LMFDB - Embedded newform 546.2.bw.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (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			11.8
Character	$\chi$	$=$	546.11
Dual form			546.2.bw.a.149.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.328251 + 1.70066i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.75073 + 0.469106i) q^{5} +(1.72767 - 0.123098i) q^{6} +(1.22850 + 2.34324i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.78450 - 1.11649i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.328251 + 1.70066i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.75073 + 0.469106i) q^{5} +(1.72767 - 0.123098i) q^{6} +(1.22850 + 2.34324i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.78450 - 1.11649i) q^{9} -1.81249i q^{10} +(0.638169 + 0.638169i) q^{11} +(-0.566057 - 1.63694i) q^{12} +(-0.922476 + 3.48555i) q^{13} +(1.94544 - 1.79311i) q^{14} +(-1.37247 + 2.82341i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.29314 - 5.70389i) q^{17} +(-0.357762 + 2.97859i) q^{18} +(4.64094 + 4.64094i) q^{19} +(-1.75073 + 0.469106i) q^{20} +(-4.38832 + 1.32009i) q^{21} +(0.451253 - 0.781594i) q^{22} +(-0.687903 + 1.19148i) q^{23} +(-1.43466 + 0.970441i) q^{24} +(-1.48514 - 0.857446i) q^{25} +(3.60553 - 0.0110823i) q^{26} +(2.81278 - 4.36901i) q^{27} +(-2.23553 - 1.41506i) q^{28} +(-5.47519 + 3.16110i) q^{29} +(3.08243 + 0.594950i) q^{30} +(-4.57998 + 1.22720i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.29479 + 0.875830i) q^{33} +(-4.65721 + 4.65721i) q^{34} +(1.05154 + 4.67868i) q^{35} +(2.96969 - 0.425345i) q^{36} +(2.57030 + 9.59250i) q^{37} +(3.28164 - 5.68397i) q^{38} +(-5.62493 - 2.71295i) q^{39} +(0.906243 + 1.56966i) q^{40} +(12.1581 + 3.25776i) q^{41} +(2.41089 + 3.89713i) q^{42} +(3.99588 + 2.30702i) q^{43} +(-0.871755 - 0.233586i) q^{44} +(-4.35116 - 3.26089i) q^{45} +(1.32893 + 0.356085i) q^{46} +(0.961209 - 3.58728i) q^{47} +(1.30869 + 1.13460i) q^{48} +(-3.98158 + 5.75734i) q^{49} +(-0.443847 + 1.65646i) q^{50} +(10.7814 - 3.72822i) q^{51} +(-0.943886 - 3.47981i) q^{52} +(4.00068 + 2.30979i) q^{53} +(-4.94814 - 1.58616i) q^{54} +(0.817891 + 1.41663i) q^{55} +(-0.788244 + 2.52560i) q^{56} +(-9.41607 + 6.36928i) q^{57} +(4.47047 + 4.47047i) q^{58} +(1.38793 - 5.17983i) q^{59} +(-0.223113 - 3.13138i) q^{60} +0.318472 q^{61} +(2.37077 + 4.10630i) q^{62} +(-0.804555 - 7.89637i) q^{63} +1.00000i q^{64} +(-3.25010 + 5.66950i) q^{65} +(1.18110 + 1.02399i) q^{66} +(-1.10352 - 1.10352i) q^{67} +(5.70389 + 3.29314i) q^{68} +(-1.80050 - 1.56099i) q^{69} +(4.24710 - 2.22664i) q^{70} +(-0.215183 - 0.803072i) q^{71} +(-1.17946 - 2.75842i) q^{72} +(-2.57872 - 9.62392i) q^{73} +(8.60040 - 4.96544i) q^{74} +(1.94572 - 2.24426i) q^{75} +(-6.33965 - 1.69870i) q^{76} +(-0.711396 + 2.27937i) q^{77} +(-1.16467 + 6.13543i) q^{78} +(-3.91647 - 6.78352i) q^{79} +(1.28162 - 1.28162i) q^{80} +(6.50691 + 6.21772i) q^{81} -12.5870i q^{82} +(7.59633 - 7.59633i) q^{83} +(3.14035 - 3.33739i) q^{84} +(-3.08967 - 11.5308i) q^{85} +(1.19420 - 4.45683i) q^{86} +(-3.57873 - 10.3491i) q^{87} +0.902507i q^{88} +(-12.6683 + 3.39445i) q^{89} +(-2.02362 + 5.04687i) q^{90} +(-9.30075 + 2.12040i) q^{91} -1.37581i q^{92} +(-0.583674 - 8.19183i) q^{93} -3.71383 q^{94} +(5.94793 + 10.3021i) q^{95} +(0.757230 - 1.55776i) q^{96} +(8.51978 - 2.28287i) q^{97} +(6.59168 + 2.35580i) q^{98} +(-1.06448 - 2.48949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−0.328251	+	1.70066i	−0.189516	+	0.981878i
$3$	−0.328251	+	1.70066i	−0.189516	+	0.981878i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.75073	+	0.469106i	0.782949	+	0.209791i	0.628085	−	0.778145i	$-0.283839\pi$
$5$	1.75073	+	0.469106i	0.782949	+	0.209791i	0.154865	+	0.987936i	$0.450506\pi$
$6$	1.72767	−	0.123098i	0.705319	−	0.0502545i
$7$	1.22850	+	2.34324i	0.464329	+	0.885663i
$7$	1.22850	+	2.34324i	0.464329	+	0.885663i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.78450	−	1.11649i	−0.928168	−	0.372162i
$10$		−	1.81249i		−	0.573159i
$11$	0.638169	+	0.638169i	0.192415	+	0.192415i	0.796739	−	0.604324i	$-0.206557\pi$
$11$	0.638169	+	0.638169i	0.192415	+	0.192415i	−0.604324	+	0.796739i	$0.706557\pi$
$12$	−0.566057	−	1.63694i	−0.163407	−	0.472544i
$13$	−0.922476	+	3.48555i	−0.255849	+	0.966717i
$13$	−0.922476	+	3.48555i	−0.255849	+	0.966717i
$14$	1.94544	−	1.79311i	0.519941	−	0.479230i
$15$	−1.37247	+	2.82341i	−0.354370	+	0.729002i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.29314	−	5.70389i	−0.798704	−	1.38340i	−0.920460	−	0.390836i	$-0.872186\pi$
$17$	−3.29314	−	5.70389i	−0.798704	−	1.38340i	0.121756	−	0.992560i	$-0.461147\pi$
$18$	−0.357762	+	2.97859i	−0.0843252	+	0.702061i
$19$	4.64094	+	4.64094i	1.06471	+	1.06471i	0.997756	+	0.0669492i	$0.0213265\pi$
$19$	4.64094	+	4.64094i	1.06471	+	1.06471i	0.0669492	+	0.997756i	$0.478673\pi$
$20$	−1.75073	+	0.469106i	−0.391475	+	0.104895i
$21$	−4.38832	+	1.32009i	−0.957610	+	0.288067i
$22$	0.451253	−	0.781594i	0.0962076	−	0.166636i
$23$	−0.687903	+	1.19148i	−0.143438	+	0.248441i	−0.928789	−	0.370609i	$-0.879149\pi$
$23$	−0.687903	+	1.19148i	−0.143438	+	0.248441i	0.785351	+	0.619050i	$0.212482\pi$
$24$	−1.43466	+	0.970441i	−0.292848	+	0.198090i
$25$	−1.48514	−	0.857446i	−0.297028	−	0.171489i
$26$	3.60553	−	0.0110823i	0.707103	−	0.00217341i
$27$	2.81278	−	4.36901i	0.541320	−	0.840816i
$28$	−2.23553	−	1.41506i	−0.422476	−	0.267421i
$29$	−5.47519	+	3.16110i	−1.01672	+	0.587002i	−0.913151	−	0.407621i	$-0.866358\pi$
$29$	−5.47519	+	3.16110i	−1.01672	+	0.587002i	−0.103565	+	0.994623i	$0.533025\pi$
$30$	3.08243	+	0.594950i	0.562772	+	0.108623i
$31$	−4.57998	+	1.22720i	−0.822589	+	0.220412i	−0.645478	−	0.763779i	$-0.723342\pi$
$31$	−4.57998	+	1.22720i	−0.822589	+	0.220412i	−0.177111	+	0.984191i	$0.556675\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−1.29479	+	0.875830i	−0.225394	+	0.152462i
$34$	−4.65721	+	4.65721i	−0.798704	+	0.798704i
$35$	1.05154	+	4.67868i	0.177742	+	0.790841i
$36$	2.96969	−	0.425345i	0.494949	−	0.0708908i
$37$	2.57030	+	9.59250i	0.422555	+	1.57700i	0.769205	+	0.639002i	$0.220653\pi$
$37$	2.57030	+	9.59250i	0.422555	+	1.57700i	−0.346650	+	0.937995i	$0.612681\pi$
$38$	3.28164	−	5.68397i	0.532353	−	0.922062i
$39$	−5.62493	−	2.71295i	−0.900710	−	0.434420i
$40$	0.906243	+	1.56966i	0.143290	+	0.248185i
$41$	12.1581	+	3.25776i	1.89878	+	0.508777i	0.997075	+	0.0764312i	$0.0243526\pi$
$41$	12.1581	+	3.25776i	1.89878	+	0.508777i	0.901708	+	0.432346i	$0.142314\pi$
$42$	2.41089	+	3.89713i	0.372008	+	0.601340i
$43$	3.99588	+	2.30702i	0.609366	+	0.351818i	0.772717	−	0.634750i	$-0.218897\pi$
$43$	3.99588	+	2.30702i	0.609366	+	0.351818i	−0.163351	+	0.986568i	$0.552230\pi$
$44$	−0.871755	−	0.233586i	−0.131422	−	0.0352144i
$45$	−4.35116	−	3.26089i	−0.648632	−	0.486105i
$46$	1.32893	+	0.356085i	0.195939	+	0.0525018i
$47$	0.961209	−	3.58728i	0.140207	−	0.523259i	−0.859715	−	0.510774i	$-0.829359\pi$
$47$	0.961209	−	3.58728i	0.140207	−	0.523259i	0.999922	−	0.0124852i	$-0.00397428\pi$
$48$	1.30869	+	1.13460i	0.188893	+	0.163766i
$49$	−3.98158	+	5.75734i	−0.568798	+	0.822478i
$50$	−0.443847	+	1.65646i	−0.0627694	+	0.234259i
$51$	10.7814	−	3.72822i	1.50969	−	0.522055i
$52$	−0.943886	−	3.47981i	−0.130893	−	0.482563i
$53$	4.00068	+	2.30979i	0.549535	+	0.317274i	0.748935	−	0.662644i	$-0.230566\pi$
$53$	4.00068	+	2.30979i	0.549535	+	0.317274i	−0.199399	+	0.979918i	$0.563899\pi$
$54$	−4.94814	−	1.58616i	−0.673357	−	0.215849i
$55$	0.817891	+	1.41663i	0.110284	+	0.191018i
$56$	−0.788244	+	2.52560i	−0.105334	+	0.337498i
$57$	−9.41607	+	6.36928i	−1.24719	+	0.843632i
$58$	4.47047	+	4.47047i	0.587002	+	0.587002i
$59$	1.38793	−	5.17983i	0.180693	−	0.674356i	−0.814818	−	0.579716i	$-0.803163\pi$
$59$	1.38793	−	5.17983i	0.180693	−	0.674356i	0.995512	−	0.0946397i	$-0.0301699\pi$
$60$	−0.223113	−	3.13138i	−0.0288038	−	0.404260i
$61$	0.318472			0.0407762			0.0203881	−	0.999792i	$-0.493510\pi$
$61$	0.318472			0.0407762			0.0203881	+	0.999792i	$0.493510\pi$
$62$	2.37077	+	4.10630i	0.301088	+	0.521501i
$63$	−0.804555	−	7.89637i	−0.101364	−	0.994849i
$64$			1.00000i			0.125000i
$65$	−3.25010	+	5.66950i	−0.403125	+	0.703216i
$66$	1.18110	+	1.02399i	0.145384	+	0.126044i
$67$	−1.10352	−	1.10352i	−0.134817	−	0.134817i	0.636478	−	0.771295i	$-0.280391\pi$
$67$	−1.10352	−	1.10352i	−0.134817	−	0.134817i	−0.771295	+	0.636478i	$0.780391\pi$
$68$	5.70389	+	3.29314i	0.691698	+	0.399352i
$69$	−1.80050	−	1.56099i	−0.216755	−	0.187922i
$70$	4.24710	−	2.22664i	0.507625	−	0.266134i
$71$	−0.215183	−	0.803072i	−0.0255375	−	0.0953072i	0.951981	−	0.306157i	$-0.0990434\pi$
$71$	−0.215183	−	0.803072i	−0.0255375	−	0.0953072i	−0.977518	+	0.210850i	$0.932377\pi$
$72$	−1.17946	−	2.75842i	−0.139001	−	0.325083i
$73$	−2.57872	−	9.62392i	−0.301816	−	1.12639i	−0.935651	−	0.352926i	$-0.885187\pi$
$73$	−2.57872	−	9.62392i	−0.301816	−	1.12639i	0.633835	−	0.773468i	$-0.281480\pi$
$74$	8.60040	−	4.96544i	0.999776	−	0.577221i
$75$	1.94572	−	2.24426i	0.224673	−	0.259145i
$76$	−6.33965	−	1.69870i	−0.727207	−	0.194855i
$77$	−0.711396	+	2.27937i	−0.0810711	+	0.259759i
$78$	−1.16467	+	6.13543i	−0.131873	+	0.694701i
