LMFDB - Embedded newform 546.2.bw.a.527.24

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			527.24
Character	$\chi$	$=$	546.527
Dual form			546.2.bw.a.431.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-1.23685 + 1.21251i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.473766 - 1.76812i) q^{5} +(-1.50853 + 0.851078i) q^{6} +(-0.491196 - 2.59976i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.0596151 - 2.99941i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-1.23685 + 1.21251i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.473766 - 1.76812i) q^{5} +(-1.50853 + 0.851078i) q^{6} +(-0.491196 - 2.59976i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.0596151 - 2.99941i) q^{9} -1.83049i q^{10} +(-2.98053 - 2.98053i) q^{11} +(-1.67740 + 0.431642i) q^{12} +(-3.58546 - 0.380134i) q^{13} +(0.198407 - 2.63830i) q^{14} +(2.72985 + 1.61246i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.234854 - 0.406780i) q^{17} +(0.833888 - 2.88178i) q^{18} +(0.932900 + 0.932900i) q^{19} +(0.473766 - 1.76812i) q^{20} +(3.75978 + 2.61993i) q^{21} +(-2.10755 - 3.65038i) q^{22} +(-4.27741 - 7.40870i) q^{23} +(-1.73197 - 0.0172103i) q^{24} +(1.42833 - 0.824649i) q^{25} +(-3.36490 - 1.29517i) q^{26} +(3.56309 + 3.78211i) q^{27} +(0.874489 - 2.49705i) q^{28} +(2.99435 + 1.72879i) q^{29} +(2.21950 + 2.26405i) q^{30} +(-1.05972 + 3.95493i) q^{31} +(0.258819 + 0.965926i) q^{32} +(7.30041 + 0.0725430i) q^{33} +(0.332134 - 0.332134i) q^{34} +(-4.36397 + 2.10017i) q^{35} +(1.55133 - 2.56776i) q^{36} +(6.47637 + 1.73534i) q^{37} +(0.659660 + 1.14256i) q^{38} +(4.89560 - 3.87725i) q^{39} +(0.915246 - 1.58525i) q^{40} +(-0.956974 - 3.57148i) q^{41} +(2.95358 + 3.50376i) q^{42} +(10.0899 - 5.82539i) q^{43} +(-1.09095 - 4.07148i) q^{44} +(-5.33156 + 1.31561i) q^{45} +(-2.21415 - 8.26333i) q^{46} +(-9.41494 + 2.52273i) q^{47} +(-1.66850 - 0.464889i) q^{48} +(-6.51745 + 2.55398i) q^{49} +(1.59310 - 0.426870i) q^{50} +(0.202746 + 0.787892i) q^{51} +(-2.91503 - 2.12193i) q^{52} +(2.77495 - 1.60212i) q^{53} +(2.46280 + 4.57544i) q^{54} +(-3.85785 + 6.68200i) q^{55} +(1.49098 - 2.18563i) q^{56} +(-2.28502 - 0.0227058i) q^{57} +(2.44487 + 2.44487i) q^{58} +(-7.93039 + 2.12494i) q^{59} +(1.55789 + 2.76135i) q^{60} +10.8980 q^{61} +(-2.04722 + 3.54590i) q^{62} +(-7.82701 + 1.31831i) q^{63} +1.00000i q^{64} +(1.02655 + 6.51961i) q^{65} +(7.03288 + 1.95956i) q^{66} +(-0.303501 - 0.303501i) q^{67} +(0.406780 - 0.234854i) q^{68} +(14.2737 + 3.97705i) q^{69} +(-4.75883 + 0.899131i) q^{70} +(-7.08791 - 1.89920i) q^{71} +(2.16306 - 2.07875i) q^{72} +(-5.97838 - 1.60190i) q^{73} +(5.80655 + 3.35242i) q^{74} +(-0.766741 + 2.75185i) q^{75} +(0.341465 + 1.27436i) q^{76} +(-6.28462 + 9.21266i) q^{77} +(5.73230 - 2.47806i) q^{78} +(-6.79835 + 11.7751i) q^{79} +(1.29435 - 1.29435i) q^{80} +(-8.99289 - 0.357620i) q^{81} -3.69746i q^{82} +(2.80080 - 2.80080i) q^{83} +(1.94610 + 4.14882i) q^{84} +(-0.830501 - 0.222532i) q^{85} +(11.2538 - 3.01545i) q^{86} +(-5.79975 + 1.49243i) q^{87} -4.21510i q^{88} +(1.52115 - 5.67702i) q^{89} +(-5.49039 - 0.109125i) q^{90} +(0.772908 + 9.50803i) q^{91} -8.55483i q^{92} +(-3.48470 - 6.17660i) q^{93} -9.74707 q^{94} +(1.20750 - 2.09145i) q^{95} +(-1.49132 - 0.880887i) q^{96} +(0.697569 - 2.60336i) q^{97} +(-6.95639 + 0.780115i) q^{98} +(-9.11750 + 8.76213i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−1.23685	+	1.21251i	−0.714098	+	0.700046i
$3$	−1.23685	+	1.21251i	−0.714098	+	0.700046i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.473766	−	1.76812i	−0.211875	−	0.790727i	−0.987243	−	0.159218i	$-0.949103\pi$
$5$	−0.473766	−	1.76812i	−0.211875	−	0.790727i	0.775369	−	0.631509i	$-0.217564\pi$
$6$	−1.50853	+	0.851078i	−0.615855	+	0.347451i
$7$	−0.491196	−	2.59976i	−0.185655	−	0.982615i
$7$	−0.491196	−	2.59976i	−0.185655	−	0.982615i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.0596151	−	2.99941i	0.0198717	−	0.999803i
$10$		−	1.83049i		−	0.578852i
$11$	−2.98053	−	2.98053i	−0.898663	−	0.898663i	0.0966553	−	0.995318i	$-0.469186\pi$
$11$	−2.98053	−	2.98053i	−0.898663	−	0.898663i	−0.995318	+	0.0966553i	$0.969186\pi$
$12$	−1.67740	+	0.431642i	−0.484225	+	0.124604i
$13$	−3.58546	−	0.380134i	−0.994427	−	0.105430i
$13$	−3.58546	−	0.380134i	−0.994427	−	0.105430i
$14$	0.198407	−	2.63830i	0.0530265	−	0.705116i
$15$	2.72985	+	1.61246i	0.704845	+	0.416335i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.234854	−	0.406780i	0.0569606	−	0.0986586i	−0.836139	−	0.548518i	$-0.815192\pi$
$17$	0.234854	−	0.406780i	0.0569606	−	0.0986586i	0.893100	+	0.449859i	$0.148526\pi$
$18$	0.833888	−	2.88178i	0.196549	−	0.679241i
$19$	0.932900	+	0.932900i	0.214022	+	0.214022i	0.805973	−	0.591952i	$-0.201642\pi$
$19$	0.932900	+	0.932900i	0.214022	+	0.214022i	−0.591952	+	0.805973i	$0.701642\pi$
$20$	0.473766	−	1.76812i	0.105937	−	0.395364i
$21$	3.75978	+	2.61993i	0.820451	+	0.571717i
$22$	−2.10755	−	3.65038i	−0.449331	−	0.778265i
$23$	−4.27741	−	7.40870i	−0.891902	−	1.54482i	−0.837592	−	0.546296i	$-0.816037\pi$
$23$	−4.27741	−	7.40870i	−0.891902	−	1.54482i	−0.0543100	−	0.998524i	$-0.517296\pi$
$24$	−1.73197	−	0.0172103i	−0.353536	−	0.00351303i
$25$	1.42833	−	0.824649i	0.285667	−	0.164930i
$26$	−3.36490	−	1.29517i	−0.659911	−	0.254003i
$27$	3.56309	+	3.78211i	0.685717	+	0.727868i
$28$	0.874489	−	2.49705i	0.165263	−	0.471898i
$29$	2.99435	+	1.72879i	0.556036	+	0.321028i	0.751553	−	0.659673i	$-0.229305\pi$
$29$	2.99435	+	1.72879i	0.556036	+	0.321028i	−0.195517	+	0.980700i	$0.562638\pi$
$30$	2.21950	+	2.26405i	0.405223	+	0.413357i
$31$	−1.05972	+	3.95493i	−0.190332	+	0.710327i	0.803094	+	0.595852i	$0.203185\pi$
$31$	−1.05972	+	3.95493i	−0.190332	+	0.710327i	−0.993426	+	0.114475i	$0.963481\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	7.30041	+	0.0725430i	1.27084	+	0.0126281i
$34$	0.332134	−	0.332134i	0.0569606	−	0.0569606i
$35$	−4.36397	+	2.10017i	−0.737645	+	0.354994i
$36$	1.55133	−	2.56776i	0.258555	−	0.427959i
$37$	6.47637	+	1.73534i	1.06471	+	0.285288i	0.748317	−	0.663341i	$-0.230862\pi$
$37$	6.47637	+	1.73534i	1.06471	+	0.285288i	0.316391	+	0.948629i	$0.397529\pi$
$38$	0.659660	+	1.14256i	0.107011	+	0.185348i
$39$	4.89560	−	3.87725i	0.783924	−	0.620857i
$40$	0.915246	−	1.58525i	0.144713	−	0.250650i
$41$	−0.956974	−	3.57148i	−0.149454	−	0.557771i	−0.999517	−	0.0310888i	$-0.990103\pi$
$41$	−0.956974	−	3.57148i	−0.149454	−	0.557771i	0.850062	−	0.526682i	$-0.176564\pi$
$42$	2.95358	+	3.50376i	0.455747	+	0.540643i
$43$	10.0899	−	5.82539i	1.53869	−	0.888364i	0.539776	−	0.841808i	$-0.318509\pi$
$43$	10.0899	−	5.82539i	1.53869	−	0.888364i	0.998916	−	0.0465558i	$-0.0148245\pi$
$44$	−1.09095	−	4.07148i	−0.164467	−	0.613798i
$45$	−5.33156	+	1.31561i	−0.794781	+	0.196120i
$46$	−2.21415	−	8.26333i	−0.326459	−	1.21836i
$47$	−9.41494	+	2.52273i	−1.37331	+	0.367977i	−0.868687	−	0.495362i	$-0.835035\pi$
$47$	−9.41494	+	2.52273i	−1.37331	+	0.367977i	−0.504624	+	0.863339i	$0.668369\pi$
$48$	−1.66850	−	0.464889i	−0.240827	−	0.0671010i
$49$	−6.51745	+	2.55398i	−0.931065	+	0.364854i
$50$	1.59310	−	0.426870i	0.225298	−	0.0603685i
$51$	0.202746	+	0.787892i	0.0283901	+	0.110327i
$52$	−2.91503	−	2.12193i	−0.404242	−	0.294259i
$53$	2.77495	−	1.60212i	0.381168	−	0.220068i	−0.297158	−	0.954828i	$-0.596039\pi$
$53$	2.77495	−	1.60212i	0.381168	−	0.220068i	0.678327	+	0.734761i	$0.262705\pi$
$54$	2.46280	+	4.57544i	0.335144	+	0.622638i
$55$	−3.85785	+	6.68200i	−0.520193	+	0.901001i
$56$	1.49098	−	2.18563i	0.199240	−	0.292067i
$57$	−2.28502	−	0.0227058i	−0.302658	−	0.00300746i
$58$	2.44487	+	2.44487i	0.321028	+	0.321028i
$59$	−7.93039	+	2.12494i	−1.03245	+	0.276644i	−0.734981	−	0.678088i	$-0.762809\pi$
$59$	−7.93039	+	2.12494i	−1.03245	+	0.276644i	−0.297468	+	0.954732i	$0.596142\pi$
$60$	1.55789	+	2.76135i	0.201123	+	0.356489i
$61$	10.8980			1.39535			0.697675	−	0.716414i	$-0.254218\pi$
$61$	10.8980			1.39535			0.697675	+	0.716414i	$0.254218\pi$
$62$	−2.04722	+	3.54590i	−0.259998	+	0.450329i
$63$	−7.82701	+	1.31831i	−0.986110	+	0.166092i
$64$			1.00000i			0.125000i
$65$	1.02655	+	6.51961i	0.127327	+	0.808658i
$66$	7.03288	+	1.95956i	0.865687	+	0.241205i
$67$	−0.303501	−	0.303501i	−0.0370786	−	0.0370786i	0.688324	−	0.725403i	$-0.258347\pi$
$67$	−0.303501	−	0.303501i	−0.0370786	−	0.0370786i	−0.725403	+	0.688324i	$0.758347\pi$
$68$	0.406780	−	0.234854i	0.0493293	−	0.0284803i
$69$	14.2737	+	3.97705i	1.71835	+	0.478780i
$70$	−4.75883	+	0.899131i	−0.568789	+	0.107467i
$71$	−7.08791	−	1.89920i	−0.841181	−	0.225394i	−0.187595	−	0.982246i	$-0.560069\pi$
$71$	−7.08791	−	1.89920i	−0.841181	−	0.225394i	−0.653585	+	0.756853i	$0.726736\pi$
$72$	2.16306	−	2.07875i	0.254919	−	0.244983i
$73$	−5.97838	−	1.60190i	−0.699716	−	0.187488i	−0.108613	−	0.994084i	$-0.534641\pi$
$73$	−5.97838	−	1.60190i	−0.699716	−	0.187488i	−0.591103	+	0.806596i	$0.701307\pi$
$74$	5.80655	+	3.35242i	0.674998	+	0.389710i
$75$	−0.766741	+	2.75185i	−0.0885357	+	0.317756i
$76$	0.341465	+	1.27436i	0.0391687	+	0.146180i
$77$	−6.28462	+	9.21266i	−0.716198	+	1.04988i
$78$	5.73230	−	2.47806i	0.649055	−	0.280585i
