LMFDB - Embedded newform 546.2.bi.e.257.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.14
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.e.17.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.21751 + 1.23193i) q^{3} +1.00000 q^{4} +(-1.57344 - 0.908426i) q^{5} +(-1.21751 - 1.23193i) q^{6} +(-2.47008 + 0.947995i) q^{7} -1.00000 q^{8} +(-0.0353243 + 2.99979i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.21751 + 1.23193i) q^{3} +1.00000 q^{4} +(-1.57344 - 0.908426i) q^{5} +(-1.21751 - 1.23193i) q^{6} +(-2.47008 + 0.947995i) q^{7} -1.00000 q^{8} +(-0.0353243 + 2.99979i) q^{9} +(1.57344 + 0.908426i) q^{10} +(1.02563 - 1.77645i) q^{11} +(1.21751 + 1.23193i) q^{12} +(-3.57560 + 0.463745i) q^{13} +(2.47008 - 0.947995i) q^{14} +(-0.796563 - 3.04440i) q^{15} +1.00000 q^{16} -5.68717 q^{17} +(0.0353243 - 2.99979i) q^{18} +(-0.796762 - 1.38003i) q^{19} +(-1.57344 - 0.908426i) q^{20} +(-4.17522 - 1.88878i) q^{21} +(-1.02563 + 1.77645i) q^{22} +8.73960i q^{23} +(-1.21751 - 1.23193i) q^{24} +(-0.849523 - 1.47142i) q^{25} +(3.57560 - 0.463745i) q^{26} +(-3.73855 + 3.60877i) q^{27} +(-2.47008 + 0.947995i) q^{28} +(-0.724381 + 0.418222i) q^{29} +(0.796563 + 3.04440i) q^{30} +(-3.97501 - 6.88493i) q^{31} -1.00000 q^{32} +(3.43719 - 0.899337i) q^{33} +5.68717 q^{34} +(4.74771 + 0.752275i) q^{35} +(-0.0353243 + 2.99979i) q^{36} +4.21819i q^{37} +(0.796762 + 1.38003i) q^{38} +(-4.92465 - 3.84029i) q^{39} +(1.57344 + 0.908426i) q^{40} +(-0.397180 + 0.229312i) q^{41} +(4.17522 + 1.88878i) q^{42} +(0.836012 - 1.44802i) q^{43} +(1.02563 - 1.77645i) q^{44} +(2.78067 - 4.68791i) q^{45} -8.73960i q^{46} +(1.94760 + 1.12445i) q^{47} +(1.21751 + 1.23193i) q^{48} +(5.20261 - 4.68325i) q^{49} +(0.849523 + 1.47142i) q^{50} +(-6.92421 - 7.00622i) q^{51} +(-3.57560 + 0.463745i) q^{52} +(-0.497067 + 0.286982i) q^{53} +(3.73855 - 3.60877i) q^{54} +(-3.22755 + 1.86343i) q^{55} +(2.47008 - 0.947995i) q^{56} +(0.730041 - 2.66176i) q^{57} +(0.724381 - 0.418222i) q^{58} -2.19150i q^{59} +(-0.796563 - 3.04440i) q^{60} +(-5.97394 + 3.44906i) q^{61} +(3.97501 + 6.88493i) q^{62} +(-2.75653 - 7.44322i) q^{63} +1.00000 q^{64} +(6.04728 + 2.51850i) q^{65} +(-3.43719 + 0.899337i) q^{66} +(-4.46448 - 2.57757i) q^{67} -5.68717 q^{68} +(-10.7666 + 10.6406i) q^{69} +(-4.74771 - 0.752275i) q^{70} +(-4.24250 + 7.34823i) q^{71} +(0.0353243 - 2.99979i) q^{72} +(5.11752 + 8.86381i) q^{73} -4.21819i q^{74} +(0.778384 - 2.83803i) q^{75} +(-0.796762 - 1.38003i) q^{76} +(-0.849335 + 5.36027i) q^{77} +(4.92465 + 3.84029i) q^{78} +(-3.68537 + 6.38325i) q^{79} +(-1.57344 - 0.908426i) q^{80} +(-8.99750 - 0.211931i) q^{81} +(0.397180 - 0.229312i) q^{82} -15.0678i q^{83} +(-4.17522 - 1.88878i) q^{84} +(8.94843 + 5.16638i) q^{85} +(-0.836012 + 1.44802i) q^{86} +(-1.39717 - 0.383200i) q^{87} +(-1.02563 + 1.77645i) q^{88} +3.86314i q^{89} +(-2.78067 + 4.68791i) q^{90} +(8.39241 - 4.53514i) q^{91} +8.73960i q^{92} +(3.64215 - 13.2794i) q^{93} +(-1.94760 - 1.12445i) q^{94} +2.89520i q^{95} +(-1.21751 - 1.23193i) q^{96} +(-1.72410 + 2.98622i) q^{97} +(-5.20261 + 4.68325i) q^{98} +(5.29275 + 3.13944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.21751	+	1.23193i	0.702931	+	0.711258i
$3$	1.21751	+	1.23193i	0.702931	+	0.711258i
$4$	1.00000			0.500000
$5$	−1.57344	−	0.908426i	−0.703664	−	0.406261i	0.105047	−	0.994467i	$-0.466501\pi$
$5$	−1.57344	−	0.908426i	−0.703664	−	0.406261i	−0.808711	+	0.588207i	$0.799834\pi$
$6$	−1.21751	−	1.23193i	−0.497048	−	0.502935i
$7$	−2.47008	+	0.947995i	−0.933603	+	0.358308i
$7$	−2.47008	+	0.947995i	−0.933603	+	0.358308i
$8$	−1.00000			−0.353553
$9$	−0.0353243	+	2.99979i	−0.0117748	+	0.999931i
$10$	1.57344	+	0.908426i	0.497566	+	0.287270i
$11$	1.02563	−	1.77645i	0.309240	−	0.535620i	−0.668956	−	0.743302i	$-0.733259\pi$
$11$	1.02563	−	1.77645i	0.309240	−	0.535620i	0.978196	+	0.207682i	$0.0665920\pi$
$12$	1.21751	+	1.23193i	0.351466	+	0.355629i
$13$	−3.57560	+	0.463745i	−0.991694	+	0.128620i
$13$	−3.57560	+	0.463745i	−0.991694	+	0.128620i
$14$	2.47008	−	0.947995i	0.660157	−	0.253362i
$15$	−0.796563	−	3.04440i	−0.205672	−	0.786060i
$16$	1.00000			0.250000
$17$	−5.68717			−1.37934			−0.689671	−	0.724123i	$-0.742245\pi$
$17$	−5.68717			−1.37934			−0.689671	+	0.724123i	$0.742245\pi$
$18$	0.0353243	−	2.99979i	0.00832601	−	0.707058i
$19$	−0.796762	−	1.38003i	−0.182790	−	0.316601i	0.760040	−	0.649876i	$-0.225179\pi$
$19$	−0.796762	−	1.38003i	−0.182790	−	0.316601i	−0.942829	+	0.333276i	$0.891846\pi$
$20$	−1.57344	−	0.908426i	−0.351832	−	0.203130i
$21$	−4.17522	−	1.88878i	−0.911109	−	0.412166i
$22$	−1.02563	+	1.77645i	−0.218666	+	0.378740i
$23$			8.73960i			1.82233i	0.412039	+	0.911166i	$0.364817\pi$
$23$			8.73960i			1.82233i	−0.412039	+	0.911166i	$0.635183\pi$
$24$	−1.21751	−	1.23193i	−0.248524	−	0.251468i
$25$	−0.849523	−	1.47142i	−0.169905	−	0.294283i
$26$	3.57560	−	0.463745i	0.701234	−	0.0909480i
$27$	−3.73855	+	3.60877i	−0.719485	+	0.694508i
$28$	−2.47008	+	0.947995i	−0.466802	+	0.179154i
$29$	−0.724381	+	0.418222i	−0.134514	+	0.0776618i	−0.565747	−	0.824579i	$-0.691412\pi$
$29$	−0.724381	+	0.418222i	−0.134514	+	0.0776618i	0.431233	+	0.902241i	$0.358079\pi$
$30$	0.796563	+	3.04440i	0.145432	+	0.555828i
$31$	−3.97501	−	6.88493i	−0.713934	−	1.23657i	−0.963369	−	0.268178i	$-0.913579\pi$
$31$	−3.97501	−	6.88493i	−0.713934	−	1.23657i	0.249436	−	0.968391i	$-0.419755\pi$
$32$	−1.00000			−0.176777
$33$	3.43719	−	0.899337i	0.598338	−	0.156555i
$34$	5.68717			0.975342
$35$	4.74771	+	0.752275i	0.802510	+	0.127158i
$36$	−0.0353243	+	2.99979i	−0.00588738	+	0.499965i
$37$			4.21819i			0.693466i	0.937964	+	0.346733i	$0.112709\pi$
$37$			4.21819i			0.693466i	−0.937964	+	0.346733i	$0.887291\pi$
$38$	0.796762	+	1.38003i	0.129252	+	0.223871i
$39$	−4.92465	−	3.84029i	−0.788575	−	0.614939i
$40$	1.57344	+	0.908426i	0.248783	+	0.143635i
$41$	−0.397180	+	0.229312i	−0.0620290	+	0.0358125i	−0.530694	−	0.847564i	$-0.678069\pi$
$41$	−0.397180	+	0.229312i	−0.0620290	+	0.0358125i	0.468665	+	0.883376i	$0.344735\pi$
$42$	4.17522	+	1.88878i	0.644251	+	0.291446i
$43$	0.836012	−	1.44802i	0.127491	−	0.220820i	−0.795213	−	0.606330i	$-0.792641\pi$
$43$	0.836012	−	1.44802i	0.127491	−	0.220820i	0.922704	+	0.385510i	$0.125974\pi$
$44$	1.02563	−	1.77645i	0.154620	−	0.267810i
$45$	2.78067	−	4.68791i	0.414518	−	0.698832i
$46$		−	8.73960i		−	1.28858i
$47$	1.94760	+	1.12445i	0.284086	+	0.164017i	0.635272	−	0.772289i	$-0.280888\pi$
$47$	1.94760	+	1.12445i	0.284086	+	0.164017i	−0.351186	+	0.936306i	$0.614221\pi$
$48$	1.21751	+	1.23193i	0.175733	+	0.177814i
$49$	5.20261	−	4.68325i	0.743230	−	0.669036i
$50$	0.849523	+	1.47142i	0.120141	+	0.208090i
$51$	−6.92421	−	7.00622i	−0.969583	−	0.981068i
$52$	−3.57560	+	0.463745i	−0.495847	+	0.0643099i
$53$	−0.497067	+	0.286982i	−0.0682774	+	0.0394200i	−0.533750	−	0.845642i	$-0.679218\pi$
$53$	−0.497067	+	0.286982i	−0.0682774	+	0.0394200i	0.465473	+	0.885062i	$0.345884\pi$
$54$	3.73855	−	3.60877i	0.508753	−	0.491091i
$55$	−3.22755	+	1.86343i	−0.435202	+	0.251264i
$56$	2.47008	−	0.947995i	0.330079	−	0.126681i
$57$	0.730041	−	2.66176i	0.0966962	−	0.352559i
$58$	0.724381	−	0.418222i	0.0951159	−	0.0549152i
$59$		−	2.19150i		−	0.285308i	−0.989773	−	0.142654i	$-0.954436\pi$
$59$		−	2.19150i		−	0.285308i	0.989773	−	0.142654i	$-0.0455637\pi$
$60$	−0.796563	−	3.04440i	−0.102836	−	0.393030i
$61$	−5.97394	+	3.44906i	−0.764885	+	0.441607i	−0.831047	−	0.556202i	$-0.812258\pi$
$61$	−5.97394	+	3.44906i	−0.764885	+	0.441607i	0.0661618	+	0.997809i	$0.478925\pi$
$62$	3.97501	+	6.88493i	0.504827	+	0.874386i
$63$	−2.75653	−	7.44322i	−0.347290	−	0.937758i
$64$	1.00000			0.125000
$65$	6.04728	+	2.51850i	0.750073	+	0.312381i
$66$	−3.43719	+	0.899337i	−0.423089	+	0.110701i
$67$	−4.46448	−	2.57757i	−0.545423	−	0.314900i	0.201851	−	0.979416i	$-0.435304\pi$
$67$	−4.46448	−	2.57757i	−0.545423	−	0.314900i	−0.747274	+	0.664516i	$0.768638\pi$
$68$	−5.68717			−0.689671
$69$	−10.7666	+	10.6406i	−1.29615	+	1.28097i
$70$	−4.74771	−	0.752275i	−0.567460	−	0.0899140i
$71$	−4.24250	+	7.34823i	−0.503493	+	0.872075i	0.496499	+	0.868037i	$0.334619\pi$
$71$	−4.24250	+	7.34823i	−0.503493	+	0.872075i	−0.999992	+	0.00403764i	$0.998715\pi$
$72$	0.0353243	−	2.99979i	0.00416300	−	0.353529i
$73$	5.11752	+	8.86381i	0.598961	+	1.03743i	0.992975	+	0.118326i	$0.0377528\pi$
$73$	5.11752	+	8.86381i	0.598961	+	1.03743i	−0.394014	+	0.919104i	$0.628914\pi$
$74$		−	4.21819i		−	0.490354i
$75$	0.778384	−	2.83803i	0.0898800	−	0.327707i
$76$	−0.796762	−	1.38003i	−0.0913948	−	0.158300i
$77$	−0.849335	+	5.36027i	−0.0967907	+	0.610860i
$78$	4.92465	+	3.84029i	0.557607	+	0.434827i
$79$	−3.68537	+	6.38325i	−0.414637	+	0.718172i	−0.995390	−	0.0959076i	$-0.969425\pi$
$79$	−3.68537	+	6.38325i	−0.414637	+	0.718172i	0.580754	+	0.814079i	$0.302758\pi$
