LMFDB - Embedded newform 546.2.bg.b.467.8

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			467.8
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.b.311.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.418670 - 1.68069i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.0916492 - 0.0529137i) q^{5} +(-1.66485 - 0.477766i) q^{6} +(-2.29863 + 1.31008i) q^{7} -1.00000 q^{8} +(-2.64943 + 1.40731i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.418670 - 1.68069i) 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} +(-2.64943 + 1.40731i) q^{9} +(-0.0916492 + 0.0529137i) q^{10} +(-0.603696 - 1.04563i) q^{11} +(-1.24618 + 1.20292i) 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} +(-0.105953 + 2.99813i) q^{18} +(-1.82371 + 3.15875i) q^{19} +0.105827i q^{20} +(3.16420 + 3.31479i) q^{21} -1.20739 q^{22} +(-0.845930 - 0.488398i) q^{23} +(0.418670 + 1.68069i) q^{24} +(-2.49440 - 4.32043i) q^{25} +(-1.64910 + 3.20632i) q^{26} +(3.47448 + 3.86367i) q^{27} +(2.28387 + 1.33563i) q^{28} -7.03811i q^{29} +(0.127302 + 0.131880i) q^{30} +(0.610707 + 1.05778i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50463 + 1.45240i) 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} +(1.80188 + 5.97940i) q^{39} +(0.0916492 + 0.0529137i) q^{40} +0.417669i q^{41} +(4.45279 - 1.08288i) q^{42} +4.90433 q^{43} +(-0.603696 + 1.04563i) q^{44} +(0.317284 + 0.0112127i) 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} +(-2.84439 + 2.74565i) q^{51} +(1.95221 + 3.03132i) q^{52} +(1.77421 - 1.02434i) q^{53} +(5.08328 - 1.07715i) 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} +(0.177863 - 0.0443067i) q^{60} +(-8.67338 - 5.00758i) q^{61} +1.22141 q^{62} +(4.24638 - 6.70584i) q^{63} +1.00000 q^{64} +(0.339316 + 0.174519i) q^{65} +(0.505498 + 2.02925i) 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} +(2.64943 - 1.40731i) q^{72} +(-3.72258 - 6.44769i) q^{73} +(2.01173 - 1.16147i) q^{74} +(-6.21697 + 6.00114i) 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} +(5.03898 - 7.45713i) q^{81} +(0.361712 + 0.208835i) q^{82} -11.6784i q^{83} +(1.28859 - 4.39767i) q^{84} +0.241549i q^{85} +(2.45216 - 4.24727i) q^{86} +(-11.8289 + 2.94664i) q^{87} +(0.603696 + 1.04563i) q^{88} +(-14.7044 - 8.48960i) q^{89} +(0.168352 - 0.269170i) q^{90} +(8.04879 - 5.12025i) q^{91} +0.976796i q^{92} +(1.52211 - 1.46927i) q^{93} +(-1.47958 + 0.854236i) q^{94} +(0.334282 - 0.192998i) q^{95} +(1.24618 - 1.20292i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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
$3$	−0.418670	−	1.68069i	−0.241719	−	0.970346i
$3$	−0.418670	−	1.68069i	−0.241719	−	0.970346i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.0916492	−	0.0529137i	−0.0409868	−	0.0236637i	0.479367	−	0.877615i	$-0.340866\pi$
$5$	−0.0916492	−	0.0529137i	−0.0409868	−	0.0236637i	−0.520353	+	0.853951i	$0.674200\pi$
$6$	−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
$9$	−2.64943	+	1.40731i	−0.883144	+	0.469102i
$10$	−0.0916492	+	0.0529137i	−0.0289820	+	0.0167328i
$11$	−0.603696	−	1.04563i	−0.182021	−	0.315270i	0.760547	−	0.649282i	$-0.224931\pi$
$11$	−0.603696	−	1.04563i	−0.182021	−	0.315270i	−0.942569	+	0.334012i	$0.891597\pi$
$12$	−1.24618	+	1.20292i	−0.359743	+	0.347254i
$13$	−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	$-0.255938\pi$
$17$	−1.14124	−	1.97669i	−0.276792	−	0.479417i	−0.970586	+	0.240756i	$0.922605\pi$
$18$	−0.105953	+	2.99813i	−0.0249733	+	0.706666i
$19$	−1.82371	+	3.15875i	−0.418387	+	0.724667i	−0.995777	−	0.0918008i	$-0.970738\pi$
$19$	−1.82371	+	3.15875i	−0.418387	+	0.724667i	0.577390	+	0.816468i	$0.304071\pi$
$20$			0.105827i			0.0236637i
$21$	3.16420	+	3.31479i	0.690485	+	0.723347i
$22$	−1.20739			−0.257417
$23$	−0.845930	−	0.488398i	−0.176389	−	0.101838i	0.409206	−	0.912442i	$-0.365806\pi$
$23$	−0.845930	−	0.488398i	−0.176389	−	0.101838i	−0.585595	+	0.810604i	$0.699139\pi$
$24$	0.418670	+	1.68069i	0.0854606	+	0.343069i
$25$	−2.49440	−	4.32043i	−0.498880	−	0.864086i
$26$	−1.64910	+	3.20632i	−0.323414	+	0.628811i
$27$	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	$-0.226688\pi$
$30$	0.127302	+	0.131880i	0.0232421	+	0.0240780i
$31$	0.610707	+	1.05778i	0.109686	+	0.189982i	0.915643	−	0.401992i	$-0.131682\pi$
$31$	0.610707	+	1.05778i	0.109686	+	0.189982i	−0.805957	+	0.591974i	$0.798349\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.50463	+	1.45240i	−0.261923	+	0.252830i
$34$	−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	$-0.272178\pi$
$37$	2.01173	+	1.16147i	0.330726	+	0.190945i	−0.325438	+	0.945564i	$0.605512\pi$
$38$	1.82371	+	3.15875i	0.295844	+	0.512417i
$39$	1.80188	+	5.97940i	0.288531	+	0.957470i
$40$	0.0916492	+	0.0529137i	0.0144910	+	0.00836639i
$41$			0.417669i			0.0652290i	0.999468	+	0.0326145i	$0.0103834\pi$
$41$			0.417669i			0.0652290i	−0.999468	+	0.0326145i	$0.989617\pi$
$42$	4.45279	−	1.08288i	0.687081	−	0.167092i
$43$	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
$45$	0.317284	+	0.0112127i	0.0472979	+	0.00167149i
$46$	−0.845930	+	0.488398i	−0.124726	+	0.0720104i
$47$	−1.47958	−	0.854236i	−0.215819	−	0.124603i	0.388194	−	0.921578i	$-0.373099\pi$
$47$	−1.47958	−	0.854236i	−0.215819	−	0.124603i	−0.604013	+	0.796975i	$0.706432\pi$
$48$	1.66485	+	0.477766i	0.240301	+	0.0689596i
$49$	3.56739	−	6.02276i	0.509628	−	0.860395i
$50$	−4.98880			−0.705523
$51$	−2.84439	+	2.74565i	−0.398295	+	0.384468i
$52$	1.95221	+	3.03132i	0.270722	+	0.420368i
$53$	1.77421	−	1.02434i	0.243706	−	0.140704i	−0.373173	−	0.927762i	$-0.621730\pi$
$53$	1.77421	−	1.02434i	0.243706	−	0.140704i	0.616879	+	0.787058i	$0.288397\pi$
$54$	5.08328	−	1.07715i	0.691747	−	0.146582i
$55$			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	−0.955303	−	0.295628i	$-0.904471\pi$
$59$	−9.04020	+	5.21936i	−1.17693	+	0.679503i	−0.221631	+	0.975131i	$0.571138\pi$
$60$	0.177863	−	0.0443067i	0.0229620	−	0.00571997i
$61$	−8.67338	−	5.00758i	−1.11051	−	0.641154i	−0.171550	−	0.985175i	$-0.554878\pi$
$61$	−8.67338	−	5.00758i	−1.11051	−	0.641154i	−0.938962	+	0.344021i	$0.888211\pi$
$62$	1.22141			0.155120
$63$	4.24638	−	6.70584i	0.534994	−	0.844856i
$64$	1.00000			0.125000
$65$	0.339316	+	0.174519i	0.0420870	+	0.0216465i
$66$	0.505498	+	2.02925i	0.0622226	+	0.249784i
$67$	5.65318	−	3.26387i	0.690646	−	0.398745i	−0.113208	−	0.993571i	$-0.536113\pi$
$67$	5.65318	−	3.26387i	0.690646	−	0.398745i	0.803854	+	0.594827i	$0.202779\pi$
$68$	−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	$0.551610\pi$
$72$	2.64943	−	1.40731i	0.312239	−	0.165853i
$73$	−3.72258	−	6.44769i	−0.435695	−	0.754645i	0.561658	−	0.827370i	$-0.310164\pi$
$73$	−3.72258	−	6.44769i	−0.435695	−	0.754645i	−0.997352	+	0.0727248i	$0.976831\pi$
$74$	2.01173	−	1.16147i	0.233858	−	0.135018i
$75$	−6.21697	+	6.00114i	−0.717874	+	0.692952i
$76$	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	0.428687	+	0.903453i	$0.358976\pi$
$79$	−5.04911	+	8.74532i	−0.568069	+	0.983925i	−0.996757	+	0.0804722i	$0.974357\pi$
$80$	0.0916492	−	0.0529137i	0.0102467	−	0.00591593i
$81$	5.03898	−	7.45713i	0.559886	−	0.828569i
$82$	0.361712	+	0.208835i	0.0399444	+	0.0230619i
$83$		−	11.6784i		−	1.28188i	−0.767593	−	0.640938i	$-0.778546\pi$
$83$		−	11.6784i		−	1.28188i	0.767593	−	0.640938i	$-0.221454\pi$
$84$	1.28859	−	4.39767i	0.140597	−	0.479825i
$85$			0.241549i			0.0261997i
$86$	2.45216	−	4.24727i	0.264424	−	0.457995i
$87$	−11.8289	+	2.94664i	−1.26819	+	0.315913i
