17.9096i	−1.55126	+	0.723363i	−0.557014	+	0.830503i	$0.688053\pi$
$614$	−15.2087	−	12.7616i	−0.613774	−	0.515017i
$615$	−5.48556	+	14.0478i	−0.221199	+	0.566463i
$616$	0.0193891	+	0.0335828i	0.000781207	+	0.00135309i
$617$	−12.5058	−	17.8602i	−0.503466	−	0.719024i	0.484311	−	0.874896i	$-0.339070\pi$
$617$	−12.5058	−	17.8602i	−0.503466	−	0.719024i	−0.987777	+	0.155872i	$0.950181\pi$
$618$	6.24901	−	19.1037i	0.251372	−	0.768465i
$619$	25.1365	−	14.5125i	1.01032	−	0.583309i	0.0990347	−	0.995084i	$-0.468425\pi$
$619$	25.1365	−	14.5125i	1.01032	−	0.583309i	0.911285	+	0.411775i	$0.135091\pi$
$620$	18.8847	+	4.43523i	0.758429	+	0.178123i
$621$	23.0660	+	8.09574i	0.925605	+	0.324871i
$622$	−0.00833482	−	0.0178741i	−0.000334196	−	0.000716685i
$623$	−7.08785	−	3.30512i	−0.283969	−	0.132417i
$624$	−10.8616	−	2.53025i	−0.434812	−	0.101291i
$625$	24.3722	+	5.56739i	0.974888	+	0.222696i
$626$		−	9.67983i		−	0.386884i
$627$	−0.0981900	+	0.00870249i	−0.00392133	+	0.000347544i
$628$	8.60450	−	8.60450i	0.343357	−	0.343357i
$629$	−2.59787	−	14.7333i	−0.103584	−	0.587454i
$630$	−15.1371	+	12.9541i	−0.603078	+	0.516105i
$631$	−6.70570	+	2.44067i	−0.266950	+	0.0971617i	−0.472027	−	0.881584i	$-0.656478\pi$
$631$	−6.70570	+	2.44067i	−0.266950	+	0.0971617i	0.205078	+	0.978746i	$0.434255\pi$
$632$	−10.0244	+	4.67446i	−0.398750	+	0.185940i
$633$	6.11982	−	5.48842i	0.243241	−	0.218145i
$634$	−14.2433	−	8.22337i	−0.565673	−	0.326592i
$635$	−0.0598326	−	1.92191i	−0.00237438	−	0.0762686i
$636$	−11.8618	+	6.01433i	−0.470349	+	0.238484i
$637$	−9.60443	+	6.72510i	−0.380542	+	0.266458i
$638$	−0.0123590	+	0.0461245i	−0.000489298	+	0.00182609i
$639$	−32.9875	−	34.4313i	−1.30497	−	1.36208i
$640$	−0.829793	−	2.07640i	−0.0328004	−	0.0820770i
$641$	4.30425	−	11.8258i	0.170008	−	0.467093i	−0.825204	−	0.564835i	$-0.808940\pi$
$641$	4.30425	−	11.8258i	0.170008	−	0.467093i	0.995212	+	0.0977423i	$0.0311621\pi$
$642$	−1.87706	+	0.395101i	−0.0740817	+	0.0155934i
$643$	−2.26631	+	25.9040i	−0.0893745	+	1.02155i	0.810596	+	0.585605i	$0.199143\pi$
$643$	−2.26631	+	25.9040i	−0.0893745	+	1.02155i	−0.899971	+	0.435950i	$0.856412\pi$
$644$	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	$0.184179\pi$
$648$	−8.31212	+	3.45089i	−0.326531	+	0.135564i
$649$	0.0255232	+	0.0304173i	0.00100187	+	0.00119398i
$650$	25.9017	+	19.1199i	1.01595	+	0.749946i
$651$	42.7033	−	12.9634i	1.67367	−	0.508074i
$652$	−1.71578	−	19.6114i	−0.0671951	−	0.768043i
$653$	23.0841	−	6.18538i	0.903353	−	0.242053i	0.222897	−	0.974842i	$-0.428449\pi$
$653$	23.0841	−	6.18538i	0.903353	−	0.242053i	0.680455	+	0.732789i	$0.261782\pi$
$654$	5.67559	+	2.42241i	0.221933	+	0.0947238i
$655$	41.2878	−	4.91095i	1.61325	−	0.191887i
$656$	−3.83471	−	0.676162i	−0.149720	−	0.0263997i
$657$	−19.5007	−	11.8225i	−0.760794	−	0.461239i
$658$	−0.0948326	−	0.353920i	−0.00369696	−	0.0137972i
$659$	−2.36293	−	1.98274i	−0.0920468	−	0.0772365i	0.595603	−	0.803279i	$-0.296913\pi$
$659$	−2.36293	−	1.98274i	−0.0920468	−	0.0772365i	−0.687650	+	0.726042i	$0.741358\pi$
$660$	0.00993474	−	0.0495824i	0.000386709	−	0.00192999i
$661$	−16.0212	+	5.83125i	−0.623154	+	0.226809i	−0.634249	−	0.773129i	$-0.718690\pi$
$661$	−16.0212	+	5.83125i	−0.623154	+	0.226809i	0.0110951	+	0.999938i	$0.496468\pi$
$662$	−3.14396	+	35.9356i	−0.122194	+	1.39668i
$663$	−0.874814	−	26.5581i	−0.0339750	−	1.03143i
$664$			5.22353i			0.202712i
$665$	20.4832	−	20.4556i	0.794303	−	0.793233i
$666$	18.0863	+	5.26373i	0.700831	+	0.203965i
$667$	−9.86884	+	14.0942i	−0.382123	+	0.545728i
