LMFDB - Embedded newform 546.2.bg.b.311.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(311,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 3]))

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

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

chi := DirichletCharacter("546.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bg (of order $6$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.14
Character	$\chi$	$=$	546.311
Dual form			546.2.bg.b.467.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.24618 - 1.20292i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0916492 + 0.0529137i) q^{5} +(1.66485 + 0.477766i) q^{6} +(2.29863 + 1.31008i) q^{7} -1.00000 q^{8} +(0.105953 - 2.99813i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.24618 - 1.20292i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0916492 + 0.0529137i) q^{5} +(1.66485 + 0.477766i) q^{6} +(2.29863 + 1.31008i) q^{7} -1.00000 q^{8} +(0.105953 - 2.99813i) q^{9} +(-0.0916492 - 0.0529137i) q^{10} +(-0.603696 + 1.04563i) q^{11} +(0.418670 + 1.68069i) q^{12} +(3.60130 - 0.175001i) q^{13} +(0.0147545 + 2.64571i) q^{14} +(-0.0505607 + 0.176187i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.14124 - 1.97669i) q^{17} +(2.64943 - 1.40731i) q^{18} +(1.82371 + 3.15875i) q^{19} -0.105827i q^{20} +(4.44044 - 1.13248i) q^{21} -1.20739 q^{22} +(0.845930 - 0.488398i) q^{23} +(-1.24618 + 1.20292i) q^{24} +(-2.49440 + 4.32043i) q^{25} +(1.95221 + 3.03132i) q^{26} +(-3.47448 - 3.86367i) q^{27} +(-2.28387 + 1.33563i) q^{28} -7.03811i q^{29} +(-0.177863 + 0.0443067i) q^{30} +(-0.610707 + 1.05778i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.505498 + 2.02925i) q^{33} +2.28248 q^{34} +(-0.279988 + 0.00156143i) q^{35} +(2.54348 + 1.59082i) q^{36} +(-2.01173 + 1.16147i) q^{37} +(-1.82371 + 3.15875i) q^{38} +(4.27738 - 4.55017i) q^{39} +(0.0916492 - 0.0529137i) q^{40} -0.417669i q^{41} +(3.20097 + 3.27929i) q^{42} +4.90433 q^{43} +(-0.603696 - 1.04563i) q^{44} +(0.148932 + 0.280382i) q^{45} +(0.845930 + 0.488398i) q^{46} +(-1.47958 + 0.854236i) q^{47} +(-1.66485 - 0.477766i) q^{48} +(3.56739 + 6.02276i) q^{49} -4.98880 q^{50} +(-0.955606 - 3.83614i) q^{51} +(-1.64910 + 3.20632i) q^{52} +(-1.77421 - 1.02434i) q^{53} +(1.60880 - 4.94083i) q^{54} -0.127775i q^{55} +(-2.29863 - 1.31008i) q^{56} +(6.07241 + 1.74261i) q^{57} +(6.09518 - 3.51906i) q^{58} +(-9.04020 - 5.21936i) q^{59} +(-0.127302 - 0.131880i) q^{60} +(-8.67338 + 5.00758i) q^{61} -1.22141 q^{62} +(4.17133 - 6.75278i) q^{63} +1.00000 q^{64} +(-0.320796 + 0.206597i) q^{65} +(-1.50463 + 1.45240i) q^{66} +(-5.65318 - 3.26387i) q^{67} +(1.14124 + 1.97669i) q^{68} +(0.466680 - 1.62622i) q^{69} +(-0.141346 - 0.241696i) q^{70} -2.72046 q^{71} +(-0.105953 + 2.99813i) q^{72} +(3.72258 - 6.44769i) q^{73} +(-2.01173 - 1.16147i) q^{74} +(2.08866 + 8.38462i) q^{75} -3.64741 q^{76} +(-2.75753 + 1.61263i) q^{77} +(6.07925 + 1.42923i) q^{78} +(-5.04911 - 8.74532i) q^{79} +(0.0916492 + 0.0529137i) q^{80} +(-8.97755 - 0.635319i) q^{81} +(0.361712 - 0.208835i) q^{82} +11.6784i q^{83} +(-1.23947 + 4.41177i) q^{84} +0.241549i q^{85} +(2.45216 + 4.24727i) q^{86} +(-8.46631 - 8.77079i) q^{87} +(0.603696 - 1.04563i) q^{88} +(-14.7044 + 8.48960i) q^{89} +(-0.168352 + 0.269170i) q^{90} +(8.50732 + 4.31572i) q^{91} +0.976796i q^{92} +(0.511369 + 2.05282i) q^{93} +(-1.47958 - 0.854236i) q^{94} +(-0.334282 - 0.192998i) q^{95} +(-0.418670 - 1.68069i) q^{96} -8.85297 q^{97} +(-3.43217 + 6.10084i) q^{98} +(3.07098 + 1.92075i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9} + 14 q^{15} - 18 q^{16} - 4 q^{18} - 23 q^{21} + 14 q^{25} + 6 q^{26} + 7 q^{30} + 18 q^{32} - 24 q^{33} - 8 q^{36} + 10 q^{39} - 16 q^{42} - 16 q^{43} + 9 q^{45} - 72 q^{47} + 12 q^{49} + 28 q^{50} - 3 q^{51} + 6 q^{52} - 9 q^{54} + 8 q^{57} - 24 q^{59} - 7 q^{60} - 36 q^{61} + 39 q^{63} + 36 q^{64} - 18 q^{65} - 24 q^{66} + 72 q^{71} - 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} + 7 q^{84} - 8 q^{86} - 24 q^{87} + 72 q^{89} - 2 q^{91} + 14 q^{93} - 72 q^{94} + 12 q^{98} - 72 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9 + 14 * q^15 - 18 * q^16 - 4 * q^18 - 23 * q^21 + 14 * q^25 + 6 * q^26 + 7 * q^30 + 18 * q^32 - 24 * q^33 - 8 * q^36 + 10 * q^39 - 16 * q^42 - 16 * q^43 + 9 * q^45 - 72 * q^47 + 12 * q^49 + 28 * q^50 - 3 * q^51 + 6 * q^52 - 9 * q^54 + 8 * q^57 - 24 * q^59 - 7 * q^60 - 36 * q^61 + 39 * q^63 + 36 * q^64 - 18 * q^65 - 24 * q^66 + 72 * q^71 - 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 + 7 * q^84 - 8 * q^86 - 24 * q^87 + 72 * q^89 - 2 * q^91 + 14 * q^93 - 72 * q^94 + 12 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.24618	−	1.20292i	0.719485	−	0.694508i
$3$	1.24618	−	1.20292i	0.719485	−	0.694508i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.0916492	+	0.0529137i	−0.0409868	+	0.0236637i	−0.520353	−	0.853951i	$-0.674200\pi$
$5$	−0.0916492	+	0.0529137i	−0.0409868	+	0.0236637i	0.479367	+	0.877615i	$0.340866\pi$
$6$	1.66485	+	0.477766i	0.679674	+	0.195047i
$7$	2.29863	+	1.31008i	0.868800	+	0.495163i
$7$	2.29863	+	1.31008i	0.868800	+	0.495163i
$8$	−1.00000			−0.353553
$9$	0.105953	−	2.99813i	0.0353175	−	0.999376i
$10$	−0.0916492	−	0.0529137i	−0.0289820	−	0.0167328i
$11$	−0.603696	+	1.04563i	−0.182021	+	0.315270i	−0.942569	−	0.334012i	$-0.891597\pi$
$11$	−0.603696	+	1.04563i	−0.182021	+	0.315270i	0.760547	+	0.649282i	$0.224931\pi$
$12$	0.418670	+	1.68069i	0.120859	+	0.485173i
$13$	3.60130	−	0.175001i	0.998821	−	0.0485364i
$13$	3.60130	−	0.175001i	0.998821	−	0.0485364i
$14$	0.0147545	+	2.64571i	0.00394331	+	0.707096i
$15$	−0.0505607	+	0.176187i	−0.0130547	+	0.0454913i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.14124	−	1.97669i	0.276792	−	0.479417i	−0.693794	−	0.720174i	$-0.744062\pi$
$17$	1.14124	−	1.97669i	0.276792	−	0.479417i	0.970586	+	0.240756i	$0.0773955\pi$
$18$	2.64943	−	1.40731i	0.624477	−	0.331705i
$19$	1.82371	+	3.15875i	0.418387	+	0.724667i	0.995777	−	0.0918008i	$-0.0292623\pi$
$19$	1.82371	+	3.15875i	0.418387	+	0.724667i	−0.577390	+	0.816468i	$0.695929\pi$
$20$		−	0.105827i		−	0.0236637i
$21$	4.44044	−	1.13248i	0.968983	−	0.247127i
$22$	−1.20739			−0.257417
$23$	0.845930	−	0.488398i	0.176389	−	0.101838i	−0.409206	−	0.912442i	$-0.634194\pi$
$23$	0.845930	−	0.488398i	0.176389	−	0.101838i	0.585595	+	0.810604i	$0.300861\pi$
$24$	−1.24618	+	1.20292i	−0.254376	+	0.245546i
$25$	−2.49440	+	4.32043i	−0.498880	+	0.864086i
$26$	1.95221	+	3.03132i	0.382859	+	0.594490i
$27$	−3.47448	−	3.86367i	−0.668664	−	0.743565i
$28$	−2.28387	+	1.33563i	−0.431612	+	0.252411i
$29$		−	7.03811i		−	1.30694i	−0.756951	−	0.653472i	$-0.773312\pi$
$29$		−	7.03811i		−	1.30694i	0.756951	−	0.653472i	$-0.226688\pi$
$30$	−0.177863	+	0.0443067i	−0.0324732	+	0.00808926i
$31$	−0.610707	+	1.05778i	−0.109686	+	0.189982i	−0.915643	−	0.401992i	$-0.868318\pi$
$31$	−0.610707	+	1.05778i	−0.109686	+	0.189982i	0.805957	+	0.591974i	$0.201651\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.505498	+	2.02925i	0.0879960	+	0.353247i
$34$	2.28248			0.391442
$35$	−0.279988	+	0.00156143i	−0.0473267	+	0.000263930i
$36$	2.54348	+	1.59082i	0.423913	+	0.265137i
$37$	−2.01173	+	1.16147i	−0.330726	+	0.190945i	−0.656163	−	0.754619i	$-0.727822\pi$
$37$	−2.01173	+	1.16147i	−0.330726	+	0.190945i	0.325438	+	0.945564i	$0.394488\pi$
