LMFDB - Embedded newform 546.2.ch.a.305.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.10
Character	$\chi$	$=$	546.305
Dual form			546.2.ch.a.401.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.222065 + 1.71776i) q^{3} +1.00000i q^{4} +(-0.998336 + 3.72584i) q^{5} +(1.37166 - 1.05761i) q^{6} +(0.528406 + 2.59245i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.90137 - 0.762906i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.222065 + 1.71776i) q^{3} +1.00000i q^{4} +(-0.998336 + 3.72584i) q^{5} +(1.37166 - 1.05761i) q^{6} +(0.528406 + 2.59245i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.90137 - 0.762906i) q^{9} +(3.34050 - 1.92864i) q^{10} +(3.62146 + 0.970367i) q^{11} +(-1.71776 - 0.222065i) q^{12} +(3.53597 - 0.704936i) q^{13} +(1.45950 - 2.20678i) q^{14} +(-6.17839 - 2.54228i) q^{15} -1.00000 q^{16} -0.858136 q^{17} +(1.51213 + 2.59104i) q^{18} +(1.11317 + 4.15440i) q^{19} +(-3.72584 - 0.998336i) q^{20} +(-4.57053 + 0.331982i) q^{21} +(-1.87460 - 3.24691i) q^{22} -5.07846 q^{23} +(1.05761 + 1.37166i) q^{24} +(-8.55508 - 4.93928i) q^{25} +(-2.99877 - 2.00184i) q^{26} +(1.95478 - 4.81444i) q^{27} +(-2.59245 + 0.528406i) q^{28} +(2.97651 + 1.71849i) q^{29} +(2.57112 + 6.16644i) q^{30} +(-1.42522 - 5.31898i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.47105 + 6.00530i) q^{33} +(0.606794 + 0.606794i) q^{34} +(-10.1866 - 0.619377i) q^{35} +(0.762906 - 2.90137i) q^{36} +(-4.06664 - 4.06664i) q^{37} +(2.15047 - 3.72473i) q^{38} +(0.425694 + 6.23047i) q^{39} +(1.92864 + 3.34050i) q^{40} +(0.774470 - 0.207519i) q^{41} +(3.46660 + 2.99711i) q^{42} +(1.15111 - 0.664595i) q^{43} +(-0.970367 + 3.62146i) q^{44} +(5.73901 - 10.0484i) q^{45} +(3.59102 + 3.59102i) q^{46} +(5.65698 + 1.51578i) q^{47} +(0.222065 - 1.71776i) q^{48} +(-6.44157 + 2.73973i) q^{49} +(2.55676 + 9.54195i) q^{50} +(0.190562 - 1.47407i) q^{51} +(0.704936 + 3.53597i) q^{52} +(4.07315 + 2.35163i) q^{53} +(-4.78656 + 2.02208i) q^{54} +(-7.23086 + 12.5242i) q^{55} +(2.20678 + 1.45950i) q^{56} +(-7.38344 + 0.989606i) q^{57} +(-0.889555 - 3.31987i) q^{58} +(10.2258 - 10.2258i) q^{59} +(2.54228 - 6.17839i) q^{60} +(-1.55221 + 2.68851i) q^{61} +(-2.75331 + 4.76887i) q^{62} +(0.444691 - 7.92479i) q^{63} -1.00000i q^{64} +(-0.903606 + 13.8782i) q^{65} +(5.99368 - 2.49909i) q^{66} +(-13.5156 - 3.62149i) q^{67} -0.858136i q^{68} +(1.12775 - 8.72357i) q^{69} +(6.76503 + 7.64096i) q^{70} +(0.326314 - 1.21782i) q^{71} +(-2.59104 + 1.51213i) q^{72} +(4.80475 - 1.28743i) q^{73} +5.75109i q^{74} +(10.3843 - 13.5987i) q^{75} +(-4.15440 + 1.11317i) q^{76} +(-0.602025 + 9.90119i) q^{77} +(4.10460 - 4.70662i) q^{78} +(7.06620 + 12.2390i) q^{79} +(0.998336 - 3.72584i) q^{80} +(7.83595 + 4.42695i) q^{81} +(-0.694371 - 0.400895i) q^{82} +(4.70571 + 4.70571i) q^{83} +(-0.331982 - 4.57053i) q^{84} +(0.856708 - 3.19728i) q^{85} +(-1.28390 - 0.344020i) q^{86} +(-3.61292 + 4.73130i) q^{87} +(3.24691 - 1.87460i) q^{88} +(-0.827250 + 0.827250i) q^{89} +(-11.1634 + 3.04721i) q^{90} +(3.69594 + 8.79432i) q^{91} -5.07846i q^{92} +(9.45321 - 1.26702i) q^{93} +(-2.92827 - 5.07191i) q^{94} -16.5899 q^{95} +(-1.37166 + 1.05761i) q^{96} +(-3.55976 - 0.953834i) q^{97} +(6.49216 + 2.61760i) q^{98} +(-9.76690 - 5.57823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.222065	+	1.71776i	−0.128209	+	0.991747i
$3$	−0.222065	+	1.71776i	−0.128209	+	0.991747i
$4$			1.00000i			0.500000i
$5$	−0.998336	+	3.72584i	−0.446469	+	1.66625i	0.265558	+	0.964095i	$0.414444\pi$
$5$	−0.998336	+	3.72584i	−0.446469	+	1.66625i	−0.712028	+	0.702151i	$0.752223\pi$
$6$	1.37166	−	1.05761i	0.559978	−	0.431769i
$7$	0.528406	+	2.59245i	0.199719	+	0.979853i
$7$	0.528406	+	2.59245i	0.199719	+	0.979853i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.90137	−	0.762906i	−0.967125	−	0.254302i
$10$	3.34050	−	1.92864i	1.05636	−	0.609888i
$11$	3.62146	+	0.970367i	1.09191	+	0.292577i	0.759466	−	0.650546i	$-0.225460\pi$
$11$	3.62146	+	0.970367i	1.09191	+	0.292577i	0.332444	+	0.943123i	$0.392127\pi$
$12$	−1.71776	−	0.222065i	−0.495874	−	0.0641046i
$13$	3.53597	−	0.704936i	0.980701	−	0.195514i
$13$	3.53597	−	0.704936i	0.980701	−	0.195514i
$14$	1.45950	−	2.20678i	0.390067	−	0.589786i
$15$	−6.17839	−	2.54228i	−1.59525	−	0.656413i
$16$	−1.00000			−0.250000
$17$	−0.858136			−0.208129			−0.104064	−	0.994571i	$-0.533185\pi$
$17$	−0.858136			−0.208129			−0.104064	+	0.994571i	$0.533185\pi$
$18$	1.51213	+	2.59104i	0.356411	+	0.610713i
$19$	1.11317	+	4.15440i	0.255378	+	0.953084i	0.967880	+	0.251414i	$0.0808955\pi$
$19$	1.11317	+	4.15440i	0.255378	+	0.953084i	−0.712501	+	0.701671i	$0.752438\pi$
$20$	−3.72584	−	0.998336i	−0.833123	−	0.223235i
$21$	−4.57053	+	0.331982i	−0.997372	+	0.0724443i
$22$	−1.87460	−	3.24691i	−0.399667	−	0.692243i
$23$	−5.07846			−1.05893			−0.529467	−	0.848331i	$-0.677608\pi$
$23$	−5.07846			−1.05893			−0.529467	+	0.848331i	$0.677608\pi$
$24$	1.05761	+	1.37166i	0.215884	+	0.279989i
$25$	−8.55508	−	4.93928i	−1.71102	−	0.987856i
$26$	−2.99877	−	2.00184i	−0.588107	−	0.392593i
$27$	1.95478	−	4.81444i	0.376198	−	0.926539i
$28$	−2.59245	+	0.528406i	−0.489927	+	0.0998594i
$29$	2.97651	+	1.71849i	0.552724	+	0.319115i	0.750220	−	0.661188i	$-0.229948\pi$
$29$	2.97651	+	1.71849i	0.552724	+	0.319115i	−0.197496	+	0.980304i	$0.563281\pi$
$30$	2.57112	+	6.16644i	0.469420	+	1.12583i
$31$	−1.42522	−	5.31898i	−0.255977	−	0.955318i	−0.967545	−	0.252700i	$-0.918681\pi$
$31$	−1.42522	−	5.31898i	−0.255977	−	0.955318i	0.711568	−	0.702617i	$-0.247985\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.47105	+	6.00530i	−0.430155	+	1.04539i
$34$	0.606794	+	0.606794i	0.104064	+	0.104064i
$35$	−10.1866	−	0.619377i	−1.72185	−	0.104694i
$36$	0.762906	−	2.90137i	0.127151	−	0.483562i
$37$	−4.06664	−	4.06664i	−0.668551	−	0.668551i	0.288830	−	0.957381i	$-0.406734\pi$
$37$	−4.06664	−	4.06664i	−0.668551	−	0.668551i	−0.957381	+	0.288830i	$0.906734\pi$
$38$	2.15047	−	3.72473i	0.348853	−	0.604231i
$39$	0.425694	+	6.23047i	0.0681656	+	0.997674i
$40$	1.92864	+	3.34050i	0.304944	+	0.528179i
$41$	0.774470	−	0.207519i	0.120952	−	0.0324090i	−0.197835	−	0.980235i	$-0.563391\pi$
$41$	0.774470	−	0.207519i	0.120952	−	0.0324090i	0.318787	+	0.947826i	$0.396724\pi$
$42$	3.46660	+	2.99711i	0.534908	+	0.462464i
$43$	1.15111	−	0.664595i	0.175543	−	0.101350i	−0.409654	−	0.912241i	$-0.634351\pi$
$43$	1.15111	−	0.664595i	0.175543	−	0.101350i	0.585197	+	0.810891i	$0.301017\pi$
$44$	−0.970367	+	3.62146i	−0.146288	+	0.545955i
$45$	5.73901	−	10.0484i	0.855522	−	1.49793i
$46$	3.59102	+	3.59102i	0.529467	+	0.529467i
$47$	5.65698	+	1.51578i	0.825156	+	0.221100i	0.646599	−	0.762830i	$-0.276191\pi$
$47$	5.65698	+	1.51578i	0.825156	+	0.221100i	0.178557	+	0.983930i	$0.442857\pi$
$48$	0.222065	−	1.71776i	0.0320523	−	0.247937i
$49$	−6.44157	+	2.73973i	−0.920225	+	0.391390i
$50$	2.55676	+	9.54195i	0.361580	+	1.34944i
$51$	0.190562	−	1.47407i	0.0266840	−	0.206411i
$52$	0.704936	+	3.53597i	0.0977570	+	0.490350i
$53$	4.07315	+	2.35163i	0.559490	+	0.323022i	0.752941	−	0.658088i	$-0.228635\pi$
$53$	4.07315	+	2.35163i	0.559490	+	0.323022i	−0.193451	+	0.981110i	$0.561968\pi$
$54$	−4.78656	+	2.02208i	−0.651369	+	0.275171i
$55$	−7.23086	+	12.5242i	−0.975009	+	1.68877i
$56$	2.20678	+	1.45950i	0.294893	+	0.195034i
$57$	−7.38344	+	0.989606i	−0.977961	+	0.131076i
$58$	−0.889555	−	3.31987i	−0.116804	−	0.435920i
$59$	10.2258	−	10.2258i	1.33128	−	1.33128i	0.427059	−	0.904224i	$-0.359550\pi$
$59$	10.2258	−	10.2258i	1.33128	−	1.33128i	0.904224	−	0.427059i	$-0.140450\pi$
$60$	2.54228	−	6.17839i	0.328206	−	0.797627i
$61$	−1.55221	+	2.68851i	−0.198741	+	0.344229i	−0.948120	−	0.317912i	$-0.897018\pi$
$61$	−1.55221	+	2.68851i	−0.198741	+	0.344229i	0.749380	+	0.662141i	$0.230352\pi$
$62$	−2.75331	+	4.76887i	−0.349671	+	0.605647i
$63$	0.444691	−	7.92479i	0.0560258	−	0.998429i
$64$		−	1.00000i		−	0.125000i
$65$	−0.903606	+	13.8782i	−0.112079	+	1.72138i
$66$	5.99368	−	2.49909i	0.737771	−	0.307617i
$67$	−13.5156	−	3.62149i	−1.65119	−	0.442435i	−0.691245	−	0.722621i	$-0.742937\pi$
$67$	−13.5156	−	3.62149i	−1.65119	−	0.442435i	−0.959946	+	0.280186i	$0.909604\pi$
$68$		−	0.858136i		−	0.104064i
$69$	1.12775	−	8.72357i	0.135765	−	1.05019i
$70$	6.76503	+	7.64096i	0.808576	+	0.913269i
$71$	0.326314	−	1.21782i	0.0387264	−	0.144529i	−0.943856	−	0.330358i	$-0.892830\pi$
$71$	0.326314	−	1.21782i	0.0387264	−	0.144529i	0.982582	+	0.185829i	$0.0594971\pi$
$72$	−2.59104	+	1.51213i	−0.305357	+	0.178206i
$73$	4.80475	−	1.28743i	0.562353	−	0.150682i	0.0335659	−	0.999437i	$-0.489314\pi$
$73$	4.80475	−	1.28743i	0.562353	−	0.150682i	0.528787	+	0.848754i	$0.322647\pi$
$74$			5.75109i			0.668551i
$75$	10.3843	−	13.5987i	1.19907	−	1.57024i
$76$	−4.15440	+	1.11317i	−0.476542	+	0.127689i
$77$	−0.602025	+	9.90119i	−0.0686071	+	1.12834i
$78$	4.10460	−	4.70662i	0.464754	−	0.532920i
$79$	7.06620	+	12.2390i	0.795010	+	1.37700i	0.922833	+	0.385200i	$0.125868\pi$
$79$	7.06620	+	12.2390i	0.795010	+	1.37700i	−0.127823	+	0.991797i	$0.540799\pi$
$80$	0.998336	−	3.72584i	0.111617	−	0.416562i
$81$	7.83595	+	4.42695i	0.870661	+	0.491884i