$668$	19.3065	+	1.68910i	0.746993	+	0.0653534i
$669$	15.0490	+	9.81536i	0.581830	+	0.379484i
$670$	−14.3615	−	0.807173i	−0.554835	−	0.0311838i
$671$	−0.0190237	+	0.0226716i	−0.000734403	+	0.000875228i
$672$	−4.04741	−	3.17511i	−0.156132	−	0.122482i
$673$	36.2702	+	9.71856i	1.39811	+	0.374623i	0.877667	−	0.479272i	$-0.159099\pi$
$673$	36.2702	+	9.71856i	1.39811	+	0.374623i	0.520446	+	0.853895i	$0.325766\pi$
$674$	1.51797	−	8.60883i	0.0584700	−	0.331600i
$675$	25.9784	+	0.350893i	0.999909	+	0.0135059i
$676$	14.2295	+	24.6461i	0.547287	+	0.947929i
$677$	7.95825	+	29.7006i	0.305860	+	1.14149i	0.932202	+	0.361938i	$0.117885\pi$
$677$	7.95825	+	29.7006i	0.305860	+	1.14149i	−0.626342	+	0.779548i	$0.715449\pi$
$678$	−13.7923	+	12.3693i	−0.529690	+	0.475041i
$679$	−11.7083	+	32.1682i	−0.449322	+	1.23450i
$680$	4.26708	−	3.19023i	0.163635	−	0.122340i
$681$	44.0181	+	10.2542i	1.68678	+	0.392941i
$682$	−0.0649688	+	0.0927851i	−0.00248778	+	0.00355292i
$683$	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	$0.505319\pi$
$684$	11.6564	−	5.92682i	0.445695	−	0.226618i
$685$	−17.5216	+	32.6546i	−0.669467	+	1.24767i
$686$	15.1481	−	2.67102i	0.578358	−	0.101980i
$687$	8.27999	−	5.15116i	0.315901	−	0.196529i
$688$	−3.15187	+	6.75921i	−0.120164	+	0.257692i
$689$	46.4585	+	16.9095i	1.76993	+	0.644201i
$690$	9.47414	−	15.5637i	0.360674	−	0.592501i
$691$	6.08746	−	10.5438i	0.231578	−	0.401105i	−0.726695	−	0.686961i	$-0.758944\pi$
$691$	6.08746	−	10.5438i	0.231578	−	0.401105i	0.958273	+	0.285856i	$0.0922778\pi$
$692$	−14.2754	−	3.82509i	−0.542671	−	0.145408i
$693$	−0.0374391	−	0.110145i	−0.00142219	−	0.00418408i
$694$	17.0622	+	3.00852i	0.647671	+	0.114202i
$695$	−22.9656	+	24.4415i	−0.871136	+	0.927119i
$696$	−0.759550	−	6.28890i	−0.0287907	−	0.238380i
$697$	−0.808611	−	9.24247i	−0.0306283	−	0.350084i
$698$	−6.40383	−	13.7331i	−0.242389	−	0.519804i
$699$	−26.8711	+	41.1991i	−1.01636	+	1.55829i
$700$	7.10092	+	13.0423i	0.268390	+	0.492951i
$701$	24.1534	−	4.25889i	0.912261	−	0.160856i	0.302231	−	0.953235i	$-0.402269\pi$
$701$	24.1534	−	4.25889i	0.912261	−	0.160856i	0.610030	+	0.792379i	$0.291158\pi$
$702$	30.4834	+	13.7895i	1.15052	+	0.520452i
$703$	−26.7886	−	5.60706i	−1.01035	−	0.211474i
$704$	0.0130566			0.000492088
$705$	−0.211927	+	0.428232i	−0.00798163	+	0.0161282i
$706$	8.10423	−	6.80026i	0.305007	−	0.255931i
$707$	7.68675	−	16.4843i	0.289090	−	0.619956i
$708$	−4.64596	−	2.48211i	−0.174606	−	0.0932833i
$709$	16.2328	−	19.3455i	0.609636	−	0.726536i	−0.369615	−	0.929185i	$-0.620510\pi$
$709$	16.2328	−	19.3455i	0.609636	−	0.726536i	0.979252	+	0.202649i	$0.0649549\pi$
$710$	−30.2115	+	18.7196i	−1.13382	+	0.702536i
$711$	32.2280	−	7.90000i	1.20865	−	0.296273i
$712$	−2.15698	+	1.51033i	−0.0808362	+	0.0566021i
$713$	−33.4322	+	23.4095i	−1.25205	+	0.876692i
$714$	4.81148	−	11.2731i	0.180065	−	0.421884i
$715$	−0.159796	+	0.0990127i	−0.00597604	+	0.00370287i
$716$	2.17495	−	2.59200i	0.0812817	−	0.0968678i
$717$	10.8626	−	20.3325i	0.405672	−	0.759330i
$718$	11.7127	−	25.1180i	0.437115	−	0.937397i
$719$	−14.6836	+	12.3210i	−0.547606	+	0.459496i	−0.874129	−	0.485693i	$-0.838567\pi$
$719$	−14.6836	+	12.3210i	−0.547606	+	0.459496i	0.326524	+	0.945189i	$0.394123\pi$
$720$	1.22896	+	6.59467i	0.0458008	+	0.245769i
$721$	−34.4659			−1.28358
$722$	−16.2250	+	9.88685i	−0.603831	+	0.367951i
$723$	5.52978	−	38.7893i	0.205655	−	1.44259i
$724$	4.44327	−	0.783468i	0.165133	−	0.0291174i
$725$	−5.17333	+	17.5394i	−0.192133	+	0.651396i
$726$	−15.9580	−	10.4082i	−0.592257	−	0.386285i
