LMFDB - Embedded newform 570.2.bh.b.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	570.13
Dual form			570.2.bh.b.307.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-1.60997 + 1.55177i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.201530 - 0.752119i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-1.60997 + 1.55177i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.201530 - 0.752119i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(-1.73909 + 1.40555i) q^{10} +(0.874161 + 1.51409i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-1.68990 + 3.62401i) q^{13} +(-0.135211 - 0.766821i) q^{14} +(0.803319 - 2.08679i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.323295 + 3.69528i) q^{17} +(0.707107 - 0.707107i) q^{18} +(0.822195 + 4.28065i) q^{19} +(-1.85497 + 1.24863i) q^{20} +(0.500507 + 0.596481i) q^{21} +(0.738873 + 1.58452i) q^{22} +(-6.35963 + 4.45306i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(0.183995 - 4.99661i) q^{25} +(-1.99932 + 3.46293i) q^{26} +(-0.258819 + 0.965926i) q^{27} +(-0.0678639 - 0.775688i) q^{28} +(-0.643029 - 0.539566i) q^{29} +(0.982137 - 2.00883i) q^{30} +(-3.62422 - 2.09244i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-1.43214 - 1.00280i) q^{33} +(-0.644129 + 3.65304i) q^{34} +(1.49157 + 0.898159i) q^{35} +(0.766044 - 0.642788i) q^{36} +(0.560810 + 0.560810i) q^{37} +(0.445983 + 4.33602i) q^{38} -3.99865i q^{39} +(-1.95674 + 1.08221i) q^{40} +(-1.42754 + 3.92212i) q^{41} +(0.446616 + 0.637833i) q^{42} +(6.64629 - 9.49188i) q^{43} +(0.597962 + 1.64289i) q^{44} +(0.153860 + 2.23077i) q^{45} +(-6.72354 + 3.88184i) q^{46} +(-4.38652 + 0.383770i) q^{47} +(-0.996195 + 0.0871557i) q^{48} +(5.53711 - 3.19685i) q^{49} +(0.618778 - 4.96156i) q^{50} +(-1.26869 - 3.48569i) q^{51} +(-2.29353 + 3.27550i) q^{52} +(8.05011 + 11.4968i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(-3.75690 - 1.08114i) q^{55} -0.778651i q^{56} +(-2.55424 - 3.53211i) q^{57} +(-0.593556 - 0.593556i) q^{58} +(9.02822 - 7.57557i) q^{59} +(1.15348 - 1.91559i) q^{60} +(-0.375507 + 2.12961i) q^{61} +(-3.42806 - 2.40035i) q^{62} +(-0.705697 - 0.329072i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-2.90295 - 8.45688i) q^{65} +(-1.33929 - 1.12380i) q^{66} +(-0.358004 - 4.09200i) q^{67} +(-0.960061 + 3.58300i) q^{68} +(3.88184 - 6.72354i) q^{69} +(1.40762 + 1.02474i) q^{70} +(13.6241 - 2.40229i) q^{71} +(0.819152 - 0.573576i) q^{72} +(0.562228 + 1.20570i) q^{73} +(0.509799 + 0.607554i) q^{74} +(1.94490 + 4.60623i) q^{75} +(0.0663765 + 4.35839i) q^{76} +(0.962608 - 0.962608i) q^{77} +(0.348505 - 3.98343i) q^{78} +(8.00565 + 2.91382i) q^{79} +(-2.04361 + 0.907549i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-1.76394 + 3.78278i) q^{82} +(9.12186 - 2.44420i) q^{83} +(0.389325 + 0.674331i) q^{84} +(-5.21374 - 6.45096i) q^{85} +(7.44827 - 8.87650i) q^{86} +(0.810813 + 0.217257i) q^{87} +(0.452499 + 1.68875i) q^{88} +(-6.59642 + 2.40090i) q^{89} +(-0.0411495 + 2.23569i) q^{90} +(3.06625 + 0.540662i) q^{91} +(-7.03628 + 3.28107i) q^{92} +(4.16896 + 0.364737i) q^{93} -4.40327 q^{94} +(-7.96631 - 5.61585i) q^{95} -1.00000 q^{96} +(-14.5292 - 1.27114i) q^{97} +(5.79466 - 2.70210i) q^{98} +(1.72176 + 0.303593i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^5 + 12 * q^7	$ 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$	−0.906308	+	0.422618i	−0.523257	+	0.243999i
$3$	−0.906308	+	0.422618i	−0.523257	+	0.243999i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−1.60997	+	1.55177i	−0.720000	+	0.693974i
$5$	−1.60997	+	1.55177i	−0.720000	+	0.693974i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	−0.201530	−	0.752119i	−0.0761710	−	0.284274i	0.917325	−	0.398139i	$-0.130344\pi$
$7$	−0.201530	−	0.752119i	−0.0761710	−	0.284274i	−0.993496	+	0.113864i	$0.963677\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	0.642788	−	0.766044i	0.214263	−	0.255348i
$10$	−1.73909	+	1.40555i	−0.549948	+	0.444474i
$11$	0.874161	+	1.51409i	0.263570	+	0.456516i	0.967188	−	0.254062i	$-0.0817668\pi$
$11$	0.874161	+	1.51409i	0.263570	+	0.456516i	−0.703618	+	0.710578i	$0.748433\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	−1.68990	+	3.62401i	−0.468695	+	1.00512i	0.519860	+	0.854252i	$0.325984\pi$
$13$	−1.68990	+	3.62401i	−0.468695	+	1.00512i	−0.988554	+	0.150867i	$0.951793\pi$
$14$	−0.135211	−	0.766821i	−0.0361367	−	0.204942i
$15$	0.803319	−	2.08679i	0.207416	−	0.538806i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−0.323295	+	3.69528i	−0.0784105	+	0.896236i	0.850510	+	0.525958i	$0.176293\pi$
$17$	−0.323295	+	3.69528i	−0.0784105	+	0.896236i	−0.928921	+	0.370278i	$0.879262\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	0.822195	+	4.28065i	0.188625	+	0.982049i
$19$	0.822195	+	4.28065i	0.188625	+	0.982049i
$20$	−1.85497	+	1.24863i	−0.414784	+	0.279202i
$21$	0.500507	+	0.596481i	0.109220	+	0.130163i
$22$	0.738873	+	1.58452i	0.157528	+	0.337821i
$23$	−6.35963	+	4.45306i	−1.32607	+	0.928527i	−0.999859	−	0.0167683i	$-0.994662\pi$
$23$	−6.35963	+	4.45306i	−1.32607	+	0.928527i	−0.326215	+	0.945296i	$0.605773\pi$
$24$	−0.984808	+	0.173648i	−0.201023	+	0.0354458i
$25$	0.183995	−	4.99661i	0.0367990	−	0.999323i
$26$	−1.99932	+	3.46293i	−0.392100	+	0.679137i
$27$	−0.258819	+	0.965926i	−0.0498097	+	0.185893i
$28$	−0.0678639	−	0.775688i	−0.0128251	−	0.146591i
$29$	−0.643029	−	0.539566i	−0.119408	−	0.100195i	0.581129	−	0.813812i	$-0.302611\pi$
$29$	−0.643029	−	0.539566i	−0.119408	−	0.100195i	−0.700536	+	0.713617i	$0.747056\pi$
$30$	0.982137	−	2.00883i	0.179313	−	0.366761i
$31$	−3.62422	−	2.09244i	−0.650929	−	0.375814i	0.137883	−	0.990449i	$-0.455970\pi$
$31$	−3.62422	−	2.09244i	−0.650929	−	0.375814i	−0.788812	+	0.614635i	$0.789304\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$	−1.43214	−	1.00280i	−0.249304	−	0.174565i
$34$	−0.644129	+	3.65304i	−0.110467	+	0.626491i
$35$	1.49157	+	0.898159i	0.252122	+	0.151817i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	0.560810	+	0.560810i	0.0921967	+	0.0921967i	0.751701	−	0.659504i	$-0.229234\pi$
$37$	0.560810	+	0.560810i	0.0921967	+	0.0921967i	−0.659504	+	0.751701i	$0.729234\pi$
$38$	0.445983	+	4.33602i	0.0723480	+	0.703396i
$39$		−	3.99865i		−	0.640296i
$40$	−1.95674	+	1.08221i	−0.309388	+	0.171112i
$41$	−1.42754	+	3.92212i	−0.222944	+	0.612532i	−0.999854	−	0.0170785i	$-0.994563\pi$
$41$	−1.42754	+	3.92212i	−0.222944	+	0.612532i	0.776911	+	0.629611i	$0.216786\pi$
$42$	0.446616	+	0.637833i	0.0689143	+	0.0984198i
$43$	6.64629	−	9.49188i	1.01355	−	1.44750i	0.123112	−	0.992393i	$-0.460713\pi$
$43$	6.64629	−	9.49188i	1.01355	−	1.44750i	0.890437	−	0.455106i	$-0.150398\pi$
$44$	0.597962	+	1.64289i	0.0901461	+	0.247674i
$45$	0.153860	+	2.23077i	0.0229361	+	0.332543i
$46$	−6.72354	+	3.88184i	−0.991332	+	0.572346i
$47$	−4.38652	+	0.383770i	−0.639839	+	0.0559787i	−0.402459	−	0.915438i	$-0.631844\pi$
$47$	−4.38652	+	0.383770i	−0.639839	+	0.0559787i	−0.237380	+	0.971417i	$0.576289\pi$
$48$	−0.996195	+	0.0871557i	−0.143788	+	0.0125798i
$49$	5.53711	−	3.19685i	0.791016	−	0.456693i
$50$	0.618778	−	4.96156i	0.0875085	−	0.701671i
$51$	−1.26869	−	3.48569i	−0.177652	−	0.488094i
$52$	−2.29353	+	3.27550i	−0.318056	+	0.454230i
$53$	8.05011	+	11.4968i	1.10577	+	1.57920i	0.770925	+	0.636926i	$0.219794\pi$
$53$	8.05011	+	11.4968i	1.10577	+	1.57920i	0.334843	+	0.942274i	$0.391317\pi$
$54$	−0.342020	+	0.939693i	−0.0465430	+	0.127876i
$55$	−3.75690	−	1.08114i	−0.506580	−	0.145781i
$56$		−	0.778651i		−	0.104052i
$57$	−2.55424	−	3.53211i	−0.338318	−	0.467840i
$58$	−0.593556	−	0.593556i	−0.0779378	−	0.0779378i
$59$	9.02822	−	7.57557i	1.17537	−	0.986255i	0.175375	−	0.984502i	$-0.443886\pi$
$59$	9.02822	−	7.57557i	1.17537	−	0.986255i	0.999998	−	0.00175378i	$-0.000558245\pi$
$60$	1.15348	−	1.91559i	0.148914	−	0.247301i
$61$	−0.375507	+	2.12961i	−0.0480787	+	0.272668i	−0.999365	−	0.0356421i	$-0.988652\pi$
$61$	−0.375507	+	2.12961i	−0.0480787	+	0.272668i	0.951286	+	0.308310i	$0.0997635\pi$
$62$	−3.42806	−	2.40035i	−0.435364	−	0.304845i
$63$	−0.705697	−	0.329072i	−0.0889095	−	0.0414592i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−2.90295	−	8.45688i	−0.360067	−	1.04895i
$66$	−1.33929	−	1.12380i	−0.164856	−	0.138330i
$67$	−0.358004	−	4.09200i	−0.0437371	−	0.499918i	−0.986194	−	0.165591i	$-0.947047\pi$
$67$	−0.358004	−	4.09200i	−0.0437371	−	0.499918i	0.942457	−	0.334327i	$-0.108509\pi$
$68$	−0.960061	+	3.58300i	−0.116425	+	0.434502i
$69$	3.88184	−	6.72354i	0.467318	−	0.809419i
$70$	1.40762	+	1.02474i	0.168243	+	0.122480i
$71$	13.6241	−	2.40229i	1.61688	−	0.285099i	0.709277	−	0.704930i	$-0.249022\pi$
$71$	13.6241	−	2.40229i	1.61688	−	0.285099i	0.907603	+	0.419830i	$0.137910\pi$
$72$	0.819152	−	0.573576i	0.0965380	−	0.0675966i
$73$	0.562228	+	1.20570i	0.0658038	+	0.141117i	0.936459	−	0.350777i	$-0.114083\pi$
$73$	0.562228	+	1.20570i	0.0658038	+	0.141117i	−0.870655	+	0.491894i	$0.836305\pi$
$74$	0.509799	+	0.607554i	0.0592629	+	0.0706267i
$75$	1.94490	+	4.60623i	0.224578	+	0.531882i
$76$	0.0663765	+	4.35839i	0.00761391	+	0.499942i
$77$	0.962608	−	0.962608i	0.109699	−	0.109699i
$78$	0.348505	−	3.98343i	0.0394604	−	0.451035i
$79$	8.00565	+	2.91382i	0.900706	+	0.327830i	0.750536	−	0.660830i	$-0.229796\pi$
$79$	8.00565	+	2.91382i	0.900706	+	0.327830i	0.150170	+	0.988660i	$0.452018\pi$
