LMFDB - Embedded newform 546.2.u.a.425.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 1, 2]))

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

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

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.7
Character	$\chi$	$=$	546.425
Dual form			546.2.u.a.185.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.685609 - 1.59058i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.587127 + 1.01693i) q^{5} +(1.38904 + 1.03468i) q^{6} +(-1.73688 - 1.99580i) q^{7} +1.00000i q^{8} +(-2.05988 + 2.18103i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.685609 - 1.59058i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.587127 + 1.01693i) q^{5} +(1.38904 + 1.03468i) q^{6} +(-1.73688 - 1.99580i) q^{7} +1.00000i q^{8} +(-2.05988 + 2.18103i) q^{9} -1.17425i q^{10} -0.918984i q^{11} +(-1.72029 - 0.201534i) q^{12} +(-0.207654 + 3.59957i) q^{13} +(2.50209 + 0.859975i) q^{14} +(2.02005 + 0.236653i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.08618 + 1.88131i) q^{17} +(0.693394 - 2.91877i) q^{18} -0.0298751i q^{19} +(0.587127 + 1.01693i) q^{20} +(-1.98366 + 4.13099i) q^{21} +(0.459492 + 0.795863i) q^{22} +(-2.48855 + 1.43677i) q^{23} +(1.59058 - 0.685609i) q^{24} +(1.81056 + 3.13599i) q^{25} +(-1.61995 - 3.22114i) q^{26} +(4.88137 + 1.78107i) q^{27} +(-2.59686 + 0.506284i) q^{28} +(-0.0565664 - 0.0326586i) q^{29} +(-1.86774 + 0.805079i) q^{30} +(3.64262 - 2.10307i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.46172 + 0.630064i) q^{33} -2.17235i q^{34} +(3.04937 - 0.594506i) q^{35} +(0.858887 + 2.87442i) q^{36} +(1.47158 + 2.54886i) q^{37} +(0.0149376 + 0.0258726i) q^{38} +(5.86776 - 2.13761i) q^{39} +(-1.01693 - 0.587127i) q^{40} +(-4.01799 + 6.95937i) q^{41} +(-0.347597 - 4.56937i) q^{42} +(2.74795 + 4.75959i) q^{43} +(-0.795863 - 0.459492i) q^{44} +(-1.00855 - 3.37530i) q^{45} +(1.43677 - 2.48855i) q^{46} +(-6.53683 + 11.3221i) q^{47} +(-1.03468 + 1.38904i) q^{48} +(-0.966466 + 6.93296i) q^{49} +(-3.13599 - 1.81056i) q^{50} +(3.73707 + 0.437804i) q^{51} +(3.01349 + 1.97962i) q^{52} +(1.75697 - 1.01439i) q^{53} +(-5.11793 + 0.898236i) q^{54} +(0.934545 + 0.539560i) q^{55} +(1.99580 - 1.73688i) q^{56} +(-0.0475187 + 0.0204827i) q^{57} +0.0653172 q^{58} +(-1.80579 + 3.12771i) q^{59} +(1.21497 - 1.63109i) q^{60} +0.759641i q^{61} +(-2.10307 + 3.64262i) q^{62} +(7.93068 + 0.322921i) q^{63} -1.00000 q^{64} +(-3.53860 - 2.32457i) q^{65} +(0.950851 - 1.27651i) q^{66} -13.0820 q^{67} +(1.08618 + 1.88131i) q^{68} +(3.99146 + 2.97318i) q^{69} +(-2.34358 + 2.03954i) q^{70} +(8.16075 - 4.71161i) q^{71} +(-2.18103 - 2.05988i) q^{72} +(-2.34499 + 1.35388i) q^{73} +(-2.54886 - 1.47158i) q^{74} +(3.74670 - 5.02991i) q^{75} +(-0.0258726 - 0.0149376i) q^{76} +(-1.83411 + 1.59617i) q^{77} +(-4.01283 + 4.78510i) q^{78} +(3.71017 - 6.42620i) q^{79} +1.17425 q^{80} +(-0.513784 - 8.98532i) q^{81} -8.03598i q^{82} -11.8735 q^{83} +(2.58571 + 3.78340i) q^{84} +(-1.27545 - 2.20914i) q^{85} +(-4.75959 - 2.74795i) q^{86} +(-0.0131637 + 0.112364i) q^{87} +0.918984 q^{88} +(-5.01737 - 8.69033i) q^{89} +(2.56108 + 2.41882i) q^{90} +(7.54470 - 5.83759i) q^{91} +2.87353i q^{92} +(-5.84251 - 4.35199i) q^{93} -13.0737i q^{94} +(0.0303810 + 0.0175405i) q^{95} +(0.201534 - 1.72029i) q^{96} +(-8.74505 + 5.04896i) q^{97} +(-2.62950 - 6.48735i) q^{98} +(2.00433 + 1.89300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.685609	−	1.59058i	−0.395837	−	0.918321i
$3$	−0.685609	−	1.59058i	−0.395837	−	0.918321i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.587127	+	1.01693i	−0.262571	+	0.454786i	−0.966924	−	0.255063i	$-0.917904\pi$
$5$	−0.587127	+	1.01693i	−0.262571	+	0.454786i	0.704353	+	0.709850i	$0.251237\pi$
$6$	1.38904	+	1.03468i	0.567075	+	0.422405i
$7$	−1.73688	−	1.99580i	−0.656481	−	0.754343i
$7$	−1.73688	−	1.99580i	−0.656481	−	0.754343i
$8$			1.00000i			0.353553i
$9$	−2.05988	+	2.18103i	−0.686627	+	0.727010i
$10$		−	1.17425i		−	0.371332i
$11$		−	0.918984i		−	0.277084i	−0.990357	−	0.138542i	$-0.955758\pi$
$11$		−	0.918984i		−	0.277084i	0.990357	−	0.138542i	$-0.0442416\pi$
$12$	−1.72029	−	0.201534i	−0.496604	−	0.0581780i
$13$	−0.207654	+	3.59957i	−0.0575928	+	0.998340i
$13$	−0.207654	+	3.59957i	−0.0575928	+	0.998340i
$14$	2.50209	+	0.859975i	0.668711	+	0.229838i
$15$	2.02005	+	0.236653i	0.521575	+	0.0611034i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.08618	+	1.88131i	−0.263436	+	0.456285i	−0.967153	−	0.254196i	$-0.918189\pi$
$17$	−1.08618	+	1.88131i	−0.263436	+	0.456285i	0.703716	+	0.710481i	$0.251523\pi$
$18$	0.693394	−	2.91877i	0.163435	−	0.687960i
$19$		−	0.0298751i		−	0.00685382i	−0.999994	−	0.00342691i	$-0.998909\pi$
$19$		−	0.0298751i		−	0.00685382i	0.999994	−	0.00342691i	$-0.00109082\pi$
$20$	0.587127	+	1.01693i	0.131286	+	0.227393i
$21$	−1.98366	+	4.13099i	−0.432870	+	0.901456i
$22$	0.459492	+	0.795863i	0.0979640	+	0.169679i
$23$	−2.48855	+	1.43677i	−0.518899	+	0.299586i	−0.736484	−	0.676455i	$-0.763515\pi$
$23$	−2.48855	+	1.43677i	−0.518899	+	0.299586i	0.217585	+	0.976041i	$0.430182\pi$
$24$	1.59058	−	0.685609i	0.324675	−	0.139949i
$25$	1.81056	+	3.13599i	0.362113	+	0.627198i
$26$	−1.61995	−	3.22114i	−0.317698	−	0.631718i
$27$	4.88137	+	1.78107i	0.939421	+	0.342767i
$28$	−2.59686	+	0.506284i	−0.490760	+	0.0956787i
$29$	−0.0565664	−	0.0326586i	−0.0105041	−	0.00606455i	0.494739	−	0.869042i	$-0.335264\pi$
$29$	−0.0565664	−	0.0326586i	−0.0105041	−	0.00606455i	−0.505243	+	0.862977i	$0.668597\pi$
$30$	−1.86774	+	0.805079i	−0.341002	+	0.146987i
$31$	3.64262	−	2.10307i	0.654234	−	0.377722i	−0.135843	−	0.990730i	$-0.543374\pi$
$31$	3.64262	−	2.10307i	0.654234	−	0.377722i	0.790076	+	0.613008i	$0.210041\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.46172	+	0.630064i	−0.254452	+	0.109680i
$34$		−	2.17235i		−	0.372555i
$35$	3.04937	−	0.594506i	0.515438	−	0.100490i
$36$	0.858887	+	2.87442i	0.143148	+	0.479071i
$37$	1.47158	+	2.54886i	0.241927	+	0.419029i	0.961263	−	0.275633i	$-0.0888873\pi$
$37$	1.47158	+	2.54886i	0.241927	+	0.419029i	−0.719336	+	0.694662i	$0.755554\pi$
$38$	0.0149376	+	0.0258726i	0.00242319	+	0.00419709i
$39$	5.86776	−	2.13761i	0.939594	−	0.342291i
$40$	−1.01693	−	0.587127i	−0.160791	−	0.0928329i
$41$	−4.01799	+	6.95937i	−0.627505	+	1.08687i	0.360546	+	0.932742i	$0.382590\pi$
$41$	−4.01799	+	6.95937i	−0.627505	+	1.08687i	−0.988051	+	0.154129i	$0.950743\pi$
$42$	−0.347597	−	4.56937i	−0.0536353	−	0.705070i
$43$	2.74795	+	4.75959i	0.419059	+	0.725831i	0.995845	−	0.0910640i	$-0.0290268\pi$
$43$	2.74795	+	4.75959i	0.419059	+	0.725831i	−0.576786	+	0.816895i	$0.695693\pi$
$44$	−0.795863	−	0.459492i	−0.119981	−	0.0692710i
$45$	−1.00855	−	3.37530i	−0.150346	−	0.503160i
$46$	1.43677	−	2.48855i	0.211840	−	0.366917i
$47$	−6.53683	+	11.3221i	−0.953495	+	1.65150i	−0.215721	+	0.976455i	$0.569210\pi$
$47$	−6.53683	+	11.3221i	−0.953495	+	1.65150i	−0.737774	+	0.675047i	$0.764123\pi$
$48$	−1.03468	+	1.38904i	−0.149343	+	0.200491i
$49$	−0.966466	+	6.93296i	−0.138067	+	0.990423i
$50$	−3.13599	−	1.81056i	−0.443496	−	0.256052i
$51$	3.73707	+	0.437804i	0.523294	+	0.0613048i
$52$	3.01349	+	1.97962i	0.417896	+	0.274523i
$53$	1.75697	−	1.01439i	0.241339	−	0.139337i	−0.374453	−	0.927246i	$-0.622170\pi$
$53$	1.75697	−	1.01439i	0.241339	−	0.139337i	0.615792	+	0.787909i	$0.288836\pi$
$54$	−5.11793	+	0.898236i	−0.696462	+	0.122234i
$55$	0.934545	+	0.539560i	0.126014	+	0.0727542i
$56$	1.99580	−	1.73688i	0.266701	−	0.232101i
$57$	−0.0475187	+	0.0204827i	−0.00629401	+	0.00271299i
$58$	0.0653172			0.00857657
$59$	−1.80579	+	3.12771i	−0.235093	+	0.407194i	−0.959300	−	0.282389i	$-0.908873\pi$
$59$	−1.80579	+	3.12771i	−0.235093	+	0.407194i	0.724206	+	0.689583i	$0.242206\pi$
$60$	1.21497	−	1.63109i	0.156852	−	0.210573i
$61$			0.759641i			0.0972621i	0.998817	+	0.0486310i	$0.0154859\pi$
$61$			0.759641i			0.0972621i	−0.998817	+	0.0486310i	$0.984514\pi$
$62$	−2.10307	+	3.64262i	−0.267090	+	0.462613i
$63$	7.93068	+	0.322921i	0.999172	+	0.0406842i
$64$	−1.00000			−0.125000
$65$	−3.53860	−	2.32457i	−0.438909	−	0.288328i
$66$	0.950851	−	1.27651i	0.117042	−	0.157127i
$67$	−13.0820			−1.59822			−0.799112	−	0.601182i	$-0.794697\pi$
$67$	−13.0820			−1.59822			−0.799112	+	0.601182i	$0.794697\pi$
$68$	1.08618	+	1.88131i	0.131718	+	0.228143i
$69$	3.99146	+	2.97318i	0.480516	+	0.357928i
$70$	−2.34358	+	2.03954i	−0.280111	+	0.243772i
$71$	8.16075	−	4.71161i	0.968503	−	0.559166i	0.0697237	−	0.997566i	$-0.477788\pi$
$71$	8.16075	−	4.71161i	0.968503	−	0.559166i	0.898780	+	0.438401i	$0.144455\pi$
$72$	−2.18103	−	2.05988i	−0.257037	−	0.242759i
$73$	−2.34499	+	1.35388i	−0.274460	+	0.158460i	−0.630913	−	0.775854i	$-0.717319\pi$
$73$	−2.34499	+	1.35388i	−0.274460	+	0.158460i	0.356453	+	0.934313i	$0.383986\pi$
$74$	−2.54886	−	1.47158i	−0.296298	−	0.171068i
$75$	3.74670	−	5.02991i	0.432632	−	0.580804i
$76$	−0.0258726	−	0.0149376i	−0.00296779	−	0.00171346i
