LMFDB - Embedded newform 409.2.g.b.49.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,2,Mod(49,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	409.g (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [132] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.26588144267$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$33$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			49.14
Character	$\chi$	$=$	409.49
Dual form			409.2.g.b.192.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.352909 + 0.203752i) q^{2} +(-1.29982 - 0.750452i) q^{3} +(-0.916970 + 1.58824i) q^{4} +1.88589 q^{5} +0.611624 q^{6} +(-0.185005 - 0.690448i) q^{7} -1.56235i q^{8} +(-0.373645 - 0.647171i) q^{9} +(-0.665547 + 0.384254i) q^{10} +(0.529954 + 0.529954i) q^{11} +(2.38379 - 1.37628i) q^{12} +(2.41294 + 2.41294i) q^{13} +(0.205970 + 0.205970i) q^{14} +(-2.45132 - 1.41527i) q^{15} +(-1.51561 - 2.62511i) q^{16} +(2.00409 + 3.47119i) q^{17} +(0.263725 + 0.152262i) q^{18} +(3.98305 + 3.98305i) q^{19} +(-1.72930 + 2.99524i) q^{20} +(-0.277675 + 1.03630i) q^{21} +(-0.295005 - 0.0790462i) q^{22} +(5.27862 - 3.04761i) q^{23} +(-1.17247 + 2.03077i) q^{24} -1.44343 q^{25} +(-1.34319 - 0.359907i) q^{26} +5.62432i q^{27} +(1.26624 + 0.339288i) q^{28} +(3.46967 - 0.929696i) q^{29} +1.15345 q^{30} +(3.04903 - 3.04903i) q^{31} +(3.77581 + 2.17996i) q^{32} +(-0.291140 - 1.08655i) q^{33} +(-1.41452 - 0.816676i) q^{34} +(-0.348899 - 1.30211i) q^{35} +1.37048 q^{36} +(-2.77507 + 10.3567i) q^{37} +(-2.21721 - 0.594100i) q^{38} +(-1.32560 - 4.94719i) q^{39} -2.94641i q^{40} +(9.99719 + 5.77188i) q^{41} +(-0.113154 - 0.422295i) q^{42} +(5.50938 - 5.50938i) q^{43} +(-1.32764 + 0.355741i) q^{44} +(-0.704652 - 1.22049i) q^{45} +(-1.24192 + 2.15106i) q^{46} +(-2.61031 + 0.699431i) q^{47} +4.54957i q^{48} +(5.61969 - 3.24453i) q^{49} +(0.509398 - 0.294101i) q^{50} -6.01590i q^{51} +(-6.04493 + 1.61973i) q^{52} +(-0.687148 + 1.19018i) q^{53} +(-1.14597 - 1.98487i) q^{54} +(0.999433 + 0.999433i) q^{55} +(-1.07872 + 0.289042i) q^{56} +(-2.18817 - 8.16634i) q^{57} +(-1.03505 + 1.03505i) q^{58} +(-8.55917 - 8.55917i) q^{59} +(4.49557 - 2.59552i) q^{60} +(-3.84312 + 3.84312i) q^{61} +(-0.454784 + 1.69728i) q^{62} +(-0.377712 + 0.377712i) q^{63} +4.28575 q^{64} +(4.55054 + 4.55054i) q^{65} +(0.324133 + 0.324133i) q^{66} +(-3.40226 - 12.6974i) q^{67} -7.35078 q^{68} -9.14835 q^{69} +(0.388437 + 0.388437i) q^{70} +(2.36375 + 4.09414i) q^{71} +(-1.01111 + 0.583762i) q^{72} +(-14.5621 + 3.90189i) q^{73} +(-1.13085 - 4.22040i) q^{74} +(1.87619 + 1.08322i) q^{75} +(-9.97838 + 2.67370i) q^{76} +(0.267862 - 0.463950i) q^{77} +(1.47582 + 1.47582i) q^{78} +(-4.66557 - 4.66557i) q^{79} +(-2.85827 - 4.95067i) q^{80} +(3.09985 - 5.36909i) q^{81} -4.70413 q^{82} -17.1469 q^{83} +(-1.39127 - 1.39127i) q^{84} +(3.77950 + 6.54628i) q^{85} +(-0.821761 + 3.06685i) q^{86} +(-5.20765 - 1.39538i) q^{87} +(0.827971 - 0.827971i) q^{88} +1.04384 q^{89} +(0.497356 + 0.287148i) q^{90} +(1.21961 - 2.11242i) q^{91} +11.1783i q^{92} +(-6.25135 + 1.67504i) q^{93} +(0.778692 - 0.778692i) q^{94} +(7.51159 + 7.51159i) q^{95} +(-3.27191 - 5.66712i) q^{96} +(16.6402 - 4.45874i) q^{97} +(-1.32216 + 2.29005i) q^{98} +(0.144957 - 0.540985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 6 q^{3} + 58 q^{4} - 4 q^{6} + 56 q^{9} - 18 q^{10} - 2 q^{11} - 30 q^{12} - 2 q^{13} - 24 q^{14} - 30 q^{15} - 58 q^{16} + 2 q^{17} - 36 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{21} - 22 q^{22} - 12 q^{23}+ \cdots - 84 q^{99}+O(q^{100}) $ 132 * q - 6 * q^3 + 58 * q^4 - 4 * q^6 + 56 * q^9 - 18 * q^10 - 2 * q^11 - 30 * q^12 - 2 * q^13 - 24 * q^14 - 30 * q^15 - 58 * q^16 + 2 * q^17 - 36 * q^18 + 6 * q^19 - 6 * q^20 + 6 * q^21 - 22 * q^22 - 12 * q^23 + 30 * q^24 + 172 * q^25 - 6 * q^26 + 30 * q^28 + 40 * q^29 - 12 * q^30 + 18 * q^31 + 36 * q^32 + 14 * q^33 - 24 * q^34 + 4 * q^35 + 20 * q^36 + 30 * q^37 - 70 * q^38 - 24 * q^39 + 84 * q^41 - 98 * q^42 - 16 * q^43 + 4 * q^44 + 12 * q^45 + 8 * q^46 + 14 * q^47 + 84 * q^49 - 36 * q^50 + 50 * q^52 - 32 * q^53 + 86 * q^54 + 14 * q^55 + 82 * q^56 + 94 * q^57 - 104 * q^58 - 18 * q^59 - 90 * q^60 + 2 * q^61 - 38 * q^62 - 62 * q^63 - 24 * q^64 - 38 * q^65 - 66 * q^66 - 100 * q^68 + 68 * q^69 - 104 * q^70 - 38 * q^71 - 48 * q^72 + 18 * q^73 - 6 * q^74 - 192 * q^75 - 22 * q^76 - 28 * q^77 - 176 * q^78 - 6 * q^79 + 32 * q^80 - 66 * q^81 - 36 * q^82 + 28 * q^83 + 60 * q^84 - 36 * q^85 + 88 * q^86 - 152 * q^87 - 96 * q^88 + 84 * q^89 - 162 * q^90 + 50 * q^91 - 144 * q^93 + 48 * q^94 + 34 * q^95 - 94 * q^96 + 28 * q^97 - 98 * q^98 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.352909	+	0.203752i	−0.249544	+	0.144074i	−0.619556	−	0.784953i	$-0.712687\pi$
$2$	−0.352909	+	0.203752i	−0.249544	+	0.144074i	0.370011	+	0.929027i	$0.379354\pi$
$3$	−1.29982	−	0.750452i	−0.750452	−	0.433273i	0.0754054	−	0.997153i	$-0.475975\pi$
$3$	−1.29982	−	0.750452i	−0.750452	−	0.433273i	−0.825857	+	0.563879i	$0.809308\pi$
$4$	−0.916970	+	1.58824i	−0.458485	+	0.794119i
$5$	1.88589			0.843395			0.421697	−	0.906737i	$-0.361434\pi$
$5$	1.88589			0.843395			0.421697	+	0.906737i	$0.361434\pi$
$6$	0.611624			0.249695
$7$	−0.185005	−	0.690448i	−0.0699253	−	0.260965i	0.922109	−	0.386929i	$-0.126464\pi$
$7$	−0.185005	−	0.690448i	−0.0699253	−	0.260965i	−0.992035	+	0.125964i	$0.959798\pi$
$8$		−	1.56235i		−	0.552373i
$9$	−0.373645	−	0.647171i	−0.124548	−	0.215724i
$10$	−0.665547	+	0.384254i	−0.210464	+	0.121512i
$11$	0.529954	+	0.529954i	0.159787	+	0.159787i	0.782472	−	0.622685i	$-0.213958\pi$
$11$	0.529954	+	0.529954i	0.159787	+	0.159787i	−0.622685	+	0.782472i	$0.713958\pi$
$12$	2.38379	−	1.37628i	0.688142	−	0.397299i
$13$	2.41294	+	2.41294i	0.669230	+	0.669230i	0.957538	−	0.288307i	$-0.0930925\pi$
$13$	2.41294	+	2.41294i	0.669230	+	0.669230i	−0.288307	+	0.957538i	$0.593093\pi$
$14$	0.205970	+	0.205970i	0.0550479	+	0.0550479i
$15$	−2.45132	−	1.41527i	−0.632927	−	0.365421i
$16$	−1.51561	−	2.62511i	−0.378902	−	0.656278i
$17$	2.00409	+	3.47119i	0.486064	+	0.841888i	0.999872	−	0.0160178i	$-0.00509884\pi$
$17$	2.00409	+	3.47119i	0.486064	+	0.841888i	−0.513808	+	0.857905i	$0.671766\pi$
$18$	0.263725	+	0.152262i	0.0621606	+	0.0358884i
$19$	3.98305	+	3.98305i	0.913775	+	0.913775i	0.996567	−	0.0827917i	$-0.0263836\pi$
$19$	3.98305	+	3.98305i	0.913775	+	0.913775i	−0.0827917	+	0.996567i	$0.526384\pi$
$20$	−1.72930	+	2.99524i	−0.386684	+	0.669756i
$21$	−0.277675	+	1.03630i	−0.0605936	+	0.226138i
$22$	−0.295005	−	0.0790462i	−0.0628952	−	0.0168527i
$23$	5.27862	−	3.04761i	1.10067	−	0.635472i	0.164272	−	0.986415i	$-0.447472\pi$
$23$	5.27862	−	3.04761i	1.10067	−	0.635472i	0.936397	+	0.350944i	$0.114139\pi$
$24$	−1.17247	+	2.03077i	−0.239329	+	0.414529i
$25$	−1.44343			−0.288685
$26$	−1.34319	−	0.359907i	−0.263422	−	0.0705836i
$27$			5.62432i			1.08240i
$28$	1.26624	+	0.339288i	0.239297	+	0.0641195i
$29$	3.46967	−	0.929696i	0.644302	−	0.172640i	0.0781509	−	0.996942i	$-0.475098\pi$
$29$	3.46967	−	0.929696i	0.644302	−	0.172640i	0.566151	+	0.824301i	$0.308432\pi$
$30$	1.15345			0.210591
$31$	3.04903	−	3.04903i	0.547623	−	0.547623i	−0.378130	−	0.925753i	$-0.623433\pi$
$31$	3.04903	−	3.04903i	0.547623	−	0.547623i	0.925753	+	0.378130i	$0.123433\pi$
$32$	3.77581	+	2.17996i	0.667475	+	0.385367i
$33$	−0.291140	−	1.08655i	−0.0506810	−	0.189144i
$34$	−1.41452	−	0.816676i	−0.242589	−	0.140059i
$35$	−0.348899	−	1.30211i	−0.0589747	−	0.220096i
$36$	1.37048			0.228414
$37$	−2.77507	+	10.3567i	−0.456219	+	1.70263i	0.228261	+	0.973600i	$0.426696\pi$
$37$	−2.77507	+	10.3567i	−0.456219	+	1.70263i	−0.684480	+	0.729032i	$0.739971\pi$
$38$	−2.21721	−	0.594100i	−0.359679	−	0.0963757i
$39$	−1.32560	−	4.94719i	−0.212265	−	0.792185i
$40$		−	2.94641i		−	0.465868i
$41$	9.99719	+	5.77188i	1.56130	+	0.901416i	0.997126	+	0.0757589i	$0.0241379\pi$
$41$	9.99719	+	5.77188i	1.56130	+	0.901416i	0.564172	+	0.825657i	$0.309195\pi$
$42$	−0.113154	−	0.422295i	−0.0174600	−	0.0651615i
$43$	5.50938	−	5.50938i	0.840172	−	0.840172i	−0.148709	−	0.988881i	$-0.547512\pi$
$43$	5.50938	−	5.50938i	0.840172	−	0.840172i	0.988881	+	0.148709i	$0.0475118\pi$
$44$	−1.32764	+	0.355741i	−0.200150	+	0.0536300i
$45$	−0.704652	−	1.22049i	−0.105043	−	0.181940i
$46$	−1.24192	+	2.15106i	−0.183110	+	0.317157i
$47$	−2.61031	+	0.699431i	−0.380753	+	0.102022i	−0.444119	−	0.895968i	$-0.646483\pi$
$47$	−2.61031	+	0.699431i	−0.380753	+	0.102022i	0.0633658	+	0.997990i	$0.479817\pi$
$48$			4.54957i			0.656673i
$49$	5.61969	−	3.24453i	0.802812	−	0.463504i
$50$	0.509398	−	0.294101i	0.0720397	−	0.0415922i
$51$		−	6.01590i		−	0.842395i
$52$	−6.04493	+	1.61973i	−0.838281	+	0.224617i
$53$	−0.687148	+	1.19018i	−0.0943870	+	0.163483i	−0.909353	−	0.416026i	$-0.863422\pi$
$53$	−0.687148	+	1.19018i	−0.0943870	+	0.163483i	0.814966	+	0.579509i	$0.196756\pi$
$54$	−1.14597	−	1.98487i	−0.155946	−	0.270107i
$55$	0.999433	+	0.999433i	0.134764	+	0.134764i
$56$	−1.07872	+	0.289042i	−0.144150	+	0.0386249i
$57$	−2.18817	−	8.16634i	−0.289830	−	1.08166i
$58$	−1.03505	+	1.03505i	−0.135909	+	0.135909i
$59$	−8.55917	−	8.55917i	−1.11431	−	1.11431i	−0.992561	−	0.121748i	$-0.961150\pi$
$59$	−8.55917	−	8.55917i	−1.11431	−	1.11431i	−0.121748	−	0.992561i	$-0.538850\pi$
