LMFDB - Embedded newform 507.2.t.b.433.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			433.4
Character	$\chi$	$=$	507.433
Dual form			507.2.t.b.322.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.123498 - 1.52980i) q^{2} +(0.845190 - 0.534466i) q^{3} +(-0.350944 + 0.0570339i) q^{4} +(-0.731801 - 0.826032i) q^{5} +(-0.922007 - 1.22697i) q^{6} +(-0.602375 + 0.578589i) q^{7} +(-0.604002 - 2.45053i) q^{8} +(0.428693 - 0.903450i) q^{9} +O(q^{10})$	\(q+(-0.123498 - 1.52980i) q^{2} +(0.845190 - 0.534466i) q^{3} +(-0.350944 + 0.0570339i) q^{4} +(-0.731801 - 0.826032i) q^{5} +(-0.922007 - 1.22697i) q^{6} +(-0.602375 + 0.578589i) q^{7} +(-0.604002 - 2.45053i) q^{8} +(0.428693 - 0.903450i) q^{9} +(-1.17329 + 1.22152i) q^{10} +(5.24852 - 2.49045i) q^{11} +(-0.266132 + 0.235772i) q^{12} +(3.38608 + 1.23872i) q^{13} +(0.959520 + 0.850060i) q^{14} +(-1.06000 - 0.307032i) q^{15} +(-4.34874 + 1.45182i) q^{16} +(-4.41268 - 4.59409i) q^{17} +(-1.43504 - 0.544240i) q^{18} +(-3.82210 + 2.20669i) q^{19} +(0.303933 + 0.248153i) q^{20} +(-0.199885 + 0.810967i) q^{21} +(-4.45809 - 7.72163i) q^{22} +(-3.20742 + 5.55542i) q^{23} +(-1.82022 - 1.74835i) q^{24} +(0.455886 - 3.75456i) q^{25} +(1.47682 - 5.33302i) q^{26} +(-0.120537 - 0.992709i) q^{27} +(0.178401 - 0.237408i) q^{28} +(1.71982 - 0.138839i) q^{29} +(-0.338790 + 1.65950i) q^{30} +(-0.273356 + 0.0331915i) q^{31} +(0.779517 + 1.82959i) q^{32} +(3.10493 - 4.91006i) q^{33} +(-6.48309 + 7.31790i) q^{34} +(0.918752 + 0.0741693i) q^{35} +(-0.0989197 + 0.341510i) q^{36} +(1.31056 - 3.07600i) q^{37} +(3.84782 + 5.57453i) q^{38} +(3.52394 - 0.762791i) q^{39} +(-1.58221 + 2.29223i) q^{40} +(3.85712 + 6.09955i) q^{41} +(1.26530 + 0.205632i) q^{42} +(-2.75176 + 1.17242i) q^{43} +(-1.69989 + 1.17335i) q^{44} +(-1.06000 + 0.307032i) q^{45} +(8.89481 + 4.22064i) q^{46} +(10.0129 - 3.79741i) q^{47} +(-2.89956 + 3.55132i) q^{48} +(-0.253771 + 6.29727i) q^{49} +(-5.80004 - 0.233734i) q^{50} +(-6.18494 - 1.52445i) q^{51} +(-1.25897 - 0.241600i) q^{52} +(-4.80848 + 1.18518i) q^{53} +(-1.50376 + 0.306995i) q^{54} +(-5.89807 - 2.51293i) q^{55} +(1.78169 + 1.12667i) q^{56} +(-2.05100 + 3.90785i) q^{57} +(-0.424791 - 2.61385i) q^{58} +(3.08401 - 9.23774i) q^{59} +(0.389511 + 0.0472952i) q^{60} +(-0.577159 - 1.99258i) q^{61} +(0.0845355 + 0.414082i) q^{62} +(0.264493 + 0.792253i) q^{63} +(-5.41642 + 2.84276i) q^{64} +(-1.45472 - 3.70351i) q^{65} +(-7.89488 - 4.14355i) q^{66} +(-0.924285 + 5.68735i) q^{67} +(1.81062 + 1.36060i) q^{68} +(0.258300 + 6.40964i) q^{69} -1.41467i q^{70} +(4.69681 - 0.189275i) q^{71} +(-2.47287 - 0.504839i) q^{72} +(7.80911 + 5.39024i) q^{73} +(-4.86753 - 1.62502i) q^{74} +(-1.62137 - 3.41697i) q^{75} +(1.21548 - 0.992413i) q^{76} +(-1.72063 + 4.53692i) q^{77} +(-1.60212 - 5.29673i) q^{78} +(4.32645 + 11.4079i) q^{79} +(4.38166 + 2.52975i) q^{80} +(-0.632445 - 0.774605i) q^{81} +(8.85476 - 6.65392i) q^{82} +(-0.413670 - 0.788183i) q^{83} +(0.0238959 - 0.296004i) q^{84} +(-0.565662 + 7.00698i) q^{85} +(2.13340 + 4.06486i) q^{86} +(1.37937 - 1.03653i) q^{87} +(-9.27305 - 11.3574i) q^{88} +(9.21906 + 5.32263i) q^{89} +(0.600606 + 1.58367i) q^{90} +(-2.75640 + 1.21298i) q^{91} +(0.808778 - 2.13257i) q^{92} +(-0.213298 + 0.174153i) q^{93} +(-7.04586 - 14.8488i) q^{94} +(4.61981 + 1.54232i) q^{95} +(1.63670 + 1.12973i) q^{96} +(13.3876 + 2.73310i) q^{97} +(9.66492 - 0.389483i) q^{98} -5.80941i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{37}{78}\right)$

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 $

$2$	−0.123498	−	1.52980i	−0.0873266	−	1.08173i	−0.880914	−	0.473277i	$-0.843071\pi$
$2$	−0.123498	−	1.52980i	−0.0873266	−	1.08173i	0.793587	−	0.608457i	$-0.208211\pi$
$3$	0.845190	−	0.534466i	0.487971	−	0.308574i
$3$	0.845190	−	0.534466i	0.487971	−	0.308574i
$4$	−0.350944	+	0.0570339i	−0.175472	+	0.0285170i
$5$	−0.731801	−	0.826032i	−0.327271	−	0.369413i	0.561728	−	0.827322i	$-0.310137\pi$
$5$	−0.731801	−	0.826032i	−0.327271	−	0.369413i	−0.888999	+	0.457909i	$0.848598\pi$
$6$	−0.922007	−	1.22697i	−0.376408	−	0.500908i
$7$	−0.602375	+	0.578589i	−0.227676	+	0.218686i	−0.797878	−	0.602818i	$-0.794044\pi$
$7$	−0.602375	+	0.578589i	−0.227676	+	0.218686i	0.570202	+	0.821504i	$0.306865\pi$
$8$	−0.604002	−	2.45053i	−0.213547	−	0.866394i
$9$	0.428693	−	0.903450i	0.142898	−	0.301150i
$10$	−1.17329	+	1.22152i	−0.371027	+	0.386280i
$11$	5.24852	−	2.49045i	1.58249	−	0.750900i	0.584327	−	0.811518i	$-0.301359\pi$
$11$	5.24852	−	2.49045i	1.58249	−	0.750900i	0.998161	+	0.0606186i	$0.0193073\pi$
$12$	−0.266132	+	0.235772i	−0.0768256	+	0.0680615i
$13$	3.38608	+	1.23872i	0.939131	+	0.343560i
$13$	3.38608	+	1.23872i	0.939131	+	0.343560i
$14$	0.959520	+	0.850060i	0.256442	+	0.227188i
$15$	−1.06000	−	0.307032i	−0.273690	−	0.0792753i
$16$	−4.34874	+	1.45182i	−1.08718	+	0.362955i
$17$	−4.41268	−	4.59409i	−1.07023	−	1.11423i	−0.993107	−	0.117210i	$-0.962605\pi$
$17$	−4.41268	−	4.59409i	−1.07023	−	1.11423i	−0.0771261	−	0.997021i	$-0.524574\pi$
$18$	−1.43504	−	0.544240i	−0.338243	−	0.128279i
$19$	−3.82210	+	2.20669i	−0.876849	+	0.506249i	−0.869618	−	0.493725i	$-0.835635\pi$
$19$	−3.82210	+	2.20669i	−0.876849	+	0.506249i	−0.00723079	+	0.999974i	$0.502302\pi$
$20$	0.303933	+	0.248153i	0.0679615	+	0.0554888i
$21$	−0.199885	+	0.810967i	−0.0436186	+	0.176967i
$22$	−4.45809	−	7.72163i	−0.950467	−	1.64626i
$23$	−3.20742	+	5.55542i	−0.668794	+	1.15838i	0.309448	+	0.950916i	$0.399856\pi$
$23$	−3.20742	+	5.55542i	−0.668794	+	1.15838i	−0.978242	+	0.207469i	$0.933478\pi$
$24$	−1.82022	−	1.74835i	−0.371551	−	0.356880i
$25$	0.455886	−	3.75456i	0.0911773	−	0.750912i
$26$	1.47682	−	5.33302i	0.289629	−	1.04589i
$27$	−0.120537	−	0.992709i	−0.0231973	−	0.191047i
$28$	0.178401	−	0.237408i	0.0337146	−	0.0448659i
$29$	1.71982	−	0.138839i	0.319363	−	0.0257817i	0.0802544	−	0.996774i	$-0.474427\pi$
$29$	1.71982	−	0.138839i	0.319363	−	0.0257817i	0.239109	+	0.970993i	$0.423145\pi$
$30$	−0.338790	+	1.65950i	−0.0618543	+	0.302983i
$31$	−0.273356	+	0.0331915i	−0.0490963	+	0.00596137i	−0.145048	−	0.989425i	$-0.546334\pi$
$31$	−0.273356	+	0.0331915i	−0.0490963	+	0.00596137i	0.0959517	+	0.995386i	$0.469411\pi$
$32$	0.779517	+	1.82959i	0.137800	+	0.323430i
$33$	3.10493	−	4.91006i	0.540500	−	0.854732i
$34$	−6.48309	+	7.31790i	−1.11184	+	1.25501i
$35$	0.918752	+	0.0741693i	0.155297	+	0.0125369i
$36$	−0.0989197	+	0.341510i	−0.0164866	+	0.0569184i
$37$	1.31056	−	3.07600i	0.215455	−	0.505692i	−0.776824	−	0.629718i	$-0.783170\pi$
$37$	1.31056	−	3.07600i	0.215455	−	0.505692i	0.992279	+	0.124026i	$0.0395807\pi$
$38$	3.84782	+	5.57453i	0.624199	+	0.904308i
$39$	3.52394	−	0.762791i	0.564282	−	0.122144i
$40$	−1.58221	+	2.29223i	−0.250169	+	0.362433i
$41$	3.85712	+	6.09955i	0.602381	+	0.952590i	0.999395	+	0.0347771i	$0.0110721\pi$
$41$	3.85712	+	6.09955i	0.602381	+	0.952590i	−0.397014	+	0.917813i	$0.629954\pi$
$42$	1.26530	+	0.205632i	0.195241	+	0.0317297i
$43$	−2.75176	+	1.17242i	−0.419639	+	0.178792i	−0.591456	−	0.806337i	$-0.701447\pi$
$43$	−2.75176	+	1.17242i	−0.419639	+	0.178792i	0.171816	+	0.985129i	$0.445036\pi$
$44$	−1.69989	+	1.17335i	−0.256269	+	0.176890i
$45$	−1.06000	+	0.307032i	−0.158015	+	0.0457696i
$46$	8.89481	+	4.22064i	1.31147	+	0.622299i
$47$	10.0129	−	3.79741i	1.46054	−	0.553909i	0.508816	−	0.860875i	$-0.330083\pi$
$47$	10.0129	−	3.79741i	1.46054	−	0.553909i	0.951720	+	0.306967i	$0.0993140\pi$
$48$	−2.89956	+	3.55132i	−0.418516	+	0.512588i
$49$	−0.253771	+	6.29727i	−0.0362530	+	0.899610i
$50$	−5.80004	−	0.233734i	−0.820250	−	0.0330549i
$51$	−6.18494	−	1.52445i	−0.866065	−	0.213466i
$52$	−1.25897	−	0.241600i	−0.174588	−	0.0335039i
$53$	−4.80848	+	1.18518i	−0.660496	+	0.162798i	−0.555295	−	0.831653i	$-0.687395\pi$
$53$	−4.80848	+	1.18518i	−0.660496	+	0.162798i	−0.105201	+	0.994451i	$0.533548\pi$
$54$	−1.50376	+	0.306995i	−0.204636	+	0.0417768i
$55$	−5.89807	−	2.51293i	−0.795295	−	0.338844i
$56$	1.78169	+	1.12667i	0.238088	+	0.150558i
$57$	−2.05100	+	3.90785i	−0.271661	+	0.517607i
$58$	−0.424791	−	2.61385i	−0.0557778	−	0.343215i
$59$	3.08401	−	9.23774i	0.401504	−	1.20265i	−0.532821	−	0.846228i	$-0.678868\pi$
$59$	3.08401	−	9.23774i	0.401504	−	1.20265i	0.934325	−	0.356423i	$-0.116004\pi$
$60$	0.389511	+	0.0472952i	0.0502856	+	0.00610578i
$61$	−0.577159	−	1.99258i	−0.0738976	−	0.255124i	0.915061	−	0.403315i	$-0.132142\pi$
$61$	−0.577159	−	1.99258i	−0.0738976	−	0.255124i	−0.988959	+	0.148191i	$0.952655\pi$
$62$	0.0845355	+	0.414082i	0.0107360	+	0.0525885i
$63$	0.264493	+	0.792253i	0.0333230	+	0.0998145i
$64$	−5.41642	+	2.84276i	−0.677052	+	0.355345i
$65$	−1.45472	−	3.70351i	−0.180435	−	0.459364i
$66$	−7.89488	−	4.14355i	−0.971792	−	0.510036i
$67$	−0.924285	+	5.68735i	−0.112919	+	0.694821i	0.867431	+	0.497557i	$0.165770\pi$
$67$	−0.924285	+	5.68735i	−0.112919	+	0.694821i	−0.980351	+	0.197263i	$0.936795\pi$
$68$	1.81062	+	1.36060i	0.219570	+	0.164996i
$69$	0.258300	+	6.40964i	0.0310956	+	0.771630i
$70$		−	1.41467i		−	0.169085i
$71$	4.69681	−	0.189275i	0.557409	−	0.0224628i	0.240037	−	0.970764i	$-0.422841\pi$
$71$	4.69681	−	0.189275i	0.557409	−	0.0224628i	0.317372	+	0.948301i	$0.397200\pi$
$72$	−2.47287	−	0.504839i	−0.291430	−	0.0594959i
$73$	7.80911	+	5.39024i	0.913988	+	0.630880i	0.929429	−	0.369001i	$-0.120300\pi$
$73$	7.80911	+	5.39024i	0.913988	+	0.630880i	−0.0154415	+	0.999881i	$0.504915\pi$
