LMFDB - Embedded newform 546.2.bv.a.317.34

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			317.34
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(1.61049 - 0.637432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.88157 - 0.772115i) q^{5} +(1.39063 - 1.03254i) q^{6} +(-2.53580 + 0.754783i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.18736 - 2.05316i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(1.61049 - 0.637432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.88157 - 0.772115i) q^{5} +(1.39063 - 1.03254i) q^{6} +(-2.53580 + 0.754783i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.18736 - 2.05316i) q^{9} +(2.58355 - 1.49161i) q^{10} +(-0.475494 - 0.127408i) q^{11} +(1.07601 - 1.35728i) q^{12} +(-3.60146 + 0.171677i) q^{13} +(-2.25405 + 1.38538i) q^{14} +(4.14857 - 3.08029i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.186739 - 0.323441i) q^{17} +(1.58143 - 2.54933i) q^{18} +(0.747436 + 2.78947i) q^{19} +(2.10946 - 2.10946i) q^{20} +(-3.60277 + 2.83197i) q^{21} -0.492267 q^{22} +(-3.98818 + 6.90774i) q^{23} +(0.688056 - 1.58952i) 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} +(3.20998 - 4.04906i) q^{30} +(4.88185 + 1.30809i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.846992 + 0.0979054i) 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} +(-5.69069 + 2.57217i) q^{39} +(1.49161 - 2.58355i) q^{40} +(-6.61487 - 6.61487i) q^{41} +(-2.74704 + 3.66794i) q^{42} -2.66245i q^{43} +(-0.475494 + 0.127408i) q^{44} +(4.71776 - 7.60521i) 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} +(-0.506912 - 0.401865i) q^{51} +(-3.03312 + 1.94941i) q^{52} +(2.82305 - 1.62989i) q^{53} +(0.921857 - 5.11372i) q^{54} -1.46854 q^{55} +(-1.25937 + 2.32680i) q^{56} +(2.98183 + 4.01597i) q^{57} +(0.150783 + 0.562729i) q^{58} +(-6.22585 - 1.66821i) q^{59} +(2.05263 - 4.74190i) q^{60} +(3.77475 - 6.53807i) q^{61} +5.05407 q^{62} +(-3.99703 + 6.85739i) q^{63} -1.00000i q^{64} +(-10.2453 + 3.27544i) q^{65} +(-0.792792 + 0.313787i) 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} +(0.0948959 - 2.99850i) q^{72} +(0.884917 - 3.30256i) q^{73} +(-2.45827 + 1.41928i) q^{74} +(4.19603 - 5.29287i) q^{75} +(2.04203 + 2.04203i) q^{76} +(1.30192 - 0.0358127i) q^{77} +(-4.83106 + 3.95739i) q^{78} +(5.68471 - 9.84621i) q^{79} +(0.772115 - 2.88157i) q^{80} +(0.569090 - 8.98199i) q^{81} +(-8.10152 - 4.67742i) q^{82} +(9.25218 + 9.25218i) q^{83} +(-1.70410 + 4.25394i) q^{84} +(-0.787834 - 0.787834i) q^{85} +(-0.689092 - 2.57173i) q^{86} +(0.371355 + 0.938240i) 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} +(8.69600 - 1.00519i) q^{93} +(6.61822 + 11.4631i) q^{94} +(4.30758 + 7.46095i) q^{95} +(-0.198887 - 1.72059i) q^{96} +(-12.1530 + 12.1530i) q^{97} +(4.67016 - 5.21437i) q^{98} +(-1.30167 + 0.697576i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$3$	1.61049	−	0.637432i	0.929817	−	0.368022i
$3$	1.61049	−	0.637432i	0.929817	−	0.368022i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.88157	−	0.772115i	1.28868	−	0.345300i	0.451520	−	0.892261i	$-0.350882\pi$
$5$	2.88157	−	0.772115i	1.28868	−	0.345300i	0.837158	+	0.546961i	$0.184215\pi$
$6$	1.39063	−	1.03254i	0.567724	−	0.421532i
$7$	−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
$9$	2.18736	−	2.05316i	0.729120	−	0.684386i
$10$	2.58355	−	1.49161i	0.816989	−	0.471689i
$11$	−0.475494	−	0.127408i	−0.143367	−	0.0384150i	0.186422	−	0.982470i	$-0.440311\pi$
$11$	−0.475494	−	0.127408i	−0.143367	−	0.0384150i	−0.329789	+	0.944055i	$0.606978\pi$
$12$	1.07601	−	1.35728i	0.310617	−	0.391812i
$13$	−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
$15$	4.14857	−	3.08029i	1.07116	−	0.795328i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.186739	−	0.323441i	−0.0452908	−	0.0784459i	0.842491	−	0.538710i	$-0.181088\pi$
$17$	−0.186739	−	0.323441i	−0.0452908	−	0.0784459i	−0.887782	+	0.460264i	$0.847755\pi$
$18$	1.58143	−	2.54933i	0.372747	−	0.600882i
$19$	0.747436	+	2.78947i	0.171473	+	0.639948i	0.997125	+	0.0757680i	$0.0241408\pi$
$19$	0.747436	+	2.78947i	0.171473	+	0.639948i	−0.825652	+	0.564180i	$0.809192\pi$
$20$	2.10946	−	2.10946i	0.471689	−	0.471689i
$21$	−3.60277	+	2.83197i	−0.786188	+	0.617988i
$22$	−0.492267			−0.104952
$23$	−3.98818	+	6.90774i	−0.831594	+	1.44036i	0.0651804	+	0.997873i	$0.479238\pi$
$23$	−3.98818	+	6.90774i	−0.831594	+	1.44036i	−0.896774	+	0.442489i	$0.854096\pi$
$24$	0.688056	−	1.58952i	0.140449	−	0.324460i
$25$	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	$0.982774\pi$
$30$	3.20998	−	4.04906i	0.586059	−	0.739254i
$31$	4.88185	+	1.30809i	0.876807	+	0.234940i	0.669029	−	0.743236i	$-0.266710\pi$
$31$	4.88185	+	1.30809i	0.876807	+	0.234940i	0.207778	+	0.978176i	$0.433377\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−0.846992	+	0.0979054i	−0.147442	+	0.0170431i
$34$	−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	−0.477053	−	0.878874i	$-0.658295\pi$
$37$	−2.74184	+	0.734674i	−0.450756	+	0.120780i	0.0262971	+	0.999654i	$0.491628\pi$
$38$	1.44393	+	2.50097i	0.234237	+	0.405711i
$39$	−5.69069	+	2.57217i	−0.911239	+	0.411877i
$40$	1.49161	−	2.58355i	0.235845	−	0.408495i
$41$	−6.61487	−	6.61487i	−1.03307	−	1.03307i	−0.999434	−	0.0336345i	$-0.989292\pi$
$41$	−6.61487	−	6.61487i	−1.03307	−	1.03307i	−0.0336345	−	0.999434i	$-0.510708\pi$
$42$	−2.74704	+	3.66794i	−0.423877	+	0.565976i
$43$		−	2.66245i		−	0.406019i	−0.979177	−	0.203010i	$-0.934928\pi$
$43$		−	2.66245i		−	0.406019i	0.979177	−	0.203010i	$-0.0650723\pi$
$44$	−0.475494	+	0.127408i	−0.0716834	+	0.0192075i
$45$	4.71776	−	7.60521i	0.703283	−	1.13372i
$46$	−2.06444	+	7.70458i	−0.304384	+	1.13598i
$47$	3.42585	+	12.7854i	0.499711	+	1.86495i	0.501860	+	0.864949i	$0.332649\pi$
$47$	3.42585	+	12.7854i	0.499711	+	1.86495i	−0.00214941	+	0.999998i	$0.500684\pi$
$48$	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
$51$	−0.506912	−	0.401865i	−0.0709819	−	0.0562724i
$52$	−3.03312	+	1.94941i	−0.420618	+	0.270334i
$53$	2.82305	−	1.62989i	0.387776	−	0.223882i	−0.293420	−	0.955984i	$-0.594794\pi$
$53$	2.82305	−	1.62989i	0.387776	−	0.223882i	0.681196	+	0.732101i	$0.261460\pi$
$54$	0.921857	−	5.11372i	0.125449	−	0.695890i
$55$	−1.46854			−0.198018
$56$	−1.25937	+	2.32680i	−0.168291	+	0.310931i
$57$	2.98183	+	4.01597i	0.394954	+	0.531929i
$58$	0.150783	+	0.562729i	0.0197988	+	0.0738899i
$59$	−6.22585	−	1.66821i	−0.810537	−	0.217183i	−0.170332	−	0.985387i	$-0.554484\pi$
$59$	−6.22585	−	1.66821i	−0.810537	−	0.217183i	−0.640205	+	0.768204i	$0.721151\pi$
$60$	2.05263	−	4.74190i	0.264993	−	0.612176i
$61$	3.77475	−	6.53807i	0.483308	−	0.837114i	−0.516508	−	0.856282i	$-0.672769\pi$
$61$	3.77475	−	6.53807i	0.483308	−	0.837114i	0.999816	+	0.0191684i	$0.00610187\pi$
$62$	5.05407			0.641867
$63$	−3.99703	+	6.85739i	−0.503578	+	0.863950i
$64$		−	1.00000i		−	0.125000i
$65$	−10.2453	+	3.27544i	−1.27078	+	0.406269i
$66$	−0.792792	+	0.313787i	−0.0975860	+	0.0386245i
$67$	2.82615	+	0.757263i	0.345269	+	0.0925144i	0.427286	−	0.904116i	$-0.359470\pi$
$67$	2.82615	+	0.757263i	0.345269	+	0.0925144i	−0.0820176	+	0.996631i	$0.526136\pi$
$68$	−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	$-0.274284\pi$
$71$	−0.908221	−	0.908221i	−0.107786	−	0.107786i	−0.758943	+	0.651157i	$0.774284\pi$
$72$	0.0948959	−	2.99850i	0.0111836	−	0.353376i
$73$	0.884917	−	3.30256i	0.103572	−	0.386535i	−0.894608	−	0.446853i	$-0.852545\pi$
$73$	0.884917	−	3.30256i	0.103572	−	0.386535i	0.998179	+	0.0603179i	$0.0192114\pi$
$74$	−2.45827	+	1.41928i	−0.285768	+	0.164988i
$75$	4.19603	−	5.29287i	0.484516	−	0.611168i
$76$	2.04203	+	2.04203i	0.234237	+	0.234237i
$77$	1.30192	−	0.0358127i	0.148368	−	0.00408123i
$78$	−4.83106	+	3.95739i	−0.547009	+	0.448086i
$79$	5.68471	−	9.84621i	0.639580	−	1.10779i	−0.345945	−	0.938255i	$-0.612442\pi$
$79$	5.68471	−	9.84621i	0.639580	−	1.10779i	0.985525	−	0.169530i	$-0.0542251\pi$
$80$	0.772115	−	2.88157i	0.0863251	−	0.322170i
$81$	0.569090	−	8.98199i	0.0632323	−	0.997999i
$82$	−8.10152	−	4.67742i	−0.894664	−	0.516534i
$83$	9.25218	+	9.25218i	1.01556	+	1.01556i	0.999877	+	0.0156815i	$0.00499178\pi$