$88$	0.603696	+	1.04563i	0.0643542	+	0.111465i
$89$	−14.7044	−	8.48960i	−1.55867	−	0.899896i	−0.997385	−	0.0722705i	$-0.976976\pi$
$89$	−14.7044	−	8.48960i	−1.55867	−	0.899896i	−0.561281	−	0.827626i	$-0.689691\pi$
$90$	0.168352	−	0.269170i	0.0177459	−	0.0283730i
$91$	8.04879	−	5.12025i	0.843743	−	0.536748i
$92$			0.976796i			0.101838i
$93$	1.52211	−	1.46927i	0.157835	−	0.152356i
$94$	−1.47958	+	0.854236i	−0.152607	+	0.0881077i
$95$	0.334282	−	0.192998i	0.0342966	−	0.0198012i
$96$	1.24618	−	1.20292i	0.127188	−	0.122773i
$97$	8.85297			0.898883			0.449441	−	0.893310i	$-0.351623\pi$
$97$	8.85297			0.898883			0.449441	+	0.893310i	$0.351623\pi$
$98$	−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	0.995327	+	0.0965644i	$0.0307854\pi$
$101$	5.84190	+	10.1185i	0.581291	+	1.00682i	−0.414036	+	0.910260i	$0.635881\pi$
$102$	0.955606	+	3.83614i	0.0946191	+	0.379835i
$103$	−0.999136	−	0.576851i	−0.0984478	−	0.0568388i	0.449968	−	0.893045i	$-0.351435\pi$
$103$	−0.999136	−	0.576851i	−0.0984478	−	0.0568388i	−0.548416	+	0.836206i	$0.684769\pi$
$104$	3.60130	−	0.175001i	0.353137	−	0.0171602i
$105$	−0.114598	−	0.471227i	−0.0111837	−	0.0459871i
$106$		−	2.04868i		−	0.198985i
$107$	−10.5362	−	6.08311i	−1.01858	−	0.588076i	−0.104886	−	0.994484i	$-0.533448\pi$
$107$	−10.5362	−	6.08311i	−1.01858	−	0.588076i	−0.913692	+	0.406408i	$0.866781\pi$
$108$	1.60880	−	4.94083i	0.154807	−	0.475431i
$109$	6.24015	−	3.60275i	0.597698	−	0.345081i	−0.170437	−	0.985368i	$-0.554518\pi$
$109$	6.24015	−	3.60275i	0.597698	−	0.345081i	0.768135	+	0.640287i	$0.221185\pi$
$110$	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	$-0.215460\pi$
$114$	4.54535	−	4.38756i	0.425711	−	0.410932i
$115$	0.0516859	+	0.0895226i	0.00481973	+	0.00834802i
$116$	−6.09518	+	3.51906i	−0.565924	+	0.326736i
$117$	9.29512	−	5.53179i	0.859334	−	0.511414i
$118$			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
$123$	0.701972	−	0.174865i	0.0632947	−	0.0157671i
$124$	0.610707	−	1.05778i	0.0548431	−	0.0949910i
$125$			1.05709i			0.0945488i
$126$	−3.68423	−	7.03039i	−0.328218	−	0.626317i
$127$	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
$129$	−2.05329	−	8.24265i	−0.180782	−	0.725725i
$130$	0.320796	−	0.206597i	0.0281357	−	0.0181197i
$131$	−6.41784	+	11.1160i	−0.560729	+	0.971212i	0.436704	+	0.899605i	$0.356146\pi$
$131$	−6.41784	+	11.1160i	−0.560729	+	0.971212i	−0.997433	+	0.0716063i	$0.977187\pi$
$132$	2.01013	+	0.576851i	0.174960	+	0.0502085i
$133$	0.0538159	−	9.65000i	0.00466643	−	0.836761i
$134$		−	6.52773i		−	0.563910i
$135$	−0.113992	−	0.537950i	−0.00981088	−	0.0462994i
$136$	1.14124	+	1.97669i	0.0978606	+	0.169500i
$137$	−2.91269	−	5.04492i	−0.248848	−	0.431017i	0.714359	−	0.699780i	$-0.246718\pi$
$137$	−2.91269	−	5.04492i	−0.248848	−	0.431017i	−0.963206	+	0.268763i	$0.913385\pi$
$138$	1.17501	+	1.21727i	0.100024	+	0.103621i
$139$			18.0901i			1.53438i	0.641420	+	0.767190i	$0.278346\pi$
$139$			18.0901i			1.53438i	−0.641420	+	0.767190i	$0.721654\pi$
$140$	−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
$143$	2.35708	+	3.65999i	0.197109	+	0.306064i
$144$	0.105953	−	2.99813i	0.00882938	−	0.249844i
$145$	−0.372412	+	0.645037i	−0.0309272	+	0.0535674i
$146$	−7.44515			−0.616165
$147$	−11.6160	−	3.47413i	−0.958068	−	0.286542i
$148$		−	2.32294i		−	0.190945i
$149$	−5.92542	+	10.2631i	−0.485429	+	0.840788i	−0.999860	−	0.0167437i	$-0.994670\pi$
$149$	−5.92542	+	10.2631i	−0.485429	+	0.840788i	0.514430	+	0.857532i	$0.328003\pi$
$150$	2.08866	+	8.38462i	0.170538	+	0.684602i
$151$	15.7115	−	9.07106i	1.27859	−	0.738192i	0.301998	−	0.953309i	$-0.402346\pi$
$151$	15.7115	−	9.07106i	1.27859	−	0.738192i	0.976588	+	0.215116i	$0.0690131\pi$
$152$	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
$156$	4.27738	−	4.55017i	0.342464	−	0.364305i
$157$	−15.3218	+	8.84604i	−1.22281	+	0.705991i	−0.965516	−	0.260342i	$-0.916165\pi$
$157$	−15.3218	+	8.84604i	−1.22281	+	0.705991i	−0.257295	+	0.966333i	$0.582831\pi$
$158$	5.04911	+	8.74532i	0.401686	+	0.695740i
$159$	−2.46440	−	2.55303i	−0.195440	−	0.202468i
$160$		−	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	$-0.403045\pi$
$163$	−4.80436	−	2.77380i	−0.376306	−	0.217261i	−0.676210	+	0.736709i	$0.736379\pi$
$164$	0.361712	−	0.208835i	0.0282450	−	0.0163072i
$165$	0.214750	−	0.0534956i	0.0167183	−	0.00416462i
$166$	−10.1138	−	5.83922i	−0.784985	−	0.453211i
$167$		−	9.21026i		−	0.712712i	−0.934350	−	0.356356i	$-0.884019\pi$
$167$		−	9.21026i		−	0.712712i	0.934350	−	0.356356i	$-0.115981\pi$
$168$	−3.16420	−	3.31479i	−0.244123	−	0.255742i
$169$	12.9387	−	1.26046i	0.995288	−	0.0969584i
$170$	0.209188	+	0.120775i	0.0160440	+	0.00926298i
$171$	0.386453	−	10.9354i	0.0295528	−	0.836252i
$172$	−2.45216	−	4.24727i	−0.186976	−	0.323851i
$173$	5.82669	−	10.0921i	0.442995	−	0.767289i	−0.554915	−	0.831907i	$-0.687249\pi$
$173$	5.82669	−	10.0921i	0.442995	−	0.767289i	0.997910	+	0.0646174i	$0.0205827\pi$
$174$	−3.36257	+	11.7174i	−0.254916	+	0.888296i
$175$	11.3938	+	6.66321i	0.861290	+	0.503691i
$176$	1.20739			0.0910106
$177$	12.5570	+	13.0086i	0.943841	+	0.977785i
$178$	−14.7044	+	8.48960i	−1.10214	+	0.636323i
$179$	−15.1632	+	8.75448i	−1.13335	+	0.654341i	−0.944776	−	0.327718i	$-0.893720\pi$
$179$	−15.1632	+	8.75448i	−1.13335	+	0.654341i	−0.188576	+	0.982059i	$0.560387\pi$
$180$	−0.148932	−	0.280382i	−0.0111007	−	0.0208985i
$181$			13.3881i			0.995127i	0.867428	+	0.497564i	$0.165772\pi$
$181$			13.3881i			0.995127i	−0.867428	+	0.497564i	$0.834228\pi$
$182$	−0.409865	−	9.53058i	−0.0303812	−	0.706454i
$183$	−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
$186$	−0.511369	−	2.05282i	−0.0374954	−	0.150520i
$187$	−1.37793	+	2.38664i	−0.100764	+	0.174528i
$188$			1.70847i			0.124603i
$189$	−13.0483	−	4.32932i	−0.949121	−	0.314912i
$190$		−	0.385996i		−	0.0280031i
$191$	12.8955	+	7.44521i	0.933084	+	0.538717i	0.887786	−	0.460257i	$-0.152243\pi$
$191$	12.8955	+	7.44521i	0.933084	+	0.538717i	0.0452987	+	0.998973i	$0.485576\pi$
$192$	−0.418670	−	1.68069i	−0.0302149	−	0.121293i
$193$	−11.3018	+	6.52508i	−0.813519	+	0.469685i	−0.848176	−	0.529714i	$-0.822299\pi$
$193$	−11.3018	+	6.52508i	−0.813519	+	0.469685i	0.0346576	+	0.999399i	$0.488966\pi$
$194$	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	$0.398360\pi$
$198$	3.19890	−	1.69917i	0.227336	−	0.120755i
$199$	13.8134	−	7.97517i	0.979206	−	0.565345i	0.0771758	−	0.997017i	$-0.475410\pi$
$199$	13.8134	−	7.97517i	0.979206	−	0.565345i	0.902030	+	0.431673i	$0.142076\pi$
$200$	2.49440	+	4.32043i	0.176381	+	0.305500i
$201$	−7.85236	−	8.13476i	−0.553863	−	0.573782i
$202$	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
$207$	2.92856	+	0.103494i	0.203549	+	0.00719334i
$208$	1.64910	−	3.20632i	0.114344	−	0.222318i
$209$	4.40386			0.304621
$210$	−0.465394	−	0.136369i	−0.0321152	−	0.00941033i
$211$	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
$213$	1.13897	+	4.57225i	0.0780412	+	0.313285i
$214$	−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
$219$	−9.27803	+	8.95594i	−0.626951	+	0.605187i
$220$	0.110657	−	0.0638876i	0.00746046	−	0.00430730i
$221$	4.45587	+	6.91893i	0.299735	+	0.465418i
$222$	−2.79432	−	2.89481i	−0.187542	−	0.194287i
$223$	−19.4124			−1.29995			−0.649975	−	0.759955i	$-0.725221\pi$
$223$	−19.4124			−1.29995			−0.649975	+	0.759955i	$0.725221\pi$
$224$	−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	0.0839133	−	0.996473i	$-0.473258\pi$
$227$	14.8984	−	8.60159i	0.988841	−	0.570908i	0.904928	+	0.425566i	$0.139925\pi$