$74$	−4.86753	−	1.62502i	−0.565839	−	0.188905i
$75$	−1.62137	−	3.41697i	−0.187220	−	0.394558i
$76$	1.21548	−	0.992413i	0.139426	−	0.113838i
$77$	−1.72063	+	4.53692i	−0.196084	+	0.517030i
$78$	−1.60212	−	5.29673i	−0.181405	−	0.599736i
$79$	4.32645	+	11.4079i	0.486764	+	1.28349i	0.923396	+	0.383850i	$0.125402\pi$
$79$	4.32645	+	11.4079i	0.486764	+	1.28349i	−0.436632	+	0.899640i	$0.643829\pi$
$80$	4.38166	+	2.52975i	0.489885	+	0.282835i
$81$	−0.632445	−	0.774605i	−0.0702717	−	0.0860672i
$82$	8.85476	−	6.65392i	0.977845	−	0.734803i
$83$	−0.413670	−	0.788183i	−0.0454062	−	0.0865143i	0.861696	−	0.507425i	$-0.169403\pi$
$83$	−0.413670	−	0.788183i	−0.0454062	−	0.0865143i	−0.907102	+	0.420911i	$0.861710\pi$
$84$	0.0238959	−	0.296004i	0.00260726	−	0.0322967i
$85$	−0.565662	+	7.00698i	−0.0613547	+	0.760014i
$86$	2.13340	+	4.06486i	0.230051	+	0.438325i
$87$	1.37937	−	1.03653i	0.147884	−	0.111128i
$88$	−9.27305	−	11.3574i	−0.988510	−	1.21071i
$89$	9.21906	+	5.32263i	0.977219	+	0.564197i	0.901429	−	0.432926i	$-0.142519\pi$
$89$	9.21906	+	5.32263i	0.977219	+	0.564197i	0.0757894	+	0.997124i	$0.475852\pi$
$90$	0.600606	+	1.58367i	0.0633094	+	0.166933i
$91$	−2.75640	+	1.21298i	−0.288950	+	0.127155i
$92$	0.808778	−	2.13257i	0.0843209	−	0.222336i
$93$	−0.213298	+	0.174153i	−0.0221180	+	0.0180588i
$94$	−7.04586	−	14.8488i	−0.726725	−	1.53154i
$95$	4.61981	+	1.54232i	0.473982	+	0.158239i
$96$	1.63670	+	1.12973i	0.167045	+	0.115303i
$97$	13.3876	+	2.73310i	1.35931	+	0.277504i	0.823730	−	0.566983i	$-0.191889\pi$
$97$	13.3876	+	2.73310i	1.35931	+	0.277504i	0.535576	+	0.844487i	$0.320094\pi$
$98$	9.66492	−	0.389483i	0.976304	−	0.0393437i
$99$		−	5.80941i		−	0.583868i
$100$	0.0541469	+	1.34364i	0.00541469	+	0.134364i
$101$	12.5366	+	9.42066i	1.24744	+	0.937391i	0.999507	−	0.0313864i	$-0.00999225\pi$
$101$	12.5366	+	9.42066i	1.24744	+	0.937391i	0.247933	+	0.968777i	$0.420249\pi$
$102$	−1.56828	+	9.65001i	−0.155283	+	0.955493i
$103$	5.84461	+	3.06749i	0.575887	+	0.302249i	0.727408	−	0.686205i	$-0.240725\pi$
$103$	5.84461	+	3.06749i	0.575887	+	0.302249i	−0.151521	+	0.988454i	$0.548417\pi$
$104$	0.990325	−	9.04590i	0.0971093	−	0.887023i
$105$	0.816161	−	0.428354i	0.0796492	−	0.0418031i
$106$	2.40694	+	7.20966i	0.233782	+	0.700264i
$107$	0.112589	+	0.551498i	0.0108844	+	0.0533153i	0.984870	−	0.173294i	$-0.0554411\pi$
$107$	0.112589	+	0.551498i	0.0108844	+	0.0533153i	−0.973986	+	0.226609i	$0.927236\pi$
$108$	0.0989197	+	0.341510i	0.00951855	+	0.0328619i
$109$	−10.6111	−	1.28843i	−1.01636	−	0.123409i	−0.404636	−	0.914478i	$-0.632602\pi$
$109$	−10.6111	−	1.28843i	−1.01636	−	0.123409i	−0.611727	+	0.791069i	$0.709525\pi$
$110$	−3.11589	+	9.33322i	−0.297088	+	0.889887i
$111$	−0.536344	−	3.30026i	−0.0509075	−	0.313247i
$112$	1.77956	−	3.39067i	0.168153	−	0.320389i
$113$	−16.2662	−	10.2861i	−1.53019	−	0.967636i	−0.992196	−	0.124691i	$-0.960206\pi$
$113$	−16.2662	−	10.2861i	−1.53019	−	0.967636i	−0.537999	−	0.842945i	$-0.680820\pi$
$114$	6.23154	+	2.65501i	0.583637	+	0.248664i
$115$	6.93615	−	1.41603i	0.646799	−	0.132045i
$116$	−0.595643	+	0.146813i	−0.0553041	+	0.0136312i
$117$	2.57071	−	2.52813i	0.237662	−	0.233726i
$118$	−14.5128	−	3.57708i	−1.33601	−	0.329297i
$119$	5.31618	+	0.214235i	0.487334	+	0.0196389i
$120$	−0.112151	+	2.78300i	−0.0102380	+	0.254052i
$121$	14.3877	−	17.6217i	1.30797	−	1.60197i
$122$	−2.97698	+	1.12902i	−0.269523	+	0.102217i
$123$	6.52000	+	3.09378i	0.587889	+	0.278957i
$124$	0.0940397	−	0.0272389i	0.00844502	−	0.00244613i
$125$	−7.97610	+	5.50550i	−0.713404	+	0.492427i
$126$	1.17933	−	0.502464i	0.105063	−	0.0447630i
$127$	3.05230	+	0.496048i	0.270848	+	0.0440171i	0.294318	−	0.955707i	$-0.404907\pi$
$127$	3.05230	+	0.496048i	0.270848	+	0.0440171i	−0.0234702	+	0.999725i	$0.507471\pi$
$128$	7.14360	+	11.2967i	0.631411	+	0.998496i
$129$	−1.69914	+	2.46164i	−0.149601	+	0.216735i
$130$	−5.48599	+	2.68281i	−0.481153	+	0.235298i
$131$	−2.94575	−	4.26766i	−0.257372	−	0.372867i	0.672903	−	0.739731i	$-0.265047\pi$
$131$	−2.94575	−	4.26766i	−0.257372	−	0.372867i	−0.930275	+	0.366863i	$0.880432\pi$
$132$	−0.809617	+	1.90024i	−0.0704681	+	0.165395i
$133$	1.02557	−	3.54068i	0.0889282	−	0.307016i
$134$	8.81468	+	0.711594i	0.761472	+	0.0614724i
$135$	−0.731801	+	0.826032i	−0.0629834	+	0.0710935i
$136$	−8.59270	+	13.5883i	−0.736818	+	1.16518i
$137$	−6.13658	−	14.4031i	−0.524284	−	1.23054i	−0.946105	−	0.323860i	$-0.895019\pi$
$137$	−6.13658	−	14.4031i	−0.524284	−	1.23054i	0.421822	−	0.906679i	$-0.361391\pi$
$138$	9.77359	−	1.18673i	0.831983	−	0.101021i
$139$	0.627448	−	3.07344i	0.0532194	−	0.260686i	−0.944472	−	0.328591i	$-0.893426\pi$
$139$	0.627448	−	3.07344i	0.0532194	−	0.260686i	0.997692	+	0.0679049i	$0.0216314\pi$
$140$	−0.326661	+	0.0263708i	−0.0276079	+	0.00222874i
$141$	6.43325	−	8.56110i	0.541777	−	0.720975i
$142$	−0.869602	−	7.16182i	−0.0729754	−	0.601006i
$143$	20.8569	−	1.93143i	1.74414	−	0.161514i
$144$	−0.552622	+	4.55125i	−0.0460519	+	0.379271i
$145$	−1.37325	−	1.31903i	−0.114043	−	0.109539i
$146$	7.28159	−	12.6121i	0.602629	−	1.04378i
$147$	3.15119	+	5.45802i	0.259906	+	0.450170i
$148$	−0.284497	+	1.15425i	−0.0233855	+	0.0948788i
$149$	−0.850675	−	0.694554i	−0.0696900	−	0.0569001i	0.596960	−	0.802271i	$-0.296375\pi$
$149$	−0.850675	−	0.694554i	−0.0696900	−	0.0569001i	−0.666650	+	0.745371i	$0.732272\pi$
$150$	−5.02706	+	2.90237i	−0.410458	+	0.236978i
$151$	11.0462	+	4.18927i	0.898926	+	0.340918i	0.760411	−	0.649443i	$-0.224998\pi$
$151$	11.0462	+	4.18927i	0.898926	+	0.340918i	0.138515	+	0.990360i	$0.455767\pi$
$152$	7.71611	+	8.03332i	0.625859	+	0.651589i
$153$	−6.04222	+	2.01719i	−0.488484	+	0.163080i
$154$	7.15309	+	2.07192i	0.576413	+	0.166960i
$155$	0.227460	+	0.201512i	0.0182700	+	0.0161858i
$156$	−1.19320	+	0.468681i	−0.0955324	+	0.0375245i
$157$	−1.95152	+	1.72890i	−0.155748	+	0.137981i	−0.737398	−	0.675458i	$-0.763946\pi$
$157$	−1.95152	+	1.72890i	−0.155748	+	0.137981i	0.581650	+	0.813439i	$0.302407\pi$
$158$	16.9175	−	8.02747i	1.34589	−	0.638631i
$159$	−3.43064	+	3.57167i	−0.272067	+	0.283252i
$160$	0.940852	−	1.98280i	0.0743809	−	0.156754i
$161$	−1.28223	−	5.20223i	−0.101054	−	0.409993i
$162$	−1.10689	+	1.06318i	−0.0869652	+	0.0835312i
$163$	−4.44388	−	5.91373i	−0.348072	−	0.463199i	0.591124	−	0.806580i	$-0.298684\pi$
$163$	−4.44388	−	5.91373i	−0.348072	−	0.463199i	−0.939196	+	0.343381i	$0.888428\pi$
$164$	−1.70151	−	1.92061i	−0.132866	−	0.149975i
$165$	−6.32806	+	1.02841i	−0.492639	+	0.0800616i
$166$	−1.15468	+	0.730173i	−0.0896203	+	0.0566724i
$167$	1.89038	+	23.4166i	0.146282	+	1.81203i	0.488669	+	0.872469i	$0.337483\pi$
$167$	1.89038	+	23.4166i	0.146282	+	1.81203i	−0.342387	+	0.939559i	$0.611235\pi$
$168$	2.10803			0.162638
$169$	9.93114	+	8.38883i	0.763934	+	0.645295i
$170$	10.7892			0.827491
$171$	0.355129	+	4.39907i	0.0271574	+	0.336405i
$172$	0.898846	−	0.568396i	0.0685363	−	0.0433398i
$173$	−0.772784	+	0.125590i	−0.0587537	+	0.00954840i	−0.189717	−	0.981839i	$-0.560757\pi$
$173$	−0.772784	+	0.125590i	−0.0587537	+	0.00954840i	0.130963	+	0.991387i	$0.458193\pi$
$174$	−1.75604	−	1.98216i	−0.133125	−	0.150267i
$175$	1.89773	+	2.52543i	0.143455	+	0.190904i
$176$	−19.2087	+	18.4502i	−1.44791	+	1.39074i
$177$	−2.33068	−	9.45594i	−0.175185	−	0.710752i
$178$	7.00403	−	14.7607i	0.524974	−	1.10636i
$179$	−15.4677	+	16.1036i	−1.15611	+	1.20364i	−0.180628	+	0.983551i	$0.557813\pi$
$179$	−15.4677	+	16.1036i	−1.15611	+	1.20364i	−0.975481	+	0.220086i	$0.929366\pi$
$180$	0.354488	−	0.168207i	0.0264220	−	0.0125374i
$181$	5.17649	−	4.58597i	0.384765	−	0.340872i	−0.448463	−	0.893801i	$-0.648028\pi$
$181$	5.17649	−	4.58597i	0.384765	−	0.340872i	0.833228	+	0.552929i	$0.186490\pi$
$182$	2.19603	+	4.06695i	0.162780	+	0.301463i
$183$	−1.55278	−	1.37564i	−0.114785	−	0.101690i
$184$	15.5510	+	4.50441i	1.14644	+	0.332069i
$185$	−3.49995	+	1.16845i	−0.257321	+	0.0859065i
$186$	0.292761	+	0.304797i	0.0214663	+	0.0223488i
$187$	−34.6014	−	13.1226i	−2.53031	−	0.959619i
$188$	−3.29740	+	1.90375i	−0.240487	+	0.138845i
$189$	0.646979	+	0.528242i	0.0470608	+	0.0384239i
$190$	1.78890	−	7.25787i	0.129781	−	0.526541i
$191$	−6.21862	−	10.7710i	−0.449963	−	0.779359i	0.548420	−	0.836203i	$-0.315230\pi$
$191$	−6.21862	−	10.7710i	−0.449963	−	0.779359i	−0.998383	+	0.0568438i	$0.981896\pi$
$192$	−3.05855	+	5.29756i	−0.220732	+	0.382319i
$193$	−12.3644	−	11.8762i	−0.890012	−	0.854868i	0.100125	−	0.994975i	$-0.468076\pi$
$193$	−12.3644	−	11.8762i	−0.890012	−	0.854868i	−0.990136	+	0.140107i	$0.955255\pi$
$194$	2.52776	−	20.8179i	0.181482	−	1.49464i
$195$	−3.20891	−	2.35268i	−0.229795	−	0.168479i
$196$	−0.270098	−	2.22446i	−0.0192927	−	0.158890i
$197$	−13.3869	+	17.8147i	−0.953776	+	1.26925i	0.00928300	+	0.999957i	$0.497045\pi$
$197$	−13.3869	+	17.8147i	−0.953776	+	1.26925i	−0.963059	+	0.269289i	$0.913211\pi$
$198$	−8.88726	+	0.717454i	−0.631590	+	0.0509872i
$199$	−3.07274	+	15.0513i	−0.217821	+	1.06696i	0.712910	+	0.701255i	$0.247377\pi$
$199$	−3.07274	+	15.0513i	−0.217821	+	1.06696i	−0.930732	+	0.365703i	$0.880829\pi$
$200$	−9.47603	+	1.15060i	−0.670057	+	0.0813596i
$201$	2.25850	+	5.30089i	0.159302	+	0.373896i
$202$	12.8635	−	20.3420i	0.905073	−	1.43126i
$203$	−0.955649	+	1.07870i	−0.0670734	+	0.0757102i
$204$	2.25751	+	0.182245i	0.158058	+	0.0127597i
$205$	2.21578	−	7.64976i	0.154757	−	0.534283i
$206$	3.97085	−	9.31993i	0.276662	−	0.649350i
$207$	3.64405	+	5.27931i	0.253279	+	0.366938i