$80$	−1.57344	−	0.908426i	−0.175916	−	0.101565i
$81$	−8.99750	−	0.211931i	−0.999723	−	0.0235479i
$82$	0.397180	−	0.229312i	0.0438612	−	0.0253233i
$83$		−	15.0678i		−	1.65391i	−0.562269	−	0.826954i	$-0.690071\pi$
$83$		−	15.0678i		−	1.65391i	0.562269	−	0.826954i	$-0.309929\pi$
$84$	−4.17522	−	1.88878i	−0.455554	−	0.206083i
$85$	8.94843	+	5.16638i	0.970594	+	0.560373i
$86$	−0.836012	+	1.44802i	−0.0901495	+	0.156143i
$87$	−1.39717	−	0.383200i	−0.149792	−	0.0410833i
$88$	−1.02563	+	1.77645i	−0.109333	+	0.189370i
$89$			3.86314i			0.409492i	0.978815	+	0.204746i	$0.0656368\pi$
$89$			3.86314i			0.409492i	−0.978815	+	0.204746i	$0.934363\pi$
$90$	−2.78067	+	4.68791i	−0.293108	+	0.494149i
$91$	8.39241	−	4.53514i	0.879763	−	0.475412i
$92$			8.73960i			0.911166i
$93$	3.64215	−	13.2794i	0.377673	−	1.37701i
$94$	−1.94760	−	1.12445i	−0.200879	−	0.115978i
$95$			2.89520i			0.297041i
$96$	−1.21751	−	1.23193i	−0.124262	−	0.125734i
$97$	−1.72410	+	2.98622i	−0.175056	+	0.303205i	−0.940180	−	0.340677i	$-0.889344\pi$
$97$	−1.72410	+	2.98622i	−0.175056	+	0.303205i	0.765125	+	0.643882i	$0.222677\pi$
$98$	−5.20261	+	4.68325i	−0.525543	+	0.473080i
$99$	5.29275	+	3.13944i	0.531941	+	0.315526i
$100$	−0.849523	−	1.47142i	−0.0849523	−	0.147142i
$101$	4.84811	−	8.39717i	0.482405	−	0.835550i	−0.517391	−	0.855749i	$-0.673097\pi$
$101$	4.84811	−	8.39717i	0.482405	−	0.835550i	0.999796	+	0.0201992i	$0.00643004\pi$
$102$	6.92421	+	7.00622i	0.685599	+	0.693720i
$103$	8.08628	+	4.66861i	0.796765	+	0.460012i	0.842339	−	0.538949i	$-0.181178\pi$
$103$	8.08628	+	4.66861i	0.796765	+	0.460012i	−0.0455739	+	0.998961i	$0.514512\pi$
$104$	3.57560	−	0.463745i	0.350617	−	0.0454740i
$105$	4.85365	+	6.76477i	0.473667	+	0.660174i
$106$	0.497067	−	0.286982i	0.0482794	−	0.0278742i
$107$			10.7060i			1.03499i	0.855687	+	0.517493i	$0.173135\pi$
$107$			10.7060i			1.03499i	−0.855687	+	0.517493i	$0.826865\pi$
$108$	−3.73855	+	3.60877i	−0.359743	+	0.347254i
$109$	−4.30381	+	2.48481i	−0.412230	+	0.238001i	−0.691748	−	0.722139i	$-0.743159\pi$
$109$	−4.30381	+	2.48481i	−0.412230	+	0.238001i	0.279517	+	0.960141i	$0.409826\pi$
$110$	3.22755	−	1.86343i	0.307735	−	0.177671i
$111$	−5.19653	+	5.13570i	−0.493233	+	0.487459i
$112$	−2.47008	+	0.947995i	−0.233401	+	0.0895771i
$113$	14.4435	+	8.33897i	1.35873	+	0.784464i	0.989453	−	0.144855i	$-0.0462714\pi$
$113$	14.4435	+	8.33897i	1.35873	+	0.784464i	0.369279	+	0.929319i	$0.379605\pi$
$114$	−0.730041	+	2.66176i	−0.0683746	+	0.249297i
$115$	7.93928	−	13.7512i	0.740342	−	1.28231i
$116$	−0.724381	+	0.418222i	−0.0672571	+	0.0388309i
$117$	−1.26483	−	10.7424i	−0.116934	−	0.993140i
$118$			2.19150i			0.201743i
$119$	14.0478	−	5.39141i	1.28776	−	0.494230i
$120$	0.796563	+	3.04440i	0.0727159	+	0.277914i
$121$	3.39615	+	5.88231i	0.308741	+	0.534755i
$122$	5.97394	−	3.44906i	0.540855	−	0.312263i
$123$	−0.766068	−	0.210109i	−0.0690741	−	0.0189449i
$124$	−3.97501	−	6.88493i	−0.356967	−	0.618285i
$125$			12.1712i			1.08862i
$126$	2.75653	+	7.44322i	0.245571	+	0.663095i
$127$	−10.6930	−	18.5208i	−0.948852	−	1.64346i	−0.747849	−	0.663869i	$-0.768913\pi$
$127$	−10.6930	−	18.5208i	−0.948852	−	1.64346i	−0.201003	−	0.979591i	$-0.564420\pi$
$128$	−1.00000			−0.0883883
$129$	2.80171	−	0.733065i	0.246677	−	0.0645428i
$130$	−6.04728	−	2.51850i	−0.530381	−	0.220887i
$131$	7.44741	−	12.8993i	0.650683	−	1.12702i	−0.332274	−	0.943183i	$-0.607816\pi$
$131$	7.44741	−	12.8993i	0.650683	−	1.12702i	0.982957	−	0.183834i	$-0.0588508\pi$
$132$	3.43719	−	0.899337i	0.299169	−	0.0782773i
$133$	3.27633	+	2.65347i	0.284094	+	0.230085i
$134$	4.46448	+	2.57757i	0.385672	+	0.222668i
$135$	9.16069	−	2.28198i	0.788427	−	0.196402i
$136$	5.68717			0.487671
$137$	11.6043			0.991424			0.495712	−	0.868487i	$-0.334907\pi$
$137$	11.6043			0.991424			0.495712	+	0.868487i	$0.334907\pi$
$138$	10.7666	−	10.6406i	0.916515	−	0.905786i
$139$	13.6556	+	7.88408i	1.15825	+	0.668719i	0.950885	−	0.309544i	$-0.100176\pi$
$139$	13.6556	+	7.88408i	1.15825	+	0.668719i	0.207370	+	0.978263i	$0.433510\pi$
$140$	4.74771	+	0.752275i	0.401255	+	0.0635788i
$141$	0.985981	+	3.76834i	0.0830346	+	0.317351i
$142$	4.24250	−	7.34823i	0.356023	−	0.616650i
$143$	−2.84344	+	6.82751i	−0.237780	+	0.570945i
$144$	−0.0353243	+	2.99979i	−0.00294369	+	0.249983i
$145$	1.51969			0.126204
$146$	−5.11752	−	8.86381i	−0.423529	−	0.733574i
$147$	12.1037	+	0.707360i	0.998297	+	0.0583421i
$148$			4.21819i			0.346733i
$149$	−2.40740	−	4.16974i	−0.197222	−	0.341599i	0.750405	−	0.660979i	$-0.229859\pi$
$149$	−2.40740	−	4.16974i	−0.197222	−	0.341599i	−0.947627	+	0.319380i	$0.896525\pi$
$150$	−0.778384	+	2.83803i	−0.0635548	+	0.231724i
$151$	−1.23569	+	0.713427i	−0.100559	+	0.0580579i	−0.549436	−	0.835536i	$-0.685157\pi$
$151$	−1.23569	+	0.713427i	−0.100559	+	0.0580579i	0.448877	+	0.893594i	$0.351824\pi$
$152$	0.796762	+	1.38003i	0.0646259	+	0.111935i
$153$	0.200895	−	17.0603i	0.0162414	−	1.37925i
$154$	0.849335	−	5.36027i	0.0684414	−	0.431943i
$155$			14.4440i			1.16017i
$156$	−4.92465	−	3.84029i	−0.394287	−	0.307469i
$157$	7.14347	−	4.12428i	0.570111	−	0.329154i	−0.187083	−	0.982344i	$-0.559903\pi$
$157$	7.14347	−	4.12428i	0.570111	−	0.329154i	0.757194	+	0.653191i	$0.226570\pi$
$158$	3.68537	−	6.38325i	0.293192	−	0.507824i
$159$	−0.958729	−	0.262950i	−0.0760321	−	0.0208533i
$160$	1.57344	+	0.908426i	0.124391	+	0.0718174i
$161$	−8.28509	−	21.5875i	−0.652957	−	1.70134i
$162$	8.99750	+	0.211931i	0.706911	+	0.0166509i
$163$	−20.7420	+	11.9754i	−1.62464	+	0.937985i	−0.638981	+	0.769223i	$0.720644\pi$
$163$	−20.7420	+	11.9754i	−1.62464	+	0.937985i	−0.985657	+	0.168762i	$0.946023\pi$
$164$	−0.397180	+	0.229312i	−0.0310145	+	0.0179062i
$165$	−6.22520	−	1.70738i	−0.484631	−	0.132920i
$166$			15.0678i			1.16949i
$167$	−20.2949	+	11.7173i	−1.57047	+	0.906711i	−0.574358	+	0.818604i	$0.694748\pi$
$167$	−20.2949	+	11.7173i	−1.57047	+	0.906711i	−0.996111	+	0.0881060i	$0.971919\pi$
$168$	4.17522	+	1.88878i	0.322126	+	0.145723i
$169$	12.5699	−	3.31634i	0.966914	−	0.255103i
$170$	−8.94843	−	5.16638i	−0.686313	−	0.396243i
$171$	4.16795	−	2.34137i	0.318731	−	0.179049i
$172$	0.836012	−	1.44802i	0.0637453	−	0.110410i
$173$	−3.80295	−	6.58691i	−0.289133	−	0.500794i	0.684470	−	0.729041i	$-0.260034\pi$
$173$	−3.80295	−	6.58691i	−0.289133	−	0.500794i	−0.973603	+	0.228248i	$0.926700\pi$
$174$	1.39717	+	0.383200i	0.105919	+	0.0290503i
$175$	3.49329	+	2.82918i	0.264068	+	0.213866i
$176$	1.02563	−	1.77645i	0.0773101	−	0.133905i
$177$	2.69978	−	2.66817i	0.202928	−	0.200552i
$178$		−	3.86314i		−	0.289554i
$179$	15.9356	+	9.20041i	1.19108	+	0.687671i	0.958552	−	0.284918i	$-0.0919664\pi$
$179$	15.9356	+	9.20041i	1.19108	+	0.687671i	0.232530	+	0.972589i	$0.425300\pi$
$180$	2.78067	−	4.68791i	0.207259	−	0.349416i
$181$		−	0.190838i		−	0.0141849i	−0.999975	−	0.00709245i	$-0.997742\pi$
$181$		−	0.190838i		−	0.0141849i	0.999975	−	0.00709245i	$-0.00225762\pi$
$182$	−8.39241	+	4.53514i	−0.622087	+	0.336167i
$183$	−11.5224	−	3.16023i	−0.851758	−	0.233611i
$184$		−	8.73960i		−	0.644292i
$185$	3.83191	−	6.63707i	0.281728	−	0.487967i
$186$	−3.64215	+	13.2794i	−0.267055	+	0.973696i
$187$	−5.83296	+	10.1030i	−0.426548	+	0.738803i
$188$	1.94760	+	1.12445i	0.142043	+	0.0820086i
$189$	5.81344	−	12.4581i	0.422866	−	0.906192i
$190$		−	2.89520i		−	0.210040i
$191$	4.50022	−	2.59820i	0.325625	−	0.187999i	−0.328272	−	0.944583i	$-0.606466\pi$
$191$	4.50022	−	2.59820i	0.325625	−	0.187999i	0.653897	+	0.756584i	$0.273133\pi$
$192$	1.21751	+	1.23193i	0.0878664	+	0.0889072i
$193$	9.53669	+	5.50601i	0.686466	+	0.396331i	0.802287	−	0.596939i	$-0.203616\pi$
$193$	9.53669	+	5.50601i	0.686466	+	0.396331i	−0.115821	+	0.993270i	$0.536950\pi$
$194$	1.72410	−	2.98622i	0.123783	−	0.214398i
$195$	4.26002	+	10.5162i	0.305066	+	0.753077i
$196$	5.20261	−	4.68325i	0.371615	−	0.334518i
$197$	11.1333	+	19.2835i	0.793218	+	1.37389i	0.923964	+	0.382478i	$0.124929\pi$
$197$	11.1333	+	19.2835i	0.793218	+	1.37389i	−0.130746	+	0.991416i	$0.541737\pi$
$198$	−5.29275	−	3.13944i	−0.376139	−	0.223110i
$199$			19.0946i			1.35358i	0.736177	+	0.676789i	$0.236629\pi$
$199$			19.0946i			1.35358i	−0.736177	+	0.676789i	$0.763371\pi$
$200$	0.849523	+	1.47142i	0.0600703	+	0.104045i
$201$	−2.26017	−	8.63817i	−0.159420	−	0.609290i
$202$	−4.84811	+	8.39717i	−0.341112	+	0.590823i
$203$	1.39281	−	1.71975i	0.0977560	−	0.120703i
$204$	−6.92421	−	7.00622i	−0.484792	−	0.490534i
$205$	0.833252			0.0581968
$206$	−8.08628	−	4.66861i	−0.563398	−	0.325278i
$207$	−26.2170	−	0.308720i	−1.82221	−	0.0214575i
$208$	−3.57560	+	0.463745i	−0.247923	+	0.0321550i
$209$	−3.26874			−0.226104
$210$	−4.85365	−	6.76477i	−0.334933	−	0.466814i
$211$	−7.80557	−	13.5196i	−0.537358	−	0.930731i	−0.999045	−	0.0436882i	$-0.986089\pi$