$79$	−3.91647	−	6.78352i	−0.440637	−	0.763206i	0.557100	−	0.830446i	$-0.311914\pi$
$79$	−3.91647	−	6.78352i	−0.440637	−	0.763206i	−0.997737	+	0.0672398i	$0.978581\pi$
$80$	1.28162	−	1.28162i	0.143290	−	0.143290i
$81$	6.50691	+	6.21772i	0.722990	+	0.690858i
$82$		−	12.5870i		−	1.39001i
$83$	7.59633	−	7.59633i	0.833806	−	0.833806i	−0.154229	−	0.988035i	$-0.549289\pi$
$83$	7.59633	−	7.59633i	0.833806	−	0.833806i	0.988035	+	0.154229i	$0.0492894\pi$
$84$	3.14035	−	3.33739i	0.342641	−	0.364139i
$85$	−3.08967	−	11.5308i	−0.335121	−	1.25069i
$86$	1.19420	−	4.45683i	0.128774	−	0.480592i
$87$	−3.57873	−	10.3491i	−0.383680	−	1.10954i
$88$			0.902507i			0.0962076i
$89$	−12.6683	+	3.39445i	−1.34283	+	0.359811i	−0.857485	−	0.514510i	$-0.827974\pi$
$89$	−12.6683	+	3.39445i	−1.34283	+	0.359811i	−0.485348	+	0.874321i	$0.661307\pi$
$90$	−2.02362	+	5.04687i	−0.213308	+	0.531987i
$91$	−9.30075	+	2.12040i	−0.974983	+	0.222279i
$92$		−	1.37581i		−	0.143438i
$93$	−0.583674	−	8.19183i	−0.0605242	−	0.849453i
$94$	−3.71383			−0.383052
$95$	5.94793	+	10.3021i	0.610245	+	1.05698i
$96$	0.757230	−	1.55776i	0.0772844	−	0.158988i
$97$	8.51978	−	2.28287i	0.865053	−	0.231790i	0.201106	−	0.979570i	$-0.435547\pi$
$97$	8.51978	−	2.28287i	0.865053	−	0.231790i	0.663947	+	0.747779i	$0.268880\pi$
$98$	6.59168	+	2.35580i	0.665860	+	0.237972i
$99$	−1.06448	−	2.48949i	−0.106984	−	0.250203i
$100$	1.71489			0.171489
$101$	−9.32931			−0.928301			−0.464151	−	0.885756i	$-0.653640\pi$
$101$	−9.32931			−0.928301			−0.464151	+	0.885756i	$0.653640\pi$
$102$	−6.39160	−	9.44907i	−0.632863	−	0.935597i
$103$	6.49600	−	3.75047i	0.640070	−	0.369544i	−0.144572	−	0.989494i	$-0.546180\pi$
$103$	6.49600	−	3.75047i	0.640070	−	0.369544i	0.784641	+	0.619950i	$0.212847\pi$
$104$	−3.11694	+	1.81236i	−0.305641	+	0.177717i
$105$	−8.30202	+	0.252528i	−0.810194	+	0.0246442i
$106$	1.19564	−	4.46218i	0.116130	−	0.433405i
$107$	4.90997	+	2.83477i	0.474665	+	0.274048i	0.718190	−	0.695847i	$-0.244971\pi$
$107$	4.90997	+	2.83477i	0.474665	+	0.274048i	−0.243526	+	0.969894i	$0.578304\pi$
$108$	−0.251437	+	5.19007i	−0.0241945	+	0.499414i
$109$	5.53098	−	1.48202i	0.529772	−	0.141952i	0.0159889	−	0.999872i	$-0.494910\pi$
$109$	5.53098	−	1.48202i	0.529772	−	0.141952i	0.513783	+	0.857920i	$0.328244\pi$
$110$	1.15667	−	1.15667i	0.110284	−	0.110284i
$111$	−17.1573	+	1.22247i	−1.62850	+	0.116032i
$112$	2.64356	+	0.107711i	0.249793	+	0.0101777i
$113$	8.49197	+	4.90284i	0.798857	+	0.461221i	0.843071	−	0.537802i	$-0.180745\pi$
$113$	8.49197	+	4.90284i	0.798857	+	0.461221i	−0.0442141	+	0.999022i	$0.514078\pi$
$114$	8.58931	+	7.44673i	0.804463	+	0.697451i
$115$	−1.76326	+	1.76326i	−0.164425	+	0.164425i
$116$	3.16110	−	5.47519i	0.293501	−	0.508358i
$117$	6.46021	−	8.67558i	0.597246	−	0.802058i
$118$	−5.36255			−0.493663
$119$	9.31998	−	14.7239i	0.854362	−	1.34973i
$120$	−2.96694	+	1.02597i	−0.270843	+	0.0936580i
$121$		−	10.1855i		−	0.925953i
$122$	−0.0824267	−	0.307621i	−0.00746256	−	0.0278507i
$123$	−9.53128	+	19.6075i	−0.859406	+	1.76795i
$124$	3.35278	−	3.35278i	0.301088	−	0.301088i
$125$	−8.60595	−	8.60595i	−0.769740	−	0.769740i
$126$	−7.41908	+	2.82087i	−0.660944	+	0.251303i
$127$	12.3064	−	7.10513i	1.09202	−	0.630478i	0.157907	−	0.987454i	$-0.449525\pi$
$127$	12.3064	−	7.10513i	1.09202	−	0.630478i	0.934114	+	0.356976i	$0.116192\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−5.23512	+	6.03836i	−0.460927	+	0.531648i
$130$	6.31751	+	1.67198i	0.554082	+	0.146642i
$131$	13.7422	−	7.93405i	1.20066	−	0.693201i	0.239958	−	0.970783i	$-0.422866\pi$
$131$	13.7422	−	7.93405i	1.20066	−	0.693201i	0.960702	+	0.277582i	$0.0895330\pi$
$132$	0.683405	−	1.40589i	0.0594828	−	0.122367i
$133$	−5.17347	+	16.5763i	−0.448597	+	1.43734i
$134$	−0.780310	+	1.35154i	−0.0674085	+	0.116755i
$135$	6.97395	−	6.32945i	0.600222	−	0.544753i
$136$	1.70466	−	6.36186i	0.146173	−	0.545525i
$137$	1.72452	−	6.43601i	0.147336	−	0.549866i	−0.852304	−	0.523046i	$-0.824795\pi$
$137$	1.72452	−	6.43601i	0.147336	−	0.549866i	0.999640	−	0.0268193i	$-0.00853786\pi$
$138$	−1.04180	+	2.14317i	−0.0886840	+	0.182439i
$139$	−11.4175	+	19.7757i	−0.968420	+	1.67735i	−0.268287	+	0.963339i	$0.586458\pi$
$139$	−11.4175	+	19.7757i	−0.968420	+	1.67735i	−0.700133	+	0.714013i	$0.746876\pi$
$140$	−3.25000	−	3.52609i	−0.274675	−	0.298009i
$141$	5.78524	+	2.81222i	0.487205	+	0.236832i
$142$	−0.720015	+	0.415701i	−0.0604223	+	0.0348848i
$143$	−2.81306	+	1.63567i	−0.235240	+	0.136782i
$144$	−2.35916	+	1.85321i	−0.196596	+	0.154434i
$145$	−11.0685	+	2.96578i	−0.919185	+	0.246295i
$146$	−8.62857	+	4.98171i	−0.714105	+	0.412289i
$147$	−8.48434	−	8.66118i	−0.699776	−	0.714362i
$148$	−7.02220	−	7.02220i	−0.577221	−	0.577221i
$149$	−7.38036	+	7.38036i	−0.604623	+	0.604623i	−0.941536	−	0.336913i	$-0.890617\pi$
$149$	−7.38036	+	7.38036i	−0.604623	+	0.604623i	0.336913	+	0.941536i	$0.390617\pi$
$150$	−2.67138	−	1.29857i	−0.218117	−	0.106028i
$151$	2.89683	+	10.8111i	0.235741	+	0.879797i	0.977814	+	0.209477i	$0.0671762\pi$
$151$	2.89683	+	10.8111i	0.235741	+	0.879797i	−0.742073	+	0.670319i	$0.766157\pi$
$152$			6.56329i			0.532353i
$153$	2.80144	+	19.5592i	0.226483	+	1.58127i
$154$	2.38583	+	0.0972099i	0.192256	+	0.00783340i
$155$	−8.59399			−0.690286
$156$	6.22781	−	0.462980i	0.498624	−	0.0370680i
$157$	4.24843	−	7.35849i	0.339061	−	0.587272i	−0.645195	−	0.764018i	$-0.723224\pi$
$157$	4.24843	−	7.35849i	0.339061	−	0.587272i	0.984256	+	0.176746i	$0.0565572\pi$
$158$	−5.53872	+	5.53872i	−0.440637	+	0.440637i
$159$	−5.24140	+	6.04561i	−0.415670	+	0.479448i
$160$	−1.56966	−	0.906243i	−0.124092	−	0.0716448i
$161$	−3.63702	−	0.148189i	−0.286637	−	0.0116790i
$162$	4.32175	−	7.89446i	0.339549	−	0.620247i
$163$	11.8900	−	11.8900i	0.931297	−	0.931297i	−0.0664901	−	0.997787i	$-0.521180\pi$
$163$	11.8900	−	11.8900i	0.931297	−	0.931297i	0.997787	+	0.0664901i	$0.0211801\pi$
$164$	−12.1581	+	3.25776i	−0.949391	+	0.254389i
$165$	−2.67768	+	0.925947i	−0.208457	+	0.0720848i
$166$	−9.30357	−	5.37142i	−0.722097	−	0.416903i
$167$	4.01048	−	14.9673i	0.310340	−	1.15821i	−0.617909	−	0.786249i	$-0.712020\pi$
$167$	4.01048	−	14.9673i	0.310340	−	1.15821i	0.928250	−	0.371957i	$-0.121313\pi$
$168$	−4.03646	−	2.16957i	−0.311419	−	0.167386i
$169$	−11.2981	−	6.43067i	−0.869083	−	0.494667i
$170$	−10.3382	+	5.96878i	−0.792906	+	0.457784i
$171$	−7.74117	−	18.1043i	−0.591982	−	1.38447i
$172$	−4.61405			−0.351818
$173$	−16.5917			−1.26144			−0.630721	−	0.776009i	$-0.717241\pi$
$173$	−16.5917			−1.26144			−0.630721	+	0.776009i	$0.717241\pi$
$174$	−9.07020	+	6.13532i	−0.687610	+	0.465118i
$175$	0.184713	−	4.53341i	0.0139630	−	0.342694i
$176$	0.871755	−	0.233586i	0.0657110	−	0.0176072i
$177$	8.35354	+	4.06068i	0.627891	+	0.305220i
$178$	6.55757	+	11.3581i	0.491511	+	0.851322i
$179$	8.73086			0.652575			0.326288	−	0.945271i	$-0.394202\pi$
$179$	8.73086			0.652575			0.326288	+	0.945271i	$0.394202\pi$
$180$	5.39866	+	0.648438i	0.402392	+	0.0483317i
$181$		−	12.7095i		−	0.944688i	−0.881414	−	0.472344i	$-0.843408\pi$
$181$		−	12.7095i		−	0.944688i	0.881414	−	0.472344i	$-0.156592\pi$
$182$	4.45536	+	8.43503i	0.330253	+	0.625246i
$183$	−0.104539	+	0.541614i	−0.00772773	+	0.0400373i
$184$	−1.32893	+	0.356085i	−0.0979697	+	0.0262509i
$185$			17.9996i			1.32336i
$186$	−7.76164	+	2.68399i	−0.569111	+	0.196800i
$187$	1.53846	−	5.74162i	0.112504	−	0.419869i
$188$	0.961209	+	3.58728i	0.0701034	+	0.261629i
$189$	13.6932	+	1.22371i	0.996031	+	0.0890121i
$190$	8.41165	−	8.41165i	0.610245	−	0.610245i
$191$		−	5.63232i		−	0.407540i	−0.979019	−	0.203770i	$-0.934680\pi$
$191$		−	5.63232i		−	0.407540i	0.979019	−	0.203770i	$-0.0653195\pi$
$192$	−1.70066	−	0.328251i	−0.122735	−	0.0236895i
$193$	4.24505	−	4.24505i	0.305566	−	0.305566i	−0.537621	−	0.843187i	$-0.680677\pi$
$193$	4.24505	−	4.24505i	0.305566	−	0.305566i	0.843187	+	0.537621i	$0.180677\pi$
$194$	−4.41017	−	7.63863i	−0.316631	−	0.548422i
$195$	−8.57507	−	7.38834i	−0.614073	−	0.529090i
$196$	0.569480	−	6.97680i	0.0406772	−	0.498343i
$197$	−0.130081	−	0.0348552i	−0.00926792	−	0.00248333i	0.254182	−	0.967156i	$-0.418194\pi$
$197$	−0.130081	−	0.0348552i	−0.00926792	−	0.00248333i	−0.263450	+	0.964673i	$0.584860\pi$
$198$	−2.12916	+	1.67253i	−0.151313	+	0.118862i
$199$	13.3757	−	7.72247i	0.948179	−	0.547431i	0.0556642	−	0.998450i	$-0.482272\pi$
$199$	13.3757	−	7.72247i	0.948179	−	0.547431i	0.892515	+	0.451018i	$0.148939\pi$
$200$	−0.443847	−	1.65646i	−0.0313847	−	0.117129i
$201$	2.23895	−	1.51449i	0.157924	−	0.106824i
$202$	2.41460	+	9.01142i	0.169891	+	0.634042i
$203$	−14.1335	−	8.94629i	−0.991976	−	0.627906i
$204$	−7.47283	+	8.61941i	−0.523203	+	0.603480i
$205$	19.7574	+	11.4069i	1.37991	+	0.796694i
$206$	−5.30396	−	5.30396i	−0.369544	−	0.369544i
$207$	3.24574	−	2.54965i	0.225595	−	0.177213i
$208$	2.55733	+	2.54166i	0.177319	+	0.176233i
$209$			5.92341i			0.409731i
$210$	2.39264	+	7.95377i	0.165108	+	0.548863i
$211$	8.34474	+	14.4535i	0.574475	+	0.995020i	0.996098	+	0.0882493i	$0.0281272\pi$
$211$	8.34474	+	14.4535i	0.574475	+	0.995020i	−0.421623	+	0.906771i	$0.638539\pi$
$212$	−4.61958			−0.317274