$77$	−1.83411	+	1.59617i	−0.209016	+	0.181900i
$78$	−4.01283	+	4.78510i	−0.454363	+	0.541806i
$79$	3.71017	−	6.42620i	0.417427	−	0.723004i	−0.578253	−	0.815857i	$-0.696265\pi$
$79$	3.71017	−	6.42620i	0.417427	−	0.723004i	0.995680	+	0.0928534i	$0.0295988\pi$
$80$	1.17425			0.131286
$81$	−0.513784	−	8.98532i	−0.0570871	−	0.998369i
$82$		−	8.03598i		−	0.887426i
$83$	−11.8735			−1.30329			−0.651645	−	0.758524i	$-0.725921\pi$
$83$	−11.8735			−1.30329			−0.651645	+	0.758524i	$0.725921\pi$
$84$	2.58571	+	3.78340i	0.282125	+	0.412802i
$85$	−1.27545	−	2.20914i	−0.138342	−	0.239615i
$86$	−4.75959	−	2.74795i	−0.513240	−	0.296319i
$87$	−0.0131637	+	0.112364i	−0.00141129	+	0.0120467i
$88$	0.918984			0.0979640
$89$	−5.01737	−	8.69033i	−0.531840	−	0.921174i	−0.999309	−	0.0371643i	$-0.988168\pi$
$89$	−5.01737	−	8.69033i	−0.531840	−	0.921174i	0.467469	−	0.884009i	$-0.345166\pi$
$90$	2.56108	+	2.41882i	0.269962	+	0.254966i
$91$	7.54470	−	5.83759i	0.790899	−	0.611946i
$92$			2.87353i			0.299586i
$93$	−5.84251	−	4.35199i	−0.605840	−	0.451280i
$94$		−	13.0737i		−	1.34845i
$95$	0.0303810	+	0.0175405i	0.00311703	+	0.00179962i
$96$	0.201534	−	1.72029i	0.0205690	−	0.175576i
$97$	−8.74505	+	5.04896i	−0.887925	+	0.512644i	−0.873263	−	0.487249i	$-0.838001\pi$
$97$	−8.74505	+	5.04896i	−0.887925	+	0.512644i	−0.0146618	+	0.999893i	$0.504667\pi$
$98$	−2.62950	−	6.48735i	−0.265619	−	0.655322i
$99$	2.00433	+	1.89300i	0.201443	+	0.190253i
$100$	3.62113			0.362113
$101$	−8.84955			−0.880563			−0.440282	−	0.897860i	$-0.645121\pi$
$101$	−8.84955			−0.880563			−0.440282	+	0.897860i	$0.645121\pi$
$102$	−3.45530	+	1.48938i	−0.342125	+	0.147471i
$103$	8.65368	+	4.99621i	0.852673	+	0.492291i	0.861552	−	0.507670i	$-0.169493\pi$
$103$	8.65368	+	4.99621i	0.852673	+	0.492291i	−0.00887895	+	0.999961i	$0.502826\pi$
$104$	−3.59957	−	0.207654i	−0.352967	−	0.0203621i
$105$	−3.03628	−	4.44266i	−0.296311	−	0.433560i
$106$	−1.01439	+	1.75697i	−0.0985261	+	0.170652i
$107$	−3.54160	+	2.04475i	−0.342380	+	0.197673i	−0.661324	−	0.750100i	$-0.730005\pi$
$107$	−3.54160	+	2.04475i	−0.342380	+	0.197673i	0.318944	+	0.947774i	$0.396672\pi$
$108$	3.98314	−	3.33686i	0.383277	−	0.321089i
$109$	3.22047	+	5.57802i	0.308465	+	0.534277i	0.978027	−	0.208479i	$-0.0668514\pi$
$109$	3.22047	+	5.57802i	0.308465	+	0.534277i	−0.669562	+	0.742756i	$0.733518\pi$
$110$	−1.07912			−0.102890
$111$	3.04523	−	4.08819i	0.289040	−	0.388033i
$112$	−0.859975	+	2.50209i	−0.0812600	+	0.236425i
$113$	18.3720	−	10.6071i	1.72829	−	0.997828i	0.831207	−	0.555963i	$-0.187650\pi$
$113$	18.3720	−	10.6071i	1.72829	−	0.997828i	0.897081	−	0.441865i	$-0.145683\pi$
$114$	0.0309111	−	0.0414979i	0.00289509	−	0.00388663i
$115$		−	3.37425i		−	0.314651i
$116$	−0.0565664	+	0.0326586i	−0.00525206	+	0.00303228i
$117$	−7.42302	−	7.86758i	−0.686259	−	0.727358i
$118$		−	3.61157i		−	0.332472i
$119$	5.64129	−	1.09983i	0.517136	−	0.100821i
$120$	−0.236653	+	2.02005i	−0.0216033	+	0.184405i
$121$	10.1555			0.923224
$122$	−0.379821	−	0.657869i	−0.0343873	−	0.0595606i
$123$	13.8242	+	1.61953i	1.24649	+	0.146028i
$124$		−	4.20614i		−	0.377722i
$125$	−10.1234			−0.905464
$126$	−7.02963	+	3.68568i	−0.626249	+	0.328347i
$127$	0.00158663	−	0.00274813i	0.000140791	−	0.000243857i	−0.865955	−	0.500122i	$-0.833289\pi$
$127$	0.00158663	−	0.00274813i	0.000140791	−	0.000243857i	0.866096	+	0.499878i	$0.166622\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	5.68649	−	7.63405i	0.500667	−	0.672141i
$130$	4.22680	+	0.243838i	0.370715	+	0.0213860i
$131$	3.60456	−	6.24329i	0.314932	−	0.545478i	−0.664491	−	0.747296i	$-0.731352\pi$
$131$	3.60456	−	6.24329i	0.314932	−	0.545478i	0.979423	+	0.201818i	$0.0646849\pi$
$132$	−0.185207	+	1.58091i	−0.0161202	+	0.137601i
$133$	−0.0596249	+	0.0518896i	−0.00517013	+	0.00449940i
$134$	11.3294	−	6.54101i	0.978708	−	0.565057i
$135$	−4.67721	+	3.91832i	−0.402550	+	0.337235i
$136$	−1.88131	−	1.08618i	−0.161321	−	0.0931388i
$137$	−17.8232	−	10.2902i	−1.52273	−	0.879151i	−0.999639	−	0.0268778i	$-0.991443\pi$
$137$	−17.8232	−	10.2902i	−1.52273	−	0.879151i	−0.523096	−	0.852274i	$-0.675223\pi$
$138$	−4.94330	−	0.579116i	−0.420801	−	0.0492976i
$139$	−5.48328	+	3.16577i	−0.465085	+	0.268517i	−0.714180	−	0.699962i	$-0.753200\pi$
$139$	−5.48328	+	3.16577i	−0.465085	+	0.268517i	0.249095	+	0.968479i	$0.419867\pi$
$140$	1.00983	−	2.93809i	0.0853461	−	0.248314i
$141$	22.4905	+	2.63480i	1.89404	+	0.221890i
$142$	−4.71161	+	8.16075i	−0.395390	+	0.684835i
$143$	3.30794	+	0.190830i	0.276624	+	0.0159580i
$144$	2.91877	+	0.693394i	0.243231	+	0.0577828i
$145$	0.0664233	−	0.0383495i	0.00551615	−	0.00318475i
$146$	1.35388	−	2.34499i	0.112048	−	0.194073i
$147$	11.6900	−	3.21606i	0.964178	−	0.265256i
$148$	2.94317			0.241927
$149$		−	7.30980i		−	0.598842i	−0.954121	−	0.299421i	$-0.903207\pi$
$149$		−	7.30980i		−	0.598842i	0.954121	−	0.299421i	$-0.0967935\pi$
$150$	−0.729782	+	6.22938i	−0.0595865	+	0.508627i
$151$	−4.87258	−	8.43956i	−0.396525	−	0.686802i	0.596769	−	0.802413i	$-0.296451\pi$
$151$	−4.87258	−	8.43956i	−0.396525	−	0.686802i	−0.993295	+	0.115611i	$0.963117\pi$
$152$	0.0298751			0.00242319
$153$	−1.86581	−	6.24426i	−0.150841	−	0.504819i
$154$	0.790303	−	2.29938i	0.0636844	−	0.185289i
$155$			4.93907i			0.396716i
$156$	1.08266	−	6.15043i	0.0866822	−	0.492429i
$157$	−7.68731	+	4.43827i	−0.613514	+	0.354213i	−0.774340	−	0.632770i	$-0.781918\pi$
$157$	−7.68731	+	4.43827i	−0.613514	+	0.354213i	0.160825	+	0.986983i	$0.448584\pi$
$158$			7.42034i			0.590330i
$159$	−2.81806	−	2.09913i	−0.223487	−	0.166472i
$160$	−1.01693	+	0.587127i	−0.0803956	+	0.0464164i
$161$	7.18983	+	2.47116i	0.566638	+	0.194755i
$162$	4.93761	+	7.52463i	0.387935	+	0.591190i
$163$	3.11766			0.244194			0.122097	−	0.992518i	$-0.461038\pi$
$163$	3.11766			0.244194			0.122097	+	0.992518i	$0.461038\pi$
$164$	4.01799	+	6.95937i	0.313752	+	0.543435i
$165$	0.217480	−	1.85639i	0.0169308	−	0.144520i
$166$	10.2828	−	5.93677i	0.798099	−	0.460783i
$167$	−3.69401	+	6.39822i	−0.285851	+	0.495109i	−0.972815	−	0.231583i	$-0.925610\pi$
$167$	−3.69401	+	6.39822i	−0.285851	+	0.495109i	0.686964	+	0.726691i	$0.258943\pi$
$168$	−4.13099	−	1.98366i	−0.318713	−	0.153043i
$169$	−12.9138	−	1.49493i	−0.993366	−	0.114994i
$170$	2.20914	+	1.27545i	0.169433	+	0.0978222i
$171$	0.0651585	+	0.0615392i	0.00498280	+	0.00470602i
$172$	5.49590			0.419059
$173$	9.97622			0.758478			0.379239	−	0.925299i	$-0.376186\pi$
$173$	9.97622			0.758478			0.379239	+	0.925299i	$0.376186\pi$
$174$	−0.0447821	−	0.103892i	−0.00339492	−	0.00787605i
$175$	3.11408	−	9.06038i	0.235402	−	0.684901i
$176$	−0.795863	+	0.459492i	−0.0599905	+	0.0346355i
$177$	6.21294	+	0.727857i	0.466993	+	0.0547091i
$178$	8.69033	+	5.01737i	0.651368	+	0.376068i
$179$		−	16.1480i		−	1.20695i	−0.797380	−	0.603477i	$-0.793781\pi$
$179$		−	16.1480i		−	1.20695i	0.797380	−	0.603477i	$-0.206219\pi$
$180$	−3.42737	−	0.814220i	−0.255461	−	0.0606884i
$181$			11.7575i			0.873927i	0.899479	+	0.436964i	$0.143946\pi$
$181$			11.7575i			0.873927i	−0.899479	+	0.436964i	$0.856054\pi$
$182$	−3.61510	+	8.82785i	−0.267969	+	0.654364i
$183$	1.20827	−	0.520817i	0.0893178	−	0.0384999i
$184$	−1.43677	−	2.48855i	−0.105920	−	0.183458i
$185$	−3.45602			−0.254092
$186$	7.23576	+	0.847681i	0.530551	+	0.0621550i
$187$	1.72890	+	0.998178i	0.126429	+	0.0729940i
$188$	6.53683	+	11.3221i	0.476748	+	0.825751i
$189$	−4.92372	−	12.8358i	−0.358148	−	0.933665i
$190$	−0.0350810			−0.00254504
$191$			1.12191i			0.0811783i	0.999176	+	0.0405892i	$0.0129235\pi$
$191$			1.12191i			0.0811783i	−0.999176	+	0.0405892i	$0.987077\pi$
$192$	0.685609	+	1.59058i	0.0494796	+	0.114790i
$193$	−16.7496			−1.20566			−0.602832	−	0.797868i	$-0.705961\pi$
$193$	−16.7496			−1.20566			−0.602832	+	0.797868i	$0.705961\pi$
$194$	5.04896	−	8.74505i	0.362494	−	0.627858i
$195$	−1.27132	+	7.22217i	−0.0910410	+	0.517190i
$196$	5.52089	+	4.30346i	0.394349	+	0.307390i
$197$	18.6511	+	10.7682i	1.32883	+	0.767202i	0.985119	−	0.171873i	$-0.0549817\pi$
$197$	18.6511	+	10.7682i	1.32883	+	0.767202i	0.343714	+	0.939075i	$0.388315\pi$
$198$	−2.68230	−	0.637218i	−0.190623	−	0.0452851i
$199$	11.2776	+	6.51112i	0.799447	+	0.461561i	0.843278	−	0.537478i	$-0.180623\pi$
$199$	11.2776	+	6.51112i	0.799447	+	0.461561i	−0.0438307	+	0.999039i	$0.513956\pi$
$200$	−3.13599	+	1.81056i	−0.221748	+	0.128026i
$201$	8.96915	+	20.8080i	0.632635	+	1.46768i
$202$	7.66394	−	4.42478i	0.539233	−	0.311326i
$203$	0.0330691	+	0.169620i	0.00232099	+	0.0119050i
$204$	2.24768	−	3.01749i	0.157369	−	0.211267i
$205$	−4.71814	−	8.17206i	−0.329529	−	0.570761i
$206$	−9.99241			−0.696204
$207$	1.99249	−	8.38717i	0.138488	−	0.582949i
$208$	3.22114	−	1.61995i	0.223346	−	0.112323i
$209$	−0.0274548			−0.00189909
$210$	4.85083	+	2.32932i	0.334739	+	0.160738i
$211$	−10.6556	+	18.4561i	−0.733562	+	1.27057i	0.221789	+	0.975095i	$0.428810\pi$