$211$	−7.80557	−	13.5196i	−0.537358	−	0.930731i	0.461688	−	0.887043i	$-0.347244\pi$
$212$	−0.497067	+	0.286982i	−0.0341387	+	0.0197100i
$213$	−14.2178	+	3.72008i	−0.974191	+	0.254896i
$214$		−	10.7060i		−	0.731846i
$215$	−2.63083	+	1.51891i	−0.179421	+	0.103589i
$216$	3.73855	−	3.60877i	0.254376	−	0.245546i
$217$	16.3455	+	13.2380i	1.10960	+	0.898657i
$218$	4.30381	−	2.48481i	0.291491	−	0.168292i
$219$	−4.68898	+	17.0963i	−0.316852	+	1.15526i
$220$	−3.22755	+	1.86343i	−0.217601	+	0.125632i
$221$	20.3351	−	2.63740i	1.36789	−	0.177411i
$222$	5.19653	−	5.13570i	0.348768	−	0.344686i
$223$	−4.91509	−	8.51319i	−0.329139	−	0.570085i	0.653202	−	0.757183i	$-0.273425\pi$
$223$	−4.91509	−	8.51319i	−0.329139	−	0.570085i	−0.982341	+	0.187098i	$0.940092\pi$
$224$	2.47008	−	0.947995i	0.165039	−	0.0633406i
$225$	4.44395	−	2.49641i	0.296263	−	0.166428i
$226$	−14.4435	−	8.33897i	−0.960768	−	0.554700i
$227$		−	11.3725i		−	0.754821i	−0.926046	−	0.377410i	$-0.876815\pi$
$227$		−	11.3725i		−	0.754821i	0.926046	−	0.377410i	$-0.123185\pi$
$228$	0.730041	−	2.66176i	0.0483481	−	0.176280i
$229$	−9.48968	+	16.4366i	−0.627096	+	1.08616i	0.361036	+	0.932552i	$0.382423\pi$
$229$	−9.48968	+	16.4366i	−0.627096	+	1.08616i	−0.988132	+	0.153610i	$0.950910\pi$
$230$	−7.93928	+	13.7512i	−0.523501	+	0.906730i
$231$	−7.63758	+	5.47988i	−0.502516	+	0.360549i
$232$	0.724381	−	0.418222i	0.0475580	−	0.0274576i
$233$	−18.2307	−	10.5255i	−1.19433	−	0.689550i	−0.235048	−	0.971984i	$-0.575525\pi$
$233$	−18.2307	−	10.5255i	−1.19433	−	0.689550i	−0.959287	+	0.282434i	$0.908858\pi$
$234$	1.26483	+	10.7424i	0.0826848	+	0.702256i
$235$	−2.04295	−	3.53850i	−0.133267	−	0.230826i
$236$		−	2.19150i		−	0.142654i
$237$	−12.3507	+	3.23156i	−0.802266	+	0.209912i
$238$	−14.0478	+	5.39141i	−0.910583	+	0.349473i
$239$	−16.6885			−1.07949			−0.539746	−	0.841828i	$-0.681480\pi$
$239$	−16.6885			−1.07949			−0.539746	+	0.841828i	$0.681480\pi$
$240$	−0.796563	−	3.04440i	−0.0514179	−	0.196515i
$241$	15.2747			0.983927			0.491963	−	0.870616i	$-0.336279\pi$
$241$	15.2747			0.983927			0.491963	+	0.870616i	$0.336279\pi$
$242$	−3.39615	−	5.88231i	−0.218313	−	0.378129i
$243$	−10.6935	−	11.3424i	−0.685988	−	0.727613i
$244$	−5.97394	+	3.44906i	−0.382443	+	0.220803i
$245$	−12.4404	+	2.64262i	−0.794787	+	0.168831i
$246$	0.766068	+	0.210109i	0.0488427	+	0.0133961i
$247$	3.48889	+	4.56495i	0.221993	+	0.290461i
$248$	3.97501	+	6.88493i	0.252414	+	0.437193i
$249$	18.5626	−	18.3453i	1.17636	−	1.16258i
$250$		−	12.1712i		−	0.769773i
$251$	−4.91975	+	8.52125i	−0.310532	+	0.537857i	−0.978478	−	0.206353i	$-0.933840\pi$
$251$	−4.91975	+	8.52125i	−0.310532	+	0.537857i	0.667946	+	0.744210i	$0.267174\pi$
$252$	−2.75653	−	7.44322i	−0.173645	−	0.468879i
$253$	15.5255	+	8.96363i	0.976077	+	0.563538i
$254$	10.6930	+	18.5208i	0.670940	+	1.16210i
$255$	4.53019	+	17.3140i	0.283692	+	1.08425i
$256$	1.00000			0.0625000
$257$	−1.53233			−0.0955843			−0.0477921	−	0.998857i	$-0.515219\pi$
$257$	−1.53233			−0.0955843			−0.0477921	+	0.998857i	$0.515219\pi$
$258$	−2.80171	+	0.733065i	−0.174427	+	0.0456387i
$259$	−3.99882	−	10.4193i	−0.248475	−	0.647422i
$260$	6.04728	+	2.51850i	0.375036	+	0.156191i
$261$	−1.22899	−	2.18777i	−0.0760726	−	0.135419i
$262$	−7.44741	+	12.8993i	−0.460103	+	0.796921i
$263$	−16.9520	−	9.78724i	−1.04530	−	0.603507i	−0.123973	−	0.992286i	$-0.539564\pi$
$263$	−16.9520	−	9.78724i	−1.04530	−	0.603507i	−0.921331	+	0.388779i	$0.872897\pi$
$264$	−3.43719	+	0.899337i	−0.211545	+	0.0553504i
$265$	1.04281			0.0640592
$266$	−3.27633	−	2.65347i	−0.200885	−	0.162694i
$267$	−4.75913	+	4.70342i	−0.291254	+	0.287845i
$268$	−4.46448	−	2.57757i	−0.272712	−	0.157450i
$269$	−13.5580			−0.826646			−0.413323	−	0.910584i	$-0.635632\pi$
$269$	−13.5580			−0.826646			−0.413323	+	0.910584i	$0.635632\pi$
$270$	−9.16069	+	2.28198i	−0.557502	+	0.138877i
$271$	−28.0556			−1.70425			−0.852127	−	0.523335i	$-0.824688\pi$
$271$	−28.0556			−1.70425			−0.852127	+	0.523335i	$0.824688\pi$
$272$	−5.68717			−0.344836
$273$	15.8049	+	4.81730i	0.956554	+	0.291556i
$274$	−11.6043			−0.701042
$275$	−3.48520			−0.210165
$276$	−10.7666	+	10.6406i	−0.648074	+	0.640487i
$277$	23.3285			1.40167			0.700836	−	0.713323i	$-0.252811\pi$
$277$	23.3285			1.40167			0.700836	+	0.713323i	$0.252811\pi$
$278$	−13.6556	−	7.88408i	−0.819010	−	0.472856i
$279$	20.7938	−	11.6810i	1.24489	−	0.699324i
$280$	−4.74771	−	0.752275i	−0.283730	−	0.0449570i
$281$	−26.6302			−1.58862			−0.794311	−	0.607512i	$-0.792168\pi$
$281$	−26.6302			−1.58862			−0.794311	+	0.607512i	$0.792168\pi$
$282$	−0.985981	−	3.76834i	−0.0587143	−	0.224401i
$283$	−23.3128	−	13.4597i	−1.38580	−	0.800093i	−0.392964	−	0.919554i	$-0.628550\pi$
$283$	−23.3128	−	13.4597i	−1.38580	−	0.800093i	−0.992839	+	0.119461i	$0.961884\pi$
$284$	−4.24250	+	7.34823i	−0.251746	+	0.436037i
$285$	−3.56669	+	3.52494i	−0.211273	+	0.208799i
$286$	2.84344	−	6.82751i	0.168136	−	0.403719i
$287$	0.763680	−	0.942943i	0.0450786	−	0.0556602i
$288$	0.0353243	−	2.99979i	0.00208150	−	0.176764i
$289$	15.3439			0.902585
$290$	−1.51969			−0.0892395
$291$	−5.77794	+	1.51179i	−0.338709	+	0.0886228i
$292$	5.11752	+	8.86381i	0.299480	+	0.518715i
$293$	−6.97220	−	4.02540i	−0.407320	−	0.235167i	0.282317	−	0.959321i	$-0.408897\pi$
$293$	−6.97220	−	4.02540i	−0.407320	−	0.235167i	−0.689638	+	0.724154i	$0.742230\pi$
$294$	−12.1037	−	0.707360i	−0.705902	−	0.0412541i
$295$	−1.99081	+	3.44819i	−0.115910	+	0.200761i
$296$		−	4.21819i		−	0.245177i
$297$	2.57641	+	10.3426i	0.149498	+	0.600140i
$298$	2.40740	+	4.16974i	0.139457	+	0.241547i
$299$	−4.05295	−	31.2493i	−0.234388	−	1.80720i
$300$	0.778384	−	2.83803i	0.0449400	−	0.163853i
$301$	−0.692308	+	4.36925i	−0.0399039	+	0.251839i
$302$	1.23569	−	0.713427i	0.0711061	−	0.0410531i
$303$	16.2474	−	4.25111i	0.933389	−	0.244220i
$304$	−0.796762	−	1.38003i	−0.0456974	−	0.0791502i
$305$	12.5329			0.717630
$306$	−0.200895	+	17.0603i	−0.0114844	+	0.975275i
$307$	13.6194			0.777300			0.388650	−	0.921385i	$-0.372942\pi$
$307$	13.6194			0.777300			0.388650	+	0.921385i	$0.372942\pi$
$308$	−0.849335	+	5.36027i	−0.0483953	+	0.305430i
$309$	4.09372	+	15.6459i	0.232884	+	0.890062i
$310$		−	14.4440i		−	0.820366i
$311$	−12.6742	−	21.9523i	−0.718685	−	1.24480i	−0.961521	−	0.274732i	$-0.911411\pi$
$311$	−12.6742	−	21.9523i	−0.718685	−	1.24480i	0.242835	−	0.970068i	$-0.421923\pi$
$312$	4.92465	+	3.84029i	0.278803	+	0.217414i
$313$	−7.41295	−	4.27987i	−0.419005	−	0.241913i	0.275647	−	0.961259i	$-0.411108\pi$
$313$	−7.41295	−	4.27987i	−0.419005	−	0.241913i	−0.694651	+	0.719347i	$0.744441\pi$
$314$	−7.14347	+	4.12428i	−0.403129	+	0.232747i
$315$	−2.42438	+	14.2156i	−0.136598	+	0.800957i
$316$	−3.68537	+	6.38325i	−0.207318	+	0.359086i
$317$	11.7752	−	20.3952i	0.661360	−	1.14551i	−0.318898	−	0.947789i	$-0.603313\pi$
$317$	11.7752	−	20.3952i	0.661360	−	1.14551i	0.980258	−	0.197721i	$-0.0633539\pi$
$318$	0.958729	+	0.262950i	0.0537628	+	0.0147455i
$319$			1.71577i			0.0960646i
$320$	−1.57344	−	0.908426i	−0.0879580	−	0.0507826i
$321$	−13.1891	+	13.0347i	−0.736142	+	0.727524i
$322$	8.28509	+	21.5875i	0.461710	+	1.20303i
$323$	4.53132	+	7.84848i	0.252129	+	0.436701i
$324$	−8.99750	−	0.211931i	−0.499861	−	0.0117739i
$325$	3.71992	+	4.86724i	0.206344	+	0.269986i
$326$	20.7420	−	11.9754i	1.14879	−	0.663256i
$327$	−8.30107	−	2.27673i	−0.459050	−	0.125903i
$328$	0.397180	−	0.229312i	0.0219306	−	0.0126616i
$329$	−5.87669	−	0.931162i	−0.323992	−	0.0513366i
$330$	6.22520	+	1.70738i	0.342686	+	0.0939883i
$331$	6.15849	−	3.55561i	0.338501	−	0.195434i	−0.321108	−	0.947043i	$-0.604055\pi$
$331$	6.15849	−	3.55561i	0.338501	−	0.195434i	0.659609	+	0.751609i	$0.270722\pi$
$332$		−	15.0678i		−	0.826954i
$333$	−12.6537	−	0.149004i	−0.693418	−	0.00816539i
$334$	20.2949	−	11.7173i	1.11049	−	0.641141i
$335$	4.68306	+	8.11130i	0.255863	+	0.443168i
$336$	−4.17522	−	1.88878i	−0.227777	−	0.103042i
$337$	19.1187			1.04146			0.520730	−	0.853722i	$-0.325660\pi$
$337$	19.1187			1.04146			0.520730	+	0.853722i	$0.325660\pi$
$338$	−12.5699	+	3.31634i	−0.683711	+	0.180385i
$339$	7.31211	+	27.9463i	0.397139	+	1.51783i
$340$	8.94843	+	5.16638i	0.485297	+	0.280186i
$341$	−16.3076			−0.883108
$342$	−4.16795	+	2.34137i	−0.225377	+	0.126607i
$343$	−8.41119	+	16.5001i	−0.454161	+	0.890919i
$344$	−0.836012	+	1.44802i	−0.0450747	+	0.0780717i
$345$	26.6068	−	6.96164i	1.43246	−	0.374802i
$346$	3.80295	+	6.58691i	0.204448	+	0.354114i
$347$			23.0701i			1.23847i	0.785207	+	0.619233i	$0.212556\pi$
$347$			23.0701i			1.23847i	−0.785207	+	0.619233i	$0.787444\pi$
$348$	−1.39717	−	0.383200i	−0.0748959	−	0.0205417i
$349$	2.11359	+	3.66085i	0.113138	+	0.195961i	0.917034	−	0.398809i	$-0.130576\pi$
$349$	2.11359	+	3.66085i	0.113138	+	0.195961i	−0.803896	+	0.594770i	$0.797243\pi$
$350$	−3.49329	−	2.82918i	−0.186724	−	0.151226i
