LMFDB - Embedded newform 546.2.bv.a.515.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			515.4
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-1.35728 - 1.07601i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.88157 - 0.772115i) q^{5} +(1.03254 + 1.39063i) q^{6} +(-2.53580 - 0.754783i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.684406 + 2.92089i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.35728 - 1.07601i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.88157 - 0.772115i) q^{5} +(1.03254 + 1.39063i) q^{6} +(-2.53580 - 0.754783i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.684406 + 2.92089i) q^{9} +(2.58355 + 1.49161i) q^{10} +(0.475494 - 0.127408i) q^{11} +(-0.637432 - 1.61049i) q^{12} +(-3.60146 - 0.171677i) q^{13} +(2.25405 + 1.38538i) q^{14} +(3.08029 + 4.14857i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.186739 - 0.323441i) q^{17} +(0.0948959 - 2.99850i) q^{18} +(0.747436 - 2.78947i) q^{19} +(-2.10946 - 2.10946i) q^{20} +(2.62964 + 3.75300i) q^{21} -0.492267 q^{22} +(3.98818 + 6.90774i) q^{23} +(0.198887 + 1.72059i) q^{24} +(3.37717 + 1.94981i) q^{25} +(3.43431 + 1.09795i) q^{26} +(2.21397 - 4.70088i) q^{27} +(-1.81868 - 1.92156i) q^{28} +0.582580i q^{29} +(-1.90160 - 4.80445i) q^{30} +(4.88185 - 1.30809i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.782470 - 0.338708i) q^{33} +(-0.264088 + 0.264088i) q^{34} +(6.72432 + 4.13290i) q^{35} +(-0.867731 + 2.87177i) q^{36} +(-2.74184 - 0.734674i) q^{37} +(-1.44393 + 2.50097i) q^{38} +(4.70346 + 4.10822i) q^{39} +(1.49161 + 2.58355i) q^{40} +(6.61487 - 6.61487i) q^{41} +(-1.56869 - 4.30572i) q^{42} +2.66245i q^{43} +(0.475494 + 0.127408i) q^{44} +(0.283096 - 8.94519i) q^{45} +(-2.06444 - 7.70458i) q^{46} +(-3.42585 + 12.7854i) q^{47} +(0.253213 - 1.71344i) q^{48} +(5.86060 + 3.82797i) q^{49} +(-2.75745 - 2.75745i) q^{50} +(-0.601482 + 0.238066i) q^{51} +(-3.03312 - 1.94941i) q^{52} +(-2.82305 - 1.62989i) q^{53} +(-3.35521 + 3.96769i) q^{54} -1.46854 q^{55} +(1.25937 + 2.32680i) q^{56} +(-4.01597 + 2.98183i) q^{57} +(0.150783 - 0.562729i) q^{58} +(6.22585 - 1.66821i) q^{59} +(0.593323 + 5.13292i) q^{60} +(3.77475 + 6.53807i) q^{61} -5.05407 q^{62} +(0.469118 - 7.92338i) q^{63} +1.00000i q^{64} +(10.2453 + 3.27544i) q^{65} +(0.668144 + 0.529685i) q^{66} +(2.82615 - 0.757263i) q^{67} +(0.323441 - 0.186739i) q^{68} +(2.01972 - 13.6670i) q^{69} +(-5.42553 - 5.73245i) q^{70} +(0.908221 - 0.908221i) q^{71} +(1.58143 - 2.54933i) q^{72} +(0.884917 + 3.30256i) q^{73} +(2.45827 + 1.41928i) q^{74} +(-2.48574 - 6.28030i) q^{75} +(2.04203 - 2.04203i) q^{76} +(-1.30192 - 0.0358127i) q^{77} +(-3.47991 - 5.18558i) q^{78} +(5.68471 + 9.84621i) q^{79} +(-0.772115 - 2.88157i) q^{80} +(-8.06318 + 3.99815i) q^{81} +(-8.10152 + 4.67742i) q^{82} +(-9.25218 + 9.25218i) q^{83} +(0.400832 + 4.56501i) q^{84} +(-0.787834 + 0.787834i) q^{85} +(0.689092 - 2.57173i) q^{86} +(0.626862 - 0.790723i) q^{87} +(-0.426316 - 0.246134i) q^{88} +(0.844833 - 3.15296i) q^{89} +(-2.58864 + 8.56712i) q^{90} +(9.00302 + 3.15366i) q^{91} +7.97637i q^{92} +(-8.03355 - 3.47748i) q^{93} +(6.61822 - 11.4631i) q^{94} +(-4.30758 + 7.46095i) q^{95} +(-0.688056 + 1.58952i) q^{96} +(-12.1530 - 12.1530i) q^{97} +(-4.67016 - 5.21437i) q^{98} +(0.697576 + 1.30167i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−1.35728	−	1.07601i	−0.783625	−	0.621234i
$3$	−1.35728	−	1.07601i	−0.783625	−	0.621234i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.88157	−	0.772115i	−1.28868	−	0.345300i	−0.451520	−	0.892261i	$-0.649118\pi$
$5$	−2.88157	−	0.772115i	−1.28868	−	0.345300i	−0.837158	+	0.546961i	$0.815785\pi$
$6$	1.03254	+	1.39063i	0.421532	+	0.567724i
$7$	−2.53580	−	0.754783i	−0.958444	−	0.285281i
$7$	−2.53580	−	0.754783i	−0.958444	−	0.285281i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.684406	+	2.92089i	0.228135	+	0.973629i
$10$	2.58355	+	1.49161i	0.816989	+	0.471689i
$11$	0.475494	−	0.127408i	0.143367	−	0.0384150i	−0.186422	−	0.982470i	$-0.559689\pi$
$11$	0.475494	−	0.127408i	0.143367	−	0.0384150i	0.329789	+	0.944055i	$0.393022\pi$
$12$	−0.637432	−	1.61049i	−0.184011	−	0.464909i
$13$	−3.60146	−	0.171677i	−0.998866	−	0.0476147i
$13$	−3.60146	−	0.171677i	−0.998866	−	0.0476147i
$14$	2.25405	+	1.38538i	0.602419	+	0.370258i
$15$	3.08029	+	4.14857i	0.795328	+	1.07116i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.186739	−	0.323441i	0.0452908	−	0.0784459i	−0.842491	−	0.538710i	$-0.818912\pi$
$17$	0.186739	−	0.323441i	0.0452908	−	0.0784459i	0.887782	+	0.460264i	$0.152245\pi$
$18$	0.0948959	−	2.99850i	0.0223672	−	0.706753i
$19$	0.747436	−	2.78947i	0.171473	−	0.639948i	−0.825652	−	0.564180i	$-0.809192\pi$
$19$	0.747436	−	2.78947i	0.171473	−	0.639948i	0.997125	−	0.0757680i	$-0.0241408\pi$
$20$	−2.10946	−	2.10946i	−0.471689	−	0.471689i
$21$	2.62964	+	3.75300i	0.573834	+	0.818972i
$22$	−0.492267			−0.104952
$23$	3.98818	+	6.90774i	0.831594	+	1.44036i	0.896774	+	0.442489i	$0.145904\pi$
$23$	3.98818	+	6.90774i	0.831594	+	1.44036i	−0.0651804	+	0.997873i	$0.520762\pi$
$24$	0.198887	+	1.72059i	0.0405976	+	0.351215i
$25$	3.37717	+	1.94981i	0.675434	+	0.389962i
$26$	3.43431	+	1.09795i	0.673524	+	0.215327i
$27$	2.21397	−	4.70088i	0.426080	−	0.904686i
$28$	−1.81868	−	1.92156i	−0.343698	−	0.363141i
$29$			0.582580i			0.108182i	0.998536	+	0.0540912i	$0.0172262\pi$
$29$			0.582580i			0.108182i	−0.998536	+	0.0540912i	$0.982774\pi$
$30$	−1.90160	−	4.80445i	−0.347184	−	0.877169i
$31$	4.88185	−	1.30809i	0.876807	−	0.234940i	0.207778	−	0.978176i	$-0.433377\pi$
$31$	4.88185	−	1.30809i	0.876807	−	0.234940i	0.669029	+	0.743236i	$0.266710\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−0.782470	−	0.338708i	−0.136210	−	0.0589614i
$34$	−0.264088	+	0.264088i	−0.0452908	+	0.0452908i
$35$	6.72432	+	4.13290i	1.13662	+	0.698587i
$36$	−0.867731	+	2.87177i	−0.144622	+	0.478628i
$37$	−2.74184	−	0.734674i	−0.450756	−	0.120780i	0.0262971	−	0.999654i	$-0.491628\pi$
$37$	−2.74184	−	0.734674i	−0.450756	−	0.120780i	−0.477053	+	0.878874i	$0.658295\pi$
$38$	−1.44393	+	2.50097i	−0.234237	+	0.405711i
$39$	4.70346	+	4.10822i	0.753156	+	0.657842i
$40$	1.49161	+	2.58355i	0.235845	+	0.408495i
$41$	6.61487	−	6.61487i	1.03307	−	1.03307i	0.0336345	−	0.999434i	$-0.489292\pi$
$41$	6.61487	−	6.61487i	1.03307	−	1.03307i	0.999434	−	0.0336345i	$-0.0107082\pi$
$42$	−1.56869	−	4.30572i	−0.242053	−	0.664387i
$43$			2.66245i			0.406019i	0.979177	+	0.203010i	$0.0650723\pi$
$43$			2.66245i			0.406019i	−0.979177	+	0.203010i	$0.934928\pi$
$44$	0.475494	+	0.127408i	0.0716834	+	0.0192075i
$45$	0.283096	−	8.94519i	0.0422014	−	1.33347i
$46$	−2.06444	−	7.70458i	−0.304384	−	1.13598i
$47$	−3.42585	+	12.7854i	−0.499711	+	1.86495i	0.00214941	+	0.999998i	$0.499316\pi$
$47$	−3.42585	+	12.7854i	−0.499711	+	1.86495i	−0.501860	+	0.864949i	$0.667351\pi$
$48$	0.253213	−	1.71344i	0.0365481	−	0.247314i
$49$	5.86060	+	3.82797i	0.837229	+	0.546852i
$50$	−2.75745	−	2.75745i	−0.389962	−	0.389962i
$51$	−0.601482	+	0.238066i	−0.0842243	+	0.0333360i
$52$	−3.03312	−	1.94941i	−0.420618	−	0.270334i
$53$	−2.82305	−	1.62989i	−0.387776	−	0.223882i	0.293420	−	0.955984i	$-0.405206\pi$
$53$	−2.82305	−	1.62989i	−0.387776	−	0.223882i	−0.681196	+	0.732101i	$0.738540\pi$
$54$	−3.35521	+	3.96769i	−0.456587	+	0.539934i
$55$	−1.46854			−0.198018
$56$	1.25937	+	2.32680i	0.168291	+	0.310931i
$57$	−4.01597	+	2.98183i	−0.531929	+	0.394954i
$58$	0.150783	−	0.562729i	0.0197988	−	0.0738899i
$59$	6.22585	−	1.66821i	0.810537	−	0.217183i	0.170332	−	0.985387i	$-0.445516\pi$
$59$	6.22585	−	1.66821i	0.810537	−	0.217183i	0.640205	+	0.768204i	$0.278849\pi$
$60$	0.593323	+	5.13292i	0.0765977	+	0.662657i
$61$	3.77475	+	6.53807i	0.483308	+	0.837114i	0.999816	−	0.0191684i	$-0.00610187\pi$
$61$	3.77475	+	6.53807i	0.483308	+	0.837114i	−0.516508	+	0.856282i	$0.672769\pi$
$62$	−5.05407			−0.641867
$63$	0.469118	−	7.92338i	0.0591033	−	0.998252i
$64$			1.00000i			0.125000i
$65$	10.2453	+	3.27544i	1.27078	+	0.406269i
$66$	0.668144	+	0.529685i	0.0822428	+	0.0651997i
$67$	2.82615	−	0.757263i	0.345269	−	0.0925144i	−0.0820176	−	0.996631i	$-0.526136\pi$
$67$	2.82615	−	0.757263i	0.345269	−	0.0925144i	0.427286	+	0.904116i	$0.359470\pi$
$68$	0.323441	−	0.186739i	0.0392230	−	0.0226454i
$69$	2.01972	−	13.6670i	0.243145	−	1.64532i
$70$	−5.42553	−	5.73245i	−0.648474	−	0.685159i
$71$	0.908221	−	0.908221i	0.107786	−	0.107786i	−0.651157	−	0.758943i	$-0.725716\pi$
$71$	0.908221	−	0.908221i	0.107786	−	0.107786i	0.758943	+	0.651157i	$0.225716\pi$
$72$	1.58143	−	2.54933i	0.186374	−	0.300441i
$73$	0.884917	+	3.30256i	0.103572	+	0.386535i	0.998179	−	0.0603179i	$-0.0192114\pi$
$73$	0.884917	+	3.30256i	0.103572	+	0.386535i	−0.894608	+	0.446853i	$0.852545\pi$
$74$	2.45827	+	1.41928i	0.285768	+	0.164988i
$75$	−2.48574	−	6.28030i	−0.287029	−	0.725187i
$76$	2.04203	−	2.04203i	0.234237	−	0.234237i
$77$	−1.30192	−	0.0358127i	−0.148368	−	0.00408123i
$78$	−3.47991	−	5.18558i	−0.394022	−	0.587152i
$79$	5.68471	+	9.84621i	0.639580	+	1.10779i	0.985525	+	0.169530i	$0.0542251\pi$
$79$	5.68471	+	9.84621i	0.639580	+	1.10779i	−0.345945	+	0.938255i	$0.612442\pi$
