LMFDB - Embedded newform 546.2.bv.a.515.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, 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:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			515.7
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.540391 + 1.64559i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.97621 - 0.529524i) q^{5} +(0.947888 - 1.44966i) q^{6} +(2.60708 + 0.450728i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.41596 - 1.77853i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.540391 + 1.64559i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.97621 - 0.529524i) q^{5} +(0.947888 - 1.44966i) q^{6} +(2.60708 + 0.450728i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.41596 - 1.77853i) q^{9} +(1.77182 + 1.02296i) q^{10} +(-4.21263 + 1.12877i) q^{11} +(-1.29079 + 1.15493i) q^{12} +(-1.63756 - 3.21223i) q^{13} +(-2.40158 - 1.11013i) q^{14} +(1.93931 - 2.96589i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.80830 - 3.13207i) q^{17} +(1.87332 + 2.34322i) q^{18} +(-0.449449 + 1.67737i) q^{19} +(-1.44669 - 1.44669i) q^{20} +(-2.15056 + 4.04662i) q^{21} +4.36124 q^{22} +(0.976570 + 1.69147i) q^{23} +(1.54572 - 0.781496i) q^{24} +(-0.705120 - 0.407101i) q^{25} +(0.750376 + 3.52660i) q^{26} +(4.23229 - 3.01458i) q^{27} +(2.03243 + 1.69388i) q^{28} -7.12520i q^{29} +(-2.64085 + 2.36290i) q^{30} +(-1.91641 + 0.513500i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.418969 - 7.54225i) q^{33} +(-2.55733 + 2.55733i) q^{34} +(-4.91346 - 2.27124i) q^{35} +(-1.20302 - 2.74823i) q^{36} +(-2.87798 - 0.771152i) q^{37} +(0.868269 - 1.50389i) q^{38} +(6.17094 - 0.958900i) q^{39} +(1.02296 + 1.77182i) q^{40} +(5.01711 - 5.01711i) q^{41} +(3.12462 - 3.35213i) q^{42} -12.4270i q^{43} +(-4.21263 - 1.12877i) q^{44} +(3.83266 + 4.79405i) q^{45} +(-0.505510 - 1.88659i) q^{46} +(-0.536532 + 2.00237i) q^{47} +(-1.69532 + 0.354805i) q^{48} +(6.59369 + 2.35017i) q^{49} +(0.575728 + 0.575728i) q^{50} +(4.17693 + 4.66828i) q^{51} +(0.187944 - 3.60065i) q^{52} +(-6.45843 - 3.72878i) q^{53} +(-4.86831 + 1.81646i) q^{54} +8.92275 q^{55} +(-1.52477 - 2.16219i) q^{56} +(-2.51739 - 1.64604i) q^{57} +(-1.84414 + 6.88241i) q^{58} +(11.3187 - 3.03283i) q^{59} +(3.16243 - 1.59888i) q^{60} +(-5.54572 - 9.60547i) q^{61} +1.98401 q^{62} +(-5.49695 - 5.72570i) q^{63} +1.00000i q^{64} +(1.53521 + 7.21516i) q^{65} +(-2.35677 + 7.17682i) q^{66} +(-7.55021 + 2.02307i) q^{67} +(3.13207 - 1.80830i) q^{68} +(-3.31120 + 0.692983i) q^{69} +(4.15819 + 3.46555i) q^{70} +(-5.58229 + 5.58229i) q^{71} +(0.450730 + 2.96595i) q^{72} +(1.97747 + 7.38003i) q^{73} +(2.58032 + 1.48975i) q^{74} +(1.05096 - 0.940347i) q^{75} +(-1.22792 + 1.22792i) q^{76} +(-11.4914 + 1.04404i) q^{77} +(-6.20885 - 0.670930i) q^{78} +(-4.09412 - 7.09122i) q^{79} +(-0.529524 - 1.97621i) q^{80} +(2.67368 + 8.59369i) q^{81} +(-6.14468 + 3.54763i) q^{82} +(-6.47658 + 6.47658i) q^{83} +(-3.88574 + 2.42920i) q^{84} +(-5.23209 + 5.23209i) q^{85} +(-3.21636 + 12.0036i) q^{86} +(11.7252 + 3.85039i) q^{87} +(3.77694 + 2.18062i) q^{88} +(0.741628 - 2.76779i) q^{89} +(-2.46128 - 5.62266i) q^{90} +(-2.82140 - 9.11261i) q^{91} +1.95314i q^{92} +(0.190597 - 3.43112i) q^{93} +(1.03650 - 1.79527i) q^{94} +(1.77641 - 3.07683i) q^{95} +(1.72938 + 0.0960666i) q^{96} +(-0.184292 - 0.184292i) q^{97} +(-5.76075 - 3.97666i) q^{98} +(12.1851 + 4.76522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.540391	+	1.64559i	−0.311995	+	0.950084i
$3$	−0.540391	+	1.64559i	−0.311995	+	0.950084i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.97621	−	0.529524i	−0.883788	−	0.236810i	−0.211747	−	0.977325i	$-0.567915\pi$
$5$	−1.97621	−	0.529524i	−0.883788	−	0.236810i	−0.672041	+	0.740514i	$0.734582\pi$
$6$	0.947888	−	1.44966i	0.386974	−	0.591820i
$7$	2.60708	+	0.450728i	0.985382	+	0.170359i
$7$	2.60708	+	0.450728i	0.985382	+	0.170359i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.41596	−	1.77853i	−0.805318	−	0.592842i
$10$	1.77182	+	1.02296i	0.560299	+	0.323489i
$11$	−4.21263	+	1.12877i	−1.27016	+	0.340337i	−0.830091	−	0.557629i	$-0.811711\pi$
$11$	−4.21263	+	1.12877i	−1.27016	+	0.340337i	−0.440065	+	0.897966i	$0.645045\pi$
$12$	−1.29079	+	1.15493i	−0.372619	+	0.333400i
$13$	−1.63756	−	3.21223i	−0.454177	−	0.890911i
$13$	−1.63756	−	3.21223i	−0.454177	−	0.890911i
$14$	−2.40158	−	1.11013i	−0.641850	−	0.296695i
$15$	1.93931	−	2.96589i	0.500727	−	0.765789i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.80830	−	3.13207i	0.438578	−	0.759639i	−0.559002	−	0.829166i	$-0.688816\pi$
$17$	1.80830	−	3.13207i	0.438578	−	0.759639i	0.997580	+	0.0695269i	$0.0221490\pi$
$18$	1.87332	+	2.34322i	0.441545	+	0.552302i
$19$	−0.449449	+	1.67737i	−0.103111	+	0.384814i	−0.998124	−	0.0612251i	$-0.980499\pi$
$19$	−0.449449	+	1.67737i	−0.103111	+	0.384814i	0.895013	+	0.446040i	$0.147166\pi$
$20$	−1.44669	−	1.44669i	−0.323489	−	0.323489i
$21$	−2.15056	+	4.04662i	−0.469290	+	0.883044i
$22$	4.36124			0.929819
$23$	0.976570	+	1.69147i	0.203629	+	0.352696i	0.949695	−	0.313176i	$-0.101393\pi$
$23$	0.976570	+	1.69147i	0.203629	+	0.352696i	−0.746066	+	0.665872i	$0.768060\pi$
$24$	1.54572	−	0.781496i	0.315520	−	0.159522i
$25$	−0.705120	−	0.407101i	−0.141024	−	0.0814202i
$26$	0.750376	+	3.52660i	0.147161	+	0.691624i
$27$	4.23229	−	3.01458i	0.814505	−	0.580156i
$28$	2.03243	+	1.69388i	0.384093	+	0.320113i
$29$		−	7.12520i		−	1.32312i	−0.749894	−	0.661558i	$-0.769896\pi$
$29$		−	7.12520i		−	1.32312i	0.749894	−	0.661558i	$-0.230104\pi$
$30$	−2.64085	+	2.36290i	−0.482152	+	0.431404i
$31$	−1.91641	+	0.513500i	−0.344197	+	0.0922273i	−0.426776	−	0.904357i	$-0.640351\pi$
$31$	−1.91641	+	0.513500i	−0.344197	+	0.0922273i	0.0825793	+	0.996584i	$0.473684\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.418969	−	7.54225i	0.0729331	−	1.31294i
$34$	−2.55733	+	2.55733i	−0.438578	+	0.438578i
$35$	−4.91346	−	2.27124i	−0.830526	−	0.383910i
$36$	−1.20302	−	2.74823i	−0.200503	−	0.458038i
$37$	−2.87798	−	0.771152i	−0.473137	−	0.126777i	0.0143683	−	0.999897i	$-0.495426\pi$
$37$	−2.87798	−	0.771152i	−0.473137	−	0.126777i	−0.487505	+	0.873120i	$0.662093\pi$
$38$	0.868269	−	1.50389i	0.140852	−	0.243963i
$39$	6.17094	−	0.958900i	0.988141	−	0.153547i
$40$	1.02296	+	1.77182i	0.161744	+	0.280149i
$41$	5.01711	−	5.01711i	0.783540	−	0.783540i	−0.196886	−	0.980426i	$-0.563083\pi$
$41$	5.01711	−	5.01711i	0.783540	−	0.783540i	0.980426	+	0.196886i	$0.0630829\pi$
$42$	3.12462	−	3.35213i	0.482139	−	0.517244i
$43$		−	12.4270i		−	1.89511i	−0.319597	−	0.947554i	$-0.603547\pi$
$43$		−	12.4270i		−	1.89511i	0.319597	−	0.947554i	$-0.396453\pi$
$44$	−4.21263	−	1.12877i	−0.635078	−	0.170169i
$45$	3.83266	+	4.79405i	0.571339	+	0.714654i
$46$	−0.505510	−	1.88659i	−0.0745333	−	0.278162i
$47$	−0.536532	+	2.00237i	−0.0782613	+	0.292075i	−0.993953	−	0.109806i	$-0.964977\pi$
$47$	−0.536532	+	2.00237i	−0.0782613	+	0.292075i	0.915692	+	0.401881i	$0.131644\pi$
$48$	−1.69532	+	0.354805i	−0.244699	+	0.0512116i
$49$	6.59369	+	2.35017i	0.941955	+	0.335738i
$50$	0.575728	+	0.575728i	0.0814202	+	0.0814202i
$51$	4.17693	+	4.66828i	0.584887	+	0.653689i
$52$	0.187944	−	3.60065i	0.0260632	−	0.499320i
$53$	−6.45843	−	3.72878i	−0.887134	−	0.512187i	−0.0141298	−	0.999900i	$-0.504498\pi$
$53$	−6.45843	−	3.72878i	−0.887134	−	0.512187i	−0.873004	+	0.487713i	$0.837831\pi$
$54$	−4.86831	+	1.81646i	−0.662493	+	0.247189i
$55$	8.92275			1.20314
$56$	−1.52477	−	2.16219i	−0.203756	−	0.288935i
$57$	−2.51739	−	1.64604i	−0.333436	−	0.218024i
$58$	−1.84414	+	6.88241i	−0.242147	+	0.903705i
$59$	11.3187	−	3.03283i	1.47357	−	0.394841i	0.569413	−	0.822051i	$-0.307170\pi$
$59$	11.3187	−	3.03283i	1.47357	−	0.394841i	0.904152	+	0.427211i	$0.140504\pi$
$60$	3.16243	−	1.59888i	0.408268	−	0.206415i
$61$	−5.54572	−	9.60547i	−0.710057	−	1.22985i	−0.964835	−	0.262855i	$-0.915336\pi$
$61$	−5.54572	−	9.60547i	−0.710057	−	1.22985i	0.254779	−	0.966999i	$-0.417997\pi$
$62$	1.98401			0.251970
$63$	−5.49695	−	5.72570i	−0.692550	−	0.721370i
$64$			1.00000i			0.125000i
$65$	1.53521	+	7.21516i	0.190420	+	0.894930i
$66$	−2.35677	+	7.17682i	−0.290099	+	0.883406i
$67$	−7.55021	+	2.02307i	−0.922405	+	0.247158i	−0.688613	−	0.725129i	$-0.741780\pi$
$67$	−7.55021	+	2.02307i	−0.922405	+	0.247158i	−0.233792	+	0.972287i	$0.575113\pi$
$68$	3.13207	−	1.80830i	0.379820	−	0.219289i
$69$	−3.31120	+	0.692983i	−0.398622	+	0.0834253i
$70$	4.15819	+	3.46555i	0.496999	+	0.414212i
$71$	−5.58229	+	5.58229i	−0.662496	+	0.662496i	−0.955968	−	0.293472i	$-0.905189\pi$
$71$	−5.58229	+	5.58229i	−0.662496	+	0.662496i	0.293472	+	0.955968i	$0.405189\pi$
$72$	0.450730	+	2.96595i	0.0531190	+	0.349540i
$73$	1.97747	+	7.38003i	0.231446	+	0.863767i	0.979719	+	0.200377i	$0.0642166\pi$
$73$	1.97747	+	7.38003i	0.231446	+	0.863767i	−0.748273	+	0.663391i	$0.769117\pi$
$74$	2.58032	+	1.48975i	0.299957	+	0.173180i
$75$	1.05096	−	0.940347i	0.121355	−	0.108582i
$76$	−1.22792	+	1.22792i	−0.140852	+	0.140852i
$77$	−11.4914	+	1.04404i	−1.30957	+	0.118979i
$78$	−6.20885	−	0.670930i	−0.703014	−	0.0759679i
$79$	−4.09412	−	7.09122i	−0.460624	−	0.797825i	0.538368	−	0.842710i	$-0.319041\pi$