$213$	1.43639	−	0.102344i	0.0984197	−	0.00701248i
$214$	1.46739	−	5.47636i	0.100309	−	0.374356i
$215$	5.91346	+	5.91346i	0.403295	+	0.403295i
$216$	5.07829	−	1.10042i	0.345534	−	0.0748740i
$217$	−8.50214	−	9.22440i	−0.577163	−	0.626193i
$218$	−2.86305	−	4.95894i	−0.193910	−	0.335862i
$219$	17.2135	−	1.22647i	1.16318	−	0.0828774i
$220$	−1.41663	−	0.817891i	−0.0955091	−	0.0551422i
$221$	22.9190	−	6.21670i	1.54170	−	0.418180i
$222$	5.62145	+	16.2563i	0.377287	+	1.09105i
$223$	−4.88471	+	18.2300i	−0.327105	+	1.22077i	0.585075	+	0.810979i	$0.301065\pi$
$223$	−4.88471	+	18.2300i	−0.327105	+	1.22077i	−0.912179	+	0.409791i	$0.865602\pi$
$224$	−0.580162	−	2.58136i	−0.0387637	−	0.172474i
$225$	3.17805	+	4.04570i	0.211870	+	0.269713i
$226$	2.53790	−	9.47156i	0.168818	−	0.630039i
$227$	5.95359	+	1.59526i	0.395154	+	0.105881i	0.450924	−	0.892563i	$-0.351095\pi$
$227$	5.95359	+	1.59526i	0.395154	+	0.105881i	−0.0557699	+	0.998444i	$0.517761\pi$
$228$	4.96991	−	10.2240i	0.329141	−	0.677101i
$229$	29.0285	+	7.77816i	1.91826	+	0.513996i	0.989779	+	0.142609i	$0.0455493\pi$
$229$	29.0285	+	7.77816i	1.91826	+	0.513996i	0.928479	+	0.371386i	$0.121117\pi$
$230$	2.15955	+	1.24681i	0.142396	+	0.0822125i
$231$	−3.64293	−	1.95805i	−0.239687	−	0.128830i
$232$	−6.10678	−	1.63631i	−0.400930	−	0.107429i
$233$	2.90989	+	5.04008i	0.190633	+	0.330187i	0.945460	−	0.325737i	$-0.105612\pi$
$233$	2.90989	+	5.04008i	0.190633	+	0.330187i	−0.754827	+	0.655924i	$0.772279\pi$
$234$	−10.0520	−	3.99468i	−0.657119	−	0.261140i
$235$	3.36563	−	5.82944i	0.219550	−	0.380271i
$236$	1.38793	+	5.17983i	0.0903466	+	0.337178i
$237$	12.8221	−	4.43389i	0.832882	−	0.288012i
$238$	−16.6343	−	5.19160i	−1.07824	−	0.336521i
$239$	4.35751	−	4.35751i	0.281864	−	0.281864i	−0.551988	−	0.833852i	$-0.686131\pi$
$239$	4.35751	−	4.35751i	0.281864	−	0.281864i	0.833852	+	0.551988i	$0.186131\pi$
$240$	1.75891	+	2.60030i	0.113537	+	0.167849i
$241$	−7.44625	−	1.99522i	−0.479655	−	0.128523i	0.0108868	−	0.999941i	$-0.496535\pi$
$241$	−7.44625	−	1.99522i	−0.479655	−	0.128523i	−0.490542	+	0.871417i	$0.663201\pi$
$242$	−9.83842	+	2.63620i	−0.632438	+	0.169461i
$243$	−12.7101	+	9.02508i	−0.815356	+	0.578959i
$244$	−0.275805	+	0.159236i	−0.0176566	+	0.0101941i
$245$	−9.67147	+	8.21176i	−0.617888	+	0.524630i
$246$	21.4063	+	4.13170i	1.36482	+	0.263428i
$247$	−20.4574	+	11.8951i	−1.30167	+	0.756865i
$248$	−4.10630	−	2.37077i	−0.260750	−	0.150544i
$249$	10.4253	+	15.4123i	0.660676	+	0.976715i
$250$	−6.08533	+	10.5401i	−0.384870	+	0.666614i
$251$	2.45017	−	4.24381i	0.154653	−	0.267867i	−0.778280	−	0.627918i	$-0.783907\pi$
$251$	2.45017	−	4.24381i	0.154653	−	0.267867i	0.932933	+	0.360051i	$0.117241\pi$
$252$	4.64495	+	6.43618i	0.292604	+	0.405441i
$253$	−1.19936	+	0.321369i	−0.0754034	+	0.0202043i
$254$	−10.0482	−	10.0482i	−0.630478	−	0.630478i
$255$	20.6242	−	1.46949i	1.29154	−	0.0920228i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.0676	−	19.1696i	0.690375	−	1.19576i	−0.281340	−	0.959608i	$-0.590779\pi$
$257$	11.0676	−	19.1696i	0.690375	−	1.19576i	0.971715	−	0.236156i	$-0.0758878\pi$
$258$	7.18756	+	3.49389i	0.447478	+	0.217520i
$259$	−19.3200	+	17.8072i	−1.20048	+	1.10649i
$260$	−0.0200864	−	6.53498i	−0.00124571	−	0.405282i
$261$	18.7750	−	2.68912i	1.16214	−	0.166452i
$262$	−11.2204	−	11.2204i	−0.693201	−	0.693201i
$263$			16.4440i			1.01398i	0.861952	+	0.506989i	$0.169242\pi$
$263$			16.4440i			1.01398i	−0.861952	+	0.506989i	$0.830758\pi$
$264$	−1.53486	−	0.296249i	−0.0944641	−	0.0182328i
$265$	5.92056	+	5.92056i	0.363697	+	0.363697i
$266$	17.3504	+	0.706938i	1.06382	+	0.0433452i
$267$	−1.61445	−	22.6587i	−0.0988025	−	1.38669i
$268$	1.50744	+	0.403918i	0.0920817	+	0.0246732i
$269$	7.62257	−	4.40089i	0.464756	−	0.268327i	−0.249286	−	0.968430i	$-0.580196\pi$
$269$	7.62257	−	4.40089i	0.464756	−	0.268327i	0.714042	+	0.700103i	$0.246863\pi$
$270$	−7.91877	−	5.09813i	−0.481921	−	0.310262i
$271$	6.01709	+	22.4561i	0.365512	+	1.36411i	0.866725	+	0.498786i	$0.166221\pi$
$271$	6.01709	+	22.4561i	0.365512	+	1.36411i	−0.501213	+	0.865324i	$0.667113\pi$
$272$	−6.58628			−0.399352
$273$	−0.553110	−	16.5135i	−0.0334757	−	0.999440i
$274$	−6.66305			−0.402530
$275$	−0.400575	−	1.49496i	−0.0241556	−	0.0901498i
$276$	2.33978	+	0.451609i	0.140838	+	0.0271837i
$277$	−7.61277	+	4.39524i	−0.457407	+	0.264084i	−0.710953	−	0.703239i	$-0.751736\pi$
$277$	−7.61277	+	4.39524i	−0.457407	+	0.264084i	0.253546	+	0.967323i	$0.418403\pi$
$278$	22.0569	+	5.91013i	1.32289	+	0.354466i
$279$	14.1231	+	1.69634i	0.845530	+	0.101557i
$280$	−2.56478	+	4.05187i	−0.153275	+	0.242146i
$281$	5.77940	+	5.77940i	0.344770	+	0.344770i	0.858157	−	0.513387i	$-0.171609\pi$
$281$	5.77940	+	5.77940i	0.344770	+	0.344770i	−0.513387	+	0.858157i	$0.671609\pi$
$282$	1.21907	−	6.31597i	0.0725944	−	0.376110i
$283$		−	18.2532i		−	1.08504i	−0.840043	−	0.542520i	$-0.817470\pi$
$283$		−	18.2532i		−	1.08504i	0.840043	−	0.542520i	$-0.182530\pi$
$284$	0.587890	+	0.587890i	0.0348848	+	0.0348848i
$285$	−19.4728	+	6.73375i	−1.15347	+	0.398873i
$286$	2.30801	+	2.29387i	0.136476	+	0.135639i
$287$	7.30252	+	32.4916i	0.431054	+	1.91792i
$288$	2.40065	+	1.79913i	0.141460	+	0.106015i
$289$	−13.1896	+	22.8450i	−0.775857	+	1.34382i
$290$	5.72945	+	9.92370i	0.336445	+	0.582740i
$291$	1.08576	+	15.2386i	0.0636486	+	0.893304i
$292$	7.04520	+	7.04520i	0.412289	+	0.412289i
$293$	−3.68965	+	0.988640i	−0.215552	+	0.0577570i	−0.364979	−	0.931016i	$-0.618924\pi$
$293$	−3.68965	+	0.988640i	−0.215552	+	0.0577570i	0.149427	+	0.988773i	$0.452257\pi$
$294$	−6.17015	+	10.4369i	−0.359850	+	0.608693i
$295$	4.85978	−	8.41738i	0.282947	−	0.490079i
$296$	−4.96544	+	8.60040i	−0.288611	+	0.499888i
$297$	4.58320	−	0.993136i	0.265944	−	0.0576276i
$298$	9.03906	+	5.21871i	0.523619	+	0.302312i
$299$	−3.51839	−	3.49683i	−0.203474	−	0.202227i
$300$	−0.562915	+	2.91645i	−0.0324999	+	0.168381i
$301$	−0.496984	+	12.1975i	−0.0286457	+	0.703052i
$302$	9.69299	−	5.59625i	0.557769	−	0.322028i
$303$	3.06235	−	15.8660i	0.175928	−	0.911478i
$304$	6.33965	−	1.69870i	0.363604	−	0.0974273i
$305$	0.557559	+	0.149397i	0.0319257	+	0.00855447i
$306$	18.1677	−	7.76829i	1.03858	−	0.444084i
$307$	11.9104	−	11.9104i	0.679761	−	0.679761i	−0.280185	−	0.959946i	$-0.590396\pi$
$307$	11.9104	−	11.9104i	0.679761	−	0.679761i	0.959946	+	0.280185i	$0.0903959\pi$
$308$	−0.523601	−	2.32969i	−0.0298349	−	0.132747i
$309$	4.24596	+	12.2786i	0.241544	+	0.698505i
$310$	2.22429	+	8.30116i	0.126331	+	0.471474i
$311$	−12.1481	+	21.0411i	−0.688853	+	1.19313i	0.283356	+	0.959015i	$0.408552\pi$
$311$	−12.1481	+	21.0411i	−0.688853	+	1.19313i	−0.972209	+	0.234114i	$0.924781\pi$
$312$	−2.05908	−	5.89578i	−0.116572	−	0.333783i
$313$	−7.76181	−	13.4438i	−0.438723	−	0.759891i	0.558868	−	0.829257i	$-0.311236\pi$
$313$	−7.76181	−	13.4438i	−0.438723	−	0.759891i	−0.997591	+	0.0693657i	$0.977902\pi$
$314$	−8.20733	−	2.19915i	−0.463166	−	0.124105i
$315$	2.29568	−	14.2018i	0.129347	−	0.800182i
$316$	6.78352	+	3.91647i	0.381603	+	0.220319i
$317$	−25.7673	−	6.90434i	−1.44724	−	0.387786i	−0.552176	−	0.833728i	$-0.686202\pi$
$317$	−25.7673	−	6.90434i	−1.44724	−	0.387786i	−0.895062	+	0.445941i	$0.852869\pi$
$318$	7.19618	+	3.49809i	0.403542	+	0.196163i
$319$	−5.51141	−	1.47678i	−0.308580	−	0.0826837i
$320$	−0.469106	+	1.75073i	−0.0262238	+	0.0978687i
$321$	−6.43269	+	7.41969i	−0.359038	+	0.414127i
$322$	0.798190	+	3.55145i	0.0444814	+	0.197914i
$323$	11.1881	−	41.7547i	0.622525	−	2.32329i
$324$	−8.74401	−	2.13125i	−0.485779	−	0.118403i
$325$	4.35867	−	4.38555i	0.241776	−	0.243267i
$326$	−14.5622	−	8.40750i	−0.806527	−	0.465648i
$327$	0.704869	+	9.89280i	0.0389794	+	0.547073i
$328$	6.29352	+	10.9007i	0.347501	+	0.601890i
$329$	9.58672	−	2.15462i	0.528533	−	0.118788i
$330$	1.58743	+	2.34679i	0.0873852	+	0.129186i
$331$	9.03647	+	9.03647i	0.496689	+	0.496689i	0.910406	−	0.413716i	$-0.135769\pi$
$331$	9.03647	+	9.03647i	0.496689	+	0.496689i	−0.413716	+	0.910406i	$0.635769\pi$
$332$	−2.78045	+	10.3768i	−0.152597	+	0.569500i
$333$	3.55289	−	29.5801i	0.194697	−	1.62098i
$334$	−15.4953			−0.847866
$335$	−1.41430	−	2.44964i	−0.0772715	−	0.133838i
$336$	−1.05093	+	4.46044i	−0.0573329	+	0.243337i
$337$		−	6.18136i		−	0.336720i	−0.985726	−	0.168360i	$-0.946153\pi$
$337$		−	6.18136i		−	0.336720i	0.985726	−	0.168360i	$-0.0538471\pi$
$338$	−3.28739	+	12.5775i	−0.178811	+	0.684125i
$339$	−11.1256	+	12.8326i	−0.604258	+	0.696972i
$340$	8.44113	+	8.44113i	0.457784	+	0.457784i
$341$	−3.70596	−	2.13964i	−0.200689	−	0.115868i
$342$	−15.4838	+	12.1631i	−0.837270	+	0.657706i
$343$	−18.3822	−	2.25693i	−0.992547	−	0.121863i
$344$	1.19420	+	4.45683i	0.0643871	+	0.240296i
$345$	−2.41992	−	3.57750i	−0.130284	−	0.192606i
$346$	4.29425	+	16.0263i	0.230860	+	0.861582i
$347$	−8.65717	+	4.99822i	−0.464741	+	0.268318i	−0.714036	−	0.700109i	$-0.753135\pi$
$347$	−8.65717	+	4.99822i	−0.464741	+	0.268318i	0.249295	+	0.968428i	$0.419801\pi$
$348$	8.27381	+	7.17320i	0.443523	+	0.384524i
$349$	−20.8799	−	5.59475i	−1.11768	−	0.299480i	−0.347733	−	0.937594i	$-0.613048\pi$