$80$	−2.04361	+	0.907549i	−0.228483	+	0.101467i
$81$	−0.173648	−	0.984808i	−0.0192942	−	0.109423i
$82$	−1.76394	+	3.78278i	−0.194794	+	0.417738i
$83$	9.12186	−	2.44420i	1.00125	−	0.268285i	0.279284	−	0.960209i	$-0.409903\pi$
$83$	9.12186	−	2.44420i	1.00125	−	0.268285i	0.721971	+	0.691923i	$0.243236\pi$
$84$	0.389325	+	0.674331i	0.0424789	+	0.0735756i
$85$	−5.21374	−	6.45096i	−0.565509	−	0.699705i
$86$	7.44827	−	8.87650i	0.803167	−	0.957178i
$87$	0.810813	+	0.217257i	0.0869283	+	0.0232924i
$88$	0.452499	+	1.68875i	0.0482366	+	0.180021i
$89$	−6.59642	+	2.40090i	−0.699219	+	0.254495i	−0.667078	−	0.744988i	$-0.732455\pi$
$89$	−6.59642	+	2.40090i	−0.699219	+	0.254495i	−0.0321418	+	0.999483i	$0.510233\pi$
$90$	−0.0411495	+	2.23569i	−0.00433754	+	0.235662i
$91$	3.06625	+	0.540662i	0.321430	+	0.0566768i
$92$	−7.03628	+	3.28107i	−0.733583	+	0.342075i
$93$	4.16896	+	0.364737i	0.432301	+	0.0378215i
$94$	−4.40327			−0.454163
$95$	−7.96631	−	5.61585i	−0.817327	−	0.576175i
$96$	−1.00000			−0.102062
$97$	−14.5292	−	1.27114i	−1.47522	−	0.129065i	−0.679029	−	0.734111i	$-0.737599\pi$
$97$	−14.5292	−	1.27114i	−1.47522	−	0.129065i	−0.796190	+	0.605046i	$0.793155\pi$
$98$	5.79466	−	2.70210i	0.585349	−	0.272953i
$99$	1.72176	+	0.303593i	0.173044	+	0.0305123i
$100$	1.04885	−	4.88875i	0.104885	−	0.488875i
$101$	−4.76557	+	1.73453i	−0.474192	+	0.172592i	−0.568050	−	0.822994i	$-0.692302\pi$
$101$	−4.76557	+	1.73453i	−0.474192	+	0.172592i	0.0938585	+	0.995586i	$0.470080\pi$
$102$	−0.960061	−	3.58300i	−0.0950602	−	0.354770i
$103$	9.01172	+	2.41468i	0.887951	+	0.237926i	0.673835	−	0.738882i	$-0.264646\pi$
$103$	9.01172	+	2.41468i	0.887951	+	0.237926i	0.214117	+	0.976808i	$0.431313\pi$
$104$	−2.57028	+	3.06314i	−0.252037	+	0.300366i
$105$	−1.73140	−	0.183642i	−0.168968	−	0.0179216i
$106$	7.01747	+	12.1546i	0.681597	+	1.18056i
$107$	−2.76933	+	0.742040i	−0.267721	+	0.0717357i	−0.390182	−	0.920738i	$-0.627588\pi$
$107$	−2.76933	+	0.742040i	−0.267721	+	0.0717357i	0.122461	+	0.992473i	$0.460921\pi$
$108$	−0.422618	+	0.906308i	−0.0406665	+	0.0872095i
$109$	−2.15828	−	12.2402i	−0.206726	−	1.17240i	−0.894701	−	0.446666i	$-0.852611\pi$
$109$	−2.15828	−	12.2402i	−0.206726	−	1.17240i	0.687975	−	0.725734i	$-0.258500\pi$
$110$	−3.64838	−	1.40446i	−0.347859	−	0.133910i
$111$	−0.745276	−	0.271258i	−0.0707384	−	0.0257467i
$112$	0.0678639	−	0.775688i	0.00641253	−	0.0732956i
$113$	−14.5206	+	14.5206i	−1.36598	+	1.36598i	−0.499900	+	0.866083i	$0.666630\pi$
$113$	−14.5206	+	14.5206i	−1.36598	+	1.36598i	−0.866083	+	0.499900i	$0.833370\pi$
$114$	−2.23668	−	3.74129i	−0.209484	−	0.350404i
$115$	3.32866	−	17.0380i	0.310399	−	1.58880i
$116$	−0.539566	−	0.643029i	−0.0500974	−	0.0597038i
$117$	1.68990	+	3.62401i	0.156232	+	0.335040i
$118$	9.65411	−	6.75988i	0.888733	−	0.622298i
$119$	2.84444	−	0.501552i	0.260749	−	0.0459772i
$120$	1.31605	−	1.80777i	0.120138	−	0.165026i
$121$	3.97168	−	6.87916i	0.361062	−	0.625378i
$122$	−0.559685	+	2.08877i	−0.0506715	+	0.189109i
$123$	−0.363774	−	4.15795i	−0.0328004	−	0.374910i
$124$	−3.20581	−	2.68999i	−0.287890	−	0.241569i
$125$	7.45739	+	8.32991i	0.667009	+	0.745050i
$126$	−0.674331	−	0.389325i	−0.0600742	−	0.0346839i
$127$	−13.4268	−	6.26103i	−1.19144	−	0.555577i	−0.277223	−	0.960806i	$-0.589414\pi$
$127$	−13.4268	−	6.26103i	−1.19144	−	0.555577i	−0.914215	+	0.405229i	$0.867192\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$	−2.01214	+	11.4114i	−0.177159	+	1.00472i
$130$	−2.15484	−	8.67771i	−0.188992	−	0.761086i
$131$	14.2664	−	11.9710i	1.24646	−	1.04591i	0.249474	−	0.968381i	$-0.419742\pi$
$131$	14.2664	−	11.9710i	1.24646	−	1.04591i	0.996990	−	0.0775266i	$-0.0247023\pi$
$132$	−1.23625	−	1.23625i	−0.107602	−	0.107602i
$133$	3.05386	−	1.48107i	0.264804	−	0.128425i
$134$		−	4.10764i		−	0.354846i
$135$	−1.08221	−	1.95674i	−0.0931416	−	0.168409i
$136$	−1.26869	+	3.48569i	−0.108789	+	0.298895i
$137$	−0.828443	−	1.18314i	−0.0707787	−	0.101082i	0.782202	−	0.623025i	$-0.214096\pi$
$137$	−0.828443	−	1.18314i	−0.0707787	−	0.101082i	−0.852981	+	0.521942i	$0.825208\pi$
$138$	4.45306	−	6.35963i	0.379070	−	0.541368i
$139$	3.35909	+	9.22903i	0.284915	+	0.782796i	0.996758	+	0.0804582i	$0.0256383\pi$
$139$	3.35909	+	9.22903i	0.284915	+	0.782796i	−0.711843	+	0.702338i	$0.752139\pi$
$140$	1.31295	+	1.14352i	0.110965	+	0.0966453i
$141$	3.81335	−	2.20164i	0.321142	−	0.185411i
$142$	13.7816	−	1.20573i	1.15653	−	0.101183i
$143$	−6.96433	+	0.609300i	−0.582386	+	0.0509522i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	1.87254	−	0.129153i	0.155506	−	0.0107255i
$146$	0.455004	+	1.25011i	0.0376564	+	0.103460i
$147$	−3.66728	+	5.23741i	−0.302472	+	0.431975i
$148$	0.454907	+	0.649674i	0.0373931	+	0.0534029i
$149$	−0.489035	+	1.34361i	−0.0400633	+	0.110073i	−0.958111	−	0.286396i	$-0.907543\pi$
$149$	−0.489035	+	1.34361i	−0.0400633	+	0.110073i	0.918048	+	0.396470i	$0.129765\pi$
$150$	1.53604	+	4.75821i	0.125417	+	0.388506i
$151$			0.249524i			0.0203059i	0.999948	+	0.0101530i	$0.00323185\pi$
$151$			0.249524i			0.0203059i	−0.999948	+	0.0101530i	$0.996768\pi$
$152$	−0.313735	+	4.34759i	−0.0254473	+	0.352636i
$153$	2.62294	+	2.62294i	0.212052	+	0.212052i
$154$	1.04284	−	0.875048i	0.0840346	−	0.0705134i
$155$	9.08188	−	2.25520i	0.729474	−	0.181142i
$156$	0.694358	−	3.93790i	0.0555931	−	0.315284i
$157$	−6.35467	−	4.44959i	−0.507158	−	0.355116i	0.291823	−	0.956472i	$-0.405738\pi$
$157$	−6.35467	−	4.44959i	−0.507158	−	0.355116i	−0.798981	+	0.601357i	$0.794627\pi$
$158$	7.72123	+	3.60047i	0.614268	+	0.286438i
$159$	−12.1546	−	7.01747i	−0.963924	−	0.556522i
$160$	−2.11493	+	0.725983i	−0.167200	+	0.0573940i
$161$	4.63088	+	3.88577i	0.364965	+	0.306242i
$162$	−0.0871557	−	0.996195i	−0.00684760	−	0.0782684i
$163$	0.561335	−	2.09493i	0.0439672	−	0.164088i	−0.940452	−	0.339928i	$-0.889597\pi$
$163$	0.561335	−	2.09493i	0.0439672	−	0.164088i	0.984419	+	0.175840i	$0.0562641\pi$
$164$	−2.08692	+	3.61465i	−0.162961	+	0.282256i
$165$	3.86182	−	0.607890i	0.300642	−	0.0473242i
$166$	9.30018	−	1.63987i	0.721834	−	0.127279i
$167$	1.44961	−	1.01503i	0.112174	−	0.0785451i	−0.516143	−	0.856502i	$-0.672633\pi$
$167$	1.44961	−	1.01503i	0.112174	−	0.0785451i	0.628317	+	0.777957i	$0.283744\pi$
$168$	0.329072	+	0.705697i	0.0253885	+	0.0544457i
$169$	−1.92142	−	2.28986i	−0.147801	−	0.176143i
$170$	−4.63166	−	6.88082i	−0.355232	−	0.527735i
$171$	3.80767	+	2.12171i	0.291180	+	0.162251i
$172$	8.19356	−	8.19356i	0.624753	−	0.624753i
$173$	−0.755115	+	8.63101i	−0.0574103	+	0.656203i	0.911908	+	0.410395i	$0.134609\pi$
$173$	−0.755115	+	8.63101i	−0.0574103	+	0.656203i	−0.969318	+	0.245809i	$0.920947\pi$
$174$	0.788792	+	0.287097i	0.0597982	+	0.0217648i
$175$	−3.79513	+	0.868580i	−0.286885	+	0.0656584i
$176$	0.303593	+	1.72176i	0.0228842	+	0.129783i
$177$	−4.98077	+	10.6813i	−0.374377	+	0.802855i
$178$	−6.78057	+	1.81685i	−0.508225	+	0.136179i
$179$	1.89496	+	3.28217i	0.141636	+	0.245321i	0.928113	−	0.372299i	$-0.121430\pi$
$179$	1.89496	+	3.28217i	0.141636	+	0.245321i	−0.786477	+	0.617620i	$0.788097\pi$
$180$	−0.235846	+	2.22360i	−0.0175789	+	0.165737i
$181$	−1.71959	+	2.04933i	−0.127816	+	0.152325i	−0.826157	−	0.563440i	$-0.809478\pi$
$181$	−1.71959	+	2.04933i	−0.127816	+	0.152325i	0.698341	+	0.715765i	$0.253922\pi$
$182$	3.00746	+	0.805846i	0.222928	+	0.0597333i
$183$	−0.559685	−	2.08877i	−0.0413731	−	0.154407i
$184$	−7.29547	+	2.65533i	−0.537829	+	0.195754i
$185$	−1.77314	−	0.0326359i	−0.130364	−	0.00239944i
$186$	4.12131	+	0.726698i	0.302189	+	0.0532841i
$187$	−5.87760	+	2.74077i	−0.429813	+	0.200425i
$188$	−4.38652	−	0.383770i	−0.319920	−	0.0279893i
$189$	0.778651			0.0566385
$190$	−7.44655	−	6.28879i	−0.540229	−	0.456237i
$191$	−23.5853			−1.70657			−0.853287	−	0.521441i	$-0.825395\pi$
$191$	−23.5853			−1.70657			−0.853287	+	0.521441i	$0.825395\pi$
$192$	−0.996195	−	0.0871557i	−0.0718942	−	0.00628992i
$193$	16.9414	−	7.89990i	1.21947	−	0.568647i	0.297058	−	0.954860i	$-0.403995\pi$
$193$	16.9414	−	7.89990i	1.21947	−	0.568647i	0.922410	+	0.386213i	$0.126217\pi$
$194$	−14.3632	−	2.53261i	−1.03121	−	0.181831i
$195$	6.20500	+	6.43770i	0.444349	+	0.461013i
$196$	6.00812	−	2.18678i	0.429151	−	0.156198i
$197$	3.09406	+	11.5472i	0.220442	+	0.822702i	0.984179	+	0.177175i	$0.0566958\pi$
$197$	3.09406	+	11.5472i	0.220442	+	0.822702i	−0.763737	+	0.645527i	$0.776638\pi$
$198$	1.68875	+	0.452499i	0.120014	+	0.0321577i
$199$	5.15642	−	6.14518i	0.365529	−	0.435620i	−0.551662	−	0.834067i	$-0.686006\pi$
$199$	5.15642	−	6.14518i	0.365529	−	0.435620i	0.917191	+	0.398447i	$0.130451\pi$
$200$	1.47094	−	4.77874i	0.104011	−	0.337908i
$201$	2.05382	+	3.55732i	0.144865	+	0.250914i
$202$	−4.89861	+	1.31258i	−0.344665	+	0.0923527i
$203$	−0.276228	+	0.592373i	−0.0193874	+	0.0415764i
$204$	−0.644129	−	3.65304i	−0.0450981	−	0.255764i
$205$	−3.78796	−	8.52970i	−0.264563	−	0.595740i
$206$	8.76698	+	3.19092i	0.610824	+	0.222322i
$207$	−0.676649	+	7.73413i	−0.0470303	+	0.537559i
$208$	−2.82747	+	2.82747i	−0.196050	+	0.196050i
$209$	−5.76257	+	4.98686i	−0.398605	+	0.344948i
$210$	−1.70881	−	0.333845i	−0.117919	−	0.0230375i
$211$	−3.01670	−	3.59516i	−0.207678	−	0.247501i	0.652144	−	0.758095i	$-0.273870\pi$
$211$	−3.01670	−	3.59516i	−0.207678	−	0.247501i	−0.859822	+	0.510594i	$0.829425\pi$