$79$	−4.09412	−	7.09122i	−0.460624	−	0.797825i	−0.998992	+	0.0448853i	$0.985708\pi$
$80$	−0.529524	−	1.97621i	−0.0592025	−	0.220947i
$81$	2.67368	+	8.59369i	0.297076	+	0.954854i
$82$	−6.14468	+	3.54763i	−0.678566	+	0.391770i
$83$	−6.47658	+	6.47658i	−0.710898	+	0.710898i	−0.966723	−	0.255825i	$-0.917653\pi$
$83$	−6.47658	+	6.47658i	−0.710898	+	0.710898i	0.255825	+	0.966723i	$0.417653\pi$
$84$	−3.88574	+	2.42920i	−0.423969	+	0.265047i
$85$	−5.23209	+	5.23209i	−0.567500	+	0.567500i
$86$	−3.21636	+	12.0036i	−0.346829	+	1.29438i
$87$	11.7252	+	3.85039i	1.25707	+	0.412805i
$88$	3.77694	+	2.18062i	0.402623	+	0.232455i
$89$	0.741628	−	2.76779i	0.0786125	−	0.293386i	−0.915416	−	0.402510i	$-0.868138\pi$
$89$	0.741628	−	2.76779i	0.0786125	−	0.293386i	0.994028	+	0.109124i	$0.0348046\pi$
$90$	−2.46128	−	5.62266i	−0.259441	−	0.592680i
$91$	−2.82140	−	9.11261i	−0.295763	−	0.955261i
$92$			1.95314i			0.203629i
$93$	0.190597	−	3.43112i	0.0197640	−	0.355791i
$94$	1.03650	−	1.79527i	0.106907	−	0.185168i
$95$	1.77641	−	3.07683i	0.182256	−	0.315677i
$96$	1.72938	+	0.0960666i	0.176505	+	0.00980475i
$97$	−0.184292	−	0.184292i	−0.0187120	−	0.0187120i	0.697689	−	0.716401i	$-0.254212\pi$
$97$	−0.184292	−	0.184292i	−0.0187120	−	0.0187120i	−0.716401	+	0.697689i	$0.754212\pi$
$98$	−5.76075	−	3.97666i	−0.581923	−	0.401703i
$99$	12.1851	+	4.76522i	1.22465	+	0.478922i
$100$	−0.407101	−	0.705120i	−0.0407101	−	0.0705120i
$101$	4.13732	−	7.16605i	0.411679	−	0.713049i	−0.583394	−	0.812189i	$-0.698276\pi$
$101$	4.13732	−	7.16605i	0.411679	−	0.713049i	0.995073	+	0.0991400i	$0.0316092\pi$
$102$	−2.82636	−	5.59028i	−0.279852	−	0.553520i
$103$	8.05782	−	4.65218i	0.793961	−	0.458393i	−0.0473944	−	0.998876i	$-0.515092\pi$
$103$	8.05782	−	4.65218i	0.793961	−	0.458393i	0.841355	+	0.540483i	$0.181758\pi$
$104$	−1.11346	+	3.42932i	−0.109183	+	0.336272i
$105$	6.39273	−	6.85819i	0.623866	−	0.669291i
$106$	5.27329	+	5.27329i	0.512187	+	0.512187i
$107$	−9.25913	+	5.34576i	−0.895113	+	0.516794i	−0.875612	−	0.483016i	$-0.839541\pi$
$107$	−9.25913	+	5.34576i	−0.895113	+	0.516794i	−0.0195018	+	0.999810i	$0.506208\pi$
$108$	5.17256	−	0.494557i	0.497730	−	0.0475888i
$109$	−15.1593	+	4.06191i	−1.45199	+	0.389061i	−0.896717	−	0.442604i	$-0.854055\pi$
$109$	−15.1593	+	4.06191i	−1.45199	+	0.389061i	−0.555278	+	0.831665i	$0.687388\pi$
$110$	−8.61871	−	2.30938i	−0.821762	−	0.220190i
$111$	2.82424	−	4.31926i	0.268065	−	0.409966i
$112$	0.913196	+	2.48316i	0.0862889	+	0.234636i
$113$			20.7267i			1.94980i	0.222637	+	0.974901i	$0.428533\pi$
$113$			20.7267i			1.94980i	−0.222637	+	0.974901i	$0.571467\pi$
$114$	2.00558	+	2.24150i	0.187840	+	0.209936i
$115$	−1.03423	−	3.85981i	−0.0964428	−	0.359929i
$116$	3.56260	−	6.17060i	0.330779	−	0.572926i
$117$	−1.75676	+	10.6730i	−0.162412	+	0.986723i
$118$	−11.7180			−1.07872
$119$	6.12610	−	7.35050i	0.561579	−	0.673819i
$120$	−3.46850	+	0.725902i	−0.316629	+	0.0662655i
$121$	6.94585	−	4.01019i	0.631441	−	0.364563i
$122$	2.87068	+	10.7135i	0.259899	+	0.969955i
$123$	5.54492	+	10.9673i	0.499968	+	0.988890i
$124$	−1.91641	−	0.513500i	−0.172099	−	0.0461137i
$125$	8.41132	+	8.41132i	0.752332	+	0.752332i
$126$	3.82772	+	6.95331i	0.341001	+	0.619450i
$127$			1.34368i			0.119233i	0.998221	+	0.0596163i	$0.0189877\pi$
$127$			1.34368i			0.119233i	−0.998221	+	0.0596163i	$0.981012\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	20.4499	+	6.71546i	1.80051	+	0.591264i
$130$	0.384520	−	7.36665i	0.0337246	−	0.646098i
$131$	−5.87615	+	3.39260i	−0.513402	+	0.296413i	−0.734231	−	0.678900i	$-0.762457\pi$
$131$	−5.87615	+	3.39260i	−0.513402	+	0.296413i	0.220829	+	0.975313i	$0.429124\pi$
$132$	4.13396	−	6.32230i	0.359815	−	0.550285i
$133$	−1.92779	+	4.17044i	−0.167160	+	0.361623i
$134$	7.81655			0.675247
$135$	−9.96019	+	3.71634i	−0.857236	+	0.319852i
$136$	−3.49337	+	0.936047i	−0.299554	+	0.0802653i
$137$	−20.0342	+	5.36816i	−1.71164	+	0.458633i	−0.975826	−	0.218550i	$-0.929867\pi$
$137$	−20.0342	+	5.36816i	−1.71164	+	0.458633i	−0.735815	+	0.677183i	$0.763201\pi$
$138$	3.37773	+	0.187631i	0.287531	+	0.0159722i
$139$	5.53614			0.469569			0.234785	−	0.972047i	$-0.424562\pi$
$139$	5.53614			0.469569			0.234785	+	0.972047i	$0.424562\pi$
$140$	−3.11956	−	4.42368i	−0.263651	−	0.373869i
$141$	−3.00514	−	1.96497i	−0.253079	−	0.165481i
$142$	6.83688	−	3.94728i	0.573739	−	0.331248i
$143$	10.5243	+	11.6835i	0.880086	+	0.977023i
$144$	0.332272	−	2.98154i	0.0276893	−	0.248462i
$145$	−3.77296	+	14.0809i	−0.313327	+	1.16935i
$146$		−	7.64037i		−	0.632322i
$147$	−7.43059	+	9.58052i	−0.612864	+	0.790188i
$148$	−2.10683	−	2.10683i	−0.173180	−	0.173180i
$149$	−0.732320	−	0.196225i	−0.0599940	−	0.0160753i	0.228697	−	0.973498i	$-0.426553\pi$
$149$	−0.732320	−	0.196225i	−0.0599940	−	0.0160753i	−0.288691	+	0.957422i	$0.593220\pi$
$150$	−1.25853	+	0.636296i	−0.102759	+	0.0519534i
$151$	−2.35869	−	8.80273i	−0.191947	−	0.716356i	−0.993036	−	0.117811i	$-0.962412\pi$
$151$	−2.35869	−	8.80273i	−0.191947	−	0.716356i	0.801089	−	0.598545i	$-0.204254\pi$
$152$	1.50389	−	0.868269i	0.121981	−	0.0704259i
$153$	−9.93926	+	4.35083i	−0.803541	+	0.351744i
$154$	11.3701	+	1.96573i	0.916226	+	0.158403i
$155$	4.05913			0.326037
$156$	5.82364	+	2.25504i	0.466264	+	0.180548i
$157$	−8.29531	+	14.3679i	−0.662038	+	1.14668i	0.318042	+	0.948077i	$0.396975\pi$
$157$	−8.29531	+	14.3679i	−0.662038	+	1.14668i	−0.980079	+	0.198606i	$0.936359\pi$
$158$	2.11927	+	7.90923i	0.168600	+	0.629224i
$159$	9.62613	−	8.61295i	0.763402	−	0.683052i
$160$			2.04592i			0.161744i
$161$	1.78360	+	4.84995i	0.140567	+	0.382230i
$162$	−0.358369	−	8.99286i	−0.0281561	−	0.706546i
$163$	13.5193	+	3.62249i	1.05891	+	0.283735i	0.745930	−	0.666024i	$-0.232005\pi$
$163$	13.5193	+	3.62249i	1.05891	+	0.283735i	0.312983	+	0.949759i	$0.398672\pi$
$164$	6.85349	−	1.83639i	0.535168	−	0.143398i
$165$	−4.82177	+	14.6832i	−0.375374	+	1.14309i
$166$	7.93216	−	4.57964i	0.615655	−	0.355449i
$167$	−13.3524	−	13.3524i	−1.03324	−	1.03324i	−0.999428	−	0.0338126i	$-0.989235\pi$
$167$	−13.3524	−	13.3524i	−1.03324	−	1.03324i	−0.0338126	−	0.999428i	$-0.510765\pi$
$168$	4.38206	−	1.34072i	0.338083	−	0.103439i
$169$	−7.63679	+	10.5204i	−0.587446	+	0.809264i
$170$	6.40798	−	3.69965i	0.491469	−	0.283750i
$171$	4.06909	−	3.25309i	0.311171	−	0.248770i
$172$	6.21352	−	10.7621i	0.473777	−	0.820606i
$173$	2.12999	+	3.68926i	0.161940	+	0.280489i	0.935565	−	0.353156i	$-0.114891\pi$
$173$	2.12999	+	3.68926i	0.161940	+	0.280489i	−0.773624	+	0.633645i	$0.781558\pi$
$174$	−10.3291	−	6.75389i	−0.783047	−	0.512011i
$175$	−1.65481	−	1.37916i	−0.125092	−	0.104255i
$176$	−3.08386	−	3.08386i	−0.232455	−	0.232455i
$177$	−1.12570	+	20.2648i	−0.0846130	+	1.52320i
$178$	−1.43272	+	2.48154i	−0.107387	+	0.185999i
$179$	9.55356	−	16.5472i	0.714066	−	1.23680i	−0.249252	−	0.968439i	$-0.580185\pi$
$179$	9.55356	−	16.5472i	0.714066	−	1.23680i	0.963319	−	0.268361i	$-0.0864819\pi$
$180$	0.922158	+	6.06810i	0.0687336	+	0.452289i
$181$			0.658571i			0.0489512i	0.999700	+	0.0244756i	$0.00779161\pi$
$181$			0.658571i			0.0489512i	−0.999700	+	0.0244756i	$0.992208\pi$
$182$	0.366747	+	9.53234i	0.0271851	+	0.706584i
$183$	18.8036	−	3.93529i	1.39000	−	0.290905i
$184$	0.505510	−	1.88659i	0.0372667	−	0.139081i
$185$	5.27914	+	3.04792i	0.388130	+	0.224087i
$186$	−1.07214	+	3.26488i	−0.0786133	+	0.239392i
$187$	−4.08232	+	15.2354i	−0.298529	+	1.11412i
$188$	−1.46583	+	1.46583i	−0.106907	+	0.106907i
$189$	12.3927	−	5.95162i	0.901434	−	0.432917i
$190$	−2.51222	+	2.51222i	−0.182256	+	0.182256i
$191$	11.4265	−	6.59710i	0.826794	−	0.477350i	−0.0259598	−	0.999663i	$-0.508264\pi$
$191$	11.4265	−	6.59710i	0.826794	−	0.477350i	0.852754	+	0.522313i	$0.174931\pi$
$192$	−1.64559	−	0.540391i	−0.118760	−	0.0389994i
$193$	−3.71437	−	13.8622i	−0.267366	−	0.997824i	−0.960786	−	0.277290i	$-0.910564\pi$
$193$	−3.71437	−	13.8622i	−0.267366	−	0.997824i	0.693420	−	0.720533i	$-0.256103\pi$
$194$	0.130314	+	0.225711i	0.00935601	+	0.0162051i
$195$	−12.7028	−	1.37267i	−0.909669	−	0.0982990i
$196$	4.53522	+	5.33215i	0.323944	+	0.380868i
$197$	6.69242	−	6.69242i	0.476815	−	0.476815i	−0.427296	−	0.904112i	$-0.640534\pi$
$197$	6.69242	−	6.69242i	0.476815	−	0.476815i	0.904112	+	0.427296i	$0.140534\pi$
$198$	−10.5366	−	7.75658i	−0.748800	−	0.551236i
$199$	7.53857	+	4.35239i	0.534395	+	0.308533i	0.742804	−	0.669509i	$-0.233495\pi$
$199$	7.53857	+	4.35239i	0.534395	+	0.308533i	−0.208409	+	0.978042i	$0.566829\pi$
$200$	0.210731	+	0.786459i	0.0149009	+	0.0556111i
$201$	0.750909	−	13.5178i	0.0529650	−	0.953474i
$202$	−5.85106	+	5.85106i	−0.411679	+	0.411679i
$203$	3.21153	−	18.5759i	0.225405	−	1.30377i
$204$	1.28319	+	6.13131i	0.0898412	+	0.429278i
$205$	−12.5715	+	7.25817i	−0.878034	+	0.506933i
$206$	−8.98733	+	2.40815i	−0.626177	+	0.167784i
$207$	0.648974	−	5.82337i	0.0451068	−	0.404752i
$208$	1.96309	−	3.02428i	0.136116	−	0.209696i
$209$		−	7.57345i		−	0.523867i
$210$	−7.94993	+	4.96994i	−0.548597	+	0.342959i
$211$	−3.35429			−0.230919			−0.115460	−	0.993312i	$-0.536834\pi$
$211$	−3.35429			−0.230919			−0.115460	+	0.993312i	$0.536834\pi$