$82$	−0.694371	−	0.400895i	−0.0766804	−	0.0442715i
$83$	4.70571	+	4.70571i	0.516519	+	0.516519i	0.916516	−	0.399998i	$-0.130989\pi$
$83$	4.70571	+	4.70571i	0.516519	+	0.516519i	−0.399998	+	0.916516i	$0.630989\pi$
$84$	−0.331982	−	4.57053i	−0.0362222	−	0.498686i
$85$	0.856708	−	3.19728i	0.0929230	−	0.346793i
$86$	−1.28390	−	0.344020i	−0.138446	−	0.0370966i
$87$	−3.61292	+	4.73130i	−0.387346	+	0.507249i
$88$	3.24691	−	1.87460i	0.346122	−	0.199833i
$89$	−0.827250	+	0.827250i	−0.0876883	+	0.0876883i	−0.749590	−	0.661902i	$-0.769749\pi$
$89$	−0.827250	+	0.827250i	−0.0876883	+	0.0876883i	0.661902	+	0.749590i	$0.269749\pi$
$90$	−11.1634	+	3.04721i	−1.17673	+	0.321204i
$91$	3.69594	+	8.79432i	0.387439	+	0.921895i
$92$		−	5.07846i		−	0.529467i
$93$	9.45321	−	1.26702i	0.980252	−	0.131384i
$94$	−2.92827	−	5.07191i	−0.302028	−	0.523128i
$95$	−16.5899			−1.70209
$96$	−1.37166	+	1.05761i	−0.139995	+	0.107942i
$97$	−3.55976	−	0.953834i	−0.361439	−	0.0968472i	0.0735295	−	0.997293i	$-0.476574\pi$
$97$	−3.55976	−	0.953834i	−0.361439	−	0.0968472i	−0.434968	+	0.900446i	$0.643240\pi$
$98$	6.49216	+	2.61760i	0.655807	+	0.264417i
$99$	−9.76690	−	5.57823i	−0.981611	−	0.560633i
$100$	4.93928	−	8.55508i	0.493928	−	0.855508i
$101$	8.62305	+	14.9356i	0.858025	+	1.48614i	0.873810	+	0.486268i	$0.161642\pi$
$101$	8.62305	+	14.9356i	0.858025	+	1.48614i	−0.0157846	+	0.999875i	$0.505025\pi$
$102$	−1.17707	+	0.907577i	−0.116547	+	0.0898635i
$103$	16.2604	−	9.38793i	1.60218	−	0.925021i	0.611133	−	0.791528i	$-0.290714\pi$
$103$	16.2604	−	9.38793i	1.60218	−	0.925021i	0.991050	−	0.133493i	$-0.0426193\pi$
$104$	2.00184	−	2.99877i	0.196297	−	0.294054i
$105$	3.32602	−	17.3605i	0.324586	−	1.69421i
$106$	−1.21730	−	4.54301i	−0.118234	−	0.441256i
$107$		−	15.5123i		−	1.49963i	−0.661647	−	0.749815i	$-0.730142\pi$
$107$		−	15.5123i		−	1.49963i	0.661647	−	0.749815i	$-0.269858\pi$
$108$	4.81444	+	1.95478i	0.463270	+	0.188099i
$109$	−0.377448	−	1.40866i	−0.0361530	−	0.134925i	0.945491	−	0.325649i	$-0.105583\pi$
$109$	−0.377448	−	1.40866i	−0.0361530	−	0.134925i	−0.981644	+	0.190725i	$0.938916\pi$
$110$	13.9689	−	3.74297i	1.33189	−	0.356878i
$111$	7.88855	−	6.08244i	0.748748	−	0.577319i
$112$	−0.528406	−	2.59245i	−0.0499297	−	0.244963i
$113$	−6.29558	+	3.63476i	−0.592239	+	0.341929i	−0.765982	−	0.642862i	$-0.777747\pi$
$113$	−6.29558	+	3.63476i	−0.592239	+	0.341929i	0.173743	+	0.984791i	$0.444414\pi$
$114$	5.92064	+	4.52112i	0.554519	+	0.423442i
$115$	5.07001	−	18.9215i	0.472781	−	1.76444i
$116$	−1.71849	+	2.97651i	−0.159558	+	0.276362i
$117$	−10.7970	−	0.652330i	−0.998180	−	0.0603079i
$118$	−14.4614			−1.33128
$119$	−0.453444	−	2.22467i	−0.0415672	−	0.203935i
$120$	−6.16644	+	2.57112i	−0.562917	+	0.234710i
$121$	2.64706	+	1.52828i	0.240642	+	0.138935i
$122$	2.99865	−	0.803485i	0.271485	−	0.0727441i
$123$	0.184484	+	1.37643i	0.0166344	+	0.124109i
$124$	5.31898	−	1.42522i	0.477659	−	0.127988i
$125$	13.3063	−	13.3063i	1.19015	−	1.19015i
$126$	−5.91811	+	5.28923i	−0.527228	+	0.471202i
$127$	−2.86221	−	1.65250i	−0.253980	−	0.146636i	0.367605	−	0.929982i	$-0.380178\pi$
$127$	−2.86221	−	1.65250i	−0.253980	−	0.146636i	−0.621585	+	0.783346i	$0.713511\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	0.885992	+	2.12492i	0.0780072	+	0.187088i
$130$	10.4523	−	9.17443i	0.916729	−	0.804651i
$131$	−10.0080	+	5.77814i	−0.874406	+	0.504839i	−0.868810	−	0.495146i	$-0.835115\pi$
$131$	−10.0080	+	5.77814i	−0.874406	+	0.504839i	−0.00559642	+	0.999984i	$0.501781\pi$
$132$	−6.00530	−	2.47105i	−0.522694	−	0.215077i
$133$	−10.1819	+	5.08104i	−0.882879	+	0.440582i
$134$	6.99618	+	12.1177i	0.604378	+	1.04681i
$135$	15.9863	+	12.0896i	1.37588	+	1.04051i
$136$	−0.606794	+	0.606794i	−0.0520321	+	0.0520321i
$137$	−13.9712	+	13.9712i	−1.19364	+	1.19364i	−0.217606	+	0.976037i	$0.569825\pi$
$137$	−13.9712	+	13.9712i	−1.19364	+	1.19364i	−0.976037	+	0.217606i	$0.930175\pi$
$138$	−6.96593	+	5.37105i	−0.592979	+	0.457215i
$139$	−2.39445	−	4.14730i	−0.203094	−	0.351770i	0.746430	−	0.665464i	$-0.231766\pi$
$139$	−2.39445	−	4.14730i	−0.203094	−	0.351770i	−0.949524	+	0.313695i	$0.898433\pi$
$140$	0.619377	−	10.1866i	0.0523469	−	0.860923i
$141$	−3.85996	+	9.38072i	−0.325068	+	0.789999i
$142$	−1.09187	+	0.630391i	−0.0916276	+	0.0529012i
$143$	13.4894	+	0.878291i	1.12804	+	0.0734463i
$144$	2.90137	+	0.762906i	0.241781	+	0.0635755i
$145$	−9.37437	+	9.37437i	−0.778499	+	0.778499i
$146$	−4.30782	−	2.48712i	−0.356518	−	0.205836i
$147$	−3.27574	−	11.6735i	−0.270179	−	0.962810i
$148$	4.06664	−	4.06664i	0.334276	−	0.334276i
$149$	6.29700	−	1.68728i	0.515871	−	0.138227i	0.00851475	−	0.999964i	$-0.497290\pi$
$149$	6.29700	−	1.68728i	0.515871	−	0.138227i	0.507356	+	0.861737i	$0.330623\pi$
$150$	−16.9585	+	2.27296i	−1.38466	+	0.185586i
$151$	16.8335	−	4.51053i	1.36989	−	0.367062i	0.502454	−	0.864604i	$-0.332431\pi$
$151$	16.8335	−	4.51053i	1.36989	−	0.367062i	0.867440	+	0.497542i	$0.165764\pi$
$152$	3.72473	+	2.15047i	0.302116	+	0.174427i
$153$	2.48977	+	0.654678i	0.201286	+	0.0529275i
$154$	7.42689	−	6.57550i	0.598476	−	0.529869i
$155$	21.2405			1.70608
$156$	−6.23047	+	0.425694i	−0.498837	+	0.0340828i
$157$	−10.1263	+	17.5393i	−0.808171	+	1.39979i	0.105959	+	0.994370i	$0.466209\pi$
$157$	−10.1263	+	17.5393i	−0.808171	+	1.39979i	−0.914130	+	0.405422i	$0.867125\pi$
$158$	3.65773	−	13.6508i	0.290994	−	1.08600i
$159$	−4.94404	+	6.47446i	−0.392088	+	0.513458i
$160$	−3.34050	+	1.92864i	−0.264089	+	0.152472i
$161$	−2.68349	−	13.1657i	−0.211489	−	1.03760i
$162$	−2.41052	−	8.67118i	−0.189389	−	0.681272i
$163$	5.94888	−	1.59400i	0.465952	−	0.124851i	−0.0182019	−	0.999834i	$-0.505794\pi$
$163$	5.94888	−	1.59400i	0.465952	−	0.124851i	0.484154	+	0.874983i	$0.339127\pi$
$164$	0.207519	+	0.774470i	0.0162045	+	0.0604759i
$165$	−19.9078	−	15.2020i	−1.54982	−	1.18348i
$166$		−	6.65488i		−	0.516519i
$167$	−4.58101	−	17.0966i	−0.354489	−	1.32297i	−0.881126	−	0.472882i	$-0.843214\pi$
$167$	−4.58101	−	17.0966i	−0.354489	−	1.32297i	0.526637	−	0.850091i	$-0.323453\pi$
$168$	−2.99711	+	3.46660i	−0.231232	+	0.267454i
$169$	12.0061	−	4.98526i	0.923549	−	0.383481i
$170$	−2.86660	+	1.65503i	−0.219858	+	0.126935i
$171$	−0.0602994	−	12.9027i	−0.00461121	−	0.986695i
$172$	0.664595	+	1.15111i	0.0506749	+	0.0877716i
$173$	1.18509	−	2.05264i	0.0901007	−	0.156059i	−0.817453	−	0.575996i	$-0.804614\pi$
$173$	1.18509	−	2.05264i	0.0901007	−	0.156059i	0.907553	+	0.419937i	$0.137948\pi$
$174$	5.90026	−	0.790814i	0.447297	−	0.0599515i
$175$	8.28427	−	24.7885i	0.626232	−	1.87384i
$176$	−3.62146	−	0.970367i	−0.272978	−	0.0731441i
$177$	15.2946	+	19.8362i	1.14961	+	1.49098i
$178$	1.16991			0.0876883
$179$	4.70383	+	8.14728i	0.351581	+	0.608956i	0.986527	−	0.163601i	$-0.0523109\pi$
$179$	4.70383	+	8.14728i	0.351581	+	0.608956i	−0.634946	+	0.772557i	$0.718978\pi$
$180$	10.0484	+	5.73901i	0.748965	+	0.427761i
$181$			24.3790i			1.81207i	0.423198	+	0.906037i	$0.360907\pi$
$181$			24.3790i			1.81207i	−0.423198	+	0.906037i	$0.639093\pi$
$182$	3.60510	−	8.83194i	0.267228	−	0.654667i
$183$	−4.27352	−	3.26335i	−0.315908	−	0.241234i
$184$	−3.59102	+	3.59102i	−0.264733	+	0.264733i
$185$	19.2115	−	11.0918i	1.41246	−	0.815483i
$186$	−7.58034	−	5.78851i	−0.555818	−	0.424434i
$187$	−3.10770	−	0.832707i	−0.227258	−	0.0608935i
$188$	−1.51578	+	5.65698i	−0.110550	+	0.412578i
$189$	13.5141	+	2.52369i	0.983006	+	0.183571i
$190$	11.7309	+	11.7309i	0.851046	+	0.851046i
$191$	−14.0745	−	8.12590i	−1.01839	−	0.587969i	−0.104755	−	0.994498i	$-0.533406\pi$
$191$	−14.0745	−	8.12590i	−1.01839	−	0.587969i	−0.913638	+	0.406529i	$0.866739\pi$
$192$	1.71776	+	0.222065i	0.123968	+	0.0160261i
$193$	0.633195	−	2.36312i	0.0455784	−	0.170101i	−0.939385	−	0.342864i	$-0.888603\pi$
$193$	0.633195	−	2.36312i	0.0455784	−	0.170101i	0.984963	+	0.172763i	$0.0552696\pi$
$194$	1.84267	+	3.19159i	0.132296	+	0.229143i
$195$	−23.6387	−	4.63404i	−1.69280	−	0.331850i
$196$	−2.73973	−	6.44157i	−0.195695	−	0.460112i
$197$	−17.2752	+	4.62888i	−1.23081	+	0.329794i	−0.814894	−	0.579610i	$-0.803205\pi$
$197$	−17.2752	+	4.62888i	−1.23081	+	0.329794i	−0.415914	+	0.909404i	$0.636538\pi$
$198$	2.96184	+	10.8506i	0.210489	+	0.771122i
$199$			8.83542i			0.626326i	0.949699	+	0.313163i	$0.101389\pi$
$199$			8.83542i			0.626326i	−0.949699	+	0.313163i	$0.898611\pi$
$200$	−9.54195	+	2.55676i	−0.674718	+	0.180790i
$201$	9.22217	−	22.4123i	0.650482	−	1.58084i
$202$	4.46362	−	16.6584i	0.314059	−	1.17208i
$203$	−2.88229	+	8.62451i	−0.202297	+	0.605322i
$204$	1.47407	+	0.190562i	0.103205	+	0.0133420i
$205$			3.09272i			0.216005i
$206$	−18.1361	−	4.85955i	−1.26360	−	0.338581i
$207$	14.7345	+	3.87439i	1.02412	+	0.269289i
$208$	−3.53597	+	0.704936i	−0.245175	+	0.0488785i
$209$			16.1252i			1.11540i
$210$	−14.6276	+	9.92388i	−1.00940	+	0.684813i
$211$	9.92000	−	17.1820i	0.682921	−	1.18285i	−0.291164	−	0.956673i	$-0.594043\pi$
$211$	9.92000	−	17.1820i	0.682921	−	1.18285i	0.974085	−	0.226181i	$-0.0726241\pi$
$212$	−2.35163	+	4.07315i	−0.161511	+	0.279745i
$213$	2.01946	+	0.830964i	0.138371	+	0.0569367i