$212$	5.93142	+	12.7200i	0.407372	+	0.873612i
$213$	−11.3323	+	7.93500i	−0.776480	+	0.543697i
$214$	−2.82346	+	0.497853i	−0.193008	+	0.0340325i
$215$	4.02894	+	25.5952i	0.274772	+	1.74558i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−0.843379	+	3.14753i	−0.0572523	+	0.213668i
$218$	−1.08326	−	12.3817i	−0.0733678	−	0.838597i
$219$	−1.01910	−	0.855128i	−0.0688646	−	0.0577842i
$220$	−3.51209	−	1.71709i	−0.236785	−	0.115766i
$221$	−12.8454	−	7.41628i	−0.864073	−	0.498873i
$222$	−0.718798	−	0.335181i	−0.0482426	−	0.0224959i
$223$	14.1240	+	9.88975i	0.945815	+	0.662267i	0.941246	−	0.337723i	$-0.109657\pi$
$223$	14.1240	+	9.88975i	0.945815	+	0.662267i	0.00456956	+	0.999990i	$0.498545\pi$
$224$	0.135211	−	0.766821i	0.00903418	−	0.0512354i
$225$	−3.70936	−	3.35271i	−0.247291	−	0.223514i
$226$	−15.7309	+	13.1998i	−1.04640	+	0.878037i
$227$	8.39623	+	8.39623i	0.557277	+	0.557277i	0.928531	−	0.371254i	$-0.121072\pi$
$227$	8.39623	+	8.39623i	0.557277	+	0.557277i	−0.371254	+	0.928531i	$0.621072\pi$
$228$	−1.90209	−	3.92199i	−0.125969	−	0.259740i
$229$		−	2.44070i		−	0.161286i	−0.996743	−	0.0806429i	$-0.974303\pi$
$229$		−	2.44070i		−	0.161286i	0.996743	−	0.0806429i	$-0.0256973\pi$
$230$	4.80095	−	16.6830i	0.316565	−	1.10005i
$231$	−0.465603	+	1.27923i	−0.0306344	+	0.0841674i
$232$	−0.481469	−	0.687609i	−0.0316100	−	0.0451437i
$233$	−3.62720	+	5.18018i	−0.237626	+	0.339365i	−0.920198	−	0.391453i	$-0.871972\pi$
$233$	−3.62720	+	5.18018i	−0.237626	+	0.339365i	0.682572	+	0.730818i	$0.260861\pi$
$234$	1.36762	+	3.75750i	0.0894040	+	0.245636i
$235$	6.46663	−	7.42474i	0.421836	−	0.484337i
$236$	10.2065	−	5.89275i	0.664389	−	0.383585i
$237$	−8.48702	+	0.742518i	−0.551291	+	0.0482317i
$238$	2.87733	−	0.251734i	0.186510	−	0.0163175i
$239$	18.6589	−	10.7727i	1.20695	−	0.696831i	0.244855	−	0.969560i	$-0.421260\pi$
$239$	18.6589	−	10.7727i	1.20695	−	0.696831i	0.962091	+	0.272729i	$0.0879262\pi$
$240$	1.46860	−	1.68619i	0.0947974	−	0.108843i
$241$	9.89419	+	27.1841i	0.637341	+	1.75108i	0.659922	+	0.751334i	$0.270589\pi$
$241$	9.89419	+	27.1841i	0.637341	+	1.75108i	−0.0225809	+	0.999745i	$0.507188\pi$
$242$	4.55613	−	6.50683i	0.292879	−	0.418275i
$243$	0.573576	+	0.819152i	0.0367949	+	0.0525486i
$244$	−0.739604	+	2.03205i	−0.0473483	+	0.130088i
$245$	−3.95378	+	13.7392i	−0.252598	+	0.877763i
$246$		−	4.17383i		−	0.266114i
$247$	−16.9025	−	4.25424i	−1.07548	−	0.270691i
$248$	−2.95916	−	2.95916i	−0.187907	−	0.187907i
$249$	−7.23425	+	6.07026i	−0.458452	+	0.384687i
$250$	6.70301	+	8.94816i	0.423936	+	0.565932i
$251$	0.280693	−	1.59189i	0.0177172	−	0.100479i	−0.974667	−	0.223662i	$-0.928199\pi$
$251$	0.280693	−	1.59189i	0.0177172	−	0.100479i	0.992384	+	0.123182i	$0.0393100\pi$
$252$	−0.637833	−	0.446616i	−0.0401797	−	0.0281341i
$253$	−12.3017	−	5.73637i	−0.773400	−	0.360643i
$254$	−12.8300	−	7.40743i	−0.805029	−	0.464783i
$255$	7.45155	+	3.64313i	0.466634	+	0.228142i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.258533	+	2.95505i	0.0161269	+	0.184331i	0.999986	+	0.00538352i	$0.00171364\pi$
$257$	0.258533	+	2.95505i	0.0161269	+	0.184331i	−0.983859	+	0.178947i	$0.942731\pi$
$258$	−2.99905	+	11.1926i	−0.186713	+	0.696822i
$259$	0.308776	−	0.534816i	0.0191864	−	0.0332319i
$260$	−1.39033	−	8.83250i	−0.0862244	−	0.547768i
$261$	−0.826663	+	0.145763i	−0.0511691	+	0.00902250i
$262$	15.2555	−	10.6820i	0.942487	−	0.659937i
$263$	−6.32981	−	13.5743i	−0.390313	−	0.837029i	−0.999047	−	0.0436542i	$-0.986100\pi$
$263$	−6.32981	−	13.5743i	−0.390313	−	0.837029i	0.608734	−	0.793375i	$-0.291678\pi$
$264$	−1.12380	−	1.33929i	−0.0691651	−	0.0824278i
$265$	−30.8008	−	6.01745i	−1.89208	−	0.369649i
$266$	3.17133	−	1.20927i	0.194446	−	0.0741451i
$267$	4.96372	−	4.96372i	0.303775	−	0.303775i
$268$	0.358004	−	4.09200i	0.0218686	−	0.249959i
$269$	5.62105	+	2.04589i	0.342721	+	0.124740i	0.507646	−	0.861566i	$-0.330516\pi$
$269$	5.62105	+	2.04589i	0.342721	+	0.124740i	−0.164925	+	0.986306i	$0.552738\pi$
$270$	−0.907549	−	2.04361i	−0.0552317	−	0.124370i
$271$	1.45518	+	8.25276i	0.0883961	+	0.501319i	0.996572	+	0.0827305i	$0.0263641\pi$
$271$	1.45518	+	8.25276i	0.0883961	+	0.501319i	−0.908176	+	0.418589i	$0.862525\pi$
$272$	−1.56766	+	3.36185i	−0.0950531	+	0.203842i
$273$	−3.00746	+	0.805846i	−0.182020	+	0.0487720i
$274$	−0.722173	−	1.25084i	−0.0436281	−	0.0755661i
$275$	7.72617	−	4.08926i	0.465906	−	0.246592i
$276$	4.99039	−	5.94732i	0.300386	−	0.357987i
$277$	9.89385	+	2.65105i	0.594464	+	0.159286i	0.543493	−	0.839414i	$-0.317102\pi$
$277$	9.89385	+	2.65105i	0.594464	+	0.159286i	0.0509714	+	0.998700i	$0.483768\pi$
$278$	2.54195	+	9.48668i	0.152456	+	0.568973i
$279$	−3.93251	+	1.43132i	−0.235433	+	0.0856906i
$280$	1.20829	+	1.25360i	0.0722091	+	0.0749171i
$281$	−9.54563	−	1.68315i	−0.569445	−	0.100408i	−0.118490	−	0.992955i	$-0.537805\pi$
$281$	−9.54563	−	1.68315i	−0.569445	−	0.100408i	−0.450955	+	0.892547i	$0.648916\pi$
$282$	3.99072	−	1.86090i	0.237644	−	0.110815i
$283$	−7.98751	−	0.698816i	−0.474808	−	0.0415403i	−0.152759	−	0.988263i	$-0.548816\pi$
$283$	−7.98751	−	0.698816i	−0.474808	−	0.0415403i	−0.322049	+	0.946723i	$0.604371\pi$
$284$	13.8342			0.820911
$285$	9.59330	+	1.72298i	0.568258	+	0.102061i
$286$	−6.99093			−0.413382
$287$	3.23759	+	0.283253i	0.191109	+	0.0167199i
$288$	0.906308	−	0.422618i	0.0534047	−	0.0249030i
$289$	3.19118	+	0.562692i	0.187717	+	0.0330995i
$290$	1.87667	+	0.0345415i	0.110202	+	0.00202835i
$291$	13.7052	−	4.98827i	0.803411	−	0.292418i
$292$	0.344318	+	1.28501i	0.0201497	+	0.0751997i
$293$	−7.09078	−	1.89997i	−0.414248	−	0.110997i	0.0456749	−	0.998956i	$-0.485456\pi$
$293$	−7.09078	−	1.89997i	−0.414248	−	0.110997i	−0.459923	+	0.887959i	$0.652123\pi$
$294$	−4.10979	+	4.89786i	−0.239688	+	0.285649i
$295$	−2.77956	+	26.2062i	−0.161832	+	1.52578i
$296$	0.396553	+	0.686850i	0.0230492	+	0.0399223i
$297$	−1.68875	+	0.452499i	−0.0979912	+	0.0262567i
$298$	−0.604278	+	1.29588i	−0.0350049	+	0.0750682i
$299$	−5.39077	−	30.5726i	−0.311756	−	1.76806i
$300$	1.11549	+	4.87398i	0.0644030	+	0.281399i
$301$	−8.47845	−	3.08590i	−0.488690	−	0.177868i
$302$	−0.0217474	+	0.248574i	−0.00125142	+	0.0143038i
$303$	3.58603	−	3.58603i	0.206012	−	0.206012i
$304$	−0.691459	+	4.30371i	−0.0396579	+	0.246834i
$305$	−2.70011	−	4.01130i	−0.154608	−	0.229686i
$306$	2.38435	+	2.84156i	0.136304	+	0.162441i
$307$	10.3901	+	22.2816i	0.592992	+	1.27168i	0.942332	+	0.334680i	$0.108628\pi$
$307$	10.3901	+	22.2816i	0.592992	+	1.27168i	−0.349340	+	0.936996i	$0.613594\pi$
$308$	1.11514	−	0.780828i	0.0635409	−	0.0444918i
$309$	−9.18788	+	1.62007i	−0.522680	+	0.0921627i
$310$	9.24387	−	1.45508i	0.525017	−	0.0826431i
$311$	3.39582	−	5.88173i	0.192559	−	0.333523i	−0.753538	−	0.657404i	$-0.771655\pi$
$311$	3.39582	−	5.88173i	0.192559	−	0.333523i	0.946098	+	0.323881i	$0.104988\pi$
$312$	1.03493	−	3.86240i	0.0585912	−	0.218665i
$313$	−0.752776	−	8.60427i	−0.0425494	−	0.486342i	−0.987335	−	0.158652i	$-0.949285\pi$
$313$	−0.752776	−	8.60427i	−0.0425494	−	0.486342i	0.944785	−	0.327690i	$-0.106270\pi$
$314$	−5.94268	−	4.98650i	−0.335365	−	0.281405i
$315$	1.64680	−	0.565287i	0.0927864	−	0.0318503i
$316$	7.37805	+	4.25972i	0.415048	+	0.239628i
$317$	−15.8306	−	7.38194i	−0.889136	−	0.414611i	−0.0762875	−	0.997086i	$-0.524307\pi$
$317$	−15.8306	−	7.38194i	−0.889136	−	0.414611i	−0.812849	+	0.582475i	$0.802084\pi$
$318$	−11.4968	−	8.05011i	−0.644706	−	0.451428i
$319$	0.254841	−	1.44527i	0.0142683	−	0.0809198i
$320$	−2.17016	+	0.538892i	−0.121316	+	0.0301250i
$321$	2.19627	−	1.84289i	0.122584	−	0.102860i
$322$	4.27460	+	4.27460i	0.238214	+	0.238214i
$323$	−16.0840	+	1.65433i	−0.894938	+	0.0920491i
$324$		−	1.00000i		−	0.0555556i
$325$	17.7968	+	9.11059i	0.987190	+	0.505364i
$326$	0.741784	−	2.03804i	0.0410836	−	0.112876i
$327$	7.12900	+	10.1813i	0.394235	+	0.563026i
$328$	−2.39401	+	3.41900i	−0.132187	+	0.188783i
$329$	1.17265	+	3.22184i	0.0646505	+	0.177626i
$330$	3.90010	−	0.268997i	0.214694	−	0.0148078i
$331$	4.74623	−	2.74024i	0.260876	−	0.150617i	−0.363858	−	0.931454i	$-0.618541\pi$
$331$	4.74623	−	2.74024i	0.260876	−	0.150617i	0.624734	+	0.780837i	$0.285207\pi$
$332$	9.40771	−	0.823068i	0.516315	−	0.0451717i
$333$	0.790088	−	0.0691237i	0.0432965	−	0.00378796i
$334$	1.53256	−	0.884823i	0.0838578	−	0.0484153i
$335$	6.92624	+	6.03246i	0.378421	+	0.329588i
$336$	0.266314	+	0.731692i	0.0145286	+	0.0399171i
$337$	7.88765	−	11.2647i	0.429668	−	0.613629i	−0.544689	−	0.838638i	$-0.683352\pi$
$337$	7.88765	−	11.2647i	0.429668	−	0.613629i	0.974357	+	0.225009i	$0.0722411\pi$
$338$	−1.71453	−	2.44861i	−0.0932583	−	0.133187i
$339$	7.02346	−	19.2968i	0.381462	−	1.04806i
$340$	−4.01433	−	7.25831i	−0.217708	−	0.393637i
$341$		−	7.31653i		−	0.396213i
$342$	3.60826	+	2.44550i	0.195112	+	0.132237i
$343$	−7.37443	−	7.37443i	−0.398182	−	0.398182i
$344$	8.87650	−	7.44827i	0.478589	−	0.401584i
$345$	4.18378	+	16.8484i	0.225247	+	0.907088i
$346$	−1.50448	+	8.53235i	−0.0808815	+	0.458702i
$347$	1.37062	+	0.959715i	0.0735785	+	0.0515202i	0.609787	−	0.792565i	$-0.291255\pi$
$347$	1.37062	+	0.959715i	0.0735785	+	0.0515202i	−0.536208	+	0.844086i	$0.680144\pi$
$348$	0.760769	+	0.354752i	0.0407815	+	0.0190167i
$349$	25.5479	+	14.7501i	1.36755	+	0.789554i	0.990614	−	0.136687i	$-0.0436455\pi$