$38$	−1.82371	+	3.15875i	−0.295844	+	0.512417i
$39$	4.27738	−	4.55017i	0.684928	−	0.728611i
$40$	0.0916492	−	0.0529137i	0.0144910	−	0.00836639i
$41$		−	0.417669i		−	0.0652290i	−0.999468	−	0.0326145i	$-0.989617\pi$
$41$		−	0.417669i		−	0.0652290i	0.999468	−	0.0326145i	$-0.0103834\pi$
$42$	3.20097	+	3.27929i	0.493921	+	0.506006i
$43$	4.90433			0.747903			0.373951	−	0.927448i	$-0.378003\pi$
$43$	4.90433			0.747903			0.373951	+	0.927448i	$0.378003\pi$
$44$	−0.603696	−	1.04563i	−0.0910106	−	0.157635i
$45$	0.148932	+	0.280382i	0.0222014	+	0.0417969i
$46$	0.845930	+	0.488398i	0.124726	+	0.0720104i
$47$	−1.47958	+	0.854236i	−0.215819	+	0.124603i	−0.604013	−	0.796975i	$-0.706432\pi$
$47$	−1.47958	+	0.854236i	−0.215819	+	0.124603i	0.388194	+	0.921578i	$0.373099\pi$
$48$	−1.66485	−	0.477766i	−0.240301	−	0.0689596i
$49$	3.56739	+	6.02276i	0.509628	+	0.860395i
$50$	−4.98880			−0.705523
$51$	−0.955606	−	3.83614i	−0.133812	−	0.537167i
$52$	−1.64910	+	3.20632i	−0.228688	+	0.444636i
$53$	−1.77421	−	1.02434i	−0.243706	−	0.140704i	0.373173	−	0.927762i	$-0.378270\pi$
$53$	−1.77421	−	1.02434i	−0.243706	−	0.140704i	−0.616879	+	0.787058i	$0.711603\pi$
$54$	1.60880	−	4.94083i	0.218930	−	0.672361i
$55$		−	0.127775i		−	0.0172292i
$56$	−2.29863	−	1.31008i	−0.307167	−	0.175066i
$57$	6.07241	+	1.74261i	0.804310	+	0.230814i
$58$	6.09518	−	3.51906i	0.800337	−	0.462075i
$59$	−9.04020	−	5.21936i	−1.17693	−	0.679503i	−0.221631	−	0.975131i	$-0.571138\pi$
$59$	−9.04020	−	5.21936i	−1.17693	−	0.679503i	−0.955303	+	0.295628i	$0.904471\pi$
$60$	−0.127302	−	0.131880i	−0.0164346	−	0.0170257i
$61$	−8.67338	+	5.00758i	−1.11051	+	0.641154i	−0.938962	−	0.344021i	$-0.888211\pi$
$61$	−8.67338	+	5.00758i	−1.11051	+	0.641154i	−0.171550	+	0.985175i	$0.554878\pi$
$62$	−1.22141			−0.155120
$63$	4.17133	−	6.75278i	0.525538	−	0.850770i
$64$	1.00000			0.125000
$65$	−0.320796	+	0.206597i	−0.0397899	+	0.0256252i
$66$	−1.50463	+	1.45240i	−0.185208	+	0.178778i
$67$	−5.65318	−	3.26387i	−0.690646	−	0.398745i	0.113208	−	0.993571i	$-0.463887\pi$
$67$	−5.65318	−	3.26387i	−0.690646	−	0.398745i	−0.803854	+	0.594827i	$0.797221\pi$
$68$	1.14124	+	1.97669i	0.138396	+	0.239709i
$69$	0.466680	−	1.62622i	0.0561817	−	0.195774i
$70$	−0.141346	−	0.241696i	−0.0168941	−	0.0288882i
$71$	−2.72046			−0.322859			−0.161430	−	0.986884i	$-0.551610\pi$
$71$	−2.72046			−0.322859			−0.161430	+	0.986884i	$0.551610\pi$
$72$	−0.105953	+	2.99813i	−0.0124866	+	0.353333i
$73$	3.72258	−	6.44769i	0.435695	−	0.754645i	−0.561658	−	0.827370i	$-0.689836\pi$
$73$	3.72258	−	6.44769i	0.435695	−	0.754645i	0.997352	+	0.0727248i	$0.0231695\pi$
$74$	−2.01173	−	1.16147i	−0.233858	−	0.135018i
$75$	2.08866	+	8.38462i	0.241178	+	0.968173i
$76$	−3.64741			−0.418387
$77$	−2.75753	+	1.61263i	−0.314250	+	0.183777i
$78$	6.07925	+	1.42923i	0.688340	+	0.161828i
$79$	−5.04911	−	8.74532i	−0.568069	−	0.983925i	−0.996757	−	0.0804722i	$-0.974357\pi$
$79$	−5.04911	−	8.74532i	−0.568069	−	0.983925i	0.428687	−	0.903453i	$-0.358976\pi$
$80$	0.0916492	+	0.0529137i	0.0102467	+	0.00591593i
$81$	−8.97755	−	0.635319i	−0.997505	−	0.0705910i
$82$	0.361712	−	0.208835i	0.0399444	−	0.0230619i
$83$			11.6784i			1.28188i	0.767593	+	0.640938i	$0.221454\pi$
$83$			11.6784i			1.28188i	−0.767593	+	0.640938i	$0.778546\pi$
$84$	−1.23947	+	4.41177i	−0.135237	+	0.481364i
$85$			0.241549i			0.0261997i
$86$	2.45216	+	4.24727i	0.264424	+	0.457995i
$87$	−8.46631	−	8.77079i	−0.907683	−	0.940327i
$88$	0.603696	−	1.04563i	0.0643542	−	0.111465i
$89$	−14.7044	+	8.48960i	−1.55867	+	0.899896i	−0.561281	+	0.827626i	$0.689691\pi$
$89$	−14.7044	+	8.48960i	−1.55867	+	0.899896i	−0.997385	+	0.0722705i	$0.976976\pi$
$90$	−0.168352	+	0.269170i	−0.0177459	+	0.0283730i
$91$	8.50732	+	4.31572i	0.891810	+	0.452411i
$92$			0.976796i			0.101838i
$93$	0.511369	+	2.05282i	0.0530264	+	0.212867i
$94$	−1.47958	−	0.854236i	−0.152607	−	0.0881077i
$95$	−0.334282	−	0.192998i	−0.0342966	−	0.0198012i
$96$	−0.418670	−	1.68069i	−0.0427303	−	0.171535i
$97$	−8.85297			−0.898883			−0.449441	−	0.893310i	$-0.648377\pi$
$97$	−8.85297			−0.898883			−0.449441	+	0.893310i	$0.648377\pi$
$98$	−3.43217	+	6.10084i	−0.346701	+	0.616278i
$99$	3.07098	+	1.92075i	0.308645	+	0.193042i
$100$	−2.49440	−	4.32043i	−0.249440	−	0.432043i
$101$	−5.84190	+	10.1185i	−0.581291	+	1.00682i	0.414036	+	0.910260i	$0.364119\pi$
$101$	−5.84190	+	10.1185i	−0.581291	+	1.00682i	−0.995327	+	0.0965644i	$0.969215\pi$
$102$	2.84439	−	2.74565i	0.281637	−	0.271860i
$103$	−0.999136	+	0.576851i	−0.0984478	+	0.0568388i	−0.548416	−	0.836206i	$-0.684769\pi$
$103$	−0.999136	+	0.576851i	−0.0984478	+	0.0568388i	0.449968	+	0.893045i	$0.351435\pi$
$104$	−3.60130	+	0.175001i	−0.353137	+	0.0171602i
$105$	−0.347039	+	0.338750i	−0.0338675	+	0.0330587i
$106$		−	2.04868i		−	0.198985i
$107$	10.5362	−	6.08311i	1.01858	−	0.588076i	0.104886	−	0.994484i	$-0.466552\pi$
$107$	10.5362	−	6.08311i	1.01858	−	0.588076i	0.913692	+	0.406408i	$0.133219\pi$
$108$	5.08328	−	1.07715i	0.489139	−	0.103649i
$109$	−6.24015	−	3.60275i	−0.597698	−	0.345081i	0.170437	−	0.985368i	$-0.445482\pi$
$109$	−6.24015	−	3.60275i	−0.597698	−	0.345081i	−0.768135	+	0.640287i	$0.778815\pi$
$110$	0.110657	−	0.0638876i	0.0105507	−	0.00609144i
$111$	−1.10982	+	3.86736i	−0.105340	+	0.367073i
$112$	−0.0147545	−	2.64571i	−0.00139417	−	0.249996i
$113$		−	13.3168i		−	1.25274i	−0.779526	−	0.626370i	$-0.784540\pi$
$113$		−	13.3168i		−	1.25274i	0.779526	−	0.626370i	$-0.215460\pi$
$114$	1.52706	+	6.13017i	0.143022	+	0.574143i
$115$	−0.0516859	+	0.0895226i	−0.00481973	+	0.00834802i
$116$	6.09518	+	3.51906i	0.565924	+	0.326736i
$117$	−0.143107	−	10.8157i	−0.0132302	−	0.999912i
$118$		−	10.4387i		−	0.960963i
$119$	5.21290	−	3.04856i	0.477866	−	0.279461i
$120$	0.0505607	−	0.176187i	0.00461554	−	0.0160836i
$121$	4.77110	+	8.26379i	0.433737	+	0.751254i
$122$	−8.67338	−	5.00758i	−0.785251	−	0.453365i
$123$	−0.502424	−	0.520493i	−0.0453020	−	0.0469313i
$124$	−0.610707	−	1.05778i	−0.0548431	−	0.0949910i
$125$		−	1.05709i		−	0.0945488i
$126$	7.93374	+	0.236084i	0.706794	+	0.0210320i
$127$	13.7882			1.22351			0.611755	−	0.791048i	$-0.290464\pi$
$127$	13.7882			1.22351			0.611755	+	0.791048i	$0.290464\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	6.11170	−	5.89953i	0.538105	−	0.519424i
$130$	−0.339316	−	0.174519i	−0.0297600	−	0.0153064i
$131$	6.41784	+	11.1160i	0.560729	+	0.971212i	0.997433	+	0.0716063i	$0.0228125\pi$
$131$	6.41784	+	11.1160i	0.560729	+	0.971212i	−0.436704	+	0.899605i	$0.643854\pi$
$132$	−2.01013	−	0.576851i	−0.174960	−	0.0502085i
$133$	0.0538159	+	9.65000i	0.00466643	+	0.836761i
$134$		−	6.52773i		−	0.563910i
$135$	0.522875	+	0.170255i	0.0450019	+	0.0146532i
$136$	−1.14124	+	1.97669i	−0.0978606	+	0.169500i
$137$	−2.91269	+	5.04492i	−0.248848	+	0.431017i	−0.963206	−	0.268763i	$-0.913385\pi$
$137$	−2.91269	+	5.04492i	−0.248848	+	0.431017i	0.714359	+	0.699780i	$0.246718\pi$
$138$	1.64169	−	0.408955i	0.139750	−	0.0348125i
$139$		−	18.0901i		−	1.53438i	−0.641420	−	0.767190i	$-0.721654\pi$
$139$		−	18.0901i		−	1.53438i	0.641420	−	0.767190i	$-0.278346\pi$
$140$	0.138642	−	0.243258i	0.0117174	−	0.0205590i
$141$	−0.816250	+	2.84436i	−0.0687406	+	0.239538i
$142$	−1.36023	−	2.35599i	−0.114148	−	0.197710i
$143$	−1.99111	+	3.87129i	−0.166505	+	0.323733i
$144$	−2.64943	+	1.40731i	−0.220786	+	0.117276i
$145$	0.372412	+	0.645037i	0.0309272	+	0.0535674i