$351$	11.6940	−	14.6373i	0.624182	−	0.781279i
$352$	−1.02563	+	1.77645i	−0.0546665	+	0.0946851i
$353$	−27.6603	−	15.9697i	−1.47221	−	0.849981i	−0.472699	−	0.881224i	$-0.656720\pi$
$353$	−27.6603	−	15.9697i	−1.47221	−	0.849981i	−0.999512	+	0.0312428i	$0.990053\pi$
$354$	−2.69978	+	2.66817i	−0.143492	+	0.141812i
$355$	13.3507	−	7.70801i	0.708579	−	0.409098i
$356$			3.86314i			0.204746i
$357$	23.7452	+	10.7418i	1.25673	+	0.568518i
$358$	−15.9356	−	9.20041i	−0.842222	−	0.486257i
$359$	12.2496	−	21.2169i	0.646509	−	1.11979i	−0.337442	−	0.941346i	$-0.609562\pi$
$359$	12.2496	−	21.2169i	0.646509	−	1.11979i	0.983951	−	0.178440i	$-0.0571049\pi$
$360$	−2.78067	+	4.68791i	−0.146554	+	0.247074i
$361$	8.23034	−	14.2554i	0.433176	−	0.750283i
$362$			0.190838i			0.0100302i
$363$	−3.11176	+	11.3456i	−0.163325	+	0.595491i
$364$	8.39241	−	4.53514i	0.439882	−	0.237706i
$365$		−	18.5956i		−	0.973337i
$366$	11.5224	+	3.16023i	0.602284	+	0.165188i
$367$	−28.7618	−	16.6056i	−1.50135	−	0.866807i	−0.999999	−	0.00156589i	$-0.999502\pi$
$367$	−28.7618	−	16.6056i	−1.50135	−	0.866807i	−0.501355	−	0.865241i	$-0.667165\pi$
$368$			8.73960i			0.455583i
$369$	−0.673858	−	1.19956i	−0.0350796	−	0.0624464i
$370$	−3.83191	+	6.63707i	−0.199212	+	0.345045i
$371$	0.955740	−	1.18009i	0.0496195	−	0.0612670i
$372$	3.64215	−	13.2794i	0.188836	−	0.688507i
$373$	2.06003	+	3.56807i	0.106664	+	0.184748i	0.914417	−	0.404774i	$-0.132650\pi$
$373$	2.06003	+	3.56807i	0.106664	+	0.184748i	−0.807753	+	0.589521i	$0.799316\pi$
$374$	5.83296	−	10.1030i	0.301615	−	0.522413i
$375$	−14.9941	+	14.8186i	−0.774292	+	0.765228i
$376$	−1.94760	−	1.12445i	−0.100440	−	0.0579888i
$377$	2.39615	−	1.83132i	0.123408	−	0.0943179i
$378$	−5.81344	+	12.4581i	−0.299011	+	0.640775i
$379$	−2.80001	+	1.61659i	−0.143827	+	0.0830385i	−0.570187	−	0.821515i	$-0.693129\pi$
$379$	−2.80001	+	1.61659i	−0.143827	+	0.0830385i	0.426360	+	0.904554i	$0.359796\pi$
$380$			2.89520i			0.148520i
$381$	9.79758	−	35.7225i	0.501945	−	1.83012i
$382$	−4.50022	+	2.59820i	−0.230251	+	0.132936i
$383$	3.61672	−	2.08811i	0.184806	−	0.106698i	−0.404743	−	0.914430i	$-0.632639\pi$
$383$	3.61672	−	2.08811i	0.184806	−	0.106698i	0.589549	+	0.807733i	$0.299306\pi$
$384$	−1.21751	−	1.23193i	−0.0621309	−	0.0628669i
$385$	6.20579	−	7.66251i	0.316276	−	0.390518i
$386$	−9.53669	−	5.50601i	−0.485405	−	0.280249i
$387$	4.31421	+	2.55901i	0.219304	+	0.130082i
$388$	−1.72410	+	2.98622i	−0.0875278	+	0.151603i
$389$	3.57665	−	2.06498i	0.181343	−	0.104699i	−0.406580	−	0.913615i	$-0.633279\pi$
$389$	3.57665	−	2.06498i	0.181343	−	0.104699i	0.587924	+	0.808916i	$0.299946\pi$
$390$	−4.26002	−	10.5162i	−0.215714	−	0.532506i
$391$		−	49.7036i		−	2.51362i
$392$	−5.20261	+	4.68325i	−0.262772	+	0.236540i
$393$	24.9584	−	6.53034i	1.25899	−	0.329412i
$394$	−11.1333	−	19.2835i	−0.560890	−	0.971490i
$395$	11.5974	−	6.69578i	0.583530	−	0.336901i
$396$	5.29275	+	3.13944i	0.265971	+	0.157763i
$397$	2.38133	+	4.12458i	0.119515	+	0.207007i	0.919576	−	0.392913i	$-0.128533\pi$
$397$	2.38133	+	4.12458i	0.119515	+	0.207007i	−0.800060	+	0.599920i	$0.795199\pi$
$398$		−	19.0946i		−	0.957124i
$399$	0.720078	+	7.26685i	0.0360490	+	0.363798i
$400$	−0.849523	−	1.47142i	−0.0424761	−	0.0735708i
$401$	−15.4809			−0.773080			−0.386540	−	0.922273i	$-0.626330\pi$
$401$	−15.4809			−0.773080			−0.386540	+	0.922273i	$0.626330\pi$
$402$	2.26017	+	8.63817i	0.112727	+	0.430833i
$403$	17.4059	+	22.7744i	0.867051	+	1.13447i
$404$	4.84811	−	8.39717i	0.241202	−	0.417775i
$405$	13.9645	+	8.50703i	0.693902	+	0.422718i
$406$	−1.39281	+	1.71975i	−0.0691240	+	0.0853498i
$407$	7.49340	+	4.32632i	0.371434	+	0.214448i
$408$	6.92421	+	7.00622i	0.342799	+	0.346860i
$409$	−39.7884			−1.96741			−0.983706	−	0.179784i	$-0.942460\pi$
$409$	−39.7884			−1.96741			−0.983706	+	0.179784i	$0.942460\pi$
$410$	−0.833252			−0.0411514
$411$	14.1284	+	14.2958i	0.696903	+	0.705158i
$412$	8.08628	+	4.66861i	0.398382	+	0.230006i
$413$	2.07753	+	5.41317i	0.102228	+	0.266365i
$414$	26.2170	+	0.308720i	1.28849	+	0.0151727i
$415$	−13.6880	+	23.7083i	−0.671918	+	1.16380i
$416$	3.57560	−	0.463745i	0.175308	−	0.0227370i
$417$	6.91323	+	26.4218i	0.338542	+	1.29388i
$418$	3.26874			0.159879
$419$	−13.1146	−	22.7152i	−0.640690	−	1.10971i	−0.985279	−	0.170954i	$-0.945315\pi$
$419$	−13.1146	−	22.7152i	−0.640690	−	1.10971i	0.344589	−	0.938754i	$-0.388018\pi$
$420$	4.85365	+	6.76477i	0.236834	+	0.330087i
$421$			14.0343i			0.683989i	0.939702	+	0.341994i	$0.111102\pi$
$421$			14.0343i			0.683989i	−0.939702	+	0.341994i	$0.888898\pi$
$422$	7.80557	+	13.5196i	0.379969	+	0.658126i
$423$	−3.44190	+	5.80266i	−0.167351	+	0.282135i
$424$	0.497067	−	0.286982i	0.0241397	−	0.0139371i
$425$	4.83138	+	8.36820i	0.234357	+	0.405917i
$426$	14.2178	−	3.72008i	0.688857	−	0.180239i
$427$	11.4864	−	14.1827i	0.555868	−	0.686350i
$428$			10.7060i			0.517493i
$429$	−11.8730	+	4.80966i	−0.573232	+	0.232212i
$430$	2.63083	−	1.51891i	0.126870	−	0.0732484i
$431$	−8.06272	+	13.9650i	−0.388368	+	0.672673i	−0.992230	−	0.124416i	$-0.960294\pi$
$431$	−8.06272	+	13.9650i	−0.388368	+	0.672673i	0.603862	+	0.797089i	$0.293628\pi$
$432$	−3.73855	+	3.60877i	−0.179871	+	0.173627i
$433$	−13.9038	−	8.02734i	−0.668172	−	0.385769i	0.127211	−	0.991876i	$-0.459397\pi$
$433$	−13.9038	−	8.02734i	−0.668172	−	0.385769i	−0.795384	+	0.606106i	$0.792731\pi$
$434$	−16.3455	−	13.2380i	−0.784608	−	0.635446i
$435$	1.85025	+	1.87216i	0.0887126	+	0.0897634i
$436$	−4.30381	+	2.48481i	−0.206115	+	0.119001i
$437$	12.0609	−	6.96338i	0.576952	−	0.333103i
$438$	4.68898	−	17.0963i	0.224048	−	0.816891i
$439$			16.1774i			0.772104i	0.922477	+	0.386052i	$0.126162\pi$
$439$			16.1774i			0.772104i	−0.922477	+	0.386052i	$0.873838\pi$
$440$	3.22755	−	1.86343i	0.153867	−	0.0888353i
$441$	13.8650	+	15.7722i	0.660238	+	0.751057i
$442$	−20.3351	+	2.63740i	−0.967241	+	0.125448i
$443$	10.8594	+	6.26970i	0.515948	+	0.297883i	0.735275	−	0.677769i	$-0.237053\pi$
$443$	10.8594	+	6.26970i	0.515948	+	0.297883i	−0.219327	+	0.975651i	$0.570386\pi$
$444$	−5.19653	+	5.13570i	−0.246616	+	0.243730i
$445$	3.50938	−	6.07842i	0.166360	−	0.288145i
$446$	4.91509	+	8.51319i	0.232736	+	0.403111i
$447$	2.20581	−	8.04248i	0.104331	−	0.380396i
$448$	−2.47008	+	0.947995i	−0.116700	+	0.0447885i
$449$	8.48307	−	14.6931i	0.400341	−	0.693411i	−0.593426	−	0.804888i	$-0.702225\pi$
$449$	8.48307	−	14.6931i	0.400341	−	0.693411i	0.993767	+	0.111478i	$0.0355584\pi$
$450$	−4.44395	+	2.49641i	−0.209490	+	0.117682i
$451$			0.940760i			0.0442986i
$452$	14.4435	+	8.33897i	0.679366	+	0.392232i
$453$	−2.38337	−	0.653685i	−0.111980	−	0.0307128i
$454$			11.3725i			0.533739i
$455$	−17.3248	−	0.488106i	−0.812199	−	0.0228828i
$456$	−0.730041	+	2.66176i	−0.0341873	+	0.124649i
$457$			9.47441i			0.443194i	0.975138	+	0.221597i	$0.0711270\pi$
$457$			9.47441i			0.443194i	−0.975138	+	0.221597i	$0.928873\pi$
$458$	9.48968	−	16.4366i	0.443424	−	0.768032i
$459$	21.2618	−	20.5237i	0.992416	−	0.957964i
$460$	7.93928	−	13.7512i	0.370171	−	0.641155i
$461$	31.5250	+	18.2010i	1.46827	+	0.847703i	0.999368	−	0.0355490i	$-0.0113180\pi$
$461$	31.5250	+	18.2010i	1.46827	+	0.847703i	0.468898	+	0.883253i	$0.344651\pi$
$462$	7.63758	−	5.47988i	0.355332	−	0.254947i
$463$		−	17.8517i		−	0.829638i	−0.909904	−	0.414819i	$-0.863845\pi$
$463$		−	17.8517i		−	0.829638i	0.909904	−	0.414819i	$-0.136155\pi$
$464$	−0.724381	+	0.418222i	−0.0336286	+	0.0194155i
$465$	−17.7941	+	17.5858i	−0.825181	+	0.815522i
$466$	18.2307	+	10.5255i	0.844522	+	0.487585i
$467$	−15.1928	+	26.3147i	−0.703039	+	1.21770i	0.264355	+	0.964425i	$0.414841\pi$
$467$	−15.1928	+	26.3147i	−0.703039	+	1.21770i	−0.967394	+	0.253274i	$0.918492\pi$
$468$	−1.26483	−	10.7424i	−0.0584670	−	0.496570i
$469$	13.4712	+	2.13450i	0.622040	+	0.0985622i
$470$	2.04295	+	3.53850i	0.0942343	+	0.163219i
$471$	13.7781	+	3.77892i	0.634862	+	0.174123i
$472$			2.19150i			0.100872i
$473$	−1.71488	−	2.97027i	−0.0788505	−	0.136573i
$474$	12.3507	−	3.23156i	0.567288	−	0.148430i
$475$	−1.35373	+	2.34474i	−0.0621136	+	0.107584i
$476$	14.0478	−	5.39141i	0.643879	−	0.247115i
$477$	−0.843328	−	1.50124i	−0.0386133	−	0.0687369i
$478$	16.6885			0.763316
$479$	19.9492	+	11.5177i	0.911504	+	0.526257i	0.880915	−	0.473275i	$-0.156928\pi$
$479$	19.9492	+	11.5177i	0.911504	+	0.526257i	0.0305891	+	0.999532i	$0.490262\pi$
$480$	0.796563	+	3.04440i	0.0363580	+	0.138957i
$481$	−1.95617	−	15.0826i	−0.0891935	−	0.687706i
$482$	−15.2747			−0.695741
$483$	16.5072	−	36.4898i	0.751104	−	1.66034i
$484$	3.39615	+	5.88231i	0.154370	+	0.267378i
$485$	5.42553	−	3.13243i	0.246361	−	0.142236i
$486$	10.6935	+	11.3424i	0.485067	+	0.514500i
$487$		−	14.2075i		−	0.643804i	−0.946773	−	0.321902i	$-0.895678\pi$
$487$		−	14.2075i		−	0.643804i	0.946773	−	0.321902i	$-0.104322\pi$
