LMFDB - Embedded newform 546.2.bv.a.515.15

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			515.15
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.15

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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	0.995277	−	0.0970716i	$-0.0309476\pi$
$5$	4.04433	+	1.08367i	1.80868	+	0.484634i	0.813400	+	0.581705i	$0.197614\pi$
$6$	−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	0.596057	−	0.802942i	$-0.296733\pi$
$11$	5.02047	−	1.34523i	1.51373	−	0.405602i	0.917672	+	0.397340i	$0.130067\pi$
$12$	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	0.138380	+	0.990379i	$0.455811\pi$
$17$	−3.25108	+	5.63104i	−0.788504	+	1.36573i	−0.926883	+	0.375349i	$0.877523\pi$
$18$	−0.655825	+	2.92744i	−0.154579	+	0.690004i
$19$	0.0105453	−	0.0393557i	0.00241926	−	0.00902881i	−0.964706	−	0.263331i	$-0.915179\pi$
$19$	0.0105453	−	0.0393557i	0.00241926	−	0.00902881i	0.967125	+	0.254302i	$0.0818457\pi$
$20$	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	0.939944	−	0.341329i	$-0.110877\pi$
$23$	0.836260	+	1.44845i	0.174372	+	0.302022i	−0.765572	+	0.643351i	$0.777544\pi$
$24$	−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	$-0.963295\pi$
$29$		−	1.23920i		−	0.230113i	0.993359	−	0.115057i	$-0.0367050\pi$
$30$	−6.96461	+	2.02161i	−1.27156	+	0.369093i
$31$	1.08666	−	0.291169i	0.195170	−	0.0522955i	−0.159910	−	0.987132i	$-0.551120\pi$
$31$	1.08666	−	0.291169i	0.195170	−	0.0522955i	0.355080	+	0.934836i	$0.384454\pi$
$32$	−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	−0.392328	−	0.919825i	$-0.628330\pi$
$37$	−7.25069	−	1.94282i	−1.19201	−	0.319397i	−0.799679	+	0.600428i	$0.794997\pi$
$38$	−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	−0.875302	−	0.483576i	$-0.839338\pi$
$41$	−2.50827	+	2.50827i	−0.391726	+	0.391726i	0.483576	+	0.875302i	$0.339338\pi$
$42$	−0.605821	−	4.54235i	−0.0934802	−	0.700900i
$43$		−	2.91255i		−	0.444160i	−0.975028	−	0.222080i	$-0.928715\pi$
$43$		−	2.91255i		−	0.444160i	0.975028	−	0.222080i	$-0.0712846\pi$
$44$	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	−0.833599	−	0.552370i	$-0.813724\pi$
$47$	1.12778	−	4.20894i	0.164504	−	0.613937i	0.998103	−	0.0615667i	$-0.0196097\pi$
$48$	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	0.351129	−	0.936327i	$-0.385798\pi$
$53$	−2.06893	−	1.19450i	−0.284189	−	0.164077i	−0.635318	+	0.772250i	$0.719131\pi$
$54$	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	0.226964	−	0.973903i	$-0.427120\pi$
$59$	6.99346	−	1.87389i	0.910471	−	0.243960i	0.683508	+	0.729943i	$0.260454\pi$
$60$	7.25053	−	0.150148i	0.936039	−	0.0193841i
$61$	1.51904	+	2.63106i	0.194494	+	0.336873i	0.946734	−	0.322015i	$-0.104360\pi$
$61$	1.51904	+	2.63106i	0.194494	+	0.336873i	−0.752241	+	0.658888i	$0.771027\pi$
$62$	−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	0.0664357	−	0.997791i	$-0.478837\pi$
$67$	5.09838	−	1.36611i	0.622866	−	0.166896i	0.556430	+	0.830894i	$0.312171\pi$
$68$	−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	−0.797762	−	0.602972i	$-0.793983\pi$
$71$	−1.64133	+	1.64133i	−0.194790	+	0.194790i	0.602972	+	0.797762i	$0.293983\pi$
$72$	−2.03168	+	2.20732i	−0.239436	+	0.260136i
$73$	−3.62026	−	13.5110i	−0.423719	−	1.58134i	−0.766705	−	0.642000i	$-0.778105\pi$
$73$	−3.62026	−	13.5110i	−0.423719	−	1.58134i	0.342986	−	0.939341i	$-0.388562\pi$
$74$	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	0.746147	−	0.665781i	$-0.231901\pi$
$79$	−1.80883	−	3.13299i	−0.203510	−	0.352489i	−0.949657	+	0.313292i	$0.898568\pi$
$80$	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	−0.0473011	+	0.998881i	$0.515062\pi$