$349$	−20.8799	−	5.59475i	−1.11768	−	0.299480i	−0.769943	+	0.638113i	$0.779715\pi$
$350$	−4.42675	+	0.994915i	−0.236620	+	0.0531805i
$351$	12.6337	+	13.8344i	0.674335	+	0.738425i
$352$	−0.451253	−	0.781594i	−0.0240519	−	0.0416591i
$353$	−7.60058	+	7.60058i	−0.404538	+	0.404538i	−0.879829	−	0.475291i	$-0.842343\pi$
$353$	−7.60058	+	7.60058i	−0.404538	+	0.404538i	0.475291	+	0.879829i	$0.342343\pi$
$354$	1.76026	−	9.11989i	0.0935569	−	0.484716i
$355$		−	1.50690i		−	0.0799782i
$356$	9.27381	−	9.27381i	0.491511	−	0.491511i
$357$	21.9810	+	20.6833i	1.16336	+	1.09467i
$358$	−2.25971	−	8.43336i	−0.119430	−	0.445717i
$359$	5.86355	−	21.8831i	0.309466	−	1.15494i	−0.619566	−	0.784945i	$-0.712691\pi$
$359$	5.86355	−	21.8831i	0.309466	−	1.15494i	0.929032	−	0.369999i	$-0.120642\pi$
$360$	−0.770932	−	5.38253i	−0.0406317	−	0.283684i
$361$			24.0767i			1.26720i
$362$	−12.2764	+	3.28946i	−0.645234	+	0.172890i
$363$	17.3221	+	3.34339i	0.909172	+	0.175483i
$364$	6.99448	−	6.48670i	0.366610	−	0.339995i
$365$		−	18.0586i		−	0.945228i
$366$	0.550216	−	0.0392032i	0.0287602	−	0.00204919i
$367$	−3.88587			−0.202841			−0.101420	−	0.994844i	$-0.532339\pi$
$367$	−3.88587			−0.202841			−0.101420	+	0.994844i	$0.532339\pi$
$368$	0.687903	+	1.19148i	0.0358594	+	0.0621103i
$369$	−30.2171	−	22.6457i	−1.57304	−	1.17889i
$370$	17.3863	−	4.65864i	0.903870	−	0.242191i
$371$	−0.497580	+	12.2121i	−0.0258331	+	0.634023i
$372$	4.60139	+	6.80250i	0.238571	+	0.352693i
$373$	7.41520			0.383944			0.191972	−	0.981400i	$-0.438512\pi$
$373$	7.41520			0.383944			0.191972	+	0.981400i	$0.438512\pi$
$374$	−5.94417			−0.307366
$375$	17.4607	−	11.8109i	0.901668	−	0.609912i
$376$	3.21627	−	1.85691i	0.165866	−	0.0957630i
$377$	−5.96743	−	22.0001i	−0.307338	−	1.13306i
$378$	−2.36203	−	13.5433i	−0.121490	−	0.696592i
$379$	−2.47437	+	9.23446i	−0.127100	+	0.474342i	−0.999906	−	0.0137247i	$-0.995631\pi$
$379$	−2.47437	+	9.23446i	−0.127100	+	0.474342i	0.872806	+	0.488067i	$0.162298\pi$
$380$	−10.3021	−	5.94793i	−0.528488	−	0.305123i
$381$	8.04382	+	23.2614i	0.412098	+	1.19172i
$382$	−5.44040	+	1.45775i	−0.278355	+	0.0745850i
$383$	−14.9808	+	14.9808i	−0.765481	+	0.765481i	−0.977307	−	0.211826i	$-0.932059\pi$
$383$	−14.9808	+	14.9808i	−0.765481	+	0.765481i	0.211826	+	0.977307i	$0.432059\pi$
$384$	0.123098	+	1.72767i	0.00628181	+	0.0881648i
$385$	−2.31473	+	3.65684i	−0.117970	+	0.186370i
$386$	−5.19911	−	3.00171i	−0.264628	−	0.152783i
$387$	−8.55078	−	10.8853i	−0.434661	−	0.553329i
$388$	−6.23692	+	6.23692i	−0.316631	+	0.316631i
$389$	−15.6838	+	27.1652i	−0.795202	+	1.37733i	0.127509	+	0.991837i	$0.459302\pi$
$389$	−15.6838	+	27.1652i	−0.795202	+	1.37733i	−0.922711	+	0.385493i	$0.874031\pi$
$390$	−4.91719	+	10.1951i	−0.248992	+	0.516250i
$391$	9.06144			0.458257
$392$	−6.88646	+	1.25565i	−0.347819	+	0.0634200i
$393$	8.98226	+	25.9752i	0.453095	+	1.31027i
$394$			0.134670i			0.00678459i
$395$	−3.67448	−	13.7133i	−0.184883	−	0.689993i
$396$	2.16661	+	1.62372i	0.108876	+	0.0815952i
$397$	18.5982	−	18.5982i	0.933419	−	0.933419i	−0.0644991	−	0.997918i	$-0.520545\pi$
$397$	18.5982	−	18.5982i	0.933419	−	0.933419i	0.997918	+	0.0644991i	$0.0205450\pi$
$398$	−10.9212	−	10.9212i	−0.547431	−	0.547431i
$399$	−26.4924	−	14.2395i	−1.32628	−	0.712866i
$400$	−1.48514	+	0.857446i	−0.0742570	+	0.0428723i
$401$	−6.01696	+	1.61224i	−0.300473	+	0.0805114i	−0.405906	−	0.913915i	$-0.633044\pi$
$401$	−6.01696	+	1.61224i	−0.300473	+	0.0805114i	0.105433	+	0.994426i	$0.466377\pi$
$402$	−2.04237	−	1.77069i	−0.101864	−	0.0883138i
$403$	−0.0525470	−	17.0958i	−0.00261755	−	0.851603i
$404$	8.07942	−	4.66466i	0.401966	−	0.232075i
$405$	8.47506	+	13.9380i	0.421129	+	0.692584i
$406$	−4.98344	+	15.9674i	−0.247324	+	0.792447i
$407$	−4.48135	+	7.76192i	−0.222132	+	0.384744i
$408$	10.2598	+	4.98733i	0.507937	+	0.246910i
$409$	−2.87061	+	10.7133i	−0.141943	+	0.529737i	0.857930	+	0.513767i	$0.171750\pi$
$409$	−2.87061	+	10.7133i	−0.141943	+	0.529737i	−0.999872	+	0.0159702i	$0.994916\pi$
$410$	5.90465	−	22.0365i	0.291610	−	1.08830i
$411$	10.3794	+	5.04546i	0.511978	+	0.248874i
$412$	−3.75047	+	6.49600i	−0.184772	+	0.320035i
$413$	13.8427	−	3.11115i	0.681153	−	0.153090i
$414$	−3.30283	−	2.47525i	−0.162325	−	0.121652i
$415$	16.8626	−	9.73563i	0.827752	−	0.477903i
$416$	1.79317	−	3.12803i	0.0879174	−	0.153364i
$417$	−29.8840	−	25.9087i	−1.46342	−	1.26875i
$418$	5.72158	−	1.53309i	0.279851	−	0.0749860i
$419$	17.9840	−	10.3830i	0.878574	−	0.507245i	0.00838623	−	0.999965i	$-0.497331\pi$
$419$	17.9840	−	10.3830i	0.878574	−	0.507245i	0.870188	+	0.492720i	$0.163997\pi$
$420$	7.06349	−	4.36971i	0.344663	−	0.213220i
$421$	−4.07675	−	4.07675i	−0.198689	−	0.198689i	0.600749	−	0.799438i	$-0.294869\pi$
$421$	−4.07675	−	4.07675i	−0.198689	−	0.198689i	−0.799438	+	0.600749i	$0.794869\pi$
$422$	11.8012	−	11.8012i	0.574475	−	0.574475i
$423$	−6.68164	+	8.91562i	−0.324873	+	0.433492i
$424$	1.19564	+	4.46218i	0.0580652	+	0.216702i
$425$			11.2948i			0.547876i
$426$	−0.470621	−	1.36096i	−0.0228017	−	0.0659386i
$427$	0.391243	+	0.746258i	0.0189336	+	0.0361140i
$428$	−5.66955			−0.274048
$429$	−1.85833	−	5.32098i	−0.0897212	−	0.256899i
$430$	4.18145	−	7.24249i	0.201647	−	0.349264i
$431$	−17.1530	+	17.1530i	−0.826229	+	0.826229i	−0.986993	−	0.160764i	$-0.948604\pi$
$431$	−17.1530	+	17.1530i	−0.826229	+	0.826229i	0.160764	+	0.986993i	$0.448604\pi$
$432$	−2.37728	−	4.62045i	−0.114377	−	0.222301i
$433$	−5.95281	−	3.43686i	−0.286074	−	0.165165i	0.350096	−	0.936714i	$-0.386149\pi$
$433$	−5.95281	−	3.43686i	−0.286074	−	0.165165i	−0.636170	+	0.771549i	$0.719482\pi$
$434$	−6.70957	+	10.5999i	−0.322070	+	0.508811i
$435$	−1.41057	−	19.7972i	−0.0676315	−	0.949204i
$436$	−4.04896	+	4.04896i	−0.193910	+	0.193910i
$437$	−8.72212	+	2.33708i	−0.417236	+	0.111798i
$438$	−5.63986	−	16.3095i	−0.269483	−	0.779299i
$439$	−8.45098	−	4.87917i	−0.403343	−	0.232870i	0.284582	−	0.958652i	$-0.408145\pi$
$439$	−8.45098	−	4.87917i	−0.403343	−	0.232870i	−0.687926	+	0.725781i	$0.741478\pi$
$440$	−0.423372	+	1.58004i	−0.0201834	+	0.0753256i
$441$	17.5147	−	11.5860i	0.834035	−	0.551712i
$442$	−11.9367	−	20.5291i	−0.567773	−	0.976468i
$443$	−34.0695	+	19.6700i	−1.61869	+	0.934552i	−0.631431	+	0.775432i	$0.717532\pi$
$443$	−34.0695	+	19.6700i	−1.61869	+	0.934552i	−0.987259	+	0.159120i	$0.949134\pi$
$444$	14.2474	−	9.63734i	0.676153	−	0.457368i
$445$	−23.7710			−1.12686
$446$	18.8731			0.893666
$447$	−10.1289	−	14.9741i	−0.479080	−	0.708251i
$448$	−2.34324	+	1.22850i	−0.110708	+	0.0580411i
$449$	−21.0377	+	5.63704i	−0.992831	+	0.266028i	−0.718439	−	0.695590i	$-0.755143\pi$
$449$	−21.0377	+	5.63704i	−0.992831	+	0.266028i	−0.274392	+	0.961618i	$0.588476\pi$
$450$	3.08531	−	4.11686i	0.145443	−	0.194071i
$451$	5.67994	+	9.83795i	0.267458	+	0.463251i
$452$	−9.80568			−0.461221
$453$	−19.3369	+	1.37777i	−0.908529	+	0.0647333i
$454$		−	6.16361i		−	0.289273i
$455$	−17.2778	−	0.650790i	−0.809994	−	0.0305095i
$456$	−11.1619	−	2.15440i	−0.522705	−	0.100889i
$457$	9.02418	−	2.41802i	0.422133	−	0.113110i	−0.0414978	−	0.999139i	$-0.513213\pi$
$457$	9.02418	−	2.41802i	0.422133	−	0.113110i	0.463631	+	0.886028i	$0.346546\pi$
$458$		−	30.0525i		−	1.40426i
$459$	−34.1832	−	1.65603i	−1.59554	−	0.0772970i
$460$	0.645399	−	2.40866i	0.0300919	−	0.112304i
$461$	−5.29013	−	19.7430i	−0.246386	−	0.919524i	−0.972682	−	0.232142i	$-0.925426\pi$
$461$	−5.29013	−	19.7430i	−0.246386	−	0.919524i	0.726296	−	0.687382i	$-0.241240\pi$
$462$	−0.948472	+	4.02558i	−0.0441269	+	0.187287i
$463$	−6.55850	+	6.55850i	−0.304799	+	0.304799i	−0.842888	−	0.538089i	$-0.819146\pi$
$463$	−6.55850	+	6.55850i	−0.304799	+	0.304799i	0.538089	+	0.842888i	$0.319146\pi$
$464$			6.32220i			0.293501i
$465$	2.82098	−	14.6155i	0.130820	−	0.677776i
$466$	4.11521	−	4.11521i	0.190633	−	0.190633i
$467$	−13.9409	−	24.1463i	−0.645106	−	1.11736i	−0.984277	−	0.176631i	$-0.943480\pi$
$467$	−13.9409	−	24.1463i	−0.645106	−	1.11736i	0.339171	−	0.940725i	$-0.389853\pi$
$468$	−1.25691	+	10.7434i	−0.0581008	+	0.496613i
$469$	1.23015	−	3.94150i	0.0568030	−	0.182002i
$470$	−6.50190	−	1.74218i	−0.299910	−	0.0803607i
$471$	11.1198	+	9.64057i	0.512371	+	0.444214i
$472$	4.64411	−	2.68128i	0.213762	−	0.123416i
$473$	1.07778	+	4.02232i	0.0495562	+	0.184946i
$474$	−7.60140	−	11.2376i	−0.349144	−	0.516159i
$475$	−2.91309	−	10.8718i	−0.133662	−	0.498833i
$476$	−0.709415	+	17.4112i	−0.0325160	+	0.798042i
$477$	−8.56104	−	10.8983i	−0.391983	−	0.499000i
$478$	−5.33684	−	3.08122i	−0.244101	−	0.140932i
$479$	15.2285	+	15.2285i	0.695810	+	0.695810i	0.963504	−	0.267694i	$-0.0862616\pi$
$479$	15.2285	+	15.2285i	0.695810	+	0.695810i	−0.267694	+	0.963504i	$0.586262\pi$
$480$	2.05646	−	2.37199i	0.0938639	−	0.108266i
$481$	−35.8062	+	0.110057i	−1.63262	+	0.00501815i
$482$			7.70893i			0.351132i
$483$	1.44588	−	6.13670i	0.0657896	−	0.279230i
$484$	5.09274	+	8.82089i	0.231488	+	0.400949i
$485$	15.9867			0.725920
$486$	12.0072	+	9.94120i	0.544657	+	0.450942i
$487$	2.06542	−	7.70827i	0.0935933	−	0.349295i	−0.903209	−	0.429201i	$-0.858795\pi$
$487$	2.06542	−	7.70827i	0.0935933	−	0.349295i	0.996802	+	0.0799059i	$0.0254620\pi$
$488$	0.225194	+	0.225194i	0.0101941	+	0.0101941i