$488$	5.97394	−	3.44906i	0.270428	−	0.156132i
$489$	−40.0065	−	10.9726i	−1.80916	−	0.496197i
$490$	12.4404	−	2.64262i	0.562000	−	0.119382i
$491$	−2.47085	+	1.42654i	−0.111508	+	0.0643790i	−0.554717	−	0.832039i	$-0.687173\pi$
$491$	−2.47085	+	1.42654i	−0.111508	+	0.0643790i	0.443209	+	0.896418i	$0.353840\pi$
$492$	−0.766068	−	0.210109i	−0.0345370	−	0.00947245i
$493$	4.11968	−	2.37850i	0.185541	−	0.107122i
$494$	−3.48889	−	4.56495i	−0.156972	−	0.205387i
$495$	−5.47588	−	9.74780i	−0.246122	−	0.438131i
$496$	−3.97501	−	6.88493i	−0.178483	−	0.309142i
$497$	3.51325	−	22.1726i	0.157591	−	0.994578i
$498$	−18.5626	+	18.3453i	−0.831809	+	0.822071i
$499$	−15.9720	−	9.22146i	−0.715007	−	0.412809i	0.0979055	−	0.995196i	$-0.468786\pi$
$499$	−15.9720	−	9.22146i	−0.715007	−	0.412809i	−0.812912	+	0.582386i	$0.802119\pi$
$500$			12.1712i			0.544312i
$501$	−39.1443	−	10.7361i	−1.74884	−	0.479652i
$502$	4.91975	−	8.52125i	0.219579	−	0.380322i
$503$	−6.05432	+	10.4864i	−0.269949	+	0.467565i	−0.968848	−	0.247655i	$-0.920340\pi$
$503$	−6.05432	+	10.4864i	−0.269949	+	0.467565i	0.698900	+	0.715220i	$0.253673\pi$
$504$	2.75653	+	7.44322i	0.122786	+	0.331547i
$505$	−15.2564	+	8.80830i	−0.678902	+	0.391964i
$506$	−15.5255	−	8.96363i	−0.690191	−	0.398482i
$507$	19.3895	+	11.4476i	0.861118	+	0.508405i
$508$	−10.6930	−	18.5208i	−0.474426	−	0.821730i
$509$			36.9477i			1.63768i	0.574023	+	0.818839i	$0.305382\pi$
$509$			36.9477i			1.63768i	−0.574023	+	0.818839i	$0.694618\pi$
$510$	−4.53019	−	17.3140i	−0.200600	−	0.766677i
$511$	−21.0435	−	17.0430i	−0.930912	−	0.753936i
$512$	−1.00000			−0.0441942
$513$	7.95895	+	2.28399i	0.351396	+	0.100841i
$514$	1.53233			0.0675883
$515$	−8.48219	−	14.6916i	−0.373770	−	0.647388i
$516$	2.80171	−	0.733065i	0.123339	−	0.0322714i
$517$	3.99504	−	2.30654i	0.175702	−	0.101441i
$518$	3.99882	+	10.4193i	0.175698	+	0.457797i
$519$	3.48449	−	12.7046i	0.152952	−	0.557672i
$520$	−6.04728	−	2.51850i	−0.265191	−	0.110443i
$521$	9.03063	+	15.6415i	0.395639	+	0.685267i	0.993183	−	0.116569i	$-0.0371898\pi$
$521$	9.03063	+	15.6415i	0.395639	+	0.685267i	−0.597543	+	0.801837i	$0.703856\pi$
$522$	1.22899	+	2.18777i	0.0537914	+	0.0957559i
$523$			39.5905i			1.73117i	0.500762	+	0.865585i	$0.333053\pi$
$523$			39.5905i			1.73117i	−0.500762	+	0.865585i	$0.666947\pi$
$524$	7.44741	−	12.8993i	0.325342	−	0.563508i
$525$	0.767761	+	7.74806i	0.0335078	+	0.338153i
$526$	16.9520	+	9.78724i	0.739142	+	0.426744i
$527$	22.6066	+	39.1558i	0.984759	+	1.70565i
$528$	3.43719	−	0.899337i	0.149585	−	0.0391386i
$529$	−53.3806			−2.32089
$530$	−1.04281			−0.0452967
$531$	6.57403	+	0.0774129i	0.285289	+	0.00335944i
$532$	3.27633	+	2.65347i	0.142047	+	0.115042i
$533$	1.31381	−	1.00412i	0.0569076	−	0.0434932i
$534$	4.75913	−	4.70342i	0.205948	−	0.203537i
$535$	9.72559	−	16.8452i	0.420474	−	0.728283i
$536$	4.46448	+	2.57757i	0.192836	+	0.111334i
$537$	8.06748	+	30.8332i	0.348137	+	1.33055i
$538$	13.5580			0.584527
$539$	−2.98358	−	14.0455i	−0.128512	−	0.604982i
$540$	9.16069	−	2.28198i	0.394214	−	0.0982009i
$541$	−21.7849	−	12.5775i	−0.936606	−	0.540750i	−0.0477116	−	0.998861i	$-0.515193\pi$
$541$	−21.7849	−	12.5775i	−0.936606	−	0.540750i	−0.888895	+	0.458111i	$0.848526\pi$
$542$	28.0556			1.20509
$543$	0.235100	−	0.232348i	0.0100891	−	0.00997102i
$544$	5.68717			0.243836
$545$	9.02906			0.386762
$546$	−15.8049	−	4.81730i	−0.676386	−	0.206161i
$547$	9.83208			0.420389			0.210195	−	0.977660i	$-0.432590\pi$
$547$	9.83208			0.420389			0.210195	+	0.977660i	$0.432590\pi$
$548$	11.6043			0.495712
$549$	−10.1354	−	18.0424i	−0.432570	−	0.770032i
$550$	3.48520			0.148609
$551$	1.15432	+	0.666446i	0.0491756	+	0.0283916i
$552$	10.7666	−	10.6406i	0.458257	−	0.452893i
$553$	3.05188	−	19.2609i	0.129779	−	0.819055i
$554$	−23.3285			−0.991131
$555$	12.8418	−	3.36005i	0.545106	−	0.142626i
$556$	13.6556	+	7.88408i	0.579127	+	0.334359i
$557$	−2.73252	+	4.73287i	−0.115781	+	0.200538i	−0.918092	−	0.396368i	$-0.870270\pi$
$557$	−2.73252	+	4.73287i	−0.115781	+	0.200538i	0.802311	+	0.596906i	$0.203604\pi$
$558$	−20.7938	+	11.6810i	−0.880270	+	0.494497i
$559$	−2.31774	+	5.56522i	−0.0980298	+	0.235384i
$560$	4.74771	+	0.752275i	0.200627	+	0.0317894i
$561$	−19.5479	+	5.11469i	−0.825313	+	0.215942i
$562$	26.6302			1.12333
$563$	−25.5357			−1.07620			−0.538101	−	0.842880i	$-0.680858\pi$
$563$	−25.5357			−1.07620			−0.538101	+	0.842880i	$0.680858\pi$
$564$	0.985981	+	3.76834i	0.0415173	+	0.158676i
$565$	−15.1507	−	26.2417i	−0.637394	−	1.10400i
$566$	23.3128	+	13.4597i	0.979910	+	0.565752i
$567$	22.4255	−	8.00610i	0.941782	−	0.336225i
$568$	4.24250	−	7.34823i	0.178012	−	0.308325i
$569$			16.5159i			0.692384i	0.938164	+	0.346192i	$0.112525\pi$
$569$			16.5159i			0.692384i	−0.938164	+	0.346192i	$0.887475\pi$
$570$	3.56669	−	3.52494i	0.149392	−	0.147643i
$571$	−1.84946	−	3.20337i	−0.0773977	−	0.134057i	0.824729	−	0.565529i	$-0.191328\pi$
$571$	−1.84946	−	3.20337i	−0.0773977	−	0.134057i	−0.902126	+	0.431472i	$0.857994\pi$
$572$	−2.84344	+	6.82751i	−0.118890	+	0.285473i
$573$	8.67989	+	2.38063i	0.362608	+	0.0994522i
$574$	−0.763680	+	0.942943i	−0.0318754	+	0.0393577i
$575$	12.8596	−	7.42449i	0.536282	−	0.309623i
$576$	−0.0353243	+	2.99979i	−0.00147184	+	0.124991i
$577$	−4.25571	−	7.37111i	−0.177168	−	0.306863i	0.763742	−	0.645522i	$-0.223360\pi$
$577$	−4.25571	−	7.37111i	−0.177168	−	0.306863i	−0.940909	+	0.338659i	$0.890027\pi$
$578$	−15.3439			−0.638224
$579$	4.82800	+	18.4522i	0.200645	+	0.766848i
$580$	1.51969			0.0631019
$581$	14.2842	+	37.2188i	0.592609	+	1.54409i
$582$	5.77794	−	1.51179i	0.239503	−	0.0626658i
$583$			1.17735i			0.0487610i
$584$	−5.11752	−	8.86381i	−0.211765	−	0.366787i
$585$	−7.76858	+	18.0516i	−0.321191	+	0.746342i
$586$	6.97220	+	4.02540i	0.288019	+	0.166288i
$587$	5.89064	−	3.40096i	0.243133	−	0.140373i	−0.373483	−	0.927637i	$-0.621837\pi$
$587$	5.89064	−	3.40096i	0.243133	−	0.140373i	0.616616	+	0.787264i	$0.288503\pi$
$588$	12.1037	+	0.707360i	0.499148	+	0.0291710i
$589$	−6.33428	+	10.9713i	−0.260999	+	0.452064i
$590$	1.99081	−	3.44819i	0.0819604	−	0.141960i
$591$	−10.2010	+	37.1935i	−0.419615	+	1.52994i
$592$			4.21819i			0.173366i
$593$	6.06317	+	3.50057i	0.248984	+	0.143751i	0.619299	−	0.785155i	$-0.287417\pi$
$593$	6.06317	+	3.50057i	0.248984	+	0.143751i	−0.370315	+	0.928906i	$0.620750\pi$
$594$	−2.57641	−	10.3426i	−0.105711	−	0.424363i
$595$	−27.0011	−	4.27832i	−1.10694	−	0.175394i
$596$	−2.40740	−	4.16974i	−0.0986111	−	0.170799i
$597$	−23.5232	+	23.2479i	−0.962742	+	0.951472i
$598$	4.05295	+	31.2493i	0.165737	+	1.27788i
$599$	36.0831	−	20.8326i	1.47432	−	0.851197i	0.474735	−	0.880129i	$-0.342544\pi$
$599$	36.0831	−	20.8326i	1.47432	−	0.851197i	0.999581	+	0.0289321i	$0.00921067\pi$
$600$	−0.778384	+	2.83803i	−0.0317774	+	0.115862i
$601$	1.93484	−	1.11708i	0.0789239	−	0.0455668i	−0.460019	−	0.887909i	$-0.652157\pi$
$601$	1.93484	−	1.11708i	0.0789239	−	0.0455668i	0.538943	+	0.842342i	$0.318824\pi$
$602$	0.692308	−	4.36925i	0.0282164	−	0.178077i
$603$	7.88987	−	13.3015i	0.321301	−	0.541677i
$604$	−1.23569	+	0.713427i	−0.0502796	+	0.0290289i
$605$		−	12.3406i		−	0.501717i
$606$	−16.2474	+	4.25111i	−0.660006	+	0.172690i
$607$	−0.586288	+	0.338493i	−0.0237967	+	0.0137390i	−0.511851	−	0.859074i	$-0.671040\pi$
$607$	−0.586288	+	0.338493i	−0.0237967	+	0.0137390i	0.488054	+	0.872813i	$0.337707\pi$
$608$	0.796762	+	1.38003i	0.0323129	+	0.0559677i
$609$	3.81438	−	0.377970i	0.154567	−	0.0153161i
$610$	−12.5329			−0.507441
$611$	−7.48529	−	3.11738i	−0.302822	−	0.126116i
$612$	0.200895	−	17.0603i	0.00812071	−	0.689623i
$613$	6.34919	+	3.66571i	0.256441	+	0.148057i	0.622710	−	0.782453i	$-0.286032\pi$
$613$	6.34919	+	3.66571i	0.256441	+	0.148057i	−0.366269	+	0.930509i	$0.619365\pi$
$614$	−13.6194			−0.549634
$615$	1.01449	+	1.02651i	0.0409084	+	0.0413929i
$616$	0.849335	−	5.36027i	0.0342207	−	0.215972i
$617$	−22.6183	+	39.1761i	−0.910579	+	1.57717i	−0.0973311	+	0.995252i	$0.531031\pi$
$617$	−22.6183	+	39.1761i	−0.910579	+	1.57717i	−0.813248	+	0.581917i	$0.802303\pi$
$618$	−4.09372	−	15.6459i	−0.164674	−	0.629369i
$619$	5.37271	+	9.30581i	0.215948	+	0.374032i	0.953565	−	0.301186i	$-0.0973826\pi$
$619$	5.37271	+	9.30581i	0.215948	+	0.374032i	−0.737618	+	0.675219i	$0.764049\pi$
$620$			14.4440i			0.580086i
$621$	−31.5392	−	32.6735i	−1.26562	−	1.31114i
$622$	12.6742	+	21.9523i	0.508187	+	0.880206i
$623$	−3.66223	−	9.54227i	−0.146724	−	0.382303i
$624$	−4.92465	−	3.84029i	−0.197144	−	0.153735i
$625$	6.80901	−	11.7935i	0.272360	−	0.471742i
$626$	7.41295	+	4.27987i	0.296281	+	0.171058i
$627$	−3.97974	−	4.02688i	−0.158935	−	0.160818i
$628$	7.14347	−	4.12428i	0.285055	−	0.164577i
$629$		−	23.9896i		−	0.956527i
$630$	2.42438	−	14.2156i	0.0965895	−	0.566362i