$349$	25.5479	+	14.7501i	1.36755	+	0.789554i	0.376933	+	0.926241i	$0.376979\pi$
$350$	−3.85639	+	0.534507i	−0.206133	+	0.0285706i
$351$	−3.06314	−	2.57028i	−0.163498	−	0.137192i
$352$	0.152376	+	1.74167i	0.00812169	+	0.0928313i
$353$	2.38595	−	8.90451i	0.126992	−	0.473939i	−0.872911	−	0.487879i	$-0.837771\pi$
$353$	2.38595	−	8.90451i	0.126992	−	0.473939i	0.999903	+	0.0139400i	$0.00443739\pi$
$354$	−5.89275	+	10.2065i	−0.313196	+	0.542472i
$355$	−18.2065	+	25.0091i	−0.966301	+	1.32734i
$356$	−6.91312	+	1.21897i	−0.366395	+	0.0646053i
$357$	−2.36597	+	1.65667i	−0.125221	+	0.0876804i
$358$	1.60169	+	3.43484i	0.0846520	+	0.181537i
$359$	14.0530	+	16.7477i	0.741688	+	0.883909i	0.996544	−	0.0830701i	$-0.0264725\pi$
$359$	14.0530	+	16.7477i	0.741688	+	0.883909i	−0.254856	+	0.966979i	$0.582028\pi$
$360$	−0.428748	+	2.19458i	−0.0225970	+	0.115664i
$361$	−17.6480	+	7.03907i	−0.928842	+	0.370477i
$362$	−1.89166	+	1.89166i	−0.0994234	+	0.0994234i
$363$	−0.692310	+	7.91314i	−0.0363369	+	0.415332i
$364$	2.92578	+	1.06490i	0.153353	+	0.0558158i
$365$	−2.77614	−	1.06869i	−0.145310	−	0.0559378i
$366$	−0.375507	−	2.12961i	−0.0196281	−	0.111316i
$367$	−10.6088	+	22.7507i	−0.553776	+	1.18758i	0.407809	+	0.913067i	$0.366293\pi$
$367$	−10.6088	+	22.7507i	−0.553776	+	1.18758i	−0.961585	+	0.274509i	$0.911485\pi$
$368$	−7.49913	+	2.00939i	−0.390919	+	0.104747i
$369$	2.08692	+	3.61465i	0.108641	+	0.188171i
$370$	−1.76355	−	0.187051i	−0.0916824	−	0.00972431i
$371$	7.02459	−	8.37158i	0.364698	−	0.434631i
$372$	4.04229	+	1.08313i	0.209583	+	0.0561576i
$373$	8.26482	+	30.8447i	0.427936	+	1.59708i	0.757427	+	0.652920i	$0.226456\pi$
$373$	8.26482	+	30.8447i	0.427936	+	1.59708i	−0.329491	+	0.944159i	$0.606877\pi$
$374$	−6.09411	+	2.21807i	−0.315119	+	0.114694i
$375$	−10.2791	−	4.39783i	−0.530808	−	0.227103i
$376$	−4.33638	−	0.764620i	−0.223632	−	0.0394323i
$377$	3.04205	−	1.41853i	0.156673	−	0.0730580i
$378$	0.775688	+	0.0678639i	0.0398971	+	0.00349054i
$379$	−15.0342			−0.772254			−0.386127	−	0.922446i	$-0.626187\pi$
$379$	−15.0342			−0.772254			−0.386127	+	0.922446i	$0.626187\pi$
$380$	−6.87011	−	6.91387i	−0.352429	−	0.354674i
$381$	14.8149			0.758988
$382$	−23.4956	−	2.05560i	−1.20214	−	0.105174i
$383$	−20.3167	+	9.47386i	−1.03814	+	0.484091i	−0.865508	−	0.500895i	$-0.833004\pi$
$383$	−20.3167	+	9.47386i	−1.03814	+	0.484091i	−0.172630	+	0.984987i	$0.555226\pi$
$384$	−0.984808	−	0.173648i	−0.0502558	−	0.00886145i
$385$	−0.0560182	+	3.04352i	−0.00285495	+	0.155112i
$386$	17.5654	−	6.39330i	0.894057	−	0.325410i
$387$	−2.99905	−	11.1926i	−0.152450	−	0.568953i
$388$	−14.0878	−	3.77480i	−0.715198	−	0.191637i
$389$	9.18723	−	10.9489i	0.465811	−	0.555132i	−0.481084	−	0.876675i	$-0.659757\pi$
$389$	9.18723	−	10.9489i	0.465811	−	0.555132i	0.946895	+	0.321542i	$0.104201\pi$
$390$	5.62031	+	6.95400i	0.284595	+	0.352130i
$391$	−14.3993	−	24.9402i	−0.728202	−	1.26128i
$392$	6.17584	−	1.65481i	0.311927	−	0.0835806i
$393$	−7.87064	+	16.8786i	−0.397021	+	0.851415i
$394$	2.07588	+	11.7729i	0.104581	+	0.593110i
$395$	−17.4104	+	7.73181i	−0.876014	+	0.389029i
$396$	1.64289	+	0.597962i	0.0825581	+	0.0300487i
$397$	1.13909	−	13.0199i	0.0571695	−	0.653450i	−0.912507	−	0.409060i	$-0.865857\pi$
$397$	1.13909	−	13.0199i	0.0571695	−	0.653450i	0.969677	−	0.244390i	$-0.0785878\pi$
$398$	5.67238	−	5.67238i	0.284331	−	0.284331i
$399$	−2.14181	+	2.63292i	−0.107225	+	0.131811i
$400$	1.88184	−	4.63235i	0.0940921	−	0.231618i
$401$	7.53482	+	8.97965i	0.376271	+	0.448422i	0.920634	−	0.390428i	$-0.127673\pi$
$401$	7.53482	+	8.97965i	0.376271	+	0.448422i	−0.544363	+	0.838850i	$0.683228\pi$
$402$	1.73596	+	3.72278i	0.0865819	+	0.185675i
$403$	13.7076	−	9.59817i	0.682825	−	0.478119i
$404$	−4.99437	+	0.880641i	−0.248479	+	0.0438135i
$405$	1.80777	+	1.31605i	0.0898287	+	0.0653949i
$406$	−0.326806	+	0.566044i	−0.0162191	+	0.0280923i
$407$	−0.358880	+	1.33936i	−0.0177890	+	0.0663895i
$408$	−0.323295	−	3.69528i	−0.0160055	−	0.182943i
$409$	−0.539122	−	0.452377i	−0.0266579	−	0.0223686i	0.629361	−	0.777113i	$-0.283317\pi$
$409$	−0.539122	−	0.452377i	−0.0266579	−	0.0223686i	−0.656019	+	0.754744i	$0.727761\pi$
$410$	−3.03013	−	8.82739i	−0.149648	−	0.435954i
$411$	1.25084	+	0.722173i	0.0616994	+	0.0356222i
$412$	8.45551	+	3.94287i	0.416573	+	0.194251i
$413$	−7.51718	−	5.26359i	−0.369896	−	0.259004i
$414$	−1.34815	+	7.64573i	−0.0662579	+	0.375767i
$415$	−10.8931	+	18.0901i	−0.534720	+	0.888010i
$416$	−3.06314	+	2.57028i	−0.150183	+	0.126018i
$417$	−6.94473	−	6.94473i	−0.340085	−	0.340085i
$418$	−6.17528	+	4.46564i	−0.302043	+	0.218422i
$419$		−	14.2025i		−	0.693838i	−0.937895	−	0.346919i	$-0.887228\pi$
$419$		−	14.2025i		−	0.693838i	0.937895	−	0.346919i	$-0.112772\pi$
$420$	−1.67321	−	0.481507i	−0.0816443	−	0.0234951i
$421$	−8.98253	+	24.6793i	−0.437782	+	1.20280i	0.503150	+	0.864199i	$0.332174\pi$
$421$	−8.98253	+	24.6793i	−0.437782	+	1.20280i	−0.940932	+	0.338596i	$0.890048\pi$
$422$	−2.69188	−	3.84440i	−0.131039	−	0.187142i
$423$	−2.52561	+	3.60695i	−0.122800	+	0.175376i
$424$	4.80023	+	13.1885i	0.233120	+	0.640492i
$425$	18.4044	+	2.29529i	0.892744	+	0.111338i
$426$	−11.9808	+	6.91712i	−0.580472	+	0.335136i
$427$	1.67739	−	0.146753i	0.0811747	−	0.00710187i
$428$	−2.85611	+	0.249877i	−0.138055	+	0.0120783i
$429$	6.05432	−	3.49547i	0.292305	−	0.168763i
$430$	1.78285	+	25.8489i	0.0859765	+	1.24655i
$431$	−8.45980	−	23.2431i	−0.407494	−	1.11958i	−0.958503	−	0.285082i	$-0.907979\pi$
$431$	−8.45980	−	23.2431i	−0.407494	−	1.11958i	0.551009	−	0.834499i	$-0.314243\pi$
$432$	−0.573576	+	0.819152i	−0.0275962	+	0.0394115i
$433$	20.8277	+	29.7450i	1.00091	+	1.42945i	0.900677	+	0.434489i	$0.143071\pi$
$433$	20.8277	+	29.7450i	1.00091	+	1.42945i	0.100236	+	0.994964i	$0.468040\pi$
$434$	−1.11450	+	3.06205i	−0.0534975	+	0.146983i
$435$	−1.64252	+	0.908422i	−0.0787526	+	0.0435555i
$436$		−	12.4290i		−	0.595243i
$437$	−24.2909	−	23.5621i	−1.16199	−	1.12713i
$438$	−0.940695	−	0.940695i	−0.0449481	−	0.0449481i
$439$	−3.22260	+	2.70408i	−0.153806	+	0.129059i	−0.716443	−	0.697645i	$-0.754231\pi$
$439$	−3.22260	+	2.70408i	−0.153806	+	0.129059i	0.562637	+	0.826704i	$0.309787\pi$
$440$	−3.34907	−	2.01666i	−0.159661	−	0.0961404i
$441$	1.11025	−	6.29657i	0.0528693	−	0.299837i
$442$	−12.1501	−	8.50761i	−0.577922	−	0.404666i
$443$	−7.07017	−	3.29688i	−0.335914	−	0.156639i	0.247341	−	0.968929i	$-0.420443\pi$
$443$	−7.07017	−	3.29688i	−0.335914	−	0.156639i	−0.583255	+	0.812289i	$0.698221\pi$
$444$	−0.686850	−	0.396553i	−0.0325964	−	0.0188196i
$445$	6.89437	−	14.1015i	0.326825	−	0.668477i
$446$	13.2083	+	11.0831i	0.625433	+	0.524801i
$447$	−0.124619	−	1.42440i	−0.00589428	−	0.0673719i
$448$	0.201530	−	0.752119i	0.00952138	−	0.0355343i
$449$	5.83935	−	10.1141i	0.275576	−	0.477312i	−0.694704	−	0.719296i	$-0.744465\pi$
$449$	5.83935	−	10.1141i	0.275576	−	0.477312i	0.970280	+	0.241984i	$0.0777981\pi$
$450$	−3.40304	−	3.66324i	−0.160421	−	0.172687i
$451$	−7.18635	+	1.26715i	−0.338392	+	0.0596676i
$452$	−16.8215	+	11.7785i	−0.791216	+	0.554015i
$453$	−0.105453	−	0.226145i	−0.00495462	−	0.0106252i
$454$	7.63250	+	9.09606i	0.358211	+	0.426899i
$455$	−5.77555	+	3.88768i	−0.270762	+	0.182257i
$456$	−1.55303	−	4.07285i	−0.0727274	−	0.190729i
$457$	10.1301	−	10.1301i	0.473868	−	0.473868i	−0.429296	−	0.903164i	$-0.641238\pi$
$457$	10.1301	−	10.1301i	0.473868	−	0.473868i	0.903164	+	0.429296i	$0.141238\pi$
$458$	0.212721	−	2.43141i	0.00993978	−	0.113612i
$459$	−3.48569	−	1.26869i	−0.162698	−	0.0592172i
$460$	6.23670	−	16.2011i	0.290788	−	0.755382i
$461$	−1.38459	−	7.85238i	−0.0644867	−	0.365722i	−0.999925	−	0.0122326i	$-0.996106\pi$
$461$	−1.38459	−	7.85238i	−0.0644867	−	0.365722i	0.935439	−	0.353489i	$-0.115005\pi$
$462$	−0.575324	+	1.23379i	−0.0267665	+	0.0574009i
$463$	16.7463	−	4.48715i	0.778265	−	0.208535i	0.152245	−	0.988343i	$-0.451350\pi$
$463$	16.7463	−	4.48715i	0.778265	−	0.208535i	0.626020	+	0.779807i	$0.284683\pi$
$464$	−0.419708	−	0.726955i	−0.0194844	−	0.0337480i
$465$	−7.27789	+	5.88207i	−0.337504	+	0.272775i
$466$	−4.06488	+	4.84433i	−0.188302	+	0.224409i
$467$	36.5683	+	9.79845i	1.69218	+	0.453418i	0.970951	−	0.239278i	$-0.0769108\pi$
$467$	36.5683	+	9.79845i	1.69218	+	0.453418i	0.721229	+	0.692697i	$0.243577\pi$
$468$	1.03493	+	3.86240i	0.0478395	+	0.178539i
$469$	−3.00553	+	1.09392i	−0.138782	+	0.0505126i
$470$	7.08913	−	6.83288i	0.326997	−	0.315177i
$471$	7.63976	+	1.34710i	0.352022	+	0.0620709i
$472$	10.6813	−	4.98077i	0.491646	−	0.229258i
$473$	20.1815	+	1.76565i	0.927947	+	0.0811848i
$474$	−8.51944			−0.391311
$475$	21.5401	−	3.32057i	0.988325	−	0.152358i
$476$	2.88832			0.132386
$477$	13.9815	+	1.22323i	0.640170	+	0.0560077i
$478$	19.5268	−	9.10551i	0.893137	−	0.416477i
$479$	−19.7611	−	3.48441i	−0.902906	−	0.159207i	−0.297125	−	0.954838i	$-0.596028\pi$
$479$	−19.7611	−	3.48441i	−0.902906	−	0.159207i	−0.605780	+	0.795632i	$0.707139\pi$
$480$	1.60997	−	1.55177i	0.0734847	−	0.0708285i
$481$	−2.98010	+	1.08467i	−0.135881	+	0.0494565i
$482$	7.48729	+	27.9430i	0.341037	+	1.27277i
$483$	−5.83921	−	1.56461i	−0.265693	−	0.0711922i
$484$	5.10590	−	6.08497i	0.232086	−	0.276590i
$485$	25.3641	−	20.4996i	1.15173	−	0.930838i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−2.36076	+	0.632564i	−0.106976	+	0.0286642i	−0.311910	−	0.950112i	$-0.600969\pi$