$208$	−16.5236	−	0.470882i	−1.14571	−	0.0326498i
$209$	−14.5647	+	21.1006i	−1.00746	+	1.45956i
$210$	−0.756092	−	1.19566i	−0.0521753	−	0.0825087i
$211$	26.9357	+	4.37748i	1.85433	+	0.301358i	0.982189	−	0.187895i	$-0.0601663\pi$
$211$	26.9357	+	4.37748i	1.85433	+	0.301358i	0.872142	+	0.489253i	$0.162730\pi$
$212$	1.61991	−	0.690180i	0.111256	−	0.0474017i
$213$	3.86854	−	2.67026i	0.265068	−	0.182963i
$214$	0.829778	−	0.240348i	0.0567225	−	0.0164299i
$215$	2.98219	+	1.41507i	0.203384	+	0.0965069i
$216$	−2.35986	+	0.894977i	−0.160568	+	0.0608955i
$217$	0.145459	−	0.178155i	0.00987439	−	0.0120939i
$218$	−0.660578	+	16.3921i	−0.0447400	+	1.11021i
$219$	9.48109	+	0.382075i	0.640672	+	0.0258182i
$220$	2.21321	+	0.545508i	0.149215	+	0.0367781i
$221$	−9.25092	−	21.0221i	−0.622285	−	1.41410i
$222$	−4.98251	+	1.22808i	−0.334404	+	0.0824232i
$223$	12.8163	−	2.61648i	0.858246	−	0.175212i	0.249302	−	0.968426i	$-0.419799\pi$
$223$	12.8163	−	2.61648i	0.858246	−	0.175212i	0.608944	+	0.793214i	$0.291594\pi$
$224$	−1.52814	−	0.651082i	−0.102103	−	0.0435022i
$225$	−3.19663	−	2.02142i	−0.213108	−	0.134762i
$226$	−13.7269	+	26.1544i	−0.913098	+	1.73976i
$227$	−1.08567	−	6.68037i	−0.0720582	−	0.443392i	−0.997860	−	0.0653831i	$-0.979173\pi$
$227$	−1.08567	−	6.68037i	−0.0720582	−	0.443392i	0.925802	−	0.378009i	$-0.123391\pi$
$228$	0.496905	−	1.48841i	0.0329083	−	0.0985725i
$229$	−6.73102	−	0.817294i	−0.444798	−	0.0540083i	−0.104926	−	0.994480i	$-0.533461\pi$
$229$	−6.73102	−	0.817294i	−0.444798	−	0.0540083i	−0.339872	+	0.940472i	$0.610384\pi$
$230$	−3.02284	−	10.4361i	−0.199320	−	0.688134i
$231$	0.970573	+	4.75418i	0.0638590	+	0.312802i
$232$	−1.37901	−	4.13063i	−0.0905362	−	0.271189i
$233$	−23.9661	+	12.5784i	−1.57007	+	0.824038i	−0.570077	+	0.821591i	$0.693087\pi$
$233$	−23.9661	+	12.5784i	−1.57007	+	0.824038i	−0.999997	+	0.00244702i	$0.999221\pi$
$234$	−4.18502	−	3.62046i	−0.273583	−	0.236677i
$235$	−10.4643	−	5.49206i	−0.682613	−	0.358263i
$236$	−0.555450	+	3.41782i	−0.0361567	+	0.222481i
$237$	9.75381	+	7.32951i	0.633578	+	0.476103i
$238$	−0.328803	−	8.15917i	−0.0213132	−	0.528880i
$239$		−	8.15647i		−	0.527598i	−0.964578	−	0.263799i	$-0.915024\pi$
$239$		−	8.15647i		−	0.527598i	0.964578	−	0.263799i	$-0.0849756\pi$
$240$	5.05540	−	0.203726i	0.326325	−	0.0131504i
$241$	3.21301	+	0.655940i	0.206968	+	0.0422528i	0.302391	−	0.953184i	$-0.402215\pi$
$241$	3.21301	+	0.655940i	0.206968	+	0.0422528i	−0.0954229	+	0.995437i	$0.530420\pi$
$242$	−28.7346	−	19.8341i	−1.84713	−	1.27498i
$243$	−0.948536	−	0.316668i	−0.0608486	−	0.0203143i
$244$	0.316195	+	0.666367i	0.0202423	+	0.0426598i
$245$	5.38746	−	4.39872i	0.344192	−	0.281024i
$246$	3.92766	−	10.3564i	0.250419	−	0.660300i
$247$	−15.6754	+	2.73752i	−0.997403	+	0.174184i
$248$	0.246445	+	0.649821i	0.0156492	+	0.0412637i
$249$	−0.770887	−	0.445072i	−0.0488530	−	0.0282053i
$250$	9.40737	+	11.5219i	0.594974	+	0.728711i
$251$	−3.81996	+	2.87051i	−0.241114	+	0.181185i	−0.714429	−	0.699708i	$-0.753314\pi$
$251$	−3.81996	+	2.87051i	−0.241114	+	0.181185i	0.473315	+	0.880893i	$0.343057\pi$
$252$	−0.138007	−	0.262951i	−0.00869365	−	0.0165644i
$253$	−2.99871	+	37.1457i	−0.188527	+	2.33533i
$254$	0.381900	−	4.73069i	0.0239626	−	0.296830i
$255$	3.26690	+	6.22456i	0.204581	+	0.389797i
$256$	6.61895	−	4.97382i	0.413684	−	0.310864i
$257$	−18.9400	−	23.1972i	−1.18144	−	1.44700i	−0.867412	−	0.497590i	$-0.834218\pi$
$257$	−18.9400	−	23.1972i	−1.18144	−	1.44700i	−0.314030	−	0.949413i	$-0.601679\pi$
$258$	3.97566	+	2.29535i	0.247514	+	0.142902i
$259$	0.990292	+	2.61119i	0.0615337	+	0.162251i
$260$	0.721749	+	1.21676i	0.0447610	+	0.0754601i
$261$	0.611842	−	1.61330i	0.0378721	−	0.0998605i
$262$	−6.16488	+	5.03347i	−0.380868	+	0.310969i
$263$	−2.98136	−	6.28308i	−0.183838	−	0.387431i	0.790519	−	0.612438i	$-0.209811\pi$
$263$	−2.98136	−	6.28308i	−0.183838	−	0.387431i	−0.974357	+	0.225006i	$0.927760\pi$
$264$	−13.9076	−	4.64305i	−0.855956	−	0.285760i
$265$	4.49785	+	3.10464i	0.276301	+	0.190717i
$266$	−5.54319	−	1.13165i	−0.339875	−	0.0693860i
$267$	10.6366	−	0.428641i	0.650951	−	0.0262324i
$268$		−	2.04866i		−	0.125142i
$269$	0.130204	+	3.23099i	0.00793870	+	0.196997i	0.998292	+	0.0584285i	$0.0186090\pi$
$269$	0.130204	+	3.23099i	0.00793870	+	0.196997i	−0.990353	+	0.138568i	$0.955750\pi$
$270$	1.35404	+	1.01750i	0.0824044	+	0.0619229i
$271$	1.20759	−	7.43061i	0.0733559	−	0.451377i	−0.924224	−	0.381850i	$-0.875287\pi$
$271$	1.20759	−	7.43061i	0.0733559	−	0.451377i	0.997580	−	0.0695268i	$-0.0221490\pi$
$272$	25.8594	+	13.5721i	1.56796	+	0.822927i
$273$	−1.68139	+	2.49840i	−0.101762	+	0.151210i
$274$	−21.2760	+	11.1665i	−1.28533	+	0.674594i
$275$	−6.95783	−	20.8413i	−0.419573	−	1.25677i
$276$	−0.456216	−	2.23469i	−0.0274610	−	0.134513i
$277$	−7.44774	−	25.7126i	−0.447491	−	1.54492i	−0.794623	−	0.607103i	$-0.792332\pi$
$277$	−7.44774	−	25.7126i	−0.447491	−	1.54492i	0.347132	−	0.937816i	$-0.387156\pi$
$278$	−4.77925	−	0.580306i	−0.286640	−	0.0348044i
$279$	−0.0871990	+	0.261193i	−0.00522047	+	0.0156372i
$280$	−0.373174	−	2.29623i	−0.0223014	−	0.137226i
$281$	−11.8878	+	22.6503i	−0.709167	+	1.35121i	0.217774	+	0.975999i	$0.430121\pi$
$281$	−11.8878	+	22.6503i	−0.709167	+	1.35121i	−0.926941	+	0.375206i	$0.877572\pi$
$282$	−13.8913	−	8.78432i	−0.827214	−	0.523099i
$283$	2.56285	+	1.09193i	0.152346	+	0.0649085i	0.466794	−	0.884366i	$-0.345409\pi$
$283$	2.56285	+	1.09193i	0.152346	+	0.0649085i	−0.314448	+	0.949275i	$0.601819\pi$
$284$	−1.63752	+	0.334302i	−0.0971690	+	0.0198372i
$285$	4.72893	−	1.16558i	0.280118	−	0.0690428i
$286$	−5.53051	−	31.6684i	−0.327026	−	1.87259i
$287$	−5.85257	−	1.44253i	−0.345466	−	0.0851498i
$288$	1.98712	+	0.0800782i	0.117092	+	0.00471865i
$289$	−0.949369	+	23.5583i	−0.0558452	+	1.38578i
$290$	−1.84826	+	2.26371i	−0.108533	+	0.132929i
$291$	12.7758	−	4.84523i	0.748932	−	0.284033i
$292$	−3.04799	−	1.44629i	−0.178370	−	0.0846376i
$293$	5.85115	−	1.69481i	0.341828	−	0.0990116i	−0.102864	−	0.994695i	$-0.532801\pi$
$293$	5.85115	−	1.69481i	0.341828	−	0.0990116i	0.444691	+	0.895684i	$0.353313\pi$
$294$	7.96053	−	5.49475i	0.464267	−	0.320461i
$295$	−9.88755	+	4.21269i	−0.575676	+	0.245272i
$296$	−8.32943	−	1.35366i	−0.484138	−	0.0786801i
$297$	−3.10493	−	4.91006i	−0.180167	−	0.284911i
$298$	−0.957474	+	1.38714i	−0.0554650	+	0.0803549i
$299$	−17.7422	+	14.8380i	−1.02606	+	0.858105i
$300$	0.763895	+	1.10669i	0.0441035	+	0.0638949i
$301$	0.979245	−	2.29837i	0.0564427	−	0.132476i
$302$	5.04456	−	17.4159i	0.290282	−	1.00217i
$303$	15.6308	+	1.26185i	0.897969	+	0.0724915i
$304$	13.4176	−	15.1453i	0.769551	−	0.868643i
$305$	−1.22357	+	1.93493i	−0.0700616	+	0.110794i
$306$	3.83211	+	8.99428i	0.219067	+	0.514169i
$307$	12.5638	−	1.52552i	0.717053	−	0.0870660i	0.246125	−	0.969238i	$-0.420843\pi$
$307$	12.5638	−	1.52552i	0.717053	−	0.0870660i	0.470927	+	0.882172i	$0.343919\pi$
$308$	0.345085	−	1.69034i	0.0196631	−	0.0963160i
$309$	6.57927	−	0.531134i	0.374282	−	0.0302152i
$310$	0.280182	−	0.372855i	0.0159133	−	0.0211767i
$311$	−0.601792	−	4.95620i	−0.0341245	−	0.281040i	−0.999775	−	0.0211972i	$-0.993252\pi$
$311$	−0.601792	−	4.95620i	−0.0341245	−	0.281040i	0.965651	−	0.259843i	$-0.0836709\pi$
$312$	−3.99771	−	8.17480i	−0.226326	−	0.462807i
$313$	−2.99850	+	24.6948i	−0.169485	+	1.39583i	0.621220	+	0.783637i	$0.286638\pi$
$313$	−2.99850	+	24.6948i	−0.169485	+	1.39583i	−0.790705	+	0.612198i	$0.790286\pi$
$314$	2.88588	+	2.77193i	0.162860	+	0.156429i
$315$	0.460871	−	0.798251i	0.0259671	−	0.0449764i
$316$	−2.16898	−	3.75678i	−0.122015	−	0.211335i
$317$	6.93509	−	28.1368i	0.389513	−	1.58032i	−0.369492	−	0.929234i	$-0.620468\pi$
$317$	6.93509	−	28.1368i	0.389513	−	1.58032i	0.759006	−	0.651084i	$-0.225686\pi$
$318$	5.88764	+	4.80711i	0.330162	+	0.269569i
$319$	8.68076	−	5.01184i	0.486029	−	0.280609i
$320$	6.31195	+	2.39381i	0.352849	+	0.133818i
$321$	0.389916	+	0.405945i	0.0217630	+	0.0226577i
$322$	−7.80003	+	2.60403i	−0.434678	+	0.145117i
$323$	27.0034	+	7.82164i	1.50251	+	0.435208i
$324$	0.266132	+	0.235772i	0.0147851	+	0.0130984i
$325$	6.19453	−	12.1485i	0.343610	−	0.673880i
$326$	−8.49803	+	7.52860i	−0.470663	+	0.416971i
$327$	−9.65705	+	4.58233i	−0.534036	+	0.253403i
$328$	12.6174	−	13.1361i	0.696681	−	0.725322i
$329$	−3.83441	+	8.08084i	−0.211398	+	0.445511i
$330$	2.35477	+	9.55368i	0.129626	+	0.525913i
$331$	−6.25184	+	6.00498i	−0.343632	+	0.330063i	−0.844595	−	0.535406i	$-0.820159\pi$
$331$	−6.25184	+	6.00498i	−0.343632	+	0.330063i	0.500963	+	0.865469i	$0.332979\pi$
$332$	0.190128	+	0.253015i	0.0104346	+	0.0138860i
$333$	−2.21719	−	2.50269i	−0.121501	−	0.137146i
$334$	35.5893	−	5.78382i	1.94736	−	0.316476i
$335$	5.37433	−	3.39852i	0.293631	−	0.185681i
$336$	−0.308130	−	3.81688i	−0.0168099	−	0.208228i
$337$	−31.0468			−1.69123			−0.845615	−	0.533794i	$-0.820766\pi$
$337$	−31.0468			−1.69123			−0.845615	+	0.533794i	$0.820766\pi$
$338$	11.6068	−	16.2287i	0.631325	−	0.882724i
$339$	−19.2456			−1.04528
$340$	−0.201120	−	2.49132i	−0.0109073	−	0.135111i
$341$	−1.35205	+	0.854987i	−0.0732179	+	0.0463002i
$342$	6.68584	−	1.08656i	0.361529	−	0.0587542i
$343$	−7.36772	−	8.31644i	−0.397819	−	0.449045i
$344$	4.53511	+	6.03513i	0.244517	+	0.325393i
$345$	5.10555	−	4.90395i	0.274874	−	0.264020i
$346$	0.287565	+	1.16670i	0.0154596	+	0.0627220i
$347$	−7.86548	+	16.5761i	−0.422241	+	0.889854i	0.575176	+	0.818029i	$0.304933\pi$