$211$	−10.6556	+	18.4561i	−0.733562	+	1.27057i	−0.955351	+	0.295472i	$0.904523\pi$
$212$		−	2.02878i		−	0.139337i
$213$	−13.0893	−	9.75000i	−0.896863	−	0.668059i
$214$	2.04475	−	3.54160i	0.139776	−	0.242099i
$215$	−6.45358			−0.440131
$216$	−1.78107	+	4.88137i	−0.121186	+	0.332135i
$217$	−10.5241	−	3.61717i	−0.714424	−	0.245550i
$218$	−5.57802	−	3.22047i	−0.377791	−	0.218118i
$219$	3.76120	+	2.80166i	0.254158	+	0.189318i
$220$	0.934545	−	0.539560i	0.0630070	−	0.0363771i
$221$	−6.54636	−	4.30042i	−0.440356	−	0.289278i
$222$	−0.593149	+	5.06309i	−0.0398096	+	0.339812i
$223$	−20.1451	−	11.6308i	−1.34902	−	0.778856i	−0.360907	−	0.932602i	$-0.617533\pi$
$223$	−20.1451	−	11.6308i	−1.34902	−	0.778856i	−0.988110	+	0.153746i	$0.950866\pi$
$224$	−0.506284	−	2.59686i	−0.0338275	−	0.173510i
$225$	−10.5692	−	2.51087i	−0.704616	−	0.167391i
$226$	−10.6071	+	18.3720i	−0.705571	+	1.22208i
$227$	−11.6786	+	20.2278i	−0.775133	+	1.34257i	0.159587	+	0.987184i	$0.448984\pi$
$227$	−11.6786	+	20.2278i	−0.775133	+	1.34257i	−0.934720	+	0.355386i	$0.884350\pi$
$228$	−0.00602087	+	0.0513938i	−0.000398742	+	0.00340363i
$229$	3.19792	+	1.84632i	0.211325	+	0.122008i	0.601927	−	0.798551i	$-0.294400\pi$
$229$	3.19792	+	1.84632i	0.211325	+	0.122008i	−0.390602	+	0.920560i	$0.627733\pi$
$230$	1.68713	+	2.92219i	0.111246	+	0.192683i
$231$	3.79631	+	1.82295i	0.249779	+	0.119941i
$232$	0.0326586	−	0.0565664i	0.00214414	−	0.00371377i
$233$	7.98666	+	4.61110i	0.523223	+	0.302083i	0.738252	−	0.674524i	$-0.235651\pi$
$233$	7.98666	+	4.61110i	0.523223	+	0.302083i	−0.215029	+	0.976608i	$0.568985\pi$
$234$	10.3623	+	3.10201i	0.677406	+	0.202785i
$235$	−7.67590	−	13.2950i	−0.500721	−	0.867273i
$236$	1.80579	+	3.12771i	0.117547	+	0.203597i
$237$	−12.7651	−	1.49545i	−0.829182	−	0.0971402i
$238$	−4.33559	+	3.77312i	−0.281034	+	0.244575i
$239$		−	13.3075i		−	0.860788i	−0.902641	−	0.430394i	$-0.858375\pi$
$239$		−	13.3075i		−	0.860788i	0.902641	−	0.430394i	$-0.141625\pi$
$240$	−0.805079	−	1.86774i	−0.0519676	−	0.120562i
$241$	−22.2936	−	12.8712i	−1.43605	−	0.829107i	−0.438482	−	0.898740i	$-0.644484\pi$
$241$	−22.2936	−	12.8712i	−1.43605	−	0.829107i	−0.997573	+	0.0696331i	$0.977817\pi$
$242$	−8.79489	+	5.07773i	−0.565357	+	0.326409i
$243$	−13.9396	+	6.97763i	−0.894226	+	0.447615i
$244$	0.657869	+	0.379821i	0.0421157	+	0.0243155i
$245$	−6.48292	−	5.05336i	−0.414179	−	0.322847i
$246$	−12.7819	+	5.50954i	−0.814942	+	0.351276i
$247$	0.107538	+	0.00620368i	0.00684245	+	0.000394731i
$248$	2.10307	+	3.64262i	0.133545	+	0.231307i
$249$	8.14061	+	18.8858i	0.515890	+	1.19684i
$250$	8.76711	−	5.06169i	0.554481	−	0.320130i
$251$	15.4915	+	26.8320i	0.977813	+	1.69362i	0.670320	+	0.742072i	$0.266157\pi$
$251$	15.4915	+	26.8320i	0.977813	+	1.69362i	0.307493	+	0.951550i	$0.400510\pi$
$252$	4.24500	−	6.70671i	0.267410	−	0.422483i
$253$	1.32036	+	2.28694i	0.0830106	+	0.143779i
$254$			0.00317326i			0.000199108i
$255$	−2.63935	+	3.54330i	−0.165282	+	0.221890i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.6430	−	27.0945i	−0.975784	−	1.69011i	−0.677322	−	0.735687i	$-0.736860\pi$
$257$	−15.6430	−	27.0945i	−0.975784	−	1.69011i	−0.298462	−	0.954421i	$-0.596474\pi$
$258$	−1.10761	+	9.45453i	−0.0689571	+	0.588613i
$259$	2.53105	−	7.36406i	0.157272	−	0.457580i
$260$	−3.78244	+	1.90223i	−0.234577	+	0.117971i
$261$	0.187749	−	0.0561001i	0.0116214	−	0.00347251i
$262$			7.20912i			0.445381i
$263$			3.27772i			0.202113i	0.994881	+	0.101056i	$0.0322222\pi$
$263$			3.27772i			0.202113i	−0.994881	+	0.101056i	$0.967778\pi$
$264$	−0.630064	−	1.46172i	−0.0387777	−	0.0899624i
$265$			2.38230i			0.146343i
$266$	0.0256919	−	0.0747502i	0.00157527	−	0.00458323i
$267$	−10.3827	+	13.9387i	−0.635411	+	0.853034i
$268$	−6.54101	+	11.3294i	−0.399556	+	0.692051i
$269$	−3.92353	+	6.79575i	−0.239222	+	0.414344i	−0.960491	−	0.278311i	$-0.910226\pi$
$269$	−3.92353	+	6.79575i	−0.239222	+	0.414344i	0.721270	+	0.692654i	$0.243559\pi$
$270$	2.09143	−	5.73197i	0.127280	−	0.348836i
$271$	9.66596	−	5.58065i	0.587165	−	0.339000i	−0.176811	−	0.984245i	$-0.556578\pi$
$271$	9.66596	−	5.58065i	0.587165	−	0.339000i	0.763976	+	0.645245i	$0.223245\pi$
$272$	2.17235			0.131718
$273$	−14.4579	−	7.99813i	−0.875030	−	0.484069i
$274$	20.5804			1.24331
$275$	2.88192	−	1.66388i	0.173787	−	0.100336i
$276$	4.57058	−	1.97012i	0.275116	−	0.118587i
$277$	−9.54535	+	16.5330i	−0.573524	+	0.993373i	0.422676	+	0.906281i	$0.361091\pi$
$277$	−9.54535	+	16.5330i	−0.573524	+	0.993373i	−0.996200	+	0.0870923i	$0.972242\pi$
$278$	3.16577	−	5.48328i	0.189870	−	0.328865i
$279$	−2.91651	+	12.2767i	−0.174607	+	0.734989i
$280$	0.594506	+	3.04937i	0.0355285	+	0.182235i
$281$			12.3375i			0.735995i	0.929827	+	0.367997i	$0.119956\pi$
$281$			12.3375i			0.735995i	−0.929827	+	0.367997i	$0.880044\pi$
$282$	−20.7947	+	8.96343i	−1.23831	+	0.533764i
$283$			10.7847i			0.641081i	0.947235	+	0.320541i	$0.103865\pi$
$283$			10.7847i			0.641081i	−0.947235	+	0.320541i	$0.896135\pi$
$284$		−	9.42323i		−	0.559166i
$285$	0.00707003	−	0.0603493i	0.000418792	−	0.00357478i
$286$	−2.96018	+	1.48871i	−0.175039	+	0.0880291i
$287$	20.8683	−	4.06849i	1.23182	−	0.240155i
$288$	−2.87442	+	0.858887i	−0.169377	+	0.0506104i
$289$	6.14044	+	10.6356i	0.361203	+	0.625621i
$290$	−0.0383495	+	0.0664233i	−0.00225196	+	0.00390051i
$291$	14.0264	+	10.4481i	0.822245	+	0.612477i
$292$			2.70776i			0.158460i
$293$	8.93398	+	15.4741i	0.521929	+	0.904007i	0.999675	+	0.0255089i	$0.00812062\pi$
$293$	8.93398	+	15.4741i	0.521929	+	0.904007i	−0.477746	+	0.878498i	$0.658546\pi$
$294$	−8.51584	+	8.63021i	−0.496654	+	0.503324i
$295$	−2.12045	−	3.67273i	−0.123457	−	0.213835i
$296$	−2.54886	+	1.47158i	−0.148149	+	0.0855340i
$297$	1.63677	−	4.48590i	0.0949752	−	0.260298i
$298$	3.65490	+	6.33047i	0.211723	+	0.366714i
$299$	−4.65498	−	9.25606i	−0.269204	−	0.535291i
$300$	−2.48268	−	5.75969i	−0.143338	−	0.332536i
$301$	4.72634	−	13.7512i	0.272422	−	0.792608i
$302$	8.43956	+	4.87258i	0.485642	+	0.280386i
$303$	6.06733	+	14.0759i	0.348559	+	0.808640i
$304$	−0.0258726	+	0.0149376i	−0.00148390	+	0.000856728i
$305$	−0.772504	−	0.446006i	−0.0442335	−	0.0255382i
$306$	4.73797	+	4.47479i	0.270851	+	0.255807i
$307$		−	15.9984i		−	0.913075i	−0.889704	−	0.456537i	$-0.849089\pi$
$307$		−	15.9984i		−	0.913075i	0.889704	−	0.456537i	$-0.150911\pi$
$308$	0.465267	+	2.38647i	0.0265110	+	0.135982i
$309$	2.01382	−	17.1898i	0.114562	−	0.977894i
$310$	−2.46953	−	4.27736i	−0.140260	−	0.242938i
$311$	7.50229	+	12.9943i	0.425416	+	0.736842i	0.996459	−	0.0840780i	$-0.0267945\pi$
$311$	7.50229	+	12.9943i	0.425416	+	0.736842i	−0.571043	+	0.820920i	$0.693461\pi$
$312$	2.13761	+	5.86776i	0.121018	+	0.332197i
$313$	−7.96283	−	4.59734i	−0.450086	−	0.259857i	0.257781	−	0.966203i	$-0.417009\pi$
$313$	−7.96283	−	4.59734i	−0.450086	−	0.259857i	−0.707866	+	0.706346i	$0.750342\pi$
$314$	4.43827	−	7.68731i	0.250466	−	0.433820i
$315$	−4.98470	+	7.87538i	−0.280856	+	0.443727i
$316$	−3.71017	−	6.42620i	−0.208713	−	0.361502i
$317$	26.2887	+	15.1778i	1.47652	+	0.852470i	0.999649	−	0.0265020i	$-0.00843682\pi$
$317$	26.2887	+	15.1778i	1.47652	+	0.852470i	0.476873	+	0.878972i	$0.341770\pi$
$318$	3.49007	+	0.408868i	0.195714	+	0.0229282i
$319$	−0.0300127	+	0.0519836i	−0.00168039	+	0.00291052i
$320$	0.587127	−	1.01693i	0.0328214	−	0.0568483i
$321$	5.68048	+	4.23130i	0.317054	+	0.236168i
$322$	−7.46216	+	1.45482i	−0.415850	+	0.0810741i
$323$	0.0562044	+	0.0324496i	0.00312730	+	0.00180555i
$324$	−8.03841	−	4.04771i	−0.446578	−	0.224873i
$325$	−11.6642	+	5.86605i	−0.647012	+	0.325390i
$326$	−2.69997	+	1.55883i	−0.149538	+	0.0863357i
$327$	6.66429	−	8.94675i	0.368536	−	0.494756i
$328$	−6.95937	−	4.01799i	−0.384267	−	0.221857i
$329$	33.9505	−	6.61899i	1.87175	−	0.364917i
$330$	0.739854	+	1.71642i	0.0407276	+	0.0944861i
$331$	30.2522			1.66281			0.831405	−	0.555666i	$-0.187537\pi$
$331$	30.2522			1.66281			0.831405	+	0.555666i	$0.187537\pi$
$332$	−5.93677	+	10.2828i	−0.325823	+	0.564341i
$333$	−8.59042	−	2.04077i	−0.470752	−	0.111834i
$334$		−	7.38803i		−	0.404255i
$335$	7.68081	−	13.3035i	0.419647	−	0.726850i
$336$	4.56937	−	0.347597i	0.249280	−	0.0189629i
$337$	−15.1212			−0.823705			−0.411852	−	0.911251i	$-0.635118\pi$
$337$	−15.1212			−0.823705			−0.411852	+	0.911251i	$0.635118\pi$
$338$	11.9311	−	5.16223i	0.648967	−	0.280789i
$339$	−29.4673	−	21.9498i	−1.60045	−	1.19215i
$340$	−2.55089			−0.138342
$341$	−1.93269	−	3.34751i	−0.104661	−	0.181278i
$342$	−0.0871986	−	0.0207152i	−0.00471516	−	0.00112015i
$343$	15.5155	−	10.1129i	0.837757	−	0.546044i
$344$	−4.75959	+	2.74795i	−0.256620	+	0.148160i
$345$	−5.36702	+	2.31342i	−0.288950	+	0.124550i
$346$	−8.63966	+	4.98811i	−0.464471	+	0.268162i
$347$	−2.80775	−	1.62106i	−0.150728	−	0.0870229i	0.422739	−	0.906251i	$-0.361069\pi$
$347$	−2.80775	−	1.62106i	−0.150728	−	0.0870229i	−0.573467	+	0.819229i	$0.694402\pi$
$348$	0.0907285	+	0.0675822i	0.00486356	+	0.00362279i