$60$	4.49557	−	2.59552i	0.580375	−	0.335080i
$61$	−3.84312	+	3.84312i	−0.492061	+	0.492061i	−0.908955	−	0.416894i	$-0.863119\pi$
$61$	−3.84312	+	3.84312i	−0.492061	+	0.492061i	0.416894	+	0.908955i	$0.363119\pi$
$62$	−0.454784	+	1.69728i	−0.0577576	+	0.215554i
$63$	−0.377712	+	0.377712i	−0.0475873	+	0.0475873i
$64$	4.28575			0.535719
$65$	4.55054	+	4.55054i	0.564425	+	0.564425i
$66$	0.324133	+	0.324133i	0.0398980	+	0.0398980i
$67$	−3.40226	−	12.6974i	−0.415652	−	1.55124i	−0.783526	−	0.621359i	$-0.786581\pi$
$67$	−3.40226	−	12.6974i	−0.415652	−	1.55124i	0.367873	−	0.929876i	$-0.380086\pi$
$68$	−7.35078			−0.891412
$69$	−9.14835			−1.10133
$70$	0.388437	+	0.388437i	0.0464271	+	0.0464271i
$71$	2.36375	+	4.09414i	0.280526	+	0.485885i	0.971514	−	0.236981i	$-0.0761578\pi$
$71$	2.36375	+	4.09414i	0.280526	+	0.485885i	−0.690989	+	0.722866i	$0.742824\pi$
$72$	−1.01111	+	0.583762i	−0.119160	+	0.0687970i
$73$	−14.5621	+	3.90189i	−1.70436	+	0.456682i	−0.974031	−	0.226414i	$-0.927300\pi$
$73$	−14.5621	+	3.90189i	−1.70436	+	0.456682i	−0.730329	+	0.683096i	$0.760633\pi$
$74$	−1.13085	−	4.22040i	−0.131459	−	0.490612i
$75$	1.87619	+	1.08322i	0.216644	+	0.125080i
$76$	−9.97838	+	2.67370i	−1.14460	+	0.306694i
$77$	0.267862	−	0.463950i	0.0305257	−	0.0528720i
$78$	1.47582	+	1.47582i	0.167103	+	0.167103i
$79$	−4.66557	−	4.66557i	−0.524917	−	0.524917i	0.394135	−	0.919052i	$-0.371044\pi$
$79$	−4.66557	−	4.66557i	−0.524917	−	0.524917i	−0.919052	+	0.394135i	$0.871044\pi$
$80$	−2.85827	−	4.95067i	−0.319564	−	0.553501i
$81$	3.09985	−	5.36909i	0.344427	−	0.596566i
$82$	−4.70413			−0.519484
$83$	−17.1469			−1.88211			−0.941057	−	0.338249i	$-0.890165\pi$
$83$	−17.1469			−1.88211			−0.941057	+	0.338249i	$0.890165\pi$
$84$	−1.39127	−	1.39127i	−0.151800	−	0.151800i
$85$	3.77950	+	6.54628i	0.409944	+	0.710044i
$86$	−0.821761	+	3.06685i	−0.0886128	+	0.330707i
$87$	−5.20765	−	1.39538i	−0.558318	−	0.149601i
$88$	0.827971	−	0.827971i	0.0882620	−	0.0882620i
$89$	1.04384			0.110647			0.0553236	−	0.998468i	$-0.482381\pi$
$89$	1.04384			0.110647			0.0553236	+	0.998468i	$0.482381\pi$
$90$	0.497356	+	0.287148i	0.0524259	+	0.0302681i
$91$	1.21961	−	2.11242i	0.127850	−	0.221442i
$92$			11.1783i			1.16542i
$93$	−6.25135	+	1.67504i	−0.648235	+	0.173694i
$94$	0.778692	−	0.778692i	0.0803159	−	0.0803159i
$95$	7.51159	+	7.51159i	0.770673	+	0.770673i
$96$	−3.27191	−	5.66712i	−0.333938	−	0.578398i
$97$	16.6402	−	4.45874i	1.68956	−	0.452717i	0.719285	−	0.694716i	$-0.244470\pi$
$97$	16.6402	−	4.45874i	1.68956	−	0.452717i	0.970276	+	0.241999i	$0.0778031\pi$
$98$	−1.32216	+	2.29005i	−0.133558	+	0.231329i
$99$	0.144957	−	0.540985i	0.0145687	−	0.0543711i
$100$	1.32358	−	2.29251i	0.132358	−	0.229251i
$101$	7.46221	+	12.9249i	0.742518	+	1.28608i	0.951345	+	0.308126i	$0.0997020\pi$
$101$	7.46221	+	12.9249i	0.742518	+	1.28608i	−0.208827	+	0.977953i	$0.566965\pi$
$102$	1.22575	+	2.12307i	0.121368	+	0.210215i
$103$		−	12.2047i		−	1.20256i	−0.799038	−	0.601281i	$-0.794657\pi$
$103$		−	12.2047i		−	1.20256i	0.799038	−	0.601281i	$-0.205343\pi$
$104$	3.76986	−	3.76986i	0.369665	−	0.369665i
$105$	−0.523663	+	1.95434i	−0.0511043	+	0.190724i
$106$		−	0.560031i		−	0.0543950i
$107$	−1.17858	+	4.39852i	−0.113938	+	0.425221i	−0.999205	−	0.0398608i	$-0.987309\pi$
$107$	−1.17858	+	4.39852i	−0.113938	+	0.425221i	0.885268	+	0.465082i	$0.153975\pi$
$108$	−8.93276	−	5.15733i	−0.859555	−	0.496265i
$109$	2.93441	−	1.69418i	0.281065	−	0.162273i	−0.352840	−	0.935684i	$-0.614784\pi$
$109$	2.93441	−	1.69418i	0.281065	−	0.162273i	0.633906	+	0.773410i	$0.281451\pi$
$110$	−0.556346	−	0.149072i	−0.0530455	−	0.0142135i
$111$	11.3793	−	11.3793i	1.08008	−	1.08008i
$112$	−1.53211	+	1.53211i	−0.144771	+	0.144771i
$113$	−2.22890	−	0.597233i	−0.209678	−	0.0561830i	0.152451	−	0.988311i	$-0.451283\pi$
$113$	−2.22890	−	0.597233i	−0.209678	−	0.0561830i	−0.362129	+	0.932128i	$0.617950\pi$
$114$	2.43613	+	2.43613i	0.228165	+	0.228165i
$115$	9.95489	−	5.74746i	0.928298	−	0.535953i
$116$	−1.70501	+	6.36318i	−0.158306	+	0.590806i
$117$	0.660005	−	2.46317i	0.0610175	−	0.227720i
$118$	4.76456	+	1.27666i	0.438613	+	0.117526i
$119$	2.02591	−	2.02591i	0.185715	−	0.185715i
$120$	−2.21114	+	3.82980i	−0.201848	+	0.349612i
$121$		−	10.4383i		−	0.948936i
$122$	0.573227	−	2.13931i	0.0518976	−	0.193684i
$123$	−8.66303	−	15.0048i	−0.781119	−	1.35294i
$124$	2.04672	+	7.63847i	0.183801	+	0.685954i
$125$	−12.1516			−1.08687
$126$	0.0563384	−	0.210258i	0.00501902	−	0.0187312i
$127$	−5.39896	+	1.44665i	−0.479080	+	0.128369i	−0.490274	−	0.871568i	$-0.663103\pi$
$127$	−5.39896	+	1.44665i	−0.479080	+	0.128369i	0.0111940	+	0.999937i	$0.496437\pi$
$128$	−9.06409	+	5.23316i	−0.801160	+	0.462550i
$129$	−11.2957	+	3.02668i	−0.994533	+	0.266484i
$130$	−2.53311	−	0.678745i	−0.222168	−	0.0595299i
$131$	13.0125	+	7.51275i	1.13690	+	0.656392i	0.945662	−	0.325151i	$-0.105415\pi$
$131$	13.0125	+	7.51275i	1.13690	+	0.656392i	0.191242	+	0.981543i	$0.438748\pi$
$132$	1.99267	+	0.533933i	0.173439	+	0.0464729i
$133$	2.01321	−	3.48698i	0.174567	−	0.302359i
$134$	3.78781	+	3.78781i	0.327217	+	0.327217i
$135$			10.6068i			0.912891i
$136$	5.42320	−	3.13109i	0.465036	−	0.268489i
$137$	−1.11575	+	1.93253i	−0.0953249	+	0.165108i	−0.909744	−	0.415169i	$-0.863722\pi$
$137$	−1.11575	+	1.93253i	−0.0953249	+	0.165108i	0.814419	+	0.580277i	$0.197056\pi$
$138$	3.22853	−	1.86399i	0.274831	−	0.158674i
$139$	4.59588	+	7.96030i	0.389818	+	0.675184i	0.992425	−	0.122854i	$-0.0392047\pi$
$139$	4.59588	+	7.96030i	0.389818	+	0.675184i	−0.602607	+	0.798038i	$0.705871\pi$
$140$	2.38799	+	0.639860i	0.201822	+	0.0540780i
$141$	3.91782	+	1.04978i	0.329940	+	0.0884072i
$142$	−1.66838	−	0.963239i	−0.140007	−	0.0808332i
$143$			2.55750i			0.213869i
$144$	−1.13260	+	1.96172i	−0.0943832	+	0.163476i
$145$	6.54342	−	1.75330i	0.543401	−	0.145604i
$146$	4.34406	−	4.34406i	0.359517	−	0.359517i
$147$	−9.73944			−0.803296
$148$	−13.9043	−	13.9043i	−1.14292	−	1.14292i
$149$	−0.0114210	+	0.00306025i	−0.000935646	+	0.000250706i	−0.259287	−	0.965800i	$-0.583487\pi$
$149$	−0.0114210	+	0.00306025i	−0.000935646	+	0.000250706i	0.258351	+	0.966051i	$0.416821\pi$
$150$	−0.882834			−0.0720831
$151$	7.17824	−	7.17824i	0.584157	−	0.584157i	−0.351886	−	0.936043i	$-0.614460\pi$
$151$	7.17824	−	7.17824i	0.584157	−	0.584157i	0.936043	+	0.351886i	$0.114460\pi$
$152$	6.22291	−	6.22291i	0.504745	−	0.504745i
$153$	1.49764	−	2.59398i	0.121077	−	0.209711i
$154$			0.218309i			0.0175919i
$155$	5.75014	−	5.75014i	0.461862	−	0.461862i
$156$	9.07286	+	2.43106i	0.726410	+	0.194641i
$157$	−2.44469	−	9.12369i	−0.195107	−	0.728150i	−0.992239	−	0.124345i	$-0.960317\pi$
$157$	−2.44469	−	9.12369i	−0.195107	−	0.728150i	0.797132	−	0.603805i	$-0.206350\pi$
$158$	2.59714	+	0.695901i	0.206617	+	0.0553629i
$159$	1.78634	−	1.03134i	0.141666	−	0.0817908i
$160$	7.12075	+	4.11117i	0.562945	+	0.325016i
$161$	−3.08079	−	3.08079i	−0.242800	−	0.242800i
$162$			2.52640i			0.198493i
$163$	−4.67724	−	2.70041i	−0.366350	−	0.211512i	0.305513	−	0.952188i	$-0.401172\pi$
$163$	−4.67724	−	2.70041i	−0.366350	−	0.211512i	−0.671863	+	0.740676i	$0.734505\pi$
$164$	−18.3342	+	10.5853i	−1.43166	+	0.826572i
$165$	−0.549058	−	2.04911i	−0.0427441	−	0.159523i
$166$	6.05128	−	3.49371i	0.469671	−	0.271164i
$167$	3.19991	+	5.54241i	0.247616	+	0.428884i	0.962864	−	0.269987i	$-0.0870194\pi$
$167$	3.19991	+	5.54241i	0.247616	+	0.428884i	−0.715248	+	0.698871i	$0.753686\pi$
$168$	1.61905	+	0.433824i	0.124913	+	0.0334703i
$169$		−	1.35540i		−	0.104261i
$170$	−2.66764	−	1.54016i	−0.204598	−	0.118125i
$171$	1.08947	−	4.06596i	0.0833140	−	0.310932i
$172$	3.69827	+	13.8021i	0.281991	+	1.05240i
$173$	15.4240	−	4.13286i	1.17267	−	0.314215i	0.380653	−	0.924718i	$-0.375699\pi$
$173$	15.4240	−	4.13286i	1.17267	−	0.314215i	0.792014	+	0.610502i	$0.209032\pi$
$174$	2.12214	−	0.568625i	0.160879	−	0.0431073i
$175$	0.267041	+	0.996611i	0.0201864	+	0.0753367i
$176$	0.587985	−	2.19439i	0.0443211	−	0.165408i
$177$	4.70214	+	17.5486i	0.353435	+	1.31904i
$178$	−0.368381	+	0.212685i	−0.0276114	+	0.0159414i
$179$	−8.50525	+	14.7315i	−0.635712	+	1.10109i	0.350652	+	0.936506i	$0.385960\pi$
$179$	−8.50525	+	14.7315i	−0.635712	+	1.10109i	−0.986364	+	0.164579i	$0.947373\pi$
$180$	2.58458			0.192643
$181$	6.70554	+	1.79674i	0.498419	+	0.133551i	0.499266	−	0.866449i	$-0.333603\pi$
$181$	6.70554	+	1.79674i	0.498419	+	0.133551i	−0.000847351		1.00000i	$0.500270\pi$
$182$			0.993989i			0.0736794i
$183$	7.87944	−	2.11129i	0.582465	−	0.156071i
$184$	−4.76143	−	8.24704i	−0.351017	−	0.607980i
$185$	−5.23347	+	19.5316i	−0.384773	+	1.43599i
$186$	1.86486	−	1.86486i	0.136738	−	0.136738i
$187$	−0.777494	+	2.90165i	−0.0568560	+	0.212189i
$188$	1.28271	−	4.78715i	0.0935516	−	0.349139i
$189$	3.88330	−	1.04053i	0.282469	−	0.0756872i
$190$	−4.18141	−	1.12041i	−0.303351	−	0.0812828i
$191$	−2.12692	+	3.68393i	−0.153898	+	0.266560i	−0.932657	−	0.360763i	$-0.882516\pi$
$191$	−2.12692	+	3.68393i	−0.153898	+	0.266560i	0.778759	+	0.627323i	$0.215850\pi$
$192$	−5.57070	−	3.21625i	−0.402031	−	0.232113i
$193$	−20.7212			−1.49154			−0.745771	−	0.666202i	$-0.767919\pi$
$193$	−20.7212			−1.49154			−0.745771	+	0.666202i	$0.767919\pi$