$631$	15.7277	+	9.08038i	0.626109	+	0.361484i	0.779244	−	0.626721i	$-0.215603\pi$
$631$	15.7277	+	9.08038i	0.626109	+	0.361484i	−0.153135	+	0.988205i	$0.548937\pi$
$632$	3.68537	−	6.38325i	0.146596	−	0.253912i
$633$	7.15193	−	26.0763i	0.284264	−	1.03644i
$634$	−11.7752	+	20.3952i	−0.467652	+	0.809998i
$635$			38.8553i			1.54192i
$636$	−0.958729	−	0.262950i	−0.0380161	−	0.0104266i
$637$	−16.4306	+	19.1581i	−0.651006	+	0.759073i
$638$		−	1.71577i		−	0.0679279i
$639$	−21.8933	−	12.9862i	−0.866086	−	0.513726i
$640$	1.57344	+	0.908426i	0.0621957	+	0.0359087i
$641$		−	14.4746i		−	0.571714i	−0.958272	−	0.285857i	$-0.907722\pi$
$641$		−	14.4746i		−	0.571714i	0.958272	−	0.285857i	$-0.0922782\pi$
$642$	13.1891	−	13.0347i	0.520531	−	0.514437i
$643$	6.24408	−	10.8151i	0.246243	−	0.426505i	−0.716238	−	0.697856i	$-0.754137\pi$
$643$	6.24408	−	10.8151i	0.246243	−	0.426505i	0.962480	+	0.271352i	$0.0874707\pi$
$644$	−8.28509	−	21.5875i	−0.326478	−	0.850668i
$645$	−5.07427	−	1.39172i	−0.199799	−	0.0547988i
$646$	−4.53132	−	7.84848i	−0.178282	−	0.308794i
$647$	16.1151	−	27.9122i	0.633550	−	1.09734i	−0.353271	−	0.935521i	$-0.614931\pi$
$647$	16.1151	−	27.9122i	0.633550	−	1.09734i	0.986820	−	0.161819i	$-0.0517361\pi$
$648$	8.99750	+	0.211931i	0.353455	+	0.00832543i
$649$	−3.89308	−	2.24767i	−0.152817	−	0.0882288i
$650$	−3.71992	−	4.86724i	−0.145907	−	0.190909i
$651$	3.59244	+	36.2540i	0.140799	+	1.42091i
$652$	−20.7420	+	11.9754i	−0.812319	+	0.468992i
$653$			36.7354i			1.43757i	0.695234	+	0.718783i	$0.255301\pi$
$653$			36.7354i			1.43757i	−0.695234	+	0.718783i	$0.744699\pi$
$654$	8.30107	+	2.27673i	0.324597	+	0.0890271i
$655$	−23.4361	+	13.5309i	−0.915725	+	0.528694i
$656$	−0.397180	+	0.229312i	−0.0155073	+	0.00895312i
$657$	−26.7704	+	15.0384i	−1.04441	+	0.586704i
$658$	5.87669	+	0.931162i	0.229097	+	0.0363005i
$659$	−39.7060	−	22.9243i	−1.54673	−	0.893003i	−0.998389	−	0.0567462i	$-0.981927\pi$
$659$	−39.7060	−	22.9243i	−1.54673	−	0.893003i	−0.548338	−	0.836257i	$-0.684739\pi$
$660$	−6.22520	−	1.70738i	−0.242316	−	0.0664598i
$661$	−7.51367	+	13.0141i	−0.292248	+	0.506188i	−0.974341	−	0.225077i	$-0.927737\pi$
$661$	−7.51367	+	13.0141i	−0.292248	+	0.506188i	0.682093	+	0.731265i	$0.261070\pi$
$662$	−6.15849	+	3.55561i	−0.239356	+	0.138193i
$663$	28.0073	+	21.8404i	1.08771	+	0.848211i
$664$			15.0678i			0.584745i
$665$	−2.74463	−	7.15138i	−0.106432	−	0.277318i
$666$	12.6537	+	0.149004i	0.490320	+	0.00577380i
$667$	−3.65509	−	6.33080i	−0.141526	−	0.245130i
$668$	−20.2949	+	11.7173i	−0.785234	+	0.453355i
$669$	4.50350	−	16.4200i	0.174115	−	0.634833i
$670$	−4.68306	−	8.11130i	−0.180923	−	0.313367i
$671$			14.1499i			0.546250i
$672$	4.17522	+	1.88878i	0.161063	+	0.0728614i
$673$	−13.8713	−	24.0258i	−0.534700	−	0.926127i	−0.999178	−	0.0405428i	$-0.987091\pi$
$673$	−13.8713	−	24.0258i	−0.534700	−	0.926127i	0.464478	−	0.885585i	$-0.346242\pi$
$674$	−19.1187			−0.736423
$675$	8.48599	+	2.43524i	0.326626	+	0.0937324i
$676$	12.5699	−	3.31634i	0.483457	−	0.127552i
$677$	0.275329	−	0.476883i	0.0105817	−	0.0183281i	−0.860686	−	0.509136i	$-0.829965\pi$
$677$	0.275329	−	0.476883i	0.0105817	−	0.0183281i	0.871268	+	0.490808i	$0.163298\pi$
$678$	−7.31211	−	27.9463i	−0.280820	−	1.07327i
$679$	1.42774	−	9.01065i	0.0547915	−	0.345797i
$680$	−8.94843	−	5.16638i	−0.343157	−	0.198122i
$681$	14.0102	−	13.8462i	0.536872	−	0.530587i
$682$	16.3076			0.624452
$683$	36.3756			1.39188			0.695938	−	0.718102i	$-0.254989\pi$
$683$	36.3756			1.39188			0.695938	+	0.718102i	$0.254989\pi$
$684$	4.16795	−	2.34137i	0.159366	−	0.0895245i
$685$	−18.2587	−	10.5417i	−0.697629	−	0.402776i
$686$	8.41119	−	16.5001i	0.321141	−	0.629975i
$687$	−31.8026	+	8.32112i	−1.21335	+	0.317471i
$688$	0.836012	−	1.44802i	0.0318727	−	0.0552051i
$689$	1.64423	−	1.25665i	0.0626401	−	0.0478744i
$690$	−26.6068	+	6.96164i	−1.01290	+	0.265025i
$691$	32.3519			1.23073			0.615363	−	0.788244i	$-0.289010\pi$
$691$	32.3519			1.23073			0.615363	+	0.788244i	$0.289010\pi$
$692$	−3.80295	−	6.58691i	−0.144567	−	0.250397i
$693$	−16.0497	−	2.73718i	−0.609678	−	0.103977i
$694$		−	23.0701i		−	0.875728i
$695$	−14.3242	−	24.8103i	−0.543348	−	0.941107i
$696$	1.39717	+	0.383200i	0.0529594	+	0.0145251i
$697$	2.25883	−	1.30414i	0.0855593	−	0.0493977i
$698$	−2.11359	−	3.66085i	−0.0800007	−	0.138565i
$699$	−9.22941	−	35.2740i	−0.349088	−	1.33419i
$700$	3.49329	+	2.82918i	0.132034	+	0.106933i
$701$		−	13.2279i		−	0.499612i	−0.968296	−	0.249806i	$-0.919633\pi$
$701$		−	13.2279i		−	0.499612i	0.968296	−	0.249806i	$-0.0803669\pi$
$702$	−11.6940	+	14.6373i	−0.441363	+	0.552448i
$703$	5.82123	−	3.36089i	0.219552	−	0.126758i
$704$	1.02563	−	1.77645i	0.0386550	−	0.0669525i
$705$	1.87187	−	6.82495i	0.0704989	−	0.257042i
$706$	27.6603	+	15.9697i	1.04101	+	0.601028i
$707$	−4.01476	+	25.3377i	−0.150990	+	0.952922i
$708$	2.69978	−	2.66817i	0.101464	−	0.100276i
$709$	23.6162	−	13.6348i	0.886926	−	0.512067i	0.0139902	−	0.999902i	$-0.495547\pi$
$709$	23.6162	−	13.6348i	0.886926	−	0.512067i	0.872936	+	0.487835i	$0.162213\pi$
$710$	−13.3507	+	7.70801i	−0.501041	+	0.289276i
$711$	−19.0182	−	11.2808i	−0.713240	−	0.423064i
$712$		−	3.86314i		−	0.144777i
$713$	60.1715	−	34.7400i	2.25344	−	1.30102i
$714$	−23.7452	−	10.7418i	−0.888643	−	0.402003i
$715$	10.6763	−	8.15963i	0.399270	−	0.305153i
$716$	15.9356	+	9.20041i	0.595541	+	0.343836i
$717$	−20.3185	−	20.5592i	−0.758809	−	0.767797i
$718$	−12.2496	+	21.2169i	−0.457151	+	0.791808i
$719$	7.69041	+	13.3202i	0.286804	+	0.496759i	0.973045	−	0.230615i	$-0.0740739\pi$
$719$	7.69041	+	13.3202i	0.286804	+	0.496759i	−0.686241	+	0.727374i	$0.740741\pi$
$720$	2.78067	−	4.68791i	0.103629	−	0.174708i
$721$	−24.3996	−	3.86611i	−0.908688	−	0.143982i
$722$	−8.23034	+	14.2554i	−0.306302	+	0.530530i
$723$	18.5971	+	18.8174i	0.691633	+	0.699826i
$724$		−	0.190838i		−	0.00709245i
$725$	1.23076	+	0.710578i	0.0457092	+	0.0263902i
$726$	3.11176	−	11.3456i	0.115488	−	0.421075i
$727$		−	34.8309i		−	1.29181i	−0.763420	−	0.645903i	$-0.776481\pi$
$727$		−	34.8309i		−	1.29181i	0.763420	−	0.645903i	$-0.223519\pi$
$728$	−8.39241	+	4.53514i	−0.311043	+	0.168084i
$729$	0.953579	−	26.9832i	0.0353177	−	0.999376i
$730$			18.5956i			0.688253i
$731$	−4.75455	+	8.23511i	−0.175853	+	0.304587i
$732$	−11.5224	−	3.16023i	−0.425879	−	0.116806i
$733$	9.43951	−	16.3497i	0.348656	−	0.603890i	−0.637355	−	0.770570i	$-0.719971\pi$
$733$	9.43951	−	16.3497i	0.348656	−	0.603890i	0.986011	+	0.166680i	$0.0533048\pi$
$734$	28.7618	+	16.6056i	1.06162	+	0.612925i
$735$	−18.4019	−	12.1083i	−0.678763	−	0.446622i
$736$		−	8.73960i		−	0.322146i
$737$	−9.15784	+	5.28728i	−0.337333	+	0.194760i
$738$	0.673858	+	1.19956i	0.0248050	+	0.0441563i
$739$	6.89197	+	3.97908i	0.253525	+	0.146373i	0.621377	−	0.783511i	$-0.286573\pi$
$739$	6.89197	+	3.97908i	0.253525	+	0.146373i	−0.367852	+	0.929884i	$0.619907\pi$
$740$	3.83191	−	6.63707i	0.140864	−	0.243984i
$741$	−1.37595	+	9.85597i	−0.0505470	+	0.362068i
$742$	−0.955740	+	1.18009i	−0.0350863	+	0.0433223i
$743$	−9.17025	−	15.8833i	−0.336424	−	0.582703i	0.647334	−	0.762207i	$-0.275884\pi$
$743$	−9.17025	−	15.8833i	−0.336424	−	0.582703i	−0.983757	+	0.179504i	$0.942551\pi$
$744$	−3.64215	+	13.2794i	−0.133528	+	0.486848i
$745$			8.74779i			0.320494i
$746$	−2.06003	−	3.56807i	−0.0754230	−	0.130636i
$747$	45.2003	+	0.532260i	1.65379	+	0.0194744i
$748$	−5.83296	+	10.1030i	−0.213274	+	0.369401i
$749$	−10.1492	−	26.4446i	−0.370844	−	0.966266i
$750$	14.9941	−	14.8186i	0.547507	−	0.541098i
$751$	−13.7928			−0.503307			−0.251654	−	0.967817i	$-0.580974\pi$
$751$	−13.7928			−0.503307			−0.251654	+	0.967817i	$0.580974\pi$
$752$	1.94760	+	1.12445i	0.0710215	+	0.0410043i
$753$	−16.4875	+	4.31393i	−0.600837	+	0.157208i
$754$	−2.39615	+	1.83132i	−0.0872627	+	0.0666929i
$755$	2.59238			0.0943465
$756$	5.81344	−	12.4581i	0.211433	−	0.453096i
$757$	21.2683	+	36.8378i	0.773010	+	1.33889i	0.935906	+	0.352249i	$0.114583\pi$
$757$	21.2683	+	36.8378i	0.773010	+	1.33889i	−0.162896	+	0.986643i	$0.552084\pi$
$758$	2.80001	−	1.61659i	0.101701	−	0.0587171i
$759$	7.85985	+	30.0397i	0.285294	+	1.09037i
$760$		−	2.89520i		−	0.105020i
$761$	27.9822	−	16.1555i	1.01435	−	0.585638i	0.101891	−	0.994796i	$-0.467511\pi$
$761$	27.9822	−	16.1555i	1.01435	−	0.585638i	0.912464	+	0.409157i	$0.134177\pi$
$762$	−9.79758	+	35.7225i	−0.354929	+	1.29409i
$763$	8.27519	−	10.2177i	0.299582	−	0.369904i
$764$	4.50022	−	2.59820i	0.162812	−	0.0939997i
$765$	−15.8142	+	26.6609i	−0.571762	+	0.963928i
$766$	−3.61672	+	2.08811i	−0.130677	+	0.0754465i
$767$	1.01630	+	7.83592i	0.0366963	+	0.282939i
$768$	1.21751	+	1.23193i	0.0439332	+	0.0444536i
$769$	6.20736	+	10.7515i	0.223843	+	0.387707i	0.955972	−	0.293459i	$-0.0948064\pi$
$769$	6.20736	+	10.7515i	0.223843	+	0.387707i	−0.732129	+	0.681166i	$0.761473\pi$