$83$	−9.53117	+	9.53117i	−1.04618	+	1.04618i	−0.998881	+	0.0473011i	$0.984938\pi$
$84$	−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	−0.766972	−	0.641680i	$-0.778238\pi$
$89$	2.05741	−	7.67837i	0.218085	−	0.813906i	0.985058	−	0.172226i	$-0.0550958\pi$
$90$	−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	0.301684	−	0.953408i	$-0.402451\pi$
$97$	−6.41874	−	6.41874i	−0.651724	−	0.651724i	−0.953408	+	0.301684i	$0.902451\pi$
$98$	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	−0.981704	−	0.190412i	$-0.939017\pi$
$101$	−3.27576	+	5.67378i	−0.325950	+	0.564562i	0.655754	+	0.754975i	$0.272351\pi$
$102$	−0.233172	−	11.2597i	−0.0230875	−	1.11487i
$103$	−10.4446	+	6.03018i	−1.02913	+	0.594171i	−0.916737	−	0.399492i	$-0.869187\pi$
$103$	−10.4446	+	6.03018i	−1.02913	+	0.594171i	−0.112398	+	0.993663i	$0.535853\pi$
$104$	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	0.473633	−	0.880722i	$-0.342942\pi$
$107$	15.2387	−	8.79805i	1.47318	−	0.850539i	0.999544	+	0.0301828i	$0.00960895\pi$
$108$	−1.65384	−	4.92593i	−0.159141	−	0.473998i
$109$	−11.5647	+	3.09875i	−1.10770	+	0.296806i	−0.765895	−	0.642966i	$-0.777704\pi$
$109$	−11.5647	+	3.09875i	−1.10770	+	0.296806i	−0.341801	+	0.939772i	$0.611037\pi$
$110$	−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	$0.112630\pi$
$113$			7.36671i			0.693002i	−0.938050	+	0.346501i	$0.887370\pi$
$114$	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	$0.100834\pi$
$127$			7.02101i			0.623014i	−0.950244	+	0.311507i	$0.899166\pi$
$128$	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	−0.316535	−	0.948581i	$-0.602519\pi$
$131$	3.96808	−	2.29097i	0.346693	−	0.200163i	0.663228	+	0.748418i	$0.269186\pi$
$132$	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	−0.739650	−	0.672991i	$-0.765009\pi$
$137$	−12.2163	+	3.27335i	−1.04371	+	0.279661i	−0.304060	+	0.952653i	$0.598342\pi$
$138$	−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	−0.0567364	−	0.998389i	$-0.518069\pi$
$149$	−7.38577	−	1.97901i	−0.605066	−	0.162127i	−0.548330	+	0.836262i	$0.684736\pi$
$150$	−21.6995	+	0.449367i	−1.77176	+	0.0366906i
$151$	−1.92180	−	7.17226i	−0.156394	−	0.583670i	−0.998982	−	0.0451114i	$-0.985636\pi$
$151$	−1.92180	−	7.17226i	−0.156394	−	0.583670i	0.842588	−	0.538559i	$-0.181031\pi$
$152$	−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	0.251067	+	0.967970i	$0.419219\pi$
$157$	−8.93077	+	15.4685i	−0.712753	+	1.23452i	−0.963820	+	0.266554i	$0.914115\pi$
$158$	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	0.980219	−	0.197916i	$-0.0634174\pi$
$163$	22.0891	+	5.91877i	1.73016	+	0.463594i	0.749936	+	0.661510i	$0.230084\pi$
$164$	−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	0.602100	−	0.798421i	$-0.294331\pi$
$167$	−2.53702	−	2.53702i	−0.196321	−	0.196321i	−0.798421	+	0.602100i	$0.794331\pi$
$168$	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	0.959712	+	0.280985i	$0.0906610\pi$
$173$	9.51216	+	16.4755i	0.723196	+	1.25261i	−0.236516	+	0.971628i	$0.576006\pi$
$174$	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	−0.902173	−	0.431374i	$-0.858029\pi$
$179$	−1.03696	+	1.79606i	−0.0775057	+	0.134244i	0.824667	+	0.565618i	$0.191362\pi$
$180$	8.50663	−	9.24205i	0.634047	−	0.688862i
$181$			4.41231i			0.327964i	0.986463	+	0.163982i	$0.0524339\pi$
$181$			4.41231i			0.327964i	−0.986463	+	0.163982i	$0.947566\pi$
$182$	−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	−0.364039	−	0.931384i	$-0.618603\pi$
$191$	3.60077	−	2.07891i	0.260543	−	0.150424i	0.624582	+	0.780959i	$0.285269\pi$
$192$	1.24984	+	1.19913i	0.0901994	+	0.0865394i