$349$	8.93794	+	5.16032i	0.478437	+	0.276226i	0.719765	−	0.694218i	$-0.244250\pi$
$349$	8.93794	+	5.16032i	0.478437	+	0.276226i	−0.241328	+	0.970444i	$0.577583\pi$
$350$	1.83332	+	9.40356i	0.0979950	+	0.502641i
$351$	−7.42471	+	17.2010i	−0.396302	+	0.918120i
$352$	0.459492	−	0.795863i	0.0244910	−	0.0424197i
$353$	22.8607			1.21675			0.608377	−	0.793648i	$-0.291821\pi$
$353$	22.8607			1.21675			0.608377	+	0.793648i	$0.291821\pi$
$354$	−5.74449	+	2.47613i	−0.305316	+	0.131605i
$355$			11.0653i			0.587283i
$356$	−10.0347			−0.531840
$357$	−5.61708	−	8.21887i	−0.297288	−	0.434989i
$358$	8.07398	+	13.9845i	0.426723	+	0.739106i
$359$	−0.0612770	−	0.0353783i	−0.00323408	−	0.00186719i	0.498382	−	0.866957i	$-0.333928\pi$
$359$	−0.0612770	−	0.0353783i	−0.00323408	−	0.00186719i	−0.501616	+	0.865090i	$0.667261\pi$
$360$	3.37530	−	1.00855i	0.177894	−	0.0531553i
$361$	18.9991			0.999953
$362$	−5.87874	−	10.1823i	−0.308980	−	0.535169i
$363$	−6.96268	−	16.1531i	−0.365446	−	0.847816i
$364$	−1.28316	−	9.45270i	−0.0672556	−	0.495456i
$365$		−	3.17960i		−	0.166428i
$366$	−0.785983	+	1.05518i	−0.0410840	+	0.0551549i
$367$		−	16.4240i		−	0.857325i	−0.903465	−	0.428662i	$-0.858985\pi$
$367$		−	16.4240i		−	0.857325i	0.903465	−	0.428662i	$-0.141015\pi$
$368$	2.48855	+	1.43677i	0.129725	+	0.0748966i
$369$	−6.90200	−	23.0988i	−0.359304	−	1.20248i
$370$	2.99300	−	1.72801i	0.155599	−	0.0898350i
$371$	−5.07618	−	1.74470i	−0.263542	−	0.0905801i
$372$	−6.69019	+	2.88376i	−0.346870	+	0.149516i
$373$	0.280532			0.0145254			0.00726269	−	0.999974i	$-0.497688\pi$
$373$	0.280532			0.0145254			0.00726269	+	0.999974i	$0.497688\pi$
$374$	−1.99636			−0.103229
$375$	6.94069	+	16.1020i	0.358416	+	0.831506i
$376$	−11.3221	−	6.53683i	−0.583894	−	0.337112i
$377$	0.129303	−	0.196833i	0.00665945	−	0.0101374i
$378$	10.6819	+	8.65425i	0.549420	+	0.445126i
$379$	−15.8106	+	27.3847i	−0.812133	+	1.40666i	0.0992346	+	0.995064i	$0.468361\pi$
$379$	−15.8106	+	27.3847i	−0.812133	+	1.40666i	−0.911368	+	0.411592i	$0.864973\pi$
$380$	0.0303810	−	0.0175405i	0.00155851	−	0.000899808i
$381$	−0.00545892		0.000639522i	−0.000279669		3.27637e-5i
$382$	−0.560953	−	0.971600i	−0.0287009	−	0.0497114i
$383$	26.3828			1.34810			0.674050	−	0.738686i	$-0.264553\pi$
$383$	26.3828			1.34810			0.674050	+	0.738686i	$0.264553\pi$
$384$	−1.38904	−	1.03468i	−0.0708844	−	0.0528006i
$385$	−0.546341	−	2.80232i	−0.0278441	−	0.142820i
$386$	14.5056	−	8.37481i	0.738315	−	0.426266i
$387$	−16.0413	−	3.81083i	−0.815423	−	0.193715i
$388$			10.0979i			0.512644i
$389$	−20.3683	+	11.7596i	−1.03271	+	0.596237i	−0.917760	−	0.397135i	$-0.870005\pi$
$389$	−20.3683	+	11.7596i	−1.03271	+	0.596237i	−0.114952	+	0.993371i	$0.536671\pi$
$390$	−2.51009	−	6.89024i	−0.127103	−	0.348901i
$391$		−	6.24232i		−	0.315688i
$392$	−6.93296	−	0.966466i	−0.350167	−	0.0488139i
$393$	−12.4018	−	1.45289i	−0.625586	−	0.0732885i
$394$	−21.5364			−1.08499
$395$	4.35668	+	7.54599i	0.219208	+	0.379680i
$396$	2.64155	−	0.789303i	0.132743	−	0.0396640i
$397$			11.1419i			0.559195i	0.960117	+	0.279598i	$0.0902010\pi$
$397$			11.1419i			0.559195i	−0.960117	+	0.279598i	$0.909799\pi$
$398$	−13.0222			−0.652746
$399$	0.123414	+	0.0592621i	0.00617842	+	0.00296681i
$400$	1.81056	−	3.13599i	0.0905282	−	0.156799i
$401$	−0.974806	+	0.562805i	−0.0486795	+	0.0281051i	−0.524142	−	0.851631i	$-0.675614\pi$
$401$	−0.974806	+	0.562805i	−0.0486795	+	0.0281051i	0.475463	+	0.879736i	$0.342281\pi$
$402$	−18.1715	−	13.5357i	−0.906313	−	0.675098i
$403$	6.81373	+	13.5486i	0.339416	+	0.674902i
$404$	−4.42478	+	7.66394i	−0.220141	+	0.381295i
$405$	9.43913	+	4.75304i	0.469034	+	0.236180i
$406$	−0.113448	−	0.130360i	−0.00563035	−	0.00646968i
$407$	2.34236	−	1.35236i	0.116106	−	0.0670340i
$408$	−0.437804	+	3.73707i	−0.0216745	+	0.185012i
$409$	−7.85440	−	4.53474i	−0.388375	−	0.224228i	0.293081	−	0.956088i	$-0.405320\pi$
$409$	−7.85440	−	4.53474i	−0.388375	−	0.224228i	−0.681456	+	0.731859i	$0.738653\pi$
$410$	8.17206	+	4.71814i	0.403589	+	0.233012i
$411$	−4.14766	+	35.4042i	−0.204589	+	1.74636i
$412$	8.65368	−	4.99621i	0.426336	−	0.246145i
$413$	9.37875	−	1.82848i	0.461498	−	0.0899737i
$414$	2.46804	+	8.25975i	0.121297	+	0.405944i
$415$	6.97127	−	12.0746i	0.342206	−	0.592719i
$416$	−1.97962	+	3.01349i	−0.0970587	+	0.147748i
$417$	8.79479	+	6.55110i	0.430683	+	0.320809i
$418$	0.0237765	−	0.0137274i	0.00116295	−	0.000671428i
$419$	14.1783	−	24.5576i	0.692657	−	1.19972i	−0.278307	−	0.960492i	$-0.589773\pi$
$419$	14.1783	−	24.5576i	0.692657	−	1.19972i	0.970964	−	0.239225i	$-0.0768934\pi$
$420$	−5.36560	+	0.408166i	−0.261815	+	0.0199165i
$421$	19.4027			0.945627			0.472814	−	0.881162i	$-0.343238\pi$
$421$	19.4027			0.945627			0.472814	+	0.881162i	$0.343238\pi$
$422$		−	21.3112i		−	1.03741i
$423$	−11.2288	−	37.5793i	−0.545963	−	1.82717i
$424$	1.01439	+	1.75697i	0.0492630	+	0.0853261i
$425$	−7.86637			−0.381575
$426$	16.2106	+	1.89911i	0.785408	+	0.0920120i
$427$	1.51609	−	1.31941i	0.0733690	−	0.0638507i
$428$			4.08949i			0.197673i
$429$	−1.96442	−	5.39238i	−0.0948433	−	0.260347i
$430$	5.58897	−	3.22679i	0.269524	−	0.155610i
$431$			17.7238i			0.853728i	0.904316	+	0.426864i	$0.140382\pi$
$431$			17.7238i			0.853728i	−0.904316	+	0.426864i	$0.859618\pi$
$432$	−0.898236	−	5.11793i	−0.0432164	−	0.246236i
$433$	0.325897	−	0.188157i	0.0156616	−	0.00904223i	−0.492149	−	0.870511i	$-0.663788\pi$
$433$	0.325897	−	0.188157i	0.0156616	−	0.00904223i	0.507810	+	0.861469i	$0.330455\pi$
$434$	10.9227	−	2.12950i	0.524308	−	0.102219i
$435$	−0.106538	−	0.0793587i	−0.00510812	−	0.00380496i
$436$	6.44094			0.308465
$437$	0.0429236	+	0.0743458i	0.00205331	+	0.00355644i
$438$	−4.65812	−	0.545707i	−0.222574	−	0.0260749i
$439$	24.2861	−	14.0216i	1.15911	−	0.669214i	0.208021	−	0.978124i	$-0.433298\pi$
$439$	24.2861	−	14.0216i	1.15911	−	0.669214i	0.951091	+	0.308911i	$0.0999645\pi$
$440$	−0.539560	+	0.934545i	−0.0257225	+	0.0445527i
$441$	−13.1302	−	16.3890i	−0.625247	−	0.780427i
$442$	7.81953	+	0.451097i	0.371937	+	0.0214565i
$443$	−13.9270	−	8.04074i	−0.661691	−	0.382027i	0.131230	−	0.991352i	$-0.458107\pi$
$443$	−13.9270	−	8.04074i	−0.661691	−	0.382027i	−0.792921	+	0.609325i	$0.791441\pi$
$444$	−2.01786	−	4.68134i	−0.0957634	−	0.222166i
$445$	11.7833			0.558583
$446$	23.2616			1.10147
$447$	−11.6268	+	5.01166i	−0.549929	+	0.237043i
$448$	1.73688	+	1.99580i	0.0820601	+	0.0942929i
$449$	30.1974	−	17.4345i	1.42510	−	0.822783i	0.428374	−	0.903602i	$-0.359087\pi$
$449$	30.1974	−	17.4345i	1.42510	−	0.822783i	0.996729	+	0.0808182i	$0.0257533\pi$
$450$	10.4087	−	3.11014i	0.490669	−	0.146613i
$451$	6.39555	+	3.69247i	0.301154	+	0.173872i
$452$		−	21.2141i		−	0.997828i
$453$	−10.0831	+	13.5365i	−0.473745	+	0.635999i
$454$		−	23.3571i		−	1.09620i
$455$	1.50675	+	11.0999i	0.0706375	+	0.520370i
$456$	−0.0204827	−	0.0475187i	−0.000959188	−	0.00222527i
$457$	−1.39850	−	2.42227i	−0.0654191	−	0.113309i	0.831461	−	0.555584i	$-0.187505\pi$
$457$	−1.39850	−	2.42227i	−0.0654191	−	0.113309i	−0.896880	+	0.442274i	$0.854172\pi$
$458$	−3.69265			−0.172546
$459$	−8.65278	+	7.24883i	−0.403877	+	0.338346i
$460$	−2.92219	−	1.68713i	−0.136248	−	0.0786627i
$461$	−11.5533	−	20.0109i	−0.538091	−	0.932001i	−0.999007	−	0.0445574i	$-0.985812\pi$
$461$	−11.5533	−	20.0109i	−0.538091	−	0.932001i	0.460916	−	0.887444i	$-0.347521\pi$
$462$	−4.19918	+	0.319436i	−0.195364	+	0.0148615i
$463$	7.03737			0.327054			0.163527	−	0.986539i	$-0.447713\pi$
$463$	7.03737			0.327054			0.163527	+	0.986539i	$0.447713\pi$
$464$			0.0653172i			0.00303228i
$465$	7.85598	−	3.38627i	0.364312	−	0.157035i
$466$	−9.22220			−0.427210
$467$	−14.7390	+	25.5287i	−0.682039	+	1.18133i	0.292319	+	0.956321i	$0.405573\pi$
$467$	−14.7390	+	25.5287i	−0.682039	+	1.18133i	−0.974358	+	0.225005i	$0.927760\pi$
$468$	−10.5250	+	2.49474i	−0.486520	+	0.115319i
$469$	22.7220	+	26.1092i	1.04920	+	1.20561i
$470$	13.2950	+	7.67590i	0.613255	+	0.354063i
$471$	12.3299	+	9.18435i	0.568132	+	0.423193i
$472$	−3.12771	−	1.80579i	−0.143965	−	0.0831181i
$473$	4.37399	−	2.52532i	0.201116	−	0.116114i
$474$	11.8026	−	5.08745i	0.542113	−	0.233674i
$475$	0.0936881	−	0.0540908i	0.00429870	−	0.00248186i
$476$	1.86817	−	5.43542i	0.0856273	−	0.249132i
$477$	−1.40674	+	5.92153i	−0.0644102	+	0.271128i
$478$	6.65373	+	11.5246i	0.304335	+	0.527123i
$479$	−14.8402			−0.678065			−0.339033	−	0.940775i	$-0.610100\pi$
$479$	−14.8402			−0.678065			−0.339033	+	0.940775i	$0.610100\pi$
$480$	1.63109	+	1.21497i	0.0744487	+	0.0554557i
$481$	−9.48036	+	4.76778i	−0.432267	+	0.217392i
$482$	25.7424			1.17253
$483$	−0.998829	−	13.1302i	−0.0454483	−	0.597447i
$484$	5.07773	−	8.79489i	0.230806	−	0.399768i
$485$		−	11.8575i		−	0.538422i
$486$	8.58324	−	13.0126i	0.389344	−	0.590264i
$487$	13.0447	−	22.5940i	0.591111	−	1.02383i	−0.402972	−	0.915212i	$-0.632023\pi$
$487$	13.0447	−	22.5940i	0.591111	−	1.02383i	0.994083	−	0.108622i	$-0.0346438\pi$
$488$	−0.759641			−0.0343873