$487$	−2.36076	+	0.632564i	−0.106976	+	0.0286642i	0.204934	+	0.978776i	$0.434302\pi$
$488$	−0.913894	+	1.95985i	−0.0413700	+	0.0887184i
$489$	0.376614	+	2.13588i	0.0170311	+	0.0965879i
$490$	−5.13618	+	13.3423i	−0.232029	+	0.602743i
$491$	−23.8462	−	8.67929i	−1.07616	−	0.391691i	−0.257685	−	0.966229i	$-0.582960\pi$
$491$	−23.8462	−	8.67929i	−1.07616	−	0.391691i	−0.818478	+	0.574538i	$0.805182\pi$
$492$	0.363774	−	4.15795i	0.0164002	−	0.187455i
$493$	2.20173	−	2.20173i	0.0991611	−	0.0991611i
$494$	−16.4674	−	5.71121i	−0.740905	−	0.256959i
$495$	−3.24309	+	2.18301i	−0.145766	+	0.0981190i
$496$	−2.68999	−	3.20581i	−0.120784	−	0.143945i
$497$	−4.55246	−	9.76279i	−0.204206	−	0.437921i
$498$	−7.73578	+	5.41665i	−0.346649	+	0.242726i
$499$	−30.8477	+	5.43928i	−1.38093	+	0.243496i	−0.814285	−	0.580465i	$-0.802871\pi$
$499$	−30.8477	+	5.43928i	−1.38093	+	0.243496i	−0.566647	+	0.823961i	$0.691760\pi$
$500$	5.89762	+	9.49832i	0.263750	+	0.424778i
$501$	−0.884823	+	1.53256i	−0.0395310	+	0.0684696i
$502$	0.418368	−	1.56137i	0.0186727	−	0.0696874i
$503$	−3.55076	−	40.5854i	−0.158321	−	1.80961i	−0.495969	−	0.868340i	$-0.665187\pi$
$503$	−3.55076	−	40.5854i	−0.158321	−	1.80961i	0.337649	−	0.941272i	$-0.390368\pi$
$504$	−0.596481	−	0.500507i	−0.0265694	−	0.0222944i
$505$	4.98082	−	10.1876i	0.221644	−	0.453343i
$506$	−11.7549	−	6.78670i	−0.522570	−	0.301706i
$507$	2.70913	+	1.26329i	0.120317	+	0.0561046i
$508$	−12.1356	−	8.49745i	−0.538431	−	0.377014i
$509$	−6.99829	+	39.6893i	−0.310194	+	1.75920i	0.287794	+	0.957692i	$0.407078\pi$
$509$	−6.99829	+	39.6893i	−0.310194	+	1.75920i	−0.597988	+	0.801505i	$0.704033\pi$
$510$	7.10567	+	4.27871i	0.314644	+	0.189465i
$511$	0.793525	−	0.665846i	0.0351035	−	0.0294553i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.34759	−	0.313735i	−0.191951	−	0.0138517i
$514$			2.96634i			0.130840i
$515$	−18.2556	+	10.0966i	−0.804439	+	0.444909i
$516$	−3.96314	+	10.8886i	−0.174468	+	0.479346i
$517$	−4.41559	−	6.30611i	−0.194197	−	0.277343i
$518$	0.354213	−	0.505869i	0.0155632	−	0.0222266i
$519$	−2.96325	−	8.14147i	−0.130072	−	0.357371i
$520$	−0.615233	−	8.92006i	−0.0269798	−	0.391171i
$521$	8.70840	−	5.02780i	0.381522	−	0.220272i	−0.296958	−	0.954890i	$-0.595972\pi$
$521$	8.70840	−	5.02780i	0.381522	−	0.220272i	0.678480	+	0.734619i	$0.262639\pi$
$522$	−0.836221	+	0.0731599i	−0.0366004	+	0.00320212i
$523$	17.5940	−	1.53928i	0.769334	−	0.0673080i	0.304271	−	0.952586i	$-0.401587\pi$
$523$	17.5940	−	1.53928i	0.769334	−	0.0673080i	0.465063	+	0.885278i	$0.346032\pi$
$524$	16.1284	−	9.31176i	0.704574	−	0.406786i
$525$	3.07248	−	2.39109i	0.134094	−	0.104356i
$526$	−5.12264	−	14.0744i	−0.223358	−	0.613671i
$527$	8.90385	−	12.7160i	0.387858	−	0.553918i
$528$	−1.00280	−	1.43214i	−0.0436411	−	0.0623260i
$529$	12.7487	−	35.0267i	0.554290	−	1.52290i
$530$	−30.1591	−	8.67902i	−1.31003	−	0.376992i
$531$		−	11.7855i		−	0.511447i
$532$	3.26465	−	0.928268i	0.141541	−	0.0402455i
$533$	−11.8014	−	11.8014i	−0.511175	−	0.511175i
$534$	5.37745	−	4.51222i	0.232705	−	0.195263i
$535$	3.30705	−	5.49203i	0.142976	−	0.237441i
$536$	0.713283	−	4.04523i	0.0308091	−	0.174727i
$537$	−3.10452	−	2.17381i	−0.133970	−	0.0938069i
$538$	5.42135	+	2.52802i	0.233731	+	0.108990i
$539$	9.68065	+	5.58913i	0.416975	+	0.240741i
$540$	−0.725983	−	2.11493i	−0.0312413	−	0.0910123i
$541$	22.3711	+	18.7716i	0.961808	+	0.807053i	0.981246	−	0.192758i	$-0.0617433\pi$
$541$	22.3711	+	18.7716i	0.961808	+	0.807053i	−0.0194382	+	0.999811i	$0.506188\pi$
$542$	0.730371	+	8.34818i	0.0313721	+	0.358585i
$543$	0.692395	−	2.58405i	0.0297135	−	0.110892i
$544$	−1.85470	+	3.21243i	−0.0795194	+	0.137732i
$545$	22.4688	+	16.3572i	0.962458	+	0.700665i
$546$	−3.06625	+	0.540662i	−0.131223	+	0.0231382i
$547$	13.3770	−	9.36667i	0.571959	−	0.400490i	−0.251507	−	0.967855i	$-0.580926\pi$
$547$	13.3770	−	9.36667i	0.571959	−	0.400490i	0.823466	+	0.567365i	$0.192037\pi$
$548$	−0.610407	−	1.30902i	−0.0260753	−	0.0559187i
$549$	1.39000	+	1.65654i	0.0593238	+	0.0706994i
$550$	8.05318	−	3.40032i	0.343389	−	0.144990i
$551$	1.78100	−	3.19621i	0.0758731	−	0.136163i
$552$	5.48975	−	5.48975i	0.233659	−	0.233659i
$553$	0.578162	−	6.60842i	0.0245860	−	0.281019i
$554$	9.62515	+	3.50327i	0.408933	+	0.148840i
$555$	1.62080	−	0.719782i	0.0687992	−	0.0305531i
$556$	1.70546	+	9.67212i	0.0723275	+	0.410189i
$557$	17.3111	−	37.1238i	0.733495	−	1.57298i	−0.0836118	−	0.996498i	$-0.526646\pi$
$557$	17.3111	−	37.1238i	0.733495	−	1.57298i	0.817107	−	0.576486i	$-0.195577\pi$
$558$	−4.04229	+	1.08313i	−0.171124	+	0.0458525i
$559$	23.1671	+	40.1265i	0.979863	+	1.69717i
$560$	1.09443	+	1.35414i	0.0462482	+	0.0572229i
$561$	4.16862	−	4.96796i	0.175999	−	0.209748i
$562$	−9.36261	−	2.50870i	−0.394938	−	0.105823i
$563$	−10.8951	−	40.6609i	−0.459172	−	1.71365i	−0.675524	−	0.737338i	$-0.736083\pi$
$563$	−10.8951	−	40.6609i	−0.459172	−	1.71365i	0.216352	−	0.976315i	$-0.430584\pi$
$564$	4.13772	−	1.50601i	0.174230	−	0.0634144i
$565$	0.845015	−	45.9104i	0.0355500	−	1.93146i
$566$	−7.89621	−	1.39231i	−0.331902	−	0.0585233i
$567$	−0.705697	+	0.329072i	−0.0296365	+	0.0138197i
$568$	13.7816	+	1.20573i	0.578263	+	0.0505915i
$569$	21.8263			0.915005			0.457503	−	0.889208i	$-0.348744\pi$
$569$	21.8263			0.915005			0.457503	+	0.889208i	$0.348744\pi$
$570$	9.40662	+	2.55254i	0.394000	+	0.106914i
$571$	41.5041			1.73689			0.868447	−	0.495783i	$-0.165119\pi$
$571$	41.5041			1.73689			0.868447	+	0.495783i	$0.165119\pi$
$572$	−6.96433	−	0.609300i	−0.291193	−	0.0254761i
$573$	21.3756	−	9.96759i	0.892977	−	0.416402i
$574$	3.20058	+	0.564349i	0.133590	+	0.0235555i
$575$	21.0801	+	32.5960i	0.879100	+	1.35935i
$576$	0.939693	−	0.342020i	0.0391539	−	0.0142508i
$577$	−12.0417	−	44.9402i	−0.501302	−	1.87088i	−0.491402	−	0.870933i	$-0.663516\pi$
$577$	−12.0417	−	44.9402i	−0.501302	−	1.87088i	−0.00989945	−	0.999951i	$-0.503151\pi$
$578$	3.13000	+	0.838681i	0.130191	+	0.0348845i
$579$	−12.0155	+	14.3195i	−0.499346	+	0.595097i
$580$	1.86652	+	0.197973i	0.0775030	+	0.00822037i
$581$	−3.67665	−	6.36815i	−0.152533	−	0.264195i
$582$	14.0878	−	3.77480i	0.583957	−	0.156471i
$583$	−10.3700	+	22.2386i	−0.429483	+	0.921030i
$584$	0.231012	+	1.31013i	0.00955933	+	0.0542137i
$585$	−8.34433	−	3.21219i	−0.344996	−	0.132808i
$586$	−6.89820	−	2.51074i	−0.284962	−	0.103718i
$587$	3.09011	−	35.3201i	0.127543	−	1.45782i	−0.615269	−	0.788318i	$-0.710952\pi$
$587$	3.09011	−	35.3201i	0.127543	−	1.45782i	0.742811	−	0.669501i	$-0.233492\pi$
$588$	−4.52103	+	4.52103i	−0.186444	+	0.186444i
$589$	5.97721	−	17.2344i	0.246287	−	0.710132i
$590$	−5.05301	+	25.8642i	−0.208029	+	1.06481i
$591$	−7.68421	−	9.15769i	−0.316086	−	0.376697i
$592$	0.335181	+	0.718798i	0.0137759	+	0.0295424i
$593$	4.72987	−	3.31189i	0.194232	−	0.136003i	−0.472415	−	0.881376i	$-0.656618\pi$
$593$	4.72987	−	3.31189i	0.194232	−	0.136003i	0.666647	+	0.745373i	$0.267729\pi$
$594$	−1.72176	+	0.303593i	−0.0706447	+	0.0124566i
$595$	−3.80116	+	5.22141i	−0.155833	+	0.214057i
$596$	−0.714922	+	1.23828i	−0.0292843	+	0.0507220i
$597$	−2.07624	+	7.74862i	−0.0849747	+	0.317130i
$598$	−2.70568	−	30.9261i	−0.110644	−	1.26466i
$599$	−2.34565	−	1.96824i	−0.0958408	−	0.0804200i	0.593608	−	0.804754i	$-0.297703\pi$
$599$	−2.34565	−	1.96824i	−0.0958408	−	0.0804200i	−0.689449	+	0.724334i	$0.742147\pi$
$600$	0.686453	+	4.95265i	0.0280243	+	0.202191i
$601$	−28.5945	−	16.5090i	−1.16639	−	0.673418i	−0.213566	−	0.976929i	$-0.568508\pi$
$601$	−28.5945	−	16.5090i	−1.16639	−	0.673418i	−0.952828	+	0.303511i	$0.901841\pi$
$602$	−8.17723	−	3.81310i	−0.333279	−	0.155411i
$603$	−3.36478	−	2.35604i	−0.137024	−	0.0959455i
$604$	−0.0433293	+	0.245733i	−0.00176304	+	0.00999872i
$605$	4.28061	+	17.2384i	0.174032	+	0.700840i
$606$	3.88493	−	3.25984i	0.157814	−	0.132422i
$607$	−22.8860	−	22.8860i	−0.928915	−	0.928915i	0.0687208	−	0.997636i	$-0.478108\pi$
$607$	−22.8860	−	22.8860i	−0.928915	−	0.928915i	−0.997636	+	0.0687208i	$0.978108\pi$
$608$	−1.06392	+	4.22706i	−0.0431477	+	0.171430i
$609$		−	0.653611i		−	0.0264857i
$610$	−2.34023	−	4.23136i	−0.0947531	−	0.171323i
$611$	6.02200	−	16.5453i	0.243624	−	0.669351i
$612$	2.12762	+	3.03856i	0.0860039	+	0.122826i
$613$	−7.48462	+	10.6892i	−0.302301	+	0.431731i	−0.941348	−	0.337437i	$-0.890440\pi$
$613$	−7.48462	+	10.6892i	−0.302301	+	0.431731i	0.639047	+	0.769168i	$0.279329\pi$
$614$	8.40856	+	23.1023i	0.339342	+	0.932334i
$615$	7.03786	+	6.12968i	0.283794	+	0.247172i
$616$	1.17895	−	0.680666i	0.0475012	−	0.0274248i
$617$	33.8655	−	2.96285i	1.36338	−	0.119280i	0.618133	−	0.786073i	$-0.287889\pi$
$617$	33.8655	−	2.96285i	1.36338	−	0.119280i	0.745243	+	0.666794i	$0.232334\pi$
$618$	−9.29412	+	0.813130i	−0.373864	+	0.0327089i
$619$	29.5227	−	17.0449i	1.18662	−	0.685093i	0.229080	−	0.973408i	$-0.426428\pi$
$619$	29.5227	−	17.0449i	1.18662	−	0.685093i	0.957536	+	0.288315i	$0.0930949\pi$
$620$	9.33551	−	0.643888i	0.374923	−	0.0258592i
$621$	−2.65533	−	7.29547i	−0.106555	−	0.292757i
$622$	3.89553	−	5.56339i	0.156196	−	0.223072i
$623$	3.13514	+	4.47744i	0.125607	+	0.179385i
$624$	1.36762	−	3.75750i	0.0547486	−	0.150420i
$625$	−24.9323	−	1.83870i	−0.997292	−	0.0735482i
$626$		−	8.63714i		−	0.345209i
$627$	3.11513	−	6.95500i	0.124406	−	0.277756i
$628$	−5.48546	−	5.48546i	−0.218894	−	0.218894i