$83$	9.25218	+	9.25218i	1.01556	+	1.01556i	0.0156815	+	0.999877i	$0.495008\pi$
$84$	−1.70410	+	4.25394i	−0.185932	+	0.464143i
$85$	−0.787834	−	0.787834i	−0.0854526	−	0.0854526i
$86$	−0.689092	−	2.57173i	−0.0743067	−	0.277316i
$87$	0.371355	+	0.938240i	0.0398135	+	0.100590i
$88$	−0.426316	+	0.246134i	−0.0454454	+	0.0262379i
$89$	−0.844833	−	3.15296i	−0.0895521	−	0.334213i	0.906585	−	0.422023i	$-0.138680\pi$
$89$	−0.844833	−	3.15296i	−0.0895521	−	0.334213i	−0.996137	+	0.0878099i	$0.972013\pi$
$90$	2.58864	−	8.56712i	0.272866	−	0.903054i
$91$	9.00302	−	3.15366i	0.943773	−	0.330594i
$92$			7.97637i			0.831594i
$93$	8.69600	−	1.00519i	0.901733	−	0.104233i
$94$	6.61822	+	11.4631i	0.682618	+	1.18233i
$95$	4.30758	+	7.46095i	0.441948	+	0.765477i
$96$	−0.198887	−	1.72059i	−0.0202988	−	0.175607i
$97$	−12.1530	+	12.1530i	−1.23395	+	1.23395i	−0.271521	+	0.962433i	$0.587527\pi$
$97$	−12.1530	+	12.1530i	−1.23395	+	1.23395i	−0.962433	+	0.271521i	$0.912473\pi$
$98$	4.67016	−	5.21437i	0.471757	−	0.526731i
$99$	−1.30167	+	0.697576i	−0.130822	+	0.0701090i
$100$	1.94981	−	3.37717i	0.194981	−	0.337717i
$101$	5.60907	+	9.71519i	0.558123	+	0.966698i	0.997653	+	0.0684698i	$0.0218117\pi$
$101$	5.60907	+	9.71519i	0.558123	+	0.966698i	−0.439530	+	0.898228i	$0.644855\pi$
$102$	−0.593650	−	0.256973i	−0.0587801	−	0.0254442i
$103$	−2.83222	−	1.63518i	−0.279067	−	0.161119i	0.353934	−	0.935270i	$-0.384844\pi$
$103$	−2.83222	−	1.63518i	−0.279067	−	0.161119i	−0.633001	+	0.774151i	$0.718177\pi$
$104$	−2.42522	+	2.66801i	−0.237813	+	0.261620i
$105$	−8.19502	+	10.9423i	−0.799752	+	1.06786i
$106$	2.30501	−	2.30501i	0.223882	−	0.223882i
$107$	−13.9686	−	8.06480i	−1.35040	−	0.779653i	−0.362094	−	0.932142i	$-0.617938\pi$
$107$	−13.9686	−	8.06480i	−1.35040	−	0.779653i	−0.988305	+	0.152488i	$0.951271\pi$
$108$	−0.433084	−	5.17807i	−0.0416735	−	0.498260i
$109$	−11.9725	−	3.20802i	−1.14676	−	0.307273i	−0.365093	−	0.930971i	$-0.618963\pi$
$109$	−11.9725	−	3.20802i	−1.14676	−	0.307273i	−0.781665	+	0.623698i	$0.785629\pi$
$110$	−1.41850	+	0.380087i	−0.135249	+	0.0362399i
$111$	−3.94741	+	2.93092i	−0.374671	+	0.278191i
$112$	−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	$-0.0866564\pi$
$114$	3.91964	+	3.10738i	0.367108	+	0.291032i
$115$	−6.15867	+	22.9845i	−0.574299	+	2.14331i
$116$	0.291290	+	0.504529i	0.0270456	+	0.0468443i
$117$	−7.52521	+	7.76989i	−0.695706	+	0.718326i
$118$	−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
$123$	−14.8697	−	6.43665i	−1.34076	−	0.580373i
$124$	4.88185	−	1.30809i	0.438403	−	0.117470i
$125$	−2.32120	+	2.32120i	−0.207615	+	0.207615i
$126$	−2.08601	+	7.65823i	−0.185837	+	0.682250i
$127$		−	2.92468i		−	0.259523i	−0.991545	−	0.129762i	$-0.958579\pi$
$127$		−	2.92468i		−	0.259523i	0.991545	−	0.129762i	$-0.0414212\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−1.69713	−	4.28784i	−0.149424	−	0.377524i
$130$	−9.04847	+	5.81552i	−0.793603	+	0.510055i
$131$	15.5403	+	8.97222i	1.35777	+	0.783906i	0.989322	−	0.145744i	$-0.0465577\pi$
$131$	15.5403	+	8.97222i	1.35777	+	0.783906i	0.368443	+	0.929650i	$0.379891\pi$
$132$	−0.684564	+	0.508285i	−0.0595837	+	0.0442405i
$133$	−4.00079	−	6.50939i	−0.346913	−	0.564436i
$134$	2.92584			0.252754
$135$	2.75010	−	15.2554i	0.236691	−	1.31297i
$136$	−0.360751	−	0.0966630i	−0.0309342	−	0.00828879i
$137$	9.18646	+	2.46150i	0.784852	+	0.210301i	0.628923	−	0.777468i	$-0.283496\pi$
$137$	9.18646	+	2.46150i	0.784852	+	0.210301i	0.155929	+	0.987768i	$0.450163\pi$
$138$	1.58639	+	13.7241i	0.135043	+	1.16827i
$139$	−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
$141$	13.6671	+	18.4071i	1.15098	+	1.55015i
$142$	−1.11234	−	0.642209i	−0.0933454	−	0.0538930i
$143$	1.73435	+	0.377224i	0.145033	+	0.0315451i
$144$	−0.684406	−	2.92089i	−0.0570339	−	0.243407i
$145$	0.449819	+	1.67875i	0.0373554	+	0.139412i
$146$		−	3.41906i		−	0.282963i
$147$	6.99838	−	9.90064i	0.577217	−	0.816591i
$148$	−2.00717	+	2.00717i	−0.164988	+	0.164988i
$149$	−3.79524	+	1.01693i	−0.310919	+	0.0833104i	−0.410904	−	0.911679i	$-0.634787\pi$
$149$	−3.79524	+	1.01693i	−0.310919	+	0.0833104i	0.0999857	+	0.994989i	$0.468120\pi$
$150$	2.68316	−	6.19853i	0.219079	−	0.506108i
$151$	2.58226	−	9.63711i	0.210141	−	0.784257i	−0.777680	−	0.628661i	$-0.783603\pi$
$151$	2.58226	−	9.63711i	0.210141	−	0.784257i	0.987821	−	0.155596i	$-0.0497299\pi$
$152$	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
$156$	−3.64219	+	5.07291i	−0.291609	+	0.406158i
$157$	10.7467	+	18.6139i	0.857682	+	1.48555i	0.874135	+	0.485684i	$0.161429\pi$
$157$	10.7467	+	18.6139i	0.857682	+	1.48555i	−0.0164529	+	0.999865i	$0.505237\pi$
$158$	2.94262	−	10.9820i	0.234103	−	0.873683i
$159$	3.50755	−	4.42442i	0.278167	−	0.350879i
$160$		−	2.98322i		−	0.235845i
$161$	4.89941	−	20.5269i	0.386127	−	1.61774i
$162$	−1.77501	−	8.82323i	−0.139458	−	0.693218i
$163$	18.4238	−	4.93665i	1.44306	−	0.386668i	0.549459	−	0.835521i	$-0.314834\pi$
$163$	18.4238	−	4.93665i	1.44306	−	0.386668i	0.893606	+	0.448853i	$0.148167\pi$
$164$	−9.03608	−	2.42121i	−0.705599	−	0.189065i
$165$	−2.36508	+	0.936097i	−0.184121	+	0.0728751i
$166$	11.3316	+	6.54228i	0.879500	+	0.507779i
$167$	−9.06640	+	9.06640i	−0.701579	+	0.701579i	−0.964749	−	0.263170i	$-0.915232\pi$
$167$	−9.06640	+	9.06640i	−0.701579	+	0.701579i	0.263170	+	0.964749i	$0.415232\pi$
$168$	−0.545031	+	4.55005i	−0.0420501	+	0.351044i
$169$	12.9411	−	1.23658i	0.995466	−	0.0951214i
$170$	−0.964896	−	0.557083i	−0.0740042	−	0.0427263i
$171$	7.36213	+	4.56697i	0.562996	+	0.349245i
$172$	−1.33122	−	2.30575i	−0.101505	−	0.175811i
$173$	−1.85430	+	3.21173i	−0.140979	+	0.244184i	−0.927866	−	0.372914i	$-0.878358\pi$
$173$	−1.85430	+	3.21173i	−0.140979	+	0.244184i	0.786886	+	0.617098i	$0.211692\pi$
$174$	0.601536	+	0.810156i	0.0456023	+	0.0614178i
$175$	−7.09216	+	7.49337i	−0.536117	+	0.566445i
$176$	−0.348086	+	0.348086i	−0.0262379	+	0.0262379i
$177$	−11.0901	+	1.28192i	−0.833579	+	0.0963549i
$178$	−1.63209	−	2.82687i	−0.122330	−	0.211883i
$179$	−5.97819	−	10.3545i	−0.446831	−	0.773934i	0.551347	−	0.834276i	$-0.314114\pi$
$179$	−5.97819	−	10.3545i	−0.446831	−	0.773934i	−0.998178	+	0.0603419i	$0.980781\pi$
$180$	0.283096	−	8.94519i	0.0211007	−	0.666735i
$181$		−	5.55672i		−	0.413028i	−0.978444	−	0.206514i	$-0.933788\pi$
$181$		−	5.55672i		−	0.413028i	0.978444	−	0.206514i	$-0.0662118\pi$
$182$	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
$186$	8.13953	−	3.22163i	0.596819	−	0.236221i
$187$	0.0475841	+	0.177586i	0.00347969	+	0.0129864i
$188$	9.35958	+	9.35958i	0.682618	+	0.682618i
$189$	−2.06606	+	13.5916i	−0.150283	+	0.988643i
$190$	6.09184	+	6.09184i	0.441948	+	0.441948i
$191$	−6.96646	−	4.02209i	−0.504076	−	0.291028i	0.226319	−	0.974053i	$-0.427331\pi$
$191$	−6.96646	−	4.02209i	−0.504076	−	0.291028i	−0.730395	+	0.683025i	$0.760664\pi$
$192$	−0.637432	−	1.61049i	−0.0460027	−	0.116227i
$193$	1.74782	−	6.52296i	0.125811	−	0.469533i	−0.874056	−	0.485825i	$-0.838519\pi$
$193$	1.74782	−	6.52296i	0.125811	−	0.469533i	0.999867	+	0.0162916i	$0.00518601\pi$
$194$	−8.59349	+	14.8844i	−0.616977	+	1.06864i
$195$	−14.4121	+	11.8058i	−1.03207	+	0.845428i
$196$	3.16145	−	6.24542i	0.225818	−	0.446101i
$197$	−9.55202	−	9.55202i	−0.680553	−	0.680553i	0.279572	−	0.960125i	$-0.409807\pi$
$197$	−9.55202	−	9.55202i	−0.680553	−	0.680553i	−0.960125	+	0.279572i	$0.909807\pi$
$198$	−1.07677	+	1.01070i	−0.0765224	+	0.0718275i
$199$	17.2076	−	9.93481i	1.21981	−	0.704260i	0.254936	−	0.966958i	$-0.417946\pi$
$199$	17.2076	−	9.93481i	1.21981	−	0.704260i	0.964878	+	0.262698i	$0.0846122\pi$
$200$	1.00930	−	3.76674i	0.0713680	−	0.266349i
$201$	5.03418	−	0.581911i	0.355084	−	0.0410448i
$202$	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
$207$	5.45907	+	23.2981i	0.379432	+	1.61933i
$208$	−1.65205	+	3.20480i	−0.114549	+	0.222213i
$209$		−	1.42160i		−	0.0983344i
$210$	−5.08371	+	12.6905i	−0.350809	+	0.875725i
$211$	−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
$213$	−2.04161	−	0.883752i	−0.139889	−	0.0605537i
$214$	−15.5800	−	4.17465i	−1.06503	−	0.285373i