$146$	7.44515			0.616165
$147$	11.6906	+	3.21418i	0.964221	+	0.265101i
$148$		−	2.32294i		−	0.190945i
$149$	−5.92542	−	10.2631i	−0.485429	−	0.840788i	0.514430	−	0.857532i	$-0.328003\pi$
$149$	−5.92542	−	10.2631i	−0.485429	−	0.840788i	−0.999860	+	0.0167437i	$0.994670\pi$
$150$	−6.21697	+	6.00114i	−0.507613	+	0.489991i
$151$	−15.7115	−	9.07106i	−1.27859	−	0.738192i	−0.301998	−	0.953309i	$-0.597654\pi$
$151$	−15.7115	−	9.07106i	−1.27859	−	0.738192i	−0.976588	+	0.215116i	$0.930987\pi$
$152$	−1.82371	−	3.15875i	−0.147922	−	0.256209i
$153$	−5.80545	−	3.63102i	−0.469342	−	0.293551i
$154$	−2.77535	−	1.58178i	−0.223644	−	0.127463i
$155$		−	0.129259i		−	0.0103823i
$156$	1.80188	+	5.97940i	0.144266	+	0.478735i
$157$	−15.3218	−	8.84604i	−1.22281	−	0.705991i	−0.257295	−	0.966333i	$-0.582831\pi$
$157$	−15.3218	−	8.84604i	−1.22281	−	0.705991i	−0.965516	+	0.260342i	$0.916165\pi$
$158$	5.04911	−	8.74532i	0.401686	−	0.695740i
$159$	−3.44319	+	0.857718i	−0.273063	+	0.0680215i
$160$			0.105827i			0.00836639i
$161$	2.58432	−	0.0144122i	0.203673	−	0.00113584i
$162$	−3.93857	−	8.09244i	−0.309443	−	0.635802i
$163$	4.80436	−	2.77380i	0.376306	−	0.217261i	−0.299904	−	0.953970i	$-0.596955\pi$
$163$	4.80436	−	2.77380i	0.376306	−	0.217261i	0.676210	+	0.736709i	$0.263621\pi$
$164$	0.361712	+	0.208835i	0.0282450	+	0.0163072i
$165$	−0.153704	−	0.159231i	−0.0119658	−	0.0123961i
$166$	−10.1138	+	5.83922i	−0.784985	+	0.453211i
$167$			9.21026i			0.712712i	0.934350	+	0.356356i	$0.115981\pi$
$167$			9.21026i			0.712712i	−0.934350	+	0.356356i	$0.884019\pi$
$168$	−4.44044	+	1.13248i	−0.342587	+	0.0873724i
$169$	12.9387	−	1.26046i	0.995288	−	0.0969584i
$170$	−0.209188	+	0.120775i	−0.0160440	+	0.00926298i
$171$	9.66357	−	5.13303i	0.738992	−	0.392532i
$172$	−2.45216	+	4.24727i	−0.186976	+	0.323851i
$173$	−5.82669	−	10.0921i	−0.442995	−	0.767289i	0.554915	−	0.831907i	$-0.312751\pi$
$173$	−5.82669	−	10.0921i	−0.442995	−	0.767289i	−0.997910	+	0.0646174i	$0.979417\pi$
$174$	3.36257	−	11.7174i	0.254916	−	0.888296i
$175$	−11.3938	+	6.66321i	−0.861290	+	0.503691i
$176$	1.20739			0.0910106
$177$	−17.5443	+	4.37038i	−1.31871	+	0.328498i
$178$	−14.7044	−	8.48960i	−1.10214	−	0.636323i
$179$	15.1632	+	8.75448i	1.13335	+	0.654341i	0.944776	−	0.327718i	$-0.106280\pi$
$179$	15.1632	+	8.75448i	1.13335	+	0.654341i	0.188576	+	0.982059i	$0.439613\pi$
$180$	−0.317284	−	0.0112127i	−0.0236490	−	0.000835744i
$181$		−	13.3881i		−	0.995127i	−0.867428	−	0.497564i	$-0.834228\pi$
$181$		−	13.3881i		−	0.995127i	0.867428	−	0.497564i	$-0.165772\pi$
$182$	0.516136	+	9.52542i	0.0382586	+	0.706071i
$183$	−4.78490	+	16.6738i	−0.353710	+	1.23256i
$184$	−0.845930	+	0.488398i	−0.0623628	+	0.0360052i
$185$	0.122915	−	0.212896i	0.00903692	−	0.0156524i
$186$	−1.52211	+	1.46927i	−0.111606	+	0.107732i
$187$	1.37793	+	2.38664i	0.100764	+	0.174528i
$188$		−	1.70847i		−	0.124603i
$189$	−2.92483	−	13.4330i	−0.212750	−	0.977107i
$190$		−	0.385996i		−	0.0280031i
$191$	−12.8955	+	7.44521i	−0.933084	+	0.538717i	−0.887786	−	0.460257i	$-0.847757\pi$
$191$	−12.8955	+	7.44521i	−0.933084	+	0.538717i	−0.0452987	+	0.998973i	$0.514424\pi$
$192$	1.24618	−	1.20292i	0.0899356	−	0.0868135i
$193$	11.3018	+	6.52508i	0.813519	+	0.469685i	0.848176	−	0.529714i	$-0.177701\pi$
$193$	11.3018	+	6.52508i	0.813519	+	0.469685i	−0.0346576	+	0.999399i	$0.511034\pi$
$194$	−4.42648	−	7.66690i	−0.317803	−	0.550451i
$195$	−0.151252	+	0.643351i	−0.0108313	+	0.0460713i
$196$	−6.99956	+	0.0780724i	−0.499969	+	0.00557660i
$197$	8.81199			0.627828			0.313914	−	0.949451i	$-0.398360\pi$
$197$	8.81199			0.627828			0.313914	+	0.949451i	$0.398360\pi$
$198$	−0.127926	+	3.61992i	−0.00909133	+	0.257256i
$199$	13.8134	+	7.97517i	0.979206	+	0.565345i	0.902030	−	0.431673i	$-0.142076\pi$
$199$	13.8134	+	7.97517i	0.979206	+	0.565345i	0.0771758	+	0.997017i	$0.475410\pi$
$200$	2.49440	−	4.32043i	0.176381	−	0.305500i
$201$	−10.9711	+	2.73296i	−0.773841	+	0.192768i
$202$	−11.6838			−0.822069
$203$	9.22047	−	16.1780i	0.647150	−	1.13547i
$204$	3.80000	+	1.09049i	0.266053	+	0.0763498i
$205$	0.0221004	+	0.0382790i	0.00154356	+	0.00267352i
$206$	−0.999136	−	0.576851i	−0.0696131	−	0.0401911i
$207$	−1.37465	−	2.58796i	−0.0955449	−	0.179875i
$208$	−1.95221	−	3.03132i	−0.135361	−	0.210184i
$209$	−4.40386			−0.304621
$210$	−0.466886	−	0.131169i	−0.0322182	−	0.00905155i
$211$	16.2666			1.11984			0.559919	−	0.828547i	$-0.310832\pi$
$211$	16.2666			1.11984			0.559919	+	0.828547i	$0.310832\pi$
$212$	1.77421	−	1.02434i	0.121853	−	0.0703518i
$213$	−3.39020	+	3.27250i	−0.232292	+	0.224228i
$214$	10.5362	+	6.08311i	0.720243	+	0.415833i
$215$	−0.449477	+	0.259506i	−0.0306541	+	0.0176982i
$216$	3.47448	+	3.86367i	0.236408	+	0.262890i
$217$	−2.78956	+	1.63136i	−0.189367	+	0.110744i
$218$		−	7.20550i		−	0.488018i
$219$	−3.11706	−	12.5130i	−0.210631	−	0.845549i
$220$	0.110657	+	0.0638876i	0.00746046	+	0.00430730i
$221$	3.76403	−	7.31837i	0.253196	−	0.492287i
$222$	−3.90414	+	0.972545i	−0.262029	+	0.0652729i
$223$	19.4124			1.29995			0.649975	−	0.759955i	$-0.274779\pi$
$223$	19.4124			1.29995			0.649975	+	0.759955i	$0.274779\pi$
$224$	2.28387	−	1.33563i	0.152598	−	0.0892407i
$225$	12.6889	+	7.93629i	0.845927	+	0.529086i
$226$	11.5327	−	6.65841i	0.767144	−	0.442911i
$227$	14.8984	+	8.60159i	0.988841	+	0.570908i	0.904928	−	0.425566i	$-0.139925\pi$
$227$	14.8984	+	8.60159i	0.988841	+	0.570908i	0.0839133	+	0.996473i	$0.473258\pi$
$228$	−4.54535	+	4.38756i	−0.301023	+	0.290573i
$229$	4.77500	+	8.27054i	0.315541	+	0.546533i	0.979552	−	0.201190i	$-0.0644808\pi$
$229$	4.77500	+	8.27054i	0.315541	+	0.546533i	−0.664012	+	0.747722i	$0.731147\pi$
$230$	−0.103372			−0.00681613
$231$	−1.49652	+	5.32674i	−0.0984640	+	0.350474i
$232$			7.03811i			0.462075i
$233$	−9.52198	+	5.49752i	−0.623806	+	0.360154i	−0.778349	−	0.627832i	$-0.783943\pi$
$233$	−9.52198	+	5.49752i	−0.623806	+	0.360154i	0.154543	+	0.987986i	$0.450609\pi$
$234$	9.29512	−	5.53179i	0.607641	−	0.361624i
$235$	0.0904015	−	0.156580i	0.00589714	−	0.0102142i
$236$	9.04020	−	5.21936i	0.588467	−	0.339752i
$237$	−16.8121	−	4.82459i	−1.09206	−	0.313391i
$238$	5.24658	+	2.99023i	0.340085	+	0.193828i
$239$	−15.2257			−0.984868			−0.492434	−	0.870350i	$-0.663893\pi$
$239$	−15.2257			−0.984868			−0.492434	+	0.870350i	$0.663893\pi$
$240$	0.177863	−	0.0443067i	0.0114810	−	0.00285998i
$241$	8.18626	−	14.1790i	0.527323	−	0.913351i	−0.472170	−	0.881508i	$-0.656529\pi$
$241$	8.18626	−	14.1790i	0.527323	−	0.913351i	0.999493	−	0.0318429i	$-0.0101376\pi$
$242$	−4.77110	+	8.26379i	−0.306698	+	0.531217i
$243$	−11.9519	+	10.0076i	−0.766716	+	0.641986i
$244$		−	10.0152i		−	0.641154i
$245$	−0.645635	−	0.363217i	−0.0412481	−	0.0232051i
$246$	0.199548	−	0.695358i	0.0127227	−	0.0443344i
$247$	7.12050	+	11.0565i	0.453067	+	0.703506i
$248$	0.610707	−	1.05778i	0.0387799	−	0.0671688i
$249$	14.0483	+	14.5535i	0.890273	+	0.922290i
$250$	0.915465	−	0.528544i	0.0578991	−	0.0334281i
$251$	5.68832			0.359044			0.179522	−	0.983754i	$-0.442545\pi$
$251$	5.68832			0.359044			0.179522	+	0.983754i	$0.442545\pi$
$252$	3.76242	+	6.98886i	0.237010	+	0.440257i
$253$			1.17938i			0.0741468i
$254$	6.89412	+	11.9410i	0.432576	+	0.749243i
$255$	0.290565	+	0.301015i	0.0181959	+	0.0188503i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.39698	−	12.8119i	−0.461411	−	0.799187i	0.537621	−	0.843187i	$-0.319323\pi$