$629$	−2.25366	+	1.89104i	−0.0898592	+	0.0754008i
$630$	1.68980	−	0.419608i	0.0673231	−	0.0167176i
$631$	−1.00168	+	5.68081i	−0.0398763	+	0.226150i	−0.998233	−	0.0594249i	$-0.981073\pi$
$631$	−1.00168	+	5.68081i	−0.0398763	+	0.226150i	0.958356	+	0.285575i	$0.0921844\pi$
$632$	6.97871	+	4.88655i	0.277598	+	0.194376i
$633$	4.25343	+	1.98341i	0.169059	+	0.0788334i
$634$	−15.1270	−	8.73358i	−0.600770	−	0.346855i
$635$	31.3325	−	10.7553i	1.24339	−	0.426812i
$636$	−10.7514	−	9.02149i	−0.426320	−	0.357725i
$637$	2.22824	+	25.4689i	0.0882860	+	1.00911i
$638$	0.379835	−	1.41756i	0.0150378	−	0.0561218i
$639$	6.91712	−	11.9808i	0.273637	−	0.473953i
$640$	−2.20887	+	0.347699i	−0.0873132	+	0.0137440i
$641$	−29.3469	+	5.17466i	−1.15913	+	0.204387i	−0.719960	−	0.694015i	$-0.755840\pi$
$641$	−29.3469	+	5.17466i	−1.15913	+	0.204387i	−0.439174	+	0.898402i	$0.644729\pi$
$642$	2.34853	−	1.64446i	0.0926889	−	0.0649015i
$643$	−6.19993	−	13.2958i	−0.244501	−	0.524335i	0.745310	−	0.666718i	$-0.232301\pi$
$643$	−6.19993	−	13.2958i	−0.244501	−	0.524335i	−0.989812	+	0.142383i	$0.954524\pi$
$644$	3.88577	+	4.63088i	0.153121	+	0.182482i
$645$	−14.4684	−	21.4944i	−0.569695	−	0.846341i
$646$	−16.1670	+	0.246217i	−0.636082	+	0.00968726i
$647$	18.1369	−	18.1369i	0.713035	−	0.713035i	−0.254134	−	0.967169i	$-0.581790\pi$
$647$	18.1369	−	18.1369i	0.713035	−	0.713035i	0.967169	+	0.254134i	$0.0817903\pi$
$648$	0.0871557	−	0.996195i	0.00342380	−	0.0391342i
$649$	19.3622	+	7.04728i	0.760034	+	0.276630i
$650$	16.9351	+	10.6270i	0.664248	+	0.416826i
$651$	−0.565844	−	3.20906i	−0.0221772	−	0.125773i
$652$	0.916588	−	1.96563i	0.0358964	−	0.0769800i
$653$	31.9565	−	8.56273i	1.25056	−	0.335085i	0.428005	−	0.903776i	$-0.359217\pi$
$653$	31.9565	−	8.56273i	1.25056	−	0.335085i	0.822551	+	0.568691i	$0.192550\pi$
$654$	6.21452	+	10.7639i	0.243007	+	0.420900i
$655$	−4.39228	+	41.4112i	−0.171621	+	1.61807i
$656$	−2.68289	+	3.19734i	−0.104749	+	0.124835i
$657$	1.28501	+	0.344318i	0.0501331	+	0.0134331i
$658$	0.887390	+	3.31178i	0.0345941	+	0.129107i
$659$	−38.8502	+	14.1403i	−1.51339	+	0.550828i	−0.959487	−	0.281754i	$-0.909084\pi$
$659$	−38.8502	+	14.1403i	−1.51339	+	0.550828i	−0.553902	+	0.832582i	$0.686862\pi$
$660$	3.90871	+	0.0719426i	0.152146	+	0.00280036i
$661$	−49.5759	−	8.74157i	−1.92828	−	0.340008i	−0.928750	−	0.370706i	$-0.879116\pi$
$661$	−49.5759	−	8.74157i	−1.92828	−	0.340008i	−0.999529	+	0.0306988i	$0.990227\pi$
$662$	4.96699	−	2.31615i	0.193048	−	0.0900196i
$663$	14.7761	+	1.29274i	0.573857	+	0.0502060i
$664$	9.44365			0.366485
$665$	−2.61834	+	7.12338i	−0.101535	+	0.276233i
$666$	0.793106			0.0307322
$667$	6.49215	+	0.567989i	0.251377	+	0.0219926i
$668$	1.60384	−	0.747884i	0.0620546	−	0.0289365i
$669$	−16.9803	−	2.99409i	−0.656497	−	0.115758i
$670$	6.37412	+	6.61316i	0.246254	+	0.255489i
$671$	−3.55267	+	1.29307i	−0.137149	+	0.0499183i
$672$	0.201530	+	0.752119i	0.00777417	+	0.0290136i
$673$	−24.7187	−	6.62334i	−0.952834	−	0.255311i	−0.251270	−	0.967917i	$-0.580848\pi$
$673$	−24.7187	−	6.62334i	−0.952834	−	0.255311i	−0.701565	+	0.712606i	$0.747515\pi$
$674$	8.83942	−	10.5344i	0.340482	−	0.405771i
$675$	4.77874	+	1.47094i	0.183934	+	0.0566167i
$676$	−1.49460	−	2.58872i	−0.0574846	−	0.0995662i
$677$	−25.4618	+	6.82248i	−0.978578	+	0.262209i	−0.712446	−	0.701727i	$-0.752413\pi$
$677$	−25.4618	+	6.82248i	−0.978578	+	0.262209i	−0.266133	+	0.963936i	$0.585746\pi$
$678$	8.67856	−	18.6112i	0.333298	−	0.714760i
$679$	1.97202	+	11.1839i	0.0756792	+	0.429198i
$680$	−3.36645	−	7.58056i	−0.129098	−	0.290701i
$681$	−11.1580	−	4.06117i	−0.427574	−	0.155624i
$682$	0.637678	−	7.28869i	0.0244180	−	0.279098i
$683$	−26.2343	+	26.2343i	−1.00383	+	1.00383i	−0.00383499	+	0.999993i	$0.501221\pi$
$683$	−26.2343	+	26.2343i	−1.00383	+	1.00383i	−0.999993	+	0.00383499i	$0.998779\pi$
$684$	3.38139	+	2.75067i	0.129291	+	0.105175i
$685$	3.16973	+	0.619260i	0.121109	+	0.0236607i
$686$	−6.70364	−	7.98909i	−0.255946	−	0.305025i
$687$	1.03148	+	2.21202i	0.0393535	+	0.0843939i
$688$	9.49188	−	6.64629i	0.361875	−	0.253387i
$689$	−55.2682	+	9.74528i	−2.10555	+	0.371265i
$690$	2.69942	+	17.1489i	0.102765	+	0.652849i
$691$	−12.0206	+	20.8203i	−0.457285	+	0.792041i	−0.998816	−	0.0486397i	$-0.984511\pi$
$691$	−12.0206	+	20.8203i	−0.457285	+	0.792041i	0.541531	+	0.840681i	$0.317845\pi$
$692$	−2.24240	+	8.36876i	−0.0852433	+	0.318132i
$693$	−0.118648	−	1.35615i	−0.00450706	−	0.0515160i
$694$	1.28175	+	1.07552i	0.0486547	+	0.0408262i
$695$	−19.7294	−	9.64590i	−0.748379	−	0.365890i
$696$	0.726955	+	0.419708i	0.0275552	+	0.0159090i
$697$	−14.0318	−	6.54314i	−0.531493	−	0.247839i
$698$	24.1651	+	16.9206i	0.914663	+	0.640454i
$699$	1.09812	−	6.22776i	0.0415348	−	0.235555i
$700$	−3.88830	+	0.196367i	−0.146964	+	0.00742197i
$701$	−14.7370	+	12.3659i	−0.556611	+	0.467052i	−0.877172	−	0.480176i	$-0.840573\pi$
$701$	−14.7370	+	12.3659i	−0.556611	+	0.467052i	0.320562	+	0.947228i	$0.396128\pi$
$702$	−2.82747	−	2.82747i	−0.106716	−	0.106716i
$703$	−1.93954	+	2.86173i	−0.0731511	+	0.107932i
$704$			1.74832i			0.0658924i
$705$	−2.72292	+	9.46202i	−0.102551	+	0.356360i
$706$	3.15295	−	8.66267i	0.118663	−	0.326024i
$707$	2.26497	+	3.23472i	0.0851830	+	0.121654i
$708$	−6.75988	+	9.65411i	−0.254052	+	0.362824i
$709$	13.9952	+	38.4516i	0.525602	+	1.44408i	0.864200	+	0.503149i	$0.167825\pi$
$709$	13.9952	+	38.4516i	0.525602	+	1.44408i	−0.338598	+	0.940931i	$0.609953\pi$
$710$	−20.3169	+	23.3271i	−0.762480	+	0.875451i
$711$	7.37805	−	4.25972i	0.276698	−	0.159752i
$712$	−6.99305	+	0.611813i	−0.262076	+	0.0229287i
$713$	32.3665	−	2.83170i	1.21213	−	0.106048i
$714$	−2.50136	+	1.44416i	−0.0936110	+	0.0540463i
$715$	10.2669	−	11.7880i	0.383958	−	0.440847i
$716$	1.29623	+	3.56136i	0.0484424	+	0.133094i
$717$	−12.3580	+	17.6490i	−0.461517	+	0.659115i
$718$	12.5398	+	17.9088i	0.467983	+	0.668349i
$719$	−4.31721	+	11.8614i	−0.161005	+	0.442357i	−0.993794	−	0.111233i	$-0.964520\pi$
$719$	−4.31721	+	11.8614i	−0.161005	+	0.442357i	0.832790	+	0.553590i	$0.186742\pi$
$720$	−0.618386	+	2.14886i	−0.0230459	+	0.0800833i
$721$		−	7.26452i		−	0.270545i
$722$	−18.1943	+	5.47416i	−0.677123	+	0.203727i
$723$	−20.4557	−	20.4557i	−0.760754	−	0.760754i
$724$	−2.04933	+	1.71959i	−0.0761627	+	0.0639081i
$725$	−2.81432	+	3.11369i	−0.104521	+	0.115640i
$726$	−1.37935	+	7.82269i	−0.0511925	+	0.290327i
$727$	13.2026	+	9.24455i	0.489657	+	0.342861i	0.792187	−	0.610278i	$-0.208942\pi$
$727$	13.2026	+	9.24455i	0.489657	+	0.342861i	−0.302530	+	0.953140i	$0.597831\pi$
$728$	2.82184	+	1.31584i	0.104584	+	0.0487684i
$729$	−0.866025	−	0.500000i	−0.0320750	−	0.0185185i
$730$	−2.67244	−	1.30658i	−0.0989113	−	0.0483587i
$731$	32.9264	+	27.6285i	1.21783	+	1.02188i
$732$	−0.188471	−	2.15423i	−0.00696607	−	0.0796226i
$733$	11.7288	−	43.7726i	0.433214	−	1.61678i	−0.312091	−	0.950052i	$-0.601029\pi$
$733$	11.7288	−	43.7726i	0.433214	−	1.61678i	0.745305	−	0.666724i	$-0.232304\pi$
$734$	−12.5513	+	21.7395i	−0.463277	+	0.802419i
$735$	−2.22308	−	14.1229i	−0.0819997	−	0.520929i
$736$	−7.64573	+	1.34815i	−0.281825	+	0.0496934i
$737$	5.88272	−	4.11912i	0.216693	−	0.151730i
$738$	1.76394	+	3.78278i	0.0649315	+	0.139246i
$739$	−2.53628	−	3.02263i	−0.0932987	−	0.111189i	0.717375	−	0.696687i	$-0.245343\pi$
$739$	−2.53628	−	3.02263i	−0.0932987	−	0.111189i	−0.810674	+	0.585498i	$0.800899\pi$
$740$	−1.74053	−	0.340042i	−0.0639833	−	0.0125002i
$741$	17.1168	−	3.28767i	0.628803	−	0.120776i
$742$	7.72749	−	7.72749i	0.283685	−	0.283685i
$743$	−3.34144	+	38.1929i	−0.122586	+	1.40116i	0.646938	+	0.762542i	$0.276049\pi$
$743$	−3.34144	+	38.1929i	−0.122586	+	1.40116i	−0.769524	+	0.638618i	$0.779507\pi$
$744$	3.93251	+	1.43132i	0.144173	+	0.0524746i
$745$	−1.29765	−	2.92205i	−0.0475423	−	0.107056i
$746$	5.54507	+	31.4477i	0.203020	+	1.15138i
$747$	3.99106	−	8.55885i	0.146025	−	0.313152i
$748$	−6.26424	+	1.67850i	−0.229043	+	0.0613719i
$749$	1.11620	+	1.93332i	0.0407852	+	0.0706420i
$750$	−9.85665	−	5.27698i	−0.359914	−	0.192688i
$751$	−20.3640	+	24.2689i	−0.743093	+	0.885584i	−0.996654	−	0.0817358i	$-0.973954\pi$
$751$	−20.3640	+	24.2689i	−0.743093	+	0.885584i	0.253561	+	0.967319i	$0.418398\pi$
$752$	−4.25323	−	1.13965i	−0.155100	−	0.0415588i
$753$	0.418368	+	1.56137i	0.0152462	+	0.0568995i
$754$	3.15410	−	1.14800i	0.114866	−	0.0418077i
$755$	−0.387204	−	0.401725i	−0.0140918	−	0.0146203i
$756$	0.766821	+	0.135211i	0.0278890	+	0.00491759i
$757$	31.4333	−	14.6576i	1.14246	−	0.532740i	0.243127	−	0.969995i	$-0.421827\pi$
$757$	31.4333	−	14.6576i	1.14246	−	0.532740i	0.899338	+	0.437255i	$0.144049\pi$
$758$	−14.9770	−	1.31032i	−0.543988	−	0.0475928i
$759$	13.5734			0.492684
$760$	−6.24138	−	7.48633i	−0.226399	−	0.271558i
$761$	−32.3987			−1.17445			−0.587226	−	0.809423i	$-0.699780\pi$
$761$	−32.3987			−1.17445			−0.587226	+	0.809423i	$0.699780\pi$
$762$	14.7585	+	1.29120i	0.534643	+	0.0467752i
$763$	−8.77114	+	4.09005i	−0.317536	+	0.148070i
$764$	−23.2270	−	4.09555i	−0.840324	−	0.148172i
$765$	−8.29305	−	0.152640i	−0.299836	−	0.00551870i
$766$	−21.0651	+	7.66708i	−0.761114	+	0.277023i
$767$	12.1971	+	45.5203i	0.440413	+	1.64364i
$768$	−0.965926	−	0.258819i	−0.0348548	−	0.00933933i
$769$	−18.7968	+	22.4012i	−0.677832	+	0.807808i	−0.989827	−	0.142275i	$-0.954558\pi$
