LMFDB - Embedded newform 546.2.bv.a.317.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.15
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(1.19913 + 1.24984i) q^{3} +(0.866025 - 0.500000i) q^{4} +(4.04433 - 1.08367i) q^{5} +(-1.48175 - 0.896896i) q^{6} +(-1.05878 - 2.42466i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.124198 + 2.99743i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(1.19913 + 1.24984i) q^{3} +(0.866025 - 0.500000i) q^{4} +(4.04433 - 1.08367i) q^{5} +(-1.48175 - 0.896896i) q^{6} +(-1.05878 - 2.42466i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.124198 + 2.99743i) q^{9} +(-3.62604 + 2.09350i) q^{10} +(5.02047 + 1.34523i) q^{11} +(1.66339 + 0.482830i) q^{12} +(-2.74774 + 2.33451i) q^{13} +(1.65025 + 2.06801i) q^{14} +(6.20407 + 3.75530i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.25108 - 5.63104i) q^{17} +(-0.655825 - 2.92744i) q^{18} +(0.0105453 + 0.0393557i) q^{19} +(2.96065 - 2.96065i) q^{20} +(1.76083 - 4.23078i) q^{21} -5.19757 q^{22} +(0.836260 - 1.44845i) q^{23} +(-1.73168 - 0.0358606i) q^{24} +(10.8521 - 6.26546i) q^{25} +(2.04990 - 2.96613i) q^{26} +(-3.89523 + 3.43906i) q^{27} +(-2.12926 - 1.57043i) q^{28} +1.23920i q^{29} +(-6.96461 - 2.02161i) q^{30} +(1.08666 + 0.291169i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(4.33885 + 7.88788i) q^{33} +(4.59773 + 4.59773i) q^{34} +(-6.90960 - 8.65874i) q^{35} +(1.39116 + 2.65795i) q^{36} +(-7.25069 + 1.94282i) q^{37} +(-0.0203720 - 0.0352853i) q^{38} +(-6.21264 - 0.634866i) q^{39} +(-2.09350 + 3.62604i) q^{40} +(-2.50827 - 2.50827i) q^{41} +(-0.605821 + 4.54235i) q^{42} +2.91255i q^{43} +(5.02047 - 1.34523i) q^{44} +(2.74594 + 12.2572i) q^{45} +(-0.432880 + 1.61553i) q^{46} +(1.12778 + 4.20894i) q^{47} +(1.68196 - 0.413553i) q^{48} +(-4.75796 + 5.13437i) q^{49} +(-8.86069 + 8.86069i) q^{50} +(3.13944 - 10.8157i) q^{51} +(-1.21236 + 3.39561i) q^{52} +(-2.06893 + 1.19450i) q^{53} +(2.87241 - 4.33004i) q^{54} +21.7622 q^{55} +(2.46317 + 0.965823i) q^{56} +(-0.0365431 + 0.0603723i) q^{57} +(-0.320728 - 1.19697i) q^{58} +(6.99346 + 1.87389i) q^{59} +(7.25053 + 0.150148i) q^{60} +(1.51904 - 2.63106i) q^{61} -1.12499 q^{62} +(7.39925 - 2.87248i) q^{63} -1.00000i q^{64} +(-8.58291 + 12.4192i) q^{65} +(-6.23254 - 6.49613i) q^{66} +(5.09838 + 1.36611i) q^{67} +(-5.63104 - 3.25108i) q^{68} +(2.81311 - 0.691676i) q^{69} +(8.91521 + 6.57537i) q^{70} +(-1.64133 - 1.64133i) q^{71} +(-2.03168 - 2.20732i) q^{72} +(-3.62026 + 13.5110i) q^{73} +(6.50079 - 3.75323i) q^{74} +(20.8438 + 6.05031i) q^{75} +(0.0288104 + 0.0288104i) q^{76} +(-2.05385 - 13.5972i) q^{77} +(6.16527 - 0.994717i) q^{78} +(-1.80883 + 3.13299i) q^{79} +(1.08367 - 4.04433i) q^{80} +(-8.96915 - 0.744551i) q^{81} +(3.07199 + 1.77361i) q^{82} +(-9.53117 - 9.53117i) q^{83} +(-0.590469 - 4.54438i) q^{84} +(-19.2507 - 19.2507i) q^{85} +(-0.753824 - 2.81331i) q^{86} +(-1.54880 + 1.48595i) q^{87} +(-4.50123 + 2.59879i) q^{88} +(2.05741 + 7.67837i) q^{89} +(-5.82476 - 11.1288i) q^{90} +(8.56965 + 4.19060i) q^{91} -1.67252i q^{92} +(0.939124 + 1.70730i) q^{93} +(-2.17871 - 3.77363i) q^{94} +(0.0852974 + 0.147739i) q^{95} +(-1.51761 + 0.834784i) q^{96} +(-6.41874 + 6.41874i) q^{97} +(3.26697 - 6.19088i) q^{98} +(-4.65577 + 14.8814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	1.19913	+	1.24984i	0.692315	+	0.721595i
$3$	1.19913	+	1.24984i	0.692315	+	0.721595i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	4.04433	−	1.08367i	1.80868	−	0.484634i	0.813400	−	0.581705i	$-0.197614\pi$
$5$	4.04433	−	1.08367i	1.80868	−	0.484634i	0.995277	+	0.0970716i	$0.0309476\pi$
$6$	−1.48175	−	0.896896i	−0.604921	−	0.366156i
$7$	−1.05878	−	2.42466i	−0.400182	−	0.916436i
$7$	−1.05878	−	2.42466i	−0.400182	−	0.916436i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.124198	+	2.99743i	−0.0413994	+	0.999143i
$10$	−3.62604	+	2.09350i	−1.14666	+	0.662022i
$11$	5.02047	+	1.34523i	1.51373	+	0.405602i	0.917672	−	0.397340i	$-0.130067\pi$
$11$	5.02047	+	1.34523i	1.51373	+	0.405602i	0.596057	+	0.802942i	$0.296733\pi$
$12$	1.66339	+	0.482830i	0.480180	+	0.139381i
$13$	−2.74774	+	2.33451i	−0.762086	+	0.647476i
$13$	−2.74774	+	2.33451i	−0.762086	+	0.647476i
$14$	1.65025	+	2.06801i	0.441049	+	0.552699i
$15$	6.20407	+	3.75530i	1.60188	+	0.969614i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.25108	−	5.63104i	−0.788504	−	1.36573i	−0.926883	−	0.375349i	$-0.877523\pi$
$17$	−3.25108	−	5.63104i	−0.788504	−	1.36573i	0.138380	−	0.990379i	$-0.455811\pi$
$18$	−0.655825	−	2.92744i	−0.154579	−	0.690004i
$19$	0.0105453	+	0.0393557i	0.00241926	+	0.00902881i	0.967125	−	0.254302i	$-0.0818457\pi$
$19$	0.0105453	+	0.0393557i	0.00241926	+	0.00902881i	−0.964706	+	0.263331i	$0.915179\pi$
$20$	2.96065	−	2.96065i	0.662022	−	0.662022i
$21$	1.76083	−	4.23078i	0.384244	−	0.923232i
$22$	−5.19757			−1.10813
$23$	0.836260	−	1.44845i	0.174372	−	0.302022i	−0.765572	−	0.643351i	$-0.777544\pi$
$23$	0.836260	−	1.44845i	0.174372	−	0.302022i	0.939944	+	0.341329i	$0.110877\pi$
$24$	−1.73168	−	0.0358606i	−0.353478	−	0.00732002i
$25$	10.8521	−	6.26546i	2.17042	−	1.25309i
$26$	2.04990	−	2.96613i	0.402018	−	0.581706i
$27$	−3.89523	+	3.43906i	−0.749638	+	0.661848i
$28$	−2.12926	−	1.57043i	−0.402393	−	0.296783i
$29$			1.23920i			0.230113i	0.993359	+	0.115057i	$0.0367050\pi$
$29$			1.23920i			0.230113i	−0.993359	+	0.115057i	$0.963295\pi$
$30$	−6.96461	−	2.02161i	−1.27156	−	0.369093i
$31$	1.08666	+	0.291169i	0.195170	+	0.0522955i	0.355080	−	0.934836i	$-0.384454\pi$
$31$	1.08666	+	0.291169i	0.195170	+	0.0522955i	−0.159910	+	0.987132i	$0.551120\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	4.33885	+	7.88788i	0.755297	+	1.37310i
$34$	4.59773	+	4.59773i	0.788504	+	0.788504i
$35$	−6.90960	−	8.65874i	−1.16794	−	1.46359i
$36$	1.39116	+	2.65795i	0.231859	+	0.442991i
$37$	−7.25069	+	1.94282i	−1.19201	+	0.319397i	−0.799679	−	0.600428i	$-0.794997\pi$
$37$	−7.25069	+	1.94282i	−1.19201	+	0.319397i	−0.392328	+	0.919825i	$0.628330\pi$
$38$	−0.0203720	−	0.0352853i	−0.00330477	−	0.00572404i
$39$	−6.21264	−	0.634866i	−0.994819	−	0.101660i
$40$	−2.09350	+	3.62604i	−0.331011	+	0.573328i
$41$	−2.50827	−	2.50827i	−0.391726	−	0.391726i	0.483576	−	0.875302i	$-0.339338\pi$
$41$	−2.50827	−	2.50827i	−0.391726	−	0.391726i	−0.875302	+	0.483576i	$0.839338\pi$
$42$	−0.605821	+	4.54235i	−0.0934802	+	0.700900i
$43$			2.91255i			0.444160i	0.975028	+	0.222080i	$0.0712846\pi$
$43$			2.91255i			0.444160i	−0.975028	+	0.222080i	$0.928715\pi$
$44$	5.02047	−	1.34523i	0.756864	−	0.202801i
$45$	2.74594	+	12.2572i	0.409340	+	1.82719i
$46$	−0.432880	+	1.61553i	−0.0638247	+	0.238197i
$47$	1.12778	+	4.20894i	0.164504	+	0.613937i	0.998103	+	0.0615667i	$0.0196097\pi$
$47$	1.12778	+	4.20894i	0.164504	+	0.613937i	−0.833599	+	0.552370i	$0.813724\pi$
$48$	1.68196	−	0.413553i	0.242769	−	0.0596912i
$49$	−4.75796	+	5.13437i	−0.679709	+	0.733482i
$50$	−8.86069	+	8.86069i	−1.25309	+	1.25309i
$51$	3.13944	−	10.8157i	0.439610	−	1.51450i
$52$	−1.21236	+	3.39561i	−0.168124	+	0.470887i
$53$	−2.06893	+	1.19450i	−0.284189	+	0.164077i	−0.635318	−	0.772250i	$-0.719131\pi$
$53$	−2.06893	+	1.19450i	−0.284189	+	0.164077i	0.351129	+	0.936327i	$0.385798\pi$
$54$	2.87241	−	4.33004i	0.390886	−	0.589244i
$55$	21.7622			2.93441
$56$	2.46317	+	0.965823i	0.329154	+	0.129063i
$57$	−0.0365431	+	0.0603723i	−0.00484025	+	0.00799651i
$58$	−0.320728	−	1.19697i	−0.0421137	−	0.157170i
$59$	6.99346	+	1.87389i	0.910471	+	0.243960i	0.683508	−	0.729943i	$-0.260454\pi$
$59$	6.99346	+	1.87389i	0.910471	+	0.243960i	0.226964	+	0.973903i	$0.427120\pi$
$60$	7.25053	+	0.150148i	0.936039	+	0.0193841i
$61$	1.51904	−	2.63106i	0.194494	−	0.336873i	−0.752241	−	0.658888i	$-0.771027\pi$
$61$	1.51904	−	2.63106i	0.194494	−	0.336873i	0.946734	+	0.322015i	$0.104360\pi$
$62$	−1.12499			−0.142874
$63$	7.39925	−	2.87248i	0.932217	−	0.361899i
$64$		−	1.00000i		−	0.125000i
$65$	−8.58291	+	12.4192i	−1.06458	+	1.54041i
$66$	−6.23254	−	6.49613i	−0.767173	−	0.799619i
$67$	5.09838	+	1.36611i	0.622866	+	0.166896i	0.556430	−	0.830894i	$-0.312171\pi$
$67$	5.09838	+	1.36611i	0.622866	+	0.166896i	0.0664357	+	0.997791i	$0.478837\pi$
$68$	−5.63104	−	3.25108i	−0.682864	−	0.394252i
$69$	2.81311	−	0.691676i	0.338658	−	0.0832680i
$70$	8.91521	+	6.57537i	1.06557	+	0.785907i
$71$	−1.64133	−	1.64133i	−0.194790	−	0.194790i	0.602972	−	0.797762i	$-0.293983\pi$
$71$	−1.64133	−	1.64133i	−0.194790	−	0.194790i	−0.797762	+	0.602972i	$0.793983\pi$
$72$	−2.03168	−	2.20732i	−0.239436	−	0.260136i
$73$	−3.62026	+	13.5110i	−0.423719	+	1.58134i	0.342986	+	0.939341i	$0.388562\pi$
$73$	−3.62026	+	13.5110i	−0.423719	+	1.58134i	−0.766705	+	0.642000i	$0.778105\pi$
$74$	6.50079	−	3.75323i	0.755702	−	0.436305i
$75$	20.8438	+	6.05031i	2.40684	+	0.698629i
$76$	0.0288104	+	0.0288104i	0.00330477	+	0.00330477i
$77$	−2.05385	−	13.5972i	−0.234058	−	1.54955i
$78$	6.16527	−	0.994717i	0.698079	−	0.112630i
$79$	−1.80883	+	3.13299i	−0.203510	+	0.352489i	−0.949657	−	0.313292i	$-0.898568\pi$
$79$	−1.80883	+	3.13299i	−0.203510	+	0.352489i	0.746147	+	0.665781i	$0.231901\pi$
$80$	1.08367	−	4.04433i	0.121158	−	0.452169i