$215$	−2.05571	−	7.67203i	−0.140199	−	0.523228i
$216$	−1.75851	−	4.88954i	−0.119652	−	0.332691i
$217$	−13.3667	+	0.367686i	−0.907394	+	0.0249601i
$218$	−12.3948			−0.839485
$219$	−0.680005	−	5.88281i	−0.0459505	−	0.397523i
$220$	−1.27180	+	0.734272i	−0.0857445	+	0.0495046i
$221$	0.728060	+	1.13280i	0.0489746	+	0.0762004i
$222$	−3.05432	+	3.85272i	−0.204993	+	0.258578i
$223$	13.2899	−	13.2899i	0.889959	−	0.889959i	−0.104560	−	0.994519i	$-0.533343\pi$
$223$	13.2899	−	13.2899i	0.889959	−	0.889959i	0.994519	+	0.104560i	$0.0333433\pi$
$224$	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	0.0259251	+	0.999664i	$0.491747\pi$
$227$	−7.47840	+	27.9098i	−0.496359	+	1.85244i	−0.522284	+	0.852772i	$0.674920\pi$
$228$	4.59033	+	1.98702i	0.304002	+	0.131593i
$229$	6.41225	−	1.71816i	0.423733	−	0.113539i	−0.0406498	−	0.999173i	$-0.512943\pi$
$229$	6.41225	−	1.71816i	0.423733	−	0.113539i	0.464383	+	0.885634i	$0.346276\pi$
$230$			23.7953i			1.56901i
$231$	2.07391	−	0.887565i	0.136453	−	0.0583975i
$232$	0.411946	+	0.411946i	0.0270456	+	0.0270456i
$233$	1.10978	−	1.92220i	0.0727044	−	0.125928i	−0.827381	−	0.561641i	$-0.810170\pi$
$233$	1.10978	−	1.92220i	0.0727044	−	0.125928i	0.900086	+	0.435713i	$0.143504\pi$
$234$	−5.25780	+	9.45280i	−0.343713	+	0.617949i
$235$	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	$-0.113327\pi$
$239$	9.10161	+	9.10161i	0.588734	+	0.588734i	−0.348554	+	0.937289i	$0.613327\pi$
$240$	−0.593323	−	5.13292i	−0.0382988	−	0.331328i
$241$	2.55818	−	9.54727i	0.164787	−	0.614993i	−0.833280	−	0.552851i	$-0.813540\pi$
$241$	2.55818	−	9.54727i	0.164787	−	0.614993i	0.998067	−	0.0621427i	$-0.0197934\pi$
$242$	−10.3911	−	2.78429i	−0.667966	−	0.178981i
$243$	−4.80890	−	14.8282i	−0.308491	−	0.951227i
$244$		−	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
$249$	20.7982	+	9.00291i	1.31803	+	0.570536i
$250$	−1.64134	+	2.84288i	−0.103807	+	0.179800i
$251$	−14.8766			−0.939002			−0.469501	−	0.882932i	$-0.655566\pi$
$251$	−14.8766			−0.939002			−0.469501	+	0.882932i	$0.655566\pi$
$252$	−0.0328339	+	7.93719i	−0.00206834	+	0.499996i
$253$	2.77646	−	2.77646i	0.174554	−	0.174554i
$254$	−0.756962	−	2.82502i	−0.0474960	−	0.177258i
$255$	−1.77099	−	0.766609i	−0.110904	−	0.0480069i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.5193	−	25.1481i	0.905688	−	1.56870i	0.0856980	−	0.996321i	$-0.472688\pi$
$257$	14.5193	−	25.1481i	0.905688	−	1.56870i	0.819990	−	0.572377i	$-0.193979\pi$
$258$	−2.74908	−	3.70249i	−0.171150	−	0.230507i
$259$	6.39825	−	3.93249i	0.397568	−	0.244353i
$260$	−7.23498	+	7.95928i	−0.448695	+	0.493613i
$261$	1.19613	+	1.27431i	0.0740385	+	0.0788780i
$262$	17.3330	+	4.64436i	1.07084	+	0.286930i
$263$	−16.0895	+	9.28926i	−0.992119	+	0.572800i	−0.905907	−	0.423476i	$-0.860810\pi$
$263$	−16.0895	+	9.28926i	−0.992119	+	0.572800i	−0.0862123	+	0.996277i	$0.527476\pi$
$264$	−0.529685	+	0.668144i	−0.0325998	+	0.0411214i
$265$	6.87636	−	6.87636i	0.422411	−	0.422411i
$266$	−5.54922	−	5.25211i	−0.340245	−	0.322027i
$267$	−3.37039	−	4.53929i	−0.206265	−	0.277800i
$268$	2.82615	−	0.757263i	0.172634	−	0.0462572i
$269$	7.03347	−	4.06078i	0.428838	−	0.247590i	−0.270013	−	0.962857i	$-0.587028\pi$
$269$	7.03347	−	4.06078i	0.428838	−	0.247590i	0.698852	+	0.715267i	$0.253695\pi$
$270$	−1.29199	−	15.4473i	−0.0786278	−	0.940096i
$271$	−23.8896	+	6.40120i	−1.45119	+	0.388845i	−0.896438	−	0.443170i	$-0.853854\pi$
$271$	−23.8896	+	6.40120i	−1.45119	+	0.388845i	−0.554753	+	0.832015i	$0.687187\pi$
$272$	−0.373477			−0.0226454
$273$	12.4890	−	10.8178i	0.755871	−	0.654721i
$274$	9.51052			0.574552
$275$	−1.85425	+	0.496844i	−0.111815	+	0.0299608i
$276$	5.08439	+	12.8459i	0.306044	+	0.773230i
$277$	12.4480	−	7.18686i	0.747929	−	0.431817i	−0.0770163	−	0.997030i	$-0.524539\pi$
$277$	12.4480	−	7.18686i	0.747929	−	0.431817i	0.824945	+	0.565213i	$0.191206\pi$
$278$	−20.6534	+	5.53407i	−1.23871	+	0.331911i
$279$	13.3641	−	7.16195i	0.800087	−	0.428775i
$280$	−1.83242	+	7.67721i	−0.109508	+	0.458801i
$281$	6.19288	−	6.19288i	0.369436	−	0.369436i	−0.497835	−	0.867272i	$-0.665872\pi$
$281$	6.19288	−	6.19288i	0.369436	−	0.369436i	0.867272	+	0.497835i	$0.165872\pi$
$282$	17.9655	+	14.2425i	1.06983	+	0.848131i
$283$	21.4880	−	12.4061i	1.27733	−	0.737466i	0.300972	−	0.953633i	$-0.402689\pi$
$283$	21.4880	−	12.4061i	1.27733	−	0.737466i	0.976356	+	0.216168i	$0.0693557\pi$
$284$	−1.24065	−	0.332432i	−0.0736192	−	0.0197262i
$285$	11.6932	+	9.26999i	0.692643	+	0.549107i
$286$	1.77288	−	0.0845112i	0.104833	−	0.00499725i
$287$	21.7668	+	11.7812i	1.28485	+	0.695423i
$288$	−1.41707	−	2.64422i	−0.0835015	−	0.155812i
$289$	8.43026	−	14.6016i	0.495897	−	0.858920i
$290$	0.868983	+	1.50512i	0.0510284	+	0.0883839i
$291$	−11.8256	+	27.3191i	−0.693230	+	1.60147i
$292$	−0.884917	−	3.30256i	−0.0517859	−	0.193267i
$293$	0.941281	−	0.941281i	0.0549902	−	0.0549902i	−0.679077	−	0.734067i	$-0.737620\pi$
$293$	0.941281	−	0.941281i	0.0549902	−	0.0549902i	0.734067	+	0.679077i	$0.237620\pi$
$294$	4.19744	−	11.3746i	0.244800	−	0.663380i
$295$	−19.2283			−1.11951
$296$	−1.41928	+	2.45827i	−0.0824941	+	0.142884i
$297$	−1.65166	+	1.95316i	−0.0958392	+	0.113334i
$298$	−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
$303$	15.2261	+	12.0708i	0.874718	+	0.693451i
$304$	2.78947	+	0.747436i	0.159987	+	0.0428684i
$305$	5.82909	−	21.7545i	0.333773	−	1.24566i
$306$	−1.11987	−	0.0354415i	−0.0640188	−	0.00202605i
$307$	1.18905	+	1.18905i	0.0678629	+	0.0678629i	0.740224	−	0.672361i	$-0.234720\pi$
$307$	1.18905	+	1.18905i	0.0678629	+	0.0678629i	−0.672361	+	0.740224i	$0.734720\pi$
$308$	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	$-0.144111\pi$
$311$	1.24862	+	2.16267i	0.0708026	+	0.122634i	−0.828451	+	0.560062i	$0.810777\pi$
$312$	−2.20512	+	5.84272i	−0.124841	+	0.330779i
$313$	15.5022	−	26.8507i	0.876239	−	1.51769i	0.0208011	−	0.999784i	$-0.493378\pi$
$313$	15.5022	−	26.8507i	0.876239	−	1.51769i	0.855437	−	0.517906i	$-0.173288\pi$
$314$	15.1982	+	15.1982i	0.857682	+	0.857682i
$315$	−6.22303	+	22.8462i	−0.350628	+	1.28724i
$316$		−	11.3694i		−	0.639580i
$317$	18.4389	−	4.94069i	1.03563	−	0.277497i	0.299330	−	0.954150i	$-0.403237\pi$
$317$	18.4389	−	4.94069i	1.03563	−	0.277497i	0.736303	+	0.676653i	$0.236570\pi$
$318$	2.24291	−	5.18148i	0.125776	−	0.290563i
$319$	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
$324$	−3.99815	−	8.06318i	−0.222119	−	0.447954i
$325$	−11.8280	+	7.60195i	−0.656100	+	0.421680i
$326$	16.5183	−	9.53687i	0.914867	−	0.528198i
$327$	−21.3265	+	2.46517i	−1.17936	+	0.136324i
$328$	−9.35483			−0.516534
$329$	−18.3375	−	29.8356i	−1.01098	−	1.64489i
$330$	−2.04221	+	1.51633i	−0.112420	+	0.0834710i
$331$	3.78955	+	14.1428i	0.208293	+	0.777359i	0.988421	+	0.151739i	$0.0484873\pi$
$331$	3.78955	+	14.1428i	0.208293	+	0.777359i	−0.780128	+	0.625620i	$0.784846\pi$
$332$	12.6387	+	3.38653i	0.693639	+	0.185860i
$333$	−4.48899	+	7.23643i	−0.245995	+	0.396554i
$334$	−6.41091	+	11.1040i	−0.350790	+	0.607585i
$335$	8.72844			0.476885
$336$	0.651179	+	4.53607i	0.0355248	+	0.247463i
$337$		−	17.4950i		−	0.953013i	−0.879171	−	0.476507i	$-0.841903\pi$
$337$		−	17.4950i		−	0.953013i	0.879171	−	0.476507i	$-0.158097\pi$
$338$	12.1800	−	4.54383i	0.662507	−	0.247152i
$339$	−3.64398	−	9.20662i	−0.197914	−	0.500035i
$340$	−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
$345$	4.73256	+	40.9420i	0.254793	+	2.20424i
$346$	−0.959854	+	3.58222i	−0.0516021	+	0.192582i
$347$	12.4022	−	7.16039i	0.665782	−	0.384390i	−0.128694	−	0.991684i	$-0.541079\pi$
$347$	12.4022	−	7.16039i	0.665782	−	0.384390i	0.794477	+	0.607295i	$0.207745\pi$
$348$	0.790723	+	0.626862i	0.0423872	+	0.0336033i
$349$	15.1284	+	15.1284i	0.809803	+	0.809803i	0.984604	−	0.174801i	$-0.0559282\pi$
$349$	15.1284	+	15.1284i	0.809803	+	0.809803i	−0.174801	+	0.984604i	$0.555928\pi$
$350$	−4.91107	+	9.07362i	−0.262508	+	0.485006i
$351$	−7.16651	+	17.3101i	−0.382520	+	0.923947i
$352$	−0.246134	+	0.426316i	−0.0131190	+	0.0227227i
$353$	0.442166	−	1.65019i	0.0235341	−	0.0878306i	−0.953160	−	0.302467i	$-0.902190\pi$