$769$	−18.7968	+	22.4012i	−0.677832	+	0.807808i	0.311995	+	0.950084i	$0.399003\pi$
$770$	−0.321065	+	3.02705i	−0.0115704	+	0.109087i
$771$	−1.48317	−	2.56892i	−0.0534150	−	0.0925175i
$772$	18.0558	−	4.83804i	0.649843	−	0.174125i
$773$	11.2592	−	24.1455i	0.404967	−	0.868454i	−0.593030	−	0.805181i	$-0.702068\pi$
$773$	11.2592	−	24.1455i	0.404967	−	0.868454i	0.997996	−	0.0632732i	$-0.0201539\pi$
$774$	−2.01214	−	11.4114i	−0.0723248	−	0.410175i
$775$	−11.1220	+	17.7238i	−0.399513	+	0.636658i
$776$	−13.7052	−	4.98827i	−0.491987	−	0.179068i
$777$	−0.0538232	+	0.615202i	−0.00193090	+	0.0220703i
$778$	10.1065	−	10.1065i	0.362337	−	0.362337i
$779$	−17.9630	−	2.88604i	−0.643590	−	0.103403i
$780$	4.99284	+	7.41738i	0.178772	+	0.265585i
$781$	15.5469	+	18.5281i	0.556313	+	0.662988i
$782$	−12.1708	−	26.1003i	−0.435226	−	0.933345i
$783$	0.687609	−	0.481469i	0.0245731	−	0.0172063i
$784$	6.29657	−	1.11025i	0.224877	−	0.0396520i
$785$	17.1356	−	2.69732i	0.611595	−	0.0962713i
$786$	−9.31176	+	16.1284i	−0.332139	+	0.575282i
$787$	0.176945	−	0.660369i	0.00630742	−	0.0235396i	−0.962700	−	0.270570i	$-0.912788\pi$
$787$	0.176945	−	0.660369i	0.00630742	−	0.0235396i	0.969008	+	0.247030i	$0.0794546\pi$
$788$	1.04190	+	11.9090i	0.0371163	+	0.424241i
$789$	11.4735	+	9.62742i	0.408468	+	0.342745i
$790$	−18.0181	+	6.18497i	−0.641054	+	0.220051i
$791$	13.8475	+	7.99489i	0.492362	+	0.284265i
$792$	1.58452	+	0.738873i	0.0563034	+	0.0262547i
$793$	−7.08313	−	4.95966i	−0.251529	−	0.176123i
$794$	2.26952	−	12.8711i	0.0805422	−	0.456778i
$795$	30.4581	−	7.56331i	1.08024	−	0.268243i
$796$	6.14518	−	5.15642i	0.217810	−	0.182764i
$797$	33.4503	+	33.4503i	1.18487	+	1.18487i	0.978467	+	0.206405i	$0.0661765\pi$
$797$	33.4503	+	33.4503i	1.18487	+	1.18487i	0.206405	+	0.978467i	$0.433823\pi$
$798$	−2.36314	+	2.43623i	−0.0836542	+	0.0862416i
$799$		−	16.3335i		−	0.577836i
$800$	2.27842	−	4.45071i	0.0805542	−	0.157356i
$801$	−2.40090	+	6.59642i	−0.0848317	+	0.233073i
$802$	6.72352	+	9.60218i	0.237416	+	0.339065i
$803$	−1.33406	+	1.90524i	−0.0470781	+	0.0672345i
$804$	1.40489	+	3.85991i	0.0495468	+	0.136129i
$805$	−13.4854	+	0.930114i	−0.475299	+	0.0327822i
$806$	14.4920	−	8.36695i	0.510458	−	0.294713i
$807$	−5.95903	+	0.521348i	−0.209768	+	0.0183523i
$808$	−5.05211	+	0.442003i	−0.177733	+	0.0155496i
$809$	4.29850	−	2.48174i	0.151127	−	0.0872533i	−0.422530	−	0.906349i	$-0.638858\pi$
$809$	4.29850	−	2.48174i	0.151127	−	0.0872533i	0.573657	+	0.819096i	$0.305524\pi$
$810$	1.68619	+	1.46860i	0.0592466	+	0.0516012i
$811$	14.1313	+	38.8254i	0.496216	+	1.36334i	0.894905	+	0.446257i	$0.147243\pi$
$811$	14.1313	+	38.8254i	0.496216	+	1.36334i	−0.398689	+	0.917086i	$0.630535\pi$
$812$	−0.374896	+	0.535407i	−0.0131563	+	0.0187891i
$813$	−4.80661	−	6.86455i	−0.168575	−	0.240750i
$814$	−0.474247	+	1.30298i	−0.0166223	+	0.0456695i
$815$	2.34713	+	4.24384i	0.0822163	+	0.148655i
$816$		−	3.70939i		−	0.129855i
$817$	46.0960	+	20.6463i	1.61269	+	0.722322i
$818$	−0.497643	−	0.497643i	−0.0173997	−	0.0173997i
$819$	2.38512	−	2.00135i	0.0833428	−	0.0699329i
$820$	−2.24924	−	9.05789i	−0.0785470	−	0.316315i
$821$	−1.19961	+	6.80332i	−0.0418666	+	0.237437i	−0.998559	−	0.0536631i	$-0.982910\pi$
$821$	−1.19961	+	6.80332i	−0.0418666	+	0.237437i	0.956692	+	0.291101i	$0.0940214\pi$
$822$	1.18314	+	0.828443i	0.0412667	+	0.0288953i
$823$	−20.9092	−	9.75012i	−0.728849	−	0.339868i	0.0225236	−	0.999746i	$-0.492830\pi$
$823$	−20.9092	−	9.75012i	−0.728849	−	0.339868i	−0.751372	+	0.659879i	$0.770608\pi$
$824$	8.07969	+	4.66481i	0.281469	+	0.162506i
$825$	−5.27410	+	6.97135i	−0.183620	+	0.242711i
$826$	−7.02983	−	5.89872i	−0.244599	−	0.205243i
$827$	−1.45997	−	16.6875i	−0.0507681	−	0.580282i	−0.978391	−	0.206764i	$-0.933707\pi$
$827$	−1.45997	−	16.6875i	−0.0507681	−	0.580282i	0.927623	−	0.373519i	$-0.121849\pi$
$828$	−2.00939	+	7.49913i	−0.0698310	+	0.260613i
$829$	21.8214	−	37.7958i	0.757889	−	1.31270i	−0.186036	−	0.982543i	$-0.559564\pi$
$829$	21.8214	−	37.7958i	0.757889	−	1.31270i	0.943925	−	0.330159i	$-0.107102\pi$
$830$	−12.4283	+	17.0719i	−0.431392	+	0.592575i
$831$	−10.0873	+	1.77866i	−0.349923	+	0.0617009i
$832$	−3.27550	+	2.29353i	−0.113558	+	0.0795139i
$833$	10.0231	+	21.4947i	0.347281	+	0.744746i
$834$	−6.31303	−	7.52358i	−0.218602	−	0.260520i
$835$	−0.758731	+	3.88363i	−0.0262570	+	0.134398i
$836$	−6.54099	+	3.91044i	−0.226225	+	0.135245i
$837$	2.95916	−	2.95916i	0.102284	−	0.102284i
$838$	1.23783	−	14.1485i	0.0427601	−	0.488750i
$839$	−2.36861	−	0.862104i	−0.0817735	−	0.0297631i	0.300809	−	0.953684i	$-0.402743\pi$
$839$	−2.36861	−	0.862104i	−0.0817735	−	0.0297631i	−0.382583	+	0.923921i	$0.624965\pi$
$840$	−1.62488	−	0.625505i	−0.0560636	−	0.0215820i
$841$	−4.91344	−	27.8655i	−0.169429	−	0.960880i
$842$	−11.0993	+	23.8025i	−0.382507	+	0.820289i
$843$	9.36261	−	2.50870i	0.322466	−	0.0864044i
$844$	−2.34657	−	4.06438i	−0.0807724	−	0.139902i
$845$	6.64676	+	0.704990i	0.228656	+	0.0242524i
$846$	−2.83037	+	3.37310i	−0.0973101	+	0.115970i
$847$	−5.97436	−	1.60082i	−0.205281	−	0.0550050i
$848$	3.63251	+	13.5567i	0.124741	+	0.465539i
$849$	7.53447	−	2.74232i	0.258582	−	0.0941163i
$850$	18.1343	+	3.89061i	0.622001	+	0.133447i
$851$	−6.06387	−	1.06922i	−0.207867	−	0.0366525i
$852$	−12.5381	+	5.84660i	−0.429548	+	0.200301i
$853$	−41.9935	−	3.67395i	−1.43783	−	0.125794i	−0.658581	−	0.752510i	$-0.728843\pi$
$853$	−41.9935	−	3.67395i	−1.43783	−	0.125794i	−0.779248	+	0.626716i	$0.784399\pi$
$854$	1.68380			0.0576184
$855$	−9.42264	+	2.49275i	−0.322248	+	0.0852502i
$856$	−2.86702			−0.0979928
$857$	−5.24401	−	0.458792i	−0.179132	−	0.0156720i	−0.00276326	−	0.999996i	$-0.500880\pi$
$857$	−5.24401	−	0.458792i	−0.179132	−	0.0156720i	−0.176369	+	0.984324i	$0.556435\pi$
$858$	6.33593	−	2.95449i	0.216305	−	0.100865i
$859$	−46.4116	−	8.18361i	−1.58354	−	0.279221i	−0.688512	−	0.725225i	$-0.741736\pi$
$859$	−46.4116	−	8.18361i	−1.58354	−	0.279221i	−0.895031	+	0.446004i	$0.852847\pi$
$860$	−0.476818	+	25.9059i	−0.0162594	+	0.883385i
$861$	−3.05396	+	1.11155i	−0.104079	+	0.0378816i
$862$	−6.40184	−	23.8920i	−0.218047	−	0.813764i
$863$	1.71561	+	0.459697i	0.0584001	+	0.0156483i	0.287901	−	0.957660i	$-0.407043\pi$
$863$	1.71561	+	0.459697i	0.0584001	+	0.0156483i	−0.229501	+	0.973308i	$0.573709\pi$
$864$	−0.642788	+	0.766044i	−0.0218681	+	0.0260614i
$865$	−12.1777	−	15.0674i	−0.414053	−	0.512307i
$866$	18.1560	+	31.4470i	0.616964	+	1.06861i
$867$	−3.13000	+	0.838681i	−0.106300	+	0.0284831i
$868$	−1.37713	+	2.95326i	−0.0467428	+	0.100240i
$869$	2.58644	+	14.6684i	0.0877390	+	0.497593i
$870$	−1.71544	+	0.761811i	−0.0581589	+	0.0258278i
$871$	15.4344	+	5.61768i	0.522976	+	0.190348i
$872$	1.08326	−	12.3817i	0.0366839	−	0.419299i
$873$	−10.3130	+	10.3130i	−0.349041	+	0.349041i
$874$	−22.1449	−	25.5895i	−0.749061	−	0.865578i
$875$	4.76220	−	7.28757i	0.160992	−	0.246365i
$876$	−0.855128	−	1.01910i	−0.0288921	−	0.0344323i
$877$	21.6001	+	46.3216i	0.729384	+	1.56417i	0.822664	+	0.568528i	$0.192487\pi$
$877$	21.6001	+	46.3216i	0.729384	+	1.56417i	−0.0932799	+	0.995640i	$0.529735\pi$
$878$	−3.44601	+	2.41292i	−0.116297	+	0.0814321i
$879$	7.22939	−	1.27474i	0.243841	−	0.0429958i
$880$	−3.16056	−	2.30087i	−0.106542	−	0.0775624i
$881$	−20.1160	+	34.8420i	−0.677727	+	1.17386i	0.297937	+	0.954585i	$0.403701\pi$
$881$	−20.1160	+	34.8420i	−0.677727	+	1.17386i	−0.975664	+	0.219272i	$0.929632\pi$
$882$	1.65481	−	6.17584i	0.0557204	−	0.207951i
$883$	0.823964	+	9.41796i	0.0277286	+	0.316939i	0.997374	+	0.0724238i	$0.0230734\pi$
$883$	0.823964	+	9.41796i	0.0277286	+	0.316939i	−0.969645	+	0.244516i	$0.921371\pi$
$884$	−11.3624	−	9.53418i	−0.382159	−	0.320669i
$885$	−8.55607	−	24.9256i	−0.287609	−	0.837863i
$886$	−6.75593	−	3.90054i	−0.226970	−	0.131041i
$887$	−39.5732	−	18.4533i	−1.32874	−	0.619600i	−0.376914	−	0.926248i	$-0.623015\pi$
$887$	−39.5732	−	18.4533i	−1.32874	−	0.619600i	−0.951823	+	0.306648i	$0.900793\pi$
$888$	−0.649674	−	0.454907i	−0.0218016	−	0.0152657i
$889$	−2.00314	+	11.3603i	−0.0671830	+	0.381014i
$890$	8.09717	−	13.4470i	0.271418	−	0.450744i
$891$	1.33929	−	1.12380i	0.0448680	−	0.0376487i
$892$	12.1921	+	12.1921i	0.408222	+	0.408222i
$893$	−5.24936	−	18.4616i	−0.175663	−	0.617795i
$894$		−	1.42984i		−	0.0478211i
$895$	−8.14402	−	2.34364i	−0.272224	−	0.0783392i
$896$	0.266314	−	0.731692i	0.00889693	−	0.0244441i
$897$	17.8062	+	25.4299i	0.594533	+	0.849081i
$898$	6.69863	−	9.56664i	0.223536	−	0.319243i
$899$	1.20147	+	3.30101i	0.0400712	+	0.110095i
$900$	−3.07081	−	3.94590i	−0.102360	−	0.131530i
$901$	−45.0862	+	26.0305i	−1.50204	+	0.867203i
$902$	−7.26944	+	0.635994i	−0.242046	+	0.0211763i
$903$	8.98824	−	0.786369i	0.299110	−	0.0261687i
$904$	−17.7840	+	10.2676i	−0.591488	+	0.341496i
$905$	−0.411608	−	5.96777i	−0.0136823	−	0.198375i
$906$	−0.0853421	−	0.234475i	−0.00283530	−	0.00778992i
$907$	−1.30249	+	1.86014i	−0.0432483	+	0.0617650i	−0.840194	−	0.542286i	$-0.817559\pi$
$907$	−1.30249	+	1.86014i	−0.0432483	+	0.0617650i	0.796946	+	0.604051i	$0.206448\pi$
$908$	6.81068	+	9.72666i	0.226020	+	0.322791i
$909$	−1.73453	+	4.76557i	−0.0575306	+	0.158064i
$910$	−6.09241	+	3.36951i	−0.201961	+	0.111698i
$911$			42.0686i			1.39380i	0.717170	+	0.696898i	$0.245437\pi$
$911$			42.0686i			1.39380i	−0.717170	+	0.696898i	$0.754563\pi$