$79$	−6.79835	+	11.7751i	−0.764874	+	1.32480i	0.175440	+	0.984490i	$0.443865\pi$
$79$	−6.79835	+	11.7751i	−0.764874	+	1.32480i	−0.940313	+	0.340310i	$0.889468\pi$
$80$	1.29435	−	1.29435i	0.144713	−	0.144713i
$81$	−8.99289	−	0.357620i	−0.999210	−	0.0397356i
$82$		−	3.69746i		−	0.408317i
$83$	2.80080	−	2.80080i	0.307428	−	0.307428i	−0.536483	−	0.843911i	$-0.680247\pi$
$83$	2.80080	−	2.80080i	0.307428	−	0.307428i	0.843911	+	0.536483i	$0.180247\pi$
$84$	1.94610	+	4.14882i	0.212337	+	0.452673i
$85$	−0.830501	−	0.222532i	−0.0900805	−	0.0241370i
$86$	11.2538	−	3.01545i	1.21353	−	0.325164i
$87$	−5.79975	+	1.49243i	−0.621798	+	0.160006i
$88$		−	4.21510i		−	0.449331i
$89$	1.52115	−	5.67702i	0.161242	−	0.601763i	−0.837248	−	0.546824i	$-0.815837\pi$
$89$	1.52115	−	5.67702i	0.161242	−	0.601763i	0.998490	−	0.0549394i	$-0.0174966\pi$
$90$	−5.49039	−	0.109125i	−0.578738	−	0.0115028i
$91$	0.772908	+	9.50803i	0.0810228	+	0.996712i
$92$		−	8.55483i		−	0.891902i
$93$	−3.48470	−	6.17660i	−0.361346	−	0.640484i
$94$	−9.74707			−1.00533
$95$	1.20750	−	2.09145i	0.123887	−	0.214579i
$96$	−1.49132	−	0.880887i	−0.152207	−	0.0899052i
$97$	0.697569	−	2.60336i	0.0708274	−	0.264331i	−0.921427	−	0.388550i	$-0.872976\pi$
$97$	0.697569	−	2.60336i	0.0708274	−	0.264331i	0.992255	+	0.124219i	$0.0396426\pi$
$98$	−6.95639	+	0.780115i	−0.702702	+	0.0788035i
$99$	−9.11750	+	8.76213i	−0.916343	+	0.880627i
$100$	1.64930			0.164930
$101$	13.2038			1.31383			0.656914	−	0.753966i	$-0.271862\pi$
$101$	13.2038			1.31383			0.656914	+	0.753966i	$0.271862\pi$
$102$	−0.00808381	+	0.813519i	−0.000800417	+	0.0805504i
$103$	−4.44902	−	2.56865i	−0.438375	−	0.253096i	0.264533	−	0.964377i	$-0.414782\pi$
$103$	−4.44902	−	2.56865i	−0.438375	−	0.253096i	−0.702908	+	0.711281i	$0.748116\pi$
$104$	−2.26651	−	2.80410i	−0.222249	−	0.274964i
$105$	2.85110	−	7.88898i	0.278239	−	0.769885i
$106$	3.09505	−	0.829317i	0.300618	−	0.0805504i
$107$	5.62240	−	3.24610i	0.543538	−	0.313812i	−0.202973	−	0.979184i	$-0.565061\pi$
$107$	5.62240	−	3.24610i	0.543538	−	0.313812i	0.746512	+	0.665372i	$0.231727\pi$
$108$	1.19467	+	5.05695i	0.114957	+	0.486605i
$109$	−2.58830	+	9.65967i	−0.247914	+	0.925229i	0.723982	+	0.689819i	$0.242310\pi$
$109$	−2.58830	+	9.65967i	−0.247914	+	0.925229i	−0.971896	+	0.235410i	$0.924357\pi$
$110$	−5.45583	+	5.45583i	−0.520193	+	0.520193i
$111$	−10.1144	+	5.70633i	−0.960021	+	0.541621i
$112$	2.00586	−	1.72527i	0.189536	−	0.163022i
$113$	14.6164	−	8.43876i	1.37499	−	0.793852i	0.383441	−	0.923565i	$-0.374739\pi$
$113$	14.6164	−	8.43876i	1.37499	−	0.793852i	0.991552	+	0.129713i	$0.0414057\pi$
$114$	−2.20128	−	0.613338i	−0.206169	−	0.0574443i
$115$	−11.0730	+	11.0730i	−1.03256	+	1.03256i
$116$	1.72879	+	2.99435i	0.160514	+	0.278018i
$117$	−1.35392	+	10.7316i	−0.125170	+	0.992135i
$118$	−8.21014			−0.755805
$119$	−1.17289	−	0.410755i	−0.107518	−	0.0376539i
$120$	0.790117	+	3.07048i	0.0721275	+	0.280295i
$121$			6.76708i			0.615189i
$122$	10.5267	+	2.82062i	0.953042	+	0.255367i
$123$	5.51411	+	3.25705i	0.497190	+	0.293678i
$124$	−2.89521	+	2.89521i	−0.259998	+	0.259998i
$125$	−8.60654	−	8.60654i	−0.769793	−	0.769793i
$126$	−7.90151	−	0.752386i	−0.703923	−	0.0670278i
$127$	1.86064	+	1.07424i	0.165105	+	0.0953236i	0.580276	−	0.814420i	$-0.302945\pi$
$127$	1.86064	+	1.07424i	0.165105	+	0.0953236i	−0.415171	+	0.909744i	$0.636278\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−5.41633	+	19.4393i	−0.476881	+	1.71153i
$130$	−0.695832	+	6.56315i	−0.0610285	+	0.575626i
$131$	3.73471	+	2.15623i	0.326303	+	0.188391i	0.654199	−	0.756323i	$-0.273006\pi$
$131$	3.73471	+	2.15623i	0.326303	+	0.188391i	−0.327896	+	0.944714i	$0.606339\pi$
$132$	6.28607	+	3.71303i	0.547132	+	0.323178i
$133$	1.96707	−	2.88355i	0.170567	−	0.250035i
$134$	−0.214608	−	0.371712i	−0.0185393	−	0.0321110i
$135$	4.99916	−	8.09181i	0.430259	−	0.696432i
$136$	0.453704	−	0.121570i	0.0389048	−	0.0104245i
$137$	−10.8780	+	2.91475i	−0.929369	+	0.249024i	−0.691585	−	0.722295i	$-0.743087\pi$
$137$	−10.8780	+	2.91475i	−0.929369	+	0.249024i	−0.237783	+	0.971318i	$0.576421\pi$
$138$	12.7580	+	7.53584i	1.08603	+	0.641493i
$139$	−11.4474	−	19.8274i	−0.970954	−	1.68174i	−0.692688	−	0.721237i	$-0.743574\pi$
$139$	−11.4474	−	19.8274i	−0.970954	−	1.68174i	−0.278266	−	0.960504i	$-0.589760\pi$
$140$	−4.82939	−	0.363182i	−0.408158	−	0.0306945i
$141$	8.58607	−	14.5360i	0.723077	−	1.22415i
$142$	−6.35485	−	3.66897i	−0.533287	−	0.307893i
$143$	9.55355	+	11.8195i	0.798908	+	0.988400i
$144$	2.62737	−	1.44808i	0.218948	−	0.120673i
$145$	1.63808	−	6.11340i	0.136035	−	0.507691i
$146$	−5.36006	−	3.09463i	−0.443602	−	0.256114i
$147$	4.96440	−	11.0614i	0.409457	−	0.912330i
$148$	4.74103	+	4.74103i	0.389710	+	0.389710i
$149$	−5.57469	+	5.57469i	−0.456696	+	0.456696i	−0.897569	−	0.440873i	$-0.854669\pi$
$149$	−5.57469	+	5.57469i	−0.456696	+	0.456696i	0.440873	+	0.897569i	$0.354669\pi$
$150$	−1.45285	+	2.45963i	−0.118624	+	0.200828i
$151$	9.60978	+	2.57493i	0.782033	+	0.209545i	0.627681	−	0.778471i	$-0.284004\pi$
$151$	9.60978	+	2.57493i	0.782033	+	0.209545i	0.154352	+	0.988016i	$0.450671\pi$
$152$			1.31932i			0.107011i
$153$	−1.20610	−	0.728674i	−0.0975072	−	0.0589098i
$154$	−8.45488	+	7.27217i	−0.681314	+	0.586008i
$155$	7.49486			0.602001
$156$	6.17834	−	0.909995i	0.494663	−	0.0728579i
$157$	5.91797	+	10.2502i	0.472305	+	0.818057i	0.999498	−	0.0316890i	$-0.0100886\pi$
$157$	5.91797	+	10.2502i	0.472305	+	0.818057i	−0.527192	+	0.849746i	$0.676755\pi$
$158$	−9.61431	+	9.61431i	−0.764874	+	0.764874i
$159$	−1.48961	+	5.34625i	−0.118134	+	0.423985i
$160$	1.58525	−	0.915246i	0.125325	−	0.0723566i
$161$	−17.1597	+	14.7594i	−1.35238	+	1.16320i
$162$	−8.59391	−	2.67297i	−0.675201	−	0.210008i
$163$	10.8440	−	10.8440i	0.849365	−	0.849365i	−0.140688	−	0.990054i	$-0.544932\pi$
$163$	10.8440	−	10.8440i	0.849365	−	0.849365i	0.990054	+	0.140688i	$0.0449316\pi$
$164$	0.956974	−	3.57148i	0.0747271	−	0.278885i
$165$	−3.33042	−	12.9424i	−0.259273	−	1.00756i
$166$	3.43027	−	1.98047i	0.266241	−	0.153714i
$167$	19.4502	−	5.21167i	1.50510	−	0.403291i	0.590297	−	0.807186i	$-0.299011\pi$
$167$	19.4502	−	5.21167i	1.50510	−	0.403291i	0.914805	+	0.403895i	$0.132344\pi$
$168$	0.805993	+	4.51114i	0.0621837	+	0.348042i
$169$	12.7110	+	2.72591i	0.977769	+	0.209685i
$170$	−0.744607	−	0.429899i	−0.0571088	−	0.0329718i
$171$	2.85376	−	2.74253i	0.218233	−	0.209727i
$172$	11.6508			0.888364
$173$	20.1644			1.53307			0.766534	−	0.642204i	$-0.221980\pi$
$173$	20.1644			1.53307			0.766534	+	0.642204i	$0.221980\pi$
$174$	−5.98840	−	0.0595057i	−0.453979	−	0.00451112i
$175$	−2.84548	−	3.30825i	−0.215098	−	0.250081i
$176$	1.09095	−	4.07148i	0.0822333	−	0.306899i
$177$	7.23221	−	12.2440i	0.543606	−	0.920312i
$178$	2.93864	−	5.08988i	0.220261	−	0.381503i
$179$	−5.50725			−0.411631			−0.205816	−	0.978591i	$-0.565985\pi$
$179$	−5.50725			−0.411631			−0.205816	+	0.978591i	$0.565985\pi$
$180$	−5.27507	−	1.52642i	−0.393180	−	0.113773i
$181$		−	16.1390i		−	1.19960i	−0.800148	−	0.599802i	$-0.795246\pi$
$181$		−	16.1390i		−	1.19960i	0.800148	−	0.599802i	$-0.204754\pi$
$182$	−1.71429	+	9.38409i	−0.127071	+	0.695595i
$183$	−13.4793	+	13.2140i	−0.996417	+	0.976809i
$184$	2.21415	−	8.26333i	0.163229	−	0.609181i
$185$		−	12.2731i		−	0.902339i
$186$	−1.76734	−	6.86805i	−0.129587	−	0.503590i
$187$	−1.91241	+	0.512428i	−0.139849	+	0.0374725i
$188$	−9.41494	−	2.52273i	−0.686655	−	0.183989i
$189$	8.08239	−	11.1209i	0.587907	−	0.808928i
$190$	1.70767	−	1.70767i	0.123887	−	0.123887i
$191$		−	0.559082i		−	0.0404538i	−0.999795	−	0.0202269i	$-0.993561\pi$
$191$		−	0.559082i		−	0.0404538i	0.999795	−	0.0202269i	$-0.00643885\pi$
$192$	−1.21251	−	1.23685i	−0.0875057	−	0.0892622i
$193$	9.44038	−	9.44038i	0.679534	−	0.679534i	−0.280361	−	0.959895i	$-0.590454\pi$
$193$	9.44038	−	9.44038i	0.679534	−	0.679534i	0.959895	+	0.280361i	$0.0904542\pi$
$194$	1.34760	−	2.33411i	0.0967520	−	0.167579i
$195$	−9.17481	−	6.81910i	−0.657022	−	0.488326i
$196$	−6.92127	−	1.04691i	−0.494376	−	0.0747796i
$197$	0.0908854	+	0.339189i	0.00647532	+	0.0241662i	0.969088	−	0.246716i	$-0.0793514\pi$
$197$	0.0908854	+	0.339189i	0.00647532	+	0.0241662i	−0.962613	+	0.270882i	$0.912685\pi$
$198$	−11.0746	+	6.10379i	−0.787040	+	0.433777i
$199$	15.3630	+	8.86980i	1.08905	+	0.628764i	0.933324	−	0.359036i	$-0.116895\pi$
$199$	15.3630	+	8.86980i	1.08905	+	0.628764i	0.155727	+	0.987800i	$0.450228\pi$
$200$	1.59310	+	0.426870i	0.112649	+	0.0301843i
$201$	0.743387	+	0.00738691i	0.0524345	+	0.000521033i
$202$	12.7539	+	3.41740i	0.897361	+	0.240447i
$203$	3.02361	−	8.63374i	0.212216	−	0.605970i
$204$	−0.218363	+	0.783707i	−0.0152884	+	0.0548705i
$205$	−5.86142	+	3.38409i	−0.409379	+	0.236355i
$206$	−3.63261	−	3.63261i	−0.253096	−	0.253096i
$207$	−22.4767	+	12.3880i	−1.56224	+	0.861028i
$208$	−1.46352	−	3.29516i	−0.101477	−	0.228478i
$209$		−	5.56106i		−	0.384667i
$210$	4.79577	−	6.88225i	0.330940	−	0.474920i
$211$	−5.30276	+	9.18465i	−0.365057	+	0.632297i	−0.988785	−	0.149344i	$-0.952284\pi$
$211$	−5.30276	+	9.18465i	−0.365057	+	0.632297i	0.623728	+	0.781641i	$0.285617\pi$
$212$	3.20423			0.220068
$213$	11.0695	−	6.24517i	0.758471	−	0.427912i