$489$	16.3180	+	24.1238i	0.737924	+	1.09092i
$490$	10.4351	+	7.21657i	0.471410	+	0.326011i
$491$	−1.14945	−	1.99091i	−0.0518741	−	0.0898485i	0.838922	−	0.544251i	$-0.183186\pi$
$491$	−1.14945	−	1.99091i	−0.0518741	−	0.0898485i	−0.890796	+	0.454403i	$0.849853\pi$
$492$	−1.54944	−	21.7463i	−0.0698540	−	0.980397i
$493$	36.0611	+	20.8199i	1.62411	+	0.937681i
$494$	16.7845	+	16.6817i	0.755171	+	0.750543i
$495$	−0.695772	−	4.85777i	−0.0312726	−	0.218341i
$496$	−1.22720	+	4.57998i	−0.0551030	+	0.205647i
$497$	1.61744	−	1.49080i	0.0725522	−	0.0668715i
$498$	12.1889	−	14.0591i	0.546196	−	0.630001i
$499$	4.30774	−	16.0767i	0.192841	−	0.719692i	−0.799974	−	0.600034i	$-0.795154\pi$
$499$	4.30774	−	16.0767i	0.192841	−	0.719692i	0.992815	−	0.119658i	$-0.0381797\pi$
$500$	11.7559	+	3.15000i	0.525742	+	0.140872i
$501$	24.1379	+	11.7335i	1.07840	+	0.524215i
$502$	−4.73336	−	1.26830i	−0.211260	−	0.0566070i
$503$	1.59511	+	0.920936i	0.0711223	+	0.0410625i	0.535139	−	0.844764i	$-0.320259\pi$
$503$	1.59511	+	0.920936i	0.0711223	+	0.0410625i	−0.464017	+	0.885826i	$0.653592\pi$
$504$	5.01467	−	6.15248i	0.223371	−	0.274053i
$505$	−16.3331	−	4.37644i	−0.726813	−	0.194749i
$506$	0.620837	+	1.07532i	0.0275996	+	0.0478039i
$507$	14.6450	−	17.1033i	0.650407	−	0.759586i
$508$	−7.10513	+	12.3064i	−0.315239	+	0.546010i
$509$	6.57749	+	24.5475i	0.291542	+	1.08805i	0.943925	+	0.330160i	$0.107103\pi$
$509$	6.57749	+	24.5475i	0.291542	+	1.08805i	−0.652383	+	0.757890i	$0.726231\pi$
$510$	−6.75734	−	19.5411i	−0.299220	−	0.865294i
$511$	19.3832	−	17.8655i	0.857464	−	0.790325i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	33.3303	−	7.22236i	1.47157	−	0.318875i
$514$	−21.3809	−	5.72899i	−0.943070	−	0.252695i
$515$	13.1321	−	3.51873i	0.578669	−	0.155054i
$516$	1.51457	−	7.84694i	0.0666750	−	0.345442i
$517$	2.90271	−	1.67588i	0.127661	−	0.0737050i
$518$	22.2008	+	14.0528i	0.975448	+	0.617444i
$519$	5.44624	−	28.2169i	0.239063	−	1.23858i
$520$	−6.30711	+	1.71078i	−0.276585	+	0.0750227i
$521$	12.5241	+	7.23078i	0.548690	+	0.316786i	0.748593	−	0.663029i	$-0.230730\pi$
$521$	12.5241	+	7.23078i	0.548690	+	0.316786i	−0.199904	+	0.979816i	$0.564063\pi$
$522$	−7.45681	−	17.4393i	−0.326376	−	0.763296i
$523$	16.2727	−	28.1851i	0.711555	−	1.23245i	−0.252718	−	0.967540i	$-0.581324\pi$
$523$	16.2727	−	28.1851i	0.711555	−	1.23245i	0.964273	−	0.264910i	$-0.0853423\pi$
$524$	−7.93405	+	13.7422i	−0.346601	+	0.600330i
$525$	7.64917	+	1.80223i	0.333837	+	0.0786558i
$526$	15.8837	−	4.25601i	0.692560	−	0.185571i
$527$	22.0824	+	22.0824i	0.961923	+	0.961923i
$528$	0.111097	+	1.55924i	0.00483486	+	0.0678570i
$529$	10.5536	+	18.2793i	0.458851	+	0.794754i
$530$	4.18647	−	7.25118i	0.181849	−	0.314971i
$531$	−9.64791	+	12.8736i	−0.418683	+	0.558668i
$532$	−3.80777	−	16.9422i	−0.165088	−	0.734537i
$533$	−22.5707	+	39.3726i	−0.977645	+	1.70541i
$534$	−21.4687	+	7.42393i	−0.929043	+	0.321265i
$535$	7.26622	+	7.26622i	0.314146	+	0.314146i
$536$		−	1.56062i		−	0.0674085i
$537$	−2.86591	+	14.8482i	−0.123673	+	0.640749i
$538$	−6.22380	−	6.22380i	−0.268327	−	0.268327i
$539$	−6.21508	+	1.13323i	−0.267702	+	0.0488119i
$540$	−2.87489	+	8.96844i	−0.123715	+	0.385940i
$541$	−26.4530	−	7.08807i	−1.13731	−	0.304740i	−0.359438	−	0.933169i	$-0.617032\pi$
$541$	−26.4530	−	7.08807i	−1.13731	−	0.304740i	−0.777867	+	0.628429i	$0.783698\pi$
$542$	20.1336	−	11.6241i	0.864811	−	0.499299i
$543$	21.6145	+	4.17190i	0.927569	+	0.179033i
$544$	1.70466	+	6.36186i	0.0730865	+	0.272763i
$545$	10.3785			0.444565
$546$	−15.8076	+	4.80826i	−0.676503	+	0.205774i
$547$	21.0848			0.901523			0.450761	−	0.892645i	$-0.351153\pi$
$547$	21.0848			0.901523			0.450761	+	0.892645i	$0.351153\pi$
$548$	1.72452	+	6.43601i	0.0736680	+	0.274933i
$549$	−0.886787	−	0.355570i	−0.0378472	−	0.0151754i
$550$	−1.34035	+	0.773851i	−0.0571527	+	0.0329971i
$551$	−40.0805	−	10.7395i	−1.70749	−	0.457520i
$552$	−0.169359	−	2.37694i	−0.00720838	−	0.101169i
$553$	11.0841	−	17.5108i	0.471343	−	0.744634i
$554$	6.21580	+	6.21580i	0.264084	+	0.264084i
$555$	−30.6112	−	5.90838i	−1.29937	−	0.250797i
$556$		−	22.8350i		−	0.968420i
$557$	8.46402	+	8.46402i	0.358632	+	0.358632i	0.863309	−	0.504676i	$-0.168388\pi$
$557$	8.46402	+	8.46402i	0.358632	+	0.358632i	−0.504676	+	0.863309i	$0.668388\pi$
$558$	−2.01679	−	14.0809i	−0.0853776	−	0.596094i
$559$	−11.7273	+	11.7997i	−0.496014	+	0.499073i
$560$	4.57762	+	1.42868i	0.193440	+	0.0603728i
$561$	9.25956	+	4.50110i	0.390939	+	0.190037i
$562$	4.08666	−	7.07830i	0.172385	−	0.298580i
$563$	−23.5056	−	40.7129i	−0.990644	−	1.71584i	−0.613512	−	0.789685i	$-0.710244\pi$
$563$	−23.5056	−	40.7129i	−0.990644	−	1.71584i	−0.377131	−	0.926160i	$-0.623089\pi$
$564$	−6.41627	+	0.457164i	−0.270174	+	0.0192501i
$565$	12.5672	+	12.5672i	0.528705	+	0.528705i
$566$	−17.6312	+	4.72427i	−0.741096	+	0.198576i
$567$	−6.57591	+	22.8857i	−0.276162	+	0.961111i
$568$	0.415701	−	0.720015i	0.0174424	−	0.0302112i
$569$	2.13169	−	3.69219i	0.0893650	−	0.154785i	−0.817878	−	0.575392i	$-0.804850\pi$
$569$	2.13169	−	3.69219i	0.0893650	−	0.154785i	0.907243	+	0.420607i	$0.138183\pi$
$570$	11.5442	+	17.0665i	0.483535	+	0.714837i
$571$	−9.82900	−	5.67478i	−0.411331	−	0.237482i	0.280031	−	0.959991i	$-0.409655\pi$
$571$	−9.82900	−	5.67478i	−0.411331	−	0.237482i	−0.691361	+	0.722509i	$0.742989\pi$
$572$	1.61835	−	2.82306i	0.0676665	−	0.118038i
$573$	9.57867	+	1.84881i	0.400155	+	0.0772353i
$574$	29.4945	−	15.4632i	1.23108	−	0.645419i
$575$	2.04326	−	1.17968i	0.0852099	−	0.0491960i
$576$	1.11649	−	2.78450i	0.0465203	−	0.116021i
$577$	−20.2604	+	5.42876i	−0.843452	+	0.226002i	−0.654574	−	0.755998i	$-0.727152\pi$
$577$	−20.2604	+	5.42876i	−0.843452	+	0.226002i	−0.188878	+	0.982001i	$0.560485\pi$
$578$	25.4803	+	6.82742i	1.05984	+	0.283983i
$579$	5.82596	+	8.61284i	0.242119	+	0.357938i
$580$	8.10267	−	8.10267i	0.336445	−	0.336445i
$581$	27.1321	+	8.46798i	1.12563	+	0.351311i
$582$	14.4384	−	4.99281i	0.598490	−	0.206959i
$583$	1.07907	+	4.02715i	0.0446905	+	0.166787i
$584$	4.98171	−	8.62857i	0.206144	−	0.357053i
$585$	15.3798	−	12.1581i	0.635878	−	0.502674i
$586$	1.90991	+	3.30805i	0.0788975	+	0.136654i
$587$	−23.1964	−	6.21546i	−0.957419	−	0.256540i	−0.253911	−	0.967227i	$-0.581717\pi$
$587$	−23.1964	−	6.21546i	−0.957419	−	0.256540i	−0.703508	+	0.710688i	$0.748384\pi$
$588$	11.6782	+	3.25863i	0.481603	+	0.134384i
$589$	−26.9508	−	15.5601i	−1.11049	−	0.641141i
$590$	−9.38837	−	2.51561i	−0.386513	−	0.103566i
$591$	0.101976	−	0.209783i	0.00419474	−	0.00862933i
$592$	9.59250	+	2.57030i	0.394249	+	0.105639i
$593$	−0.971782	+	3.62674i	−0.0399063	+	0.148932i	−0.983004	−	0.183583i	$-0.941231\pi$
$593$	−0.971782	+	3.62674i	−0.0399063	+	0.148932i	0.943098	+	0.332515i	$0.107897\pi$
$594$	−2.14551	−	4.16999i	−0.0880315	−	0.171097i
$595$	23.2238	−	21.4054i	0.952083	−	0.877536i
$596$	2.70140	−	10.0818i	0.110654	−	0.412965i
$597$	8.74272	+	25.2825i	0.357816	+	1.03474i
$598$	−2.46705	+	4.30355i	−0.100885	+	0.175985i
$599$	6.17618	+	3.56582i	0.252352	+	0.145695i	0.620841	−	0.783937i	$-0.286791\pi$
$599$	6.17618	+	3.56582i	0.252352	+	0.145695i	−0.368489	+	0.929632i	$0.620125\pi$
$600$	2.96277	−	0.211099i	0.120954	−	0.00861809i
$601$	−19.7330	−	34.1785i	−0.804924	−	1.39417i	−0.916342	−	0.400396i	$-0.868872\pi$
$601$	−19.7330	−	34.1785i	−0.804924	−	1.39417i	0.111418	−	0.993774i	$-0.464461\pi$
$602$	11.9105	−	2.67690i	0.485436	−	0.109102i
$603$	1.84070	+	4.30484i	0.0749589	+	0.175307i
$604$	−7.91429	−	7.91429i	−0.322028	−	0.322028i
$605$	4.77807	−	17.8320i	0.194256	−	0.724974i
$606$	−16.1180	+	1.14842i	−0.654748	+	0.0466513i
$607$	−6.17751			−0.250737			−0.125369	−	0.992110i	$-0.540011\pi$
$607$	−6.17751			−0.250737			−0.125369	+	0.992110i	$0.540011\pi$
$608$	−3.28164	−	5.68397i	−0.133088	−	0.230516i
$609$	19.8539	−	21.0997i	0.804522	−	0.855001i
$610$		−	0.577227i		−	0.0233712i
$611$	11.6169	+	6.65952i	0.469971	+	0.269415i
$612$	−12.2057	−	15.5381i	−0.493388	−	0.628090i
$613$	−6.91119	−	6.91119i	−0.279140	−	0.279140i	0.553625	−	0.832766i	$-0.313244\pi$
$613$	−6.91119	−	6.91119i	−0.279140	−	0.279140i	−0.832766	+	0.553625i	$0.813244\pi$
$614$	−14.5872	−	8.42190i	−0.588690	−	0.339880i
$615$	−25.8847	+	29.8563i	−1.04377	+	1.20392i
$616$	−2.11479	+	1.10873i	−0.0852075	+	0.0446719i
$617$	−1.15991	−	4.32885i	−0.0466963	−	0.174273i	0.938639	−	0.344900i	$-0.112087\pi$
$617$	−1.15991	−	4.32885i	−0.0466963	−	0.174273i	−0.985336	+	0.170627i	$0.945421\pi$
$618$	10.7613	−	7.27922i	0.432882	−	0.292813i
$619$	11.4373	+	42.6846i	0.459704	+	1.71564i	0.673878	+	0.738843i	$0.264628\pi$
$619$	11.4373	+	42.6846i	0.459704	+	1.71564i	−0.214173	+	0.976796i	$0.568706\pi$
$620$	7.44261	−	4.29700i	0.298903	−	0.172571i
$621$	3.27068	+	6.35683i	0.131248	+	0.255091i
$622$	23.4683	+	6.28830i	0.940991	+	0.252138i
$623$	−23.5170	−	25.5147i	−0.942187	−	1.02223i
$624$	−5.16195	+	3.51486i	−0.206644	+	0.140707i
$625$	−6.74235	−	11.6781i	−0.269694	−	0.467123i
$626$	−10.9769	+	10.9769i	−0.438723	+	0.438723i
$627$	−10.0737	−	1.94436i	−0.402306	−	0.0776504i
$628$			8.49685i			0.339061i
$629$	46.2502	−	46.2502i	1.84412	−	1.84412i