$347$	−7.86548	+	16.5761i	−0.422241	+	0.889854i	−0.997417	+	0.0718245i	$0.977118\pi$
$348$	−0.424965	+	0.442436i	−0.0227805	+	0.0237170i
$349$	−14.6052	+	6.93026i	−0.781800	+	0.370969i	−0.777388	−	0.629022i	$-0.783456\pi$
$349$	−14.6052	+	6.93026i	−0.781800	+	0.370969i	−0.00441191	+	0.999990i	$0.501404\pi$
$350$	3.62904	−	3.21505i	0.193980	−	0.171851i
$351$	0.821542	−	3.51071i	0.0438507	−	0.187388i
$352$	8.64783	+	7.66131i	0.460931	+	0.408349i
$353$	−25.3324	−	7.33761i	−1.34831	−	0.390542i	−0.475976	−	0.879458i	$-0.657905\pi$
$353$	−25.3324	−	7.33761i	−1.34831	−	0.390542i	−0.872331	+	0.488917i	$0.837392\pi$
$354$	−14.1779	+	4.73328i	−0.753546	+	0.251571i
$355$	−3.59348	−	3.74121i	−0.190722	−	0.198563i
$356$	−3.53894	−	1.34214i	−0.187564	−	0.0711335i
$357$	4.60769	−	2.66025i	0.243865	−	0.140795i
$358$	26.5455	+	21.6737i	1.40297	+	1.14549i
$359$	−0.543252	+	2.20406i	−0.0286718	+	0.116326i	−0.983534	−	0.180723i	$-0.942156\pi$
$359$	−0.543252	+	2.20406i	−0.0286718	+	0.116326i	0.954862	+	0.297049i	$0.0960024\pi$
$360$	1.39263	+	2.41211i	0.0733981	+	0.127129i
$361$	0.238945	−	0.413865i	0.0125761	−	0.0217824i
$362$	−7.65492	−	7.35265i	−0.402333	−	0.386447i
$363$	2.74213	−	22.5834i	0.143924	−	1.18532i
$364$	0.898162	−	0.582895i	0.0470765	−	0.0305520i
$365$	−1.26220	−	10.3952i	−0.0660666	−	0.544108i
$366$	−1.91269	+	2.54533i	−0.0999781	+	0.133047i
$367$	14.2638	−	1.15149i	0.744563	−	0.0601073i	0.297638	−	0.954679i	$-0.403801\pi$
$367$	14.2638	−	1.15149i	0.744563	−	0.0601073i	0.446925	+	0.894571i	$0.352519\pi$
$368$	5.88276	−	28.8157i	0.306660	−	1.50212i
$369$	7.16416	−	0.869887i	0.372951	−	0.0452845i
$370$	2.21974	+	5.20993i	0.115399	+	0.270851i
$371$	2.21077	−	3.49606i	0.114778	−	0.181506i
$372$	0.0649232	−	0.0732831i	0.00336611	−	0.00379955i
$373$	−6.28673	−	0.507517i	−0.325515	−	0.0262783i	−0.0833707	−	0.996519i	$-0.526569\pi$
$373$	−6.28673	−	0.507517i	−0.325515	−	0.0262783i	−0.242144	+	0.970240i	$0.577851\pi$
$374$	−15.8018	+	54.5540i	−0.817089	+	2.82092i
$375$	−3.79882	+	8.91615i	−0.196170	+	0.460428i
$376$	−15.3535	−	22.2434i	−0.791796	−	1.14711i
$377$	5.99545	+	1.66026i	0.308782	+	0.0855080i
$378$	0.728205	−	1.05499i	0.0374548	−	0.0542627i
$379$	9.38734	+	14.8449i	0.482195	+	0.762531i	0.995407	−	0.0957310i	$-0.0305189\pi$
$379$	9.38734	+	14.8449i	0.482195	+	0.762531i	−0.513212	+	0.858262i	$0.671545\pi$
$380$	−1.70926	−	0.277781i	−0.0876831	−	0.0142499i
$381$	2.84490	−	1.21210i	0.145749	−	0.0620977i
$382$	−15.7095	+	10.8435i	−0.803766	+	0.554799i
$383$	−29.7537	+	8.61826i	−1.52034	+	0.440372i	−0.930238	−	0.366956i	$-0.880400\pi$
$383$	−29.7537	+	8.61826i	−1.52034	+	0.440372i	−0.590103	+	0.807328i	$0.700913\pi$
$384$	12.0754	+	5.72985i	0.616220	+	0.292400i
$385$	5.00680	−	1.89883i	0.255170	−	0.0967733i
$386$	−16.6413	+	20.3818i	−0.847018	+	1.03741i
$387$	−0.120440	+	2.98868i	−0.00612230	+	0.151923i
$388$	−4.85418	−	0.195617i	−0.246434	−	0.00993094i
$389$	36.7271	+	9.05241i	1.86214	+	0.458975i	0.998946	−	0.0459040i	$-0.0146168\pi$
$389$	36.7271	+	9.05241i	1.86214	+	0.458975i	0.863190	+	0.504879i	$0.168463\pi$
$390$	−3.20284	+	5.19955i	−0.162182	+	0.263290i
$391$	39.6755	−	9.77912i	2.00647	−	0.494551i
$392$	15.5849	−	3.18169i	0.787158	−	0.160699i
$393$	−4.77064	−	2.03258i	−0.240647	−	0.102530i
$394$	28.9063	+	18.2792i	1.45628	+	0.920893i
$395$	6.25720	−	11.9221i	0.314834	−	0.599866i
$396$	0.331334	+	2.03878i	0.0166501	+	0.102452i
$397$	−8.66410	+	25.9522i	−0.434839	+	1.30250i	0.472214	+	0.881484i	$0.343455\pi$
$397$	−8.66410	+	25.9522i	−0.434839	+	1.30250i	−0.907053	+	0.421017i	$0.861673\pi$
$398$	23.4050	+	2.84188i	1.17319	+	0.142451i
$399$	−1.02557	−	3.54068i	−0.0513427	−	0.177256i
$400$	3.46843	+	16.9895i	0.173421	+	0.849474i
$401$	−6.20955	−	18.5999i	−0.310090	−	0.928833i	−0.982111	−	0.188301i	$-0.939702\pi$
$401$	−6.20955	−	18.5999i	−0.310090	−	0.928833i	0.672021	−	0.740532i	$-0.265426\pi$
$402$	7.83040	−	4.10971i	0.390545	−	0.204974i
$403$	−0.966723	−	0.226223i	−0.0481559	−	0.0112690i
$404$	−4.93695	−	2.59111i	−0.245622	−	0.128913i
$405$	−0.177025	+	1.08928i	−0.00879643	+	0.0541266i
$406$	1.76823	+	1.32874i	0.0877556	+	0.0659441i
$407$	−0.782130	−	19.4084i	−0.0387687	−	0.962036i
$408$			16.0772i			0.795939i
$409$	−1.71907	+	0.0692760i	−0.0850023	+	0.00342548i	−0.0827307	−	0.996572i	$-0.526364\pi$
$409$	−1.71907	+	0.0692760i	−0.0850023	+	0.00342548i	−0.00227167	+	0.999997i	$0.500723\pi$
$410$	−11.9763	−	2.44497i	−0.591466	−	0.120749i
$411$	−12.8845	−	8.89355i	−0.635547	−	0.438687i
$412$	−2.22608	−	0.743175i	−0.109671	−	0.0366136i
$413$	3.48712	+	7.34896i	0.171590	+	0.361619i
$414$	7.62628	−	6.22666i	0.374811	−	0.306024i
$415$	−0.348340	+	0.918498i	−0.0170994	+	0.0450873i
$416$	0.373154	+	7.16076i	0.0182954	+	0.351085i
$417$	−1.11234	−	2.93299i	−0.0544714	−	0.143629i
$418$	34.0785	+	19.6752i	1.66683	+	0.962346i
$419$	3.89294	+	4.76799i	0.190183	+	0.232932i	0.860891	−	0.508790i	$-0.169907\pi$
$419$	3.89294	+	4.76799i	0.190183	+	0.232932i	−0.670708	+	0.741722i	$0.734010\pi$
$420$	−0.261996	+	0.196877i	−0.0127841	+	0.00960662i
$421$	−0.652224	−	1.24271i	−0.0317875	−	0.0605660i	0.869044	−	0.494734i	$-0.164735\pi$
$421$	−0.652224	−	1.24271i	−0.0317875	−	0.0605660i	−0.900832	+	0.434168i	$0.857042\pi$
$422$	3.37016	−	41.7469i	0.164057	−	2.03221i
$423$	0.861703	−	10.6741i	0.0418974	−	0.518993i
$424$	5.80866	+	11.0675i	0.282094	+	0.537484i
$425$	−19.2605	+	14.4733i	−0.934271	+	0.702059i
$426$	−4.56273	−	5.58833i	−0.221065	−	0.270755i
$427$	1.50055	+	0.866345i	0.0726169	+	0.0419254i
$428$	−0.0709665	−	0.187123i	−0.00343030	−	0.00904495i
$429$	16.5958	−	12.7797i	0.801251	−	0.617011i
$430$	1.79648	−	4.73693i	0.0866339	−	0.228435i
$431$	19.8548	−	16.2109i	0.956370	−	0.780852i	−0.0193636	−	0.999813i	$-0.506164\pi$
$431$	19.8548	−	16.2109i	0.956370	−	0.780852i	0.975734	+	0.218960i	$0.0702666\pi$
$432$	1.96542	+	4.14203i	0.0945613	+	0.199284i
$433$	−13.5172	−	4.51271i	−0.649596	−	0.216867i	−0.0272737	−	0.999628i	$-0.508683\pi$
$433$	−13.5172	−	4.51271i	−0.649596	−	0.216867i	−0.622323	+	0.782761i	$0.713811\pi$
$434$	−0.290506	−	0.200522i	−0.0139447	−	0.00962534i
$435$	−1.86564	−	0.380872i	−0.0894504	−	0.0182614i
$436$	3.79740	−	0.153030i	0.181862	−	0.00732880i
$437$		−	28.3111i		−	1.35430i
$438$	−0.586400	−	14.5514i	−0.0280193	−	0.695292i
$439$	9.02515	+	6.78196i	0.430747	+	0.323685i	0.793905	−	0.608042i	$-0.208045\pi$
$439$	9.02515	+	6.78196i	0.430747	+	0.323685i	−0.363157	+	0.931728i	$0.618301\pi$
$440$	−2.59557	+	15.9712i	−0.123739	+	0.761398i
$441$	5.58048	+	2.92886i	0.265737	+	0.139470i
$442$	−31.0171	+	16.7483i	−1.47534	+	0.796635i
$443$	31.8640	−	16.7235i	1.51391	−	0.794559i	0.515837	−	0.856687i	$-0.327481\pi$
$443$	31.8640	−	16.7235i	1.51391	−	0.794559i	0.998068	+	0.0621279i	$0.0197887\pi$
$444$	0.376453	+	1.12762i	0.0178657	+	0.0535143i
$445$	−2.34985	−	11.5103i	−0.111394	−	0.545643i
$446$	−5.58549	−	19.2833i	−0.264481	−	0.913093i
$447$	−1.09020	−	0.132374i	−0.0515646	−	0.00626107i
$448$	1.61793	−	4.84629i	0.0764399	−	0.228966i
$449$	0.289229	+	1.77970i	0.0136496	+	0.0839892i	0.992981	−	0.118271i	$-0.0377353\pi$
$449$	0.289229	+	1.77970i	0.0136496	+	0.0839892i	−0.979332	+	0.202261i	$0.935171\pi$
$450$	−2.69760	+	5.13985i	−0.127166	+	0.242295i
$451$	35.4348	+	22.4076i	1.66856	+	1.05513i
$452$	6.29518	+	2.68212i	0.296100	+	0.126157i
$453$	11.5751	−	2.36308i	0.543848	−	0.111027i
$454$	−10.0856	+	2.48587i	−0.473339	+	0.116668i
$455$	3.01910	+	1.38922i	0.141537	+	0.0651277i
$456$	10.8151	+	2.66569i	0.506464	+	0.124832i
$457$	−22.5236	−	0.907671i	−1.05361	−	0.0424590i	−0.492590	−	0.870261i	$-0.663950\pi$
$457$	−22.5236	−	0.907671i	−1.05361	−	0.0424590i	−0.561020	+	0.827802i	$0.689591\pi$
$458$	−0.419028	+	10.3981i	−0.0195799	+	0.485870i
$459$	−4.02871	+	4.93427i	−0.188044	+	0.230312i
$460$	−2.35344	+	0.892541i	−0.109730	+	0.0416150i
$461$	−5.02011	−	2.38207i	−0.233810	−	0.110944i	0.308184	−	0.951327i	$-0.400279\pi$
$461$	−5.02011	−	2.38207i	−0.233810	−	0.110944i	−0.541993	+	0.840383i	$0.682330\pi$
$462$	7.15309	−	2.07192i	0.332792	−	0.0963944i
$463$	32.8499	−	22.6747i	1.52667	−	1.05378i	0.551003	−	0.834503i	$-0.314245\pi$
$463$	32.8499	−	22.6747i	1.52667	−	1.05378i	0.975663	−	0.219277i	$-0.0703700\pi$
$464$	−7.27750	+	3.10065i	−0.337849	+	0.143944i
$465$	0.299948	+	0.0487463i	0.0139097	+	0.00226055i
$466$	22.2022	+	35.1100i	1.02850	+	1.62644i
$467$	13.2047	−	19.1303i	0.611041	−	0.885246i	−0.388300	−	0.921533i	$-0.626938\pi$
$467$	13.2047	−	19.1303i	0.611041	−	0.885246i	0.999341	+	0.0362867i	$0.0115530\pi$
$468$	−0.757987	+	1.03385i	−0.0350379	+	0.0477897i
$469$	−2.73387	−	3.96070i	−0.126239	−	0.182888i
$470$	−7.10946	+	16.6865i	−0.327935	+	0.769691i
$471$	−0.725370	+	2.50427i	−0.0334233	+	0.115391i
$472$	−24.5001	−	1.97785i	−1.12771	−	0.0910381i
$473$	−11.5228	+	13.0066i	−0.529820	+	0.598043i
$474$	10.0081	−	15.8266i	0.459689	−	0.726939i
$475$	6.54271	+	15.3563i	0.300200	+	0.704595i
$476$	−1.87790	+	0.228018i	−0.0860734	+	0.0104512i
$477$	−0.990605	+	4.85230i	−0.0453567	+	0.222172i
$478$	−12.4778	+	1.00731i	−0.570721	+	0.0460733i
$479$	−22.1138	+	29.4281i	−1.01040	+	1.34460i	−0.0726303	+	0.997359i	$0.523139\pi$
$479$	−22.1138	+	29.4281i	−1.01040	+	1.34460i	−0.937774	+	0.347245i	$0.887117\pi$
$480$	−0.264542	−	2.17870i	−0.0120746	−	0.0994436i
$481$	8.24799	−	8.79219i	0.376076	−	0.400889i
