LMFDB - Embedded newform 546.2.ch.a.137.12

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			137.12
Character	$\chi$	$=$	546.137
Dual form			546.2.ch.a.275.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.480095 + 1.66418i) q^{3} -1.00000i q^{4} +(3.07620 + 0.824266i) q^{5} +(-1.51623 - 0.837278i) q^{6} +(1.73277 - 1.99938i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.53902 + 1.59793i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.480095 + 1.66418i) q^{3} -1.00000i q^{4} +(3.07620 + 0.824266i) q^{5} +(-1.51623 - 0.837278i) q^{6} +(1.73277 - 1.99938i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.53902 + 1.59793i) q^{9} +(-2.75805 + 1.59236i) q^{10} +(-1.03991 + 3.88100i) q^{11} +(1.66418 - 0.480095i) q^{12} +(2.68244 - 2.40926i) q^{13} +(0.188523 + 2.63903i) q^{14} +(0.105139 + 5.51509i) q^{15} -1.00000 q^{16} -3.84291 q^{17} +(0.665448 - 2.92527i) q^{18} +(6.83462 - 1.83133i) q^{19} +(0.824266 - 3.07620i) q^{20} +(4.15923 + 1.92375i) q^{21} +(-2.00895 - 3.47961i) q^{22} +5.71656 q^{23} +(-0.837278 + 1.51623i) q^{24} +(4.45348 + 2.57122i) q^{25} +(-0.193169 + 3.60037i) q^{26} +(-3.87822 - 3.45823i) q^{27} +(-1.99938 - 1.73277i) q^{28} +(-2.37022 - 1.36845i) q^{29} +(-3.97410 - 3.82542i) q^{30} +(-2.10902 + 0.565110i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.95795 + 0.132645i) q^{33} +(2.71735 - 2.71735i) q^{34} +(6.97836 - 4.72223i) q^{35} +(1.59793 + 2.53902i) q^{36} +(-6.20889 + 6.20889i) q^{37} +(-3.53786 + 6.12776i) q^{38} +(5.29727 + 3.30740i) q^{39} +(1.59236 + 2.75805i) q^{40} +(1.09733 + 4.09530i) q^{41} +(-4.30132 + 1.58072i) q^{42} +(-6.57787 + 3.79774i) q^{43} +(3.88100 + 1.03991i) q^{44} +(-9.12765 + 2.82274i) q^{45} +(-4.04222 + 4.04222i) q^{46} +(0.212620 - 0.793509i) q^{47} +(-0.480095 - 1.66418i) q^{48} +(-0.995036 - 6.92892i) q^{49} +(-4.96721 + 1.33096i) q^{50} +(-1.84496 - 6.39531i) q^{51} +(-2.40926 - 2.68244i) q^{52} +(-4.39567 - 2.53784i) q^{53} +(5.18766 - 0.296978i) q^{54} +(-6.39795 + 11.0816i) q^{55} +(2.63903 - 0.188523i) q^{56} +(6.32894 + 10.4949i) q^{57} +(2.64364 - 0.708361i) q^{58} +(-9.69186 - 9.69186i) q^{59} +(5.51509 - 0.105139i) q^{60} +(-2.81947 + 4.88346i) q^{61} +(1.09171 - 1.89090i) q^{62} +(-1.20465 + 7.84531i) q^{63} +1.00000i q^{64} +(10.2376 - 5.20032i) q^{65} +(4.82622 - 5.01381i) q^{66} +(2.32494 - 8.67678i) q^{67} +3.84291i q^{68} +(2.74449 + 9.51340i) q^{69} +(-1.59532 + 8.27357i) q^{70} +(11.0094 + 2.94997i) q^{71} +(-2.92527 - 0.665448i) q^{72} +(1.12460 + 4.19705i) q^{73} -8.78070i q^{74} +(-2.14089 + 8.64584i) q^{75} +(-1.83133 - 6.83462i) q^{76} +(5.95767 + 8.80404i) q^{77} +(-6.08442 + 1.40705i) q^{78} +(-0.236397 - 0.409451i) q^{79} +(-3.07620 - 0.824266i) q^{80} +(3.89322 - 8.11436i) q^{81} +(-3.67175 - 2.11988i) q^{82} +(-2.22692 + 2.22692i) q^{83} +(1.92375 - 4.15923i) q^{84} +(-11.8216 - 3.16758i) q^{85} +(1.96585 - 7.33666i) q^{86} +(1.13942 - 4.60147i) q^{87} +(-3.47961 + 2.00895i) q^{88} +(-10.9217 - 10.9217i) q^{89} +(4.45825 - 8.45020i) q^{90} +(-0.168975 - 9.53790i) q^{91} -5.71656i q^{92} +(-1.95298 - 3.23849i) q^{93} +(0.410751 + 0.711441i) q^{94} +22.5342 q^{95} +(1.51623 + 0.837278i) q^{96} +(1.05243 - 3.92771i) q^{97} +(5.60308 + 4.19589i) q^{98} +(-3.56122 - 11.5156i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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
$3$	0.480095	+	1.66418i	0.277183	+	0.960817i
$3$	0.480095	+	1.66418i	0.277183	+	0.960817i
$4$		−	1.00000i		−	0.500000i
$5$	3.07620	+	0.824266i	1.37572	+	0.368623i	0.869564	−	0.493820i	$-0.164400\pi$
$5$	3.07620	+	0.824266i	1.37572	+	0.368623i	0.506155	+	0.862442i	$0.331066\pi$
$6$	−1.51623	−	0.837278i	−0.619000	−	0.341817i
$7$	1.73277	−	1.99938i	0.654924	−	0.755694i
$7$	1.73277	−	1.99938i	0.654924	−	0.755694i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.53902	+	1.59793i	−0.846339	+	0.532644i
$10$	−2.75805	+	1.59236i	−0.872171	+	0.503548i
$11$	−1.03991	+	3.88100i	−0.313545	+	1.17017i	0.611792	+	0.791019i	$0.290449\pi$
$11$	−1.03991	+	3.88100i	−0.313545	+	1.17017i	−0.925337	+	0.379146i	$0.876218\pi$
$12$	1.66418	−	0.480095i	0.480409	−	0.138591i
$13$	2.68244	−	2.40926i	0.743975	−	0.668208i
$13$	2.68244	−	2.40926i	0.743975	−	0.668208i
$14$	0.188523	+	2.63903i	0.0503850	+	0.705309i
$15$	0.105139	+	5.51509i	0.0271467	+	1.42399i
$16$	−1.00000			−0.250000
$17$	−3.84291			−0.932042			−0.466021	−	0.884774i	$-0.654313\pi$
$17$	−3.84291			−0.932042			−0.466021	+	0.884774i	$0.654313\pi$
$18$	0.665448	−	2.92527i	0.156848	−	0.689492i
$19$	6.83462	−	1.83133i	1.56797	−	0.420136i	0.632794	−	0.774320i	$-0.281908\pi$
$19$	6.83462	−	1.83133i	1.56797	−	0.420136i	0.935176	+	0.354183i	$0.115241\pi$
$20$	0.824266	−	3.07620i	0.184311	−	0.687860i
$21$	4.15923	+	1.92375i	0.907618	+	0.419797i
$22$	−2.00895	−	3.47961i	−0.428310	−	0.741855i
$23$	5.71656			1.19198			0.595992	−	0.802990i	$-0.296759\pi$
$23$	5.71656			1.19198			0.595992	+	0.802990i	$0.296759\pi$
$24$	−0.837278	+	1.51623i	−0.170909	+	0.309500i
$25$	4.45348	+	2.57122i	0.890696	+	0.514243i
$26$	−0.193169	+	3.60037i	−0.0378836	+	0.706091i
$27$	−3.87822	−	3.45823i	−0.746364	−	0.665537i
$28$	−1.99938	−	1.73277i	−0.377847	−	0.327462i
$29$	−2.37022	−	1.36845i	−0.440139	−	0.254115i	0.263517	−	0.964655i	$-0.415117\pi$
$29$	−2.37022	−	1.36845i	−0.440139	−	0.254115i	−0.703657	+	0.710540i	$0.748451\pi$
$30$	−3.97410	−	3.82542i	−0.725569	−	0.698422i
$31$	−2.10902	+	0.565110i	−0.378791	+	0.101497i	−0.443191	−	0.896427i	$-0.646153\pi$
$31$	−2.10902	+	0.565110i	−0.378791	+	0.101497i	0.0643995	+	0.997924i	$0.479487\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−6.95795	+	0.132645i	−1.21122	+	0.0230906i
$34$	2.71735	−	2.71735i	0.466021	−	0.466021i
$35$	6.97836	−	4.72223i	1.17956	−	0.798203i
$36$	1.59793	+	2.53902i	0.266322	+	0.423170i
$37$	−6.20889	+	6.20889i	−1.02074	+	1.02074i	−0.0209547	+	0.999780i	$0.506671\pi$
$37$	−6.20889	+	6.20889i	−1.02074	+	1.02074i	−0.999780	+	0.0209547i	$0.993329\pi$
$38$	−3.53786	+	6.12776i	−0.573917	+	0.994053i
$39$	5.29727	+	3.30740i	0.848242	+	0.529608i
$40$	1.59236	+	2.75805i	0.251774	+	0.436086i
$41$	1.09733	+	4.09530i	0.171375	+	0.639579i	0.997141	+	0.0755661i	$0.0240764\pi$
$41$	1.09733	+	4.09530i	0.171375	+	0.639579i	−0.825766	+	0.564013i	$0.809257\pi$
$42$	−4.30132	+	1.58072i	−0.663708	+	0.243910i
$43$	−6.57787	+	3.79774i	−1.00312	+	0.579149i	−0.909169	−	0.416428i	$-0.863282\pi$
$43$	−6.57787	+	3.79774i	−1.00312	+	0.579149i	−0.0939474	+	0.995577i	$0.529949\pi$
$44$	3.88100	+	1.03991i	0.585083	+	0.156772i
$45$	−9.12765	+	2.82274i	−1.36067	+	0.420789i
$46$	−4.04222	+	4.04222i	−0.595992	+	0.595992i
$47$	0.212620	−	0.793509i	0.0310138	−	0.115745i	−0.948684	−	0.316227i	$-0.897584\pi$
$47$	0.212620	−	0.793509i	0.0310138	−	0.115745i	0.979697	+	0.200481i	$0.0642506\pi$
$48$	−0.480095	−	1.66418i	−0.0692957	−	0.240204i
$49$	−0.995036	−	6.92892i	−0.142148	−	0.989845i
$50$	−4.96721	+	1.33096i	−0.702470	+	0.188226i
$51$	−1.84496	−	6.39531i	−0.258346	−	0.895522i
$52$	−2.40926	−	2.68244i	−0.334104	−	0.371987i
$53$	−4.39567	−	2.53784i	−0.603792	−	0.348599i	0.166740	−	0.986001i	$-0.446676\pi$
$53$	−4.39567	−	2.53784i	−0.603792	−	0.348599i	−0.770532	+	0.637401i	$0.780009\pi$
$54$	5.18766	−	0.296978i	0.705951	−	0.0404135i
$55$	−6.39795	+	11.0816i	−0.862699	+	1.49424i
$56$	2.63903	−	0.188523i	0.352655	−	0.0251925i
$57$	6.32894	+	10.4949i	0.838289	+	1.39008i
$58$	2.64364	−	0.708361i	0.347127	−	0.0930124i
$59$	−9.69186	−	9.69186i	−1.26177	−	1.26177i	−0.950233	−	0.311539i	$-0.899156\pi$
$59$	−9.69186	−	9.69186i	−1.26177	−	1.26177i	−0.311539	−	0.950233i	$-0.600844\pi$
$60$	5.51509	−	0.105139i	0.711995	−	0.0135733i
$61$	−2.81947	+	4.88346i	−0.360996	+	0.625263i	−0.988125	−	0.153652i	$-0.950896\pi$
$61$	−2.81947	+	4.88346i	−0.360996	+	0.625263i	0.627129	+	0.778915i	$0.284230\pi$
$62$	1.09171	−	1.89090i	0.138647	−	0.240144i
$63$	−1.20465	+	7.84531i	−0.151772	+	0.988416i
$64$			1.00000i			0.125000i
$65$	10.2376	−	5.20032i	1.26982	−	0.645020i
$66$	4.82622	−	5.01381i	0.594067	−	0.617157i
$67$	2.32494	−	8.67678i	0.284036	−	1.06004i	−0.665505	−	0.746394i	$-0.731784\pi$
$67$	2.32494	−	8.67678i	0.284036	−	1.06004i	0.949541	−	0.313644i	$-0.101550\pi$
$68$			3.84291i			0.466021i
$69$	2.74449	+	9.51340i	0.330398	+	1.14528i
$70$	−1.59532	+	8.27357i	−0.190678	+	0.988881i
$71$	11.0094	+	2.94997i	1.30658	+	0.350097i	0.843935	−	0.536446i	$-0.180234\pi$
$71$	11.0094	+	2.94997i	1.30658	+	0.350097i	0.462646	+	0.886543i	$0.346900\pi$
$72$	−2.92527	−	0.665448i	−0.344746	−	0.0784238i
$73$	1.12460	+	4.19705i	0.131624	+	0.491227i	0.999989	−	0.00469823i	$-0.00149550\pi$
$73$	1.12460	+	4.19705i	0.131624	+	0.491227i	−0.868365	+	0.495926i	$0.834829\pi$
$74$		−	8.78070i		−	1.02074i
$75$	−2.14089	+	8.64584i	−0.247208	+	0.998335i
$76$	−1.83133	−	6.83462i	−0.210068	−	0.783985i
$77$	5.95767	+	8.80404i	0.678939	+	1.00331i
$78$	−6.08442	+	1.40705i	−0.688925	+	0.159317i
$79$	−0.236397	−	0.409451i	−0.0265967	−	0.0460669i	0.852421	−	0.522857i	$-0.175134\pi$
$79$	−0.236397	−	0.409451i	−0.0265967	−	0.0460669i	−0.879017	+	0.476790i	$0.841800\pi$