$630$	−14.3121	+	1.45825i	−0.570207	+	0.0580979i
$631$	5.66403	+	21.1384i	0.225481	+	0.841508i	0.982211	+	0.187780i	$0.0601292\pi$
$631$	5.66403	+	21.1384i	0.225481	+	0.841508i	−0.756730	+	0.653728i	$0.773204\pi$
$632$	2.02731	−	7.56603i	0.0806422	−	0.300961i
$633$	−27.3197	+	9.44720i	−1.08586	+	0.375493i
$634$			26.6763i			1.05945i
$635$	24.8783	−	6.66612i	0.987265	−	0.264537i
$636$	1.51638	−	7.85635i	0.0601285	−	0.311525i
$637$	−16.3946	−	19.1890i	−0.649577	−	0.760296i
$638$			5.70583i			0.225896i
$639$	−0.297444	+	2.47641i	−0.0117667	+	0.0979651i
$640$	1.81249			0.0716448
$641$	−22.7521	−	39.4077i	−0.898653	−	1.55651i	−0.829218	−	0.558926i	$-0.811214\pi$
$641$	−22.7521	−	39.4077i	−0.898653	−	1.55651i	−0.0694349	−	0.997586i	$-0.522120\pi$
$642$	8.83177	+	4.29315i	0.348562	+	0.169437i
$643$	18.4734	−	4.94992i	0.728518	−	0.195206i	0.124549	−	0.992213i	$-0.460252\pi$
$643$	18.4734	−	4.94992i	0.728518	−	0.195206i	0.603969	+	0.797008i	$0.293585\pi$
$644$	3.22385	−	1.69017i	0.127037	−	0.0666022i
$645$	−11.9979	+	8.11571i	−0.472417	+	0.319556i
$646$	−43.2277			−1.70077
$647$	−13.5573			−0.532994			−0.266497	−	0.963836i	$-0.585866\pi$
$647$	−13.5573			−0.532994			−0.266497	+	0.963836i	$0.585866\pi$
$648$	0.204486	+	8.99768i	0.00803297	+	0.353462i
$649$	4.19134	−	2.41987i	0.164524	−	0.0949882i
$650$	−5.36422	−	3.07509i	−0.210402	−	0.120615i
$651$	18.4784	−	11.4313i	0.724226	−	0.448030i
$652$	−4.35204	+	16.2420i	−0.170439	+	0.636088i
$653$	−6.83940	−	3.94873i	−0.267647	−	0.154526i	0.360171	−	0.932886i	$-0.382718\pi$
$653$	−6.83940	−	3.94873i	−0.267647	−	0.154526i	−0.627818	+	0.778360i	$0.716052\pi$
$654$	9.37328	−	3.24130i	0.366524	−	0.126745i
$655$	27.7807	−	7.44383i	1.08548	−	0.290854i
$656$	8.90038	−	8.90038i	0.347501	−	0.347501i
$657$	−3.56453	+	29.6769i	−0.139065	+	1.15781i
$658$	−4.56243	−	8.70240i	−0.177862	−	0.339255i
$659$	27.0573	+	15.6216i	1.05400	+	0.608530i	0.923768	−	0.382953i	$-0.125093\pi$
$659$	27.0573	+	15.6216i	1.05400	+	0.608530i	0.130237	+	0.991483i	$0.458426\pi$
$660$	1.85597	−	2.14073i	0.0722434	−	0.0833279i
$661$	27.4906	−	27.4906i	1.06926	−	1.06926i	0.0718449	−	0.997416i	$-0.477111\pi$
$661$	27.4906	−	27.4906i	1.06926	−	1.06926i	0.997416	−	0.0718449i	$-0.0228887\pi$
$662$	6.38975	−	11.0674i	0.248345	−	0.430146i
$663$	3.04932	+	41.0181i	0.118426	+	1.59301i
$664$	10.7428			0.416903
$665$	−16.8334	+	26.5936i	−0.652770	+	1.03126i
$666$	−29.4917	+	4.22405i	−1.14278	+	0.163679i
$667$		−	8.69812i		−	0.336792i
$668$	4.01048	+	14.9673i	0.155170	+	0.579103i
$669$	−29.3996	−	14.2913i	−1.13666	−	0.552532i
$670$	−2.00012	+	2.00012i	−0.0772715	+	0.0772715i
$671$	0.203239	+	0.203239i	0.00784596	+	0.00784596i
$672$	4.58046	−	0.139327i	0.176695	−	0.00537465i
$673$	−26.8382	+	15.4950i	−1.03453	+	0.597289i	−0.918281	−	0.395930i	$-0.870422\pi$
$673$	−26.8382	+	15.4950i	−1.03453	+	0.597289i	−0.116254	+	0.993219i	$0.537089\pi$
$674$	−5.97073	+	1.59985i	−0.229984	+	0.0616240i
$675$	−7.92356	+	4.07678i	−0.304978	+	0.156915i
$676$	12.9998	−	0.0799149i	0.499991	−	0.00307365i
$677$	11.6126	−	6.70454i	0.446309	−	0.257676i	−0.259961	−	0.965619i	$-0.583710\pi$
$677$	11.6126	−	6.70454i	0.446309	−	0.257676i	0.706270	+	0.707943i	$0.250376\pi$
$678$	15.2749	+	7.42515i	0.586627	+	0.285161i
$679$	15.8159	+	17.1594i	0.606957	+	0.658519i
$680$	5.96878	−	10.3382i	0.228892	−	0.396453i
$681$	−4.66727	+	9.60140i	−0.178850	+	0.367927i
$682$	−1.10756	+	4.13347i	−0.0424106	+	0.158279i
$683$	0.0581129	−	0.216880i	0.00222363	−	0.00829869i	−0.964805	−	0.262966i	$-0.915299\pi$
$683$	0.0581129	−	0.216880i	0.00222363	−	0.00829869i	0.967029	+	0.254667i	$0.0819660\pi$
$684$	15.7562	+	11.8082i	0.602453	+	0.451497i
$685$	6.03834	−	10.4587i	0.230713	−	0.399607i
$686$	2.57764	+	18.3400i	0.0984148	+	0.700225i
$687$	−22.7567	+	46.8145i	−0.868221	+	1.78608i
$688$	3.99588	−	2.30702i	0.152342	−	0.0879545i
$689$	−11.7414	+	11.8138i	−0.447312	+	0.450071i
$690$	−2.82928	+	3.26339i	−0.107709	+	0.124235i
$691$	−33.8220	+	9.06259i	−1.28665	+	0.344757i	−0.836387	−	0.548139i	$-0.815337\pi$
$691$	−33.8220	+	9.06259i	−1.28665	+	0.344757i	−0.450263	+	0.892896i	$0.648670\pi$
$692$	14.3688	−	8.29585i	0.546221	−	0.315361i
$693$	4.52578	−	5.55266i	0.171920	−	0.210928i
$694$	7.06855	+	7.06855i	0.268318	+	0.268318i
$695$	−29.2658	+	29.2658i	−1.11012	+	1.11012i
$696$	4.78736	−	9.84844i	0.181464	−	0.373304i
$697$	−21.4566	−	80.0770i	−0.812725	−	3.03313i
$698$			21.6165i			0.818195i
$699$	−9.52665	+	3.29433i	−0.360331	+	0.124603i
$700$	2.10674	+	4.01841i	0.0796273	+	0.151882i
$701$	−4.70332			−0.177642			−0.0888209	−	0.996048i	$-0.528310\pi$
$701$	−4.70332			−0.177642			−0.0888209	+	0.996048i	$0.528310\pi$
$702$	10.0932	−	15.7838i	0.380942	−	0.595721i
$703$	−32.5896	+	56.4469i	−1.22914	+	2.12893i
$704$	−0.638169	+	0.638169i	−0.0240519	+	0.0240519i
$705$	8.80914	+	7.63732i	0.331772	+	0.287638i
$706$	9.30877	+	5.37442i	0.350340	+	0.202269i
$707$	−11.4610	−	21.8609i	−0.431037	−	0.822162i
$708$	−9.26472	+	0.660118i	−0.348190	+	0.0248088i
$709$	−25.3424	+	25.3424i	−0.951753	+	0.951753i	−0.998889	−	0.0471355i	$-0.984991\pi$
$709$	−25.3424	+	25.3424i	−0.951753	+	0.951753i	0.0471355	+	0.998889i	$0.484991\pi$
$710$	−1.45556	+	0.390016i	−0.0546261	+	0.0146370i
$711$	3.33170	+	23.2614i	0.124948	+	0.872371i
$712$	−11.3581	−	6.55757i	−0.425661	−	0.245755i
$713$	1.68839	−	6.30116i	0.0632308	−	0.235980i
$714$	14.2894	−	26.5852i	0.534767	−	0.994928i
$715$	−5.69221	+	1.54399i	−0.212877	+	0.0577420i
$716$	−7.56115	+	4.36543i	−0.282573	+	0.163144i
$717$	5.98029	+	8.84100i	0.223338	+	0.330173i
$718$	−22.6550			−0.845477
$719$	17.3600			0.647418			0.323709	−	0.946157i	$-0.395070\pi$
$719$	17.3600			0.647418			0.323709	+	0.946157i	$0.395070\pi$
$720$	−4.99959	+	2.13776i	−0.186324	+	0.0796698i
$721$	16.7686	+	10.6143i	0.624495	+	0.395296i
$722$	23.2563	−	6.23151i	0.865511	−	0.231913i
$723$	5.83743	−	12.0086i	0.217096	−	0.446606i
$724$	6.35474	+	11.0067i	0.236172	+	0.409062i
$725$	10.8419			0.402658
$726$	−1.25381	−	17.5972i	−0.0465333	−	0.653092i
$727$			2.82499i			0.104773i	0.998627	+	0.0523865i	$0.0166828\pi$
$727$			2.82499i			0.104773i	−0.998627	+	0.0523865i	$0.983317\pi$
$728$	−8.07597	−	5.07727i	−0.299315	−	0.188176i
$729$	−11.1765	−	24.5782i	−0.413945	−	0.910302i
$730$	−17.4432	+	4.67390i	−0.645603	+	0.172989i
$731$		−	30.3894i		−	1.12399i
$732$	−0.180274	−	0.521321i	−0.00666311	−	0.0192686i
$733$	2.60022	−	9.70415i	0.0960413	−	0.358431i	−0.901134	−	0.433541i	$-0.857264\pi$
$733$	2.60022	−	9.70415i	0.0960413	−	0.358431i	0.997175	+	0.0751097i	$0.0239307\pi$
$734$	1.00574	+	3.75346i	0.0371225	+	0.138543i
$735$	−10.7908	−	19.1434i	−0.398023	−	0.706116i
$736$	0.972841	−	0.972841i	0.0358594	−	0.0358594i
$737$		−	1.40847i		−	0.0518816i
$738$	−14.0533	+	35.0486i	−0.517308	+	1.29016i
$739$	−0.663354	+	0.663354i	−0.0244019	+	0.0244019i	−0.719202	−	0.694801i	$-0.755493\pi$
$739$	−0.663354	+	0.663354i	−0.0244019	+	0.0244019i	0.694801	+	0.719202i	$0.255493\pi$
$740$	−8.99980	−	15.5881i	−0.330839	−	0.573030i
$741$	−13.5143	−	38.6957i	−0.496461	−	1.42152i
$742$	11.9248	−	2.68011i	0.437773	−	0.0983899i
$743$	−33.4454	−	8.96168i	−1.22699	−	0.328772i	−0.413586	−	0.910465i	$-0.635724\pi$
$743$	−33.4454	−	8.96168i	−1.22699	−	0.328772i	−0.813408	+	0.581693i	$0.802390\pi$
$744$	5.37978	−	6.20522i	0.197232	−	0.227494i
$745$	−16.3832	+	9.45884i	−0.600233	+	0.346545i
$746$	−1.91919	−	7.16253i	−0.0702667	−	0.262239i
$747$	−29.6332	+	12.6708i	−1.08422	+	0.463600i
$748$	1.53846	+	5.74162i	0.0562518	+	0.209935i
$749$	−0.610673	+	14.9878i	−0.0223135	+	0.547641i
$750$	−15.9276	−	13.8089i	−0.581595	−	0.504229i
$751$	19.2427	+	11.1098i	0.702178	+	0.405403i	0.808158	−	0.588966i	$-0.200465\pi$
$751$	19.2427	+	11.1098i	0.702178	+	0.405403i	−0.105980	+	0.994368i	$0.533798\pi$
$752$	−2.62607	−	2.62607i	−0.0957630	−	0.0957630i
$753$	6.41302	+	5.55994i	0.233703	+	0.202615i
$754$	−19.7059	+	11.4581i	−0.717648	+	0.417281i
$755$			20.2863i			0.738292i
$756$	−12.4705	+	5.78681i	−0.453547	+	0.210464i
$757$	19.9696	+	34.5883i	0.725807	+	1.25713i	0.958641	+	0.284618i	$0.0918667\pi$
$757$	19.9696	+	34.5883i	0.725807	+	1.25713i	−0.232834	+	0.972516i	$0.574800\pi$
$758$	9.56022			0.347243
$759$	−0.152847	−	2.14520i	−0.00554800	−	0.0778660i
$760$	−3.07888	+	11.4905i	−0.111683	+	0.416805i
$761$	−2.06228	−	2.06228i	−0.0747577	−	0.0747577i	0.668739	−	0.743497i	$-0.266834\pi$
$761$	−2.06228	−	2.06228i	−0.0747577	−	0.0747577i	−0.743497	+	0.668739i	$0.766834\pi$
$762$	20.3869	−	13.7902i	0.738538	−	0.499567i
$763$	10.2675	+	11.1398i	0.371710	+	0.403287i
$764$	2.81616	+	4.87773i	0.101885	+	0.176470i
$765$	−4.27080	+	35.5571i	−0.154411	+	1.28557i
$766$	18.3476	+	10.5930i	0.662926	+	0.382741i
$767$	16.7742	+	9.61596i	0.605681	+	0.347212i
$768$	1.63694	−	0.566057i	0.0590681	−	0.0204258i
$769$	9.05425	−	33.7909i	0.326505	−	1.21853i	−0.586286	−	0.810104i	$-0.699411\pi$
$769$	9.05425	−	33.7909i	0.326505	−	1.21853i	0.912791	−	0.408427i	$-0.133923\pi$
$770$	4.13134	+	1.28940i	0.148883	+	0.0464666i
$771$	28.9680	+	25.1146i	1.04326	+	0.904480i
$772$	−1.55380	+	5.79885i	−0.0559224	+	0.208705i