$81$	−8.96915	−	0.744551i	−0.996572	−	0.0827279i
$82$	3.07199	+	1.77361i	0.339244	+	0.195863i
$83$	−9.53117	−	9.53117i	−1.04618	−	1.04618i	−0.998881	−	0.0473011i	$-0.984938\pi$
$83$	−9.53117	−	9.53117i	−1.04618	−	1.04618i	−0.0473011	−	0.998881i	$-0.515062\pi$
$84$	−0.590469	−	4.54438i	−0.0644255	−	0.495832i
$85$	−19.2507	−	19.2507i	−2.08803	−	2.08803i
$86$	−0.753824	−	2.81331i	−0.0812870	−	0.303367i
$87$	−1.54880	+	1.48595i	−0.166049	+	0.159311i
$88$	−4.50123	+	2.59879i	−0.479833	+	0.277032i
$89$	2.05741	+	7.67837i	0.218085	+	0.813906i	0.985058	+	0.172226i	$0.0550958\pi$
$89$	2.05741	+	7.67837i	0.218085	+	0.813906i	−0.766972	+	0.641680i	$0.778238\pi$
$90$	−5.82476	−	11.1288i	−0.613983	−	1.17308i
$91$	8.56965	+	4.19060i	0.898343	+	0.439294i
$92$		−	1.67252i		−	0.174372i
$93$	0.939124	+	1.70730i	0.0973826	+	0.177038i
$94$	−2.17871	−	3.77363i	−0.224716	−	0.389220i
$95$	0.0852974	+	0.147739i	0.00875133	+	0.0151577i
$96$	−1.51761	+	0.834784i	−0.154890	+	0.0851997i
$97$	−6.41874	+	6.41874i	−0.651724	+	0.651724i	−0.953408	−	0.301684i	$-0.902451\pi$
$97$	−6.41874	+	6.41874i	−0.651724	+	0.651724i	0.301684	+	0.953408i	$0.402451\pi$
$98$	3.26697	−	6.19088i	0.330013	−	0.625373i
$99$	−4.65577	+	14.8814i	−0.467922	+	1.49564i
$100$	6.26546	−	10.8521i	0.626546	−	1.08521i
$101$	−3.27576	−	5.67378i	−0.325950	−	0.564562i	0.655754	−	0.754975i	$-0.272351\pi$
$101$	−3.27576	−	5.67378i	−0.325950	−	0.564562i	−0.981704	+	0.190412i	$0.939017\pi$
$102$	−0.233172	+	11.2597i	−0.0230875	+	1.11487i
$103$	−10.4446	−	6.03018i	−1.02913	−	0.594171i	−0.112398	−	0.993663i	$-0.535853\pi$
$103$	−10.4446	−	6.03018i	−1.02913	−	0.594171i	−0.916737	+	0.399492i	$0.869187\pi$
$104$	0.292198	−	3.59369i	0.0286524	−	0.352390i
$105$	2.53657	−	19.0188i	0.247544	−	1.85605i
$106$	1.68927	−	1.68927i	0.164077	−	0.164077i
$107$	15.2387	+	8.79805i	1.47318	+	0.850539i	0.999544	−	0.0301828i	$-0.00960895\pi$
$107$	15.2387	+	8.79805i	1.47318	+	0.850539i	0.473633	+	0.880722i	$0.342942\pi$
$108$	−1.65384	+	4.92593i	−0.159141	+	0.473998i
$109$	−11.5647	−	3.09875i	−1.10770	−	0.296806i	−0.341801	−	0.939772i	$-0.611037\pi$
$109$	−11.5647	−	3.09875i	−1.10770	−	0.296806i	−0.765895	+	0.642966i	$0.777704\pi$
$110$	−21.0207	+	5.63247i	−2.00424	+	0.537035i
$111$	−11.1227	−	6.73252i	−1.05572	−	0.639023i
$112$	−2.62921	−	0.295399i	−0.248437	−	0.0279126i
$113$		−	7.36671i		−	0.693002i	−0.938050	−	0.346501i	$-0.887370\pi$
$113$		−	7.36671i		−	0.693002i	0.938050	−	0.346501i	$-0.112630\pi$
$114$	0.0196724	−	0.0677732i	0.00184249	−	0.00634755i
$115$	1.81247	−	6.76422i	0.169013	−	0.630766i
$116$	0.619599	+	1.07318i	0.0575283	+	0.0996420i
$117$	−6.65626	−	8.52609i	−0.615371	−	0.788238i
$118$	−7.24017			−0.666511
$119$	−10.2112	+	13.8448i	−0.936058	+	1.26915i
$120$	−7.04234	+	1.73154i	−0.642874	+	0.158068i
$121$	13.8692	+	8.00738i	1.26084	+	0.727944i
$122$	−0.786315	+	2.93457i	−0.0711896	+	0.265683i
$123$	0.127206	−	6.14266i	0.0114698	−	0.553865i
$124$	1.08666	−	0.291169i	0.0975848	−	0.0261478i
$125$	22.2964	−	22.2964i	1.99425	−	1.99425i
$126$	−6.40367	+	4.68967i	−0.570484	+	0.417789i
$127$		−	7.02101i		−	0.623014i	−0.950244	−	0.311507i	$-0.899166\pi$
$127$		−	7.02101i		−	0.623014i	0.950244	−	0.311507i	$-0.100834\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−3.64022	+	3.49252i	−0.320504	+	0.307499i
$130$	5.07613	−	14.2174i	0.445206	−	1.24695i
$131$	3.96808	+	2.29097i	0.346693	+	0.200163i	0.663228	−	0.748418i	$-0.269186\pi$
$131$	3.96808	+	2.29097i	0.346693	+	0.200163i	−0.316535	+	0.948581i	$0.602519\pi$
$132$	7.70149	+	4.66168i	0.670329	+	0.405747i
$133$	0.0842590	−	0.0672379i	0.00730618	−	0.00583026i
$134$	−5.27823			−0.455970
$135$	−12.0268	+	18.1299i	−1.03510	+	1.56037i
$136$	6.28061	+	1.68288i	0.538558	+	0.144306i
$137$	−12.2163	−	3.27335i	−1.04371	−	0.279661i	−0.304060	−	0.952653i	$-0.598342\pi$
$137$	−12.2163	−	3.27335i	−1.04371	−	0.279661i	−0.739650	+	0.672991i	$0.765009\pi$
$138$	−2.53823	+	1.39619i	−0.216069	+	0.118852i
$139$	−5.27391			−0.447327			−0.223663	−	0.974666i	$-0.571802\pi$
$139$	−5.27391			−0.447327			−0.223663	+	0.974666i	$0.571802\pi$
$140$	−10.3133	−	4.04389i	−0.871630	−	0.341771i
$141$	−3.90815	+	6.45659i	−0.329125	+	0.543743i
$142$	2.01021	+	1.16060i	0.168693	+	0.0973950i
$143$	−16.9354	+	8.02398i	−1.41621	+	0.670999i
$144$	2.53375	+	1.60627i	0.211146	+	0.133856i
$145$	1.34289	+	5.01172i	0.111521	+	0.416201i
$146$		−	13.9876i		−	1.15762i
$147$	−12.1225	+	0.210065i	−0.999850	+	0.0173258i
$148$	−5.30787	+	5.30787i	−0.436305	+	0.436305i
$149$	−7.38577	+	1.97901i	−0.605066	+	0.162127i	−0.548330	−	0.836262i	$-0.684736\pi$
$149$	−7.38577	+	1.97901i	−0.605066	+	0.162127i	−0.0567364	+	0.998389i	$0.518069\pi$
$150$	−21.6995	−	0.449367i	−1.77176	−	0.0366906i
$151$	−1.92180	+	7.17226i	−0.156394	+	0.583670i	0.842588	+	0.538559i	$0.181031\pi$
$151$	−1.92180	+	7.17226i	−0.156394	+	0.583670i	−0.998982	+	0.0451114i	$0.985636\pi$
$152$	−0.0352853	−	0.0203720i	−0.00286202	−	0.00165239i
$153$	17.2824	−	9.04552i	1.39720	−	0.731287i
$154$	5.50309	+	12.6024i	0.443452	+	1.01553i
$155$	4.71033			0.378343
$156$	−5.69774	+	2.55651i	−0.456184	+	0.204685i
$157$	−8.93077	−	15.4685i	−0.712753	−	1.23452i	−0.963820	−	0.266554i	$-0.914115\pi$
$157$	−8.93077	−	15.4685i	−0.712753	−	1.23452i	0.251067	−	0.967970i	$-0.419219\pi$
$158$	0.936321	−	3.49440i	0.0744897	−	0.277999i
$159$	−3.97383	−	1.15348i	−0.315145	−	0.0914768i
$160$			4.18699i			0.331011i
$161$	−4.39741	−	0.494061i	−0.346564	−	0.0389374i
$162$	8.85624	−	1.60221i	0.695812	−	0.125881i
$163$	22.0891	−	5.91877i	1.73016	−	0.463594i	0.749936	−	0.661510i	$-0.230084\pi$
$163$	22.0891	−	5.91877i	1.73016	−	0.463594i	0.980219	+	0.197916i	$0.0634174\pi$
$164$	−3.42636	−	0.918090i	−0.267554	−	0.0716908i
$165$	26.0956	+	27.1993i	2.03154	+	2.11746i
$166$	11.6733	+	6.73955i	0.906020	+	0.523091i
$167$	−2.53702	+	2.53702i	−0.196321	+	0.196321i	−0.798421	−	0.602100i	$-0.794331\pi$
$167$	−2.53702	+	2.53702i	−0.196321	+	0.196321i	0.602100	+	0.798421i	$0.294331\pi$
$168$	1.74652	+	4.23670i	0.134747	+	0.326869i
$169$	2.10014	−	12.8292i	0.161549	−	0.986865i
$170$	23.5771	+	13.6123i	1.80828	+	1.04401i
$171$	−0.119276	+	0.0267209i	−0.00912123	+	0.00204340i
$172$	1.45628	+	2.52234i	0.111040	+	0.192327i
$173$	9.51216	−	16.4755i	0.723196	−	1.25261i	−0.236516	−	0.971628i	$-0.576006\pi$
$173$	9.51216	−	16.4755i	0.723196	−	1.25261i	0.959712	−	0.280985i	$-0.0906610\pi$
$174$	1.11143	−	1.83618i	0.0842575	−	0.139200i
$175$	−26.6816	−	19.6789i	−2.01694	−	1.48758i
$176$	3.67524	−	3.67524i	0.277032	−	0.277032i
$177$	6.04397	+	10.9877i	0.454293	+	0.825889i
$178$	−3.97462	−	6.88424i	−0.297910	−	0.515996i
$179$	−1.03696	−	1.79606i	−0.0775057	−	0.134244i	0.824667	−	0.565618i	$-0.191362\pi$
$179$	−1.03696	−	1.79606i	−0.0775057	−	0.134244i	−0.902173	+	0.431374i	$0.858029\pi$
$180$	8.50663	+	9.24205i	0.634047	+	0.688862i
$181$		−	4.41231i		−	0.327964i	−0.986463	−	0.163982i	$-0.947566\pi$
$181$		−	4.41231i		−	0.327964i	0.986463	−	0.163982i	$-0.0524339\pi$
$182$	−9.36225	−	1.82982i	−0.693976	−	0.135635i
$183$	5.10993	−	1.25641i	0.377737	−	0.0928765i
$184$	0.432880	+	1.61553i	0.0319124	+	0.119099i
$185$	−27.2188	+	15.7148i	−2.00116	+	1.15537i
$186$	−1.34901	−	1.40606i	−0.0989139	−	0.103097i
$187$	−8.74692	−	32.6439i	−0.639638	−	2.38716i
$188$	3.08116	+	3.08116i	0.224716	+	0.224716i
$189$	12.4628	+	5.80340i	0.906533	+	0.422136i
$190$	−0.120629	−	0.120629i	−0.00875133	−	0.00875133i
$191$	3.60077	+	2.07891i	0.260543	+	0.150424i	0.624582	−	0.780959i	$-0.285269\pi$
$191$	3.60077	+	2.07891i	0.260543	+	0.150424i	−0.364039	+	0.931384i	$0.618603\pi$
$192$	1.24984	−	1.19913i	0.0901994	−	0.0865394i
$193$	0.892300	−	3.33011i	0.0642292	−	0.239707i	−0.926347	−	0.376672i	$-0.877068\pi$
$193$	0.892300	−	3.33011i	0.0642292	−	0.239707i	0.990576	+	0.136966i	$0.0437350\pi$
$194$	4.53874	−	7.86132i	0.325862	−	0.564410i
$195$	−25.8139	+	4.16487i	−1.84857	+	0.298253i
$196$	−1.55333	+	6.82548i	−0.110952	+	0.487534i
$197$	−1.23026	−	1.23026i	−0.0876527	−	0.0876527i	0.661921	−	0.749574i	$-0.269741\pi$
$197$	−1.23026	−	1.23026i	−0.0876527	−	0.0876527i	−0.749574	+	0.661921i	$0.769741\pi$
$198$	0.645530	−	15.5794i	0.0458758	−	1.10718i
$199$	14.4696	−	8.35403i	1.02572	−	0.592201i	0.109966	−	0.993935i	$-0.464926\pi$
$199$	14.4696	−	8.35403i	1.02572	−	0.592201i	0.915756	+	0.401734i	$0.131592\pi$
$200$	−3.24324	+	12.1039i	−0.229332	+	0.855877i
$201$	4.40618	+	8.01029i	0.310788	+	0.565002i
$202$	4.63262	+	4.63262i	0.325950	+	0.325950i
$203$	3.00464	−	1.31204i	0.210884	−	0.0920872i
$204$	−2.68899	−	10.9364i	−0.188267	−	0.765698i
$205$	−12.8624	−	7.42611i	−0.898349	−	0.518662i
$206$	11.6494	+	3.12145i	0.811653	+	0.217482i
$207$	4.23775	+	2.68652i	0.294544	+	0.186726i
$208$	0.647874	+	3.54687i	0.0449220	+	0.245931i
$209$			0.211770i			0.0146484i
$210$	2.47229	+	19.0273i	0.170604	+	1.31301i
$211$	−2.75269			−0.189503			−0.0947515	−	0.995501i	$-0.530206\pi$
$211$	−2.75269			−0.189503			−0.0947515	+	0.995501i	$0.530206\pi$
$212$	−1.19450	+	2.06893i	−0.0820384	+	0.142095i
$213$	0.0832394	−	4.01956i	0.00570347	−	0.275416i