$194$	−4.96401	+	4.96401i	−0.356395	+	0.356395i
$195$	−2.49993	−	9.32985i	−0.179023	−	0.668125i
$196$			11.9005i			0.850038i
$197$	−0.809306	−	1.40176i	−0.0576607	−	0.0998712i	0.835754	−	0.549104i	$-0.185031\pi$
$197$	−0.809306	−	1.40176i	−0.0576607	−	0.0998712i	−0.893415	+	0.449233i	$0.851697\pi$
$198$	0.0590704	+	0.220454i	0.00419795	+	0.0156670i
$199$	−5.55946	−	20.7482i	−0.394100	−	1.47080i	−0.823308	−	0.567594i	$-0.807874\pi$
$199$	−5.55946	−	20.7482i	−0.394100	−	1.47080i	0.429209	−	0.903205i	$-0.358793\pi$
$200$			2.25513i			0.159462i
$201$	−5.10646	+	19.0576i	−0.360182	+	1.34422i
$202$	−5.26696	−	3.04088i	−0.370582	−	0.213956i
$203$	−1.28381	−	2.22363i	−0.0901061	−	0.156068i
$204$	9.55469	+	5.51640i	0.668962	+	0.386225i
$205$	18.8536	+	10.8851i	1.31679	+	0.760250i
$206$	2.48673	+	4.30714i	0.173258	+	0.300092i
$207$	−3.94466	−	2.27745i	−0.274173	−	0.158294i
$208$	2.67717	−	9.99133i	0.185628	−	0.692774i
$209$			4.22167i			0.292019i
$210$	−0.213395	−	0.796401i	−0.0147257	−	0.0549569i
$211$	−3.17496	−	11.8491i	−0.218573	−	0.815727i	−0.984878	−	0.173249i	$-0.944573\pi$
$211$	−3.17496	−	11.8491i	−0.218573	−	0.815727i	0.766305	−	0.642477i	$-0.222093\pi$
$212$	−1.26019	−	2.18271i	−0.0865501	−	0.149909i
$213$		−	7.09553i		−	0.486178i
$214$	−0.480277	−	1.79242i	−0.0328310	−	0.122527i
$215$	10.3901	−	10.3901i	0.708597	−	0.708597i
$216$	8.78713			0.597889
$217$	−2.66929	−	1.54111i	−0.181203	−	0.104618i
$218$	−0.690386	+	1.19578i	−0.0467588	+	0.0809887i
$219$	21.8562	+	5.85636i	1.47691	+	0.395736i
$220$	−2.50379	+	0.670888i	−0.168805	+	0.0452313i
$221$	−3.54003	+	13.2116i	−0.238128	+	0.888706i
$222$	−1.69730	+	6.33441i	−0.113915	+	0.425138i
$223$	−15.2292	+	15.2292i	−1.01982	+	1.01982i	−0.0200211	+	0.999800i	$0.506373\pi$
$223$	−15.2292	+	15.2292i	−1.01982	+	1.01982i	−0.999800	+	0.0200211i	$0.993627\pi$
$224$	0.806609	−	3.01030i	0.0538938	−	0.201134i
$225$	0.539328	+	0.934144i	0.0359552	+	0.0622763i
$226$	0.908287	−	0.243375i	0.0604184	−	0.0161891i
$227$			4.47123i			0.296766i	0.988930	+	0.148383i	$0.0474069\pi$
$227$			4.47123i			0.296766i	−0.988930	+	0.148383i	$0.952593\pi$
$228$	14.9766	+	4.01296i	0.991849	+	0.265765i
$229$	15.6146			1.03184			0.515921	−	0.856636i	$-0.327450\pi$
$229$	15.6146			1.03184			0.515921	+	0.856636i	$0.327450\pi$
$230$	−2.34211	+	4.05666i	−0.154434	+	0.267488i
$231$	−0.696344	+	0.402034i	−0.0458161	+	0.0264519i
$232$	−1.45251	−	5.42083i	−0.0953618	−	0.355895i
$233$	−3.55399	+	13.2637i	−0.232829	+	0.868931i	0.746286	+	0.665625i	$0.231835\pi$
$233$	−3.55399	+	13.2637i	−0.232829	+	0.868931i	−0.979115	+	0.203306i	$0.934832\pi$
$234$	0.268955	+	1.00375i	0.0175821	+	0.0656174i
$235$	−4.92275	+	1.31905i	−0.321125	+	0.0860452i
$236$	21.4425	−	5.74550i	1.39579	−	0.374000i
$237$	2.56312	+	9.56568i	0.166492	+	0.621358i
$238$	−0.302179	+	1.12775i	−0.0195873	+	0.0731009i
$239$	0.0880973	+	0.0508630i	0.00569854	+	0.00329005i	0.502847	−	0.864376i	$-0.332286\pi$
$239$	0.0880973	+	0.0508630i	0.00569854	+	0.00329005i	−0.497148	+	0.867666i	$0.665619\pi$
$240$			8.57997i			0.553835i
$241$	1.81062	+	0.485153i	0.116632	+	0.0312515i	0.316663	−	0.948538i	$-0.397438\pi$
$241$	1.81062	+	0.485153i	0.116632	+	0.0312515i	−0.200031	+	0.979790i	$0.564104\pi$
$242$	2.12682	+	3.68377i	0.136717	+	0.236802i
$243$	6.55392	−	3.78391i	0.420434	−	0.242738i
$244$	−2.57976	−	9.62781i	−0.165152	−	0.616357i
$245$	10.5981	−	6.11882i	0.677088	−	0.390917i
$246$	6.11452	+	3.53022i	0.389848	+	0.225079i
$247$			19.2218i			1.22305i
$248$	−4.76365	−	4.76365i	−0.302492	−	0.302492i
$249$	22.2879	+	12.8679i	1.41244	+	0.815470i
$250$	4.28840	−	2.47591i	0.271222	−	0.156590i
$251$	−8.76625	−	2.34891i	−0.553321	−	0.148262i	−0.0286848	−	0.999589i	$-0.509132\pi$
$251$	−8.76625	−	2.34891i	−0.553321	−	0.148262i	−0.524636	+	0.851327i	$0.675799\pi$
$252$	−0.253546	−	0.946248i	−0.0159719	−	0.0596080i
$253$	4.41252	+	1.18233i	0.277413	+	0.0743325i
$254$	1.61058	−	1.61058i	0.101057	−	0.101057i
$255$		−	11.3453i		−	0.710471i
$256$	−2.15322	+	3.72948i	−0.134576	+	0.233092i
$257$	−6.06417	+	6.06417i	−0.378272	+	0.378272i	−0.870479	−	0.492206i	$-0.836191\pi$
$257$	−6.06417	+	6.06417i	−0.378272	+	0.378272i	0.492206	+	0.870479i	$0.336191\pi$
$258$	3.36967	−	3.36967i	0.209786	−	0.209786i
$259$	7.66417			0.476228
$260$	−11.4001	+	3.05464i	−0.707002	+	0.189441i
$261$	−1.89810	−	1.89810i	−0.117489	−	0.117489i
$262$	−6.12295			−0.378277
$263$	−9.04021	+	9.04021i	−0.557443	+	0.557443i	−0.928579	−	0.371135i	$-0.878969\pi$
$263$	−9.04021	+	9.04021i	−0.557443	+	0.557443i	0.371135	+	0.928579i	$0.378969\pi$
$264$	−1.69757	+	0.454862i	−0.104478	+	0.0279948i
$265$	−1.29588	+	2.24454i	−0.0796055	+	0.137881i
$266$			1.64078i			0.100603i
$267$	−1.35681	−	0.783354i	−0.0830353	−	0.0479405i
$268$	23.2863	+	6.23954i	1.42244	+	0.381141i
$269$	−17.2200	−	4.61409i	−1.04992	−	0.281326i	−0.307703	−	0.951482i	$-0.599560\pi$
$269$	−17.2200	−	4.61409i	−1.04992	−	0.281326i	−0.742220	+	0.670156i	$0.766227\pi$
$270$	−2.16116	−	3.74325i	−0.131524	−	0.227807i
$271$	−14.7856	+	8.53650i	−0.898164	+	0.518555i	−0.876604	−	0.481212i	$-0.840197\pi$
$271$	−14.7856	+	8.53650i	−0.898164	+	0.518555i	−0.0215600	+	0.999768i	$0.506863\pi$
$272$	6.07484	−	10.5219i	0.368342	−	0.637986i
$273$	−3.17054	+	1.83051i	−0.191890	+	0.110788i
$274$		−	0.909345i		−	0.0549355i
$275$	−0.764949	−	0.764949i	−0.0461282	−	0.0461282i
$276$	8.38876	−	14.5298i	0.504944	−	0.874589i
$277$	15.7522	+	4.22078i	0.946455	+	0.253602i	0.698858	−	0.715261i	$-0.253692\pi$
$277$	15.7522	+	4.22078i	0.946455	+	0.253602i	0.247598	+	0.968863i	$0.420359\pi$
$278$	−3.24386	−	1.87284i	−0.194554	−	0.112326i
$279$	−3.11250	−	0.833992i	−0.186341	−	0.0499298i
$280$	−2.03434	+	0.545101i	−0.121575	+	0.0325760i
$281$	−8.27251	+	4.77613i	−0.493496	+	0.284920i	−0.726024	−	0.687670i	$-0.758634\pi$
$281$	−8.27251	+	4.77613i	−0.493496	+	0.284920i	0.232527	+	0.972590i	$0.425300\pi$
$282$	−1.59653	+	0.427789i	−0.0950720	+	0.0254745i
$283$	−2.49756	+	9.32101i	−0.148464	+	0.554077i	0.851112	+	0.524984i	$0.175929\pi$
$283$	−2.49756	+	9.32101i	−0.148464	+	0.554077i	−0.999577	+	0.0290931i	$0.990738\pi$
$284$	−8.66996			−0.514468
$285$	−4.12663	−	15.4008i	−0.244441	−	0.912265i
$286$	−0.521095	−	0.902564i	−0.0308130	−	0.0533697i
$287$	2.13565	−	7.97037i	0.126064	−	0.470476i
$288$		−	3.25813i		−	0.191987i
$289$	0.467219	−	0.809248i	0.0274835	−	0.0476028i
$290$	−1.95199	+	1.95199i	−0.114625	+	0.114625i
$291$	−24.9754	−	6.69214i	−1.46408	−	0.392300i
$292$	7.15584	−	26.7059i	0.418764	−	1.56285i
$293$	7.68829	−	28.6931i	0.449155	−	1.67627i	−0.255573	−	0.966790i	$-0.582264\pi$
$293$	7.68829	−	28.6931i	0.449155	−	1.67627i	0.704728	−	0.709478i	$-0.251069\pi$
$294$	3.43714	−	1.98443i	0.200458	−	0.115734i
$295$	−16.1416	−	16.1416i	−0.939802	−	0.939802i
$296$	16.1808	+	4.33562i	0.940488	+	0.252003i
$297$	−2.98063	+	2.98063i	−0.172954	+	0.172954i
$298$	0.00340705	−	0.00340705i	0.000197365	−	0.000197365i
$299$	20.0907	+	5.38330i	1.16188	+	0.311324i
$300$	−3.44083	+	1.98656i	−0.198656	+	0.114694i
$301$	−4.82320	−	2.78468i	−0.278005	−	0.160506i
$302$	−1.07068	+	3.99585i	−0.0616109	+	0.229935i
$303$		−	22.4001i		−	1.28685i
$304$	4.41921	−	16.4927i	0.253459	−	0.945922i
$305$	−7.24769	+	7.24769i	−0.415001	+	0.415001i
$306$			1.22059i			0.0697763i
$307$	6.59725	+	11.4268i	0.376525	+	0.652160i	0.990554	−	0.137123i	$-0.0437856\pi$
$307$	6.59725	+	11.4268i	0.376525	+	0.652160i	−0.614029	+	0.789283i	$0.710452\pi$
$308$	0.491242	+	0.850856i	0.0279911	+	0.0484820i
$309$	−9.15901	+	15.8639i	−0.521038	+	0.902464i
$310$	−0.857672	+	3.20088i	−0.0487125	+	0.181798i
$311$	1.52294	−	2.63781i	0.0863581	−	0.149577i	−0.819611	−	0.572920i	$-0.805810\pi$
$311$	1.52294	−	2.63781i	0.0863581	−	0.149577i	0.905969	+	0.423344i	$0.139144\pi$
$312$	−7.72923	+	2.07104i	−0.437581	+	0.117250i
$313$	−8.14021	−	14.0992i	−0.460112	−	0.796937i	0.538854	−	0.842399i	$-0.318857\pi$
$313$	−8.14021	−	14.0992i	−0.460112	−	0.796937i	−0.998966	+	0.0454622i	$0.985524\pi$
$314$	2.72172	+	2.72172i	0.153596	+	0.153596i
$315$	−0.712323	+	0.712323i	−0.0401348	+	0.0401348i
$316$	11.6882	−	3.13185i	0.657514	−	0.176180i
$317$			0.377492i			0.0212021i	0.999944	+	0.0106010i	$0.00337448\pi$
$317$			0.377492i			0.0212021i	−0.999944	+	0.0106010i	$0.996626\pi$
$318$	−0.420276	+	0.727940i	−0.0235679	+	0.0408209i
$319$	2.33146	+	1.34607i	0.130537	+	0.0753655i
$320$	8.08244			0.451822
$321$	4.83282	−	4.83282i	0.269742	−	0.269742i
$322$	1.71496	+	0.459521i	0.0955708	+	0.0256081i
$323$	−5.84353	+	21.8084i	−0.325143	+	1.21345i
$324$	5.68493	+	9.84659i	0.315830	+	0.547033i
$325$	−3.48291	−	3.48291i	−0.193197	−	0.193197i
$326$	2.20085			0.121894
$327$	−5.08561			−0.281235
$328$	9.01767	−	15.6191i	0.497918	−	0.862419i
$329$	0.965842	+	1.67289i	0.0532486	+	0.0922292i
$330$	0.611278	+	0.611278i	0.0336497	+	0.0336497i
$331$	6.76797	+	6.76797i	0.372001	+	0.372001i	0.868206	−	0.496204i	$-0.165273\pi$
$331$	6.76797	+	6.76797i	0.372001	+	0.372001i	−0.496204	+	0.868206i	$0.665273\pi$
$332$	15.7232	−	27.2333i	0.862921	−	1.49462i
$333$	7.73945	−	2.07378i	0.424119	−	0.113642i
$334$	−2.25855	−	1.30398i	−0.123583	−	0.0713504i
$335$	−6.41628	−	23.9459i	−0.350559	−	1.30830i
$336$	3.14124	−	0.841693i	0.171369	−	0.0459181i