$80$	−0.772115	−	2.88157i	−0.0863251	−	0.322170i
$81$	−8.06318	+	3.99815i	−0.895908	+	0.444239i
$82$	−8.10152	+	4.67742i	−0.894664	+	0.516534i
$83$	−9.25218	+	9.25218i	−1.01556	+	1.01556i	−0.0156815	+	0.999877i	$0.504992\pi$
$83$	−9.25218	+	9.25218i	−1.01556	+	1.01556i	−0.999877	+	0.0156815i	$0.995008\pi$
$84$	0.400832	+	4.56501i	0.0437343	+	0.498084i
$85$	−0.787834	+	0.787834i	−0.0854526	+	0.0854526i
$86$	0.689092	−	2.57173i	0.0743067	−	0.277316i
$87$	0.626862	−	0.790723i	0.0672066	−	0.0847744i
$88$	−0.426316	−	0.246134i	−0.0454454	−	0.0262379i
$89$	0.844833	−	3.15296i	0.0895521	−	0.334213i	−0.906585	−	0.422023i	$-0.861320\pi$
$89$	0.844833	−	3.15296i	0.0895521	−	0.334213i	0.996137	+	0.0878099i	$0.0279868\pi$
$90$	−2.58864	+	8.56712i	−0.272866	+	0.903054i
$91$	9.00302	+	3.15366i	0.943773	+	0.330594i
$92$			7.97637i			0.831594i
$93$	−8.03355	−	3.47748i	−0.833040	−	0.360598i
$94$	6.61822	−	11.4631i	0.682618	−	1.18233i
$95$	−4.30758	+	7.46095i	−0.441948	+	0.765477i
$96$	−0.688056	+	1.58952i	−0.0702244	+	0.162230i
$97$	−12.1530	−	12.1530i	−1.23395	−	1.23395i	−0.962433	−	0.271521i	$-0.912473\pi$
$97$	−12.1530	−	12.1530i	−1.23395	−	1.23395i	−0.271521	−	0.962433i	$-0.587527\pi$
$98$	−4.67016	−	5.21437i	−0.471757	−	0.526731i
$99$	0.697576	+	1.30167i	0.0701090	+	0.130822i
$100$	1.94981	+	3.37717i	0.194981	+	0.337717i
$101$	−5.60907	+	9.71519i	−0.558123	+	0.966698i	0.439530	+	0.898228i	$0.355145\pi$
$101$	−5.60907	+	9.71519i	−0.558123	+	0.966698i	−0.997653	+	0.0684698i	$0.978188\pi$
$102$	0.642603	−	0.0742796i	0.0636272	−	0.00735478i
$103$	−2.83222	+	1.63518i	−0.279067	+	0.161119i	−0.633001	−	0.774151i	$-0.718177\pi$
$103$	−2.83222	+	1.63518i	−0.279067	+	0.161119i	0.353934	+	0.935270i	$0.384844\pi$
$104$	2.42522	+	2.66801i	0.237813	+	0.261620i
$105$	−4.67974	−	12.8449i	−0.456696	−	1.25354i
$106$	2.30501	+	2.30501i	0.223882	+	0.223882i
$107$	13.9686	−	8.06480i	1.35040	−	0.779653i	0.362094	−	0.932142i	$-0.382062\pi$
$107$	13.9686	−	8.06480i	1.35040	−	0.779653i	0.988305	+	0.152488i	$0.0487287\pi$
$108$	4.26780	−	2.96410i	0.410669	−	0.285220i
$109$	−11.9725	+	3.20802i	−1.14676	+	0.307273i	−0.781665	−	0.623698i	$-0.785629\pi$
$109$	−11.9725	+	3.20802i	−1.14676	+	0.307273i	−0.365093	+	0.930971i	$0.618963\pi$
$110$	1.41850	+	0.380087i	0.135249	+	0.0362399i
$111$	2.93092	+	3.94741i	0.278191	+	0.374671i
$112$	−0.614240	−	2.57346i	−0.0580403	−	0.243169i
$113$		−	5.71666i		−	0.537778i	−0.963171	−	0.268889i	$-0.913344\pi$
$113$		−	5.71666i		−	0.537778i	0.963171	−	0.268889i	$-0.0866564\pi$
$114$	4.65089	−	1.84082i	0.435595	−	0.172409i
$115$	−6.15867	−	22.9845i	−0.574299	−	2.14331i
$116$	−0.291290	+	0.504529i	−0.0270456	+	0.0468443i
$117$	−1.96341	−	10.6370i	−0.181518	−	0.983388i
$118$	−6.44548			−0.593354
$119$	−0.717660	+	0.679235i	−0.0657878	+	0.0622654i
$120$	0.755390	−	5.11158i	0.0689574	−	0.466621i
$121$	−9.31642	+	5.37884i	−0.846947	+	0.488985i
$122$	−1.95396	−	7.29227i	−0.176903	−	0.660211i
$123$	−16.0959	+	1.86055i	−1.45132	+	0.167760i
$124$	4.88185	+	1.30809i	0.438403	+	0.117470i
$125$	2.32120	+	2.32120i	0.207615	+	0.207615i
$126$	−2.50385	+	7.53198i	−0.223061	+	0.671002i
$127$			2.92468i			0.259523i	0.991545	+	0.129762i	$0.0414212\pi$
$127$			2.92468i			0.259523i	−0.991545	+	0.129762i	$0.958579\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	2.86482	−	3.61368i	0.252233	−	0.318167i
$130$	−9.04847	−	5.81552i	−0.793603	−	0.510055i
$131$	−15.5403	+	8.97222i	−1.35777	+	0.783906i	−0.989322	−	0.145744i	$-0.953442\pi$
$131$	−15.5403	+	8.97222i	−1.35777	+	0.783906i	−0.368443	+	0.929650i	$0.620109\pi$
$132$	−0.508285	−	0.684564i	−0.0442405	−	0.0595837i
$133$	−4.00079	+	6.50939i	−0.346913	+	0.564436i
$134$	−2.92584			−0.252754
$135$	−10.0094	+	11.8365i	−0.861468	+	1.01872i
$136$	−0.360751	+	0.0966630i	−0.0309342	+	0.00828879i
$137$	−9.18646	+	2.46150i	−0.784852	+	0.210301i	−0.628923	−	0.777468i	$-0.716504\pi$
$137$	−9.18646	+	2.46150i	−0.784852	+	0.210301i	−0.155929	+	0.987768i	$0.549837\pi$
$138$	−5.48819	+	12.6786i	−0.467186	+	1.07927i
$139$	−21.3820			−1.81360			−0.906799	−	0.421563i	$-0.861482\pi$
$139$	−21.3820			−1.81360			−0.906799	+	0.421563i	$0.861482\pi$
$140$	3.75699	+	6.94135i	0.317523	+	0.586651i
$141$	18.4071	−	13.6671i	1.55015	−	1.15098i
$142$	−1.11234	+	0.642209i	−0.0933454	+	0.0538930i
$143$	−1.73435	+	0.377224i	−0.145033	+	0.0315451i
$144$	−2.18736	+	2.05316i	−0.182280	+	0.171096i
$145$	0.449819	−	1.67875i	0.0373554	−	0.139412i
$146$		−	3.41906i		−	0.282963i
$147$	−3.83554	−	11.5017i	−0.316350	−	0.948643i
$148$	−2.00717	−	2.00717i	−0.164988	−	0.164988i
$149$	3.79524	+	1.01693i	0.310919	+	0.0833104i	0.410904	−	0.911679i	$-0.365213\pi$
$149$	3.79524	+	1.01693i	0.310919	+	0.0833104i	−0.0999857	+	0.994989i	$0.531880\pi$
$150$	0.775582	+	6.70966i	0.0633260	+	0.547842i
$151$	2.58226	+	9.63711i	0.210141	+	0.784257i	0.987821	+	0.155596i	$0.0497299\pi$
$151$	2.58226	+	9.63711i	0.210141	+	0.784257i	−0.777680	+	0.628661i	$0.783603\pi$
$152$	−2.50097	+	1.44393i	−0.202855	+	0.117119i
$153$	1.07254	+	0.324078i	0.0867097	+	0.0262001i
$154$	1.24829	+	0.371555i	0.100590	+	0.0299408i
$155$	−15.0774			−1.21105
$156$	2.01920	+	5.90955i	0.161666	+	0.473143i
$157$	10.7467	−	18.6139i	0.857682	−	1.48555i	−0.0164529	−	0.999865i	$-0.505237\pi$
$157$	10.7467	−	18.6139i	0.857682	−	1.48555i	0.874135	−	0.485684i	$-0.161429\pi$
$158$	−2.94262	−	10.9820i	−0.234103	−	0.873683i
$159$	2.07789	+	5.24984i	0.164787	+	0.416339i
$160$			2.98322i			0.235845i
$161$	−4.89941	−	20.5269i	−0.386127	−	1.61774i
$162$	8.82323	−	1.77501i	0.693218	−	0.139458i
$163$	18.4238	+	4.93665i	1.44306	+	0.386668i	0.893606	−	0.448853i	$-0.148167\pi$
$163$	18.4238	+	4.93665i	1.44306	+	0.386668i	0.549459	+	0.835521i	$0.314834\pi$
$164$	9.03608	−	2.42121i	0.705599	−	0.189065i
$165$	1.99322	+	1.58017i	0.155172	+	0.123016i
$166$	11.3316	−	6.54228i	0.879500	−	0.507779i
$167$	9.06640	+	9.06640i	0.701579	+	0.701579i	0.964749	−	0.263170i	$-0.0847681\pi$
$167$	9.06640	+	9.06640i	0.701579	+	0.701579i	−0.263170	+	0.964749i	$0.584768\pi$
$168$	0.794338	−	4.51321i	0.0612845	−	0.348201i
$169$	12.9411	+	1.23658i	0.995466	+	0.0951214i
$170$	0.964896	−	0.557083i	0.0740042	−	0.0427263i
$171$	8.65927	+	0.274047i	0.662191	+	0.0209569i
$172$	−1.33122	+	2.30575i	−0.101505	+	0.175811i
$173$	1.85430	+	3.21173i	0.140979	+	0.244184i	0.927866	−	0.372914i	$-0.121642\pi$
$173$	1.85430	+	3.21173i	0.140979	+	0.244184i	−0.786886	+	0.617098i	$0.788308\pi$
$174$	−0.810156	+	0.601536i	−0.0614178	+	0.0456023i
$175$	−7.09216	−	7.49337i	−0.536117	−	0.566445i
$176$	0.348086	+	0.348086i	0.0262379	+	0.0262379i
$177$	−10.2452	−	4.43485i	−0.770078	−	0.333344i
$178$	−1.63209	+	2.82687i	−0.122330	+	0.211883i
$179$	5.97819	−	10.3545i	0.446831	−	0.773934i	−0.551347	−	0.834276i	$-0.685886\pi$
$179$	5.97819	−	10.3545i	0.446831	−	0.773934i	0.998178	+	0.0603419i	$0.0192191\pi$
$180$	4.71776	−	7.60521i	0.351641	−	0.566859i
$181$			5.55672i			0.413028i	0.978444	+	0.206514i	$0.0662118\pi$
$181$			5.55672i			0.413028i	−0.978444	+	0.206514i	$0.933788\pi$
$182$	−7.88002	−	5.37636i	−0.584106	−	0.398522i
$183$	1.91163	−	12.9356i	0.141312	−	0.956230i
$184$	2.06444	−	7.70458i	0.152192	−	0.567989i
$185$	7.33356	+	4.23403i	0.539174	+	0.311292i
$186$	6.85977	+	5.43823i	0.502983	+	0.398750i
$187$	0.0475841	−	0.177586i	0.00347969	−	0.0129864i
$188$	−9.35958	+	9.35958i	−0.682618	+	0.682618i
$189$	−9.16236	+	10.2495i	−0.666463	+	0.745538i
$190$	6.09184	−	6.09184i	0.441948	−	0.441948i
$191$	6.96646	−	4.02209i	0.504076	−	0.291028i	−0.226319	−	0.974053i	$-0.572669\pi$
$191$	6.96646	−	4.02209i	0.504076	−	0.291028i	0.730395	+	0.683025i	$0.239336\pi$
$192$	1.07601	−	1.35728i	0.0776543	−	0.0979531i
$193$	1.74782	+	6.52296i	0.125811	+	0.469533i	0.999867	−	0.0162916i	$-0.00518601\pi$
$193$	1.74782	+	6.52296i	0.125811	+	0.469533i	−0.874056	+	0.485825i	$0.838519\pi$
$194$	8.59349	+	14.8844i	0.616977	+	1.06864i
$195$	−10.3813	−	15.4697i	−0.743423	−	1.10781i
$196$	3.16145	+	6.24542i	0.225818	+	0.446101i
$197$	9.55202	−	9.55202i	0.680553	−	0.680553i	−0.279572	−	0.960125i	$-0.590193\pi$
$197$	9.55202	−	9.55202i	0.680553	−	0.680553i	0.960125	+	0.279572i	$0.0901925\pi$
$198$	−0.336911	−	1.43786i	−0.0239432	−	0.102184i
$199$	17.2076	+	9.93481i	1.21981	+	0.704260i	0.964878	−	0.262698i	$-0.0846122\pi$
$199$	17.2076	+	9.93481i	1.21981	+	0.704260i	0.254936	+	0.966958i	$0.417946\pi$
$200$	−1.00930	−	3.76674i	−0.0713680	−	0.266349i
$201$	−4.65069	−	2.01314i	−0.328034	−	0.141996i
$202$	7.93242	−	7.93242i	0.558123	−	0.558123i
$203$	0.439722	−	1.47731i	0.0308624	−	0.103687i
$204$	−0.639932	−	0.0945692i	−0.0448042	−	0.00662117i
$205$	−24.1687	+	13.9538i	−1.68801	+	0.974574i
$206$	3.15893	−	0.846433i	0.220093	−	0.0589738i
$207$	−17.4472	+	16.3767i	−1.21266	+	1.13826i
$208$	−1.65205	−	3.20480i	−0.114549	−	0.222213i
$209$		−	1.42160i		−	0.0983344i
$210$	1.19577	+	13.6184i	0.0825160	+	0.939762i
$211$	−8.11047			−0.558348			−0.279174	−	0.960241i	$-0.590061\pi$
$211$	−8.11047			−0.558348			−0.279174	+	0.960241i	$0.590061\pi$
$212$	−1.62989	−	2.82305i	−0.111941	−	0.193888i
$213$	−2.20996	+	0.255454i	−0.151424	+	0.0175034i