$214$	6.27098	−	1.68030i	0.428675	−	0.114863i
$215$	−15.0802	−	15.0802i	−1.02846	−	1.02846i
$216$	−0.154872	+	5.19384i	−0.0105377	+	0.353396i
$217$	10.8024	+	0.812367i	0.733314	+	0.0551470i
$218$	−5.00021	+	8.66062i	−0.338657	+	0.586571i
$219$	9.33671	−	5.26755i	0.630916	−	0.355948i
$220$	−6.68200	+	3.85785i	−0.450500	+	0.260097i
$221$	−0.996691	+	1.36921i	−0.0670447	+	0.0921034i
$222$	−11.2467	+	2.89408i	−0.754830	+	0.194238i
$223$	−14.7587	+	3.95458i	−0.988316	+	0.264818i	−0.716543	−	0.697543i	$-0.754277\pi$
$223$	−14.7587	+	3.95458i	−0.988316	+	0.264818i	−0.271773	+	0.962361i	$0.587610\pi$
$224$	2.38404	−	1.14733i	0.159290	−	0.0766589i
$225$	−2.38831	−	4.33332i	−0.159221	−	0.288888i
$226$	16.3024	−	4.36823i	1.08442	−	0.290570i
$227$	4.46575	+	16.6664i	0.296402	+	1.10619i	0.940097	+	0.340906i	$0.110734\pi$
$227$	4.46575	+	16.6664i	0.296402	+	1.10619i	−0.643695	+	0.765282i	$0.722600\pi$
$228$	−1.96753	−	1.16217i	−0.130303	−	0.0769667i
$229$	6.91392	+	25.8031i	0.456884	+	1.70512i	0.682488	+	0.730897i	$0.260898\pi$
$229$	6.91392	+	25.8031i	0.456884	+	1.70512i	−0.225604	+	0.974219i	$0.572435\pi$
$230$	−13.5616	+	7.82977i	−0.894223	+	0.516280i
$231$	−3.39734	−	19.0149i	−0.223529	−	1.25109i
$232$	0.894886	+	3.33976i	0.0587521	+	0.219266i
$233$	9.56424	−	16.5657i	0.626574	−	1.08526i	−0.361660	−	0.932310i	$-0.617790\pi$
$233$	9.56424	−	16.5657i	0.626574	−	1.08526i	0.988234	−	0.152948i	$-0.0488767\pi$
$234$	−4.08533	+	10.0155i	−0.267066	+	0.654733i
$235$	8.92096	+	15.4516i	0.581940	+	1.00795i
$236$	−7.93039	−	2.12494i	−0.516224	−	0.138322i
$237$	−5.86890	−	22.8072i	−0.381226	−	1.48148i
$238$	−1.02661	−	0.700325i	−0.0665453	−	0.0453953i
$239$	−8.38717	+	8.38717i	−0.542521	+	0.542521i	−0.924267	−	0.381746i	$-0.875323\pi$
$239$	−8.38717	+	8.38717i	−0.542521	+	0.542521i	0.381746	+	0.924267i	$0.375323\pi$
$240$	−0.0315032	+	3.17035i	−0.00203353	+	0.204645i
$241$	−5.36483	−	20.0218i	−0.345579	−	1.28972i	−0.891934	−	0.452165i	$-0.850652\pi$
$241$	−5.36483	−	20.0218i	−0.345579	−	1.28972i	0.546355	−	0.837554i	$-0.316015\pi$
$242$	−1.75145	+	6.53650i	−0.112587	+	0.420182i
$243$	11.5565	−	10.4617i	0.741351	−	0.671118i
$244$	9.43798	+	5.44902i	0.604204	+	0.348838i
$245$	7.60349	+	10.3136i	0.485769	+	0.658915i
$246$	4.48323	+	4.57322i	0.285840	+	0.291578i
$247$	−2.99024	−	3.69950i	−0.190265	−	0.235393i
$248$	−3.54590	+	2.04722i	−0.225165	+	0.129999i
$249$	−0.0681687	+	6.86020i	−0.00432002	+	0.434748i
$250$	−6.08574	−	10.5408i	−0.384896	−	0.666660i
$251$	3.06317	+	5.30557i	0.193346	+	0.334884i	0.946357	−	0.323123i	$-0.104733\pi$
$251$	3.06317	+	5.30557i	0.193346	+	0.334884i	−0.753011	+	0.658008i	$0.771399\pi$
$252$	−7.43754	−	2.77181i	−0.468521	−	0.174608i
$253$	−9.33287	+	34.8308i	−0.586753	+	2.18979i
$254$	1.51921	+	1.51921i	0.0953236	+	0.0953236i
$255$	1.29703	−	0.731756i	0.0812233	−	0.0458243i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.45182	−	7.71078i	−0.277697	−	0.480985i	0.693115	−	0.720827i	$-0.256238\pi$
$257$	−4.45182	−	7.71078i	−0.277697	−	0.480985i	−0.970812	+	0.239842i	$0.922904\pi$
$258$	−10.2630	+	17.3751i	−0.638948	+	1.08172i
$259$	1.33028	−	17.6894i	0.0826598	−	1.09916i
$260$	−2.37079	+	6.15942i	−0.147030	+	0.381991i
$261$	5.36385	−	8.87821i	0.332014	−	0.549547i
$262$	3.04938	+	3.04938i	0.188391	+	0.188391i
$263$		−	4.57153i		−	0.281893i	−0.990017	−	0.140946i	$-0.954985\pi$
$263$		−	4.57153i		−	0.281893i	0.990017	−	0.140946i	$-0.0450145\pi$
$264$	5.11087	+	5.21346i	0.314552	+	0.320867i
$265$	−4.14741	−	4.14741i	−0.254773	−	0.254773i
$266$	2.64636	−	2.27618i	0.162259	−	0.139561i
$267$	5.00203	+	8.86607i	0.306119	+	0.542595i
$268$	−0.111089	−	0.414591i	−0.00678585	−	0.0253251i
$269$	1.50862	+	0.871005i	0.0919824	+	0.0531061i	0.545286	−	0.838250i	$-0.316421\pi$
$269$	1.50862	+	0.871005i	0.0919824	+	0.0531061i	−0.453303	+	0.891356i	$0.649755\pi$
$270$	6.92313	−	6.52221i	0.421328	−	0.396929i
$271$	10.6559	+	2.85523i	0.647298	+	0.173443i	0.567507	−	0.823369i	$-0.307908\pi$
$271$	10.6559	+	2.85523i	0.647298	+	0.173443i	0.0797910	+	0.996812i	$0.474575\pi$
$272$	0.469709			0.0284803
$273$	−12.4846	−	10.8229i	−0.755602	−	0.655030i
$274$	−11.2617			−0.680345
$275$	−6.71508	−	1.79930i	−0.404934	−	0.108502i
$276$	10.3729	+	10.5811i	0.624372	+	0.636906i
$277$	−22.8768	−	13.2079i	−1.37453	−	0.793586i	−0.383036	−	0.923733i	$-0.625122\pi$
$277$	−22.8768	−	13.2079i	−1.37453	−	0.793586i	−0.991495	+	0.130148i	$0.958455\pi$
$278$	−5.92560	−	22.1146i	−0.355394	−	1.32635i
$279$	11.7993	+	3.41431i	0.706405	+	0.204409i
$280$	−4.57083	−	1.60075i	−0.273160	−	0.0956628i
$281$	−9.29793	−	9.29793i	−0.554668	−	0.554668i	0.373117	−	0.927784i	$-0.378289\pi$
$281$	−9.29793	−	9.29793i	−0.554668	−	0.554668i	−0.927784	+	0.373117i	$0.878289\pi$
$282$	12.0557	−	11.8185i	0.717906	−	0.703779i
$283$		−	10.0191i		−	0.595572i	−0.954633	−	0.297786i	$-0.903752\pi$
$283$		−	10.0191i		−	0.595572i	0.954633	−	0.297786i	$-0.0962482\pi$
$284$	−5.18871	−	5.18871i	−0.307893	−	0.307893i
$285$	1.04242	+	4.05094i	0.0617474	+	0.239957i
$286$	6.16890	+	13.8894i	0.364774	+	0.821300i
$287$	−8.81490	+	4.24219i	−0.520327	+	0.250409i
$288$	2.91263	−	0.718720i	0.171629	−	0.0423510i
$289$	8.38969	+	14.5314i	0.493511	+	0.854786i
$290$	3.16453	−	5.48113i	0.185828	−	0.321863i
$291$	2.29382	+	4.06579i	0.134466	+	0.238341i
$292$	−4.37647	−	4.37647i	−0.256114	−	0.256114i
$293$	−0.0253299	+	0.0945323i	−0.00147979	+	0.00552264i	−0.966662	−	0.256057i	$-0.917577\pi$
$293$	−0.0253299	+	0.0945323i	−0.00147979	+	0.00552264i	0.965182	+	0.261579i	$0.0842433\pi$
$294$	7.65814	−	9.39962i	0.446632	−	0.548197i
$295$	7.51430	+	13.0151i	0.437499	+	0.757771i
$296$	3.35242	+	5.80655i	0.194855	+	0.337499i
$297$	0.652801	−	21.8926i	0.0378794	−	1.27034i
$298$	−6.82757	+	3.94190i	−0.395511	+	0.228348i
$299$	12.5202	+	28.1895i	0.724061	+	1.63024i
$300$	−2.03994	+	1.99980i	−0.117776	+	0.115458i
$301$	−20.1007	−	23.3698i	−1.15859	−	1.34701i
$302$	8.61589	+	4.97439i	0.495789	+	0.286244i
$303$	−16.3312	+	16.0098i	−0.938202	+	0.919740i
$304$	−0.341465	+	1.27436i	−0.0195844	+	0.0730898i
$305$	−5.16312	−	19.2690i	−0.295639	−	1.10334i
$306$	−0.976406	−	1.01601i	−0.0558174	−	0.0580812i
$307$	18.6298	−	18.6298i	1.06326	−	1.06326i	0.0654016	−	0.997859i	$-0.479167\pi$
$307$	18.6298	−	18.6298i	1.06326	−	1.06326i	0.997859	−	0.0654016i	$-0.0208328\pi$
$308$	−10.0490	+	4.83609i	−0.572593	+	0.275562i
$309$	8.61731	−	2.21747i	0.490222	−	0.126147i
$310$	7.23948	+	1.93981i	0.411175	+	0.110174i
$311$	3.37427	+	5.84441i	0.191337	+	0.331406i	0.945694	−	0.325059i	$-0.105384\pi$
$311$	3.37427	+	5.84441i	0.191337	+	0.331406i	−0.754356	+	0.656465i	$0.772051\pi$
$312$	6.20334	+	0.720085i	0.351195	+	0.0407668i
$313$	3.77452	−	6.53766i	0.213348	−	0.369530i	−0.739412	−	0.673253i	$-0.764896\pi$
$313$	3.77452	−	6.53766i	0.213348	−	0.369530i	0.952760	+	0.303723i	$0.0982297\pi$
$314$	3.06337	+	11.4326i	0.172876	+	0.645181i
$315$	6.03911	+	13.2145i	0.340265	+	0.744554i
$316$	−11.7751	+	6.79835i	−0.662400	+	0.382437i
$317$	6.03948	+	22.5397i	0.339211	+	1.26595i	0.899231	+	0.437474i	$0.144127\pi$
$317$	6.03948	+	22.5397i	0.339211	+	1.26595i	−0.560020	+	0.828479i	$0.689207\pi$
$318$	−2.82257	+	4.77854i	−0.158282	+	0.267967i
$319$	−3.77204	−	14.0774i	−0.211193	−	0.788185i
$320$	1.76812	−	0.473766i	0.0988409	−	0.0264843i
$321$	−3.01815	+	10.8322i	−0.168457	+	0.604594i
$322$	−20.3950	+	9.81517i	−1.13657	+	0.546978i
$323$	0.598580	−	0.160389i	0.0333059	−	0.00892429i
$324$	−7.60926	−	4.80615i	−0.422737	−	0.267009i
$325$	−5.43471	+	2.41379i	−0.301463	+	0.133893i
$326$	13.2811	−	7.66785i	0.735572	−	0.424683i
$327$	−8.51114	−	15.0860i	−0.470667	−	0.834255i
$328$	1.84873	−	3.20210i	0.102079	−	0.176806i
$329$	11.1831	+	23.2374i	0.616542	+	1.28112i
$330$	0.132789	−	13.3633i	0.00730981	−	0.735628i
$331$	−16.1178	−	16.1178i	−0.885916	−	0.885916i	0.108212	−	0.994128i	$-0.465488\pi$
$331$	−16.1178	−	16.1178i	−0.885916	−	0.885916i	−0.994128	+	0.108212i	$0.965488\pi$
$332$	3.82597	−	1.02517i	0.209977	−	0.0562633i
$333$	5.59107	−	19.3218i	0.306389	−	1.05883i
$334$	20.1363			1.10181
$335$	−0.392838	+	0.680415i	−0.0214630	+	0.0371751i
$336$	−0.389040	+	4.56603i	−0.0212238	+	0.249097i
$337$		−	7.04042i		−	0.383516i	−0.981442	−	0.191758i	$-0.938581\pi$
$337$		−	7.04042i		−	0.383516i	0.981442	−	0.191758i	$-0.0614189\pi$
$338$	11.5724	+	5.92287i	0.629454	+	0.322162i
$339$	−7.84618	+	28.1601i	−0.426146	+	1.52945i
$340$	−0.607969	−	0.607969i	−0.0329718	−	0.0329718i
$341$	14.9463	−	8.62926i	0.809388	−	0.467301i
$342$	3.46634	−	1.91047i	0.187438	−	0.103307i
$343$	9.84107	+	15.6893i	0.531368	+	0.847141i
$344$	11.2538	+	3.01545i	0.606764	+	0.162582i
$345$	0.269505	−	27.1218i	0.0145097	−	1.46019i
$346$	19.4773	+	5.21892i	1.04710	+	0.280571i
$347$	−28.5564	−	16.4871i	−1.53299	−	0.885072i	−0.999222	−	0.0394416i	$-0.987442\pi$
$347$	−28.5564	−	16.4871i	−1.53299	−	0.885072i	−0.533768	−	0.845631i	$-0.679225\pi$
$348$	−5.76895	−	1.60739i	−0.309248	−	0.0861651i
$349$	−0.715205	−	2.66918i	−0.0382841	−	0.142878i	0.944138	−	0.329549i	$-0.106897\pi$
$349$	−0.715205	−	2.66918i	−0.0382841	−	0.142878i	−0.982422	+	0.186671i	$0.940230\pi$