$727$	−13.7219	−	29.4267i	−0.508917	−	1.09138i	−0.978073	−	0.208261i	$-0.933220\pi$
$727$	−13.7219	−	29.4267i	−0.508917	−	1.09138i	0.469156	−	0.883115i	$-0.344558\pi$
$728$	1.66672	+	19.0507i	0.0617728	+	0.706066i
$729$	26.4748	−	5.29965i	0.980547	−	0.196283i
$730$	−11.6392	+	12.3872i	−0.430788	+	0.458472i
$731$	−17.4999	−	3.08570i	−0.647256	−	0.114129i
$732$	1.22061	−	3.73152i	0.0451152	−	0.137921i
$733$	6.09148	+	1.63221i	0.224994	+	0.0602869i	0.369555	−	0.929209i	$-0.379510\pi$
$733$	6.09148	+	1.63221i	0.224994	+	0.0602869i	−0.144561	+	0.989496i	$0.546177\pi$
$734$	5.08733	−	8.81152i	0.187777	−	0.325239i
$735$	6.02415	+	3.66710i	0.222204	+	0.135263i
$736$	4.42081	+	1.60904i	0.162953	+	0.0593101i
$737$	0.0354959	−	0.0761212i	0.00130751	−	0.00280396i
$738$	10.8890	+	4.22944i	0.400831	+	0.155688i
$739$	−23.1972	+	4.09030i	−0.853324	+	0.150464i	−0.583167	−	0.812352i	$-0.698187\pi$
$739$	−23.1972	+	4.09030i	−0.853324	+	0.150464i	−0.270157	+	0.962816i	$0.587076\pi$
$740$	6.63829	−	12.3716i	0.244028	−	0.454790i
$741$	−45.6994	−	16.5747i	−1.67881	−	0.608886i
$742$	16.1255	+	16.1255i	0.591986	+	0.591986i
$743$	−16.7315	+	23.8951i	−0.613820	+	0.876625i	−0.998930	−	0.0462451i	$-0.985274\pi$
$743$	−16.7315	+	23.8951i	−0.613820	+	0.876625i	0.385110	+	0.922871i	$0.374163\pi$
$744$	3.40910	−	14.6342i	0.124984	−	0.536517i
$745$	8.97503	−	6.71006i	0.328820	−	0.245838i
$746$	4.65777	−	12.7971i	0.170533	−	0.468535i
$747$	3.05095	−	15.3707i	0.111628	−	0.562385i
$748$	0.00805172	+	0.0300494i	0.000294400	+	0.00109872i
$749$	1.64460	+	2.84852i	0.0600922	+	0.104083i
$750$	4.27838	−	18.8864i	0.156224	−	0.689633i
$751$	−6.24535	+	35.4191i	−0.227896	+	1.29246i	0.629175	+	0.777264i	$0.283393\pi$
$751$	−6.24535	+	35.4191i	−0.227896	+	1.29246i	−0.857071	+	0.515199i	$0.827718\pi$
$752$	−0.119165	−	0.0319301i	−0.00434549	−	0.00116437i
$753$	29.2662	−	37.3066i	1.06652	−	1.35953i
$754$	−15.1368	+	18.0394i	−0.551251	+	0.656955i
$755$	−4.50735	−	0.253330i	−0.164039	−	0.00921963i
$756$	10.0554	+	11.7070i	0.365711	+	0.425781i
$757$	23.0384	+	2.01560i	0.837345	+	0.0732582i	0.497757	−	0.867316i	$-0.334157\pi$
$757$	23.0384	+	2.01560i	0.837345	+	0.0732582i	0.339588	+	0.940574i	$0.389713\pi$
$758$	−0.353648	+	0.505062i	−0.0128451	+	0.0183447i
$759$	0.0638596	+	0.0850943i	0.00231795	+	0.00308873i
$760$	−2.51631	−	9.41638i	−0.0912761	−	0.341568i
$761$			11.4937i			0.416648i	0.978060	+	0.208324i	$0.0668008\pi$
$761$			11.4937i			0.416648i	−0.978060	+	0.208324i	$0.933199\pi$
$762$	−1.48862	+	0.0490345i	−0.0539269	+	0.00177633i
$763$	0.922240	−	10.5413i	0.0333873	−	0.381619i
$764$	−21.5375	+	7.83902i	−0.779200	+	0.283606i
$765$	−14.4196	+	6.89523i	−0.521342	+	0.249298i
$766$	−6.45917	−	5.41989i	−0.233379	−	0.195828i
$767$	5.06808	+	18.9143i	0.182998	+	0.682957i
$768$	−1.60721	+	0.645658i	−0.0579952	+	0.0232982i
$769$	−16.9086	−	2.98143i	−0.609738	−	0.107513i	−0.139751	−	0.990187i	$-0.544630\pi$
$769$	−16.9086	−	2.98143i	−0.609738	−	0.107513i	−0.469987	+	0.882673i	$0.655741\pi$
$770$	−0.0861036	+	0.0102415i	−0.00310296	+	0.000369080i
$771$	−20.8583	+	48.8699i	−0.751192	+	1.76001i
$772$	19.6244	−	5.25834i	0.706297	−	0.189252i
$773$	3.25322	+	37.1845i	0.117010	+	1.33743i	0.796897	+	0.604116i	$0.206474\pi$
$773$	3.25322	+	37.1845i	0.117010	+	1.33743i	−0.679886	+	0.733318i	$0.737971\pi$
$774$	13.2226	−	18.0487i	0.475276	−	0.648746i
$775$	−25.7610	+	34.8983i	−0.925362	+	1.25359i
$776$	7.40886	+	8.82953i	0.265962	+	0.316962i
$777$	−1.06337	−	32.2825i	−0.0381483	−	1.15813i