$482$	0.606657	−	4.99627i	0.0276325	−	0.227574i
$483$	−3.86414	−	3.71156i	−0.175825	−	0.168882i
$484$	−4.04424	+	7.00482i	−0.183829	+	0.318401i
$485$	−7.53944	−	13.0587i	−0.342348	−	0.592964i
$486$	−0.367297	+	1.49018i	−0.0166609	+	0.0675960i
$487$	−4.47540	−	3.65405i	−0.202800	−	0.165581i	0.525603	−	0.850730i	$-0.323840\pi$
$487$	−4.47540	−	3.65405i	−0.202800	−	0.165581i	−0.728403	+	0.685149i	$0.759737\pi$
$488$	−4.53429	+	2.61787i	−0.205257	+	0.118505i
$489$	−6.91661	−	2.62313i	−0.312780	−	0.118622i
$490$	−7.39452	−	7.69851i	−0.334050	−	0.347783i
$491$	−24.3836	+	8.14044i	−1.10042	+	0.367373i	−0.808158	−	0.588966i	$-0.799535\pi$
$491$	−24.3836	+	8.14044i	−1.10042	+	0.367373i	−0.292259	+	0.956339i	$0.594407\pi$
$492$	−2.46460	−	0.713881i	−0.111113	−	0.0321843i
$493$	−8.22688	−	7.28838i	−0.370520	−	0.328252i
$494$	6.12376	+	23.6422i	0.275521	+	1.06371i
$495$	−4.79876	+	4.25133i	−0.215688	+	0.191083i
$496$	1.14057	−	0.541206i	0.0512130	−	0.0243009i
$497$	−2.71973	+	2.83154i	−0.121997	+	0.127012i
$498$	−0.585669	+	1.23427i	−0.0262444	+	0.0553090i
$499$	−6.81283	−	27.6408i	−0.304984	−	1.23737i	−0.900795	−	0.434245i	$-0.857015\pi$
$499$	−6.81283	−	27.6408i	−0.304984	−	1.23737i	0.595811	−	0.803125i	$-0.296831\pi$
$500$	2.48516	−	2.38703i	0.111140	−	0.106751i
$501$	14.1131	+	18.7811i	0.630526	+	0.839078i
$502$	4.86308	+	5.48928i	0.217050	+	0.244999i
$503$	−14.5620	+	2.36655i	−0.649286	+	0.105519i	−0.476129	−	0.879375i	$-0.657961\pi$
$503$	−14.5620	+	2.36655i	−0.649286	+	0.105519i	−0.173156	+	0.984894i	$0.555397\pi$
$504$	1.78169	−	1.12667i	0.0793627	−	0.0501859i
$505$	−1.39254	−	17.2497i	−0.0619672	−	0.767602i
$506$	57.1959			2.54267
$507$	12.8772	+	1.78230i	0.571898	+	0.0791548i
$508$	−1.09948			−0.0487815
$509$	0.637967	+	7.90264i	0.0282774	+	0.350278i	0.995389	+	0.0959244i	$0.0305807\pi$
$509$	0.637967	+	7.90264i	0.0282774	+	0.350278i	−0.967111	+	0.254354i	$0.918137\pi$
$510$	9.11889	−	5.76644i	0.403791	−	0.255342i
$511$	−7.82275	+	1.27132i	−0.346058	+	0.0562399i
$512$	9.30002	+	10.4976i	0.411007	+	0.463931i
$513$	2.65130	+	3.52824i	0.117058	+	0.155776i
$514$	−33.1481	+	31.8392i	−1.46210	+	1.40437i
$515$	−1.74325	−	7.07263i	−0.0768166	−	0.311657i
$516$	0.455907	−	0.960805i	0.0200702	−	0.0422971i
$517$	43.0958	−	44.8675i	1.89535	−	1.97327i
$518$	3.87230	−	1.83743i	0.170139	−	0.0807320i
$519$	−0.586026	+	0.519174i	−0.0257237	+	0.0227892i
$520$	−8.19693	+	5.80176i	−0.359459	+	0.254424i
$521$	−15.1231	−	13.3979i	−0.662554	−	0.586972i	0.263364	−	0.964697i	$-0.415168\pi$
$521$	−15.1231	−	13.3979i	−0.662554	−	0.586972i	−0.925918	+	0.377725i	$0.876706\pi$
$522$	−2.54359	−	0.736758i	−0.111330	−	0.0322470i
$523$	3.95643	−	1.32085i	0.173003	−	0.0577568i	−0.228847	−	0.973462i	$-0.573496\pi$
$523$	3.95643	−	1.32085i	0.173003	−	0.0577568i	0.401850	+	0.915706i	$0.368367\pi$
$524$	1.27720	+	1.32970i	0.0557946	+	0.0580883i
$525$	2.95370	+	1.12019i	0.128910	+	0.0488891i
$526$	−9.24368	+	5.33684i	−0.403044	+	0.232697i
$527$	1.35872	+	1.10936i	0.0591868	+	0.0483245i
$528$	−6.37401	+	25.8604i	−0.277393	+	1.12543i
$529$	−9.07512	−	15.7186i	−0.394571	−	0.683416i
$530$	4.19401	−	7.26424i	0.182176	−	0.315539i
$531$	−7.02375	−	6.74640i	−0.304805	−	0.292769i
$532$	−0.157979	+	1.30107i	−0.00684924	+	0.0564086i
$533$	5.50490	+	25.4315i	0.238444	+	1.10156i
$534$	−1.96934	−	16.2190i	−0.0852218	−	0.701865i
$535$	0.373162	−	0.496589i	0.0161332	−	0.0214694i
$536$	14.4953	−	1.17018i	0.626102	−	0.0505442i
$537$	−4.46633	+	21.8775i	−0.192736	+	0.944085i
$538$	4.92669	−	0.598209i	0.212405	−	0.0257906i
$539$	14.3511	+	33.6833i	0.618147	+	1.45084i
$540$	0.209709	−	0.331628i	0.00902444	−	0.0142710i
$541$	9.46842	−	10.6876i	0.407079	−	0.459497i	−0.508839	−	0.860861i	$-0.669925\pi$
$541$	9.46842	−	10.6876i	0.407079	−	0.459497i	0.915919	+	0.401364i	$0.131464\pi$
$542$	−11.5165	−	0.929708i	−0.494676	−	0.0399344i
$543$	1.92407	−	6.64267i	0.0825699	−	0.285064i
$544$	4.96556	−	11.6546i	0.212897	−	0.499687i
$545$	6.70096	+	9.70802i	0.287038	+	0.415846i
$546$	4.02971	+	2.26365i	0.172456	+	0.0968752i
$547$	−15.7736	+	22.8521i	−0.674432	+	0.977083i	0.325075	+	0.945688i	$0.394610\pi$
$547$	−15.7736	+	22.8521i	−0.674432	+	0.977083i	−0.999507	+	0.0313951i	$0.990005\pi$
$548$	2.97506	+	4.70468i	0.127088	+	0.200974i
$549$	−2.04762	−	0.332771i	−0.0873905	−	0.0142023i
$550$	−31.0237	+	13.2180i	−1.32286	+	0.563616i
$551$	−6.26696	+	4.32577i	−0.266982	+	0.184284i
$552$	15.5510	−	4.50441i	0.661895	−	0.191720i
$553$	−9.20664	−	4.36860i	−0.391506	−	0.185772i
$554$	−38.4154	+	14.5690i	−1.63211	+	0.618979i
$555$	−2.33362	+	2.85817i	−0.0990568	+	0.121323i
$556$	−0.0449084	+	1.11439i	−0.00190454	+	0.0472607i
$557$	6.24469	+	0.251652i	0.264596	+	0.0106629i	0.172209	−	0.985060i	$-0.444909\pi$
$557$	6.24469	+	0.251652i	0.264596	+	0.0106629i	0.0923866	+	0.995723i	$0.470550\pi$
$558$	0.410343	+	0.101140i	0.0173712	+	0.00428161i
$559$	−10.7700	+	0.561234i	−0.455522	+	0.0237377i
$560$	−4.10309	+	1.01132i	−0.173387	+	0.0427361i
$561$	−36.2584	+	7.40220i	−1.53083	+	0.312521i
$562$	36.1187	+	15.3887i	1.52357	+	0.649134i
$563$	−4.67408	−	2.95571i	−0.196989	−	0.124568i	0.432330	−	0.901716i	$-0.357692\pi$
$563$	−4.67408	−	2.95571i	−0.196989	−	0.124568i	−0.629319	+	0.777147i	$0.716666\pi$
$564$	−1.76944	+	3.37138i	−0.0745067	+	0.141961i
$565$	3.40695	+	20.9638i	0.143331	+	0.881953i
$566$	1.35393	−	4.05551i	0.0569099	−	0.170466i
$567$	0.829147	+	0.100677i	0.0348209	+	0.00422803i
$568$	−3.30071	−	11.3954i	−0.138495	−	0.478139i
$569$	0.916645	+	4.49002i	0.0384277	+	0.188232i	0.994474	−	0.104985i	$-0.0334795\pi$
$569$	0.916645	+	4.49002i	0.0384277	+	0.188232i	−0.956046	+	0.293217i	$0.905274\pi$
$570$	−2.36712	−	7.09039i	−0.0991477	−	0.296984i
$571$	−4.71383	+	2.47401i	−0.197268	+	0.103534i	−0.560465	−	0.828178i	$-0.689377\pi$
$571$	−4.71383	+	2.47401i	−0.197268	+	0.103534i	0.363197	+	0.931712i	$0.381685\pi$
$572$	−7.20944	+	1.86738i	−0.301442	+	0.0780789i
$573$	−11.0126	−	5.77987i	−0.460059	−	0.241458i
$574$	−1.48400	+	9.13142i	−0.0619410	+	0.381138i
$575$	19.3959	+	14.5751i	0.808867	+	0.607824i
$576$	0.246311	+	6.11214i	0.0102629	+	0.254672i
$577$			28.8252i			1.20001i	0.799996	+	0.600005i	$0.204835\pi$
$577$			28.8252i			1.20001i	−0.799996	+	0.600005i	$0.795165\pi$
$578$	36.1569	−	1.45707i	1.50393	−	0.0606062i
$579$	−16.7977	−	3.42928i	−0.698090	−	0.142516i
$580$	0.557165	+	0.384583i	0.0231350	+	0.0159689i
$581$	0.705219	+	0.235437i	0.0292574	+	0.00976756i
$582$	−8.99004	−	18.9461i	−0.372649	−	0.785342i
$583$	−22.2858	+	18.1958i	−0.922982	+	0.753591i
$584$	8.49224	−	22.3922i	0.351411	−	0.926596i
$585$	−3.96957	−	0.273405i	−0.164121	−	0.0113039i
$586$	−3.31533	−	8.74180i	−0.136955	−	0.361120i
$587$	25.5390	+	14.7450i	1.05411	+	0.608590i	0.923797	−	0.382884i	$-0.125069\pi$
$587$	25.5390	+	14.7450i	1.05411	+	0.608590i	0.130311	+	0.991473i	$0.458402\pi$
$588$	−1.41718	−	1.73573i	−0.0584436	−	0.0715805i
$589$	0.971551	−	0.730073i	0.0400321	−	0.0300822i
$590$	7.66568	+	14.6057i	0.315591	+	0.601309i
$591$	−1.79311	+	22.2117i	−0.0737587	+	0.913665i
$592$	−1.23348	+	15.2794i	−0.0506959	+	0.627981i
$593$	−17.1537	−	32.6836i	−0.704418	−	1.34216i	−0.929865	−	0.367901i	$-0.880077\pi$
$593$	−17.1537	−	32.6836i	−0.704418	−	1.34216i	0.225447	−	0.974255i	$-0.427616\pi$
$594$	−7.12797	+	5.35632i	−0.292464	+	0.219772i
$595$	−3.71342	−	4.54812i	−0.152235	−	0.186455i
$596$	0.338152	+	0.195232i	0.0138513	+	0.00799702i
$597$	5.44735	+	14.3635i	0.222945	+	0.587858i
$598$	24.8904	+	25.3096i	1.01784	+	1.03499i
$599$	−6.56405	+	17.3080i	−0.268200	+	0.707185i	0.731480	+	0.681863i	$0.238830\pi$
$599$	−6.56405	+	17.3080i	−0.268200	+	0.707185i	−0.999679	+	0.0253214i	$0.991939\pi$
$600$	−7.39409	+	6.03709i	−0.301863	+	0.246463i
$601$	−7.84102	−	16.5246i	−0.319842	−	0.674053i	0.678313	−	0.734773i	$-0.262711\pi$
$601$	−7.84102	−	16.5246i	−0.319842	−	0.674053i	−0.998155	+	0.0607206i	$0.980660\pi$
$602$	−3.63699	−	1.21421i	−0.148233	−	0.0494874i
$603$	4.74201	+	3.27317i	0.193109	+	0.133294i
$604$	−4.11552	−	0.840190i	−0.167458	−	0.0341868i
$605$	−25.0850	+	1.01089i	−1.01985	+	0.0410986i
$606$		−	24.0680i		−	0.977694i
$607$	1.06466	+	26.4192i	0.0432131	+	1.07232i	0.864761	+	0.502183i	$0.167470\pi$
$607$	1.06466	+	26.4192i	0.0432131	+	1.07232i	−0.821548	+	0.570139i	$0.806889\pi$
$608$	−7.01673	−	5.27273i	−0.284566	−	0.213838i
$609$	−0.231174	+	1.42247i	−0.00936765	+	0.0576415i
$610$	3.11117	+	1.63287i	0.125967	+	0.0661128i
$611$	38.6086	−	0.455099i	1.56194	−	0.0184113i
$612$	2.00543	−	1.05253i	0.0810648	−	0.0425461i
$613$	−7.81136	−	23.3979i	−0.315498	−	0.945031i	−0.980215	−	0.197936i	$-0.936576\pi$
$613$	−7.81136	−	23.3979i	−0.315498	−	0.945031i	0.664717	−	0.747095i	$-0.268552\pi$
$614$	−3.88535	−	19.0317i	−0.156800	−	0.768057i
$615$	−2.21578	−	7.64976i	−0.0893489	−	0.308468i
$616$	12.1571	+	1.47614i	0.489825	+	0.0594755i
$617$	5.07779	−	15.2098i	0.204424	−	0.612325i	−0.795555	−	0.605881i	$-0.792821\pi$
$617$	5.07779	−	15.2098i	0.204424	−	0.612325i	0.999979	−	0.00644356i	$-0.00205106\pi$
$618$	−1.62506	−	9.99940i	−0.0653695	−	0.402235i
$619$	12.0798	−	23.0161i	0.485528	−	0.925096i	−0.512273	−	0.858822i	$-0.671197\pi$
$619$	12.0798	−	23.0161i	0.485528	−	0.925096i	0.997801	−	0.0662739i	$-0.0211111\pi$
$620$	−0.0913186	−	0.0577464i	−0.00366744	−	0.00231915i
$621$	5.90153	+	2.51441i	0.236820	+	0.100900i
$622$	−7.50769	+	1.53271i	−0.301031	+	0.0614559i