$228$	−1.52706	−	6.13017i	−0.101132	−	0.405980i
$229$	−4.77500	+	8.27054i	−0.315541	+	0.546533i	−0.979552	−	0.201190i	$-0.935519\pi$
$229$	−4.77500	+	8.27054i	−0.315541	+	0.546533i	0.664012	+	0.747722i	$0.268853\pi$
$230$	0.103372			0.00681613
$231$	1.55584	−	5.30972i	0.102367	−	0.349354i
$232$			7.03811i			0.462075i
$233$	9.52198	+	5.49752i	0.623806	+	0.360154i	0.778349	−	0.627832i	$-0.216057\pi$
$233$	9.52198	+	5.49752i	0.623806	+	0.360154i	−0.154543	+	0.987986i	$0.549391\pi$
$234$	−0.143107	−	10.8157i	−0.00935519	−	0.707045i
$235$	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	$0.663893\pi$
$240$	−0.127302	−	0.131880i	−0.00821732	−	0.00851284i
$241$	−8.18626	−	14.1790i	−0.527323	−	0.913351i	−0.999493	−	0.0318429i	$-0.989862\pi$
$241$	−8.18626	−	14.1790i	−0.527323	−	0.913351i	0.472170	−	0.881508i	$-0.343471\pi$
$242$	−4.77110	−	8.26379i	−0.306698	−	0.531217i
$243$	−14.6428	−	5.34688i	−0.939334	−	0.343003i
$244$			10.0152i			0.641154i
$245$	−0.645635	+	0.363217i	−0.0412481	+	0.0232051i
$246$	0.199548	−	0.695358i	0.0127227	−	0.0443344i
$247$	6.01493	−	11.6948i	0.382721	−	0.744120i
$248$	−0.610707	−	1.05778i	−0.0387799	−	0.0671688i
$249$	−19.6278	+	4.88941i	−1.24386	+	0.309854i
$250$	0.915465	+	0.528544i	0.0578991	+	0.0334281i
$251$	−5.68832			−0.359044			−0.179522	−	0.983754i	$-0.557455\pi$
$251$	−5.68832			−0.359044			−0.179522	+	0.983754i	$0.557455\pi$
$252$	−7.93062	−	0.324556i	−0.499582	−	0.0204451i
$253$			1.17938i			0.0741468i
$254$	6.89412	−	11.9410i	0.432576	−	0.749243i
$255$	0.405969	−	0.101129i	0.0254228	−	0.00633296i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.39698	−	12.8119i	0.461411	−	0.799187i	−0.537621	−	0.843187i	$-0.680677\pi$
$257$	7.39698	−	12.8119i	0.461411	−	0.799187i	0.999032	+	0.0439995i	$0.0140100\pi$
$258$	−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
$261$	9.90478	+	18.6470i	0.613090	+	1.15422i
$262$	6.41784	+	11.1160i	0.396496	+	0.686750i
$263$	−20.3349	+	11.7403i	−1.25390	+	0.723940i	−0.971882	−	0.235468i	$-0.924338\pi$
$263$	−20.3349	+	11.7403i	−1.25390	+	0.723940i	−0.282020	+	0.959409i	$0.591004\pi$
$264$	1.50463	−	1.45240i	0.0926038	−	0.0893890i
$265$	−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	0.997551	+	0.0699465i	$0.0222829\pi$
$269$	9.17404	+	15.8899i	0.559351	+	0.968824i	−0.438200	+	0.898878i	$0.644384\pi$
$270$	−0.522875	−	0.170255i	−0.0318211	−	0.0103614i
$271$	−11.0400	+	19.1219i	−0.670634	+	1.16157i	0.307091	+	0.951680i	$0.400644\pi$
$271$	−11.0400	+	19.1219i	−0.670634	+	1.16157i	−0.977725	+	0.209891i	$0.932689\pi$
$272$	2.28248			0.138396
$273$	−11.9753	−	11.3838i	−0.724780	−	0.688981i
$274$	−5.82537			−0.351924
$275$	−3.01172	+	5.21645i	−0.181614	+	0.314564i
$276$	1.64169	−	0.408955i	0.0988182	−	0.0246162i
$277$	−1.11567	−	1.93239i	−0.0670338	−	0.116106i	0.830561	−	0.556928i	$-0.188020\pi$
$277$	−1.11567	−	1.93239i	−0.0670338	−	0.116106i	−0.897594	+	0.440822i	$0.854687\pi$
$278$	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	$0.252916\pi$
$282$	2.05516	+	2.12907i	0.122383	+	0.126784i
$283$	−4.21753	+	2.43499i	−0.250706	+	0.144745i	−0.620088	−	0.784533i	$-0.712903\pi$
$283$	−4.21753	+	2.43499i	−0.250706	+	0.144745i	0.369381	+	0.929278i	$0.379570\pi$
$284$	1.36023	+	2.35599i	0.0807148	+	0.139802i
$285$	−0.464323	−	0.481022i	−0.0275041	−	0.0284933i
$286$	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
$291$	−3.70647	−	14.8791i	−0.217277	−	0.872228i
$292$	−3.72258	+	6.44769i	−0.217847	+	0.377323i
$293$			3.97126i			0.232003i	0.993249	+	0.116002i	$0.0370078\pi$
$293$			3.97126i			0.232003i	−0.993249	+	0.116002i	$0.962992\pi$
$294$	−8.81667	+	8.32264i	−0.514198	+	0.485386i
$295$	1.10470			0.0643183
$296$	−2.01173	−	1.16147i	−0.116929	−	0.0675091i
$297$	1.94245	−	5.96552i	0.112713	−	0.346154i
$298$	5.92542	+	10.2631i	0.343250	+	0.594527i
$299$	3.13192	+	1.61083i	0.181124	+	0.0931568i
$300$	8.30563	+	2.38348i	0.479526	+	0.137610i
$301$	−11.2732	+	6.42505i	−0.649778	+	0.370334i
$302$		−	18.1421i		−	1.04396i
$303$	14.5602	−	14.0547i	0.836460	−	0.807422i
$304$	−1.82371	−	3.15875i	−0.104597	−	0.181167i
$305$	0.529939	+	0.917880i	0.0303442	+	0.0525577i
$306$	6.04728	−	3.21215i	0.345700	−	0.183627i
$307$	−3.58652			−0.204694			−0.102347	−	0.994749i	$-0.532635\pi$
$307$	−3.58652			−0.204694			−0.102347	+	0.994749i	$0.532635\pi$
$308$	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	0.894493	+	0.447082i	$0.147537\pi$
$311$	14.7153	+	25.4877i	0.834431	+	1.44528i	−0.0600623	+	0.998195i	$0.519130\pi$
$312$	−1.80188	−	5.97940i	−0.102011	−	0.338517i
$313$	−12.7524	−	7.36260i	−0.720809	−	0.416159i	0.0942416	−	0.995549i	$-0.469957\pi$
$313$	−12.7524	−	7.36260i	−0.720809	−	0.416159i	−0.815050	+	0.579390i	$0.803291\pi$
$314$			17.6921i			0.998421i
$315$	−0.744008	+	0.389893i	−0.0419201	+	0.0219680i
$316$	10.0982			0.568069
$317$	13.3964	−	23.2033i	0.752420	−	1.30323i	−0.194227	−	0.980957i	$-0.562220\pi$
$317$	13.3964	−	23.2033i	0.752420	−	1.30323i	0.946647	−	0.322272i	$-0.104447\pi$
$318$	−3.44319	+	0.857718i	−0.193084	+	0.0480984i
$319$	−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
$324$	−8.97755	−	0.635319i	−0.498753	−	0.0352955i
$325$	9.73917	+	15.1226i	0.540232	+	0.838853i
$326$	−4.80436	+	2.77380i	−0.266089	+	0.153626i
$327$	−8.66767	−	8.97939i	−0.479323	−	0.496561i
$328$		−	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	$-0.348783\pi$
$331$	−1.52884	−	0.882679i	−0.0840329	−	0.0485164i	−0.541428	+	0.840747i	$0.682116\pi$
$332$	−10.1138	+	5.83922i	−0.555068	+	0.320469i
$333$	−6.96448	−	0.246122i	−0.381651	−	0.0134874i
$334$	−7.97632	−	4.60513i	−0.436445	−	0.251982i
$335$	−0.690813			−0.0377431
$336$	−4.45279	+	1.08288i	−0.242920	+	0.0590760i
$337$	−19.9939			−1.08913			−0.544567	−	0.838717i	$-0.683306\pi$
$337$	−19.9939			−1.08913			−0.544567	+	0.838717i	$0.683306\pi$
$338$	5.37778	−	11.8355i	0.292513	−	0.643767i
$339$	−22.3814	+	5.57534i	−1.21559	+	0.302811i
$340$	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
$345$	0.128820	−	0.124348i	0.00693545	−	0.00669469i
$346$	−5.82669	−	10.0921i	−0.313245	−	0.542556i
$347$	−5.40323	+	3.11955i	−0.290060	+	0.167466i	−0.637969	−	0.770062i	$-0.720225\pi$
$347$	−5.40323	+	3.11955i	−0.290060	+	0.167466i	0.347909	+	0.937528i	$0.386892\pi$
$348$	8.46631	+	8.77079i	0.453842	+	0.470163i
$349$	−5.19865			−0.278278			−0.139139	−	0.990273i	$-0.544433\pi$
$349$	−5.19865			−0.278278			−0.139139	+	0.990273i	$0.544433\pi$
$350$	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	0.198386	−	0.980124i	$-0.436430\pi$
$353$	21.5387	−	12.4354i	1.14639	−	0.661869i	0.948005	+	0.318255i	$0.103097\pi$
$354$	17.5443	−	4.37038i	0.932466	−	0.232283i
$355$	0.249328	+	0.143950i	0.0132330	+	0.00764005i
$356$			16.9792i			0.899896i
$357$	2.94119	−	10.0376i	0.155665	−	0.531247i
$358$			17.5090i			0.925378i
$359$	−15.5010	+	26.8486i	−0.818113	+	1.41701i	0.0889571	+	0.996035i	$0.471647\pi$
$359$	−15.5010	+	26.8486i	−0.818113	+	1.41701i	−0.907071	+	0.420979i	$0.861687\pi$
$360$	−0.317284	−	0.0112127i	−0.0167223	−	0.000590960i
$361$	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
$364$	−8.45866	−	4.41034i	−0.443354	−	0.231165i
$365$			0.787901i			0.0412406i
$366$	12.0475	+	12.4807i	0.629731	+	0.652378i
$367$	14.7620	−	8.52284i	0.770570	−	0.444889i	−0.0625080	−	0.998044i	$-0.519910\pi$
$367$	14.7620	−	8.52284i	0.770570	−	0.444889i	0.833078	+	0.553156i	$0.186577\pi$
$368$	0.845930	−	0.488398i	0.0440972	−	0.0254595i