$350$	−1.89228	−	3.93199i	−0.101147	−	0.210174i
$351$	−11.3376	−	14.9151i	−0.605156	−	0.796107i
$352$	2.10755	−	3.65038i	0.112333	−	0.194566i
$353$	−2.22532	+	2.22532i	−0.118442	+	0.118442i	−0.763843	−	0.645402i	$-0.776690\pi$
$353$	−2.22532	+	2.22532i	−0.118442	+	0.118442i	0.645402	+	0.763843i	$0.276690\pi$
$354$	10.1547	−	9.95492i	0.539718	−	0.529098i
$355$			13.4321i			0.712899i
$356$	4.15587	−	4.15587i	0.220261	−	0.220261i
$357$	1.94874	−	0.914099i	0.103138	−	0.0483793i
$358$	−5.31960	−	1.42538i	−0.281150	−	0.0753338i
$359$	21.2293	−	5.68837i	1.12044	−	0.300220i	0.349377	−	0.936982i	$-0.386393\pi$
$359$	21.2293	−	5.68837i	1.12044	−	0.300220i	0.771061	+	0.636762i	$0.219727\pi$
$360$	−4.70026	−	2.83970i	−0.247725	−	0.149665i
$361$		−	17.2594i		−	0.908389i
$362$	4.17709	−	15.5891i	0.219543	−	0.819345i
$363$	−8.20518	−	8.36989i	−0.430660	−	0.439305i
$364$	−4.08466	+	8.62065i	−0.214094	+	0.451845i
$365$			11.3294i			0.593008i
$366$	−16.4400	+	9.27508i	−0.859334	+	0.484816i
$367$	5.38521			0.281106			0.140553	−	0.990073i	$-0.455112\pi$
$367$	5.38521			0.281106			0.140553	+	0.990073i	$0.455112\pi$
$368$	4.27741	−	7.40870i	0.222976	−	0.386205i
$369$	−10.7694	+	2.65744i	−0.560631	+	0.138341i
$370$	3.17652	−	11.8549i	0.165140	−	0.616309i
$371$	−5.52816	−	6.42723i	−0.287008	−	0.333685i
$372$	0.0704665	−	7.09144i	0.00365352	−	0.367674i
$373$	−25.4457			−1.31753			−0.658765	−	0.752349i	$-0.728921\pi$
$373$	−25.4457			−1.31753			−0.658765	+	0.752349i	$0.728921\pi$
$374$	−1.97987			−0.102377
$375$	21.0806	+	0.209474i	1.08860	+	0.0108172i
$376$	−8.44121	−	4.87353i	−0.435322	−	0.251333i
$377$	−10.0789	−	7.33674i	−0.519091	−	0.377862i
$378$	10.6853	−	8.65011i	0.549592	−	0.444914i
$379$	12.0881	−	3.23899i	0.620923	−	0.166376i	0.0653756	−	0.997861i	$-0.479175\pi$
$379$	12.0881	−	3.23899i	0.620923	−	0.166376i	0.555547	+	0.831485i	$0.312509\pi$
$380$	2.09145	−	1.20750i	0.107289	−	0.0619435i
$381$	−3.60388	+	0.927376i	−0.184632	+	0.0475109i
$382$	0.144701	−	0.540032i	0.00740355	−	0.0276304i
$383$	−6.83241	+	6.83241i	−0.349120	+	0.349120i	−0.859782	−	0.510662i	$-0.829400\pi$
$383$	−6.83241	+	6.83241i	−0.349120	+	0.349120i	0.510662	+	0.859782i	$0.329400\pi$
$384$	−0.851078	−	1.50853i	−0.0434314	−	0.0769819i
$385$	19.2665	+	6.74730i	0.981913	+	0.343874i
$386$	11.5621	−	6.67536i	0.588493	−	0.339767i
$387$	−16.8712	−	30.6109i	−0.857612	−	1.55604i
$388$	1.90579	−	1.90579i	0.0967520	−	0.0967520i
$389$	17.1024	+	29.6221i	0.867124	+	1.50190i	0.864923	+	0.501905i	$0.167367\pi$
$389$	17.1024	+	29.6221i	0.867124	+	1.50190i	0.00220090	+	0.999998i	$0.499299\pi$
$390$	−7.09727	−	8.96136i	−0.359384	−	0.453776i
$391$	−4.01828			−0.203213
$392$	−6.41447	−	2.80260i	−0.323980	−	0.141553i
$393$	−7.23376	+	1.86144i	−0.364895	+	0.0938973i
$394$			0.351154i			0.0176909i
$395$	24.0406	+	6.44165i	1.20961	+	0.324115i
$396$	−12.2771	+	3.02948i	−0.616945	+	0.152237i
$397$	3.88127	−	3.88127i	0.194795	−	0.194795i	−0.602969	−	0.797764i	$-0.706016\pi$
$397$	3.88127	−	3.88127i	0.194795	−	0.194795i	0.797764	+	0.602969i	$0.206016\pi$
$398$	12.5438	+	12.5438i	0.628764	+	0.628764i
$399$	1.06336	+	5.95163i	0.0532347	+	0.297954i
$400$	1.42833	+	0.824649i	0.0714167	+	0.0412325i
$401$	2.20534	−	8.23043i	0.110129	−	0.411008i	−0.888747	−	0.458398i	$-0.848424\pi$
$401$	2.20534	−	8.23043i	0.110129	−	0.411008i	0.998876	+	0.0473896i	$0.0150902\pi$
$402$	0.716145	+	0.199538i	0.0357180	+	0.00995204i
$403$	5.30299	−	13.7774i	0.264161	−	0.686302i
$404$	11.4348	+	6.60190i	0.568904	+	0.328457i
$405$	3.62821	+	16.0699i	0.180287	+	0.798522i
$406$	5.15516	−	7.55699i	0.255846	−	0.375047i
$407$	−14.1308	−	24.4752i	−0.700436	−	1.21319i
$408$	−0.413760	+	0.700486i	−0.0204842	+	0.0346792i
$409$	11.6697	−	3.12688i	0.577029	−	0.154614i	0.0415104	−	0.999138i	$-0.486783\pi$
$409$	11.6697	−	3.12688i	0.577029	−	0.154614i	0.535518	+	0.844524i	$0.320116\pi$
$410$	−6.53756	+	1.75173i	−0.322867	+	0.0865120i
$411$	9.92030	−	16.7948i	0.489332	−	0.828428i
$412$	−2.56865	−	4.44902i	−0.126548	−	0.219188i
$413$	9.41970	+	19.5733i	0.463513	+	0.963139i
$414$	−24.9171	+	6.14852i	−1.22461	+	0.302183i
$415$	−6.27908	−	3.62523i	−0.308228	−	0.177956i
$416$	−0.560803	−	3.56167i	−0.0274956	−	0.174625i
$417$	38.1998	+	10.6435i	1.87065	+	0.521216i
$418$	1.43931	−	5.37158i	0.0703989	−	0.262732i
$419$	−4.97007	−	2.86947i	−0.242804	−	0.140183i	0.373661	−	0.927565i	$-0.378102\pi$
$419$	−4.97007	−	2.86947i	−0.242804	−	0.140183i	−0.616465	+	0.787383i	$0.711436\pi$
$420$	6.41361	−	5.40650i	0.312952	−	0.263810i
$421$	7.51201	+	7.51201i	0.366113	+	0.366113i	0.866057	−	0.499944i	$-0.166646\pi$
$421$	7.51201	+	7.51201i	0.366113	+	0.366113i	−0.499944	+	0.866057i	$0.666646\pi$
$422$	−7.49923	+	7.49923i	−0.365057	+	0.365057i
$423$	7.00541	+	28.3896i	0.340615	+	1.38035i
$424$	3.09505	+	0.829317i	0.150309	+	0.0402752i
$425$		−	0.774690i		−	0.0375780i
$426$	12.3087	−	3.16736i	0.596359	−	0.153459i
$427$	−5.35308	−	28.3322i	−0.259053	−	1.37109i
$428$	6.49219			0.313812
$429$	−26.1477	−	3.03523i	−1.26242	−	0.146542i
$430$	−10.6633	−	18.4694i	−0.514232	−	0.890676i
$431$	−8.75759	+	8.75759i	−0.421838	+	0.421838i	−0.885836	−	0.463998i	$-0.846415\pi$
$431$	−8.75759	+	8.75759i	−0.421838	+	0.421838i	0.463998	+	0.885836i	$0.346415\pi$
$432$	−1.49386	+	4.97678i	−0.0718734	+	0.239446i
$433$	−17.3783	+	10.0334i	−0.835149	+	0.482174i	−0.855612	−	0.517617i	$-0.826819\pi$
$433$	−17.3783	+	10.0334i	−0.835149	+	0.482174i	0.0204632	+	0.999791i	$0.493486\pi$
$434$	10.2241	+	3.58055i	0.490770	+	0.171872i
$435$	5.38653	+	9.54759i	0.258264	+	0.457772i
$436$	−7.07137	+	7.07137i	−0.338657	+	0.338657i
$437$	2.92117	−	10.9020i	0.139739	−	0.521512i
$438$	10.3819	−	2.67155i	0.496067	−	0.127651i
$439$	−13.1405	+	7.58665i	−0.627160	+	0.362091i	−0.779651	−	0.626214i	$-0.784604\pi$
$439$	−13.1405	+	7.58665i	−0.627160	+	0.362091i	0.152491	+	0.988305i	$0.451270\pi$
$440$	−7.45280	+	1.99697i	−0.355298	+	0.0952019i
$441$	7.27189	+	19.7008i	0.346280	+	0.938131i
$442$	−1.31711	+	1.06460i	−0.0626485	+	0.0506377i
$443$	30.6703	+	17.7075i	1.45719	+	0.841309i	0.998872	−	0.0474791i	$-0.0151187\pi$
$443$	30.6703	+	17.7075i	1.45719	+	0.841309i	0.458318	+	0.888788i	$0.348452\pi$
$444$	−11.6125	−	0.115392i	−0.551106	−	0.00547626i
$445$	−10.7583			−0.509994
$446$	−15.2793			−0.723497
$447$	0.135682	−	13.6545i	0.00641755	−	0.645834i
$448$	2.59976	−	0.491196i	0.122827	−	0.0232068i
$449$	1.63891	−	6.11648i	0.0773448	−	0.288655i	−0.916410	−	0.400241i	$-0.868926\pi$
$449$	1.63891	−	6.11648i	0.0773448	−	0.288655i	0.993755	+	0.111586i	$0.0355931\pi$
$450$	−1.18538	−	4.80380i	−0.0558795	−	0.226453i
$451$	−7.79259	+	13.4972i	−0.366939	+	0.635557i
$452$	16.8775			0.793852
$453$	−15.0080	+	8.46718i	−0.705139	+	0.397823i
$454$			17.2543i			0.809785i
$455$	16.4452	−	5.87118i	0.770961	−	0.275245i
$456$	−1.59969	−	1.63181i	−0.0749126	−	0.0764163i
$457$	−6.05003	+	22.5790i	−0.283008	+	1.05620i	0.667274	+	0.744812i	$0.267461\pi$
$457$	−6.05003	+	22.5790i	−0.283008	+	1.05620i	−0.950282	+	0.311390i	$0.899206\pi$
$458$			26.7133i			1.24823i
$459$	2.37529	−	0.561147i	0.110869	−	0.0261921i
$460$	−15.1260	+	4.05299i	−0.705251	+	0.188972i
$461$	−13.1547	−	3.52480i	−0.612677	−	0.164166i	−0.0608805	−	0.998145i	$-0.519391\pi$
$461$	−13.1547	−	3.52480i	−0.612677	−	0.164166i	−0.551797	+	0.833979i	$0.686058\pi$
$462$	1.63984	−	19.2463i	0.0762923	−	0.895418i
$463$	7.45241	−	7.45241i	0.346343	−	0.346343i	−0.512402	−	0.858745i	$-0.671244\pi$
$463$	7.45241	−	7.45241i	0.346343	−	0.346343i	0.858745	+	0.512402i	$0.171244\pi$
$464$			3.45757i			0.160514i
$465$	−9.27004	+	9.08763i	−0.429888	+	0.421429i
$466$	13.5259	−	13.5259i	0.626574	−	0.626574i
$467$	−5.79547	+	10.0380i	−0.268182	+	0.464505i	−0.968392	−	0.249432i	$-0.919756\pi$
$467$	−5.79547	+	10.0380i	−0.268182	+	0.464505i	0.700210	+	0.713937i	$0.253090\pi$
$468$	−6.53832	+	8.61686i	−0.302234	+	0.398315i
$469$	−0.639950	+	0.938108i	−0.0295502	+	0.0433178i
$470$	4.61783	+	17.2340i	0.213005	+	0.794944i
$471$	−19.7482	−	5.50240i	−0.909950	−	0.253537i
$472$	−7.11019	−	4.10507i	−0.327273	−	0.188951i
$473$	−47.4359	−	12.7104i	−2.18110	−	0.584425i
$474$	0.234003	−	23.5490i	0.0107481	−	1.08164i
$475$	2.10181	+	0.563178i	0.0964375	+	0.0258404i
$476$	−0.810373	−	0.942168i	−0.0371434	−	0.0431842i
$477$	−4.63997	−	8.41871i	−0.212450	−	0.385466i
$478$	−10.2721	+	5.93062i	−0.469837	+	0.271260i
$479$	−15.5030	−	15.5030i	−0.708352	−	0.708352i	0.257836	−	0.966189i	$-0.416990\pi$
$479$	−15.5030	−	15.5030i	−0.708352	−	0.708352i	−0.966189	+	0.257836i	$0.916990\pi$
$480$	−0.850976	+	3.05417i	−0.0388416	+	0.139403i
$481$	−22.5611	−	8.68387i	−1.02870	−	0.395950i
$482$		−	20.7281i		−	0.944140i
$483$	3.32817	−	39.0616i	0.151437	−	1.77736i
$484$	−3.38354	+	5.86046i	−0.153797	+	0.266385i
$485$	−4.93354			−0.224020
$486$	13.8704	−	7.11417i	0.629175	−	0.322705i
$487$	−6.89989	+	1.84882i	−0.312664	+	0.0837780i	−0.411739	−	0.911302i	$-0.635078\pi$
$487$	−6.89989	+	1.84882i	−0.312664	+	0.0837780i	0.0990748	+	0.995080i	$0.468412\pi$
$488$	7.70607	+	7.70607i	0.348838	+	0.348838i
$489$	−0.263931	+	26.5609i	−0.0119354	+	1.20112i