$212$	−3.72878	−	6.45843i	−0.256093	−	0.443567i
$213$	−6.16956	−	12.2028i	−0.422732	−	0.836122i
$214$	10.3272	−	2.76717i	0.705954	−	0.189160i
$215$	−6.58042	+	24.5584i	−0.448781	+	1.67487i
$216$	−5.12431	−	0.861053i	−0.348665	−	0.0585872i
$217$	−5.22767	+	0.474954i	−0.354877	+	0.0322420i
$218$	15.6940			1.06293
$219$	−13.2131	−	0.733984i	−0.892861	−	0.0495981i
$220$	7.72733	+	4.46137i	0.520976	+	0.300786i
$221$	−13.0221	−	0.679721i	−0.875963	−	0.0457230i
$222$	−3.84591	+	3.44112i	−0.258121	+	0.230953i
$223$	9.79258	+	9.79258i	0.655759	+	0.655759i	0.954374	−	0.298614i	$-0.0965244\pi$
$223$	9.79258	+	9.79258i	0.655759	+	0.655759i	−0.298614	+	0.954374i	$0.596524\pi$
$224$	−0.239391	−	2.63490i	−0.0159950	−	0.176052i
$225$	0.979498	+	2.23761i	0.0652998	+	0.149174i
$226$	5.36446	−	20.0204i	0.356839	−	1.33174i
$227$	−2.20020	−	8.21127i	−0.146033	−	0.545001i	−0.999707	−	0.0241943i	$-0.992298\pi$
$227$	−2.20020	−	8.21127i	−0.146033	−	0.545001i	0.853675	−	0.520807i	$-0.174369\pi$
$228$	−1.35710	−	2.68421i	−0.0898760	−	0.177766i
$229$	−15.9252	−	4.26713i	−1.05236	−	0.281980i	−0.309136	−	0.951018i	$-0.600040\pi$
$229$	−15.9252	−	4.26713i	−1.05236	−	0.281980i	−0.743228	+	0.669038i	$0.766706\pi$
$230$			3.99597i			0.263487i
$231$	4.49179	−	19.4744i	0.295538	−	1.28132i
$232$	−5.03827	+	5.03827i	−0.330779	+	0.330779i
$233$	−7.84624	−	13.5901i	−0.514024	−	0.890317i	−0.999868	−	0.0162705i	$-0.994821\pi$
$233$	−7.84624	−	13.5901i	−0.514024	−	0.890317i	0.485843	−	0.874046i	$-0.338513\pi$
$234$	4.45929	−	9.85468i	0.291513	−	0.644221i
$235$	2.12060	−	3.67299i	0.138333	−	0.239599i
$236$	11.3187	+	3.03283i	0.736783	+	0.197420i
$237$	13.8817	−	2.90522i	0.901713	−	0.188715i
$238$	−7.81981	+	5.51449i	−0.506883	+	0.357451i
$239$	−1.89482	+	1.89482i	−0.122566	+	0.122566i	−0.765729	−	0.643163i	$-0.777622\pi$
$239$	−1.89482	+	1.89482i	−0.122566	+	0.122566i	0.643163	+	0.765729i	$0.277622\pi$
$240$	3.53819	+	0.196545i	0.228389	+	0.0126869i
$241$	−6.68380	−	24.9443i	−0.430542	−	1.60680i	−0.751516	−	0.659715i	$-0.770677\pi$
$241$	−6.68380	−	24.9443i	−0.430542	−	1.60680i	0.320974	−	0.947088i	$-0.395990\pi$
$242$	−7.74709	+	2.07583i	−0.498002	+	0.133439i
$243$	−15.5865	−	0.244156i	−0.999877	−	0.0156626i
$244$		−	11.0914i		−	0.710057i
$245$	−11.7860	−	8.13593i	−0.752982	−	0.519786i
$246$	−2.51743	−	12.0287i	−0.160505	−	0.766925i
$247$	6.12408	−	1.30306i	0.389666	−	0.0829115i
$248$	1.71820	+	0.992006i	0.109106	+	0.0629924i
$249$	−7.15794	−	14.1577i	−0.453616	−	0.897209i
$250$	−5.94770	−	10.3017i	−0.376166	−	0.651538i
$251$	−7.80900			−0.492900			−0.246450	−	0.969156i	$-0.579264\pi$
$251$	−7.80900			−0.492900			−0.246450	+	0.969156i	$0.579264\pi$
$252$	−1.89765	−	7.70707i	−0.119541	−	0.485500i
$253$	−6.02321	−	6.02321i	−0.378676	−	0.378676i
$254$	0.347771	−	1.29790i	0.0218211	−	0.0814374i
$255$	−5.78252	−	11.4373i	−0.362116	−	0.716230i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.84625	+	4.92985i	0.177544	+	0.307516i	0.941039	−	0.338299i	$-0.109851\pi$
$257$	2.84625	+	4.92985i	0.177544	+	0.307516i	−0.763495	+	0.645814i	$0.776518\pi$
$258$	−18.0150	−	11.7795i	−1.12156	−	0.733357i
$259$	−7.15553	−	3.30764i	−0.444623	−	0.205527i
$260$	−2.27805	+	7.01612i	−0.141278	+	0.435121i
$261$	−12.6724	+	17.2142i	−0.784399	+	1.06553i
$262$	6.55400	−	1.75614i	0.404907	−	0.108495i
$263$	−23.6148	−	13.6340i	−1.45615	−	0.840710i	−0.457334	−	0.889295i	$-0.651196\pi$
$263$	−23.6148	−	13.6340i	−1.45615	−	0.840710i	−0.998819	+	0.0485845i	$0.984529\pi$
$264$	−5.62943	+	5.03692i	−0.346468	+	0.310001i
$265$	10.7887	+	10.7887i	0.662747	+	0.662747i
$266$	2.94149	−	3.52939i	0.180354	−	0.216401i
$267$	4.15390	+	2.71611i	0.254214	+	0.166223i
$268$	−7.55021	−	2.02307i	−0.461202	−	0.123579i
$269$	24.7504	+	14.2897i	1.50906	+	0.871256i	0.999944	+	0.0105569i	$0.00336042\pi$
$269$	24.7504	+	14.2897i	1.50906	+	0.871256i	0.509115	+	0.860699i	$0.329973\pi$
$270$	10.5827	−	1.01182i	0.644040	−	0.0615777i
$271$	−3.66271	−	0.981420i	−0.222494	−	0.0596170i	0.145850	−	0.989307i	$-0.453408\pi$
$271$	−3.66271	−	0.981420i	−0.222494	−	0.0596170i	−0.368344	+	0.929690i	$0.620075\pi$
$272$	3.61661			0.219289
$273$	16.5203	+	0.281493i	0.999855	+	0.0170367i
$274$	20.7410			1.25301
$275$	3.42993	+	0.919048i	0.206833	+	0.0554207i
$276$	−3.21407	−	1.05546i	−0.193465	−	0.0635312i
$277$	7.30789	+	4.21921i	0.439088	+	0.253508i	0.703211	−	0.710981i	$-0.251749\pi$
$277$	7.30789	+	4.21921i	0.439088	+	0.253508i	−0.264123	+	0.964489i	$0.585082\pi$
$278$	−5.34750	−	1.43286i	−0.320722	−	0.0859371i
$279$	5.54323	+	2.16779i	0.331865	+	0.129782i
$280$	1.86833	+	5.08035i	0.111654	+	0.303609i
$281$	4.00546	+	4.00546i	0.238946	+	0.238946i	0.816413	−	0.577468i	$-0.195959\pi$
$281$	4.00546	+	4.00546i	0.238946	+	0.238946i	−0.577468	+	0.816413i	$0.695959\pi$
$282$	2.39417	+	2.67581i	0.142571	+	0.159342i
$283$	−25.2706	−	14.5900i	−1.50218	−	0.867286i	−0.999997	−	0.00252638i	$-0.999196\pi$
$283$	−25.2706	−	14.5900i	−1.50218	−	0.867286i	−0.502186	−	0.864759i	$-0.667471\pi$
$284$	−7.62555	+	2.04326i	−0.452493	+	0.121245i
$285$	4.10326	+	4.58594i	0.243056	+	0.271648i
$286$	−7.14179	−	14.0093i	−0.422303	−	0.828386i
$287$	15.3413	−	10.8186i	0.905570	−	0.638603i
$288$	−1.09263	+	2.79395i	−0.0643838	+	0.164635i
$289$	1.96008	+	3.39496i	0.115299	+	0.199703i
$290$	7.28880	−	12.6246i	0.428013	−	0.741340i
$291$	0.402859	−	0.203680i	0.0236160	−	0.0119399i
$292$	−1.97747	+	7.38003i	−0.115723	+	0.431884i
$293$	8.81162	+	8.81162i	0.514780	+	0.514780i	0.915987	−	0.401207i	$-0.131409\pi$
$293$	8.81162	+	8.81162i	0.514780	+	0.514780i	−0.401207	+	0.915987i	$0.631409\pi$
$294$	9.65702	−	7.33089i	0.563209	−	0.427546i
$295$	−23.9740			−1.39582
$296$	1.48975	+	2.58032i	0.0865900	+	0.149978i
$297$	−14.4263	+	17.4766i	−0.837100	+	1.01410i
$298$	0.656580	+	0.379077i	0.0380347	+	0.0219593i
$299$	3.83419	−	5.90684i	0.221737	−	0.341602i
$300$	1.38033	−	0.288883i	0.0796936	−	0.0166786i
$301$	5.60123	−	32.3983i	0.322849	−	1.86740i
$302$			9.11326i			0.524409i
$303$	9.55664	+	10.6808i	0.549015	+	0.613597i
$304$	−1.67737	+	0.449449i	−0.0962036	+	0.0257777i
$305$	5.87318	+	21.9190i	0.336297	+	1.25508i
$306$	10.7267	−	1.63011i	0.613203	−	0.0931873i
$307$	3.24026	−	3.24026i	0.184931	−	0.184931i	−0.608569	−	0.793501i	$-0.708256\pi$
$307$	3.24026	−	3.24026i	0.184931	−	0.184931i	0.793501	+	0.608569i	$0.208256\pi$
$308$	−10.4739	−	4.84154i	−0.596805	−	0.275873i
$309$	3.30123	+	15.7739i	0.187801	+	0.897346i
$310$	−3.92082	−	1.05058i	−0.222688	−	0.0596690i
$311$	−2.46001	+	4.26087i	−0.139494	+	0.241611i	−0.927305	−	0.374306i	$-0.877881\pi$
$311$	−2.46001	+	4.26087i	−0.139494	+	0.241611i	0.787811	+	0.615917i	$0.211214\pi$
$312$	−5.04156	−	3.68547i	−0.285422	−	0.208649i
$313$	−3.42968	−	5.94038i	−0.193857	−	0.335770i	0.752668	−	0.658400i	$-0.228766\pi$
$313$	−3.42968	−	5.94038i	−0.193857	−	0.335770i	−0.946525	+	0.322630i	$0.895433\pi$
$314$	11.7313	−	11.7313i	0.662038	−	0.662038i
$315$	7.83122	+	14.2259i	0.441239	+	0.801541i
$316$		−	8.18824i		−	0.460624i
$317$	7.02606	+	1.88263i	0.394623	+	0.105739i	0.450673	−	0.892689i	$-0.351184\pi$
$317$	7.02606	+	1.88263i	0.394623	+	0.105739i	−0.0560503	+	0.998428i	$0.517851\pi$
$318$	−11.5273	+	5.82805i	−0.646420	+	0.326821i
$319$	8.04271	+	30.0158i	0.450305	+	1.68056i
$320$	0.529524	−	1.97621i	0.0296013	−	0.110473i
$321$	−3.79340	−	18.1256i	−0.211727	−	1.01167i
$322$	−0.467563	−	5.14633i	−0.0260563	−	0.286794i
$323$	4.44090	+	4.44090i	0.247098	+	0.247098i
$324$	−1.98137	+	8.77919i	−0.110076	+	0.487733i
$325$	−0.153025	+	2.93166i	−0.00848829	+	0.162619i
$326$	−12.1211	−	6.99810i	−0.671324	−	0.387589i
$327$	1.50767	−	27.1410i	0.0833744	−	1.50090i
$328$	−7.09526			−0.391770
$329$	−2.30130	+	4.97849i	−0.126875	+	0.274473i
$330$	8.45777	−	12.9349i	0.465585	−	0.712045i
$331$	−7.56826	+	28.2451i	−0.415989	+	1.55249i	0.366856	+	0.930278i	$0.380434\pi$
$331$	−7.56826	+	28.2451i	−0.415989	+	1.55249i	−0.782846	+	0.622216i	$0.786233\pi$
$332$	−8.84718	+	2.37059i	−0.485552	+	0.130103i
$333$	5.58155	+	6.98163i	0.305867	+	0.382591i
$334$	9.44158	+	16.3533i	0.516620	+	0.894813i
$335$	15.9921			0.873739
$336$	−4.57975	+	0.160873i	−0.249846	+	0.00877633i
$337$			34.9072i			1.90152i	0.309935	+	0.950758i	$0.399693\pi$
$337$			34.9072i			1.90152i	−0.309935	+	0.950758i	$0.600307\pi$
$338$	10.0995	−	8.18540i	0.549338	−	0.445227i
$339$	−34.1077	−	11.2005i	−1.85248	−	0.608328i
$340$	−7.14717	+	1.91508i	−0.387610	+	0.103860i
$341$	7.49350	−	4.32637i	0.405796	−	0.234286i
$342$	−4.77240	+	2.08908i	−0.258062	+	0.112965i
$343$	16.1310	+	9.09902i	0.870990	+	0.491301i
$344$	−8.78725	+	8.78725i	−0.473777	+	0.473777i
$345$	6.91057	+	0.383879i	0.372053	+	0.0206674i
$346$	−1.10257	−	4.11483i	−0.0592743	−	0.221215i
$347$	9.28926	+	5.36316i	0.498674	+	0.287909i	0.728166	−	0.685401i	$-0.240373\pi$
$347$	9.28926	+	5.36316i	0.498674	+	0.287909i	−0.229492	+	0.973311i	$0.573706\pi$
$348$	8.22910	+	9.19712i	0.441126	+	0.493018i
$349$	24.1788	−	24.1788i	1.29426	−	1.29426i	0.362136	−	0.932125i	$-0.382048\pi$
$349$	24.1788	−	24.1788i	1.29426	−	1.29426i	0.932125	−	0.362136i	$-0.117952\pi$
$350$	1.24147	+	1.76046i	0.0663593	+	0.0941007i