$214$	−10.9688	+	10.9688i	−0.749815	+	0.749815i
$215$	1.32698	+	4.95235i	0.0904992	+	0.337748i
$216$	−2.02208	−	4.78656i	−0.137585	−	0.325684i
$217$	13.0361	−	6.50539i	0.884948	−	0.441614i
$218$	−0.729174	+	1.26297i	−0.0493859	+	0.0855389i
$219$	1.14452	+	8.53928i	0.0773397	+	0.577031i
$220$	−12.5242	−	7.23086i	−0.844383	−	0.487505i
$221$	−3.03434	+	0.604931i	−0.204112	+	0.0406920i
$222$	−9.87898	−	1.27712i	−0.663034	−	0.0857144i
$223$	1.25289	+	4.67584i	0.0838995	+	0.313117i	0.995104	−	0.0988382i	$-0.0315126\pi$
$223$	1.25289	+	4.67584i	0.0838995	+	0.313117i	−0.911204	+	0.411955i	$0.864846\pi$
$224$	−1.45950	+	2.20678i	−0.0975168	+	0.147446i
$225$	21.0533	+	20.8574i	1.40355	+	1.39049i
$226$	7.02181	+	1.88149i	0.467084	+	0.125155i
$227$	7.10864	+	7.10864i	0.471817	+	0.471817i	0.902502	−	0.430685i	$-0.141728\pi$
$227$	7.10864	+	7.10864i	0.471817	+	0.471817i	−0.430685	+	0.902502i	$0.641728\pi$
$228$	−0.989606	−	7.38344i	−0.0655382	−	0.488980i
$229$	−0.443341	+	1.65457i	−0.0292968	+	0.109337i	−0.979026	−	0.203736i	$-0.934692\pi$
$229$	−0.443341	+	1.65457i	−0.0292968	+	0.109337i	0.949729	+	0.313073i	$0.101358\pi$
$230$	−16.9646	+	9.79451i	−1.11861	+	0.645831i
$231$	−16.8741	−	3.23284i	−1.11024	−	0.212705i
$232$	3.31987	−	0.889555i	0.217960	−	0.0584022i
$233$	7.49512	+	12.9819i	0.491022	+	0.850474i	0.999947	−	0.0103366i	$-0.00329030\pi$
$233$	7.49512	+	12.9819i	0.491022	+	0.850474i	−0.508925	+	0.860811i	$0.669957\pi$
$234$	7.17334	+	8.09587i	0.468936	+	0.529244i
$235$	−11.2951	+	19.5638i	−0.736814	+	1.27620i
$236$	10.2258	+	10.2258i	0.665641	+	0.665641i
$237$	−22.5928	+	9.42016i	−1.46756	+	0.611905i
$238$	−1.25245	+	1.89372i	−0.0811842	+	0.122751i
$239$	7.39507	+	7.39507i	0.478347	+	0.478347i	0.904603	−	0.426256i	$-0.140168\pi$
$239$	7.39507	+	7.39507i	0.478347	+	0.478347i	−0.426256	+	0.904603i	$0.640168\pi$
$240$	6.17839	+	2.54228i	0.398813	+	0.164103i
$241$	5.84548	+	5.84548i	0.376540	+	0.376540i	0.869852	−	0.493312i	$-0.164214\pi$
$241$	5.84548	+	5.84548i	0.376540	+	0.376540i	−0.493312	+	0.869852i	$0.664214\pi$
$242$	−0.791097	−	2.95241i	−0.0508536	−	0.189788i
$243$	−9.34452	+	12.4772i	−0.599451	+	0.800411i
$244$	−2.68851	−	1.55221i	−0.172114	−	0.0993703i
$245$	−3.77694	−	26.7354i	−0.241300	−	1.70806i
$246$	0.842835	−	1.10373i	0.0537372	−	0.0703716i
$247$	6.86471	+	13.9051i	0.436791	+	0.884761i
$248$	−4.76887	−	2.75331i	−0.302824	−	0.174835i
$249$	−9.12823	+	7.03829i	−0.578478	+	0.446033i
$250$	−18.8179			−1.19015
$251$	0.193651	+	0.335414i	0.0122232	+	0.0211711i	0.872072	−	0.489377i	$-0.162776\pi$
$251$	0.193651	+	0.335414i	0.0122232	+	0.0211711i	−0.859849	+	0.510548i	$0.829442\pi$
$252$	7.92479	+	0.444691i	0.499215	+	0.0280129i
$253$	−18.3914	−	4.92797i	−1.15626	−	0.309819i
$254$	0.855396	+	3.19238i	0.0536723	+	0.200308i
$255$	5.30190	+	2.18162i	0.332018	+	0.136618i
$256$	1.00000			0.0625000
$257$	−27.7372			−1.73020			−0.865100	−	0.501599i	$-0.832745\pi$
$257$	−27.7372			−1.73020			−0.865100	+	0.501599i	$0.832745\pi$
$258$	0.876051	−	2.12903i	0.0545406	−	0.132548i
$259$	8.39371	−	12.6914i	0.521560	−	0.788604i
$260$	−13.8782	−	0.903606i	−0.860690	−	0.0560393i
$261$	−7.32492	−	7.25678i	−0.453401	−	0.449183i
$262$	11.1625	+	2.99099i	0.689623	+	0.184784i
$263$	−8.05209	+	4.64888i	−0.496513	+	0.286662i	−0.727273	−	0.686349i	$-0.759212\pi$
$263$	−8.05209	+	4.64888i	−0.496513	+	0.286662i	0.230759	+	0.973011i	$0.425879\pi$
$264$	2.49909	+	5.99368i	0.153808	+	0.368886i
$265$	−12.8282	+	12.8282i	−0.788029	+	0.788029i
$266$	10.7925	+	3.60682i	0.661731	+	0.221149i
$267$	−1.23731	−	1.60472i	−0.0757222	−	0.0982071i
$268$	3.62149	−	13.5156i	0.221218	−	0.825595i
$269$		−	14.8168i		−	0.903394i	−0.892171	−	0.451697i	$-0.850819\pi$
$269$		−	14.8168i		−	0.903394i	0.892171	−	0.451697i	$-0.149181\pi$
$270$	−2.75537	−	19.8527i	−0.167686	−	1.20820i
$271$	21.1857	+	21.1857i	1.28694	+	1.28694i	0.936637	+	0.350301i	$0.113921\pi$
$271$	21.1857	+	21.1857i	1.28694	+	1.28694i	0.350301	+	0.936637i	$0.386079\pi$
$272$	0.858136			0.0520321
$273$	−15.9272	+	4.39581i	−0.963960	+	0.266046i
$274$	19.7583			1.19364
$275$	−26.1889	−	26.1889i	−1.57925	−	1.57925i
$276$	8.72357	+	1.12775i	0.525097	+	0.0678825i
$277$			18.5553i			1.11488i	0.830217	+	0.557441i	$0.188217\pi$
$277$			18.5553i			1.11488i	−0.830217	+	0.557441i	$0.811783\pi$
$278$	−1.23946	+	4.62572i	−0.0743377	+	0.277432i
$279$	0.0772028	+	16.5197i	0.00462201	+	0.989007i
$280$	−7.64096	+	6.76503i	−0.456635	+	0.404288i
$281$	19.6555	−	19.6555i	1.17255	−	1.17255i	0.190951	−	0.981600i	$-0.438843\pi$
$281$	19.6555	−	19.6555i	1.17255	−	1.17255i	0.981600	−	0.190951i	$-0.0611570\pi$
$282$	9.36258	−	3.90376i	0.557533	−	0.232466i
$283$	−19.2652	+	11.1228i	−1.14520	+	0.661181i	−0.947713	−	0.319125i	$-0.896611\pi$
$283$	−19.2652	+	11.1228i	−1.14520	+	0.661181i	−0.197486	+	0.980306i	$0.563278\pi$
$284$	1.21782	+	0.326314i	0.0722644	+	0.0193632i
$285$	3.68404	−	28.4975i	0.218224	−	1.68804i
$286$	−8.91740	−	10.1595i	−0.527297	−	0.600743i
$287$	0.947216	+	1.89812i	0.0559124	+	0.112042i
$288$	−1.51213	−	2.59104i	−0.0891028	−	0.152678i
$289$	−16.2636			−0.956682
$290$	13.2574			0.778499
$291$	2.42895	−	5.90298i	0.142388	−	0.346039i
$292$	1.28743	+	4.80475i	0.0753410	+	0.281177i
$293$	0.436492	+	0.116958i	0.0255001	+	0.00683274i	0.271547	−	0.962425i	$-0.412465\pi$
$293$	0.436492	+	0.116958i	0.0255001	+	0.00683274i	−0.246046	+	0.969258i	$0.579132\pi$
$294$	−5.93808	+	10.5707i	−0.346316	+	0.616494i
$295$	27.8909	+	48.3084i	1.62387	+	2.81262i
$296$	−5.75109			−0.334276
$297$	11.7509	−	15.5384i	0.681858	−	0.901631i
$298$	−5.64574	−	3.25957i	−0.327049	−	0.188822i
$299$	−17.9573	+	3.57999i	−1.03850	+	0.207036i
$300$	13.5987	+	10.3843i	0.785122	+	0.599535i
$301$	2.33118	+	2.63302i	0.134367	+	0.151765i
$302$	−15.0925	−	8.71368i	−0.868478	−	0.501416i
$303$	−27.5705	+	11.4956i	−1.58389	+	0.660407i
$304$	−1.11317	−	4.15440i	−0.0638445	−	0.238271i
$305$	−8.46734	−	8.46734i	−0.484838	−	0.484838i
$306$	−1.29761	−	2.22346i	−0.0741794	−	0.127107i
$307$	−1.88568	−	1.88568i	−0.107622	−	0.107622i	0.651245	−	0.758867i	$-0.274247\pi$
$307$	−1.88568	−	1.88568i	−0.107622	−	0.107622i	−0.758867	+	0.651245i	$0.774247\pi$
$308$	−9.90119	−	0.602025i	−0.564172	−	0.0343036i
$309$	12.5153	+	30.0161i	0.711972	+	1.70756i
$310$	−15.0193	−	15.0193i	−0.853040	−	0.853040i
$311$	6.16349	−	10.6755i	0.349499	−	0.605351i	−0.636661	−	0.771144i	$-0.719685\pi$
$311$	6.16349	−	10.6755i	0.349499	−	0.605351i	0.986161	+	0.165793i	$0.0530183\pi$
$312$	4.70662	+	4.10460i	0.266460	+	0.232377i
$313$	3.28838	+	5.69564i	0.185870	+	0.321937i	0.943869	−	0.330319i	$-0.107156\pi$
$313$	3.28838	+	5.69564i	0.185870	+	0.321937i	−0.757999	+	0.652256i	$0.773823\pi$
$314$	19.5626	−	5.24178i	1.10398	−	0.295811i
$315$	29.0825	+	9.56845i	1.63862	+	0.539121i
$316$	−12.2390	+	7.06620i	−0.688499	+	0.397505i
$317$	0.110640	−	0.412915i	0.00621418	−	0.0231916i	−0.962749	−	0.270396i	$-0.912845\pi$
$317$	0.110640	−	0.412915i	0.00621418	−	0.0231916i	0.968963	+	0.247205i	$0.0795120\pi$
$318$	8.07410	−	1.08217i	0.452773	−	0.0606854i
$319$	9.11174	+	9.11174i	0.510159	+	0.510159i
$320$	3.72584	+	0.998336i	0.208281	+	0.0558087i
$321$	26.6463	+	3.44473i	1.48725	+	0.192266i
$322$	−7.41201	+	11.2070i	−0.413055	+	0.624544i
$323$	−0.955250	−	3.56504i	−0.0531515	−	0.198364i
$324$	−4.42695	+	7.83595i	−0.245942	+	0.435330i
$325$	−33.7324	−	11.4343i	−1.87113	−	0.634263i
$326$	−5.33362	−	3.07937i	−0.295402	−	0.170550i
$327$	2.50355	−	0.335551i	0.138446	−	0.0185560i
$328$	0.400895	−	0.694371i	0.0221357	−	0.0383402i
$329$	−0.940407	+	15.4664i	−0.0518463	+	0.852689i
$330$	3.32750	+	24.8264i	0.183173	+	1.36665i
$331$	−3.19075	−	11.9080i	−0.175379	−	0.654525i	−0.996487	−	0.0837510i	$-0.973310\pi$
$331$	−3.19075	−	11.9080i	−0.175379	−	0.654525i	0.821107	−	0.570774i	$-0.193357\pi$
$332$	−4.70571	+	4.70571i	−0.258259	+	0.258259i
$333$	8.69637	+	14.9013i	0.476558	+	0.816586i
$334$	−8.84984	+	15.3284i	−0.484241	+	0.838731i
$335$	26.9862	−	46.7414i	1.47441	−	2.55376i
$336$	4.57053	−	0.331982i	0.249343	−	0.0181111i
$337$			16.3884i			0.892732i	0.894850	+	0.446366i	$0.147282\pi$
$337$			16.3884i			0.892732i	−0.894850	+	0.446366i	$0.852718\pi$
$338$	−12.0147	−	4.96451i	−0.653515	−	0.270034i
$339$	−4.84560	−	11.6214i	−0.263177	−	0.631190i
$340$	3.19728	+	0.856708i	0.173397	+	0.0464615i
$341$		−	20.6455i		−	1.11801i
$342$	−9.08095	+	9.16623i	−0.491042	+	0.495653i
$343$	−10.5064	−	15.2518i	−0.567291	−	0.823517i
$344$	0.344020	−	1.28390i	0.0185483	−	0.0692232i
$345$	31.3767	+	12.9109i	1.68927	+	0.695097i
$346$	−2.28942	+	0.613447i	−0.123080	+	0.0329791i
$347$			11.5331i			0.619130i	0.950878	+	0.309565i	$0.100183\pi$
$347$			11.5331i			0.619130i	−0.950878	+	0.309565i	$0.899817\pi$
$348$	−4.73130	−	3.61292i	−0.253624	−	0.193673i
$349$	28.2682	−	7.57445i	1.51316	−	0.405451i	0.595680	−	0.803222i	$-0.296883\pi$
$349$	28.2682	−	7.57445i	1.51316	−	0.405451i	0.917485	+	0.397771i	$0.130216\pi$
$350$	−23.3860	+	11.6703i	−1.25003	+	0.623803i
$351$	3.51817	−	18.4017i	0.187786	−	0.982210i
$352$	1.87460	+	3.24691i	0.0999167	+	0.173061i