$490$	4.67504	+	11.9301i	0.211197	+	0.538949i
$491$	−18.1562	+	31.4474i	−0.819376	+	1.41920i	0.0867668	+	0.996229i	$0.472346\pi$
$491$	−18.1562	+	31.4474i	−0.819376	+	1.41920i	−0.906143	+	0.422972i	$0.860987\pi$
$492$	3.14683	+	5.57774i	0.141870	+	0.251464i
$493$	1.40647	−	0.812026i	0.0633443	−	0.0365718i
$494$	−1.93085	−	4.34737i	−0.0868732	−	0.195598i
$495$	19.8121	+	11.9696i	0.890486	+	0.537995i
$496$	−3.95493	+	1.05972i	−0.177582	+	0.0475829i
$497$	−1.45590	+	19.3597i	−0.0653060	+	0.868402i
$498$	−1.84140	+	6.60880i	−0.0825150	+	0.296147i
$499$	35.3246	−	9.46520i	1.58135	−	0.423720i	0.642004	−	0.766702i	$-0.278103\pi$
$499$	35.3246	−	9.46520i	1.58135	−	0.423720i	0.939342	+	0.342981i	$0.111437\pi$
$500$	−3.15021	−	11.7568i	−0.140882	−	0.525778i
$501$	−17.7378	+	30.0297i	−0.792468	+	1.34163i
$502$	1.58561	+	5.91759i	0.0707694	+	0.264115i
$503$	26.7281	−	15.4315i	1.19175	−	0.688056i	0.233045	−	0.972466i	$-0.425131\pi$
$503$	26.7281	−	15.4315i	1.19175	−	0.688056i	0.958703	+	0.284410i	$0.0917976\pi$
$504$	−6.46672	−	4.60234i	−0.288051	−	0.205005i
$505$	−6.25552	−	23.3459i	−0.278367	−	1.03888i
$506$	−18.0297	+	31.2284i	−0.801519	+	1.38827i
$507$	−19.0268	+	12.0407i	−0.845012	+	0.534747i
$508$	1.07424	+	1.86064i	0.0476618	+	0.0825527i
$509$	3.50851	+	0.940103i	0.155512	+	0.0416693i	0.335735	−	0.941956i	$-0.391015\pi$
$509$	3.50851	+	0.940103i	0.155512	+	0.0416693i	−0.180223	+	0.983626i	$0.557682\pi$
$510$	1.44223	−	0.371125i	0.0638630	−	0.0164337i
$511$	−1.22799	+	16.3292i	−0.0543232	+	0.722359i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.204326	+	6.85234i	−0.00902119	+	0.302538i
$514$	−2.30443	−	8.60026i	−0.101644	−	0.379341i
$515$	−2.43387	+	9.08334i	−0.107249	+	0.400260i
$516$	−14.4103	+	14.1268i	−0.634379	+	0.621896i
$517$	35.5805	+	20.5424i	1.56483	+	0.903455i
$518$	5.86330	−	16.7423i	0.257619	−	0.735615i
$519$	−24.9404	+	24.4496i	−1.09476	+	1.07322i
$520$	−3.88418	+	5.33594i	−0.170333	+	0.233996i
$521$	17.9997	−	10.3922i	0.788583	−	0.455289i	−0.0508804	−	0.998705i	$-0.516203\pi$
$521$	17.9997	−	10.3922i	0.788583	−	0.455289i	0.839463	+	0.543416i	$0.182869\pi$
$522$	7.47893	−	7.18742i	0.327344	−	0.314585i
$523$	−5.11816	−	8.86491i	−0.223801	−	0.387635i	0.732158	−	0.681135i	$-0.238513\pi$
$523$	−5.11816	−	8.86491i	−0.223801	−	0.387635i	−0.955959	+	0.293500i	$0.905180\pi$
$524$	2.15623	+	3.73471i	0.0941956	+	0.163151i
$525$	7.53075	+	0.641642i	0.328669	+	0.0280036i
$526$	1.18320	−	4.41576i	0.0515900	−	0.192536i
$527$	1.35991	+	1.35991i	0.0592385	+	0.0592385i
$528$	3.58738	+	6.35861i	0.156121	+	0.276723i
$529$	−25.0925	+	43.4615i	−1.09098	+	1.88963i
$530$	−2.93266	−	5.07952i	−0.127387	−	0.220640i
$531$	5.90079	+	23.9131i	0.256073	+	1.03774i
$532$	3.14531	−	1.51369i	0.136366	−	0.0656267i
$533$	2.07355	+	13.1692i	0.0898154	+	0.570419i
$534$	2.53688	+	9.85859i	0.109782	+	0.426623i
$535$	−8.40319	−	8.40319i	−0.363302	−	0.363302i
$536$		−	0.429216i		−	0.0185393i
$537$	6.81167	−	6.67763i	0.293945	−	0.288161i
$538$	1.23179	+	1.23179i	0.0531061	+	0.0531061i
$539$	27.0376	+	11.8132i	1.16459	+	0.508832i
$540$	8.37530	−	4.50813i	0.360416	−	0.193999i
$541$	5.72876	+	21.3800i	0.246298	+	0.919199i	0.972726	+	0.231956i	$0.0745125\pi$
$541$	5.72876	+	21.3800i	0.246298	+	0.919199i	−0.726428	+	0.687243i	$0.758821\pi$
$542$	9.55379	+	5.51588i	0.410370	+	0.236927i
$543$	19.5688	+	19.9616i	0.839778	+	0.856635i
$544$	0.453704	+	0.121570i	0.0194524	+	0.00521225i
$545$	18.3057			0.784130
$546$	−9.25803	−	13.6854i	−0.396207	−	0.585679i
$547$	34.8653			1.49073			0.745366	−	0.666655i	$-0.232275\pi$
$547$	34.8653			1.49073			0.745366	+	0.666655i	$0.232275\pi$
$548$	−10.8780	−	2.91475i	−0.464684	−	0.124512i
$549$	0.649688	−	32.6876i	0.0277280	−	1.39507i
$550$	−6.02057	−	3.47598i	−0.256718	−	0.148216i
$551$	1.18064	+	4.40621i	0.0502970	+	0.187711i
$552$	7.28083	+	12.9052i	0.309892	+	0.549283i
$553$	33.9516	+	11.8902i	1.44377	+	0.505621i
$554$	−18.6788	−	18.6788i	−0.793586	−	0.793586i
$555$	14.8814	+	15.1801i	0.631679	+	0.644359i
$556$		−	22.8948i		−	0.970954i
$557$	16.4908	+	16.4908i	0.698738	+	0.698738i	0.964138	−	0.265401i	$-0.0855042\pi$
$557$	16.4908	+	16.4908i	0.698738	+	0.698738i	−0.265401	+	0.964138i	$0.585504\pi$
$558$	10.5135	+	6.35185i	0.445074	+	0.268895i
$559$	−38.3912	+	17.0512i	−1.62378	+	0.721189i
$560$	−4.00078	−	2.72922i	−0.169064	−	0.115331i
$561$	1.74404	−	2.95262i	0.0736335	−	0.124660i
$562$	−6.57463	−	11.3876i	−0.277334	−	0.480357i
$563$	4.24907	−	7.35961i	0.179077	−	0.310170i	−0.762488	−	0.647003i	$-0.776022\pi$
$563$	4.24907	−	7.35961i	0.179077	−	0.310170i	0.941565	+	0.336832i	$0.109356\pi$
$564$	14.7038	−	8.29552i	0.619140	−	0.349304i
$565$	−21.8455	−	21.8455i	−0.919047	−	0.919047i
$566$	2.59313	−	9.67769i	0.108997	−	0.406783i
$567$	3.48755	+	23.5550i	0.146463	+	0.989216i
$568$	−3.66897	−	6.35485i	−0.153947	−	0.266644i
$569$	16.3458	+	28.3118i	0.685253	+	1.18689i	0.973357	+	0.229294i	$0.0736418\pi$
$569$	16.3458	+	28.3118i	0.685253	+	1.18689i	−0.288104	+	0.957599i	$0.593025\pi$
$570$	−0.0415628	+	4.18270i	−0.00174088	+	0.175194i
$571$	−36.1272	+	20.8580i	−1.51187	+	0.872881i	−0.511971	+	0.859003i	$0.671085\pi$
$571$	−36.1272	+	20.8580i	−1.51187	+	0.872881i	−0.999904	+	0.0138789i	$0.995582\pi$
$572$	2.36384	+	15.0128i	0.0988372	+	0.627717i
$573$	0.677895	+	0.691503i	0.0283195	+	0.0288879i
$574$	−9.61250	+	1.81618i	−0.401218	+	0.0758059i
$575$	−12.2192	−	7.05473i	−0.509574	−	0.294203i
$576$	2.99941	+	0.0596151i	0.124975	+	0.00248396i
$577$	−1.11933	+	4.17739i	−0.0465983	+	0.173907i	−0.985303	−	0.170815i	$-0.945360\pi$
$577$	−1.11933	+	4.17739i	−0.0465983	+	0.173907i	0.938705	+	0.344722i	$0.112027\pi$
$578$	4.34282	+	16.2076i	0.180638	+	0.674149i
$579$	−0.229769	+	23.1230i	−0.00954889	+	0.960958i
$580$	4.47532	−	4.47532i	0.185828	−	0.185828i
$581$	−8.65715	−	5.90566i	−0.359159	−	0.245008i
$582$	1.16336	+	4.52094i	0.0482228	+	0.187399i
$583$	−13.0460	−	3.49565i	−0.540308	−	0.144775i
$584$	−3.09463	−	5.36006i	−0.128057	−	0.221801i
$585$	19.6162	−	2.69036i	0.811029	−	0.111233i
$586$	−0.0489335	+	0.0847554i	−0.00202143	+	0.00350121i
$587$	0.699999	+	2.61243i	0.0288920	+	0.107827i	0.978866	−	0.204502i	$-0.0655576\pi$
$587$	0.699999	+	2.61243i	0.0288920	+	0.107827i	−0.949974	+	0.312329i	$0.898891\pi$
$588$	9.83000	−	7.09726i	0.405382	−	0.292686i
$589$	−4.67817	+	2.70094i	−0.192761	+	0.111290i
$590$	3.88969	+	14.5165i	0.160136	+	0.597635i
$591$	−0.523684	−	0.309327i	−0.0215415	−	0.0127240i
$592$	1.73534	+	6.47637i	0.0713219	+	0.266177i
$593$	−29.2182	+	7.82899i	−1.19985	+	0.321498i	−0.802771	−	0.596288i	$-0.796642\pi$
$593$	−29.2182	+	7.82899i	−1.19985	+	0.321498i	−0.397076	+	0.917786i	$0.629975\pi$
$594$	6.29677	−	20.9776i	0.258360	−	0.860723i
$595$	−0.170590	+	2.26841i	−0.00699350	+	0.0929956i
$596$	−7.61516	+	2.04048i	−0.311929	+	0.0835812i
$597$	−29.7565	+	7.65716i	−1.21785	+	0.313387i
$598$	4.79757	+	30.4695i	0.196187	+	1.24599i
$599$	−14.5428	+	8.39629i	−0.594203	+	0.343063i	−0.766758	−	0.641937i	$-0.778131\pi$
$599$	−14.5428	+	8.39629i	−0.594203	+	0.343063i	0.172555	+	0.985000i	$0.444798\pi$
$600$	−2.48802	+	1.40368i	−0.101573	+	0.0573051i
$601$	−8.57728	+	14.8563i	−0.349875	+	0.606001i	−0.986227	−	0.165398i	$-0.947109\pi$
$601$	−8.57728	+	14.8563i	−0.349875	+	0.606001i	0.636352	+	0.771399i	$0.280442\pi$
$602$	−13.3672	−	27.7759i	−0.544808	−	1.13206i
$603$	−0.928418	+	0.892231i	−0.0378081	+	0.0363345i
$604$	7.03485	+	7.03485i	0.286244	+	0.286244i
$605$	11.9650	−	3.20601i	0.486447	−	0.130343i
$606$	−19.9183	+	11.2375i	−0.809128	+	0.456491i
$607$	28.6947			1.16468			0.582341	−	0.812945i	$-0.302137\pi$
$607$	28.6947			1.16468			0.582341	+	0.812945i	$0.302137\pi$
$608$	−0.659660	+	1.14256i	−0.0267527	+	0.0463371i
$609$	6.72878	+	14.3449i	0.272664	+	0.581283i
$610$		−	19.9488i		−	0.807702i
$611$	34.7158	−	5.46619i	1.40445	−	0.221138i
$612$	−0.680174	−	1.23410i	−0.0274944	−	0.0498855i
$613$	−19.5456	−	19.5456i	−0.789438	−	0.789438i	0.191964	−	0.981402i	$-0.438514\pi$
$613$	−19.5456	−	19.5456i	−0.789438	−	0.789438i	−0.981402	+	0.191964i	$0.938514\pi$
$614$	22.8168	−	13.1733i	0.920811	−	0.531630i
$615$	3.14646	−	11.2927i	0.126877	−	0.455365i
$616$	−10.9582	+	2.07044i	−0.441520	+	0.0834205i
$617$	4.46425	+	1.19619i	0.179724	+	0.0481569i	0.347559	−	0.937658i	$-0.387011\pi$
$617$	4.46425	+	1.19619i	0.179724	+	0.0481569i	−0.167835	+	0.985815i	$0.553677\pi$
$618$	8.89761	+	0.0884141i	0.357914	+	0.00355654i
$619$	−27.1861	−	7.28449i	−1.09270	−	0.292788i	−0.332912	−	0.942958i	$-0.608031\pi$
$619$	−27.1861	−	7.28449i	−1.09270	−	0.292788i	−0.759789	+	0.650169i	$0.774698\pi$
$620$	6.49074	+	3.74743i	0.260674	+	0.150500i
$621$	12.7797	−	42.5755i	0.512832	−	1.70850i
$622$	1.74665	+	6.51860i	0.0700344	+	0.261372i
$623$	−15.5061	−	1.16609i	−0.621237	−	0.0467186i
$624$	5.80560	+	2.30109i	0.232410	+	0.0921174i
$625$	−7.01666	+	12.1532i	−0.280666	+	0.486129i
$626$	5.33798	−	5.33798i	0.213348	−	0.213348i
$627$	6.74287	+	6.87822i	0.269284	+	0.274690i
$628$			11.8359i			0.472305i
$629$	2.22690	−	2.22690i	0.0887925	−	0.0887925i
$630$	2.41316	+	14.3273i	0.0961427	+	0.570812i