$214$	−16.9965	−	4.55420i	−1.16186	−	0.311319i
$215$	3.15626	+	11.7793i	0.215255	+	0.803342i
$216$	0.322561	−	5.18613i	0.0219475	−	0.352872i
$217$	−0.444547	−	2.94306i	−0.0301778	−	0.199788i
$218$	11.9726			0.810889
$219$	−21.2277	+	11.6766i	−1.43443	+	0.789033i
$220$	18.8466	−	10.8811i	1.27064	−	0.733604i
$221$	22.0788	+	7.88295i	1.48518	+	0.530265i
$222$	12.4862	+	3.62435i	0.838019	+	0.243251i
$223$	−8.39459	+	8.39459i	−0.562143	+	0.562143i	−0.929916	−	0.367773i	$-0.880120\pi$
$223$	−8.39459	+	8.39459i	−0.562143	+	0.562143i	0.367773	+	0.929916i	$0.380120\pi$
$224$	2.61608	−	0.395156i	0.174794	−	0.0264025i
$225$	17.4324	+	33.3065i	1.16216	+	2.22043i
$226$	1.90665	+	7.11570i	0.126828	+	0.473329i
$227$	2.18092	−	8.13930i	0.144753	−	0.540224i	−0.855014	−	0.518606i	$-0.826451\pi$
$227$	2.18092	−	8.13930i	0.144753	−	0.540224i	0.999766	−	0.0216187i	$-0.00688199\pi$
$228$	−0.00146111	+	0.0705555i	−9.67641e−5	+	0.00467265i
$229$	−28.9686	+	7.76212i	−1.91430	+	0.512936i	−0.922343	+	0.386371i	$0.873728\pi$
$229$	−28.9686	+	7.76212i	−1.91430	+	0.512936i	−0.991958	+	0.126564i	$0.959605\pi$
$230$			7.00283i			0.461753i
$231$	14.5315	−	18.8718i	0.956106	−	1.24167i
$232$	−0.876246	−	0.876246i	−0.0575283	−	0.0575283i
$233$	−4.08975	+	7.08365i	−0.267928	+	0.464066i	−0.968327	−	0.249687i	$-0.919672\pi$
$233$	−4.08975	+	7.08365i	−0.267928	+	0.464066i	0.700398	+	0.713752i	$0.253006\pi$
$234$	8.63616	+	6.51281i	0.564564	+	0.425756i
$235$	9.12223	+	15.8002i	0.595069	+	1.03069i
$236$	6.99346	−	1.87389i	0.455236	−	0.121980i
$237$	−6.08475	+	1.49610i	−0.395247	+	0.0971819i
$238$	6.27994	−	16.0159i	0.407068	−	1.03816i
$239$	−1.18354	−	1.18354i	−0.0765568	−	0.0765568i	0.667792	−	0.744348i	$-0.267240\pi$
$239$	−1.18354	−	1.18354i	−0.0765568	−	0.0765568i	−0.744348	+	0.667792i	$0.767240\pi$
$240$	6.35422	−	3.49523i	0.410163	−	0.225616i
$241$	−2.59183	+	9.67284i	−0.166954	+	0.623082i	0.830828	+	0.556529i	$0.187867\pi$
$241$	−2.59183	+	9.67284i	−0.166954	+	0.623082i	−0.997783	+	0.0665537i	$0.978800\pi$
$242$	−15.4691	−	4.14493i	−0.994390	−	0.266446i
$243$	−9.82456	−	12.1028i	−0.630246	−	0.776396i
$244$		−	3.03809i		−	0.194494i
$245$	−13.6788	+	25.9212i	−0.873904	+	1.65604i
$246$	1.46697	+	5.96628i	0.0935304	+	0.380396i
$247$	−0.120852	−	0.0835210i	−0.00768962	−	0.00531431i
$248$	−0.974271	+	0.562496i	−0.0618663	+	0.0357185i
$249$	0.483370	−	23.3415i	0.0306323	−	1.47921i
$250$	−15.7659	+	27.3074i	−0.997126	+	1.72707i
$251$	−2.66714			−0.168349			−0.0841743	−	0.996451i	$-0.526825\pi$
$251$	−2.66714			−0.168349			−0.0841743	+	0.996451i	$0.526825\pi$
$252$	4.97169	−	6.18727i	0.313187	−	0.389761i
$253$	6.14691	−	6.14691i	0.386453	−	0.386453i
$254$	1.81717	+	6.78177i	0.114019	+	0.425526i
$255$	0.976289	−	47.1442i	0.0611376	−	2.95228i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.22876	−	5.59238i	0.201405	−	0.348843i	−0.747577	−	0.664176i	$-0.768783\pi$
$257$	3.22876	−	5.59238i	0.201405	−	0.348843i	0.948981	+	0.315333i	$0.102116\pi$
$258$	2.61226	−	4.31567i	0.162632	−	0.268682i
$259$	12.3876	+	15.5235i	0.769726	+	0.964580i
$260$	−1.22343	+	15.0468i	−0.0758741	+	0.933161i
$261$	−3.71441	−	0.153906i	−0.229916	−	0.00952656i
$262$	−4.42582	−	1.18590i	−0.273428	−	0.0732649i
$263$	3.47681	−	2.00734i	0.214389	−	0.123778i	−0.388960	−	0.921255i	$-0.627166\pi$
$263$	3.47681	−	2.00734i	0.214389	−	0.123778i	0.603350	+	0.797477i	$0.293832\pi$
$264$	−8.64560	−	2.50955i	−0.532100	−	0.154452i
$265$	−7.07298	+	7.07298i	−0.434489	+	0.434489i
$266$	−0.0639855	+	0.0867546i	−0.00392320	+	0.00531927i
$267$	−7.12964	+	11.7788i	−0.436327	+	0.720849i
$268$	5.09838	−	1.36611i	0.311433	−	0.0834482i
$269$	−2.95341	+	1.70515i	−0.180073	+	0.103965i	−0.587327	−	0.809350i	$-0.699820\pi$
$269$	−2.95341	+	1.70515i	−0.180073	+	0.103965i	0.407254	+	0.913315i	$0.366486\pi$
$270$	6.92462	−	20.6248i	0.421419	−	1.25519i
$271$	29.3133	−	7.85448i	1.78066	−	0.477125i	0.789953	−	0.613167i	$-0.210105\pi$
$271$	29.3133	−	7.85448i	1.78066	−	0.477125i	0.990703	+	0.136042i	$0.0434382\pi$
$272$	−6.50217			−0.394252
$273$	5.03850	+	15.7357i	0.304944	+	0.952370i
$274$	12.6473			0.764049
$275$	62.9111	−	16.8570i	3.79368	−	1.01651i
$276$	2.09038	−	2.00556i	0.125826	−	0.120721i
$277$	−3.21931	+	1.85867i	−0.193430	+	0.111677i	−0.593587	−	0.804770i	$-0.702289\pi$
$277$	−3.21931	+	1.85867i	−0.193430	+	0.111677i	0.400157	+	0.916446i	$0.368955\pi$
$278$	5.09420	−	1.36499i	0.305530	−	0.0818665i
$279$	−1.00772	+	3.22102i	−0.0603306	+	0.192837i
$280$	11.0085	+	1.23683i	0.657883	+	0.0739149i
$281$	15.0107	−	15.0107i	0.895462	−	0.895462i	−0.0995691	−	0.995031i	$-0.531746\pi$
$281$	15.0107	−	15.0107i	0.895462	−	0.895462i	0.995031	+	0.0995691i	$0.0317464\pi$
$282$	2.10389	−	7.24809i	0.125285	−	0.431617i
$283$	−9.63544	+	5.56302i	−0.572767	+	0.330687i	−0.758254	−	0.651959i	$-0.773947\pi$
$283$	−9.63544	+	5.56302i	−0.572767	+	0.330687i	0.185487	+	0.982647i	$0.440614\pi$
$284$	−2.24210	−	0.600769i	−0.133044	−	0.0356491i
$285$	−0.0823684	+	0.283766i	−0.00487908	+	0.0168089i
$286$	14.2816	−	12.1338i	0.844487	−	0.717485i
$287$	−3.42599	+	8.73741i	−0.202230	+	0.515753i
$288$	−2.86315	−	0.895758i	−0.168713	−	0.0527830i
$289$	−12.6391	+	21.8916i	−0.743476	+	1.28774i
$290$	−2.59426	−	4.49339i	−0.152340	−	0.263861i
$291$	−15.7193	−	0.325524i	−0.921480	−	0.0190826i
$292$	3.62026	+	13.5110i	0.211859	+	0.790670i
$293$	5.14645	−	5.14645i	0.300659	−	0.300659i	−0.540613	−	0.841272i	$-0.681808\pi$
$293$	5.14645	−	5.14645i	0.300659	−	0.300659i	0.841272	+	0.540613i	$0.181808\pi$
$294$	11.6551	−	3.34045i	0.679739	−	0.194819i
$295$	30.3145			1.76498
$296$	3.75323	−	6.50079i	0.218152	−	0.377851i
$297$	−24.1822	+	12.0257i	−1.40320	+	0.697803i
$298$	6.62190	−	3.82316i	0.383597	−	0.221470i
$299$	1.08358	+	5.93221i	0.0626652	+	0.343068i
$300$	21.0764	−	5.18220i	1.21685	−	0.299194i
$301$	7.06195	−	3.08376i	0.407044	−	0.177745i
$302$		−	7.42527i		−	0.427276i
$303$	3.16327	−	10.8977i	0.181725	−	0.626059i
$304$	0.0393557	+	0.0105453i	0.00225720	+	0.000604816i
$305$	3.29230	−	12.2870i	0.188516	−	0.703553i
$306$	−14.3524	+	13.2103i	−0.820471	+	0.755184i
$307$	7.36830	+	7.36830i	0.420531	+	0.420531i	0.885386	−	0.464856i	$-0.153894\pi$
$307$	7.36830	+	7.36830i	0.420531	+	0.420531i	−0.464856	+	0.885386i	$0.653894\pi$
$308$	−8.57731	−	10.7486i	−0.488738	−	0.612460i
$309$	−4.98760	−	20.2850i	−0.283734	−	1.15397i
$310$	−4.54983	+	1.21912i	−0.258413	+	0.0692416i
$311$	−1.39247	−	2.41183i	−0.0789597	−	0.136762i	0.823842	−	0.566820i	$-0.191827\pi$
$311$	−1.39247	−	2.41183i	−0.0789597	−	0.136762i	−0.902801	+	0.430058i	$0.858493\pi$
$312$	4.84192	−	3.94408i	0.274120	−	0.223290i
$313$	−9.64584	+	16.7071i	−0.545215	+	0.944341i	0.453378	+	0.891318i	$0.350219\pi$
$313$	−9.64584	+	16.7071i	−0.545215	+	0.944341i	−0.998593	+	0.0530224i	$0.983115\pi$
$314$	12.6300	+	12.6300i	0.712753	+	0.712753i
$315$	26.8121	−	19.6356i	1.51069	−	1.10634i
$316$			3.61767i			0.203510i
$317$	8.28772	−	2.22069i	0.465485	−	0.124726i	−0.0184511	−	0.999830i	$-0.505874\pi$
$317$	8.28772	−	2.22069i	0.465485	−	0.124726i	0.483936	+	0.875104i	$0.339207\pi$
$318$	4.13697	+	0.0856708i	0.231990	+	0.00480418i
$319$	−1.66701	+	6.22136i	−0.0933345	+	0.348329i
$320$	−1.08367	−	4.04433i	−0.0605792	−	0.226085i
$321$	7.27692	+	29.5958i	0.406158	+	1.65188i
$322$	4.37544	−	0.660907i	0.243834	−	0.0368309i
$323$	0.187330	−	0.187330i	0.0104233	−	0.0104233i
$324$	−8.13979	+	3.83977i	−0.452210	+	0.213321i
$325$	−15.1920	+	42.5501i	−0.842698	+	2.36026i
$326$	−19.8046	+	11.4342i	−1.09687	+	0.633281i
$327$	−9.99456	−	18.1698i	−0.552701	−	1.00479i
$328$	3.54723			0.195863
$329$	9.01117	−	7.19083i	0.496802	−	0.396443i
$330$	−32.2461	−	19.5184i	−1.77509	−	1.07445i
$331$	4.87091	+	18.1785i	0.267730	+	0.999181i	0.960558	+	0.278079i	$0.0896976\pi$
$331$	4.87091	+	18.1785i	0.267730	+	0.999181i	−0.692829	+	0.721102i	$0.743636\pi$
$332$	−13.0198	−	3.48865i	−0.714555	−	0.191465i
$333$	−4.92293	−	21.9747i	−0.269775	−	1.20421i
$334$	1.79395	−	3.10720i	0.0981603	−	0.170019i
$335$	22.0999			1.20745
$336$	−2.78355	−	3.64031i	−0.151855	−	0.198595i
$337$			19.6080i			1.06812i	0.845448	+	0.534058i	$0.179334\pi$
$337$			19.6080i			1.06812i	−0.845448	+	0.534058i	$0.820666\pi$
$338$	1.29187	+	12.9357i	0.0702685	+	0.703607i
$339$	9.20721	−	8.83361i	0.500067	−	0.479776i
$340$	−26.2969	−	7.04623i	−1.42615	−	0.382135i
$341$	5.06384	+	2.92361i	0.274223	+	0.158322i
$342$	0.108295	−	0.0566812i	0.00585594	−	0.00306497i
$343$	17.4868	+	6.10027i	0.944196	+	0.329384i
$344$	−2.05949	−	2.05949i	−0.111040	−	0.111040i
$345$	10.6276	−	5.84585i	0.572169	−	0.314730i
$346$	−4.92386	+	18.3761i	−0.264708	+	0.987904i
$347$	−6.56921	+	3.79274i	−0.352654	+	0.203605i	−0.665853	−	0.746083i	$-0.731932\pi$
$347$	−6.56921	+	3.79274i	−0.352654	+	0.203605i	0.313200	+	0.949687i	$0.398599\pi$
$348$	−0.598323	+	2.06127i	−0.0320735	+	0.110496i
$349$	−3.65238	−	3.65238i	−0.195507	−	0.195507i	0.602564	−	0.798071i	$-0.294146\pi$
$349$	−3.65238	−	3.65238i	−0.195507	−	0.195507i	−0.798071	+	0.602564i	$0.794146\pi$
$350$	30.8657	+	12.1026i	1.64984	+	0.646913i
$351$	2.67457	−	18.5431i	0.142758	−	0.989758i