$353$	−4.17655	+	15.5871i	−0.222295	+	0.829617i	0.761175	+	0.648547i	$0.224623\pi$
$353$	−4.17655	+	15.5871i	−0.222295	+	0.829617i	−0.983470	+	0.181071i	$0.942044\pi$
$354$	3.21137	−	24.8412i	0.170683	−	1.32030i
$355$	4.21164	+	2.43159i	0.223531	+	0.129055i
$356$	−0.827250	−	0.827250i	−0.0438441	−	0.0438441i
$357$	3.92214	−	0.284885i	0.207582	−	0.0150777i
$358$	2.43488	−	9.08711i	0.128688	−	0.480268i
$359$	8.06012	+	2.15970i	0.425397	+	0.113985i	0.465165	−	0.885224i	$-0.345995\pi$
$359$	8.06012	+	2.15970i	0.425397	+	0.113985i	−0.0397678	+	0.999209i	$0.512662\pi$
$360$	−3.04721	−	11.1634i	−0.160602	−	0.588363i
$361$	0.434597	−	0.250915i	0.0228735	−	0.0132060i
$362$	17.2385	−	17.2385i	0.906037	−	0.906037i
$363$	−3.21303	+	4.20763i	−0.168641	+	0.220843i
$364$	−8.79432	+	3.69594i	−0.460948	+	0.193720i
$365$			19.1870i			1.00429i
$366$	0.714298	+	5.32937i	0.0373369	+	0.278571i
$367$	−7.87954	−	13.6478i	−0.411309	−	0.712408i	0.583724	−	0.811952i	$-0.301595\pi$
$367$	−7.87954	−	13.6478i	−0.411309	−	0.712408i	−0.995033	+	0.0995443i	$0.968262\pi$
$368$	5.07846			0.264733
$369$	−2.40534	+	0.0112411i	−0.125217	+	0.000585189i
$370$	−21.4277	−	5.74152i	−1.11397	−	0.298488i
$371$	−3.94421	+	11.8020i	−0.204773	+	0.612732i
$372$	1.26702	+	9.45321i	0.0656918	+	0.490126i
$373$	10.7604	−	18.6376i	0.557152	−	0.965016i	−0.440580	−	0.897713i	$-0.645227\pi$
$373$	10.7604	−	18.6376i	0.557152	−	0.965016i	0.997733	−	0.0673028i	$-0.0214394\pi$
$374$	1.60867	+	2.78629i	0.0831821	+	0.144076i
$375$	19.9021	+	25.8118i	1.02774	+	1.33292i
$376$	5.07191	−	2.92827i	0.261564	−	0.151014i
$377$	11.7363	+	3.97827i	0.604448	+	0.204891i
$378$	−7.77140	−	11.3404i	−0.399718	−	0.583289i
$379$	−3.78995	−	14.1443i	−0.194677	−	0.726544i	−0.992350	−	0.123454i	$-0.960603\pi$
$379$	−3.78995	−	14.1443i	−0.194677	−	0.726544i	0.797674	−	0.603090i	$-0.206064\pi$
$380$		−	16.5899i		−	0.851046i
$381$	3.47419	−	4.54962i	0.177988	−	0.233084i
$382$	4.20628	+	15.6980i	0.215212	+	0.803181i
$383$	17.4647	−	4.67965i	0.892405	−	0.239119i	0.216653	−	0.976249i	$-0.430486\pi$
$383$	17.4647	−	4.67965i	0.892405	−	0.239119i	0.675751	+	0.737130i	$0.263819\pi$
$384$	−1.05761	−	1.37166i	−0.0539711	−	0.0699973i
$385$	−36.2892	−	12.1278i	−1.84947	−	0.618088i
$386$	−2.11871	+	1.22324i	−0.107840	+	0.0622613i
$387$	−3.84683	+	1.05005i	−0.195546	+	0.0533770i
$388$	0.953834	−	3.55976i	0.0484236	−	0.180719i
$389$	17.0678	−	29.5624i	0.865374	−	1.49887i	−0.00130104	−	0.999999i	$-0.500414\pi$
$389$	17.0678	−	29.5624i	0.865374	−	1.49887i	0.866675	−	0.498873i	$-0.166253\pi$
$390$	13.4383	+	19.9919i	0.680477	+	1.01233i
$391$	4.35801			0.220394
$392$	−2.61760	+	6.49216i	−0.132209	+	0.327904i
$393$	−7.70301	−	18.4745i	−0.388566	−	0.931915i
$394$	15.4885	+	8.94231i	0.780301	+	0.450507i
$395$	−52.6551	+	14.1089i	−2.64936	+	0.709895i
$396$	5.57823	−	9.76690i	0.280317	−	0.490805i
$397$	−5.99288	+	1.60579i	−0.300774	+	0.0805921i	−0.406050	−	0.913851i	$-0.633094\pi$
$397$	−5.99288	+	1.60579i	−0.300774	+	0.0805921i	0.105276	+	0.994443i	$0.466427\pi$
$398$	6.24759	−	6.24759i	0.313163	−	0.313163i
$399$	−6.46696	−	18.6183i	−0.323753	−	0.932079i
$400$	8.55508	+	4.93928i	0.427754	+	0.246964i
$401$	−9.57756	+	9.57756i	−0.478281	+	0.478281i	−0.904581	−	0.426301i	$-0.859817\pi$
$401$	−9.57756	+	9.57756i	−0.478281	+	0.478281i	0.426301	+	0.904581i	$0.359817\pi$
$402$	−22.3689	+	9.32681i	−1.11566	+	0.465179i
$403$	−8.78906	−	17.8031i	−0.437814	−	0.886834i
$404$	−14.9356	+	8.62305i	−0.743072	+	0.429013i
$405$	−24.3170	+	24.7759i	−1.20832	+	1.23112i
$406$	8.13653	−	4.06036i	0.403809	−	0.201512i
$407$	−10.7810	−	18.6733i	−0.534395	−	0.925600i
$408$	−0.907577	−	1.17707i	−0.0449317	−	0.0582737i
$409$	−10.8715	+	10.8715i	−0.537563	+	0.537563i	−0.922812	−	0.385250i	$-0.874115\pi$
$409$	−10.8715	+	10.8715i	−0.537563	+	0.537563i	0.385250	+	0.922812i	$0.374115\pi$
$410$	2.18689	−	2.18689i	0.108003	−	0.108003i
$411$	−20.8967	−	27.1017i	−1.03076	−	1.33683i
$412$	9.38793	+	16.2604i	0.462510	+	0.801091i
$413$	31.9132	+	21.1064i	1.57034	+	1.03858i
$414$	−7.67928	−	13.1585i	−0.377416	−	0.646705i
$415$	−22.2306	+	12.8348i	−1.09126	+	0.630037i
$416$	2.99877	+	2.00184i	0.147027	+	0.0981484i
$417$	7.65578	−	3.19211i	0.374905	−	0.156318i
$418$	11.4022	−	11.4022i	0.557700	−	0.557700i
$419$	−19.8136	−	11.4394i	−0.967957	−	0.558850i	−0.0693443	−	0.997593i	$-0.522091\pi$
$419$	−19.8136	−	11.4394i	−0.967957	−	0.558850i	−0.898613	+	0.438742i	$0.855424\pi$
$420$	17.3605	+	3.32602i	0.847106	+	0.162293i
$421$	15.0535	−	15.0535i	0.733661	−	0.733661i	−0.237682	−	0.971343i	$-0.576388\pi$
$421$	15.0535	−	15.0535i	0.733661	−	0.733661i	0.971343	+	0.237682i	$0.0763875\pi$
$422$	−19.1640	+	5.13497i	−0.932888	+	0.249967i
$423$	−15.2566	−	8.71361i	−0.741803	−	0.423670i
$424$	4.54301	−	1.21730i	0.220628	−	0.0591171i
$425$	7.34142	+	4.23857i	0.356111	+	0.205601i
$426$	−0.840392	−	2.01555i	−0.0407171	−	0.0976539i
$427$	−7.79003	−	2.60341i	−0.376986	−	0.125988i
$428$	15.5123			0.749815
$429$	−4.50421	+	22.9765i	−0.217465	+	1.10931i
$430$	2.56353	−	4.44016i	0.123624	−	0.214123i
$431$	−4.26352	+	15.9117i	−0.205366	+	0.766438i	0.783971	+	0.620797i	$0.213191\pi$
$431$	−4.26352	+	15.9117i	−0.205366	+	0.766438i	−0.989338	+	0.145641i	$0.953476\pi$
$432$	−1.95478	+	4.81444i	−0.0940494	+	0.231635i
$433$	30.5376	−	17.6309i	1.46754	−	0.847287i	0.468204	−	0.883620i	$-0.344901\pi$
$433$	30.5376	−	17.6309i	1.46754	−	0.847287i	0.999340	+	0.0363331i	$0.0115677\pi$
$434$	−13.8179	−	4.61791i	−0.663281	−	0.221667i
$435$	−14.0212	−	18.1846i	−0.672264	−	0.871885i
$436$	1.40866	−	0.377448i	0.0674624	−	0.0180765i
$437$	−5.65318	−	21.0980i	−0.270428	−	1.00925i
$438$	5.22888	−	6.84748i	0.249846	−	0.327185i
$439$		−	40.3976i		−	1.92807i	−0.265772	−	0.964036i	$-0.585627\pi$
$439$		−	40.3976i		−	1.92807i	0.265772	−	0.964036i	$-0.414373\pi$
$440$	3.74297	+	13.9689i	0.178439	+	0.665944i
$441$	20.7796	−	3.03467i	0.989504	−	0.144508i
$442$	2.57335	+	1.71785i	0.122402	+	0.0817099i
$443$	14.1384	−	8.16280i	0.671735	−	0.387826i	−0.124999	−	0.992157i	$-0.539893\pi$
$443$	14.1384	−	8.16280i	0.671735	−	0.387826i	0.796734	+	0.604330i	$0.206559\pi$
$444$	6.08244	+	7.88855i	0.288660	+	0.374374i
$445$	−2.25633	−	3.90807i	−0.106960	−	0.185260i
$446$	2.42039	−	4.19224i	0.114609	−	0.198508i
$447$	1.49999	+	11.1914i	0.0709470	+	0.529335i
$448$	2.59245	−	0.528406i	0.122482	−	0.0249648i
$449$	−10.2311	−	2.74141i	−0.482834	−	0.129375i	0.00918765	−	0.999958i	$-0.497075\pi$
$449$	−10.2311	−	2.74141i	−0.482834	−	0.129375i	−0.492022	+	0.870583i	$0.663742\pi$
$450$	−0.138497	−	29.6353i	−0.00652883	−	1.39702i
$451$	3.00608			0.141551
$452$	−3.63476	−	6.29558i	−0.170965	−	0.296119i
$453$	4.00986	+	29.9175i	0.188400	+	1.40565i
$454$		−	10.0531i		−	0.471817i
$455$	−36.4560	+	4.99078i	−1.70908	+	0.233971i
$456$	−4.52112	+	5.92064i	−0.211721	+	0.277259i
$457$	1.13291	−	1.13291i	0.0529955	−	0.0529955i	−0.680112	−	0.733108i	$-0.738069\pi$
$457$	1.13291	−	1.13291i	0.0529955	−	0.0529955i	0.733108	+	0.680112i	$0.238069\pi$
$458$	1.48345	−	0.856469i	0.0693170	−	0.0400202i
$459$	−1.67747	+	4.13145i	−0.0782975	+	0.192839i
$460$	18.9215	+	5.07001i	0.882222	+	0.236391i
$461$	2.74435	−	10.2421i	0.127817	−	0.477020i	−0.872107	−	0.489315i	$-0.837247\pi$
$461$	2.74435	−	10.2421i	0.127817	−	0.477020i	0.999924	+	0.0122944i	$0.00391354\pi$
$462$	9.64586	+	14.2178i	0.448766	+	0.661471i
$463$	13.8266	+	13.8266i	0.642577	+	0.642577i	0.951188	−	0.308611i	$-0.0998643\pi$
$463$	13.8266	+	13.8266i	0.642577	+	0.642577i	−0.308611	+	0.951188i	$0.599864\pi$
$464$	−2.97651	−	1.71849i	−0.138181	−	0.0797788i
$465$	−4.71677	+	36.4861i	−0.218735	+	1.69200i
$466$	3.87976	−	14.4795i	0.179726	−	0.670748i
$467$	−8.30570	−	14.3859i	−0.384342	−	0.665699i	0.607336	−	0.794445i	$-0.292238\pi$
$467$	−8.30570	−	14.3859i	−0.384342	−	0.665699i	−0.991678	+	0.128746i	$0.958905\pi$
$468$	0.652330	−	10.7970i	0.0301540	−	0.499090i
$469$	2.24681	−	36.9520i	0.103748	−	1.70629i
$470$	21.8205	−	5.84679i	1.00651	−	0.269692i
$471$	−27.8796	−	21.2895i	−1.28463	−	0.980967i
$472$		−	14.4614i		−	0.665641i
$473$	4.81361	−	1.28980i	0.221330	−	0.0593052i
$474$	22.6366	+	9.31447i	1.03973	+	0.427828i
$475$	10.9965	−	41.0395i	0.504554	−	1.88302i
$476$	2.22467	−	0.453444i	0.101968	−	0.0207836i
$477$	−10.0237	−	9.93040i	−0.458952	−	0.454682i
$478$		−	10.4582i		−	0.478347i
$479$	3.94268	+	1.05644i	0.180146	+	0.0482699i	0.347764	−	0.937582i	$-0.386941\pi$
$479$	3.94268	+	1.05644i	0.180146	+	0.0482699i	−0.167618	+	0.985852i	$0.553608\pi$
$480$	−2.57112	−	6.16644i	−0.117355	−	0.281458i
$481$	−17.2462	−	11.5128i	−0.786360	−	0.524938i
$482$		−	8.26675i		−	0.376540i
$483$	23.2113	−	1.68596i	1.05615	−	0.0767137i
$484$	−1.52828	+	2.64706i	−0.0694673	+	0.120321i
$485$	7.10766	−	12.3108i	0.322742	−	0.559006i
$486$	15.4303	−	2.21513i	0.699931	−	0.100480i
$487$	3.94660	−	3.94660i	0.178838	−	0.178838i	−0.612011	−	0.790849i	$-0.709639\pi$
$487$	3.94660	−	3.94660i	0.178838	−	0.178838i	0.790849	+	0.612011i	$0.209639\pi$
$488$	0.803485	+	2.99865i	0.0363721	+	0.135742i
$489$	1.41706	+	10.5727i	0.0640818	+	0.478114i