$80$	−3.07620	−	0.824266i	−0.343930	−	0.0921557i
$81$	3.89322	−	8.11436i	0.432580	−	0.901595i
$82$	−3.67175	−	2.11988i	−0.405477	−	0.234102i
$83$	−2.22692	+	2.22692i	−0.244436	+	0.244436i	−0.818682	−	0.574247i	$-0.805295\pi$
$83$	−2.22692	+	2.22692i	−0.244436	+	0.244436i	0.574247	+	0.818682i	$0.305295\pi$
$84$	1.92375	−	4.15923i	0.209899	−	0.453809i
$85$	−11.8216	−	3.16758i	−1.28223	−	0.343572i
$86$	1.96585	−	7.33666i	0.211983	−	0.791133i
$87$	1.13942	−	4.60147i	0.122159	−	0.493330i
$88$	−3.47961	+	2.00895i	−0.370928	+	0.214155i
$89$	−10.9217	−	10.9217i	−1.15770	−	1.15770i	−0.984969	−	0.172729i	$-0.944742\pi$
$89$	−10.9217	−	10.9217i	−1.15770	−	1.15770i	−0.172729	−	0.984969i	$-0.555258\pi$
$90$	4.45825	−	8.45020i	0.469941	−	0.890730i
$91$	−0.168975	−	9.53790i	−0.0177134	−	0.999843i
$92$		−	5.71656i		−	0.595992i
$93$	−1.95298	−	3.23849i	−0.202514	−	0.335816i
$94$	0.410751	+	0.711441i	0.0423657	+	0.0733795i
$95$	22.5342			2.31196
$96$	1.51623	+	0.837278i	0.154750	+	0.0854543i
$97$	1.05243	−	3.92771i	0.106858	−	0.398798i	−0.891692	−	0.452643i	$-0.850481\pi$
$97$	1.05243	−	3.92771i	0.106858	−	0.398798i	0.998549	+	0.0538451i	$0.0171477\pi$
$98$	5.60308	+	4.19589i	0.565997	+	0.423849i
$99$	−3.56122	−	11.5156i	−0.357916	−	1.15736i
$100$	2.57122	−	4.45348i	0.257122	−	0.445348i
$101$	3.53014	+	6.11439i	0.351263	+	0.608405i	0.986471	−	0.163936i	$-0.0524191\pi$
$101$	3.53014	+	6.11439i	0.351263	+	0.608405i	−0.635208	+	0.772341i	$0.719086\pi$
$102$	5.82675	+	3.21758i	0.576934	+	0.318588i
$103$	12.6406	−	7.29808i	1.24552	−	0.719101i	0.275308	−	0.961356i	$-0.411220\pi$
$103$	12.6406	−	7.29808i	1.24552	−	0.719101i	0.970213	+	0.242255i	$0.0778870\pi$
$104$	3.60037	+	0.193169i	0.353046	+	0.0189418i
$105$	11.2089	+	9.34616i	1.09388	+	0.912092i
$106$	4.90273	−	1.31368i	0.476196	−	0.127596i
$107$		−	6.38549i		−	0.617309i	−0.951174	−	0.308654i	$-0.900121\pi$
$107$		−	6.38549i		−	0.617309i	0.951174	−	0.308654i	$-0.0998786\pi$
$108$	−3.45823	+	3.87822i	−0.332769	+	0.373182i
$109$	−10.3549	+	2.77459i	−0.991821	+	0.265758i	−0.718015	−	0.696027i	$-0.754949\pi$
$109$	−10.3549	+	2.77459i	−0.991821	+	0.265758i	−0.273806	+	0.961785i	$0.588282\pi$
$110$	−3.31182	−	12.3599i	−0.315770	−	1.17847i
$111$	−13.3136	−	7.35188i	−1.26367	−	0.697810i
$112$	−1.73277	+	1.99938i	−0.163731	+	0.188924i
$113$	−0.771567	+	0.445464i	−0.0725829	+	0.0419058i	−0.535852	−	0.844312i	$-0.680010\pi$
$113$	−0.771567	+	0.445464i	−0.0725829	+	0.0419058i	0.463269	+	0.886218i	$0.346676\pi$
$114$	−11.8962	−	2.94575i	−1.11418	−	0.275895i
$115$	17.5853	+	4.71196i	1.63984	+	0.439393i
$116$	−1.36845	+	2.37022i	−0.127057	+	0.220070i
$117$	−2.96093	+	10.4035i	−0.273738	+	0.961804i
$118$	13.7064			1.26177
$119$	−6.65887	+	7.68343i	−0.610417	+	0.704339i
$120$	−3.82542	+	3.97410i	−0.349211	+	0.362784i
$121$	−4.45446	−	2.57178i	−0.404951	−	0.233798i
$122$	−1.45946	−	5.44679i	−0.132134	−	0.493130i
$123$	−6.28851	+	3.79230i	−0.567016	+	0.341940i
$124$	0.565110	+	2.10902i	0.0507484	+	0.189396i
$125$	0.320753	+	0.320753i	0.0286890	+	0.0286890i
$126$	−4.69565	−	6.39929i	−0.418322	−	0.570094i
$127$	7.40405	+	4.27473i	0.657004	+	0.379321i	0.791134	−	0.611642i	$-0.209491\pi$
$127$	7.40405	+	4.27473i	0.657004	+	0.379321i	−0.134131	+	0.990964i	$0.542824\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−9.47814	−	9.12352i	−0.834503	−	0.803281i
$130$	−3.56189	+	10.9163i	−0.312399	+	0.957419i
$131$	7.82728	−	4.51908i	0.683872	−	0.394834i	−0.117440	−	0.993080i	$-0.537469\pi$
$131$	7.82728	−	4.51908i	0.683872	−	0.394834i	0.801312	+	0.598246i	$0.204135\pi$
$132$	0.132645	+	6.95795i	0.0115453	+	0.605612i
$133$	8.18129	−	16.8383i	0.709407	−	1.46006i
$134$	4.49143	+	7.77939i	0.388001	+	0.672037i
$135$	−9.07970	−	13.8349i	−0.781456	−	1.19072i
$136$	−2.71735	−	2.71735i	−0.233011	−	0.233011i
$137$	−6.87860	−	6.87860i	−0.587679	−	0.587679i	0.349324	−	0.937002i	$-0.386411\pi$
$137$	−6.87860	−	6.87860i	−0.587679	−	0.587679i	−0.937002	+	0.349324i	$0.886411\pi$
$138$	−8.66764	−	4.78635i	−0.737839	−	0.407441i
$139$	8.55373	+	14.8155i	0.725518	+	1.25663i	0.958760	+	0.284216i	$0.0917332\pi$
$139$	8.55373	+	14.8155i	0.725518	+	1.25663i	−0.233242	+	0.972419i	$0.574934\pi$
$140$	−4.72223	−	6.97836i	−0.399102	−	0.589779i
$141$	1.42262	−	0.0271206i	0.119807	−	0.00228397i
$142$	−9.87079	+	5.69891i	−0.828339	+	0.478242i
$143$	6.56083	+	12.9160i	0.548644	+	1.08009i
$144$	2.53902	−	1.59793i	0.211585	−	0.133161i
$145$	−6.16332	−	6.16332i	−0.511836	−	0.511836i
$146$	−3.76297	−	2.17255i	−0.311426	−	0.179802i
$147$	11.0533	−	4.98246i	0.911659	−	0.410946i
$148$	6.20889	+	6.20889i	0.510368	+	0.510368i
$149$	−1.73858	−	6.48845i	−0.142430	−	0.531555i	−0.999856	−	0.0169487i	$-0.994605\pi$
$149$	−1.73858	−	6.48845i	−0.142430	−	0.531555i	0.857427	−	0.514606i	$-0.172062\pi$
$150$	−4.59969	−	7.62737i	−0.375563	−	0.622772i
$151$	−0.420790	−	1.57041i	−0.0342434	−	0.127798i	0.946688	−	0.322151i	$-0.104406\pi$
$151$	−0.420790	−	1.57041i	−0.0342434	−	0.127798i	−0.980932	+	0.194353i	$0.937739\pi$
$152$	6.12776	+	3.53786i	0.497027	+	0.286959i
$153$	9.75721	−	6.14071i	0.788824	−	0.496447i
$154$	−10.4381	−	2.01269i	−0.841126	−	0.162187i
$155$	−6.95357			−0.558524
$156$	3.30740	−	5.29727i	0.264804	−	0.424121i
$157$	0.529427	−	0.916994i	0.0422528	−	0.0731841i	−0.844126	−	0.536146i	$-0.819880\pi$
$157$	0.529427	−	0.916994i	0.0422528	−	0.0731841i	0.886378	+	0.462961i	$0.153213\pi$
$158$	0.456684	+	0.122368i	0.0363318	+	0.00973508i
$159$	2.11310	−	8.53361i	0.167580	−	0.676759i
$160$	2.75805	−	1.59236i	0.218043	−	0.125887i
$161$	9.90546	−	11.4296i	0.780660	−	0.900776i
$162$	2.98479	+	8.49064i	0.234508	+	0.667088i
$163$	1.09955	+	4.10359i	0.0861236	+	0.321418i	0.995525	−	0.0945028i	$-0.0301261\pi$
$163$	1.09955	+	4.10359i	0.0861236	+	0.321418i	−0.909401	+	0.415921i	$0.863459\pi$
$164$	4.09530	−	1.09733i	0.319789	−	0.0856873i
$165$	−21.5134	−	5.32716i	−1.67482	−	0.414719i
$166$		−	3.14933i		−	0.244436i
$167$	17.4044	−	4.66350i	1.34680	−	0.360873i	0.487845	−	0.872930i	$-0.337783\pi$
$167$	17.4044	−	4.66350i	1.34680	−	0.360873i	0.858951	+	0.512058i	$0.171117\pi$
$168$	1.58072	+	4.30132i	0.121955	+	0.331854i
$169$	1.39096	−	12.9254i	0.106997	−	0.994259i
$170$	10.5989	−	6.11929i	0.812901	−	0.469328i
$171$	−14.4269	+	15.5711i	−1.10325	+	1.19075i
$172$	3.79774	+	6.57787i	0.289575	+	0.501558i
$173$	6.02142	−	10.4294i	0.457800	−	0.792933i	−0.541044	−	0.840994i	$-0.681971\pi$
$173$	6.02142	−	10.4294i	0.457800	−	0.792933i	0.998844	+	0.0480611i	$0.0153042\pi$
$174$	2.44804	+	4.05942i	0.185586	+	0.307744i
$175$	12.8577	−	4.44887i	0.971949	−	0.336303i
$176$	1.03991	−	3.88100i	0.0783862	−	0.292541i
$177$	11.4760	−	20.7820i	0.862591	−	1.56207i
$178$	15.4456			1.15770
$179$	−3.32667	−	5.76195i	−0.248647	−	0.430669i	0.714504	−	0.699631i	$-0.246652\pi$
$179$	−3.32667	−	5.76195i	−0.248647	−	0.430669i	−0.963151	+	0.268963i	$0.913319\pi$
$180$	2.82274	+	9.12765i	0.210394	+	0.680335i
$181$			20.6106i			1.53198i	0.642854	+	0.765989i	$0.277750\pi$
$181$			20.6106i			1.53198i	−0.642854	+	0.765989i	$0.722250\pi$
$182$	6.86379	+	6.62483i	0.508778	+	0.491065i
$183$	−9.48059	−	2.34759i	−0.700826	−	0.173539i
$184$	4.04222	+	4.04222i	0.297996	+	0.297996i
$185$	−24.2176	+	13.9820i	−1.78051	+	1.02798i
$186$	3.67092	+	0.908995i	0.269165	+	0.0666508i
$187$	3.99628	−	14.9143i	0.292237	−	1.09064i
$188$	−0.793509	−	0.212620i	−0.0578726	−	0.0155069i
$189$	−13.6344	+	1.76173i	−0.991755	+	0.128147i
$190$	−15.9341	+	15.9341i	−1.15598	+	1.15598i
$191$	−17.5045	−	10.1062i	−1.26658	−	0.731259i	−0.292240	−	0.956345i	$-0.594400\pi$
$191$	−17.5045	−	10.1062i	−1.26658	−	0.731259i	−0.974339	+	0.225086i	$0.927734\pi$
$192$	−1.66418	+	0.480095i	−0.120102	+	0.0346479i
$193$	−7.77269	−	2.08269i	−0.559491	−	0.149915i	−0.0320184	−	0.999487i	$-0.510194\pi$
$193$	−7.77269	−	2.08269i	−0.559491	−	0.149915i	−0.527472	+	0.849572i	$0.676860\pi$
$194$	2.03313	+	3.52149i	0.145970	+	0.252828i
$195$	13.5693	+	14.5406i	0.971718	+	1.04127i
$196$	−6.92892	+	0.995036i	−0.494923	+	0.0710740i
$197$	−5.46537	−	20.3970i	−0.389391	−	1.45323i	−0.831127	−	0.556083i	$-0.812304\pi$
$197$	−5.46537	−	20.3970i	−0.389391	−	1.45323i	0.441736	−	0.897145i	$-0.354363\pi$
$198$	10.6609	+	5.62462i	0.757641	+	0.399724i
$199$		−	14.7137i		−	1.04303i	−0.853243	−	0.521513i	$-0.825368\pi$
$199$		−	14.7137i		−	1.04303i	0.853243	−	0.521513i	$-0.174632\pi$
$200$	1.33096	+	4.96721i	0.0941131	+	0.351235i
$201$	15.5559	−	0.296556i	1.09723	−	0.0209174i
$202$	−6.81972	−	1.82734i	−0.479834	−	0.128571i
$203$	−6.84309	+	2.36777i	−0.480291	+	0.166185i
$204$	−6.39531	+	1.84496i	−0.447761	+	0.129173i
$205$			13.5025i			0.943054i
$206$	−3.77777	+	14.0988i	−0.263209	+	0.982311i
$207$	−14.5144	+	9.13467i	−1.00882	+	0.634904i
$208$	−2.68244	+	2.40926i	−0.185994	+	0.167052i
$209$			28.4296i			1.96652i
$210$	−14.5347	+	1.31719i	−1.00299	+	0.0908946i
$211$	9.22393	−	15.9763i	0.635002	−	1.09986i	−0.351513	−	0.936183i	$-0.614333\pi$
$211$	9.22393	−	15.9763i	0.635002	−	1.09986i	0.986515	−	0.163672i	$-0.0523340\pi$
$212$	−2.53784	+	4.39567i	−0.174300	+	0.301896i