$214$	−15.5800	+	4.17465i	−1.06503	+	0.285373i
$215$	2.05571	−	7.67203i	0.140199	−	0.523228i
$216$	−4.88954	+	1.75851i	−0.332691	+	0.119652i
$217$	−13.3667	−	0.367686i	−0.907394	−	0.0249601i
$218$	12.3948			0.839485
$219$	2.35250	−	5.43466i	0.158967	−	0.367241i
$220$	−1.27180	−	0.734272i	−0.0857445	−	0.0495046i
$221$	−0.728060	+	1.13280i	−0.0489746	+	0.0762004i
$222$	−1.80939	−	4.57148i	−0.121438	−	0.306818i
$223$	13.2899	+	13.2899i	0.889959	+	0.889959i	0.994519	−	0.104560i	$-0.0333433\pi$
$223$	13.2899	+	13.2899i	0.889959	+	0.889959i	−0.104560	+	0.994519i	$0.533343\pi$
$224$	−0.0727504	+	2.64475i	−0.00486084	+	0.176710i
$225$	−3.38382	+	11.1988i	−0.225588	+	0.746587i
$226$	−1.47958	+	5.52187i	−0.0984202	+	0.367309i
$227$	7.47840	+	27.9098i	0.496359	+	1.85244i	0.522284	+	0.852772i	$0.325080\pi$
$227$	7.47840	+	27.9098i	0.496359	+	1.85244i	−0.0259251	+	0.999664i	$0.508253\pi$
$228$	−4.96885	+	0.574359i	−0.329070	+	0.0380378i
$229$	6.41225	+	1.71816i	0.423733	+	0.113539i	0.464383	−	0.885634i	$-0.346276\pi$
$229$	6.41225	+	1.71816i	0.423733	+	0.113539i	−0.0406498	+	0.999173i	$0.512943\pi$
$230$			23.7953i			1.56901i
$231$	1.72854	+	1.44949i	0.113729	+	0.0953695i
$232$	0.411946	−	0.411946i	0.0270456	−	0.0270456i
$233$	−1.10978	−	1.92220i	−0.0727044	−	0.125928i	0.827381	−	0.561641i	$-0.189830\pi$
$233$	−1.10978	−	1.92220i	−0.0727044	−	0.125928i	−0.900086	+	0.435713i	$0.856496\pi$
$234$	−0.856538	+	10.7827i	−0.0559936	+	0.704886i
$235$	19.7436	−	34.1970i	1.28793	−	2.23077i
$236$	6.22585	+	1.66821i	0.405269	+	0.108591i
$237$	2.87888	−	19.4808i	0.187004	−	1.26542i
$238$	0.869006	−	0.470347i	0.0563293	−	0.0304881i
$239$	−9.10161	+	9.10161i	−0.588734	+	0.588734i	−0.937289	−	0.348554i	$-0.886673\pi$
$239$	−9.10161	+	9.10161i	−0.588734	+	0.588734i	0.348554	+	0.937289i	$0.386673\pi$
$240$	−2.05263	+	4.74190i	−0.132496	+	0.306088i
$241$	2.55818	+	9.54727i	0.164787	+	0.614993i	0.998067	+	0.0621427i	$0.0197934\pi$
$241$	2.55818	+	9.54727i	0.164787	+	0.614993i	−0.833280	+	0.552851i	$0.813540\pi$
$242$	10.3911	−	2.78429i	0.667966	−	0.178981i
$243$	15.2460	+	3.24946i	0.978032	+	0.208453i
$244$			7.54951i			0.483308i
$245$	−13.9321	−	15.5556i	−0.890091	−	0.993812i
$246$	16.0290	+	2.36876i	1.02197	+	0.151027i
$247$	−3.17075	+	9.91784i	−0.201750	+	0.631057i
$248$	−4.37695	−	2.52703i	−0.277937	−	0.160467i
$249$	22.5132	−	2.60234i	1.42672	−	0.164917i
$250$	−1.64134	−	2.84288i	−0.103807	−	0.179800i
$251$	14.8766			0.939002			0.469501	−	0.882932i	$-0.344434\pi$
$251$	14.8766			0.939002			0.469501	+	0.882932i	$0.344434\pi$
$252$	4.36796	−	6.62729i	0.275155	−	0.417480i
$253$	2.77646	+	2.77646i	0.174554	+	0.174554i
$254$	0.756962	−	2.82502i	0.0474960	−	0.177258i
$255$	1.91703	−	0.221593i	0.120049	−	0.0138767i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.5193	−	25.1481i	−0.905688	−	1.56870i	−0.819990	−	0.572377i	$-0.806021\pi$
$257$	−14.5193	−	25.1481i	−0.905688	−	1.56870i	−0.0856980	−	0.996321i	$-0.527312\pi$
$258$	−3.70249	+	2.74908i	−0.230507	+	0.171150i
$259$	6.39825	+	3.93249i	0.397568	+	0.244353i
$260$	7.23498	+	7.95928i	0.448695	+	0.493613i
$261$	−1.70165	+	0.398721i	−0.105330	+	0.0246802i
$262$	17.3330	−	4.64436i	1.07084	−	0.286930i
$263$	16.0895	+	9.28926i	0.992119	+	0.572800i	0.905907	−	0.423476i	$-0.139190\pi$
$263$	16.0895	+	9.28926i	0.992119	+	0.572800i	0.0862123	+	0.996277i	$0.472524\pi$
$264$	0.313787	+	0.792792i	0.0193123	+	0.0487930i
$265$	6.87636	+	6.87636i	0.422411	+	0.422411i
$266$	5.54922	−	5.25211i	0.340245	−	0.322027i
$267$	−4.53929	+	3.37039i	−0.277800	+	0.206265i
$268$	2.82615	+	0.757263i	0.172634	+	0.0462572i
$269$	−7.03347	−	4.06078i	−0.428838	−	0.247590i	0.270013	−	0.962857i	$-0.412972\pi$
$269$	−7.03347	−	4.06078i	−0.428838	−	0.247590i	−0.698852	+	0.715267i	$0.746305\pi$
$270$	12.7318	−	8.84257i	0.774833	−	0.538141i
$271$	−23.8896	−	6.40120i	−1.45119	−	0.388845i	−0.554753	−	0.832015i	$-0.687187\pi$
$271$	−23.8896	−	6.40120i	−1.45119	−	0.388845i	−0.896438	+	0.443170i	$0.853854\pi$
$272$	0.373477			0.0226454
$273$	−8.82623	−	13.9677i	−0.534188	−	0.845366i
$274$	9.51052			0.574552
$275$	1.85425	+	0.496844i	0.111815	+	0.0299608i
$276$	8.58265	−	10.8261i	0.516615	−	0.651657i
$277$	12.4480	+	7.18686i	0.747929	+	0.431817i	0.824945	−	0.565213i	$-0.191206\pi$
$277$	12.4480	+	7.18686i	0.747929	+	0.431817i	−0.0770163	+	0.997030i	$0.524539\pi$
$278$	20.6534	+	5.53407i	1.23871	+	0.331911i
$279$	7.16195	+	13.3641i	0.428775	+	0.800087i
$280$	−1.83242	−	7.67721i	−0.109508	−	0.458801i
$281$	−6.19288	−	6.19288i	−0.369436	−	0.369436i	0.497835	−	0.867272i	$-0.334128\pi$
$281$	−6.19288	−	6.19288i	−0.369436	−	0.369436i	−0.867272	+	0.497835i	$0.834128\pi$
$282$	−21.3172	+	8.43734i	−1.26942	+	0.502436i
$283$	21.4880	+	12.4061i	1.27733	+	0.737466i	0.976356	−	0.216168i	$-0.0693557\pi$
$283$	21.4880	+	12.4061i	1.27733	+	0.737466i	0.300972	+	0.953633i	$0.402689\pi$
$284$	1.24065	−	0.332432i	0.0736192	−	0.0197262i
$285$	13.8746	−	5.49158i	0.821862	−	0.325293i
$286$	1.77288	+	0.0845112i	0.104833	+	0.00499725i
$287$	−21.7668	+	11.7812i	−1.28485	+	0.695423i
$288$	2.64422	−	1.41707i	0.155812	−	0.0835015i
$289$	8.43026	+	14.6016i	0.495897	+	0.858920i
$290$	−0.868983	+	1.50512i	−0.0510284	+	0.0883839i
$291$	3.41826	+	29.5718i	0.200382	+	1.73353i
$292$	−0.884917	+	3.30256i	−0.0517859	+	0.193267i
$293$	−0.941281	−	0.941281i	−0.0549902	−	0.0549902i	0.679077	−	0.734067i	$-0.262380\pi$
$293$	−0.941281	−	0.941281i	−0.0549902	−	0.0549902i	−0.734067	+	0.679077i	$0.762380\pi$
$294$	0.727993	+	12.1025i	0.0424574	+	0.705831i
$295$	−19.2283			−1.11951
$296$	1.41928	+	2.45827i	0.0824941	+	0.142884i
$297$	0.453800	−	2.51732i	0.0263322	−	0.146070i
$298$	−3.40272	−	1.96456i	−0.197114	−	0.113804i
$299$	−13.1774	−	25.5626i	−0.762068	−	1.47832i
$300$	0.987434	−	6.68177i	0.0570095	−	0.385772i
$301$	2.00957	−	6.75144i	0.115830	−	0.389147i
$302$		−	9.97707i		−	0.574116i
$303$	18.0667	−	7.15080i	1.03791	−	0.410803i
$304$	2.78947	−	0.747436i	0.159987	−	0.0428684i
$305$	−5.82909	−	21.7545i	−0.333773	−	1.24566i
$306$	−0.952116	−	0.590629i	−0.0544289	−	0.0337640i
$307$	1.18905	−	1.18905i	0.0678629	−	0.0678629i	−0.672361	−	0.740224i	$-0.734720\pi$
$307$	1.18905	−	1.18905i	0.0678629	−	0.0678629i	0.740224	+	0.672361i	$0.234720\pi$
$308$	−1.10959	−	0.681977i	−0.0632250	−	0.0388592i
$309$	5.60358	+	0.828098i	0.318777	+	0.0471089i
$310$	14.5637	+	3.90232i	0.827160	+	0.221637i
$311$	−1.24862	+	2.16267i	−0.0708026	+	0.122634i	−0.899253	−	0.437428i	$-0.855889\pi$
$311$	−1.24862	+	2.16267i	−0.0708026	+	0.122634i	0.828451	+	0.560062i	$0.189223\pi$
$312$	−0.420895	−	6.23080i	−0.0238285	−	0.352749i
$313$	15.5022	+	26.8507i	0.876239	+	1.51769i	0.855437	+	0.517906i	$0.173288\pi$
$313$	15.5022	+	26.8507i	0.876239	+	1.51769i	0.0208011	+	0.999784i	$0.493378\pi$
$314$	−15.1982	+	15.1982i	−0.857682	+	0.857682i
$315$	−7.46956	+	22.4696i	−0.420862	+	1.26602i
$316$			11.3694i			0.639580i
$317$	−18.4389	−	4.94069i	−1.03563	−	0.277497i	−0.299330	−	0.954150i	$-0.596763\pi$
$317$	−18.4389	−	4.94069i	−1.03563	−	0.277497i	−0.736303	+	0.676653i	$0.763430\pi$
$318$	−0.648326	−	5.60875i	−0.0363563	−	0.314523i
$319$	0.0742255	+	0.277013i	0.00415583	+	0.0155098i
$320$	0.772115	−	2.88157i	0.0431625	−	0.161085i
$321$	−27.6371	−	4.08422i	−1.54255	−	0.227959i
$322$	−0.580284	+	21.0955i	−0.0323380	+	1.17561i
$323$	−0.762653	−	0.762653i	−0.0424351	−	0.0424351i
$324$	−8.98199	−	0.569090i	−0.498999	−	0.0316161i
$325$	−11.8280	−	7.60195i	−0.656100	−	0.421680i
$326$	−16.5183	−	9.53687i	−0.914867	−	0.528198i
$327$	19.7019	+	8.52835i	1.08952	+	0.471619i
$328$	−9.35483			−0.516534
$329$	18.3375	−	29.8356i	1.01098	−	1.64489i
$330$	−1.51633	−	2.04221i	−0.0834710	−	0.112420i
$331$	3.78955	−	14.1428i	0.208293	−	0.777359i	−0.780128	−	0.625620i	$-0.784846\pi$
$331$	3.78955	−	14.1428i	0.208293	−	0.777359i	0.988421	−	0.151739i	$-0.0484873\pi$
$332$	−12.6387	+	3.38653i	−0.693639	+	0.185860i
$333$	0.269368	−	8.51143i	0.0147613	−	0.466423i
$334$	−6.41091	−	11.1040i	−0.350790	−	0.607585i
$335$	−8.72844			−0.476885
$336$	−1.93538	+	4.15383i	−0.105583	+	0.226610i
$337$			17.4950i			0.953013i	0.879171	+	0.476507i	$0.158097\pi$
$337$			17.4950i			0.953013i	−0.879171	+	0.476507i	$0.841903\pi$
$338$	−12.1800	−	4.54383i	−0.662507	−	0.247152i
$339$	−6.15118	+	7.75909i	−0.334086	+	0.421416i
$340$	−1.07620	+	0.288367i	−0.0583652	+	0.0156389i
$341$	2.15463	−	1.24398i	0.116680	−	0.0673651i
$342$	−8.29329	−	2.50589i	−0.448450	−	0.135503i
$343$	−11.9721	−	14.1305i	−0.646430	−	0.762973i
$344$	1.88263	−	1.88263i	0.101505	−	0.101505i
$345$	−16.3725	+	37.8231i	−0.881465	+	2.03633i
$346$	−0.959854	−	3.58222i	−0.0516021	−	0.192582i
$347$	−12.4022	−	7.16039i	−0.665782	−	0.384390i	0.128694	−	0.991684i	$-0.458921\pi$
$347$	−12.4022	−	7.16039i	−0.665782	−	0.384390i	−0.794477	+	0.607295i	$0.792255\pi$
$348$	0.938240	−	0.371355i	0.0502949	−	0.0199067i
$349$	15.1284	−	15.1284i	0.809803	−	0.809803i	−0.174801	−	0.984604i	$-0.555928\pi$
$349$	15.1284	−	15.1284i	0.809803	−	0.809803i	0.984604	+	0.174801i	$0.0559282\pi$
$350$	4.91107	+	9.07362i	0.262508	+	0.485006i
$351$	−8.78058	+	16.5500i	−0.468673	+	0.883372i