$353$	0.442166	−	1.65019i	0.0235341	−	0.0878306i	0.976694	+	0.214636i	$0.0688566\pi$
$354$	−10.3804	+	4.10855i	−0.551711	+	0.218367i
$355$	−3.31835	−	1.91585i	−0.176120	−	0.101683i
$356$	−2.30813	−	2.30813i	−0.122330	−	0.122330i
$357$	1.58875	+	0.636442i	0.0840857	+	0.0336841i
$358$	−8.45444	−	8.45444i	−0.446831	−	0.446831i
$359$	−3.59997	−	13.4353i	−0.189999	−	0.709087i	−0.993505	−	0.113790i	$-0.963701\pi$
$359$	−3.59997	−	13.4353i	−0.189999	−	0.709087i	0.803506	−	0.595297i	$-0.202966\pi$
$360$	−2.04174	−	8.71366i	−0.107609	−	0.459250i
$361$	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
$366$	−1.50150	−	12.9896i	−0.0784845	−	0.678979i
$367$	13.9526	+	24.1666i	0.728319	+	1.26148i	0.957593	+	0.288123i	$0.0930312\pi$
$367$	13.9526	+	24.1666i	0.728319	+	1.26148i	−0.229275	+	0.973362i	$0.573635\pi$
$368$	3.98818	+	6.90774i	0.207898	+	0.360091i
$369$	−28.0505	−	0.887735i	−1.46025	−	0.0462136i
$370$	−5.98783	+	5.98783i	−0.311292	+	0.311292i
$371$	−5.92849	+	6.26387i	−0.307792	+	0.325204i
$372$	7.02836	−	5.21852i	0.364404	−	0.270567i
$373$	12.3242	−	21.3461i	0.638122	−	1.10526i	−0.347722	−	0.937598i	$-0.613045\pi$
$373$	12.3242	−	21.3461i	0.638122	−	1.10526i	0.985844	−	0.167662i	$-0.0536218\pi$
$374$	0.0919254	+	0.159219i	0.00475335	+	0.00823304i
$375$	−2.25867	+	5.21789i	−0.116637	+	0.269451i
$376$	11.4631	+	6.61822i	0.591164	+	0.341309i
$377$	−0.100016	−	2.09814i	−0.00515107	−	0.108060i
$378$	1.52211	+	13.6632i	0.0782887	+	0.702759i
$379$	−5.55621	+	5.55621i	−0.285403	+	0.285403i	−0.835259	−	0.549856i	$-0.814682\pi$
$379$	−5.55621	+	5.55621i	−0.285403	+	0.285403i	0.549856	+	0.835259i	$0.314682\pi$
$380$	7.46095	+	4.30758i	0.382738	+	0.220974i
$381$	−1.86428	−	4.71016i	−0.0955101	−	0.241309i
$382$	−7.77008	−	2.08199i	−0.397552	−	0.106524i
$383$	−10.6284	+	2.84788i	−0.543087	+	0.145520i	−0.519925	−	0.854212i	$-0.674040\pi$
$383$	−10.6284	+	2.84788i	−0.543087	+	0.145520i	−0.0231622	+	0.999732i	$0.507373\pi$
$384$	−1.03254	−	1.39063i	−0.0526915	−	0.0709655i
$385$	3.72394	−	1.10843i	0.189789	−	0.0564909i
$386$		−	6.75307i		−	0.343722i
$387$	−5.46642	−	5.82373i	−0.277874	−	0.296037i
$388$	−4.44832	+	16.6014i	−0.225829	+	0.842806i
$389$	2.28311	+	3.95446i	0.115758	+	0.200499i	0.918083	−	0.396389i	$-0.129737\pi$
$389$	2.28311	+	3.95446i	0.115758	+	0.200499i	−0.802324	+	0.596888i	$0.796404\pi$
$390$	−10.8655	+	15.1336i	−0.550195	+	0.766321i
$391$	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
$396$	−0.778487	+	1.25495i	−0.0391205	+	0.0630637i
$397$	−15.0698	+	4.03794i	−0.756331	+	0.202658i	−0.616325	−	0.787492i	$-0.711379\pi$
$397$	−15.0698	+	4.03794i	−0.756331	+	0.202658i	−0.140007	+	0.990151i	$0.544712\pi$
$398$	14.0499	−	14.0499i	0.704260	−	0.704260i
$399$	−10.5925	−	7.93308i	−0.530290	−	0.397151i
$400$		−	3.89962i		−	0.194981i
$401$	5.19661	+	19.3940i	0.259506	+	0.968491i	0.965528	+	0.260300i	$0.0838216\pi$
$401$	5.19661	+	19.3940i	0.259506	+	0.968491i	−0.706021	+	0.708191i	$0.749512\pi$
$402$	4.71204	−	1.86503i	0.235015	−	0.0930190i
$403$	−17.8064	−	3.87293i	−0.886999	−	0.192924i
$404$	9.71519	+	5.60907i	0.483349	+	0.279062i
$405$	−5.29525	−	26.3217i	−0.263123	−	1.30793i
$406$	−0.807094	−	1.31316i	−0.0400554	−	0.0651711i
$407$	1.39733			0.0692632
$408$	−0.642603	+	0.0742796i	−0.0318136	+	0.00367739i
$409$	−21.8252	−	5.84805i	−1.07919	−	0.289167i	−0.324925	−	0.945740i	$-0.605339\pi$
$409$	−21.8252	−	5.84805i	−1.07919	−	0.289167i	−0.754263	+	0.656572i	$0.772006\pi$
$410$	−26.9566	−	7.22301i	−1.33129	−	0.356719i
$411$	16.3637	−	1.89152i	0.807164	−	0.0933016i
$412$	−3.27037			−0.161119
$413$	17.0467	−	0.468911i	0.838812	−	0.0230736i
$414$	11.3030	+	21.0913i	0.555514	+	1.03658i
$415$	33.8046	+	19.5171i	1.65940	+	0.958056i
$416$	−0.766299	+	3.52318i	−0.0375709	+	0.172738i
$417$	−34.4355	+	13.6296i	−1.68631	+	0.667443i
$418$	−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	$0.983404\pi$
$420$	−1.62595	+	13.5738i	−0.0793382	+	0.662334i
$421$	−27.5364	+	27.5364i	−1.34204	+	1.34204i	−0.448021	+	0.894023i	$0.647871\pi$
$421$	−27.5364	+	27.5364i	−1.34204	+	1.34204i	−0.894023	+	0.448021i	$0.852129\pi$
$422$	−7.83411	+	2.09914i	−0.381359	+	0.102185i
$423$	33.7441	+	20.9325i	1.64069	+	1.01777i
$424$	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
$429$	3.03360	−	0.498012i	0.146464	−	0.0240442i
$430$	−3.97134	−	6.87855i	−0.191515	−	0.331713i
$431$	−1.82189	+	6.79937i	−0.0877572	+	0.327514i	−0.995822	−	0.0913153i	$-0.970893\pi$
$431$	−1.82189	+	6.79937i	−0.0877572	+	0.327514i	0.908065	+	0.418830i	$0.137560\pi$
$432$	−2.96410	−	4.26780i	−0.142610	−	0.205335i
$433$			4.80709i			0.231014i	0.993307	+	0.115507i	$0.0368493\pi$
$433$			4.80709i			0.231014i	−0.993307	+	0.115507i	$0.963151\pi$
$434$	−12.8161	+	3.81473i	−0.615194	+	0.183113i
$435$	1.79452	+	2.41688i	0.0860405	+	0.115880i
$436$	−11.9725	+	3.20802i	−0.573379	+	0.153636i
$437$	−22.2498	−	5.96182i	−1.06435	−	0.285193i
$438$	−2.17942	−	5.50636i	−0.104137	−	0.263104i
$439$	−17.8083	−	10.2816i	−0.849942	−	0.490715i	0.0106890	−	0.999943i	$-0.496598\pi$
$439$	−17.8083	−	10.2816i	−0.849942	−	0.490715i	−0.860631	+	0.509228i	$0.829931\pi$
$440$	−1.03842	+	1.03842i	−0.0495046	+	0.0495046i
$441$	4.95984	−	20.4059i	0.236183	−	0.971709i
$442$	0.996442	+	0.905766i	0.0473959	+	0.0430829i
$443$	−14.5938	−	8.42571i	−0.693370	−	0.400318i	0.111503	−	0.993764i	$-0.464434\pi$
$443$	−14.5938	−	8.42571i	−0.693370	−	0.400318i	−0.804873	+	0.593446i	$0.797767\pi$
$444$	−1.95309	+	4.51196i	−0.0926896	+	0.214128i
$445$	−4.86890	−	8.43317i	−0.230808	−	0.399771i
$446$	9.39739	−	16.2768i	0.444980	−	0.770727i
$447$	−5.46398	+	4.05697i	−0.258437	+	0.191888i
$448$	0.754783	+	2.53580i	0.0356602	+	0.119805i
$449$	−19.6778	+	19.6778i	−0.928651	+	0.928651i	−0.997619	−	0.0689678i	$-0.978029\pi$
$449$	−19.6778	+	19.6778i	−0.928651	+	0.928651i	0.0689678	+	0.997619i	$0.478029\pi$
$450$	0.370058	−	11.6930i	0.0174447	−	0.551214i
$451$	2.30254	+	3.98812i	0.108422	+	0.187793i
$452$	−2.85833	−	4.95077i	−0.134444	−	0.232865i
$453$	−1.98431	−	17.1665i	−0.0932308	−	0.806552i
$454$			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	0.659516	+	0.751691i	$0.270761\pi$
$457$	9.92354	+	37.0352i	0.464204	+	1.73243i	−0.195312	+	0.980741i	$0.562572\pi$
$458$	5.74906	−	3.31922i	0.268636	−	0.155097i
$459$	−1.93389	+	0.161747i	−0.0902664	+	0.00754970i
$460$	6.15867	+	22.9845i	0.287150	+	1.07166i
$461$	17.5692	+	17.5692i	0.818281	+	0.818281i	0.985859	−	0.167578i	$-0.0535947\pi$
$461$	17.5692	+	17.5692i	0.818281	+	0.818281i	−0.167578	+	0.985859i	$0.553595\pi$
$462$	1.77352	−	1.39409i	0.0825118	−	0.0648589i
$463$	−24.8187	−	24.8187i	−1.15342	−	1.15342i	−0.985861	−	0.167563i	$-0.946410\pi$
$463$	−24.8187	−	24.8187i	−1.15342	−	1.15342i	−0.167563	−	0.985861i	$-0.553590\pi$
$464$	0.504529	+	0.291290i	0.0234222	+	0.0135228i
$465$	24.2820	−	9.61083i	1.12605	−	0.445691i
$466$	0.574466	−	2.14394i	0.0266116	−	0.0993160i
$467$	7.40191	−	12.8205i	0.342520	−	0.593262i	−0.642380	−	0.766386i	$-0.722053\pi$
$467$	7.40191	−	12.8205i	0.342520	−	0.593262i	0.984900	+	0.173125i	$0.0553863\pi$
$468$	−2.63208	+	10.4915i	−0.121668	+	0.484971i
$469$	−7.73812	+	0.212856i	−0.357313	+	0.00982878i
$470$	27.9217	+	27.9217i	1.28793	+	1.28793i
$471$	29.1726	+	23.1272i	1.34420	+	1.06564i
$472$	−5.58195	+	3.22274i	−0.256930	+	0.148339i
$473$	−0.339217	+	1.26598i	−0.0155972	+	0.0582097i
$474$	−2.26123	−	19.5622i	−0.103862	−	0.898520i
$475$	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	$-0.148157\pi$
$479$	31.5839	+	8.46289i	1.44311	+	0.386679i	0.549487	+	0.835502i	$0.314823\pi$
$480$	−1.90160	−	4.80445i	−0.0867959	−	0.219292i
$481$	9.74851	−	3.11661i	0.444494	−	0.142105i
$482$		−	9.88406i		−	0.450206i
$483$	−5.19405	−	36.1814i	−0.236337	−	1.64631i
$484$	−10.7577			−0.488985
$485$	−25.6363	+	44.4034i	−1.16408	+	2.01625i
$486$	−8.48285	−	13.0783i	−0.384790	−	0.593243i
$487$	15.5694	+	4.17182i	0.705518	+	0.189043i	0.593701	−	0.804686i	$-0.297666\pi$
$487$	15.5694	+	4.17182i	0.705518	+	0.189043i	0.111817	+	0.993729i	$0.464333\pi$
$488$	−1.95396	−	7.29227i	−0.0884515	−	0.330105i