$489$	−2.13750	−	4.95889i	−0.0966610	−	0.224249i
$490$	8.14105	+	1.13488i	0.367775	+	0.0512685i
$491$	−19.2964	−	11.1408i	−0.870834	−	0.502776i	−0.00320842	−	0.999995i	$-0.501021\pi$
$491$	−19.2964	−	11.1408i	−0.870834	−	0.502776i	−0.867625	+	0.497219i	$0.834355\pi$
$492$	8.31465	−	11.1623i	0.374853	−	0.503237i
$493$	0.122882	−	0.0709460i	0.00553433	−	0.00319525i
$494$	−0.0962321	+	0.0483962i	−0.00432968	+	0.00217745i
$495$	−3.10185	+	0.926842i	−0.139418	+	0.0416585i
$496$	−3.64262	−	2.10307i	−0.163558	−	0.0944305i
$497$	−23.5777	−	8.10374i	−1.05761	−	0.363502i
$498$	−16.4929	−	12.2853i	−0.739063	−	0.550517i
$499$	−11.3535	+	19.6649i	−0.508254	+	0.880321i	0.491701	+	0.870764i	$0.336375\pi$
$499$	−11.3535	+	19.6649i	−0.508254	+	0.880321i	−0.999954	+	0.00955703i	$0.996958\pi$
$500$	−5.06169	+	8.76711i	−0.226366	+	0.392077i
$501$	12.7095	+	1.48894i	0.567819	+	0.0665210i
$502$	−26.8320	−	15.4915i	−1.19757	−	0.691418i
$503$	−13.8434	−	23.9774i	−0.617246	−	1.06910i	−0.989986	−	0.141165i	$-0.954915\pi$
$503$	−13.8434	−	23.9774i	−0.617246	−	1.06910i	0.372740	−	0.927936i	$-0.378418\pi$
$504$	−0.322921	+	7.93068i	−0.0143840	+	0.353261i
$505$	5.19581	−	8.99940i	0.231210	−	0.400468i
$506$	−2.28694	−	1.32036i	−0.101667	−	0.0586974i
$507$	6.47599	+	21.5653i	0.287609	+	0.957748i
$508$	−0.00158663	−	0.00274813i	−7.03954e−5	−	0.000121928i
$509$	9.55630	+	16.5520i	0.423575	+	0.733654i	0.996286	−	0.0861033i	$-0.0274415\pi$
$509$	9.55630	+	16.5520i	0.423575	+	0.733654i	−0.572711	+	0.819757i	$0.694108\pi$
$510$	0.514093	−	4.38826i	0.0227644	−	0.194316i
$511$	6.77505	+	2.32860i	0.299711	+	0.103011i
$512$		−	1.00000i		−	0.0441942i
$513$	0.0532096	−	0.145832i	0.00234926	−	0.00643862i
$514$	27.0945	+	15.6430i	1.19509	+	0.689984i
$515$	−10.1616	+	5.86681i	−0.447774	+	0.258523i
$516$	−3.76804	−	8.74167i	−0.165879	−	0.384830i
$517$	10.4049	+	6.00725i	0.457605	+	0.264198i
$518$	1.49008	+	7.64299i	0.0654702	+	0.335813i
$519$	−6.83978	−	15.8680i	−0.300233	−	0.696526i
$520$	2.32457	−	3.53860i	0.101939	−	0.155178i
$521$	−7.05557	−	12.2206i	−0.309110	−	0.535394i	0.669058	−	0.743210i	$-0.266698\pi$
$521$	−7.05557	−	12.2206i	−0.309110	−	0.535394i	−0.978168	+	0.207816i	$0.933365\pi$
$522$	−0.134546	+	0.142459i	−0.00588891	+	0.00623526i
$523$	−1.17718	+	0.679646i	−0.0514745	+	0.0297188i	−0.525516	−	0.850783i	$-0.676128\pi$
$523$	−1.17718	+	0.679646i	−0.0514745	+	0.0297188i	0.474042	+	0.880502i	$0.342795\pi$
$524$	−3.60456	−	6.24329i	−0.157466	−	0.272739i
$525$	−16.5463	+	1.25869i	−0.722139	+	0.0549338i
$526$	−1.63886	−	2.83858i	−0.0714576	−	0.123768i
$527$			9.13721i			0.398023i
$528$	1.27651	+	0.950851i	0.0555529	+	0.0413805i
$529$	−7.37141	+	12.7677i	−0.320496	+	0.555115i
$530$	−1.19115	−	2.06313i	−0.0517402	−	0.0896166i
$531$	−3.10193	−	10.3812i	−0.134612	−	0.450506i
$532$	0.0151253	+	0.0775815i	0.000655765	+	0.00336358i
$533$	−24.2164	−	15.9082i	−1.04893	−	0.689059i
$534$	2.02234	−	17.2626i	0.0875154	−	0.747026i
$535$		−	4.80210i		−	0.207613i
$536$		−	13.0820i		−	0.565057i
$537$	−25.6846	+	11.0712i	−1.10837	+	0.477757i
$538$		−	7.84705i		−	0.338310i
$539$	6.37128	+	0.888167i	0.274430	+	0.0382560i
$540$	1.05476	+	6.00974i	0.0453895	+	0.258618i
$541$	16.1920	−	28.0454i	0.696150	−	1.20577i	−0.273642	−	0.961832i	$-0.588228\pi$
$541$	16.1920	−	28.0454i	0.696150	−	1.20577i	0.969792	−	0.243935i	$-0.0784383\pi$
$542$	−5.58065	+	9.66596i	−0.239709	+	0.415189i
$543$	18.7012	−	8.06104i	0.802546	−	0.345932i
$544$	−1.88131	+	1.08618i	−0.0806606	+	0.0465694i
$545$	−7.56329			−0.323976
$546$	16.5199	−	0.302349i	0.706988	−	0.0129393i
$547$	−20.9799			−0.897036			−0.448518	−	0.893774i	$-0.648048\pi$
$547$	−20.9799			−0.897036			−0.448518	+	0.893774i	$0.648048\pi$
$548$	−17.8232	+	10.2902i	−0.761367	+	0.439576i
$549$	−1.65680	−	1.56477i	−0.0707105	−	0.0667828i
$550$	−1.66388	+	2.88192i	−0.0709481	+	0.122886i
$551$	−0.000975680		0.00168993i	−4.15654e−5		7.19934e-5i
$552$	−2.97318	+	3.99146i	−0.126547	+	0.169888i
$553$	−19.2696	+	3.75680i	−0.819425	+	0.159755i
$554$		−	19.0907i		−	0.811086i
$555$	2.36948	+	5.49707i	0.100579	+	0.233338i
$556$			6.33154i			0.268517i
$557$		−	2.04448i		−	0.0866275i	−0.999062	−	0.0433137i	$-0.986208\pi$
$557$		−	2.04448i		−	0.0866275i	0.999062	−	0.0433137i	$-0.0137915\pi$
$558$	−3.61260	−	12.0902i	−0.152933	−	0.511820i
$559$	−17.7031	+	8.90309i	−0.748761	+	0.376561i
$560$	−2.03954	−	2.34358i	−0.0861864	−	0.0990343i
$561$	0.402335	−	3.43430i	0.0169866	−	0.144996i
$562$	−6.16876	−	10.6846i	−0.260214	−	0.450703i
$563$	17.3267	−	30.0108i	0.730235	−	1.26480i	−0.226548	−	0.974000i	$-0.572744\pi$
$563$	17.3267	−	30.0108i	0.730235	−	1.26480i	0.956783	−	0.290804i	$-0.0939227\pi$
$564$	13.5270	−	18.1599i	0.569591	−	0.764670i
$565$			24.9107i			1.04800i
$566$	−5.39233	−	9.33979i	−0.226656	−	0.392580i
$567$	−17.0406	+	16.6319i	−0.715636	+	0.698473i
$568$	4.71161	+	8.16075i	0.197695	+	0.342418i
$569$	−8.82762	+	5.09663i	−0.370073	+	0.213662i	−0.673490	−	0.739196i	$-0.735206\pi$
$569$	−8.82762	+	5.09663i	−0.370073	+	0.213662i	0.303417	+	0.952858i	$0.401872\pi$
$570$	0.0240518	+	0.0557990i	0.00100742	+	0.00233716i
$571$	4.05162	+	7.01761i	0.169555	+	0.293678i	0.938263	−	0.345922i	$-0.112434\pi$
$571$	4.05162	+	7.01761i	0.169555	+	0.293678i	−0.768709	+	0.639599i	$0.779100\pi$
$572$	1.81924	−	2.76935i	0.0760661	−	0.115792i
$573$	1.78448	−	0.769189i	0.0745478	−	0.0321333i
$574$	−16.0382	+	13.9576i	−0.669424	+	0.582578i
$575$	−9.01136	−	5.20271i	−0.375800	−	0.216968i
$576$	2.05988	−	2.18103i	0.0858284	−	0.0908763i
$577$	14.1521	−	8.17074i	0.589161	−	0.340153i	−0.175604	−	0.984461i	$-0.556188\pi$
$577$	14.1521	−	8.17074i	0.589161	−	0.340153i	0.764766	+	0.644308i	$0.222855\pi$
$578$	−10.6356	−	6.14044i	−0.442381	−	0.255409i
$579$	11.4837	+	26.6416i	0.477246	+	1.10719i
$580$		−	0.0766990i		−	0.00318475i
$581$	20.6230	+	23.6973i	0.855585	+	0.983128i
$582$	−17.3713	−	2.03508i	−0.720063	−	0.0843567i
$583$	−0.932206	−	1.61463i	−0.0386080	−	0.0668711i
$584$	−1.35388	−	2.34499i	−0.0560239	−	0.0970363i
$585$	12.3591	−	2.92945i	0.510984	−	0.121118i
$586$	−15.4741	−	8.93398i	−0.639229	−	0.369059i
$587$	11.5145	−	19.9438i	0.475256	−	0.823167i	−0.524343	−	0.851507i	$-0.675689\pi$
$587$	11.5145	−	19.9438i	0.475256	−	0.823167i	0.999598	+	0.0283405i	$0.00902228\pi$
$588$	3.05983	−	11.7319i	0.126185	−	0.483815i
$589$	−0.0628294	−	0.108824i	−0.00258884	−	0.00448400i
$590$	3.67273	+	2.12045i	0.151204	+	0.0872976i
$591$	4.34032	−	37.0487i	0.178537	−	1.52398i
$592$	1.47158	−	2.54886i	0.0604817	−	0.104757i
$593$	3.13509	−	5.43014i	0.128743	−	0.222989i	−0.794447	−	0.607334i	$-0.792239\pi$
$593$	3.13509	−	5.43014i	0.128743	−	0.222989i	0.923190	+	0.384344i	$0.125572\pi$
$594$	0.825464	+	4.70329i	0.0338692	+	0.192978i
$595$	−2.19370	+	6.38256i	−0.0899330	+	0.261659i
$596$	−6.33047	−	3.65490i	−0.259306	−	0.149710i
$597$	2.62443	−	22.4020i	0.107411	−	0.916852i
$598$	8.65936	+	5.68849i	0.354107	+	0.232620i
$599$	4.15122	−	2.39671i	0.169614	−	0.0979269i	−0.412790	−	0.910826i	$-0.635446\pi$
$599$	4.15122	−	2.39671i	0.169614	−	0.0979269i	0.582404	+	0.812900i	$0.302112\pi$
$600$	5.02991	+	3.74670i	0.205345	+	0.152958i
$601$	42.1719	+	24.3480i	1.72023	+	0.993174i	0.918434	+	0.395574i	$0.129454\pi$
$601$	42.1719	+	24.3480i	1.72023	+	0.993174i	0.801794	+	0.597601i	$0.203879\pi$
$602$	2.78249	+	14.2721i	0.113406	+	0.581687i
$603$	26.9474	−	28.5323i	1.09738	−	1.16192i
$604$	−9.74517			−0.396525
$605$	−5.96255	+	10.3274i	−0.242412	+	0.419870i
$606$	−12.2924	−	9.15643i	−0.499345	−	0.371954i
$607$		−	35.3201i		−	1.43360i	−0.697279	−	0.716800i	$-0.745606\pi$
$607$		−	35.3201i		−	1.43360i	0.697279	−	0.716800i	$-0.254394\pi$
$608$	0.0149376	−	0.0258726i	0.000605798	−	0.00104927i
$609$	0.247121	−	0.168892i	0.0100138	−	0.00684384i
$610$	0.892011			0.0361165
$611$	−39.3974	−	25.8809i	−1.59385	−	1.04703i
$612$	−6.34059	−	1.50630i	−0.256303	−	0.0608884i
$613$	41.7258			1.68529			0.842645	−	0.538469i	$-0.180997\pi$
$613$	41.7258			1.68529			0.842645	+	0.538469i	$0.180997\pi$
$614$	7.99918	+	13.8550i	0.322821	+	0.559142i
$615$	−9.76350	+	13.1074i	−0.393702	+	0.528542i
$616$	−1.59617	−	1.83411i	−0.0643115	−	0.0738985i
$617$	−25.8310	+	14.9135i	−1.03992	+	0.600395i	−0.919809	−	0.392366i	$-0.871657\pi$
$617$	−25.8310	+	14.9135i	−1.03992	+	0.600395i	−0.120106	+	0.992761i	$0.538323\pi$
$618$	6.85089	+	15.8937i	0.275583	+	0.639339i
$619$	11.2355	−	6.48683i	0.451594	−	0.260728i	−0.256909	−	0.966436i	$-0.582704\pi$
$619$	11.2355	−	6.48683i	0.451594	−	0.260728i	0.708503	+	0.705708i	$0.249371\pi$
$620$	4.27736	+	2.46953i	0.171783	+	0.0991789i
$621$	−14.7065	+	2.58111i	−0.590152	+	0.103576i
$622$	−12.9943	−	7.50229i	−0.521026	−	0.300814i
$623$	−8.62962	+	25.1078i	−0.345738	+	1.00592i
$624$	−4.78510	−	4.01283i	−0.191557	−	0.160642i
$625$	−3.10911	+	5.38514i	−0.124364	+	0.215405i
$626$	9.19469			0.367494
$627$	0.0188232	+	0.0436689i	0.000751727	+	0.00174397i