$490$	−16.2341	+	21.5755i	−0.733382	+	0.974682i
$491$	13.4071	−	23.2219i	0.605056	−	1.04799i	−0.386986	−	0.922085i	$-0.626484\pi$
$491$	13.4071	−	23.2219i	0.605056	−	1.04799i	0.992043	−	0.125903i	$-0.0401827\pi$
$492$	−1.37643	+	0.184484i	−0.0620544	+	0.00831718i
$493$	−2.55425	−	1.47470i	−0.115038	−	0.0664170i
$494$	4.97831	−	14.6865i	0.223985	−	0.660776i
$495$	30.5342	−	30.8210i	1.37241	−	1.38530i
$496$	1.42522	+	5.31898i	0.0639941	+	0.238829i
$497$	3.32957	+	0.202449i	0.149351	+	0.00908106i
$498$	11.4315	+	1.47781i	0.512256	+	0.0662224i
$499$	−0.664159	−	0.177961i	−0.0297318	−	0.00796662i	0.243922	−	0.969795i	$-0.421566\pi$
$499$	−0.664159	−	0.177961i	−0.0297318	−	0.00796662i	−0.273654	+	0.961828i	$0.588232\pi$
$500$	13.3063	+	13.3063i	0.595075	+	0.595075i
$501$	30.3850	−	4.07252i	1.35750	−	0.181947i
$502$	0.100241	−	0.374105i	0.00447398	−	0.0166971i
$503$	5.03003	−	2.90409i	0.224278	−	0.129487i	−0.383652	−	0.923478i	$-0.625334\pi$
$503$	5.03003	−	2.90409i	0.224278	−	0.129487i	0.607929	+	0.793991i	$0.292000\pi$
$504$	−5.28923	−	5.91811i	−0.235601	−	0.263614i
$505$	−64.2562	+	17.2174i	−2.85936	+	0.766164i
$506$	9.52011	+	16.4893i	0.423221	+	0.733040i
$507$	5.89732	+	21.7307i	0.261909	+	0.965093i
$508$	1.65250	−	2.86221i	0.0733178	−	0.126990i
$509$	17.3856	+	17.3856i	0.770601	+	0.770601i	0.978212	−	0.207611i	$-0.0665687\pi$
$509$	17.3856	+	17.3856i	0.770601	+	0.770601i	−0.207611	+	0.978212i	$0.566569\pi$
$510$	−2.20637	−	5.29165i	−0.0976998	−	0.234318i
$511$	5.87645	+	11.7758i	0.259959	+	0.520930i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	22.1771	+	2.76166i	0.979143	+	0.121930i
$514$	19.6132	+	19.6132i	0.865100	+	0.865100i
$515$	18.7446	+	69.9559i	0.825987	+	3.08262i
$516$	−2.12492	+	0.885992i	−0.0935442	+	0.0390036i
$517$	19.0157	+	10.9787i	0.836308	+	0.482842i
$518$	−14.9094	+	3.03891i	−0.655082	+	0.133522i
$519$	3.26276	+	2.49151i	0.143219	+	0.109365i
$520$	9.17443	+	10.4523i	0.402325	+	0.458365i
$521$	4.56253	+	2.63418i	0.199888	+	0.115405i	0.596603	−	0.802536i	$-0.296517\pi$
$521$	4.56253	+	2.63418i	0.199888	+	0.115405i	−0.396715	+	0.917942i	$0.629850\pi$
$522$	0.0481865	+	10.3108i	0.00210906	+	0.451292i
$523$	−10.5961			−0.463333			−0.231667	−	0.972795i	$-0.574418\pi$
$523$	−10.5961			−0.463333			−0.231667	+	0.972795i	$0.574418\pi$
$524$	−5.77814	−	10.0080i	−0.252419	−	0.437203i
$525$	40.7410	+	19.7350i	1.77808	+	0.861307i
$526$	8.98094	+	2.40644i	0.391588	+	0.104926i
$527$	1.22303	+	4.56441i	0.0532760	+	0.198829i
$528$	2.47105	−	6.00530i	0.107539	−	0.261347i
$529$	2.79081			0.121339
$530$	18.1418			0.788029
$531$	−37.4701	+	21.8675i	−1.62606	+	0.948969i
$532$	−5.08104	−	10.1819i	−0.220291	−	0.441440i
$533$	2.59221	−	1.27973i	0.112281	−	0.0554313i
$534$	−0.259795	+	2.00962i	−0.0112424	+	0.0869646i
$535$	57.7963	+	15.4865i	2.49875	+	0.669539i
$536$	−12.1177	+	6.99618i	−0.523406	+	0.302189i
$537$	−15.0396	+	6.27081i	−0.649006	+	0.270606i
$538$	−10.4770	+	10.4770i	−0.451697	+	0.451697i
$539$	−25.9864	+	3.67113i	−1.11931	+	0.158127i
$540$	−12.0896	+	15.9863i	−0.520255	+	0.687941i
$541$	9.65396	−	36.0291i	0.415056	−	1.54901i	−0.369667	−	0.929164i	$-0.620528\pi$
$541$	9.65396	−	36.0291i	0.415056	−	1.54901i	0.784723	−	0.619846i	$-0.212805\pi$
$542$		−	29.9611i		−	1.28694i
$543$	−41.8771	−	5.41371i	−1.79712	−	0.232324i
$544$	−0.606794	−	0.606794i	−0.0260161	−	0.0260161i
$545$	5.62525			0.240959
$546$	14.3706	+	8.15395i	0.615003	+	0.348957i
$547$	−33.0367			−1.41255			−0.706274	−	0.707938i	$-0.749625\pi$
$547$	−33.0367			−1.41255			−0.706274	+	0.707938i	$0.749625\pi$
$548$	−13.9712	−	13.9712i	−0.596821	−	0.596821i
$549$	6.55464	−	6.61619i	0.279745	−	0.282372i
$550$			37.0368i			1.57925i
$551$	−3.82593	+	14.2786i	−0.162990	+	0.608288i
$552$	−5.37105	−	6.96593i	−0.228607	−	0.296490i
$553$	−27.9952	+	24.7859i	−1.19048	+	1.05400i
$554$	13.1206	−	13.1206i	0.557441	−	0.557441i
$555$	14.7868	+	35.4638i	0.627663	+	1.50535i
$556$	4.14730	−	2.39445i	0.175885	−	0.101547i
$557$	−14.4507	−	3.87204i	−0.612294	−	0.164064i	−0.0606720	−	0.998158i	$-0.519324\pi$
$557$	−14.4507	−	3.87204i	−0.612294	−	0.164064i	−0.551622	+	0.834094i	$0.685991\pi$
$558$	11.6266	−	11.7358i	0.492192	−	0.496814i
$559$	3.60180	−	3.16145i	0.152340	−	0.133715i
$560$	10.1866	+	0.619377i	0.430461	+	0.0261735i
$561$	2.12050	−	5.15336i	0.0895275	−	0.217575i
$562$	−27.7971			−1.17255
$563$	−20.9032			−0.880965			−0.440482	−	0.897761i	$-0.645193\pi$
$563$	−20.9032			−0.880965			−0.440482	+	0.897761i	$0.645193\pi$
$564$	−9.38072	−	3.85996i	−0.394999	−	0.162534i
$565$	−7.25742	−	27.0850i	−0.305322	−	1.13948i
$566$	21.4876	+	5.75758i	0.903190	+	0.242009i
$567$	−7.33609	+	22.6535i	−0.308087	+	0.951358i
$568$	−0.630391	−	1.09187i	−0.0264506	−	0.0458138i
$569$	16.1978			0.679047			0.339523	−	0.940598i	$-0.389734\pi$
$569$	16.1978			0.679047			0.339523	+	0.940598i	$0.389734\pi$
$570$	−22.7558	+	17.5457i	−0.953134	+	0.734910i
$571$	20.6308	+	11.9112i	0.863372	+	0.498468i	0.865140	−	0.501530i	$-0.167229\pi$
$571$	20.6308	+	11.9112i	0.863372	+	0.498468i	−0.00176774	+	0.999998i	$0.500563\pi$
$572$	−0.878291	+	13.4894i	−0.0367232	+	0.564020i
$573$	17.0838	−	22.3720i	0.713684	−	0.934605i
$574$	0.672390	−	2.01196i	0.0280650	−	0.0839774i
$575$	43.4467	+	25.0840i	1.81185	+	1.04607i
$576$	−0.762906	+	2.90137i	−0.0317878	+	0.120891i
$577$	3.92043	+	14.6312i	0.163209	+	0.609106i	0.998262	+	0.0589355i	$0.0187706\pi$
$577$	3.92043	+	14.6312i	0.163209	+	0.609106i	−0.835052	+	0.550171i	$0.814563\pi$
$578$	11.5001	+	11.5001i	0.478341	+	0.478341i
$579$	3.91865	+	1.61244i	0.162854	+	0.0670107i
$580$	−9.37437	−	9.37437i	−0.389250	−	0.389250i
$581$	−9.71278	+	14.6858i	−0.402954	+	0.609271i
$582$	−5.89157	+	2.45651i	−0.244213	+	0.101826i
$583$	12.4688	+	12.4688i	0.516405	+	0.516405i
$584$	2.48712	−	4.30782i	0.102918	−	0.178259i
$585$	13.2095	−	39.5765i	0.546145	−	1.63629i
$586$	−0.225945	−	0.391348i	−0.00933370	−	0.0161664i
$587$	15.7504	−	4.22031i	0.650089	−	0.174191i	0.0813201	−	0.996688i	$-0.474086\pi$
$587$	15.7504	−	4.22031i	0.650089	−	0.174191i	0.568769	+	0.822497i	$0.307420\pi$
$588$	11.6735	−	3.27574i	0.481405	−	0.135089i
$589$	20.5107	−	11.8418i	0.845128	−	0.487935i
$590$	14.4374	−	53.8810i	0.594377	−	2.21825i
$591$	−4.11507	−	30.7025i	−0.169271	−	1.26293i
$592$	4.06664	+	4.06664i	0.167138	+	0.167138i
$593$	−26.4266	−	7.08098i	−1.08521	−	0.290781i	−0.328481	−	0.944511i	$-0.606537\pi$
$593$	−26.4266	−	7.08098i	−1.08521	−	0.290781i	−0.756728	+	0.653730i	$0.773203\pi$
$594$	−19.2965	+	2.67817i	−0.791745	+	0.109887i
$595$	8.74147	+	0.531510i	0.358365	+	0.0217898i
$596$	1.68728	+	6.29700i	0.0691136	+	0.257935i
$597$	−15.1771	−	1.96204i	−0.621157	−	0.0803008i
$598$	15.2292	+	10.1663i	0.622766	+	0.415730i
$599$	14.2351	+	8.21862i	0.581629	+	0.335804i	0.761780	−	0.647835i	$-0.224326\pi$
$599$	14.2351	+	8.21862i	0.581629	+	0.335804i	−0.180152	+	0.983639i	$0.557659\pi$
$600$	−2.27296	−	16.9585i	−0.0927931	−	0.692329i
$601$	0.289361	−	0.501188i	0.0118033	−	0.0204439i	−0.860063	−	0.510187i	$-0.829576\pi$
$601$	0.289361	−	0.501188i	0.0118033	−	0.0204439i	0.871867	+	0.489743i	$0.162909\pi$
$602$	0.213433	−	3.51023i	0.00869889	−	0.143066i
$603$	36.4509	+	20.8184i	1.48440	+	0.847791i
$604$	4.51053	+	16.8335i	0.183531	+	0.684947i
$605$	−8.33679	+	8.33679i	−0.338939	+	0.338939i
$606$	27.6239	+	11.3667i	1.12215	+	0.461739i
$607$	−1.18100	+	2.04556i	−0.0479355	+	0.0830267i	−0.888998	−	0.457912i	$-0.848598\pi$
$607$	−1.18100	+	2.04556i	−0.0479355	+	0.0830267i	0.841062	+	0.540939i	$0.181931\pi$
$608$	−2.15047	+	3.72473i	−0.0872133	+	0.151058i
$609$	−14.1747	−	6.86627i	−0.574390	−	0.278235i
$610$			11.9746i			0.484838i
$611$	21.0714	+	1.37195i	0.852459	+	0.0555033i
$612$	−0.654678	+	2.48977i	−0.0264638	+	0.100643i
$613$	−20.9385	−	5.61046i	−0.845699	−	0.226604i	−0.190148	−	0.981755i	$-0.560897\pi$
$613$	−20.9385	−	5.61046i	−0.845699	−	0.226604i	−0.655551	+	0.755151i	$0.727563\pi$
$614$			2.66676i			0.107622i
$615$	−5.31255	−	0.686785i	−0.214223	−	0.0276938i
$616$	6.57550	+	7.42689i	0.264934	+	0.299238i
$617$	0.234904	−	0.876672i	0.00945687	−	0.0352935i	−0.961036	−	0.276423i	$-0.910851\pi$
$617$	0.234904	−	0.876672i	0.00945687	−	0.0352935i	0.970493	+	0.241129i	$0.0775177\pi$
$618$	12.3749	−	30.0743i	0.497792	−	1.20976i
$619$	−20.5782	+	5.51391i	−0.827107	+	0.221623i	−0.647451	−	0.762107i	$-0.724165\pi$
$619$	−20.5782	+	5.51391i	−0.827107	+	0.221623i	−0.179656	+	0.983730i	$0.557498\pi$
$620$			21.2405i			0.853040i
$621$	−9.92728	+	24.4500i	−0.398368	+	0.981143i
$622$	−11.9069	+	3.19046i	−0.477425	+	0.127926i
$623$	−2.58173	−	1.70748i	−0.103435	−	0.0684087i
$624$	−0.425694	−	6.23047i	−0.0170414	−	0.249419i
$625$	11.5965	+	20.0858i	0.463862	+	0.803432i
$626$	1.70219	−	6.35267i	0.0680333	−	0.253904i
$627$	−27.6991	−	3.58083i	−1.10620	−	0.143005i
$628$	−17.5393	−	10.1263i	−0.699896	−	0.404085i
$629$	3.48973	+	3.48973i	0.139145	+	0.139145i
$630$	−13.7985	−	27.3304i	−0.549747	−	1.08887i
$631$	8.90953	−	33.2508i	0.354683	−	1.32369i	−0.526200	−	0.850361i	$-0.676384\pi$
$631$	8.90953	−	33.2508i	0.354683	−	1.32369i	0.880883	−	0.473334i	$-0.156950\pi$