$351$	−16.6141	−	8.65853i	−0.886798	−	0.462158i
$352$	2.18062	+	3.77694i	0.116227	+	0.201312i
$353$	−4.75212	−	17.7352i	−0.252930	−	0.943948i	−0.969230	−	0.246155i	$-0.920833\pi$
$353$	−4.75212	−	17.7352i	−0.252930	−	0.943948i	0.716300	−	0.697792i	$-0.245834\pi$
$354$	6.33227	−	19.2830i	0.336557	−	1.02488i
$355$	13.9877	−	8.07582i	0.742392	−	0.428620i
$356$	2.02617	−	2.02617i	0.107387	−	0.107387i
$357$	8.78544	+	14.0532i	0.464975	+	0.743775i
$358$	−13.5108	+	13.5108i	−0.714066	+	0.714066i
$359$	4.33385	−	16.1741i	0.228732	−	0.853639i	−0.752143	−	0.659000i	$-0.770980\pi$
$359$	4.33385	−	16.1741i	0.228732	−	0.853639i	0.980875	−	0.194639i	$-0.0623535\pi$
$360$	0.679803	−	6.10000i	0.0358288	−	0.321498i
$361$	13.8429	+	7.99222i	0.728575	+	0.420643i
$362$	0.170451	−	0.636131i	0.00895870	−	0.0334343i
$363$	2.84567	+	13.5971i	0.149359	+	0.713663i
$364$	2.11290	−	9.30245i	0.110746	−	0.487581i
$365$		−	15.6316i		−	0.818196i
$366$	−19.1814	−	1.06552i	−1.00263	−	0.0556954i
$367$	2.70085	−	4.67801i	0.140983	−	0.244190i	−0.786884	−	0.617101i	$-0.788307\pi$
$367$	2.70085	−	4.67801i	0.140983	−	0.244190i	0.927867	+	0.372911i	$0.121640\pi$
$368$	−0.976570	+	1.69147i	−0.0509072	+	0.0881739i
$369$	−21.0442	+	3.19805i	−1.09552	+	0.166484i
$370$	−4.31040	−	4.31040i	−0.224087	−	0.224087i
$371$	−15.1570	−	12.6322i	−0.786910	−	0.655831i
$372$	1.88062	−	2.87614i	0.0975057	−	0.149121i
$373$	−5.47339	−	9.48020i	−0.283402	−	0.490866i	0.688819	−	0.724934i	$-0.258130\pi$
$373$	−5.47339	−	9.48020i	−0.283402	−	0.490866i	−0.972220	+	0.234068i	$0.924796\pi$
$374$	7.88644	−	13.6597i	0.407798	−	0.706327i
$375$	−18.3870	+	9.29621i	−0.949502	+	0.480054i
$376$	1.79527	−	1.03650i	0.0925841	−	0.0534535i
$377$	−22.8877	+	11.6679i	−1.17878	+	0.600929i
$378$	−13.5108	+	2.54137i	−0.694920	+	0.130714i
$379$	10.3217	+	10.3217i	0.530188	+	0.530188i	0.920628	−	0.390440i	$-0.127677\pi$
$379$	10.3217	+	10.3217i	0.530188	+	0.530188i	−0.390440	+	0.920628i	$0.627677\pi$
$380$	3.07683	−	1.77641i	0.157838	−	0.0911280i
$381$	−2.21116	−	0.726115i	−0.113281	−	0.0372000i
$382$	−12.7446	+	3.41491i	−0.652072	+	0.174722i
$383$	−5.40009	−	1.44695i	−0.275932	−	0.0739357i	0.118200	−	0.992990i	$-0.462288\pi$
$383$	−5.40009	−	1.44695i	−0.275932	−	0.0739357i	−0.394131	+	0.919054i	$0.628954\pi$
$384$	1.44966	+	0.947888i	0.0739775	+	0.0483717i
$385$	23.2623	+	4.02174i	1.18556	+	0.204967i
$386$			14.3512i			0.730457i
$387$	−22.1018	+	30.0232i	−1.12350	+	1.52616i
$388$	−0.0674555	−	0.251748i	−0.00342454	−	0.0127805i
$389$	13.3021	−	23.0398i	0.674441	−	1.16817i	−0.302191	−	0.953247i	$-0.597718\pi$
$389$	13.3021	−	23.0398i	0.674441	−	1.16817i	0.976632	−	0.214918i	$-0.0689485\pi$
$390$	11.9147	+	4.61363i	0.603325	+	0.233620i
$391$	7.06374			0.357229
$392$	−3.00062	−	6.32426i	−0.151554	−	0.319423i
$393$	−2.40742	−	11.5031i	−0.121438	−	0.580254i
$394$	−8.19651	+	4.73226i	−0.412934	+	0.238408i
$395$	4.33586	+	16.1817i	0.218161	+	0.814188i
$396$	8.16998	+	10.2193i	0.410557	+	0.513541i
$397$	4.55398	+	1.22024i	0.228558	+	0.0612418i	0.371280	−	0.928521i	$-0.378919\pi$
$397$	4.55398	+	1.22024i	0.228558	+	0.0612418i	−0.142722	+	0.989763i	$0.545586\pi$
$398$	−6.15522	−	6.15522i	−0.308533	−	0.308533i
$399$	−5.82110	−	5.42602i	−0.291419	−	0.271641i
$400$		−	0.814202i		−	0.0407101i
$401$	5.97373	−	22.2943i	0.298314	−	1.11332i	−0.640236	−	0.768178i	$-0.721163\pi$
$401$	5.97373	−	22.2943i	0.298314	−	1.11332i	0.938550	−	0.345144i	$-0.112170\pi$
$402$	−4.22399	+	12.8629i	−0.210674	+	0.641541i
$403$	4.78771	+	5.31505i	0.238493	+	0.264761i
$404$	7.16605	−	4.13732i	0.356524	−	0.205839i
$405$	−0.733194	−	18.3987i	−0.0364327	−	0.914239i
$406$	−7.90990	+	17.1118i	−0.392562	+	0.849242i
$407$	12.9943			0.644104
$408$	0.347435	−	6.25450i	0.0172006	−	0.309644i
$409$	4.87027	−	1.30498i	0.240819	−	0.0645273i	−0.136391	−	0.990655i	$-0.543550\pi$
$409$	4.87027	−	1.30498i	0.240819	−	0.0645273i	0.377210	+	0.926128i	$0.376884\pi$
$410$	14.0217	−	3.75711i	0.692483	−	0.185550i
$411$	1.99251	−	35.8691i	0.0982835	−	1.76929i
$412$	9.30437			0.458393
$413$	30.8756	−	2.80517i	1.51929	−	0.138033i
$414$	−2.13406	+	5.45698i	−0.104883	+	0.268196i
$415$	16.2286	−	9.36958i	0.796630	−	0.459935i
$416$	−2.67894	+	2.41315i	−0.131346	+	0.118314i
$417$	−2.99168	+	9.11023i	−0.146503	+	0.446130i
$418$	−1.96015	+	7.31539i	−0.0958743	+	0.357808i
$419$			31.2952i			1.52887i	0.644701	+	0.764435i	$0.276982\pi$
$419$			31.2952i			1.52887i	−0.644701	+	0.764435i	$0.723018\pi$
$420$	8.96536	−	2.74300i	0.437465	−	0.133845i
$421$	−3.76960	−	3.76960i	−0.183719	−	0.183719i	0.609255	−	0.792974i	$-0.291468\pi$
$421$	−3.76960	−	3.76960i	−0.183719	−	0.183719i	−0.792974	+	0.609255i	$0.791468\pi$
$422$	3.24000	+	0.868155i	0.157721	+	0.0422611i
$423$	4.85750	−	3.88339i	0.236180	−	0.188817i
$424$	1.93016	+	7.20344i	0.0937367	+	0.349830i
$425$	−2.55014	+	1.47232i	−0.123700	+	0.0714182i
$426$	2.80102	+	13.3838i	0.135710	+	0.648447i
$427$	−10.1287	−	27.5418i	−0.490160	−	1.33284i
$428$	−10.6915			−0.516794
$429$	−24.9135	+	11.0051i	−1.20284	+	0.531330i
$430$	12.7124	−	22.0185i	0.613046	−	1.06183i
$431$	4.86532	+	18.1576i	0.234354	+	0.874622i	0.978439	+	0.206536i	$0.0662192\pi$
$431$	4.86532	+	18.1576i	0.234354	+	0.874622i	−0.744085	+	0.668085i	$0.767114\pi$
$432$	4.72685	+	2.15798i	0.227421	+	0.103826i
$433$		−	13.1033i		−	0.629706i	−0.949140	−	0.314853i	$-0.898045\pi$
$433$		−	13.1033i		−	0.629706i	0.949140	−	0.314853i	$-0.101955\pi$
$434$	5.17247	+	0.894251i	0.248286	+	0.0429254i
$435$	−21.1325	−	13.8179i	−1.01323	−	0.662519i
$436$	−15.1593	−	4.06191i	−0.725997	−	0.194530i
$437$	−3.27613	+	0.877837i	−0.156719	+	0.0419926i
$438$	12.5729	+	4.12879i	0.600759	+	0.197281i
$439$	25.4749	−	14.7079i	1.21585	−	0.701971i	0.251822	−	0.967773i	$-0.418970\pi$
$439$	25.4749	−	14.7079i	1.21585	−	0.701971i	0.964028	+	0.265802i	$0.0856368\pi$
$440$	−6.30934	−	6.30934i	−0.300786	−	0.300786i
$441$	−11.7502	−	17.4050i	−0.559534	−	0.828807i
$442$	12.4025	+	4.02694i	0.589926	+	0.191542i
$443$	13.4694	−	7.77657i	0.639951	−	0.369476i	−0.144645	−	0.989484i	$-0.546204\pi$
$443$	13.4694	−	7.77657i	0.639951	−	0.369476i	0.784596	+	0.620008i	$0.212871\pi$
$444$	4.60549	−	2.32847i	0.218567	−	0.110504i
$445$	−2.93123	+	5.07703i	−0.138953	+	0.240674i
$446$	−6.92440	−	11.9934i	−0.327880	−	0.567904i
$447$	0.718645	−	1.09906i	0.0339907	−	0.0519839i
$448$	−0.450728	+	2.60708i	−0.0212949	+	0.123173i
$449$	1.03071	+	1.03071i	0.0486424	+	0.0486424i	0.731010	−	0.682367i	$-0.239049\pi$
$449$	1.03071	+	1.03071i	0.0486424	+	0.0486424i	−0.682367	+	0.731010i	$0.739049\pi$
$450$	−0.366985	−	2.41488i	−0.0172999	−	0.113839i
$451$	−15.4720	+	26.7984i	−0.728550	+	1.26189i
$452$	−10.3633	+	17.9498i	−0.487451	+	0.844289i
$453$	15.7603	+	0.875480i	0.740485	+	0.0411336i
$454$			8.50093i			0.398968i
$455$	0.750336	+	19.5024i	0.0351763	+	0.914288i
$456$	0.616132	+	2.94399i	0.0288530	+	0.137865i
$457$	−1.55490	+	5.80298i	−0.0727353	+	0.271452i	−0.992710	−	0.120525i	$-0.961542\pi$
$457$	−1.55490	+	5.80298i	−0.0727353	+	0.271452i	0.919975	+	0.391977i	$0.128209\pi$
$458$	14.2781	+	8.24347i	0.667172	+	0.385192i
$459$	−1.78862	−	18.7071i	−0.0834855	−	0.873174i
$460$	1.03423	−	3.85981i	0.0482214	−	0.179965i
$461$	22.0789	−	22.0789i	1.02832	−	1.02832i	0.0287282	−	0.999587i	$-0.490854\pi$
$461$	22.0789	−	22.0789i	1.02832	−	1.02832i	0.999587	−	0.0287282i	$-0.00914572\pi$
$462$	−9.37908	+	17.6483i	−0.436354	+	0.821071i
$463$	19.2289	−	19.2289i	0.893641	−	0.893641i	−0.101223	−	0.994864i	$-0.532276\pi$
$463$	19.2289	−	19.2289i	0.893641	−	0.893641i	0.994864	+	0.101223i	$0.0322756\pi$
$464$	6.17060	−	3.56260i	0.286463	−	0.165389i
$465$	−2.19352	+	6.67968i	−0.101722	+	0.309763i
$466$	4.06151	+	15.1578i	0.188146	+	0.702171i
$467$	19.8990	+	34.4661i	0.920818	+	1.59490i	0.798153	+	0.602455i	$0.205811\pi$
$467$	19.8990	+	34.4661i	0.920818	+	1.59490i	0.122664	+	0.992448i	$0.460856\pi$
$468$	−6.85792	+	8.36474i	−0.317007	+	0.386660i
$469$	−20.5958	+	1.87121i	−0.951027	+	0.0864044i
$470$	−2.99898	+	2.99898i	−0.138333	+	0.138333i
$471$	−19.1610	−	21.4150i	−0.882892	−	0.986750i
$472$	−10.1480	−	5.85898i	−0.467102	−	0.269681i
$473$	14.0273	+	52.3506i	0.644976	+	2.40708i
$474$	−14.1606	−	0.786616i	−0.650418	−	0.0361305i
$475$	0.999774	−	0.999774i	0.0458728	−	0.0458728i
$476$	8.98061	−	3.30267i	0.411625	−	0.151378i
$477$	8.97155	+	20.4951i	0.410779	+	0.938404i
$478$	2.32067	−	1.33984i	0.106145	−	0.0612828i
$479$	7.91329	−	2.12036i	0.361567	−	0.0968817i	−0.0734618	−	0.997298i	$-0.523405\pi$
$479$	7.91329	−	2.12036i	0.361567	−	0.0968817i	0.435029	+	0.900416i	$0.356738\pi$
$480$	−3.36676	−	1.10560i	−0.153671	−	0.0504634i
$481$	2.23575	+	10.5075i	0.101941	+	0.479102i
$482$			25.8242i			1.17626i
$483$	−8.94489	+	0.314207i	−0.407007	+	0.0142969i
$484$	8.02038			0.364563
$485$	0.266613	+	0.461786i	0.0121063	+	0.0209686i
$486$	14.9923	+	4.26993i	0.680062	+	0.193688i
$487$	0.493434	−	0.132215i	0.0223596	−	0.00599125i	−0.247622	−	0.968857i	$-0.579649\pi$
$487$	0.493434	−	0.132215i	0.0223596	−	0.00599125i	0.269982	+	0.962866i	$0.412982\pi$
$488$	−2.87068	+	10.7135i	−0.129949	+	0.484978i