$628$			8.87654i			0.354213i
$629$	−6.39359			−0.254929
$630$	0.379191	−	9.31263i	0.0151073	−	0.371024i
$631$	−14.7342	−	25.5203i	−0.586557	−	1.01595i	−0.994679	−	0.103020i	$-0.967150\pi$
$631$	−14.7342	−	25.5203i	−0.586557	−	1.01595i	0.408122	−	0.912927i	$-0.366184\pi$
$632$	6.42620	+	3.71017i	0.255620	+	0.147583i
$633$	36.6614	+	4.29494i	1.45716	+	0.170709i
$634$	−30.3556			−1.20557
$635$	0.00186311	+	0.00322700i	7.39351e−5	+	0.000128059i
$636$	−3.22693	+	1.39095i	−0.127956	+	0.0551546i
$637$	−24.7550	−	4.91851i	−0.980827	−	0.194879i
$638$		−	0.0600255i		−	0.00237643i
$639$	−6.53401	+	27.5042i	−0.258481	+	1.08805i
$640$			1.17425i			0.0464164i
$641$	−24.6081	−	14.2075i	−0.971963	−	0.561163i	−0.0721291	−	0.997395i	$-0.522979\pi$
$641$	−24.6081	−	14.2075i	−0.971963	−	0.561163i	−0.899834	+	0.436232i	$0.856313\pi$
$642$	−7.03510	−	0.824174i	−0.277653	−	0.0325275i
$643$	−27.7370	+	16.0140i	−1.09384	+	0.631530i	−0.934597	−	0.355709i	$-0.884239\pi$
$643$	−27.7370	+	16.0140i	−1.09384	+	0.631530i	−0.159245	+	0.987239i	$0.550906\pi$
$644$	5.73500	−	4.99099i	0.225991	−	0.196673i
$645$	4.42464	+	10.2649i	0.174220	+	0.404181i
$646$	−0.0648993			−0.00255343
$647$	15.0516			0.591741			0.295870	−	0.955228i	$-0.404390\pi$
$647$	15.0516			0.591741			0.295870	+	0.955228i	$0.404390\pi$
$648$	8.98532	−	0.513784i	0.352977	−	0.0201833i
$649$	2.87432	+	1.65949i	0.112827	+	0.0651406i
$650$	7.16845	−	10.9122i	0.281170	−	0.428013i
$651$	1.46204	+	19.2194i	0.0573018	+	0.753268i
$652$	1.55883	−	2.69997i	0.0610485	−	0.105739i
$653$	11.8120	−	6.81968i	0.462240	−	0.266875i	−0.250745	−	0.968053i	$-0.580676\pi$
$653$	11.8120	−	6.81968i	0.462240	−	0.266875i	0.712986	+	0.701178i	$0.247342\pi$
$654$	−1.29807	+	11.0803i	−0.0507586	+	0.433272i
$655$	4.23267	+	7.33120i	0.165384	+	0.286454i
$656$	8.03598			0.313752
$657$	1.87754	−	7.90332i	0.0732500	−	0.308338i
$658$	−26.0925	+	22.7075i	−1.01719	+	0.885229i
$659$	7.63539	−	4.40829i	0.297432	−	0.171723i	−0.343856	−	0.939022i	$-0.611733\pi$
$659$	7.63539	−	4.40829i	0.297432	−	0.171723i	0.641289	+	0.767300i	$0.278400\pi$
$660$	−1.49894	−	1.11654i	−0.0583464	−	0.0434613i
$661$			28.6027i			1.11252i	0.831010	+	0.556258i	$0.187763\pi$
$661$			28.6027i			1.11252i	−0.831010	+	0.556258i	$0.812237\pi$
$662$	−26.1992	+	15.1261i	−1.01826	+	0.587892i
$663$	−2.35192	+	13.3609i	−0.0913410	+	0.518895i
$664$		−	11.8735i		−	0.460783i
$665$	−0.0177609	−	0.0911003i	−0.000688739	−	0.00353272i
$666$	8.45990	−	2.52785i	0.327815	−	0.0979521i
$667$	0.187691			0.00726743
$668$	3.69401	+	6.39822i	0.142926	+	0.247554i
$669$	−4.68801	+	40.0166i	−0.181249	+	1.54713i
$670$			15.3616i			0.593471i
$671$	0.698098			0.0269498
$672$	−3.78340	+	2.58571i	−0.145948	+	0.0997461i
$673$	9.49994	−	16.4544i	0.366196	−	0.634270i	−0.622771	−	0.782404i	$-0.713993\pi$
$673$	9.49994	−	16.4544i	0.366196	−	0.634270i	0.988967	+	0.148134i	$0.0473267\pi$
$674$	13.0953	−	7.56060i	0.504414	−	0.291224i
$675$	3.25263	+	18.5327i	0.125194	+	0.713323i
$676$	−7.75152	+	10.4362i	−0.298136	+	0.401392i
$677$	−24.1275	+	41.7901i	−0.927297	+	1.60612i	−0.139471	+	0.990226i	$0.544540\pi$
$677$	−24.1275	+	41.7901i	−0.927297	+	1.60612i	−0.787825	+	0.615899i	$0.788793\pi$
$678$	36.4943	+	4.27538i	1.40156	+	0.164195i
$679$	25.2659	+	8.68395i	0.969615	+	0.333259i
$680$	2.20914	−	1.27545i	0.0847165	−	0.0489111i
$681$	40.1809	+	4.70726i	1.53974	+	0.180383i
$682$	3.34751	+	1.93269i	0.128183	+	0.0740063i
$683$	6.11835	+	3.53243i	0.234112	+	0.135165i	0.612468	−	0.790496i	$-0.290177\pi$
$683$	6.11835	+	3.53243i	0.234112	+	0.135165i	−0.378356	+	0.925660i	$0.623510\pi$
$684$	0.0858738	−	0.0256594i	0.00328347	−	0.000981110i
$685$	20.9289	−	12.0833i	0.799652	−	0.461679i
$686$	−8.38035	+	16.5157i	−0.319963	+	0.630574i
$687$	0.744195	−	6.35241i	0.0283928	−	0.242359i
$688$	2.74795	−	4.75959i	0.104765	−	0.181458i
$689$	3.28652	+	6.53498i	0.125206	+	0.248963i
$690$	3.49126	−	4.68699i	0.132910	−	0.178431i
$691$	−23.8298	+	13.7581i	−0.906527	+	0.523384i	−0.879312	−	0.476246i	$-0.841997\pi$
$691$	−23.8298	+	13.7581i	−0.906527	+	0.523384i	−0.0272151	+	0.999630i	$0.508664\pi$
$692$	4.98811	−	8.63966i	0.189619	−	0.328430i
$693$	0.296759	−	7.28817i	0.0112729	−	0.276855i
$694$	3.24211			0.123069
$695$		−	7.43483i		−	0.282019i
$696$	−0.112364	−	0.0131637i	−0.00425916	−	0.000498968i
$697$	−8.72849	−	15.1182i	−0.330615	−	0.572643i
$698$	−10.3206			−0.390642
$699$	1.85859	−	15.8648i	0.0702984	−	0.600063i
$700$	−6.28948	−	7.22706i	−0.237720	−	0.273157i
$701$		−	1.43708i		−	0.0542779i	−0.999632	−	0.0271389i	$-0.991360\pi$
$701$		−	1.43708i		−	0.0542779i	0.999632	−	0.0271389i	$-0.00863965\pi$
$702$	−2.17050	−	18.6088i	−0.0819204	−	0.702345i
$703$	0.0761474	−	0.0439637i	0.00287195	−	0.00165812i
$704$			0.918984i			0.0346355i
$705$	−15.8842	+	21.3243i	−0.598232	+	0.803121i
$706$	−19.7980	+	11.4304i	−0.745106	+	0.430187i
$707$	15.3706	+	17.6620i	0.578073	+	0.664247i
$708$	3.73681	−	5.01664i	0.140438	−	0.188537i
$709$	19.0147			0.714111			0.357056	−	0.934083i	$-0.383781\pi$
$709$	19.0147			0.714111			0.357056	+	0.934083i	$0.383781\pi$
$710$	−5.53263	−	9.58279i	−0.207636	−	0.359636i
$711$	6.37323	+	21.3292i	0.239015	+	0.799907i
$712$	8.69033	−	5.01737i	0.325684	−	0.188034i
$713$	−6.04323	+	10.4672i	−0.226321	+	0.391999i
$714$	8.97397	+	4.30921i	0.335842	+	0.161268i
$715$	−2.13624	+	3.25192i	−0.0798910	+	0.121615i
$716$	−13.9845	−	8.07398i	−0.522627	−	0.301739i
$717$	−21.1666	+	9.12372i	−0.790480	+	0.340731i
$718$	0.0707566			0.00264061
$719$	38.3391			1.42981			0.714904	−	0.699222i	$-0.246470\pi$
$719$	38.3391			1.42981			0.714904	+	0.699222i	$0.246470\pi$
$720$	−2.41882	+	2.56108i	−0.0901442	+	0.0954459i
$721$	−5.05900	−	25.9489i	−0.188407	−	0.966387i
$722$	−16.4537	+	9.49955i	−0.612344	+	0.353537i
$723$	−5.18798	+	44.2843i	−0.192943	+	1.64695i
$724$	10.1823	+	5.87874i	0.378422	+	0.218482i
$725$		−	0.236522i		−	0.00878421i
$726$	14.1064	+	10.5076i	0.523537	+	0.389975i
$727$			36.3302i			1.34741i	0.738998	+	0.673707i	$0.235299\pi$
$727$			36.3302i			1.34741i	−0.738998	+	0.673707i	$0.764701\pi$
$728$	5.83759	+	7.54470i	0.216356	+	0.279625i
$729$	20.6556	+	17.3881i	0.765022	+	0.644004i
$730$	1.58980	+	2.75361i	0.0588411	+	0.101916i
$731$	−11.9390			−0.441581
$732$	0.153094	−	1.30680i	0.00565851	−	0.0483007i
$733$	−16.1295	−	9.31236i	−0.595756	−	0.343960i	0.171614	−	0.985164i	$-0.445102\pi$
$733$	−16.1295	−	9.31236i	−0.595756	−	0.343960i	−0.767370	+	0.641204i	$0.778435\pi$
$734$	8.21199	+	14.2236i	0.303110	+	0.525002i
$735$	−3.59301	+	13.7762i	−0.132530	+	0.508144i
$736$	−2.87353			−0.105920
$737$			12.0222i			0.442842i
$738$	17.5267	+	16.5532i	0.645168	+	0.609331i
$739$	−33.0261			−1.21488			−0.607442	−	0.794364i	$-0.707804\pi$
$739$	−33.0261			−1.21488			−0.607442	+	0.794364i	$0.707804\pi$
$740$	−1.72801	+	2.99300i	−0.0635229	+	0.110025i
$741$	−0.0638612	−	0.175300i	−0.00234600	−	0.00643981i
$742$	5.26844	−	1.02714i	0.193411	−	0.0377074i
$743$	2.44292	+	1.41042i	0.0896221	+	0.0517434i	0.544141	−	0.838994i	$-0.316856\pi$
$743$	2.44292	+	1.41042i	0.0896221	+	0.0517434i	−0.454519	+	0.890737i	$0.650189\pi$
$744$	4.35199	−	5.84251i	0.159552	−	0.214197i
$745$	7.43357	+	4.29178i	0.272345	+	0.157239i
$746$	−0.242947	+	0.140266i	−0.00889494	+	0.00513549i
$747$	24.4581	−	25.8966i	0.894874	−	0.947505i
$748$	1.72890	−	0.998178i	0.0632147	−	0.0364970i
$749$	10.2323	+	3.51686i	0.373879	+	0.128503i
$750$	−14.0618	−	10.4744i	−0.513466	−	0.382472i
$751$	−21.7233	−	37.6258i	−0.792693	−	1.37298i	−0.924294	−	0.381682i	$-0.875345\pi$
$751$	−21.7233	−	37.6258i	−0.792693	−	1.37298i	0.131601	−	0.991303i	$-0.457988\pi$
$752$	13.0737			0.476748
$753$	32.0573	−	43.0367i	1.16823	−	1.56834i
$754$	−0.0135634	+	0.235114i	−0.000493949	+	0.00856234i
$755$	11.4433			0.416464
$756$	−13.5780	−	2.15382i	−0.493826	−	0.0783338i
$757$	4.02158	−	6.96557i	0.146167	−	0.253168i	−0.783641	−	0.621214i	$-0.786640\pi$
$757$	4.02158	−	6.96557i	0.146167	−	0.253168i	0.929808	+	0.368046i	$0.119973\pi$
$758$		−	31.6211i		−	1.14853i
$759$	2.73230	−	3.66809i	0.0991762	−	0.133143i
$760$	−0.0175405	+	0.0303810i	−0.000636260	+	0.00110204i
$761$	34.6666			1.25666			0.628332	−	0.777945i	$-0.283738\pi$
$761$	34.6666			1.25666			0.628332	+	0.777945i	$0.283738\pi$
$762$	0.00504732	−	0.00217562i	0.000182845	−	7.88143e-5i
$763$	5.53905	−	16.1158i	0.200527	−	0.583431i
$764$	0.971600	+	0.560953i	0.0351512	+	0.0202946i
$765$	7.44546	+	1.76877i	0.269191	+	0.0639501i
$766$	−22.8482	+	13.1914i	−0.825539	+	0.476625i
$767$	−10.8834	−	7.14953i	−0.392978	−	0.258155i
$768$	1.72029	+	0.201534i	0.0620755	+	0.00727225i
$769$	37.8048	+	21.8266i	1.36328	+	0.787089i	0.990059	−	0.140655i	$-0.0449207\pi$
$769$	37.8048	+	21.8266i	1.36328	+	0.787089i	0.373219	+	0.927743i	$0.378254\pi$
$770$	1.87431	+	2.15371i	0.0675453	+	0.0776144i
$771$	−32.3709	+	43.4577i	−1.16581	+	1.56509i