$352$	−0.246134	−	0.426316i	−0.0131190	−	0.0227227i
$353$	−0.442166	−	1.65019i	−0.0235341	−	0.0878306i	0.953160	−	0.302467i	$-0.0978101\pi$
$353$	−0.442166	−	1.65019i	−0.0235341	−	0.0878306i	−0.976694	+	0.214636i	$0.931143\pi$
$354$	8.74830	+	6.93540i	0.464967	+	0.368612i
$355$	−3.31835	+	1.91585i	−0.176120	+	0.101683i
$356$	2.30813	−	2.30813i	0.122330	−	0.122330i
$357$	1.70493	−	0.149701i	0.0902344	−	0.00792304i
$358$	−8.45444	+	8.45444i	−0.446831	+	0.446831i
$359$	3.59997	−	13.4353i	0.189999	−	0.709087i	−0.803506	−	0.595297i	$-0.797034\pi$
$359$	3.59997	−	13.4353i	0.189999	−	0.709087i	0.993505	−	0.113790i	$-0.0362990\pi$
$360$	−6.52538	+	6.12503i	−0.343918	+	0.322817i
$361$	9.23201	+	5.33010i	0.485895	+	0.280532i
$362$	1.43818	−	5.36738i	0.0755893	−	0.282103i
$363$	18.4326	+	2.72398i	0.967463	+	0.142972i
$364$	6.22001	+	7.23266i	0.326017	+	0.379095i
$365$		−	10.1998i		−	0.533882i
$366$	−5.19449	+	12.0001i	−0.271520	+	0.627256i
$367$	13.9526	−	24.1666i	0.728319	−	1.26148i	−0.229275	−	0.973362i	$-0.573635\pi$
$367$	13.9526	−	24.1666i	0.728319	−	1.26148i	0.957593	−	0.288123i	$-0.0930312\pi$
$368$	−3.98818	+	6.90774i	−0.207898	+	0.360091i
$369$	23.8485	+	14.7940i	1.24151	+	0.770147i
$370$	−5.98783	−	5.98783i	−0.311292	−	0.311292i
$371$	5.92849	+	6.26387i	0.307792	+	0.325204i
$372$	−5.21852	−	7.02836i	−0.270567	−	0.364404i
$373$	12.3242	+	21.3461i	0.638122	+	1.10526i	0.985844	+	0.167662i	$0.0536218\pi$
$373$	12.3242	+	21.3461i	0.638122	+	1.10526i	−0.347722	+	0.937598i	$0.613045\pi$
$374$	−0.0919254	+	0.159219i	−0.00475335	+	0.00823304i
$375$	−0.652881	−	5.64816i	−0.0337146	−	0.291670i
$376$	11.4631	−	6.61822i	0.591164	−	0.341309i
$377$	0.100016	−	2.09814i	0.00515107	−	0.108060i
$378$	11.5029	−	7.52882i	0.591646	−	0.387241i
$379$	−5.55621	−	5.55621i	−0.285403	−	0.285403i	0.549856	−	0.835259i	$-0.314682\pi$
$379$	−5.55621	−	5.55621i	−0.285403	−	0.285403i	−0.835259	+	0.549856i	$0.814682\pi$
$380$	−7.46095	+	4.30758i	−0.382738	+	0.220974i
$381$	3.14698	−	3.96960i	0.161225	−	0.203369i
$382$	−7.77008	+	2.08199i	−0.397552	+	0.106524i
$383$	10.6284	+	2.84788i	0.543087	+	0.145520i	0.519925	−	0.854212i	$-0.325960\pi$
$383$	10.6284	+	2.84788i	0.543087	+	0.145520i	0.0231622	+	0.999732i	$0.492627\pi$
$384$	−1.39063	+	1.03254i	−0.0709655	+	0.0526915i
$385$	3.72394	+	1.10843i	0.189789	+	0.0564909i
$386$		−	6.75307i		−	0.343722i
$387$	−7.77671	+	1.82219i	−0.395312	+	0.0926274i
$388$	−4.44832	−	16.6014i	−0.225829	−	0.842806i
$389$	−2.28311	+	3.95446i	−0.115758	+	0.200499i	−0.918083	−	0.396389i	$-0.870263\pi$
$389$	−2.28311	+	3.95446i	−0.115758	+	0.200499i	0.802324	+	0.596888i	$0.203596\pi$
$390$	6.02373	+	17.6295i	0.305024	+	0.892705i
$391$	2.97899			0.150654
$392$	−1.43729	−	6.85085i	−0.0725942	−	0.346020i
$393$	30.7467	+	4.54376i	1.55097	+	0.229202i
$394$	−11.6988	+	6.75430i	−0.589376	+	0.340276i
$395$	−8.77850	−	32.7618i	−0.441694	−	1.64843i
$396$	−0.0467141	+	1.47606i	−0.00234747	+	0.0741750i
$397$	−15.0698	−	4.03794i	−0.756331	−	0.202658i	−0.140007	−	0.990151i	$-0.544712\pi$
$397$	−15.0698	−	4.03794i	−0.756331	−	0.202658i	−0.616325	+	0.787492i	$0.711379\pi$
$398$	−14.0499	−	14.0499i	−0.704260	−	0.704260i
$399$	12.4344	−	4.53016i	0.622496	−	0.226792i
$400$			3.89962i			0.194981i
$401$	−5.19661	+	19.3940i	−0.259506	+	0.968491i	0.706021	+	0.708191i	$0.250488\pi$
$401$	−5.19661	+	19.3940i	−0.259506	+	0.968491i	−0.965528	+	0.260300i	$0.916178\pi$
$402$	3.97118	+	3.14823i	0.198064	+	0.157020i
$403$	−17.8064	+	3.87293i	−0.886999	+	0.192924i
$404$	−9.71519	+	5.60907i	−0.483349	+	0.279062i
$405$	26.3217	−	5.29525i	1.30793	−	0.263123i
$406$	−0.807094	+	1.31316i	−0.0400554	+	0.0651711i
$407$	−1.39733			−0.0692632
$408$	0.593650	+	0.256973i	0.0293901	+	0.0127221i
$409$	−21.8252	+	5.84805i	−1.07919	+	0.289167i	−0.754263	−	0.656572i	$-0.772006\pi$
$409$	−21.8252	+	5.84805i	−1.07919	+	0.289167i	−0.324925	+	0.945740i	$0.605339\pi$
$410$	26.9566	−	7.22301i	1.33129	−	0.356719i
$411$	15.1172	+	6.54377i	0.745676	+	0.322781i
$412$	−3.27037			−0.161119
$413$	−17.0467	−	0.468911i	−0.838812	−	0.0230736i
$414$	21.0913	−	11.3030i	1.03658	−	0.555514i
$415$	33.8046	−	19.5171i	1.65940	−	0.958056i
$416$	0.766299	+	3.52318i	0.0375709	+	0.172738i
$417$	29.0213	+	23.0072i	1.42118	+	1.12667i
$418$	−0.367938	+	1.37316i	−0.0179964	+	0.0671636i
$419$			2.13344i			0.104226i	0.998641	+	0.0521128i	$0.0165955\pi$
$419$			2.13344i			0.104226i	−0.998641	+	0.0521128i	$0.983404\pi$
$420$	2.36969	−	13.4639i	0.115629	−	0.656971i
$421$	−27.5364	−	27.5364i	−1.34204	−	1.34204i	−0.894023	−	0.448021i	$-0.852129\pi$
$421$	−27.5364	−	27.5364i	−1.34204	−	1.34204i	−0.448021	−	0.894023i	$-0.647871\pi$
$422$	7.83411	+	2.09914i	0.381359	+	0.102185i
$423$	−39.6895	−	1.25608i	−1.92977	−	0.0610729i
$424$	0.843692	+	3.14870i	0.0409733	+	0.152914i
$425$	1.26130	−	0.728210i	0.0611819	−	0.0353234i
$426$	2.20078	+	0.325231i	0.106628	+	0.0157575i
$427$	−4.63721	−	19.4284i	−0.224410	−	0.940205i
$428$	16.1296			0.779653
$429$	2.75989	+	1.35417i	0.133249	+	0.0653802i
$430$	−3.97134	+	6.87855i	−0.191515	+	0.331713i
$431$	1.82189	+	6.79937i	0.0877572	+	0.327514i	0.995822	−	0.0913153i	$-0.0291071\pi$
$431$	1.82189	+	6.79937i	0.0877572	+	0.327514i	−0.908065	+	0.418830i	$0.862440\pi$
$432$	5.17807	−	0.433084i	0.249130	−	0.0208368i
$433$		−	4.80709i		−	0.231014i	−0.993307	−	0.115507i	$-0.963151\pi$
$433$		−	4.80709i		−	0.231014i	0.993307	−	0.115507i	$-0.0368493\pi$
$434$	12.8161	+	3.81473i	0.615194	+	0.183113i
$435$	−2.41688	+	1.79452i	−0.115880	+	0.0860405i
$436$	−11.9725	−	3.20802i	−0.573379	−	0.153636i
$437$	22.2498	−	5.96182i	1.06435	−	0.285193i
$438$	−3.67894	+	4.64061i	−0.175786	+	0.221737i
$439$	−17.8083	+	10.2816i	−0.849942	+	0.490715i	−0.860631	−	0.509228i	$-0.829931\pi$
$439$	−17.8083	+	10.2816i	−0.849942	+	0.490715i	0.0106890	+	0.999943i	$0.496598\pi$
$440$	1.03842	+	1.03842i	0.0495046	+	0.0495046i
$441$	−7.17003	+	19.7381i	−0.341430	+	0.939907i
$442$	0.996442	−	0.905766i	0.0473959	−	0.0430829i
$443$	14.5938	−	8.42571i	0.693370	−	0.400318i	−0.111503	−	0.993764i	$-0.535566\pi$
$443$	14.5938	−	8.42571i	0.693370	−	0.400318i	0.804873	+	0.593446i	$0.202233\pi$
$444$	0.564552	+	4.88402i	0.0267925	+	0.231785i
$445$	−4.86890	+	8.43317i	−0.230808	+	0.399771i
$446$	−9.39739	−	16.2768i	−0.444980	−	0.770727i
$447$	−4.05697	−	5.46398i	−0.191888	−	0.258437i
$448$	0.754783	−	2.53580i	0.0356602	−	0.119805i
$449$	19.6778	+	19.6778i	0.928651	+	0.928651i	0.997619	−	0.0689678i	$-0.0219706\pi$
$449$	19.6778	+	19.6778i	0.928651	+	0.928651i	−0.0689678	+	0.997619i	$0.521971\pi$
$450$	6.16698	−	9.94141i	0.290714	−	0.468643i
$451$	2.30254	−	3.98812i	0.108422	−	0.187793i
$452$	2.85833	−	4.95077i	0.134444	−	0.232865i
$453$	6.86478	−	15.8588i	0.322536	−	0.745110i
$454$		−	28.8943i		−	1.35608i
$455$	−23.5079	−	16.0389i	−1.10207	−	0.751914i
$456$	4.94820	+	0.731246i	0.231721	+	0.0342437i
$457$	9.92354	−	37.0352i	0.464204	−	1.73243i	−0.195312	−	0.980741i	$-0.562572\pi$
$457$	9.92354	−	37.0352i	0.464204	−	1.73243i	0.659516	−	0.751691i	$-0.270761\pi$
$458$	−5.74906	−	3.31922i	−0.268636	−	0.155097i
$459$	−1.10702	−	1.59393i	−0.0516714	−	0.0743981i
$460$	6.15867	−	22.9845i	0.287150	−	1.07166i
$461$	−17.5692	+	17.5692i	−0.818281	+	0.818281i	−0.985859	−	0.167578i	$-0.946405\pi$
$461$	−17.5692	+	17.5692i	−0.818281	+	0.818281i	0.167578	+	0.985859i	$0.446405\pi$
$462$	−1.29448	−	1.84748i	−0.0602249	−	0.0859525i
$463$	−24.8187	+	24.8187i	−1.15342	+	1.15342i	−0.167563	+	0.985861i	$0.553590\pi$
$463$	−24.8187	+	24.8187i	−1.15342	+	1.15342i	−0.985861	+	0.167563i	$0.946410\pi$
$464$	−0.504529	+	0.291290i	−0.0234222	+	0.0135228i
$465$	20.4642	+	16.2234i	0.949006	+	0.752344i
$466$	0.574466	+	2.14394i	0.0266116	+	0.0993160i
$467$	−7.40191	−	12.8205i	−0.342520	−	0.593262i	0.642380	−	0.766386i	$-0.277947\pi$
$467$	−7.40191	−	12.8205i	−0.342520	−	0.593262i	−0.984900	+	0.173125i	$0.944614\pi$
$468$	3.61812	−	10.1936i	0.167248	−	0.471199i
$469$	−7.73812	−	0.212856i	−0.357313	−	0.00982878i
$470$	−27.9217	+	27.9217i	−1.28793	+	1.28793i
$471$	−34.6150	+	13.7006i	−1.59497	+	0.631291i
$472$	−5.58195	−	3.22274i	−0.256930	−	0.148339i
$473$	0.339217	+	1.26598i	0.0155972	+	0.0582097i
$474$	−7.82280	+	18.0719i	−0.359313	+	0.830072i
$475$	7.96315	−	7.96315i	0.365374	−	0.365374i
$476$	−0.961130	+	0.229405i	−0.0440533	+	0.0105148i
$477$	2.82861	−	9.36132i	0.129513	−	0.428625i
$478$	11.1472	−	6.43581i	0.509859	−	0.294367i
$479$	−31.5839	+	8.46289i	−1.44311	+	0.386679i	−0.893621	−	0.448823i	$-0.851843\pi$
$479$	−31.5839	+	8.46289i	−1.44311	+	0.386679i	−0.549487	+	0.835502i	$0.685177\pi$
$480$	3.20998	−	4.04906i	0.146515	−	0.184814i
$481$	9.74851	+	3.11661i	0.444494	+	0.142105i
$482$		−	9.88406i		−	0.450206i
$483$	−15.4373	+	33.1325i	−0.702420	+	1.50758i
$484$	−10.7577			−0.488985
$485$	25.6363	+	44.4034i	1.16408	+	2.01625i
$486$	−13.8855	−	7.08469i	−0.629859	−	0.321368i
$487$	15.5694	−	4.17182i	0.705518	−	0.189043i	0.111817	−	0.993729i	$-0.464333\pi$
$487$	15.5694	−	4.17182i	0.705518	−	0.189043i	0.593701	+	0.804686i	$0.297666\pi$
$488$	1.95396	−	7.29227i	0.0884515	−	0.330105i