$193$	0.892300	+	3.33011i	0.0642292	+	0.239707i	0.990576	−	0.136966i	$-0.0437350\pi$
$193$	0.892300	+	3.33011i	0.0642292	+	0.239707i	−0.926347	+	0.376672i	$0.877068\pi$
$194$	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	−0.749574	−	0.661921i	$-0.769741\pi$
$197$	−1.23026	+	1.23026i	−0.0876527	+	0.0876527i	0.661921	+	0.749574i	$0.269741\pi$
$198$	0.645530	+	15.5794i	0.0458758	+	1.10718i
$199$	14.4696	+	8.35403i	1.02572	+	0.592201i	0.915756	−	0.401734i	$-0.131592\pi$
$199$	14.4696	+	8.35403i	1.02572	+	0.592201i	0.109966	+	0.993935i	$0.464926\pi$
$200$	−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	0.367773	−	0.929916i	$-0.380120\pi$
$223$	−8.39459	−	8.39459i	−0.562143	−	0.562143i	−0.929916	+	0.367773i	$0.880120\pi$
$224$	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	0.999766	+	0.0216187i	$0.00688199\pi$
$227$	2.18092	+	8.13930i	0.144753	+	0.540224i	−0.855014	+	0.518606i	$0.826451\pi$
$228$	−0.00146111	−	0.0705555i	−9.67641e−5	−	0.00467265i
$229$	−28.9686	−	7.76212i	−1.91430	−	0.512936i	−0.991958	−	0.126564i	$-0.959605\pi$
$229$	−28.9686	−	7.76212i	−1.91430	−	0.512936i	−0.922343	−	0.386371i	$-0.873728\pi$
$230$		−	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	0.700398	−	0.713752i	$-0.253006\pi$
$233$	−4.08975	−	7.08365i	−0.267928	−	0.464066i	−0.968327	+	0.249687i	$0.919672\pi$
$234$	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	−0.744348	−	0.667792i	$-0.767240\pi$
$239$	−1.18354	+	1.18354i	−0.0765568	+	0.0765568i	0.667792	+	0.744348i	$0.267240\pi$
$240$	6.35422	+	3.49523i	0.410163	+	0.225616i
$241$	−2.59183	−	9.67284i	−0.166954	−	0.623082i	−0.997783	−	0.0665537i	$-0.978800\pi$
$241$	−2.59183	−	9.67284i	−0.166954	−	0.623082i	0.830828	−	0.556529i	$-0.187867\pi$
$242$	−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	0.948981	−	0.315333i	$-0.102116\pi$
$257$	3.22876	+	5.59238i	0.201405	+	0.348843i	−0.747577	+	0.664176i	$0.768783\pi$
$258$	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	0.603350	−	0.797477i	$-0.293832\pi$
$263$	3.47681	+	2.00734i	0.214389	+	0.123778i	−0.388960	+	0.921255i	$0.627166\pi$
$264$	−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	0.407254	−	0.913315i	$-0.366486\pi$
$269$	−2.95341	−	1.70515i	−0.180073	−	0.103965i	−0.587327	+	0.809350i	$0.699820\pi$
$270$	6.92462	+	20.6248i	0.421419	+	1.25519i
$271$	29.3133	+	7.85448i	1.78066	+	0.477125i	0.990703	−	0.136042i	$-0.0434382\pi$
$271$	29.3133	+	7.85448i	1.78066	+	0.477125i	0.789953	+	0.613167i	$0.210105\pi$
$272$	−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	0.400157	−	0.916446i	$-0.368955\pi$
$277$	−3.21931	−	1.85867i	−0.193430	−	0.111677i	−0.593587	+	0.804770i	$0.702289\pi$
$278$	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	0.995031	−	0.0995691i	$-0.0317464\pi$
$281$	15.0107	+	15.0107i	0.895462	+	0.895462i	−0.0995691	+	0.995031i	$0.531746\pi$
$282$	2.10389	+	7.24809i	0.125285	+	0.431617i
$283$	−9.63544	−	5.56302i	−0.572767	−	0.330687i	0.185487	−	0.982647i	$-0.440614\pi$
$283$	−9.63544	−	5.56302i	−0.572767	−	0.330687i	−0.758254	+	0.651959i	$0.773947\pi$
$284$	−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	0.841272	−	0.540613i	$-0.181808\pi$
$293$	5.14645	+	5.14645i	0.300659	+	0.300659i	−0.540613	+	0.841272i	$0.681808\pi$
$294$	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	−0.464856	−	0.885386i	$-0.653894\pi$
$307$	7.36830	−	7.36830i	0.420531	−	0.420531i	0.885386	+	0.464856i	$0.153894\pi$
$308$	−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	−0.902801	−	0.430058i	$-0.858493\pi$
$311$	−1.39247	+	2.41183i	−0.0789597	+	0.136762i	0.823842	+	0.566820i	$0.191827\pi$
$312$	4.84192	+	3.94408i	0.274120	+	0.223290i