$623$	−8.63295	+	2.12783i	−0.345872	+	0.0852498i
$624$	−14.2173	+	8.43331i	−0.569146	+	0.337603i
$625$	−7.97654	−	1.96604i	−0.319061	−	0.0786416i
$626$	38.1485	+	1.53733i	1.52472	+	0.0614442i
$627$	−1.03238	+	25.6183i	−0.0412294	+	1.02310i
$628$	0.586269	−	0.718049i	0.0233947	−	0.0286533i
$629$	−19.9145	+	7.55259i	−0.794045	+	0.301141i
$630$	−1.27808	−	0.606458i	−0.0509201	−	0.0241619i
$631$	20.9611	−	6.07147i	0.834450	−	0.241701i	0.166626	−	0.986020i	$-0.446713\pi$
$631$	20.9611	−	6.07147i	0.834450	−	0.241701i	0.667824	+	0.744319i	$0.267226\pi$
$632$	25.3423	−	17.4925i	1.00806	−	0.695814i
$633$	25.1054	−	10.6964i	0.997851	−	0.425144i
$634$	−43.9002	−	7.13447i	−1.74350	−	0.283346i
$635$	−1.82393	−	2.88431i	−0.0723804	−	0.114460i
$636$	1.00026	−	1.44912i	0.0396627	−	0.0574613i
$637$	−8.65985	+	21.0087i	−0.343116	+	0.832396i
$638$	−8.73919	−	12.6609i	−0.345988	−	0.501250i
$639$	1.84249	−	4.32448i	0.0728877	−	0.171074i
$640$	4.10374	−	14.1678i	0.162215	−	0.560030i
$641$	−28.8042	−	2.32532i	−1.13770	−	0.0918446i	−0.502774	−	0.864418i	$-0.667687\pi$
$641$	−28.8042	−	2.32532i	−1.13770	−	0.0918446i	−0.634925	+	0.772573i	$0.718969\pi$
$642$	0.572862	−	0.646628i	0.0226091	−	0.0255204i
$643$	10.2232	−	16.1667i	0.403165	−	0.637554i	−0.581187	−	0.813770i	$-0.697411\pi$
$643$	10.2232	−	16.1667i	0.403165	−	0.637554i	0.984351	+	0.176216i	$0.0563858\pi$
$644$	0.746695	+	1.75256i	0.0294239	+	0.0690605i
$645$	3.27683	−	0.397879i	0.129025	−	0.0156665i
$646$	8.63068	−	42.2759i	0.339570	−	1.66332i
$647$	22.9607	−	1.85358i	0.902677	−	0.0728716i	0.379594	−	0.925153i	$-0.376064\pi$
$647$	22.9607	−	1.85358i	0.902677	−	0.0728716i	0.523083	+	0.852282i	$0.324782\pi$
$648$	−1.51620	+	2.01769i	−0.0595618	+	0.0792624i
$649$	−6.81967	−	56.1650i	−0.267695	−	2.20467i
$650$	−19.3499	−	7.97608i	−0.758965	−	0.312847i
$651$	0.0277228	−	0.228317i	0.00108654	−	0.00894847i
$652$	1.89684	+	1.82194i	0.0742859	+	0.0713525i
$653$	10.0794	−	17.4581i	0.394439	−	0.683189i	−0.598590	−	0.801055i	$-0.704272\pi$
$653$	10.0794	−	17.4581i	0.394439	−	0.683189i	0.993029	+	0.117867i	$0.0376055\pi$
$654$	8.20269	+	14.2075i	0.320750	+	0.555556i
$655$	−1.36952	+	5.55637i	−0.0535116	+	0.217105i
$656$	−25.6291	−	20.9255i	−1.00065	−	0.817003i
$657$	8.21753	−	4.74439i	0.320596	−	0.185096i
$658$	12.8356	+	4.86791i	0.500385	+	0.189771i
$659$	−5.31110	−	5.52944i	−0.206891	−	0.215396i	0.609670	−	0.792655i	$-0.291302\pi$
$659$	−5.31110	−	5.52944i	−0.206891	−	0.215396i	−0.816561	+	0.577259i	$0.804122\pi$
$660$	2.16214	−	0.721828i	0.0841612	−	0.0280971i
$661$	−17.5226	−	5.07548i	−0.681550	−	0.197413i	−0.0806558	−	0.996742i	$-0.525701\pi$
$661$	−17.5226	−	5.07548i	−0.681550	−	0.197413i	−0.600894	+	0.799329i	$0.705189\pi$
$662$	9.95852	+	8.82248i	0.387049	+	0.342895i
$663$	−19.0544	−	12.8233i	−0.740010	−	0.498017i
$664$	−1.68161	+	1.48978i	−0.0652591	+	0.0578145i
$665$	−3.67523	+	1.74392i	−0.142519	+	0.0676262i
$666$	−3.55480	+	3.70094i	−0.137746	+	0.143408i
$667$	−4.74490	+	9.99966i	−0.183723	+	0.387188i
$668$	−1.99896	−	8.11008i	−0.0773419	−	0.313789i
$669$	9.43383	−	9.06132i	0.364733	−	0.350331i
$670$	−5.86279	−	7.80195i	−0.226499	−	0.301416i
$671$	−7.99167	−	9.02073i	−0.308515	−	0.348241i
$672$	−1.63955	+	0.266453i	−0.0632472	+	0.0102787i
$673$	27.7914	−	17.5742i	1.07128	−	0.677437i	0.122212	−	0.992504i	$-0.461001\pi$
$673$	27.7914	−	17.5742i	1.07128	−	0.677437i	0.949070	+	0.315067i	$0.102027\pi$
$674$	3.83424	+	47.4955i	0.147689	+	1.82946i
$675$	−3.78214			−0.145575
$676$	−3.96372	−	2.37760i	−0.152451	−	0.0914460i
$677$	23.7992			0.914677			0.457338	−	0.889293i	$-0.348803\pi$
$677$	23.7992			0.914677			0.457338	+	0.889293i	$0.348803\pi$
$678$	2.37680	+	29.4420i	0.0912805	+	1.13071i
$679$	−9.64571	+	6.09958i	−0.370168	+	0.234080i
$680$	17.5125	−	2.84606i	0.671573	−	0.109141i
$681$	−4.48802	−	5.06593i	−0.171981	−	0.194127i
$682$	1.47494	+	1.96279i	0.0564783	+	0.0751590i
$683$	5.85232	−	5.62123i	0.223933	−	0.215090i	−0.572359	−	0.820003i	$-0.693972\pi$
$683$	5.85232	−	5.62123i	0.223933	−	0.215090i	0.796292	+	0.604913i	$0.206792\pi$
$684$	−0.375526	−	1.52357i	−0.0143586	−	0.0582552i
$685$	−7.40666	+	15.6092i	−0.282994	+	0.596397i
$686$	−11.8126	+	12.2982i	−0.451007	+	0.469548i
$687$	−6.12581	+	2.90673i	−0.233714	+	0.110899i
$688$	10.2645	−	9.09359i	0.391332	−	0.346690i
$689$	−17.7500	−	1.94323i	−0.676223	−	0.0740313i
$690$	−8.13260	−	7.20485i	−0.309603	−	0.274284i
$691$	−12.2005	−	3.53393i	−0.464131	−	0.134437i	0.0379099	−	0.999281i	$-0.487930\pi$
$691$	−12.2005	−	3.53393i	−0.464131	−	0.134437i	−0.502041	+	0.864844i	$0.667417\pi$
$692$	0.264041	−	0.0881498i	0.0100373	−	0.00335095i
$693$	3.36126	+	3.49945i	0.127684	+	0.132933i
$694$	26.3296	+	9.98550i	0.999458	+	0.379044i
$695$	−2.99793	+	1.73086i	−0.113718	+	0.0656551i
$696$	−3.37320	−	2.75413i	−0.127861	−	0.104395i
$697$	11.0016	−	44.6354i	0.416716	−	1.69068i
$698$	12.4057	+	21.4872i	0.469561	+	0.813304i
$699$	−13.5332	+	23.4402i	−0.511873	+	0.886591i
$700$	−0.810033	−	0.778047i	−0.0306164	−	0.0294074i
$701$	−3.73869	+	30.7908i	−0.141208	+	1.16295i	0.733980	+	0.679171i	$0.237661\pi$
$701$	−3.73869	+	30.7908i	−0.141208	+	1.16295i	−0.875188	+	0.483783i	$0.839262\pi$
$702$	−5.47215	−	0.823231i	−0.206533	−	0.0310708i
$703$	1.77868	+	14.6488i	0.0670843	+	0.552489i
$704$	−21.3484	+	28.4096i	−0.804599	+	1.07073i
$705$	−11.7796	+	0.950948i	−0.443646	+	0.0358148i
$706$	−8.09659	+	39.6597i	−0.304719	+	1.49261i
$707$	−13.0024	+	1.57878i	−0.489007	+	0.0593762i
$708$	1.35725	+	3.18558i	0.0510085	+	0.119721i
$709$	11.8369	−	18.7186i	0.444544	−	0.702991i	−0.546361	−	0.837550i	$-0.683987\pi$
$709$	11.8369	−	18.7186i	0.444544	−	0.702991i	0.990906	+	0.134559i	$0.0429617\pi$
$710$	−5.27952	+	5.95934i	−0.198137	+	0.223650i
$711$	12.1612	+	0.981753i	0.456081	+	0.0368186i
$712$	7.47494	−	25.8065i	0.280135	−	0.967139i
$713$	0.692377	−	1.62507i	0.0259297	−	0.0608593i
$714$	−4.63870	−	6.72032i	−0.173599	−	0.251501i
$715$	−16.8585	−	15.8151i	−0.630473	−	0.591450i
$716$	4.50984	−	6.53363i	0.168541	−	0.244173i
$717$	−4.35935	−	6.89377i	−0.162803	−	0.257452i
$718$	3.43887	+	0.558871i	0.128338	+	0.0208569i
$719$	13.6589	−	5.81951i	0.509390	−	0.217031i	−0.121951	−	0.992536i	$-0.538915\pi$
$719$	13.6589	−	5.81951i	0.509390	−	0.217031i	0.631341	+	0.775505i	$0.282505\pi$
$720$	4.16389	−	2.87413i	0.155179	−	0.107112i
$721$	−5.29546	+	1.53385i	−0.197213	+	0.0571236i
$722$	−0.662641	−	0.314427i	−0.0246610	−	0.0117018i
$723$	3.06618	−	1.16285i	0.114032	−	0.0432468i
$724$	−1.55510	+	1.90465i	−0.0577949	+	0.0707859i
$725$	0.262766	−	6.52048i	0.00975890	−	0.242165i
$726$	−34.8868	−	1.40589i	−1.29477	−	0.0521775i
$727$	13.4457	+	3.31406i	0.498673	+	0.122912i	0.480626	−	0.876925i	$-0.340409\pi$
$727$	13.4457	+	3.31406i	0.498673	+	0.122912i	0.0180461	+	0.999837i	$0.494255\pi$
$728$	4.63731	+	6.02202i	0.171870	+	0.223191i
$729$	−0.970942	+	0.239316i	−0.0359608	+	0.00886354i
$730$	−15.7467	+	3.21471i	−0.582810	+	0.118982i
$731$	17.5288	+	7.46834i	0.648327	+	0.276226i
$732$	0.623396	+	0.394212i	0.0230414	+	0.0145705i
$733$	23.1210	−	44.0533i	0.853992	−	1.62715i	0.0775229	−	0.996991i	$-0.475299\pi$
$733$	23.1210	−	44.0533i	0.853992	−	1.62715i	0.776469	−	0.630155i	$-0.217009\pi$
$734$	−3.52311	−	21.6786i	−0.130040	−	0.800170i
$735$	2.20246	−	6.59717i	0.0812389	−	0.243340i
$736$	−12.6644	−	1.53774i	−0.466816	−	0.0566817i
$737$	9.31296	+	32.1521i	0.343047	+	1.18434i
$738$	−2.21552	−	10.8523i	−0.0815543	−	0.399479i
$739$	−2.75221	−	8.24389i	−0.101242	−	0.303256i	0.885718	−	0.464224i	$-0.153667\pi$
$739$	−2.75221	−	8.24389i	−0.101242	−	0.303256i	−0.986960	+	0.160968i	$0.948539\pi$
$740$	1.16164	−	0.609678i	0.0427029	−	0.0224122i
$741$	−11.7856	+	10.6917i	−0.432955	+	0.392769i
$742$	−5.62131	−	2.95029i	−0.206365	−	0.108309i
$743$	1.38992	−	8.55254i	0.0509914	−	0.313762i	−0.949008	−	0.315253i	$-0.897910\pi$
$743$	1.38992	−	8.55254i	0.0509914	−	0.313762i	0.999999	+	0.00149099i	$0.000474597\pi$
$744$	0.555600	+	0.417506i	0.0203693	+	0.0153065i
$745$	0.0488000	+	1.21096i	0.00178789	+	0.0443662i
$746$			9.68014i			0.354415i
$747$	−0.889422	+	0.0358425i	−0.0325422	+	0.00131141i
$748$	12.8916	+	2.63184i	0.471363	+	0.0962295i
$749$	−0.386912	−	0.267066i	−0.0141374	−	0.00975837i
$750$	14.1091	+	4.71031i	0.515191	+	0.171996i
$751$	−1.60277	−	3.37777i	−0.0584860	−	0.123257i	0.872103	−	0.489322i	$-0.162756\pi$
$751$	−1.60277	−	3.37777i	−0.0584860	−	0.123257i	−0.930589	+	0.366066i	$0.880705\pi$
$752$	−38.0305	+	31.0509i	−1.38683	+	1.13231i
$753$	−1.69440	+	4.46777i	−0.0617474	+	0.162815i
$754$	1.79945	−	9.37690i	0.0655320	−	0.341487i
$755$	−4.62314	−	12.1902i	−0.168253	−	0.443647i
$756$	−0.257181	−	0.148484i	−0.00935358	−	0.00540029i
$757$	−5.62761	−	6.89257i	−0.204539	−	0.250515i	0.662141	−	0.749379i	$-0.269648\pi$
$757$	−5.62761	−	6.89257i	−0.204539	−	0.250515i	−0.866680	+	0.498865i	$0.833751\pi$
$758$	21.5504	−	16.1941i	0.782747	−	0.588196i
$759$	17.3186	+	32.9978i	0.628626	+	1.19775i
$760$	0.989128	−	12.2526i	0.0358795	−	0.444447i
$761$	−2.60650	+	32.2873i	−0.0944855	+	1.17041i	0.759639	+	0.650345i	$0.225376\pi$
$761$	−2.60650	+	32.2873i	−0.0944855	+	1.17041i	−0.854125	+	0.520068i	$0.825907\pi$
$762$	−2.20561	−	4.20244i	−0.0799009	−	0.152238i
$763$	7.13736	−	5.36338i	0.258390	−	0.194167i
$764$	2.79670	+	3.42533i	0.101181	+	0.123924i
$765$	6.08796	+	3.51489i	0.220111	+	0.127081i