$213$	0.376282	+	19.7380i	0.0257824	+	1.35243i
$214$	4.51522	+	4.51522i	0.308654	+	0.308654i
$215$	−23.3652	+	6.26069i	−1.59349	+	0.426976i
$216$	−0.296978	−	5.18766i	−0.0202068	−	0.352975i
$217$	−2.52457	+	5.19593i	−0.171379	+	0.352723i
$218$	5.36010	−	9.28396i	0.363032	−	0.628789i
$219$	−6.44475	+	3.88652i	−0.435496	+	0.262626i
$220$	11.0816	+	6.39795i	0.747120	+	0.431350i
$221$	−10.3084	+	9.25855i	−0.693416	+	0.622798i
$222$	14.6127	−	4.21557i	0.980740	−	0.282930i
$223$	18.7357	−	5.02021i	1.25464	−	0.336178i	0.430510	−	0.902586i	$-0.358334\pi$
$223$	18.7357	−	5.02021i	1.25464	−	0.336178i	0.824125	+	0.566407i	$0.191667\pi$
$224$	−0.188523	−	2.63903i	−0.0125962	−	0.176327i
$225$	−15.4161	+	0.587993i	−1.02774	+	0.0391995i
$226$	0.230589	−	0.860571i	0.0153386	−	0.0572443i
$227$	−4.34998	+	4.34998i	−0.288719	+	0.288719i	−0.836573	−	0.547855i	$-0.815445\pi$
$227$	−4.34998	+	4.34998i	−0.288719	+	0.288719i	0.547855	+	0.836573i	$0.315445\pi$
$228$	10.4949	−	6.32894i	0.695039	−	0.419144i
$229$	−19.5254	−	5.23182i	−1.29028	−	0.345728i	−0.452511	−	0.891759i	$-0.649472\pi$
$229$	−19.5254	−	5.23182i	−1.29028	−	0.345728i	−0.837765	+	0.546030i	$0.816138\pi$
$230$	−15.7665	+	9.10281i	−1.03961	+	0.600222i
$231$	−11.7913	+	14.1414i	−0.775811	+	0.930438i
$232$	−0.708361	−	2.64364i	−0.0465062	−	0.173563i
$233$	11.0321	+	19.1081i	0.722735	+	1.25181i	0.959899	+	0.280345i	$0.0904488\pi$
$233$	11.0321	+	19.1081i	0.722735	+	1.25181i	−0.237164	+	0.971470i	$0.576218\pi$
$234$	−5.26269	−	9.45008i	−0.344033	−	0.617771i
$235$	1.30813	−	2.26574i	0.0853327	−	0.147801i
$236$	−9.69186	+	9.69186i	−0.630886	+	0.630886i
$237$	0.567910	−	0.589984i	0.0368897	−	0.0383236i
$238$	−0.724478	−	10.1415i	−0.0469609	−	0.657378i
$239$	−14.3931	+	14.3931i	−0.931014	+	0.931014i	−0.997769	−	0.0667552i	$-0.978735\pi$
$239$	−14.3931	+	14.3931i	−0.931014	+	0.931014i	0.0667552	+	0.997769i	$0.478735\pi$
$240$	−0.105139	−	5.51509i	−0.00678667	−	0.355998i
$241$	1.31409	−	1.31409i	0.0846479	−	0.0846479i	−0.663515	−	0.748163i	$-0.730936\pi$
$241$	1.31409	−	1.31409i	0.0846479	−	0.0846479i	0.748163	+	0.663515i	$0.230936\pi$
$242$	4.96830	−	1.33125i	0.319375	−	0.0855762i
$243$	15.3729	+	2.58338i	0.986172	+	0.165724i
$244$	4.88346	+	2.81947i	0.312632	+	0.180498i
$245$	2.65034	−	22.1349i	0.169324	−	1.41415i
$246$	1.76509	−	7.12821i	0.112538	−	0.454478i
$247$	13.9213	−	21.3788i	0.885792	−	1.36030i
$248$	−1.89090	−	1.09171i	−0.120072	−	0.0693236i
$249$	−4.77513	−	2.63687i	−0.302612	−	0.167105i
$250$	−0.453613			−0.0286890
$251$	0.926227	+	1.60427i	0.0584629	+	0.101261i	0.893776	−	0.448514i	$-0.148047\pi$
$251$	0.926227	+	1.60427i	0.0584629	+	0.101261i	−0.835313	+	0.549775i	$0.814713\pi$
$252$	7.84531	+	1.20465i	0.494208	+	0.0758860i
$253$	−5.94471	+	22.1860i	−0.373741	+	1.39482i
$254$	−8.25815	+	2.21276i	−0.518162	+	0.138841i
$255$	−0.404039	−	21.1940i	−0.0253019	−	1.32722i
$256$	1.00000			0.0625000
$257$	18.3595			1.14524			0.572618	−	0.819823i	$-0.305928\pi$
$257$	18.3595			1.14524			0.572618	+	0.819823i	$0.305928\pi$
$258$	13.1534	−	0.250753i	0.818892	−	0.0156112i
$259$	1.65537	+	23.1725i	0.102859	+	1.43987i
$260$	−5.20032	−	10.2376i	−0.322510	−	0.634909i
$261$	8.20473	−	0.312941i	0.507860	−	0.0193705i
$262$	−2.33925	+	8.73019i	−0.144519	+	0.539353i
$263$	15.1227	−	8.73109i	0.932505	−	0.538382i	0.0449018	−	0.998991i	$-0.485702\pi$
$263$	15.1227	−	8.73109i	0.932505	−	0.538382i	0.887603	+	0.460610i	$0.152369\pi$
$264$	−5.01381	−	4.82622i	−0.308579	−	0.297033i
$265$	−11.4301	−	11.4301i	−0.702147	−	0.702147i
$266$	6.12142	+	17.6915i	0.375328	+	1.08474i
$267$	12.9323	−	23.4192i	0.791442	−	1.43323i
$268$	−8.67678	−	2.32494i	−0.530019	−	0.142018i
$269$			4.74274i			0.289170i	0.989492	+	0.144585i	$0.0461847\pi$
$269$			4.74274i			0.289170i	−0.989492	+	0.144585i	$0.953815\pi$
$270$	16.2031	+	3.36245i	0.986088	+	0.204632i
$271$	−5.56652	+	5.56652i	−0.338142	+	0.338142i	−0.855668	−	0.517526i	$-0.826853\pi$
$271$	−5.56652	+	5.56652i	−0.338142	+	0.338142i	0.517526	+	0.855668i	$0.326853\pi$
$272$	3.84291			0.233011
$273$	15.7917	−	4.86030i	0.955757	−	0.294159i
$274$	9.72781			0.587679
$275$	−14.6101	+	14.6101i	−0.881023	+	0.881023i
$276$	9.51340	−	2.74449i	0.572640	−	0.165199i
$277$		−	4.01656i		−	0.241332i	−0.992693	−	0.120666i	$-0.961497\pi$
$277$		−	4.01656i		−	0.241332i	0.992693	−	0.120666i	$-0.0385029\pi$
$278$	−16.5245	−	4.42774i	−0.991076	−	0.265558i
$279$	4.45183	−	4.80490i	0.266524	−	0.287662i
$280$	8.27357	+	1.59532i	0.494440	+	0.0953388i
$281$	6.88328	+	6.88328i	0.410622	+	0.410622i	0.881955	−	0.471333i	$-0.156227\pi$
$281$	6.88328	+	6.88328i	0.410622	+	0.410622i	−0.471333	+	0.881955i	$0.656227\pi$
$282$	−0.986770	+	1.02512i	−0.0587613	+	0.0610453i
$283$	−20.9789	+	12.1122i	−1.24706	+	0.719993i	−0.970523	−	0.241009i	$-0.922522\pi$
$283$	−20.9789	+	12.1122i	−1.24706	+	0.719993i	−0.276541	+	0.961002i	$0.589188\pi$
$284$	2.94997	−	11.0094i	0.175049	−	0.653290i
$285$	10.8186	+	37.5010i	0.640836	+	2.22137i
$286$	−13.7722	−	4.49376i	−0.814365	−	0.265721i
$287$	10.0895	+	4.90222i	0.595563	+	0.289369i
$288$	−0.665448	+	2.92527i	−0.0392119	+	0.172373i
$289$	−2.23205			−0.131297
$290$	8.71625			0.511836
$291$	7.04169	−	0.134242i	0.412791	−	0.00786938i
$292$	4.19705	−	1.12460i	0.245614	−	0.0658120i
$293$	−6.78684	+	25.3288i	−0.396492	+	1.47973i	0.422733	+	0.906254i	$0.361071\pi$
$293$	−6.78684	+	25.3288i	−0.396492	+	1.47973i	−0.819225	+	0.573472i	$0.805596\pi$
$294$	−4.29272	+	11.3390i	−0.250357	+	0.661303i
$295$	−21.8254	−	37.8028i	−1.27073	−	2.20096i
$296$	−8.78070			−0.510368
$297$	17.4544	−	11.4551i	1.01281	−	0.664694i
$298$	5.81739	+	3.35867i	0.336992	+	0.194563i
$299$	15.3343	−	13.7727i	0.886807	−	0.796493i
$300$	8.64584	+	2.14089i	0.499168	+	0.123604i
$301$	−3.80481	+	19.7323i	−0.219305	+	1.13735i
$302$	1.40799	+	0.812904i	0.0810208	+	0.0467774i
$303$	−8.48067	+	8.81030i	−0.487202	+	0.506138i
$304$	−6.83462	+	1.83133i	−0.391993	+	0.105034i
$305$	−12.6985	+	12.6985i	−0.727115	+	0.727115i
$306$	−2.55726	+	11.2415i	−0.146189	+	0.642636i
$307$	0.653635	−	0.653635i	0.0373049	−	0.0373049i	−0.688208	−	0.725513i	$-0.741602\pi$
$307$	0.653635	−	0.653635i	0.0373049	−	0.0373049i	0.725513	+	0.688208i	$0.241602\pi$
$308$	8.80404	−	5.95767i	0.501657	−	0.339470i
$309$	18.2141	+	17.5326i	1.03616	+	0.997395i
$310$	4.91692	−	4.91692i	0.279262	−	0.279262i
$311$	−14.4497	+	25.0277i	−0.819370	+	1.41919i	0.0867779	+	0.996228i	$0.472343\pi$
$311$	−14.4497	+	25.0277i	−0.819370	+	1.41919i	−0.906147	+	0.422962i	$0.860990\pi$
$312$	1.40705	+	6.08442i	0.0796586	+	0.344463i
$313$	2.95108	+	5.11143i	0.166805	+	0.288915i	0.937295	−	0.348537i	$-0.113322\pi$
$313$	2.95108	+	5.11143i	0.166805	+	0.288915i	−0.770490	+	0.637452i	$0.779988\pi$
$314$	0.274051	+	1.02277i	0.0154656	+	0.0577185i
$315$	−10.1724	+	23.1408i	−0.573148	+	1.30384i
$316$	−0.409451	+	0.236397i	−0.0230334	+	0.0132984i
$317$	18.5533	+	4.97135i	1.04206	+	0.279219i	0.738966	−	0.673743i	$-0.235314\pi$
$317$	18.5533	+	4.97135i	1.04206	+	0.279219i	0.303092	+	0.952961i	$0.401981\pi$
$318$	4.53999	+	7.52836i	0.254590	+	0.422169i
$319$	7.77577	−	7.77577i	0.435359	−	0.435359i
$320$	−0.824266	+	3.07620i	−0.0460779	+	0.171965i
$321$	10.6266	−	3.06564i	0.593121	−	0.171107i
$322$	1.07770	+	15.0861i	0.0600581	+	0.840718i
$323$	−26.2648	+	7.03764i	−1.46141	+	0.391585i
$324$	−8.11436	−	3.89322i	−0.450798	−	0.216290i
$325$	18.1409	−	3.83244i	1.00628	−	0.212585i
$326$	−3.67918	−	2.12417i	−0.203771	−	0.117647i
$327$	−9.58877	−	15.9004i	−0.530260	−	0.879295i
$328$	−2.11988	+	3.67175i	−0.117051	+	0.202738i
$329$	−1.21811	−	1.80008i	−0.0671563	−	0.0992414i
$330$	18.9791	−	11.4454i	1.04477	−	0.630049i
$331$	−30.8250	+	8.25954i	−1.69430	+	0.453985i	−0.971493	−	0.237069i	$-0.923813\pi$
$331$	−30.8250	+	8.25954i	−1.69430	+	0.453985i	−0.722803	+	0.691054i	$0.757147\pi$
$332$	2.22692	+	2.22692i	0.122218	+	0.122218i
$333$	5.84309	−	25.6859i	0.320200	−	1.40758i
$334$	−9.00920	+	15.6044i	−0.492961	+	0.853834i
$335$	14.3039	−	24.7752i	0.781508	−	1.35361i
$336$	−4.15923	−	1.92375i	−0.226904	−	0.104949i
$337$			0.708948i			0.0386189i	0.999814	+	0.0193094i	$0.00614677\pi$
$337$			0.708948i			0.0386189i	−0.999814	+	0.0193094i	$0.993853\pi$
$338$	8.15606	+	10.1232i	0.443631	+	0.550628i
$339$	−1.11176	−	1.07016i	−0.0603825	−	0.0581233i
$340$	−3.16758	+	11.8216i	−0.171786	+	0.641114i
$341$		−	8.77277i		−	0.475072i
$342$	−0.809048	−	21.2117i	−0.0437483	−	1.14700i
$343$	−15.5777	−	10.0167i	−0.841117	−	0.540854i
$344$	−7.33666	−	1.96585i	−0.395566	−	0.105992i
$345$	0.601031	+	31.5273i	0.0323584	+	1.69738i
$346$	3.11692	+	11.6325i	0.167566	+	0.625367i
$347$		−	7.05414i		−	0.378686i	−0.981911	−	0.189343i	$-0.939364\pi$
$347$		−	7.05414i		−	0.378686i	0.981911	−	0.189343i	$-0.0606358\pi$
$348$	−4.60147	−	1.13942i	−0.246665	−	0.0610793i
$349$	−3.38816	−	12.6448i	−0.181364	−	0.676859i	−0.995380	−	0.0960166i	$-0.969390\pi$
$349$	−3.38816	−	12.6448i	−0.181364	−	0.676859i	0.814016	−	0.580843i	$-0.197277\pi$
$350$	−5.94592	+	12.2376i	−0.317823	+	0.654126i