$778$	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
$782$	−0.976957	+	11.1667i	−0.0349359	+	0.399319i
$783$	−1.43816	+	18.9493i	−0.0513956	+	0.677193i
$784$	−0.622802	+	1.71113i	−0.0222429	+	0.0611119i
$785$	10.0974	+	25.2669i	0.360393	+	0.901815i
$786$	−3.86176	−	31.9744i	−0.137744	−	1.14049i
$787$	−7.76152	+	28.9664i	−0.276668	+	1.03254i	0.678047	+	0.735019i	$0.262827\pi$
$787$	−7.76152	+	28.9664i	−0.276668	+	1.03254i	−0.954715	+	0.297521i	$0.903840\pi$
$788$	−1.49978	+	1.05016i	−0.0534276	+	0.0374104i
$789$	5.02711	+	9.91472i	0.178970	+	0.352973i
$790$	−0.769596	−	24.7205i	−0.0273810	−	0.879517i
$791$	27.5118	+	15.8839i	0.978207	+	0.564768i
$792$	−0.0384202	−	0.00762605i	−0.00136520	−	0.000270980i
$793$	−13.2277	+	6.16818i	−0.469729	+	0.219038i
$794$	14.6686	−	5.33894i	0.520569	−	0.189472i
$795$	−1.90342	−	29.6773i	−0.0675074	−	1.05255i
$796$	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	$0.195622\pi$
$798$	−15.8734	−	15.8376i	−0.561914	−	0.560643i
$799$		−	0.293945i		−	0.0103990i
$800$	4.99843	+	0.125101i	0.176721	+	0.00442300i
$801$	7.22926	−	3.18445i	0.255433	−	0.112517i
$802$	−20.3407	−	9.48502i	−0.718255	−	0.334928i
$803$	−0.0419447	−	0.0899508i	−0.00148020	−	0.00317429i
$804$	−0.605143	+	11.1255i	−0.0213417	+	0.392367i
$805$	−30.4158	−	7.14341i	−1.07202	−	0.251772i
$806$	−48.3754	+	27.9295i	−1.70395	+	0.983776i
$807$	39.9019	+	13.0523i	1.40461	+	0.459461i
$808$	−3.51260	−	5.01651i	−0.123573	−	0.176480i
$809$	1.84919	+	3.20290i	0.0650142	+	0.112608i	0.896700	−	0.442638i	$-0.145957\pi$
$809$	1.84919	+	3.20290i	0.0650142	+	0.112608i	−0.831686	+	0.555246i	$0.812624\pi$
$810$	0.235460	−	20.1232i	0.00827324	−	0.707058i
$811$	29.8059	+	25.0101i	1.04663	+	0.878224i	0.992735	−	0.120322i	$-0.0383928\pi$
$811$	29.8059	+	25.0101i	1.04663	+	0.878224i	0.0538922	+	0.998547i	$0.482837\pi$
$812$	−9.84446	+	4.59055i	−0.345473	+	0.161097i
$813$	−2.94473	−	13.9899i	−0.103276	−	0.490649i
$814$	0.0526964	+	0.0628011i	0.00184701	+	0.00220118i
$815$	41.8137	+	13.7613i	1.46467	+	0.482037i
$816$	−2.47710	−	3.30080i	−0.0867160	−	0.115551i
$817$	−17.1410	+	27.6222i	−0.599689	+	0.966380i
$818$	−22.5652	−	22.5652i	−0.788974	−	0.788974i
$819$	6.22261	−	57.0319i	0.217436	−	1.99286i
$820$	4.76974	−	7.28425i	0.166567	−	0.254377i
$821$	−10.1863	−	27.9865i	−0.355503	−	0.976736i	−0.980571	−	0.196165i	$-0.937151\pi$
$821$	−10.1863	−	27.9865i	−0.355503	−	0.976736i	0.625068	−	0.780570i	$-0.285071\pi$
$822$	25.3187	+	13.5265i	0.883089	+	0.471791i
$823$	24.5553	−	2.14831i	0.855946	−	0.0748855i	0.349270	−	0.937022i	$-0.386430\pi$
$823$	24.5553	−	2.14831i	0.855946	−	0.0748855i	0.506676	+	0.862137i	$0.330874\pi$
$824$	−5.80232	+	10.0499i	−0.202133	+	0.350105i
$825$	0.0931339	+	0.0641219i	0.00324251	+	0.00223244i
$826$	−1.56843	+	8.89503i	−0.0545728	+	0.309498i
$827$	17.4521	+	24.9241i	0.606867	+	0.866696i	0.998574	−	0.0533939i	$-0.0170039\pi$
$827$	17.4521	+	24.9241i	0.606867	+	0.866696i	−0.391706	+	0.920090i	$0.628115\pi$
$828$	−12.0688	−	7.31686i	−0.419421	−	0.254278i
$829$	25.6487	+	14.8083i	0.890816	+	0.514313i	0.874209	−	0.485549i	$-0.161380\pi$
$829$	25.6487	+	14.8083i	0.890816	+	0.514313i	0.0166068	+	0.999862i	$0.494714\pi$
$830$	−10.7343	−	4.60446i	−0.372593	−	0.159823i
$831$	5.18005	−	1.57250i	0.179694	−	0.0545493i
$832$	5.83559	+	2.72118i	0.202313	+	0.0943399i
$833$	−4.32221	−	0.378144i	−0.149756	−	0.0131019i
$834$	18.9644	+	17.7549i	0.656683	+	0.614801i
$835$	−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
$838$	−12.9784	−	9.08755i	−0.448330	−	0.313924i