$489$	26.5246	−	19.6944i	1.19948	−	0.890610i
$490$	9.43131	−	18.6315i	0.426063	−	0.841684i
$491$	−31.5653			−1.42452			−0.712260	−	0.701915i	$-0.752328\pi$
$491$	−31.5653			−1.42452			−0.712260	+	0.701915i	$0.752328\pi$
$492$	−16.0959	+	1.86055i	−0.725658	+	0.0838801i
$493$	0.188430	−	0.108790i	0.00848647	−	0.00489966i
$494$	−5.62964	−	8.75925i	−0.253289	−	0.394097i
$495$	−3.21223	+	3.01515i	−0.144379	+	0.135521i
$496$	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	−0.974763	−	0.223243i	$-0.928336\pi$
$499$	−5.41067	−	20.1929i	−0.242215	−	0.903959i	0.732548	−	0.680716i	$-0.238331\pi$
$500$	−0.849619	+	3.17082i	−0.0379961	+	0.141804i
$501$	−8.82214	+	20.3806i	−0.394144	+	0.910537i
$502$	−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	$-0.0181792\pi$
$504$	2.02258	+	7.67523i	0.0900929	+	0.341882i
$505$	23.6642	+	23.6642i	1.05304	+	1.05304i
$506$	1.96325	−	3.40045i	0.0872772	−	0.151169i
$507$	20.0532	−	10.2405i	0.890594	−	0.454798i
$508$	−1.46234	−	2.53284i	−0.0648808	−	0.112377i
$509$	17.4226	−	4.66837i	0.772243	−	0.206922i	0.148881	−	0.988855i	$-0.452433\pi$
$509$	17.4226	−	4.66837i	0.772243	−	0.206922i	0.623362	+	0.781933i	$0.285766\pi$
$510$	−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
$513$	14.7678	+	2.66220i	0.652013	+	0.117539i
$514$	7.51574	−	28.0491i	0.331505	−	1.23719i
$515$	−9.42379	−	2.52510i	−0.415262	−	0.111269i
$516$	−3.61368	−	2.86482i	−0.159083	−	0.126117i
$517$		−	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	$-0.847709\pi$
$521$	−21.2930	+	12.2935i	−0.932865	+	0.538590i	−0.0451486	+	0.998980i	$0.514376\pi$
$522$	1.48519	+	0.921310i	0.0650049	+	0.0403247i
$523$	−20.8457	+	36.1057i	−0.911517	+	1.57879i	−0.0995948	+	0.995028i	$0.531755\pi$
$523$	−20.8457	+	36.1057i	−0.911517	+	1.57879i	−0.811922	+	0.583766i	$0.801579\pi$
$524$	17.9444			0.783906
$525$	−6.64534	+	16.5888i	−0.290026	+	0.723993i
$526$	−13.1370	+	13.1370i	−0.572800	+	0.572800i
$527$	−0.488542	−	1.82326i	−0.0212812	−	0.0794225i
$528$	−0.338708	+	0.782470i	−0.0147404	+	0.0340526i
$529$	−20.3112	−	35.1800i	−0.883096	−	1.52957i
$530$	4.86232	−	8.42179i	0.211206	−	0.365819i
$531$	−17.0433	+	9.13367i	−0.739616	+	0.396368i
$532$	−6.71949	−	3.63690i	−0.291327	−	0.157680i
$533$	24.9588	+	22.6876i	1.08109	+	0.982708i
$534$	−4.43040	−	3.51229i	−0.191722	−	0.151992i
$535$	−46.4786	−	12.4539i	−2.00944	−	0.538429i
$536$	2.53385	−	1.46292i	0.109446	−	0.0631885i
$537$	−16.2281	−	12.8652i	−0.700296	−	0.555174i
$538$	5.74280	−	5.74280i	0.247590	−	0.247590i
$539$	−3.27439	+	1.07349i	−0.141038	+	0.0462383i
$540$	−5.24603	−	14.5866i	−0.225753	−	0.627707i
$541$	−24.7657	+	6.63595i	−1.06476	+	0.285302i	−0.748339	−	0.663317i	$-0.769148\pi$
$541$	−24.7657	+	6.63595i	−1.06476	+	0.285302i	−0.316422	+	0.948618i	$0.602482\pi$
$542$	−21.4188	+	12.3662i	−0.920018	+	0.531173i
$543$	−3.54203	−	8.94904i	−0.152003	−	0.384040i
$544$	−0.360751	+	0.0966630i	−0.0154671	+	0.00414439i
$545$	−36.9766			−1.58390
$546$	9.26364	−	13.6816i	0.396447	−	0.585517i
$547$	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
$549$	−5.16693	−	22.0513i	−0.220519	−	0.941125i
$550$	−1.66247	+	0.959828i	−0.0708880	+	0.0409272i
$551$	−1.62509	+	0.435441i	−0.0692311	+	0.0185504i
$552$	8.23590	+	11.0922i	0.350543	+	0.472116i
$553$	−6.98356	+	29.2588i	−0.296971	+	1.24421i
$554$	10.1638	−	10.1638i	0.431817	−	0.431817i
$555$	−9.11172	+	11.4935i	−0.386771	+	0.487873i
$556$	−18.5174	+	10.6910i	−0.785311	+	0.453399i
$557$	21.4532	+	5.74838i	0.909003	+	0.243567i	0.682879	−	0.730532i	$-0.260728\pi$
$557$	21.4532	+	5.74838i	0.909003	+	0.243567i	0.226125	+	0.974098i	$0.427394\pi$
$558$	11.0551	−	10.3768i	0.467998	−	0.439285i
$559$	0.457082	+	9.58870i	0.0193325	+	0.405559i
$560$	0.217031	+	7.88988i	0.00917122	+	0.333408i
$561$	0.189833	+	0.255669i	0.00801475	+	0.0107944i
$562$	4.37903	−	7.58470i	0.184718	−	0.319941i
$563$	−1.46940	−	2.54508i	−0.0619280	−	0.107262i	0.833399	−	0.552672i	$-0.186392\pi$
$563$	−1.46940	−	2.54508i	−0.0619280	−	0.107262i	−0.895327	+	0.445409i	$0.853058\pi$
$564$	21.0396	+	9.10742i	0.885928	+	0.383492i
$565$	−4.41392	−	16.4730i	−0.185695	−	0.693022i
$566$	17.5449	−	17.5449i	0.737466	−	0.737466i
$567$	5.33636	+	23.2061i	0.224106	+	0.974565i
$568$	−1.28442			−0.0538930
$569$	−11.2238	+	19.4402i	−0.470526	+	0.814976i	−0.999432	−	0.0337051i	$-0.989269\pi$
$569$	−11.2238	+	19.4402i	−0.470526	+	0.814976i	0.528905	+	0.848681i	$0.322603\pi$
$570$	13.6940	+	5.92771i	0.573578	+	0.248285i
$571$	−31.4173	+	18.1388i	−1.31477	+	0.759084i	−0.982882	−	0.184234i	$-0.941020\pi$
$571$	−31.4173	+	18.1388i	−1.31477	+	0.759084i	−0.331890	+	0.943318i	$0.607686\pi$
$572$	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
$576$	−2.05316	−	2.18736i	−0.0855482	−	0.0911400i
$577$	−21.9929	−	5.89299i	−0.915577	−	0.245328i	−0.229883	−	0.973218i	$-0.573835\pi$
$577$	−21.9929	−	5.89299i	−0.915577	−	0.245328i	−0.685694	+	0.727890i	$0.740501\pi$
$578$	4.36382	−	16.2860i	0.181511	−	0.677409i
$579$	−1.34309	−	11.6193i	−0.0558171	−	0.482881i
$580$	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
$585$	−15.6852	+	28.1998i	−0.648503	+	1.16592i
$586$	0.665586	−	1.15283i	0.0274951	−	0.0476229i
$587$	15.2745	+	15.2745i	0.630447	+	0.630447i	0.948180	−	0.317733i	$-0.102922\pi$
$587$	15.2745	+	15.2745i	0.630447	+	0.630447i	−0.317733	+	0.948180i	$0.602922\pi$
$588$	1.11045	−	12.0734i	0.0457943	−	0.497898i
$589$			14.5955i			0.601397i
$590$	−18.5731	+	4.97665i	−0.764643	+	0.204885i
$591$	−21.4722	−	9.29467i	−0.883248	−	0.382332i
$592$	−0.734674	+	2.74184i	−0.0301949	+	0.112689i
$593$	11.3778	+	42.4626i	0.467231	+	1.74373i	0.649385	+	0.760460i	$0.275026\pi$
$593$	11.3778	+	42.4626i	0.467231	+	1.74373i	−0.182154	+	0.983270i	$0.558307\pi$
$594$	−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
$597$	21.3799	−	26.9686i	0.875021	−	1.10375i
$598$	6.11228	−	28.1022i	0.249950	−	1.14918i
$599$	18.6340	−	10.7583i	0.761363	−	0.439573i	−0.0684221	−	0.997656i	$-0.521796\pi$
$599$	18.6340	−	10.7583i	0.761363	−	0.439573i	0.829785	+	0.558084i	$0.188463\pi$
$600$	−0.775582	−	6.70966i	−0.0316630	−	0.273921i
$601$	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
$603$	7.73658	−	4.14611i	0.315058	−	0.168843i
$604$	−2.58226	−	9.63711i	−0.105070	−	0.392128i
$605$	−30.9990	−	8.30616i	−1.26029	−	0.337693i
$606$	17.8315	+	7.71871i	0.724354	+	0.313551i
$607$	−18.1150	+	31.3761i	−0.735266	+	1.27352i	0.219340	+	0.975648i	$0.429609\pi$
$607$	−18.1150	+	31.3761i	−0.735266	+	1.27352i	−0.954606	+	0.297870i	$0.903724\pi$
$608$	2.88787			0.117119
$609$	−1.64985	−	2.09890i	−0.0668554	−	0.0850517i
$610$		−	22.5219i		−	0.911884i
$611$	−14.5330	−	45.4581i	−0.587943	−	1.83904i
$612$	−1.09089	+	0.255610i	−0.0440964	+	0.0103324i
$613$	14.4606	+	3.87470i	0.584057	+	0.156497i	0.538735	−	0.842475i	$-0.318902\pi$
$613$	14.4606	+	3.87470i	0.584057	+	0.156497i	0.0453211	+	0.998972i	$0.485569\pi$
$614$	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	$-0.212757\pi$
$617$	4.10076	+	4.10076i	0.165090	+	0.165090i	−0.619727	+	0.784817i	$0.712757\pi$
$618$	−5.62697	+	0.650432i	−0.226350	+	0.0261642i
$619$	3.53669	−	13.1991i	0.142152	−	0.530517i	−0.857714	−	0.514127i	$-0.828116\pi$
$619$	3.53669	−	13.1991i	0.142152	−	0.530517i	0.999866	−	0.0163900i	$-0.00521733\pi$
$620$	13.0574	−	7.53871i	0.524399	−	0.302762i
$621$	23.6427	+	34.0415i	0.948750	+	1.36604i
$622$	1.76581	+	1.76581i	0.0708026	+	0.0708026i
$623$	4.52213	+	7.35762i	0.181175	+	0.294777i
$624$	−0.617777	+	6.21437i	−0.0247309	+	0.248774i
$625$	−14.6455	+	25.3668i	−0.585821	+	1.01467i
$626$	8.02455	−	29.9480i	0.320726	−	1.19696i
$627$	−0.906176	−	2.28948i	−0.0361892	−	0.0914330i
$628$	18.6139	+	10.7467i	0.742774	+	0.428841i
$629$	0.749631	+	0.749631i	0.0298898	+	0.0298898i
$630$	−0.0979508	+	23.6784i	−0.00390245	+	0.943370i
$631$	26.9483	+	26.9483i	1.07279	+	1.07279i	0.997134	+	0.0756614i	$0.0241068\pi$
$631$	26.9483	+	26.9483i	1.07279	+	1.07279i	0.0756614	+	0.997134i	$0.475893\pi$
$632$	−2.94262	−	10.9820i	−0.117051	−	0.436841i
$633$	−13.0618	+	5.16987i	−0.519161	+	0.205484i