$352$	−2.59879	+	4.50123i	−0.138516	+	0.239916i
$353$	−4.06354	+	15.1653i	−0.216280	+	0.807170i	0.769431	+	0.638729i	$0.220540\pi$
$353$	−4.06354	+	15.1653i	−0.216280	+	0.807170i	−0.985712	+	0.168440i	$0.946127\pi$
$354$	−8.68186	−	9.04905i	−0.461436	−	0.480951i
$355$	−8.41674	−	4.85941i	−0.446714	−	0.257911i
$356$	5.62096	+	5.62096i	0.297910	+	0.297910i
$357$	−29.5483	+	3.83933i	−1.56386	+	0.203199i
$358$	1.46648	+	1.46648i	0.0775057	+	0.0775057i
$359$	−0.0873569	−	0.326020i	−0.00461052	−	0.0172067i	0.963582	−	0.267412i	$-0.0861685\pi$
$359$	−0.0873569	−	0.326020i	−0.00461052	−	0.0172067i	−0.968193	+	0.250205i	$0.919502\pi$
$360$	−10.6088	−	6.72545i	−0.559132	−	0.354463i
$361$	16.4530	−	9.49917i	0.865950	−	0.499956i
$362$	1.14199	+	4.26196i	0.0600216	+	0.224004i
$363$	6.62295	+	26.9361i	0.347615	+	1.41378i
$364$	9.51683	−	0.655656i	0.498818	−	0.0343657i
$365$			58.5660i			3.06548i
$366$	−4.61063	+	2.53615i	−0.241002	+	0.132567i
$367$	−11.9398	−	20.6804i	−0.623255	−	1.07951i	−0.988876	−	0.148745i	$-0.952477\pi$
$367$	−11.9398	−	20.6804i	−0.623255	−	1.07951i	0.365621	−	0.930764i	$-0.380857\pi$
$368$	−0.836260	−	1.44845i	−0.0435931	−	0.0755054i
$369$	7.82988	−	7.20683i	0.407607	−	0.375173i
$370$	22.2240	−	22.2240i	1.15537	−	1.15537i
$371$	5.08679	+	3.75174i	0.264093	+	0.194781i
$372$	1.66695	+	1.00900i	0.0864275	+	0.0523142i
$373$	6.59425	−	11.4216i	0.341437	−	0.591387i	−0.643263	−	0.765646i	$-0.722420\pi$
$373$	6.59425	−	11.4216i	0.341437	−	0.591387i	0.984700	+	0.174259i	$0.0557530\pi$
$374$	16.8977	+	29.2678i	0.873762	+	1.51340i
$375$	54.6031	+	1.13075i	2.81969	+	0.0583919i
$376$	−3.77363	−	2.17871i	−0.194610	−	0.112358i
$377$	−2.89292	−	3.40499i	−0.148993	−	0.175366i
$378$	−13.5401	−	2.38006i	−0.696430	−	0.122417i
$379$	−17.7321	+	17.7321i	−0.910835	+	0.910835i	−0.996338	−	0.0855028i	$-0.972750\pi$
$379$	−17.7321	+	17.7321i	−0.910835	+	0.910835i	0.0855028	+	0.996338i	$0.472750\pi$
$380$	0.147739	+	0.0852974i	0.00757887	+	0.00437566i
$381$	8.77514	−	8.41907i	0.449564	−	0.431322i
$382$	−4.01614	−	1.07612i	−0.205484	−	0.0550592i
$383$	−5.68924	+	1.52443i	−0.290706	+	0.0778946i	−0.401225	−	0.915979i	$-0.631415\pi$
$383$	−5.68924	+	1.52443i	−0.290706	+	0.0778946i	0.110519	+	0.993874i	$0.464749\pi$
$384$	−0.896896	+	1.48175i	−0.0457695	+	0.0756151i
$385$	−23.0414	−	52.7660i	−1.17430	−	2.68920i
$386$			3.44758i			0.175477i
$387$	−8.73017	−	0.361734i	−0.443779	−	0.0183880i
$388$	−2.34942	+	8.76816i	−0.119274	+	0.445136i
$389$	−2.36400	−	4.09456i	−0.119859	−	0.207602i	0.799852	−	0.600197i	$-0.204911\pi$
$389$	−2.36400	−	4.09456i	−0.119859	−	0.207602i	−0.919712	+	0.392594i	$0.871578\pi$
$390$	23.8564	−	10.7041i	1.20802	−	0.542023i
$391$	−10.8750			−0.549973
$392$	−0.266162	−	6.99494i	−0.0134432	−	0.353298i
$393$	1.89488	+	7.70663i	0.0955840	+	0.388748i
$394$	1.50676	+	0.869929i	0.0759095	+	0.0438264i
$395$	−3.92037	+	14.6310i	−0.197255	+	0.736167i
$396$	3.40870	+	15.2156i	0.171294	+	0.764611i
$397$	20.2204	−	5.41804i	1.01483	−	0.271924i	0.287186	−	0.957875i	$-0.407280\pi$
$397$	20.2204	−	5.41804i	1.01483	−	0.271924i	0.727647	+	0.685951i	$0.240614\pi$
$398$	−11.8144	+	11.8144i	−0.592201	+	0.592201i
$399$	0.185074	+	0.0246836i	0.00926527	+	0.00123572i
$400$		−	12.5309i		−	0.626546i
$401$	10.0045	+	37.3372i	0.499599	+	1.86453i	0.502576	+	0.864533i	$0.332386\pi$
$401$	10.0045	+	37.3372i	0.499599	+	1.86453i	−0.00297753	+	0.999996i	$0.500948\pi$
$402$	−6.32926	−	6.59694i	−0.315675	−	0.329026i
$403$	−3.66559	+	1.73676i	−0.182596	+	0.0865140i
$404$	−5.67378	−	3.27576i	−0.282281	−	0.162975i
$405$	−37.0810	+	6.70842i	−1.84257	+	0.333344i
$406$	−2.56267	+	2.04499i	−0.127183	+	0.101491i
$407$	−39.0154			−1.93392
$408$	5.42790	+	9.86775i	0.268721	+	0.488526i
$409$	−4.20530	−	1.12681i	−0.207939	−	0.0557170i	0.153346	−	0.988173i	$-0.450995\pi$
$409$	−4.20530	−	1.12681i	−0.207939	−	0.0557170i	−0.361285	+	0.932456i	$0.617662\pi$
$410$	14.3461	+	3.84404i	0.708506	+	0.189843i
$411$	−10.5577	−	19.1936i	−0.520774	−	0.946751i
$412$	−12.0604			−0.594171
$413$	−2.86100	−	18.9408i	−0.140780	−	0.932017i
$414$	−4.78867	−	1.49817i	−0.235351	−	0.0736312i
$415$	−48.8758	−	28.2185i	−2.39922	−	1.38519i
$416$	−1.54379	−	3.25833i	−0.0756908	−	0.159753i
$417$	−6.32407	−	6.59154i	−0.309691	−	0.322789i
$418$	−0.0548101	−	0.204554i	−0.00268085	−	0.0100051i
$419$		−	35.1233i		−	1.71588i	−0.513747	−	0.857942i	$-0.671743\pi$
$419$		−	35.1233i		−	1.71588i	0.513747	−	0.857942i	$-0.328257\pi$
$420$	−7.31267	−	17.7391i	−0.356822	−	0.865577i
$421$	−17.6207	+	17.6207i	−0.858779	+	0.858779i	−0.991194	−	0.132415i	$-0.957727\pi$
$421$	−17.6207	+	17.6207i	−0.858779	+	0.858779i	0.132415	+	0.991194i	$0.457727\pi$
$422$	2.65889	−	0.712448i	0.129433	−	0.0346814i
$423$	−12.7561	+	2.85770i	−0.620221	+	0.138946i
$424$	0.618317	−	2.30759i	0.0300281	−	0.112066i
$425$	−70.5621	−	40.7391i	−3.42276	−	1.97613i
$426$	0.959936	+	3.90414i	0.0465090	+	0.189156i
$427$	−7.98777	−	0.897448i	−0.386555	−	0.0434305i
$428$	17.5961			0.850539
$429$	−30.3363	−	11.5448i	−1.46465	−	0.557387i
$430$	−6.09742	−	10.5610i	−0.294044	−	0.509299i
$431$	−8.05608	+	30.0657i	−0.388048	+	1.44821i	0.445259	+	0.895402i	$0.353112\pi$
$431$	−8.05608	+	30.0657i	−0.388048	+	1.44821i	−0.833306	+	0.552811i	$0.813555\pi$
$432$	1.03070	+	5.09290i	0.0495895	+	0.245032i
$433$		−	20.3783i		−	0.979320i	−0.871913	−	0.489660i	$-0.837121\pi$
$433$		−	20.3783i		−	0.979320i	0.871913	−	0.489660i	$-0.162879\pi$
$434$	1.19112	+	2.72772i	0.0571756	+	0.130935i
$435$	−4.65356	+	7.68807i	−0.223121	+	0.368615i
$436$	−11.5647	+	3.09875i	−0.553848	+	0.148403i
$437$	0.0658232	+	0.0176373i	0.00314875	+	0.000843705i
$438$	17.4823	−	16.7729i	0.835334	−	0.801439i
$439$	−7.80862	−	4.50831i	−0.372685	−	0.215170i	0.301946	−	0.953325i	$-0.402364\pi$
$439$	−7.80862	−	4.50831i	−0.372685	−	0.215170i	−0.674631	+	0.738155i	$0.735697\pi$
$440$	−15.3882	+	15.3882i	−0.733604	+	0.733604i
$441$	−14.7990	−	14.8993i	−0.704713	−	0.709492i
$442$	−23.3668	−	1.89992i	−1.11144	−	0.0903701i
$443$	−23.3482	−	13.4801i	−1.10931	−	0.640459i	−0.170658	−	0.985330i	$-0.554589\pi$
$443$	−23.3482	−	13.4801i	−1.10931	−	0.640459i	−0.938650	+	0.344871i	$0.887923\pi$
$444$	−12.9988	−	0.269187i	−0.616896	−	0.0127750i
$445$	16.6417	+	28.8243i	0.788892	+	1.36640i
$446$	5.93587	−	10.2812i	0.281072	−	0.486830i
$447$	−11.3299	−	6.85795i	−0.535887	−	0.324370i
$448$	−2.42466	+	1.05878i	−0.114554	+	0.0500227i
$449$	18.9064	−	18.9064i	0.892250	−	0.892250i	−0.102485	−	0.994735i	$-0.532679\pi$
$449$	18.9064	−	18.9064i	0.892250	−	0.892250i	0.994735	+	0.102485i	$0.0326793\pi$
$450$	−25.4588	−	27.6598i	−1.20014	−	1.30389i
$451$	−9.21849	−	15.9669i	−0.434082	−	0.751851i
$452$	−3.68336	−	6.37976i	−0.173250	−	0.300079i
$453$	−11.2686	+	6.19849i	−0.529447	+	0.291230i
$454$			8.42642i			0.395472i
$455$	39.1997	+	7.66146i	1.83771	+	0.359175i
$456$	−0.0168498	−	0.0685296i	−0.000789064	−	0.00320919i
$457$	5.62441	+	20.9906i	0.263099	+	0.981898i	0.963404	+	0.268054i	$0.0863806\pi$
$457$	5.62441	+	20.9906i	0.263099	+	0.981898i	−0.700305	+	0.713844i	$0.746953\pi$
$458$	25.9726	−	14.9953i	1.21362	−	0.700683i
$459$	32.0292	+	10.7535i	1.49500	+	0.501932i
$460$	−1.81247	−	6.76422i	−0.0845067	−	0.315383i
$461$	−16.1114	−	16.1114i	−0.750384	−	0.750384i	0.224167	−	0.974551i	$-0.428034\pi$
$461$	−16.1114	−	16.1114i	−0.750384	−	0.750384i	−0.974551	+	0.224167i	$0.928034\pi$
$462$	−9.15202	+	21.9898i	−0.425791	+	1.02306i
$463$	24.7561	+	24.7561i	1.15051	+	1.15051i	0.986450	+	0.164062i	$0.0524597\pi$
$463$	24.7561	+	24.7561i	1.15051	+	1.15051i	0.164062	+	0.986450i	$0.447540\pi$
$464$	1.07318	+	0.619599i	0.0498210	+	0.0287642i
$465$	5.64828	+	5.88716i	0.261933	+	0.273010i
$466$	2.11701	−	7.90079i	0.0980686	−	0.365997i
$467$	−10.8534	+	18.7986i	−0.502234	+	0.869894i	0.497763	+	0.867313i	$0.334155\pi$
$467$	−10.8534	+	18.7986i	−0.502234	+	0.869894i	−0.999997	+	0.00258128i	$0.999178\pi$
$468$	−10.0275	−	4.05568i	−0.463523	−	0.187474i
$469$	−2.08572	−	13.8082i	−0.0963098	−	0.637606i
$470$	−12.9008	−	12.9008i	−0.595069	−	0.595069i
$471$	8.62409	−	29.7107i	0.397377	−	1.36900i
$472$	−6.27017	+	3.62008i	−0.288608	+	0.166628i
$473$	−3.91806	+	14.6224i	−0.180152	+	0.672338i
$474$	5.49020	−	3.01997i	0.252173	−	0.138712i
$475$	0.361020	+	0.361020i	0.0165647	+	0.0165647i
$476$	−1.92073	+	17.0956i	−0.0880366	+	0.783574i
$477$	−3.32346	−	6.34982i	−0.152171	−	0.290738i
$478$	1.44953	+	0.836889i	0.0663002	+	0.0382784i
$479$	23.1157	+	6.19382i	1.05618	+	0.283003i	0.744804	−	0.667284i	$-0.232543\pi$
$479$	23.1157	+	6.19382i	1.05618	+	0.283003i	0.311377	+	0.950286i	$0.399210\pi$
$480$	−5.23307	+	5.02073i	−0.238856	+	0.229164i
$481$	15.3875	−	22.2652i	0.701609	−	1.01520i
$482$		−	10.0141i		−	0.456128i
$483$	−4.65554	−	6.08849i	−0.211835	−	0.277036i
$484$	16.0148			0.727944
$485$	−19.0037	+	32.9153i	−0.862912	+	1.49461i
$486$	12.6222	+	9.14763i	0.572556	+	0.414945i
$487$	28.1495	+	7.54264i	1.27558	+	0.341790i	0.832165	−	0.554528i	$-0.187101\pi$
$487$	28.1495	+	7.54264i	1.27558	+	0.341790i	0.443412	+	0.896318i	$0.353768\pi$
$488$	0.786315	+	2.93457i	0.0355948	+	0.132842i