$313$	−9.64584	−	16.7071i	−0.545215	−	0.944341i	−0.998593	−	0.0530224i	$-0.983115\pi$
$313$	−9.64584	−	16.7071i	−0.545215	−	0.944341i	0.453378	−	0.891318i	$-0.350219\pi$
$314$	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	0.483936	−	0.875104i	$-0.339207\pi$
$317$	8.28772	+	2.22069i	0.465485	+	0.124726i	−0.0184511	+	0.999830i	$0.505874\pi$
$318$	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	−0.692829	−	0.721102i	$-0.743636\pi$
$331$	4.87091	−	18.1785i	0.267730	−	0.999181i	0.960558	−	0.278079i	$-0.0896976\pi$
$332$	−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	$-0.820666\pi$
$337$		−	19.6080i		−	1.06812i	0.845448	−	0.534058i	$-0.179334\pi$
$338$	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	0.313200	−	0.949687i	$-0.398599\pi$
$347$	−6.56921	−	3.79274i	−0.352654	−	0.203605i	−0.665853	+	0.746083i	$0.731932\pi$
$348$	−0.598323	−	2.06127i	−0.0320735	−	0.110496i
$349$	−3.65238	+	3.65238i	−0.195507	+	0.195507i	−0.798071	−	0.602564i	$-0.794146\pi$
$349$	−3.65238	+	3.65238i	−0.195507	+	0.195507i	0.602564	+	0.798071i	$0.294146\pi$
$350$	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	−0.985712	−	0.168440i	$-0.946127\pi$
$353$	−4.06354	−	15.1653i	−0.216280	−	0.807170i	0.769431	−	0.638729i	$-0.220540\pi$
$354$	−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	−0.968193	−	0.250205i	$-0.919502\pi$
$359$	−0.0873569	+	0.326020i	−0.00461052	+	0.0172067i	0.963582	+	0.267412i	$0.0861685\pi$
$360$	−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	0.365621	+	0.930764i	$0.380857\pi$
$367$	−11.9398	+	20.6804i	−0.623255	+	1.07951i	−0.988876	+	0.148745i	$0.952477\pi$
$368$	−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	0.984700	−	0.174259i	$-0.0557530\pi$
$373$	6.59425	+	11.4216i	0.341437	+	0.591387i	−0.643263	+	0.765646i	$0.722420\pi$
$374$	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	0.0855028	−	0.996338i	$-0.472750\pi$
$379$	−17.7321	−	17.7321i	−0.910835	−	0.910835i	−0.996338	+	0.0855028i	$0.972750\pi$
$380$	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	0.110519	−	0.993874i	$-0.464749\pi$
$383$	−5.68924	−	1.52443i	−0.290706	−	0.0778946i	−0.401225	+	0.915979i	$0.631415\pi$
$384$	−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	−0.919712	−	0.392594i	$-0.871578\pi$
$389$	−2.36400	+	4.09456i	−0.119859	+	0.207602i	0.799852	+	0.600197i	$0.204911\pi$
$390$	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	0.727647	−	0.685951i	$-0.240614\pi$
$397$	20.2204	+	5.41804i	1.01483	+	0.271924i	0.287186	+	0.957875i	$0.407280\pi$
$398$	−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	−0.00297753	−	0.999996i	$-0.500948\pi$
$401$	10.0045	−	37.3372i	0.499599	−	1.86453i	0.502576	−	0.864533i	$-0.332386\pi$
$402$	−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	−0.361285	−	0.932456i	$-0.617662\pi$
$409$	−4.20530	+	1.12681i	−0.207939	+	0.0557170i	0.153346	+	0.988173i	$0.450995\pi$
$410$	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	$0.328257\pi$
$419$			35.1233i			1.71588i	−0.513747	+	0.857942i	$0.671743\pi$
$420$	−7.31267	+	17.7391i	−0.356822	+	0.865577i
$421$	−17.6207	−	17.6207i	−0.858779	−	0.858779i	0.132415	−	0.991194i	$-0.457727\pi$
$421$	−17.6207	−	17.6207i	−0.858779	−	0.858779i	−0.991194	+	0.132415i	$0.957727\pi$
$422$	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	−0.833306	−	0.552811i	$-0.813555\pi$
$431$	−8.05608	−	30.0657i	−0.388048	−	1.44821i	0.445259	−	0.895402i	$-0.353112\pi$
$432$	1.03070	−	5.09290i	0.0495895	−	0.245032i
$433$			20.3783i			0.979320i	0.871913	+	0.489660i	$0.162879\pi$
$433$			20.3783i			0.979320i	−0.871913	+	0.489660i	$0.837121\pi$