$257$	−7.39698	−	12.8119i	−0.461411	−	0.799187i	−0.999032	+	0.0439995i	$0.985990\pi$
$258$	8.16499	+	2.34312i	0.508330	+	0.145876i
$259$	−6.14583	+	0.0342739i	−0.381883	+	0.00212968i
$260$	−0.0185198	−	0.381116i	−0.00114855	−	0.0236358i
$261$	−21.1012	−	0.745706i	−1.30613	−	0.0461581i
$262$	−6.41784	+	11.1160i	−0.396496	+	0.686750i
$263$	20.3349	+	11.7403i	1.25390	+	0.723940i	0.971882	−	0.235468i	$-0.0756624\pi$
$263$	20.3349	+	11.7403i	1.25390	+	0.723940i	0.282020	+	0.959409i	$0.408996\pi$
$264$	−0.505498	−	2.02925i	−0.0311113	−	0.124892i
$265$	0.216806			0.0133183
$266$	−8.33023	+	4.87160i	−0.510759	+	0.298697i
$267$	−8.11209	+	28.2679i	−0.496452	+	1.72997i
$268$	5.65318	−	3.26387i	0.345323	−	0.199372i
$269$	−9.17404	+	15.8899i	−0.559351	+	0.968824i	0.438200	+	0.898878i	$0.355616\pi$
$269$	−9.17404	+	15.8899i	−0.559351	+	0.968824i	−0.997551	+	0.0699465i	$0.977717\pi$
$270$	0.113992	+	0.537950i	0.00693734	+	0.0327386i
$271$	11.0400	+	19.1219i	0.670634	+	1.16157i	0.977725	+	0.209891i	$0.0673110\pi$
$271$	11.0400	+	19.1219i	0.670634	+	1.16157i	−0.307091	+	0.951680i	$0.599356\pi$
$272$	−2.28248			−0.138396
$273$	15.7932	−	4.85547i	0.955847	−	0.293866i
$274$	−5.82537			−0.351924
$275$	−3.01172	−	5.21645i	−0.181614	−	0.314564i
$276$	1.17501	+	1.21727i	0.0707273	+	0.0732710i
$277$	−1.11567	+	1.93239i	−0.0670338	+	0.116106i	−0.897594	−	0.440822i	$-0.854687\pi$
$277$	−1.11567	+	1.93239i	−0.0670338	+	0.116106i	0.830561	+	0.556928i	$0.188020\pi$
$278$	15.6665	−	9.04503i	0.939612	−	0.542485i
$279$	3.10664	+	1.94305i	0.185990	+	0.116327i
$280$	0.279988	−	0.00156143i	0.0167325	−	9.33134e-5i
$281$	23.4884			1.40120			0.700600	−	0.713554i	$-0.252916\pi$
$281$	23.4884			1.40120			0.700600	+	0.713554i	$0.252916\pi$
$282$	−2.87141	+	0.715285i	−0.170990	+	0.0425946i
$283$	−4.21753	−	2.43499i	−0.250706	−	0.144745i	0.369381	−	0.929278i	$-0.379570\pi$
$283$	−4.21753	−	2.43499i	−0.250706	−	0.144745i	−0.620088	+	0.784533i	$0.712903\pi$
$284$	1.36023	−	2.35599i	0.0807148	−	0.139802i
$285$	−0.648739	+	0.161605i	−0.0384280	+	0.00957264i
$286$	−4.34818	+	0.211294i	−0.257114	+	0.0124941i
$287$	0.547179	−	0.960067i	0.0322990	−	0.0566710i
$288$	−2.54348	−	1.59082i	−0.149876	−	0.0937401i
$289$	5.89514	+	10.2107i	0.346773	+	0.600628i
$290$	−0.372412	+	0.645037i	−0.0218688	+	0.0378779i
$291$	−11.0324	+	10.6494i	−0.646733	+	0.624281i
$292$	3.72258	+	6.44769i	0.217847	+	0.377323i
$293$		−	3.97126i		−	0.232003i	−0.993249	−	0.116002i	$-0.962992\pi$
$293$		−	3.97126i		−	0.232003i	0.993249	−	0.116002i	$-0.0370078\pi$
$294$	3.06172	+	11.7314i	0.178563	+	0.684189i
$295$	1.10470			0.0643183
$296$	2.01173	−	1.16147i	0.116929	−	0.0675091i
$297$	6.13752	−	1.30054i	0.356135	−	0.0754653i
$298$	5.92542	−	10.2631i	0.343250	−	0.594527i
$299$	2.96098	−	1.90691i	0.171238	−	0.110279i
$300$	−8.30563	−	2.38348i	−0.479526	−	0.137610i
$301$	11.2732	+	6.42505i	0.649778	+	0.370334i
$302$		−	18.1421i		−	1.04396i
$303$	4.89165	+	19.6368i	0.281018	+	1.12811i
$304$	1.82371	−	3.15875i	0.104597	−	0.181167i
$305$	0.529939	−	0.917880i	0.0303442	−	0.0525577i
$306$	0.241835	−	6.84317i	0.0138248	−	0.391198i
$307$	3.58652			0.204694			0.102347	−	0.994749i	$-0.467365\pi$
$307$	3.58652			0.204694			0.102347	+	0.994749i	$0.467365\pi$
$308$	−0.0178145	−	3.19441i	−0.00101508	−	0.182018i
$309$	−0.551200	+	1.92075i	−0.0313567	+	0.109267i
$310$	0.111942	−	0.0646295i	0.00635785	−	0.00367071i
$311$	−14.7153	+	25.4877i	−0.834431	+	1.44528i	0.0600623	+	0.998195i	$0.480870\pi$
$311$	−14.7153	+	25.4877i	−0.834431	+	1.44528i	−0.894493	+	0.447082i	$0.852463\pi$
$312$	−4.27738	+	4.55017i	−0.242159	+	0.257603i
$313$	−12.7524	+	7.36260i	−0.720809	+	0.416159i	−0.815050	−	0.579390i	$-0.803291\pi$
$313$	−12.7524	+	7.36260i	−0.720809	+	0.416159i	0.0942416	+	0.995549i	$0.469957\pi$
$314$		−	17.6921i		−	0.998421i
$315$	−0.0249841	+	0.839607i	−0.00140770	+	0.0473065i
$316$	10.0982			0.568069
$317$	13.3964	+	23.2033i	0.752420	+	1.30323i	0.946647	+	0.322272i	$0.104447\pi$
$317$	13.3964	+	23.2033i	0.752420	+	1.30323i	−0.194227	+	0.980957i	$0.562220\pi$
$318$	−2.46440	−	2.55303i	−0.138197	−	0.143167i
$319$	7.35928	+	4.24888i	0.412040	+	0.237892i
$320$	−0.0916492	+	0.0529137i	−0.00512334	+	0.00295796i
$321$	5.81260	−	20.2550i	0.324428	−	1.13052i
$322$	1.30464	+	2.23088i	0.0727048	+	0.124322i
$323$	8.32515			0.463224
$324$	5.03898	−	7.45713i	0.279943	−	0.414285i
$325$	−8.22701	+	15.9957i	−0.456352	+	0.887281i
$326$	4.80436	+	2.77380i	0.266089	+	0.153626i
$327$	−12.1102	+	3.01673i	−0.669696	+	0.166825i
$328$			0.417669i			0.0230619i
$329$	−4.52012	+	0.0252077i	−0.249202	+	0.00138974i
$330$	0.0610466	−	0.212727i	0.00336051	−	0.0117102i
$331$	1.52884	−	0.882679i	0.0840329	−	0.0485164i	−0.457395	−	0.889264i	$-0.651217\pi$
$331$	1.52884	−	0.882679i	0.0840329	−	0.0485164i	0.541428	+	0.840747i	$0.317884\pi$
$332$	−10.1138	−	5.83922i	−0.555068	−	0.320469i
$333$	3.26909	+	6.15447i	0.179145	+	0.337263i
$334$	−7.97632	+	4.60513i	−0.436445	+	0.251982i
$335$	0.690813			0.0377431
$336$	−3.20097	−	3.27929i	−0.174627	−	0.178900i
$337$	−19.9939			−1.08913			−0.544567	−	0.838717i	$-0.683306\pi$
$337$	−19.9939			−1.08913			−0.544567	+	0.838717i	$0.683306\pi$
$338$	7.56096	+	10.5751i	0.411262	+	0.575207i
$339$	−16.0191	−	16.5952i	−0.870038	−	0.901328i
$340$	−0.209188	−	0.120775i	−0.0113448	−	0.00654992i
$341$	−0.737363	−	1.27715i	−0.0399304	−	0.0691615i
$342$	9.27712	+	5.80238i	0.501649	+	0.313757i
$343$	0.309832	+	18.5177i	0.0167294	+	0.999860i
$344$	−4.90433			−0.264424
$345$	0.0432786	+	0.173736i	0.00233004	+	0.00935362i
$346$	5.82669	−	10.0921i	0.313245	−	0.542556i
$347$	5.40323	+	3.11955i	0.290060	+	0.167466i	0.637969	−	0.770062i	$-0.279775\pi$
$347$	5.40323	+	3.11955i	0.290060	+	0.167466i	−0.347909	+	0.937528i	$0.613108\pi$
$348$	11.8289	−	2.94664i	0.634094	−	0.157957i
$349$	5.19865			0.278278			0.139139	−	0.990273i	$-0.455567\pi$
$349$	5.19865			0.278278			0.139139	+	0.990273i	$0.455567\pi$
$350$	−11.4674	−	6.53571i	−0.612959	−	0.349349i
$351$	−13.1888	−	13.3062i	−0.703966	−	0.710234i
$352$	0.603696	+	1.04563i	0.0321771	+	0.0557324i
$353$	21.5387	+	12.4354i	1.14639	+	0.661869i	0.948005	−	0.318255i	$-0.103097\pi$
$353$	21.5387	+	12.4354i	1.14639	+	0.661869i	0.198386	+	0.980124i	$0.436430\pi$
$354$	−12.5570	−	13.0086i	−0.667396	−	0.691398i
$355$	0.249328	−	0.143950i	0.0132330	−	0.00764005i
$356$		−	16.9792i		−	0.899896i
$357$	2.82906	−	10.0698i	0.149730	−	0.532950i
$358$			17.5090i			0.925378i
$359$	−15.5010	−	26.8486i	−0.818113	−	1.41701i	−0.907071	−	0.420979i	$-0.861687\pi$
$359$	−15.5010	−	26.8486i	−0.818113	−	1.41701i	0.0889571	−	0.996035i	$-0.471647\pi$
$360$	−0.148932	−	0.280382i	−0.00784938	−	0.0147774i
$361$	2.84819	−	4.93321i	0.149905	−	0.259643i
$362$	11.5944	−	6.69403i	0.609388	−	0.351831i
$363$	15.8864	+	4.55894i	0.833819	+	0.239282i
$364$	−7.99119	+	5.20970i	−0.418852	+	0.273062i
$365$			0.787901i			0.0412406i
$366$	−16.8324	+	4.19304i	−0.879841	+	0.219174i
$367$	14.7620	+	8.52284i	0.770570	+	0.444889i	0.833078	−	0.553156i	$-0.186577\pi$
$367$	14.7620	+	8.52284i	0.770570	+	0.444889i	−0.0625080	+	0.998044i	$0.519910\pi$
$368$	−0.845930	−	0.488398i	−0.0440972	−	0.0254595i
$369$	−1.25223	−	0.0442532i	−0.0651883	−	0.00230373i
$370$	0.245831			0.0127801
$371$	−2.73628	−	4.67892i	−0.142061	−	0.242917i
$372$	−2.03348	−	0.583550i	−0.105431	−	0.0302557i