$632$	13.6508	+	3.65773i	0.543002	+	0.145497i
$633$	27.3115	+	20.8557i	1.08554	+	0.828938i
$634$	−0.370210	+	0.213741i	−0.0147029	+	0.00848873i
$635$	9.01439	−	9.01439i	0.357725	−	0.357725i
$636$	−6.47446	−	4.94404i	−0.256729	−	0.196044i
$637$	−20.8459	+	14.2285i	−0.825943	+	0.563753i
$638$		−	12.8859i		−	0.510159i
$639$	−1.87584	+	3.28441i	−0.0742072	+	0.129929i
$640$	−1.92864	−	3.34050i	−0.0762361	−	0.132045i
$641$	−14.4271			−0.569836			−0.284918	−	0.958552i	$-0.591966\pi$
$641$	−14.4271			−0.569836			−0.284918	+	0.958552i	$0.591966\pi$
$642$	−16.4060	−	21.2776i	−0.647494	−	0.839760i
$643$	25.2212	+	6.75799i	0.994626	+	0.266509i	0.719193	−	0.694811i	$-0.244512\pi$
$643$	25.2212	+	6.75799i	0.994626	+	0.266509i	0.275434	+	0.961320i	$0.411179\pi$
$644$	13.1657	−	2.68349i	0.518800	−	0.105744i
$645$	−8.80161	+	1.17968i	−0.346563	+	0.0464500i
$646$	−1.84540	+	3.19633i	−0.0726063	+	0.125758i
$647$	2.60423	+	4.51065i	0.102383	+	0.177332i	0.912666	−	0.408707i	$-0.134020\pi$
$647$	2.60423	+	4.51065i	0.102383	+	0.177332i	−0.810283	+	0.586039i	$0.800687\pi$
$648$	8.67118	−	2.41052i	0.340636	−	0.0946943i
$649$	46.9550	−	27.1095i	1.84314	−	1.06414i
$650$	15.7671	+	31.9377i	0.618436	+	1.25270i
$651$	8.27981	+	23.8375i	0.324511	+	0.934263i
$652$	1.59400	+	5.94888i	0.0624257	+	0.232976i
$653$		−	0.381461i		−	0.0149277i	−0.999972	−	0.00746385i	$-0.997624\pi$
$653$		−	0.381461i		−	0.0149277i	0.999972	−	0.00746385i	$-0.00237584\pi$
$654$	−2.00755	−	1.53300i	−0.0785012	−	0.0599452i
$655$	−11.5371	−	43.0569i	−0.450790	−	1.68237i
$656$	−0.774470	+	0.207519i	−0.0302380	+	0.00810224i
$657$	−14.9226	+	0.0697389i	−0.582184	+	0.00272077i
$658$	11.6014	−	10.2714i	0.452268	−	0.400422i
$659$	−41.4586	+	23.9362i	−1.61500	+	0.932420i	−0.626812	+	0.779170i	$0.715641\pi$
$659$	−41.4586	+	23.9362i	−1.61500	+	0.932420i	−0.988187	+	0.153250i	$0.951026\pi$
$660$	15.2020	−	19.9078i	0.591739	−	0.774911i
$661$	−2.62621	+	9.80114i	−0.102148	+	0.381220i	−0.998006	−	0.0631196i	$-0.979895\pi$
$661$	−2.62621	+	9.80114i	−0.102148	+	0.381220i	0.895858	+	0.444340i	$0.146562\pi$
$662$	−6.16405	+	10.6765i	−0.239573	+	0.414952i
$663$	−0.365303	−	5.34659i	−0.0141872	−	0.207644i
$664$	6.65488			0.258259
$665$	−8.76622	−	43.0086i	−0.339940	−	1.66780i
$666$	4.38755	−	16.6861i	0.170014	−	0.646572i
$667$	−15.1161	−	8.72729i	−0.585298	−	0.337922i
$668$	17.0966	−	4.58101i	0.661486	−	0.177245i
$669$	−8.31017	+	1.11382i	−0.321290	+	0.0430626i
$670$	−52.1333	+	13.9691i	−2.01408	+	0.539672i
$671$	−8.23012	+	8.23012i	−0.317720	+	0.317720i
$672$	−3.46660	−	2.99711i	−0.133727	−	0.115616i
$673$	−43.7483	−	25.2581i	−1.68637	−	0.973628i	−0.957258	−	0.289237i	$-0.906599\pi$
$673$	−43.7483	−	25.2581i	−1.68637	−	0.973628i	−0.729115	−	0.684391i	$-0.760068\pi$
$674$	11.5883	−	11.5883i	0.446366	−	0.446366i
$675$	−40.5032	+	31.5327i	−1.55897	+	1.21369i
$676$	4.98526	+	12.0061i	0.191741	+	0.461774i
$677$	25.0911	−	14.4864i	0.964331	−	0.556757i	0.0668277	−	0.997765i	$-0.478712\pi$
$677$	25.0911	−	14.4864i	0.964331	−	0.556757i	0.897503	+	0.441008i	$0.145379\pi$
$678$	−4.79124	+	11.6440i	−0.184006	+	0.447183i
$679$	0.591768	−	9.73250i	0.0227100	−	0.373499i
$680$	−1.65503	−	2.86660i	−0.0634676	−	0.109929i
$681$	−13.7895	+	10.6323i	−0.528414	+	0.407432i
$682$	−14.5985	+	14.5985i	−0.559007	+	0.559007i
$683$	17.1453	−	17.1453i	0.656046	−	0.656046i	−0.298396	−	0.954442i	$-0.596452\pi$
$683$	17.1453	−	17.1453i	0.656046	−	0.656046i	0.954442	+	0.298396i	$0.0964517\pi$
$684$	12.9027	−	0.0602994i	0.493347	−	0.00230560i
$685$	−38.1066	−	66.0025i	−1.45598	−	2.52183i
$686$	−3.35549	+	18.2137i	−0.128113	+	0.695404i
$687$	−2.74370	−	1.12897i	−0.104679	−	0.0430731i
$688$	−1.15111	+	0.664595i	−0.0438858	+	0.0253375i
$689$	16.0603	+	5.44399i	0.611848	+	0.207400i
$690$	−13.0573	−	31.3161i	−0.497085	−	1.19218i
$691$	−16.9978	+	16.9978i	−0.646628	+	0.646628i	−0.952176	−	0.305549i	$-0.901160\pi$
$691$	−16.9978	+	16.9978i	−0.646628	+	0.646628i	0.305549	+	0.952176i	$0.401160\pi$
$692$	2.05264	+	1.18509i	0.0780295	+	0.0450503i
$693$	9.30038	−	28.2678i	0.353292	−	1.07380i
$694$	8.15514	−	8.15514i	0.309565	−	0.309565i
$695$	17.8426	−	4.78092i	0.676810	−	0.181351i
$696$	0.790814	+	5.90026i	0.0299757	+	0.223649i
$697$	−0.664601	+	0.178079i	−0.0251735	+	0.00674523i
$698$	−25.3446	−	14.6327i	−0.959308	−	0.553857i
$699$	−23.9642	+	9.99196i	−0.906409	+	0.377931i
$700$	24.7885	+	8.28427i	0.936919	+	0.313116i
$701$	−32.8796			−1.24185			−0.620923	−	0.783872i	$-0.713242\pi$
$701$	−32.8796			−1.24185			−0.620923	+	0.783872i	$0.713242\pi$
$702$	−15.4997	+	10.5242i	−0.584998	+	0.397212i
$703$	12.3676	−	21.4213i	0.466452	−	0.807919i
$704$	0.970367	−	3.62146i	0.0365721	−	0.136489i
$705$	−31.0975	−	23.7467i	−1.17120	−	0.894353i
$706$	13.9750	−	8.06847i	0.525956	−	0.303661i
$707$	−34.1632	+	30.2468i	−1.28484	+	1.13755i
$708$	−19.8362	+	15.2946i	−0.745489	+	0.574807i
$709$	−23.0329	+	6.17165i	−0.865019	+	0.231781i	−0.663933	−	0.747792i	$-0.731114\pi$
$709$	−23.0329	+	6.17165i	−0.865019	+	0.231781i	−0.201087	+	0.979573i	$0.564447\pi$
$710$	−1.25868	−	4.69747i	−0.0472376	−	0.176293i
$711$	−11.1645	−	40.9008i	−0.418700	−	1.53390i
$712$			1.16991i			0.0438441i
$713$	7.23792	+	27.0123i	0.271062	+	1.01162i
$714$	−2.97482	−	2.57193i	−0.111330	−	0.0962520i
$715$	−16.7393	+	49.3825i	−0.626015	+	1.84680i
$716$	−8.14728	+	4.70383i	−0.304478	+	0.175790i
$717$	−14.3451	+	11.0607i	−0.535728	+	0.413071i
$718$	−4.17222	−	7.22650i	−0.155706	−	0.269691i
$719$	−13.3323	+	23.0923i	−0.497212	+	0.861196i	−0.999995	−	0.00321648i	$-0.998976\pi$
$719$	−13.3323	+	23.0923i	−0.497212	+	0.861196i	0.502783	+	0.864413i	$0.332309\pi$
$720$	−5.73901	+	10.0484i	−0.213880	+	0.374482i
$721$	32.9298	+	37.1935i	1.22637	+	1.38516i
$722$	−0.484730	−	0.129883i	−0.0180398	−	0.00483374i
$723$	−11.3392	+	8.74303i	−0.421709	+	0.325157i
$724$	−24.3790			−0.906037
$725$	−16.9762	−	29.4036i	−0.630480	−	1.09202i
$726$	5.24720	−	0.703285i	0.194742	−	0.0261013i
$727$			33.7416i			1.25141i	0.780061	+	0.625703i	$0.215188\pi$
$727$			33.7416i			1.25141i	−0.780061	+	0.625703i	$0.784812\pi$
$728$	8.83194	+	3.60510i	0.327334	+	0.133614i
$729$	−19.3577	−	18.8223i	−0.716951	−	0.697124i
$730$	13.5673	−	13.5673i	0.502147	−	0.502147i
$731$	−0.987812	+	0.570313i	−0.0365355	+	0.0210938i
$732$	3.26335	−	4.27352i	0.120617	−	0.157954i
$733$	38.0696	+	10.2007i	1.40613	+	0.376772i	0.880543	−	0.473966i	$-0.157178\pi$
$733$	38.0696	+	10.2007i	1.40613	+	0.376772i	0.525589	+	0.850738i	$0.323845\pi$
$734$	−4.07875	+	15.2221i	−0.150549	+	0.561858i
$735$	46.7637	−	0.550869i	1.72491	−	0.0203191i
$736$	−3.59102	−	3.59102i	−0.132367	−	0.132367i
$737$	−45.4319	−	26.2301i	−1.67351	−	0.966199i
$738$	1.70878	+	1.69289i	0.0629012	+	0.0623160i
$739$	4.02512	−	15.0220i	0.148067	−	0.552592i	−0.851533	−	0.524301i	$-0.824327\pi$
$739$	4.02512	−	15.0220i	0.148067	−	0.552592i	0.999600	−	0.0282912i	$-0.00900658\pi$
$740$	11.0918	+	19.2115i	0.407742	+	0.706229i
$741$	−25.4100	+	8.70406i	−0.933460	+	0.319752i
$742$	11.1343	−	5.55633i	0.408753	−	0.203979i
$743$	2.98428	−	0.799634i	0.109482	−	0.0293357i	−0.203662	−	0.979041i	$-0.565284\pi$
$743$	2.98428	−	0.799634i	0.109482	−	0.0293357i	0.313144	+	0.949706i	$0.398618\pi$
$744$	5.78851	−	7.58034i	0.212217	−	0.277909i
$745$			25.1461i			0.921282i
$746$	−20.7875	+	5.56999i	−0.761084	+	0.203932i
$747$	−10.0630	−	17.2430i	−0.368186	−	0.630890i
$748$	0.832707	−	3.10770i	0.0304468	−	0.113629i
$749$	40.2148	−	8.19679i	1.46942	−	0.299504i
$750$	4.17880	−	32.3246i	0.152588	−	1.18033i
$751$			54.6734i			1.99506i	0.0702453	+	0.997530i	$0.477622\pi$
$751$			54.6734i			1.99506i	−0.0702453	+	0.997530i	$0.522378\pi$
$752$	−5.65698	−	1.51578i	−0.206289	−	0.0552750i
$753$	−0.619162	+	0.258162i	−0.0225635	+	0.00940795i
$754$	−5.48573	−	11.1119i	−0.199778	−	0.404670i
$755$			67.2221i			2.44646i
$756$	−2.52369	+	13.5141i	−0.0917856	+	0.491503i
$757$	0.0583063	−	0.100989i	0.00211918	−	0.00367052i	−0.864964	−	0.501834i	$-0.832659\pi$
$757$	0.0583063	−	0.100989i	0.00211918	−	0.00367052i	0.867083	+	0.498164i	$0.165992\pi$
$758$	−7.32163	+	12.6814i	−0.265933	+	0.460610i
$759$	12.5491	−	30.4977i	0.455505	−	1.10700i
$760$	−11.7309	+	11.7309i	−0.425523	+	0.425523i
$761$	4.49619	+	16.7800i	0.162987	+	0.608274i	0.998288	+	0.0584826i	$0.0186262\pi$
$761$	4.49619	+	16.7800i	0.162987	+	0.608274i	−0.835302	+	0.549792i	$0.814707\pi$
$762$	−5.67369	+	0.760447i	−0.205536	+	0.0275481i
$763$	3.45242	−	1.72286i	0.124986	−	0.0623716i
$764$	8.12590	−	14.0745i	0.293985	−	0.509196i
$765$	−4.92485	+	8.62291i	−0.178058	+	0.311762i
$766$	−15.6584	−	9.04040i	−0.565762	−	0.326643i
$767$	28.9495	−	43.3665i	1.04531	−	1.56587i
$768$	−0.222065	+	1.71776i	−0.00801307	+	0.0619842i
$769$	−1.17842	−	4.39791i	−0.0424948	−	0.158593i	0.941418	−	0.337242i	$-0.109494\pi$
$769$	−1.17842	−	4.39791i	−0.0424948	−	0.158593i	−0.983913	+	0.178649i	$0.942827\pi$
$770$	17.0847	+	34.2360i	0.615691	+	1.23378i
$771$	6.15946	−	47.6458i	0.221828	−	1.71592i
$772$	2.36312	+	0.633195i	0.0850505	+	0.0227892i