$766$	16.8588	+	44.4529i	0.609132	+	1.60615i
$767$	21.8857	−	27.4595i	0.790247	−	0.991506i
$768$	2.93594	−	7.74143i	0.105941	−	0.279345i
$769$	−4.53879	+	3.70581i	−0.163673	+	0.133635i	−0.710742	−	0.703452i	$-0.751641\pi$
$769$	−4.53879	+	3.70581i	−0.163673	+	0.133635i	0.547069	+	0.837087i	$0.315743\pi$
$770$	−3.52317	−	7.42492i	−0.126966	−	0.267575i
$771$	−28.4060	−	9.48331i	−1.02302	−	0.341533i
$772$	5.01657	+	3.46269i	0.180550	+	0.124625i
$773$	−22.6467	−	4.62335i	−0.814545	−	0.166290i	−0.225346	−	0.974279i	$-0.572351\pi$
$773$	−22.6467	−	4.62335i	−0.814545	−	0.166290i	−0.589199	+	0.807988i	$0.700556\pi$
$774$	4.58697	−	0.184849i	0.164875	−	0.00664425i
$775$			1.04147i			0.0374105i
$776$	−1.38859	−	34.4576i	−0.0498476	−	1.23695i
$777$	2.23257	+	1.67767i	0.0800932	+	0.0601861i
$778$	9.31266	−	57.3031i	0.333875	−	2.05442i
$779$	−28.2021	−	14.8016i	−1.01044	−	0.530322i
$780$	1.26033	+	0.642641i	0.0451271	+	0.0230102i
$781$	24.1799	−	12.6906i	0.865226	−	0.454105i
$782$	−19.8600	−	59.4879i	−0.710191	−	2.12728i
$783$	−0.345128	−	1.69055i	−0.0123339	−	0.0604153i
$784$	−8.03893	−	27.7536i	−0.287105	−	0.991200i
$785$	2.85625	+	0.346812i	0.101944	+	0.0123782i
$786$	−2.52028	+	7.54916i	−0.0898954	+	0.269270i
$787$	2.48311	+	15.2792i	0.0885134	+	0.544645i	0.992997	+	0.118137i	$0.0376922\pi$
$787$	2.48311	+	15.2792i	0.0885134	+	0.544645i	−0.904484	+	0.426508i	$0.859744\pi$
$788$	3.68200	−	7.01547i	0.131166	−	0.249916i
$789$	−5.87791	−	3.71696i	−0.209259	−	0.132327i
$790$	−19.0112	−	8.09993i	−0.676389	−	0.288182i
$791$	15.7498	−	3.21534i	0.559998	−	0.114324i
$792$	−14.2362	+	3.50890i	−0.505860	+	0.124683i
$793$	0.513947	−	7.46200i	0.0182508	−	0.264983i
$794$	40.7717	+	10.0493i	1.44693	+	0.356637i
$795$	5.46086	+	0.220065i	0.193677	+	0.00780491i
$796$	0.219926	−	5.45741i	0.00779507	−	0.193433i
$797$	−2.96304	+	3.62907i	−0.104956	+	0.128548i	−0.824412	−	0.565990i	$-0.808494\pi$
$797$	−2.96304	+	3.62907i	−0.104956	+	0.128548i	0.719456	+	0.694538i	$0.244391\pi$
$798$	−5.28988	+	2.00619i	−0.187260	+	0.0710183i
$799$	−61.6296	−	29.2436i	−2.18030	−	1.03456i
$800$	7.22469	−	2.09266i	0.255432	−	0.0739866i
$801$	8.76087	−	6.04720i	0.309550	−	0.213667i
$802$	−27.6873	+	11.7964i	−0.977671	+	0.416547i
$803$	54.4104	+	8.84255i	1.92010	+	0.312047i
$804$	−1.09494	−	1.73150i	−0.0386155	−	0.0610655i
$805$	−3.35887	+	4.86616i	−0.118385	+	0.171510i
$806$	−0.226688	+	1.50683i	−0.00798475	+	0.0530760i
$807$	1.83690	+	2.66121i	0.0646619	+	0.0936790i
$808$	15.5135	−	36.4115i	0.545763	−	1.28095i
$809$	0.146880	−	0.507090i	0.00516404	−	0.0178283i	−0.957895	−	0.287120i	$-0.907302\pi$
$809$	0.146880	−	0.507090i	0.00516404	−	0.0178283i	0.963059	+	0.269291i	$0.0867894\pi$
$810$	1.68824	+	0.136289i	0.0593187	+	0.00478870i
$811$	−5.07868	+	5.73264i	−0.178337	+	0.201300i	−0.830881	−	0.556450i	$-0.812163\pi$
$811$	−5.07868	+	5.73264i	−0.178337	+	0.201300i	0.652545	+	0.757750i	$0.273702\pi$
$812$	0.273856	−	0.433069i	0.00961048	−	0.0151978i
$813$	−2.95076	−	6.92569i	−0.103488	−	0.242895i
$814$	−29.5944	+	3.59341i	−1.03728	+	0.125949i
$815$	−1.63290	+	7.99847i	−0.0571979	+	0.280174i
$816$	29.1099	−	2.35000i	1.01905	−	0.0822663i
$817$	7.93034	−	10.5534i	0.277447	−	0.369215i
$818$	0.318281	+	2.62128i	0.0111284	+	0.0916508i
$819$	−0.0857854	+	3.01027i	−0.00299758	+	0.105187i
$820$	−0.341319	+	2.81101i	−0.0119194	+	0.0981648i
$821$	−28.7141	−	27.5802i	−1.00213	−	0.962557i	−0.00282904	−	0.999996i	$-0.500901\pi$
$821$	−28.7141	−	27.5802i	−1.00213	−	0.962557i	−0.999299	+	0.0374390i	$0.988080\pi$
$822$	−12.0142	+	20.8091i	−0.419042	+	0.725802i
$823$	−22.9771	−	39.7975i	−0.800931	−	1.38725i	−0.919004	−	0.394249i	$-0.871005\pi$
$823$	−22.9771	−	39.7975i	−0.800931	−	1.38725i	0.118072	−	0.993005i	$-0.462329\pi$
$824$	3.98682	−	16.1752i	0.138888	−	0.563489i
$825$	−17.0196	−	13.8961i	−0.592547	−	0.483800i
$826$	10.8118	−	6.24220i	0.376191	−	0.217194i
$827$	−36.2167	−	13.7352i	−1.25938	−	0.477619i	−0.367553	−	0.930002i	$-0.619804\pi$
$827$	−36.2167	−	13.7352i	−1.25938	−	0.477619i	−0.891823	+	0.452384i	$0.850574\pi$
$828$	−1.57996	−	1.64491i	−0.0549073	−	0.0571645i
$829$	−29.3691	+	9.80486i	−1.02003	+	0.340537i	−0.777013	−	0.629485i	$-0.783266\pi$
$829$	−29.3691	+	9.80486i	−1.02003	+	0.340537i	−0.243019	+	0.970021i	$0.578138\pi$
$830$	1.44814	+	0.419459i	0.0502657	+	0.0145596i
$831$	−20.0372	−	17.7515i	−0.695084	−	0.615791i
$832$	−21.8618	+	2.91638i	−0.757923	+	0.101107i
$833$	30.0500	−	26.6220i	1.04117	−	0.922398i
$834$	−4.34953	+	2.06388i	−0.150612	+	0.0714662i
$835$	17.9595	−	18.6978i	0.621513	−	0.647063i
$836$	3.90794	−	8.23580i	0.135159	−	0.284841i
$837$	0.0658990	+	0.267363i	0.00227780	+	0.00924140i
$838$	6.81331	−	6.54427i	0.235362	−	0.226068i
$839$	0.784584	+	1.04409i	0.0270869	+	0.0360461i	0.812783	−	0.582567i	$-0.197951\pi$
$839$	0.784584	+	1.04409i	0.0270869	+	0.0360461i	−0.785696	+	0.618613i	$0.787695\pi$
$840$	−1.54266	−	1.74130i	−0.0532268	−	0.0600806i
$841$	−25.6859	+	4.17437i	−0.885722	+	0.143944i
$842$	−1.82055	+	1.15125i	−0.0627404	+	0.0396746i
$843$	2.05837	+	25.4975i	0.0708940	+	0.878180i
$844$	−9.70259			−0.333977
$845$	−0.338169	−	14.3424i	−0.0116334	−	0.493393i
$846$	−16.4357			−0.565071
$847$	1.52895	+	18.9395i	0.0525354	+	0.650767i
$848$	19.1901	−	12.1351i	0.658992	−	0.416721i
$849$	2.74970	−	0.446870i	0.0943694	−	0.0153365i
$850$	24.5200	+	27.6773i	0.841028	+	0.949324i
$851$	12.8850	+	17.1468i	0.441691	+	0.587784i
$852$	−1.20534	+	1.15775i	−0.0412944	+	0.0396638i
$853$	11.5813	+	46.9873i	0.396537	+	1.60881i	0.742012	+	0.670387i	$0.233872\pi$
$853$	11.5813	+	46.9873i	0.396537	+	1.60881i	−0.345475	+	0.938428i	$0.612282\pi$
$854$	1.14002	−	2.40254i	0.0390107	−	0.0822134i
$855$	3.37389	−	3.51259i	0.115384	−	0.120128i
$856$	1.28346	−	0.609009i	0.0438677	−	0.0208155i
$857$	3.02232	−	2.67754i	0.103240	−	0.0914630i	−0.609924	−	0.792460i	$-0.708800\pi$
$857$	3.02232	−	2.67754i	0.103240	−	0.0914630i	0.713164	+	0.700997i	$0.247261\pi$
$858$	−21.6000	−	23.8100i	−0.737412	−	0.812859i
$859$	−8.20805	−	7.27170i	−0.280055	−	0.248107i	0.511388	−	0.859350i	$-0.329131\pi$
$859$	−8.20805	−	7.27170i	−0.280055	−	0.248107i	−0.791443	+	0.611243i	$0.790670\pi$
$860$	−1.12729	−	0.326523i	−0.0384402	−	0.0111344i
$861$	−5.71751	+	1.90879i	−0.194852	+	0.0650513i
$862$	−27.2515	−	28.3718i	−0.928191	−	0.966349i
$863$	15.1945	+	5.76250i	0.517225	+	0.196158i	0.599384	−	0.800462i	$-0.295412\pi$
$863$	15.1945	+	5.76250i	0.517225	+	0.196158i	−0.0821588	+	0.996619i	$0.526181\pi$
$864$	1.72229	−	0.994367i	0.0585936	−	0.0338290i
$865$	0.669265	+	0.546438i	0.0227557	+	0.0185795i
$866$	−5.23420	+	21.2360i	−0.177865	+	0.721628i
$867$	11.7887	+	20.4187i	0.400366	+	0.693455i
$868$	−0.0408870	+	0.0708184i	−0.00138780	+	0.00240373i
$869$	51.1183	+	49.0998i	1.73407	+	1.66560i
$870$	−0.352256	+	2.90109i	−0.0119426	+	0.0983563i
$871$	−10.1748	+	18.1129i	−0.344758	+	0.613733i
$872$	3.25182	+	26.7811i	0.110121	+	0.906924i
$873$	8.20839	−	10.9234i	0.277812	−	0.369701i
$874$	−43.3104	+	3.49638i	−1.46500	+	0.118267i
$875$	1.61918	−	7.93127i	0.0547383	−	0.268126i
$876$	−3.34912	+	0.406657i	−0.113156	+	0.0137397i
$877$	8.09648	+	19.0031i	0.273399	+	0.641690i	0.998918	−	0.0465117i	$-0.0148105\pi$
$877$	8.09648	+	19.0031i	0.273399	+	0.641690i	−0.725519	+	0.688202i	$0.758400\pi$
$878$	9.26047	−	14.6443i	0.312526	−	0.494220i
$879$	4.03952	−	4.55967i	0.136250	−	0.153794i
$880$	29.2975	+	2.36514i	0.987617	+	0.0797287i
$881$	0.458832	−	1.58407i	0.0154585	−	0.0533688i	−0.952418	−	0.304794i	$-0.901412\pi$
$881$	0.458832	−	1.58407i	0.0154585	−	0.0533688i	0.967877	+	0.251426i	$0.0808994\pi$
$882$	3.79140	−	8.89874i	0.127663	−	0.299636i
$883$	7.41325	+	10.7400i	0.249476	+	0.361428i	0.927636	−	0.373486i	$-0.121838\pi$
$883$	7.41325	+	10.7400i	0.249476	+	0.361428i	−0.678160	+	0.734914i	$0.737222\pi$
$884$	4.44553	+	6.84995i	0.149519	+	0.230389i
$885$	−6.10532	+	8.84508i	−0.205228	+	0.297324i
$886$	−29.5189	−	46.6803i	−0.991705	−	1.56826i
$887$	57.6457	+	9.36834i	1.93555	+	0.314558i	0.999322	−	0.0368273i	$-0.0117251\pi$
$887$	57.6457	+	9.36834i	1.93555	+	0.314558i	0.936231	+	0.351385i	$0.114289\pi$
$888$	−7.76344	+	3.30769i	−0.260524	+	0.110999i
$889$	−2.12564	+	1.46722i	−0.0712917	+	0.0492091i
$890$	−17.3184	+	5.01632i	−0.580513	+	0.168148i
$891$	−5.24852	−	2.49045i	−0.175832	−	0.0834333i
$892$	−4.34859	+	1.64920i	−0.145602	+	0.0552194i
$893$	−29.8907	+	36.6095i	−1.00025	+	1.22509i
$894$	−0.0678683	+	1.68413i	−0.00226986	+	0.0563259i
$895$	24.6213	+	0.992206i	0.823000	+	0.0331658i
$896$	−10.8393	−	2.67164i	−0.362115	−	0.0892532i
$897$	−7.06514	+	22.0236i	−0.235898	+	0.735345i
$898$	2.68687	−	0.662254i	0.0896620	−	0.0220997i
$899$	−0.465517	+	0.0950360i	−0.0155259	+	0.00316963i
$900$	1.23713	+	0.527090i	0.0412375	+	0.0175697i
$901$	26.6632	+	16.8608i	0.888278	+	0.561713i
$902$	29.9031	−	56.9756i	0.995664	−	1.89708i
$903$	−0.400753	−	2.46593i	−0.0133362	−	0.0820612i
$904$	−15.3816	+	46.0737i	−0.511586	+	1.53239i
$905$	−7.57632	−	0.919932i	−0.251845	−	0.0305796i
$906$	−5.04456	−	17.4159i	−0.167594	−	0.578603i
$907$	−5.38685	−	26.3865i	−0.178867	−	0.876150i	−0.965835	−	0.259156i	$-0.916555\pi$
$907$	−5.38685	−	26.3865i	−0.178867	−	0.876150i	0.786968	−	0.616994i	$-0.211650\pi$
$908$	0.762016	+	2.28252i	0.0252884	+	0.0757479i
$909$	13.8855	−	7.28765i	0.460551	−	0.241716i
$910$	1.75238	−	4.79019i	0.0580909	−	0.158793i