$337$	−21.9555	+	12.6760i	−1.19599	+	0.690508i	−0.959660	−	0.281164i	$-0.909279\pi$
$337$	−21.9555	+	12.6760i	−1.19599	+	0.690508i	−0.236335	+	0.971672i	$0.575946\pi$
$338$	0.276165	+	0.478332i	0.0150214	+	0.0260178i
$339$	2.44898	+	2.44898i	0.133010	+	0.133010i
$340$	−13.8627			−0.751813
$341$	3.23169			0.175006
$342$	0.443964	+	1.65690i	0.0240068	+	0.0895947i
$343$	−6.81795	−	6.81795i	−0.368135	−	0.368135i
$344$	−8.60755	−	8.60755i	−0.464088	−	0.464088i
$345$	−17.2528			−0.928858
$346$	−4.60120	+	4.60120i	−0.247362	+	0.247362i
$347$	5.57237	−	20.7964i	0.299141	−	1.11641i	−0.638732	−	0.769429i	$-0.720541\pi$
$347$	5.57237	−	20.7964i	0.299141	−	1.11641i	0.937873	−	0.346979i	$-0.112793\pi$
$348$	6.99146	−	6.99146i	0.374782	−	0.374782i
$349$	−6.91054	+	3.98980i	−0.369913	+	0.213569i	−0.673420	−	0.739260i	$-0.735176\pi$
$349$	−6.91054	+	3.98980i	−0.369913	+	0.213569i	0.303507	+	0.952829i	$0.401842\pi$
$350$	−0.297303	−	0.297303i	−0.0158915	−	0.0158915i
$351$	−13.5712	+	13.5712i	−0.724375	+	0.724375i
$352$	0.845723	+	3.15628i	0.0450772	+	0.168230i
$353$	−22.3972	+	6.00130i	−1.19208	+	0.319417i	−0.799708	−	0.600389i	$-0.795012\pi$
$353$	−22.3972	+	6.00130i	−1.19208	+	0.319417i	−0.392373	+	0.919806i	$0.628346\pi$
$354$	−5.23500	−	5.23500i	−0.278237	−	0.278237i
$355$	4.45777	+	7.72109i	0.236594	+	0.409793i
$356$	−0.957173	+	1.65787i	−0.0507301	+	0.0878670i
$357$	−4.15367	+	1.11297i	−0.219835	+	0.0589047i
$358$		−	6.93184i		−	0.366359i
$359$	9.19452	−	5.30846i	0.485268	−	0.280170i	−0.237341	−	0.971426i	$-0.576276\pi$
$359$	9.19452	−	5.30846i	0.485268	−	0.280170i	0.722609	+	0.691257i	$0.242943\pi$
$360$	−1.90683	+	1.10091i	−0.100499	+	0.0580231i
$361$			12.7294i			0.669970i
$362$	−2.73253	+	0.732180i	−0.143619	+	0.0384825i
$363$	−7.83344	+	13.5679i	−0.411149	+	0.712131i
$364$	2.23669	+	3.87405i	0.117234	+	0.203056i
$365$	−27.4624	+	7.35853i	−1.43745	+	0.385163i
$366$	−2.35054	+	2.35054i	−0.122865	+	0.122865i
$367$	1.95232	+	7.28616i	0.101910	+	0.380334i	0.997976	−	0.0635864i	$-0.0202538\pi$
$367$	1.95232	+	7.28616i	0.101910	+	0.380334i	−0.896066	+	0.443921i	$0.853587\pi$
$368$	−16.0007	−	9.23798i	−0.834092	−	0.481563i
$369$		−	8.62652i		−	0.449079i
$370$	−2.13266	−	7.95920i	−0.110872	−	0.413779i
$371$	0.948880	+	0.254252i	0.0492634	+	0.0132001i
$372$	3.07193	−	11.4646i	0.159272	−	0.594412i
$373$	−23.9012			−1.23756			−0.618779	−	0.785565i	$-0.712373\pi$
$373$	−23.9012			−1.23756			−0.618779	+	0.785565i	$0.712373\pi$
$374$	−0.316832	−	1.18243i	−0.0163830	−	0.0611422i
$375$	15.7949	+	9.11917i	0.815644	+	0.470912i
$376$	1.09275	+	4.07821i	0.0563544	+	0.210318i
$377$	10.6154	+	6.12883i	0.546723	+	0.315651i
$378$	−1.15844	+	1.15844i	−0.0595838	+	0.0595838i
$379$	7.11419			0.365431			0.182716	−	0.983166i	$-0.441511\pi$
$379$	7.11419			0.365431			0.182716	+	0.983166i	$0.441511\pi$
$380$	−18.8181	+	5.04230i	−0.965349	+	0.258664i
$381$	8.10332	+	2.17128i	0.415146	+	0.111238i
$382$		−	1.73346i		−	0.0886914i
$383$	15.2911	+	4.09724i	0.781340	+	0.209359i	0.627375	−	0.778717i	$-0.284129\pi$
$383$	15.2911	+	4.09724i	0.781340	+	0.209359i	0.153964	+	0.988076i	$0.450796\pi$
$384$	15.7089			0.801643
$385$	0.505157	−	0.874957i	0.0257452	−	0.0445920i
$386$	7.31269	−	4.22198i	0.372206	−	0.214893i
$387$	−5.62406	−	1.50696i	−0.285887	−	0.0766032i
$388$	−8.17706	+	30.5172i	−0.415128	+	1.54928i
$389$	−19.4958	+	33.7677i	−0.988476	+	1.71209i	−0.363139	+	0.931735i	$0.618295\pi$
$389$	−19.4958	+	33.7677i	−0.988476	+	1.71209i	−0.625337	+	0.780355i	$0.715038\pi$
$390$	2.78322	+	2.78322i	0.140934	+	0.140934i
$391$	21.1577	+	12.2154i	1.06999	+	0.617760i
$392$	−5.06908	−	8.77990i	−0.256027	−	0.443452i
$393$	−11.2759	−	19.5305i	−0.568794	−	0.985181i
$394$	0.571223	+	0.329796i	0.0287778	+	0.0166149i
$395$	−8.79873	−	8.79873i	−0.442712	−	0.442712i
$396$	0.726293	+	0.726293i	0.0364976	+	0.0364976i
$397$	6.62191	−	3.82316i	0.332344	−	0.191879i	−0.324537	−	0.945873i	$-0.605209\pi$
$397$	6.62191	−	3.82316i	0.332344	−	0.191879i	0.656881	+	0.753994i	$0.271875\pi$
$398$	6.18947	+	6.18947i	0.310250	+	0.310250i
$399$	−5.23362	+	3.02163i	−0.262009	+	0.151271i
$400$	2.18767	+	3.78915i	0.109383	+	0.189458i
$401$		−	26.9888i		−	1.34775i	−0.738843	−	0.673877i	$-0.764628\pi$
$401$		−	26.9888i		−	1.34775i	0.738843	−	0.673877i	$-0.235372\pi$
$402$	−2.08090	−	7.76604i	−0.103786	−	0.387335i
$403$	14.7143			0.732971
$404$	−27.3705			−1.36173
$405$	5.84596	−	10.1255i	0.290488	−	0.503140i
$406$	0.906139	+	0.523160i	0.0449709	+	0.0259640i
$407$	−6.95923	+	4.01792i	−0.344956	+	0.199161i
$408$	−9.39892			−0.465316
$409$	−20.0662	−	2.51972i	−0.992208	−	0.124592i
$409$	−20.0662	−	2.51972i	−0.992208	−	0.124592i
$410$	−8.87146			−0.438130
$411$	2.90055	−	1.67463i	0.143073	−	0.0826035i
$412$	19.3839	+	11.1913i	0.954978	+	0.551357i
$413$	−4.32617	+	7.49315i	−0.212877	+	0.368714i
$414$	1.85614			0.0912243
$415$	−32.3371			−1.58736
$416$	3.85068	+	14.3709i	0.188795	+	0.704594i
$417$		−	13.7960i		−	0.675591i
$418$	−0.860174	−	1.48986i	−0.0420725	−	0.0728716i
$419$	11.6081	−	6.70195i	0.567094	−	0.327412i	−0.188894	−	0.981997i	$-0.560490\pi$
$419$	11.6081	−	6.70195i	0.567094	−	0.327412i	0.755988	+	0.654586i	$0.227157\pi$
$420$	−2.62377	−	2.62377i	−0.128027	−	0.128027i
$421$	−24.7744	+	14.3035i	−1.20743	+	0.697111i	−0.962197	−	0.272354i	$-0.912198\pi$
$421$	−24.7744	+	14.3035i	−1.20743	+	0.697111i	−0.245234	+	0.969464i	$0.578865\pi$
$422$	3.53475	+	3.53475i	0.172069	+	0.172069i
$423$	1.42798	+	1.42798i	0.0694308	+	0.0694308i
$424$	1.85947	+	1.07356i	0.0903037	+	0.0521368i
$425$	−2.89276	−	5.01041i	−0.140319	−	0.243041i
$426$	1.44573	+	2.50408i	0.0700458	+	0.121323i
$427$	3.36447	+	1.94248i	0.162818	+	0.0940031i
$428$	−5.90518	−	5.90518i	−0.285438	−	0.285438i
$429$	1.91928	−	3.32429i	0.0926636	−	0.160498i
$430$	−1.54975	+	5.78374i	−0.0747356	+	0.278917i
$431$	18.4462	+	4.94264i	0.888521	+	0.238078i	0.674080	−	0.738659i	$-0.264540\pi$
$431$	18.4462	+	4.94264i	0.888521	+	0.238078i	0.214441	+	0.976737i	$0.431207\pi$
$432$	14.7645	−	8.52427i	0.710356	−	0.410124i
$433$	18.8371	−	32.6268i	0.905253	−	1.56794i	0.0846757	−	0.996409i	$-0.473015\pi$
$433$	18.8371	−	32.6268i	0.905253	−	1.56794i	0.820577	−	0.571536i	$-0.193652\pi$
$434$	1.25602			0.0602909
$435$	−9.82104	−	2.63154i	−0.470883	−	0.126173i
$436$			6.21406i			0.297599i
$437$	33.1639	+	8.88623i	1.58644	+	0.425086i
$438$	−8.90651	+	2.38649i	−0.425569	+	0.114031i
$439$	−13.0281			−0.621797			−0.310899	−	0.950443i	$-0.600630\pi$
$439$	−13.0281			−0.621797			−0.310899	+	0.950443i	$0.600630\pi$
$440$	1.56146	−	1.56146i	0.0744397	−	0.0744397i
$441$	−4.19953	−	2.42460i	−0.199978	−	0.115457i
$442$	−1.44258	−	5.38376i	−0.0686163	−	0.256080i
$443$	−7.62815	−	4.40411i	−0.362424	−	0.209246i	0.307719	−	0.951477i	$-0.400434\pi$
$443$	−7.62815	−	4.40411i	−0.362424	−	0.209246i	−0.670144	+	0.742231i	$0.733768\pi$
$444$	7.63857	+	28.5075i	0.362510	+	1.35291i
$445$	1.96857			0.0933192
$446$	2.27154	−	8.47748i	0.107560	−	0.401421i
$447$	0.0171418	+	0.00459314i	0.000810781	+	0.000217248i
$448$	−0.792885	−	2.95909i	−0.0374603	−	0.139804i
$449$		−	27.4944i		−	1.29754i	−0.760983	−	0.648772i	$-0.775283\pi$
$449$		−	27.4944i		−	1.29754i	0.760983	−	0.648772i	$-0.224717\pi$
$450$	−0.380667	−	0.219778i	−0.0179448	−	0.0103605i
$451$	2.23922	+	8.35688i	0.105441	+	0.393510i
$452$	2.99239	−	2.99239i	0.140750	−	0.140750i
$453$	−14.7173	+	3.94350i	−0.691481	+	0.185282i
$454$	−0.911023	−	1.57794i	−0.0427564	−	0.0740563i
$455$	2.30004	−	3.98379i	0.107828	−	0.186763i
$456$	−12.7587	+	3.41867i	−0.597479	+	0.160094i
$457$		−	20.8614i		−	0.975854i	−0.872884	−	0.487927i	$-0.837753\pi$
$457$		−	20.8614i		−	0.975854i	0.872884	−	0.487927i	$-0.162247\pi$
$458$	−5.51054	+	3.18151i	−0.257490	+	0.148662i
$459$	−19.5231	+	11.2717i	−0.911260	+	0.526116i
$460$			21.0810i			0.982907i
$461$	37.2998	−	9.99445i	1.73722	−	0.465488i	0.755397	−	0.655267i	$-0.227444\pi$
$461$	37.2998	−	9.99445i	1.73722	−	0.465488i	0.981827	+	0.189779i	$0.0607773\pi$
$462$	0.163831	−	0.283763i	0.00762209	−	0.0132018i
$463$	−7.61580	−	13.1910i	−0.353936	−	0.613036i	0.632999	−	0.774153i	$-0.281824\pi$
$463$	−7.61580	−	13.1910i	−0.353936	−	0.613036i	−0.986935	+	0.161117i	$0.948490\pi$
$464$	−7.69923	−	7.69923i	−0.357428	−	0.357428i
$465$	−11.7893	+	3.15894i	−0.546718	+	0.146493i
$466$	−1.44826	−	5.40499i	−0.0670895	−	0.250382i
$467$	−7.67934	+	7.67934i	−0.355357	+	0.355357i	−0.862098	−	0.506741i	$-0.830850\pi$
$467$	−7.67934	+	7.67934i	−0.355357	+	0.355357i	0.506741	+	0.862098i	$0.330850\pi$
$468$	3.30690	+	3.30690i	0.152862	+	0.152862i
$469$	−8.13747	+	4.69817i	−0.375753	+	0.216941i
$470$	1.46853	−	1.46853i	0.0677380	−	0.0677380i
$471$	−3.66924	+	13.6938i	−0.169070	+	0.630976i
$472$	−13.3724	+	13.3724i	−0.615514	+	0.615514i
$473$	5.83943			0.268497
$474$	−2.85357	−	2.85357i	−0.131069	−	0.131069i
$475$	−5.74924	−	5.74924i	−0.263793	−	0.263793i
$476$	1.35993	+	5.07533i	0.0623323	+	0.232627i
$477$	1.02700			0.0470229
$478$	−0.0414537			−0.00189605
$479$	1.69327	+	1.69327i	0.0773675	+	0.0773675i	0.744732	−	0.667364i	$-0.232578\pi$
$479$	1.69327	+	1.69327i	0.0773675	+	0.0773675i	−0.667364	+	0.744732i	$0.732578\pi$
$480$	−6.17046	−	10.6876i	−0.281642	−	0.487818i