$351$	−18.7349	+	0.0671330i	−0.999994	+	0.00358329i
$352$	2.00895	+	3.47961i	0.107078	+	0.185464i
$353$	3.51011	+	0.940531i	0.186824	+	0.0500594i	0.351018	−	0.936369i	$-0.385836\pi$
$353$	3.51011	+	0.940531i	0.186824	+	0.0500594i	−0.164194	+	0.986428i	$0.552502\pi$
$354$	6.58035	+	22.8099i	0.349742	+	1.21233i
$355$	31.4357	+	18.1494i	1.66843	+	0.963271i
$356$	−10.9217	+	10.9217i	−0.578849	+	0.578849i
$357$	−15.9835	−	7.39280i	−0.845938	−	0.391269i
$358$	6.42662	+	1.72201i	0.339658	+	0.0910110i
$359$	−2.00341	+	7.47684i	−0.105736	+	0.394613i	−0.998428	−	0.0560556i	$-0.982148\pi$
$359$	−2.00341	+	7.47684i	−0.105736	+	0.394613i	0.892691	+	0.450668i	$0.148814\pi$
$360$	−8.45020	−	4.45825i	−0.445365	−	0.234970i
$361$	26.9038	−	15.5329i	1.41599	−	0.817523i
$362$	−14.5739	−	14.5739i	−0.765989	−	0.765989i
$363$	2.14136	−	8.64774i	0.112392	−	0.453889i
$364$	−9.53790	+	0.168975i	−0.499922	+	0.00885670i
$365$			13.8379i			0.724311i
$366$	8.36379	−	5.04379i	0.437182	−	0.263643i
$367$	7.28011	+	12.6095i	0.380019	+	0.658211i	0.991064	−	0.133384i	$-0.0425843\pi$
$367$	7.28011	+	12.6095i	0.380019	+	0.658211i	−0.611046	+	0.791595i	$0.709251\pi$
$368$	−5.71656			−0.297996
$369$	−9.33016	−	8.64458i	−0.485709	−	0.450019i
$370$	7.23763	−	27.0112i	0.376266	−	1.40425i
$371$	−12.6908	+	4.39113i	−0.658873	+	0.227976i
$372$	−3.23849	+	1.95298i	−0.167908	+	0.101257i
$373$	−2.88327	+	4.99397i	−0.149290	+	0.258578i	−0.930965	−	0.365108i	$-0.881032\pi$
$373$	−2.88327	+	4.99397i	−0.149290	+	0.258578i	0.781675	+	0.623686i	$0.214366\pi$
$374$	7.72022	+	13.3718i	0.399203	+	0.691440i
$375$	−0.379800	+	0.687784i	−0.0196128	+	0.0355170i
$376$	0.711441	−	0.410751i	0.0366898	−	0.0211829i
$377$	−9.65492	+	2.03969i	−0.497254	+	0.105050i
$378$	8.39523	−	10.8867i	0.431804	−	0.559951i
$379$	15.2479	−	4.08565i	0.783230	−	0.209866i	0.155022	−	0.987911i	$-0.450455\pi$
$379$	15.2479	−	4.08565i	0.783230	−	0.209866i	0.628208	+	0.778045i	$0.283789\pi$
$380$		−	22.5342i		−	1.15598i
$381$	−3.55929	+	14.3740i	−0.182348	+	0.736402i
$382$	19.5237	−	5.23136i	0.998919	−	0.267660i
$383$	2.87687	+	10.7366i	0.147001	+	0.548616i	0.999658	+	0.0261447i	$0.00832305\pi$
$383$	2.87687	+	10.7366i	0.147001	+	0.548616i	−0.852657	+	0.522471i	$0.825010\pi$
$384$	0.837278	−	1.51623i	0.0427271	−	0.0773750i
$385$	11.0701	+	31.9937i	0.564185	+	1.63055i
$386$	6.96881	−	4.02344i	0.354703	−	0.204788i
$387$	10.6328	−	20.1535i	0.540496	−	1.02446i
$388$	−3.92771	−	1.05243i	−0.199399	−	0.0534288i
$389$	12.9910	−	22.5010i	0.658668	−	1.14085i	−0.322293	−	0.946640i	$-0.604454\pi$
$389$	12.9910	−	22.5010i	0.658668	−	1.14085i	0.980961	−	0.194206i	$-0.0622130\pi$
$390$	−19.8767	−	0.686809i	−1.00650	−	0.0347779i
$391$	−21.9682			−1.11098
$392$	4.19589	−	5.60308i	0.211924	−	0.282998i
$393$	11.2784	+	10.8564i	0.568921	+	0.547635i
$394$	18.2875	+	10.5583i	0.921310	+	0.531918i
$395$	−0.389708	−	1.45441i	−0.0196083	−	0.0731793i
$396$	−11.5156	+	3.56122i	−0.578682	+	0.178958i
$397$	−3.78484	−	14.1252i	−0.189955	−	0.708923i	−0.993515	−	0.113699i	$-0.963730\pi$
$397$	−3.78484	−	14.1252i	−0.189955	−	0.708923i	0.803560	−	0.595224i	$-0.202937\pi$
$398$	10.4042	+	10.4042i	0.521513	+	0.521513i
$399$	31.9498	+	5.53119i	1.59949	+	0.276906i
$400$	−4.45348	−	2.57122i	−0.222674	−	0.128561i
$401$	2.12030	+	2.12030i	0.105883	+	0.105883i	0.758063	−	0.652181i	$-0.226146\pi$
$401$	2.12030	+	2.12030i	0.105883	+	0.105883i	−0.652181	+	0.758063i	$0.726146\pi$
$402$	−10.7900	+	11.2094i	−0.538157	+	0.559075i
$403$	−4.29582	+	6.59704i	−0.213990	+	0.328622i
$404$	6.11439	−	3.53014i	0.304202	−	0.175631i
$405$	18.6647	−	21.7524i	0.927458	−	1.08088i
$406$	3.16453	−	6.51306i	0.157053	−	0.323238i
$407$	−17.6400	−	30.5534i	−0.874383	−	1.51448i
$408$	3.21758	−	5.82675i	0.159294	−	0.288467i
$409$	−10.8976	−	10.8976i	−0.538853	−	0.538853i	0.384339	−	0.923192i	$-0.374429\pi$
$409$	−10.8976	−	10.8976i	−0.538853	−	0.538853i	−0.923192	+	0.384339i	$0.874429\pi$
$410$	−9.54769	−	9.54769i	−0.471527	−	0.471527i
$411$	8.14488	−	14.7496i	0.401757	−	0.727546i
$412$	−7.29808	−	12.6406i	−0.359551	−	0.622760i
$413$	−36.1714	+	2.58397i	−1.77988	+	0.127149i
$414$	3.80407	−	16.7224i	0.186960	−	0.821864i
$415$	−8.68601	+	5.01487i	−0.426380	+	0.246170i
$416$	0.193169	−	3.60037i	0.00947091	−	0.176523i
$417$	−20.5491	+	21.3478i	−1.00629	+	1.04541i
$418$	−20.1028	−	20.1028i	−0.983258	−	0.983258i
$419$	−17.6526	−	10.1917i	−0.862386	−	0.497899i	0.00242467	−	0.999997i	$-0.499228\pi$
$419$	−17.6526	−	10.1917i	−0.862386	−	0.497899i	−0.864811	+	0.502098i	$0.832562\pi$
$420$	9.34616	−	11.2089i	0.456046	−	0.546940i
$421$	−26.0846	−	26.0846i	−1.27129	−	1.27129i	−0.945413	−	0.325874i	$-0.894341\pi$
$421$	−26.0846	−	26.0846i	−1.27129	−	1.27129i	−0.325874	−	0.945413i	$-0.605659\pi$
$422$	4.77466	+	17.8193i	0.232427	+	0.867429i
$423$	0.728128	+	2.35449i	0.0354028	+	0.114479i
$424$	−1.31368	−	4.90273i	−0.0637981	−	0.238098i
$425$	−17.1143	−	9.88095i	−0.830166	−	0.479297i
$426$	−14.2229	−	13.6908i	−0.689104	−	0.663322i
$427$	4.87841	+	14.0991i	0.236083	+	0.682303i
$428$	−6.38549			−0.308654
$429$	−18.3447	+	17.1193i	−0.885691	+	0.826528i
$430$	12.0947	−	20.9487i	0.583259	−	1.01023i
$431$	−28.9223	−	7.74971i	−1.39314	−	0.373290i	−0.517263	−	0.855827i	$-0.673049\pi$
$431$	−28.9223	−	7.74971i	−1.39314	−	0.373290i	−0.875876	+	0.482536i	$0.839716\pi$
$432$	3.87822	+	3.45823i	0.186591	+	0.166384i
$433$	−27.1564	+	15.6787i	−1.30505	+	0.753472i	−0.981266	−	0.192659i	$-0.938289\pi$
$433$	−27.1564	+	15.6787i	−1.30505	+	0.753472i	−0.323785	+	0.946131i	$0.604956\pi$
$434$	−1.88894	−	5.45922i	−0.0906720	−	0.262051i
$435$	7.29792	−	13.2159i	0.349908	−	0.633653i
$436$	2.77459	+	10.3549i	0.132879	+	0.495910i
$437$	39.0705	−	10.4689i	1.86900	−	0.500796i
$438$	1.80894	−	7.30531i	0.0864347	−	0.349061i
$439$			2.59361i			0.123786i	0.998083	+	0.0618931i	$0.0197138\pi$
$439$			2.59361i			0.123786i	−0.998083	+	0.0618931i	$0.980286\pi$
$440$	−12.3599	+	3.31182i	−0.589235	+	0.157885i
$441$	13.5984	+	16.0026i	0.647541	+	0.762031i
$442$	0.742333	−	13.8359i	0.0353092	−	0.658107i
$443$	18.5688	−	10.7207i	0.882233	−	0.509357i	0.0108387	−	0.999941i	$-0.496550\pi$
$443$	18.5688	−	10.7207i	0.882233	−	0.509357i	0.871394	+	0.490584i	$0.163217\pi$
$444$	−7.35188	+	13.3136i	−0.348905	+	0.631835i
$445$	−24.5950	−	42.5998i	−1.16591	−	2.01942i
$446$	−9.69831	+	16.7980i	−0.459228	+	0.795407i
$447$	9.96330	−	6.00838i	0.471248	−	0.284187i
$448$	1.99938	+	1.73277i	0.0944618	+	0.0818656i
$449$	−6.92873	+	25.8584i	−0.326987	+	1.22033i	0.585313	+	0.810808i	$0.300972\pi$
$449$	−6.92873	+	25.8584i	−0.326987	+	1.22033i	−0.912299	+	0.409524i	$0.865695\pi$
$450$	10.4851	−	11.3166i	0.494270	−	0.533470i
$451$	−17.0350			−0.802146
$452$	0.445464	+	0.771567i	0.0209529	+	0.0362915i
$453$	2.41143	−	1.45422i	0.113299	−	0.0683251i
$454$		−	6.15181i		−	0.288719i
$455$	7.34196	−	29.4798i	0.344196	−	1.38203i
$456$	−2.94575	+	11.8962i	−0.137947	+	0.557092i
$457$	−2.12609	−	2.12609i	−0.0994545	−	0.0994545i	0.655629	−	0.755083i	$-0.272404\pi$
$457$	−2.12609	−	2.12609i	−0.0994545	−	0.0994545i	−0.755083	+	0.655629i	$0.772404\pi$
$458$	17.5060	−	10.1071i	0.818002	−	0.472274i
$459$	14.9037	+	13.2897i	0.695643	+	0.620309i
$460$	4.71196	−	17.5853i	0.219696	−	0.819918i
$461$	−10.9743	−	2.94055i	−0.511123	−	0.136955i	−0.00596583	−	0.999982i	$-0.501899\pi$
$461$	−10.9743	−	2.94055i	−0.511123	−	0.136955i	−0.505158	+	0.863027i	$0.668566\pi$
$462$	−1.66179	−	18.3372i	−0.0773135	−	0.853124i
$463$	29.5393	−	29.5393i	1.37281	−	1.37281i	0.516548	−	0.856258i	$-0.327217\pi$
$463$	29.5393	−	29.5393i	1.37281	−	1.37281i	0.856258	−	0.516548i	$-0.172783\pi$
$464$	2.37022	+	1.36845i	0.110035	+	0.0635286i
$465$	−3.33837	−	11.5720i	−0.154813	−	0.536640i
$466$	−21.3123	−	5.71062i	−0.987275	−	0.264540i
$467$	−0.847286	−	1.46754i	−0.0392077	−	0.0679097i	0.845756	−	0.533570i	$-0.179150\pi$
$467$	−0.847286	−	1.46754i	−0.0392077	−	0.0679097i	−0.884963	+	0.465661i	$0.845817\pi$
$468$	10.4035	+	2.96093i	0.480902	+	0.136869i
$469$	−13.3196	−	19.6833i	−0.615042	−	0.908889i
$470$	0.677136	+	2.52710i	0.0312339	+	0.116567i
$471$	1.78022	+	0.440819i	0.0820283	+	0.0203119i
$472$		−	13.7064i		−	0.630886i
$473$	−7.89861	−	29.4780i	−0.363179	−	1.35540i
$474$	0.0156086	+	0.818754i	0.000716926	+	0.0376066i
$475$	35.1466	+	9.41751i	1.61264	+	0.432105i
$476$	7.68343	+	6.65887i	0.352170	+	0.305209i
$477$	15.2160	−	0.580361i	0.696692	−	0.0265729i
$478$		−	20.3550i		−	0.931014i
$479$	6.85229	−	25.5731i	0.313089	−	1.16846i	−0.612666	−	0.790342i	$-0.709903\pi$
$479$	6.85229	−	25.5731i	0.313089	−	1.16846i	0.925755	−	0.378123i	$-0.123430\pi$
$480$	3.97410	+	3.82542i	0.181392	+	0.174606i
$481$	−1.69616	+	31.6138i	−0.0773383	+	1.44146i
$482$			1.85840i			0.0846479i
$483$	23.7765	+	10.9972i	1.08187	+	0.500392i
$484$	−2.57178	+	4.45446i	−0.116899	+	0.202475i
$485$	6.47495	−	11.2149i	0.294012	−	0.509244i
$486$	−12.6970	+	9.04356i	−0.575948	+	0.410224i
$487$	17.6662	+	17.6662i	0.800531	+	0.800531i	0.983178	−	0.182648i	$-0.0584668\pi$
$487$	17.6662	+	17.6662i	0.800531	+	0.800531i	−0.182648	+	0.983178i	$0.558467\pi$