$631$	−5.68895	−	1.52435i	−0.226474	−	0.0606834i	0.143798	−	0.989607i	$-0.454069\pi$
$631$	−5.68895	−	1.52435i	−0.226474	−	0.0606834i	−0.370271	+	0.928924i	$0.620735\pi$
$632$	−13.1334	+	3.51908i	−0.522418	+	0.139982i
$633$	−4.57778	−	17.7897i	−0.181951	−	0.707079i
$634$			23.3348i			0.926742i
$635$	1.01788	−	3.79878i	0.0403933	−	0.150750i
$636$	−3.96317	+	3.88518i	−0.157150	+	0.154057i
$637$	24.3389	−	6.67968i	0.964342	−	0.264659i
$638$		−	14.5740i		−	0.576991i
$639$	−6.11902	+	21.1463i	−0.242065	+	0.836535i
$640$	1.83049			0.0723566
$641$	−12.0856	+	20.9329i	−0.477353	+	0.826800i	−0.999663	−	0.0259555i	$-0.991737\pi$
$641$	−12.0856	+	20.9329i	−0.477353	+	0.826800i	0.522310	+	0.852756i	$0.325071\pi$
$642$	−5.71889	+	9.68194i	−0.225707	+	0.382116i
$643$	8.11515	−	30.2861i	0.320030	−	1.19437i	−0.599184	−	0.800611i	$-0.704508\pi$
$643$	8.11515	−	30.2861i	0.320030	−	1.19437i	0.919214	−	0.393757i	$-0.128825\pi$
$644$	−22.2405	+	4.20210i	−0.876397	+	0.165586i
$645$	36.9371	+	0.367038i	1.45440	+	0.0144521i
$646$	0.619696			0.0243816
$647$	−44.0152			−1.73042			−0.865208	−	0.501413i	$-0.832814\pi$
$647$	−44.0152			−1.73042			−0.865208	+	0.501413i	$0.832814\pi$
$648$	−6.10606	−	6.61181i	−0.239869	−	0.259736i
$649$	29.9702	+	17.3033i	1.17643	+	0.679213i
$650$	−5.87426	+	0.924932i	−0.230407	+	0.0362788i
$651$	−14.3460	+	12.0933i	−0.562264	+	0.473973i
$652$	14.8131	−	3.96917i	0.580127	−	0.155445i
$653$	27.6747	−	15.9780i	1.08300	−	0.625268i	0.151293	−	0.988489i	$-0.451656\pi$
$653$	27.6747	−	15.9780i	1.08300	−	0.625268i	0.931703	+	0.363221i	$0.118323\pi$
$654$	−4.31660	−	16.7748i	−0.168792	−	0.655945i
$655$	2.04310	−	7.62496i	0.0798306	−	0.297932i
$656$	2.61450	−	2.61450i	0.102079	−	0.102079i
$657$	−5.16116	+	17.8361i	−0.201356	+	0.695852i
$658$	4.78772	+	25.3400i	0.186645	+	0.987855i
$659$	−8.48563	+	4.89918i	−0.330553	+	0.190845i	−0.656087	−	0.754686i	$-0.727789\pi$
$659$	−8.48563	+	4.89918i	−0.330553	+	0.190845i	0.325534	+	0.945531i	$0.394456\pi$
$660$	3.58695	−	12.8736i	0.139622	−	0.501105i
$661$	28.5622	−	28.5622i	1.11094	−	1.11094i	0.117917	−	0.993023i	$-0.462378\pi$
$661$	28.5622	−	28.5622i	1.11094	−	1.11094i	0.993023	−	0.117917i	$-0.0376216\pi$
$662$	−11.3970	−	19.7402i	−0.442958	−	0.767226i
$663$	−0.427432	−	2.90202i	−0.0166001	−	0.112705i
$664$	3.96093			0.153714
$665$	−6.03039	−	2.11189i	−0.233849	−	0.0818957i
$666$	10.4014	−	17.2164i	0.403047	−	0.667121i
$667$		−	29.5789i		−	1.14530i
$668$	19.4502	+	5.21167i	0.752551	+	0.201645i
$669$	13.4594	−	22.7864i	0.520369	−	0.880973i
$670$	−0.555557	+	0.555557i	−0.0214630	+	0.0214630i
$671$	−32.4819	−	32.4819i	−1.25395	−	1.25395i
$672$	−1.55756	+	4.30976i	−0.0600842	+	0.166253i
$673$	−15.1655	−	8.75581i	−0.584588	−	0.337512i	0.178367	−	0.983964i	$-0.442919\pi$
$673$	−15.1655	−	8.75581i	−0.584588	−	0.337512i	−0.762954	+	0.646452i	$0.776252\pi$
$674$	1.82219	−	6.80052i	0.0701883	−	0.261946i
$675$	8.20820	+	2.46382i	0.315934	+	0.0948325i
$676$	9.64509	+	8.71620i	0.370965	+	0.335239i
$677$	−37.4927	−	21.6464i	−1.44096	−	0.831938i	−0.443046	−	0.896499i	$-0.646102\pi$
$677$	−37.4927	−	21.6464i	−1.44096	−	0.831938i	−0.997914	+	0.0645604i	$0.979435\pi$
$678$	−14.8672	+	25.1698i	−0.570971	+	0.966641i
$679$	−7.11074	−	0.534746i	−0.272885	−	0.0205217i
$680$	−0.429899	−	0.744607i	−0.0164859	−	0.0285544i
$681$	−25.7317	−	15.1991i	−0.986042	−	0.582431i
$682$	16.6704	−	4.46683i	0.638344	−	0.171044i
$683$	−7.14274	+	1.91389i	−0.273309	+	0.0732331i	−0.392871	−	0.919594i	$-0.628518\pi$
$683$	−7.14274	+	1.91389i	−0.273309	+	0.0732331i	0.119561	+	0.992827i	$0.461851\pi$
$684$	3.84270	−	0.948221i	0.146929	−	0.0362561i
$685$	10.3072	+	17.8527i	0.393819	+	0.682115i
$686$	5.44506	+	17.7017i	0.207893	+	0.675855i
$687$	−39.8381	−	23.5314i	−1.51992	−	0.897780i
$688$	10.0899	+	5.82539i	0.384673	+	0.222091i
$689$	−10.5585	+	4.68947i	−0.402246	+	0.178655i
$690$	7.27996	−	26.1279i	0.277143	−	0.994671i
$691$	−1.90039	+	7.09235i	−0.0722943	+	0.269806i	−0.992606	−	0.121380i	$-0.961268\pi$
$691$	−1.90039	+	7.09235i	−0.0722943	+	0.269806i	0.920312	+	0.391185i	$0.127935\pi$
$692$	17.4628	+	10.0822i	0.663838	+	0.383267i
$693$	27.2579	+	19.3993i	1.03544	+	0.736920i
$694$	−23.3162	−	23.3162i	−0.885072	−	0.885072i
$695$	−29.6339	+	29.6339i	−1.12408	+	1.12408i
$696$	−5.15635	−	3.04573i	−0.195451	−	0.115448i
$697$	−1.67755	−	0.449499i	−0.0635419	−	0.0170260i
$698$		−	2.76334i		−	0.104594i
$699$	8.25665	+	32.0862i	0.312295	+	1.21361i
$700$	−0.810129	−	4.28777i	−0.0306200	−	0.162063i
$701$	−8.78964			−0.331980			−0.165990	−	0.986127i	$-0.553082\pi$
$701$	−8.78964			−0.331980			−0.165990	+	0.986127i	$0.553082\pi$
$702$	−7.09098	−	17.3412i	−0.267632	−	0.654502i
$703$	4.42291	+	7.66070i	0.166813	+	0.288929i
$704$	2.98053	−	2.98053i	0.112333	−	0.112333i
$705$	−29.7692	−	8.29452i	−1.12117	−	0.312390i
$706$	−2.72544	+	1.57354i	−0.102573	+	0.0592208i
$707$	−6.48566	−	34.3267i	−0.243918	−	1.29099i
$708$	12.3852	−	6.98747i	0.465466	−	0.262605i
$709$	−4.37369	+	4.37369i	−0.164257	+	0.164257i	−0.784450	−	0.620192i	$-0.787055\pi$
$709$	−4.37369	+	4.37369i	−0.164257	+	0.164257i	0.620192	+	0.784450i	$0.287055\pi$
$710$	−3.47647	+	12.9744i	−0.130470	+	0.486919i
$711$	34.9130	+	21.0930i	1.30934	+	0.791049i
$712$	5.08988	−	2.93864i	0.190751	−	0.110130i
$713$	33.8338	−	9.06573i	1.26708	−	0.339514i
$714$	2.11892	−	0.378582i	0.0792987	−	0.0141681i
$715$	16.3722	−	22.4915i	0.612287	−	0.841135i
$716$	−4.76942	−	2.75363i	−0.178242	−	0.102908i
$717$	0.204135	−	20.5433i	0.00762357	−	0.767202i
$718$	21.9782			0.820217
$719$	18.9811			0.707876			0.353938	−	0.935269i	$-0.384842\pi$
$719$	18.9811			0.707876			0.353938	+	0.935269i	$0.384842\pi$
$720$	−3.80513	−	3.95946i	−0.141809	−	0.147560i
$721$	−4.49250	+	12.8281i	−0.167310	+	0.477743i
$722$	4.46706	−	16.6713i	0.166247	−	0.620441i
$723$	30.9123	+	18.2591i	1.14964	+	0.679064i
$724$	8.06951	−	13.9768i	0.299901	−	0.519444i
$725$	5.70257			0.211788
$726$	−5.75931	−	10.2083i	−0.213748	−	0.378867i
$727$		−	34.8355i		−	1.29198i	−0.763347	−	0.645989i	$-0.776445\pi$
$727$		−	34.8355i		−	1.29198i	0.763347	−	0.645989i	$-0.223555\pi$
$728$	−6.17666	+	7.26972i	−0.228922	+	0.269434i
$729$	−1.60876	+	26.9520i	−0.0595838	+	0.998223i
$730$	−2.93227	+	10.9434i	−0.108528	+	0.405032i
$731$		−	5.47248i		−	0.202407i
$732$	−18.2804	+	4.70405i	−0.675663	+	0.173867i
$733$	−43.7567	+	11.7246i	−1.61619	+	0.433057i	−0.949879	−	0.312617i	$-0.898794\pi$
$733$	−43.7567	+	11.7246i	−1.61619	+	0.433057i	−0.666311	+	0.745674i	$0.732128\pi$
$734$	5.20172	+	1.39380i	0.191999	+	0.0514459i
$735$	−21.9099	−	3.53713i	−0.808157	−	0.130469i
$736$	6.04918	−	6.04918i	0.222976	−	0.222976i
$737$			1.80919i			0.0666423i
$738$	−11.0902	−	0.220425i	−0.408236	−	0.00811395i
$739$	1.74707	−	1.74707i	0.0642669	−	0.0642669i	−0.674243	−	0.738510i	$-0.735530\pi$
$739$	1.74707	−	1.74707i	0.0642669	−	0.0642669i	0.738510	+	0.674243i	$0.235530\pi$
$740$	6.13657	−	10.6289i	0.225585	−	0.390724i
$741$	8.18419	+	0.950022i	0.300654	+	0.0348999i
$742$	−3.67630	−	7.63902i	−0.134961	−	0.280437i
$743$	−9.90850	−	36.9790i	−0.363507	−	1.35663i	−0.869433	−	0.494051i	$-0.835516\pi$
$743$	−9.90850	−	36.9790i	−0.363507	−	1.35663i	0.505925	−	0.862577i	$-0.331151\pi$
$744$	1.90347	−	6.83157i	0.0697845	−	0.250458i
$745$	12.4978	+	7.21562i	0.457884	+	0.264360i
$746$	−24.5787	−	6.58584i	−0.899890	−	0.241125i
$747$	−8.23378	−	8.56772i	−0.301258	−	0.313477i
$748$	−1.91241	−	0.512428i	−0.0699245	−	0.0187362i
$749$	−11.2008	−	13.0224i	−0.409267	−	0.475828i
$750$	20.3081	+	5.65840i	0.741546	+	0.206615i
$751$	40.6036	−	23.4425i	1.48165	−	0.855430i	0.481865	−	0.876246i	$-0.339960\pi$
$751$	40.6036	−	23.4425i	1.48165	−	0.855430i	0.999783	+	0.0208160i	$0.00662640\pi$
$752$	−6.89222	−	6.89222i	−0.251333	−	0.251333i
$753$	−10.2218	−	2.84807i	−0.372502	−	0.103789i
$754$	−7.83661	−	9.69537i	−0.285393	−	0.353085i
$755$		−	18.2112i		−	0.662772i
$756$	12.5600	−	5.58981i	0.456803	−	0.203299i
$757$	−2.02231	+	3.50275i	−0.0735022	+	0.127309i	−0.900434	−	0.434993i	$-0.856751\pi$
$757$	−2.02231	+	3.50275i	−0.0735022	+	0.127309i	0.826932	+	0.562302i	$0.190084\pi$
$758$	12.5145			0.454547
$759$	−30.6894	−	54.3968i	−1.11396	−	1.97448i
$760$	2.33271	−	0.625049i	0.0846165	−	0.0226729i
$761$	−7.31358	−	7.31358i	−0.265117	−	0.265117i	0.562012	−	0.827129i	$-0.310028\pi$
$761$	−7.31358	−	7.31358i	−0.265117	−	0.265117i	−0.827129	+	0.562012i	$0.810028\pi$
$762$	−3.72110	−	0.0369760i	−0.134801	−	0.00133950i
$763$	26.3841	+	1.98415i	0.955170	+	0.0718312i
$764$	0.279541	−	0.484179i	0.0101134	−	0.0175170i
$765$	−0.716975	+	2.47775i	−0.0259223	+	0.0895831i
$766$	−8.36796	+	4.83125i	−0.302347	+	0.174560i
$767$	29.2418	−	4.60427i	1.05586	−	0.166251i
$768$	−0.431642	−	1.67740i	−0.0155755	−	0.0605281i
$769$	−5.89522	+	1.57962i	−0.212587	+	0.0569625i	−0.363541	−	0.931578i	$-0.618432\pi$
$769$	−5.89522	+	1.57962i	−0.212587	+	0.0569625i	0.150954	+	0.988541i	$0.451766\pi$
$770$	16.8637	+	11.5039i	0.607726	+	0.414573i
$771$	14.8557	+	4.13921i	0.535015	+	0.149070i
$772$	12.8958	−	3.45542i	0.464130	−	0.124363i
$773$	−6.99903	−	26.1207i	−0.251738	−	0.939498i	−0.969876	−	0.243598i	$-0.921672\pi$