$481$	−31.6862	+	18.2941i	−1.44477	+	0.834138i
$482$	−0.737833	+	0.197702i	−0.0336074	+	0.00900507i
$483$	1.69249	+	6.31646i	0.0770110	+	0.287409i
$484$	16.5785	+	9.57161i	0.753569	+	0.435073i
$485$	31.3816	−	8.40869i	1.42497	−	0.381819i
$486$	−1.54196	+	2.67075i	−0.0699447	+	0.121148i
$487$	−23.0244	−	23.0244i	−1.04334	−	1.04334i	−0.999017	−	0.0443197i	$-0.985888\pi$
$487$	−23.0244	−	23.0244i	−1.04334	−	1.04334i	−0.0443197	−	0.999017i	$-0.514112\pi$
$488$	6.00428	+	6.00428i	0.271801	+	0.271801i
$489$	4.05305	+	7.02009i	0.183285	+	0.317459i
$490$	−2.49344	+	4.31877i	−0.112642	+	0.195102i
$491$	35.1553			1.58654			0.793268	−	0.608873i	$-0.208378\pi$
$491$	35.1553			1.58654			0.793268	+	0.608873i	$0.208378\pi$
$492$	31.7750			1.43253
$493$	10.1807	+	10.1807i	0.458516	+	0.458516i
$494$	−3.91648	−	6.78354i	−0.176211	−	0.305206i
$495$	0.273372	−	1.02024i	0.0122871	−	0.0458563i
$496$	−12.6252	−	3.38291i	−0.566888	−	0.151897i
$497$	2.38949	−	2.38949i	0.107183	−	0.107183i
$498$	−10.4874			−0.469954
$499$	16.3175	+	9.42091i	0.730471	+	0.421738i	0.818595	−	0.574372i	$-0.194754\pi$
$499$	16.3175	+	9.42091i	0.730471	+	0.421738i	−0.0881233	+	0.996110i	$0.528087\pi$
$500$	11.1426	−	19.2996i	0.498314	−	0.863105i
$501$		−	9.60551i		−	0.429143i
$502$	3.57228	−	0.957190i	0.159439	−	0.0427215i
$503$	−2.45715	+	2.45715i	−0.109559	+	0.109559i	−0.759761	−	0.650202i	$-0.774684\pi$
$503$	−2.45715	+	2.45715i	−0.109559	+	0.109559i	0.650202	+	0.759761i	$0.274684\pi$
$504$	0.590117	+	0.590117i	0.0262859	+	0.0262859i
$505$	14.0729	+	24.3750i	0.626236	+	1.08467i
$506$	−1.79812	+	0.481805i	−0.0799362	+	0.0214188i
$507$	−1.01716	+	1.76177i	−0.0451737	+	0.0782431i
$508$	2.65306	−	9.90137i	0.117711	−	0.439302i
$509$	21.7219	−	37.6234i	0.962805	−	1.66763i	0.247405	−	0.968912i	$-0.420422\pi$
$509$	21.7219	−	37.6234i	0.962805	−	1.66763i	0.715400	−	0.698715i	$-0.246245\pi$
$510$	2.31163	+	4.00386i	0.102361	+	0.177294i
$511$	5.38811	+	9.33248i	0.238356	+	0.412845i
$512$		−	22.6875i		−	1.00266i
$513$	−22.4020	+	22.4020i	−0.989071	+	0.989071i
$514$	0.904512	−	3.37569i	0.0398963	−	0.148895i
$515$		−	23.0166i		−	1.01423i
$516$	5.55075	−	20.7157i	0.244358	−	0.911957i
$517$	−1.75401	−	1.01268i	−0.0771413	−	0.0445375i
$518$	−2.70475	+	1.56159i	−0.118840	+	0.0686124i
$519$	−23.1500	−	6.20302i	−1.01617	−	0.272282i
$520$	7.10953	−	7.10953i	0.311773	−	0.311773i
$521$	1.15643	−	1.15643i	0.0506642	−	0.0506642i	−0.681321	−	0.731985i	$-0.738594\pi$
$521$	1.15643	−	1.15643i	0.0506642	−	0.0506642i	0.731985	+	0.681321i	$0.238594\pi$
$522$	1.05660	+	0.283114i	0.0462460	+	0.0123916i
$523$	3.89350	+	3.89350i	0.170251	+	0.170251i	0.787090	−	0.616839i	$-0.211587\pi$
$523$	3.89350	+	3.89350i	0.170251	+	0.170251i	−0.616839	+	0.787090i	$0.711587\pi$
$524$	−23.8641	+	13.7779i	−1.04251	+	0.601892i
$525$	0.400803	−	1.49582i	0.0174925	−	0.0652828i
$526$	1.34841	−	5.03233i	0.0587935	−	0.219420i
$527$	16.6943	+	4.47323i	0.727216	+	0.194857i
$528$	−2.41106	+	2.41106i	−0.104928	+	0.104928i
$529$	7.07591	−	12.2558i	0.307648	−	0.532862i
$530$		−	1.05616i		−	0.0458765i
$531$	−2.34116	+	8.73734i	−0.101598	+	0.379168i
$532$	3.69210	+	6.39491i	0.160073	+	0.277254i
$533$	10.1954	+	38.0499i	0.441613	+	1.64812i
$534$	0.638440			0.0276280
$535$	−2.22267	+	8.29512i	−0.0960945	+	0.358629i
$536$	−19.8377	+	5.31551i	−0.856860	+	0.229595i
$537$	22.1106	−	12.7656i	0.954142	−	0.550874i
$538$	7.01723	−	1.88026i	0.302534	−	0.0810638i
$539$	4.69762	+	1.25872i	0.202341	+	0.0542171i
$540$	−16.8462	−	9.72615i	−0.724945	−	0.418547i
$541$	0.945664	+	0.253390i	0.0406572	+	0.0108941i	0.279090	−	0.960265i	$-0.409967\pi$
$541$	0.945664	+	0.253390i	0.0406572	+	0.0108941i	−0.238433	+	0.971159i	$0.576634\pi$
$542$	3.47866	−	6.02521i	0.149421	−	0.258805i
$543$	−7.36763	−	7.36763i	−0.316175	−	0.316175i
$544$			17.4754i			0.749252i
$545$	5.53397	−	3.19504i	0.237049	−	0.136860i
$546$	0.745941	−	1.29201i	0.0319233	−	0.0552928i
$547$	14.9372	−	8.62397i	0.638666	−	0.368734i	−0.145434	−	0.989368i	$-0.546458\pi$
$547$	14.9372	−	8.62397i	0.638666	−	0.368734i	0.784101	+	0.620634i	$0.213125\pi$
$548$	−2.04622	−	3.54415i	−0.0874101	−	0.151399i
$549$	3.92311	+	1.05120i	0.167434	+	0.0448639i
$550$	0.425817	+	0.114097i	0.0181569	+	0.00486513i
$551$	17.5229	+	10.1169i	0.746502	+	0.430993i
$552$			14.2929i			0.608346i
$553$	−2.35818	+	4.08449i	−0.100280	+	0.173690i
$554$	−6.41907	+	1.71998i	−0.272720	+	0.0730751i
$555$	21.4601	−	21.4601i	0.910930	−	0.910930i
$556$	−16.8572			−0.714903
$557$	7.47466	+	7.47466i	0.316712	+	0.316712i	0.847503	−	0.530791i	$-0.178105\pi$
$557$	7.47466	+	7.47466i	0.316712	+	0.316712i	−0.530791	+	0.847503i	$0.678105\pi$
$558$	1.26836	−	0.339855i	0.0536938	−	0.0143872i
$559$	26.5876			1.12454
$560$	−2.88939	+	2.88939i	−0.122099	+	0.122099i
$561$	3.18815	−	3.18815i	0.134604	−	0.134604i
$562$	1.94629	−	3.37108i	0.0820994	−	0.142200i
$563$		−	40.8941i		−	1.72348i	−0.507349	−	0.861741i	$-0.669375\pi$
$563$		−	40.8941i		−	1.72348i	0.507349	−	0.861741i	$-0.330625\pi$
$564$	−5.25983	+	5.25983i	−0.221479	+	0.221479i
$565$	−4.20346	−	1.12631i	−0.176841	−	0.0473844i
$566$	−1.01777	−	3.79835i	−0.0427799	−	0.159657i
$567$	−4.28057	−	1.14697i	−0.179767	−	0.0481684i
$568$	6.39646	−	3.69300i	0.268390	−	0.154955i
$569$	14.4715	+	8.35513i	0.606677	+	0.350265i	0.771664	−	0.636031i	$-0.219425\pi$
$569$	14.4715	+	8.35513i	0.606677	+	0.350265i	−0.164987	+	0.986296i	$0.552758\pi$
$570$	4.59427	+	4.59427i	0.192433	+	0.192433i
$571$		−	6.07048i		−	0.254042i	−0.991900	−	0.127021i	$-0.959458\pi$
$571$		−	6.07048i		−	0.254042i	0.991900	−	0.127021i	$-0.0405415\pi$
$572$	−4.06192	−	2.34515i	−0.169837	−	0.0980556i
$573$	5.52923	−	3.19230i	0.230987	−	0.133360i
$574$	0.870288	+	3.24796i	0.0363251	+	0.135567i
$575$	−7.61930	+	4.39901i	−0.317747	+	0.183451i
$576$	−1.60135	−	2.77361i	−0.0667228	−	0.115567i
$577$	14.3488	+	3.84474i	0.597347	+	0.160059i	0.544809	−	0.838560i	$-0.316602\pi$
$577$	14.3488	+	3.84474i	0.597347	+	0.160059i	0.0525382	+	0.998619i	$0.483269\pi$
$578$			0.380788i			0.0158387i
$579$	26.9338	+	15.5502i	1.11933	+	0.646246i
$580$	−3.21545	+	12.0002i	−0.133514	+	0.498283i
$581$	3.17226	+	11.8390i	0.131607	+	0.491166i
$582$	10.1776	−	2.72707i	0.421874	−	0.113041i
$583$	−0.994895	+	0.266581i	−0.0412043	+	0.0110407i
$584$	6.09611	+	22.7510i	0.252259	+	0.941442i
$585$	1.24470	−	4.64527i	0.0514618	−	0.192058i
$586$	3.13301	+	11.6925i	0.129423	+	0.483015i
$587$	−35.9691	+	20.7668i	−1.48460	+	0.857136i	−0.999847	−	0.0175131i	$-0.994425\pi$
$587$	−35.9691	+	20.7668i	−1.48460	+	0.857136i	−0.484757	+	0.874649i	$0.661092\pi$
$588$	8.93078	−	15.4686i	0.368299	−	0.637913i
$589$	24.2889			1.00081
$590$	8.98542	+	2.40764i	0.369924	+	0.0991208i
$591$			2.42938i			0.0999314i
$592$	31.3934	−	8.41185i	1.29026	−	0.345725i
$593$	3.17574	+	5.50054i	0.130412	+	0.225880i	0.923835	−	0.382790i	$-0.125037\pi$
$593$	3.17574	+	5.50054i	0.130412	+	0.225880i	−0.793424	+	0.608670i	$0.791703\pi$
$594$	0.444581	−	1.65920i	0.0182414	−	0.0680778i
$595$	3.82064	−	3.82064i	0.156631	−	0.156631i
$596$	0.00561232	−	0.0209455i	0.000229890	−	0.000857960i
$597$	−8.34421	+	31.1410i	−0.341506	+	1.27452i
$598$	−8.18706	+	2.19372i	−0.334794	+	0.0897078i
$599$	12.7448	+	3.41496i	0.520738	+	0.139531i	0.509608	−	0.860407i	$-0.329790\pi$
$599$	12.7448	+	3.41496i	0.520738	+	0.139531i	0.0111303	+	0.999938i	$0.496457\pi$
$600$	1.69237	−	2.93127i	0.0690906	−	0.119668i
$601$	−15.6160	−	9.01591i	−0.636991	−	0.367767i	0.146464	−	0.989216i	$-0.453211\pi$
$601$	−15.6160	−	9.01591i	−0.636991	−	0.367767i	−0.783454	+	0.621449i	$0.786544\pi$
$602$	2.26953			0.0924993
$603$	−6.94616	+	6.94616i	−0.282870	+	0.282870i
$604$	4.81853	+	17.9830i	0.196063	+	0.731717i
$605$		−	19.6855i		−	0.800328i
$606$	4.56407	+	7.90520i	0.185403	+	0.321127i
$607$	−1.47634	−	5.50979i	−0.0599229	−	0.223635i	0.929470	−	0.368897i	$-0.120264\pi$
$607$	−1.47634	−	5.50979i	−0.0599229	−	0.223635i	−0.989393	+	0.145261i	$0.953598\pi$
$608$	6.35633	+	23.7222i	0.257783	+	0.962060i
$609$			3.85376i			0.156162i
$610$	1.08104	−	4.03451i	0.0437701	−	0.163352i
$611$	−7.98622	−	4.61085i	−0.323088	−	0.186535i
$612$	2.74658	+	4.75721i	0.111024	+	0.192299i
$613$	−15.2728	−	8.81774i	−0.616861	−	0.356145i	0.158785	−	0.987313i	$-0.449242\pi$
$613$	−15.2728	−	8.81774i	−0.616861	−	0.356145i	−0.775646	+	0.631168i	$0.782576\pi$
$614$	−4.65646	−	2.68841i	−0.187919	−	0.108495i
$615$	−16.3375	−	28.2974i	−0.658792	−	1.14106i
$616$	−0.724850	−	0.418493i	−0.0292051	−	0.0168615i
$617$	−7.97065	+	29.7469i	−0.320886	+	1.19756i	0.597497	+	0.801871i	$0.296162\pi$
$617$	−7.97065	+	29.7469i	−0.320886	+	1.19756i	−0.918383	+	0.395693i	$0.870505\pi$
$618$		−	7.46467i		−	0.300273i
$619$	−1.82741	−	6.81998i	−0.0734497	−	0.274118i	0.919428	−	0.393259i	$-0.128653\pi$
$619$	−1.82741	−	6.81998i	−0.0734497	−	0.274118i	−0.992877	+	0.119141i	$0.961986\pi$
$620$	3.85989	+	14.4053i	0.155017	+	0.578530i
$621$	17.1408	+	29.6887i	0.687835	+	1.19136i
$622$			1.24121i			0.0497680i
$623$	−0.193116	−	0.720720i	−0.00773704	−	0.0288750i
$624$	−10.9778	+	10.9778i	−0.439466	+	0.439466i
$625$	−15.6994			−0.627976
$626$	5.74550	+	3.31717i	0.229636	+	0.132581i
$627$	3.16816	−	5.48741i	0.126524	−	0.219146i
$628$	16.7323	+	4.48341i	0.667692	+	0.178907i