$773$	−34.7582	−	34.7582i	−1.25017	−	1.25017i	−0.955645	−	0.294520i	$-0.904840\pi$
$773$	−34.7582	−	34.7582i	−1.25017	−	1.25017i	−0.294520	−	0.955645i	$-0.595160\pi$
$774$	3.46262	+	1.97763i	0.124461	+	0.0710843i
$775$	−14.0791	+	52.5439i	−0.505736	+	1.88743i
$776$	−3.19159	+	1.84267i	−0.114571	+	0.0661478i
$777$	19.9368	+	17.2367i	0.715227	+	0.618362i
$778$	−32.9725	+	8.83497i	−1.18212	+	0.316749i
$779$	1.72423	+	2.98645i	0.0617769	+	0.107001i
$780$	4.63404	−	23.6387i	0.165925	−	0.846402i
$781$	2.36347	−	4.09364i	0.0845715	−	0.146482i
$782$	−3.08158	−	3.08158i	−0.110197	−	0.110197i
$783$	14.0920	−	10.9710i	0.503606	−	0.392070i
$784$	6.44157	−	2.73973i	0.230056	−	0.0978475i
$785$	−55.2393	−	55.2393i	−1.97158	−	1.97158i
$786$	−7.61659	+	18.5103i	−0.271675	+	0.660240i
$787$	29.1310	+	29.1310i	1.03841	+	1.03841i	0.999232	+	0.0391744i	$0.0124728\pi$
$787$	29.1310	+	29.1310i	1.03841	+	1.03841i	0.0391744	+	0.999232i	$0.487527\pi$
$788$	−4.62888	−	17.2752i	−0.164897	−	0.615404i
$789$	−6.19755	−	14.8639i	−0.220639	−	0.529168i
$790$	47.2092	+	27.2563i	1.67963	+	0.969734i
$791$	−12.7495	−	14.4003i	−0.453322	−	0.512017i
$792$	−10.8506	+	2.96184i	−0.385561	+	0.105244i
$793$	−3.59335	+	10.6007i	−0.127604	+	0.376442i
$794$	5.37307	+	3.10214i	0.190683	+	0.110091i
$795$	−19.1870	−	24.8844i	−0.680493	−	0.882558i
$796$	−8.83542			−0.313163
$797$	3.17850	+	5.50533i	0.112588	+	0.195009i	0.916813	−	0.399316i	$-0.130753\pi$
$797$	3.17850	+	5.50533i	0.112588	+	0.195009i	−0.804225	+	0.594325i	$0.797419\pi$
$798$	−8.59228	+	17.7379i	−0.304163	+	0.627916i
$799$	−4.85446	−	1.30075i	−0.171739	−	0.0460172i
$800$	−2.55676	−	9.54195i	−0.0903951	−	0.337359i
$801$	3.03128	−	1.76905i	0.107105	−	0.0625062i
$802$	13.5447			0.478281
$803$	18.6495			0.658125
$804$	22.4123	+	9.22217i	0.790420	+	0.325241i
$805$	51.7322	+	3.14549i	1.82332	+	0.110864i
$806$	−6.37386	+	18.8035i	−0.224510	+	0.662324i
$807$	25.4516	+	3.29028i	0.895939	+	0.115823i
$808$	16.6584	+	4.46362i	0.586042	+	0.157030i
$809$	−6.33120	+	3.65532i	−0.222593	+	0.128514i	−0.607150	−	0.794587i	$-0.707687\pi$
$809$	−6.33120	+	3.65532i	−0.222593	+	0.128514i	0.384557	+	0.923101i	$0.374354\pi$
$810$	34.7139	−	0.324470i	1.21972	−	0.0114007i
$811$	−3.16405	+	3.16405i	−0.111105	+	0.111105i	−0.760474	−	0.649369i	$-0.775033\pi$
$811$	−3.16405	+	3.16405i	−0.111105	+	0.111105i	0.649369	+	0.760474i	$0.275033\pi$
$812$	−8.62451	−	2.88229i	−0.302661	−	0.101148i
$813$	−41.0964	+	31.6872i	−1.44131	+	1.11132i
$814$	−5.58067	+	20.8273i	−0.195602	+	0.729998i
$815$			23.7559i			0.832133i
$816$	−0.190562	+	1.47407i	−0.00667100	+	0.0516027i
$817$	4.04238	+	4.04238i	0.141425	+	0.141425i
$818$	15.3747			0.537563
$819$	−4.01405	−	28.3353i	−0.140262	−	0.990114i
$820$	−3.09272			−0.108003
$821$	0.575204	+	0.575204i	0.0200747	+	0.0200747i	0.717073	−	0.696998i	$-0.245481\pi$
$821$	0.575204	+	0.575204i	0.0200747	+	0.0200747i	−0.696998	+	0.717073i	$0.745481\pi$
$822$	−4.38762	+	33.9400i	−0.153036	+	1.18379i
$823$		−	41.4123i		−	1.44354i	−0.692132	−	0.721771i	$-0.743328\pi$
$823$		−	41.4123i		−	1.44354i	0.692132	−	0.721771i	$-0.256672\pi$
$824$	4.85955	−	18.1361i	0.169291	−	0.631801i
$825$	50.8019	−	39.1706i	1.76869	−	1.36374i
$826$	−7.64151	−	37.4905i	−0.265882	−	1.30446i
$827$	15.6164	−	15.6164i	0.543037	−	0.543037i	−0.381381	−	0.924418i	$-0.624551\pi$
$827$	15.6164	−	15.6164i	0.543037	−	0.543037i	0.924418	+	0.381381i	$0.124551\pi$
$828$	−3.87439	+	14.7345i	−0.134644	+	0.512060i
$829$	31.4583	−	18.1624i	1.09259	−	0.630808i	0.158326	−	0.987387i	$-0.449390\pi$
$829$	31.4583	−	18.1624i	1.09259	−	0.630808i	0.934265	+	0.356579i	$0.116057\pi$
$830$	24.7950	+	6.64380i	0.860647	+	0.230610i
$831$	−31.8735	−	4.12048i	−1.10568	−	0.142938i
$832$	−0.704936	−	3.53597i	−0.0244392	−	0.122588i
$833$	5.52775	−	2.35106i	0.191525	−	0.0814595i
$834$	−7.67061	−	3.15629i	−0.265612	−	0.109294i
$835$	68.2725			2.36267
$836$	−16.1252			−0.557700
$837$	−28.3939	−	3.53582i	−0.981437	−	0.122216i
$838$	5.92146	+	22.0992i	0.204553	+	0.763404i
$839$	47.9933	+	12.8598i	1.65691	+	0.443968i	0.961536	−	0.274677i	$-0.0885711\pi$
$839$	47.9933	+	12.8598i	1.65691	+	0.443968i	0.695376	+	0.718646i	$0.255238\pi$
$840$	−9.92388	−	14.6276i	−0.342407	−	0.504700i
$841$	−8.59359	−	14.8845i	−0.296331	−	0.513260i
$842$	−21.2888			−0.733661
$843$	29.3986	+	38.1282i	1.01254	+	1.31321i
$844$	17.1820	+	9.92000i	0.591427	+	0.341461i
$845$	6.58812	+	49.7099i	0.226638	+	1.71007i
$846$	4.62661	+	16.9495i	0.159066	+	0.582736i
$847$	−2.56327	+	7.66992i	−0.0880749	+	0.263542i
$848$	−4.07315	−	2.35163i	−0.139873	−	0.0807554i
$849$	−14.8281	−	35.5629i	−0.508899	−	1.22052i
$850$	−2.19405	−	8.18829i	−0.0752552	−	0.280856i
$851$	20.6523	+	20.6523i	0.707951	+	0.707951i
$852$	−0.830964	+	2.01946i	−0.0284684	+	0.0691855i
$853$	10.0034	+	10.0034i	0.342509	+	0.342509i	0.857310	−	0.514801i	$-0.172134\pi$
$853$	10.0034	+	10.0034i	0.342509	+	0.342509i	−0.514801	+	0.857310i	$0.672134\pi$
$854$	3.66750	+	7.34927i	0.125499	+	0.251487i
$855$	48.1336	+	12.6566i	1.64614	+	0.432846i
$856$	−10.9688	−	10.9688i	−0.374908	−	0.374908i
$857$	2.65429	−	4.59736i	0.0906687	−	0.157043i	−0.817124	−	0.576462i	$-0.804433\pi$
$857$	2.65429	−	4.59736i	0.0906687	−	0.157043i	0.907793	+	0.419419i	$0.137766\pi$
$858$	19.4318	−	13.0619i	0.663390	−	0.445924i
$859$	−15.0092	−	25.9966i	−0.512106	−	0.886993i	−0.999901	−	0.0140355i	$-0.995532\pi$
$859$	−15.0092	−	25.9966i	−0.512106	−	0.886993i	0.487796	−	0.872958i	$-0.337801\pi$
$860$	−4.95235	+	1.32698i	−0.168874	+	0.0452496i
$861$	−3.47085	+	1.20558i	−0.118286	+	0.0410861i
$862$	14.2660	−	8.23648i	0.485902	−	0.280536i
$863$	3.99159	−	14.8968i	0.135875	−	0.507093i	−0.864118	−	0.503290i	$-0.832123\pi$
$863$	3.99159	−	14.8968i	0.135875	−	0.507093i	0.999993	−	0.00380322i	$-0.00121061\pi$
$864$	4.78656	−	2.02208i	0.162842	−	0.0687927i
$865$	6.46467	+	6.46467i	0.219805	+	0.219805i
$866$	−34.0603	−	9.12643i	−1.15742	−	0.310129i
$867$	3.61157	−	27.9369i	0.122655	−	0.948787i
$868$	6.50539	+	13.0361i	0.220807	+	0.442474i
$869$	13.7136	+	51.1799i	0.465202	+	1.73616i
$870$	−2.94399	+	22.7729i	−0.0998107	+	0.772074i
$871$	−50.3436	−	3.27785i	−1.70583	−	0.111066i
$872$	−1.26297	−	0.729174i	−0.0427695	−	0.0246930i
$873$	9.60050	+	5.48319i	0.324928	+	0.185578i
$874$	−10.9211	+	18.9159i	−0.369412	+	0.639841i
$875$	41.5270	+	27.4647i	1.40387	+	0.928477i
$876$	−8.53928	+	1.14452i	−0.288515	+	0.0386698i
$877$	−12.8780	−	48.0613i	−0.434858	−	1.62291i	−0.741405	−	0.671058i	$-0.765840\pi$
$877$	−12.8780	−	48.0613i	−0.434858	−	1.62291i	0.306547	−	0.951856i	$-0.400826\pi$
$878$	−28.5654	+	28.5654i	−0.964036	+	0.964036i
$879$	−0.297834	+	0.723815i	−0.0100457	+	0.0244137i
$880$	7.23086	−	12.5242i	0.243752	−	0.422191i
$881$	−21.7730	+	37.7119i	−0.733550	+	1.27055i	0.221806	+	0.975091i	$0.428805\pi$
$881$	−21.7730	+	37.7119i	−0.733550	+	1.27055i	−0.955356	+	0.295456i	$0.904529\pi$
$882$	−16.8392	−	12.5475i	−0.567006	−	0.422498i
$883$		−	3.45829i		−	0.116381i	−0.998306	−	0.0581904i	$-0.981467\pi$
$883$		−	3.45829i		−	0.116381i	0.998306	−	0.0581904i	$-0.0185331\pi$
$884$	−0.604931	−	3.03434i	−0.0203460	−	0.102056i
$885$	−89.1756	+	37.1821i	−2.99760	+	1.24986i
$886$	−15.7693	−	4.22538i	−0.529781	−	0.141954i
$887$		−	26.5982i		−	0.893079i	−0.894764	−	0.446539i	$-0.852656\pi$
$887$		−	26.5982i		−	0.893079i	0.894764	−	0.446539i	$-0.147344\pi$
$888$	1.27712	−	9.87898i	0.0428572	−	0.331517i
$889$	2.77161	−	8.29333i	0.0929567	−	0.278149i
$890$	−1.16796	+	4.35889i	−0.0391501	+	0.146110i
$891$	24.0818	+	23.6358i	0.806770	+	0.791828i
$892$	−4.67584	+	1.25289i	−0.156559	+	0.0419498i
$893$			25.1887i			0.842907i
$894$	6.85287	−	8.97417i	0.229194	−	0.300141i
$895$	−35.0514	+	9.39201i	−1.17164	+	0.313940i
$896$	−2.20678	−	1.45950i	−0.0737232	−	0.0487584i
$897$	−2.16187	−	31.6412i	−0.0721828	−	1.05647i
$898$	5.29600	+	9.17294i	0.176730	+	0.306105i
$899$	4.89844	−	18.2812i	0.163372	−	0.609713i
$900$	−20.8574	+	21.0533i	−0.695247	+	0.701776i
$901$	−3.49532	−	2.01802i	−0.116446	−	0.0672301i
$902$	−2.12562	−	2.12562i	−0.0707753	−	0.0707753i
$903$	−5.04057	+	3.41971i	−0.167740	+	0.113801i
$904$	−1.88149	+	7.02181i	−0.0625774	+	0.233542i
$905$	−90.8321	−	24.3384i	−3.01936	−	0.809036i
$906$	18.3195	−	23.9903i	0.608625	−	0.797024i
$907$	−3.19977	+	1.84739i	−0.106247	+	0.0613416i	−0.552182	−	0.833724i	$-0.686205\pi$
$907$	−3.19977	+	1.84739i	−0.106247	+	0.0613416i	0.445935	+	0.895065i	$0.352871\pi$
$908$	−7.10864	+	7.10864i	−0.235908	+	0.235908i
$909$	−13.6243	−	49.9122i	−0.451888	−	1.65548i
$910$	29.3073	+	22.2493i	0.971528	+	0.737556i
$911$			36.0850i			1.19555i	0.801664	+	0.597774i	$0.203948\pi$
$911$			36.0850i			1.19555i	−0.801664	+	0.597774i	$0.796052\pi$
$912$	7.38344	−	0.989606i	0.244490	−	0.0327691i
$913$	12.4753	+	21.6078i	0.412871	+	0.715113i
$914$	−1.60218			−0.0529955
$915$	16.4251	−	12.6645i	0.542998	−	0.418676i
$916$	−1.65457	−	0.443341i	−0.0546686	−	0.0146484i
$917$	−20.2678	−	22.8921i	−0.669303	−	0.755964i
$918$	4.10752	−	1.73522i	0.135568	−	0.0572709i
$919$	1.62216	−	2.80966i	0.0535101	−	0.0926821i	−0.838030	−	0.545625i	$-0.816292\pi$