$770$	−6.20579	+	7.66251i	−0.223641	+	0.276138i
$771$	−1.86563	−	1.88773i	−0.0671892	−	0.0679850i
$772$	9.53669	+	5.50601i	0.343233	+	0.198166i
$773$			12.5201i			0.450318i	0.974322	+	0.225159i	$0.0722901\pi$
$773$			12.5201i			0.450318i	−0.974322	+	0.225159i	$0.927710\pi$
$774$	−4.31421	−	2.55901i	−0.155071	−	0.0919818i
$775$	−6.75373	+	11.6978i	−0.242601	+	0.420197i
$776$	1.72410	−	2.98622i	0.0618915	−	0.107199i
$777$	7.96724	−	17.6119i	0.285823	−	0.631823i
$778$	−3.57665	+	2.06498i	−0.128229	+	0.0740331i
$779$	0.632915	+	0.365414i	0.0226765	+	0.0130923i
$780$	4.26002	+	10.5162i	0.152533	+	0.376539i
$781$	8.70251	+	15.0732i	0.311400	+	0.539361i
$782$			49.7036i			1.77740i
$783$	1.19887	−	4.17767i	0.0428442	−	0.149298i
$784$	5.20261	−	4.68325i	0.185808	−	0.167259i
$785$	−14.9864			−0.534889
$786$	−24.9584	+	6.53034i	−0.890237	+	0.232929i
$787$	39.3805			1.40376			0.701882	−	0.712294i	$-0.252344\pi$
$787$	39.3805			1.40376			0.701882	+	0.712294i	$0.252344\pi$
$788$	11.1333	+	19.2835i	0.396609	+	0.686947i
$789$	−8.58204	−	32.7998i	−0.305529	−	1.16770i
$790$	−11.5974	+	6.69578i	−0.412618	+	0.238225i
$791$	−43.5820	−	6.90556i	−1.54960	−	0.245533i
$792$	−5.29275	−	3.13944i	−0.188070	−	0.111555i
$793$	19.7610	−	15.1029i	0.701733	−	0.536318i
$794$	−2.38133	−	4.12458i	−0.0845101	−	0.146376i
$795$	1.26963	+	1.28467i	0.0450292	+	0.0455626i
$796$			19.0946i			0.676789i
$797$	−15.1983	+	26.3242i	−0.538350	+	0.932449i	0.460643	+	0.887585i	$0.347619\pi$
$797$	−15.1983	+	26.3242i	−0.538350	+	0.932449i	−0.998993	+	0.0448640i	$0.985715\pi$
$798$	−0.720078	−	7.26685i	−0.0254905	−	0.257244i
$799$	−11.0763	−	6.39492i	−0.391852	−	0.226236i
$800$	0.849523	+	1.47142i	0.0300352	+	0.0520224i
$801$	−11.5886	−	0.136462i	−0.409463	−	0.00482166i
$802$	15.4809			0.546650
$803$	20.9948			0.740891
$804$	−2.26017	−	8.63817i	−0.0797099	−	0.304645i
$805$	−6.57458	+	41.4931i	−0.231723	+	1.46244i
$806$	−17.4059	−	22.7744i	−0.613098	−	0.802193i
$807$	−16.5071	−	16.7026i	−0.581076	−	0.587959i
$808$	−4.84811	+	8.39717i	−0.170556	+	0.295412i
$809$	−14.1316	−	8.15889i	−0.496841	−	0.286851i	0.230567	−	0.973056i	$-0.425942\pi$
$809$	−14.1316	−	8.15889i	−0.496841	−	0.286851i	−0.727408	+	0.686205i	$0.759275\pi$
$810$	−13.9645	−	8.50703i	−0.490663	−	0.298907i
$811$	−5.92788			−0.208156			−0.104078	−	0.994569i	$-0.533189\pi$
$811$	−5.92788			−0.208156			−0.104078	+	0.994569i	$0.533189\pi$
$812$	1.39281	−	1.71975i	0.0488780	−	0.0603514i
$813$	−34.1580	−	34.5626i	−1.19797	−	1.21216i
$814$	−7.49340	−	4.32632i	−0.262644	−	0.151637i
$815$	43.5150			1.52427
$816$	−6.92421	−	7.00622i	−0.242396	−	0.245267i
$817$	−2.66441			−0.0932159
$818$	39.7884			1.39117
$819$	13.3080	+	25.3357i	0.465020	+	0.885300i
$820$	0.833252			0.0290984
$821$	33.2585			1.16073			0.580364	−	0.814357i	$-0.302910\pi$
$821$	33.2585			1.16073			0.580364	+	0.814357i	$0.302910\pi$
$822$	−14.1284	−	14.2958i	−0.492785	−	0.498622i
$823$	3.16826			0.110439			0.0552193	−	0.998474i	$-0.482414\pi$
$823$	3.16826			0.110439			0.0552193	+	0.998474i	$0.482414\pi$
$824$	−8.08628	−	4.66861i	−0.281699	−	0.162639i
$825$	−4.24327	−	4.29353i	−0.147732	−	0.149482i
$826$	−2.07753	−	5.41317i	−0.0722864	−	0.188348i
$827$	−24.0773			−0.837250			−0.418625	−	0.908159i	$-0.637488\pi$
$827$	−24.0773			−0.837250			−0.418625	+	0.908159i	$0.637488\pi$
$828$	−26.2170	−	0.308720i	−0.911103	−	0.0107288i
$829$	30.2946	+	17.4906i	1.05218	+	0.607474i	0.923258	−	0.384182i	$-0.125516\pi$
$829$	30.2946	+	17.4906i	1.05218	+	0.607474i	0.128918	+	0.991655i	$0.458850\pi$
$830$	13.6880	−	23.7083i	0.475118	−	0.822928i
$831$	28.4027	+	28.7391i	0.985279	+	0.996949i
$832$	−3.57560	+	0.463745i	−0.123962	+	0.0160775i
$833$	−29.5882	+	26.6345i	−1.02517	+	0.922829i
$834$	−6.91323	−	26.4218i	−0.239386	−	0.914912i
$835$	42.5772			1.47344
$836$	−3.26874			−0.113052
$837$	39.7069	+	11.3948i	1.37247	+	0.393861i
$838$	13.1146	+	22.7152i	0.453036	+	0.784682i
$839$	−1.10165	−	0.636039i	−0.0380332	−	0.0219585i	0.480863	−	0.876796i	$-0.340324\pi$
$839$	−1.10165	−	0.636039i	−0.0380332	−	0.0219585i	−0.518896	+	0.854837i	$0.673657\pi$
$840$	−4.85365	−	6.76477i	−0.167467	−	0.233407i
$841$	−14.1502	+	24.5088i	−0.487937	+	0.845132i
$842$		−	14.0343i		−	0.483653i
$843$	−32.4226	−	32.8066i	−1.11669	−	1.12992i
$844$	−7.80557	−	13.5196i	−0.268679	−	0.465365i
$845$	−22.7906	−	6.20075i	−0.784021	−	0.213312i
$846$	3.44190	−	5.80266i	0.118335	−	0.199500i
$847$	−13.9652	−	11.3102i	−0.479849	−	0.388625i
$848$	−0.497067	+	0.286982i	−0.0170694	+	0.00985500i
$849$	−11.8022	−	45.1072i	−0.405052	−	1.54807i
$850$	−4.83138	−	8.36820i	−0.165715	−	0.287027i
$851$	−36.8653			−1.26373
$852$	−14.2178	+	3.72008i	−0.487095	+	0.127448i
$853$	−8.88125			−0.304088			−0.152044	−	0.988374i	$-0.548586\pi$
$853$	−8.88125			−0.304088			−0.152044	+	0.988374i	$0.548586\pi$
$854$	−11.4864	+	14.1827i	−0.393058	+	0.485323i
$855$	−8.68499	−	0.102271i	−0.297020	−	0.00349758i
$856$		−	10.7060i		−	0.365923i
$857$	14.1680	+	24.5397i	0.483969	+	0.838259i	0.999830	−	0.0184131i	$-0.00586142\pi$
$857$	14.1680	+	24.5397i	0.483969	+	0.838259i	−0.515861	+	0.856672i	$0.672528\pi$
$858$	11.8730	−	4.80966i	0.405337	−	0.164199i
$859$	15.6163	+	9.01607i	0.532821	+	0.307624i	0.742164	−	0.670218i	$-0.233799\pi$
$859$	15.6163	+	9.01607i	0.532821	+	0.307624i	−0.209343	+	0.977842i	$0.567133\pi$
$860$	−2.63083	+	1.51891i	−0.0897106	+	0.0517944i
$861$	2.09143	−	0.207242i	0.0712759	−	0.00706278i
$862$	8.06272	−	13.9650i	0.274617	−	0.475651i
$863$	−20.8330	+	36.0838i	−0.709163	+	1.22831i	0.256005	+	0.966675i	$0.417594\pi$
$863$	−20.8330	+	36.0838i	−0.709163	+	1.22831i	−0.965168	+	0.261631i	$0.915740\pi$
$864$	3.73855	−	3.60877i	0.127188	−	0.122773i
$865$			13.8188i			0.469854i
$866$	13.9038	+	8.02734i	0.472469	+	0.272780i
$867$	18.6815	+	18.9027i	0.634456	+	0.641971i
$868$	16.3455	+	13.2380i	0.554802	+	0.449328i
$869$	7.55968	+	13.0938i	0.256445	+	0.444175i
$870$	−1.85025	−	1.87216i	−0.0627293	−	0.0634723i
$871$	17.1585	+	7.14598i	0.581395	+	0.242132i
$872$	4.30381	−	2.48481i	0.145745	−	0.0841462i
$873$	−8.89715	−	5.27742i	−0.301123	−	0.178614i
$874$	−12.0609	+	6.96338i	−0.407967	+	0.235540i
$875$	−11.5382	−	30.0638i	−0.390063	−	1.01634i
$876$	−4.68898	+	17.0963i	−0.158426	+	0.577629i
$877$	−32.0440	+	18.5006i	−1.08205	+	0.624722i	−0.931449	−	0.363873i	$-0.881454\pi$
$877$	−32.0440	+	18.5006i	−1.08205	+	0.624722i	−0.150601	+	0.988595i	$0.548121\pi$
$878$		−	16.1774i		−	0.545960i
$879$	−3.52972	−	13.4903i	−0.119054	−	0.455016i
$880$	−3.22755	+	1.86343i	−0.108801	+	0.0628161i
$881$	12.5417	+	21.7228i	0.422540	+	0.731861i	0.996187	−	0.0872416i	$-0.0278052\pi$
$881$	12.5417	+	21.7228i	0.422540	+	0.731861i	−0.573647	+	0.819103i	$0.694472\pi$
$882$	−13.8650	−	15.7722i	−0.466859	−	0.531077i
$883$	23.5431			0.792287			0.396144	−	0.918189i	$-0.370348\pi$
$883$	23.5431			0.792287			0.396144	+	0.918189i	$0.370348\pi$
$884$	20.3351	−	2.63740i	0.683943	−	0.0887054i
$885$	−6.67178	+	1.74566i	−0.224269	+	0.0586798i
$886$	−10.8594	−	6.26970i	−0.364830	−	0.210635i
$887$	−29.4455			−0.988682			−0.494341	−	0.869268i	$-0.664591\pi$
$887$	−29.4455			−0.988682			−0.494341	+	0.869268i	$0.664591\pi$
$888$	5.19653	−	5.13570i	0.174384	−	0.172343i
$889$	43.9703	+	35.6111i	1.47472	+	1.19436i
$890$	−3.50938	+	6.07842i	−0.117635	+	0.203749i
$891$	−9.60463	+	15.7663i	−0.321767	+	0.528189i
$892$	−4.91509	−	8.51319i	−0.164569	−	0.285043i
$893$		−	3.58366i		−	0.119923i
$894$	−2.20581	+	8.04248i	−0.0737732	+	0.268981i
$895$	−16.7158	−	28.9526i	−0.558748	−	0.967779i
$896$	2.47008	−	0.947995i	0.0825197	−	0.0316703i
$897$	33.5626	−	43.0394i	1.12062	−	1.43704i
$898$	−8.48307	+	14.6931i	−0.283084	+	0.490315i
$899$	5.75885	+	3.32487i	0.192068	+	0.110891i
$900$	4.44395	−	2.49641i	0.148132	−	0.0832138i
$901$	2.82691	−	1.63212i	0.0941780	−	0.0543737i
$902$		−	0.940760i		−	0.0313239i
$903$	−6.22552	+	4.46674i	−0.207172	+	0.148644i
$904$	−14.4435	−	8.33897i	−0.480384	−	0.277350i
$905$	−0.173363	+	0.300273i	−0.00576277	+	0.00998141i
$906$	2.38337	+	0.653685i	0.0791821	+	0.0217172i
$907$	−6.92697	+	11.9979i	−0.230006	+	0.398383i	−0.957810	−	0.287403i	$-0.907208\pi$
$907$	−6.92697	+	11.9979i	−0.230006	+	0.398383i	0.727803	+	0.685786i	$0.240541\pi$
$908$		−	11.3725i		−	0.377410i
$909$	25.0185	+	14.8399i	0.829812	+	0.492210i
$910$	17.3248	+	0.488106i	0.574311	+	0.0161806i
$911$		−	27.4426i		−	0.909213i	−0.890692	−	0.454607i	$-0.849780\pi$
$911$		−	27.4426i		−	0.909213i	0.890692	−	0.454607i	$-0.150220\pi$
$912$	0.730041	−	2.66176i	0.0241741	−	0.0881398i
$913$	−26.7672	−	15.4541i	−0.885866	−	0.511455i
$914$		−	9.47441i		−	0.313386i
$915$	15.2589	+	15.4397i	0.504444	+	0.510420i
$916$	−9.48968	+	16.4366i	−0.313548	+	0.543081i
$917$	−6.16726	+	38.9224i	−0.203661	+	1.28533i
$918$	−21.2618	+	20.5237i	−0.701744	+	0.677383i