$434$	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	−0.674631	−	0.738155i	$-0.735697\pi$
$439$	−7.80862	+	4.50831i	−0.372685	+	0.215170i	0.301946	+	0.953325i	$0.402364\pi$
$440$	−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	−0.938650	−	0.344871i	$-0.887923\pi$
$443$	−23.3482	+	13.4801i	−1.10931	+	0.640459i	−0.170658	+	0.985330i	$0.554589\pi$
$444$	−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	0.994735	−	0.102485i	$-0.0326793\pi$
$449$	18.9064	+	18.9064i	0.892250	+	0.892250i	−0.102485	+	0.994735i	$0.532679\pi$
$450$	−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	−0.700305	−	0.713844i	$-0.746953\pi$
$457$	5.62441	−	20.9906i	0.263099	−	0.981898i	0.963404	−	0.268054i	$-0.0863806\pi$
$458$	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	−0.974551	−	0.224167i	$-0.928034\pi$
$461$	−16.1114	+	16.1114i	−0.750384	+	0.750384i	0.224167	+	0.974551i	$0.428034\pi$
$462$	−9.15202	−	21.9898i	−0.425791	−	1.02306i
$463$	24.7561	−	24.7561i	1.15051	−	1.15051i	0.164062	−	0.986450i	$-0.447540\pi$
$463$	24.7561	−	24.7561i	1.15051	−	1.15051i	0.986450	−	0.164062i	$-0.0524597\pi$
$464$	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	−0.999997	−	0.00258128i	$-0.999178\pi$
$467$	−10.8534	−	18.7986i	−0.502234	−	0.869894i	0.497763	−	0.867313i	$-0.334155\pi$
$468$	−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	0.311377	−	0.950286i	$-0.399210\pi$
$479$	23.1157	−	6.19382i	1.05618	−	0.283003i	0.744804	+	0.667284i	$0.232543\pi$
$480$	−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	0.443412	−	0.896318i	$-0.353768\pi$
$487$	28.1495	−	7.54264i	1.27558	−	0.341790i	0.832165	+	0.554528i	$0.187101\pi$
$488$	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	−0.947356	−	0.320183i	$-0.896256\pi$
$499$	0.740955	−	2.76528i	0.0331697	−	0.123791i	0.980526	+	0.196392i	$0.0629224\pi$
$500$	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	$0.0950041\pi$
$503$			13.1898i			0.588105i	−0.955789	+	0.294053i	$0.904996\pi$
$504$	−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	0.973570	−	0.228391i	$-0.0733464\pi$
$509$	38.4104	+	10.2920i	1.70251	+	0.456186i	0.728941	+	0.684577i	$0.240013\pi$
$510$	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	0.977634	−	0.210313i	$-0.0674484\pi$
$521$	29.3150	+	16.9250i	1.28431	+	0.741499i	0.306680	+	0.951813i	$0.400782\pi$
$522$	3.62768	+	0.812697i	0.158779	+	0.0355708i
$523$	13.5259	+	23.4276i	0.591448	+	1.02442i	0.994038	+	0.109038i	$0.0347770\pi$
$523$	13.5259	+	23.4276i	0.591448	+	1.02442i	−0.402589	+	0.915381i	$0.631890\pi$
$524$	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	0.807485	−	0.589889i	$-0.200828\pi$
$541$	28.1867	+	7.55261i	1.21184	+	0.324712i	0.404358	+	0.914601i	$0.367495\pi$
$542$	−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	−0.573079	−	0.819500i	$-0.694251\pi$
$557$	−15.5678	+	4.17139i	−0.659631	+	0.176747i	−0.0865512	+	0.996247i	$0.527585\pi$
$558$	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	−0.807566	−	0.589777i	$-0.799216\pi$
$563$	2.53836	−	4.39656i	0.106979	−	0.185293i	0.914545	+	0.404484i	$0.132549\pi$
$564$	−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	0.993115	−	0.117145i	$-0.0373743\pi$
$569$	9.42476	+	16.3242i	0.395107	+	0.684345i	−0.598008	+	0.801490i	$0.704041\pi$
$570$	0.00611764	+	0.295416i	0.000256240	+	0.0123736i
$571$	−16.7331	−	9.66085i	−0.700258	−	0.404294i	0.107186	−	0.994239i	$-0.465816\pi$
$571$	−16.7331	−	9.66085i	−0.700258	−	0.404294i	−0.807443	+	0.589945i	$0.799149\pi$
$572$	−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	−0.253446	−	0.967350i	$-0.581564\pi$
$577$	0.257942	−	0.0691154i	0.0107383	−	0.00287731i	0.264184	+	0.964472i	$0.414897\pi$