$489$	−19.6944	−	26.5246i	−0.890610	−	1.19948i
$490$	9.43131	+	18.6315i	0.426063	+	0.841684i
$491$	31.5653			1.42452			0.712260	−	0.701915i	$-0.247672\pi$
$491$	31.5653			1.42452			0.712260	+	0.701915i	$0.247672\pi$
$492$	−14.8697	−	6.43665i	−0.670378	−	0.290187i
$493$	0.188430	+	0.108790i	0.00848647	+	0.00489966i
$494$	5.62964	−	8.75925i	0.253289	−	0.394097i
$495$	−1.00508	−	4.28945i	−0.0451750	−	0.192797i
$496$	3.57377	+	3.57377i	0.160467	+	0.160467i
$497$	−2.98858	+	1.61756i	−0.134056	+	0.0725575i
$498$	−22.4196	−	3.31318i	−1.00465	−	0.148467i
$499$	−5.41067	+	20.1929i	−0.242215	+	0.903959i	0.732548	+	0.680716i	$0.238331\pi$
$499$	−5.41067	+	20.1929i	−0.242215	+	0.903959i	−0.974763	+	0.223243i	$0.928336\pi$
$500$	0.849619	+	3.17082i	0.0379961	+	0.141804i
$501$	−2.55009	−	22.0612i	−0.113930	−	0.985620i
$502$	−14.3697	−	3.85034i	−0.641350	−	0.171849i
$503$		−	2.56037i		−	0.114161i	−0.998370	−	0.0570807i	$-0.981821\pi$
$503$		−	2.56037i		−	0.114161i	0.998370	−	0.0570807i	$-0.0181792\pi$
$504$	−5.93439	+	5.27096i	−0.264339	+	0.234787i
$505$	23.6642	−	23.6642i	1.05304	−	1.05304i
$506$	−1.96325	−	3.40045i	−0.0872772	−	0.151169i
$507$	−16.2340	−	15.6031i	−0.720979	−	0.692957i
$508$	−1.46234	+	2.53284i	−0.0648808	+	0.112377i
$509$	−17.4226	−	4.66837i	−0.772243	−	0.206922i	−0.148881	−	0.988855i	$-0.547567\pi$
$509$	−17.4226	−	4.66837i	−0.772243	−	0.206922i	−0.623362	+	0.781933i	$0.714234\pi$
$510$	−1.90906	−	0.282121i	−0.0845346	−	0.0124925i
$511$	0.248738	−	9.04255i	0.0110035	−	0.400019i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−11.4582	−	9.68942i	−0.505890	−	0.427798i
$514$	7.51574	+	28.0491i	0.331505	+	1.23719i
$515$	9.42379	−	2.52510i	0.415262	−	0.111269i
$516$	4.28784	−	1.69713i	0.188762	−	0.0747119i
$517$			6.51587i			0.286568i
$518$	−5.16244	−	5.45448i	−0.226824	−	0.239656i
$519$	0.939063	−	6.35446i	0.0412203	−	0.278930i
$520$	−4.92845	−	9.56062i	−0.216127	−	0.419261i
$521$	21.2930	+	12.2935i	0.932865	+	0.538590i	0.887717	−	0.460390i	$-0.152291\pi$
$521$	21.2930	+	12.2935i	0.932865	+	0.538590i	0.0451486	+	0.998980i	$0.485624\pi$
$522$	1.74687	+	0.0552844i	0.0764582	+	0.00241973i
$523$	−20.8457	−	36.1057i	−0.911517	−	1.57879i	−0.811922	−	0.583766i	$-0.801579\pi$
$523$	−20.8457	−	36.1057i	−0.911517	−	1.57879i	−0.0995948	−	0.995028i	$-0.531755\pi$
$524$	−17.9444			−0.783906
$525$	1.56309	+	17.8018i	0.0682189	+	0.776935i
$526$	−13.1370	−	13.1370i	−0.572800	−	0.572800i
$527$	0.488542	−	1.82326i	0.0212812	−	0.0794225i
$528$	−0.0979054	−	0.846992i	−0.00426079	−	0.0368606i
$529$	−20.3112	+	35.1800i	−0.883096	+	1.52957i
$530$	−4.86232	−	8.42179i	−0.211206	−	0.365819i
$531$	9.13367	+	17.0433i	0.396368	+	0.739616i
$532$	−6.71949	+	3.63690i	−0.291327	+	0.157680i
$533$	−24.9588	+	22.6876i	−1.08109	+	0.982708i
$534$	5.25694	−	2.08070i	0.227490	−	0.0900405i
$535$	−46.4786	+	12.4539i	−2.00944	+	0.538429i
$536$	−2.53385	−	1.46292i	−0.109446	−	0.0631885i
$537$	−19.2557	+	7.62139i	−0.830943	+	0.328887i
$538$	5.74280	+	5.74280i	0.247590	+	0.247590i
$539$	3.27439	+	1.07349i	0.141038	+	0.0462383i
$540$	−14.5866	+	5.24603i	−0.627707	+	0.225753i
$541$	−24.7657	−	6.63595i	−1.06476	−	0.285302i	−0.316422	−	0.948618i	$-0.602482\pi$
$541$	−24.7657	−	6.63595i	−1.06476	−	0.285302i	−0.748339	+	0.663317i	$0.769148\pi$
$542$	21.4188	+	12.3662i	0.920018	+	0.531173i
$543$	5.97908	−	7.54201i	0.256587	−	0.323659i
$544$	−0.360751	−	0.0966630i	−0.0154671	−	0.00414439i
$545$	36.9766			1.58390
$546$	4.91037	+	15.7762i	0.210144	+	0.675159i
$547$	5.31392			0.227207			0.113603	−	0.993526i	$-0.463761\pi$
$547$	5.31392			0.227207			0.113603	+	0.993526i	$0.463761\pi$
$548$	−9.18646	−	2.46150i	−0.392426	−	0.105150i
$549$	−16.5135	+	15.5003i	−0.704779	+	0.661538i
$550$	−1.66247	−	0.959828i	−0.0708880	−	0.0409272i
$551$	1.62509	+	0.435441i	0.0692311	+	0.0185504i
$552$	−11.0922	+	8.23590i	−0.472116	+	0.350543i
$553$	−6.98356	−	29.2588i	−0.296971	−	1.24421i
$554$	−10.1638	−	10.1638i	−0.431817	−	0.431817i
$555$	−5.39782	−	13.6377i	−0.229125	−	0.578890i
$556$	−18.5174	−	10.6910i	−0.785311	−	0.453399i
$557$	−21.4532	+	5.74838i	−0.909003	+	0.243567i	−0.682879	−	0.730532i	$-0.739272\pi$
$557$	−21.4532	+	5.74838i	−0.909003	+	0.243567i	−0.226125	+	0.974098i	$0.572606\pi$
$558$	−3.45904	−	14.7624i	−0.146433	−	0.624941i
$559$	0.457082	−	9.58870i	0.0193325	−	0.405559i
$560$	−0.217031	+	7.88988i	−0.00917122	+	0.333408i
$561$	−0.255669	+	0.189833i	−0.0107944	+	0.00801475i
$562$	4.37903	+	7.58470i	0.184718	+	0.319941i
$563$	1.46940	−	2.54508i	0.0619280	−	0.107262i	−0.833399	−	0.552672i	$-0.813608\pi$
$563$	1.46940	−	2.54508i	0.0619280	−	0.107262i	0.895327	+	0.445409i	$0.146942\pi$
$564$	22.7746	−	2.63255i	0.958982	−	0.110850i
$565$	−4.41392	+	16.4730i	−0.185695	+	0.693022i
$566$	−17.5449	−	17.5449i	−0.737466	−	0.737466i
$567$	23.4644	−	4.05257i	0.985411	−	0.170192i
$568$	−1.28442			−0.0538930
$569$	11.2238	+	19.4402i	0.470526	+	0.814976i	0.999432	−	0.0337051i	$-0.0107307\pi$
$569$	11.2238	+	19.4402i	0.470526	+	0.814976i	−0.528905	+	0.848681i	$0.677397\pi$
$570$	−14.8232	+	1.71344i	−0.620875	+	0.0717681i
$571$	−31.4173	−	18.1388i	−1.31477	−	0.759084i	−0.331890	−	0.943318i	$-0.607686\pi$
$571$	−31.4173	−	18.1388i	−1.31477	−	0.759084i	−0.982882	+	0.184234i	$0.941020\pi$
$572$	−1.69060	−	0.540487i	−0.0706875	−	0.0225989i
$573$	−13.7832	−	2.03689i	−0.575803	−	0.0850923i
$574$	24.0743	−	5.74612i	1.00484	−	0.239838i
$575$			31.1048i			1.29716i
$576$	−2.92089	+	0.684406i	−0.121704	+	0.0285169i
$577$	−21.9929	+	5.89299i	−0.915577	+	0.245328i	−0.685694	−	0.727890i	$-0.740501\pi$
$577$	−21.9929	+	5.89299i	−0.915577	+	0.245328i	−0.229883	+	0.973218i	$0.573835\pi$
$578$	−4.36382	−	16.2860i	−0.181511	−	0.677409i
$579$	4.64649	−	10.7341i	0.193102	−	0.446096i
$580$	1.22893	−	1.22893i	0.0510284	−	0.0510284i
$581$	30.4451	−	16.4783i	1.26308	−	0.683636i
$582$	4.35196	−	29.4489i	0.180395	−	1.22070i
$583$	−1.55000	−	0.415322i	−0.0641946	−	0.0172009i
$584$	1.70953	−	2.96099i	0.0707408	−	0.122527i
$585$	−2.55524	+	32.1672i	−0.105646	+	1.32995i
$586$	0.665586	+	1.15283i	0.0274951	+	0.0476229i
$587$	−15.2745	+	15.2745i	−0.630447	+	0.630447i	−0.948180	−	0.317733i	$-0.897078\pi$
$587$	−15.2745	+	15.2745i	−0.630447	+	0.630447i	0.317733	+	0.948180i	$0.397078\pi$
$588$	2.42917	−	11.8785i	0.100177	−	0.489862i
$589$		−	14.5955i		−	0.601397i
$590$	18.5731	+	4.97665i	0.764643	+	0.204885i
$591$	−23.2428	+	2.68668i	−0.956081	+	0.110515i
$592$	−0.734674	−	2.74184i	−0.0301949	−	0.112689i
$593$	−11.3778	+	42.4626i	−0.467231	+	1.74373i	0.182154	+	0.983270i	$0.441693\pi$
$593$	−11.3778	+	42.4626i	−0.467231	+	1.74373i	−0.649385	+	0.760460i	$0.724974\pi$
$594$	−1.08987	+	2.31409i	−0.0447178	+	0.0949484i
$595$	2.59244	−	1.40315i	0.106280	−	0.0575235i
$596$	2.77831	+	2.77831i	0.113804	+	0.113804i
$597$	−12.6655	−	31.9998i	−0.518366	−	1.30967i
$598$	6.11228	+	28.1022i	0.249950	+	1.14918i
$599$	−18.6340	−	10.7583i	−0.761363	−	0.439573i	0.0684221	−	0.997656i	$-0.478204\pi$
$599$	−18.6340	−	10.7583i	−0.761363	−	0.439573i	−0.829785	+	0.558084i	$0.811537\pi$
$600$	−2.68316	+	6.19853i	−0.109539	+	0.253054i
$601$	11.5937			0.472916			0.236458	−	0.971642i	$-0.424013\pi$
$601$	11.5937			0.472916			0.236458	+	0.971642i	$0.424013\pi$
$602$	−3.68850	+	6.00128i	−0.150332	+	0.244594i
$603$	4.14611	+	7.73658i	0.168843	+	0.315058i
$604$	−2.58226	+	9.63711i	−0.105070	+	0.392128i
$605$	30.9990	−	8.30616i	1.26029	−	0.337693i
$606$	−19.3019	+	2.23114i	−0.784084	+	0.0906337i
$607$	−18.1150	−	31.3761i	−0.735266	−	1.27352i	−0.954606	−	0.297870i	$-0.903724\pi$
$607$	−18.1150	−	31.3761i	−0.735266	−	1.27352i	0.219340	−	0.975648i	$-0.429609\pi$
$608$	−2.88787			−0.117119
$609$	−2.18642	+	1.53197i	−0.0885983	+	0.0620787i
$610$			22.5219i			0.911884i
$611$	14.5330	−	45.4581i	0.587943	−	1.83904i
$612$	0.766808	+	0.816929i	0.0309964	+	0.0330224i
$613$	14.4606	−	3.87470i	0.584057	−	0.156497i	0.0453211	−	0.998972i	$-0.485569\pi$
$613$	14.4606	−	3.87470i	0.584057	−	0.156497i	0.538735	+	0.842475i	$0.318902\pi$
$614$	−1.45629	+	0.840788i	−0.0587710	+	0.0339315i
$615$	47.8180	+	7.06655i	1.92821	+	0.284951i
$616$	0.895276	+	0.945923i	0.0360717	+	0.0381123i
$617$	−4.10076	+	4.10076i	−0.165090	+	0.165090i	−0.784817	−	0.619727i	$-0.787243\pi$
$617$	−4.10076	+	4.10076i	−0.165090	+	0.165090i	0.619727	+	0.784817i	$0.287243\pi$
$618$	−5.19832	−	2.25020i	−0.209107	−	0.0905161i
$619$	3.53669	+	13.1991i	0.142152	+	0.530517i	0.999866	+	0.0163900i	$0.00521733\pi$
$619$	3.53669	+	13.1991i	0.142152	+	0.530517i	−0.857714	+	0.514127i	$0.828116\pi$
$620$	−13.0574	−	7.53871i	−0.524399	−	0.302762i
$621$	41.3022	−	3.45444i	1.65740	−	0.138622i
$622$	1.76581	−	1.76581i	0.0708026	−	0.0708026i
$623$	−4.52213	+	7.35762i	−0.181175	+	0.294777i
$624$	−1.20610	+	6.12742i	−0.0482825	+	0.245293i
$625$	−14.6455	−	25.3668i	−0.585821	−	1.01467i
$626$	−8.02455	−	29.9480i	−0.320726	−	1.19696i
$627$	−1.52966	+	1.92951i	−0.0610887	+	0.0770573i
$628$	18.6139	−	10.7467i	0.742774	−	0.428841i
$629$	−0.749631	+	0.749631i	−0.0298898	+	0.0298898i
$630$	13.0306	−	19.7707i	0.519151	−	0.787683i
$631$	26.9483	−	26.9483i	1.07279	−	1.07279i	0.0756614	−	0.997134i	$-0.475893\pi$