$489$	33.8852	+	20.5105i	1.53234	+	0.927519i
$490$	6.50378	−	28.5782i	0.293811	−	1.29103i
$491$	−4.50540			−0.203326			−0.101663	−	0.994819i	$-0.532416\pi$
$491$	−4.50540			−0.203326			−0.101663	+	0.994819i	$0.532416\pi$
$492$	−2.96117	−	5.38330i	−0.133500	−	0.242698i
$493$	6.97798	−	4.02874i	0.314272	−	0.181445i
$494$	0.138351	+	0.0493963i	0.00622470	+	0.00222244i
$495$	−2.70283	+	65.2306i	−0.121483	+	2.93190i
$496$	0.795489	−	0.795489i	0.0357185	−	0.0357185i
$497$	−2.24186	+	5.71748i	−0.100561	+	0.256464i
$498$	5.57433	+	22.6713i	0.249791	+	1.01592i
$499$	0.740955	+	2.76528i	0.0331697	+	0.123791i	0.980526	−	0.196392i	$-0.0629224\pi$
$499$	0.740955	+	2.76528i	0.0331697	+	0.123791i	−0.947356	+	0.320183i	$0.896256\pi$
$500$	8.16105	−	30.4575i	0.364973	−	1.36210i
$501$	−6.21308	−	0.128664i	−0.277580	−	0.00574829i
$502$	2.57626	−	0.690308i	0.114984	−	0.0308099i
$503$		−	13.1898i		−	0.588105i	−0.955789	−	0.294053i	$-0.904996\pi$
$503$		−	13.1898i		−	0.588105i	0.955789	−	0.294053i	$-0.0950041\pi$
$504$	−3.20090	+	7.26321i	−0.142580	+	0.323529i
$505$	−19.3968	−	19.3968i	−0.863144	−	0.863144i
$506$	−4.34652	+	7.52840i	−0.193227	+	0.334678i
$507$	18.5528	−	12.7590i	0.823960	−	0.566648i
$508$	−3.51050	−	6.08037i	−0.155753	−	0.269773i
$509$	38.4104	−	10.2920i	1.70251	−	0.456186i	0.728941	−	0.684577i	$-0.240013\pi$
$509$	38.4104	−	10.2920i	1.70251	−	0.456186i	0.973570	+	0.228391i	$0.0733464\pi$
$510$	11.2588	+	45.7905i	0.498547	+	2.02764i
$511$	36.5926	−	5.52728i	1.61876	−	0.244513i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.176423	−	0.117034i	−0.00778927	−	0.00516716i
$514$	−1.67133	+	6.23749i	−0.0737192	+	0.275124i
$515$	−48.7760	−	13.0695i	−2.14933	−	0.575911i
$516$	−1.40627	+	4.84472i	−0.0619075	+	0.213277i
$517$			22.6480i			0.996056i
$518$	−15.9832	−	11.7884i	−0.702263	−	0.517951i
$519$	31.9981	−	7.86756i	1.40456	−	0.345348i
$520$	−2.71264	−	14.8507i	−0.118957	−	0.651247i
$521$	29.3150	−	16.9250i	1.28431	−	0.741499i	0.306680	−	0.951813i	$-0.400782\pi$
$521$	29.3150	−	16.9250i	1.28431	−	0.741499i	0.977634	+	0.210313i	$0.0674484\pi$
$522$	3.62768	−	0.812697i	0.158779	−	0.0355708i
$523$	13.5259	−	23.4276i	0.591448	−	1.02442i	−0.402589	−	0.915381i	$-0.631890\pi$
$523$	13.5259	−	23.4276i	0.591448	−	1.02442i	0.994038	−	0.109038i	$-0.0347770\pi$
$524$	4.58195			0.200163
$525$	−7.39912	−	56.9452i	−0.322924	−	2.48529i
$526$	−2.83881	+	2.83881i	−0.123778	+	0.123778i
$527$	−1.89323	−	7.06563i	−0.0824704	−	0.307784i
$528$	9.00053	+	0.186388i	0.391698	+	0.00811151i
$529$	10.1013	+	17.4960i	0.439189	+	0.760697i
$530$	5.00135	−	8.66259i	0.217245	−	0.376279i
$531$	−6.48543	+	20.7297i	−0.281444	+	0.899591i
$532$	0.0393515	−	0.100359i	0.00170610	−	0.00435112i
$533$	12.7476	+	1.03649i	0.552162	+	0.0448956i
$534$	3.83813	−	13.2227i	0.166092	−	0.572202i
$535$	71.1643	+	19.0684i	3.07670	+	0.824400i
$536$	−4.57108	+	2.63912i	−0.197441	+	0.113992i
$537$	1.00135	−	3.44973i	0.0432113	−	0.148867i
$538$	2.41145	−	2.41145i	0.103965	−	0.103965i
$539$	−30.7941	+	19.3764i	−1.32640	+	0.834601i
$540$	−1.35056	+	21.7143i	−0.0581189	+	0.934435i
$541$	28.1867	−	7.55261i	1.21184	−	0.324712i	0.404358	−	0.914601i	$-0.367495\pi$
$541$	28.1867	−	7.55261i	1.21184	−	0.324712i	0.807485	+	0.589889i	$0.200828\pi$
$542$	−26.2816	+	15.1737i	−1.12889	+	0.651765i
$543$	5.51467	−	5.29091i	0.236657	−	0.227054i
$544$	6.28061	−	1.68288i	0.269279	−	0.0721531i
$545$	−50.1294			−2.14731
$546$	−8.93952	−	13.8955i	−0.382576	−	0.594672i
$547$	30.9138			1.32178			0.660890	−	0.750483i	$-0.270179\pi$
$547$	30.9138			1.32178			0.660890	+	0.750483i	$0.270179\pi$
$548$	−12.2163	+	3.27335i	−0.521855	+	0.139831i
$549$	7.69776	+	4.88000i	0.328532	+	0.208273i
$550$	−56.4045	+	32.5652i	−2.40510	+	1.38858i
$551$	−0.0487695	+	0.0130677i	−0.00207765	+	0.000556705i
$552$	−1.50008	+	2.47825i	−0.0638475	+	0.105482i
$553$	9.51160	+	1.06865i	0.404474	+	0.0454438i
$554$	2.62856	−	2.62856i	0.111677	−	0.111677i
$555$	−52.2797	−	15.1751i	−2.21915	−	0.644149i
$556$	−4.56734	+	2.63695i	−0.193698	+	0.111832i
$557$	−15.5678	−	4.17139i	−0.659631	−	0.176747i	−0.0865512	−	0.996247i	$-0.527585\pi$
$557$	−15.5678	−	4.17139i	−0.659631	−	0.176747i	−0.573079	+	0.819500i	$0.694251\pi$
$558$	0.139722	−	3.37208i	0.00591490	−	0.142752i
$559$	−6.79938	−	8.00294i	−0.287583	−	0.338488i
$560$	−10.9535	+	1.65452i	−0.462869	+	0.0699160i
$561$	30.3110	−	50.0764i	1.27973	−	2.11423i
$562$	−10.6141	+	18.3842i	−0.447731	+	0.775492i
$563$	2.53836	+	4.39656i	0.106979	+	0.185293i	0.914545	−	0.404484i	$-0.132549\pi$
$563$	2.53836	+	4.39656i	0.106979	+	0.185293i	−0.807566	+	0.589777i	$0.799216\pi$
$564$	−0.156260	+	7.54564i	−0.00657972	+	0.317729i
$565$	−7.98311	−	29.7934i	−0.335852	−	1.25342i
$566$	7.86730	−	7.86730i	0.330687	−	0.330687i
$567$	7.69109	+	22.5355i	0.322995	+	0.946401i
$568$	2.32119			0.0973950
$569$	9.42476	−	16.3242i	0.395107	−	0.684345i	−0.598008	−	0.801490i	$-0.704041\pi$
$569$	9.42476	−	16.3242i	0.395107	−	0.684345i	0.993115	+	0.117145i	$0.0373743\pi$
$570$	0.00611764	−	0.295416i	0.000256240	−	0.0123736i
$571$	−16.7331	+	9.66085i	−0.700258	+	0.404294i	−0.807443	−	0.589945i	$-0.799149\pi$
$571$	−16.7331	+	9.66085i	−0.700258	+	0.404294i	0.107186	+	0.994239i	$0.465816\pi$
$572$	−10.6545	+	15.4167i	−0.445487	+	0.644603i
$573$	1.71948	+	6.99326i	0.0718322	+	0.292148i
$574$	1.04785	−	9.32640i	0.0437363	−	0.389277i
$575$		−	20.9582i		−	0.874018i
$576$	2.99743	+	0.124198i	0.124893	+	0.00517493i
$577$	0.257942	+	0.0691154i	0.0107383	+	0.00287731i	0.264184	−	0.964472i	$-0.414897\pi$
$577$	0.257942	+	0.0691154i	0.0107383	+	0.00287731i	−0.253446	+	0.967350i	$0.581564\pi$
$578$	6.54248	−	24.4169i	0.272131	−	1.01561i
$579$	5.23208	−	2.87799i	0.217438	−	0.119605i
$580$	3.66883	+	3.66883i	0.152340	+	0.152340i
$581$	−13.0184	+	33.2013i	−0.540095	+	1.37742i
$582$	15.2679	−	3.75401i	0.632875	−	0.155609i
$583$	−11.9939	+	3.21375i	−0.496735	+	0.133100i
$584$	−6.99380	−	12.1136i	−0.289405	−	0.501265i
$585$	−36.1596	−	27.2691i	−1.49501	−	1.12744i
$586$	−3.63909	+	6.30309i	−0.150329	+	0.260378i
$587$	16.9696	+	16.9696i	0.700408	+	0.700408i	0.964498	−	0.264090i	$-0.0850715\pi$
$587$	16.9696	+	16.9696i	0.700408	+	0.700408i	−0.264090	+	0.964498i	$0.585072\pi$
$588$	−10.3934	+	6.24319i	−0.428616	+	0.257465i
$589$			0.0458366i			0.00188867i
$590$	−29.2816	+	7.84598i	−1.20550	+	0.323014i
$591$	0.0623924	−	3.01287i	0.00256648	−	0.123933i
$592$	−1.94282	+	7.25069i	−0.0798493	+	0.298002i
$593$	8.99679	+	33.5765i	0.369454	+	1.37882i	0.861281	+	0.508129i	$0.169663\pi$
$593$	8.99679	+	33.5765i	0.369454	+	1.37882i	−0.491827	+	0.870693i	$0.663671\pi$
$594$	20.2458	−	17.8748i	0.830694	−	0.733411i
$595$	−26.2941	+	67.0585i	−1.07795	+	2.74913i
$596$	−5.40676	+	5.40676i	−0.221470	+	0.221470i
$597$	27.7921	+	8.06716i	1.13745	+	0.330167i
$598$	−2.58203	−	5.44962i	−0.105587	−	0.222852i
$599$	4.66976	−	2.69609i	0.190801	−	0.110159i	−0.401556	−	0.915834i	$-0.631531\pi$
$599$	4.66976	−	2.69609i	0.190801	−	0.110159i	0.592358	+	0.805675i	$0.298197\pi$
$600$	−19.0170	+	10.4606i	−0.776367	+	0.427052i
$601$	−33.9734			−1.38580			−0.692901	−	0.721033i	$-0.743668\pi$
$601$	−33.9734			−1.38580			−0.692901	+	0.721033i	$0.743668\pi$
$602$	−6.02319	+	4.80645i	−0.245487	+	0.195896i
$603$	−4.72802	+	15.1124i	−0.192540	+	0.615423i
$604$	1.92180	+	7.17226i	0.0781969	+	0.291835i
$605$	64.7689	+	17.3548i	2.63323	+	0.705572i
$606$	−0.234942	+	11.3451i	−0.00954385	+	0.460864i
$607$	−20.9467	+	36.2808i	−0.850201	+	1.47259i	0.0308253	+	0.999525i	$0.490186\pi$
$607$	−20.9467	+	36.2808i	−0.850201	+	1.47259i	−0.881026	+	0.473067i	$0.843147\pi$
$608$	−0.0407440			−0.00165239
$609$	5.24277	+	2.18201i	0.212448	+	0.0884196i
$610$			12.7205i			0.515036i
$611$	−12.9246	−	8.93225i	−0.522875	−	0.361360i
$612$	10.4443	−	16.4749i	0.422184	−	0.665957i
$613$	26.9839	+	7.23030i	1.08987	+	0.292029i	0.758632	−	0.651519i	$-0.225868\pi$
$613$	26.9839	+	7.23030i	1.08987	+	0.292029i	0.331236	+	0.943548i	$0.392535\pi$
$614$	−9.02428	−	5.21017i	−0.364190	−	0.210265i
$615$	−6.14218	−	24.9808i	−0.247677	−	1.00732i
$616$	11.0670	+	8.16241i	0.445902	+	0.328873i
$617$	−7.65580	−	7.65580i	−0.308211	−	0.308211i	0.536004	−	0.844215i	$-0.319933\pi$
$617$	−7.65580	−	7.65580i	−0.308211	−	0.308211i	−0.844215	+	0.536004i	$0.819933\pi$
$618$	10.0678	+	18.3029i	0.404986	+	0.736251i
$619$	7.91213	−	29.5285i	0.318015	−	1.18685i	−0.603134	−	0.797640i	$-0.706081\pi$
$619$	7.91213	−	29.5285i	0.318015	−	1.18685i	0.921149	−	0.389210i	$-0.127252\pi$
$620$	4.07927	−	2.35517i	0.163827	−	0.0945857i
$621$	1.72387	+	8.51799i	0.0691763	+	0.341815i
$622$	1.96925	+	1.96925i	0.0789597	+	0.0789597i
$623$	16.4391	−	13.1183i	0.658619	−	0.525572i
$624$	−3.65613	+	5.06287i	−0.146362	+	0.202677i
$625$	34.6846	−	60.0755i	1.38738	−	2.40302i
$626$	4.99306	−	18.6343i	0.199563	−	0.744778i
$627$	−0.264678	+	0.253939i	−0.0105702	+	0.0101413i
$628$	−15.4685	−	8.93077i	−0.617262	−	0.356376i
$629$	34.5127	+	34.5127i	1.37611	+	1.37611i
$630$	−20.8164	+	25.9060i	−0.829347	+	1.03212i
$631$	−32.9747	−	32.9747i	−1.31270	−	1.31270i	−0.919415	−	0.393288i	$-0.871338\pi$