$839$	41.3668	−	34.7108i	1.42814	−	1.19835i	0.481337	−	0.876536i	$-0.340152\pi$
$839$	41.3668	−	34.7108i	1.42814	−	1.19835i	0.946803	−	0.321815i	$-0.104293\pi$
$840$	10.0925	−	5.51859i	0.348226	−	0.190409i
$841$	14.6820	+	5.34382i	0.506277	+	0.184270i
$842$	3.78503	−	0.331147i	0.130441	−	0.0114121i
$843$	−12.2448	+	15.6088i	−0.421733	+	0.537597i
$844$	−4.11020	+	2.37303i	−0.141479	+	0.0816829i
$845$	−63.1906	+	7.51618i	−2.17382	+	0.258564i
$846$	0.332003	+	0.163559i	0.0114145	+	0.00562326i
$847$	−8.45551	+	31.5564i	−0.290535	+	1.08429i
$848$	7.41676	−	1.98732i	0.254693	−	0.0682447i
$849$	1.03595	−	19.0459i	0.0355537	−	0.653652i
$850$	2.79451	+	11.5809i	0.0958511	+	0.397223i
$851$	10.1030	+	27.7579i	0.346328	+	0.951528i
$852$	14.5424	+	23.3755i	0.498215	+	0.800832i
$853$	8.34814	+	5.84543i	0.285835	+	0.200144i	0.707697	−	0.706516i	$-0.249734\pi$
$853$	8.34814	+	5.84543i	0.285835	+	0.200144i	−0.421862	+	0.906660i	$0.638623\pi$
$854$	−6.73220			−0.230371
$855$	1.90457	+	29.1783i	0.0651350	+	0.997876i
$856$	1.10747			0.0378525
$857$	−40.9322	−	28.6610i	−1.39822	−	0.979043i	−0.998038	−	0.0626057i	$-0.980059\pi$
$857$	−40.9322	−	28.6610i	−1.39822	−	0.979043i	−0.400179	−	0.916437i	$-0.631052\pi$
$858$	0.0769183	+	0.123639i	0.00262595	+	0.00422096i
$859$	−1.80928	−	4.97097i	−0.0617320	−	0.169607i	0.904992	−	0.425428i	$-0.139876\pi$
$859$	−1.80928	−	4.97097i	−0.0617320	−	0.169607i	−0.966724	+	0.255821i	$0.917654\pi$
$860$	−11.1118	−	12.4352i	−0.378909	−	0.424037i
$861$	1.08792	−	20.0013i	0.0370761	−	0.681641i
$862$	−17.7238	+	4.74907i	−0.603674	+	0.161754i
$863$	2.62607	−	9.80064i	0.0893926	−	0.333618i	−0.906717	−	0.421739i	$-0.861420\pi$
$863$	2.62607	−	9.80064i	0.0893926	−	0.333618i	0.996110	+	0.0881215i	$0.0280864\pi$
$864$	5.10648	−	0.961174i	0.173726	−	0.0326998i
$865$	20.4441	−	25.9641i	0.695121	−	0.882806i
$866$	−18.5065	+	10.6847i	−0.628875	+	0.363081i
$867$	−12.1048	+	15.4304i	−0.411101	+	0.524044i
$868$	−25.6677	+	2.24563i	−0.871218	+	0.0762217i
$869$	0.135706	+	0.0493928i	0.00460350	+	0.00167554i
$870$	13.5932	+	3.98270i	0.460851	+	0.135026i
$871$	31.7296	−	26.6243i	1.07512	−	0.902129i
$872$	−2.91847	−	2.04353i	−0.0988318	−	0.0692028i
$873$	−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
$876$	9.61137	+	8.99837i	0.324738	+	0.304027i
$877$	36.2431	+	3.17086i	1.22384	+	0.107072i	0.680697	−	0.732565i	$-0.261677\pi$
$877$	36.2431	+	3.17086i	1.22384	+	0.107072i	0.543147	+	0.839638i	$0.317233\pi$
$878$	16.4935	+	7.69105i	0.556629	+	0.259560i
$879$	−52.3368	+	15.8878i	−1.76527	+	0.535881i
$880$	−0.0115092	+	0.0268311i	−0.000387974	+	0.000904477i
$881$	−43.8420	−	25.3122i	−1.47707	−	0.852790i	−0.477410	−	0.878681i	$-0.658424\pi$
$881$	−43.8420	−	25.3122i	−1.47707	−	0.852790i	−0.999665	+	0.0258910i	$0.991758\pi$
$882$	2.83209	−	4.67141i	0.0953614	−	0.157294i
$883$	28.0735	+	40.0931i	0.944748	+	1.34924i	0.937022	+	0.349270i	$0.113570\pi$
$883$	28.0735	+	40.0931i	0.944748	+	1.34924i	0.00772593	+	0.999970i	$0.497541\pi$
$884$	−2.66405	+	15.1086i	−0.0896017	+	0.508157i
$885$	9.19605	−	7.35946i	0.309122	−	0.247386i
$886$	−8.00259	+	13.8609i	−0.268852	+	0.465666i
$887$	0.679322	−	0.0594329i	0.0228094	−	0.00199556i	−0.0757453	−	0.997127i	$-0.524134\pi$
$887$	0.679322	−	0.0594329i	0.0228094	−	0.00199556i	0.0985547	+	0.995132i	$0.468578\pi$
$888$	−9.59228	−	5.12468i	−0.321896	−	0.171973i
$889$	0.873509	+	2.39995i	0.0292966	+	0.0804916i
$890$	−1.20237	−	5.76391i	−0.0403037	−	0.193207i
$891$	0.108601	+	0.0448807i	0.00363826	+	0.00150356i