$631$	26.9483	−	26.9483i	1.07279	−	1.07279i	0.997134	−	0.0756614i	$-0.0241068\pi$
$632$	2.94262	−	10.9820i	0.117051	−	0.436841i
$633$	11.0082	+	8.72694i	0.437535	+	0.346865i
$634$	16.5319	+	9.54469i	0.656565	+	0.379068i
$635$	2.25819	−	8.42767i	0.0896134	−	0.334442i
$636$	−0.825417	+	5.58544i	−0.0327299	+	0.221477i
$637$	−20.4496	−	14.7924i	−0.810241	−	0.586096i
$638$		−	0.286785i		−	0.0113539i
$639$	3.27440	+	2.03122i	0.129533	+	0.0803538i
$640$	−1.49161	+	2.58355i	−0.0589611	+	0.102124i
$641$	−22.0062	+	38.1158i	−0.869191	+	1.50548i	−0.00636716	+	0.999980i	$0.502027\pi$
$641$	−22.0062	+	38.1158i	−0.869191	+	1.50548i	−0.862824	+	0.505504i	$0.831307\pi$
$642$	25.6383	+	11.0981i	1.01186	+	0.438006i
$643$	27.9829	+	27.9829i	1.10354	+	1.10354i	0.993980	+	0.109559i	$0.0349438\pi$
$643$	27.9829	+	27.9829i	1.10354	+	1.10354i	0.109559	+	0.993980i	$0.465056\pi$
$644$	6.02043	−	20.2265i	0.237238	−	0.797036i
$645$	−11.0454	+	8.20111i	−0.434910	+	0.322918i
$646$	0.539277	+	0.934055i	0.0212176	+	0.0367499i
$647$	−12.7841	+	22.1426i	−0.502593	+	0.870516i	0.497403	+	0.867520i	$0.334287\pi$
$647$	−12.7841	+	22.1426i	−0.502593	+	0.870516i	−0.999996	+	0.00299663i	$0.999046\pi$
$648$	8.52864	+	2.87441i	0.335037	+	0.112917i
$649$	2.74781	−	1.58645i	0.107861	−	0.0622736i
$650$	9.45745	+	10.4042i	0.370952	+	0.408088i
$651$	17.7468	+	14.8818i	0.695550	+	0.583264i
$652$	13.4872	+	13.4872i	0.528198	+	0.528198i
$653$	9.80664	−	5.66186i	0.383763	−	0.221566i	−0.295691	−	0.955284i	$-0.595550\pi$
$653$	9.80664	−	5.66186i	0.383763	−	0.221566i	0.679454	+	0.733718i	$0.262217\pi$
$654$	−16.8233	−	13.3370i	−0.657841	−	0.521517i
$655$	51.7082	−	13.8552i	2.02041	−	0.541366i
$656$	9.03608	+	2.42121i	0.352800	+	0.0945323i
$657$	−9.04075	+	4.84503i	−0.352713	+	0.189023i
$658$	−25.4347	+	24.0729i	−0.991547	+	0.938457i
$659$		−	12.4449i		−	0.484783i	−0.970179	−	0.242391i	$-0.922068\pi$
$659$		−	12.4449i		−	0.484783i	0.970179	−	0.242391i	$-0.0779318\pi$
$660$	0.936097	+	2.36508i	0.0364375	+	0.0920604i
$661$	2.47664	+	9.24295i	0.0963302	+	0.359509i	0.997218	−	0.0745433i	$-0.0237499\pi$
$661$	2.47664	+	9.24295i	0.0963302	+	0.359509i	−0.900888	+	0.434053i	$0.857083\pi$
$662$	−7.32086	+	12.6801i	−0.284533	+	0.492826i
$663$	2.20708	−	0.754127i	0.0857160	−	0.0292878i
$664$	13.0846			0.507779
$665$	16.5546	−	15.6682i	0.641959	−	0.607587i
$666$	−2.46311	+	8.15169i	−0.0954436	+	0.315872i
$667$	−4.02431	+	2.32344i	−0.155822	+	0.0899638i
$668$	3.31853	+	12.3849i	0.128398	+	0.479188i
$669$	−3.73803	−	32.3382i	−0.144521	−	1.25027i
$670$	8.43102	+	2.25909i	0.325719	+	0.0872761i
$671$	2.62788	+	2.62788i	0.101448	+	0.101448i
$672$	2.94452	−	3.51138i	0.113587	−	0.135454i
$673$			7.76392i			0.299277i	0.988741	+	0.149638i	$0.0478110\pi$
$673$			7.76392i			0.299277i	−0.988741	+	0.149638i	$0.952189\pi$
$674$	4.52804	−	16.8989i	0.174414	−	0.650920i
$675$	16.6428	−	11.5589i	0.640582	−	0.444901i
$676$	10.5890	+	7.54144i	0.407269	+	0.290055i
$677$	−12.1599	+	7.02053i	−0.467344	+	0.269821i	−0.715127	−	0.698995i	$-0.753631\pi$
$677$	−12.1599	+	7.02053i	−0.467344	+	0.269821i	0.247784	+	0.968815i	$0.420298\pi$
$678$	7.94978	−	5.90266i	0.305309	−	0.226690i
$679$	21.6448	+	39.9906i	0.830651	+	1.53470i
$680$	1.11417			0.0427263
$681$	19.8809	−	45.9281i	0.761838	−	1.75997i
$682$	−2.40318	+	0.643930i	−0.0920224	+	0.0246573i
$683$	30.3629	−	8.13572i	1.16181	−	0.311305i	0.374119	−	0.927381i	$-0.377945\pi$
$683$	30.3629	−	8.13572i	1.16181	−	0.311305i	0.787687	+	0.616076i	$0.211279\pi$
$684$	7.36213	+	4.56697i	0.281498	+	0.174622i
$685$	28.3720			1.08404
$686$	7.90689	+	16.7476i	0.301886	+	0.639425i
$687$	−6.85445	−	9.23166i	−0.261514	−	0.352210i
$688$	−2.30575	+	1.33122i	−0.0879057	+	0.0507524i
$689$	9.88729	+	6.35463i	0.376676	+	0.242092i
$690$	25.6040	−	32.2968i	0.974726	−	1.22952i
$691$	−3.69969	+	13.8074i	−0.140743	+	0.525259i	0.859165	+	0.511698i	$0.170983\pi$
$691$	−3.69969	+	13.8074i	−0.140743	+	0.525259i	−0.999908	+	0.0135610i	$0.995683\pi$
$692$			3.70859i			0.140979i
$693$	−0.786441	−	3.82729i	−0.0298744	−	0.145387i
$694$	10.1263	+	10.1263i	0.384390	+	0.384390i
$695$	61.6138	+	16.5094i	2.33714	+	0.626236i
$696$	−1.00238	+	0.115867i	−0.0379953	+	0.00439194i
$697$	−0.904267	−	3.37477i	−0.0342515	−	0.127829i
$698$	−18.5284	+	10.6974i	−0.701310	+	0.404901i
$699$	−0.562023	+	3.80310i	−0.0212577	+	0.143846i
$700$	−2.39530	−	10.0355i	−0.0905340	−	0.379307i
$701$	5.06325			0.191236			0.0956181	−	0.995418i	$-0.469517\pi$
$701$	5.06325			0.191236			0.0956181	+	0.995418i	$0.469517\pi$
$702$	12.7648	−	13.7135i	0.481778	−	0.517581i
$703$	−4.09870	+	7.09916i	−0.154585	+	0.267750i
$704$	0.127408	+	0.475494i	0.00480188	+	0.0179208i
$705$	−63.5939	+	25.1705i	−2.39508	+	0.947975i
$706$			1.70840i			0.0642965i
$707$	21.5564	−	20.4022i	0.810711	−	0.767303i
$708$	−6.65520	−	8.96331i	−0.250118	−	0.336862i
$709$	18.3917	+	4.92803i	0.690714	+	0.185076i	0.587067	−	0.809538i	$-0.300282\pi$
$709$	18.3917	+	4.92803i	0.690714	+	0.185076i	0.103646	+	0.994614i	$0.466949\pi$
$710$	3.70114	−	0.991718i	0.138901	−	0.0372185i
$711$	−24.8690	+	23.3432i	−0.932661	+	0.875439i
$712$	−2.82687	+	1.63209i	−0.105941	+	0.0611652i
$713$	28.5057	+	28.5057i	1.06755	+	1.06755i
$714$	−1.68558	−	0.296667i	−0.0630812	−	0.0111025i
$715$	5.28890	+	0.252116i	0.197794	+	0.00942859i
$716$	10.3545	−	5.97819i	0.386967	−	0.223416i
$717$	22.1468	−	2.55999i	0.827089	−	0.0956047i
$718$	−6.95461	+	12.0457i	−0.259544	+	0.449543i
$719$	21.6555	+	37.5084i	0.807614	+	1.39883i	0.914512	+	0.404558i	$0.132575\pi$
$719$	21.6555	+	37.5084i	0.807614	+	1.39883i	−0.106899	+	0.994270i	$0.534092\pi$
$720$	7.88831	−	4.22743i	0.293980	−	0.157547i
$721$	8.41616	−	2.00879i	0.313434	−	0.0748113i
$722$	−7.53791	−	7.53791i	−0.280532	−	0.280532i
$723$	6.80079	−	15.7109i	0.252924	−	0.584295i
$724$	−2.77836	+	4.81226i	−0.103257	+	0.178846i
$725$	−1.13592	+	1.96747i	−0.0421870	+	0.0730701i
$726$	−17.0996	−	7.40188i	−0.634624	−	0.274710i
$727$		−	26.4056i		−	0.979328i	−0.871911	−	0.489664i	$-0.837119\pi$
$727$		−	26.4056i		−	0.979328i	0.871911	−	0.489664i	$-0.162881\pi$
$728$	−4.13612	−	8.59607i	−0.153295	−	0.318592i
$729$	−17.1966	−	20.8153i	−0.636912	−	0.770936i
$730$	−2.63991	+	9.85226i	−0.0977073	+	0.364648i
$731$	0.861144	+	0.497182i	0.0318506	+	0.0183889i
$732$	8.12335	−	10.2468i	0.300247	−	0.378732i
$733$	−6.59585	+	24.6161i	−0.243623	+	0.909215i	0.730447	+	0.682969i	$0.239312\pi$
$733$	−6.59585	+	24.6161i	−0.243623	+	0.909215i	−0.974070	+	0.226245i	$0.927355\pi$
$734$	−19.7319	+	19.7319i	−0.728319	+	0.728319i
$735$	2.17177	+	36.1044i	0.0801068	+	1.33173i
$736$	5.64014	−	5.64014i	0.207898	−	0.207898i
$737$	1.24733	−	0.720148i	0.0459461	−	0.0265270i
$738$	−19.2069	−	20.4624i	−0.707017	−	0.753231i
$739$	6.39753	+	23.8759i	0.235337	+	0.878289i	0.977997	+	0.208620i	$0.0668973\pi$
$739$	6.39753	+	23.8759i	0.235337	+	0.878289i	−0.742660	+	0.669669i	$0.766436\pi$
$740$	4.23403	+	7.33356i	0.155646	+	0.269587i
$741$	14.9753	−	10.0495i	0.550131	−	0.369178i
$742$	−4.10527	−	7.58484i	−0.150709	−	0.278448i
$743$	4.42963	−	4.42963i	0.162507	−	0.162507i	−0.621169	−	0.783677i	$-0.713342\pi$
$743$	4.42963	−	4.42963i	0.162507	−	0.162507i	0.783677	+	0.621169i	$0.213342\pi$
$744$	3.22163	+	8.13953i	0.118111	+	0.298410i
$745$	−10.1511	−	5.86073i	−0.371907	−	0.214721i
$746$	−6.37947	−	23.8085i	−0.233569	−	0.871691i
$747$	−33.3568	−	20.6923i	−1.22046	−	0.757093i
$748$	0.130002	−	0.130002i	0.00475335	−	0.00475335i
$749$	−41.5089	+	9.90745i	−1.51670	+	0.362010i
$750$	−0.831216	+	5.62468i	−0.0303517	+	0.205384i
$751$	17.6566	−	10.1940i	0.644299	−	0.371986i	−0.141970	−	0.989871i	$-0.545344\pi$
$751$	17.6566	−	10.1940i	0.644299	−	0.371986i	0.786268	+	0.617885i	$0.212010\pi$
$752$	−12.7854	+	3.42585i	−0.466237	+	0.124928i
$753$	−20.1917	−	16.0073i	−0.735825	−	0.583340i
$754$	−0.639646	+	2.00076i	−0.0232945	+	0.0728634i
$755$		−	29.7638i		−	1.08322i
$756$	−13.0596	+	4.29511i	−0.474972	+	0.156212i
$757$	−15.9128			−0.578362			−0.289181	−	0.957274i	$-0.593383\pi$
$757$	−15.9128			−0.578362			−0.289181	+	0.957274i	$0.593383\pi$
$758$	3.92883	+	6.80493i	0.142702	+	0.247166i
$759$	−0.780929	−	6.75592i	−0.0283459	−	0.245224i
$760$	8.32160	−	2.22977i	0.301856	−	0.0808822i
$761$	8.80566	−	32.8632i	0.319205	−	1.19129i	−0.600805	−	0.799395i	$-0.705153\pi$
$761$	8.80566	−	32.8632i	0.319205	−	1.19129i	0.920010	−	0.391894i	$-0.128180\pi$
$762$	−4.06716	+	3.01984i	−0.147338	+	0.109397i
$763$	32.7813	+	0.901730i	1.18676	+	0.0326448i
$764$	8.04418			0.291028
$765$	−2.84038	−	1.76198i	−0.102694	−	0.0637044i
$766$	−9.52919	−	5.50168i	−0.344303	−	0.198784i
$767$	−22.7086	+	4.93916i	−0.819959	+	0.178343i
$768$	1.61049	−	0.637432i	0.0581136	−	0.0230014i
$769$	2.08636	+	2.08636i	0.0752360	+	0.0752360i	0.743723	−	0.668487i	$-0.233058\pi$
$769$	2.08636	+	2.08636i	0.0752360	+	0.0752360i	−0.668487	+	0.743723i	$0.733058\pi$
$770$	−3.31017	−	2.03449i	−0.119290	−	0.0733179i
$771$	−7.35294	+	49.7559i	−0.264810	+	1.79192i
$772$	−1.74782	+	6.52296i	−0.0629055	+	0.234767i
$773$	4.43238	+	16.5419i	0.159422	+	0.594970i	0.998686	+	0.0512461i	$0.0163193\pi$