$488$	−5.44679	+	1.45946i	−0.246565	+	0.0660668i
$489$	−6.30123	+	3.79997i	−0.284952	+	0.171841i
$490$	13.7777	+	17.5258i	0.622412	+	0.791736i
$491$	−0.424561	+	0.735361i	−0.0191602	+	0.0331864i	−0.875447	−	0.483315i	$-0.839433\pi$
$491$	−0.424561	+	0.735361i	−0.0191602	+	0.0331864i	0.856286	+	0.516501i	$0.172766\pi$
$492$	3.79230	+	6.28851i	0.170970	+	0.283508i
$493$	9.10855	+	5.25882i	0.410228	+	0.236846i
$494$	5.27324	+	24.9610i	0.237254	+	1.12305i
$495$	−1.46310	−	38.3598i	−0.0657615	−	1.72415i
$496$	2.10902	−	0.565110i	0.0946978	−	0.0253742i
$497$	24.9749	−	16.9004i	1.12028	−	0.758088i
$498$	5.24107	−	1.51198i	0.234858	−	0.0677534i
$499$	−8.85639	+	33.0525i	−0.396467	+	1.47963i	0.422801	+	0.906223i	$0.361047\pi$
$499$	−8.85639	+	33.0525i	−0.396467	+	1.47963i	−0.819268	+	0.573411i	$0.805620\pi$
$500$	0.320753	−	0.320753i	0.0143445	−	0.0143445i
$501$	16.1167	+	26.7253i	0.720042	+	1.19400i
$502$	−1.78933	−	0.479451i	−0.0798619	−	0.0213989i
$503$	−29.5585	+	17.0656i	−1.31795	+	0.760917i	−0.983398	−	0.181462i	$-0.941917\pi$
$503$	−29.5585	+	17.0656i	−1.31795	+	0.760917i	−0.334549	+	0.942379i	$0.608584\pi$
$504$	−6.39929	+	4.69565i	−0.285047	+	0.209161i
$505$	5.81956	+	21.7189i	0.258967	+	0.966477i
$506$	−11.4843	−	19.8914i	−0.510539	−	0.884280i
$507$	22.1780	−	3.89058i	0.984959	−	0.172787i
$508$	4.27473	−	7.40405i	0.189661	−	0.328502i
$509$	−22.9477	+	22.9477i	−1.01714	+	1.01714i	−0.0172866	+	0.999851i	$0.505503\pi$
$509$	−22.9477	+	22.9477i	−1.01714	+	1.01714i	−0.999851	+	0.0172866i	$0.994497\pi$
$510$	15.2721	+	14.7007i	0.676261	+	0.650959i
$511$	10.3402	+	5.02402i	0.457422	+	0.222249i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−32.8394	−	16.5334i	−1.44989	−	0.729968i
$514$	−12.9821	+	12.9821i	−0.572618	+	0.572618i
$515$	44.9008	−	12.0311i	1.97856	−	0.530155i
$516$	−9.12352	+	9.47814i	−0.401640	+	0.417252i
$517$	2.85850	+	1.65036i	0.125717	+	0.0725826i
$518$	−17.5559	−	15.2149i	−0.771364	−	0.668504i
$519$	20.2473	+	5.01365i	0.888758	+	0.220075i
$520$	10.9163	+	3.56189i	0.478709	+	0.156199i
$521$	−13.0040	−	7.50785i	−0.569715	−	0.328925i	0.187321	−	0.982299i	$-0.440020\pi$
$521$	−13.0040	−	7.50785i	−0.569715	−	0.328925i	−0.757035	+	0.653374i	$0.773353\pi$
$522$	−5.58034	+	6.02290i	−0.244245	+	0.263615i
$523$	11.9584			0.522905			0.261453	−	0.965216i	$-0.415798\pi$
$523$	11.9584			0.522905			0.261453	+	0.965216i	$0.415798\pi$
$524$	−4.51908	−	7.82728i	−0.197417	−	0.341936i
$525$	13.5767	+	19.2617i	0.592534	+	0.840648i
$526$	−4.51954	+	16.8672i	−0.197061	+	0.735443i
$527$	8.10477	−	2.17167i	0.353049	−	0.0945993i
$528$	6.95795	−	0.132645i	0.302806	−	0.00577264i
$529$	9.67903			0.420827
$530$	16.1646			0.702147
$531$	40.0947	+	9.12086i	1.73996	+	0.395812i
$532$	−16.8383	−	8.18129i	−0.730032	−	0.354704i
$533$	12.8102	+	8.34164i	0.554870	+	0.361317i
$534$	7.41536	+	25.7044i	0.320894	+	1.11234i
$535$	5.26334	−	19.6431i	0.227554	−	0.849244i
$536$	7.77939	−	4.49143i	0.336018	−	0.194000i
$537$	7.99184	−	8.30247i	0.344873	−	0.358278i
$538$	−3.35362	−	3.35362i	−0.144585	−	0.144585i
$539$	27.9259	+	3.34372i	1.20285	+	0.144024i
$540$	−13.8349	+	9.07970i	−0.595360	+	0.390728i
$541$	6.92295	+	1.85500i	0.297641	+	0.0797526i	0.404549	−	0.914516i	$-0.367428\pi$
$541$	6.92295	+	1.85500i	0.297641	+	0.0797526i	−0.106908	+	0.994269i	$0.534095\pi$
$542$		−	7.87225i		−	0.338142i
$543$	−34.2999	+	9.89506i	−1.47195	+	0.424638i
$544$	−2.71735	+	2.71735i	−0.116505	+	0.116505i
$545$	−34.1408			−1.46243
$546$	−7.72966	+	14.6032i	−0.330799	+	0.624958i
$547$	22.6826			0.969837			0.484918	−	0.874559i	$-0.338849\pi$
$547$	22.6826			0.969837			0.484918	+	0.874559i	$0.338849\pi$
$548$	−6.87860	+	6.87860i	−0.293839	+	0.293839i
$549$	−0.644764	−	16.9045i	−0.0275178	−	0.721467i
$550$		−	20.6618i		−	0.881023i
$551$	−18.7057	−	5.01217i	−0.796888	−	0.213526i
$552$	−4.78635	+	8.66764i	−0.203720	+	0.368919i
$553$	−1.22827	−	0.236837i	−0.0522313	−	0.0100713i
$554$	2.84014	+	2.84014i	0.120666	+	0.120666i
$555$	−34.8954	−	33.5898i	−1.48123	−	1.42581i
$556$	14.8155	−	8.55373i	0.628317	−	0.362759i
$557$	−5.55942	+	20.7481i	−0.235560	+	0.879123i	0.742335	+	0.670029i	$0.233718\pi$
$557$	−5.55942	+	20.7481i	−0.235560	+	0.879123i	−0.977895	+	0.209094i	$0.932948\pi$
$558$	0.249655	+	6.54549i	0.0105687	+	0.277093i
$559$	−8.49502	+	26.0350i	−0.359301	+	1.10116i
$560$	−6.97836	+	4.72223i	−0.294890	+	0.199551i
$561$	26.7388	−	0.509743i	1.12891	−	0.0215214i
$562$	−9.73443			−0.410622
$563$	−9.67895			−0.407919			−0.203959	−	0.978979i	$-0.565381\pi$
$563$	−9.67895			−0.407919			−0.203959	+	0.978979i	$0.565381\pi$
$564$	−0.0271206	−	1.42262i	−0.00114198	−	0.0599033i
$565$	−2.74068	+	0.734362i	−0.115301	+	0.0308948i
$566$	6.26971	−	23.3989i	0.263536	−	0.983528i
$567$	−9.47763	−	21.8443i	−0.398023	−	0.917375i
$568$	5.69891	+	9.87079i	0.239121	+	0.414169i
$569$	21.2472			0.890730			0.445365	−	0.895349i	$-0.353074\pi$
$569$	21.2472			0.890730			0.445365	+	0.895349i	$0.353074\pi$
$570$	−34.1671	−	18.8674i	−1.43110	−	0.790267i
$571$	−1.49319	−	0.862095i	−0.0624881	−	0.0360775i	0.468430	−	0.883500i	$-0.344820\pi$
$571$	−1.49319	−	0.862095i	−0.0624881	−	0.0360775i	−0.530919	+	0.847423i	$0.678153\pi$
$572$	12.9160	−	6.56083i	0.540043	−	0.274322i
$573$	8.41479	−	33.9826i	0.351533	−	1.41964i
$574$	−10.6007	+	3.66795i	−0.442466	+	0.153097i
$575$	25.4586	+	14.6985i	1.06170	+	0.612970i
$576$	−1.59793	−	2.53902i	−0.0665805	−	0.105792i
$577$	−17.2532	+	4.62299i	−0.718261	+	0.192457i	−0.599396	−	0.800453i	$-0.704592\pi$
$577$	−17.2532	+	4.62299i	−0.718261	+	0.192457i	−0.118865	+	0.992910i	$0.537926\pi$
$578$	1.57830	−	1.57830i	0.0656485	−	0.0656485i
$579$	−0.265656	−	13.9351i	−0.0110403	−	0.579122i
$580$	−6.16332	+	6.16332i	−0.255918	+	0.255918i
$581$	0.593723	+	8.31118i	0.0246318	+	0.344806i
$582$	−4.88431	+	5.07415i	−0.202461	+	0.210330i
$583$	14.4205	−	14.4205i	0.597235	−	0.597235i
$584$	−2.17255	+	3.76297i	−0.0899009	+	0.155713i
$585$	−17.6837	+	29.5627i	−0.731130	+	1.22227i
$586$	−13.1112	−	22.7092i	−0.541618	−	0.938109i
$587$	4.79136	+	17.8816i	0.197761	+	0.738053i	0.991535	+	0.129840i	$0.0414465\pi$
$587$	4.79136	+	17.8816i	0.197761	+	0.738053i	−0.793774	+	0.608213i	$0.791887\pi$
$588$	−4.98246	−	11.0533i	−0.205473	−	0.455830i
$589$	−13.3795	+	7.72463i	−0.551291	+	0.318288i
$590$	42.1635	+	11.2977i	1.73584	+	0.465118i
$591$	31.3205	−	18.8879i	1.28835	−	0.776944i
$592$	6.20889	−	6.20889i	0.255184	−	0.255184i
$593$	−7.65269	+	28.5602i	−0.314258	+	1.17283i	0.610420	+	0.792078i	$0.291001\pi$
$593$	−7.65269	+	28.5602i	−0.314258	+	1.17283i	−0.924678	+	0.380750i	$0.875666\pi$
$594$	−4.24213	+	20.4421i	−0.174057	+	0.838751i
$595$	−26.8172	+	18.1471i	−1.09940	+	0.743959i
$596$	−6.48845	+	1.73858i	−0.265777	+	0.0712149i
$597$	24.4863	−	7.06397i	1.00216	−	0.289109i
$598$	−1.10426	+	20.5817i	−0.0451567	+	0.841650i
$599$	20.9863	+	12.1164i	0.857476	+	0.495064i	0.863166	−	0.504920i	$-0.168478\pi$
$599$	20.9863	+	12.1164i	0.857476	+	0.495064i	−0.00569046	+	0.999984i	$0.501811\pi$
$600$	−7.62737	+	4.59969i	−0.311386	+	0.187782i
$601$	2.40179	−	4.16002i	0.0979711	−	0.169691i	−0.812874	−	0.582440i	$-0.802098\pi$
$601$	2.40179	−	4.16002i	0.0979711	−	0.169691i	0.910845	+	0.412749i	$0.135431\pi$
$602$	−11.2624	−	16.6432i	−0.459022	−	0.678327i
$603$	7.96185	+	25.7456i	0.324232	+	1.04844i
$604$	−1.57041	+	0.420790i	−0.0638991	+	0.0171217i
$605$	−11.5830	−	11.5830i	−0.470915	−	0.470915i
$606$	−0.233085	−	12.2266i	−0.00946843	−	0.496670i
$607$	−16.9432	+	29.3465i	−0.687704	+	1.19114i	0.284875	+	0.958565i	$0.408048\pi$
$607$	−16.9432	+	29.3465i	−0.687704	+	1.19114i	−0.972579	+	0.232573i	$0.925286\pi$
$608$	3.53786	−	6.12776i	0.143479	−	0.248513i
$609$	−7.22574	−	10.2514i	−0.292802	−	0.415408i
$610$		−	17.9584i		−	0.727115i
$611$	−1.34143	−	2.64080i	−0.0542683	−	0.106835i
$612$	−6.14071	−	9.75721i	−0.248223	−	0.394412i
$613$	−7.28333	+	27.1818i	−0.294171	+	1.09786i	0.647703	+	0.761893i	$0.275730\pi$
$613$	−7.28333	+	27.1818i	−0.294171	+	1.09786i	−0.941874	+	0.335968i	$0.890937\pi$
$614$			0.924380i			0.0373049i
$615$	−22.4706	+	6.48247i	−0.906102	+	0.261398i
$616$	−2.01269	+	10.4381i	−0.0810937	+	0.420563i
$617$	28.0661	+	7.52029i	1.12990	+	0.302756i	0.774883	−	0.632105i	$-0.217809\pi$
$617$	28.0661	+	7.52029i	1.12990	+	0.302756i	0.355016	+	0.934860i	$0.384475\pi$
$618$	−25.2767	+	0.481870i	−1.01678	+	0.0193837i
$619$	0.974909	+	3.63841i	0.0391849	+	0.146240i	0.982747	−	0.184956i	$-0.0592144\pi$
$619$	0.974909	+	3.63841i	0.0391849	+	0.146240i	−0.943562	+	0.331196i	$0.892548\pi$
$620$			6.95357i			0.279262i
$621$	−22.1701	−	19.7692i	−0.889655	−	0.793310i
$622$	−7.47974	−	27.9148i	−0.299910	−	1.11928i
$623$	−40.7614	+	2.91186i	−1.63307	+	0.116661i
$624$	−5.29727	−	3.30740i	−0.212061	−	0.132402i
$625$	−12.1338	−	21.0163i	−0.485351	−	0.840652i
$626$	−5.70106	−	1.52759i	−0.227860	−	0.0610549i
$627$	−47.3121	+	13.6489i	−1.88946	+	0.545085i
$628$	−0.916994	−	0.529427i	−0.0365920	−	0.0211264i
$629$	23.8602	−	23.8602i	0.951368	−	0.951368i
$630$	−9.17005	−	23.5560i	−0.365344	−	0.938492i