$919$	1.62216	−	2.80966i	0.0535101	−	0.0926821i	0.891540	+	0.452943i	$0.149626\pi$
$920$	−9.79451	−	16.9646i	−0.322916	−	0.559306i
$921$	3.65789	−	2.82040i	0.120532	−	0.0929354i
$922$	−9.18278	+	5.30168i	−0.302419	+	0.174602i
$923$	0.295351	−	4.53621i	0.00972160	−	0.149311i
$924$	3.23284	−	16.8741i	0.106353	−	0.555118i
$925$	14.7042	+	54.8767i	0.483470	+	1.80433i
$926$		−	19.5538i		−	0.642577i
$927$	−54.3396	+	14.8328i	−1.78475	+	0.487172i
$928$	0.889555	+	3.31987i	0.0292011	+	0.108980i
$929$	4.49526	−	1.20450i	0.147485	−	0.0395184i	−0.184321	−	0.982866i	$-0.559009\pi$
$929$	4.49526	−	1.20450i	0.147485	−	0.0395184i	0.331806	+	0.943348i	$0.392342\pi$
$930$	29.1348	−	22.4643i	0.955368	−	0.736633i
$931$	−18.5525	−	23.7111i	−0.608033	−	0.777099i
$932$	−12.9819	+	7.49512i	−0.425237	+	0.245511i
$933$	16.9692	+	12.9580i	0.555546	+	0.424227i
$934$	−4.29934	+	16.0454i	−0.140679	+	0.525021i
$935$	6.20506	−	10.7475i	0.202927	−	0.351480i
$936$	−8.09587	+	7.17334i	−0.264622	+	0.234468i
$937$	34.1925			1.11702			0.558510	−	0.829498i	$-0.311373\pi$
$937$	34.1925			1.11702			0.558510	+	0.829498i	$0.311373\pi$
$938$	−27.7178	+	24.5403i	−0.905017	+	0.801270i
$939$	−10.5140	+	4.38384i	−0.343110	+	0.143061i
$940$	−19.5638	−	11.2951i	−0.638099	−	0.368407i
$941$	17.9297	−	4.80425i	0.584491	−	0.156614i	0.0455568	−	0.998962i	$-0.485494\pi$
$941$	17.9297	−	4.80425i	0.584491	−	0.156614i	0.538934	+	0.842348i	$0.318827\pi$
$942$	4.65994	+	34.7678i	0.151829	+	1.13280i
$943$	−3.93312	+	1.05388i	−0.128080	+	0.0343189i
$944$	−10.2258	+	10.2258i	−0.332821	+	0.332821i
$945$	−22.8945	+	47.8319i	−0.744757	+	1.55597i
$946$	−4.31576	−	2.49171i	−0.140318	−	0.0810124i
$947$	17.0524	−	17.0524i	0.554128	−	0.554128i	−0.373502	−	0.927630i	$-0.621843\pi$
$947$	17.0524	−	17.0524i	0.554128	−	0.554128i	0.927630	+	0.373502i	$0.121843\pi$
$948$	−9.42016	−	22.5928i	−0.305952	−	0.733780i
$949$	16.0819	−	7.93934i	0.522040	−	0.257722i
$950$	−36.7950	+	21.2436i	−1.19379	+	0.689233i
$951$	0.684719	+	0.281747i	0.0222035	+	0.00913627i
$952$	−1.89372	−	1.25245i	−0.0613757	−	0.0405921i
$953$	−0.921008	−	1.59523i	−0.0298344	−	0.0516747i	0.850723	−	0.525615i	$-0.176165\pi$
$953$	−0.921008	−	1.59523i	−0.0298344	−	0.0516747i	−0.880557	+	0.473940i	$0.842831\pi$
$954$	0.0659399	+	14.1097i	0.00213488	+	0.456817i
$955$	44.3268	−	44.3268i	1.43438	−	1.43438i
$956$	−7.39507	+	7.39507i	−0.239174	+	0.239174i
$957$	−17.6751	+	13.6284i	−0.571356	+	0.440542i
$958$	−2.04088	−	3.53491i	−0.0659380	−	0.114208i
$959$	−43.6022	−	28.8372i	−1.40799	−	0.931202i
$960$	−2.54228	+	6.17839i	−0.0820516	+	0.199407i
$961$	0.586446	−	0.338585i	0.0189176	−	0.0109221i
$962$	4.05415	+	20.3357i	0.130711	+	0.655649i
$963$	−11.8344	+	45.0070i	−0.381359	+	1.45033i
$964$	−5.84548	+	5.84548i	−0.188270	+	0.188270i
$965$	8.17245	+	4.71837i	0.263081	+	0.151890i
$966$	−17.6050	−	15.2207i	−0.566432	−	0.489719i
$967$	−3.86855	+	3.86855i	−0.124404	+	0.124404i	−0.766568	−	0.642163i	$-0.778037\pi$
$967$	−3.86855	+	3.86855i	−0.124404	+	0.124404i	0.642163	+	0.766568i	$0.278037\pi$
$968$	2.95241	−	0.791097i	0.0948941	−	0.0254268i
$969$	6.33600	−	0.849216i	0.203542	−	0.0272808i
$970$	−13.7310	+	3.67920i	−0.440874	+	0.118132i
$971$	36.3369	+	20.9791i	1.16611	+	0.673252i	0.952760	−	0.303725i	$-0.0982303\pi$
$971$	36.3369	+	20.9791i	1.16611	+	0.673252i	0.213347	+	0.976977i	$0.431564\pi$
$972$	−12.4772	−	9.34452i	−0.400206	−	0.299726i
$973$	9.48643	−	8.39894i	0.304121	−	0.269258i
$974$	−5.58134			−0.178838
$975$	27.1322	−	55.4048i	0.868926	−	1.77437i
$976$	1.55221	−	2.68851i	0.0496852	−	0.0860572i
$977$	2.65945	−	9.92520i	0.0850833	−	0.317535i	−0.910247	−	0.414067i	$-0.864108\pi$
$977$	2.65945	−	9.92520i	0.0850833	−	0.317535i	0.995330	+	0.0965312i	$0.0307747\pi$
$978$	6.47401	−	8.47804i	0.207016	−	0.271098i
$979$	−3.79858	+	2.19311i	−0.121403	+	0.0700922i
$980$	26.7354	−	3.77694i	0.854032	−	0.120650i
$981$	0.0204461	+	4.37500i	0.000652792	+	0.139683i
$982$	−25.9006	+	6.94005i	−0.826522	+	0.221466i
$983$	−5.56888	−	20.7833i	−0.177620	−	0.662885i	−0.996091	−	0.0883374i	$-0.971845\pi$
$983$	−5.56888	−	20.7833i	−0.177620	−	0.662885i	0.818471	−	0.574548i	$-0.194822\pi$
$984$	1.10373	+	0.842835i	0.0351858	+	0.0268686i
$985$		−	68.9858i		−	2.19807i
$986$	0.763360	+	2.84890i	0.0243103	+	0.0907274i
$987$	−26.3587	−	5.04993i	−0.839005	−	0.160741i
$988$	−13.9051	+	6.86471i	−0.442380	+	0.218395i
$989$	−5.84589	+	3.37512i	−0.185888	+	0.107323i
$990$	−43.3847	+	0.202753i	−1.37886	+	0.00644393i
$991$	21.4247	+	37.1086i	0.680577	+	1.17879i	0.974805	+	0.223059i	$0.0716042\pi$
$991$	21.4247	+	37.1086i	0.680577	+	1.17879i	−0.294228	+	0.955735i	$0.595063\pi$
$992$	2.75331	−	4.76887i	0.0874176	−	0.151412i
$993$	21.1637	−	2.83657i	0.671608	−	0.0900160i
$994$	−2.21121	−	2.49751i	−0.0701352	−	0.0792163i
$995$	−32.9194	−	8.82072i	−1.04361	−	0.279636i
$996$	−7.03829	−	9.12823i	−0.223017	−	0.289239i
$997$	37.7733			1.19629			0.598147	−	0.801387i	$-0.295904\pi$
$997$	37.7733			1.19629			0.598147	+	0.801387i	$0.295904\pi$
$998$	0.343794	+	0.595468i	0.0108826	+	0.0188492i
$999$	−27.5280	+	11.6292i	−0.870946	+	0.367932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.305.10	yes	152
3.2	odd	2	inner	546.2.ch.a.305.35	yes	152
7.2	even	3		546.2.bw.a.149.5	yes	152
13.11	odd	12		546.2.bw.a.11.24	yes	152
21.2	odd	6		546.2.bw.a.149.24	yes	152
39.11	even	12		546.2.bw.a.11.5	✓	152
91.37	odd	12	inner	546.2.ch.a.401.35	yes	152
273.128	even	12	inner	546.2.ch.a.401.10	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.5	✓	152	39.11	even	12
546.2.bw.a.11.24	yes	152	13.11	odd	12
546.2.bw.a.149.5	yes	152	7.2	even	3
546.2.bw.a.149.24	yes	152	21.2	odd	6
546.2.ch.a.305.10	yes	152	1.1	even	1	trivial
546.2.ch.a.305.35	yes	152	3.2	odd	2	inner
546.2.ch.a.401.10	yes	152	273.128	even	12	inner
546.2.ch.a.401.35	yes	152	91.37	odd	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.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.222065 + 1.71776i) q^{3} +1.00000i q^{4} +(-0.998336 + 3.72584i) q^{5} +(1.37166 - 1.05761i) q^{6} +(0.528406 + 2.59245i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.90137 - 0.762906i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.222065 + 1.71776i) q^{3} +1.00000i q^{4} +(-0.998336 + 3.72584i) q^{5} +(1.37166 - 1.05761i) q^{6} +(0.528406 + 2.59245i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.90137 - 0.762906i) q^{9} +(3.34050 - 1.92864i) q^{10} +(3.62146 + 0.970367i) q^{11} +(-1.71776 - 0.222065i) q^{12} +(3.53597 - 0.704936i) q^{13} +(1.45950 - 2.20678i) q^{14} +(-6.17839 - 2.54228i) q^{15} -1.00000 q^{16} -0.858136 q^{17} +(1.51213 + 2.59104i) q^{18} +(1.11317 + 4.15440i) q^{19} +(-3.72584 - 0.998336i) q^{20} +(-4.57053 + 0.331982i) q^{21} +(-1.87460 - 3.24691i) q^{22} -5.07846 q^{23} +(1.05761 + 1.37166i) q^{24} +(-8.55508 - 4.93928i) q^{25} +(-2.99877 - 2.00184i) q^{26} +(1.95478 - 4.81444i) q^{27} +(-2.59245 + 0.528406i) q^{28} +(2.97651 + 1.71849i) q^{29} +(2.57112 + 6.16644i) q^{30} +(-1.42522 - 5.31898i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.47105 + 6.00530i) q^{33} +(0.606794 + 0.606794i) q^{34} +(-10.1866 - 0.619377i) q^{35} +(0.762906 - 2.90137i) q^{36} +(-4.06664 - 4.06664i) q^{37} +(2.15047 - 3.72473i) q^{38} +(0.425694 + 6.23047i) q^{39} +(1.92864 + 3.34050i) q^{40} +(0.774470 - 0.207519i) q^{41} +(3.46660 + 2.99711i) q^{42} +(1.15111 - 0.664595i) q^{43} +(-0.970367 + 3.62146i) q^{44} +(5.73901 - 10.0484i) q^{45} +(3.59102 + 3.59102i) q^{46} +(5.65698 + 1.51578i) q^{47} +(0.222065 - 1.71776i) q^{48} +(-6.44157 + 2.73973i) q^{49} +(2.55676 + 9.54195i) q^{50} +(0.190562 - 1.47407i) q^{51} +(0.704936 + 3.53597i) q^{52} +(4.07315 + 2.35163i) q^{53} +(-4.78656 + 2.02208i) q^{54} +(-7.23086 + 12.5242i) q^{55} +(2.20678 + 1.45950i) q^{56} +(-7.38344 + 0.989606i) q^{57} +(-0.889555 - 3.31987i) q^{58} +(10.2258 - 10.2258i) q^{59} +(2.54228 - 6.17839i) q^{60} +(-1.55221 + 2.68851i) q^{61} +(-2.75331 + 4.76887i) q^{62} +(0.444691 - 7.92479i) q^{63} -1.00000i q^{64} +(-0.903606 + 13.8782i) q^{65} +(5.99368 - 2.49909i) q^{66} +(-13.5156 - 3.62149i) q^{67} -0.858136i q^{68} +(1.12775 - 8.72357i) q^{69} +(6.76503 + 7.64096i) q^{70} +(0.326314 - 1.21782i) q^{71} +(-2.59104 + 1.51213i) q^{72} +(4.80475 - 1.28743i) q^{73} +5.75109i q^{74} +(10.3843 - 13.5987i) q^{75} +(-4.15440 + 1.11317i) q^{76} +(-0.602025 + 9.90119i) q^{77} +(4.10460 - 4.70662i) q^{78} +(7.06620 + 12.2390i) q^{79} +(0.998336 - 3.72584i) q^{80} +(7.83595 + 4.42695i) q^{81} +(-0.694371 - 0.400895i) q^{82} +(4.70571 + 4.70571i) q^{83} +(-0.331982 - 4.57053i) q^{84} +(0.856708 - 3.19728i) q^{85} +(-1.28390 - 0.344020i) q^{86} +(-3.61292 + 4.73130i) q^{87} +(3.24691 - 1.87460i) q^{88} +(-0.827250 + 0.827250i) q^{89} +(-11.1634 + 3.04721i) q^{90} +(3.69594 + 8.79432i) q^{91} -5.07846i q^{92} +(9.45321 - 1.26702i) q^{93} +(-2.92827 - 5.07191i) q^{94} -16.5899 q^{95} +(-1.37166 + 1.05761i) q^{96} +(-3.55976 - 0.953834i) q^{97} +(6.49216 + 2.61760i) q^{98} +(-9.76690 - 5.57823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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