$634$	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
$639$	−3.85133	−	0.121886i	−0.152356	−	0.00482173i
$640$	−1.49161	−	2.58355i	−0.0589611	−	0.102124i
$641$	22.0062	+	38.1158i	0.869191	+	1.50548i	0.862824	+	0.505504i	$0.168693\pi$
$641$	22.0062	+	38.1158i	0.869191	+	1.50548i	0.00636716	+	0.999980i	$0.497973\pi$
$642$	−27.7525	+	3.20796i	−1.09530	+	0.126608i
$643$	27.9829	−	27.9829i	1.10354	−	1.10354i	0.109559	−	0.993980i	$-0.465056\pi$
$643$	27.9829	−	27.9829i	1.10354	−	1.10354i	0.993980	−	0.109559i	$-0.0349438\pi$
$644$	−6.02043	−	20.2265i	−0.237238	−	0.797036i
$645$	−8.20111	−	11.0454i	−0.322918	−	0.434910i
$646$	0.539277	−	0.934055i	0.0212176	−	0.0367499i
$647$	12.7841	+	22.1426i	0.502593	+	0.870516i	0.999996	+	0.00299663i	$0.000953858\pi$
$647$	12.7841	+	22.1426i	0.502593	+	0.870516i	−0.497403	+	0.867520i	$0.665713\pi$
$648$	−5.94882	−	6.75363i	−0.233692	−	0.265308i
$649$	2.74781	+	1.58645i	0.107861	+	0.0622736i
$650$	−9.45745	+	10.4042i	−0.370952	+	0.408088i
$651$	−21.2927	+	9.11255i	−0.834525	+	0.357149i
$652$	13.4872	−	13.4872i	0.528198	−	0.528198i
$653$	−9.80664	−	5.66186i	−0.383763	−	0.221566i	0.295691	−	0.955284i	$-0.404450\pi$
$653$	−9.80664	−	5.66186i	−0.383763	−	0.221566i	−0.679454	+	0.733718i	$0.737783\pi$
$654$	−19.9618	+	7.90087i	−0.780568	+	0.308949i
$655$	51.7082	+	13.8552i	2.02041	+	0.541366i
$656$	−9.03608	+	2.42121i	−0.352800	+	0.0945323i
$657$	−4.84503	−	9.04075i	−0.189023	−	0.352713i
$658$	−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	$-0.0779318\pi$
$660$	−1.58017	+	1.99322i	−0.0615079	+	0.0775860i
$661$	2.47664	−	9.24295i	0.0963302	−	0.359509i	−0.900888	−	0.434053i	$-0.857083\pi$
$661$	2.47664	−	9.24295i	0.0963302	−	0.359509i	0.997218	+	0.0745433i	$0.0237499\pi$
$662$	7.32086	+	12.6801i	0.284533	+	0.492826i
$663$	1.89462	+	1.36028i	0.0735808	+	0.0528288i
$664$	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
$669$	12.9319	−	29.8747i	0.499975	−	1.15502i
$670$	8.43102	−	2.25909i	0.325719	−	0.0872761i
$671$	−2.62788	+	2.62788i	−0.101448	+	0.101448i
$672$	1.80301	+	4.21297i	0.0695527	+	0.162519i
$673$		−	7.76392i		−	0.299277i	−0.988741	−	0.149638i	$-0.952189\pi$
$673$		−	7.76392i		−	0.299277i	0.988741	−	0.149638i	$-0.0478110\pi$
$674$	−4.52804	−	16.8989i	−0.174414	−	0.650920i
$675$	−1.68886	−	20.1925i	−0.0650044	−	0.777210i
$676$	10.5890	−	7.54144i	0.407269	−	0.290055i
$677$	12.1599	+	7.02053i	0.467344	+	0.269821i	0.715127	−	0.698995i	$-0.246369\pi$
$677$	12.1599	+	7.02053i	0.467344	+	0.269821i	−0.247784	+	0.968815i	$0.579702\pi$
$678$	−5.90266	−	7.94978i	−0.226690	−	0.305309i
$679$	21.6448	−	39.9906i	0.830651	−	1.53470i
$680$	−1.11417			−0.0427263
$681$	5.74669	+	49.7154i	0.220214	+	1.90510i
$682$	−2.40318	−	0.643930i	−0.0920224	−	0.0246573i
$683$	−30.3629	−	8.13572i	−1.16181	−	0.311305i	−0.374119	−	0.927381i	$-0.622055\pi$
$683$	−30.3629	−	8.13572i	−1.16181	−	0.311305i	−0.787687	+	0.616076i	$0.788721\pi$
$684$	8.65927	+	0.274047i	0.331096	+	0.0104784i
$685$	28.3720			1.08404
$686$	−7.90689	+	16.7476i	−0.301886	+	0.639425i
$687$	9.23166	−	6.85445i	0.352210	−	0.261514i
$688$	−2.30575	−	1.33122i	−0.0879057	−	0.0507524i
$689$	−9.88729	+	6.35463i	−0.376676	+	0.242092i
$690$	15.1679	+	38.3221i	0.577431	+	1.45890i
$691$	−3.69969	−	13.8074i	−0.140743	−	0.525259i	−0.999908	−	0.0135610i	$-0.995683\pi$
$691$	−3.69969	−	13.8074i	−0.140743	−	0.525259i	0.859165	−	0.511698i	$-0.170983\pi$
$692$			3.70859i			0.140979i
$693$	2.77425	−	2.75139i	0.105385	−	0.104517i
$694$	10.1263	−	10.1263i	0.384390	−	0.384390i
$695$	−61.6138	+	16.5094i	−2.33714	+	0.626236i
$696$	0.926023	+	0.400848i	0.0351008	+	0.0151941i
$697$	−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	$-0.530483\pi$
$701$	−5.06325			−0.191236			−0.0956181	+	0.995418i	$0.530483\pi$
$702$	−2.44212	+	18.5751i	−0.0921719	+	0.701074i
$703$	−4.09870	−	7.09916i	−0.154585	−	0.267750i
$704$	−0.127408	+	0.475494i	−0.00480188	+	0.0179208i
$705$	53.5952	+	42.4887i	2.01851	+	1.60022i
$706$		−	1.70840i		−	0.0642965i
$707$	−21.5564	−	20.4022i	−0.810711	−	0.767303i
$708$	−8.96331	+	6.65520i	−0.336862	+	0.250118i
$709$	18.3917	−	4.92803i	0.690714	−	0.185076i	0.103646	−	0.994614i	$-0.466949\pi$
$709$	18.3917	−	4.92803i	0.690714	−	0.185076i	0.587067	+	0.809538i	$0.300282\pi$
$710$	−3.70114	−	0.991718i	−0.138901	−	0.0372185i
$711$	−7.78130	−	33.2088i	−0.291822	−	1.24543i
$712$	−2.82687	−	1.63209i	−0.105941	−	0.0611652i
$713$	−28.5057	+	28.5057i	−1.06755	+	1.06755i
$714$	1.69934	+	0.203557i	0.0635962	+	0.00761792i
$715$	5.28890	−	0.252116i	0.197794	−	0.00942859i
$716$	−10.3545	−	5.97819i	−0.386967	−	0.223416i
$717$	20.4597	+	8.85640i	0.764082	+	0.330748i
$718$	−6.95461	−	12.0457i	−0.259544	−	0.449543i
$719$	−21.6555	+	37.5084i	−0.807614	+	1.39883i	0.106899	+	0.994270i	$0.465908\pi$
$719$	−21.6555	+	37.5084i	−0.807614	+	1.39883i	−0.914512	+	0.404558i	$0.867425\pi$
$720$	−4.22743	−	7.88831i	−0.157547	−	0.293980i
$721$	8.41616	+	2.00879i	0.313434	+	0.0748113i
$722$	7.53791	−	7.53791i	0.280532	−	0.280532i
$723$	−1.96581	−	17.0064i	−0.0731091	−	0.632477i
$724$	−2.77836	−	4.81226i	−0.103257	−	0.178846i
$725$	1.13592	+	1.96747i	0.0421870	+	0.0730701i
$726$	−18.5096	+	2.13956i	−0.686955	+	0.0794064i
$727$			26.4056i			0.979328i	0.871911	+	0.489664i	$0.162881\pi$
$727$			26.4056i			0.979328i	−0.871911	+	0.489664i	$0.837119\pi$
$728$	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
$732$	−4.81230	−	12.1584i	−0.177868	−	0.449388i
$733$	−6.59585	−	24.6161i	−0.243623	−	0.909215i	−0.974070	−	0.226245i	$-0.927355\pi$
$733$	−6.59585	−	24.6161i	−0.243623	−	0.909215i	0.730447	−	0.682969i	$-0.239312\pi$
$734$	19.7319	+	19.7319i	0.728319	+	0.728319i
$735$	12.5219	−	33.9330i	0.461877	−	1.25164i
$736$	5.64014	+	5.64014i	0.207898	+	0.207898i
$737$	−1.24733	−	0.720148i	−0.0459461	−	0.0265270i
$738$	−27.3244	+	6.40251i	−1.00583	+	0.235680i
$739$	6.39753	−	23.8759i	0.235337	−	0.878289i	−0.742660	−	0.669669i	$-0.766436\pi$
$739$	6.39753	−	23.8759i	0.235337	−	0.878289i	0.977997	−	0.208620i	$-0.0668973\pi$
$740$	−4.23403	+	7.33356i	−0.155646	+	0.269587i
$741$	−11.4284	−	13.9515i	−0.419833	−	0.512520i
$742$	−4.10527	+	7.58484i	−0.150709	+	0.278448i
$743$	−4.42963	−	4.42963i	−0.162507	−	0.162507i	0.621169	−	0.783677i	$-0.286658\pi$
$743$	−4.42963	−	4.42963i	−0.162507	−	0.162507i	−0.783677	+	0.621169i	$0.786658\pi$
$744$	5.43823	−	6.85977i	0.199375	−	0.251492i
$745$	−10.1511	+	5.86073i	−0.371907	+	0.214721i
$746$	6.37947	−	23.8085i	0.233569	−	0.871691i
$747$	39.2340	+	1.24167i	1.43550	+	0.0454303i
$748$	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	0.786268	−	0.617885i	$-0.212010\pi$
$751$	17.6566	+	10.1940i	0.644299	+	0.371986i	−0.141970	+	0.989871i	$0.545344\pi$
$752$	12.7854	+	3.42585i	0.466237	+	0.124928i
$753$	−23.9586	+	9.48281i	−0.873100	+	0.345573i
$754$	−0.639646	−	2.00076i	−0.0232945	−	0.0728634i
$755$		−	29.7638i		−	1.08322i
$756$	5.00654	+	12.8037i	0.182086	+	0.465666i
$757$	−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
$759$	2.70166	−	6.24126i	0.0980639	−	0.226544i
$760$	8.32160	+	2.22977i	0.301856	+	0.0808822i
$761$	−8.80566	−	32.8632i	−0.319205	−	1.19129i	−0.920010	−	0.391894i	$-0.871820\pi$
$761$	−8.80566	−	32.8632i	−0.319205	−	1.19129i	0.600805	−	0.799395i	$-0.294847\pi$
$762$	−3.01984	−	4.06716i	−0.109397	−	0.147338i
$763$	32.7813	−	0.901730i	1.18676	−	0.0326448i
$764$	−8.04418			−0.291028
$765$	−3.34083	−	0.105730i	−0.120788	−	0.00382267i
$766$	−9.52919	+	5.50168i	−0.344303	+	0.198784i
$767$	22.7086	+	4.93916i	0.819959	+	0.178343i
$768$	−1.35728	−	1.07601i	−0.0489765	−	0.0388272i
$769$	2.08636	−	2.08636i	0.0752360	−	0.0752360i	−0.668487	−	0.743723i	$-0.733058\pi$
$769$	2.08636	−	2.08636i	0.0752360	−	0.0752360i	0.743723	+	0.668487i	$0.233058\pi$
$770$	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	0.839264	+	0.543723i	$0.182986\pi$
$773$	−4.43238	+	16.5419i	−0.159422	+	0.594970i	−0.998686	+	0.0512461i	$0.983681\pi$
$774$	−6.78745	−	4.21048i	−0.243970	−	0.151342i
$775$	19.0374	−	5.10105i	0.683843	−	0.183235i
$776$			17.1870i			0.616977i
$777$	7.79763	−	10.4117i	0.279739	−	0.373517i