$578$	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	−0.264090	−	0.964498i	$-0.585072\pi$
$587$	16.9696	−	16.9696i	0.700408	−	0.700408i	0.964498	+	0.264090i	$0.0850715\pi$
$588$	−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	−0.491827	−	0.870693i	$-0.663671\pi$
$593$	8.99679	−	33.5765i	0.369454	−	1.37882i	0.861281	−	0.508129i	$-0.169663\pi$
$594$	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	0.592358	−	0.805675i	$-0.298197\pi$
$599$	4.66976	+	2.69609i	0.190801	+	0.110159i	−0.401556	+	0.915834i	$0.631531\pi$
$600$	−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	−0.881026	−	0.473067i	$-0.843147\pi$
$607$	−20.9467	−	36.2808i	−0.850201	−	1.47259i	0.0308253	−	0.999525i	$-0.490186\pi$
$608$	−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	0.331236	−	0.943548i	$-0.392535\pi$
$613$	26.9839	−	7.23030i	1.08987	−	0.292029i	0.758632	+	0.651519i	$0.225868\pi$
$614$	−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	−0.844215	−	0.536004i	$-0.819933\pi$
$617$	−7.65580	+	7.65580i	−0.308211	+	0.308211i	0.536004	+	0.844215i	$0.319933\pi$
$618$	10.0678	−	18.3029i	0.404986	−	0.736251i
$619$	7.91213	+	29.5285i	0.318015	+	1.18685i	0.921149	+	0.389210i	$0.127252\pi$
$619$	7.91213	+	29.5285i	0.318015	+	1.18685i	−0.603134	+	0.797640i	$0.706081\pi$
$620$	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	−0.393288	+	0.919415i	$0.628662\pi$
$631$	−32.9747	+	32.9747i	−1.31270	+	1.31270i	−0.919415	+	0.393288i	$0.871338\pi$
$632$	−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	−0.285243	−	0.958455i	$-0.592074\pi$
$641$	17.4042	−	30.1450i	0.687425	−	1.19065i	0.972668	−	0.232199i	$-0.0745922\pi$
$642$	−14.6889	+	26.7040i	−0.579726	+	1.05392i
$643$	22.7474	+	22.7474i	0.897070	+	0.897070i	0.995176	−	0.0981062i	$-0.0312785\pi$
$643$	22.7474	+	22.7474i	0.897070	+	0.897070i	−0.0981062	+	0.995176i	$0.531278\pi$
$644$	−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	−0.327068	+	0.945001i	$0.606061\pi$
$647$	−24.9765	+	43.2606i	−0.981929	+	1.70075i	−0.654861	+	0.755750i	$0.727273\pi$
$648$	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	−0.375477	−	0.926832i	$-0.622521\pi$
$653$	6.11871	−	3.53264i	0.239444	−	0.138243i	0.614921	+	0.788589i	$0.289188\pi$
$654$	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	$0.0591146\pi$
$659$			9.48022i			0.369297i	−0.982805	+	0.184648i	$0.940885\pi$
$660$	36.1991	−	10.5075i	1.40905	−	0.409002i
$661$	−3.18735	−	11.8954i	−0.123974	−	0.462676i	0.875827	−	0.482625i	$-0.160316\pi$
$661$	−3.18735	−	11.8954i	−0.123974	−	0.462676i	−0.999801	+	0.0199485i	$0.993650\pi$
$662$	−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	$0.0265912\pi$
$673$			4.32932i			0.166883i	−0.996513	+	0.0834415i	$0.973409\pi$
$674$	−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	−0.0149048	−	0.999889i	$-0.504745\pi$
$677$	21.9491	−	12.6723i	0.843572	−	0.487037i	0.858477	+	0.512852i	$0.171411\pi$
$678$	−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	−0.592705	−	0.805419i	$-0.701940\pi$
$683$	−18.3801	+	4.92492i	−0.703293	+	0.188447i	−0.110588	+	0.993866i	$0.535273\pi$
$684$	−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	−0.521172	−	0.853452i	$-0.674505\pi$
$691$	9.38184	−	35.0135i	0.356902	−	1.33198i	0.878074	−	0.478525i	$-0.158828\pi$
$692$			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	0.685917	−	0.727679i	$-0.259401\pi$
$709$	24.3930	+	6.53609i	0.916099	+	0.245468i	0.230182	+	0.973148i	$0.426068\pi$
$710$	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	0.999998	+	0.00195263i	$0.000621541\pi$
$719$	13.4524	+	23.3002i	0.501690	+	0.868953i	−0.498308	+	0.867000i	$0.666045\pi$