$773$	4.43238	+	16.5419i	0.159422	+	0.594970i	−0.839264	+	0.543723i	$0.817014\pi$
$774$	7.98334	+	0.252655i	0.286955	+	0.00908150i
$775$	19.0374	+	5.10105i	0.683843	+	0.183235i
$776$			17.1870i			0.616977i
$777$	−4.45281	−	12.2221i	−0.159744	−	0.438464i
$778$	3.22881	−	3.22881i	0.115758	−	0.115758i
$779$	−13.5078	−	23.3961i	−0.483966	−	0.838254i
$780$	−1.25563	−	18.5879i	−0.0449586	−	0.665552i
$781$	0.316139	−	0.547568i	0.0113123	−	0.0195935i
$782$	−2.87748	−	0.771020i	−0.102899	−	0.0275716i
$783$	2.73864	+	1.28982i	0.0978711	+	0.0460943i
$784$	−0.384813	+	6.98941i	−0.0137433	+	0.249622i
$785$	−45.3395	+	45.3395i	−1.61824	+	1.61824i
$786$	−28.5231	−	12.3468i	−1.01738	−	0.440395i
$787$	−2.35688	−	8.79601i	−0.0840138	−	0.313544i	0.911112	−	0.412159i	$-0.135225\pi$
$787$	−2.35688	−	8.79601i	−0.0840138	−	0.313544i	−0.995126	+	0.0986155i	$0.968559\pi$
$788$	13.0483	−	3.49628i	0.464826	−	0.124550i
$789$	−11.8425	−	29.9205i	−0.421606	−	1.06520i
$790$			33.9175i			1.20673i
$791$	−4.31484	+	14.4963i	−0.153418	+	0.515430i
$792$	0.427156	−	1.41368i	0.0151783	−	0.0502328i
$793$	−12.4722	−	24.1946i	−0.442901	−	0.859177i
$794$	13.5112	+	7.80070i	0.479495	+	0.276836i
$795$	−1.93410	−	16.7322i	−0.0685955	−	0.593428i
$796$	9.93481	+	17.2076i	0.352130	+	0.609907i
$797$	13.8457			0.490440			0.245220	−	0.969468i	$-0.421140\pi$
$797$	13.8457			0.490440			0.245220	+	0.969468i	$0.421140\pi$
$798$	−13.1832	+	1.15755i	−0.466679	+	0.0409768i
$799$	3.49559	+	3.49559i	0.123665	+	0.123665i
$800$	1.00930	−	3.76674i	0.0356840	−	0.133175i
$801$	9.78765	+	0.309758i	0.345830	+	0.0109447i
$802$	10.0391	−	17.3882i	0.354492	−	0.613999i
$803$	0.841545	+	1.45760i	0.0296975	+	0.0514375i
$804$	−3.02104	−	4.06878i	−0.106544	−	0.143495i
$805$	−1.73112	+	62.9326i	−0.0610138	+	2.21808i
$806$	18.2020	+	0.867669i	0.641139	+	0.0305623i
$807$	5.17694	+	13.0797i	0.182237	+	0.460427i
$808$	10.8359	−	2.90347i	0.381205	−	0.102144i
$809$	−26.8210	−	15.4851i	−0.942977	−	0.544428i	−0.0520847	−	0.998643i	$-0.516587\pi$
$809$	−26.8210	−	15.4851i	−0.942977	−	0.544428i	−0.890892	+	0.454215i	$0.849920\pi$
$810$	−26.7953	−	1.69772i	−0.941490	−	0.0596519i
$811$	21.3040	+	21.3040i	0.748083	+	0.748083i	0.974119	−	0.226036i	$-0.0725766\pi$
$811$	21.3040	+	21.3040i	0.748083	+	0.748083i	−0.226036	+	0.974119i	$0.572577\pi$
$812$	1.11946	−	1.05953i	0.0392855	−	0.0371821i
$813$	25.5371	+	34.3937i	0.895625	+	1.20624i
$814$	1.34972	+	0.361656i	0.0473076	+	0.0126760i
$815$	−49.2779	−	28.4506i	−1.72613	−	0.996582i
$816$	−0.506912	−	0.401865i	−0.0177455	−	0.0140681i
$817$	7.42681	+	1.99001i	0.259831	+	0.0696215i
$818$	22.5951			0.790020
$819$	−3.04977	+	28.4552i	−0.106568	+	0.994305i
$820$	−27.9076			−0.974574
$821$	−19.0589	−	5.10681i	−0.665159	−	0.178229i	−0.0895861	−	0.995979i	$-0.528554\pi$
$821$	−19.0589	−	5.10681i	−0.665159	−	0.178229i	−0.575573	+	0.817750i	$0.695221\pi$
$822$	−12.9084	−	10.2334i	−0.450233	−	0.356931i
$823$	14.8852	+	8.59396i	0.518865	+	0.299567i	0.736470	−	0.676470i	$-0.236491\pi$
$823$	14.8852	+	8.59396i	0.518865	+	0.299567i	−0.217605	+	0.976037i	$0.569825\pi$
$824$	3.15893	+	0.846433i	0.110047	+	0.0294869i
$825$	−1.98212	−	2.66954i	−0.0690085	−	0.0929415i
$826$	16.3445	+	4.86494i	0.568697	+	0.169273i
$827$	20.6419	+	20.6419i	0.717790	+	0.717790i	0.968152	−	0.250362i	$-0.0805496\pi$
$827$	20.6419	+	20.6419i	0.717790	+	0.717790i	−0.250362	+	0.968152i	$0.580550\pi$
$828$	−23.2981	+	5.45907i	−0.809664	+	0.189716i
$829$	16.4326	+	9.48736i	0.570728	+	0.329510i	0.757440	−	0.652905i	$-0.226450\pi$
$829$	16.4326	+	9.48736i	0.570728	+	0.329510i	−0.186712	+	0.982415i	$0.559783\pi$
$830$	−37.7041	+	10.1028i	−1.30873	+	0.350673i
$831$	−9.16228	−	23.1488i	−0.317836	−	0.803021i
$832$	0.171677	−	3.60146i	0.00595184	−	0.124858i
$833$	2.33252	−	1.18073i	0.0808171	−	0.0409099i
$834$	−22.0777	−	29.7346i	−0.764489	−	1.02962i
$835$	−19.1252	−	33.1258i	−0.661854	−	1.14637i
$836$	0.710802	−	1.23115i	0.0245836	−	0.0425800i
$837$	4.65913	−	25.8451i	0.161043	−	0.893338i
$838$	0.552176	−	2.06075i	0.0190746	−	0.0711874i
$839$	3.44017	+	3.44017i	0.118768	+	0.118768i	0.763993	−	0.645225i	$-0.223236\pi$
$839$	3.44017	+	3.44017i	0.118768	+	0.118768i	−0.645225	+	0.763993i	$0.723236\pi$
$840$	−5.77366	+	12.3918i	−0.199210	+	0.427558i
$841$	28.6606			0.988297
$842$	19.4712	+	33.7251i	0.671022	+	1.16224i
$843$	1.74186	+	15.0691i	0.0599928	+	0.519006i
$844$	−7.02387	−	4.05523i	−0.241772	−	0.139587i
$845$	−36.3358	−	13.5553i	−1.24999	−	0.466316i
$846$	38.0120	+	11.4857i	1.30688	+	0.394886i
$847$	27.6845	−	6.60780i	0.951250	−	0.227047i
$848$		−	3.25978i		−	0.111941i
$849$	−15.8161	−	39.9598i	−0.542807	−	1.37142i
$850$	−1.40679	+	0.376949i	−0.0482526	+	0.0129292i
$851$	−5.86003	−	21.8699i	−0.200879	−	0.749692i
$852$	−2.04161	−	0.883752i	−0.0699444	−	0.0302768i
$853$	−33.6661	+	33.6661i	−1.15271	+	1.15271i	−0.166698	+	0.986008i	$0.553310\pi$
$853$	−33.6661	+	33.6661i	−1.15271	+	1.15271i	−0.986008	+	0.166698i	$0.946690\pi$
$854$	−0.549230	+	19.9666i	−0.0187943	+	0.683242i
$855$	−24.7407	−	7.47564i	−0.846115	−	0.255662i
$856$	−15.5800	−	4.17465i	−0.532513	−	0.142686i
$857$	8.00696	−	13.8685i	0.273513	−	0.473738i	−0.696246	−	0.717803i	$-0.745148\pi$
$857$	8.00696	−	13.8685i	0.273513	−	0.473738i	0.969759	+	0.244065i	$0.0784811\pi$
$858$	−2.31536	−	2.02234i	−0.0790451	−	0.0690417i
$859$	2.08126	+	3.60485i	0.0710117	+	0.122996i	0.899345	−	0.437240i	$-0.144044\pi$
$859$	2.08126	+	3.60485i	0.0710117	+	0.122996i	−0.828333	+	0.560236i	$0.810711\pi$
$860$	5.61632	−	5.61632i	0.191515	−	0.191515i
$861$	42.2203	+	7.43091i	1.43886	+	0.253245i
$862$		−	7.03923i		−	0.239757i
$863$	−8.23152	−	2.20563i	−0.280204	−	0.0750805i	0.115980	−	0.993252i	$-0.462999\pi$
$863$	−8.23152	−	2.20563i	−0.280204	−	0.0750805i	−0.396184	+	0.918171i	$0.629666\pi$
$864$	−5.11372	−	0.921857i	−0.173972	−	0.0313622i
$865$	−2.86346	−	10.6866i	−0.0973605	−	0.363354i
$866$	−1.24417	+	4.64329i	−0.0422785	+	0.157786i
$867$	4.26930	−	28.8895i	0.144993	−	0.981139i
$868$	−11.3921	−	7.00180i	−0.386673	−	0.237657i
$869$	3.95753	+	3.95753i	0.134250	+	0.134250i
$870$	2.79898	−	1.10784i	0.0948942	−	0.0375591i
$871$	−10.3083	+	2.24207i	−0.349282	+	0.0759696i
$872$	10.7343	+	6.19742i	0.363508	+	0.209871i
$873$	27.1800	−	43.8153i	0.919905	−	1.48292i
$874$	−23.0347			−0.779160
$875$	−4.13411	−	7.63812i	−0.139758	−	0.258216i
$876$	4.75466	−	3.53031i	0.160645	−	0.119278i
$877$	1.00074	−	3.73481i	0.0337926	−	0.126116i	−0.946969	−	0.321325i	$-0.895872\pi$
$877$	1.00074	−	3.73481i	0.0337926	−	0.126116i	0.980762	+	0.195209i	$0.0625386\pi$
$878$	19.8625	−	5.32215i	0.670329	−	0.179614i
$879$	0.264752	+	2.29041i	0.00892987	+	0.0772535i
$880$	−0.734272	−	1.27180i	−0.0247523	−	0.0428722i
$881$	−47.5999			−1.60368			−0.801841	−	0.597538i	$-0.796146\pi$
$881$	−47.5999			−1.60368			−0.801841	+	0.597538i	$0.796146\pi$
$882$	12.0343	−	17.2098i	0.405216	−	0.579483i
$883$			32.0280i			1.07783i	0.842361	+	0.538914i	$0.181165\pi$
$883$			32.0280i			1.07783i	−0.842361	+	0.538914i	$0.818835\pi$
$884$	−1.19692	+	0.617005i	−0.0402567	+	0.0207521i
$885$	26.0981	+	20.6898i	0.877279	+	0.695481i
$886$	−16.2772	+	4.36147i	−0.546844	+	0.146526i
$887$	−8.43763	+	4.87147i	−0.283308	+	0.163568i	−0.634920	−	0.772578i	$-0.718967\pi$
$887$	−8.43763	+	4.87147i	−0.283308	+	0.163568i	0.351612	+	0.936146i	$0.385634\pi$
$888$	0.718761	−	4.86371i	0.0241200	−	0.163216i
$889$	2.20750	−	7.41641i	0.0740371	−	0.248738i
$890$	6.88566	−	6.88566i	0.230808	−	0.230808i
$891$	−3.32459	+	2.92841i	−0.111378	+	0.0981054i
$892$	4.86445	+	18.1544i	0.162874	+	0.607853i
$893$	33.1039	+	19.1126i	1.10778	+	0.639578i
$894$	2.50455	+	6.32782i	0.0837647	+	0.211634i
$895$	−25.2215	+	25.2215i	−0.843062	+	0.843062i
$896$	−1.38538	+	2.25405i	−0.0462823	+	0.0753024i
$897$	−9.62026	+	48.8746i	−0.321211	+	1.63187i
$898$	−13.9143	−	24.1002i	−0.464326	−	0.804235i
$899$	0.762066	+	2.84407i	0.0254163	+	0.0948551i
$900$	−8.52988	+	8.00653i	−0.284329	+	0.266884i
$901$	−1.05434	+	0.608726i	−0.0351253	+	0.0202796i
$902$	−3.25628	+	3.25628i	−0.108422	+	0.108422i
$903$	−9.99216	+	7.00126i	−0.332518	+	0.232987i
$904$	−4.04229	+	4.04229i	−0.134444	+	0.134444i
$905$	4.29043	−	16.0121i	0.142619	−	0.532260i
$906$	−10.7354	+	13.5417i	−0.356661	+	0.449891i
$907$	−24.5858	−	14.1946i	−0.816358	−	0.471325i	0.0328009	−	0.999462i	$-0.489557\pi$
$907$	−24.5858	−	14.1946i	−0.816358	−	0.471325i	−0.849159	+	0.528137i	$0.822891\pi$
$908$	−7.47840	+	27.9098i	−0.248179	+	0.926218i
$909$	−32.2159	−	9.73432i	−1.06853	−	0.322867i
$910$	18.5557	+	21.5767i	0.615115	+	0.715259i
$911$		−	24.4891i		−	0.811361i	−0.914015	−	0.405681i	$-0.867035\pi$
$911$		−	24.4891i		−	0.811361i	0.914015	−	0.405681i	$-0.132965\pi$
$912$	−4.59033	−	1.98702i	−0.152001	−	0.0657967i
$913$	−3.22055	+	5.57816i	−0.106585	+	0.184610i
$914$	−19.1708	+	33.2048i	−0.634114	+	1.09832i
$915$	−15.4963	+	35.7990i	−0.512292	+	1.18348i
$916$	4.69409	+	4.69409i	0.155097	+	0.155097i
$917$	46.1793	−	11.0222i	1.52498	−	0.363985i
$918$	0.656764	+	1.82613i	0.0216764	+	0.0602714i
$919$	−7.43086	−	12.8706i	−0.245121	−	0.424563i	0.717044	−	0.697027i	$-0.245494\pi$