$489$	−13.2668	+	20.2897i	−0.599947	+	0.917533i
$490$	9.27870	+	10.9092i	0.419169	+	0.492826i
$491$	9.85382			0.444697			0.222348	−	0.974967i	$-0.428628\pi$
$491$	9.85382			0.444697			0.222348	+	0.974967i	$0.428628\pi$
$492$	−0.681617	+	12.2704i	−0.0307297	+	0.553194i
$493$	−22.3166	−	12.8845i	−1.00509	−	0.580289i
$494$	−6.25267	−	0.326373i	−0.281321	−	0.0146842i
$495$	−21.5570	−	15.8694i	−0.968913	−	0.713274i
$496$	−1.40291	−	1.40291i	−0.0629924	−	0.0629924i
$497$	−17.0696	+	12.0374i	−0.765674	+	0.539949i
$498$	3.24975	+	15.5279i	0.145625	+	0.695822i
$499$	−3.16359	+	11.8067i	−0.141622	+	0.528539i	0.858261	+	0.513214i	$0.171545\pi$
$499$	−3.16359	+	11.8067i	−0.141622	+	0.528539i	−0.999883	+	0.0153254i	$0.995122\pi$
$500$	3.07876	+	11.4901i	0.137686	+	0.513852i
$501$	29.1882	−	14.7571i	1.30403	−	0.659300i
$502$	7.54292	+	2.02112i	0.336657	+	0.0902069i
$503$			20.1854i			0.900022i	0.893023	+	0.450011i	$0.148580\pi$
$503$			20.1854i			0.900022i	−0.893023	+	0.450011i	$0.851420\pi$
$504$	−0.161750	+	7.93561i	−0.00720492	+	0.353480i
$505$	−11.9708	+	11.9708i	−0.532694	+	0.532694i
$506$	4.25905	+	7.37689i	0.189338	+	0.327943i
$507$	−13.1855	−	18.2522i	−0.585588	−	0.810609i
$508$	−0.671842	+	1.16366i	−0.0298082	+	0.0516293i
$509$	−23.6534	−	6.33791i	−1.04842	−	0.280923i	−0.306820	−	0.951767i	$-0.599265\pi$
$509$	−23.6534	−	6.33791i	−1.04842	−	0.280923i	−0.741598	+	0.670845i	$0.765932\pi$
$510$	2.62530	+	12.5442i	0.116250	+	0.555466i
$511$	1.82903	+	20.1316i	0.0809117	+	0.890570i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	3.15436	+	8.45401i	0.139268	+	0.373254i
$514$	−1.47333	−	5.49853i	−0.0649857	−	0.242530i
$515$	−18.3874	+	4.92688i	−0.810245	+	0.217104i
$516$	14.3524	+	16.0407i	0.631828	+	0.706152i
$517$		−	9.04085i		−	0.397616i
$518$	6.05563	+	5.04692i	0.266069	+	0.221749i
$519$	−7.22204	+	1.51146i	−0.317012	+	0.0663458i
$520$	4.01633	−	6.18745i	0.176128	−	0.271337i
$521$	3.53113	+	2.03870i	0.154702	+	0.0893170i	0.575352	−	0.817906i	$-0.304865\pi$
$521$	3.53113	+	2.03870i	0.154702	+	0.0893170i	−0.420651	+	0.907223i	$0.638198\pi$
$522$	16.6959	−	13.3477i	0.730760	−	0.584215i
$523$	9.70637	+	16.8119i	0.424430	+	0.735134i	0.996367	−	0.0851631i	$-0.0271411\pi$
$523$	9.70637	+	16.8119i	0.424430	+	0.735134i	−0.571937	+	0.820298i	$0.693808\pi$
$524$	−6.78520			−0.296413
$525$	3.16378	−	1.97786i	0.138079	−	0.0863207i
$526$	19.2814	+	19.2814i	0.840710	+	0.840710i
$527$	−1.85713	+	6.93090i	−0.0808978	+	0.301915i
$528$	6.74127	−	3.40829i	0.293376	−	0.148327i
$529$	9.59262	−	16.6149i	0.417071	−	0.722387i
$530$	−7.62879	−	13.2134i	−0.331373	−	0.573955i
$531$	−32.7394	−	12.8034i	−1.42077	−	0.555620i
$532$	−3.75473	+	2.64782i	−0.162788	+	0.114797i
$533$	−24.3319	−	7.90027i	−1.05393	−	0.342199i
$534$	−3.30937	−	3.69867i	−0.143211	−	0.160057i
$535$	21.1287	−	5.66141i	0.913472	−	0.244764i
$536$	6.76933	+	3.90827i	0.292391	+	0.168812i
$537$	22.0674	+	24.6633i	0.952278	+	1.06430i
$538$	−20.2086	−	20.2086i	−0.871256	−	0.871256i
$539$	−30.4296	−	2.45762i	−1.31069	−	0.105857i
$540$	−10.4839	−	1.76165i	−0.451157	−	0.0758092i
$541$	22.8291	+	6.11704i	0.981499	+	0.262992i	0.713676	−	0.700476i	$-0.247029\pi$
$541$	22.8291	+	6.11704i	0.981499	+	0.262992i	0.267823	+	0.963468i	$0.413696\pi$
$542$	3.28390	+	1.89596i	0.141055	+	0.0814384i
$543$	−1.08374	−	0.355886i	−0.0465078	−	0.0152725i
$544$	−3.49337	−	0.936047i	−0.149777	−	0.0401327i
$545$	32.1088			1.37539
$546$	−15.8845	−	4.54767i	−0.679796	−	0.194622i
$547$	−21.5260			−0.920387			−0.460193	−	0.887819i	$-0.652220\pi$
$547$	−21.5260			−0.920387			−0.460193	+	0.887819i	$0.652220\pi$
$548$	−20.0342	−	5.36816i	−0.855820	−	0.229316i
$549$	−3.68538	+	33.0696i	−0.157288	+	1.41138i
$550$	−3.07519	−	1.77546i	−0.131127	−	0.0757060i
$551$	11.9516	+	3.20241i	0.509154	+	0.136427i
$552$	2.83138	+	1.85136i	0.120512	+	0.0787990i
$553$	−7.47746	−	20.3327i	−0.317974	−	0.864634i
$554$	−5.96686	−	5.96686i	−0.253508	−	0.253508i
$555$	−7.86843	+	7.04026i	−0.333996	+	0.298842i
$556$	4.79444	+	2.76807i	0.203329	+	0.117392i
$557$	−20.0631	+	5.37588i	−0.850099	+	0.227783i	−0.657463	−	0.753487i	$-0.728370\pi$
$557$	−20.0631	+	5.37588i	−0.850099	+	0.227783i	−0.192636	+	0.981270i	$0.561704\pi$
$558$	−4.79328	−	3.52862i	−0.202916	−	0.149378i
$559$	−39.9185	+	20.3500i	−1.68837	+	0.860715i
$560$	−0.489775	−	5.39080i	−0.0206968	−	0.227803i
$561$	−22.8653	−	14.9509i	−0.965372	−	0.631229i
$562$	−2.83229	−	4.90566i	−0.119473	−	0.206933i
$563$	19.8770	−	34.4279i	0.837714	−	1.45096i	−0.0540870	−	0.998536i	$-0.517225\pi$
$563$	19.8770	−	34.4279i	0.837714	−	1.45096i	0.891801	−	0.452427i	$-0.149442\pi$
$564$	−1.62004	−	3.20429i	−0.0682161	−	0.134925i
$565$	10.9753	−	40.9603i	0.461733	−	1.72321i
$566$	20.6334	+	20.6334i	0.867286	+	0.867286i
$567$	3.09707	+	23.6095i	0.130065	+	0.991505i
$568$	7.89455			0.331248
$569$	−17.0013	−	29.4471i	−0.712731	−	1.23449i	−0.963828	−	0.266525i	$-0.914125\pi$
$569$	−17.0013	−	29.4471i	−0.712731	−	1.23449i	0.251097	−	0.967962i	$-0.419209\pi$
$570$	−2.77652	−	5.49168i	−0.116296	−	0.230021i
$571$	−9.50529	−	5.48788i	−0.397784	−	0.229661i	0.287743	−	0.957708i	$-0.407095\pi$
$571$	−9.50529	−	5.48788i	−0.397784	−	0.229661i	−0.685527	+	0.728047i	$0.740428\pi$
$572$	3.27257	+	15.3804i	0.136833	+	0.643085i
$573$	4.68136	+	22.3684i	0.195567	+	0.934454i
$574$	−17.6187	+	6.47936i	−0.735388	+	0.270443i
$575$		−	1.59025i		−	0.0663180i
$576$	1.77853	−	2.41596i	0.0741053	−	0.100665i
$577$	0.918038	−	0.245987i	0.0382184	−	0.0102406i	−0.239659	−	0.970857i	$-0.577036\pi$
$577$	0.918038	−	0.245987i	0.0382184	−	0.0102406i	0.277878	+	0.960616i	$0.410369\pi$
$578$	−1.01461	−	3.78658i	−0.0422023	−	0.157501i
$579$	24.8188	+	1.37867i	1.03143	+	0.0572956i
$580$	−10.3079	+	10.3079i	−0.428013	+	0.428013i
$581$	−19.8041	+	13.9658i	−0.821614	+	0.579398i
$582$	−0.441849	+	0.0924721i	−0.0183152	+	0.00383309i
$583$	31.4159	+	8.41787i	1.30111	+	0.348632i
$584$	3.82019	−	6.61676i	0.158080	−	0.273803i
$585$	9.12335	−	20.1619i	0.377204	−	0.833593i
$586$	−6.23076	−	10.7920i	−0.257390	−	0.445813i
$587$	−9.10194	+	9.10194i	−0.375677	+	0.375677i	−0.869540	−	0.493863i	$-0.835585\pi$
$587$	−9.10194	+	9.10194i	−0.375677	+	0.375677i	0.493863	+	0.869540i	$0.335585\pi$
$588$	−11.2253	+	4.58168i	−0.462925	+	0.188945i
$589$		−	3.44531i		−	0.141962i
$590$	23.1571	+	6.20493i	0.953364	+	0.255453i
$591$	7.39648	+	14.6295i	0.304251	+	0.601778i
$592$	−0.771152	−	2.87798i	−0.0316942	−	0.118284i
$593$	6.06292	−	22.6271i	0.248974	−	0.929185i	−0.722370	−	0.691507i	$-0.756947\pi$
$593$	6.06292	−	22.6271i	0.248974	−	0.929185i	0.971344	−	0.237678i	$-0.0763863\pi$
$594$	18.4580	−	13.1473i	0.757342	−	0.539440i
$595$	−15.9987	+	11.2822i	−0.655883	+	0.462525i
$596$	−0.536096	−	0.536096i	−0.0219593	−	0.0219593i
$597$	−11.2360	+	10.0534i	−0.459861	+	0.411459i
$598$	−5.23235	+	4.71321i	−0.213967	+	0.192738i
$599$	19.8542	+	11.4628i	0.811221	+	0.468359i	0.847380	−	0.530987i	$-0.178179\pi$
$599$	19.8542	+	11.4628i	0.811221	+	0.468359i	−0.0361585	+	0.999346i	$0.511512\pi$
$600$	−1.40807	−	0.0782176i	−0.0574842	−	0.00319322i
$601$	−7.81297			−0.318698			−0.159349	−	0.987222i	$-0.550939\pi$
$601$	−7.81297			−0.318698			−0.159349	+	0.987222i	$0.550939\pi$
$602$	−13.7957	+	29.8446i	−0.562269	+	1.21638i
$603$	21.8391	+	8.54060i	0.889355	+	0.347800i
$604$	2.35869	−	8.80273i	0.0959735	−	0.358178i
$605$	−15.8499	+	4.24698i	−0.644392	+	0.172664i
$606$	−6.46660	−	12.7903i	−0.262688	−	0.519571i
$607$	−18.4186	−	31.9020i	−0.747588	−	1.29486i	−0.948976	−	0.315349i	$-0.897878\pi$
$607$	−18.4186	−	31.9020i	−0.747588	−	1.29486i	0.201388	−	0.979512i	$-0.435455\pi$
$608$	1.73654			0.0704259
$609$	28.8329	+	15.3231i	1.16837	+	0.620925i
$610$		−	22.6922i		−	0.918781i
$611$	7.31066	−	1.55553i	0.295758	−	0.0629301i
$612$	−10.7831	−	1.20170i	−0.435880	−	0.0485757i
$613$	0.640775	−	0.171695i	0.0258806	−	0.00693470i	−0.245855	−	0.969306i	$-0.579069\pi$
$613$	0.640775	−	0.171695i	0.0258806	−	0.00693470i	0.271736	+	0.962372i	$0.412402\pi$
$614$	−3.96849	+	2.29121i	−0.160155	+	0.0924657i
$615$	−5.15047	−	24.6099i	−0.207687	−	0.992366i
$616$	8.86390	+	7.38741i	0.357137	+	0.297647i
$617$	−19.3269	+	19.3269i	−0.778070	+	0.778070i	−0.979502	−	0.201432i	$-0.935440\pi$
$617$	−19.3269	+	19.3269i	−0.778070	+	0.778070i	0.201432	+	0.979502i	$0.435440\pi$
$618$	0.893839	−	16.0908i	0.0359555	−	0.647268i
$619$	5.96820	+	22.2736i	0.239882	+	0.895252i	0.975887	+	0.218276i	$0.0700433\pi$
$619$	5.96820	+	22.2736i	0.239882	+	0.895252i	−0.736005	+	0.676976i	$0.763290\pi$
$620$	3.51531	+	2.02957i	0.141178	+	0.0815094i
$621$	9.23220	+	4.21484i	0.370475	+	0.169136i
$622$	3.47898	−	3.47898i	0.139494	−	0.139494i
$623$	3.18101	−	6.88158i	0.127444	−	0.275705i
$624$	3.91590	+	4.86474i	0.156762	+	0.194746i
$625$	−10.1330	−	17.5509i	−0.405321	−	0.702037i
$626$	1.77533	+	6.62563i	0.0709565	+	0.264813i
$627$	12.4628	+	4.09262i	0.497717	+	0.163444i
$628$	−14.3679	+	8.29531i	−0.573341	+	0.331019i
$629$	−7.61956	+	7.61956i	−0.303812	+	0.303812i
$630$	−3.88244	−	15.7681i	−0.154680	−	0.628215i
$631$	22.0518	−	22.0518i	0.877867	−	0.877867i	−0.115447	−	0.993314i	$-0.536830\pi$