$892$	−7.33502	−	7.33502i	−0.245595	−	0.245595i
$893$	−0.499217	−	0.199893i	−0.0167057	−	0.00668916i
$894$	−5.21014	−	6.94263i	−0.174253	−	0.232196i
$895$	3.40936	+	6.75432i	0.113962	+	0.225772i
$896$	1.90908	+	2.27516i	0.0637780	+	0.0760077i
$897$	10.8069	+	51.3419i	0.360832	+	1.71426i
$898$	−11.6687	+	5.44122i	−0.389390	+	0.181576i
$899$	−24.3051	−	20.3944i	−0.810620	−	0.680191i
$900$	−14.6353	−	3.28760i	−0.487843	−	0.109587i
$901$	9.14753	+	15.8440i	0.304748	+	0.527840i
$902$	0.0291609	+	0.0416461i	0.000970952	+	0.00138666i
$903$	−36.4640	−	11.9277i	−1.21345	−	0.396929i
$904$	9.26320	−	5.34811i	0.308090	−	0.177876i
$905$	−2.30666	+	9.82149i	−0.0766759	+	0.326477i
$906$	−0.189923	+	3.49173i	−0.00630978	+	0.116005i
$907$	−9.78002	−	20.9733i	−0.324740	−	0.696408i	0.674378	−	0.738386i	$-0.264412\pi$
$907$	−9.78002	−	20.9733i	−0.324740	−	0.696408i	−0.999119	+	0.0419782i	$0.986634\pi$
$908$	−23.6495	−	11.0279i	−0.784836	−	0.365975i
$909$	7.40611	+	16.8132i	0.245645	+	0.557657i
$910$	−40.6182	−	13.3678i	−1.34648	−	0.443139i
$911$			25.0000i			0.828286i	0.910212	+	0.414143i	$0.135919\pi$
$911$			25.0000i			0.828286i	−0.910212	+	0.414143i	$0.864081\pi$
$912$	−7.29036	+	1.96229i	−0.241408	+	0.0649780i
$913$	0.0482256	−	0.0482256i	0.00159604	−	0.00159604i
$914$	5.43399	+	30.8177i	0.179741	+	1.01936i
$915$	6.59229	+	5.79763i	0.217934	+	0.191664i
$916$	−5.29053	+	1.92559i	−0.174804	+	0.0636234i
$917$	−50.0519	+	23.3396i	−1.65286	+	0.770741i
$918$	5.36118	+	11.1597i	0.176945	+	0.368326i
$919$	−14.0895	−	8.13460i	−0.464771	−	0.268336i	0.249277	−	0.968432i	$-0.419807\pi$
$919$	−14.0895	−	8.13460i	−0.464771	−	0.268336i	−0.714048	+	0.700097i	$0.753140\pi$
$920$	−7.20345	+	7.66637i	−0.237491	+	0.252753i
$921$	−15.5509	−	30.6702i	−0.512419	−	1.01062i
$922$	9.74177	−	6.82126i	0.320828	−	0.224646i
$923$	26.4880	−	98.8547i	0.871864	−	3.25384i
$924$	0.00805350	+	0.0666811i	0.000264941	+	0.00219365i
$925$	19.5720	+	24.5470i	0.643523	+	0.807101i
$926$	4.07847	−	11.2055i	0.134027	−	0.368235i
$927$	22.9438	−	26.1838i	0.753573	−	0.859989i
$928$	−0.318753	+	3.64337i	−0.0104636	+	0.119599i
$929$	−0.604747	−	3.42969i	−0.0198411	−	0.112524i	0.973279	−	0.229627i	$-0.0737506\pi$
$929$	−0.604747	−	3.42969i	−0.0198411	−	0.112524i	−0.993120	+	0.117102i	$0.962639\pi$
$930$	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
$933$	−0.00112458	−	0.0341407i	−3.68172e−5	−	0.00111772i
$934$	2.48307	+	2.95920i	0.0812484	+	0.0968281i
$935$	−0.0688487	−	0.00994192i	−0.00225159	−	0.000325136i
$936$	−15.5824	−	11.4158i	−0.509326	−	0.373136i
$937$	−0.537476	−	6.14337i	−0.0175586	−	0.200695i	−0.999907	−	0.0136352i	$-0.995660\pi$
$937$	−0.537476	−	6.14337i	−0.0175586	−	0.200695i	0.982348	−	0.187060i	$-0.0598959\pi$
$938$	18.4545	−	4.94487i	0.602561	−	0.161456i
$939$	6.58151	−	15.4201i	0.214779	−	0.503218i
$940$	0.170658	−	0.216736i	0.00556624	−	0.00706915i
$941$	3.79454	+	0.669080i	0.123699	+	0.0218114i	0.235155	−	0.971958i	$-0.424440\pi$
$941$	3.79454	+	0.669080i	0.123699	+	0.0218114i	−0.111456	+	0.993769i	$0.535551\pi$
$942$	19.5575	−	7.85676i	0.637218	−	0.255987i
$943$	4.74125	+	17.6946i	0.154396	+	0.576215i
$944$	2.32966	+	1.95481i	0.0758239	+	0.0636238i
$945$	−32.9215	+	10.3441i	−1.07094	+	0.336494i
$946$	0.0915029	−	0.0333043i	0.00297502	−	0.00108282i
$947$	0.909155	−	10.3917i	0.0295436	−	0.337684i	−0.967010	−	0.254737i	$-0.918011\pi$
$947$	0.909155	−	10.3917i	0.0295436	−	0.337684i	0.996554	−	0.0829474i	$-0.0264333\pi$
$948$	−19.1473	+	0.630705i	−0.621877	+	0.0204844i
$949$		−	48.9451i		−	1.58883i