$631$	−32.9747	−	32.9747i	−1.31270	−	1.31270i	−0.393288	−	0.919415i	$-0.628662\pi$
$632$	−0.936321	−	3.49440i	−0.0372449	−	0.139000i
$633$	−3.30082	−	3.44042i	−0.131196	−	0.136744i
$634$	−7.43057	+	4.29004i	−0.295105	+	0.170379i
$635$	−7.60848	−	28.3952i	−0.301933	−	1.12683i
$636$	−4.01818	+	0.987975i	−0.159331	+	0.0391758i
$637$	1.08741	−	25.2154i	0.0430846	−	0.999071i
$638$		−	6.44082i		−	0.254995i
$639$	5.12362	−	4.71592i	0.202687	−	0.186559i
$640$	2.09350	+	3.62604i	0.0827527	+	0.143332i
$641$	17.4042	+	30.1450i	0.687425	+	1.19065i	0.972668	+	0.232199i	$0.0745922\pi$
$641$	17.4042	+	30.1450i	0.687425	+	1.19065i	−0.285243	+	0.958455i	$0.592074\pi$
$642$	−14.6889	−	26.7040i	−0.579726	−	1.05392i
$643$	22.7474	−	22.7474i	0.897070	−	0.897070i	−0.0981062	−	0.995176i	$-0.531278\pi$
$643$	22.7474	−	22.7474i	0.897070	−	0.897070i	0.995176	+	0.0981062i	$0.0312785\pi$
$644$	−4.05530	+	1.77083i	−0.159801	+	0.0697806i
$645$	−10.9375	+	18.0697i	−0.430664	+	0.711493i
$646$	−0.132462	+	0.229431i	−0.00521165	+	0.00902685i
$647$	−24.9765	−	43.2606i	−0.981929	−	1.70075i	−0.654861	−	0.755750i	$-0.727273\pi$
$647$	−24.9765	−	43.2606i	−0.981929	−	1.70075i	−0.327068	−	0.945001i	$-0.606061\pi$
$648$	6.86862	−	5.81567i	0.269825	−	0.228461i
$649$	32.5897	+	18.8156i	1.27926	+	0.738579i
$650$	3.66151	−	45.0322i	0.143616	−	1.76631i
$651$	3.14529	−	4.08471i	0.123274	−	0.160093i
$652$	16.1704	−	16.1704i	0.633281	−	0.633281i
$653$	6.11871	+	3.53264i	0.239444	+	0.138243i	0.614921	−	0.788589i	$-0.289188\pi$
$653$	6.11871	+	3.53264i	0.239444	+	0.138243i	−0.375477	+	0.926832i	$0.622521\pi$
$654$	14.3567	+	14.9639i	0.561391	+	0.585134i
$655$	18.5309	+	4.96534i	0.724062	+	0.194012i
$656$	−3.42636	+	0.918090i	−0.133777	+	0.0358454i
$657$	−40.0486	−	12.5295i	−1.56244	−	0.488822i
$658$	−6.84300	+	9.27807i	−0.266768	+	0.361697i
$659$		−	9.48022i		−	0.369297i	−0.982805	−	0.184648i	$-0.940885\pi$
$659$		−	9.48022i		−	0.369297i	0.982805	−	0.184648i	$-0.0591146\pi$
$660$	36.1991	+	10.5075i	1.40905	+	0.409002i
$661$	−3.18735	+	11.8954i	−0.123974	+	0.462676i	−0.999801	−	0.0199485i	$-0.993650\pi$
$661$	−3.18735	+	11.8954i	−0.123974	+	0.462676i	0.875827	+	0.482625i	$0.160316\pi$
$662$	−9.40988	−	16.2984i	−0.365726	−	0.633455i
$663$	16.6229	+	37.0477i	0.645579	+	1.43881i
$664$	13.4791			0.523091
$665$	0.267907	−	0.363241i	0.0103890	−	0.0140859i
$666$	10.4427	+	19.9518i	0.404645	+	0.773117i
$667$	1.79491	+	1.03629i	0.0694992	+	0.0401254i
$668$	−0.928614	+	3.46564i	−0.0359292	+	0.134090i
$669$	−20.5580	−	0.425728i	−0.794820	−	0.0164596i
$670$	−21.3469	+	5.71988i	−0.824702	+	0.220978i
$671$	11.1657	−	11.1657i	0.431047	−	0.431047i
$672$	3.63088	+	2.79583i	0.140064	+	0.107852i
$673$		−	4.32932i		−	0.166883i	−0.996513	−	0.0834415i	$-0.973409\pi$
$673$		−	4.32932i		−	0.166883i	0.996513	−	0.0834415i	$-0.0265912\pi$
$674$	−5.07493	−	18.9399i	−0.195479	−	0.729537i
$675$	−20.7241	+	61.7264i	−0.797672	+	2.37585i
$676$	−4.59584	−	12.1605i	−0.176763	−	0.467712i
$677$	21.9491	+	12.6723i	0.843572	+	0.487037i	0.858477	−	0.512852i	$-0.171411\pi$
$677$	21.9491	+	12.6723i	0.843572	+	0.487037i	−0.0149048	+	0.999889i	$0.504745\pi$
$678$	−6.60717	+	10.9156i	−0.253747	+	0.419211i
$679$	22.3593	+	8.76723i	0.858072	+	0.336455i
$680$	27.2245			1.04401
$681$	12.7880	−	7.03424i	0.490038	−	0.269553i
$682$	−5.64799	−	1.51337i	−0.216273	−	0.0579500i
$683$	−18.3801	−	4.92492i	−0.703293	−	0.188447i	−0.110588	−	0.993866i	$-0.535273\pi$
$683$	−18.3801	−	4.92492i	−0.703293	−	0.188447i	−0.592705	+	0.805419i	$0.701940\pi$
$684$	−0.0899351	+	0.0827788i	−0.00343876	+	0.00316512i
$685$	−52.9540			−2.02327
$686$	−18.4698	−	1.36650i	−0.705179	−	0.0521732i
$687$	−44.4384	−	26.8984i	−1.69543	−	1.02624i
$688$	2.52234	+	1.45628i	0.0961635	+	0.0555200i
$689$	2.89631	−	8.11210i	0.110341	−	0.309046i
$690$	−8.75242	+	8.39727i	−0.333199	+	0.319679i
$691$	9.38184	+	35.0135i	0.356902	+	1.33198i	0.878074	+	0.478525i	$0.158828\pi$
$691$	9.38184	+	35.0135i	0.356902	+	1.33198i	−0.521172	+	0.853452i	$0.674505\pi$
$692$		−	19.0243i		−	0.723196i
$693$	41.0118	−	4.46752i	1.55791	−	0.169707i
$694$	5.36374	−	5.36374i	0.203605	−	0.203605i
$695$	−21.3294	+	5.71519i	−0.809070	+	0.216790i
$696$	0.0444385	−	2.14589i	0.00168444	−	0.0813399i
$697$	−5.96958	+	22.2788i	−0.226114	+	0.843868i
$698$	4.47323	+	2.58262i	0.169314	+	0.0977537i
$699$	−13.7576	+	3.38266i	−0.520358	+	0.127944i
$700$	−32.9464	−	3.70162i	−1.24526	−	0.139908i
$701$	27.8910			1.05343			0.526714	−	0.850042i	$-0.323424\pi$
$701$	27.8910			1.05343			0.526714	+	0.850042i	$0.323424\pi$
$702$	2.21588	+	18.6035i	0.0836329	+	0.702144i
$703$	−0.152922	−	0.264868i	−0.00576755	−	0.00998969i
$704$	1.34523	−	5.02047i	0.0507003	−	0.189216i
$705$	−8.80898	+	30.3477i	−0.331765	+	1.14296i
$706$		−	15.7003i		−	0.590889i
$707$	−10.2887	+	13.9499i	−0.386946	+	0.524640i
$708$	10.7281	+	6.49368i	0.403187	+	0.244047i
$709$	24.3930	−	6.53609i	0.916099	−	0.245468i	0.230182	−	0.973148i	$-0.426068\pi$
$709$	24.3930	−	6.53609i	0.916099	−	0.245468i	0.685917	+	0.727679i	$0.259401\pi$
$710$	9.38765	+	2.51541i	0.352312	+	0.0944018i
$711$	−9.16626	−	5.81096i	−0.343762	−	0.217928i
$712$	−6.88424	−	3.97462i	−0.257998	−	0.148955i
$713$	1.33047	−	1.33047i	0.0498266	−	0.0498266i
$714$	27.5478	−	11.3562i	1.03095	−	0.424994i
$715$	−59.7969	+	50.8040i	−2.23628	+	1.89996i
$716$	−1.79606	−	1.03696i	−0.0671219	−	0.0387529i
$717$	0.0600228	−	2.89845i	0.00224159	−	0.108245i
$718$	0.168760	+	0.292302i	0.00629809	+	0.0109086i
$719$	13.4524	−	23.3002i	0.501690	−	0.868953i	−0.498308	−	0.867000i	$-0.666045\pi$
$719$	13.4524	−	23.3002i	0.501690	−	0.868953i	0.999998	−	0.00195263i	$-0.000621541\pi$
$720$	11.9880	+	3.75053i	0.446766	+	0.139774i
$721$	−3.56262	+	31.7092i	−0.132679	+	1.18091i
$722$	−13.4339	+	13.4339i	−0.499956	+	0.499956i
$723$	−15.1974	+	8.35957i	−0.565198	+	0.310896i
$724$	−2.20615	−	3.82117i	−0.0819910	−	0.142013i
$725$	7.76414	+	13.4479i	0.288353	+	0.499442i
$726$	−13.3689	−	24.3041i	−0.496165	−	0.902011i
$727$			11.7770i			0.436786i	0.975861	+	0.218393i	$0.0700815\pi$
$727$			11.7770i			0.436786i	−0.975861	+	0.218393i	$0.929919\pi$
$728$	−9.02286	+	3.09645i	−0.334409	+	0.114762i
$729$	3.34569	−	26.7919i	0.123914	−	0.992293i
$730$	−15.1580	−	56.5704i	−0.561022	−	2.09376i
$731$	16.4007	−	9.46895i	0.606602	−	0.350222i
$732$	3.79712	−	3.64305i	0.140346	−	0.134651i
$733$	−7.70015	−	28.7374i	−0.284412	−	1.06144i	−0.949268	−	0.314468i	$-0.898174\pi$
$733$	−7.70015	−	28.7374i	−0.284412	−	1.06144i	0.664857	−	0.746971i	$-0.268493\pi$
$734$	16.8855	+	16.8855i	0.623255	+	0.623255i
$735$	−48.7998	+	13.9864i	−1.80001	+	0.515898i
$736$	1.18265	+	1.18265i	0.0435931	+	0.0435931i
$737$	23.7585	+	13.7170i	0.875157	+	0.505272i
$738$	−5.69782	+	8.98779i	−0.209740	+	0.330845i
$739$	−5.11564	+	19.0918i	−0.188182	+	0.702304i	0.805745	+	0.592262i	$0.201765\pi$
$739$	−5.11564	+	19.0918i	−0.188182	+	0.702304i	−0.993927	+	0.110042i	$0.964902\pi$
$740$	−15.7148	+	27.2188i	−0.577686	+	1.00058i
$741$	−0.0405287	−	0.251198i	−0.00148886	−	0.00922798i
$742$	−5.88449	−	2.30734i	−0.216026	−	0.0847052i
$743$	20.1411	+	20.1411i	0.738906	+	0.738906i	0.972366	−	0.233460i	$-0.0750048\pi$
$743$	20.1411	+	20.1411i	0.738906	+	0.738906i	−0.233460	+	0.972366i	$0.575005\pi$
$744$	−1.87130	−	0.543180i	−0.0686053	−	0.0199139i
$745$	−27.7259	+	16.0075i	−1.01580	+	0.586471i
$746$	−3.41343	+	12.7391i	−0.124975	+	0.466412i
$747$	29.7528	−	27.3852i	1.08860	−	1.00197i
$748$	−23.8970	−	23.8970i	−0.873762	−	0.873762i
$749$	5.19787	−	46.2638i	0.189926	−	1.69044i
$750$	−53.0352	+	13.0401i	−1.93657	+	0.476157i
$751$	22.3293	+	12.8918i	0.814807	+	0.470429i	0.848623	−	0.528999i	$-0.177432\pi$
$751$	22.3293	+	12.8918i	0.814807	+	0.470429i	−0.0338151	+	0.999428i	$0.510766\pi$
$752$	4.20894	+	1.12778i	0.153484	+	0.0411260i
$753$	−3.19824	−	3.33350i	−0.116550	−	0.121480i
$754$	3.67562	+	2.54023i	0.133858	+	0.0925097i
$755$			31.0895i			1.13146i
$756$	13.6948	−	1.20549i	0.498074	−	0.0438431i
$757$	19.6394			0.713807			0.356903	−	0.934141i	$-0.383833\pi$
$757$	19.6394			0.713807			0.356903	+	0.934141i	$0.383833\pi$
$758$	12.5385	−	21.7173i	0.455418	−	0.788806i
$759$	15.0536	+	0.311738i	0.546410	+	0.0113154i
$760$	−0.164782	−	0.0441532i	−0.00597727	−	0.00160160i
$761$	−4.50906	−	16.8280i	−0.163453	−	0.610016i	−0.998232	−	0.0594308i	$-0.981071\pi$
$761$	−4.50906	−	16.8280i	−0.163453	−	0.610016i	0.834779	−	0.550585i	$-0.185595\pi$
$762$	−6.29712	+	10.4034i	−0.228120	+	0.376874i
$763$	4.73106	+	31.3213i	0.171276	+	1.13391i
$764$	4.15781			0.150424
$765$	60.0933	−	55.3115i	2.17268	−	1.99979i
$766$	5.10083	−	2.94497i	0.184300	−	0.106406i
$767$	−23.5908	+	11.1773i	−0.851816	+	0.403590i
$768$	0.482830	−	1.66339i	0.0174226	−	0.0600225i
$769$	29.8709	−	29.8709i	1.07717	−	1.07717i	0.0804097	−	0.996762i	$-0.474377\pi$
$769$	29.8709	−	29.8709i	1.07717	−	1.07717i	0.996762	−	0.0804097i	$-0.0256229\pi$
$770$	35.9131	+	45.0045i	1.29422	+	1.62185i
$771$	10.8613	−	2.67053i	0.391159	−	0.0961767i
$772$	−0.892300	−	3.33011i	−0.0321146	−	0.119853i
$773$	7.66877	−	28.6202i	0.275827	−	1.02940i	−0.679459	−	0.733714i	$-0.737785\pi$