$778$	3.22881	+	3.22881i	0.115758	+	0.115758i
$779$	13.5078	−	23.3961i	0.483966	−	0.838254i
$780$	−6.57838	+	17.4302i	−0.235544	+	0.624100i
$781$	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
$786$	30.8751	−	3.56891i	1.10128	−	0.127299i
$787$	−2.35688	+	8.79601i	−0.0840138	+	0.313544i	−0.995126	−	0.0986155i	$-0.968559\pi$
$787$	−2.35688	+	8.79601i	−0.0840138	+	0.313544i	0.911112	+	0.412159i	$0.135225\pi$
$788$	−13.0483	−	3.49628i	−0.464826	−	0.124550i
$789$	−19.9907	+	25.2162i	−0.711687	+	0.897721i
$790$		−	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
$795$	6.69110	−	15.4575i	0.237309	−	0.548222i
$796$	9.93481	−	17.2076i	0.352130	−	0.609907i
$797$	−13.8457			−0.490440			−0.245220	−	0.969468i	$-0.578860\pi$
$797$	−13.8457			−0.490440			−0.245220	+	0.969468i	$0.578860\pi$
$798$	−12.2848	−	4.92122i	−0.434879	−	0.174209i
$799$	3.49559	−	3.49559i	0.123665	−	0.123665i
$800$	−1.00930	−	3.76674i	−0.0356840	−	0.133175i
$801$	−8.32148	−	5.16208i	−0.294025	−	0.182393i
$802$	10.0391	+	17.3882i	0.354492	+	0.613999i
$803$	−0.841545	+	1.45760i	−0.0296975	+	0.0514375i
$804$	4.06878	−	3.02104i	0.143495	−	0.106544i
$805$	−1.73112	−	62.9326i	−0.0610138	−	2.21808i
$806$	−18.2020	+	0.867669i	−0.641139	+	0.0305623i
$807$	8.73887	−	11.0232i	0.307623	−	0.388035i
$808$	10.8359	+	2.90347i	0.381205	+	0.102144i
$809$	26.8210	−	15.4851i	0.942977	−	0.544428i	0.0520847	−	0.998643i	$-0.483413\pi$
$809$	26.8210	−	15.4851i	0.942977	−	0.544428i	0.890892	+	0.454215i	$0.150080\pi$
$810$	−11.9274	−	24.0543i	−0.419085	−	0.845180i
$811$	21.3040	−	21.3040i	0.748083	−	0.748083i	−0.226036	−	0.974119i	$-0.572577\pi$
$811$	21.3040	−	21.3040i	0.748083	−	0.748083i	0.974119	+	0.226036i	$0.0725766\pi$
$812$	−1.11946	−	1.05953i	−0.0392855	−	0.0371821i
$813$	−34.3937	+	25.5371i	−1.20624	+	0.895625i
$814$	1.34972	−	0.361656i	0.0473076	−	0.0126760i
$815$	49.2779	−	28.4506i	1.72613	−	0.996582i
$816$	−0.601482	+	0.238066i	−0.0210561	+	0.00833399i
$817$	7.42681	−	1.99001i	0.259831	−	0.0696215i
$818$	−22.5951			−0.790020
$819$	13.2179	−	25.3828i	0.461870	−	0.886947i
$820$	−27.9076			−0.974574
$821$	19.0589	−	5.10681i	0.665159	−	0.178229i	0.0895861	−	0.995979i	$-0.471446\pi$
$821$	19.0589	−	5.10681i	0.665159	−	0.178229i	0.575573	+	0.817750i	$0.304779\pi$
$822$	15.3166	−	6.06231i	0.534228	−	0.211447i
$823$	14.8852	−	8.59396i	0.518865	−	0.299567i	−0.217605	−	0.976037i	$-0.569825\pi$
$823$	14.8852	−	8.59396i	0.518865	−	0.299567i	0.736470	+	0.676470i	$0.236491\pi$
$824$	−3.15893	+	0.846433i	−0.110047	+	0.0294869i
$825$	−2.66954	+	1.98212i	−0.0929415	+	0.0690085i
$826$	16.3445	−	4.86494i	0.568697	−	0.169273i
$827$	−20.6419	+	20.6419i	−0.717790	+	0.717790i	−0.968152	−	0.250362i	$-0.919450\pi$
$827$	−20.6419	+	20.6419i	−0.717790	+	0.717790i	0.250362	+	0.968152i	$0.419450\pi$
$828$	16.3767	+	17.4472i	0.569131	+	0.606332i
$829$	16.4326	−	9.48736i	0.570728	−	0.329510i	−0.186712	−	0.982415i	$-0.559783\pi$
$829$	16.4326	−	9.48736i	0.570728	−	0.329510i	0.757440	+	0.652905i	$0.226450\pi$
$830$	37.7041	+	10.1028i	1.30873	+	0.350673i
$831$	15.4663	−	19.5091i	0.536519	−	0.676765i
$832$	0.171677	+	3.60146i	0.00595184	+	0.124858i
$833$	−2.33252	−	1.18073i	−0.0808171	−	0.0409099i
$834$	−29.7346	+	22.0777i	−1.02962	+	0.764489i
$835$	−19.1252	+	33.1258i	−0.661854	+	1.14637i
$836$	−0.710802	−	1.23115i	−0.0245836	−	0.0425800i
$837$	16.9575	−	20.0530i	0.586136	−	0.693132i
$838$	0.552176	+	2.06075i	0.0190746	+	0.0711874i
$839$	−3.44017	+	3.44017i	−0.118768	+	0.118768i	−0.763993	−	0.645225i	$-0.776764\pi$
$839$	−3.44017	+	3.44017i	−0.118768	+	0.118768i	0.645225	+	0.763993i	$0.276764\pi$
$840$	1.94261	+	13.5321i	0.0670265	+	0.466903i
$841$	28.6606			0.988297
$842$	−19.4712	+	33.7251i	−0.671022	+	1.16224i
$843$	6.02603	−	13.9211i	0.207548	−	0.479469i
$844$	−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
$849$	26.6981	−	33.6770i	0.916278	−	1.15579i
$850$	−1.40679	−	0.376949i	−0.0482526	−	0.0129292i
$851$	5.86003	−	21.8699i	0.200879	−	0.749692i
$852$	−2.20996	+	0.255454i	−0.0757121	+	0.00875169i
$853$	−33.6661	−	33.6661i	−1.15271	−	1.15271i	−0.986008	−	0.166698i	$-0.946690\pi$
$853$	−33.6661	−	33.6661i	−1.15271	−	1.15271i	−0.166698	−	0.986008i	$-0.553310\pi$
$854$	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	$-0.254852\pi$
$857$	−8.00696	−	13.8685i	−0.273513	−	0.473738i	−0.969759	+	0.244065i	$0.921519\pi$
$858$	2.80134	−	1.26620i	0.0956362	−	0.0432272i
$859$	2.08126	−	3.60485i	0.0710117	−	0.122996i	−0.828333	−	0.560236i	$-0.810711\pi$
$859$	2.08126	−	3.60485i	0.0710117	−	0.122996i	0.899345	+	0.437240i	$0.144044\pi$
$860$	−5.61632	−	5.61632i	−0.191515	−	0.191515i
$861$	42.5650	+	5.09868i	1.45061	+	0.173762i
$862$			7.03923i			0.239757i
$863$	8.23152	−	2.20563i	0.280204	−	0.0750805i	−0.115980	−	0.993252i	$-0.537001\pi$
$863$	8.23152	−	2.20563i	0.280204	−	0.0750805i	0.396184	+	0.918171i	$0.370334\pi$
$864$	−3.96769	−	3.35521i	−0.134983	−	0.114147i
$865$	−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
$870$	2.35890	+	1.87007i	0.0799743	+	0.0634013i
$871$	−10.3083	−	2.24207i	−0.349282	−	0.0759696i
$872$	−10.7343	+	6.19742i	−0.363508	+	0.209871i
$873$	−1.63097	+	51.5352i	−0.0552001	+	1.74420i
$874$	−23.0347			−0.779160
$875$	4.13411	−	7.63812i	0.139758	−	0.258216i
$876$	−3.53031	−	4.75466i	−0.119278	−	0.160645i
$877$	1.00074	+	3.73481i	0.0337926	+	0.126116i	0.980762	−	0.195209i	$-0.0625386\pi$
$877$	1.00074	+	3.73481i	0.0337926	+	0.126116i	−0.946969	+	0.321325i	$0.895872\pi$
$878$	−19.8625	−	5.32215i	−0.670329	−	0.179614i
$879$	0.915921	−	2.11593i	0.0308932	−	0.0713684i
$880$	−0.734272	+	1.27180i	−0.0247523	+	0.0428722i
$881$	47.5999			1.60368			0.801841	−	0.597538i	$-0.203854\pi$
$881$	47.5999			1.60368			0.801841	+	0.597538i	$0.203854\pi$
$882$	−0.490596	−	20.9943i	−0.0165192	−	0.706914i
$883$		−	32.0280i		−	1.07783i	−0.842361	−	0.538914i	$-0.818835\pi$
$883$		−	32.0280i		−	1.07783i	0.842361	−	0.538914i	$-0.181165\pi$
$884$	1.19692	+	0.617005i	0.0402567	+	0.0207521i
$885$	−30.9670	+	12.2567i	−1.04094	+	0.412006i
$886$	−16.2772	−	4.36147i	−0.546844	−	0.146526i
$887$	8.43763	+	4.87147i	0.283308	+	0.163568i	0.634920	−	0.772578i	$-0.281033\pi$
$887$	8.43763	+	4.87147i	0.283308	+	0.163568i	−0.351612	+	0.936146i	$0.614366\pi$
$888$	−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
$891$	−1.41498	+	4.19837i	−0.0474035	+	0.140651i
$892$	4.86445	−	18.1544i	0.162874	−	0.607853i
$893$	−33.1039	+	19.1126i	−1.10778	+	0.639578i
$894$	−4.22778	+	5.33292i	−0.141398	+	0.178359i
$895$	−25.2215	−	25.2215i	−0.843062	−	0.843062i
$896$	1.38538	+	2.25405i	0.0462823	+	0.0753024i
$897$	4.92762	−	49.5681i	0.164528	−	1.65503i
$898$	−13.9143	+	24.1002i	−0.464326	+	0.804235i
$899$	−0.762066	+	2.84407i	−0.0254163	+	0.0948551i
$900$	−2.66892	−	11.3904i	−0.0889642	−	0.379679i
$901$	−1.05434	−	0.608726i	−0.0351253	−	0.0202796i
$902$	3.25628	+	3.25628i	0.108422	+	0.108422i
$903$	7.53998	+	9.59217i	0.250915	+	0.319207i
$904$	−4.04229	−	4.04229i	−0.134444	−	0.134444i
$905$	−4.29043	−	16.0121i	−0.142619	−	0.532260i
$906$	−6.35971	−	16.0680i	−0.211287	−	0.533823i
$907$	−24.5858	+	14.1946i	−0.816358	+	0.471325i	−0.849159	−	0.528137i	$-0.822891\pi$
$907$	−24.5858	+	14.1946i	−0.816358	+	0.471325i	0.0328009	+	0.999462i	$0.489557\pi$
$908$	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	$-0.132965\pi$
$912$	4.96885	−	0.574359i	0.164535	−	0.0190189i
$913$	−3.22055	−	5.57816i	−0.106585	−	0.184610i
$914$	19.1708	+	33.2048i	0.634114	+	1.09832i
$915$	−4.47930	−	38.7510i	−0.148081	−	1.28107i
$916$	4.69409	−	4.69409i	0.155097	−	0.155097i
$917$	−46.1793	−	11.0222i	−1.52498	−	0.363985i
$918$	−1.82613	+	0.656764i	−0.0602714	+	0.0216764i
$919$	−7.43086	+	12.8706i	−0.245121	+	0.424563i	−0.962166	−	0.272465i	$-0.912161\pi$
$919$	−7.43086	+	12.8706i	−0.245121	+	0.424563i	0.717044	+	0.697027i	$0.245494\pi$
$920$	11.8976	+	20.6073i	0.392254	+	0.679403i
$921$	2.67290	+	1.15702i	0.0880751	+	0.0381251i
$922$	21.5178	+	12.4233i	0.708652	+	0.409140i
$923$	3.42684	+	3.11500i	0.112796	+	0.102532i
$924$	1.35228	−	1.80561i	0.0444866	−	0.0594002i