$369$	−0.587789	−	1.10659i	−0.0305991	−	0.0576066i
$370$	−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	0.431502	+	0.902112i	$0.357984\pi$
$373$	−10.9216	+	18.9168i	−0.565501	+	0.979476i	−0.997003	+	0.0773640i	$0.975350\pi$
$374$	1.37793	+	2.38664i	0.0712508	+	0.123410i
$375$	1.77664	−	0.442571i	0.0917451	−	0.0228542i
$376$	1.47958	+	0.854236i	0.0763035	+	0.0440538i
$377$	1.23167	+	25.3464i	0.0634344	+	1.30540i
$378$	−10.2734	+	9.13546i	−0.528408	+	0.469878i
$379$		−	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
$381$	−5.77272	−	23.1738i	−0.295745	−	1.18723i
$382$	12.8955	−	7.44521i	0.659790	−	0.380930i
$383$	13.3338	+	7.69829i	0.681327	+	0.393364i	0.800355	−	0.599527i	$-0.204644\pi$
$383$	13.3338	+	7.69829i	0.681327	+	0.393364i	−0.119028	+	0.992891i	$0.537978\pi$
$384$	−1.66485	−	0.477766i	−0.0849592	−	0.0243809i
$385$	−0.167395	−	0.293708i	−0.00853125	−	0.0149687i
$386$			13.0502i			0.664235i
$387$	−12.9937	+	6.90189i	−0.660506	+	0.350843i
$388$	−4.42648	−	7.66690i	−0.224721	−	0.389228i
$389$	−9.83397	+	5.67765i	−0.498602	+	0.287868i	−0.728136	−	0.685433i	$-0.759613\pi$
$389$	−9.83397	+	5.67765i	−0.498602	+	0.287868i	0.229534	+	0.973301i	$0.426280\pi$
$390$	−0.481533	−	0.452663i	−0.0243834	−	0.0229215i
$391$			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
$396$	0.127926	−	3.61992i	0.00642854	−	0.181908i
$397$	12.6212	−	21.8606i	0.633440	−	1.09715i	−0.353404	−	0.935471i	$-0.614976\pi$
$397$	12.6212	−	21.8606i	0.633440	−	1.09715i	0.986843	−	0.161679i	$-0.0516909\pi$
$398$		−	15.9503i		−	0.799519i
$399$	−16.2412	+	3.94971i	−0.813076	+	0.197733i
$400$	4.98880			0.249440
$401$	−17.2752	+	29.9215i	−0.862681	+	1.49421i	0.00665018	+	0.999978i	$0.497883\pi$
$401$	−17.2752	+	29.9215i	−0.862681	+	1.49421i	−0.869331	+	0.494230i	$0.835450\pi$
$402$	−10.9711	+	2.73296i	−0.547188	+	0.136308i
$403$	−2.38445	−	3.70249i	−0.118778	−	0.184434i
$404$	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
$408$	2.84439	−	2.74565i	0.140818	−	0.135930i
$409$	4.95129	+	8.57588i	0.244825	+	0.424050i	0.962083	−	0.272759i	$-0.0879360\pi$
$409$	4.95129	+	8.57588i	0.244825	+	0.424050i	−0.717257	+	0.696809i	$0.754603\pi$
$410$	−0.0221004	−	0.0382790i	−0.00109146	−	0.00189047i
$411$	−7.25949	+	7.00747i	−0.358084	+	0.345653i
$412$			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
$416$	−1.95221	−	3.03132i	−0.0957148	−	0.148623i
$417$	30.4038	−	7.57376i	1.48888	−	0.370889i
$418$	2.20193	−	3.81385i	0.107700	−	0.186542i
$419$	−26.9663			−1.31739			−0.658694	−	0.752411i	$-0.728891\pi$
$419$	−26.9663			−1.31739			−0.658694	+	0.752411i	$0.728891\pi$
$420$	−0.350796	+	0.334859i	−0.0171171	+	0.0163394i
$421$		−	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
$423$	5.12222	+	0.181017i	0.249051	+	0.00880135i
$424$	−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
$429$	5.16447	−	5.49384i	0.249343	−	0.265245i
$430$	−0.449477	+	0.259506i	−0.0216757	+	0.0125145i
$431$	−11.0130	−	19.0751i	−0.530478	−	0.918816i	−0.999368	−	0.0355586i	$-0.988679\pi$
$431$	−11.0130	−	19.0751i	−0.530478	−	0.918816i	0.468889	−	0.883257i	$-0.344654\pi$
$432$	−5.08328	+	1.07715i	−0.244569	+	0.0518245i
$433$		−	35.6522i		−	1.71334i	−0.515868	−	0.856668i	$-0.672530\pi$
$433$		−	35.6522i		−	1.71334i	0.515868	−	0.856668i	$-0.327470\pi$
$434$	−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
$438$	3.11706	+	12.5130i	0.148939	+	0.597894i
$439$	−8.95324	−	5.16916i	−0.427315	−	0.246710i	0.270887	−	0.962611i	$-0.412683\pi$
$439$	−8.95324	−	5.16916i	−0.427315	−	0.246710i	−0.698202	+	0.715901i	$0.746016\pi$
$440$		−	0.127775i		−	0.00609144i
$441$	−0.975693	+	20.9773i	−0.0464616	+	0.998920i
$442$	8.21991	−	0.399436i	0.390981	−	0.0189992i
$443$	−33.8232	−	19.5279i	−1.60699	−	0.927796i	−0.990039	−	0.140795i	$-0.955034\pi$
$443$	−33.8232	−	19.5279i	−1.60699	−	0.927796i	−0.616952	−	0.787001i	$-0.711633\pi$
$444$	−3.90414	+	0.972545i	−0.185282	+	0.0461549i
$445$	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	$0.389437\pi$
$450$	13.2175	−	7.02077i	0.623078	−	0.330962i
$451$	0.436729	−	0.252145i	0.0205647	−	0.0118731i
$452$	−11.5327	+	6.65841i	−0.542453	+	0.313185i
$453$	−21.8236	−	22.6084i	−1.02536	−	1.06224i
$454$		−	17.2032i		−	0.807385i
$455$	−1.00860	+	0.0433750i	−0.0472837	+	0.00203345i
$456$	−6.07241	−	1.74261i	−0.284367	−	0.0816052i
$457$	35.3848	+	20.4294i	1.65523	+	0.955647i	0.974872	+	0.222766i	$0.0715085\pi$
$457$	35.3848	+	20.4294i	1.65523	+	0.955647i	0.680357	+	0.732881i	$0.261825\pi$
$458$	4.77500	+	8.27054i	0.223121	+	0.386457i
$459$	3.67206	−	11.2773i	0.171397	−	0.526381i
$460$	0.0516859	−	0.0895226i	0.00240987	−	0.00417401i
$461$			12.6945i			0.591242i	0.955305	+	0.295621i	$0.0955265\pi$
$461$			12.6945i			0.591242i	−0.955305	+	0.295621i	$0.904474\pi$
$462$	−3.82043	−	4.00225i	−0.177742	−	0.186202i
$463$		−	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
$465$	−0.217244	+	0.0541168i	−0.0100745	+	0.00250961i
$466$	9.52198	−	5.49752i	0.441097	−	0.254668i
$467$	7.65871	−	13.2653i	0.354403	−	0.613844i	−0.632613	−	0.774468i	$-0.718017\pi$
$467$	7.65871	−	13.2653i	0.354403	−	0.613844i	0.987016	+	0.160624i	$0.0513508\pi$
$468$	−9.43823	−	5.28392i	−0.436282	−	0.244249i
$469$	−8.71865	+	14.9085i	−0.402590	+	0.688412i
$470$	0.180803			0.00833982
$471$	21.2822	+	22.0476i	0.980632	+	1.01590i
$472$	9.04020	−	5.21936i	0.416109	−	0.240241i
$473$	−2.96072	−	5.12812i	−0.136134	−	0.235791i
$474$	12.5843	−	12.1474i	0.578014	−	0.557948i
$475$	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	0.726078	−	0.687612i	$-0.241341\pi$
$479$	36.8694	−	21.2866i	1.68461	−	0.972608i	0.958529	−	0.284996i	$-0.0919922\pi$
$480$	−0.177863	+	0.0443067i	−0.00811829	+	0.00202231i
$481$	−7.44809	−	3.83075i	−0.339604	−	0.174667i
$482$	−16.3725			−0.745748
$483$	−1.05775	−	4.34947i	−0.0481295	−	0.197908i
$484$	−9.54220			−0.433737
$485$	−0.811367	−	0.468443i	−0.0368423	−	0.0212709i
$486$	−11.9519	+	10.0076i	−0.542150	+	0.453953i
$487$	4.29100	−	2.47741i	0.194444	−	0.112262i	−0.399617	−	0.916682i	$-0.630857\pi$
$487$	4.29100	−	2.47741i	0.194444	−	0.112262i	0.594061	+	0.804420i	$0.297524\pi$
$488$	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	$-0.306225\pi$
$492$	−0.502424	−	0.520493i	−0.0226510	−	0.0234656i
$493$	−13.9121	+	8.03218i	−0.626572	+	0.361751i
$494$	−7.12050	−	11.0565i	−0.320366	−	0.497454i
$495$	−0.179819	−	0.338532i	−0.00808225	−	0.0152159i
$496$	−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	$-0.534367\pi$
$499$	−22.8436	−	13.1887i	−1.02262	−	0.590409i	−0.914861	+	0.403769i	$0.867700\pi$
$500$	0.915465	−	0.528544i	0.0409409	−	0.0236372i
$501$	−15.4796	+	3.85606i	−0.691577	+	0.172276i
$502$	−2.84416	+	4.92623i	−0.126941	+	0.219868i
$503$	33.8590			1.50970			0.754849	−	0.655898i	$-0.227710\pi$
$503$	33.8590			1.50970			0.754849	+	0.655898i	$0.227710\pi$
$504$	−4.24638	+	6.70584i	−0.189149	+	0.298702i
$505$		−	1.23647i		−	0.0550220i
$506$	1.02137	+	0.589688i	0.0454054	+	0.0262148i
$507$	−7.53550	−	21.2183i	−0.334663	−	0.942338i
$508$	−6.89412	−	11.9410i	−0.305877	−	0.529795i
$509$	−34.0447	−	19.6557i	−1.50901	−	0.871225i	−0.999945	−	0.0104951i	$-0.996659\pi$
$509$	−34.0447	−	19.6557i	−1.50901	−	0.871225i	−0.509061	−	0.860730i	$-0.670007\pi$
$510$	0.115404	−	0.402144i	0.00511017	−	0.0178072i
$511$	17.0038	+	9.94399i	0.752204	+	0.439896i
$512$	−1.00000			−0.0441942
$513$	−18.5408	+	3.92882i	−0.818597	+	0.173461i
$514$	−7.39698	−	12.8119i	−0.326267	−	0.565111i