$772$	−8.37481	+	14.5056i	−0.301416	+	0.522068i
$773$	−15.3590	+	26.6026i	−0.552426	+	0.956830i	0.445673	+	0.895196i	$0.352964\pi$
$773$	−15.3590	+	26.6026i	−0.552426	+	0.956830i	−0.998099	+	0.0616338i	$0.980369\pi$
$774$	15.7976	−	4.72036i	0.567831	−	0.169670i
$775$	13.1904	+	7.61548i	0.473813	+	0.273556i
$776$	−5.04896	−	8.74505i	−0.181247	−	0.313929i
$777$	−13.4484	+	1.02303i	−0.482459	+	0.0367011i
$778$	11.7596	−	20.3683i	0.421603	−	0.730238i
$779$	0.207912	+	0.120038i	0.00744922	+	0.00430081i
$780$	5.61892	+	4.71208i	0.201190	+	0.168719i
$781$	−4.32990	−	7.49960i	−0.154936	−	0.268357i
$782$	3.12116	+	5.40601i	0.111612	+	0.193319i
$783$	−0.217954	−	0.260167i	−0.00778905	−	0.00929763i
$784$	6.48735	−	2.62950i	0.231691	−	0.0939106i
$785$		−	10.4233i		−	0.372024i
$786$	11.4667	−	4.94264i	0.409003	−	0.176298i
$787$	−42.6182	−	24.6056i	−1.51918	−	0.877096i	−0.999745	−	0.0225831i	$-0.992811\pi$
$787$	−42.6182	−	24.6056i	−1.51918	−	0.877096i	−0.519430	−	0.854513i	$-0.673856\pi$
$788$	18.6511	−	10.7682i	0.664416	−	0.383601i
$789$	5.21346	−	2.24723i	0.185604	−	0.0800035i
$790$	−7.54599	−	4.35668i	−0.268474	−	0.155004i
$791$	−53.0796	−	18.2436i	−1.88729	−	0.648668i
$792$	−1.89300	+	2.00433i	−0.0672647	+	0.0712208i
$793$	−2.73438	−	0.157742i	−0.0971007	−	0.00560160i
$794$	−5.57094	−	9.64915i	−0.197705	−	0.342436i
$795$	3.78923	−	1.63332i	0.134390	−	0.0579280i
$796$	11.2776	−	6.51112i	0.399724	−	0.230780i
$797$	5.88110	+	10.1864i	0.208319	+	0.360819i	0.951185	−	0.308621i	$-0.0998674\pi$
$797$	5.88110	+	10.1864i	0.208319	+	0.360819i	−0.742866	+	0.669440i	$0.766534\pi$
$798$	−0.136511	+	0.0103845i	−0.00483242	+	0.000367607i
$799$	−14.2003	−	24.5957i	−0.502371	−	0.870132i
$800$			3.62113i			0.128026i
$801$	29.2891	+	6.95802i	1.03488	+	0.245850i
$802$	0.562805	−	0.974806i	0.0198733	−	0.0344216i
$803$	1.24419	+	2.15501i	0.0439066	+	0.0760485i
$804$	22.5048	+	2.63648i	0.793684	+	0.0929815i
$805$	−6.73435	+	5.86069i	−0.237355	+	0.206562i
$806$	−12.6751	−	8.32654i	−0.446463	−	0.293290i
$807$	13.4992	+	1.58145i	0.475193	+	0.0556697i
$808$		−	8.84955i		−	0.311326i
$809$			49.2392i			1.73116i	0.500773	+	0.865579i	$0.333049\pi$
$809$			49.2392i			1.73116i	−0.500773	+	0.865579i	$0.666951\pi$
$810$	−10.5510	+	0.603312i	−0.370726	+	0.0211982i
$811$		−	24.8223i		−	0.871628i	−0.900037	−	0.435814i	$-0.856461\pi$
$811$		−	24.8223i		−	0.871628i	0.900037	−	0.435814i	$-0.143539\pi$
$812$	0.163429	+	0.0561712i	0.00573525	+	0.00197122i
$813$	−15.5035	−	11.5483i	−0.543732	−	0.405018i
$814$	−1.35236	+	2.34236i	−0.0474002	+	0.0820996i
$815$	−1.83046	+	3.17045i	−0.0641183	+	0.111056i
$816$	−1.48938	−	3.45530i	−0.0521389	−	0.120960i
$817$	0.142193	−	0.0820954i	0.00497472	−	0.00287215i
$818$	9.06948			0.317107
$819$	−2.80921	+	28.4800i	−0.0981618	+	0.995170i
$820$	−9.43628			−0.329529
$821$	−30.3151	+	17.5025i	−1.05801	+	0.610840i	−0.924880	−	0.380259i	$-0.875835\pi$
$821$	−30.3151	+	17.5025i	−1.05801	+	0.610840i	−0.133126	+	0.991099i	$0.542501\pi$
$822$	−14.1101	−	32.7348i	−0.492147	−	1.14176i
$823$	2.66903	−	4.62290i	0.0930365	−	0.161144i	−0.815751	−	0.578403i	$-0.803676\pi$
$823$	2.66903	−	4.62290i	0.0930365	−	0.161144i	0.908787	+	0.417259i	$0.137009\pi$
$824$	−4.99621	+	8.65368i	−0.174051	+	0.301465i
$825$	−4.62240	−	3.44316i	−0.160931	−	0.119875i
$826$	−7.20799	+	6.27289i	−0.250798	+	0.218262i
$827$		−	19.8191i		−	0.689178i	−0.938754	−	0.344589i	$-0.888018\pi$
$827$		−	19.8191i		−	0.689178i	0.938754	−	0.344589i	$-0.111982\pi$
$828$	−6.26726	−	5.91913i	−0.217802	−	0.205704i
$829$			9.20374i			0.319659i	0.987145	+	0.159830i	$0.0510945\pi$
$829$			9.20374i			0.319659i	−0.987145	+	0.159830i	$0.948906\pi$
$830$			13.9425i			0.483953i
$831$	32.8415	+	3.84743i	1.13926	+	0.133466i
$832$	0.207654	−	3.59957i	0.00719910	−	0.124793i
$833$	−11.9933	−	9.34864i	−0.415544	−	0.323911i
$834$	−10.8921	−	1.27602i	−0.377161	−	0.0441851i
$835$	−4.33771	−	7.51313i	−0.150113	−	0.260003i
$836$	−0.0137274	+	0.0237765i	−0.000474771	+	0.000822328i
$837$	21.5267	−	3.77810i	0.744071	−	0.130590i
$838$			28.3567i			0.979565i
$839$	−16.4881	−	28.5582i	−0.569231	−	0.985937i	−0.996642	−	0.0818800i	$-0.973908\pi$
$839$	−16.4881	−	28.5582i	−0.569231	−	0.985937i	0.427411	−	0.904057i	$-0.359426\pi$
$840$	4.44266	−	3.03628i	0.153287	−	0.104762i
$841$	−14.4979	−	25.1110i	−0.499926	−	0.865898i
$842$	−16.8032	+	9.70133i	−0.579076	+	0.334330i
$843$	19.6238	−	8.45872i	0.675880	−	0.291334i
$844$	10.6556	+	18.4561i	0.366781	+	0.635284i
$845$	9.10225	−	12.2547i	0.313127	−	0.421575i
$846$	28.5141	+	26.9302i	0.980334	+	0.925879i
$847$	−17.6389	−	20.2683i	−0.606079	−	0.696428i
$848$	−1.75697	−	1.01439i	−0.0603346	−	0.0348342i
$849$	17.1538	−	7.39406i	0.588718	−	0.253763i
$850$	6.81247	−	3.93318i	0.233666	−	0.134907i
$851$	−7.32422	−	4.22864i	−0.251071	−	0.144956i
$852$	−14.9884	+	6.46065i	−0.513494	+	0.221338i
$853$		−	8.39823i		−	0.287550i	−0.989610	−	0.143775i	$-0.954076\pi$
$853$		−	8.39823i		−	0.287550i	0.989610	−	0.143775i	$-0.0459241\pi$
$854$	−0.653272	+	1.90069i	−0.0223545	+	0.0650402i
$855$	−0.100838	+	0.0301306i	−0.00344857	+	0.00103044i
$856$	−2.04475	−	3.54160i	−0.0698880	−	0.121050i
$857$	20.9307	+	36.2531i	0.714980	+	1.23838i	0.962967	+	0.269618i	$0.0868974\pi$
$857$	20.9307	+	36.2531i	0.714980	+	1.23838i	−0.247988	+	0.968763i	$0.579769\pi$
$858$	4.39743	+	3.68772i	0.150126	+	0.125897i
$859$	−22.3299	−	12.8922i	−0.761887	−	0.439875i	0.0680860	−	0.997679i	$-0.478311\pi$
$859$	−22.3299	−	12.8922i	−0.761887	−	0.439875i	−0.829973	+	0.557804i	$0.811644\pi$
$860$	−3.22679	+	5.58897i	−0.110033	+	0.190582i
$861$	−20.7788	−	30.4033i	−0.708138	−	1.03614i
$862$	−8.86192	−	15.3493i	−0.301838	−	0.522799i
$863$	23.6109	+	13.6317i	0.803724	+	0.464030i	0.844772	−	0.535127i	$-0.179736\pi$
$863$	23.6109	+	13.6317i	0.803724	+	0.464030i	−0.0410479	+	0.999157i	$0.513070\pi$
$864$	3.33686	+	3.98314i	0.113522	+	0.135509i
$865$	−5.85730	+	10.1451i	−0.199154	+	0.344945i
$866$	−0.188157	+	0.325897i	−0.00639382	+	0.0110744i
$867$	12.7067	−	17.0587i	0.431544	−	0.579344i
$868$	−8.39462	+	7.30557i	−0.284932	+	0.247967i
$869$	−5.90557	−	3.40958i	−0.200333	−	0.115662i
$870$	0.131944	+	0.0154575i	0.00447333	+	0.000524058i
$871$	2.71653	−	47.0896i	0.0920462	−	1.59557i
$872$	−5.57802	+	3.22047i	−0.188895	+	0.109059i
$873$	7.00183	−	29.4735i	0.236976	−	0.997525i
$874$	−0.0743458	−	0.0429236i	−0.00251478	−	0.00145191i
$875$	17.5832	+	20.2043i	0.594419	+	0.683030i
$876$	4.30690	−	1.85646i	0.145517	−	0.0627241i
$877$	19.3834			0.654531			0.327266	−	0.944932i	$-0.393873\pi$
$877$	19.3834			0.654531			0.327266	+	0.944932i	$0.393873\pi$
$878$	−14.0216	+	24.2861i	−0.473205	+	0.819616i
$879$	18.4876	−	24.8194i	0.623570	−	0.837137i
$880$		−	1.07912i		−	0.0363771i
$881$	2.46823	−	4.27510i	0.0831568	−	0.144032i	−0.821447	−	0.570284i	$-0.806833\pi$
$881$	2.46823	−	4.27510i	0.0831568	−	0.144032i	0.904604	+	0.426252i	$0.140166\pi$
$882$	19.5656	+	7.62816i	0.658807	+	0.256854i
$883$	50.5405			1.70082			0.850411	−	0.526118i	$-0.176353\pi$
$883$	50.5405			1.70082			0.850411	+	0.526118i	$0.176353\pi$
$884$	−6.99746	+	3.51910i	−0.235350	+	0.118360i
$885$	−4.38796	+	5.89080i	−0.147500	+	0.198017i
$886$	16.0815			0.540268
$887$	25.8419	+	44.7595i	0.867687	+	1.50288i	0.864354	+	0.502883i	$0.167727\pi$
$887$	25.8419	+	44.7595i	0.867687	+	1.50288i	0.00333264	+	0.999994i	$0.498939\pi$
$888$	4.08819	+	3.04523i	0.137191	+	0.102191i
$889$	−0.00824051	+	0.00160657i	−0.000276378	+	5.38827e-5i
$890$	−10.2047	+	5.89166i	−0.342061	+	0.197489i
$891$	−8.25737	+	0.472159i	−0.276632	+	0.0158179i
$892$	−20.1451	+	11.6308i	−0.674509	+	0.389428i
$893$	0.338250	+	0.195289i	0.0113191	+	0.00653509i
$894$	7.56328	−	10.1536i	0.252954	−	0.339588i
$895$	16.4214	+	9.48089i	0.548907	+	0.316911i
$896$	−2.50209	−	0.859975i	−0.0835889	−	0.0287297i
$897$	−11.5310	+	13.7501i	−0.385009	+	0.459104i
$898$	−17.4345	+	30.1974i	−0.581796	+	1.00770i
$899$	−0.274733			−0.00916286
$900$	−7.45909	+	7.89779i	−0.248636	+	0.263260i
$901$			4.40722i			0.146826i
$902$	−7.38494			−0.245892
$903$	−25.1128	+	1.91036i	−0.835703	+	0.0635727i
$904$	10.6071	+	18.3720i	0.352785	+	0.611042i
$905$	−11.9566	−	6.90313i	−0.397450	−	0.229468i
$906$	1.96399	−	16.7645i	0.0652491	−	0.556962i
$907$	6.18953			0.205520			0.102760	−	0.994706i	$-0.467233\pi$
$907$	6.18953			0.205520			0.102760	+	0.994706i	$0.467233\pi$
$908$	11.6786	+	20.2278i	0.387566	+	0.671285i
$909$	18.2290	−	19.3011i	0.604618	−	0.640178i
$910$	−6.85481	−	8.85939i	−0.227235	−	0.293686i
$911$			24.1747i			0.800943i	0.916309	+	0.400472i	$0.131154\pi$
$911$			24.1747i			0.800943i	−0.916309	+	0.400472i	$0.868846\pi$
$912$	0.0414979	+	0.0309111i	0.00137413	+	0.00102357i
$913$			10.9116i			0.361121i
$914$	2.42227	+	1.39850i	0.0801217	+	0.0462583i
$915$	−0.179771	+	1.53451i	−0.00594305	+	0.0507295i
$916$	3.19792	−	1.84632i	0.105662	−	0.0610042i
$917$	−18.7211	+	3.64986i	−0.618225	+	0.120529i