$773$	7.66877	−	28.6202i	0.275827	−	1.02940i	0.955285	−	0.295685i	$-0.0955479\pi$
$774$	8.52632	−	1.91013i	0.306472	−	0.0686580i
$775$	13.6168	−	3.64862i	0.489131	−	0.131062i
$776$		−	9.07747i		−	0.325862i
$777$	−4.54758	+	34.0970i	−0.163143	+	1.22322i
$778$	3.34320	+	3.34320i	0.119859	+	0.119859i
$779$	0.0722641	−	0.125165i	0.00258913	−	0.00448451i
$780$	−20.2731	+	16.5139i	−0.725893	+	0.591291i
$781$	−6.03228	−	10.4482i	−0.215852	−	0.373867i
$782$	10.5045	−	2.81466i	0.375638	−	0.100652i
$783$	−4.26168	−	4.82697i	−0.152300	−	0.172502i
$784$	2.06752	+	6.68770i	0.0738399	+	0.238847i
$785$	−52.8818	−	52.8818i	−1.88743	−	1.88743i
$786$	−3.82494	−	6.95361i	−0.136431	−	0.248027i
$787$	3.43589	−	12.8229i	0.122476	−	0.457088i	−0.877261	−	0.480014i	$-0.840632\pi$
$787$	3.43589	−	12.8229i	0.122476	−	0.457088i	0.999737	+	0.0229262i	$0.00729829\pi$
$788$	−1.68057	−	0.450308i	−0.0598679	−	0.0160416i
$789$	6.67798	+	1.93841i	0.237743	+	0.0690092i
$790$		−	15.1471i		−	0.538911i
$791$	−17.8618	+	7.79974i	−0.635092	+	0.277327i
$792$	−7.23063	−	13.8149i	−0.256929	−	0.490890i
$793$	1.96830	+	10.7757i	0.0698963	+	0.382656i
$794$	−18.1291	+	10.4669i	−0.643378	+	0.371455i
$795$	−17.3215	−	0.358703i	−0.614329	−	0.0127219i
$796$	8.35403	−	14.4696i	0.296101	−	0.512861i
$797$	−51.6511			−1.82957			−0.914787	−	0.403936i	$-0.867642\pi$
$797$	−51.6511			−1.82957			−0.914787	+	0.403936i	$0.867642\pi$
$798$	−0.185156	+	0.0240581i	−0.00655445	+	0.000851647i
$799$	20.0342	−	20.0342i	0.708759	−	0.708759i
$800$	3.24324	+	12.1039i	0.114666	+	0.427939i
$801$	−23.2709	+	5.21331i	−0.822237	+	0.184203i
$802$	−19.3271	−	33.4756i	−0.682465	−	1.18206i
$803$	−36.3508	+	62.9614i	−1.28279	+	2.22186i
$804$	7.82101	+	4.73402i	0.275826	+	0.166956i
$805$	−18.3199	+	2.76721i	−0.645693	+	0.0975314i
$806$	3.09118	−	2.62630i	0.108882	−	0.0925075i
$807$	−5.67268	−	1.64660i	−0.199688	−	0.0579630i
$808$	6.32828	+	1.69566i	0.222628	+	0.0596530i
$809$	10.7402	−	6.20086i	0.377605	−	0.218010i	−0.299171	−	0.954200i	$-0.596710\pi$
$809$	10.7402	−	6.20086i	0.377605	−	0.218010i	0.676776	+	0.736189i	$0.263377\pi$
$810$	34.0812	−	16.0771i	1.19749	−	0.564892i
$811$	−7.12154	+	7.12154i	−0.250071	+	0.250071i	−0.821000	−	0.570929i	$-0.806583\pi$
$811$	−7.12154	+	7.12154i	−0.250071	+	0.250071i	0.570929	+	0.821000i	$0.306583\pi$
$812$	1.94607	−	2.63858i	0.0682937	−	0.0925960i
$813$	44.9671	+	27.2184i	1.57707	+	0.954592i
$814$	37.6860	−	10.0979i	1.32089	−	0.353932i
$815$	82.9217	−	47.8748i	2.90462	−	1.67698i
$816$	−7.79691	−	8.12667i	−0.272947	−	0.284490i
$817$	−0.114625	+	0.0307138i	−0.00401024	+	0.00107454i
$818$	4.35364			0.152222
$819$	−13.6254	+	25.1664i	−0.476109	+	0.879386i
$820$	−14.8522			−0.518662
$821$	−21.0339	+	5.63602i	−0.734088	+	0.196698i	−0.606449	−	0.795122i	$-0.707407\pi$
$821$	−21.0339	+	5.63602i	−0.734088	+	0.196698i	−0.127639	+	0.991821i	$0.540740\pi$
$822$	15.1657	+	15.8071i	0.528963	+	0.551334i
$823$	−26.2071	+	15.1307i	−0.913523	+	0.527423i	−0.881563	−	0.472066i	$-0.843508\pi$
$823$	−26.2071	+	15.1307i	−0.913523	+	0.527423i	−0.0319601	+	0.999489i	$0.510175\pi$
$824$	11.6494	−	3.12145i	0.405827	−	0.108741i
$825$	96.5068	+	58.4151i	3.35993	+	2.03375i
$826$	7.66575	+	17.5549i	0.266726	+	0.610815i
$827$	−37.0084	+	37.0084i	−1.28691	+	1.28691i	−0.350252	+	0.936656i	$0.613904\pi$
$827$	−37.0084	+	37.0084i	−1.28691	+	1.28691i	−0.936656	+	0.350252i	$0.886096\pi$
$828$	5.01326	+	0.207724i	0.174223	+	0.00721892i
$829$	−20.4767	+	11.8222i	−0.711184	+	0.410602i	−0.811499	−	0.584353i	$-0.801348\pi$
$829$	−20.4767	+	11.8222i	−0.711184	+	0.410602i	0.100315	+	0.994956i	$0.468015\pi$
$830$	54.5139	+	14.6070i	1.89221	+	0.507015i
$831$	−6.18340	−	1.79484i	−0.214500	−	0.0622625i
$832$	2.33451	+	2.74774i	0.0809345	+	0.0952607i
$833$	44.3804	+	10.1000i	1.53769	+	0.349945i
$834$	7.81460	+	4.73015i	0.270597	+	0.163792i
$835$	−7.51124	+	13.0098i	−0.259937	+	0.450224i
$836$	0.105885	+	0.183398i	0.00366211	+	0.00634295i
$837$	−5.23414	+	2.60291i	−0.180918	+	0.0899699i
$838$	9.09057	+	33.9265i	0.314028	+	1.17197i
$839$	−7.02486	+	7.02486i	−0.242525	+	0.242525i	−0.817894	−	0.575369i	$-0.804858\pi$
$839$	−7.02486	+	7.02486i	−0.242525	+	0.242525i	0.575369	+	0.817894i	$0.304858\pi$
$840$	11.6547	+	15.2420i	0.402125	+	0.525897i
$841$	27.4644			0.947048
$842$	12.4597	−	21.5808i	0.429389	−	0.743724i
$843$	36.7606	+	0.761260i	1.26610	+	0.0262192i
$844$	−2.38390	+	1.37634i	−0.0820572	+	0.0473757i
$845$	−5.40905	−	54.1615i	−0.186077	−	1.86321i
$846$	11.5818	−	6.06184i	0.398190	−	0.208410i
$847$	4.73074	−	42.1062i	0.162550	−	1.44678i
$848$			2.38899i			0.0820384i
$849$	−18.5070	−	5.37199i	−0.635158	−	0.184366i
$850$	78.7018	+	21.0881i	2.69945	+	0.723315i
$851$	−3.24940	+	12.1269i	−0.111388	+	0.415706i
$852$	−1.93769	−	3.52266i	−0.0663843	−	0.120684i
$853$	−1.33595	−	1.33595i	−0.0457419	−	0.0457419i	0.683866	−	0.729608i	$-0.260297\pi$
$853$	−1.33595	−	1.33595i	−0.0457419	−	0.0457419i	−0.729608	+	0.683866i	$0.760297\pi$
$854$	7.94787	−	1.20052i	0.271971	−	0.0410809i
$855$	−0.453432	+	0.237324i	−0.0155071	+	0.00811630i
$856$	−16.9965	+	4.55420i	−0.580929	+	0.155660i
$857$	19.4163	+	33.6301i	0.663250	+	1.14878i	0.979757	+	0.200192i	$0.0641566\pi$
$857$	19.4163	+	33.6301i	0.663250	+	1.14878i	−0.316507	+	0.948590i	$0.602510\pi$
$858$	32.2907	+	3.29976i	1.10239	+	0.112652i
$859$	−11.6019	+	20.0951i	−0.395852	+	0.685635i	−0.993210	−	0.116339i	$-0.962884\pi$
$859$	−11.6019	+	20.0951i	−0.395852	+	0.685635i	0.597358	+	0.801975i	$0.296217\pi$
$860$	8.62305	+	8.62305i	0.294044	+	0.294044i
$861$	−15.0286	+	6.19531i	−0.512172	+	0.211135i
$862$		−	31.1263i		−	1.06017i
$863$	33.6970	−	9.02909i	1.14706	−	0.307354i	0.365273	−	0.930900i	$-0.380976\pi$
$863$	33.6970	−	9.02909i	1.14706	−	0.307354i	0.781786	+	0.623547i	$0.214309\pi$
$864$	−2.31372	−	4.65260i	−0.0787143	−	0.158285i
$865$	20.6162	−	76.9405i	0.700970	−	2.61606i
$866$	5.27430	+	19.6840i	0.179228	+	0.668888i
$867$	−42.5168	+	10.4539i	−1.44395	+	0.355032i
$868$	−1.85652	−	2.32649i	−0.0630144	−	0.0789663i
$869$	−13.2958	+	13.2958i	−0.451029	+	0.451029i
$870$	2.50517	−	8.63054i	0.0849333	−	0.292603i
$871$	−17.1982	+	8.14850i	−0.582739	+	0.276102i
$872$	10.3686	−	5.98632i	0.351125	−	0.202722i
$873$	−18.4425	−	20.0369i	−0.624185	−	0.678147i
$874$	−0.0681452			−0.00230504
$875$	−77.6683	−	30.4542i	−2.62567	−	1.02954i
$876$	−12.5454	+	20.7261i	−0.423870	+	0.700270i
$877$	8.36760	+	31.2283i	0.282554	+	1.05451i	0.950608	+	0.310393i	$0.100461\pi$
$877$	8.36760	+	31.2283i	0.282554	+	1.05451i	−0.668054	+	0.744112i	$0.732873\pi$
$878$	8.70938	+	2.33367i	0.293927	+	0.0787576i
$879$	12.6035	+	0.261000i	0.425105	+	0.00880332i
$880$	10.8811	−	18.8466i	0.366802	−	0.635319i
$881$	18.3096			0.616866			0.308433	−	0.951246i	$-0.400195\pi$
$881$	18.3096			0.616866			0.308433	+	0.951246i	$0.400195\pi$
$882$	18.1510	+	10.5614i	0.611174	+	0.355621i
$883$		−	11.8777i		−	0.399716i	−0.979825	−	0.199858i	$-0.935952\pi$
$883$		−	11.8777i		−	0.399716i	0.979825	−	0.199858i	$-0.0640481\pi$
$884$	23.0623	−	4.21258i	0.775670	−	0.141685i
$885$	36.3509	+	37.8883i	1.22192	+	1.27360i
$886$	26.0416	+	6.97782i	0.874884	+	0.234424i
$887$	−18.4001	−	10.6233i	−0.617814	−	0.356695i	0.158204	−	0.987407i	$-0.449430\pi$
$887$	−18.4001	−	10.6233i	−0.617814	−	0.356695i	−0.776017	+	0.630712i	$0.782763\pi$
$888$	12.6255	−	3.10432i	0.423686	−	0.104174i
$889$	−17.0236	+	7.43372i	−0.570952	+	0.249319i
$890$	−23.5349	−	23.5349i	−0.788892	−	0.788892i
$891$	−44.0278	−	15.8036i	−1.47499	−	0.529440i
$892$	−3.07263	+	11.4672i	−0.102879	+	0.383951i
$893$	−0.153753	+	0.0887692i	−0.00514514	+	0.00297055i
$894$	12.7188	+	3.69187i	0.425381	+	0.123475i
$895$	−6.14013	−	6.14013i	−0.205242	−	0.205242i
$896$	2.06801	−	1.65025i	0.0690874	−	0.0551311i
$897$	−6.11496	+	8.46776i	−0.204172	+	0.282730i
$898$	−13.3689	+	23.1556i	−0.446125	+	0.772711i
$899$	−0.360816	+	1.34659i	−0.0120339	+	0.0449111i
$900$	31.7502	+	20.1281i	1.05834	+	0.670936i
$901$	13.4525	+	7.76682i	0.448168	+	0.258750i
$902$	13.0369	+	13.0369i	0.434082	+	0.434082i
$903$	12.3224	+	5.12850i	0.410063	+	0.170666i
$904$	5.20905	+	5.20905i	0.173250	+	0.173250i
$905$	−4.78150	−	17.8448i	−0.158942	−	0.593181i
$906$	9.28039	−	8.90382i	0.308320	−	0.295810i
$907$	16.4197	−	9.47991i	0.545207	−	0.314775i	−0.201980	−	0.979390i	$-0.564738\pi$
$907$	16.4197	−	9.47991i	0.545207	−	0.314775i	0.747186	+	0.664614i	$0.231404\pi$
$908$	−2.18092	−	8.13930i	−0.0723763	−	0.270112i
$909$	17.4136	−	9.11417i	0.577572	−	0.302298i
$910$	−39.8469	+	2.74523i	−1.32091	+	0.0910034i
$911$		−	40.7162i		−	1.34899i	−0.738281	−	0.674493i	$-0.764362\pi$
$911$		−	40.7162i		−	1.34899i	0.738281	−	0.674493i	$-0.235638\pi$
$912$	0.0340124	+	0.0618334i	0.00112626	+	0.00204751i
$913$	−35.0293	−	60.6726i	−1.15930	−	2.00797i
$914$	−10.8655	−	18.8196i	−0.359399	−	0.622498i
$915$	19.3047	−	10.6188i	0.638193	−	0.351048i
$916$	−21.2065	+	21.2065i	−0.700683	+	0.700683i
$917$	1.35350	−	12.0469i	0.0446966	−	0.397824i
$918$	−33.7211	−	2.09735i	−1.11296	−	0.0692228i
$919$	−9.93773	+	17.2126i	−0.327815	+	0.567793i	−0.982078	−	0.188474i	$-0.939646\pi$