$919$	−7.43086	−	12.8706i	−0.245121	−	0.424563i	−0.962166	+	0.272465i	$0.912161\pi$
$920$	−11.8976	+	20.6073i	−0.392254	+	0.679403i
$921$	−2.89331	+	0.334443i	−0.0953378	+	0.0110203i
$922$	21.5178	−	12.4233i	0.708652	−	0.409140i
$923$	−3.42684	+	3.11500i	−0.112796	+	0.102532i
$924$	0.772213	+	2.11957i	0.0254039	+	0.0697286i
$925$	−7.82719	−	7.82719i	−0.257356	−	0.257356i
$926$	30.3966	−	17.5495i	0.998895	−	0.576712i
$927$	−6.71457	−	7.15347i	−0.220536	−	0.234951i
$928$	0.562729	−	0.150783i	0.0184725	−	0.00494969i
$929$	24.1066	+	6.45934i	0.790912	+	0.211924i	0.631590	−	0.775303i	$-0.282403\pi$
$929$	24.1066	+	6.45934i	0.790912	+	0.211924i	0.159322	+	0.987227i	$0.449069\pi$
$930$	−15.5680	−	20.9672i	−0.510495	−	0.687541i
$931$	15.0584	−	13.4868i	0.493519	−	0.442012i
$932$		−	2.21957i		−	0.0727044i
$933$	4.02178	−	1.59182i	0.131667	−	0.0521138i
$934$	3.83151	+	14.2994i	0.125371	+	0.467891i
$935$	−0.274234	+	0.474987i	−0.00896841	+	0.0155337i
$936$	−6.13313	+	8.90981i	−0.200468	+	0.291226i
$937$	21.9030			0.715541			0.357771	−	0.933809i	$-0.383537\pi$
$937$	21.9030			0.715541			0.357771	+	0.933809i	$0.383537\pi$
$938$	7.41936	+	2.20838i	0.242251	+	0.0721060i
$939$	7.85073	−	53.1244i	0.256199	−	1.73365i
$940$	34.1970	−	19.7436i	1.11538	−	0.643967i
$941$	11.0414	+	41.2069i	0.359938	+	1.34331i	0.874155	+	0.485648i	$0.161416\pi$
$941$	11.0414	+	41.2069i	0.359938	+	1.34331i	−0.514216	+	0.857661i	$0.671917\pi$
$942$	36.9815	−	4.27476i	1.20492	−	0.139279i
$943$	72.0751	+	19.3125i	2.34709	+	0.628900i
$944$	4.55764	+	4.55764i	0.148339	+	0.148339i
$945$	34.3157	−	22.4601i	1.11629	−	0.730628i
$946$		−	1.31064i		−	0.0426124i
$947$	−8.88682	+	33.1661i	−0.288783	+	1.07775i	0.657247	+	0.753675i	$0.271721\pi$
$947$	−8.88682	+	33.1661i	−0.288783	+	1.07775i	−0.946030	+	0.324078i	$0.894946\pi$
$948$	12.2336	−	15.4315i	0.397329	−	0.501191i
$949$	−2.62002	−	12.0459i	−0.0850495	−	0.391028i
$950$	−9.75283	+	5.63080i	−0.316424	+	0.182687i
$951$	19.7105	+	26.5464i	0.639157	+	0.860824i
$952$	0.987754	+	0.0271706i	0.0320133	+	0.000880605i
$953$	−38.4250			−1.24471			−0.622354	−	0.782736i	$-0.713824\pi$
$953$	−38.4250			−1.24471			−0.622354	+	0.782736i	$0.713824\pi$
$954$	−5.15511	+	8.31024i	−0.166903	+	0.269054i
$955$	−23.1799	+	6.21103i	−0.750083	+	0.200984i
$956$	−12.4330	+	3.33142i	−0.402113	+	0.107746i
$957$	0.197324	−	0.455851i	0.00637859	−	0.0147356i
$958$	32.6981			1.05643
$959$	25.1530	+	0.691895i	0.812232	+	0.0223424i
$960$	−4.14857	+	3.08029i	−0.133895	+	0.0994160i
$961$	−4.72538	+	2.72820i	−0.152432	+	0.0880065i
$962$	−8.60970	−	5.53352i	−0.277588	−	0.178408i
$963$	33.1166	+	35.2812i	1.06717	+	1.13692i
$964$	−2.55818	+	9.54727i	−0.0823935	+	0.307497i
$965$		−	20.1459i		−	0.648520i
$966$	23.4866	−	28.0081i	0.755668	−	0.901145i
$967$	−37.3805	−	37.3805i	−1.20208	−	1.20208i	−0.973534	−	0.228543i	$-0.926604\pi$
$967$	−37.3805	−	37.3805i	−1.20208	−	1.20208i	−0.228543	−	0.973534i	$-0.573396\pi$
$968$	10.3911	+	2.78429i	0.333983	+	0.0894905i
$969$	0.214510	+	1.85575i	0.00689105	+	0.0596154i
$970$	−13.2703	−	49.5255i	−0.426085	−	1.59017i
$971$	37.7590	−	21.8002i	1.21174	−	0.699600i	0.248604	−	0.968605i	$-0.420028\pi$
$971$	37.7590	−	21.8002i	1.21174	−	0.699600i	0.963139	+	0.269005i	$0.0866948\pi$
$972$	11.5787	+	10.4371i	0.371387	+	0.334771i
$973$	54.2206	+	16.1388i	1.73823	+	0.517386i
$974$	−16.1187			−0.516475
$975$	7.87413	+	23.0450i	0.252174	+	0.738031i
$976$	−3.77475	+	6.53807i	−0.120827	+	0.209278i
$977$	3.44656	+	12.8627i	0.110265	+	0.411515i	0.998889	−	0.0471214i	$-0.0150048\pi$
$977$	3.44656	+	12.8627i	0.110265	+	0.411515i	−0.888624	+	0.458636i	$0.848338\pi$
$978$	12.1582	+	30.7181i	0.388777	+	0.982256i
$979$		−	1.60685i		−	0.0513552i
$980$	−4.28776	−	20.4376i	−0.136968	−	0.652856i
$981$	−17.5643	−	32.7748i	−0.560786	−	1.04642i
$982$	−30.4897	−	8.16969i	−0.972966	−	0.260705i
$983$	0.274991	−	0.0736836i	0.00877085	−	0.00235014i	−0.254431	−	0.967091i	$-0.581888\pi$
$983$	0.274991	−	0.0736836i	0.00877085	−	0.00235014i	0.263202	+	0.964741i	$0.415221\pi$
$984$	12.6971	+	10.0659i	0.404769	+	0.320889i
$985$	−34.9001	+	20.1496i	−1.11201	+	0.642019i
$986$	−0.153853	−	0.153853i	−0.00489966	−	0.00489966i
$987$	−56.9924	+	20.7638i	−1.81409	+	0.660920i
$988$	−7.70487	+	7.00373i	−0.245125	+	0.222818i
$989$	−18.3915	+	10.6183i	−0.584815	+	0.337643i
$990$	−0.139359	+	4.40343i	−0.00442911	+	0.139950i
$991$	18.1504	−	31.4374i	0.576566	−	0.998642i	−0.419304	−	0.907846i	$-0.637726\pi$
$991$	18.1504	−	31.4374i	0.576566	−	0.998642i	0.995870	−	0.0907955i	$-0.0289410\pi$
$992$	−2.52703	−	4.37695i	−0.0802334	−	0.138968i
$993$	−20.3613	+	15.1181i	−0.646146	+	0.479759i
$994$	3.30540	−	0.788942i	0.104841	−	0.0250237i
$995$	−41.9141	−	41.9141i	−1.32877	−	1.32877i
$996$	20.7982	+	9.00291i	0.659016	+	0.285268i
$997$	8.60792	−	14.9094i	0.272616	−	0.472184i	−0.696915	−	0.717154i	$-0.745445\pi$
$997$	8.60792	−	14.9094i	0.272616	−	0.472184i	0.969531	+	0.244970i	$0.0787780\pi$
$998$	10.4526	−	18.1045i	0.330872	−	0.573087i
$999$	−9.52399	+	11.2625i	−0.301326	+	0.356331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.515.4	yes	144
3.2	odd	2	inner	546.2.bv.a.515.34	yes	144
7.2	even	3	inner	546.2.bv.a.359.34	yes	144
13.5	odd	4	inner	546.2.bv.a.473.4	yes	144
21.2	odd	6	inner	546.2.bv.a.359.4	yes	144
39.5	even	4	inner	546.2.bv.a.473.34	yes	144
91.44	odd	12	inner	546.2.bv.a.317.34	yes	144
273.44	even	12	inner	546.2.bv.a.317.4	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.4	✓	144	273.44	even	12	inner
546.2.bv.a.317.34	yes	144	91.44	odd	12	inner
546.2.bv.a.359.4	yes	144	21.2	odd	6	inner
546.2.bv.a.359.34	yes	144	7.2	even	3	inner
546.2.bv.a.473.4	yes	144	13.5	odd	4	inner
546.2.bv.a.473.34	yes	144	39.5	even	4	inner
546.2.bv.a.515.4	yes	144	1.1	even	1	trivial
546.2.bv.a.515.34	yes	144	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.35728 - 1.07601i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.88157 - 0.772115i) q^{5} +(1.03254 + 1.39063i) q^{6} +(-2.53580 - 0.754783i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.684406 + 2.92089i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.35728 - 1.07601i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.88157 - 0.772115i) q^{5} +(1.03254 + 1.39063i) q^{6} +(-2.53580 - 0.754783i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.684406 + 2.92089i) q^{9} +(2.58355 + 1.49161i) q^{10} +(0.475494 - 0.127408i) q^{11} +(-0.637432 - 1.61049i) q^{12} +(-3.60146 - 0.171677i) q^{13} +(2.25405 + 1.38538i) q^{14} +(3.08029 + 4.14857i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.186739 - 0.323441i) q^{17} +(0.0948959 - 2.99850i) q^{18} +(0.747436 - 2.78947i) q^{19} +(-2.10946 - 2.10946i) q^{20} +(2.62964 + 3.75300i) q^{21} -0.492267 q^{22} +(3.98818 + 6.90774i) q^{23} +(0.198887 + 1.72059i) q^{24} +(3.37717 + 1.94981i) q^{25} +(3.43431 + 1.09795i) q^{26} +(2.21397 - 4.70088i) q^{27} +(-1.81868 - 1.92156i) q^{28} +0.582580i q^{29} +(-1.90160 - 4.80445i) q^{30} +(4.88185 - 1.30809i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.782470 - 0.338708i) q^{33} +(-0.264088 + 0.264088i) q^{34} +(6.72432 + 4.13290i) q^{35} +(-0.867731 + 2.87177i) q^{36} +(-2.74184 - 0.734674i) q^{37} +(-1.44393 + 2.50097i) q^{38} +(4.70346 + 4.10822i) q^{39} +(1.49161 + 2.58355i) q^{40} +(6.61487 - 6.61487i) q^{41} +(-1.56869 - 4.30572i) q^{42} +2.66245i q^{43} +(0.475494 + 0.127408i) q^{44} +(0.283096 - 8.94519i) q^{45} +(-2.06444 - 7.70458i) q^{46} +(-3.42585 + 12.7854i) q^{47} +(0.253213 - 1.71344i) q^{48} +(5.86060 + 3.82797i) q^{49} +(-2.75745 - 2.75745i) q^{50} +(-0.601482 + 0.238066i) q^{51} +(-3.03312 - 1.94941i) q^{52} +(-2.82305 - 1.62989i) q^{53} +(-3.35521 + 3.96769i) q^{54} -1.46854 q^{55} +(1.25937 + 2.32680i) q^{56} +(-4.01597 + 2.98183i) q^{57} +(0.150783 - 0.562729i) q^{58} +(6.22585 - 1.66821i) q^{59} +(0.593323 + 5.13292i) q^{60} +(3.77475 + 6.53807i) q^{61} -5.05407 q^{62} +(0.469118 - 7.92338i) q^{63} +1.00000i q^{64} +(10.2453 + 3.27544i) q^{65} +(0.668144 + 0.529685i) q^{66} +(2.82615 - 0.757263i) q^{67} +(0.323441 - 0.186739i) q^{68} +(2.01972 - 13.6670i) q^{69} +(-5.42553 - 5.73245i) q^{70} +(0.908221 - 0.908221i) q^{71} +(1.58143 - 2.54933i) q^{72} +(0.884917 + 3.30256i) q^{73} +(2.45827 + 1.41928i) q^{74} +(-2.48574 - 6.28030i) q^{75} +(2.04203 - 2.04203i) q^{76} +(-1.30192 - 0.0358127i) q^{77} +(-3.47991 - 5.18558i) q^{78} +(5.68471 + 9.84621i) q^{79} +(-0.772115 - 2.88157i) q^{80} +(-8.06318 + 3.99815i) q^{81} +(-8.10152 + 4.67742i) q^{82} +(-9.25218 + 9.25218i) q^{83} +(0.400832 + 4.56501i) q^{84} +(-0.787834 + 0.787834i) q^{85} +(0.689092 - 2.57173i) q^{86} +(0.626862 - 0.790723i) q^{87} +(-0.426316 - 0.246134i) q^{88} +(0.844833 - 3.15296i) q^{89} +(-2.58864 + 8.56712i) q^{90} +(9.00302 + 3.15366i) q^{91} +7.97637i q^{92} +(-8.03355 - 3.47748i) q^{93} +(6.61822 - 11.4631i) q^{94} +(-4.30758 + 7.46095i) q^{95} +(-0.688056 + 1.58952i) q^{96} +(-12.1530 - 12.1530i) q^{97} +(-4.67016 - 5.21437i) q^{98} +(0.697576 + 1.30167i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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