$950$	21.5687	+	3.12941i	0.699779	+	0.101532i
$951$	−17.0986	−	22.7843i	−0.554460	−	0.738831i
$952$	−4.05894	+	5.79676i	−0.131551	+	0.187874i
$953$	−0.320834	−	0.0280694i	−0.0103928	−	0.000909256i	0.0819581	−	0.996636i	$-0.473883\pi$
$953$	−0.320834	−	0.0280694i	−0.0103928	−	0.000909256i	−0.0923510	+	0.995727i	$0.529438\pi$
$954$	−22.9853	+	1.51589i	−0.744175	+	0.0490789i
$955$	2.87591	−	51.1694i	0.0930622	−	1.65580i
$956$	−8.55500	+	10.1955i	−0.276689	+	0.329745i
$957$	−0.0510491	+	0.0650740i	−0.00165018	+	0.00210354i
$958$	−33.1051	−	8.87049i	−1.06958	−	0.286592i
$959$	8.54734	−	48.4744i	0.276008	−	1.56532i
$960$	0.0899109	−	3.87194i	0.00290186	−	0.124966i
$961$	−22.1304	−	38.3310i	−0.713885	−	1.23649i
$962$	10.4638	+	39.0514i	0.337367	+	1.25907i
$963$	−3.25883	−	0.646848i	−0.105014	−	0.0208444i
$964$	−7.73699	+	21.2572i	−0.249192	+	0.684649i
$965$	−6.49277	+	44.9630i	−0.209010	+	1.44741i
$966$	−5.49071	+	23.5700i	−0.176661	+	0.758351i
$967$	−8.99097	+	12.8404i	−0.289130	+	0.412920i	−0.937272	−	0.348599i	$-0.886657\pi$
$967$	−8.99097	+	12.8404i	−0.289130	+	0.412920i	0.648142	+	0.761520i	$0.275546\pi$
$968$	7.77805	+	7.77805i	0.249996	+	0.249996i
$969$	−9.01199	−	15.5685i	−0.289507	−	0.500133i
$970$	−24.6754	+	7.44202i	−0.792279	+	0.238949i
$971$	31.1862	−	5.49897i	1.00081	−	0.176470i	0.350846	−	0.936433i	$-0.385894\pi$
$971$	31.1862	−	5.49897i	1.00081	−	0.176470i	0.649966	+	0.759963i	$0.274783\pi$
$972$	−15.5877	−	0.154238i	−0.499976	−	0.00494717i
$973$	18.8261	−	40.3727i	0.603537	−	1.29429i
$974$	7.18324	+	2.61449i	0.230166	+	0.0837736i
$975$	28.2619	+	48.0695i	0.905107	+	1.53946i
$976$	−1.13336	+	1.96304i	−0.0362781	+	0.0628355i
$977$	−1.76397	−	0.472655i	−0.0564345	−	0.0151216i	0.230491	−	0.973074i	$-0.425967\pi$
$977$	−1.76397	−	0.472655i	−0.0564345	−	0.0151216i	−0.286926	+	0.957953i	$0.592633\pi$
$978$	10.6009	−	32.4080i	0.338981	−	1.03629i
$979$	0.0338580	+	0.00597009i	0.00108211	+	0.000190805i
$980$	−2.96737	−	2.78819i	−0.0947893	−	0.0890655i
$981$	7.39428	+	7.71790i	0.236081	+	0.246414i
$982$	2.24572	+	25.6687i	0.0716638	+	0.819120i
$983$	2.95739	+	6.34214i	0.0943261	+	0.202283i	0.947810	−	0.318837i	$-0.103292\pi$
$983$	2.95739	+	6.34214i	0.0943261	+	0.202283i	−0.853484	+	0.521120i	$0.825514\pi$
$984$	−5.64902	−	3.68443i	−0.180084	−	0.117455i
$985$	−0.836030	−	4.00774i	−0.0266381	−	0.127697i
$986$	−8.58170	+	1.51319i	−0.273297	+	0.0481896i
$987$	0.0895672	−	0.628280i	0.00285095	−	0.0199984i
$988$	23.8478	+	14.7988i	0.758698	+	0.470812i
$989$	35.0862			1.11568
$990$	0.0495383	−	0.0722308i	0.00157443	−	0.00229565i
$991$	6.19973	−	5.20219i	0.196941	−	0.165253i	−0.538985	−	0.842316i	$-0.681192\pi$
$991$	6.19973	−	5.20219i	0.196941	−	0.165253i	0.735925	+	0.677063i	$0.236747\pi$
$992$	−3.66634	+	7.86249i	−0.116406	+	0.249634i
$993$	−29.4418	+	55.1085i	−0.934306	+	1.74882i
$994$	30.3438	−	36.1623i	0.962446	−	1.14700i
$995$	−3.07671	−	0.722590i	−0.0975383	−	0.0229077i
$996$	−3.55158	+	8.32118i	−0.112536	+	0.263667i
$997$	19.7974	−	13.8623i	0.626989	−	0.439022i	−0.216416	−	0.976301i	$-0.569437\pi$
$997$	19.7974	−	13.8623i	0.626989	−	0.439022i	0.843405	+	0.537279i	$0.180548\pi$
$998$	2.44519	−	1.71214i	0.0774013	−	0.0541970i
$999$	25.2330	+	20.6825i	0.798336	+	0.654365i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.17	✓	480	57.17	odd	18	inner
570.2.bi.a.17.35	yes	480	19.17	even	9	inner
570.2.bi.a.47.7	yes	480	1.1	even	1	trivial
570.2.bi.a.47.35	yes	480	3.2	odd	2	inner
570.2.bi.a.473.7	yes	480	285.188	even	36	inner