$911$	36.0196	+	18.9045i	1.19338	+	0.626336i	0.940048	−	0.341043i	$-0.110780\pi$
$911$	36.0196	+	18.9045i	1.19338	+	0.626336i	0.253335	+	0.967379i	$0.418473\pi$
$912$	3.24575	−	19.9719i	0.107478	−	0.661336i
$913$	−4.13409	−	3.10657i	−0.136818	−	0.102812i
$914$	1.39307	+	34.5688i	0.0460788	+	1.14343i
$915$			2.28934i			0.0756832i
$916$	2.40882	−	0.0970723i	0.0795898	−	0.00320736i
$917$	4.24367	+	0.866352i	0.140138	+	0.0286095i
$918$	8.04600	+	5.55375i	0.265557	+	0.183301i
$919$	−38.5758	−	12.8785i	−1.27250	−	0.424822i	−0.401386	−	0.915909i	$-0.631472\pi$
$919$	−38.5758	−	12.8785i	−1.27250	−	0.424822i	−0.871111	+	0.491087i	$0.836600\pi$
$920$	−7.65946	−	16.1420i	−0.252525	−	0.532185i
$921$	9.80344	−	8.00426i	0.323034	−	0.263749i
$922$	−3.02412	+	7.97396i	−0.0995942	+	0.262608i
$923$	16.1383	+	5.17714i	0.531197	+	0.170408i
$924$	−0.611766	−	1.61309i	−0.0201256	−	0.0530669i
$925$	−10.9516	−	6.32290i	−0.360086	−	0.207896i
$926$	−38.7447	−	47.4536i	−1.27323	−	1.55942i
$927$	5.27686	−	3.96531i	0.173315	−	0.130238i
$928$	1.59465	+	3.03835i	0.0523470	+	0.0997388i
$929$	1.01537	−	12.5776i	0.0333131	−	0.412657i	−0.958512	−	0.285052i	$-0.907989\pi$
$929$	1.01537	−	12.5776i	0.0333131	−	0.412657i	0.991825	−	0.127605i	$-0.0407289\pi$
$930$	0.0375291	−	0.464881i	0.00123063	−	0.0152441i
$931$	−12.9262	−	24.6288i	−0.423638	−	0.807175i
$932$	7.69337	−	5.78119i	0.252005	−	0.189369i
$933$	−3.15755	−	3.86730i	−0.103374	−	0.126610i
$934$	−30.8964	−	17.8380i	−1.01096	−	0.583679i
$935$	14.4817	+	38.1850i	0.473601	+	1.24878i
$936$	−7.74798	−	4.77262i	−0.253251	−	0.155998i
$937$	−16.9451	+	44.6806i	−0.553573	+	1.45965i	0.307686	+	0.951488i	$0.400445\pi$
$937$	−16.9451	+	44.6806i	−0.553573	+	1.45965i	−0.861260	+	0.508165i	$0.830324\pi$
$938$	−5.72146	+	4.67143i	−0.186812	+	0.152528i
$939$	10.6642	+	22.4744i	0.348014	+	0.733425i
$940$	3.98560	+	1.33059i	0.129996	+	0.0433990i
$941$	18.8151	+	12.9871i	0.613356	+	0.423369i	0.833828	−	0.552024i	$-0.186144\pi$
$941$	18.8151	+	12.9871i	0.613356	+	0.423369i	−0.220472	+	0.975393i	$0.570760\pi$
$942$	3.92062	+	0.800400i	0.127741	+	0.0260784i
$943$	−46.2570	+	1.86409i	−1.50633	+	0.0607032i
$944$			44.6499i			1.45323i
$945$	−0.0371148	−	0.920993i	−0.00120734	−	0.0299599i
$946$	21.3205	+	16.0213i	0.693191	+	0.520899i
$947$	−3.32178	+	20.4398i	−0.107943	+	0.664203i	0.875532	+	0.483160i	$0.160511\pi$
$947$	−3.32178	+	20.4398i	−0.107943	+	0.664203i	−0.983475	+	0.181042i	$0.942053\pi$
$948$	−3.84107	−	2.01595i	−0.124752	−	0.0654750i
$949$	19.7653	+	27.9251i	0.641609	+	0.906488i
$950$	22.6841	−	11.9055i	0.735969	−	0.386266i
$951$	−9.17667	−	27.4875i	−0.297574	−	0.891343i
$952$	−2.68600	−	13.1569i	−0.0870536	−	0.426417i
$953$	11.5732	+	39.9553i	0.374892	+	1.29428i	0.897239	+	0.441545i	$0.145570\pi$
$953$	11.5732	+	39.9553i	0.374892	+	1.29428i	−0.522346	+	0.852733i	$0.674943\pi$
$954$	7.54541	+	0.916178i	0.244292	+	0.0296624i
$955$	−4.34637	+	13.0190i	−0.140645	+	0.421284i
$956$	0.465195	+	2.86246i	0.0150455	+	0.0925787i
$957$	4.65824	−	8.87553i	0.150579	−	0.286905i
$958$	47.7502	+	30.1954i	1.54274	+	0.975569i
$959$	12.0300	+	5.12550i	0.388469	+	0.165511i
$960$	6.61421	−	1.35030i	0.213473	−	0.0435807i
$961$	−30.0256	+	7.40064i	−0.968567	+	0.238730i
$962$	−14.4689	−	11.5320i	−0.466497	−	0.371806i
$963$	0.546517	+	0.134704i	0.0176113	+	0.00434079i
$964$	−1.16500	−	0.0469477i	−0.0375220	−	0.00151208i
$965$	−0.761823	+	18.9044i	−0.0245239	+	0.608556i
$966$	−5.20074	+	6.36975i	−0.167331	+	0.204943i
$967$	−41.5306	+	15.7505i	−1.33553	+	0.506501i	−0.915978	−	0.401229i	$-0.868583\pi$
$967$	−41.5306	+	15.7505i	−1.33553	+	0.506501i	−0.419555	+	0.907730i	$0.637814\pi$
$968$	−51.8728	−	24.6139i	−1.66725	−	0.791122i
$969$	27.0034	−	7.82164i	0.867475	−	0.251267i
$970$	−19.0461	+	13.1466i	−0.611534	+	0.422111i
$971$	28.9740	−	12.3447i	0.929821	−	0.396160i	0.126677	−	0.991944i	$-0.459569\pi$
$971$	28.9740	−	12.3447i	0.929821	−	0.396160i	0.803144	+	0.595784i	$0.203159\pi$
$972$	0.350944	+	0.0570339i	0.0112565	+	0.00182936i
$973$	1.40030	+	2.21440i	0.0448916	+	0.0709904i
$974$	−5.03727	+	7.29774i	−0.161404	+	0.233835i
$975$	−1.25743	−	13.5786i	−0.0402701	−	0.434863i
$976$	5.40279	+	7.82729i	0.172939	+	0.250546i
$977$	4.60732	−	10.8138i	0.147401	−	0.345963i	−0.829870	−	0.557957i	$-0.811585\pi$
$977$	4.60732	−	10.8138i	0.147401	−	0.345963i	0.977271	+	0.211994i	$0.0679956\pi$
$978$	−3.15867	+	10.9050i	−0.101003	+	0.348704i
$979$	61.6422	+	4.97627i	1.97009	+	0.159042i
$980$	−1.63982	+	1.85097i	−0.0523821	+	0.0591271i
$981$	−5.71295	+	9.03430i	−0.182400	+	0.288443i
$982$	15.4646	+	36.2968i	0.493495	+	1.15828i
$983$	−36.7564	+	4.46304i	−1.17235	+	0.142349i	−0.683454	−	0.729994i	$-0.739523\pi$
$983$	−36.7564	+	4.46304i	−1.17235	+	0.142349i	−0.488895	+	0.872343i	$0.662600\pi$
$984$	3.64331	−	17.8461i	0.116145	−	0.568914i
$985$	24.5121	−	1.97882i	0.781019	−	0.0630504i
$986$	−10.1338	+	13.4856i	−0.322725	+	0.429469i
$987$	1.07813	+	8.87920i	0.0343173	+	0.282628i
$988$	5.34506	−	1.85475i	0.170049	−	0.0590073i
$989$	2.31280	−	19.0476i	0.0735427	−	0.605679i
$990$	7.09634	+	6.81613i	0.225537	+	0.216631i
$991$	−18.2774	+	31.6573i	−0.580600	+	1.00563i	0.414808	+	0.909909i	$0.363849\pi$
$991$	−18.2774	+	31.6573i	−0.580600	+	1.00563i	−0.995408	+	0.0957198i	$0.969485\pi$
$992$	−0.273813	−	0.474258i	−0.00869357	−	0.0150577i
$993$	−2.07454	+	8.41674i	−0.0658335	+	0.267097i
$994$	4.66758	+	3.81096i	0.148047	+	0.120876i
$995$	14.6815	−	8.47637i	0.465435	−	0.268719i
$996$	0.295922	+	0.112228i	0.00937665	+	0.00355610i
$997$	17.7682	+	18.4986i	0.562724	+	0.585857i	0.940396	−	0.340082i	$-0.110455\pi$
$997$	17.7682	+	18.4986i	0.562724	+	0.585857i	−0.377672	+	0.925939i	$0.623275\pi$
$998$	−41.4435	+	13.8359i	−1.31187	+	0.437967i
$999$	−3.21155	−	0.930236i	−0.101609	−	0.0294314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.433.4	yes	360
169.153	even	78	inner	507.2.t.b.322.4	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.322.4	✓	360	169.153	even	78	inner
507.2.t.b.433.4	yes	360	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.123498 - 1.52980i) q^{2} +(0.845190 - 0.534466i) q^{3} +(-0.350944 + 0.0570339i) q^{4} +(-0.731801 - 0.826032i) q^{5} +(-0.922007 - 1.22697i) q^{6} +(-0.602375 + 0.578589i) q^{7} +(-0.604002 - 2.45053i) q^{8} +(0.428693 - 0.903450i) q^{9} +O(q^{10})\)	\(q+(-0.123498 - 1.52980i) q^{2} +(0.845190 - 0.534466i) q^{3} +(-0.350944 + 0.0570339i) q^{4} +(-0.731801 - 0.826032i) q^{5} +(-0.922007 - 1.22697i) q^{6} +(-0.602375 + 0.578589i) q^{7} +(-0.604002 - 2.45053i) q^{8} +(0.428693 - 0.903450i) q^{9} +(-1.17329 + 1.22152i) q^{10} +(5.24852 - 2.49045i) q^{11} +(-0.266132 + 0.235772i) q^{12} +(3.38608 + 1.23872i) q^{13} +(0.959520 + 0.850060i) q^{14} +(-1.06000 - 0.307032i) q^{15} +(-4.34874 + 1.45182i) q^{16} +(-4.41268 - 4.59409i) q^{17} +(-1.43504 - 0.544240i) q^{18} +(-3.82210 + 2.20669i) q^{19} +(0.303933 + 0.248153i) q^{20} +(-0.199885 + 0.810967i) q^{21} +(-4.45809 - 7.72163i) q^{22} +(-3.20742 + 5.55542i) q^{23} +(-1.82022 - 1.74835i) q^{24} +(0.455886 - 3.75456i) q^{25} +(1.47682 - 5.33302i) q^{26} +(-0.120537 - 0.992709i) q^{27} +(0.178401 - 0.237408i) q^{28} +(1.71982 - 0.138839i) q^{29} +(-0.338790 + 1.65950i) q^{30} +(-0.273356 + 0.0331915i) q^{31} +(0.779517 + 1.82959i) q^{32} +(3.10493 - 4.91006i) q^{33} +(-6.48309 + 7.31790i) q^{34} +(0.918752 + 0.0741693i) q^{35} +(-0.0989197 + 0.341510i) q^{36} +(1.31056 - 3.07600i) q^{37} +(3.84782 + 5.57453i) q^{38} +(3.52394 - 0.762791i) q^{39} +(-1.58221 + 2.29223i) q^{40} +(3.85712 + 6.09955i) q^{41} +(1.26530 + 0.205632i) q^{42} +(-2.75176 + 1.17242i) q^{43} +(-1.69989 + 1.17335i) q^{44} +(-1.06000 + 0.307032i) q^{45} +(8.89481 + 4.22064i) q^{46} +(10.0129 - 3.79741i) q^{47} +(-2.89956 + 3.55132i) q^{48} +(-0.253771 + 6.29727i) q^{49} +(-5.80004 - 0.233734i) q^{50} +(-6.18494 - 1.52445i) q^{51} +(-1.25897 - 0.241600i) q^{52} +(-4.80848 + 1.18518i) q^{53} +(-1.50376 + 0.306995i) q^{54} +(-5.89807 - 2.51293i) q^{55} +(1.78169 + 1.12667i) q^{56} +(-2.05100 + 3.90785i) q^{57} +(-0.424791 - 2.61385i) q^{58} +(3.08401 - 9.23774i) q^{59} +(0.389511 + 0.0472952i) q^{60} +(-0.577159 - 1.99258i) q^{61} +(0.0845355 + 0.414082i) q^{62} +(0.264493 + 0.792253i) q^{63} +(-5.41642 + 2.84276i) q^{64} +(-1.45472 - 3.70351i) q^{65} +(-7.89488 - 4.14355i) q^{66} +(-0.924285 + 5.68735i) q^{67} +(1.81062 + 1.36060i) q^{68} +(0.258300 + 6.40964i) q^{69} -1.41467i q^{70} +(4.69681 - 0.189275i) q^{71} +(-2.47287 - 0.504839i) q^{72} +(7.80911 + 5.39024i) q^{73} +(-4.86753 - 1.62502i) q^{74} +(-1.62137 - 3.41697i) q^{75} +(1.21548 - 0.992413i) q^{76} +(-1.72063 + 4.53692i) q^{77} +(-1.60212 - 5.29673i) q^{78} +(4.32645 + 11.4079i) q^{79} +(4.38166 + 2.52975i) q^{80} +(-0.632445 - 0.774605i) q^{81} +(8.85476 - 6.65392i) q^{82} +(-0.413670 - 0.788183i) q^{83} +(0.0238959 - 0.296004i) q^{84} +(-0.565662 + 7.00698i) q^{85} +(2.13340 + 4.06486i) q^{86} +(1.37937 - 1.03653i) q^{87} +(-9.27305 - 11.3574i) q^{88} +(9.21906 + 5.32263i) q^{89} +(0.600606 + 1.58367i) q^{90} +(-2.75640 + 1.21298i) q^{91} +(0.808778 - 2.13257i) q^{92} +(-0.213298 + 0.174153i) q^{93} +(-7.04586 - 14.8488i) q^{94} +(4.61981 + 1.54232i) q^{95} +(1.63670 + 1.12973i) q^{96} +(13.3876 + 2.73310i) q^{97} +(9.66492 - 0.389483i) q^{98} -5.80941i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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