$912$	−1.19215	−	4.19271i	−0.0394760	−	0.138834i
$913$	11.6747	+	11.6747i	0.386377	+	0.386377i
$914$	10.9745	−	9.20870i	0.363004	−	0.304597i
$915$	4.14238	+	2.49435i	0.136943	+	0.0824608i
$916$	0.423822	−	2.40362i	0.0140035	−	0.0794177i
$917$	−11.8787	−	8.31755i	−0.392269	−	0.274670i
$918$	−3.36185	−	1.56766i	−0.110958	−	0.0517404i
$919$	−9.03750	−	5.21780i	−0.298119	−	0.172119i	0.343478	−	0.939161i	$-0.388395\pi$
$919$	−9.03750	−	5.21780i	−0.298119	−	0.172119i	−0.641598	+	0.767041i	$0.721728\pi$
$920$	7.62499	−	15.5959i	0.251389	−	0.514182i
$921$	−18.8332	−	15.8029i	−0.620575	−	0.520724i
$922$	−0.694938	−	7.94318i	−0.0228866	−	0.261595i
$923$	−14.3174	+	53.4334i	−0.471264	+	1.75878i
$924$	−0.680666	+	1.17895i	−0.0223923	+	0.0387846i
$925$	2.90534	−	2.69897i	0.0955270	−	0.0887415i
$926$	17.0736	−	3.01054i	0.561074	−	0.0989325i
$927$	7.64238	−	5.35125i	0.251009	−	0.175758i
$928$	−0.354752	−	0.760769i	−0.0116453	−	0.0249735i
$929$	−2.84814	−	3.39428i	−0.0934444	−	0.111363i	0.717296	−	0.696769i	$-0.245380\pi$
$929$	−2.84814	−	3.39428i	−0.0934444	−	0.111363i	−0.810740	+	0.585406i	$0.800935\pi$
$930$	−7.76285	+	5.22538i	−0.254554	+	0.171347i
$931$	18.2372	+	21.0740i	0.597700	+	0.690673i
$932$	−4.47162	+	4.47162i	−0.146473	+	0.146473i
$933$	−0.591931	+	6.76580i	−0.0193789	+	0.221502i
$934$	35.5752	+	12.9483i	1.16406	+	0.423682i
$935$	5.20969	−	13.5333i	0.170375	−	0.442585i
$936$	0.694358	+	3.93790i	0.0226958	+	0.128714i
$937$	−0.724239	+	1.55314i	−0.0236599	+	0.0507387i	−0.917783	−	0.397083i	$-0.870022\pi$
$937$	−0.724239	+	1.55314i	−0.0236599	+	0.0507387i	0.894123	+	0.447822i	$0.147800\pi$
$938$	−3.08943	+	0.827810i	−0.100873	+	0.0270290i
$939$	4.31857	+	7.47998i	0.140931	+	0.244100i
$940$	7.65768	−	6.18902i	0.249766	−	0.201864i
$941$	4.25279	−	5.06827i	0.138637	−	0.165221i	−0.692259	−	0.721650i	$-0.743384\pi$
$941$	4.25279	−	5.06827i	0.138637	−	0.165221i	0.830895	+	0.556429i	$0.187829\pi$
$942$	7.49328	+	2.00782i	0.244144	+	0.0654183i
$943$	−8.38685	−	31.3001i	−0.273113	−	1.01927i
$944$	11.0747	−	4.03088i	0.360452	−	0.131194i
$945$	−1.25360	+	1.20829i	−0.0407797	+	0.0393057i
$946$	19.9508	+	3.51787i	0.648657	+	0.114376i
$947$	41.5836	−	19.3908i	1.35129	−	0.630115i	0.393961	−	0.919127i	$-0.371105\pi$
$947$	41.5836	−	19.3908i	1.35129	−	0.630115i	0.957325	+	0.289012i	$0.0933268\pi$
$948$	−8.48702	−	0.742518i	−0.275646	−	0.0241159i
$949$	−5.31958			−0.172681
$950$	21.7475	−	1.43060i	0.705582	−	0.0464147i
$951$	17.4672			0.566411
$952$	2.87733	+	0.251734i	0.0932548	+	0.00815874i
$953$	43.0435	−	20.0715i	1.39432	−	0.650181i	0.427117	−	0.904196i	$-0.359529\pi$
$953$	43.0435	−	20.0715i	1.39432	−	0.650181i	0.967200	+	0.254016i	$0.0817515\pi$
$954$	13.8217	+	2.43714i	0.447495	+	0.0789054i
$955$	37.9716	−	36.5991i	1.22873	−	1.18432i
$956$	20.2461	−	7.36899i	0.654807	−	0.238330i
$957$	0.379835	+	1.41756i	0.0122783	+	0.0458233i
$958$	−19.3822	−	5.19344i	−0.626210	−	0.167792i
$959$	−0.722906	+	0.861525i	−0.0233438	+	0.0278201i
$960$	1.73909	−	1.40555i	0.0561288	−	0.0453640i
$961$	−6.74336	−	11.6798i	−0.217528	−	0.376769i
$962$	−3.06329	+	0.820806i	−0.0987645	+	0.0264639i
$963$	−1.21166	+	2.59840i	−0.0390450	+	0.0837324i
$964$	5.02341	+	28.4892i	0.161793	+	0.917575i
$965$	−15.0162	+	39.0078i	−0.483390	+	1.25570i
$966$	−5.68062	−	2.06758i	−0.182771	−	0.0665232i
$967$	−0.682487	+	7.80086i	−0.0219473	+	0.250859i	0.977293	+	0.211892i	$0.0679624\pi$
$967$	−0.682487	+	7.80086i	−0.0219473	+	0.250859i	−0.999240	+	0.0389673i	$0.987593\pi$
$968$	5.61681	−	5.61681i	0.180531	−	0.180531i
$969$	13.8779	−	8.29672i	0.445823	−	0.266529i
$970$	27.0543	−	18.2109i	0.868660	−	0.584718i
$971$	29.1162	+	34.6994i	0.934385	+	1.11356i	0.993331	+	0.115295i	$0.0367814\pi$
$971$	29.1162	+	34.6994i	0.934385	+	1.11356i	−0.0589465	+	0.998261i	$0.518774\pi$
$972$	0.422618	+	0.906308i	0.0135555	+	0.0290698i
$973$	6.26437	−	4.38636i	0.200827	−	0.140620i
$974$	−2.40691	+	0.424403i	−0.0771223	+	0.0135987i
$975$	−19.9797	−	0.735732i	−0.639863	−	0.0235623i
$976$	−1.08123	+	1.87274i	−0.0346093	+	0.0599451i
$977$	12.2933	−	45.8791i	0.393297	−	1.46780i	−0.431366	−	0.902177i	$-0.641968\pi$
$977$	12.2933	−	45.8791i	0.393297	−	1.46780i	0.824662	−	0.565626i	$-0.191365\pi$
$978$	0.189026	+	2.16058i	0.00604439	+	0.0690877i
$979$	−9.40152	−	7.88881i	−0.300474	−	0.252128i
$980$	−6.27949	+	12.8439i	−0.200591	+	0.410283i
$981$	−10.7639	−	6.21452i	−0.343664	−	0.198414i
$982$	−22.9990	−	10.7246i	−0.733927	−	0.342236i
$983$	−13.3760	−	9.36597i	−0.426628	−	0.298728i	0.340473	−	0.940254i	$-0.389413\pi$
$983$	−13.3760	−	9.36597i	−0.426628	−	0.298728i	−0.767101	+	0.641526i	$0.778302\pi$
$984$	0.724779	−	4.11042i	0.0231051	−	0.131036i
$985$	−22.8999	−	13.7893i	−0.729653	−	0.439364i
$986$	2.38525	−	2.00146i	0.0759618	−	0.0637395i
$987$	−2.42439	−	2.42439i	−0.0771693	−	0.0771693i
$988$	−15.9070	−	7.12471i	−0.506070	−	0.226667i
$989$			89.9612i			2.86060i
$990$	−3.42101	+	1.89205i	−0.108727	+	0.0601333i
$991$	3.71590	−	10.2094i	0.118040	−	0.324311i	−0.866576	−	0.499045i	$-0.833684\pi$
$991$	3.71590	−	10.2094i	0.118040	−	0.324311i	0.984616	+	0.174734i	$0.0559065\pi$
$992$	−2.40035	−	3.42806i	−0.0762113	−	0.108841i
$993$	−3.14347	+	4.48934i	−0.0997550	+	0.142465i
$994$	−3.68426	−	10.1224i	−0.116857	−	0.321063i
$995$	1.23426	+	17.8951i	0.0391287	+	0.567314i
$996$	−8.17844	+	4.72182i	−0.259144	+	0.149617i
$997$	27.8304	−	2.43485i	0.881398	−	0.0771123i	0.362535	−	0.931970i	$-0.381911\pi$
$997$	27.8304	−	2.43485i	0.881398	−	0.0771123i	0.518862	+	0.854858i	$0.326356\pi$
$998$	−31.2044	+	2.73003i	−0.987757	+	0.0864175i
$999$	−0.686850	+	0.396553i	−0.0217310	+	0.0125464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.b.13.7	✓	120
5.2	odd	4	inner	570.2.bh.b.127.5	yes	120
19.3	odd	18	inner	570.2.bh.b.193.5	yes	120
95.22	even	36	inner	570.2.bh.b.307.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.b.13.7	✓	120	1.1	even	1	trivial
570.2.bh.b.127.5	yes	120	5.2	odd	4	inner
570.2.bh.b.193.5	yes	120	19.3	odd	18	inner
570.2.bh.b.307.7	yes	120	95.22	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-1.60997 + 1.55177i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.201530 - 0.752119i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-1.60997 + 1.55177i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.201530 - 0.752119i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(-1.73909 + 1.40555i) q^{10} +(0.874161 + 1.51409i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-1.68990 + 3.62401i) q^{13} +(-0.135211 - 0.766821i) q^{14} +(0.803319 - 2.08679i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.323295 + 3.69528i) q^{17} +(0.707107 - 0.707107i) q^{18} +(0.822195 + 4.28065i) q^{19} +(-1.85497 + 1.24863i) q^{20} +(0.500507 + 0.596481i) q^{21} +(0.738873 + 1.58452i) q^{22} +(-6.35963 + 4.45306i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(0.183995 - 4.99661i) q^{25} +(-1.99932 + 3.46293i) q^{26} +(-0.258819 + 0.965926i) q^{27} +(-0.0678639 - 0.775688i) q^{28} +(-0.643029 - 0.539566i) q^{29} +(0.982137 - 2.00883i) q^{30} +(-3.62422 - 2.09244i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-1.43214 - 1.00280i) q^{33} +(-0.644129 + 3.65304i) q^{34} +(1.49157 + 0.898159i) q^{35} +(0.766044 - 0.642788i) q^{36} +(0.560810 + 0.560810i) q^{37} +(0.445983 + 4.33602i) q^{38} -3.99865i q^{39} +(-1.95674 + 1.08221i) q^{40} +(-1.42754 + 3.92212i) q^{41} +(0.446616 + 0.637833i) q^{42} +(6.64629 - 9.49188i) q^{43} +(0.597962 + 1.64289i) q^{44} +(0.153860 + 2.23077i) q^{45} +(-6.72354 + 3.88184i) q^{46} +(-4.38652 + 0.383770i) q^{47} +(-0.996195 + 0.0871557i) q^{48} +(5.53711 - 3.19685i) q^{49} +(0.618778 - 4.96156i) q^{50} +(-1.26869 - 3.48569i) q^{51} +(-2.29353 + 3.27550i) q^{52} +(8.05011 + 11.4968i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(-3.75690 - 1.08114i) q^{55} -0.778651i q^{56} +(-2.55424 - 3.53211i) q^{57} +(-0.593556 - 0.593556i) q^{58} +(9.02822 - 7.57557i) q^{59} +(1.15348 - 1.91559i) q^{60} +(-0.375507 + 2.12961i) q^{61} +(-3.42806 - 2.40035i) q^{62} +(-0.705697 - 0.329072i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-2.90295 - 8.45688i) q^{65} +(-1.33929 - 1.12380i) q^{66} +(-0.358004 - 4.09200i) q^{67} +(-0.960061 + 3.58300i) q^{68} +(3.88184 - 6.72354i) q^{69} +(1.40762 + 1.02474i) q^{70} +(13.6241 - 2.40229i) q^{71} +(0.819152 - 0.573576i) q^{72} +(0.562228 + 1.20570i) q^{73} +(0.509799 + 0.607554i) q^{74} +(1.94490 + 4.60623i) q^{75} +(0.0663765 + 4.35839i) q^{76} +(0.962608 - 0.962608i) q^{77} +(0.348505 - 3.98343i) q^{78} +(8.00565 + 2.91382i) q^{79} +(-2.04361 + 0.907549i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-1.76394 + 3.78278i) q^{82} +(9.12186 - 2.44420i) q^{83} +(0.389325 + 0.674331i) q^{84} +(-5.21374 - 6.45096i) q^{85} +(7.44827 - 8.87650i) q^{86} +(0.810813 + 0.217257i) q^{87} +(0.452499 + 1.68875i) q^{88} +(-6.59642 + 2.40090i) q^{89} +(-0.0411495 + 2.23569i) q^{90} +(3.06625 + 0.540662i) q^{91} +(-7.03628 + 3.28107i) q^{92} +(4.16896 + 0.364737i) q^{93} -4.40327 q^{94} +(-7.96631 - 5.61585i) q^{95} -1.00000 q^{96} +(-14.5292 - 1.27114i) q^{97} +(5.79466 - 2.70210i) q^{98} +(1.72176 + 0.303593i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^5 + 12 * q^7	\( 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more