$515$	0.0610466	+	0.105736i	0.00269004	+	0.00465928i
$516$	−6.11170	+	5.89953i	−0.269052	+	0.259712i
$517$			2.06280i			0.0907216i
$518$	−3.10260	+	5.30531i	−0.136320	+	0.233102i
$519$	−19.4012	−	5.56759i	−0.851617	−	0.244390i
$520$	−0.339316	−	0.174519i	−0.0148800	−	0.00765318i
$521$	−8.81970	−	15.2762i	−0.386398	−	0.669261i	0.605564	−	0.795797i	$-0.292948\pi$
$521$	−8.81970	−	15.2762i	−0.386398	−	0.669261i	−0.991962	+	0.126535i	$0.959614\pi$
$522$	21.1012	+	0.745706i	0.923573	+	0.0326387i
$523$	17.8468	+	10.3039i	0.780387	+	0.450557i	0.836567	−	0.547864i	$-0.184559\pi$
$523$	17.8468	+	10.3039i	0.780387	+	0.450557i	−0.0561804	+	0.998421i	$0.517892\pi$
$524$	12.8357			0.560729
$525$	6.42854	−	21.9391i	0.280565	−	0.957501i
$526$			23.4807i			1.02381i
$527$	1.39393	−	2.41435i	0.0607204	−	0.105171i
$528$	−0.505498	−	2.02925i	−0.0219990	−	0.0883118i
$529$	−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
$534$	20.4247	+	21.1592i	0.883862	+	0.915649i
$535$	0.643759	+	1.11502i	0.0278321	+	0.0482067i
$536$	−5.65318	+	3.26387i	−0.244180	+	0.140978i
$537$	21.0619	+	21.8194i	0.908890	+	0.941577i
$538$	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	$-0.193766\pi$
$541$	17.1036	+	9.87474i	0.735339	+	0.424548i	−0.0850330	+	0.996378i	$0.527100\pi$
$542$	11.0400	+	19.1219i	0.474210	+	0.821355i
$543$	22.5012	−	5.60518i	0.965618	−	0.240541i
$544$	1.14124	−	1.97669i	0.0489303	−	0.0847498i
$545$	−0.762539			−0.0326636
$546$	−15.8463	+	4.67902i	−0.678161	+	0.200244i
$547$	−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
$549$	30.0267	+	1.06113i	1.28151	+	0.0452880i
$550$	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
$555$	−0.306350	+	0.295715i	−0.0130039	+	0.0125524i
$556$	15.6665	−	9.04503i	0.664406	−	0.383595i
$557$	−4.88652	−	8.46370i	−0.207049	−	0.358619i	0.743735	−	0.668475i	$-0.233052\pi$
$557$	−4.88652	−	8.46370i	−0.207049	−	0.358619i	−0.950783	+	0.309856i	$0.899719\pi$
$558$	−3.23605	+	1.71890i	−0.136993	+	0.0727670i
$559$	−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	$-0.172285\pi$
$563$	−0.418795	−	0.725375i	−0.0176501	−	0.0305709i	−0.874716	+	0.484637i	$0.838952\pi$
$564$	2.87141	−	0.715285i	0.120908	−	0.0301189i
$565$	−0.704642	+	1.22048i	−0.0296445	+	0.0513458i
$566$			4.86999i			0.204701i
$567$	−1.81333	+	23.7426i	−0.0761527	+	0.997096i
$568$	2.72046			0.114148
$569$	−23.1014	−	13.3376i	−0.968463	−	0.559142i	−0.0696956	−	0.997568i	$-0.522203\pi$
$569$	−23.1014	−	13.3376i	−0.968463	−	0.559142i	−0.898767	+	0.438426i	$0.855536\pi$
$570$	−0.648739	+	0.161605i	−0.0271727	+	0.00676888i
$571$	11.7217	+	20.3025i	0.490536	+	0.849633i	0.999941	−	0.0108941i	$-0.00346775\pi$
$571$	11.7217	+	20.3025i	0.490536	+	0.849633i	−0.509405	+	0.860527i	$0.670134\pi$
$572$	1.99111	−	3.87129i	0.0832523	−	0.161867i
$573$	7.11414	−	24.7904i	0.297197	−	1.03563i
$574$	−1.10503	−	0.00616251i	−0.0461231	−	0.000257218i
$575$			4.87304i			0.203220i
$576$	−2.64943	+	1.40731i	−0.110393	+	0.0586378i
$577$	2.28855	+	3.96389i	0.0952736	+	0.165019i	0.909723	−	0.415216i	$-0.136294\pi$
$577$	2.28855	+	3.96389i	0.0952736	+	0.165019i	−0.814449	+	0.580235i	$0.802961\pi$
$578$	−5.89514	−	10.2107i	−0.245205	−	0.424708i
$579$	15.6983	+	16.2629i	0.652400	+	0.675863i
$580$	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
$585$	−1.14460	+	0.0151446i	−0.0473233	+	0.000626153i
$586$	3.43921	+	1.98563i	0.142072	+	0.0820256i
$587$		−	36.9891i		−	1.52670i	−0.645982	−	0.763352i	$-0.723552\pi$
$587$		−	36.9891i		−	1.52670i	0.645982	−	0.763352i	$-0.276448\pi$
$588$	2.79929	+	11.7968i	0.115441	+	0.486491i
$589$	−4.45500			−0.183565
$590$	0.552351	−	0.956700i	0.0227399	−	0.0393867i
$591$	−3.68931	−	14.8102i	−0.151758	−	0.609211i
$592$	−2.01173	+	1.16147i	−0.0826814	+	0.0477362i
$593$	−24.0004	−	13.8566i	−0.985579	−	0.569024i	−0.0816289	−	0.996663i	$-0.526012\pi$
$593$	−24.0004	−	13.8566i	−0.985579	−	0.569024i	−0.903950	+	0.427639i	$0.859346\pi$
$594$	−4.19506	−	4.66497i	−0.172125	−	0.191406i
$595$	−0.316448	−	0.555232i	−0.0129731	−	0.0227623i
$596$	11.8508			0.485429
$597$	−19.1870	−	19.8771i	−0.785273	−	0.813515i
$598$	2.96098	−	1.90691i	0.121084	−	0.0779792i
$599$	10.8738	−	6.27799i	0.444291	−	0.256512i	−0.261125	−	0.965305i	$-0.584093\pi$
$599$	10.8738	−	6.27799i	0.444291	−	0.256512i	0.705416	+	0.708793i	$0.250760\pi$
$600$	6.21697	−	6.00114i	0.253807	−	0.244996i
$601$		−	10.7277i		−	0.437594i	−0.975770	−	0.218797i	$-0.929787\pi$
$601$		−	10.7277i		−	0.437594i	0.975770	−	0.218797i	$-0.0702132\pi$
$602$	−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
$606$	−4.89165	−	19.6368i	−0.198710	−	0.797692i
$607$	27.0857	+	15.6379i	1.09937	+	0.634724i	0.936057	−	0.351849i	$-0.114447\pi$
$607$	27.0857	+	15.6379i	1.09937	+	0.634724i	0.163318	+	0.986574i	$0.447780\pi$
$608$	−3.64741			−0.147922
$609$	23.3299	−	22.2700i	0.945374	−	0.902425i
$610$	1.05988			0.0429132
$611$	5.47790	+	2.81743i	0.221612	+	0.113981i
$612$	0.241835	−	6.84317i	0.00977560	−	0.276619i
$613$	10.8577	−	6.26872i	0.438540	−	0.253191i	−0.264438	−	0.964403i	$-0.585187\pi$
$613$	10.8577	−	6.26872i	0.438540	−	0.253191i	0.702978	+	0.711212i	$0.251853\pi$
$614$	−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	$0.449165\pi$
$618$	1.38782	+	1.43773i	0.0558261	+	0.0578338i
$619$	−5.53340	−	9.58414i	−0.222406	−	0.385219i	0.733132	−	0.680086i	$-0.238058\pi$
$619$	−5.53340	−	9.58414i	−0.222406	−	0.385219i	−0.955538	+	0.294868i	$0.904724\pi$
$620$	−0.111942	+	0.0646295i	−0.00449568	+	0.00259558i
$621$	−1.05216	−	4.96533i	−0.0422216	−	0.199252i
$622$	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
$627$	−1.84376	−	7.40152i	−0.0736327	−	0.295588i
$628$	15.3218	+	8.84604i	0.611406	+	0.352995i
$629$		−	5.30207i		−	0.211407i
$630$	−0.0343469	+	0.839276i	−0.00136841	+	0.0334376i
$631$			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
$633$	−6.81033	−	27.3391i	−0.270686	−	1.08663i
$634$	−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
$637$	−11.7933	+	22.3141i	−0.467267	+	0.884116i
$638$			8.49776i			0.336430i
$639$	7.20767	−	3.82852i	0.285131	−	0.151454i
$640$	−0.0916492	+	0.0529137i	−0.00362275	+	0.00209160i
$641$	5.02205	−	2.89948i	0.198359	−	0.114523i	−0.397531	−	0.917589i	$-0.630133\pi$
$641$	5.02205	−	2.89948i	0.198359	−	0.114523i	0.595890	+	0.803066i	$0.296800\pi$
$642$	14.6350	+	15.1613i	0.577598	+	0.598371i
$643$	17.1073			0.674646			0.337323	−	0.941389i	$-0.390479\pi$
$643$	17.1073			0.674646			0.337323	+	0.941389i	$0.390479\pi$
$644$	−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	$-0.0825174\pi$
$647$	6.64633	+	11.5118i	0.261294	+	0.452575i	−0.705292	+	0.708917i	$0.749184\pi$
$648$	−5.03898	+	7.45713i	−0.197950	+	0.292944i
$649$	10.9151	+	6.30182i	0.428454	+	0.247368i
$650$	17.9662	−	0.873043i	0.704691	−	0.0342436i
$651$	−1.57391	+	5.37138i	−0.0616863	+	0.210521i
$652$			5.54760i			0.217261i
$653$	−20.2462	−	11.6891i	−0.792295	−	0.457432i	0.0484750	−	0.998824i	$-0.484564\pi$
$653$	−20.2462	−	11.6891i	−0.792295	−	0.457432i	−0.840770	+	0.541393i	$0.817897\pi$
$654$	−12.1102	+	3.01673i	−0.473547	+	0.117963i
$655$	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	$0.990036\pi$
$660$	−0.153704	−	0.159231i	−0.00598291	−	0.00619807i
$661$	−3.91663	−	6.78381i	−0.152339	−	0.263860i	0.779748	−	0.626094i	$-0.215347\pi$
$661$	−3.91663	−	6.78381i	−0.152339	−	0.263860i	−0.932087	+	0.362234i	$0.882014\pi$
$662$	−1.52884	+	0.882679i	−0.0594202	+	0.0343063i
$663$	9.76303	−	10.3857i	0.379165	−	0.403347i