$629$	−41.5116	+	11.1230i	−1.65518	+	0.443503i
$630$	0.106248	−	0.396522i	0.00423302	−	0.0157978i
$631$	−6.80514	+	25.3971i	−0.270908	+	1.01104i	0.687626	+	0.726065i	$0.258653\pi$
$631$	−6.80514	+	25.3971i	−0.270908	+	1.01104i	−0.958534	+	0.284978i	$0.908014\pi$
$632$	−7.28923	+	7.28923i	−0.289950	+	0.289950i
$633$	−4.76531	+	17.7844i	−0.189404	+	0.706865i
$634$	−0.0769148	−	0.133220i	−0.00305468	−	0.00529085i
$635$	−10.1818	+	2.72821i	−0.404054	+	0.108266i
$636$			3.78284i			0.149999i
$637$	21.3889	+	5.73113i	0.847457	+	0.227075i
$638$	−1.09706			−0.0434330
$639$	1.76641	−	3.05951i	0.0698780	−	0.121032i
$640$	−17.0939	+	9.86915i	−0.675694	+	0.390112i
$641$	−4.21439	−	15.7283i	−0.166458	−	0.621231i	−0.997850	−	0.0655434i	$-0.979122\pi$
$641$	−4.21439	−	15.7283i	−0.166458	−	0.621231i	0.831391	−	0.555687i	$-0.187545\pi$
$642$	−0.720849	+	2.69024i	−0.0284496	+	0.106175i
$643$	5.17366	+	19.3084i	0.204029	+	0.761448i	0.989743	+	0.142858i	$0.0456292\pi$
$643$	5.17366	+	19.3084i	0.204029	+	0.761448i	−0.785714	+	0.618590i	$0.787704\pi$
$644$	7.71803	−	2.06804i	0.304133	−	0.0814922i
$645$	−21.3025	+	5.70798i	−0.838784	+	0.224751i
$646$	−2.38126	−	8.88699i	−0.0936895	−	0.349654i
$647$	10.5687	−	39.4430i	0.415500	−	1.55067i	−0.368333	−	0.929694i	$-0.620071\pi$
$647$	10.5687	−	39.4430i	0.415500	−	1.55067i	0.783833	−	0.620972i	$-0.213262\pi$
$648$	−8.38838	−	4.84303i	−0.329527	−	0.190252i
$649$		−	9.07193i		−	0.356104i
$650$	1.93880	+	0.519499i	0.0760459	+	0.0203764i
$651$	2.31306	+	4.00634i	0.0906560	+	0.157021i
$652$	8.57778	−	4.95239i	0.335932	−	0.193950i
$653$	−0.771043	−	2.87757i	−0.0301732	−	0.112608i	0.949197	−	0.314683i	$-0.101898\pi$
$653$	−0.771043	−	2.87757i	−0.0301732	−	0.112608i	−0.979370	+	0.202075i	$0.935232\pi$
$654$	1.79476	−	1.03620i	0.0701805	−	0.0405187i
$655$	24.5401	+	14.1682i	0.958859	+	0.553598i
$656$		−	34.9916i		−	1.36619i
$657$	7.96622	+	7.96622i	0.310792	+	0.310792i
$658$	−0.681708	−	0.393584i	−0.0265758	−	0.0153435i
$659$	37.1949	−	21.4745i	1.44891	−	0.836528i	0.450492	−	0.892780i	$-0.351249\pi$
$659$	37.1949	−	21.4745i	1.44891	−	0.836528i	0.998417	+	0.0562526i	$0.0179152\pi$
$660$	3.75795	+	1.00694i	0.146278	+	0.0391950i
$661$	−5.87852	−	21.9389i	−0.228648	−	0.853326i	−0.980910	−	0.194462i	$-0.937704\pi$
$661$	−5.87852	−	21.9389i	−0.228648	−	0.853326i	0.752262	−	0.658864i	$-0.228963\pi$
$662$	−3.76747	−	1.00949i	−0.146427	−	0.0392349i
$663$	14.5160	−	14.5160i	0.563756	−	0.563756i
$664$			26.7894i			1.03963i
$665$	3.79668	−	6.57605i	0.147229	−	0.255008i
$666$	−2.30878	+	2.30878i	−0.0894636	+	0.0894636i
$667$	15.4817	−	15.4817i	0.599456	−	0.599456i
$668$	−11.7369			−0.454114
$669$	31.2239	−	8.36643i	1.20719	−	0.323465i
$670$	7.14339	+	7.14339i	0.275973	+	0.275973i
$671$	−4.07335			−0.157250
$672$	−3.30753	+	3.30753i	−0.127591	+	0.127591i
$673$	−8.33794	+	2.23414i	−0.321404	+	0.0861200i	−0.415914	−	0.909404i	$-0.636538\pi$
$673$	−8.33794	+	2.23414i	−0.321404	+	0.0861200i	0.0945099	+	0.995524i	$0.469872\pi$
$674$	5.16554	−	8.94697i	0.198969	−	0.344624i
$675$		−	8.11829i		−	0.312473i
$676$	2.15269	+	1.24286i	0.0827959	+	0.0478023i
$677$	−24.6744	−	6.61149i	−0.948314	−	0.254100i	−0.248668	−	0.968589i	$-0.579993\pi$
$677$	−24.6744	−	6.61149i	−0.948314	−	0.254100i	−0.699647	+	0.714489i	$0.746659\pi$
$678$	−1.36325	−	0.365282i	−0.0523554	−	0.0140286i
$679$	−6.15706	−	10.6643i	−0.236286	−	0.409260i
$680$	10.2276	−	5.90488i	0.392209	−	0.226442i
$681$	3.35544	−	5.81180i	0.128581	−	0.222709i
$682$	−1.14049	+	0.658464i	−0.0436717	+	0.0252139i
$683$			30.0336i			1.14920i	0.818433	+	0.574601i	$0.194843\pi$
$683$			30.0336i			1.14920i	−0.818433	+	0.574601i	$0.805157\pi$
$684$	5.45871	+	5.45871i	0.208719	+	0.208719i
$685$	−2.10418	+	3.64454i	−0.0803965	+	0.139251i
$686$	3.79529	+	1.01694i	0.144905	+	0.0388271i
$687$	−20.2962	−	11.7180i	−0.774348	−	0.447070i
$688$	−22.8128	−	6.11267i	−0.869729	−	0.233043i
$689$	−4.52988	+	1.21378i	−0.172575	+	0.0462412i
$690$	6.08865	−	3.51529i	0.231791	−	0.133825i
$691$	8.35612	−	2.23902i	0.317882	−	0.0851762i	−0.0963502	−	0.995347i	$-0.530717\pi$
$691$	8.35612	−	2.23902i	0.317882	−	0.0851762i	0.414232	+	0.910171i	$0.364050\pi$
$692$	−7.57942	+	28.2868i	−0.288126	+	1.07530i
$693$	−0.400340			−0.0152077
$694$	2.27077	+	8.47461i	0.0861971	+	0.321692i
$695$	8.66732	+	15.0122i	0.328770	+	0.569447i
$696$	−2.18007	+	8.13615i	−0.0826355	+	0.308400i
$697$			46.2695i			1.75258i
$698$	1.62586	−	2.81607i	0.0615398	−	0.106590i
$699$	14.5733	−	14.5733i	0.551212	−	0.551212i
$700$	−1.82773	−	0.489738i	−0.0690815	−	0.0185103i
$701$	−0.433969	+	1.61960i	−0.0163908	+	0.0611713i	−0.973637	−	0.228104i	$-0.926748\pi$
$701$	−0.433969	+	1.61960i	−0.0163908	+	0.0611713i	0.957246	+	0.289275i	$0.0934142\pi$
$702$	2.02423	−	7.55454i	0.0763997	−	0.285128i
$703$	−52.3046	+	30.1981i	−1.97270	+	1.13894i
$704$	2.27125	+	2.27125i	0.0856009	+	0.0856009i
$705$	7.38858	+	1.97976i	0.278270	+	0.0745622i
$706$	6.68138	−	6.68138i	0.251457	−	0.251457i
$707$	7.54345	−	7.54345i	0.283701	−	0.283701i
$708$	−32.1831	−	8.62345i	−1.20952	−	0.324089i
$709$	24.7862	−	14.3103i	0.930867	−	0.537436i	0.0437812	−	0.999041i	$-0.486060\pi$
$709$	24.7862	−	14.3103i	0.930867	−	0.537436i	0.887086	+	0.461605i	$0.152726\pi$
$710$	−3.14638	−	1.81656i	−0.118081	−	0.0681743i
$711$	−1.27616	+	4.76268i	−0.0478596	+	0.178615i
$712$		−	1.63084i		−	0.0611185i
$713$	6.80242	−	25.3870i	0.254753	−	0.950750i
$714$	1.23910	−	1.23910i	0.0463720	−	0.0463720i
$715$			4.82316i			0.180376i
$716$	−15.5981	−	27.0167i	−0.582929	−	1.00966i
$717$	−0.0763404	−	0.132225i	−0.00285098	−	0.00493805i
$718$	−2.16322	+	3.74681i	−0.0807306	+	0.139830i
$719$	−9.04899	+	33.7713i	−0.337471	+	1.25946i	0.563695	+	0.825983i	$0.309379\pi$
$719$	−9.04899	+	33.7713i	−0.337471	+	1.25946i	−0.901166	+	0.433474i	$0.857287\pi$
$720$	−2.13595	+	3.69958i	−0.0796023	+	0.137875i
$721$	−8.42669	+	2.25793i	−0.313826	+	0.0840895i
$722$	−2.59365	−	4.49233i	−0.0965256	−	0.167187i
$723$	−1.98939	−	1.98939i	−0.0739863	−	0.0739863i
$724$	−9.00244	+	9.00244i	−0.334573	+	0.334573i
$725$	−5.00822	+	1.34195i	−0.186001	+	0.0498387i
$726$		−	6.38432i		−	0.236944i
$727$	7.35658	−	12.7420i	0.272840	−	0.472573i	−0.696748	−	0.717316i	$-0.745370\pi$
$727$	7.35658	−	12.7420i	0.272840	−	0.472573i	0.969588	+	0.244743i	$0.0787036\pi$
$728$	−3.30033	−	1.90545i	−0.122318	−	0.0706206i
$729$	−29.9576			−1.10954
$730$	8.19241	−	8.19241i	0.303215	−	0.303215i
$731$	30.1654	+	8.08279i	1.11571	+	0.298953i
$732$	−3.87198	+	14.4504i	−0.143112	+	0.534103i
$733$	15.6789	+	27.1567i	0.579115	+	1.00306i	0.995581	+	0.0939052i	$0.0299351\pi$
$733$	15.6789	+	27.1567i	0.579115	+	1.00306i	−0.416466	+	0.909151i	$0.636732\pi$
$734$	−2.17356	−	2.17356i	−0.0802276	−	0.0802276i
$735$	−18.3675			−0.677495
$736$	26.5748			0.979558
$737$	4.92600	−	8.53208i	0.181451	−	0.314283i
$738$	1.75767	+	3.04438i	0.0647008	+	0.112065i
$739$	−30.2837	−	30.2837i	−1.11401	−	1.11401i	−0.992603	−	0.121402i	$-0.961261\pi$
$739$	−30.2837	−	30.2837i	−1.11401	−	1.11401i	−0.121402	−	0.992603i	$-0.538739\pi$
$740$	−26.2219	−	26.2219i	−0.963936	−	0.963936i
$741$	14.4250	−	24.9849i	0.529916	−	0.917842i
$742$	−0.386673	+	0.103609i	−0.0141952	+	0.00380359i
$743$	−46.3544	−	26.7627i	−1.70058	−	0.981830i	−0.945172	−	0.326574i	$-0.894106\pi$
$743$	−46.3544	−	26.7627i	−1.70058	−	0.981830i	−0.755407	−	0.655256i	$-0.772561\pi$
$744$	2.61700	+	9.76677i	0.0959438	+	0.358067i
$745$	−0.0215388	+	0.00577129i	−0.000789119	+	0.000211444i
$746$	8.43496	−	4.86992i	0.308826	−	0.178301i
$747$	6.40683	+	11.0970i	0.234414	+	0.406017i
$748$	−3.89557	−	3.89557i	−0.142436	−	0.142436i
$749$	3.25500			0.118935
$750$	−7.43220			−0.271386
$751$	−6.13628	−	22.9009i	−0.223916	−	0.835666i	−0.982836	−	0.184482i	$-0.940939\pi$
$751$	−6.13628	−	22.9009i	−0.223916	−	0.835666i	0.758920	−	0.651184i	$-0.225727\pi$
$752$	5.79230	+	5.79230i	0.211223	+	0.211223i
$753$	9.63181	+	9.63181i	0.351003	+	0.351003i
$754$	−4.99504			−0.181909
$755$	13.5374	−	13.5374i	0.492675	−	0.492675i
$756$	−1.90827	+	7.12174i	−0.0694029	+	0.259015i
$757$	−28.6199	+	28.6199i	−1.04021	+	1.04021i	−0.0410519	+	0.999157i	$0.513071\pi$
$757$	−28.6199	+	28.6199i	−1.04021	+	1.04021i	−0.999157	+	0.0410519i	$0.986929\pi$
$758$	−2.51066	+	1.44953i	−0.0911913	+	0.0526493i
$759$	−4.84820	−	4.84820i	−0.175979	−	0.175979i
$760$	11.7357	−	11.7357i	0.425699	−	0.425699i
$761$	5.37799	+	20.0709i	0.194952	+	0.727571i	0.992279	+	0.124024i	$0.0395799\pi$
$761$	5.37799	+	20.0709i	0.194952	+	0.727571i	−0.797327	+	0.603547i	$0.793753\pi$
$762$	−3.30214	+	0.884805i	−0.119624	+	0.0320531i
$763$	−1.71263	−	1.71263i	−0.0620012	−	0.0620012i
$764$	−3.90064	−	6.75611i	−0.141120	−	0.244428i
$765$	2.82438	−	4.89196i	0.102116	−	0.176869i
$766$	−6.23119	+	1.66964i	−0.225142	+	0.0603267i
$767$		−	41.3056i		−	1.49146i
$768$	5.59759	−	3.23177i	0.201986	−	0.116616i
$769$	11.2308	−	6.48409i	0.404992	−	0.233822i	−0.283644	−	0.958930i	$-0.591543\pi$
$769$	11.2308	−	6.48409i	0.404992	−	0.233822i	0.688636	+	0.725108i	$0.258210\pi$
$770$			0.411707i			0.0148369i
$771$	12.4332	−	3.33146i	0.447771	−	0.119980i
$772$	19.0007	−	32.9102i	0.683850	−	1.18446i
$773$	8.45446	+	14.6436i	0.304086	+	0.526692i	0.977057	−	0.212976i	$-0.0683157\pi$