$773$	−6.99903	−	26.1207i	−0.251738	−	0.939498i	0.718139	−	0.695900i	$-0.244994\pi$
$774$	−8.37365	−	33.9345i	−0.300985	−	1.21975i
$775$	1.74780	+	6.52287i	0.0627827	+	0.234308i
$776$	2.33411	−	1.34760i	0.0837897	−	0.0483760i
$777$	19.8033	+	23.4921i	0.710438	+	0.842776i
$778$	8.85283	+	33.0392i	0.317389	+	1.18451i
$779$	2.43907	−	4.22459i	0.0873887	−	0.151362i
$780$	−4.53607	−	10.4929i	−0.162417	−	0.375707i
$781$	15.4651	+	26.7863i	0.553385	+	0.958490i
$782$	−3.88136	−	1.04001i	−0.138797	−	0.0371906i
$783$	4.13066	+	17.4848i	0.147618	+	0.624855i
$784$	−5.47054	−	4.36729i	−0.195376	−	0.155975i
$785$	15.3199	−	15.3199i	0.546790	−	0.546790i
$786$	−7.46905	−	0.0742187i	−0.266412	−	0.00264729i
$787$	−3.20226	−	11.9510i	−0.114148	−	0.426007i	0.885074	−	0.465451i	$-0.154108\pi$
$787$	−3.20226	−	11.9510i	−0.114148	−	0.426007i	−0.999222	+	0.0394444i	$0.987441\pi$
$788$	−0.0908854	+	0.339189i	−0.00323766	+	0.0120831i
$789$	5.54305	+	5.65432i	0.197338	+	0.201299i
$790$	21.5542	+	12.4443i	0.766864	+	0.442749i
$791$	−29.1182	−	33.8539i	−1.03532	−	1.20371i
$792$	−12.6428	−	0.251284i	−0.449243	−	0.00892898i
$793$	−39.0744	−	4.14271i	−1.38757	−	0.147112i
$794$	4.75356	−	2.74447i	0.168698	−	0.0973976i
$795$	10.1585	+	0.100944i	0.360286	+	0.00358011i
$796$	8.86980	+	15.3630i	0.314382	+	0.544525i
$797$	1.57225	+	2.72322i	0.0556919	+	0.0964613i	0.892527	−	0.450993i	$-0.148930\pi$
$797$	1.57225	+	2.72322i	0.0556919	+	0.0964613i	−0.836835	+	0.547455i	$0.815597\pi$
$798$	−0.513267	+	6.02405i	−0.0181695	+	0.213249i
$799$	−1.18495	+	4.42228i	−0.0419204	+	0.156449i
$800$	1.16623	+	1.16623i	0.0412325	+	0.0412325i
$801$	−16.9370	−	4.90100i	−0.598440	−	0.173168i
$802$	4.26038	−	7.37920i	0.150439	−	0.260569i
$803$	13.0442	+	22.5932i	0.460320	+	0.797297i
$804$	0.640098	+	0.378091i	0.0225745	+	0.0133342i
$805$	34.2260	+	23.3480i	1.20631	+	0.822909i
$806$	8.68815	−	11.9354i	0.306027	−	0.420408i
$807$	−2.92205	+	0.751924i	−0.102861	+	0.0264690i
$808$	9.33650	+	9.33650i	0.328457	+	0.328457i
$809$			26.4193i			0.928854i	0.885611	+	0.464427i	$0.153740\pi$
$809$			26.4193i			0.928854i	−0.885611	+	0.464427i	$0.846260\pi$
$810$	−0.654621	+	16.4614i	−0.0230010	+	0.578395i
$811$	17.2238	+	17.2238i	0.604809	+	0.604809i	0.941585	−	0.336776i	$-0.109336\pi$
$811$	17.2238	+	17.2238i	0.604809	+	0.604809i	−0.336776	+	0.941585i	$0.609336\pi$
$812$	6.93539	−	5.96524i	0.243385	−	0.209339i
$813$	−16.6418	+	9.38889i	−0.583652	+	0.329283i
$814$	−7.31462	−	27.2985i	−0.256377	−	0.956814i
$815$	−24.3109	−	14.0359i	−0.851575	−	0.491657i
$816$	−0.580961	+	0.569529i	−0.0203377	+	0.0199375i
$817$	14.8474	+	3.97834i	0.519443	+	0.139184i
$818$	12.0813			0.422414
$819$	28.5645	−	1.75144i	0.998125	−	0.0612004i
$820$	−6.76818			−0.236355
$821$	−4.83739	−	1.29617i	−0.168826	−	0.0452368i	0.173416	−	0.984849i	$-0.444520\pi$
$821$	−4.83739	−	1.29617i	−0.168826	−	0.0452368i	−0.342242	+	0.939612i	$0.611186\pi$
$822$	13.9291	−	13.6550i	0.485833	−	0.476273i
$823$	−28.9493	−	16.7139i	−1.00911	−	0.582610i	−0.0981789	−	0.995169i	$-0.531302\pi$
$823$	−28.9493	−	16.7139i	−1.00911	−	0.582610i	−0.910931	+	0.412559i	$0.864635\pi$
$824$	−1.32963	−	4.96224i	−0.0463198	−	0.172868i
$825$	10.4872	−	5.91666i	0.365119	−	0.205992i
$826$	4.03279	+	21.3443i	0.140319	+	0.742665i
$827$	8.82801	+	8.82801i	0.306980	+	0.306980i	0.843737	−	0.536757i	$-0.180351\pi$
$827$	8.82801	+	8.82801i	0.306980	+	0.306980i	−0.536757	+	0.843737i	$0.680351\pi$
$828$	−25.6594	−	0.509997i	−0.891726	−	0.0177236i
$829$		−	23.5195i		−	0.816867i	−0.912788	−	0.408434i	$-0.866075\pi$
$829$		−	23.5195i		−	0.816867i	0.912788	−	0.408434i	$-0.133925\pi$
$830$	−5.12685	−	5.12685i	−0.177956	−	0.177956i
$831$	44.3100	−	11.4022i	1.53710	−	0.395537i
$832$	0.380134	−	3.58546i	0.0131788	−	0.124303i
$833$	−0.491745	+	3.25098i	−0.0170379	+	0.112640i
$834$	34.1434	+	20.1677i	1.18229	+	0.698350i
$835$	−18.4297	−	31.9212i	−0.637786	−	1.10468i
$836$	2.78053	−	4.81602i	0.0961667	−	0.166566i
$837$	−18.7339	+	10.0838i	−0.647538	+	0.348547i
$838$	−4.05804	−	4.05804i	−0.140183	−	0.140183i
$839$	13.6496	−	50.9411i	0.471237	−	1.75868i	−0.164097	−	0.986444i	$-0.552471\pi$
$839$	13.6496	−	50.9411i	0.471237	−	1.75868i	0.635335	−	0.772237i	$-0.280862\pi$
$840$	7.59438	−	3.56232i	0.262031	−	0.122912i
$841$	−8.52259	−	14.7616i	−0.293882	−	0.509019i
$842$	5.31179	+	9.20030i	0.183057	+	0.317063i
$843$	22.7741	+	0.226302i	0.784380	+	0.00779426i
$844$	−9.18465	+	5.30276i	−0.316149	+	0.182528i
$845$	−1.20231	−	23.7660i	−0.0413608	−	0.817575i
$846$	−0.581073	+	29.2354i	−0.0199777	+	1.00513i
$847$	17.5927	−	3.32396i	0.604494	−	0.114213i
$848$	2.77495	+	1.60212i	0.0952921	+	0.0550169i
$849$	12.1483	+	12.3921i	0.416928	+	0.425297i
$850$	0.200505	−	0.748293i	0.00687725	−	0.0256662i
$851$	−14.8455	−	55.4042i	−0.508898	−	1.89923i
$852$	12.7091	+	0.126288i	0.435406	+	0.00432656i
$853$	−7.75900	+	7.75900i	−0.265663	+	0.265663i	−0.827350	−	0.561687i	$-0.810153\pi$
$853$	−7.75900	+	7.75900i	−0.265663	+	0.265663i	0.561687	+	0.827350i	$0.310153\pi$
$854$	2.16224	−	28.7523i	0.0739905	−	0.983884i
$855$	−6.20114	−	3.74647i	−0.212074	−	0.128127i
$856$	6.27098	+	1.68030i	0.214338	+	0.0574316i
$857$	11.7558	+	20.3616i	0.401570	+	0.695539i	0.993916	−	0.110145i	$-0.0351314\pi$
$857$	11.7558	+	20.3616i	0.401570	+	0.695539i	−0.592346	+	0.805684i	$0.701798\pi$
$858$	−24.4712	−	9.69934i	−0.835432	−	0.331130i
$859$	12.7497	−	22.0832i	0.435015	−	0.753468i	−0.562282	−	0.826946i	$-0.690076\pi$
$859$	12.7497	−	22.0832i	0.435015	−	0.753468i	0.997297	+	0.0734777i	$0.0234098\pi$
$860$	−5.51975	−	20.6000i	−0.188222	−	0.702454i
$861$	5.75902	−	15.9352i	0.196267	−	0.543069i
$862$	−10.7258	+	6.19255i	−0.365323	+	0.210919i
$863$	8.35227	+	31.1711i	0.284315	+	1.06108i	0.949339	+	0.314255i	$0.101755\pi$
$863$	8.35227	+	31.1711i	0.284315	+	1.06108i	−0.665024	+	0.746822i	$0.731579\pi$
$864$	−2.73105	+	4.42056i	−0.0929120	+	0.150391i
$865$	−9.55319	−	35.6530i	−0.324818	−	1.21224i
$866$	−19.3830	+	5.19366i	−0.658661	+	0.176488i
$867$	−27.9963	−	7.80055i	−0.950805	−	0.264921i
$868$	8.94896	+	6.10473i	0.303748	+	0.207208i
$869$	55.3586	−	14.8333i	1.87791	−	0.503185i
$870$	2.73189	+	10.6164i	0.0926197	+	0.359930i
$871$	0.972820	+	1.20356i	0.0329627	+	0.0407811i
$872$	−8.66062	+	5.00021i	−0.293286	+	0.169329i
$873$	−7.76696	−	2.24749i	−0.262872	−	0.0760661i
$874$	5.64327	−	9.77444i	0.190887	−	0.330625i
$875$	−18.1474	+	26.6024i	−0.613494	+	0.899325i
$876$	10.7196	+	0.106519i	0.362182	+	0.00359894i
$877$	10.6940	+	10.6940i	0.361112	+	0.361112i	0.864222	−	0.503110i	$-0.167811\pi$
$877$	10.6940	+	10.6940i	0.361112	+	0.361112i	−0.503110	+	0.864222i	$0.667811\pi$
$878$	−14.6563	+	3.92714i	−0.494626	+	0.132535i
$879$	−0.0832925	−	0.147636i	−0.00280939	−	0.00497962i
$880$	−7.71571			−0.260097
$881$	0.216879	−	0.375646i	0.00730684	−	0.0126558i	−0.862349	−	0.506315i	$-0.831007\pi$
$881$	0.216879	−	0.375646i	0.00730684	−	0.0126558i	0.869656	+	0.493659i	$0.164341\pi$
$882$	1.92518	+	20.9116i	0.0648241	+	0.704129i
$883$			8.07035i			0.271589i	0.990737	+	0.135794i	$0.0433587\pi$
$883$			8.07035i			0.271589i	−0.990737	+	0.135794i	$0.956641\pi$
$884$	−1.54777	+	0.687429i	−0.0520570	+	0.0231208i
$885$	−25.0751	−	6.98664i	−0.842892	−	0.234853i
$886$	25.0422	+	25.0422i	0.841309	+	0.841309i
$887$	−19.2581	+	11.1187i	−0.646623	+	0.373328i	−0.787161	−	0.616747i	$-0.788450\pi$
$887$	−19.2581	+	11.1187i	−0.646623	+	0.373328i	0.140538	+	0.990075i	$0.455117\pi$
$888$	−11.1870	−	3.11700i	−0.375410	−	0.104600i
$889$	1.87883	−	5.36488i	0.0630138	−	0.179932i
$890$	−10.3917	−	2.78446i	−0.348332	−	0.0933353i
$891$	25.7377	+	27.8695i	0.862244	+	0.933662i
$892$	−14.7587	−	3.95458i	−0.494158	−	0.132409i
$893$	−11.1366	−	6.42975i	−0.372674	−	0.215163i
$894$	3.66509	−	13.1541i	0.122579	−	0.439938i
$895$	2.60915	+	9.73748i	0.0872143	+	0.325488i
$896$	2.63830	+	0.198407i	0.0881395	+	0.00662831i
$897$	−49.6659	−	19.6854i	−1.65830	−	0.657278i
$898$	3.16612	−	5.48389i	0.105655	−	0.183000i
$899$	−10.0104	+	10.0104i	−0.333866	+	0.333866i
$900$	0.0983232	−	4.94692i	0.00327744	−	0.164897i
$901$		−	1.50506i		−	0.0501407i
$902$	−11.0204	+	11.0204i	−0.366939	+	0.366939i
$903$	53.1979	+	4.53262i	1.77031	+	0.150836i
$904$	16.3024	+	4.36823i	0.542211	+	0.145285i
$905$	−28.5357	+	7.64613i	−0.948560	+	0.254166i
$906$	−16.6881	+	4.29431i	−0.554426	+	0.142669i
$907$		−	20.7043i		−	0.687476i	−0.939066	−	0.343738i	$-0.888307\pi$
$907$		−	20.7043i		−	0.687476i	0.939066	−	0.343738i	$-0.111693\pi$
$908$	−4.46575	+	16.6664i	−0.148201	+	0.553094i
$909$	0.787147	−	39.6036i	0.0261080	−	1.31357i
$910$	17.4044	−	1.41480i	0.576949	−	0.0469003i
$911$			53.6626i			1.77792i	0.457985	+	0.888960i	$0.348571\pi$
$911$			53.6626i			1.77792i	−0.457985	+	0.888960i	$0.651429\pi$
$912$	−1.12284	−	1.99023i	−0.0371811	−	0.0659032i
$913$	−16.6957			−0.552548
$914$	−11.6878	+	20.2438i	−0.386597	+	0.669605i
$915$	29.7500	+	17.5726i	0.983505	+	0.580933i
$916$	−6.91392	+	25.8031i	−0.228442	+	0.852558i
$917$	3.77121	−	10.7685i	0.124536	−	0.355606i
$918$	2.43959	+	0.0727447i	0.0805186	+	0.00240093i
$919$	−31.6973			−1.04560			−0.522798	−	0.852457i	$-0.675112\pi$