$373$	−10.9216	−	18.9168i	−0.565501	−	0.979476i	−0.997003	−	0.0773640i	$-0.975350\pi$
$373$	−10.9216	−	18.9168i	−0.565501	−	0.979476i	0.431502	−	0.902112i	$-0.357984\pi$
$374$	−1.37793	+	2.38664i	−0.0712508	+	0.123410i
$375$	−1.27160	−	1.31733i	−0.0656649	−	0.0680265i
$376$	1.47958	−	0.854236i	0.0763035	−	0.0440538i
$377$	−1.23167	−	25.3464i	−0.0634344	−	1.30540i
$378$	10.1709	−	9.24948i	0.523135	−	0.475742i
$379$		−	29.5625i		−	1.51852i	−0.650786	−	0.759261i	$-0.725560\pi$
$379$		−	29.5625i		−	1.51852i	0.650786	−	0.759261i	$-0.274440\pi$
$380$	0.334282	−	0.192998i	0.0171483	−	0.00990059i
$381$	17.1827	−	16.5862i	0.880297	−	0.849737i
$382$	−12.8955	−	7.44521i	−0.659790	−	0.380930i
$383$	13.3338	−	7.69829i	0.681327	−	0.393364i	−0.119028	−	0.992891i	$-0.537978\pi$
$383$	13.3338	−	7.69829i	0.681327	−	0.393364i	0.800355	+	0.599527i	$0.204644\pi$
$384$	1.66485	+	0.477766i	0.0849592	+	0.0243809i
$385$	0.167395	−	0.293708i	0.00853125	−	0.0149687i
$386$			13.0502i			0.664235i
$387$	0.519626	−	14.7038i	0.0264141	−	0.747436i
$388$	4.42648	−	7.66690i	0.224721	−	0.389228i
$389$	9.83397	+	5.67765i	0.498602	+	0.287868i	0.728136	−	0.685433i	$-0.240387\pi$
$389$	9.83397	+	5.67765i	0.498602	+	0.287868i	−0.229534	+	0.973301i	$0.573720\pi$
$390$	−0.632784	+	0.190688i	−0.0320423	+	0.00965585i
$391$		−	2.22952i		−	0.112752i
$392$	−3.56739	−	6.02276i	−0.180181	−	0.304196i
$393$	21.3695	+	6.13245i	1.07795	+	0.309341i
$394$	4.40599	+	7.63140i	0.221971	+	0.384465i
$395$	0.925494	+	0.534334i	0.0465666	+	0.0268853i
$396$	−3.19890	+	1.69917i	−0.160751	+	0.0853866i
$397$	−12.6212	−	21.8606i	−0.633440	−	1.09715i	−0.986843	−	0.161679i	$-0.948309\pi$
$397$	−12.6212	−	21.8606i	−0.633440	−	1.09715i	0.353404	−	0.935471i	$-0.385024\pi$
$398$			15.9503i			0.799519i
$399$	11.6753	+	11.9609i	0.584494	+	0.598796i
$400$	4.98880			0.249440
$401$	−17.2752	−	29.9215i	−0.862681	−	1.49421i	−0.869331	−	0.494230i	$-0.835450\pi$
$401$	−17.2752	−	29.9215i	−0.862681	−	1.49421i	0.00665018	−	0.999978i	$-0.497883\pi$
$402$	−7.85236	−	8.13476i	−0.391640	−	0.405725i
$403$	−2.01423	+	3.91624i	−0.100336	+	0.195082i
$404$	−5.84190	−	10.1185i	−0.290645	−	0.503412i
$405$	0.856402	−	0.416809i	0.0425550	−	0.0207114i
$406$	18.6208	−	0.103844i	0.924135	−	0.00515369i
$407$		−	2.80470i		−	0.139024i
$408$	0.955606	+	3.83614i	0.0473095	+	0.189917i
$409$	−4.95129	+	8.57588i	−0.244825	+	0.424050i	−0.962083	−	0.272759i	$-0.912064\pi$
$409$	−4.95129	+	8.57588i	−0.244825	+	0.424050i	0.717257	+	0.696809i	$0.245397\pi$
$410$	−0.0221004	+	0.0382790i	−0.00109146	+	0.00189047i
$411$	2.43891	+	9.79064i	0.120302	+	0.482937i
$412$		−	1.15370i		−	0.0568388i
$413$	−13.9423	−	23.8407i	−0.686056	−	1.17313i
$414$	1.55391	−	2.48446i	0.0763705	−	0.122105i
$415$	−0.617949	−	1.07032i	−0.0303339	−	0.0525399i
$416$	1.64910	−	3.20632i	0.0808536	−	0.157203i
$417$	−21.7610	−	22.5436i	−1.06564	−	1.10396i
$418$	−2.20193	−	3.81385i	−0.107700	−	0.186542i
$419$	26.9663			1.31739			0.658694	−	0.752411i	$-0.271109\pi$
$419$	26.9663			1.31739			0.658694	+	0.752411i	$0.271109\pi$
$420$	−0.119847	−	0.469920i	−0.00584793	−	0.0229297i
$421$		−	10.6473i		−	0.518917i	−0.965754	−	0.259458i	$-0.916456\pi$
$421$		−	10.6473i		−	0.518917i	0.965754	−	0.259458i	$-0.0835440\pi$
$422$	8.13330	+	14.0873i	0.395923	+	0.685758i
$423$	2.40434	+	4.52648i	0.116903	+	0.220085i
$424$	1.77421	+	1.02434i	0.0861630	+	0.0497463i
$425$	5.69342	+	9.86130i	0.276172	+	0.478343i
$426$	−4.52917	−	1.29974i	−0.219439	−	0.0629728i
$427$	−26.4972	+	0.147769i	−1.28229	+	0.00715104i
$428$			12.1662i			0.588076i
$429$	2.17557	+	7.21948i	0.105038	+	0.348560i
$430$	−0.449477	−	0.259506i	−0.0216757	−	0.0125145i
$431$	−11.0130	+	19.0751i	−0.530478	+	0.918816i	0.468889	+	0.883257i	$0.344654\pi$
$431$	−11.0130	+	19.0751i	−0.530478	+	0.918816i	−0.999368	+	0.0355586i	$0.988679\pi$
$432$	−1.60880	+	4.94083i	−0.0774034	+	0.237716i
$433$			35.6522i			1.71334i	0.515868	+	0.856668i	$0.327470\pi$
$433$			35.6522i			1.71334i	−0.515868	+	0.856668i	$0.672530\pi$
$434$	−2.80758	−	1.60015i	−0.134768	−	0.0768095i
$435$	1.24002	+	0.355852i	0.0594546	+	0.0170618i
$436$	6.24015	−	3.60275i	0.298849	−	0.172541i
$437$	3.08546	+	1.78139i	0.147597	+	0.0852154i
$438$	9.27803	−	8.95594i	0.443322	−	0.427932i
$439$	−8.95324	+	5.16916i	−0.427315	+	0.246710i	−0.698202	−	0.715901i	$-0.746016\pi$
$439$	−8.95324	+	5.16916i	−0.427315	+	0.246710i	0.270887	+	0.962611i	$0.412683\pi$
$440$			0.127775i			0.00609144i
$441$	18.4350	−	10.0574i	0.877857	−	0.478923i
$442$	8.21991	−	0.399436i	0.390981	−	0.0189992i
$443$	33.8232	−	19.5279i	1.60699	−	0.927796i	0.616952	−	0.787001i	$-0.288367\pi$
$443$	33.8232	−	19.5279i	1.60699	−	0.927796i	0.990039	−	0.140795i	$-0.0449660\pi$
$444$	−2.79432	−	2.89481i	−0.132613	−	0.137382i
$445$	0.898432	−	1.55613i	0.0425898	−	0.0737676i
$446$	9.70620	+	16.8116i	0.459602	+	0.796054i
$447$	−19.7299	−	5.66193i	−0.933193	−	0.267800i
$448$	2.29863	+	1.31008i	0.108600	+	0.0618953i
$449$	14.4259			0.680801			0.340400	−	0.940281i	$-0.389437\pi$
$449$	14.4259			0.680801			0.340400	+	0.940281i	$0.389437\pi$
$450$	−0.528576	+	14.9571i	−0.0249173	+	0.705083i
$451$	0.436729	+	0.252145i	0.0205647	+	0.0118731i
$452$	11.5327	+	6.65841i	0.542453	+	0.313185i
$453$	−30.4913	+	7.59555i	−1.43260	+	0.356870i
$454$			17.2032i			0.807385i
$455$	−1.00805	+	0.0546213i	−0.0472581	+	0.00256069i
$456$	−6.07241	−	1.74261i	−0.284367	−	0.0816052i
$457$	−35.3848	+	20.4294i	−1.65523	+	0.955647i	−0.680357	+	0.732881i	$0.738175\pi$
$457$	−35.3848	+	20.4294i	−1.65523	+	0.955647i	−0.974872	+	0.222766i	$0.928491\pi$
$458$	−4.77500	+	8.27054i	−0.223121	+	0.386457i
$459$	−11.6025	+	2.45858i	−0.541558	+	0.114757i
$460$	−0.0516859	−	0.0895226i	−0.00240987	−	0.00417401i
$461$		−	12.6945i		−	0.591242i	−0.955305	−	0.295621i	$-0.904474\pi$
$461$		−	12.6945i		−	0.591242i	0.955305	−	0.295621i	$-0.0955265\pi$
$462$	−5.36135	+	1.36734i	−0.249433	+	0.0636146i
$463$		−	30.2556i		−	1.40610i	−0.711141	−	0.703049i	$-0.751821\pi$
$463$		−	30.2556i		−	1.40610i	0.711141	−	0.703049i	$-0.248179\pi$
$464$	−6.09518	+	3.51906i	−0.282962	+	0.163368i
$465$	−0.155489	−	0.161081i	−0.00721061	−	0.00746993i
$466$	−9.52198	−	5.49752i	−0.441097	−	0.254668i
$467$	−7.65871	−	13.2653i	−0.354403	−	0.613844i	0.632613	−	0.774468i	$-0.281983\pi$
$467$	−7.65871	−	13.2653i	−0.354403	−	0.613844i	−0.987016	+	0.160624i	$0.948649\pi$
$468$	9.43823	+	5.28392i	0.436282	+	0.244249i
$469$	−8.71865	−	14.9085i	−0.402590	−	0.688412i
$470$	0.180803			0.00833982
$471$	−29.7349	+	7.40713i	−1.37011	+	0.341303i
$472$	9.04020	+	5.21936i	0.416109	+	0.240241i
$473$	−2.96072	+	5.12812i	−0.136134	+	0.235791i
$474$	−4.22782	−	16.9720i	−0.194190	−	0.779549i
$475$	−18.1962			−0.834900
$476$	0.0336769	+	6.03879i	0.00154358	+	0.276787i
$477$	−3.25908	+	5.21076i	−0.149223	+	0.238585i
$478$	−7.61285	−	13.1858i	−0.348203	−	0.603106i
$479$	36.8694	+	21.2866i	1.68461	+	0.972608i	0.958529	+	0.284996i	$0.0919922\pi$
$479$	36.8694	+	21.2866i	1.68461	+	0.972608i	0.726078	+	0.687612i	$0.241341\pi$
$480$	0.127302	+	0.131880i	0.00581052	+	0.00601949i
$481$	−7.04158	+	4.53486i	−0.321068	+	0.206772i
$482$	16.3725			0.745748
$483$	3.20320	−	3.12670i	0.145751	−	0.142270i
$484$	−9.54220			−0.433737
$485$	0.811367	−	0.468443i	0.0368423	−	0.0212709i
$486$	−14.6428	−	5.34688i	−0.664210	−	0.242539i
$487$	−4.29100	−	2.47741i	−0.194444	−	0.112262i	0.399617	−	0.916682i	$-0.369143\pi$