$919$	−9.93773	+	17.2126i	−0.327815	+	0.567793i	0.654263	+	0.756267i	$0.272979\pi$
$920$	3.50142	+	6.06463i	0.115438	+	0.199945i
$921$	−0.373680	+	18.0447i	−0.0123132	+	0.594593i
$922$	19.7324	+	11.3925i	0.649851	+	0.375192i
$923$	8.34165	+	0.678249i	0.274569	+	0.0223248i
$924$	3.14880	−	23.6092i	0.103588	−	0.776686i
$925$	−66.5125	+	66.5125i	−2.18692	+	2.18692i
$926$	−30.3199	−	17.5052i	−0.996373	−	0.575256i
$927$	19.3722	−	30.5579i	0.636267	−	1.00365i
$928$	−1.19697	−	0.320728i	−0.0392926	−	0.0105284i
$929$	−18.3708	+	4.92245i	−0.602727	+	0.161500i	−0.547263	−	0.836961i	$-0.684330\pi$
$929$	−18.3708	+	4.92245i	−0.602727	+	0.161500i	−0.0554636	+	0.998461i	$0.517664\pi$
$930$	−6.97952	−	4.22468i	−0.228868	−	0.138533i
$931$	−0.252241	−	0.133109i	−0.00826686	−	0.00436248i
$932$			8.17950i			0.267928i
$933$	1.34465	−	4.63245i	0.0440220	−	0.151660i
$934$	5.61811	−	20.9671i	0.183830	−	0.686064i
$935$	−70.7507	−	122.544i	−2.31380	−	4.00761i
$936$	10.7355	+	1.32217i	0.350902	+	0.0432166i
$937$	7.62390			0.249062			0.124531	−	0.992216i	$-0.460257\pi$
$937$	7.62390			0.249062			0.124531	+	0.992216i	$0.460257\pi$
$938$	5.58849	+	12.7979i	0.182471	+	0.417867i
$939$	−32.4478	+	7.97813i	−1.05889	+	0.260357i
$940$	15.8002	+	9.12223i	0.515344	+	0.297534i
$941$	7.01312	−	26.1733i	0.228621	−	0.853226i	−0.752300	−	0.658820i	$-0.771056\pi$
$941$	7.01312	−	26.1733i	0.228621	−	0.853226i	0.980921	−	0.194405i	$-0.0622777\pi$
$942$	−0.640526	+	30.9305i	−0.0208695	+	1.00777i
$943$	−5.73066	+	1.53552i	−0.186616	+	0.0500036i
$944$	5.11957	−	5.11957i	0.166628	−	0.166628i
$945$	56.6925	+	9.96529i	1.84421	+	0.324171i
$946$		−	15.1382i		−	0.492186i
$947$	−6.06543	−	22.6365i	−0.197100	−	0.735587i	−0.991713	−	0.128471i	$-0.958993\pi$
$947$	−6.06543	−	22.6365i	−0.197100	−	0.735587i	0.794613	−	0.607116i	$-0.207674\pi$
$948$	−4.52150	+	4.33803i	−0.146852	+	0.140893i
$949$	−21.5940	−	45.5762i	−0.700970	−	1.47947i
$950$	−0.442157	−	0.255280i	−0.0143455	−	0.00828237i
$951$	12.7135	+	7.69544i	0.412264	+	0.249542i
$952$	−2.56937	−	17.0102i	−0.0832738	−	0.551303i
$953$	50.7316			1.64336			0.821679	−	0.569950i	$-0.193037\pi$
$953$	50.7316			1.64336			0.821679	+	0.569950i	$0.193037\pi$
$954$	4.85367	+	5.27328i	0.157143	+	0.170729i
$955$	16.8156	+	4.50571i	0.544139	+	0.145801i
$956$	−1.61675	−	0.433206i	−0.0522893	−	0.0140109i
$957$	−9.77465	+	5.37669i	−0.315970	+	0.173804i
$958$	−23.9311			−0.773178
$959$	4.99764	+	33.0862i	0.161382	+	1.06841i
$960$	3.75530	−	6.20407i	0.121202	−	0.200235i
$961$	−25.7507	−	14.8672i	−0.830669	−	0.479587i
$962$	−9.10053	+	25.4891i	−0.293413	+	0.821800i
$963$	−28.2641	+	44.5841i	−0.910799	+	1.43670i
$964$	2.59183	+	9.67284i	0.0834772	+	0.311541i
$965$		−	14.4350i		−	0.464679i
$966$	6.07273	+	4.67609i	0.195387	+	0.150451i
$967$	34.6269	−	34.6269i	1.11353	−	1.11353i	0.120857	−	0.992670i	$-0.461436\pi$
$967$	34.6269	−	34.6269i	1.11353	−	1.11353i	0.992670	−	0.120857i	$-0.0385642\pi$
$968$	−15.4691	+	4.14493i	−0.497195	+	0.133223i
$969$	0.458764	+	0.00950036i	0.0147376	+	0.000305195i
$970$	9.83702	−	36.7122i	0.315848	−	1.17876i
$971$	32.3883	+	18.6994i	1.03939	+	0.600092i	0.919660	−	0.392715i	$-0.128464\pi$
$971$	32.3883	+	18.6994i	1.03939	+	0.600092i	0.119729	+	0.992807i	$0.461797\pi$
$972$	−14.5597	−	5.56906i	−0.467003	−	0.178628i
$973$	5.58391	+	12.7874i	0.179012	+	0.409946i
$974$	−29.1425			−0.933787
$975$	−71.3979	+	32.0354i	−2.28656	+	1.02595i
$976$	−1.51904	−	2.63106i	−0.0486234	−	0.0842183i
$977$	0.869806	−	3.24616i	0.0278276	−	0.103854i	−0.950615	−	0.310372i	$-0.899546\pi$
$977$	0.869806	−	3.24616i	0.0278276	−	0.103854i	0.978443	+	0.206518i	$0.0662131\pi$
$978$	−38.0391	−	11.0415i	−1.21636	−	0.353070i
$979$			41.3167i			1.32049i
$980$	1.11442	+	29.2878i	0.0355988	+	0.935563i
$981$	10.7246	−	34.2794i	0.342410	−	1.09446i
$982$	4.35189	−	1.16608i	0.138874	−	0.0372112i
$983$	36.5128	+	9.78356i	1.16458	+	0.312047i	0.788792	−	0.614660i	$-0.210707\pi$
$983$	36.5128	+	9.78356i	1.16458	+	0.312047i	0.375784	+	0.926707i	$0.377373\pi$
$984$	4.25357	+	4.43347i	0.135599	+	0.141334i
$985$	−6.30880	−	3.64238i	−0.201015	−	0.116056i
$986$	−5.69750	+	5.69750i	−0.181445	+	0.181445i
$987$	19.7929	+	2.63981i	0.630015	+	0.0840262i
$988$	−0.146421	−	0.0119053i	−0.00465828	−	0.000378759i
$989$	4.21867	+	2.43565i	0.134146	+	0.0774492i
$990$	−14.2722	−	63.7075i	−0.453600	−	2.02476i
$991$	−15.2692	−	26.4471i	−0.485043	−	0.840119i	0.514810	−	0.857305i	$-0.327863\pi$
$991$	−15.2692	−	26.4471i	−0.485043	−	0.840119i	−0.999852	+	0.0171858i	$0.994529\pi$
$992$	−0.562496	+	0.974271i	−0.0178593	+	0.0309331i
$993$	−16.8794	+	27.8862i	−0.535651	+	0.884940i
$994$	0.685677	−	6.10290i	0.0217484	−	0.193572i
$995$	49.4667	−	49.4667i	1.56820	−	1.56820i
$996$	−11.2521	−	20.4560i	−0.356538	−	0.648174i
$997$	14.9662	+	25.9222i	0.473984	+	0.820964i	0.999556	−	0.0297848i	$-0.00948220\pi$
$997$	14.9662	+	25.9222i	0.473984	+	0.820964i	−0.525573	+	0.850749i	$0.676149\pi$
$998$	−1.43141	−	2.47928i	−0.0453106	−	0.0784803i
$999$	21.5617	−	32.5033i	0.682181	−	1.02836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.317.15	✓	144
3.2	odd	2	inner	546.2.bv.a.317.28	yes	144
7.4	even	3	inner	546.2.bv.a.473.28	yes	144
13.8	odd	4	inner	546.2.bv.a.359.15	yes	144
21.11	odd	6	inner	546.2.bv.a.473.15	yes	144
39.8	even	4	inner	546.2.bv.a.359.28	yes	144
91.60	odd	12	inner	546.2.bv.a.515.28	yes	144
273.242	even	12	inner	546.2.bv.a.515.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.15	✓	144	1.1	even	1	trivial
546.2.bv.a.317.28	yes	144	3.2	odd	2	inner
546.2.bv.a.359.15	yes	144	13.8	odd	4	inner
546.2.bv.a.359.28	yes	144	39.8	even	4	inner
546.2.bv.a.473.15	yes	144	21.11	odd	6	inner
546.2.bv.a.473.28	yes	144	7.4	even	3	inner
546.2.bv.a.515.15	yes	144	273.242	even	12	inner
546.2.bv.a.515.28	yes	144	91.60	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.19913 + 1.24984i) q^{3} +(0.866025 - 0.500000i) q^{4} +(4.04433 - 1.08367i) q^{5} +(-1.48175 - 0.896896i) q^{6} +(-1.05878 - 2.42466i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.124198 + 2.99743i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.19913 + 1.24984i) q^{3} +(0.866025 - 0.500000i) q^{4} +(4.04433 - 1.08367i) q^{5} +(-1.48175 - 0.896896i) q^{6} +(-1.05878 - 2.42466i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.124198 + 2.99743i) q^{9} +(-3.62604 + 2.09350i) q^{10} +(5.02047 + 1.34523i) q^{11} +(1.66339 + 0.482830i) q^{12} +(-2.74774 + 2.33451i) q^{13} +(1.65025 + 2.06801i) q^{14} +(6.20407 + 3.75530i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.25108 - 5.63104i) q^{17} +(-0.655825 - 2.92744i) q^{18} +(0.0105453 + 0.0393557i) q^{19} +(2.96065 - 2.96065i) q^{20} +(1.76083 - 4.23078i) q^{21} -5.19757 q^{22} +(0.836260 - 1.44845i) q^{23} +(-1.73168 - 0.0358606i) q^{24} +(10.8521 - 6.26546i) q^{25} +(2.04990 - 2.96613i) q^{26} +(-3.89523 + 3.43906i) q^{27} +(-2.12926 - 1.57043i) q^{28} +1.23920i q^{29} +(-6.96461 - 2.02161i) q^{30} +(1.08666 + 0.291169i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(4.33885 + 7.88788i) q^{33} +(4.59773 + 4.59773i) q^{34} +(-6.90960 - 8.65874i) q^{35} +(1.39116 + 2.65795i) q^{36} +(-7.25069 + 1.94282i) q^{37} +(-0.0203720 - 0.0352853i) q^{38} +(-6.21264 - 0.634866i) q^{39} +(-2.09350 + 3.62604i) q^{40} +(-2.50827 - 2.50827i) q^{41} +(-0.605821 + 4.54235i) q^{42} +2.91255i q^{43} +(5.02047 - 1.34523i) q^{44} +(2.74594 + 12.2572i) q^{45} +(-0.432880 + 1.61553i) q^{46} +(1.12778 + 4.20894i) q^{47} +(1.68196 - 0.413553i) q^{48} +(-4.75796 + 5.13437i) q^{49} +(-8.86069 + 8.86069i) q^{50} +(3.13944 - 10.8157i) q^{51} +(-1.21236 + 3.39561i) q^{52} +(-2.06893 + 1.19450i) q^{53} +(2.87241 - 4.33004i) q^{54} +21.7622 q^{55} +(2.46317 + 0.965823i) q^{56} +(-0.0365431 + 0.0603723i) q^{57} +(-0.320728 - 1.19697i) q^{58} +(6.99346 + 1.87389i) q^{59} +(7.25053 + 0.150148i) q^{60} +(1.51904 - 2.63106i) q^{61} -1.12499 q^{62} +(7.39925 - 2.87248i) q^{63} -1.00000i q^{64} +(-8.58291 + 12.4192i) q^{65} +(-6.23254 - 6.49613i) q^{66} +(5.09838 + 1.36611i) q^{67} +(-5.63104 - 3.25108i) q^{68} +(2.81311 - 0.691676i) q^{69} +(8.91521 + 6.57537i) q^{70} +(-1.64133 - 1.64133i) q^{71} +(-2.03168 - 2.20732i) q^{72} +(-3.62026 + 13.5110i) q^{73} +(6.50079 - 3.75323i) q^{74} +(20.8438 + 6.05031i) q^{75} +(0.0288104 + 0.0288104i) q^{76} +(-2.05385 - 13.5972i) q^{77} +(6.16527 - 0.994717i) q^{78} +(-1.80883 + 3.13299i) q^{79} +(1.08367 - 4.04433i) q^{80} +(-8.96915 - 0.744551i) q^{81} +(3.07199 + 1.77361i) q^{82} +(-9.53117 - 9.53117i) q^{83} +(-0.590469 - 4.54438i) q^{84} +(-19.2507 - 19.2507i) q^{85} +(-0.753824 - 2.81331i) q^{86} +(-1.54880 + 1.48595i) q^{87} +(-4.50123 + 2.59879i) q^{88} +(2.05741 + 7.67837i) q^{89} +(-5.82476 - 11.1288i) q^{90} +(8.56965 + 4.19060i) q^{91} -1.67252i q^{92} +(0.939124 + 1.70730i) q^{93} +(-2.17871 - 3.77363i) q^{94} +(0.0852974 + 0.147739i) q^{95} +(-1.51761 + 0.834784i) q^{96} +(-6.41874 + 6.41874i) q^{97} +(3.26697 - 6.19088i) q^{98} +(-4.65577 + 14.8814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

L-functions

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