$664$			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
$669$	8.12738	+	32.6262i	0.314223	+	1.26140i
$670$	−0.345406	+	0.598261i	−0.0133442	+	0.0231129i
$671$			12.0922i			0.466815i
$672$	−1.28859	+	4.39767i	−0.0497086	+	0.169644i
$673$	−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
$675$	8.02598	−	24.6488i	0.308920	−	0.948733i
$676$	−7.56096	−	10.5751i	−0.290806	−	0.406733i
$677$	−9.98440	+	17.2935i	−0.383732	+	0.664643i	−0.991592	−	0.129401i	$-0.958695\pi$
$677$	−9.98440	+	17.2935i	−0.383732	+	0.664643i	0.607861	+	0.794044i	$0.292028\pi$
$678$	−6.36232	+	22.1706i	−0.244344	+	0.851455i
$679$	−20.3497	+	11.5981i	−0.780950	+	0.445093i
$680$		−	0.241549i		−	0.00926298i
$681$	−20.6941	−	21.4383i	−0.793000	−	0.821519i
$682$	−0.737363	−	1.27715i	−0.0282351	−	0.0489046i
$683$	20.4986	+	35.5046i	0.784357	+	1.35855i	0.929383	+	0.369118i	$0.120340\pi$
$683$	20.4986	+	35.5046i	0.784357	+	1.35855i	−0.145026	+	0.989428i	$0.546327\pi$
$684$	−9.66357	+	5.13303i	−0.369496	+	0.196266i
$685$			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
$689$	−6.21019	+	3.99944i	−0.236589	+	0.152366i
$690$	−0.0432786	−	0.173736i	−0.00164759	−	0.00661401i
$691$	3.60774	−	6.24879i	0.137245	−	0.237715i	−0.789208	−	0.614126i	$-0.789509\pi$
$691$	3.60774	−	6.24879i	0.137245	−	0.237715i	0.926453	+	0.376411i	$0.122842\pi$
$692$	−11.6534			−0.442995
$693$	−9.57537	−	0.391866i	−0.363738	−	0.0148858i
$694$			6.23911i			0.236833i
$695$	0.957212	−	1.65794i	0.0363091	−	0.0628892i
$696$	11.8289	−	2.94664i	0.448372	−	0.111692i
$697$	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	$-0.125009\pi$
$702$	−18.1179	+	4.76872i	−0.683817	+	0.179984i
$703$	−7.33760	+	4.23636i	−0.276743	+	0.159777i
$704$	−0.603696	−	1.04563i	−0.0227527	−	0.0394088i
$705$	0.225314	−	0.217492i	0.00848581	−	0.00819123i
$706$		−	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	$-0.498831\pi$
$709$	−22.9129	−	13.2288i	−0.860513	−	0.496817i	−0.864184	+	0.503176i	$0.832165\pi$
$710$	0.249328	−	0.143950i	0.00935711	−	0.00540233i
$711$	1.06993	−	30.2758i	0.0401256	−	1.13543i
$712$	14.7044	+	8.48960i	0.551072	+	0.318161i
$713$		−	1.19307i		−	0.0446809i
$714$	−7.22223	−	7.56595i	−0.270285	−	0.283149i
$715$	−0.0223607	−	0.460157i	−0.000836244	−	0.0172089i
$716$	15.1632	+	8.75448i	0.566676	+	0.327170i
$717$	6.37453	+	25.5897i	0.238061	+	0.955663i
$718$	15.5010	+	26.8486i	0.578494	+	1.00198i
$719$	6.33059	−	10.9649i	0.236091	−	0.408922i	−0.723498	−	0.690326i	$-0.757467\pi$
$719$	6.33059	−	10.9649i	0.236091	−	0.408922i	0.959589	+	0.281405i	$0.0908003\pi$
$720$	−0.168352	+	0.269170i	−0.00627413	+	0.0100314i
$721$	3.05236	+	0.0170223i	0.113676	+	0.000633945i
$722$	5.69638			0.211997
$723$	−20.4032	+	19.6949i	−0.758802	+	0.732460i
$724$	11.5944	−	6.69403i	0.430903	−	0.248782i
$725$	−30.4077	+	17.5559i	−1.12931	+	0.652008i
$726$	−11.8913	+	11.4785i	−0.441329	+	0.426008i
$727$		−	18.4770i		−	0.685274i	−0.939468	−	0.342637i	$-0.888680\pi$
$727$		−	18.4770i		−	0.685274i	0.939468	−	0.342637i	$-0.111320\pi$
$728$	−8.04879	+	5.12025i	−0.298308	+	0.189769i
$729$	−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
$732$	16.8324	−	4.19304i	0.622142	−	0.154979i
$733$	−1.52428	+	2.64013i	−0.0563005	+	0.0975153i	−0.892802	−	0.450449i	$-0.851264\pi$
$733$	−1.52428	+	2.64013i	−0.0563005	+	0.0975153i	0.836502	+	0.547965i	$0.184597\pi$
$734$		−	17.0457i		−	0.629168i
$735$	0.880763	+	0.933044i	0.0324874	+	0.0344159i
$736$		−	0.976796i		−	0.0360052i
$737$	−6.82561	−	3.94077i	−0.251425	−	0.145160i
$738$	−1.25223	−	0.0442532i	−0.0460951	−	0.00162898i
$739$	−29.4714	+	17.0153i	−1.08412	+	0.625919i	−0.932006	−	0.362443i	$-0.881943\pi$
$739$	−29.4714	+	17.0153i	−1.08412	+	0.625919i	−0.152118	+	0.988362i	$0.548609\pi$
$740$	−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	$0.891059\pi$
$744$	−1.52211	+	1.46927i	−0.0558031	+	0.0538659i
$745$	1.08612	−	0.627072i	0.0397924	−	0.0229741i
$746$	10.9216	+	18.9168i	0.399869	+	0.692594i
$747$	16.4351	+	30.9412i	0.601331	+	1.13208i
$748$	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	−0.918802	−	0.394718i	$-0.870842\pi$
$751$	−3.22181	+	5.58034i	−0.117566	+	0.203630i	0.801237	+	0.598347i	$0.204176\pi$
$752$	1.47958	−	0.854236i	0.0539547	−	0.0311508i
$753$	2.38153	+	9.56030i	0.0867876	+	0.348397i
$754$	22.5664	+	11.6065i	0.821821	+	0.422685i
$755$	−1.91993			−0.0698735
$756$	2.77483	+	13.4648i	0.100920	+	0.489709i
$757$	−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
$759$	1.98217	−	0.493769i	0.0719480	−	0.0179227i
$760$	−0.334282	+	0.192998i	−0.0121257	+	0.00700077i
$761$	2.67214	+	1.54276i	0.0968650	+	0.0559250i	0.547650	−	0.836708i	$-0.315523\pi$
$761$	2.67214	+	1.54276i	0.0968650	+	0.0559250i	−0.450785	+	0.892633i	$0.648856\pi$
$762$	−22.9554	−	6.58756i	−0.831587	−	0.238642i
$763$	−9.62391	+	16.4565i	−0.348409	+	0.595764i
$764$		−	14.8904i		−	0.538717i
$765$	−0.339934	−	0.639968i	−0.0122903	−	0.0231381i
$766$	13.3338	−	7.69829i	0.481771	−	0.278151i
$767$	31.6431	−	20.3785i	1.14257	−	0.735826i
$768$	−1.24618	+	1.20292i	−0.0449678	+	0.0434067i
$769$	−44.6644			−1.61064			−0.805320	−	0.592840i	$-0.798007\pi$
$769$	−44.6644			−1.61064			−0.805320	+	0.592840i	$0.798007\pi$
$770$	−0.338056	−	0.00188526i	−0.0121827	−	6.79401e-5i
$771$	−24.6298	−	7.06805i	−0.887020	−	0.254550i
$772$	11.3018	+	6.52508i	0.406759	+	0.234843i
$773$	−44.2470	+	25.5460i	−1.59145	+	0.918826i	−0.598396	+	0.801201i	$0.704195\pi$
$773$	−44.2470	+	25.5460i	−1.59145	+	0.918826i	−0.993058	+	0.117626i	$0.962472\pi$
$774$	−0.519626	+	14.7038i	−0.0186776	+	0.528517i
$775$	3.04669	−	5.27703i	0.109440	−	0.189556i
$776$	−8.85297			−0.317803
$777$	2.51547	+	10.3436i	0.0902419	+	0.371074i
$778$			11.3553i			0.407107i
$779$	−1.31931	−	0.761706i	−0.0472693	−	0.0272910i
$780$	−0.632784	+	0.190688i	−0.0226573	+	0.00682772i
$781$	1.64233	+	2.84460i	0.0587672	+	0.101788i
$782$	1.93082	+	1.11476i	0.0690460	+	0.0398637i
$783$	27.1930	−	24.4538i	0.971797	−	0.873907i
$784$	3.43217	+	6.10084i	0.122577	+	0.217887i
$785$	1.87231			0.0668254
$786$	15.9956	−	15.4403i	0.570545	−	0.550739i
$787$	16.0516	+	27.8022i	0.572178	+	0.991042i	0.996342	+	0.0854563i	$0.0272348\pi$
$787$	16.0516	+	27.8022i	0.572178	+	0.991042i	−0.424164	+	0.905586i	$0.639432\pi$
$788$	−4.40599	−	7.63140i	−0.156957	−	0.271858i
$789$	28.2455	+	29.2613i	1.00556	+	1.04173i
$790$		−	1.06867i		−	0.0380215i
$791$	17.4461	+	30.6104i	0.620310	+	1.08838i
$792$	−3.07098	−	1.92075i	−0.109122	−	0.0682507i
$793$	32.1118	+	16.5159i	1.14032	+	0.586499i
$794$	−12.6212	−	21.8606i	−0.447910	−	0.775802i
$795$	0.0907700	+	0.364383i	0.00321928	+	0.0129233i
$796$	−13.8134	−	7.97517i	−0.489603	−	0.282672i
$797$	−14.8107			−0.524621			−0.262311	−	0.964983i	$-0.584485\pi$
$797$	−14.8107			−0.524621			−0.262311	+	0.964983i	$0.584485\pi$
$798$	−4.70004	+	16.0401i	−0.166379	+	0.567814i
$799$			3.89956i			0.137956i
$800$	2.49440	−	4.32043i	0.0881904	−	0.152750i
$801$	50.9058	+	1.79899i	1.79867	+	0.0635642i
$802$	17.2752	+	29.9215i	0.610008	+	1.05656i
$803$	−4.49461	+	7.78489i	−0.158611	+	0.274723i
$804$	−3.11873	+	10.8677i	−0.109989	+	0.383275i
$805$	−0.236088	−	0.138067i	−0.00832101	−	0.00486621i
$806$	−4.39868	+	0.213748i	−0.154937	+	0.00752895i
$807$	22.8651	−	22.0713i	0.804889	−	0.776947i
$808$	−5.84190	−	10.1185i	−0.205517	−	0.355966i
$809$	−41.4000	+	23.9023i	−1.45555	+	0.840361i	−0.998788	−	0.0492291i	$-0.984324\pi$
$809$	−41.4000	+	23.9023i	−1.45555	+	0.840361i	−0.456760	+	0.889590i	$0.650990\pi$