$631$	7.68584	+	2.05942i	0.305969	+	0.0819840i	0.408537	−	0.912742i	$-0.366039\pi$
$631$	7.68584	+	2.05942i	0.305969	+	0.0819840i	−0.102568	+	0.994726i	$0.532706\pi$
$632$	0.122368	−	0.456684i	0.00486754	−	0.0181659i
$633$	31.0159	+	7.68017i	1.23277	+	0.305260i
$634$	−16.6344	+	9.60390i	−0.660638	+	0.381420i
$635$	19.2529	+	19.2529i	0.764026	+	0.764026i
$636$	−8.53361	−	2.11310i	−0.338380	−	0.0837898i
$637$	−19.3627	−	16.1891i	−0.767177	−	0.641436i
$638$			10.9966i			0.435359i
$639$	−32.6670	+	10.1023i	−1.29229	+	0.399641i
$640$	−1.59236	−	2.75805i	−0.0629435	−	0.109021i
$641$	18.0757			0.713946			0.356973	−	0.934115i	$-0.383809\pi$
$641$	18.0757			0.713946			0.356973	+	0.934115i	$0.383809\pi$
$642$	−5.34643	+	9.68190i	−0.211007	+	0.382114i
$643$	−9.46354	+	35.3184i	−0.373206	+	1.39282i	0.482743	+	0.875762i	$0.339641\pi$
$643$	−9.46354	+	35.3184i	−0.373206	+	1.39282i	−0.855949	+	0.517061i	$0.827026\pi$
$644$	−11.4296	−	9.90546i	−0.450388	−	0.390330i
$645$	−21.6365	−	35.8783i	−0.851935	−	1.41271i
$646$	13.5957	−	23.5484i	0.534915	−	0.926500i
$647$	12.8885	+	22.3236i	0.506700	+	0.877630i	0.999970	+	0.00775374i	$0.00246812\pi$
$647$	12.8885	+	22.3236i	0.506700	+	0.877630i	−0.493270	+	0.869876i	$0.664199\pi$
$648$	8.49064	−	2.98479i	0.333544	−	0.117254i
$649$	47.6927	−	27.5354i	1.87210	−	1.08086i
$650$	−10.1176	+	15.5375i	−0.396846	+	0.609431i
$651$	−9.85902	−	1.70681i	−0.386406	−	0.0668951i
$652$	4.10359	−	1.09955i	0.160709	−	0.0430618i
$653$			2.61814i			0.102456i	0.998687	+	0.0512280i	$0.0163135\pi$
$653$			2.61814i			0.102456i	−0.998687	+	0.0512280i	$0.983686\pi$
$654$	18.0236	+	4.46301i	0.704778	+	0.174517i
$655$	27.8032	−	7.44985i	1.08636	−	0.291090i
$656$	−1.09733	−	4.09530i	−0.0428437	−	0.159895i
$657$	−9.56197	−	8.85935i	−0.373048	−	0.345636i
$658$	2.13418	+	0.411515i	0.0831988	+	0.0160425i
$659$	1.55081	−	0.895360i	0.0604110	−	0.0348783i	−0.469490	−	0.882938i	$-0.655562\pi$
$659$	1.55081	−	0.895360i	0.0604110	−	0.0348783i	0.529901	+	0.848059i	$0.322229\pi$
$660$	−5.32716	+	21.5134i	−0.207359	+	0.837408i
$661$	30.3550	+	8.13360i	1.18067	+	0.316361i	0.795194	−	0.606356i	$-0.207369\pi$
$661$	30.3550	+	8.13360i	1.18067	+	0.316361i	0.385480	+	0.922716i	$0.374036\pi$
$662$	15.9562	−	27.6369i	0.620155	−	1.07414i
$663$	−20.3569	−	12.7100i	−0.790598	−	0.493617i
$664$	−3.14933			−0.122218
$665$	39.0465	−	45.0544i	1.51416	−	1.74713i
$666$	14.0310	+	22.2943i	0.543689	+	0.863888i
$667$	−13.5495	−	7.82281i	−0.524639	−	0.302901i
$668$	−4.66350	−	17.4044i	−0.180436	−	0.673398i
$669$	17.3495	+	28.7695i	0.670769	+	1.11229i
$670$	7.40427	+	27.6331i	0.286052	+	1.06756i
$671$	−16.0207	−	16.0207i	−0.618473	−	0.618473i
$672$	4.30132	−	1.58072i	0.165927	−	0.0609776i
$673$	6.26032	+	3.61440i	0.241318	+	0.139325i	0.615782	−	0.787916i	$-0.288840\pi$
$673$	6.26032	+	3.61440i	0.241318	+	0.139325i	−0.374465	+	0.927241i	$0.622173\pi$
$674$	−0.501302	−	0.501302i	−0.0193094	−	0.0193094i
$675$	−8.37972	−	25.3729i	−0.322535	−	0.976604i
$676$	−12.9254	−	1.39096i	−0.497130	−	0.0534986i
$677$	16.8876	−	9.75008i	0.649045	−	0.374726i	−0.139045	−	0.990286i	$-0.544403\pi$
$677$	16.8876	−	9.75008i	0.649045	−	0.374726i	0.788090	+	0.615560i	$0.211070\pi$
$678$	1.54285	−	0.0294127i	0.0592529	−	0.00112959i
$679$	−6.02937	−	8.91000i	−0.231386	−	0.341935i
$680$	−6.11929	−	10.5989i	−0.234664	−	0.406450i
$681$	−9.32758	−	5.15077i	−0.357434	−	0.197378i
$682$	6.20328	+	6.20328i	0.237536	+	0.237536i
$683$	−5.48698	−	5.48698i	−0.209953	−	0.209953i	0.594294	−	0.804248i	$-0.297431\pi$
$683$	−5.48698	−	5.48698i	−0.209953	−	0.209953i	−0.804248	+	0.594294i	$0.797431\pi$
$684$	15.5711	+	14.4269i	0.595374	+	0.551626i
$685$	−15.4902	−	26.8298i	−0.591849	−	1.02511i
$686$	18.0980	−	3.93219i	0.690985	−	0.150132i
$687$	−0.667342	−	35.0057i	−0.0254607	−	1.33555i
$688$	6.57787	−	3.79774i	0.250779	−	0.144787i
$689$	−17.9054	+	3.78269i	−0.682143	+	0.144109i
$690$	−22.7182	−	21.8682i	−0.864867	−	0.832508i
$691$	1.45252	+	1.45252i	0.0552566	+	0.0552566i	0.734195	−	0.678939i	$-0.237560\pi$
$691$	1.45252	+	1.45252i	0.0552566	+	0.0552566i	−0.678939	+	0.734195i	$0.737560\pi$
$692$	−10.4294	−	6.02142i	−0.396466	−	0.228900i
$693$	−29.1949	−	12.8337i	−1.10902	−	0.487511i
$694$	4.98803	+	4.98803i	0.189343	+	0.189343i
$695$	14.1011	+	52.6260i	0.534885	+	1.99622i
$696$	4.05942	−	2.44804i	0.153872	−	0.0927928i
$697$	−4.21695	−	15.7379i	−0.159728	−	0.596114i
$698$	11.3370	+	6.54542i	0.429112	+	0.247748i
$699$	−26.5030	+	27.5331i	−1.00243	+	1.04140i
$700$	−4.44887	−	12.8577i	−0.168152	−	0.485975i
$701$	9.39372			0.354796			0.177398	−	0.984139i	$-0.443232\pi$
$701$	9.39372			0.354796			0.177398	+	0.984139i	$0.443232\pi$
$702$	13.2001	−	13.2950i	0.498205	−	0.501788i
$703$	−31.0649	+	53.8060i	−1.17163	+	2.02933i
$704$	−3.88100	−	1.03991i	−0.146271	−	0.0391931i
$705$	4.39863	+	1.08919i	0.165662	+	0.0410213i
$706$	−3.14708	+	1.81697i	−0.118442	+	0.0683824i
$707$	18.3419	+	3.53672i	0.689818	+	0.133012i
$708$	−20.7820	−	11.4760i	−0.781037	−	0.431295i
$709$	−5.30576	−	19.8014i	−0.199262	−	0.743656i	−0.991122	−	0.132954i	$-0.957554\pi$
$709$	−5.30576	−	19.8014i	−0.199262	−	0.743656i	0.791860	−	0.610702i	$-0.209113\pi$
$710$	−35.0620	+	9.39483i	−1.31585	+	0.352582i
$711$	1.25449	+	0.661858i	0.0470471	+	0.0248216i
$712$		−	15.4456i		−	0.578849i
$713$	−12.0563	+	3.23048i	−0.451513	+	0.120983i
$714$	16.5296	−	6.07457i	0.618604	−	0.227335i
$715$	9.53624	+	45.1400i	0.356635	+	1.68814i
$716$	−5.76195	+	3.32667i	−0.215334	+	0.124323i
$717$	−30.8629	−	17.0427i	−1.15260	−	0.636473i
$718$	−3.87030	−	6.70355i	−0.144438	−	0.250174i
$719$	−17.1293	+	29.6689i	−0.638816	+	1.10646i	0.346877	+	0.937911i	$0.387242\pi$
$719$	−17.1293	+	29.6689i	−0.638816	+	1.10646i	−0.985693	+	0.168552i	$0.946091\pi$
$720$	9.12765	−	2.82274i	0.340168	−	0.105197i
$721$	7.31167	−	37.9193i	0.272301	−	1.41219i
$722$	−8.04044	+	30.0073i	−0.299234	+	1.11676i
$723$	2.81777	+	1.55600i	0.104794	+	0.0578682i
$724$	20.6106			0.765989
$725$	−7.03716	−	12.1887i	−0.261353	−	0.452677i
$726$	4.60071	+	7.62905i	0.170748	+	0.283140i
$727$			24.9097i			0.923850i	0.886919	+	0.461925i	$0.152841\pi$
$727$			24.9097i			0.923850i	−0.886919	+	0.461925i	$0.847159\pi$
$728$	6.62483	−	6.86379i	0.245532	−	0.254389i
$729$	3.08124	+	26.8236i	0.114120	+	0.993467i
$730$	−9.78490	−	9.78490i	−0.362155	−	0.362155i
$731$	25.2782	−	14.5944i	0.934947	−	0.539792i
$732$	−2.34759	+	9.48059i	−0.0867694	+	0.350413i
$733$	−10.8257	+	40.4020i	−0.399856	+	1.49228i	0.413494	+	0.910507i	$0.364308\pi$
$733$	−10.8257	+	40.4020i	−0.399856	+	1.49228i	−0.813350	+	0.581775i	$0.802358\pi$
$734$	−14.0641	−	3.76846i	−0.519115	−	0.139096i
$735$	38.1090	−	6.21621i	1.40567	−	0.229288i
$736$	4.04222	−	4.04222i	0.148998	−	0.148998i
$737$	31.2568	+	18.0461i	1.15136	+	0.664738i
$738$	12.7101	−	0.484781i	0.467864	−	0.0178450i
$739$	−6.39772	−	1.71426i	−0.235344	−	0.0630602i	0.139219	−	0.990262i	$-0.455541\pi$
$739$	−6.39772	−	1.71426i	−0.235344	−	0.0630602i	−0.374563	+	0.927201i	$0.622207\pi$
$740$	13.9820	+	24.2176i	0.513989	+	0.890256i
$741$	42.2618	+	12.9038i	1.55253	+	0.474032i
$742$	5.86875	−	12.0787i	0.215448	−	0.443424i
$743$	−11.4893	−	42.8788i	−0.421503	−	1.57307i	−0.771444	−	0.636298i	$-0.780465\pi$
$743$	−11.4893	−	42.8788i	−0.421503	−	1.57307i	0.349941	−	0.936772i	$-0.386202\pi$
$744$	0.908995	−	3.67092i	0.0333254	−	0.134583i
$745$		−	21.3928i		−	0.783773i
$746$	−1.49249	−	5.57005i	−0.0546440	−	0.203934i
$747$	2.09572	−	9.21264i	0.0766783	−	0.337073i
$748$	−14.9143	−	3.99628i	−0.545322	−	0.146119i
$749$	−12.7670	−	11.0646i	−0.466497	−	0.404291i
$750$	−0.217777	−	0.754896i	−0.00795211	−	0.0275649i
$751$		−	35.9644i		−	1.31236i	−0.754604	−	0.656180i	$-0.772171\pi$
$751$		−	35.9644i		−	1.31236i	0.754604	−	0.656180i	$-0.227829\pi$
$752$	−0.212620	+	0.793509i	−0.00775346	+	0.0289363i
$753$	−2.22513	+	2.31162i	−0.0810882	+	0.0842400i
$754$	5.38478	−	8.26934i	0.196102	−	0.301152i
$755$		−	5.17774i		−	0.188437i
$756$	1.76173	+	13.6344i	0.0640734	+	0.495878i
$757$	−16.2869	+	28.2098i	−0.591959	+	1.02530i	0.402010	+	0.915635i	$0.368312\pi$
$757$	−16.2869	+	28.2098i	−0.591959	+	1.02530i	−0.993968	+	0.109667i	$0.965022\pi$
$758$	−7.89287	+	13.6709i	−0.286682	+	0.496548i
$759$	−39.7755	+	0.758273i	−1.44376	+	0.0275236i
$760$	15.9341	+	15.9341i	0.577990	+	0.577990i
$761$	−14.6687	+	3.93046i	−0.531739	+	0.142479i	−0.514691	−	0.857376i	$-0.672093\pi$
$761$	−14.6687	+	3.93046i	−0.531739	+	0.142479i	−0.0170478	+	0.999855i	$0.505427\pi$
$762$	−7.64714	−	12.6807i	−0.277027	−	0.459375i
$763$	−12.3952	+	25.5111i	−0.448736	+	0.923565i
$764$	−10.1062	+	17.5045i	−0.365630	+	0.633289i
$765$	35.0767	−	10.8475i	1.26820	−	0.392193i
$766$	−9.62619	−	5.55768i	−0.347808	−	0.200807i
$767$	−49.3480	−	2.64765i	−1.78185	−	0.0956011i
$768$	0.480095	+	1.66418i	0.0173239	+	0.0600511i
$769$	34.5536	−	9.25861i	1.24604	−	0.333874i	0.425232	−	0.905085i	$-0.360193\pi$
$769$	34.5536	−	9.25861i	1.24604	−	0.333874i	0.820804	+	0.571211i	$0.193526\pi$
$770$	−30.4507	−	14.7952i	−1.09737	−	0.533183i
$771$	8.81431	+	30.5536i	0.317440	+	1.10036i