$720$	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	$-0.929919\pi$
$727$		−	11.7770i		−	0.436786i	0.975861	−	0.218393i	$-0.0700815\pi$
$728$	−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	0.664857	+	0.746971i	$0.268493\pi$
$733$	−7.70015	+	28.7374i	−0.284412	+	1.06144i	−0.949268	+	0.314468i	$0.898174\pi$
$734$	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	−0.993927	−	0.110042i	$-0.964902\pi$
$739$	−5.11564	−	19.0918i	−0.188182	−	0.702304i	0.805745	−	0.592262i	$-0.201765\pi$
$740$	−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	−0.233460	−	0.972366i	$-0.575005\pi$
$743$	20.1411	−	20.1411i	0.738906	−	0.738906i	0.972366	+	0.233460i	$0.0750048\pi$
$744$	−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	−0.0338151	−	0.999428i	$-0.510766\pi$
$751$	22.3293	−	12.8918i	0.814807	−	0.470429i	0.848623	+	0.528999i	$0.177432\pi$
$752$	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	0.834779	+	0.550585i	$0.185595\pi$
$761$	−4.50906	+	16.8280i	−0.163453	+	0.610016i	−0.998232	+	0.0594308i	$0.981071\pi$
$762$	−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	0.996762	+	0.0804097i	$0.0256229\pi$
$769$	29.8709	+	29.8709i	1.07717	+	1.07717i	0.0804097	+	0.996762i	$0.474377\pi$
$770$	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	0.955285	+	0.295685i	$0.0955479\pi$
$773$	7.66877	+	28.6202i	0.275827	+	1.02940i	−0.679459	+	0.733714i	$0.737785\pi$
$774$	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	0.999737	−	0.0229262i	$-0.00729829\pi$
$787$	3.43589	+	12.8229i	0.122476	+	0.457088i	−0.877261	+	0.480014i	$0.840632\pi$
$788$	−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	0.676776	−	0.736189i	$-0.263377\pi$
$809$	10.7402	+	6.20086i	0.377605	+	0.218010i	−0.299171	+	0.954200i	$0.596710\pi$
$810$	34.0812	+	16.0771i	1.19749	+	0.564892i
$811$	−7.12154	−	7.12154i	−0.250071	−	0.250071i	0.570929	−	0.821000i	$-0.306583\pi$
$811$	−7.12154	−	7.12154i	−0.250071	−	0.250071i	−0.821000	+	0.570929i	$0.806583\pi$
$812$	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	−0.127639	−	0.991821i	$-0.540740\pi$
$821$	−21.0339	−	5.63602i	−0.734088	−	0.196698i	−0.606449	+	0.795122i	$0.707407\pi$
$822$	15.1657	−	15.8071i	0.528963	−	0.551334i
$823$	−26.2071	−	15.1307i	−0.913523	−	0.527423i	−0.0319601	−	0.999489i	$-0.510175\pi$
$823$	−26.2071	−	15.1307i	−0.913523	−	0.527423i	−0.881563	+	0.472066i	$0.843508\pi$
$824$	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	−0.936656	−	0.350252i	$-0.886096\pi$
$827$	−37.0084	−	37.0084i	−1.28691	−	1.28691i	−0.350252	−	0.936656i	$-0.613904\pi$
$828$	5.01326	−	0.207724i	0.174223	−	0.00721892i
$829$	−20.4767	−	11.8222i	−0.711184	−	0.410602i	0.100315	−	0.994956i	$-0.468015\pi$
$829$	−20.4767	−	11.8222i	−0.711184	−	0.410602i	−0.811499	+	0.584353i	$0.801348\pi$
$830$	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	0.575369	−	0.817894i	$-0.304858\pi$
$839$	−7.02486	−	7.02486i	−0.242525	−	0.242525i	−0.817894	+	0.575369i	$0.804858\pi$
$840$	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	−0.729608	−	0.683866i	$-0.760297\pi$
$853$	−1.33595	+	1.33595i	−0.0457419	+	0.0457419i	0.683866	+	0.729608i	$0.260297\pi$
$854$	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	−0.316507	−	0.948590i	$-0.602510\pi$
$857$	19.4163	−	33.6301i	0.663250	−	1.14878i	0.979757	−	0.200192i	$-0.0641566\pi$
$858$	32.2907	−	3.29976i	1.10239	−	0.112652i
$859$	−11.6019	−	20.0951i	−0.395852	−	0.685635i	0.597358	−	0.801975i	$-0.296217\pi$
$859$	−11.6019	−	20.0951i	−0.395852	−	0.685635i	−0.993210	+	0.116339i	$0.962884\pi$