$631$	22.0518	−	22.0518i	0.877867	−	0.877867i	0.993314	+	0.115447i	$0.0368299\pi$
$632$	−2.11927	+	7.90923i	−0.0843001	+	0.314612i
$633$	1.81263	−	5.51981i	0.0720456	−	0.219393i
$634$	−6.29939	−	3.63695i	−0.250181	−	0.144442i
$635$	0.711513	−	2.65540i	0.0282355	−	0.105376i
$636$	12.6429	−	2.64597i	0.501325	−	0.104920i
$637$	−3.24829	−	25.0290i	−0.128702	−	0.991683i
$638$		−	31.0747i		−	1.23026i
$639$	23.4148	−	3.55831i	0.926276	−	0.140765i
$640$	−1.02296	+	1.77182i	−0.0404361	+	0.0700374i
$641$	20.1784	−	34.9501i	0.797000	−	1.38044i	−0.124562	−	0.992212i	$-0.539752\pi$
$641$	20.1784	−	34.9501i	0.797000	−	1.38044i	0.921562	−	0.388232i	$-0.126914\pi$
$642$	−1.02710	+	18.4897i	−0.0405363	+	0.729732i
$643$	−6.13057	−	6.13057i	−0.241766	−	0.241766i	0.575814	−	0.817580i	$-0.304685\pi$
$643$	−6.13057	−	6.13057i	−0.241766	−	0.241766i	−0.817580	+	0.575814i	$0.804685\pi$
$644$	−0.880336	+	5.09198i	−0.0346901	+	0.200652i
$645$	−36.8572	−	24.0999i	−1.45125	−	0.948931i
$646$	−3.14019	−	5.43897i	−0.123549	−	0.213993i
$647$	−16.8741	+	29.2268i	−0.663389	+	1.14902i	0.316330	+	0.948649i	$0.397549\pi$
$647$	−16.8741	+	29.2268i	−0.663389	+	1.14902i	−0.979719	+	0.200374i	$0.935784\pi$
$648$	4.18607	−	7.96723i	0.164445	−	0.312982i
$649$	−44.2580	+	25.5524i	−1.73728	+	1.00302i
$650$	0.906579	−	2.79216i	0.0355590	−	0.109517i
$651$	2.04340	−	8.85928i	0.0800873	−	0.347223i
$652$	9.89681	+	9.89681i	0.387589	+	0.387589i
$653$	−7.23789	+	4.17880i	−0.283240	+	0.163529i	−0.634889	−	0.772603i	$-0.718954\pi$
$653$	−7.23789	+	4.17880i	−0.283240	+	0.163529i	0.351649	+	0.936132i	$0.385621\pi$
$654$	−8.48091	+	25.8260i	−0.331630	+	1.00988i
$655$	13.4090	−	3.59292i	0.523932	−	0.140387i
$656$	6.85349	+	1.83639i	0.267584	+	0.0716989i
$657$	8.34810	−	21.3468i	0.325690	−	0.832819i
$658$	3.51142	−	4.21323i	0.136889	−	0.164249i
$659$		−	47.8017i		−	1.86209i	−0.364904	−	0.931045i	$-0.618898\pi$
$659$		−	47.8017i		−	1.86209i	0.364904	−	0.931045i	$-0.381102\pi$
$660$	−11.5174	+	10.3052i	−0.448314	+	0.401128i
$661$	3.83392	+	14.3084i	0.149122	+	0.556532i	0.999537	+	0.0304196i	$0.00968434\pi$
$661$	3.83392	+	14.3084i	0.149122	+	0.556532i	−0.850415	+	0.526113i	$0.823649\pi$
$662$	14.6208	−	25.3239i	0.568252	−	0.984241i
$663$	8.15559	−	21.0618i	0.316737	−	0.817973i
$664$	9.15927			0.355449
$665$	6.01806	−	7.22086i	0.233370	−	0.280013i
$666$	−3.58439	−	8.18835i	−0.138892	−	0.317292i
$667$	12.0520	−	6.95825i	0.466657	−	0.269425i
$668$	−4.88732	−	18.2397i	−0.189096	−	0.705717i
$669$	−21.4064	+	10.8228i	−0.827620	+	0.418433i
$670$	−15.4471	−	4.13905i	−0.596775	−	0.159905i
$671$	34.2044	+	34.2044i	1.32045	+	1.32045i
$672$	4.46534	+	1.02994i	0.172254	+	0.0397306i
$673$			38.1300i			1.46980i	0.678173	+	0.734902i	$0.262772\pi$
$673$			38.1300i			1.46980i	−0.678173	+	0.734902i	$0.737228\pi$
$674$	9.03464	−	33.7178i	0.348001	−	1.29876i
$675$	−4.21151	+	0.402669i	−0.162101	+	0.0154988i
$676$	−11.8739	+	5.29256i	−0.456687	+	0.203560i
$677$	14.4620	−	8.34967i	0.555822	−	0.320904i	−0.195645	−	0.980675i	$-0.562680\pi$
$677$	14.4620	−	8.34967i	0.555822	−	0.320904i	0.751467	+	0.659771i	$0.229347\pi$
$678$	30.0466	+	19.6466i	1.15393	+	0.754523i
$679$	−0.397398	−	0.563529i	−0.0152507	−	0.0216263i
$680$	7.39930			0.283750
$681$	14.7014	+	0.816655i	0.563358	+	0.0312943i
$682$	−8.35791	+	2.23949i	−0.320041	+	0.0857547i
$683$	−22.1748	+	5.94172i	−0.848496	+	0.227354i	−0.656766	−	0.754094i	$-0.728076\pi$
$683$	−22.1748	+	5.94172i	−0.848496	+	0.227354i	−0.191729	+	0.981448i	$0.561410\pi$
$684$	5.15048	−	0.782710i	0.196934	−	0.0299277i
$685$	42.4344			1.62134
$686$	−13.2263	−	12.9640i	−0.504983	−	0.494967i
$687$	15.6278	−	23.9004i	0.596237	−	0.911858i
$688$	10.7621	−	6.21352i	0.410303	−	0.236888i
$689$	−1.40161	+	26.8520i	−0.0533969	+	1.02298i
$690$	−6.57575	−	2.15939i	−0.250334	−	0.0822064i
$691$	−10.0065	+	37.3446i	−0.380663	+	1.42066i	0.464227	+	0.885716i	$0.346332\pi$
$691$	−10.0065	+	37.3446i	−0.380663	+	1.42066i	−0.844891	+	0.534939i	$0.820335\pi$
$692$			4.25998i			0.161940i
$693$	29.6196	+	17.9154i	1.12516	+	0.680551i
$694$	−7.58465	−	7.58465i	−0.287909	−	0.287909i
$695$	−10.9406	−	2.93152i	−0.414999	−	0.111199i
$696$	−5.56831	−	11.0136i	−0.211066	−	0.417469i
$697$	−6.64149	−	24.7864i	−0.251565	−	0.938852i
$698$	−29.6129	+	17.0970i	−1.12086	+	0.647130i
$699$	26.6038	−	5.56777i	1.00625	−	0.210592i
$700$	−0.743526	−	2.02179i	−0.0281026	−	0.0764166i
$701$	−33.0964			−1.25003			−0.625016	−	0.780612i	$-0.714908\pi$
$701$	−33.0964			−1.25003			−0.625016	+	0.780612i	$0.714908\pi$
$702$	13.8070	+	12.6636i	0.521113	+	0.477955i
$703$	2.58701	−	4.48083i	0.0975709	−	0.168998i
$704$	−1.12877	−	4.21263i	−0.0425422	−	0.158769i
$705$	4.89829	+	5.47450i	0.184480	+	0.206181i
$706$			18.3608i			0.691018i
$707$	14.0163	−	16.8176i	0.527136	−	0.632492i
$708$	−11.1073	+	16.9870i	−0.417438	+	0.638411i
$709$	−47.0107	−	12.5965i	−1.76553	−	0.473071i	−0.777700	−	0.628636i	$-0.783614\pi$
$709$	−47.0107	−	12.5965i	−1.76553	−	0.473071i	−0.987826	+	0.155565i	$0.950280\pi$
$710$	−15.6013	+	4.18035i	−0.585506	+	0.156886i
$711$	−2.72072	+	24.4136i	−0.102035	+	0.915581i
$712$	−2.48154	+	1.43272i	−0.0929995	+	0.0536933i
$713$	−2.74008	−	2.74008i	−0.102617	−	0.102617i
$714$	−4.84885	−	15.8482i	−0.181464	−	0.593104i
$715$	−14.6115	−	28.6619i	−0.546440	−	1.07189i
$716$	16.5472	−	9.55356i	0.618400	−	0.357033i
$717$	−2.09416	−	4.14204i	−0.0782077	−	0.154687i
$718$	−8.37235	+	14.5013i	−0.312453	+	0.541185i
$719$	−19.6014	−	33.9506i	−0.731009	−	1.26614i	−0.956453	−	0.291888i	$-0.905717\pi$
$719$	−19.6014	−	33.9506i	−0.731009	−	1.26614i	0.225444	−	0.974256i	$-0.427617\pi$
$720$	−2.23544	+	5.71621i	−0.0833098	+	0.213030i
$721$	23.1042	−	8.49671i	0.860446	−	0.316434i
$722$	−11.3027	−	11.3027i	−0.420643	−	0.420643i
$723$	44.6600	+	2.48084i	1.66092	+	0.0922636i
$724$	−0.329286	+	0.570340i	−0.0122378	+	0.0211965i
$725$	−2.90068	+	5.02412i	−0.107728	+	0.186591i
$726$	0.770490	−	13.8703i	0.0285956	−	0.514776i
$727$			35.3118i			1.30964i	0.755784	+	0.654821i	$0.227256\pi$
$727$			35.3118i			1.30964i	−0.755784	+	0.654821i	$0.772744\pi$
$728$	−4.44856	+	8.43862i	−0.164875	+	0.312756i
$729$	8.82461	−	25.5172i	0.326837	−	0.945081i
$730$	−4.04576	+	15.0990i	−0.149740	+	0.558838i
$731$	−38.9224	−	22.4719i	−1.43960	−	0.831152i
$732$	18.2520	+	5.99371i	0.674613	+	0.221534i
$733$	6.67970	−	24.9290i	0.246720	−	0.920773i	−0.725790	−	0.687916i	$-0.758526\pi$
$733$	6.67970	−	24.9290i	0.246720	−	0.920773i	0.972511	−	0.232857i	$-0.0748076\pi$
$734$	−3.81958	+	3.81958i	−0.140983	+	0.140983i
$735$	19.7575	−	14.9984i	0.728767	−	0.553226i
$736$	1.38108	−	1.38108i	0.0509072	−	0.0509072i
$737$	29.5226	−	17.0449i	1.08748	−	0.627857i
$738$	21.1548	+	2.35756i	0.778720	+	0.0867829i
$739$	6.24936	+	23.3229i	0.229886	+	0.857948i	0.980388	+	0.197079i	$0.0631454\pi$
$739$	6.24936	+	23.3229i	0.229886	+	0.857948i	−0.750501	+	0.660869i	$0.770188\pi$
$740$	3.04792	+	5.27914i	0.112044	+	0.194065i
$741$	−1.16510	+	10.7819i	−0.0428009	+	0.396083i
$742$	11.3710	+	16.1247i	0.417444	+	0.591956i
$743$	8.33082	−	8.33082i	0.305628	−	0.305628i	−0.537583	−	0.843211i	$-0.680662\pi$
$743$	8.33082	−	8.33082i	0.305628	−	0.305628i	0.843211	+	0.537583i	$0.180662\pi$
$744$	−2.56094	+	2.29140i	−0.0938886	+	0.0840066i
$745$	1.34331	+	0.775562i	0.0492152	+	0.0284144i
$746$	2.83324	+	10.5738i	0.103732	+	0.387134i
$747$	27.1659	−	4.12836i	0.993949	−	0.151049i
$748$	−11.1531	+	11.1531i	−0.407798	+	0.407798i
$749$	−26.5487	+	9.76345i	−0.970069	+	0.356749i
$750$	20.1665	−	4.22054i	0.736378	−	0.154112i
$751$	37.9371	−	21.9030i	1.38434	−	0.799251i	0.391674	−	0.920104i	$-0.371896\pi$
$751$	37.9371	−	21.9030i	1.38434	−	0.799251i	0.992670	+	0.120853i	$0.0385629\pi$
$752$	−2.00237	+	0.536532i	−0.0730188	+	0.0195653i
$753$	4.21991	−	12.8504i	0.153782	−	0.468296i
$754$	25.1277	−	5.34658i	0.915098	−	0.194711i
$755$			18.6450i			0.678562i
$756$	13.7082	+	1.04207i	0.498562	+	0.0378999i
$757$	8.41018			0.305673			0.152837	−	0.988251i	$-0.451159\pi$
$757$	8.41018			0.305673			0.152837	+	0.988251i	$0.451159\pi$
$758$	−7.29852	−	12.6414i	−0.265094	−	0.459156i
$759$	13.1666	−	6.65686i	0.477919	−	0.241629i
$760$	−3.43176	+	0.919538i	−0.124483	+	0.0333552i
$761$	−11.6888	+	43.6231i	−0.423718	+	1.58134i	0.342989	+	0.939340i	$0.388561\pi$
$761$	−11.6888	+	43.6231i	−0.423718	+	1.58134i	−0.766707	+	0.641998i	$0.778106\pi$
$762$	1.94788	+	1.27366i	0.0705643	+	0.0461399i
$763$	−41.3522	+	3.75700i	−1.49705	+	0.136013i
$764$	13.1942			0.477350
$765$	21.9459	−	3.33508i	0.793456	−	0.120580i
$766$	4.84159	+	2.79529i	0.174934	+	0.100998i
$767$	−28.2771	−	31.3917i	−1.02103	−	1.13349i
$768$	−1.15493	−	1.29079i	−0.0416750	−	0.0465773i
$769$	−24.1688	−	24.1688i	−0.871549	−	0.871549i	0.121092	−	0.992641i	$-0.461360\pi$
$769$	−24.1688	−	24.1688i	−0.871549	−	0.871549i	−0.992641	+	0.121092i	$0.961360\pi$
$770$	−21.4287	−	9.90542i	−0.772238	−	0.356967i
$771$	−9.65062	+	2.01973i	−0.347559	+	0.0727386i
$772$	3.71437	−	13.8622i	0.133683	−	0.498912i
$773$	−12.8361	−	47.9049i	−0.461681	−	1.72302i	−0.667664	−	0.744463i	$-0.732706\pi$