$487$	−4.29100	−	2.47741i	−0.194444	−	0.112262i	−0.594061	+	0.804420i	$0.702476\pi$
$488$	8.67338	−	5.00758i	0.392625	−	0.226682i
$489$	2.65045	−	9.23594i	0.119858	−	0.417664i
$490$	−0.00826220	−	0.740745i	−0.000373248	−	0.0334635i
$491$		−	36.3557i		−	1.64071i	−0.571853	−	0.820356i	$-0.693775\pi$
$491$		−	36.3557i		−	1.64071i	0.571853	−	0.820356i	$-0.306225\pi$
$492$	0.701972	−	0.174865i	0.0316474	−	0.00788354i
$493$	−13.9121	−	8.03218i	−0.626572	−	0.361751i
$494$	−6.01493	+	11.6948i	−0.270625	+	0.526172i
$495$	−0.383086	−	0.0135381i	−0.0172184	−	0.000608493i
$496$	1.22141			0.0548431
$497$	−6.25333	−	3.56401i	−0.280500	−	0.159868i
$498$	−5.57956	+	19.4429i	−0.250026	+	0.871257i
$499$	22.8436	−	13.1887i	1.02262	−	0.590409i	0.107757	−	0.994177i	$-0.465633\pi$
$499$	22.8436	−	13.1887i	1.02262	−	0.590409i	0.914861	+	0.403769i	$0.132300\pi$
$500$	0.915465	+	0.528544i	0.0409409	+	0.0236372i
$501$	11.0792	+	11.4777i	0.494984	+	0.512785i
$502$	2.84416	+	4.92623i	0.126941	+	0.219868i
$503$	−33.8590			−1.50970			−0.754849	−	0.655898i	$-0.772290\pi$
$503$	−33.8590			−1.50970			−0.754849	+	0.655898i	$0.772290\pi$
$504$	−4.17133	+	6.75278i	−0.185806	+	0.300793i
$505$		−	1.23647i		−	0.0550220i
$506$	−1.02137	+	0.589688i	−0.0454054	+	0.0262148i
$507$	14.6078	−	17.1351i	0.648757	−	0.760996i
$508$	−6.89412	+	11.9410i	−0.305877	+	0.529795i
$509$	−34.0447	+	19.6557i	−1.50901	+	0.871225i	−0.509061	+	0.860730i	$0.670007\pi$
$509$	−34.0447	+	19.6557i	−1.50901	+	0.871225i	−0.999945	+	0.0104951i	$0.996659\pi$
$510$	−0.115404	+	0.402144i	−0.00511017	+	0.0178072i
$511$	17.0038	−	9.94399i	0.752204	−	0.439896i
$512$	−1.00000			−0.0441942
$513$	5.86796	−	18.0212i	0.259077	−	0.795657i
$514$	7.39698	−	12.8119i	0.326267	−	0.565111i
$515$	0.0610466	−	0.105736i	0.00269004	−	0.00465928i
$516$	2.05329	+	8.24265i	0.0903911	+	0.362862i
$517$		−	2.06280i		−	0.0907216i
$518$	−3.10260	−	5.30531i	−0.136320	−	0.233102i
$519$	−19.4012	−	5.56759i	−0.851617	−	0.244390i
$520$	0.320796	−	0.206597i	0.0140679	−	0.00905987i
$521$	8.81970	−	15.2762i	0.386398	−	0.669261i	−0.605564	−	0.795797i	$-0.707052\pi$
$521$	8.81970	−	15.2762i	0.386398	−	0.669261i	0.991962	+	0.126535i	$0.0403857\pi$
$522$	−9.90478	−	18.6470i	−0.433520	−	0.816157i
$523$	17.8468	−	10.3039i	0.780387	−	0.450557i	−0.0561804	−	0.998421i	$-0.517892\pi$
$523$	17.8468	−	10.3039i	0.780387	−	0.450557i	0.836567	+	0.547864i	$0.184559\pi$
$524$	−12.8357			−0.560729
$525$	−6.18345	+	22.0094i	−0.269868	+	0.960571i
$526$			23.4807i			1.02381i
$527$	1.39393	+	2.41435i	0.0607204	+	0.105171i
$528$	1.50463	−	1.45240i	0.0654808	−	0.0632076i
$529$	−11.0229	+	19.0923i	−0.479258	+	0.830099i
$530$	0.108403	+	0.187759i	0.00470872	+	0.00815575i
$531$	−16.6062	+	26.5507i	−0.720646	+	1.15220i
$532$	−8.38405	−	4.77839i	−0.363495	−	0.207170i
$533$	−0.0730924	−	1.50415i	−0.00316598	−	0.0651521i
$534$	−28.5368	+	7.10868i	−1.23491	+	0.307622i
$535$	−0.643759	+	1.11502i	−0.0278321	+	0.0482067i
$536$	5.65318	+	3.26387i	0.244180	+	0.140978i
$537$	29.4271	−	7.33047i	1.26987	−	0.316333i
$538$	−18.3481			−0.791042
$539$	−8.45122	+	0.0942640i	−0.364020	+	0.00406024i
$540$	−0.408882	+	0.367695i	−0.0175955	+	0.0158231i
$541$	−17.1036	+	9.87474i	−0.735339	+	0.424548i	−0.820372	−	0.571830i	$-0.806234\pi$
$541$	−17.1036	+	9.87474i	−0.735339	+	0.424548i	0.0850330	+	0.996378i	$0.472900\pi$
$542$	−11.0400	+	19.1219i	−0.474210	+	0.821355i
$543$	−16.1048	−	16.6840i	−0.691124	−	0.715979i
$544$	−1.14124	−	1.97669i	−0.0489303	−	0.0847498i
$545$	0.762539			0.0326636
$546$	12.1015	+	11.2496i	0.517898	+	0.481437i
$547$	−25.0148			−1.06956			−0.534778	−	0.844992i	$-0.679605\pi$
$547$	−25.0148			−1.06956			−0.534778	+	0.844992i	$0.679605\pi$
$548$	−2.91269	−	5.04492i	−0.124424	−	0.215508i
$549$	14.0944	+	26.5345i	0.601534	+	1.13246i
$550$	3.01172	−	5.21645i	0.128420	−	0.222430i
$551$	22.2316	−	12.8354i	0.947100	−	0.546808i
$552$	−0.466680	+	1.62622i	−0.0198632	+	0.0692167i
$553$	−0.148995	−	26.7170i	−0.00633589	−	1.13612i
$554$	−2.23133			−0.0948002
$555$	−0.102922	−	0.413165i	−0.00436879	−	0.0175379i
$556$	15.6665	+	9.04503i	0.664406	+	0.383595i
$557$	−4.88652	+	8.46370i	−0.207049	+	0.358619i	−0.950783	−	0.309856i	$-0.899719\pi$
$557$	−4.88652	+	8.46370i	−0.207049	+	0.358619i	0.743735	+	0.668475i	$0.233052\pi$
$558$	−0.129412	+	3.66195i	−0.00547844	+	0.155023i
$559$	17.6620	−	0.858260i	0.747021	−	0.0363005i
$560$	0.141346	+	0.241696i	0.00597298	+	0.0102135i
$561$	4.58809	+	1.31665i	0.193709	+	0.0555891i
$562$	11.7442	+	20.3416i	0.495399	+	0.858057i
$563$	0.418795	−	0.725375i	0.0176501	−	0.0305709i	−0.857065	−	0.515208i	$-0.827715\pi$
$563$	0.418795	−	0.725375i	0.0176501	−	0.0305709i	0.874716	+	0.484637i	$0.161048\pi$
$564$	−2.05516	−	2.12907i	−0.0865378	−	0.0896501i
$565$	0.704642	+	1.22048i	0.0296445	+	0.0513458i
$566$		−	4.86999i		−	0.204701i
$567$	−19.8037	−	13.2216i	−0.831679	−	0.555257i
$568$	2.72046			0.114148
$569$	23.1014	−	13.3376i	0.968463	−	0.559142i	0.0696956	−	0.997568i	$-0.477797\pi$
$569$	23.1014	−	13.3376i	0.968463	−	0.559142i	0.898767	+	0.438426i	$0.144464\pi$
$570$	−0.464323	−	0.481022i	−0.0194484	−	0.0201478i
$571$	11.7217	−	20.3025i	0.490536	−	0.849633i	−0.509405	−	0.860527i	$-0.670134\pi$
$571$	11.7217	−	20.3025i	0.490536	−	0.849633i	0.999941	+	0.0108941i	$0.00346775\pi$
$572$	−2.35708	−	3.65999i	−0.0985544	−	0.153032i
$573$	−7.11414	+	24.7904i	−0.297197	+	1.03563i
$574$	1.10503	−	0.00616251i	0.0461231	−	0.000257218i
$575$			4.87304i			0.203220i
$576$	0.105953	−	2.99813i	0.00441469	−	0.124922i
$577$	−2.28855	+	3.96389i	−0.0952736	+	0.165019i	−0.909723	−	0.415216i	$-0.863706\pi$
$577$	−2.28855	+	3.96389i	−0.0952736	+	0.165019i	0.814449	+	0.580235i	$0.197039\pi$
$578$	−5.89514	+	10.2107i	−0.245205	+	0.424708i
$579$	21.9332	−	5.46370i	0.911515	−	0.227064i
$580$	−0.744825			−0.0309272
$581$	−15.2997	+	26.8444i	−0.634737	+	1.11369i
$582$	−14.7389	−	4.22965i	−0.610947	−	0.175325i
$583$	2.14216	−	1.23678i	0.0887193	−	0.0512221i
$584$	−3.72258	+	6.44769i	−0.154041	+	0.266807i
$585$	0.585414	+	0.983678i	0.0242039	+	0.0406701i
$586$	3.43921	−	1.98563i	0.142072	−	0.0820256i
$587$			36.9891i			1.52670i	0.645982	+	0.763352i	$0.276448\pi$
$587$			36.9891i			1.52670i	−0.645982	+	0.763352i	$0.723552\pi$
$588$	−8.62884	+	8.51723i	−0.355847	+	0.351245i
$589$	−4.45500			−0.183565
$590$	0.552351	+	0.956700i	0.0227399	+	0.0393867i
$591$	10.9814	−	10.6001i	0.451713	−	0.436032i
$592$	2.01173	+	1.16147i	0.0826814	+	0.0477362i
$593$	−24.0004	+	13.8566i	−0.985579	+	0.569024i	−0.903950	−	0.427639i	$-0.859346\pi$
$593$	−24.0004	+	13.8566i	−0.985579	+	0.569024i	−0.0816289	+	0.996663i	$0.526012\pi$
$594$	4.19506	+	4.66497i	0.172125	+	0.191406i
$595$	−0.316448	+	0.555232i	−0.0129731	+	0.0227623i
$596$	11.8508			0.485429
$597$	26.8076	−	6.67792i	1.09716	−	0.273309i
$598$	3.13192	+	1.61083i	0.128074	+	0.0658718i
$599$	−10.8738	−	6.27799i	−0.444291	−	0.256512i	0.261125	−	0.965305i	$-0.415907\pi$
$599$	−10.8738	−	6.27799i	−0.444291	−	0.256512i	−0.705416	+	0.708793i	$0.749240\pi$
$600$	−2.08866	−	8.38462i	−0.0852691	−	0.342301i
$601$			10.7277i			0.437594i	0.975770	+	0.218797i	$0.0702132\pi$
$601$			10.7277i			0.437594i	−0.975770	+	0.218797i	$0.929787\pi$
$602$	0.0723610	+	12.9754i	0.00294922	+	0.528839i
$603$	−10.3845	+	16.6032i	−0.422888	+	0.676133i