$860$	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	0.781786	−	0.623547i	$-0.214309\pi$
$863$	33.6970	+	9.02909i	1.14706	+	0.307354i	0.365273	+	0.930900i	$0.380976\pi$
$864$	−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	−0.668054	−	0.744112i	$-0.732873\pi$
$877$	8.36760	−	31.2283i	0.282554	−	1.05451i	0.950608	−	0.310393i	$-0.100461\pi$
$878$	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	$0.0640481\pi$
$883$			11.8777i			0.399716i	−0.979825	+	0.199858i	$0.935952\pi$
$884$	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	−0.776017	−	0.630712i	$-0.782763\pi$
$887$	−18.4001	+	10.6233i	−0.617814	+	0.356695i	0.158204	+	0.987407i	$0.449430\pi$
$888$	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	0.747186	−	0.664614i	$-0.231404\pi$
$907$	16.4197	+	9.47991i	0.545207	+	0.314775i	−0.201980	+	0.979390i	$0.564738\pi$
$908$	−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	$0.235638\pi$
$911$			40.7162i			1.34899i	−0.738281	+	0.674493i	$0.764362\pi$
$912$	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	0.654263	−	0.756267i	$-0.272979\pi$
$919$	−9.93773	−	17.2126i	−0.327815	−	0.567793i	−0.982078	+	0.188474i	$0.939646\pi$
$920$	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	−0.0554636	−	0.998461i	$-0.517664\pi$
$929$	−18.3708	−	4.92245i	−0.602727	−	0.161500i	−0.547263	+	0.836961i	$0.684330\pi$
$930$	−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	0.980921	+	0.194405i	$0.0622777\pi$
$941$	7.01312	+	26.1733i	0.228621	+	0.853226i	−0.752300	+	0.658820i	$0.771056\pi$
$942$	−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	0.794613	+	0.607116i	$0.207674\pi$
$947$	−6.06543	+	22.6365i	−0.197100	+	0.735587i	−0.991713	+	0.128471i	$0.958993\pi$
$948$	−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	0.992670	+	0.120857i	$0.0385642\pi$
$967$	34.6269	+	34.6269i	1.11353	+	1.11353i	0.120857	+	0.992670i	$0.461436\pi$
$968$	−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	0.119729	−	0.992807i	$-0.461797\pi$
$971$	32.3883	−	18.6994i	1.03939	−	0.600092i	0.919660	+	0.392715i	$0.128464\pi$
$972$	−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	0.978443	−	0.206518i	$-0.0662131\pi$
$977$	0.869806	+	3.24616i	0.0278276	+	0.103854i	−0.950615	+	0.310372i	$0.899546\pi$
$978$	−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	0.375784	−	0.926707i	$-0.377373\pi$
$983$	36.5128	−	9.78356i	1.16458	−	0.312047i	0.788792	+	0.614660i	$0.210707\pi$
$984$	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	−0.999852	−	0.0171858i	$-0.994529\pi$
$991$	−15.2692	+	26.4471i	−0.485043	+	0.840119i	0.514810	+	0.857305i	$0.327863\pi$
$992$	−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	−0.525573	−	0.850749i	$-0.676149\pi$
$997$	14.9662	−	25.9222i	0.473984	−	0.820964i	0.999556	+	0.0297848i	$0.00948220\pi$
$998$	−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.515.15	yes	144
3.2	odd	2	inner	546.2.bv.a.515.28	yes	144
7.2	even	3	inner	546.2.bv.a.359.28	yes	144
13.5	odd	4	inner	546.2.bv.a.473.15	yes	144
21.2	odd	6	inner	546.2.bv.a.359.15	yes	144
39.5	even	4	inner	546.2.bv.a.473.28	yes	144
91.44	odd	12	inner	546.2.bv.a.317.28	yes	144
273.44	even	12	inner	546.2.bv.a.317.15	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.15	✓	144	273.44	even	12	inner
546.2.bv.a.317.28	yes	144	91.44	odd	12	inner
546.2.bv.a.359.15	yes	144	21.2	odd	6	inner
546.2.bv.a.359.28	yes	144	7.2	even	3	inner
546.2.bv.a.473.15	yes	144	13.5	odd	4	inner
546.2.bv.a.473.28	yes	144	39.5	even	4	inner
546.2.bv.a.515.15	yes	144	1.1	even	1	trivial
546.2.bv.a.515.28	yes	144	3.2	odd	2	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

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