$773$	−12.8361	−	47.9049i	−0.461681	−	1.72302i	0.205983	−	0.978556i	$-0.433961\pi$
$774$	29.1193	−	23.2798i	1.04667	−	0.836775i
$775$	1.56034	+	0.418093i	0.0560492	+	0.0150183i
$776$			0.260628i			0.00935601i
$777$	9.30981	−	9.98767i	0.333988	−	0.358306i
$778$	−18.8119	+	18.8119i	−0.674441	+	0.674441i
$779$	6.16060	+	10.6705i	0.220726	+	0.382309i
$780$	−10.3146	−	7.54018i	−0.369323	−	0.269982i
$781$	17.2150	−	29.8173i	0.616001	−	1.06695i
$782$	−6.82305	−	1.82823i	−0.243992	−	0.0653774i
$783$	−21.4795	−	30.1559i	−0.767614	−	1.07768i
$784$	1.26154	+	6.88538i	0.0450550	+	0.245907i
$785$	24.0014	−	24.0014i	0.856647	−	0.856647i
$786$	−0.651830	+	11.7342i	−0.0232500	+	0.418546i
$787$	2.55022	+	9.51756i	0.0909056	+	0.339264i	0.996367	−	0.0851645i	$-0.0271416\pi$
$787$	2.55022	+	9.51756i	0.0909056	+	0.339264i	−0.905461	+	0.424429i	$0.860475\pi$
$788$	9.14202	−	2.44960i	0.325671	−	0.0872633i
$789$	35.1973	−	31.4927i	1.25306	−	1.12117i
$790$		−	16.7525i		−	0.596027i
$791$	−9.34211	+	54.0360i	−0.332167	+	1.92130i
$792$	−5.24663	−	11.9857i	−0.186431	−	0.425892i
$793$	−21.7735	+	33.5436i	−0.773199	+	1.19117i
$794$	−4.08299	−	2.35731i	−0.144900	−	0.0836579i
$795$	−23.5840	+	11.9237i	−0.836438	+	0.422891i
$796$	4.35239	+	7.53857i	0.154267	+	0.267197i
$797$	−21.8817			−0.775089			−0.387544	−	0.921851i	$-0.626677\pi$
$797$	−21.8817			−0.775089			−0.387544	+	0.921851i	$0.626677\pi$
$798$	4.21839	+	6.74774i	0.149329	+	0.238868i
$799$	5.30134	+	5.30134i	0.187548	+	0.187548i
$800$	−0.210731	+	0.786459i	−0.00745047	+	0.0278055i
$801$	−6.71434	+	5.36786i	−0.237240	+	0.189664i
$802$	−11.5404	+	19.9885i	−0.407504	+	0.705818i
$803$	−16.6607	−	28.8572i	−0.587944	−	1.01835i
$804$	7.40922	−	11.3313i	0.261303	−	0.399625i
$805$	−0.956598	−	10.5290i	−0.0337157	−	0.371098i
$806$	−3.24894	−	6.37309i	−0.114439	−	0.224483i
$807$	−36.8899	+	33.0071i	−1.29858	+	1.16191i
$808$	−7.99269	+	2.14164i	−0.281182	+	0.0753425i
$809$	−43.4161	−	25.0663i	−1.52643	−	0.881284i	−0.999508	−	0.0313705i	$-0.990013\pi$
$809$	−43.4161	−	25.0663i	−1.52643	−	0.881284i	−0.526922	−	0.849914i	$-0.676654\pi$
$810$	−4.05372	+	17.9615i	−0.142433	+	0.631104i
$811$	33.8652	+	33.8652i	1.18917	+	1.18917i	0.977298	+	0.211871i	$0.0679558\pi$
$811$	33.8652	+	33.8652i	1.18917	+	1.18917i	0.211871	+	0.977298i	$0.432044\pi$
$812$	12.0692	−	14.4815i	0.423547	−	0.508200i
$813$	3.59431	−	5.49698i	0.126058	−	0.192788i
$814$	−12.5515	−	3.36318i	−0.439931	−	0.117879i
$815$	−24.7988	−	14.3176i	−0.868663	−	0.501523i
$816$	−1.95438	+	5.95146i	−0.0684170	+	0.208343i
$817$	20.8447	+	5.58533i	0.729265	+	0.195406i
$818$	−5.04207			−0.176292
$819$	−9.39065	+	27.0336i	−0.328136	+	0.944631i
$820$	−14.5163			−0.506933
$821$	26.3039	+	7.04810i	0.918011	+	0.245980i	0.686735	−	0.726908i	$-0.259043\pi$
$821$	26.3039	+	7.04810i	0.918011	+	0.245980i	0.231276	+	0.972888i	$0.425710\pi$
$822$	−11.2082	+	34.1312i	−0.390932	+	1.19046i
$823$	5.93612	+	3.42722i	0.206920	+	0.119465i	0.599879	−	0.800091i	$-0.295215\pi$
$823$	5.93612	+	3.42722i	0.206920	+	0.119465i	−0.392959	+	0.919556i	$0.628549\pi$
$824$	−8.98733	−	2.40815i	−0.313089	−	0.0838918i
$825$	−3.36588	+	5.14763i	−0.117185	+	0.179217i
$826$	−30.5496	−	5.28161i	−1.06296	−	0.183771i
$827$	10.6442	+	10.6442i	0.370137	+	0.370137i	0.867527	−	0.497390i	$-0.165708\pi$
$827$	10.6442	+	10.6442i	0.370137	+	0.370137i	−0.497390	+	0.867527i	$0.665708\pi$
$828$	3.47371	−	4.71870i	0.120720	−	0.163986i
$829$	22.0563	+	12.7342i	0.766046	+	0.442277i	0.831462	−	0.555581i	$-0.187504\pi$
$829$	22.0563	+	12.7342i	0.766046	+	0.442277i	−0.0654163	+	0.997858i	$0.520838\pi$
$830$	−18.1006	+	4.85005i	−0.628282	+	0.168348i
$831$	−10.8922	+	9.74579i	−0.377847	+	0.338078i
$832$	3.21223	−	1.63756i	0.111364	−	0.0567722i
$833$	19.2843	−	16.4021i	0.668161	−	0.568299i
$834$	5.24764	−	8.02551i	0.181711	−	0.277901i
$835$	19.3167	+	33.4576i	0.668483	+	1.15785i
$836$	3.78673	−	6.55880i	0.130967	−	0.226841i
$837$	−6.56281	+	7.95045i	−0.226844	+	0.274808i
$838$	8.09979	−	30.2288i	0.279803	−	1.04424i
$839$	−17.3774	−	17.3774i	−0.599933	−	0.599933i	0.340362	−	0.940295i	$-0.389451\pi$
$839$	−17.3774	−	17.3774i	−0.599933	−	0.599933i	−0.940295	+	0.340362i	$0.889451\pi$
$840$	−9.36981	+	0.329133i	−0.323289	+	0.0113562i
$841$	−21.7684			−0.750635
$842$	2.66551	+	4.61680i	0.0918595	+	0.159105i
$843$	−8.75587	+	4.42684i	−0.301568	+	0.152469i
$844$	−2.90490	−	1.67715i	−0.0999909	−	0.0577298i
$845$	20.6627	−	16.7467i	0.710819	−	0.576104i
$846$	−5.69708	+	2.49385i	−0.195870	+	0.0857404i
$847$	19.9159	−	7.32417i	0.684317	−	0.251662i
$848$		−	7.45755i		−	0.256093i
$849$	37.6652	−	33.7009i	1.29267	−	1.15661i
$850$	2.84431	−	0.762131i	0.0975591	−	0.0261409i
$851$	−1.50617	−	5.62109i	−0.0516308	−	0.192689i
$852$	0.758403	−	13.6527i	0.0259824	−	0.467734i
$853$	9.14555	−	9.14555i	0.313138	−	0.313138i	−0.532986	−	0.846124i	$-0.678930\pi$
$853$	9.14555	−	9.14555i	0.313138	−	0.313138i	0.846124	+	0.532986i	$0.178930\pi$
$854$	2.65519	+	29.2248i	0.0908586	+	1.00005i
$855$	−9.76396	+	4.27410i	−0.333921	+	0.146171i
$856$	10.3272	+	2.76717i	0.352977	+	0.0945799i
$857$	0.343950	−	0.595739i	0.0117491	−	0.0203501i	−0.860091	−	0.510141i	$-0.829593\pi$
$857$	0.343950	−	0.595739i	0.0117491	−	0.0203501i	0.871840	+	0.489790i	$0.162927\pi$
$858$	26.9129	−	4.18199i	0.918792	−	0.142771i
$859$	15.8952	+	27.5313i	0.542337	+	0.939356i	0.998769	+	0.0495975i	$0.0157939\pi$
$859$	15.8952	+	27.5313i	0.542337	+	0.939356i	−0.456432	+	0.889758i	$0.650873\pi$
$860$	−17.9780	+	17.9780i	−0.613046	+	0.613046i
$861$	9.51274	+	31.0919i	0.324193	+	1.05961i
$862$		−	18.7982i		−	0.640268i
$863$	−41.4737	−	11.1128i	−1.41178	−	0.378285i	−0.529220	−	0.848485i	$-0.677515\pi$
$863$	−41.4737	−	11.1128i	−1.41178	−	0.378285i	−0.882560	+	0.470199i	$0.844182\pi$
$864$	−4.00726	−	3.30785i	−0.136330	−	0.112535i
$865$	−2.25576	−	8.41862i	−0.0766982	−	0.286242i
$866$	−3.39139	+	12.6568i	−0.115244	+	0.430097i
$867$	−6.64592	+	1.39089i	−0.225707	+	0.0472371i
$868$	−4.76477	−	2.20251i	−0.161727	−	0.0747582i
$869$	25.2514	+	25.2514i	0.856594	+	0.856594i
$870$	16.8361	+	18.8166i	0.570797	+	0.637942i
$871$	18.8625	+	20.9401i	0.639131	+	0.709527i
$872$	13.5914	+	7.84702i	0.460264	+	0.265733i
$873$	0.117473	+	0.773010i	0.00397586	+	0.0261624i
$874$	3.39170			0.114726
$875$	18.1377	+	25.7202i	0.613167	+	0.869501i
$876$	−11.0759	−	7.24222i	−0.374221	−	0.244692i
$877$	−9.70257	+	36.2105i	−0.327632	+	1.22274i	0.584006	+	0.811749i	$0.301484\pi$
$877$	−9.70257	+	36.2105i	−0.327632	+	1.22274i	−0.911639	+	0.410992i	$0.865182\pi$
$878$	−28.4135	+	7.61339i	−0.958911	+	0.256939i
$879$	−19.2621	+	9.73862i	−0.649693	+	0.328476i
$880$	4.46137	+	7.72733i	0.150393	+	0.260488i
$881$	37.1385			1.25123			0.625614	−	0.780133i	$-0.284848\pi$
$881$	37.1385			1.25123			0.625614	+	0.780133i	$0.284848\pi$
$882$	6.84511	+	19.8531i	0.230487	+	0.668488i
$883$		−	20.8239i		−	0.700781i	−0.936604	−	0.350391i	$-0.886049\pi$
$883$		−	20.8239i		−	0.700781i	0.936604	−	0.350391i	$-0.113951\pi$
$884$	−10.9376	−	7.09972i	−0.367873	−	0.238790i
$885$	12.9553	−	39.4515i	0.435489	−	1.32615i
$886$	−15.0232	+	4.02545i	−0.504713	+	0.135238i
$887$	23.6361	−	13.6463i	0.793622	−	0.458198i	−0.0476138	−	0.998866i	$-0.515162\pi$
$887$	23.6361	−	13.6463i	0.793622	−	0.458198i	0.841236	+	0.540668i	$0.181828\pi$
$888$	−5.05121	+	1.05714i	−0.169508	+	0.0354753i
$889$	−0.605637	+	3.50309i	−0.0203124	+	0.117490i
$890$	4.14538	−	4.14538i	0.138953	−	0.138953i
$891$	−20.9635	−	33.1840i	−0.702305	−	1.11171i
$892$	3.58433	+	13.3769i	0.120012	+	0.447892i
$893$	−3.11756	−	1.79992i	−0.104325	−	0.0602322i
$894$	−0.978616	+	0.875615i	−0.0327298	+	0.0292849i
$895$	−27.6420	+	27.6420i	−0.923970	+	0.923970i
$896$	1.11013	−	2.40158i	0.0370869	−	0.0802313i
$897$	7.64830	+	9.50152i	0.255369	+	0.317246i
$898$	−0.728825	−	1.26236i	−0.0243212	−	0.0421256i
$899$	3.65879	+	13.6548i	0.122027	+	0.455413i
$900$	−0.270537	+	2.42758i	−0.00901789	+	0.0809193i
$901$	−23.3576	+	13.4855i	−0.778155	+	0.449268i
$902$	21.8808	−	21.8808i	0.728550	−	0.728550i
$903$	50.2875	+	26.7251i	1.67346	+	0.889354i
$904$	14.6560	−	14.6560i	0.487451	−	0.487451i
$905$	0.348729	−	1.30147i	0.0115921	−	0.0432625i
$906$	−14.9967	−	4.92472i	−0.498233	−	0.163613i
$907$	18.2193	+	10.5189i	0.604961	+	0.349275i	0.770991	−	0.636846i	$-0.219761\pi$
$907$	18.2193	+	10.5189i	0.604961	+	0.349275i	−0.166030	+	0.986121i	$0.553095\pi$
$908$	2.20020	−	8.21127i	0.0730163	−	0.272500i
$909$	−22.7406	+	9.95452i	−0.754258	+	0.330171i
$910$	4.32283	−	19.0321i	0.143300	−	0.630908i
$911$			19.4559i			0.644603i	0.946637	+	0.322301i	$0.104456\pi$
$911$			19.4559i			0.644603i	−0.946637	+	0.322301i	$0.895544\pi$
$912$	0.166823	−	3.00314i	0.00552407	−	0.0994440i
$913$	19.9729	−	34.5940i	0.661006	−	1.14490i
$914$	3.00384	−	5.20281i	0.0993583	−	0.172094i
$915$	−39.2436	−	2.17996i	−1.29735	−	0.0720674i
$916$	−11.6580	−	11.6580i	−0.385192	−	0.385192i
$917$	−16.8487	+	6.19621i	−0.556394	+	0.204617i
$918$	−3.11409	+	18.5326i	−0.102780	+	0.611668i
$919$	−11.3876	−	19.7238i	−0.375641	−	0.650629i	0.614782	−	0.788697i	$-0.289244\pi$
$919$	−11.3876	−	19.7238i	−0.375641	−	0.650629i	−0.990423	+	0.138068i	$0.955911\pi$