$604$	15.7115	−	9.07106i	0.639293	−	0.369096i
$605$	−0.874535	−	0.504913i	−0.0355549	−	0.0205276i
$606$	−14.5602	+	14.0547i	−0.591466	+	0.570933i
$607$	27.0857	−	15.6379i	1.09937	−	0.634724i	0.163318	−	0.986574i	$-0.447780\pi$
$607$	27.0857	−	15.6379i	1.09937	−	0.634724i	0.936057	+	0.351849i	$0.114447\pi$
$608$	3.64741			0.147922
$609$	−7.97049	−	31.2523i	−0.322981	−	1.26641i
$610$	1.05988			0.0429132
$611$	−5.17892	+	3.33529i	−0.209517	+	0.134931i
$612$	6.04728	−	3.21215i	0.244447	−	0.129844i
$613$	−10.8577	−	6.26872i	−0.438540	−	0.253191i	0.264438	−	0.964403i	$-0.414813\pi$
$613$	−10.8577	−	6.26872i	−0.438540	−	0.253191i	−0.702978	+	0.711212i	$0.748147\pi$
$614$	1.79326	+	3.10602i	0.0723702	+	0.125349i
$615$	0.0735879	+	0.0211177i	0.00296735	+	0.000851546i
$616$	2.75753	−	1.61263i	0.111104	−	0.0649748i
$617$	7.90025			0.318052			0.159026	−	0.987274i	$-0.449165\pi$
$617$	7.90025			0.318052			0.159026	+	0.987274i	$0.449165\pi$
$618$	−1.93902	+	0.483020i	−0.0779986	+	0.0194299i
$619$	5.53340	−	9.58414i	0.222406	−	0.385219i	−0.733132	−	0.680086i	$-0.761942\pi$
$619$	5.53340	−	9.58414i	0.222406	−	0.385219i	0.955538	+	0.294868i	$0.0952755\pi$
$620$	0.111942	+	0.0646295i	0.00449568	+	0.00259558i
$621$	−4.82618	−	1.57147i	−0.193668	−	0.0630609i
$622$	−29.4307			−1.18006
$623$	−44.9221	+	0.250520i	−1.79976	+	0.0100369i
$624$	−6.07925	−	1.42923i	−0.243365	−	0.0572150i
$625$	−12.4161	−	21.5053i	−0.496643	−	0.860210i
$626$	−12.7524	−	7.36260i	−0.509689	−	0.294269i
$627$	−5.48802	+	5.29750i	−0.219170	+	0.211562i
$628$	15.3218	−	8.84604i	0.611406	−	0.352995i
$629$			5.30207i			0.211407i
$630$	−0.739613	+	0.398167i	−0.0294669	+	0.0158633i
$631$			18.1982i			0.724461i	0.932089	+	0.362230i	$0.117985\pi$
$631$			18.1982i			0.724461i	−0.932089	+	0.362230i	$0.882015\pi$
$632$	5.04911	+	8.74532i	0.200843	+	0.347870i
$633$	20.2712	−	19.5675i	0.805707	−	0.777737i
$634$	−13.3964	+	23.2033i	−0.532041	+	0.921522i
$635$	−1.26368	+	0.729587i	−0.0501477	+	0.0289528i
$636$	0.978788	−	3.41075i	0.0388115	−	0.135245i
$637$	13.9013	+	21.0655i	0.550788	+	0.834645i
$638$			8.49776i			0.336430i
$639$	−0.288240	+	8.15629i	−0.0114026	+	0.322658i
$640$	−0.0916492	−	0.0529137i	−0.00362275	−	0.00209160i
$641$	−5.02205	−	2.89948i	−0.198359	−	0.114523i	0.397531	−	0.917589i	$-0.369867\pi$
$641$	−5.02205	−	2.89948i	−0.198359	−	0.114523i	−0.595890	+	0.803066i	$0.703200\pi$
$642$	20.4476	−	5.09362i	0.807003	−	0.201029i
$643$	−17.1073			−0.674646			−0.337323	−	0.941389i	$-0.609521\pi$
$643$	−17.1073			−0.674646			−0.337323	+	0.941389i	$0.609521\pi$
$644$	−1.27968	+	2.24529i	−0.0504264	+	0.0884769i
$645$	−0.247966	+	0.864079i	−0.00976366	+	0.0340231i
$646$	4.16258	+	7.20979i	0.163774	+	0.283666i
$647$	−6.64633	+	11.5118i	−0.261294	+	0.452575i	−0.966586	−	0.256342i	$-0.917483\pi$
$647$	−6.64633	+	11.5118i	−0.261294	+	0.452575i	0.705292	+	0.708917i	$0.250816\pi$
$648$	8.97755	+	0.635319i	0.352671	+	0.0249577i
$649$	10.9151	−	6.30182i	0.428454	−	0.247368i
$650$	−17.9662	+	0.873043i	−0.704691	+	0.0342436i
$651$	−1.51390	+	5.38860i	−0.0593345	+	0.211196i
$652$			5.54760i			0.217261i
$653$	20.2462	−	11.6891i	0.792295	−	0.457432i	−0.0484750	−	0.998824i	$-0.515436\pi$
$653$	20.2462	−	11.6891i	0.792295	−	0.457432i	0.840770	+	0.541393i	$0.182103\pi$
$654$	−8.66767	−	8.97939i	−0.338933	−	0.351122i
$655$	−1.17638	−	0.679183i	−0.0459650	−	0.0265379i
$656$	−0.361712	+	0.208835i	−0.0141225	+	0.00815362i
$657$	−18.9366	−	11.8439i	−0.738787	−	0.462075i
$658$	−2.28189	−	3.90193i	−0.0889574	−	0.152113i
$659$			1.60689i			0.0625954i	0.999510	+	0.0312977i	$0.00996400\pi$
$659$			1.60689i			0.0625954i	−0.999510	+	0.0312977i	$0.990036\pi$
$660$	0.214750	−	0.0534956i	0.00835914	−	0.00208231i
$661$	3.91663	−	6.78381i	0.152339	−	0.263860i	−0.779748	−	0.626094i	$-0.784653\pi$
$661$	3.91663	−	6.78381i	0.152339	−	0.263860i	0.932087	+	0.362234i	$0.117986\pi$
$662$	1.52884	+	0.882679i	0.0594202	+	0.0343063i
$663$	−4.11275	−	13.6479i	−0.159726	−	0.530040i
$664$		−	11.6784i		−	0.453211i
$665$	−0.515549	−	0.881567i	−0.0199921	−	0.0341857i
$666$	−3.69539	+	5.90835i	−0.143193	+	0.228944i
$667$	−3.43740	−	5.95375i	−0.133097	−	0.230530i
$668$	−7.97632	−	4.60513i	−0.308613	−	0.178178i
$669$	24.1914	−	23.3516i	0.935295	−	0.902826i
$670$	0.345406	+	0.598261i	0.0133442	+	0.0231129i
$671$		−	12.0922i		−	0.466815i
$672$	1.23947	−	4.41177i	0.0478135	−	0.170188i
$673$	−26.3985			−1.01759			−0.508793	−	0.860889i	$-0.669908\pi$
$673$	−26.3985			−1.01759			−0.508793	+	0.860889i	$0.669908\pi$
$674$	−9.99693	−	17.3152i	−0.385067	−	0.666956i
$675$	25.3595	−	5.37369i	0.976087	−	0.206834i
$676$	−5.37778	+	11.8355i	−0.206838	+	0.455212i
$677$	9.98440	+	17.2935i	0.383732	+	0.664643i	0.991592	−	0.129401i	$-0.0413055\pi$
$677$	9.98440	+	17.2935i	0.383732	+	0.664643i	−0.607861	+	0.794044i	$0.707972\pi$
$678$	6.36232	−	22.1706i	0.244344	−	0.851455i
$679$	−20.3497	−	11.5981i	−0.780950	−	0.445093i
$680$		−	0.241549i		−	0.00926298i
$681$	28.9132	−	7.20245i	1.10796	−	0.275998i
$682$	0.737363	−	1.27715i	0.0282351	−	0.0489046i
$683$	20.4986	−	35.5046i	0.784357	−	1.35855i	−0.145026	−	0.989428i	$-0.546327\pi$
$683$	20.4986	−	35.5046i	0.784357	−	1.35855i	0.929383	−	0.369118i	$-0.120340\pi$
$684$	−0.386453	+	10.9354i	−0.0147764	+	0.418126i
$685$		−	0.616484i		−	0.0235546i
$686$	−15.8819	+	9.52716i	−0.606372	+	0.363749i
$687$	15.8993	+	4.56266i	0.606598	+	0.174076i
$688$	−2.45216	−	4.24727i	−0.0934879	−	0.161926i
$689$	−6.56871	−	3.37846i	−0.250248	−	0.128709i
$690$	−0.128820	+	0.124348i	−0.00490411	+	0.00473386i
$691$	−3.60774	−	6.24879i	−0.137245	−	0.237715i	0.789208	−	0.614126i	$-0.210491\pi$
$691$	−3.60774	−	6.24879i	−0.137245	−	0.237715i	−0.926453	+	0.376411i	$0.877158\pi$
$692$	11.6534			0.442995
$693$	4.54271	+	8.43830i	0.172563	+	0.320545i
$694$			6.23911i			0.236833i
$695$	0.957212	+	1.65794i	0.0363091	+	0.0628892i
$696$	8.46631	+	8.77079i	0.320914	+	0.332456i
$697$	−0.825602	−	0.476661i	−0.0312719	−	0.0180548i
$698$	2.59933	+	4.50217i	0.0983860	+	0.170410i
$699$	−5.25306	+	18.3051i	−0.198689	+	0.692364i
$700$	−0.0736074	−	13.1989i	−0.00278210	−	0.498872i
$701$		−	20.2655i		−	0.765419i	−0.923869	−	0.382709i	$-0.874991\pi$
$701$		−	20.2655i		−	0.765419i	0.923869	−	0.382709i	$-0.125009\pi$
$702$	4.92913	−	18.0749i	0.186038	−	0.682195i
$703$	−7.33760	−	4.23636i	−0.276743	−	0.159777i
$704$	−0.603696	+	1.04563i	−0.0227527	+	0.0394088i
$705$	−0.0756967	−	0.303874i	−0.00285090	−	0.0114445i
$706$			24.8708i			0.936024i
$707$	−26.6843	+	15.6053i	−1.00357	+	0.586896i
$708$	4.98727	−	17.3790i	0.187433	−	0.653141i
$709$	22.9129	−	13.2288i	0.860513	−	0.496817i	−0.00367133	−	0.999993i	$-0.501169\pi$
$709$	22.9129	−	13.2288i	0.860513	−	0.496817i	0.864184	+	0.503176i	$0.167835\pi$
$710$	0.249328	+	0.143950i	0.00935711	+	0.00540233i
$711$	−26.7546	+	14.2113i	−1.00337	+	0.532965i
$712$	14.7044	−	8.48960i	0.551072	−	0.318161i
$713$			1.19307i			0.0446809i
$714$	10.1352	−	2.58486i	0.379301	−	0.0967358i
$715$	−0.0223607	−	0.460157i	−0.000836244	−	0.0172089i
$716$	−15.1632	+	8.75448i	−0.566676	+	0.327170i
$717$	−18.9740	+	18.3153i	−0.708598	+	0.683999i
$718$	15.5010	−	26.8486i	0.578494	−	1.00198i
$719$	−6.33059	−	10.9649i	−0.236091	−	0.408922i	0.723498	−	0.690326i	$-0.242533\pi$
$719$	−6.33059	−	10.9649i	−0.236091	−	0.408922i	−0.959589	+	0.281405i	$0.909200\pi$
$720$	0.168352	−	0.269170i	0.00627413	−	0.0100314i