$918$	3.86911	−	10.6041i	0.127700	−	0.349986i
$919$	−49.8887			−1.64568			−0.822839	−	0.568275i	$-0.807611\pi$
$919$	−49.8887			−1.64568			−0.822839	+	0.568275i	$0.807611\pi$
$920$	3.37425			0.111246
$921$	−25.4467	+	10.9686i	−0.838496	+	0.361428i
$922$	20.0109	+	11.5533i	0.659024	+	0.380488i
$923$	15.2652	+	30.3536i	0.502459	+	0.999100i
$924$	3.47688	−	2.37623i	0.114381	−	0.0781722i
$925$	−5.32879	+	9.22974i	−0.175210	+	0.303472i
$926$	−6.09454	+	3.51868i	−0.200279	+	0.115631i
$927$	−28.7224	+	8.58236i	−0.943368	+	0.281882i
$928$	−0.0326586	−	0.0565664i	−0.00107207	−	0.00185688i
$929$	−22.5164			−0.738739			−0.369369	−	0.929283i	$-0.620426\pi$
$929$	−22.5164			−0.738739			−0.369369	+	0.929283i	$0.620426\pi$
$930$	−5.11034	+	6.86058i	−0.167575	+	0.224967i
$931$	0.207123	+	0.0288733i	0.00678818	+	0.000946284i
$932$	7.98666	−	4.61110i	0.261612	−	0.151042i
$933$	15.5249	−	20.8420i	0.508262	−	0.682337i
$934$		−	29.4780i		−	0.964548i
$935$	−2.03016	+	1.17211i	−0.0663934	+	0.0383322i
$936$	7.86758	−	7.42302i	0.257160	−	0.242629i
$937$			50.9552i			1.66463i	0.554300	+	0.832317i	$0.312986\pi$
$937$			50.9552i			1.66463i	−0.554300	+	0.832317i	$0.687014\pi$
$938$	−32.7324	−	11.2502i	−1.06875	−	0.367332i
$939$	−1.85305	+	15.8175i	−0.0604719	+	0.516184i
$940$	−15.3518			−0.500721
$941$	−7.47373	−	12.9449i	−0.243637	−	0.421991i	0.718111	−	0.695929i	$-0.245007\pi$
$941$	−7.47373	−	12.9449i	−0.243637	−	0.421991i	−0.961747	+	0.273938i	$0.911674\pi$
$942$	−15.2702	−	1.78893i	−0.497530	−	0.0582865i
$943$		−	23.0917i		−	0.751968i
$944$	3.61157			0.117547
$945$	15.9440	+	2.52913i	0.518657	+	0.0822727i
$946$	−2.52532	+	4.37399i	−0.0821053	+	0.142211i
$947$	2.33684	−	1.34918i	0.0759372	−	0.0438424i	−0.461551	−	0.887114i	$-0.652707\pi$
$947$	2.33684	−	1.34918i	0.0759372	−	0.0438424i	0.537488	+	0.843272i	$0.319373\pi$
$948$	−7.67765	+	10.3072i	−0.249359	+	0.334761i
$949$	−4.38643	−	8.72208i	−0.142390	−	0.283131i
$950$	−0.0540908	+	0.0936881i	−0.00175494	+	0.00303964i
$951$	6.11770	−	52.2203i	0.198380	−	1.69336i
$952$	1.09983	+	5.64129i	0.0356456	+	0.182835i
$953$	−17.2962	+	9.98599i	−0.560280	+	0.323478i	−0.753258	−	0.657725i	$-0.771519\pi$
$953$	−17.2962	+	9.98599i	−0.560280	+	0.323478i	0.192978	+	0.981203i	$0.438185\pi$
$954$	−1.74249	−	5.83156i	−0.0564152	−	0.188804i
$955$	−1.14090	−	0.658701i	−0.0369188	−	0.0213151i
$956$	−11.5246	−	6.65373i	−0.372732	−	0.215197i
$957$	0.103261	+	0.0120972i	0.00333795	+	0.000391047i
$958$	12.8520	−	7.42009i	0.415229	−	0.239732i
$959$	10.4195	+	53.4444i	0.336464	+	1.72581i
$960$	−2.02005	−	0.236653i	−0.0651969	−	0.00763793i
$961$	−6.65421	+	11.5254i	−0.214652	+	0.371788i
$962$	5.82634	−	8.86920i	0.187849	−	0.285954i
$963$	2.83563	−	11.9363i	0.0913769	−	0.384641i
$964$	−22.2936	+	12.8712i	−0.718027	+	0.414553i
$965$	9.83415	−	17.0332i	0.316572	−	0.548319i
$966$	7.43013	+	10.8717i	0.239061	+	0.349791i
$967$	−27.3039			−0.878035			−0.439017	−	0.898479i	$-0.644673\pi$
$967$	−27.3039			−0.878035			−0.439017	+	0.898479i	$0.644673\pi$
$968$			10.1555i			0.326409i
$969$	0.0130794	−	0.111645i	0.000420172	−	0.00358657i
$970$	5.92875	+	10.2689i	0.190361	+	0.329715i
$971$	15.4806			0.496798			0.248399	−	0.968658i	$-0.420096\pi$
$971$	15.4806			0.496798			0.248399	+	0.968658i	$0.420096\pi$
$972$	−0.926997	+	15.5609i	−0.0297335	+	0.499115i
$973$	15.8421	+	5.44497i	0.507874	+	0.174558i
$974$			26.0894i			0.835957i
$975$	17.3275	+	14.5310i	0.554923	+	0.465364i
$976$	0.657869	−	0.379821i	0.0210579	−	0.0121578i
$977$			22.4348i			0.717752i	0.933385	+	0.358876i	$0.116840\pi$
$977$			22.4348i			0.717752i	−0.933385	+	0.358876i	$0.883160\pi$
$978$	4.33057	+	3.22577i	0.138476	+	0.103149i
$979$	−7.98628	+	4.61088i	−0.255242	+	0.147364i
$980$	−7.61780	+	3.08769i	−0.243342	+	0.0986328i
$981$	−18.7996	−	4.46611i	−0.600225	−	0.142592i
$982$	22.2815			0.711033
$983$	−1.46260	−	2.53330i	−0.0466498	−	0.0807999i	0.841758	−	0.539856i	$-0.181521\pi$
$983$	−1.46260	−	2.53330i	−0.0466498	−	0.0807999i	−0.888407	+	0.459056i	$0.848188\pi$
$984$	−1.61953	+	13.8242i	−0.0516287	+	0.440699i
$985$	−21.9011	+	12.6446i	−0.697826	+	0.402890i
$986$	−0.0709460	+	0.122882i	−0.00225938	+	0.00391336i
$987$	−33.8048	−	49.4629i	−1.07602	−	1.57442i
$988$	0.0591413	−	0.0900284i	0.00188154	−	0.00286418i
$989$	−13.6768	−	7.89633i	−0.434898	−	0.251089i
$990$	2.22286	−	2.35359i	0.0706471	−	0.0748021i
$991$	−16.6048			−0.527470			−0.263735	−	0.964595i	$-0.584954\pi$
$991$	−16.6048			−0.527470			−0.263735	+	0.964595i	$0.584954\pi$
$992$	4.20614			0.133545
$993$	−20.7412	−	48.1185i	−0.658201	−	1.52699i
$994$	24.4708	−	4.77083i	0.776166	−	0.151321i
$995$	−13.2427	+	7.64570i	−0.419823	+	0.242385i
$996$	20.4259	+	2.39293i	0.647219	+	0.0758228i
$997$	37.7832	+	21.8141i	1.19661	+	0.690860i	0.959797	−	0.280696i	$-0.0905652\pi$
$997$	37.7832	+	21.8141i	1.19661	+	0.690860i	0.236809	+	0.971556i	$0.423899\pi$
$998$		−	22.7071i		−	0.718779i
$999$	2.64366	+	15.0629i	0.0836416	+	0.476569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.425.7	yes	76
3.2	odd	2	inner	546.2.u.a.425.32	yes	76
7.3	odd	6		546.2.bb.a.269.13	yes	76
13.3	even	3		546.2.bb.a.341.19	yes	76
21.17	even	6		546.2.bb.a.269.38	yes	76
39.29	odd	6		546.2.bb.a.341.32	yes	76
91.3	odd	6	inner	546.2.u.a.185.32	yes	76
273.185	even	6	inner	546.2.u.a.185.7	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.7	✓	76	273.185	even	6	inner
546.2.u.a.185.32	yes	76	91.3	odd	6	inner
546.2.u.a.425.7	yes	76	1.1	even	1	trivial
546.2.u.a.425.32	yes	76	3.2	odd	2	inner
546.2.bb.a.269.13	yes	76	7.3	odd	6
546.2.bb.a.269.38	yes	76	21.17	even	6
546.2.bb.a.341.19	yes	76	13.3	even	3
546.2.bb.a.341.32	yes	76	39.29	odd	6

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.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.685609 - 1.59058i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.587127 + 1.01693i) q^{5} +(1.38904 + 1.03468i) q^{6} +(-1.73688 - 1.99580i) q^{7} +1.00000i q^{8} +(-2.05988 + 2.18103i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.685609 - 1.59058i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.587127 + 1.01693i) q^{5} +(1.38904 + 1.03468i) q^{6} +(-1.73688 - 1.99580i) q^{7} +1.00000i q^{8} +(-2.05988 + 2.18103i) q^{9} -1.17425i q^{10} -0.918984i q^{11} +(-1.72029 - 0.201534i) q^{12} +(-0.207654 + 3.59957i) q^{13} +(2.50209 + 0.859975i) q^{14} +(2.02005 + 0.236653i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.08618 + 1.88131i) q^{17} +(0.693394 - 2.91877i) q^{18} -0.0298751i q^{19} +(0.587127 + 1.01693i) q^{20} +(-1.98366 + 4.13099i) q^{21} +(0.459492 + 0.795863i) q^{22} +(-2.48855 + 1.43677i) q^{23} +(1.59058 - 0.685609i) q^{24} +(1.81056 + 3.13599i) q^{25} +(-1.61995 - 3.22114i) q^{26} +(4.88137 + 1.78107i) q^{27} +(-2.59686 + 0.506284i) q^{28} +(-0.0565664 - 0.0326586i) q^{29} +(-1.86774 + 0.805079i) q^{30} +(3.64262 - 2.10307i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.46172 + 0.630064i) q^{33} -2.17235i q^{34} +(3.04937 - 0.594506i) q^{35} +(0.858887 + 2.87442i) q^{36} +(1.47158 + 2.54886i) q^{37} +(0.0149376 + 0.0258726i) q^{38} +(5.86776 - 2.13761i) q^{39} +(-1.01693 - 0.587127i) q^{40} +(-4.01799 + 6.95937i) q^{41} +(-0.347597 - 4.56937i) q^{42} +(2.74795 + 4.75959i) q^{43} +(-0.795863 - 0.459492i) q^{44} +(-1.00855 - 3.37530i) q^{45} +(1.43677 - 2.48855i) q^{46} +(-6.53683 + 11.3221i) q^{47} +(-1.03468 + 1.38904i) q^{48} +(-0.966466 + 6.93296i) q^{49} +(-3.13599 - 1.81056i) q^{50} +(3.73707 + 0.437804i) q^{51} +(3.01349 + 1.97962i) q^{52} +(1.75697 - 1.01439i) q^{53} +(-5.11793 + 0.898236i) q^{54} +(0.934545 + 0.539560i) q^{55} +(1.99580 - 1.73688i) q^{56} +(-0.0475187 + 0.0204827i) q^{57} +0.0653172 q^{58} +(-1.80579 + 3.12771i) q^{59} +(1.21497 - 1.63109i) q^{60} +0.759641i q^{61} +(-2.10307 + 3.64262i) q^{62} +(7.93068 + 0.322921i) q^{63} -1.00000 q^{64} +(-3.53860 - 2.32457i) q^{65} +(0.950851 - 1.27651i) q^{66} -13.0820 q^{67} +(1.08618 + 1.88131i) q^{68} +(3.99146 + 2.97318i) q^{69} +(-2.34358 + 2.03954i) q^{70} +(8.16075 - 4.71161i) q^{71} +(-2.18103 - 2.05988i) q^{72} +(-2.34499 + 1.35388i) q^{73} +(-2.54886 - 1.47158i) q^{74} +(3.74670 - 5.02991i) q^{75} +(-0.0258726 - 0.0149376i) q^{76} +(-1.83411 + 1.59617i) q^{77} +(-4.01283 + 4.78510i) q^{78} +(3.71017 - 6.42620i) q^{79} +1.17425 q^{80} +(-0.513784 - 8.98532i) q^{81} -8.03598i q^{82} -11.8735 q^{83} +(2.58571 + 3.78340i) q^{84} +(-1.27545 - 2.20914i) q^{85} +(-4.75959 - 2.74795i) q^{86} +(-0.0131637 + 0.112364i) q^{87} +0.918984 q^{88} +(-5.01737 - 8.69033i) q^{89} +(2.56108 + 2.41882i) q^{90} +(7.54470 - 5.83759i) q^{91} +2.87353i q^{92} +(-5.84251 - 4.35199i) q^{93} -13.0737i q^{94} +(0.0303810 + 0.0175405i) q^{95} +(0.201534 - 1.72029i) q^{96} +(-8.74505 + 5.04896i) q^{97} +(-2.62950 - 6.48735i) q^{98} +(2.00433 + 1.89300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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