$773$	8.45446	+	14.6436i	0.304086	+	0.526692i	−0.672972	+	0.739668i	$0.734982\pi$
$774$	2.29183	−	0.614093i	0.0823780	−	0.0220731i
$775$	−4.40105	+	4.40105i	−0.158091	+	0.158091i
$776$	−6.96610	−	25.9978i	−0.250068	−	0.933268i
$777$	−9.96205	−	5.75159i	−0.357386	−	0.206337i
$778$		−	15.8892i		−	0.569656i
$779$	16.8296	+	62.8090i	0.602984	+	2.25037i
$780$	17.1104	+	4.58472i	0.612650	+	0.164159i
$781$	−0.917025	+	3.42238i	−0.0328137	+	0.122463i
$782$	−9.95566			−0.356014
$783$	5.22891	+	19.5146i	0.186866	+	0.697393i
$784$	−17.0345	−	9.83487i	−0.608375	−	0.351245i
$785$	−4.61040	−	17.2063i	−0.164552	−	0.614118i
$786$	7.95874	+	4.59498i	0.283879	+	0.163898i
$787$	−17.3458	+	17.3458i	−0.618311	+	0.618311i	−0.945098	−	0.326787i	$-0.894034\pi$
$787$	−17.3458	+	17.3458i	−0.618311	+	0.618311i	0.326787	+	0.945098i	$0.394034\pi$
$788$	2.96844			0.105746
$789$	18.5349	−	4.96641i	0.659860	−	0.176809i
$790$	4.89791	+	1.31239i	0.174260	+	0.0466928i
$791$			1.64943i			0.0586471i
$792$	−0.845206	−	0.226472i	−0.0300331	−	0.00804734i
$793$	−18.5465			−0.658604
$794$	−1.55795	+	2.69846i	−0.0552897	+	0.0957646i
$795$	3.36883	−	1.94500i	0.119480	−	0.0689819i
$796$	38.0509	+	10.1957i	1.34868	+	0.361378i
$797$	−4.04652	+	15.1018i	−0.143335	+	0.534934i	0.856489	+	0.516166i	$0.172641\pi$
$797$	−4.04652	+	15.1018i	−0.143335	+	0.534934i	−0.999824	+	0.0187685i	$0.994025\pi$
$798$	1.23133	−	2.13272i	0.0435885	−	0.0754975i
$799$	−7.65916	−	7.65916i	−0.270962	−	0.270962i
$800$	−5.45010	−	3.14662i	−0.192690	−	0.111250i
$801$	−0.390026	−	0.675545i	−0.0137809	−	0.0238692i
$802$	5.49902	+	9.52458i	0.194177	+	0.336324i
$803$	−9.78504	−	5.64939i	−0.345306	−	0.199363i
$804$	−25.5855	−	25.5855i	−0.902332	−	0.902332i
$805$	−5.81003	−	5.81003i	−0.204777	−	0.204777i
$806$	−5.19281	+	2.99807i	−0.182909	+	0.105602i
$807$	18.9203	+	18.9203i	0.666026	+	0.666026i
$808$	20.1932	−	11.6586i	0.710395	−	0.410147i
$809$	19.8471	+	34.3762i	0.697787	+	1.20860i	0.969232	+	0.246149i	$0.0791651\pi$
$809$	19.8471	+	34.3762i	0.697787	+	1.20860i	−0.271445	+	0.962454i	$0.587502\pi$
$810$			4.76451i			0.167408i
$811$	−3.35237	−	12.5112i	−0.117718	−	0.439329i	0.881758	−	0.471702i	$-0.156360\pi$
$811$	−3.35237	−	12.5112i	−0.117718	−	0.439329i	−0.999476	+	0.0323732i	$0.989693\pi$
$812$	4.70888			0.165249
$813$	25.6249			0.898705
$814$	1.63732	−	2.83592i	0.0573879	−	0.0993988i
$815$	−8.82076	−	5.09267i	−0.308978	−	0.178388i
$816$	−15.7924	+	9.11775i	−0.552845	+	0.319185i
$817$	43.8883			1.53546
$818$	7.59493	−	3.19929i	0.265550	−	0.111861i
$819$	−1.82280			−0.0636937
$820$	−34.5763	+	19.9627i	−1.20746	+	0.697126i
$821$	−32.6543	−	18.8530i	−1.13964	−	0.657973i	−0.193301	−	0.981140i	$-0.561919\pi$
$821$	−32.6543	−	18.8530i	−1.13964	−	0.657973i	−0.946342	+	0.323166i	$0.895253\pi$
$822$	−0.682419	+	1.18198i	−0.0238021	+	0.0412265i
$823$	−28.0596			−0.978097			−0.489048	−	0.872257i	$-0.662656\pi$
$823$	−28.0596			−0.978097			−0.489048	+	0.872257i	$0.662656\pi$
$824$	−19.0679			−0.664262
$825$	0.420239	+	1.56835i	0.0146308	+	0.0546031i
$826$		−	3.52587i		−	0.122681i
$827$	−11.1607	−	19.3308i	−0.388094	−	0.672199i	0.604099	−	0.796909i	$-0.293533\pi$
$827$	−11.1607	−	19.3308i	−0.388094	−	0.672199i	−0.992193	+	0.124711i	$0.960200\pi$
$828$	7.23427	−	4.17671i	0.251408	−	0.145151i
$829$	−34.3290	−	34.3290i	−1.19229	−	1.19229i	−0.976422	−	0.215873i	$-0.930740\pi$
$829$	−34.3290	−	34.3290i	−1.19229	−	1.19229i	−0.215873	−	0.976422i	$-0.569260\pi$
$830$	11.4120	−	6.58875i	0.396118	−	0.228699i
$831$	−17.3075	−	17.3075i	−0.600390	−	0.600390i
$832$	10.3413	+	10.3413i	0.358519	+	0.358519i
$833$	22.5248	+	13.0047i	0.780436	+	0.450585i
$834$	2.81095	+	4.86872i	0.0973354	+	0.168590i
$835$	6.03467	+	10.4524i	0.208838	+	0.361719i
$836$	−6.70502	−	3.87114i	−0.231898	−	0.133886i
$837$	17.1487	+	17.1487i	0.592747	+	0.592747i
$838$	−2.73107	+	4.73036i	−0.0943433	+	0.163407i
$839$	13.3167	−	49.6987i	0.459744	−	1.71579i	−0.214009	−	0.976832i	$-0.568652\pi$
$839$	13.3167	−	49.6987i	0.459744	−	1.71579i	0.673753	−	0.738957i	$-0.264681\pi$
$840$	3.05335	+	0.818144i	0.105351	+	0.0282286i
$841$	−13.9404	+	8.04851i	−0.480705	+	0.277535i
$842$	5.82874	−	10.0957i	0.200872	−	0.347920i
$843$	14.3370			0.493793
$844$	21.7306	+	5.82269i	0.747997	+	0.200425i
$845$		−	2.55613i		−	0.0879334i
$846$	−0.794901	−	0.212993i	−0.0273292	−	0.00732285i
$847$	−7.20711	+	1.93114i	−0.247639	+	0.0663547i
$848$	4.16579			0.143054
$849$	10.2413	−	10.2413i	0.351482	−	0.351482i
$850$	2.04176	+	1.17881i	0.0700319	+	0.0404329i
$851$	16.9147	+	63.1265i	0.579828	+	2.16395i
$852$	11.2694	+	6.50639i	0.386083	+	0.222905i
$853$	−12.6813	−	47.3273i	−0.434200	−	1.62045i	−0.742974	−	0.669320i	$-0.766586\pi$
$853$	−12.6813	−	47.3273i	−0.434200	−	1.62045i	0.308775	−	0.951135i	$-0.400081\pi$
$854$	−1.58314			−0.0541738
$855$	2.05462	−	7.66795i	0.0702666	−	0.262238i
$856$	6.87202	+	1.84135i	0.234881	+	0.0629361i
$857$	6.79004	+	25.3408i	0.231943	+	0.865624i	0.979503	+	0.201429i	$0.0645586\pi$
$857$	6.79004	+	25.3408i	0.231943	+	0.865624i	−0.747560	+	0.664194i	$0.768775\pi$
$858$			1.56423i			0.0534019i
$859$	26.6664	+	15.3959i	0.909847	+	0.525301i	0.880382	−	0.474265i	$-0.157286\pi$
$859$	26.6664	+	15.3959i	0.909847	+	0.525301i	0.0294654	+	0.999566i	$0.490620\pi$
$860$	6.97453	+	26.0293i	0.237829	+	0.887591i
$861$	−8.75734	+	8.75734i	−0.298449	+	0.298449i
$862$	−7.51689	+	2.01414i	−0.256026	+	0.0686020i
$863$	−25.4613	−	44.1003i	−0.866714	−	1.50119i	−0.865335	−	0.501193i	$-0.832895\pi$
$863$	−25.4613	−	44.1003i	−0.866714	−	1.50119i	−0.00137857	−	0.999999i	$-0.500439\pi$
$864$	−12.2608	+	21.2363i	−0.417121	+	0.722475i
$865$	29.0880	−	7.79411i	0.989022	−	0.265008i
$866$			15.3524i			0.521695i
$867$	−1.21460	+	0.701251i	−0.0412501	+	0.0238157i
$868$	4.89531	−	2.82631i	0.166158	−	0.0959312i
$869$		−	4.94507i		−	0.167750i
$870$	4.00211	−	1.07236i	0.135684	−	0.0363565i
$871$	22.4287	−	38.8476i	0.759967	−	1.31630i
$872$	−2.64690	−	4.58456i	−0.0896353	−	0.155253i
$873$	−9.10311	−	9.10311i	−0.308093	−	0.308093i
$874$	−13.5144	+	3.62117i	−0.457132	+	0.122488i
$875$	2.24810	+	8.39004i	0.0759998	+	0.283635i
$876$	−29.3428	+	29.3428i	−0.991402	+	0.991402i
$877$	−9.70447	−	9.70447i	−0.327697	−	0.327697i	0.524013	−	0.851710i	$-0.324434\pi$
$877$	−9.70447	−	9.70447i	−0.327697	−	0.327697i	−0.851710	+	0.524013i	$0.824434\pi$
$878$	4.59773	−	2.65450i	0.155166	−	0.0895851i
$879$	−31.5262	+	31.5262i	−1.06335	+	1.06335i
$880$	1.10887	−	4.13838i	0.0373801	−	0.139505i
$881$	0.605271	−	0.605271i	0.0203921	−	0.0203921i	−0.696837	−	0.717229i	$-0.745410\pi$
$881$	0.605271	−	0.605271i	0.0203921	−	0.0203921i	0.717229	+	0.696837i	$0.245410\pi$
$882$	1.97607			0.0665377
$883$	23.3240	+	23.3240i	0.784916	+	0.784916i	0.980656	−	0.195740i	$-0.0627109\pi$
$883$	23.3240	+	23.3240i	0.784916	+	0.784916i	−0.195740	+	0.980656i	$0.562711\pi$
$884$	−17.7370	−	17.7370i	−0.596560	−	0.596560i
$885$	8.86771	+	33.0947i	0.298085	+	1.11247i
$886$	3.58939			0.120588
$887$	−20.8082			−0.698671			−0.349335	−	0.936998i	$-0.613593\pi$
$887$	−20.8082			−0.698671			−0.349335	+	0.936998i	$0.613593\pi$
$888$	−17.7784	−	17.7784i	−0.596604	−	0.596604i
$889$	1.99767	+	3.46007i	0.0669997	+	0.116047i
$890$	−0.694726	+	0.401100i	−0.0232873	+	0.0134449i
$891$	4.48814	−	1.20259i	0.150359	−	0.0402884i
$892$	−10.2229	−	38.1523i	−0.342287	−	1.27743i
$893$	−13.1829	−	7.61114i	−0.441148	−	0.254697i
$894$	−0.00698537	+	0.00187172i	−0.000233626	+	6.25998e-5i
$895$	−16.0399	+	27.7820i	−0.536156	+	0.928650i
$896$	5.29013	+	5.29013i	0.176731	+	0.176731i
$897$	−22.0745	−	22.0745i	−0.737045	−	0.737045i
$898$	5.60205	+	9.70303i	0.186943	+	0.323794i
$899$	7.74448	−	13.4138i	0.258293	−	0.447376i
$900$	−1.97819			−0.0659397
$901$	−5.50844			−0.183513
$902$	−2.49297	−	2.49297i	−0.0830068	−	0.0830068i
$903$	4.17953	+	7.23916i	0.139086	+	0.240904i
$904$	−0.933085	+	3.48232i	−0.0310339	+	0.115820i
$905$	12.6459	+	3.38846i	0.420364	+	0.112636i
$906$	4.39038	−	4.39038i	0.145861	−	0.145861i
$907$	−38.1871			−1.26798			−0.633991	−	0.773341i	$-0.718584\pi$
$907$	−38.1871			−1.26798			−0.633991	+	0.773341i	$0.718584\pi$
$908$	−7.10139	−	4.09999i	−0.235668	−	0.136063i
$909$	5.57643	−	9.65866i	0.184959	−	0.320358i
$910$			1.87455i			0.0621408i
$911$	−33.6520	+	9.01703i	−1.11494	+	0.298747i	−0.768834	−	0.639448i	$-0.779163\pi$
$911$	−33.6520	+	9.01703i	−1.11494	+	0.298747i	−0.346106	+	0.938195i	$0.612496\pi$
$912$	−18.1212	+	18.1212i	−0.600052	+	0.600052i
$913$	−9.08705	−	9.08705i	−0.300737	−	0.300737i
$914$	4.25055	+	7.36217i	0.140596	+	0.243519i
$915$	14.8597	−	3.98165i	0.491248	−	0.131629i
$916$	−14.3181	+	24.7997i	−0.473084	+	0.819406i
$917$	2.77979	−	10.3743i	0.0917969	−	0.342591i
$918$	4.59325	−	7.95574i	0.151600	−	0.262578i
$919$	12.8474	+	22.2523i	0.423795	+	0.734035i	0.996307	−	0.0858615i	$-0.0273643\pi$
$919$	12.8474	+	22.2523i	0.423795	+	0.734035i	−0.572512	+	0.819897i	$0.694031\pi$
$920$	−8.97952	−	15.5530i	−0.296046	−	0.512767i
$921$		−	19.8037i		−	0.652553i
$922$	−11.1270	+	11.1270i	−0.366449	+	0.366449i
$923$	−4.17533	+	15.5825i	−0.137433	+	0.512905i
$924$		−	1.47461i		−	0.0485112i
$925$	4.00561	−	14.9491i	0.131704	−	0.491525i