$721$	−3.05236	+	0.0170223i	−0.113676	+	0.000633945i
$722$	5.69638			0.211997
$723$	−6.85467	−	27.5171i	−0.254928	−	1.02337i
$724$	11.5944	+	6.69403i	0.430903	+	0.248782i
$725$	30.4077	+	17.5559i	1.12931	+	0.652008i
$726$	3.99503	+	16.0375i	0.148269	+	0.595207i
$727$			18.4770i			0.685274i	0.939468	+	0.342637i	$0.111320\pi$
$727$			18.4770i			0.685274i	−0.939468	+	0.342637i	$0.888680\pi$
$728$	−8.50732	−	4.31572i	−0.315302	−	0.159951i
$729$	−2.85596	+	26.8485i	−0.105776	+	0.994390i
$730$	−0.682342	+	0.393950i	−0.0252546	+	0.0145808i
$731$	5.59702	−	9.69432i	0.207013	−	0.358557i
$732$	−12.0475	−	12.4807i	−0.445287	−	0.461301i
$733$	1.52428	+	2.64013i	0.0563005	+	0.0975153i	0.892802	−	0.450449i	$-0.148736\pi$
$733$	1.52428	+	2.64013i	0.0563005	+	0.0975153i	−0.836502	+	0.547965i	$0.815403\pi$
$734$			17.0457i			0.629168i
$735$	−1.24150	+	0.324014i	−0.0457935	+	0.0119514i
$736$		−	0.976796i		−	0.0360052i
$737$	6.82561	−	3.94077i	0.251425	−	0.145160i
$738$	−0.587789	−	1.10659i	−0.0216368	−	0.0407340i
$739$	29.4714	+	17.0153i	1.08412	+	0.625919i	0.932006	−	0.362443i	$-0.118057\pi$
$739$	29.4714	+	17.0153i	1.08412	+	0.625919i	0.152118	+	0.988362i	$0.451391\pi$
$740$	0.122915	+	0.212896i	0.00451846	+	0.00782620i
$741$	22.1735	+	5.21299i	0.814565	+	0.191504i
$742$	2.68392	−	4.70915i	0.0985300	−	0.172878i
$743$	−51.3542			−1.88400			−0.942002	−	0.335607i	$-0.891059\pi$
$743$	−51.3542			−1.88400			−0.942002	+	0.335607i	$0.891059\pi$
$744$	−0.511369	−	2.05282i	−0.0187477	−	0.0752599i
$745$	1.08612	+	0.627072i	0.0397924	+	0.0229741i
$746$	10.9216	−	18.9168i	0.399869	−	0.692594i
$747$	35.0135	+	1.23736i	1.28108	+	0.0452727i
$748$	−2.75585			−0.100764
$749$	32.1883	−	0.179507i	1.17613	−	0.00655903i
$750$	0.505041	−	1.75990i	0.0184415	−	0.0642624i
$751$	−3.22181	−	5.58034i	−0.117566	−	0.203630i	0.801237	−	0.598347i	$-0.204176\pi$
$751$	−3.22181	−	5.58034i	−0.117566	−	0.203630i	−0.918802	+	0.394718i	$0.870842\pi$
$752$	1.47958	+	0.854236i	0.0539547	+	0.0311508i
$753$	7.08870	−	6.84261i	0.258326	−	0.249359i
$754$	21.3348	−	13.7398i	0.776966	−	0.500376i
$755$	1.91993			0.0698735
$756$	13.0957	+	4.18352i	0.476287	+	0.152153i
$757$	−33.0813			−1.20236			−0.601180	−	0.799114i	$-0.705302\pi$
$757$	−33.0813			−1.20236			−0.601180	+	0.799114i	$0.705302\pi$
$758$	25.6019	−	14.7812i	0.929902	−	0.536879i
$759$	1.41870	+	1.46972i	0.0514955	+	0.0533475i
$760$	0.334282	+	0.192998i	0.0121257	+	0.00700077i
$761$	2.67214	−	1.54276i	0.0968650	−	0.0559250i	−0.450785	−	0.892633i	$-0.648856\pi$
$761$	2.67214	−	1.54276i	0.0968650	−	0.0559250i	0.547650	+	0.836708i	$0.315523\pi$
$762$	22.9554	+	6.58756i	0.831587	+	0.238642i
$763$	−9.62391	−	16.4565i	−0.348409	−	0.595764i
$764$		−	14.8904i		−	0.538717i
$765$	0.724195	+	0.0255927i	0.0261833	+	0.000925308i
$766$	13.3338	+	7.69829i	0.481771	+	0.278151i
$767$	−33.4699	−	17.2145i	−1.20853	−	0.621578i
$768$	0.418670	+	1.68069i	0.0151074	+	0.0606466i
$769$	44.6644			1.61064			0.805320	−	0.592840i	$-0.201993\pi$
$769$	44.6644			1.61064			0.805320	+	0.592840i	$0.201993\pi$
$770$	0.338056	−	0.00188526i

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.24618 - 1.20292i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0916492 + 0.0529137i) q^{5} +(1.66485 + 0.477766i) q^{6} +(2.29863 + 1.31008i) q^{7} -1.00000 q^{8} +(0.105953 - 2.99813i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.24618 - 1.20292i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0916492 + 0.0529137i) q^{5} +(1.66485 + 0.477766i) q^{6} +(2.29863 + 1.31008i) q^{7} -1.00000 q^{8} +(0.105953 - 2.99813i) q^{9} +(-0.0916492 - 0.0529137i) q^{10} +(-0.603696 + 1.04563i) q^{11} +(0.418670 + 1.68069i) q^{12} +(3.60130 - 0.175001i) q^{13} +(0.0147545 + 2.64571i) q^{14} +(-0.0505607 + 0.176187i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.14124 - 1.97669i) q^{17} +(2.64943 - 1.40731i) q^{18} +(1.82371 + 3.15875i) q^{19} -0.105827i q^{20} +(4.44044 - 1.13248i) q^{21} -1.20739 q^{22} +(0.845930 - 0.488398i) q^{23} +(-1.24618 + 1.20292i) q^{24} +(-2.49440 + 4.32043i) q^{25} +(1.95221 + 3.03132i) q^{26} +(-3.47448 - 3.86367i) q^{27} +(-2.28387 + 1.33563i) q^{28} -7.03811i q^{29} +(-0.177863 + 0.0443067i) q^{30} +(-0.610707 + 1.05778i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.505498 + 2.02925i) q^{33} +2.28248 q^{34} +(-0.279988 + 0.00156143i) q^{35} +(2.54348 + 1.59082i) q^{36} +(-2.01173 + 1.16147i) q^{37} +(-1.82371 + 3.15875i) q^{38} +(4.27738 - 4.55017i) q^{39} +(0.0916492 - 0.0529137i) q^{40} -0.417669i q^{41} +(3.20097 + 3.27929i) q^{42} +4.90433 q^{43} +(-0.603696 - 1.04563i) q^{44} +(0.148932 + 0.280382i) q^{45} +(0.845930 + 0.488398i) q^{46} +(-1.47958 + 0.854236i) q^{47} +(-1.66485 - 0.477766i) q^{48} +(3.56739 + 6.02276i) q^{49} -4.98880 q^{50} +(-0.955606 - 3.83614i) q^{51} +(-1.64910 + 3.20632i) q^{52} +(-1.77421 - 1.02434i) q^{53} +(1.60880 - 4.94083i) q^{54} -0.127775i q^{55} +(-2.29863 - 1.31008i) q^{56} +(6.07241 + 1.74261i) q^{57} +(6.09518 - 3.51906i) q^{58} +(-9.04020 - 5.21936i) q^{59} +(-0.127302 - 0.131880i) q^{60} +(-8.67338 + 5.00758i) q^{61} -1.22141 q^{62} +(4.17133 - 6.75278i) q^{63} +1.00000 q^{64} +(-0.320796 + 0.206597i) q^{65} +(-1.50463 + 1.45240i) q^{66} +(-5.65318 - 3.26387i) q^{67} +(1.14124 + 1.97669i) q^{68} +(0.466680 - 1.62622i) q^{69} +(-0.141346 - 0.241696i) q^{70} -2.72046 q^{71} +(-0.105953 + 2.99813i) q^{72} +(3.72258 - 6.44769i) q^{73} +(-2.01173 - 1.16147i) q^{74} +(2.08866 + 8.38462i) q^{75} -3.64741 q^{76} +(-2.75753 + 1.61263i) q^{77} +(6.07925 + 1.42923i) q^{78} +(-5.04911 - 8.74532i) q^{79} +(0.0916492 + 0.0529137i) q^{80} +(-8.97755 - 0.635319i) q^{81} +(0.361712 - 0.208835i) q^{82} +11.6784i q^{83} +(-1.23947 + 4.41177i) q^{84} +0.241549i q^{85} +(2.45216 + 4.24727i) q^{86} +(-8.46631 - 8.77079i) q^{87} +(0.603696 - 1.04563i) q^{88} +(-14.7044 + 8.48960i) q^{89} +(-0.168352 + 0.269170i) q^{90} +(8.50732 + 4.31572i) q^{91} +0.976796i q^{92} +(0.511369 + 2.05282i) q^{93} +(-1.47958 - 0.854236i) q^{94} +(-0.334282 - 0.192998i) q^{95} +(-0.418670 - 1.68069i) q^{96} -8.85297 q^{97} +(-3.43217 + 6.10084i) q^{98} +(3.07098 + 1.92075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9} + 14 q^{15} - 18 q^{16} - 4 q^{18} - 23 q^{21} + 14 q^{25} + 6 q^{26} + 7 q^{30} + 18 q^{32} - 24 q^{33} - 8 q^{36} + 10 q^{39} - 16 q^{42} - 16 q^{43} + 9 q^{45} - 72 q^{47} + 12 q^{49} + 28 q^{50} - 3 q^{51} + 6 q^{52} - 9 q^{54} + 8 q^{57} - 24 q^{59} - 7 q^{60} - 36 q^{61} + 39 q^{63} + 36 q^{64} - 18 q^{65} - 24 q^{66} + 72 q^{71} - 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} + 7 q^{84} - 8 q^{86} - 24 q^{87} + 72 q^{89} - 2 q^{91} + 14 q^{93} - 72 q^{94} + 12 q^{98} - 72 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9 + 14 * q^15 - 18 * q^16 - 4 * q^18 - 23 * q^21 + 14 * q^25 + 6 * q^26 + 7 * q^30 + 18 * q^32 - 24 * q^33 - 8 * q^36 + 10 * q^39 - 16 * q^42 - 16 * q^43 + 9 * q^45 - 72 * q^47 + 12 * q^49 + 28 * q^50 - 3 * q^51 + 6 * q^52 - 9 * q^54 + 8 * q^57 - 24 * q^59 - 7 * q^60 - 36 * q^61 + 39 * q^63 + 36 * q^64 - 18 * q^65 - 24 * q^66 + 72 * q^71 - 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 + 7 * q^84 - 8 * q^86 - 24 * q^87 + 72 * q^89 - 2 * q^91 + 14 * q^93 - 72 * q^94 + 12 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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