$810$	−0.0672341	+	0.950070i	−0.00236237	+	0.0333821i
$811$	−37.9398			−1.33225			−0.666123	−	0.745842i	$-0.732047\pi$
$811$	−37.9398			−1.33225			−0.666123	+	0.745842i	$0.732047\pi$
$812$	9.40033	−	16.0742i	0.329887	−	0.564093i
$813$	36.7601	+	10.5491i	1.28923	+	0.369973i
$814$	−2.42894	−	1.40235i	−0.0851344	−	0.0491524i
$815$	0.293544	+	0.508433i	0.0102824	+	0.0178096i
$816$	−0.955606	−	3.83614i	−0.0334529	−	0.134292i
$817$	−8.94405	+	15.4916i	−0.312913	+	0.541981i
$818$	9.90258			0.346235
$819$	−14.1190	+	24.8929i	−0.493357	+	0.869827i
$820$	−0.0442008			−0.00154356
$821$	7.70294	−	13.3419i	0.268835	−	0.465635i	−0.699727	−	0.714411i	$-0.746695\pi$
$821$	7.70294	−	13.3419i	0.268835	−	0.465635i	0.968561	+	0.248776i	$0.0800282\pi$
$822$	2.43891	+	9.79064i	0.0850666	+	0.341488i
$823$	5.07586	+	8.79165i	0.176933	+	0.306458i	0.940829	−	0.338883i	$-0.110049\pi$
$823$	5.07586	+	8.79165i	0.176933	+	0.306458i	−0.763895	+	0.645340i	$0.776716\pi$
$824$	0.999136	+	0.576851i	0.0348065	+	0.0200956i
$825$	10.0281	+	2.87780i	0.349135	+	0.100192i
$826$	−13.6755	−	23.9948i	−0.475833	−	0.834885i
$827$	−52.1371			−1.81299			−0.906493	−	0.422221i	$-0.861251\pi$
$827$	−52.1371			−1.81299			−0.906493	+	0.422221i	$0.861251\pi$
$828$	−1.37465	−	2.58796i	−0.0477725	−	0.0899377i
$829$	3.42966	−	1.98012i	0.119117	−	0.0687722i	−0.439258	−	0.898361i	$-0.644758\pi$
$829$	3.42966	−	1.98012i	0.119117	−	0.0687722i	0.558375	+	0.829589i	$0.311425\pi$
$830$	0.617949	+	1.07032i	0.0214493	+	0.0371513i
$831$	−2.78065	+	2.68412i	−0.0964597	+	0.0931111i
$832$	−3.60130	+	0.175001i	−0.124853	+	0.00606705i
$833$	−15.9764	−	0.178199i	−0.553549	−	0.00617423i
$834$	8.64282	−	30.1173i	0.299276	−	1.04288i
$835$	−0.487349	+	0.844113i	−0.0168654	+	0.0292117i
$836$	−2.20193	−	3.81385i	−0.0761553	−	0.131905i
$837$	−1.96501	+	6.03479i	−0.0679207	+	0.208593i
$838$	−13.4831	+	23.3535i	−0.465767	+	0.806733i
$839$		−	30.7002i		−	1.05989i	−0.848033	−	0.529944i	$-0.822213\pi$
$839$		−	30.7002i		−	1.05989i	0.848033	−	0.529944i	$-0.177787\pi$
$840$	0.114598	+	0.471227i	0.00395402	+	0.0162589i
$841$	−20.5350			−0.708104
$842$	−9.22081	−	5.32364i	−0.317770	−	0.183465i
$843$	−9.83388	−	39.4767i	−0.338697	−	1.35965i
$844$	−8.13330	−	14.0873i	−0.279960	−	0.484904i
$845$	−1.25252	−	0.569117i	−0.0430880	−	0.0195782i
$846$	2.71787	−	4.34546i	0.0934424	−	0.149400i
$847$	−0.140791	+	25.2459i	−0.00483763	+	0.867460i
$848$			2.04868i			0.0703518i
$849$	5.85822	+	6.06890i	0.201054	+	0.208284i
$850$	5.69342	+	9.86130i	0.195283	+	0.338240i
$851$	−1.13452	−	1.96505i	−0.0388909	−	0.0673609i
$852$	3.39020	−	3.27250i	0.116146	−	0.112114i
$853$	−36.8069			−1.26024			−0.630122	−	0.776496i	$-0.716995\pi$
$853$	−36.8069			−1.26024			−0.630122	+	0.776496i	$0.716995\pi$
$854$	13.3766	−	22.8734i	0.457737	−	0.782710i
$855$	−0.614051	+	0.981773i	−0.0210001	+	0.0335759i
$856$	10.5362	+	6.08311i	0.360122	+	0.207916i
$857$	24.8881	+	43.1074i	0.850160	+	1.47252i	0.881064	+	0.472998i	$0.156828\pi$
$857$	24.8881	+	43.1074i	0.850160	+	1.47252i	−0.0309036	+	0.999522i	$0.509838\pi$
$858$	−2.17557	−	7.21948i	−0.0742728	−	0.246469i
$859$	33.0379	+	19.0744i	1.12724	+	0.650811i	0.943239	−	0.332116i	$-0.107762\pi$
$859$	33.0379	+	19.0744i	1.12724	+	0.650811i	0.183999	+	0.982927i	$0.441096\pi$
$860$			0.519012i			0.0176982i
$861$	−1.38449	+	1.32159i	−0.0471832	+	0.0450396i
$862$	−22.0260			−0.750210
$863$	5.64656	−	9.78013i	0.192211	−	0.332919i	−0.753772	−	0.657137i	$-0.771767\pi$
$863$	5.64656	−	9.78013i	0.192211	−	0.332919i	0.945983	+	0.324217i	$0.105101\pi$
$864$	−1.60880	+	4.94083i	−0.0547325	+	0.168090i
$865$	−1.06802	+	0.616623i	−0.0363138	+	0.0209658i
$866$	−30.8757	−	17.8261i	−1.04920	−	0.605756i
$867$	−19.6291	−	5.63299i	−0.666639	−	0.191307i
$868$	−0.0180214	+	3.23151i	−0.000611685	+	0.109684i
$869$	12.1925			0.413603
$870$	0.928189	−	0.895967i	0.0314686	−	0.0303761i
$871$	−19.7876	+	12.7435i	−0.670479	+	0.431796i
$872$	−6.24015	+	3.60275i	−0.211318	+	0.122005i
$873$	−23.4553	+	12.4588i	−0.793843	+	0.421668i
$874$		−	3.56278i		−	0.120513i
$875$	−1.38487	−	2.42985i	−0.0468171	−	0.0821441i
$876$	12.3951	+	3.55704i	0.418791	+	0.120181i
$877$	0.700269	+	0.404301i	0.0236464	+	0.0136523i	0.511777	−	0.859119i	$-0.328988\pi$
$877$	0.700269	+	0.404301i	0.0236464	+	0.0136523i	−0.488130	+	0.872771i	$0.662321\pi$
$878$	−8.95324	+	5.16916i	−0.302157	+	0.174451i
$879$	6.67445	−	1.66264i	0.225124	−	0.0560796i
$880$	−0.110657	−	0.0638876i	−0.00373023	−	0.00215365i
$881$	−32.2390			−1.08616			−0.543079	−	0.839681i	$-0.682742\pi$
$881$	−32.2390			−1.08616			−0.543079	+	0.839681i	$0.682742\pi$
$882$	17.6790	+	11.3336i	0.595284	+	0.381623i
$883$	−15.8943			−0.534886			−0.267443	−	0.963574i	$-0.586179\pi$
$883$	−15.8943			−0.534886			−0.267443	+	0.963574i	$0.586179\pi$
$884$	3.76403	−	7.31837i	0.126598	−	0.246143i
$885$	−0.462505	−	1.85666i	−0.0155469	−	0.0624110i
$886$	−33.8232	+	19.5279i	−1.13631	+	0.656051i
$887$	14.9312	−	25.8616i	0.501340	−	0.868347i	−0.498659	−	0.866798i	$-0.666174\pi$
$887$	14.9312	−	25.8616i	0.501340	−	0.868347i	0.999999	−	0.00154824i	$-0.000492819\pi$
$888$	−1.10982	+	3.86736i	−0.0372432	+	0.129780i
$889$	−31.6941	+	18.0637i	−1.06299	+	0.605836i
$890$	1.79686			0.0602310
$891$	−10.8394	−	0.767079i	−0.363134	−	0.0256981i
$892$	9.70620	+	16.8116i	0.324988	+	0.562895i
$893$	5.39664	−	3.11575i	0.180592	−	0.104265i
$894$	14.7683	−	14.2557i	0.493927	−	0.476780i
$895$	1.85293			0.0619365
$896$	−0.0147545	+	2.64571i	−0.000492914	+	0.0883870i
$897$	1.39607	−	5.93819i	0.0466133	−	0.198270i
$898$	7.21296	−	12.4932i	0.240699	−	0.416904i
$899$	7.44474	−	4.29822i	0.248296	−	0.143354i
$900$	0.528576	−	14.9571i	0.0176192	−	0.498569i
$901$	−4.04959	−	2.33803i	−0.134911	−	0.0778912i
$902$		−	0.504291i		−	0.0167910i
$903$	15.5183	+	16.2568i	0.516416	+	0.540993i
$904$			13.3168i			0.442911i
$905$	0.708412	−	1.22701i	0.0235484	−	0.0407870i
$906$	−30.4913	+	7.59555i	−1.01300	+	0.252345i
$907$	10.7037	+	18.5394i	0.355411	+	0.615590i	0.987188	−	0.159560i	$-0.0510076\pi$
$907$	10.7037	+	18.5394i	0.355411	+	0.615590i	−0.631777	+	0.775150i	$0.717674\pi$
$908$	−14.8984	−	8.60159i	−0.494420	−	0.285454i
$909$	−29.7175	−	18.5868i	−0.985667	−	0.616487i
$910$	−0.466734	+	0.895157i	−0.0154721	+	0.0296742i
$911$		−	3.64882i		−	0.120891i	−0.998172	−	0.0604454i	$-0.980748\pi$
$911$		−	3.64882i		−	0.120891i	0.998172	−	0.0604454i	$-0.0192521\pi$
$912$	−4.54535	+	4.38756i	−0.150512	+	0.145287i
$913$	−12.2114	+	7.05023i	−0.404137	+	0.233329i
$914$	35.3848	−	20.4294i	1.17042	−	0.675744i
$915$	1.32080	−	1.27495i	0.0436644	−	0.0421486i
$916$	9.54999			0.315541
$917$	0.189384	−	33.9595i	0.00625403	−	1.12144i
$918$	−7.93044	−	8.81877i	−0.261744	−	0.291063i
$919$	2.25933	−	3.91327i	0.0745283	−	0.129087i	−0.826353	−	0.563153i	$-0.809588\pi$
$919$	2.25933	−	3.91327i	0.0745283	−	0.129087i	0.900881	+	0.434066i	$0.142922\pi$
$920$	−0.0516859	−	0.0895226i	−0.00170403	−	0.00295147i
$921$	1.50157	+	6.02783i	0.0494784	+	0.198624i
$922$	10.9938	+	6.34725i	0.362060	+	0.209035i
$923$	9.79720	−	0.476082i	0.322479	−	0.0156704i
$924$	−5.37627	+	1.30746i	−0.176866	+	0.0430123i
$925$		−	11.5887i		−	0.381034i
$926$	−26.2022	−	15.1278i	−0.861056	−	0.497131i
$927$	3.45895	+	0.122238i	0.113607	+	0.00401482i
$928$	6.09518	−	3.51906i	0.200084	−	0.115519i
$929$	−14.5504	−	8.40067i	−0.477383	−	0.275617i	0.241942	−	0.970291i	$-0.422215\pi$
$929$	−14.5504	−	8.40067i	−0.477383	−	0.275617i	−0.719325	+	0.694674i	$0.755549\pi$