$919$	−31.6973			−1.04560			−0.522798	+	0.852457i	$0.675112\pi$
$920$	−15.6595			−0.516280
$921$	−0.453431	+	45.6313i	−0.0149411	+	1.50360i
$922$	−11.7942	−	6.80939i	−0.388422	−	0.224255i
$923$	24.6915	+	9.50386i	0.812729	+	0.312823i
$924$	6.56527	−	18.1661i	0.215982	−	0.597620i
$925$	10.6815	−	2.86209i	0.351204	−	0.0941049i
$926$	9.12730	−	5.26965i	0.299942	−	0.173172i
$927$	−7.96964	+	13.1913i	−0.261757	+	0.433259i
$928$	−0.894886	+	3.33976i	−0.0293761	+	0.109633i
$929$	−28.2429	+	28.2429i	−0.926621	+	0.926621i	−0.997486	−	0.0708652i	$-0.977424\pi$
$929$	−28.2429	+	28.2429i	−0.926621	+	0.926621i	0.0708652	+	0.997486i	$0.477424\pi$
$930$	−11.3062	+	6.37871i	−0.370746	+	0.209166i
$931$	−8.46274	−	3.69752i	−0.277355	−	0.121181i
$932$	16.5657	−	9.56424i	0.542629	−	0.313287i
$933$	−11.2599	−	3.13733i	−0.368633	−	0.102712i
$934$	−8.19603	+	8.19603i	−0.268182	+	0.268182i
$935$	1.81207	+	3.13859i	0.0592610	+	0.102643i
$936$	−8.54574	+	6.63101i	−0.279326	+	0.216741i
$937$	36.5451			1.19388			0.596938	−	0.802288i	$-0.296384\pi$
$937$	36.5451			1.19388			0.596938	+	0.802288i	$0.296384\pi$
$938$	−0.860945	+	0.740511i	−0.0281108	+	0.0241786i
$939$	3.25848	+	12.6628i	0.106337	+	0.413235i
$940$			17.8419i			0.581940i
$941$	−27.2251	−	7.29494i	−0.887512	−	0.237808i	−0.213867	−	0.976863i	$-0.568606\pi$
$941$	−27.2251	−	7.29494i	−0.887512	−	0.237808i	−0.673645	+	0.739055i	$0.735272\pi$
$942$	−17.6512	−	10.4261i	−0.575107	−	0.339702i
$943$	−22.3666	+	22.3666i	−0.728357	+	0.728357i
$944$	−5.80544	−	5.80544i	−0.188951	−	0.188951i
$945$	−23.4923	−	9.02191i	−0.764204	−	0.293483i
$946$	−42.5299	−	24.5546i	−1.38277	−	0.798340i
$947$	−5.99476	+	22.3727i	−0.194804	+	0.727017i	0.797514	+	0.603300i	$0.206148\pi$
$947$	−5.99476	+	22.3727i	−0.194804	+	0.727017i	−0.992318	+	0.123716i	$0.960519\pi$
$948$	6.32096	−	22.6860i	0.205295	−	0.736808i
$949$	20.8263	+	8.01613i	0.676049	+	0.260215i
$950$	1.88443	+	1.08798i	0.0611390	+	0.0352986i
$951$	−34.7996	−	20.5553i	−1.12846	−	0.666551i
$952$	−0.538909	−	1.11980i	−0.0174661	−	0.0362931i
$953$	−14.4888	−	25.0954i	−0.469339	−	0.812920i	0.530046	−	0.847969i	$-0.322175\pi$
$953$	−14.4888	−	25.0954i	−0.469339	−	0.812920i	−0.999386	+	0.0350490i	$0.988841\pi$
$954$	−2.30295	−	9.33276i	−0.0745607	−	0.302159i
$955$	−0.988524	+	0.264874i	−0.0319879	+	0.00857113i
$956$	−11.4571	+	3.06992i	−0.370549	+	0.0992882i
$957$	21.7345	+	12.8381i	0.702578	+	0.414996i
$958$	−10.9623	−	18.9873i	−0.354176	−	0.613451i
$959$	12.9209	+	26.8484i	0.417236	+	0.866979i
$960$	−1.61246	+	2.72985i	−0.0520418	+	0.0881056i
$961$	12.3283	+	7.11774i	0.397687	+	0.229605i
$962$	−19.5448	−	14.2272i	−0.630149	−	0.458704i
$963$	−9.40119	−	17.0574i	−0.302949	−	0.549667i
$964$	5.36483	−	20.0218i	0.172790	−	0.644860i
$965$	−21.1643	−	12.2192i	−0.681302	−	0.393350i
$966$	13.3246	−	36.8692i	0.428714	−	1.18625i
$967$	−30.6197	−	30.6197i	−0.984663	−	0.984663i	0.0152208	−	0.999884i	$-0.495155\pi$
$967$	−30.6197	−	30.6197i	−0.984663	−	0.984663i	−0.999884	+	0.0152208i	$0.995155\pi$
$968$	−4.78505	+	4.78505i	−0.153797	+	0.153797i
$969$	−0.545882	+	0.924165i	−0.0175363	+	0.0296885i
$970$	−4.76543	−	1.27689i	−0.153009	−	0.0409986i
$971$		−	1.70826i		−	0.0548206i	−0.999624	−	0.0274103i	$-0.991274\pi$
$971$		−	1.70826i		−	0.0548206i	0.999624	−	0.0274103i	$-0.00872607\pi$
$972$	15.2391	−	3.28183i	0.488794	−	0.105265i
$973$	−45.9236	+	39.4995i	−1.47224	+	1.26630i
$974$	−7.14329			−0.228886
$975$	3.79519	−	9.57516i	0.121543	−	0.306651i
$976$	5.44902	+	9.43798i	0.174419	+	0.302102i
$977$	21.3728	−	21.3728i	0.683776	−	0.683776i	−0.277073	−	0.960849i	$-0.589364\pi$
$977$	21.3728	−	21.3728i	0.683776	−	0.683776i	0.960849	+	0.277073i	$0.0893645\pi$
$978$	−7.12940	+	25.5875i	−0.227973	+	0.818199i
$979$	−21.4544	+	12.3867i	−0.685684	+	0.395880i
$980$	1.42799	+	12.7336i	0.0456156	+	0.406761i
$981$	28.8190	+	8.33923i	0.920119	+	0.266251i
$982$	−25.6767	+	25.6767i	−0.819376	+	0.819376i
$983$	15.8322	−	59.0866i	0.504969	−	1.88457i	0.0400888	−	0.999196i	$-0.487236\pi$
$983$	15.8322	−	59.0866i	0.504969	−	1.88457i	0.464880	−	0.885374i	$-0.346097\pi$
$984$	1.59598	+	6.20214i	0.0508780	+	0.197717i
$985$	0.556668	−	0.321393i	0.0177369	−	0.0102404i
$986$	1.56871	−	0.420336i	0.0499581	−	0.0133862i
$987$	−42.0075	−	15.1816i	−1.33711	−	0.483237i
$988$	−0.739879	−	4.69898i	−0.0235387	−	0.149495i
$989$	−86.3172	−	49.8352i	−2.74473	−	1.58467i
$990$	16.0390	+	16.6895i	0.509753	+	0.530427i
$991$	48.3629			1.53630			0.768148	−	0.640272i	$-0.221178\pi$
$991$	48.3629			1.53630			0.768148	+	0.640272i	$0.221178\pi$
$992$	−4.09445			−0.129999
$993$	39.4785	+	0.392292i	1.25281	+	0.0124490i
$994$	−6.41695	+	18.3232i	−0.203533	+	0.581178i
$995$	8.40443	−	31.3658i	0.266438	−	0.994361i
$996$	−3.48914	+	5.90702i	−0.110558	+	0.187171i
$997$	2.04093	−	3.53500i	0.0646370	−	0.111954i	−0.831896	−	0.554932i	$-0.812744\pi$
$997$	2.04093	−	3.53500i	0.0646370	−	0.111954i	0.896533	+	0.442977i	$0.146078\pi$
$998$	36.5707			1.15763
$999$	16.5126	+	30.6775i	0.522437	+	0.970594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.527.24	yes	152
3.2	odd	2	inner	546.2.bw.a.527.5	yes	152
7.4	even	3		546.2.ch.a.137.18	yes	152
13.2	odd	12		546.2.ch.a.275.27	yes	152
21.11	odd	6		546.2.ch.a.137.27	yes	152
39.2	even	12		546.2.ch.a.275.18	yes	152
91.67	odd	12	inner	546.2.bw.a.431.5	✓	152
273.158	even	12	inner	546.2.bw.a.431.24	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.5	✓	152	91.67	odd	12	inner
546.2.bw.a.431.24	yes	152	273.158	even	12	inner
546.2.bw.a.527.5	yes	152	3.2	odd	2	inner
546.2.bw.a.527.24	yes	152	1.1	even	1	trivial
546.2.ch.a.137.18	yes	152	7.4	even	3
546.2.ch.a.137.27	yes	152	21.11	odd	6
546.2.ch.a.275.18	yes	152	39.2	even	12
546.2.ch.a.275.27	yes	152	13.2	odd	12

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)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.23685 + 1.21251i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.473766 - 1.76812i) q^{5} +(-1.50853 + 0.851078i) q^{6} +(-0.491196 - 2.59976i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.0596151 - 2.99941i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.23685 + 1.21251i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.473766 - 1.76812i) q^{5} +(-1.50853 + 0.851078i) q^{6} +(-0.491196 - 2.59976i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.0596151 - 2.99941i) q^{9} -1.83049i q^{10} +(-2.98053 - 2.98053i) q^{11} +(-1.67740 + 0.431642i) q^{12} +(-3.58546 - 0.380134i) q^{13} +(0.198407 - 2.63830i) q^{14} +(2.72985 + 1.61246i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.234854 - 0.406780i) q^{17} +(0.833888 - 2.88178i) q^{18} +(0.932900 + 0.932900i) q^{19} +(0.473766 - 1.76812i) q^{20} +(3.75978 + 2.61993i) q^{21} +(-2.10755 - 3.65038i) q^{22} +(-4.27741 - 7.40870i) q^{23} +(-1.73197 - 0.0172103i) q^{24} +(1.42833 - 0.824649i) q^{25} +(-3.36490 - 1.29517i) q^{26} +(3.56309 + 3.78211i) q^{27} +(0.874489 - 2.49705i) q^{28} +(2.99435 + 1.72879i) q^{29} +(2.21950 + 2.26405i) q^{30} +(-1.05972 + 3.95493i) q^{31} +(0.258819 + 0.965926i) q^{32} +(7.30041 + 0.0725430i) q^{33} +(0.332134 - 0.332134i) q^{34} +(-4.36397 + 2.10017i) q^{35} +(1.55133 - 2.56776i) q^{36} +(6.47637 + 1.73534i) q^{37} +(0.659660 + 1.14256i) q^{38} +(4.89560 - 3.87725i) q^{39} +(0.915246 - 1.58525i) q^{40} +(-0.956974 - 3.57148i) q^{41} +(2.95358 + 3.50376i) q^{42} +(10.0899 - 5.82539i) q^{43} +(-1.09095 - 4.07148i) q^{44} +(-5.33156 + 1.31561i) q^{45} +(-2.21415 - 8.26333i) q^{46} +(-9.41494 + 2.52273i) q^{47} +(-1.66850 - 0.464889i) q^{48} +(-6.51745 + 2.55398i) q^{49} +(1.59310 - 0.426870i) q^{50} +(0.202746 + 0.787892i) q^{51} +(-2.91503 - 2.12193i) q^{52} +(2.77495 - 1.60212i) q^{53} +(2.46280 + 4.57544i) q^{54} +(-3.85785 + 6.68200i) q^{55} +(1.49098 - 2.18563i) q^{56} +(-2.28502 - 0.0227058i) q^{57} +(2.44487 + 2.44487i) q^{58} +(-7.93039 + 2.12494i) q^{59} +(1.55789 + 2.76135i) q^{60} +10.8980 q^{61} +(-2.04722 + 3.54590i) q^{62} +(-7.82701 + 1.31831i) q^{63} +1.00000i q^{64} +(1.02655 + 6.51961i) q^{65} +(7.03288 + 1.95956i) q^{66} +(-0.303501 - 0.303501i) q^{67} +(0.406780 - 0.234854i) q^{68} +(14.2737 + 3.97705i) q^{69} +(-4.75883 + 0.899131i) q^{70} +(-7.08791 - 1.89920i) q^{71} +(2.16306 - 2.07875i) q^{72} +(-5.97838 - 1.60190i) q^{73} +(5.80655 + 3.35242i) q^{74} +(-0.766741 + 2.75185i) q^{75} +(0.341465 + 1.27436i) q^{76} +(-6.28462 + 9.21266i) q^{77} +(5.73230 - 2.47806i) q^{78} +(-6.79835 + 11.7751i) q^{79} +(1.29435 - 1.29435i) q^{80} +(-8.99289 - 0.357620i) q^{81} -3.69746i q^{82} +(2.80080 - 2.80080i) q^{83} +(1.94610 + 4.14882i) q^{84} +(-0.830501 - 0.222532i) q^{85} +(11.2538 - 3.01545i) q^{86} +(-5.79975 + 1.49243i) q^{87} -4.21510i q^{88} +(1.52115 - 5.67702i) q^{89} +(-5.49039 - 0.109125i) q^{90} +(0.772908 + 9.50803i) q^{91} -8.55483i q^{92} +(-3.48470 - 6.17660i) q^{93} -9.74707 q^{94} +(1.20750 - 2.09145i) q^{95} +(-1.49132 - 0.880887i) q^{96} +(0.697569 - 2.60336i) q^{97} +(-6.95639 + 0.780115i) q^{98} +(-9.11750 + 8.76213i) 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

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