$772$	−2.08269	+	7.77269i	−0.0749575	+	0.279745i
$773$	18.6416	−	18.6416i	0.670491	−	0.670491i	−0.287338	−	0.957829i	$-0.592770\pi$
$773$	18.6416	−	18.6416i	0.670491	−	0.670491i	0.957829	+	0.287338i	$0.0927703\pi$
$774$	6.73216	+	21.7692i	0.241982	+	0.782479i
$775$	−10.8455	−	2.90604i	−0.389582	−	0.104388i
$776$	3.52149	−	2.03313i	0.126414	−	0.0729852i
$777$	−37.7686	+	13.8798i	−1.35494	+	0.497936i
$778$	6.72461	+	25.0966i	0.241089	+	0.899757i
$779$	14.9997	+	25.9803i	0.537421	+	0.930840i
$780$	14.5406	−	13.5693i	0.520637	−	0.485859i
$781$	−22.8977	+	39.6599i	−0.819343	+	1.41914i
$782$	15.5339	−	15.5339i	0.555490	−	0.555490i
$783$	4.45984	+	13.5039i	0.159382	+	0.482591i
$784$	0.995036	+	6.92892i	0.0355370	+	0.247461i
$785$	2.38447	−	2.38447i	0.0851054	−	0.0851054i
$786$	−15.6517	+	0.298381i	−0.558278	+	0.0106429i
$787$	−22.6376	+	22.6376i	−0.806945	+	0.806945i	−0.984170	−	0.177226i	$-0.943288\pi$
$787$	−22.6376	+	22.6376i	−0.806945	+	0.806945i	0.177226	+	0.984170i	$0.443288\pi$
$788$	−20.3970	+	5.46537i	−0.726614	+	0.194696i
$789$	21.7905	+	20.9752i	0.775761	+	0.746736i
$790$	1.30399	+	0.752858i	0.0463938	+	0.0267855i
$791$	−0.446293	+	2.31454i	−0.0158684	+	0.0822956i
$792$	5.62462	−	10.6609i	0.199862	−	0.378820i
$793$	4.20246	+	19.8924i	0.149234	+	0.706400i
$794$	12.6643	+	7.31174i	0.449439	+	0.259484i
$795$	13.5343	−	24.5094i	0.480011	−	0.869258i
$796$	−14.7137			−0.521513
$797$	4.76025	+	8.24500i	0.168617	+	0.292053i	0.937934	−	0.346814i	$-0.112737\pi$
$797$	4.76025	+	8.24500i	0.168617	+	0.292053i	−0.769317	+	0.638867i	$0.779403\pi$
$798$	−26.5031	+	18.6808i	−0.938198	+	0.661292i
$799$	−0.817080	+	3.04938i	−0.0289062	+	0.107879i
$800$	4.96721	−	1.33096i	0.175617	−	0.0470565i
$801$	45.1825	+	10.2783i	1.59645	+	0.363164i
$802$	−2.99855			−0.105883
$803$	−17.4582			−0.616087
$804$	−0.296556	−	15.5559i	−0.0104587	−	0.548616i
$805$	39.8922	−	26.9949i	1.40602	−	0.951446i
$806$	−1.62721	−	7.70242i	−0.0573160	−	0.271306i
$807$	−7.89278	+	2.27696i	−0.277839	+	0.0801529i
$808$	−1.82734	+	6.81972i	−0.0642855	+	0.239917i
$809$	−43.9742	+	25.3885i	−1.54605	+	0.892614i	−0.547615	+	0.836731i	$0.684464\pi$
$809$	−43.9742	+	25.3885i	−1.54605	+	0.892614i	−0.998437	+	0.0558829i	$0.982203\pi$
$810$	2.18328	+	28.5792i	0.0767127	+	1.00417i
$811$	14.8857	+	14.8857i	0.522708	+	0.522708i	0.918388	−	0.395680i	$-0.129491\pi$
$811$	14.8857	+	14.8857i	0.522708	+	0.522708i	−0.395680	+	0.918388i	$0.629491\pi$
$812$	2.36777	+	6.84309i	0.0830925	+	0.240145i
$813$	−11.9362	−	6.59125i	−0.418620	−	0.231165i
$814$	34.0779	+	9.13114i	1.19443	+	0.320046i
$815$			13.5298i			0.473928i
$816$	1.84496	+	6.39531i	0.0645866	+	0.223881i
$817$	−38.0024	+	38.0024i	−1.32953	+	1.32953i
$818$	15.4116			0.538853
$819$	15.6699	+	23.9469i	0.547552	+	0.836772i
$820$	13.5025			0.471527
$821$	−5.23137	+	5.23137i	−0.182576	+	0.182576i	−0.792477	−	0.609901i	$-0.791209\pi$
$821$	−5.23137	+	5.23137i	−0.182576	+	0.182576i	0.609901	+	0.792477i	$0.291209\pi$
$822$	4.67027	+	16.1889i	0.162894	+	0.564652i
$823$			8.09325i			0.282113i	0.990002	+	0.141056i	$0.0450499\pi$
$823$			8.09325i			0.282113i	−0.990002	+	0.141056i	$0.954950\pi$
$824$	14.0988	+	3.77777i	0.491155	+	0.131605i
$825$	−31.3282	−	17.2997i	−1.09071	−	0.602297i
$826$	23.7499	−	27.4042i	0.826365	−	0.953514i
$827$	18.6269	+	18.6269i	0.647721	+	0.647721i	0.952442	−	0.304721i	$-0.0985631\pi$
$827$	18.6269	+	18.6269i	0.647721	+	0.647721i	−0.304721	+	0.952442i	$0.598563\pi$
$828$	9.13467	+	14.5144i	0.317452	+	0.504412i
$829$	42.1225	−	24.3194i	1.46298	−	0.844649i	0.463828	−	0.885925i	$-0.346476\pi$
$829$	42.1225	−	24.3194i	1.46298	−	0.844649i	0.999148	+	0.0412762i	$0.0131424\pi$
$830$	2.59589	−	9.68799i	0.0901046	−	0.336275i
$831$	6.68429	−	1.92833i	0.231876	−	0.0668930i
$832$	2.40926	+	2.68244i	0.0835259	+	0.0929969i
$833$	3.82383	+	26.6272i	0.132488	+	0.922578i
$834$	−0.564777	−	29.6256i	−0.0195566	−	1.02585i
$835$	57.3835			1.98584
$836$	28.4296			0.983258
$837$	10.1335	+	5.10186i	0.350266	+	0.176346i
$838$	19.6889	−	5.27563i	0.680142	−	0.182244i
$839$	−6.78037	+	25.3047i	−0.234084	+	0.873614i	0.744475	+	0.667650i	$0.232700\pi$
$839$	−6.78037	+	25.3047i	−0.234084	+	0.873614i	−0.978560	+	0.205964i	$0.933967\pi$
$840$	1.31719	+	14.5347i	0.0454473	+	0.501493i
$841$	−10.7547	−	18.6277i	−0.370852	−	0.642334i
$842$	36.8892			1.27129
$843$	−8.15042	+	14.7597i	−0.280715	+	0.508350i
$844$	−15.9763	−	9.22393i	−0.549928	−	0.317501i
$845$	14.9328	−	38.6145i	0.513705	−	1.32838i
$846$	−2.17974	−	1.15001i	−0.0749409	−	0.0395381i
$847$	−12.8605	+	4.44985i	−0.441892	+	0.152899i
$848$	4.39567	+	2.53784i	0.150948	+	0.0871499i
$849$	−30.2287	−	29.0977i	−1.03745	−	0.998631i
$850$	19.0885	−	5.11476i	0.654731	−	0.175435i
$851$	−35.4935	+	35.4935i	−1.21670	+	1.21670i
$852$	19.7380	−	0.376282i	0.676213	−	0.0128912i
$853$	−6.71790	+	6.71790i	−0.230016	+	0.230016i	−0.812700	−	0.582683i	$-0.802003\pi$
$853$	−6.71790	+	6.71790i	−0.230016	+	0.230016i	0.582683	+	0.812700i	$0.302003\pi$
$854$	−13.4191	−	6.52000i	−0.459193	−	0.223110i
$855$	−57.2147	+	36.0081i	−1.95670	+	1.23145i
$856$	4.51522	−	4.51522i	0.154327	−	0.154327i
$857$	16.0255	−	27.7569i	0.547419	−	0.948158i	−0.451031	−	0.892508i	$-0.648944\pi$
$857$	16.0255	−	27.7569i	0.547419	−	0.948158i	0.998450	−	0.0556499i	$-0.0177231\pi$
$858$	0.866492	−	25.0768i	0.0295815	−	0.856109i
$859$	12.8306	+	22.2232i	0.437774	+	0.758247i	0.997517	−	0.0704193i	$-0.0224337\pi$
$859$	12.8306	+	22.2232i	0.437774	+	0.758247i	−0.559744	+	0.828666i	$0.689100\pi$
$860$	6.26069	+	23.3652i	0.213488	+	0.796747i
$861$	−3.31429	+	19.1443i	−0.112951	+	0.652436i
$862$	25.9310	−	14.9713i	0.883214	−	0.509924i
$863$	4.52440	+	1.21231i	0.154012	+	0.0412675i	0.335001	−	0.942218i	$-0.391263\pi$
$863$	4.52440	+	1.21231i	0.154012	+	0.0412675i	−0.180989	+	0.983485i	$0.557930\pi$
$864$	−5.18766	+	0.296978i	−0.176488	+	0.0101034i
$865$	27.1197	−	27.1197i	0.922098	−	0.922098i
$866$	8.11591	−	30.2890i	0.275790	−	1.02926i
$867$	−1.07160	−	3.71454i	−0.0363933	−	0.126152i
$868$	5.19593	+	2.52457i	0.176361	+	0.0856895i
$869$	1.83491	−	0.491663i	0.0622451	−	0.0166785i
$870$	4.18463	+	14.5054i	0.141872	+	0.491781i
$871$	−14.6681	−	28.8763i	−0.497009	−	0.978436i
$872$	−9.28396	−	5.36010i	−0.314395	−	0.181516i
$873$	3.60408	+	11.6542i	0.121980	+	0.394436i
$874$	−20.2244	+	35.0297i	−0.684100	+	1.18490i
$875$	1.19710	−	0.0855167i	0.0404693	−	0.00289099i
$876$	3.88652	+	6.44475i	0.131313	+	0.217748i
$877$	21.9186	−	5.87308i	0.740139	−	0.198320i	0.130999	−	0.991382i	$-0.458181\pi$
$877$	21.9186	−	5.87308i	0.740139	−	0.198320i	0.609140	+	0.793063i	$0.291515\pi$
$878$	−1.83396	−	1.83396i	−0.0618931	−	0.0618931i
$879$	−45.4102	+	0.865691i	−1.53165	+	0.0291990i
$880$	6.39795	−	11.0816i	0.215675	−	0.373560i
$881$	25.3493	−	43.9063i	0.854039	−	1.47924i	−0.0234939	−	0.999724i	$-0.507479\pi$
$881$	25.3493	−	43.9063i	0.854039	−	1.47924i	0.877533	−	0.479516i	$-0.159188\pi$
$882$	−20.9311	−	1.70009i	−0.704786	−	0.0572449i
$883$		−	24.3319i		−	0.818833i	−0.912348	−	0.409417i	$-0.865732\pi$
$883$		−	24.3319i		−	0.818833i	0.912348	−	0.409417i	$-0.134268\pi$
$884$	9.25855	+	10.3084i	0.311399	+	0.346708i
$885$	52.4325	−	54.4705i	1.76250	−	1.83101i
$886$	−5.54946	+	20.7109i	−0.186438	+	0.695795i
$887$		−	2.99906i		−	0.100699i	−0.998732	−	0.0503493i	$-0.983967\pi$
$887$		−	2.99906i		−	0.100699i	0.998732	−	0.0503493i	$-0.0160334\pi$
$888$	−4.21557	−	14.6127i	−0.141465	−	0.490370i
$889$	21.3763	−	7.39640i	0.716939	−	0.248067i
$890$	47.5139	+	12.7313i	1.59267	+	0.426754i
$891$	27.4432	+	23.5478i	0.919382	+	0.788881i
$892$	−5.02021	−	18.7357i	−0.168089	−	0.627318i
$893$		−	5.81272i		−	0.194515i
$894$	−2.79655	+	11.2937i	−0.0935306	+	0.377717i
$895$	−5.48411	−	20.4670i	−0.183314	−	0.684136i
$896$	−2.63903	+	0.188523i	−0.0881637	+	0.00629812i
$897$	30.2822	+	18.9070i	1.01109	+	0.631285i
$898$	−13.3853	−	23.1840i	−0.446672	−	0.773659i
$899$	5.77217	+	1.54665i	0.192513	+	0.0515836i
$900$	0.587993	+	15.4161i	0.0195998	+	0.513870i
$901$	16.8922	+	9.75270i	0.562760	+	0.324909i
$902$	12.0456	−	12.0456i	0.401073	−	0.401073i
$903$	−34.6648	+	3.14146i	−1.15357	+	0.104541i
$904$	−0.860571	−	0.230589i	−0.0286222	−	0.00766929i
$905$	−16.9887	+	63.4025i	−0.564722	+	2.10757i
$906$	−0.676853	+	2.73343i	−0.0224869	+	0.0908120i
$907$	2.54569	−	1.46975i	0.0845281	−	0.0488023i	−0.457140	−	0.889395i	$-0.651126\pi$
$907$	2.54569	−	1.46975i	0.0845281	−	0.0488023i	0.541668	+	0.840592i	$0.317793\pi$
$908$	4.34998	+	4.34998i	0.144359	+	0.144359i
$909$	−18.7335	−	9.88361i	−0.621350	−	0.327819i
$910$	15.6538	+	26.0369i	0.518918	+	0.863115i
$911$			3.73575i			0.123771i	0.998083	+	0.0618855i	$0.0197114\pi$
$911$			3.73575i			0.123771i	−0.998083	+	0.0618855i	$0.980289\pi$
$912$	−6.32894	−	10.4949i	−0.209572	−	0.347520i
$913$	−6.32686	−	10.9585i	−0.209389	−	0.362672i
$914$	3.00675			0.0994545
$915$	−27.2292	−	15.0362i	−0.900169	−	0.497081i
$916$	−5.23182	+	19.5254i	−0.172864	+	0.645138i
$917$	4.52749	−	23.4802i	0.149511	−	0.775385i
$918$	−19.9357	+	1.14126i	−0.657976	+	0.0376671i