$773$	5.09265	+	1.36457i	0.183170	+	0.0490802i	0.349238	−	0.937034i	$-0.386440\pi$
$773$	5.09265	+	1.36457i	0.183170	+	0.0490802i	−0.166068	+	0.986114i	$0.553107\pi$
$774$	−8.30126	+	11.0767i	−0.298382	+	0.398145i
$775$	7.85417	+	2.10452i	0.282130	+	0.0755965i
$776$	7.63863	+	4.41017i	0.274211	+	0.158316i
$777$	−23.9423	−	38.7019i	−0.858924	−	1.38842i
$778$	30.2988	+	8.11855i	1.08627	+	0.291064i
$779$	41.3062	+	71.5444i	1.47995	+	2.56334i
$780$	11.1204	+	2.11095i	0.398174	+	0.0755843i
$781$	0.375173	−	0.649819i	0.0134247	−	0.0232523i
$782$	−2.34527	−	8.75268i	−0.0838668	−	0.312995i
$783$	−1.58963	+	32.8126i	−0.0568088	+	1.17263i
$784$	2.99521	+	6.32682i	0.106972	+	0.225958i
$785$	10.8898	−	10.8898i	0.388672	−	0.388672i
$786$	22.7653	−	15.3991i	0.812012	−	0.549266i
$787$	4.09910	+	1.09835i	0.146117	+	0.0391520i	0.331136	−	0.943583i	$-0.392568\pi$
$787$	4.09910	+	1.09835i	0.146117	+	0.0391520i	−0.185019	+	0.982735i	$0.559235\pi$
$788$	0.130081	−	0.0348552i	0.00463396	−	0.00124167i
$789$	−27.9656	−	5.39775i	−0.995603	−	0.192165i
$790$	−12.2950	+	7.09855i	−0.437438	+	0.252555i
$791$	−1.05618	+	25.9219i	−0.0375534	+	0.921676i
$792$	1.00764	−	2.51303i	0.0358048	−	0.0892967i
$793$	−0.293783	+	1.11005i	−0.0104325	+	0.0394190i
$794$	−22.7781	−	13.1509i	−0.808364	−	0.466709i
$795$	−12.0123	+	8.12544i	−0.426032	+	0.288180i
$796$	−7.72247	+	13.3757i	−0.273716	+	0.474090i
$797$	−5.97249	+	10.3447i	−0.211557	+	0.366427i	−0.952202	−	0.305470i	$-0.901187\pi$
$797$	−5.97249	+	10.3447i	−0.211557	+	0.366427i	0.740645	+	0.671896i	$0.234520\pi$
$798$	−6.89755	+	29.2752i	−0.244171	+	1.03633i
$799$	−23.6269	+	6.33080i	−0.835858	+	0.223968i
$800$	1.21261	+	1.21261i	0.0428723	+	0.0428723i
$801$	39.0647	+	4.69210i	1.38028	+	0.165787i
$802$	3.11461	+	5.39466i	0.109981	+	0.190492i
$803$	4.49603	−	7.78734i	0.158661	−	0.274809i
$804$	−1.18175	+	2.43106i	−0.0416770	+	0.0857370i
$805$	−6.29792	−	1.96559i	−0.221972	−	0.0692779i
$806$	−16.4997	+	4.47548i	−0.581176	+	0.157642i
$807$	4.98232	+	14.4080i	0.175386	+	0.507186i
$808$	−6.59682	−	6.59682i	−0.232075	−	0.232075i
$809$			27.8941i			0.980703i	0.871525	+	0.490352i	$0.163132\pi$
$809$			27.8941i			0.980703i	−0.871525	+	0.490352i	$0.836868\pi$
$810$	11.2695	−	11.7937i	0.395971	−	0.414388i
$811$	−13.1791	−	13.1791i	−0.462781	−	0.462781i	0.436785	−	0.899566i	$-0.356117\pi$
$811$	−13.1791	−	13.1791i	−0.462781	−	0.462781i	−0.899566	+	0.436785i	$0.856117\pi$
$812$	16.7131	+	0.680970i	0.586515	+	0.0238974i
$813$	−40.1653	+	2.86181i	−1.40866	+	0.100368i
$814$	8.65730	+	2.31972i	0.303438	+	0.0813060i
$815$	26.3938	−	15.2385i	0.924536	−	0.533781i
$816$	2.16195	−	11.2010i	0.0756835	−	0.392115i
$817$	7.83790	+	29.2514i	0.274213	+	1.02338i
$818$	11.0912			0.387794
$819$	28.2654	+	4.47990i	0.987672	+	0.156540i
$820$	−22.8138			−0.796694
$821$	−10.7288	−	40.0405i	−0.374438	−	1.39742i	−0.854164	−	0.520004i	$-0.825930\pi$
$821$	−10.7288	−	40.0405i	−0.374438	−	1.39742i	0.479725	−	0.877419i	$-0.340736\pi$
$822$	2.18715	−	11.3316i	0.0762857	−	0.395235i
$823$	15.0426	−	8.68488i	0.524354	−	0.302736i	−0.214360	−	0.976755i	$-0.568767\pi$
$823$	15.0426	−	8.68488i	0.524354	−	0.302736i	0.738714	+	0.674019i	$0.235433\pi$
$824$	7.24535	+	1.94138i	0.252404	+	0.0676313i
$825$	2.67392	−	0.190519i	0.0930939	−	0.00663301i
$826$	−6.58789	−	12.5658i	−0.229222	−	0.437219i
$827$	19.6554	+	19.6554i	0.683486	+	0.683486i	0.960784	−	0.277298i	$-0.0894388\pi$
$827$	19.6554	+	19.6554i	0.683486	+	0.683486i	−0.277298	+	0.960784i	$0.589439\pi$
$828$	−1.53607	+	3.83093i	−0.0533821	+	0.133134i
$829$		−	5.36288i		−	0.186261i	−0.995654	−	0.0931303i	$-0.970313\pi$
$829$		−	5.36288i		−	0.186261i	0.995654	−	0.0931303i	$-0.0296873\pi$
$830$	−13.7683	−	13.7683i	−0.477903	−	0.477903i
$831$	−4.97591	−	14.3895i	−0.172613	−	0.499166i
$832$	−3.48555	−	0.922476i	−0.120840	−	0.0319811i
$833$	45.9512	+	3.75076i	1.59211	+	0.129956i
$834$	−17.2913	+	35.5713i	−0.598750	+	1.23174i
$835$	14.0425	−	24.3224i	0.485962	−	0.841710i
$836$	−2.96171	−	5.12982i	−0.102433	−	0.177419i
$837$	−7.52084	+	23.4618i	−0.259958	+	0.810960i
$838$	−14.6838	−	14.6838i	−0.507245	−	0.507245i
$839$	−18.8876	+	5.06091i	−0.652071	+	0.174722i	−0.569665	−	0.821877i	$-0.692927\pi$
$839$	−18.8876	+	5.06091i	−0.652071	+	0.174722i	−0.0824061	+	0.996599i	$0.526260\pi$
$840$	−6.04898	−	5.69185i	−0.208710	−	0.196387i
$841$	5.48511	−	9.50049i	0.189142	−	0.327603i
$842$	−2.88270	+	4.99298i	−0.0993443	+	0.172069i
$843$	−11.7259	+	7.93172i	−0.403862	+	0.273183i
$844$	−14.4535	−	8.34474i	−0.497510	−	0.287238i
$845$	−16.7632	−	16.5583i	−0.576671	−	0.569624i
$846$	10.3412	+	4.14644i	0.355536	+	0.142558i
$847$	23.8671	−	12.5128i	0.820082	−	0.429947i
$848$	4.00068	−	2.30979i	0.137384	−	0.0793186i
$849$	31.0425	+	5.99162i	1.06538	+	0.205632i
$850$	10.9099	−	2.92330i	0.374207	−	0.100268i
$851$	−13.1974	−	3.53624i	−0.452401	−	0.121221i
$852$	−1.19278	+	0.806827i	−0.0408639	+	0.0276414i
$853$	23.1719	−	23.1719i	0.793391	−	0.793391i	−0.188653	−	0.982044i	$-0.560412\pi$
$853$	23.1719	−	23.1719i	0.793391	−	0.793391i	0.982044	+	0.188653i	$0.0604120\pi$
$854$	0.619569	−	0.571057i	0.0212012	−	0.0195412i
$855$	−5.05985	−	35.3271i	−0.173043	−	1.20816i
$856$	1.46739	+	5.47636i	0.0501543	+	0.187178i
$857$	−11.3306	+	19.6252i	−0.387046	+	0.670383i	−0.992051	−	0.125839i	$-0.959838\pi$
$857$	−11.3306	+	19.6252i	−0.387046	+	0.670383i	0.605005	+	0.796222i	$0.293171\pi$
$858$	−4.65870	+	3.17218i	−0.159045	+	0.108297i
$859$	2.02468	+	3.50686i	0.0690813	+	0.119652i	0.898497	−	0.438979i	$-0.144660\pi$
$859$	2.02468	+	3.50686i	0.0690813	+	0.119652i	−0.829416	+	0.558632i	$0.811327\pi$
$860$	−8.07794	−	2.16448i	−0.275456	−	0.0738081i
$861$	−57.6544	+	1.75371i	−1.96486	+	0.0597664i
$862$	21.0080	+	12.1290i	0.715535	+	0.413114i
$863$	16.4191	+	4.39948i	0.558912	+	0.149760i	0.527207	−	0.849737i	$-0.323239\pi$
$863$	16.4191	+	4.39948i	0.558912	+	0.149760i	0.0317057	+	0.999497i	$0.489906\pi$
$864$	−3.84772	+	3.49214i	−0.130902	+	0.118805i
$865$	−29.0475	−	7.78326i	−0.987646	−	0.264639i
$866$	−1.77905	+	6.63950i	−0.0604545	+	0.225619i
$867$	−34.5221	−	29.9299i	−1.17243	−	1.01647i
$868$	11.9753	+	3.73750i	0.406467	+	0.126859i
$869$	1.82966	−	6.82840i	0.0620671	−	0.231638i
$870$	−18.7576	+	6.48640i	−0.635941	+	0.219910i
$871$	4.86436	−	2.82841i	0.164823	−	0.0958370i
$872$	4.95894	+	2.86305i	0.167931	+	0.0969550i
$873$	−26.2722	−	3.15558i	−0.889178	−	0.106800i
$874$	4.51490	+	7.82004i	0.152719	+	0.264517i
$875$	9.59344	−	30.7382i	0.324318	−	1.03914i
$876$	−14.2941	+	9.66891i	−0.482953	+	0.326682i
$877$	−30.4418	−	30.4418i	−1.02795	−	1.02795i	−0.999598	−	0.0283488i	$-0.990975\pi$
$877$	−30.4418	−	30.4418i	−1.02795	−	1.02795i	−0.0283488	−	0.999598i	$-0.509025\pi$
$878$	−2.52565	+	9.42584i	−0.0852364	+	0.318107i
$879$	−0.470210	−	6.59938i	−0.0158598	−	0.222591i
$880$	1.63578			0.0551422
$881$	2.80656	+	4.86111i	0.0945554	+	0.163775i	0.909423	−	0.415872i	$-0.136524\pi$
$881$	2.80656	+	4.86111i	0.0945554	+	0.163775i	−0.814868	+	0.579647i	$0.803190\pi$
$882$	−15.7243	−	13.9193i	−0.529465	−	0.468686i
$883$			48.7239i			1.63969i	0.572586	+	0.819844i	$0.305940\pi$
$883$			48.7239i			1.63969i	−0.572586	+	0.819844i	$0.694060\pi$
$884$	−16.7401	+	16.8433i	−0.563031	+	0.566502i
$885$	12.7199	+	11.0278i	0.427574	+	0.370697i
$886$	27.8176	+	27.8176i	0.934552	+	0.934552i
$887$	15.6708	+	9.04754i	0.526174	+	0.303787i	0.739457	−	0.673204i	$-0.235082\pi$
$887$	15.6708	+	9.04754i	0.526174	+	0.303787i	−0.213283	+	0.976990i	$0.568416\pi$
$888$	−12.9965	−	11.2676i	−0.436133	−	0.378117i
$889$	31.7675	+	20.1084i	1.06545	+	0.674413i
$890$	6.15240	+	22.9611i	0.206229	+	0.769656i
$891$	0.184550	+	8.12047i	0.00618266	+	0.272046i
$892$	−4.88471	−	18.2300i	−0.163552	−	0.610385i
$893$	21.1093	−	12.1875i	0.706396	−	0.407838i
$894$	−11.8423	+	13.6593i	−0.396067	+	0.456837i
$895$	15.2854	+	4.09570i	0.510933	+	0.136904i
$896$	1.79311	+	1.94544i	0.0599038	+	0.0649926i
$897$	7.10184	−	4.83576i	0.237124	−	0.161461i
$898$	10.8899	+	18.8619i	0.363401	+	0.629430i
$899$	21.1969	−	21.1969i	0.706958	−	0.706958i
$900$	−4.77512	−	1.91465i	−0.159171	−	0.0638218i
$901$		−	30.4259i		−	1.01363i
$902$	8.03265	−	8.03265i	0.267458	−	0.267458i
$903$	−20.5807	−	4.84904i	−0.684883	−	0.161366i
$904$	2.53790	+	9.47156i	0.0844092	+	0.315019i
$905$	5.96210	−	22.2508i	0.198187	−	0.739643i
$906$	6.33560	+	18.3215i	0.210486	+	0.608690i
$907$			2.00781i			0.0666683i	0.999444	+	0.0333342i	$0.0106126\pi$
$907$			2.00781i			0.0666683i	−0.999444	+	0.0333342i	$0.989387\pi$
$908$	−5.95359	+	1.59526i	−0.197577	+	0.0529406i
$909$	25.9775	+	10.4161i	0.861619	+	0.345479i
$910$	3.84320	+	16.8575i	0.127401	+	0.558820i
$911$			39.1948i			1.29858i	0.760540	+	0.649291i	$0.224934\pi$
$911$			39.1948i			1.29858i	−0.760540	+	0.649291i	$0.775066\pi$
$912$	0.807926	+	11.3392i	0.0267531	+	0.375478i
$913$	9.69549			0.320874
$914$	−4.67126	−	8.09086i	−0.154512	−	0.267622i
$915$	−0.437093	+	0.899179i	−0.0144499	+	0.0297259i
$916$	−29.0285	+	7.77816i	−0.959129	+	0.256998i
$917$	35.4737	+	22.4543i	1.17144	+	0.741507i
$918$	7.24767	+	33.4471i	0.239209	+	1.10392i