$930$	−0.0617555	+	0.215197i	−0.00202504	+	0.00705660i
$931$	12.5185	+	22.2523i	0.410279	+	0.729289i
$932$		−	10.9950i		−	0.360154i
$933$	36.6761	−	35.4029i	1.20072	−	1.15904i
$934$	−7.65871	−	13.2653i	−0.250601	−	0.434053i
$935$	0.252572	−	0.145822i	0.00825997	−	0.00476890i
$936$	−9.29512	+	5.53179i	−0.303821	+	0.180812i
$937$		−	24.5999i		−	0.803645i	−0.915718	−	0.401822i	$-0.868377\pi$
$937$		−	24.5999i		−	0.803645i	0.915718	−	0.401822i	$-0.131623\pi$
$938$	8.55183	+	15.0048i	0.279227	+	0.489925i
$939$	−7.03521	+	24.5153i	−0.229585	+	0.800027i
$940$	0.0904015	−	0.156580i	0.00294857	−	0.00510708i
$941$	−36.5960	+	21.1287i	−1.19299	+	0.688776i	−0.958984	−	0.283459i	$-0.908518\pi$
$941$	−36.5960	+	21.1287i	−1.19299	+	0.688776i	−0.234010	+	0.972234i	$0.575185\pi$
$942$	29.7349	−	7.40713i	0.968815	−	0.241337i
$943$	0.203989	−	0.353319i	0.00664279	−	0.0115057i
$944$		−	10.4387i		−	0.339752i
$945$	0.966782	+	1.08721i	0.0314494	+	0.0353669i
$946$	−5.92145			−0.192523
$947$	4.10191	−	7.10472i	0.133294	−	0.230872i	−0.791650	−	0.610974i	$-0.790778\pi$
$947$	4.10191	−	7.10472i	0.133294	−	0.230872i	0.924945	+	0.380102i	$0.124111\pi$
$948$	−4.22782	−	16.9720i	−0.137313	−	0.551224i
$949$	14.5345	+	22.5686i	0.471809	+	0.732609i
$950$	9.09811	−	15.7584i	0.295182	−	0.511269i
$951$	−44.6063	−	12.8007i	−1.44646	−	0.415092i
$952$	−5.21290	−	3.04856i	−0.168951	−	0.0988043i
$953$			53.5038i			1.73316i	0.499041	+	0.866578i	$0.333686\pi$
$953$			53.5038i			1.73316i	−0.499041	+	0.866578i	$0.666314\pi$
$954$	2.88312	+	5.42783i	0.0933443	+	0.175732i
$955$	−0.787907	−	1.36469i	−0.0254961	−	0.0441605i
$956$	7.61285	+	13.1858i	0.246217	+	0.426460i
$957$	10.2222	+	10.5898i	0.330435	+	0.342319i
$958$		−	42.5731i		−	1.37548i
$959$	13.3044	+	7.78056i	0.429622	+	0.251247i
$960$	−0.0505607	+	0.176187i	−0.00163184	+	0.00568641i
$961$	14.7541	−	25.5548i	0.475938	−	0.824349i
$962$	−7.04158	+	4.53486i	−0.227029	+	0.146210i
$963$	36.4759	+	1.28904i	1.17542	+	0.0415388i
$964$	−8.18626	+	14.1790i	−0.263662	+	0.456675i
$965$	1.38106			0.0444580
$966$	−4.29563	−	1.25869i	−0.138210	−	0.0404978i
$967$		−	28.2530i		−	0.908555i	−0.890860	−	0.454278i	$-0.849897\pi$
$967$		−	28.2530i		−	0.908555i	0.890860	−	0.454278i	$-0.150103\pi$
$968$	−4.77110	+	8.26379i	−0.153349	+	0.265608i
$969$	−3.48549	−	13.9920i	−0.111970	−	0.449488i
$970$	−0.811367	+	0.468443i	−0.0260514	+	0.0150408i
$971$	7.54548	−	13.0692i	0.242146	−	0.419409i	−0.719179	−	0.694825i	$-0.755482\pi$
$971$	7.54548	−	13.0692i	0.242146	−	0.419409i	0.961325	+	0.275415i	$0.0888153\pi$
$972$	2.69085	+	15.3545i	0.0863091	+	0.492494i
$973$	−23.6994	−	41.5824i	−0.759768	−	1.33307i
$974$		−	4.95482i		−	0.158763i
$975$	21.3390	−	22.6999i	0.683394	−	0.726979i
$976$	8.67338	−	5.00758i	0.277628	−	0.160289i
$977$	−12.0405	−	20.8547i	−0.385208	−	0.667200i	0.606590	−	0.795015i	$-0.292537\pi$
$977$	−12.0405	−	20.8547i	−0.385208	−	0.667200i	−0.991798	+	0.127815i	$0.959204\pi$
$978$	6.67333	+	6.91333i	0.213390	+	0.221064i
$979$			20.5006i			0.655201i
$980$	0.637373	+	0.377528i	0.0203601	+	0.0120597i
$981$	−11.4627	+	18.3270i	−0.365975	+	0.585138i
$982$	−31.4850	−	18.1779i	−1.00473	−	0.580079i
$983$	−23.0577	+	13.3124i	−0.735427	+	0.424599i	−0.820404	−	0.571784i	$-0.806252\pi$
$983$	−23.0577	+	13.3124i	−0.735427	+	0.424599i	0.0849773	+	0.996383i	$0.472918\pi$
$984$	−0.701972	+	0.174865i	−0.0223781	+	0.00557451i
$985$	−0.807611	−	0.466275i	−0.0257326	−	0.0148567i
$986$			16.0644i			0.511593i
$987$	−1.85007	−	7.60747i	−0.0588884	−	0.242148i
$988$	−13.1354	+	0.638299i	−0.417894	+	0.0203070i
$989$	−4.14872	−	2.39526i	−0.131922	−	0.0761650i
$990$	−0.383086	−	0.0135381i	−0.0121753	−	0.000430269i
$991$	3.04456	+	5.27333i	0.0967135	+	0.167513i	0.910322	−	0.413900i	$-0.135834\pi$
$991$	3.04456	+	5.27333i	0.0967135	+	0.167513i	−0.813609	+	0.581412i	$0.802500\pi$
$992$	−0.610707	+	1.05778i	−0.0193900	+	0.0335844i
$993$	−0.843428	+	2.93906i	−0.0267654	+	0.0932684i
$994$	0.0401391	−	7.19755i	0.00127314	−	0.228292i
$995$	−1.68798			−0.0535126
$996$	14.0483	+	14.5535i	0.445136	+	0.461145i
$997$	27.4812	−	15.8663i	0.870339	−	0.502491i	0.00287843	−	0.999996i	$-0.499084\pi$
$997$	27.4812	−	15.8663i	0.870339	−	0.502491i	0.867461	+	0.497505i	$0.165750\pi$
$998$	−22.8436	+	13.1887i	−0.723100	+	0.417482i
$999$	2.50216	+	11.8082i	0.0791648	+	0.373594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bg.b.467.8	yes	36
3.2	odd	2		546.2.bg.a.467.14	yes	36
7.3	odd	6	inner	546.2.bg.b.311.14	yes	36
13.12	even	2		546.2.bg.a.467.8	yes	36
21.17	even	6		546.2.bg.a.311.8	✓	36
39.38	odd	2	inner	546.2.bg.b.467.14	yes	36
91.38	odd	6		546.2.bg.a.311.14	yes	36
273.38	even	6	inner	546.2.bg.b.311.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.8	✓	36	21.17	even	6
546.2.bg.a.311.14	yes	36	91.38	odd	6
546.2.bg.a.467.8	yes	36	13.12	even	2
546.2.bg.a.467.14	yes	36	3.2	odd	2
546.2.bg.b.311.8	yes	36	273.38	even	6	inner
546.2.bg.b.311.14	yes	36	7.3	odd	6	inner
546.2.bg.b.467.8	yes	36	1.1	even	1	trivial
546.2.bg.b.467.14	yes	36	39.38	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.418670 - 1.68069i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.0916492 - 0.0529137i) q^{5} +(-1.66485 - 0.477766i) q^{6} +(-2.29863 + 1.31008i) q^{7} -1.00000 q^{8} +(-2.64943 + 1.40731i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.418670 - 1.68069i) 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} +(-2.64943 + 1.40731i) q^{9} +(-0.0916492 + 0.0529137i) q^{10} +(-0.603696 - 1.04563i) q^{11} +(-1.24618 + 1.20292i) 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} +(-0.105953 + 2.99813i) q^{18} +(-1.82371 + 3.15875i) q^{19} +0.105827i q^{20} +(3.16420 + 3.31479i) q^{21} -1.20739 q^{22} +(-0.845930 - 0.488398i) q^{23} +(0.418670 + 1.68069i) q^{24} +(-2.49440 - 4.32043i) q^{25} +(-1.64910 + 3.20632i) q^{26} +(3.47448 + 3.86367i) q^{27} +(2.28387 + 1.33563i) q^{28} -7.03811i q^{29} +(0.127302 + 0.131880i) q^{30} +(0.610707 + 1.05778i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50463 + 1.45240i) 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} +(1.80188 + 5.97940i) q^{39} +(0.0916492 + 0.0529137i) q^{40} +0.417669i q^{41} +(4.45279 - 1.08288i) q^{42} +4.90433 q^{43} +(-0.603696 + 1.04563i) q^{44} +(0.317284 + 0.0112127i) 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} +(-2.84439 + 2.74565i) q^{51} +(1.95221 + 3.03132i) q^{52} +(1.77421 - 1.02434i) q^{53} +(5.08328 - 1.07715i) 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} +(0.177863 - 0.0443067i) q^{60} +(-8.67338 - 5.00758i) q^{61} +1.22141 q^{62} +(4.24638 - 6.70584i) q^{63} +1.00000 q^{64} +(0.339316 + 0.174519i) q^{65} +(0.505498 + 2.02925i) 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} +(2.64943 - 1.40731i) q^{72} +(-3.72258 - 6.44769i) q^{73} +(2.01173 - 1.16147i) q^{74} +(-6.21697 + 6.00114i) 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} +(5.03898 - 7.45713i) q^{81} +(0.361712 + 0.208835i) q^{82} -11.6784i q^{83} +(1.28859 - 4.39767i) q^{84} +0.241549i q^{85} +(2.45216 - 4.24727i) q^{86} +(-11.8289 + 2.94664i) q^{87} +(0.603696 + 1.04563i) q^{88} +(-14.7044 - 8.48960i) q^{89} +(0.168352 - 0.269170i) q^{90} +(8.04879 - 5.12025i) q^{91} +0.976796i q^{92} +(1.52211 - 1.46927i) q^{93} +(-1.47958 + 0.854236i) q^{94} +(0.334282 - 0.192998i) q^{95} +(1.24618 - 1.20292i) 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

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