$919$	4.90314	−	8.49249i	0.161740	−	0.280142i	−0.773753	−	0.633487i	$-0.781623\pi$
$919$	4.90314	−	8.49249i	0.161740	−	0.280142i	0.935493	+	0.353346i	$0.114956\pi$
$920$	9.10281	+	15.7665i	0.300111	+	0.519807i
$921$	1.40158	+	0.773962i	0.0461835	+	0.0255029i
$922$	9.83928	−	5.68071i	0.324039	−	0.187084i
$923$	36.6394	−	18.6115i	1.20600	−	0.612603i
$924$	14.1414	+	11.7913i	0.465219	+	0.387905i
$925$	−43.6156	+	11.6868i	−1.43407	+	0.384258i
$926$			41.7748i			1.37281i
$927$	−20.4330	+	38.7289i	−0.671107	+	1.27202i
$928$	−2.64364	+	0.708361i	−0.0867817	+	0.0232531i
$929$	−14.0570	−	52.4613i	−0.461194	−	1.72120i	−0.669209	−	0.743074i	$-0.733367\pi$
$929$	−14.0570	−	52.4613i	−0.461194	−	1.72120i	0.208015	−	0.978126i	$-0.433300\pi$
$930$	10.5432	+	5.82207i	0.345727	+	0.190913i
$931$	−19.4898	−	45.5343i	−0.638754	−	1.49233i
$932$	19.1081	−	11.0321i	0.625907	−	0.361368i
$933$	−48.5879	−	12.0314i	−1.59070	−	0.393889i
$934$	1.63683	+	0.438587i	0.0535587	+	0.0143510i
$935$	24.5867	−	42.5855i	0.804072	−	1.39269i
$936$	−9.45008	+	5.26269i	−0.308886	+	0.172016i
$937$	1.62142			0.0529693			0.0264847	−	0.999649i	$-0.491569\pi$
$937$	1.62142			0.0529693			0.0264847	+	0.999649i	$0.491569\pi$
$938$	23.3366	+	4.49979i	0.761965	+	0.146923i
$939$	−7.08955	+	7.36512i	−0.231359	+	0.240351i
$940$	−2.26574	−	1.30813i	−0.0739003	−	0.0426664i
$941$	9.30450	+	34.7249i	0.303318	+	1.13200i	0.934383	+	0.356269i	$0.115951\pi$
$941$	9.30450	+	34.7249i	0.303318	+	1.13200i	−0.631065	+	0.775730i	$0.717382\pi$
$942$	−1.57051	+	0.947100i	−0.0511701	+	0.0308582i
$943$	6.27297	+	23.4110i	0.204276	+	0.762368i
$944$	9.69186	+	9.69186i	0.315443	+	0.315443i
$945$	−43.3942	−	5.81893i	−1.41161	−	0.189290i
$946$	26.4293	+	15.2589i	0.859290	+	0.496111i
$947$	−11.7923	−	11.7923i	−0.383198	−	0.383198i	0.489055	−	0.872253i	$-0.337342\pi$
$947$	−11.7923	−	11.7923i	−0.383198	−	0.383198i	−0.872253	+	0.489055i	$0.837342\pi$
$948$	−0.589984	−	0.567910i	−0.0191618	−	0.0184449i
$949$	13.1284	+	8.54889i	0.426167	+	0.277509i
$950$	−31.5116	+	18.1932i	−1.02237	+	0.590266i
$951$	0.634117	+	33.2628i	0.0205626	+	1.07862i
$952$	−10.1415	+	0.724478i	−0.328689	+	0.0234805i
$953$	−0.652511	−	1.13018i	−0.0211369	−	0.0366102i	0.855263	−	0.518193i	$-0.173395\pi$
$953$	−0.652511	−	1.13018i	−0.0211369	−	0.0366102i	−0.876400	+	0.481583i	$0.840062\pi$
$954$	−10.3490	+	11.1697i	−0.335060	+	0.361633i
$955$	−45.5171	−	45.5171i	−1.47290	−	1.47290i
$956$	14.3931	+	14.3931i	0.465507	+	0.465507i
$957$	16.6734	+	9.20720i	0.538975	+	0.297627i
$958$	13.2376	+	22.9282i	0.427688	+	0.740777i
$959$	−25.6719	+	1.83392i	−0.828990	+	0.0592203i
$960$	−5.51509	+	0.105139i	−0.177999	+	0.00339334i
$961$	−22.7182	+	13.1163i	−0.732844	+	0.423108i
$962$	−21.1550	−	23.5537i	−0.682063	−	0.759401i
$963$	10.2036	+	16.2129i	0.328806	+	0.522453i
$964$	−1.31409	−	1.31409i	−0.0423240	−	0.0423240i
$965$	−22.1937	−	12.8135i	−0.714440	−	0.412482i
$966$	−24.5887	+	9.03628i	−0.791129	+	0.290738i
$967$	−37.9506	−	37.9506i	−1.22041	−	1.22041i	−0.967486	−	0.252923i	$-0.918608\pi$
$967$	−37.9506	−	37.9506i	−1.22041	−	1.22041i	−0.252923	−	0.967486i	$-0.581392\pi$
$968$	−1.33125	−	4.96830i	−0.0427881	−	0.159687i
$969$	−24.3216	−	40.3308i	−0.781321	−	1.29561i
$970$	3.35168	+	12.5086i	0.107616	+	0.401628i
$971$	7.52464	+	4.34435i	0.241477	+	0.139417i	0.615855	−	0.787859i	$-0.288811\pi$
$971$	7.52464	+	4.34435i	0.241477	+	0.139417i	−0.374378	+	0.927276i	$0.622144\pi$
$972$	2.58338	−	15.3729i	0.0828619	−	0.493086i
$973$	44.4434	+	8.56965i	1.42479	+	0.274731i
$974$	−24.9837			−0.800531
$975$	15.0872	+	28.3499i	0.483178	+	0.907923i
$976$	2.81947	−	4.88346i	0.0902490	−	0.156316i
$977$	33.6764	+	9.02357i	1.07740	+	0.288690i	0.753532	−	0.657411i	$-0.228349\pi$
$977$	33.6764	+	9.02357i	1.07740	+	0.288690i	0.323872	+	0.946101i	$0.395015\pi$
$978$	1.76866	−	7.14263i	0.0565556	−	0.228396i
$979$	53.7447	−	31.0295i	1.71769	−	0.991708i
$980$	−22.1349	−	2.65034i	−0.707074	−	0.0846620i
$981$	21.8577	−	23.5912i	0.697863	−	0.753209i
$982$	−0.219769	−	0.820188i	−0.00701310	−	0.0261733i
$983$	16.1750	−	4.33408i	0.515903	−	0.138236i	0.00853213	−	0.999964i	$-0.497284\pi$
$983$	16.1750	−	4.33408i	0.515903	−	0.138236i	0.507371	+	0.861728i	$0.330617\pi$
$984$	−7.12821	−	1.76509i	−0.227239	−	0.0562690i
$985$		−	67.2503i		−	2.14277i
$986$	−10.1593	+	2.72217i	−0.323537	+	0.0866915i
$987$	2.41085	−	2.89136i	0.0767382	−	0.0920330i
$988$	−21.3788	−	13.9213i	−0.680150	−	0.442896i
$989$	−37.6028	+	21.7100i	−1.19570	+	0.690337i
$990$	28.1590	+	26.0899i	0.894953	+	0.829192i
$991$	17.7497	+	30.7433i	0.563837	+	0.976594i	0.997157	+	0.0753540i	$0.0240087\pi$
$991$	17.7497	+	30.7433i	0.563837	+	0.976594i	−0.433320	+	0.901240i	$0.642658\pi$
$992$	−1.09171	+	1.89090i	−0.0346618	+	0.0600360i
$993$	−28.5443	−	47.3331i	−0.905827	−	1.50207i
$994$	−5.70951	+	29.6103i	−0.181095	+	0.939183i
$995$	12.1280	−	45.2623i	0.384483	−	1.43491i
$996$	−2.63687	+	4.77513i	−0.0835523	+	0.151306i
$997$	−13.7853			−0.436586			−0.218293	−	0.975883i	$-0.570049\pi$
$997$	−13.7853			−0.436586			−0.218293	+	0.975883i	$0.570049\pi$
$998$	−17.1092	−	29.6341i	−0.541584	−	0.938050i
$999$	45.5513	−	2.60767i	1.44118	−	0.0825030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.137.12	yes	152
3.2	odd	2	inner	546.2.ch.a.137.35	yes	152
7.2	even	3		546.2.bw.a.527.22	yes	152
13.2	odd	12		546.2.bw.a.431.3	✓	152
21.2	odd	6		546.2.bw.a.527.3	yes	152
39.2	even	12		546.2.bw.a.431.22	yes	152
91.2	odd	12	inner	546.2.ch.a.275.35	yes	152
273.2	even	12	inner	546.2.ch.a.275.12	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.3	✓	152	13.2	odd	12
546.2.bw.a.431.22	yes	152	39.2	even	12
546.2.bw.a.527.3	yes	152	21.2	odd	6
546.2.bw.a.527.22	yes	152	7.2	even	3
546.2.ch.a.137.12	yes	152	1.1	even	1	trivial
546.2.ch.a.137.35	yes	152	3.2	odd	2	inner
546.2.ch.a.275.12	yes	152	273.2	even	12	inner
546.2.ch.a.275.35	yes	152	91.2	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.480095 + 1.66418i) q^{3} -1.00000i q^{4} +(3.07620 + 0.824266i) q^{5} +(-1.51623 - 0.837278i) q^{6} +(1.73277 - 1.99938i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.53902 + 1.59793i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.480095 + 1.66418i) q^{3} -1.00000i q^{4} +(3.07620 + 0.824266i) q^{5} +(-1.51623 - 0.837278i) q^{6} +(1.73277 - 1.99938i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.53902 + 1.59793i) q^{9} +(-2.75805 + 1.59236i) q^{10} +(-1.03991 + 3.88100i) q^{11} +(1.66418 - 0.480095i) q^{12} +(2.68244 - 2.40926i) q^{13} +(0.188523 + 2.63903i) q^{14} +(0.105139 + 5.51509i) q^{15} -1.00000 q^{16} -3.84291 q^{17} +(0.665448 - 2.92527i) q^{18} +(6.83462 - 1.83133i) q^{19} +(0.824266 - 3.07620i) q^{20} +(4.15923 + 1.92375i) q^{21} +(-2.00895 - 3.47961i) q^{22} +5.71656 q^{23} +(-0.837278 + 1.51623i) q^{24} +(4.45348 + 2.57122i) q^{25} +(-0.193169 + 3.60037i) q^{26} +(-3.87822 - 3.45823i) q^{27} +(-1.99938 - 1.73277i) q^{28} +(-2.37022 - 1.36845i) q^{29} +(-3.97410 - 3.82542i) q^{30} +(-2.10902 + 0.565110i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.95795 + 0.132645i) q^{33} +(2.71735 - 2.71735i) q^{34} +(6.97836 - 4.72223i) q^{35} +(1.59793 + 2.53902i) q^{36} +(-6.20889 + 6.20889i) q^{37} +(-3.53786 + 6.12776i) q^{38} +(5.29727 + 3.30740i) q^{39} +(1.59236 + 2.75805i) q^{40} +(1.09733 + 4.09530i) q^{41} +(-4.30132 + 1.58072i) q^{42} +(-6.57787 + 3.79774i) q^{43} +(3.88100 + 1.03991i) q^{44} +(-9.12765 + 2.82274i) q^{45} +(-4.04222 + 4.04222i) q^{46} +(0.212620 - 0.793509i) q^{47} +(-0.480095 - 1.66418i) q^{48} +(-0.995036 - 6.92892i) q^{49} +(-4.96721 + 1.33096i) q^{50} +(-1.84496 - 6.39531i) q^{51} +(-2.40926 - 2.68244i) q^{52} +(-4.39567 - 2.53784i) q^{53} +(5.18766 - 0.296978i) q^{54} +(-6.39795 + 11.0816i) q^{55} +(2.63903 - 0.188523i) q^{56} +(6.32894 + 10.4949i) q^{57} +(2.64364 - 0.708361i) q^{58} +(-9.69186 - 9.69186i) q^{59} +(5.51509 - 0.105139i) q^{60} +(-2.81947 + 4.88346i) q^{61} +(1.09171 - 1.89090i) q^{62} +(-1.20465 + 7.84531i) q^{63} +1.00000i q^{64} +(10.2376 - 5.20032i) q^{65} +(4.82622 - 5.01381i) q^{66} +(2.32494 - 8.67678i) q^{67} +3.84291i q^{68} +(2.74449 + 9.51340i) q^{69} +(-1.59532 + 8.27357i) q^{70} +(11.0094 + 2.94997i) q^{71} +(-2.92527 - 0.665448i) q^{72} +(1.12460 + 4.19705i) q^{73} -8.78070i q^{74} +(-2.14089 + 8.64584i) q^{75} +(-1.83133 - 6.83462i) q^{76} +(5.95767 + 8.80404i) q^{77} +(-6.08442 + 1.40705i) q^{78} +(-0.236397 - 0.409451i) q^{79} +(-3.07620 - 0.824266i) q^{80} +(3.89322 - 8.11436i) q^{81} +(-3.67175 - 2.11988i) q^{82} +(-2.22692 + 2.22692i) q^{83} +(1.92375 - 4.15923i) q^{84} +(-11.8216 - 3.16758i) q^{85} +(1.96585 - 7.33666i) q^{86} +(1.13942 - 4.60147i) q^{87} +(-3.47961 + 2.00895i) q^{88} +(-10.9217 - 10.9217i) q^{89} +(4.45825 - 8.45020i) q^{90} +(-0.168975 - 9.53790i) q^{91} -5.71656i q^{92} +(-1.95298 - 3.23849i) q^{93} +(0.410751 + 0.711441i) q^{94} +22.5342 q^{95} +(1.51623 + 0.837278i) q^{96} +(1.05243 - 3.92771i) q^{97} +(5.60308 + 4.19589i) q^{98} +(-3.56122 - 11.5156i) 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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