$925$	−7.82719	+	7.82719i	−0.257356	+	0.257356i
$926$	−30.3966	−	17.5495i	−0.998895	−	0.576712i
$927$	−9.55237	+	2.23826i	−0.313741	+	0.0735140i
$928$	0.562729	+	0.150783i	0.0184725	+	0.00494969i
$929$	−24.1066	+	6.45934i	−0.790912	+	0.211924i	−0.631590	−	0.775303i	$-0.717597\pi$
$929$	−24.1066	+	6.45934i	−0.790912	+	0.211924i	−0.159322	+	0.987227i	$0.550931\pi$
$930$	20.9672	−	15.5680i	0.687541	−	0.510495i
$931$	15.0584	+	13.4868i	0.493519	+	0.442012i
$932$		−	2.21957i		−	0.0727044i
$933$	3.38944	+	2.68705i	0.110965	+	0.0879701i
$934$	3.83151	−	14.2994i	0.125371	−	0.467891i
$935$	0.274234	+	0.474987i	0.00896841	+	0.0155337i
$936$	0.173010	+	10.8153i	0.00565502	+	0.353508i
$937$	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	0.514216	+	0.857661i	$0.328083\pi$
$941$	−11.0414	+	41.2069i	−0.359938	+	1.34331i	−0.874155	+	0.485648i	$0.838584\pi$
$942$	34.1643	+	14.7887i	1.11313	+	0.481842i
$943$	72.0751	−	19.3125i	2.34709	−	0.628900i
$944$	−4.55764	+	4.55764i	−0.148339	+	0.148339i
$945$	4.54078	+	40.7604i	0.147712	+	1.32594i
$946$			1.31064i			0.0426124i
$947$	8.88682	+	33.1661i	0.288783	+	1.07775i	0.946030	+	0.324078i	$0.105054\pi$
$947$	8.88682	+	33.1661i	0.288783	+	1.07775i	−0.657247	+	0.753675i	$0.728279\pi$
$948$	−7.24724	−	18.3104i	−0.235379	−	0.594693i
$949$	−2.62002	+	12.0459i	−0.0850495	+	0.391028i
$950$	9.75283	+	5.63080i	0.316424	+	0.182687i
$951$	26.5464	−	19.7105i	0.860824	−	0.639157i
$952$	0.987754	−	0.0271706i	0.0320133	−	0.000880605i
$953$	38.4250			1.24471			0.622354	−	0.782736i	$-0.286176\pi$
$953$	38.4250			1.24471			0.622354	+	0.782736i	$0.286176\pi$
$954$	0.309339	−	9.77443i	0.0100152	−	0.316459i
$955$	−23.1799	−	6.21103i	−0.750083	−	0.200984i
$956$	12.4330	+	3.33142i	0.402113	+	0.107746i
$957$	−0.0570377	−	0.493441i	−0.00184377	−	0.0159507i
$958$	32.6981			1.05643
$959$	−25.1530	+	0.691895i	−0.812232	+	0.0223424i
$960$	−3.08029	−	4.14857i	−0.0994160	−	0.133895i
$961$	−4.72538	−	2.72820i	−0.152432	−	0.0880065i
$962$	8.60970	−	5.53352i	0.277588	−	0.178408i
$963$	−47.1127	+	11.0392i	−1.51819	+	0.355733i
$964$	−2.55818	−	9.54727i	−0.0823935	−	0.307497i
$965$		−	20.1459i		−	0.648520i
$966$	−14.3815	−	33.6042i	−0.462717	−	1.08120i
$967$	−37.3805	+	37.3805i	−1.20208	+	1.20208i	−0.228543	+	0.973534i	$0.573396\pi$
$967$	−37.3805	+	37.3805i	−1.20208	+	1.20208i	−0.973534	+	0.228543i	$0.926604\pi$
$968$	−10.3911	+	2.78429i	−0.333983	+	0.0894905i
$969$	0.742106	−	1.71438i	0.0238399	−	0.0550740i
$970$	−13.2703	+	49.5255i	−0.426085	+	1.59017i
$971$	−37.7590	−	21.8002i	−1.21174	−	0.699600i	−0.248604	−	0.968605i	$-0.579972\pi$
$971$	−37.7590	−	21.8002i	−1.21174	−	0.699600i	−0.963139	+	0.269005i	$0.913305\pi$
$972$	−11.5787	−	10.4371i	−0.371387	−	0.334771i
$973$	54.2206	−	16.1388i	1.73823	−	0.517386i
$974$	16.1187			0.516475
$975$	−14.2032	+	19.7824i	−0.454866	+	0.633545i
$976$	−3.77475	−	6.53807i	−0.120827	−	0.209278i
$977$	−3.44656	+	12.8627i	−0.110265	+	0.411515i	−0.998889	−	0.0471214i	$-0.984995\pi$
$977$	−3.44656	+	12.8627i	−0.110265	+	0.411515i	0.888624	+	0.458636i	$0.151662\pi$
$978$	20.5235	−	25.8884i	0.656270	−	0.827819i
$979$			1.60685i			0.0513552i
$980$	4.28776	−	20.4376i	0.136968	−	0.652856i
$981$	−32.7748	+	17.5643i	−1.04642	+	0.560786i
$982$	−30.4897	+	8.16969i	−0.972966	+	0.260705i
$983$	−0.274991	−	0.0736836i	−0.00877085	−	0.00235014i	0.254431	−	0.967091i	$-0.418112\pi$
$983$	−0.274991	−	0.0736836i	−0.00877085	−	0.00235014i	−0.263202	+	0.964741i	$0.584779\pi$
$984$	−15.0659	+	5.96307i	−0.480283	+	0.190096i
$985$	−34.9001	−	20.1496i	−1.11201	−	0.642019i
$986$	0.153853	−	0.153853i	0.00489966	−	0.00489966i
$987$	−48.5505	−	36.3610i	−1.54538	−	1.15738i
$988$	−7.70487	−	7.00373i	−0.245125	−	0.222818i
$989$	18.3915	+	10.6183i	0.584815	+	0.337643i
$990$	−2.32240	+	3.74380i	−0.0738108	+	0.118986i
$991$	18.1504	+	31.4374i	0.576566	+	0.998642i	0.995870	+	0.0907955i	$0.0289410\pi$
$991$	18.1504	+	31.4374i	0.576566	+	0.998642i	−0.419304	+	0.907846i	$0.637726\pi$
$992$	2.52703	−	4.37695i	0.0802334	−	0.138968i
$993$	15.1181	+	20.3613i	0.479759	+	0.646146i
$994$	3.30540	+	0.788942i	0.104841	+	0.0250237i
$995$	41.9141	−	41.9141i	1.32877	−	1.32877i
$996$	22.5132	−	2.60234i	0.713358	−	0.0824584i
$997$	8.60792	+	14.9094i	0.272616	+	0.472184i	0.969531	−	0.244970i	$-0.0787780\pi$
$997$	8.60792	+	14.9094i	0.272616	+	0.472184i	−0.696915	+	0.717154i	$0.745445\pi$
$998$	−10.4526	−	18.1045i	−0.330872	−	0.573087i
$999$	−2.61675	+	14.5156i	−0.0827903	+	0.459254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.317.34	yes	144
3.2	odd	2	inner	546.2.bv.a.317.4	✓	144
7.4	even	3	inner	546.2.bv.a.473.4	yes	144
13.8	odd	4	inner	546.2.bv.a.359.34	yes	144
21.11	odd	6	inner	546.2.bv.a.473.34	yes	144
39.8	even	4	inner	546.2.bv.a.359.4	yes	144
91.60	odd	12	inner	546.2.bv.a.515.4	yes	144
273.242	even	12	inner	546.2.bv.a.515.34	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.4	✓	144	3.2	odd	2	inner
546.2.bv.a.317.34	yes	144	1.1	even	1	trivial
546.2.bv.a.359.4	yes	144	39.8	even	4	inner
546.2.bv.a.359.34	yes	144	13.8	odd	4	inner
546.2.bv.a.473.4	yes	144	7.4	even	3	inner
546.2.bv.a.473.34	yes	144	21.11	odd	6	inner
546.2.bv.a.515.4	yes	144	91.60	odd	12	inner
546.2.bv.a.515.34	yes	144	273.242	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.61049 - 0.637432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.88157 - 0.772115i) q^{5} +(1.39063 - 1.03254i) q^{6} +(-2.53580 + 0.754783i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.18736 - 2.05316i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.61049 - 0.637432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.88157 - 0.772115i) q^{5} +(1.39063 - 1.03254i) q^{6} +(-2.53580 + 0.754783i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.18736 - 2.05316i) q^{9} +(2.58355 - 1.49161i) q^{10} +(-0.475494 - 0.127408i) q^{11} +(1.07601 - 1.35728i) q^{12} +(-3.60146 + 0.171677i) q^{13} +(-2.25405 + 1.38538i) q^{14} +(4.14857 - 3.08029i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.186739 - 0.323441i) q^{17} +(1.58143 - 2.54933i) q^{18} +(0.747436 + 2.78947i) q^{19} +(2.10946 - 2.10946i) q^{20} +(-3.60277 + 2.83197i) q^{21} -0.492267 q^{22} +(-3.98818 + 6.90774i) q^{23} +(0.688056 - 1.58952i) 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} +(3.20998 - 4.04906i) q^{30} +(4.88185 + 1.30809i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.846992 + 0.0979054i) 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} +(-5.69069 + 2.57217i) q^{39} +(1.49161 - 2.58355i) q^{40} +(-6.61487 - 6.61487i) q^{41} +(-2.74704 + 3.66794i) q^{42} -2.66245i q^{43} +(-0.475494 + 0.127408i) q^{44} +(4.71776 - 7.60521i) 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} +(-0.506912 - 0.401865i) q^{51} +(-3.03312 + 1.94941i) q^{52} +(2.82305 - 1.62989i) q^{53} +(0.921857 - 5.11372i) q^{54} -1.46854 q^{55} +(-1.25937 + 2.32680i) q^{56} +(2.98183 + 4.01597i) q^{57} +(0.150783 + 0.562729i) q^{58} +(-6.22585 - 1.66821i) q^{59} +(2.05263 - 4.74190i) q^{60} +(3.77475 - 6.53807i) q^{61} +5.05407 q^{62} +(-3.99703 + 6.85739i) q^{63} -1.00000i q^{64} +(-10.2453 + 3.27544i) q^{65} +(-0.792792 + 0.313787i) 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} +(0.0948959 - 2.99850i) q^{72} +(0.884917 - 3.30256i) q^{73} +(-2.45827 + 1.41928i) q^{74} +(4.19603 - 5.29287i) q^{75} +(2.04203 + 2.04203i) q^{76} +(1.30192 - 0.0358127i) q^{77} +(-4.83106 + 3.95739i) q^{78} +(5.68471 - 9.84621i) q^{79} +(0.772115 - 2.88157i) q^{80} +(0.569090 - 8.98199i) q^{81} +(-8.10152 - 4.67742i) q^{82} +(9.25218 + 9.25218i) q^{83} +(-1.70410 + 4.25394i) q^{84} +(-0.787834 - 0.787834i) q^{85} +(-0.689092 - 2.57173i) q^{86} +(0.371355 + 0.938240i) 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} +(8.69600 - 1.00519i) q^{93} +(6.61822 + 11.4631i) q^{94} +(4.30758 + 7.46095i) q^{95} +(-0.198887 - 1.72059i) q^{96} +(-12.1530 + 12.1530i) q^{97} +(4.67016 - 5.21437i) q^{98} +(-1.30167 + 0.697576i) 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

L-functions

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