$926$	5.37537	+	3.10347i	0.176646	+	0.101986i
$927$	−7.89851	+	4.56021i	−0.259421	+	0.149777i
$928$	15.1275	+	4.05341i	0.496585	+	0.133060i
$929$	9.39124	−	9.39124i	0.308116	−	0.308116i	−0.536062	−	0.844179i	$-0.680089\pi$
$929$	9.39124	−	9.39124i	0.308116	−	0.308116i	0.844179	+	0.536062i	$0.180089\pi$
$930$	3.51692	−	3.51692i	0.115324	−	0.115324i
$931$	35.3066	+	9.46038i	1.15713	+	0.310052i
$932$	−17.8070	−	17.8070i	−0.583286	−	0.583286i
$933$	−3.95910	+	2.28579i	−0.129615	+	0.0748333i
$934$	1.14543	−	4.27479i	0.0374795	−	0.139875i
$935$	−1.46627	+	5.47218i	−0.0479521	+	0.178960i
$936$	−3.84833	−	1.03116i	−0.125787	−	0.0337044i
$937$	11.6409	−	11.6409i	0.380290	−	0.380290i	−0.490916	−	0.871207i	$-0.663338\pi$
$937$	11.6409	−	11.6409i	0.380290	−	0.380290i	0.871207	+	0.490916i	$0.163338\pi$
$938$	1.91452	−	3.31605i	0.0625114	−	0.108273i
$939$			24.4353i			0.797417i
$940$	2.41906	−	9.02804i	0.0789009	−	0.294462i
$941$	−16.7155	−	28.9521i	−0.544910	−	0.943813i	−0.998613	−	0.0526591i	$-0.983230\pi$
$941$	−16.7155	−	28.9521i	−0.544910	−	0.943813i	0.453702	−	0.891153i	$-0.350103\pi$
$942$	−1.49523	−	5.58027i	−0.0487172	−	0.181815i
$943$	70.3618			2.29130
$944$	−9.49642	+	35.4411i	−0.309082	+	1.15351i
$945$	7.32347	−	1.96232i	0.238233	−	0.0638342i
$946$	−2.06079	+	1.18980i	−0.0670019	+	0.0386836i
$947$	17.9719	−	4.81556i	0.584009	−	0.156485i	0.0452951	−	0.998974i	$-0.485577\pi$
$947$	17.9719	−	4.81556i	0.584009	−	0.156485i	0.538714	+	0.842489i	$0.318911\pi$
$948$	−17.5429	−	4.70060i	−0.569766	−	0.152668i
$949$	−44.5525	−	25.7224i	−1.44623	−	0.834984i
$950$	3.20038	+	0.857539i	0.103834	+	0.0278222i
$951$	0.283290	−	0.490672i	0.00918629	−	0.0159111i
$952$	−3.16517	−	3.16517i	−0.102584	−	0.102584i
$953$		−	13.2708i		−	0.429884i	−0.976627	−	0.214942i	$-0.931044\pi$
$953$		−	13.2708i		−	0.429884i	0.976627	−	0.214942i	$-0.0689562\pi$
$954$	−0.362436	+	0.209253i	−0.0117343	+	0.00677480i
$955$	−4.01113	+	6.94748i	−0.129797	+	0.224815i
$956$	−0.161565	+	0.0932797i	−0.00522539	+	0.00301688i
$957$	−2.02032	−	3.49930i	−0.0653077	−	0.113116i
$958$	−0.942577	−	0.252563i	−0.0304533	−	0.00815993i
$959$	1.54073	+	0.412838i	0.0497529	+	0.0133312i
$960$	−10.5057	−	6.06548i	−0.339071	−	0.195763i
$961$			12.4068i			0.400219i
$962$	7.45491	−	12.9123i	0.240356	−	0.416309i
$963$	3.28697	−	0.880741i	0.105921	−	0.0283815i
$964$	−2.43082	+	2.43082i	−0.0782914	+	0.0782914i
$965$	−39.0778			−1.25796
$966$	−1.88429	−	1.88429i	−0.0606260	−	0.0606260i
$967$	7.79053	−	2.08747i	0.250527	−	0.0671284i	−0.131370	−	0.991333i	$-0.541938\pi$
$967$	7.79053	−	2.08747i	0.250527	−	0.0671284i	0.381897	+	0.924205i	$0.375271\pi$
$968$	−16.3082			−0.524167
$969$	23.9617	−	23.9617i	0.769759	−	0.769759i
$970$	−9.36157	+	9.36157i	−0.300582	+	0.300582i
$971$	−29.2184	+	50.6077i	−0.937662	+	1.62408i	−0.167844	+	0.985814i	$0.553680\pi$
$971$	−29.2184	+	50.6077i	−0.937662	+	1.62408i	−0.769818	+	0.638264i	$0.779653\pi$
$972$			13.8789i			0.445167i
$973$	4.64592	−	4.64592i	0.148941	−	0.148941i
$974$	12.8168	+	3.43425i	0.410677	+	0.110041i
$975$	1.91340	+	7.14091i	0.0612779	+	0.228692i
$976$	15.9133	+	4.26395i	0.509372	+	0.136486i
$977$	−14.4008	+	8.31431i	−0.460722	+	0.265998i	−0.712348	−	0.701826i	$-0.752368\pi$
$977$	−14.4008	+	8.31431i	−0.460722	+	0.265998i	0.251626	+	0.967825i	$0.419035\pi$
$978$	−2.86072	−	1.65163i	−0.0914756	−	0.0528135i
$979$	0.553188	+	0.553188i	0.0176800	+	0.0176800i
$980$			22.4431i			0.716918i
$981$	−2.19285	−	1.26604i	−0.0700124	−	0.0404217i
$982$	−12.4066	+	7.16296i	−0.395911	+	0.228579i
$983$	5.22404	+	19.4964i	0.166621	+	0.621838i	0.997828	+	0.0658746i	$0.0209837\pi$
$983$	5.22404	+	19.4964i	0.166621	+	0.621838i	−0.831207	+	0.555963i	$0.812350\pi$
$984$	−23.4427	+	13.5347i	−0.747326	+	0.431469i
$985$	−1.52626	−	2.64356i	−0.0486307	−	0.0842309i
$986$	−5.66720	−	1.51852i	−0.180480	−	0.0483596i
$987$		−	2.89927i		−	0.0922848i
$988$	−30.5288	−	17.6258i	−0.971250	−	0.560751i
$989$	12.2915	−	45.8724i	0.390846	−	1.45866i
$990$	0.111400	+	0.415751i	0.00354053	+	0.0132134i
$991$	−34.5360	+	9.25388i	−1.09707	+	0.293959i	−0.761571	−	0.648081i	$-0.775572\pi$
$991$	−34.5360	+	9.25388i	−1.09707	+	0.293959i	−0.335500	+	0.942040i	$0.608905\pi$
$992$	18.1593	−	4.86578i	0.576560	−	0.154489i
$993$	−3.71811	−	13.8762i	−0.117991	−	0.440347i
$994$	−0.356408	+	1.33013i	−0.0113046	+	0.0421893i
$995$	−10.4845	−	39.1288i	−0.332382	−	1.24046i
$996$	−40.8746	+	23.5990i	−1.29516	+	0.747762i
$997$	21.6095	−	37.4288i	0.684380	−	1.18538i	−0.289251	−	0.957253i	$-0.593406\pi$
$997$	21.6095	−	37.4288i	0.684380	−	1.18538i	0.973631	−	0.228127i	$-0.0732603\pi$
$998$	−7.67812			−0.243047
$999$	−58.2494	−	15.6079i	−1.84293	−	0.493812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.2.g.b.49.14	✓	132
409.192	even	12	inner	409.2.g.b.192.14	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.2.g.b.49.14	✓	132	1.1	even	1	trivial
409.2.g.b.192.14	yes	132	409.192	even	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	409.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.352909 + 0.203752i) q^{2} +(-1.29982 - 0.750452i) q^{3} +(-0.916970 + 1.58824i) q^{4} +1.88589 q^{5} +0.611624 q^{6} +(-0.185005 - 0.690448i) q^{7} -1.56235i q^{8} +(-0.373645 - 0.647171i) q^{9} +(-0.665547 + 0.384254i) q^{10} +(0.529954 + 0.529954i) q^{11} +(2.38379 - 1.37628i) q^{12} +(2.41294 + 2.41294i) q^{13} +(0.205970 + 0.205970i) q^{14} +(-2.45132 - 1.41527i) q^{15} +(-1.51561 - 2.62511i) q^{16} +(2.00409 + 3.47119i) q^{17} +(0.263725 + 0.152262i) q^{18} +(3.98305 + 3.98305i) q^{19} +(-1.72930 + 2.99524i) q^{20} +(-0.277675 + 1.03630i) q^{21} +(-0.295005 - 0.0790462i) q^{22} +(5.27862 - 3.04761i) q^{23} +(-1.17247 + 2.03077i) q^{24} -1.44343 q^{25} +(-1.34319 - 0.359907i) q^{26} +5.62432i q^{27} +(1.26624 + 0.339288i) q^{28} +(3.46967 - 0.929696i) q^{29} +1.15345 q^{30} +(3.04903 - 3.04903i) q^{31} +(3.77581 + 2.17996i) q^{32} +(-0.291140 - 1.08655i) q^{33} +(-1.41452 - 0.816676i) q^{34} +(-0.348899 - 1.30211i) q^{35} +1.37048 q^{36} +(-2.77507 + 10.3567i) q^{37} +(-2.21721 - 0.594100i) q^{38} +(-1.32560 - 4.94719i) q^{39} -2.94641i q^{40} +(9.99719 + 5.77188i) q^{41} +(-0.113154 - 0.422295i) q^{42} +(5.50938 - 5.50938i) q^{43} +(-1.32764 + 0.355741i) q^{44} +(-0.704652 - 1.22049i) q^{45} +(-1.24192 + 2.15106i) q^{46} +(-2.61031 + 0.699431i) q^{47} +4.54957i q^{48} +(5.61969 - 3.24453i) q^{49} +(0.509398 - 0.294101i) q^{50} -6.01590i q^{51} +(-6.04493 + 1.61973i) q^{52} +(-0.687148 + 1.19018i) q^{53} +(-1.14597 - 1.98487i) q^{54} +(0.999433 + 0.999433i) q^{55} +(-1.07872 + 0.289042i) q^{56} +(-2.18817 - 8.16634i) q^{57} +(-1.03505 + 1.03505i) q^{58} +(-8.55917 - 8.55917i) q^{59} +(4.49557 - 2.59552i) q^{60} +(-3.84312 + 3.84312i) q^{61} +(-0.454784 + 1.69728i) q^{62} +(-0.377712 + 0.377712i) q^{63} +4.28575 q^{64} +(4.55054 + 4.55054i) q^{65} +(0.324133 + 0.324133i) q^{66} +(-3.40226 - 12.6974i) q^{67} -7.35078 q^{68} -9.14835 q^{69} +(0.388437 + 0.388437i) q^{70} +(2.36375 + 4.09414i) q^{71} +(-1.01111 + 0.583762i) q^{72} +(-14.5621 + 3.90189i) q^{73} +(-1.13085 - 4.22040i) q^{74} +(1.87619 + 1.08322i) q^{75} +(-9.97838 + 2.67370i) q^{76} +(0.267862 - 0.463950i) q^{77} +(1.47582 + 1.47582i) q^{78} +(-4.66557 - 4.66557i) q^{79} +(-2.85827 - 4.95067i) q^{80} +(3.09985 - 5.36909i) q^{81} -4.70413 q^{82} -17.1469 q^{83} +(-1.39127 - 1.39127i) q^{84} +(3.77950 + 6.54628i) q^{85} +(-0.821761 + 3.06685i) q^{86} +(-5.20765 - 1.39538i) q^{87} +(0.827971 - 0.827971i) q^{88} +1.04384 q^{89} +(0.497356 + 0.287148i) q^{90} +(1.21961 - 2.11242i) q^{91} +11.1783i q^{92} +(-6.25135 + 1.67504i) q^{93} +(0.778692 - 0.778692i) q^{94} +(7.51159 + 7.51159i) q^{95} +(-3.27191 - 5.66712i) q^{96} +(16.6402 - 4.45874i) q^{97} +(-1.32216 + 2.29005i) q^{98} +(0.144957 - 0.540985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 6 q^{3} + 58 q^{4} - 4 q^{6} + 56 q^{9} - 18 q^{10} - 2 q^{11} - 30 q^{12} - 2 q^{13} - 24 q^{14} - 30 q^{15} - 58 q^{16} + 2 q^{17} - 36 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{21} - 22 q^{22} - 12 q^{23}+ \cdots - 84 q^{99}+O(q^{100}) \) 132 * q - 6 * q^3 + 58 * q^4 - 4 * q^6 + 56 * q^9 - 18 * q^10 - 2 * q^11 - 30 * q^12 - 2 * q^13 - 24 * q^14 - 30 * q^15 - 58 * q^16 + 2 * q^17 - 36 * q^18 + 6 * q^19 - 6 * q^20 + 6 * q^21 - 22 * q^22 - 12 * q^23 + 30 * q^24 + 172 * q^25 - 6 * q^26 + 30 * q^28 + 40 * q^29 - 12 * q^30 + 18 * q^31 + 36 * q^32 + 14 * q^33 - 24 * q^34 + 4 * q^35 + 20 * q^36 + 30 * q^37 - 70 * q^38 - 24 * q^39 + 84 * q^41 - 98 * q^42 - 16 * q^43 + 4 * q^44 + 12 * q^45 + 8 * q^46 + 14 * q^47 + 84 * q^49 - 36 * q^50 + 50 * q^52 - 32 * q^53 + 86 * q^54 + 14 * q^55 + 82 * q^56 + 94 * q^57 - 104 * q^58 - 18 * q^59 - 90 * q^60 + 2 * q^61 - 38 * q^62 - 62 * q^63 - 24 * q^64 - 38 * q^65 - 66 * q^66 - 100 * q^68 + 68 * q^69 - 104 * q^70 - 38 * q^71 - 48 * q^72 + 18 * q^73 - 6 * q^74 - 192 * q^75 - 22 * q^76 - 28 * q^77 - 176 * q^78 - 6 * q^79 + 32 * q^80 - 66 * q^81 - 36 * q^82 + 28 * q^83 + 60 * q^84 - 36 * q^85 + 88 * q^86 - 152 * q^87 - 96 * q^88 + 84 * q^89 - 162 * q^90 + 50 * q^91 - 144 * q^93 + 48 * q^94 + 34 * q^95 - 94 * q^96 + 28 * q^97 - 98 * q^98 - 84 * q^99

Introduction

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