$919$	22.0343	+	38.1646i	0.726845	+	1.25893i	0.958210	+	0.286066i	$0.0923476\pi$
$919$	22.0343	+	38.1646i	0.726845	+	1.25893i	−0.231365	+	0.972867i	$0.574319\pi$
$920$	−7.93928	+	13.7512i	−0.261750	+	0.453365i
$921$	16.5818	+	16.7782i	0.546389	+	0.552861i
$922$	−31.5250	−	18.2010i	−1.03822	−	0.599417i
$923$	11.7618	−	28.2418i	0.387144	−	0.929590i
$924$	−7.63758	+	5.47988i	−0.251258	+	0.180275i
$925$	6.20671	−	3.58345i	0.204075	−	0.117823i
$926$			17.8517i			0.586643i
$927$	−14.2905	+	24.0922i	−0.469362	+	0.791293i
$928$	0.724381	−	0.418222i	0.0237790	−	0.0137288i
$929$	−36.2869	+	20.9503i	−1.19053	+	0.687356i	−0.958428	−	0.285335i	$-0.907895\pi$
$929$	−36.2869	+	20.9503i	−1.19053	+	0.687356i	−0.232107	+	0.972690i	$0.574562\pi$
$930$	17.7941	−	17.5858i	0.583491	−	0.576661i
$931$	−10.6083	−	3.44834i	−0.347672	−	0.113015i
$932$	−18.2307	−	10.5255i	−0.597167	−	0.344775i
$933$	11.6128	−	42.3409i	0.380187	−	1.38618i
$934$	15.1928	−	26.3147i	0.497124	−	0.861044i
$935$	18.3556	−	10.5976i	0.600293	−	0.346579i
$936$	1.26483	+	10.7424i	0.0413424	+	0.351128i
$937$			1.71598i			0.0560586i	0.999607	+	0.0280293i	$0.00892317\pi$
$937$			1.71598i			0.0560586i	−0.999607	+	0.0280293i	$0.991077\pi$
$938$	−13.4712	−	2.13450i	−0.439849	−	0.0696940i
$939$	−3.75285	−	14.3431i	−0.122470	−	0.468068i
$940$	−2.04295	−	3.53850i	−0.0666337	−	0.115413i
$941$	1.26611	−	0.730989i	0.0412740	−	0.0238296i	−0.479221	−	0.877694i	$-0.659081\pi$
$941$	1.26611	−	0.730989i	0.0412740	−	0.0238296i	0.520495	+	0.853865i	$0.325747\pi$
$942$	−13.7781	−	3.77892i	−0.448915	−	0.123124i
$943$	−2.00409	−	3.47119i	−0.0652622	−	0.113038i
$944$		−	2.19150i		−	0.0713271i
$945$	−20.4644	+	14.3210i	−0.665706	+	0.465861i
$946$	1.71488	+	2.97027i	0.0557557	+	0.0965717i
$947$	15.2680			0.496145			0.248072	−	0.968742i	$-0.420203\pi$
$947$	15.2680			0.496145			0.248072	+	0.968742i	$0.420203\pi$
$948$	−12.3507	+	3.23156i	−0.401133	+	0.104956i
$949$	−22.4088	−	29.3202i	−0.727420	−	0.951775i
$950$	1.35373	−	2.34474i	0.0439209	−	0.0760733i
$951$	39.4620	−	10.3252i	1.27964	−	0.334817i
$952$	−14.0478	+	5.39141i	−0.455291	+	0.174737i
$953$	−20.0074	−	11.5513i	−0.648104	−	0.374183i	0.139625	−	0.990204i	$-0.455410\pi$
$953$	−20.0074	−	11.5513i	−0.648104	−	0.374183i	−0.787729	+	0.616021i	$0.788743\pi$
$954$	0.843328	+	1.50124i	0.0273037	+	0.0486043i
$955$	−9.44111			−0.305507
$956$	−16.6885			−0.539746
$957$	−2.11371	+	2.08897i	−0.0683267	+	0.0675268i
$958$	−19.9492	−	11.5177i	−0.644530	−	0.372120i
$959$	−28.6636	+	11.0008i	−0.925596	+	0.355235i
$960$	−0.796563	−	3.04440i	−0.0257090	−	0.0982575i
$961$	−16.1015	+	27.8886i	−0.519402	+	0.899631i
$962$	1.95617	+	15.0826i	0.0630693	+	0.486282i
$963$	−32.1157	−	0.378181i	−1.03491	−	0.0121867i
$964$	15.2747			0.491963
$965$	−10.0036	−	17.3268i	−0.322028	−	0.557768i
$966$	−16.5072	+	36.4898i	−0.531111	+	1.17404i
$967$		−	14.3674i		−	0.462026i	−0.972951	−	0.231013i	$-0.925796\pi$
$967$		−	14.3674i		−	0.462026i	0.972951	−	0.231013i	$-0.0742040\pi$
$968$	−3.39615	−	5.88231i	−0.109156	−	0.189064i
$969$	−4.15187	+	15.1379i	−0.133377	+	0.486300i
$970$	−5.42553	+	3.13243i	−0.174203	+	0.100576i
$971$	−15.6985	−	27.1905i	−0.503788	−	0.872586i	−0.999990	−	0.00437930i	$-0.998606\pi$
$971$	−15.6985	−	27.1905i	−0.503788	−	0.872586i	0.496203	−	0.868207i	$-0.334727\pi$
$972$	−10.6935	−	11.3424i	−0.342994	−	0.363806i
$973$	−41.2046	−	6.52886i	−1.32096	−	0.209306i
$974$			14.2075i			0.455238i
$975$	−1.46707	+	10.5086i	−0.0469838	+	0.336545i
$976$	−5.97394	+	3.44906i	−0.191221	+	0.110402i
$977$	−21.8776	+	37.8931i	−0.699926	+	1.21231i	0.268566	+	0.963261i	$0.413450\pi$
$977$	−21.8776	+	37.8931i	−0.699926	+	1.21231i	−0.968492	+	0.249046i	$0.919883\pi$
$978$	40.0065	+	10.9726i	1.27927	+	0.350864i
$979$	6.86267	+	3.96217i	0.219332	+	0.126631i
$980$	−12.4404	+	2.64262i	−0.397394	+	0.0844155i
$981$	−7.30188	−	12.9983i	−0.233131	−	0.415004i
$982$	2.47085	−	1.42654i	0.0788479	−	0.0455228i
$983$	3.21594	−	1.85672i	0.102572	−	0.0592202i	−0.447836	−	0.894116i	$-0.647805\pi$
$983$	3.21594	−	1.85672i	0.102572	−	0.0592202i	0.550409	+	0.834895i	$0.314472\pi$
$984$	0.766068	+	0.210109i	0.0244214	+	0.00669804i
$985$		−	40.4553i		−	1.28901i
$986$	−4.11968	+	2.37850i	−0.131197	+	0.0757469i
$987$	−6.00782	−	8.37340i	−0.191231	−	0.266528i
$988$	3.48889	+	4.56495i	0.110996	+	0.145230i
$989$	12.6551	+	7.30641i	0.402408	+	0.232330i
$990$	5.47588	+	9.74780i	0.174035	+	0.309805i
$991$	21.0267	−	36.4192i	0.667934	−	1.15690i	−0.310547	−	0.950558i	$-0.600512\pi$
$991$	21.0267	−	36.4192i	0.667934	−	1.15690i	0.978481	−	0.206337i	$-0.0661544\pi$
$992$	3.97501	+	6.88493i	0.126207	+	0.218597i
$993$	11.8783	+	3.25786i	0.376947	+	0.103385i
$994$	−3.51325	+	22.1726i	−0.111434	+	0.703273i
$995$	17.3460	−	30.0442i	0.549905	−	0.952464i
$996$	18.5626	−	18.3453i	0.588178	−	0.581292i
$997$		−	45.1553i		−	1.43008i	−0.699083	−	0.715041i	$-0.746408\pi$
$997$		−	45.1553i		−	1.43008i	0.699083	−	0.715041i	$-0.253592\pi$
$998$	15.9720	+	9.22146i	0.505586	+	0.291900i
$999$	−15.2225	−	15.7699i	−0.481618	−	0.498938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.e.257.14	yes	34
3.2	odd	2		546.2.bi.f.257.15	yes	34
7.3	odd	6		546.2.bn.f.101.8	yes	34
13.4	even	6		546.2.bn.e.173.10	yes	34
21.17	even	6		546.2.bn.e.101.10	yes	34
39.17	odd	6		546.2.bn.f.173.8	yes	34
91.17	odd	6		546.2.bi.f.17.15	yes	34
273.17	even	6	inner	546.2.bi.e.17.14	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.14	✓	34	273.17	even	6	inner
546.2.bi.e.257.14	yes	34	1.1	even	1	trivial
546.2.bi.f.17.15	yes	34	91.17	odd	6
546.2.bi.f.257.15	yes	34	3.2	odd	2
546.2.bn.e.101.10	yes	34	21.17	even	6
546.2.bn.e.173.10	yes	34	13.4	even	6
546.2.bn.f.101.8	yes	34	7.3	odd	6
546.2.bn.f.173.8	yes	34	39.17	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.21751 + 1.23193i) q^{3} +1.00000 q^{4} +(-1.57344 - 0.908426i) q^{5} +(-1.21751 - 1.23193i) q^{6} +(-2.47008 + 0.947995i) q^{7} -1.00000 q^{8} +(-0.0353243 + 2.99979i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.21751 + 1.23193i) q^{3} +1.00000 q^{4} +(-1.57344 - 0.908426i) q^{5} +(-1.21751 - 1.23193i) q^{6} +(-2.47008 + 0.947995i) q^{7} -1.00000 q^{8} +(-0.0353243 + 2.99979i) q^{9} +(1.57344 + 0.908426i) q^{10} +(1.02563 - 1.77645i) q^{11} +(1.21751 + 1.23193i) q^{12} +(-3.57560 + 0.463745i) q^{13} +(2.47008 - 0.947995i) q^{14} +(-0.796563 - 3.04440i) q^{15} +1.00000 q^{16} -5.68717 q^{17} +(0.0353243 - 2.99979i) q^{18} +(-0.796762 - 1.38003i) q^{19} +(-1.57344 - 0.908426i) q^{20} +(-4.17522 - 1.88878i) q^{21} +(-1.02563 + 1.77645i) q^{22} +8.73960i q^{23} +(-1.21751 - 1.23193i) q^{24} +(-0.849523 - 1.47142i) q^{25} +(3.57560 - 0.463745i) q^{26} +(-3.73855 + 3.60877i) q^{27} +(-2.47008 + 0.947995i) q^{28} +(-0.724381 + 0.418222i) q^{29} +(0.796563 + 3.04440i) q^{30} +(-3.97501 - 6.88493i) q^{31} -1.00000 q^{32} +(3.43719 - 0.899337i) q^{33} +5.68717 q^{34} +(4.74771 + 0.752275i) q^{35} +(-0.0353243 + 2.99979i) q^{36} +4.21819i q^{37} +(0.796762 + 1.38003i) q^{38} +(-4.92465 - 3.84029i) q^{39} +(1.57344 + 0.908426i) q^{40} +(-0.397180 + 0.229312i) q^{41} +(4.17522 + 1.88878i) q^{42} +(0.836012 - 1.44802i) q^{43} +(1.02563 - 1.77645i) q^{44} +(2.78067 - 4.68791i) q^{45} -8.73960i q^{46} +(1.94760 + 1.12445i) q^{47} +(1.21751 + 1.23193i) q^{48} +(5.20261 - 4.68325i) q^{49} +(0.849523 + 1.47142i) q^{50} +(-6.92421 - 7.00622i) q^{51} +(-3.57560 + 0.463745i) q^{52} +(-0.497067 + 0.286982i) q^{53} +(3.73855 - 3.60877i) q^{54} +(-3.22755 + 1.86343i) q^{55} +(2.47008 - 0.947995i) q^{56} +(0.730041 - 2.66176i) q^{57} +(0.724381 - 0.418222i) q^{58} -2.19150i q^{59} +(-0.796563 - 3.04440i) q^{60} +(-5.97394 + 3.44906i) q^{61} +(3.97501 + 6.88493i) q^{62} +(-2.75653 - 7.44322i) q^{63} +1.00000 q^{64} +(6.04728 + 2.51850i) q^{65} +(-3.43719 + 0.899337i) q^{66} +(-4.46448 - 2.57757i) q^{67} -5.68717 q^{68} +(-10.7666 + 10.6406i) q^{69} +(-4.74771 - 0.752275i) q^{70} +(-4.24250 + 7.34823i) q^{71} +(0.0353243 - 2.99979i) q^{72} +(5.11752 + 8.86381i) q^{73} -4.21819i q^{74} +(0.778384 - 2.83803i) q^{75} +(-0.796762 - 1.38003i) q^{76} +(-0.849335 + 5.36027i) q^{77} +(4.92465 + 3.84029i) q^{78} +(-3.68537 + 6.38325i) q^{79} +(-1.57344 - 0.908426i) q^{80} +(-8.99750 - 0.211931i) q^{81} +(0.397180 - 0.229312i) q^{82} -15.0678i q^{83} +(-4.17522 - 1.88878i) q^{84} +(8.94843 + 5.16638i) q^{85} +(-0.836012 + 1.44802i) q^{86} +(-1.39717 - 0.383200i) q^{87} +(-1.02563 + 1.77645i) q^{88} +3.86314i q^{89} +(-2.78067 + 4.68791i) q^{90} +(8.39241 - 4.53514i) q^{91} +8.73960i q^{92} +(3.64215 - 13.2794i) q^{93} +(-1.94760 - 1.12445i) q^{94} +2.89520i q^{95} +(-1.21751 - 1.23193i) q^{96} +(-1.72410 + 2.98622i) q^{97} +(-5.20261 + 4.68325i) q^{98} +(5.29275 + 3.13944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more