$920$	−1.99799	+	3.46061i	−0.0658716	+	0.114093i
$921$	3.58114	+	7.08315i	0.118003	+	0.233398i
$922$	−27.0410	+	15.6121i	−0.890547	+	0.514158i
$923$	27.0729	+	8.79025i	0.891116	+	0.289334i
$924$	13.6272	−	14.6194i	0.448302	−	0.480943i
$925$	1.71538	+	1.71538i	0.0564014	+	0.0564014i
$926$	−23.5504	+	13.5969i	−0.773915	+	0.446820i
$927$	−27.7414	−	3.09158i	−0.911146	−	0.101541i
$928$	−6.88241	+	1.84414i	−0.225926	+	0.0605367i
$929$	−55.6070	−	14.8999i	−1.82441	−	0.488849i	−0.827092	−	0.562067i	$-0.810006\pi$
$929$	−55.6070	−	14.8999i	−1.82441	−	0.488849i	−0.997316	+	0.0732185i	$0.976673\pi$
$930$	3.84761	−	5.88436i	0.126168	−	0.192956i
$931$	−6.90562	+	10.0038i	−0.226323	+	0.327860i
$932$		−	15.6925i		−	0.514024i
$933$	−5.68228	−	6.35071i	−0.186030	−	0.207913i
$934$	−10.3005	−	38.4420i	−0.337043	−	1.25786i
$935$	16.1350	−	27.9467i	0.527672	−	0.913955i
$936$	8.78920	−	6.30476i	0.287284	−	0.206078i
$937$	−6.71198			−0.219271			−0.109635	−	0.993972i	$-0.534968\pi$
$937$	−6.71198			−0.219271			−0.109635	+	0.993972i	$0.534968\pi$
$938$	20.3783	+	3.52314i	0.665376	+	0.115035i
$939$	11.6288	−	2.43373i	0.379492	−	0.0794218i
$940$	3.67299	−	2.12060i	0.119800	−	0.0691664i
$941$	0.0271903	+	0.101476i	0.000886378	+	0.00330801i	0.966368	−	0.257165i	$-0.0827883\pi$
$941$	0.0271903	+	0.101476i	0.000886378	+	0.00330801i	−0.965481	+	0.260473i	$0.916122\pi$
$942$	12.9655	+	25.6445i	0.422439	+	0.835544i
$943$	13.3858	+	3.58672i	0.435903	+	0.116800i
$944$	8.28584	+	8.28584i	0.269681	+	0.269681i
$945$	−27.6420	+	5.19945i	−0.899195	+	0.169138i
$946$		−	54.1973i		−	1.76211i
$947$	6.32509	−	23.6055i	0.205538	−	0.767077i	−0.783747	−	0.621080i	$-0.786694\pi$
$947$	6.32509	−	23.6055i	0.205538	−	0.767077i	0.989285	−	0.145997i	$-0.0466391\pi$
$948$	13.4745	+	4.42485i	0.437632	+	0.143712i
$949$	20.4681	−	18.4373i	0.664423	−	0.598501i
$950$	−1.22447	+	0.706947i	−0.0397270	+	0.0229364i
$951$	−6.89485	+	10.5447i	−0.223581	+	0.341935i
$952$	−9.52939	+	0.865782i	−0.308849	+	0.0280601i
$953$	29.6280			0.959745			0.479873	−	0.877338i	$-0.340683\pi$
$953$	29.6280			0.959745			0.479873	+	0.877338i	$0.340683\pi$
$954$	−3.36134	−	22.1187i	−0.108827	−	0.716120i
$955$	−26.0745	+	6.98664i	−0.843751	+	0.226083i
$956$	−2.58837	+	0.693551i	−0.0837138	+	0.0224311i
$957$	−53.7400	−	2.98524i	−1.73717	−	0.0964989i
$958$	−8.19244			−0.264686
$959$	−54.6504	+	4.96519i	−1.76475	+	0.160334i
$960$	2.96589	+	1.93931i	0.0957236	+	0.0625908i
$961$	−23.4378	+	13.5318i	−0.756060	+	0.436511i
$962$	0.559981	−	10.7281i	0.0180545	−	0.345889i
$963$	31.8772	+	3.55249i	1.02723	+	0.114477i
$964$	6.68380	−	24.9443i	0.215271	−	0.803401i
$965$			29.3615i			0.945179i
$966$	8.72143	+	2.01161i	0.280607	+	0.0647224i
$967$	−16.5860	−	16.5860i	−0.533371	−	0.533371i	0.388203	−	0.921574i	$-0.373096\pi$
$967$	−16.5860	−	16.5860i	−0.533371	−	0.533371i	−0.921574	+	0.388203i	$0.873096\pi$
$968$	−7.74709	−	2.07583i	−0.249001	−	0.0667196i
$969$	−9.70773	+	4.90809i	−0.311857	+	0.157671i
$970$	−0.138009	−	0.515056i	−0.00443120	−	0.0165374i
$971$	14.8816	−	8.59189i	0.477573	−	0.275727i	−0.241832	−	0.970318i	$-0.577748\pi$
$971$	14.8816	−	8.59189i	0.477573	−	0.275727i	0.719404	+	0.694591i	$0.244415\pi$
$972$	−13.3763	−	8.00472i	−0.429044	−	0.256751i
$973$	14.4331	+	2.49530i	0.462705	+	0.0799955i
$974$	−0.510841			−0.0163684
$975$	−4.74162	−	1.83606i	−0.151853	−	0.0588009i
$976$	5.54572	−	9.60547i	0.177514	−	0.307464i
$977$	3.03420	+	11.3238i	0.0970727	+	0.362280i	0.997326	−	0.0730872i	$-0.0232851\pi$
$977$	3.03420	+	11.3238i	0.0970727	+	0.362280i	−0.900253	+	0.435367i	$0.856618\pi$
$978$	18.0662	−	16.1646i	0.577692	−	0.516888i
$979$			12.4968i			0.399400i
$980$	−6.13904	−	12.9389i	−0.196104	−	0.413319i
$981$	43.8483	+	17.1478i	1.39997	+	0.547486i
$982$	−9.51806	−	2.55036i	−0.303733	−	0.0813851i
$983$	−30.0137	+	8.04214i	−0.957287	+	0.256504i	−0.703452	−	0.710743i	$-0.748359\pi$
$983$	−30.0137	+	8.04214i	−0.957287	+	0.256504i	−0.253835	+	0.967247i	$0.581692\pi$
$984$	3.83421	−	11.6759i	0.122230	−	0.372215i
$985$	−16.7694	+	9.68183i	−0.534318	+	0.308489i
$986$	18.2215	+	18.2215i	0.580289	+	0.580289i
$987$	−6.94897	−	6.47734i	−0.221188	−	0.206176i
$988$	5.95514	+	1.93356i	0.189458	+	0.0615148i
$989$	21.0200	−	12.1359i	0.668396	−	0.385899i
$990$	16.7151	+	20.9080i	0.531242	+	0.664499i
$991$	15.0966	−	26.1481i	0.479560	−	0.830622i	−0.520165	−	0.854066i	$-0.674130\pi$
$991$	15.0966	−	26.1481i	0.479560	−	0.830622i	0.999725	+	0.0234433i	$0.00746292\pi$
$992$	0.992006	+	1.71820i	0.0314962	+	0.0545531i
$993$	−42.3902	−	27.7177i	−1.34521	−	0.879595i
$994$	19.6034	−	7.20927i	0.621783	−	0.228664i
$995$	−12.5931	−	12.5931i	−0.399228	−	0.399228i
$996$	0.879900	−	15.8399i	0.0278807	−	0.501907i
$997$	21.3620	−	37.0001i	0.676541	−	1.17180i	−0.299474	−	0.954104i	$-0.596811\pi$
$997$	21.3620	−	37.0001i	0.676541	−	1.17180i	0.976016	−	0.217700i	$-0.0698553\pi$
$998$	6.11158	−	10.5856i	0.193459	−	0.335080i
$999$	−14.5051	+	5.41216i	−0.458923	+	0.171233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.515.7	yes	144
3.2	odd	2	inner	546.2.bv.a.515.24	yes	144
7.2	even	3	inner	546.2.bv.a.359.24	yes	144
13.5	odd	4	inner	546.2.bv.a.473.7	yes	144
21.2	odd	6	inner	546.2.bv.a.359.7	yes	144
39.5	even	4	inner	546.2.bv.a.473.24	yes	144
91.44	odd	12	inner	546.2.bv.a.317.24	yes	144
273.44	even	12	inner	546.2.bv.a.317.7	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.7	✓	144	273.44	even	12	inner
546.2.bv.a.317.24	yes	144	91.44	odd	12	inner
546.2.bv.a.359.7	yes	144	21.2	odd	6	inner
546.2.bv.a.359.24	yes	144	7.2	even	3	inner
546.2.bv.a.473.7	yes	144	13.5	odd	4	inner
546.2.bv.a.473.24	yes	144	39.5	even	4	inner
546.2.bv.a.515.7	yes	144	1.1	even	1	trivial
546.2.bv.a.515.24	yes	144	3.2	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.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.540391 + 1.64559i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.97621 - 0.529524i) q^{5} +(0.947888 - 1.44966i) q^{6} +(2.60708 + 0.450728i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.41596 - 1.77853i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.540391 + 1.64559i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.97621 - 0.529524i) q^{5} +(0.947888 - 1.44966i) q^{6} +(2.60708 + 0.450728i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.41596 - 1.77853i) q^{9} +(1.77182 + 1.02296i) q^{10} +(-4.21263 + 1.12877i) q^{11} +(-1.29079 + 1.15493i) q^{12} +(-1.63756 - 3.21223i) q^{13} +(-2.40158 - 1.11013i) q^{14} +(1.93931 - 2.96589i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.80830 - 3.13207i) q^{17} +(1.87332 + 2.34322i) q^{18} +(-0.449449 + 1.67737i) q^{19} +(-1.44669 - 1.44669i) q^{20} +(-2.15056 + 4.04662i) q^{21} +4.36124 q^{22} +(0.976570 + 1.69147i) q^{23} +(1.54572 - 0.781496i) q^{24} +(-0.705120 - 0.407101i) q^{25} +(0.750376 + 3.52660i) q^{26} +(4.23229 - 3.01458i) q^{27} +(2.03243 + 1.69388i) q^{28} -7.12520i q^{29} +(-2.64085 + 2.36290i) q^{30} +(-1.91641 + 0.513500i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.418969 - 7.54225i) q^{33} +(-2.55733 + 2.55733i) q^{34} +(-4.91346 - 2.27124i) q^{35} +(-1.20302 - 2.74823i) q^{36} +(-2.87798 - 0.771152i) q^{37} +(0.868269 - 1.50389i) q^{38} +(6.17094 - 0.958900i) q^{39} +(1.02296 + 1.77182i) q^{40} +(5.01711 - 5.01711i) q^{41} +(3.12462 - 3.35213i) q^{42} -12.4270i q^{43} +(-4.21263 - 1.12877i) q^{44} +(3.83266 + 4.79405i) q^{45} +(-0.505510 - 1.88659i) q^{46} +(-0.536532 + 2.00237i) q^{47} +(-1.69532 + 0.354805i) q^{48} +(6.59369 + 2.35017i) q^{49} +(0.575728 + 0.575728i) q^{50} +(4.17693 + 4.66828i) q^{51} +(0.187944 - 3.60065i) q^{52} +(-6.45843 - 3.72878i) q^{53} +(-4.86831 + 1.81646i) q^{54} +8.92275 q^{55} +(-1.52477 - 2.16219i) q^{56} +(-2.51739 - 1.64604i) q^{57} +(-1.84414 + 6.88241i) q^{58} +(11.3187 - 3.03283i) q^{59} +(3.16243 - 1.59888i) q^{60} +(-5.54572 - 9.60547i) q^{61} +1.98401 q^{62} +(-5.49695 - 5.72570i) q^{63} +1.00000i q^{64} +(1.53521 + 7.21516i) q^{65} +(-2.35677 + 7.17682i) q^{66} +(-7.55021 + 2.02307i) q^{67} +(3.13207 - 1.80830i) q^{68} +(-3.31120 + 0.692983i) q^{69} +(4.15819 + 3.46555i) q^{70} +(-5.58229 + 5.58229i) q^{71} +(0.450730 + 2.96595i) q^{72} +(1.97747 + 7.38003i) q^{73} +(2.58032 + 1.48975i) q^{74} +(1.05096 - 0.940347i) q^{75} +(-1.22792 + 1.22792i) q^{76} +(-11.4914 + 1.04404i) q^{77} +(-6.20885 - 0.670930i) q^{78} +(-4.09412 - 7.09122i) q^{79} +(-0.529524 - 1.97621i) q^{80} +(2.67368 + 8.59369i) q^{81} +(-6.14468 + 3.54763i) q^{82} +(-6.47658 + 6.47658i) q^{83} +(-3.88574 + 2.42920i) q^{84} +(-5.23209 + 5.23209i) q^{85} +(-3.21636 + 12.0036i) q^{86} +(11.7252 + 3.85039i) q^{87} +(3.77694 + 2.18062i) q^{88} +(0.741628 - 2.76779i) q^{89} +(-2.46128 - 5.62266i) q^{90} +(-2.82140 - 9.11261i) q^{91} +1.95314i q^{92} +(0.190597 - 3.43112i) q^{93} +(1.03650 - 1.79527i) q^{94} +(1.77641 - 3.07683i) q^{95} +(1.72938 + 0.0960666i) q^{96} +(-0.184292 - 0.184292i) q^{97} +(-5.76075 - 3.97666i) q^{98} +(12.1851 + 4.76522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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