570.2.bi.a.473.35	yes	480	95.93	odd	36	inner
570.2.bi.a.503.17	yes	480	5.3	odd	4	inner
570.2.bi.a.503.35	yes	480	15.8	even	4	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)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.914939 - 1.47068i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.23254 - 0.125477i) q^{5} +(-0.0940712 + 1.72949i) q^{6} +(2.86881 - 0.768695i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-1.32577 + 2.69116i) q^{9} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.914939 - 1.47068i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.23254 - 0.125477i) q^{5} +(-0.0940712 + 1.72949i) q^{6} +(2.86881 - 0.768695i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-1.32577 + 2.69116i) q^{9} +(1.75682 + 1.38332i) q^{10} +(-0.0113073 + 0.00652828i) q^{11} +(1.06906 - 1.36276i) q^{12} +(-6.41436 + 0.561184i) q^{13} +(-2.79090 - 1.01580i) q^{14} +(1.85810 + 3.39815i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-1.95177 - 1.36664i) q^{17} +(2.62959 - 1.44403i) q^{18} +(-3.64828 + 2.38539i) q^{19} +(-0.645665 - 2.14082i) q^{20} +(-3.75528 - 3.51578i) q^{21} +(0.0130069 + 0.00113795i) q^{22} +(4.26375 + 1.98822i) q^{23} +(-1.65737 + 0.503124i) q^{24} +(4.96851 + 0.560267i) q^{25} +(5.57622 + 3.21943i) q^{26} +(5.17082 - 0.512457i) q^{27} +(1.70353 + 2.43289i) q^{28} +(-0.635081 + 3.60172i) q^{29} +(0.427031 - 3.84937i) q^{30} +(-4.33765 + 7.51303i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(0.0199465 + 0.0106564i) q^{33} +(0.814920 + 2.23897i) q^{34} +(-6.50120 + 1.35618i) q^{35} +(-2.98230 - 0.325391i) q^{36} +(4.43986 + 4.43986i) q^{37} +(4.35670 + 0.138572i) q^{38} +(6.69406 + 8.91999i) q^{39} +(-0.699027 + 2.12400i) q^{40} +(2.50293 + 2.98287i) q^{41} +(1.05958 + 5.03390i) q^{42} +(6.75921 - 3.15187i) q^{43} +(-0.0100019 - 0.00839260i) q^{44} +(3.29753 - 5.84177i) q^{45} +(-2.35226 - 4.07424i) q^{46} +(0.0707611 + 0.101057i) q^{47} +(1.64622 + 0.538492i) q^{48} +(1.57699 - 0.910476i) q^{49} +(-3.74861 - 3.30877i) q^{50} +(-0.224140 + 4.12081i) q^{51} +(-2.72118 - 5.83559i) q^{52} +(-6.95899 - 3.24503i) q^{53} +(-4.52962 - 2.54608i) q^{54} +(0.0260632 - 0.0131559i) q^{55} -2.97001i q^{56} +(6.84608 + 3.18295i) q^{57} +(2.58609 - 2.58609i) q^{58} +(-0.528090 - 2.99495i) q^{59} +(-2.55771 + 2.90828i) q^{60} +(2.13003 - 0.775267i) q^{61} +(7.86249 - 3.66634i) q^{62} +(-1.73472 + 8.73953i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(14.3908 - 0.448011i) q^{65} +(-0.0102269 - 0.0201701i) q^{66} +(-5.26945 + 3.68971i) q^{67} +(0.616680 - 2.30148i) q^{68} +(-0.977043 - 8.08969i) q^{69} +(6.10334 + 2.61802i) q^{70} +(-5.43621 + 14.9359i) q^{71} +(2.25632 + 1.97712i) q^{72} +(-0.662516 + 7.57259i) 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} +(-0.367157 - 11.1464i) q^{78} +(-7.10969 - 8.47300i) q^{79} +(1.79088 - 1.33893i) q^{80} +(-5.48464 - 7.13573i) q^{81} +(-0.339372 - 3.87904i) q^{82} +(-5.04554 + 1.35195i) q^{83} +(2.01937 - 4.73128i) q^{84} +(4.18592 + 3.29599i) q^{85} +(-7.34466 - 1.29506i) q^{86} +(5.87802 - 2.36136i) q^{87} +(0.00337929 + 0.0126117i) q^{88} +(-2.01714 - 1.69258i) q^{89} +(-6.05188 + 2.89391i) q^{90} +(-17.9702 + 6.54061i) q^{91} +(-0.410027 + 4.68663i) q^{92} +(15.0179 - 0.494684i) q^{93} -0.123368i q^{94} +(8.44426 - 4.86770i) q^{95} +(-1.03963 - 1.38534i) q^{96} +(-6.61112 + 9.44166i) q^{97} +(-1.81402 - 0.158706i) q^{98} +(-0.00257767 - 0.0390848i) 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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