$919$	−5.45574			−0.179968			−0.0899842	−	0.995943i	$-0.528682\pi$
$919$	−5.45574			−0.179968			−0.0899842	+	0.995943i	$0.528682\pi$
$920$	−2.49363			−0.0822125
$921$	16.3459	+	24.1651i	0.538616	+	0.796267i
$922$	−17.7011	+	10.2197i	−0.582955	+	0.336569i
$923$	2.99765	−	0.00921381i	0.0986688	−	0.000303276i
$924$	4.13389	−	0.125744i	0.135995	−	0.00413666i
$925$	4.40779	−	16.4501i	0.144927	−	0.540876i
$926$	8.03248	+	4.63756i	0.263964	+	0.152400i
$927$	−22.2755	+	3.19048i	−0.731623	+	0.104789i
$928$	6.10678	−	1.63631i	0.200465	−	0.0537144i
$929$	42.6189	−	42.6189i	1.39828	−	1.39828i	0.593302	−	0.804980i	$-0.297824\pi$
$929$	42.6189	−	42.6189i	1.39828	−	1.39828i	0.804980	−	0.593302i	$-0.202176\pi$
$930$	−14.8476	+	1.05790i	−0.486872	+	0.0346899i
$931$	−45.1978	+	8.24120i	−1.48130	+	0.270095i
$932$	−5.04008	−	2.90989i	−0.165093	−	0.0953167i
$933$	−31.7961	−	27.5665i	−1.04096	−	0.902486i
$934$	−19.7153	+	19.7153i	−0.645106	+	0.645106i
$935$	5.38686	−	9.33032i	0.176169	−	0.305134i
$936$	10.7026	−	1.56651i	0.349826	−	0.0512029i
$937$	26.9548			0.880575			0.440287	−	0.897857i	$-0.354877\pi$
$937$	26.9548			0.880575			0.440287	+	0.897857i	$0.354877\pi$
$938$	−4.12559	−	0.168096i	−0.134705	−	0.00548852i
$939$	25.4113	−	8.78726i	0.829265	−	0.286761i
$940$			6.73126i			0.219550i
$941$	−5.51692	−	20.5894i	−0.179846	−	0.671196i	−0.995675	−	0.0929026i	$-0.970385\pi$
$941$	−5.51692	−	20.5894i	−0.179846	−	0.671196i	0.815829	−	0.578294i	$-0.196281\pi$
$942$	6.43407	−	13.2360i	0.209633	−	0.431253i
$943$	−12.2452	+	12.2452i	−0.398758	+	0.398758i
$944$	−3.79190	−	3.79190i	−0.123416	−	0.123416i
$945$	23.3989	+	8.56593i	0.761168	+	0.278650i
$946$	3.60631	−	2.08211i	0.117251	−	0.0676951i
$947$	−27.4435	+	7.35345i	−0.891793	+	0.238955i	−0.675488	−	0.737371i	$-0.736067\pi$
$947$	−27.4435	+	7.35345i	−0.891793	+	0.238955i	−0.216304	+	0.976326i	$0.569400\pi$
$948$	−8.88728	+	10.2509i	−0.288646	+	0.332934i
$949$	35.9234	−	0.110417i	1.16612	−	0.00358429i
$950$	−9.74740	+	5.62766i	−0.316247	+	0.182585i
$951$	20.2001	−	41.5552i	0.655033	−	1.34752i
$952$	17.0016	−	3.82111i	0.551024	−	0.123843i
$953$	2.18676	−	3.78759i	0.0708363	−	0.122692i	−0.828432	−	0.560090i	$-0.810767\pi$
$953$	2.18676	−	3.78759i	0.0708363	−	0.122692i	0.899268	+	0.437398i	$0.144100\pi$
$954$	−8.31122	+	11.0900i	−0.269086	+	0.359053i
$955$	2.64215	−	9.86066i	0.0854981	−	0.319083i
$956$	−1.59496	+	5.95247i	−0.0515847	+	0.192517i
$957$	4.32062	−	8.88829i	0.139666	−	0.287318i
$958$	10.7682	−	18.6511i	0.347905	−	0.602589i
$959$	17.1997	−	3.86565i	0.555408	−	0.124828i
$960$	−2.82341	−	1.37247i	−0.0911252	−	0.0442962i
$961$	−7.37658	+	4.25887i	−0.237954	+	0.137383i
$962$	9.37362	+	34.5576i	0.302218	+	1.11418i
$963$	−10.5068	−	13.3754i	−0.338578	−	0.431015i
$964$	7.44625	−	1.99522i	0.239828	−	0.0642616i
$965$	9.42331	−	5.44055i	0.303347	−	0.175138i
$966$	−6.30182	+	0.191687i	−0.202758	+	0.00616742i
$967$	28.0679	+	28.0679i	0.902603	+	0.902603i	0.995661	−	0.0930581i	$-0.0296642\pi$
$967$	28.0679	+	28.0679i	0.902603	+	0.902603i	−0.0930581	+	0.995661i	$0.529664\pi$
$968$	7.20222	−	7.20222i	0.231488	−	0.231488i
$969$	67.3382	+	32.7333i	2.16321	+	1.05154i
$970$	−4.13767	−	15.4420i	−0.132853	−	0.495813i
$971$		−	1.51892i		−	0.0487444i	−0.999703	−	0.0243722i	$-0.992241\pi$
$971$		−	1.51892i		−	0.0487444i	0.999703	−	0.0243722i	$-0.00775868\pi$
$972$	6.49477	−	14.1710i	0.208320	−	0.454536i
$973$	−60.3656	−	2.45958i	−1.93523	−	0.0788505i
$974$	−7.98018			−0.255702
$975$	6.02760	+	8.85219i	0.193038	+	0.283497i
$976$	0.159236	−	0.275805i	0.00509703	−	0.00882831i
$977$	23.7210	−	23.7210i	0.758904	−	0.758904i	−0.217219	−	0.976123i	$-0.569699\pi$
$977$	23.7210	−	23.7210i	0.758904	−	0.758904i	0.976123	+	0.217219i	$0.0696987\pi$
$978$	19.0784	−	22.0056i	0.610059	−	0.703663i
$979$	−10.2507	−	5.91826i	−0.327614	−	0.189148i
$980$	4.26986	−	11.9473i	0.136396	−	0.381643i
$981$	−17.0557	−	2.04858i	−0.544546	−	0.0654060i
$982$	−1.62557	+	1.62557i	−0.0518741	+	0.0518741i
$983$	40.4506	−	10.8387i	1.29018	−	0.345701i	0.452448	−	0.891791i	$-0.350551\pi$
$983$	40.4506	−	10.8387i	1.29018	−	0.345701i	0.837727	+	0.546089i	$0.183884\pi$
$984$	−20.6042	+	7.12498i	−0.656839	+	0.227136i
$985$	−0.211386	−	0.122044i	−0.00673533	−	0.00388864i
$986$	10.7772	−	40.2210i	0.343215	−	1.28090i
$987$	0.517436	+	17.0110i	0.0164702	+	0.541467i
$988$	11.7691	−	20.5301i	0.374424	−	0.653150i
$989$	−5.49756	+	3.17402i	−0.174812	+	0.100928i
$990$	−4.51217	+	1.92935i	−0.143406	+	0.0613187i
$991$	−38.5173			−1.22354			−0.611771	−	0.791035i	$-0.709542\pi$
$991$	−38.5173			−1.22354			−0.611771	+	0.791035i	$0.709542\pi$
$992$	4.74155			0.150544
$993$	−18.3342	+	12.4018i	−0.581819	+	0.393558i
$994$	−1.85863	−	1.17648i	−0.0589520	−	0.0373158i
$995$	27.0399	−	7.24532i	0.857222	−	0.229692i
$996$	−16.7347	−	8.13480i	−0.530260	−	0.257761i
$997$	4.48797	+	7.77340i	0.142136	+	0.246186i	0.928301	−	0.371831i	$-0.121270\pi$
$997$	4.48797	+	7.77340i	0.142136	+	0.246186i	−0.786165	+	0.618017i	$0.787936\pi$
$998$	−16.6438			−0.526851
$999$	49.1394	+	15.7519i	1.55470	+	0.498369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.11.8	✓	152
3.2	odd	2	inner	546.2.bw.a.11.27	yes	152
7.2	even	3		546.2.ch.a.401.5	yes	152
13.6	odd	12		546.2.ch.a.305.37	yes	152
21.2	odd	6		546.2.ch.a.401.37	yes	152
39.32	even	12		546.2.ch.a.305.5	yes	152
91.58	odd	12	inner	546.2.bw.a.149.27	yes	152
273.149	even	12	inner	546.2.bw.a.149.8	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.8	✓	152	1.1	even	1	trivial
546.2.bw.a.11.27	yes	152	3.2	odd	2	inner
546.2.bw.a.149.8	yes	152	273.149	even	12	inner
546.2.bw.a.149.27	yes	152	91.58	odd	12	inner
546.2.ch.a.305.5	yes	152	39.32	even	12
546.2.ch.a.305.37	yes	152	13.6	odd	12
546.2.ch.a.401.5	yes	152	7.2	even	3
546.2.ch.a.401.37	yes	152	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.328251 + 1.70066i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.75073 + 0.469106i) q^{5} +(1.72767 - 0.123098i) q^{6} +(1.22850 + 2.34324i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.78450 - 1.11649i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.328251 + 1.70066i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.75073 + 0.469106i) q^{5} +(1.72767 - 0.123098i) q^{6} +(1.22850 + 2.34324i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.78450 - 1.11649i) q^{9} -1.81249i q^{10} +(0.638169 + 0.638169i) q^{11} +(-0.566057 - 1.63694i) q^{12} +(-0.922476 + 3.48555i) q^{13} +(1.94544 - 1.79311i) q^{14} +(-1.37247 + 2.82341i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.29314 - 5.70389i) q^{17} +(-0.357762 + 2.97859i) q^{18} +(4.64094 + 4.64094i) q^{19} +(-1.75073 + 0.469106i) q^{20} +(-4.38832 + 1.32009i) q^{21} +(0.451253 - 0.781594i) q^{22} +(-0.687903 + 1.19148i) q^{23} +(-1.43466 + 0.970441i) q^{24} +(-1.48514 - 0.857446i) q^{25} +(3.60553 - 0.0110823i) q^{26} +(2.81278 - 4.36901i) q^{27} +(-2.23553 - 1.41506i) q^{28} +(-5.47519 + 3.16110i) q^{29} +(3.08243 + 0.594950i) q^{30} +(-4.57998 + 1.22720i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.29479 + 0.875830i) q^{33} +(-4.65721 + 4.65721i) q^{34} +(1.05154 + 4.67868i) q^{35} +(2.96969 - 0.425345i) q^{36} +(2.57030 + 9.59250i) q^{37} +(3.28164 - 5.68397i) q^{38} +(-5.62493 - 2.71295i) q^{39} +(0.906243 + 1.56966i) q^{40} +(12.1581 + 3.25776i) q^{41} +(2.41089 + 3.89713i) q^{42} +(3.99588 + 2.30702i) q^{43} +(-0.871755 - 0.233586i) q^{44} +(-4.35116 - 3.26089i) q^{45} +(1.32893 + 0.356085i) q^{46} +(0.961209 - 3.58728i) q^{47} +(1.30869 + 1.13460i) q^{48} +(-3.98158 + 5.75734i) q^{49} +(-0.443847 + 1.65646i) q^{50} +(10.7814 - 3.72822i) q^{51} +(-0.943886 - 3.47981i) q^{52} +(4.00068 + 2.30979i) q^{53} +(-4.94814 - 1.58616i) q^{54} +(0.817891 + 1.41663i) q^{55} +(-0.788244 + 2.52560i) q^{56} +(-9.41607 + 6.36928i) q^{57} +(4.47047 + 4.47047i) q^{58} +(1.38793 - 5.17983i) q^{59} +(-0.223113 - 3.13138i) q^{60} +0.318472 q^{61} +(2.37077 + 4.10630i) q^{62} +(-0.804555 - 7.89637i) q^{63} +1.00000i q^{64} +(-3.25010 + 5.66950i) q^{65} +(1.18110 + 1.02399i) q^{66} +(-1.10352 - 1.10352i) q^{67} +(5.70389 + 3.29314i) q^{68} +(-1.80050 - 1.56099i) q^{69} +(4.24710 - 2.22664i) q^{70} +(-0.215183 - 0.803072i) q^{71} +(-1.17946 - 2.75842i) q^{72} +(-2.57872 - 9.62392i) q^{73} +(8.60040 - 4.96544i) q^{74} +(1.94572 - 2.24426i) q^{75} +(-6.33965 - 1.69870i) q^{76} +(-0.711396 + 2.27937i) q^{77} +(-1.16467 + 6.13543i) q^{78} +(-3.91647 - 6.78352i) q^{79} +(1.28162 - 1.28162i) q^{80} +(6.50691 + 6.21772i) q^{81} -12.5870i q^{82} +(7.59633 - 7.59633i) q^{83} +(3.14035 - 3.33739i) q^{84} +(-3.08967 - 11.5308i) q^{85} +(1.19420 - 4.45683i) q^{86} +(-3.57873 - 10.3491i) q^{87} +0.902507i q^{88} +(-12.6683 + 3.39445i) q^{89} +(-2.02362 + 5.04687i) q^{90} +(-9.30075 + 2.12040i) q^{91} -1.37581i q^{92} +(-0.583674 - 8.19183i) q^{93} -3.71383 q^{94} +(5.94793 + 10.3021i) q^{95} +(0.757230 - 1.55776i) q^{96} +(8.51978 - 2.28287i) q^{97} +(6.59168 + 2.35580i) q^{98} +(-1.06448 - 2.48949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

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