LMFDB - Embedded newform 570.2.u.f.61.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [570,2,Mod(61,570)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("570.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(570, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,0,0,3,3,0,0,-3,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	570.61
Dual form			570.2.u.f.271.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(1.43969 - 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(2.14543 + 3.71599i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.794263 + 4.50449i) q^{13} +(2.20574 - 1.85083i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(5.08512 + 1.85083i) q^{17} -1.00000 q^{18} +(-3.79086 - 2.15160i) q^{19} -1.00000 q^{20} +(2.70574 + 0.984808i) q^{21} +(0.745100 + 4.22567i) q^{22} +(-0.0432332 - 0.0362770i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-2.28699 + 3.96118i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(2.70574 - 0.984808i) q^{28} +(7.59879 - 2.76573i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-1.88666 + 3.26779i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-3.28699 + 2.75811i) q^{33} +(4.14543 + 3.47843i) q^{34} +(0.500000 + 2.83564i) q^{35} +(-0.939693 - 0.342020i) q^{36} -11.5963 q^{37} +(-2.82635 - 3.31839i) q^{38} -4.57398 q^{39} +(-0.939693 - 0.342020i) q^{40} +(-1.37686 - 7.80856i) q^{41} +(2.20574 + 1.85083i) q^{42} +(3.28106 - 2.75314i) q^{43} +(-0.745100 + 4.22567i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-0.0282185 - 0.0488759i) q^{46} +(-1.59967 + 0.582232i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.939693 + 5.32926i) q^{51} +(-3.50387 + 2.94010i) q^{52} +(-3.52094 - 2.95442i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(-4.03209 - 1.46756i) q^{55} +2.87939 q^{56} +(1.46064 - 4.10689i) q^{57} +8.08647 q^{58} +(-5.13816 - 1.87014i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(7.67752 + 6.44220i) q^{61} +(-2.89053 + 2.42544i) q^{62} +(-0.500000 + 2.83564i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.28699 - 3.96118i) q^{65} +(-4.03209 + 1.46756i) q^{66} +(13.1814 - 4.79763i) q^{67} +(2.70574 + 4.68647i) q^{68} +(0.0282185 - 0.0488759i) q^{69} +(-0.500000 + 2.83564i) q^{70} +(8.98158 - 7.53644i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-2.79813 - 15.8690i) q^{73} +(-10.8969 - 3.96616i) q^{74} +1.00000 q^{75} +(-1.52094 - 4.08494i) q^{76} +12.3550 q^{77} +(-4.29813 - 1.56439i) q^{78} +(0.0778483 + 0.441500i) q^{79} +(-0.766044 - 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(1.37686 - 7.80856i) q^{82} +(7.82160 - 13.5474i) q^{83} +(1.43969 + 2.49362i) q^{84} +(-5.08512 + 1.85083i) q^{85} +(4.02481 - 1.46491i) q^{86} +(4.04323 + 7.00309i) q^{87} +(-2.14543 + 3.71599i) q^{88} +(-0.337496 + 1.91404i) q^{89} +(0.766044 - 0.642788i) q^{90} +(10.0890 + 8.46567i) q^{91} +(-0.00980018 - 0.0555796i) q^{92} +(-3.54576 - 1.29055i) q^{93} -1.70233 q^{94} +(4.28699 - 0.788496i) q^{95} -1.00000 q^{96} +(-11.1099 - 4.04369i) q^{97} +(-0.224155 - 1.27125i) q^{98} +(-3.28699 - 2.75811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 15 q^{13} + 3 q^{14} + 9 q^{17} - 6 q^{18} + 9 q^{19} - 6 q^{20} + 6 q^{21} + 3 q^{22} + 15 q^{23} - 6 q^{26} - 3 q^{27} + 6 q^{28} + 3 q^{29} - 3 q^{30}+ \cdots - 12 q^{99}+O(q^{100}) $ 6 * q + 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 15 * q^13 + 3 * q^14 + 9 * q^17 - 6 * q^18 + 9 * q^19 - 6 * q^20 + 6 * q^21 + 3 * q^22 + 15 * q^23 - 6 * q^26 - 3 * q^27 + 6 * q^28 + 3 * q^29 - 3 * q^30 - 18 * q^31 - 12 * q^33 + 9 * q^34 + 3 * q^35 - 42 * q^37 - 18 * q^38 - 12 * q^39 - 12 * q^41 + 3 * q^42 - 15 * q^43 - 3 * q^44 + 3 * q^45 - 15 * q^46 - 24 * q^47 + 12 * q^49 + 3 * q^50 + 3 * q^52 - 18 * q^53 - 15 * q^55 + 6 * q^56 + 18 * q^58 + 3 * q^59 + 21 * q^61 - 3 * q^63 - 3 * q^64 - 6 * q^65 - 15 * q^66 + 30 * q^67 + 6 * q^68 + 15 * q^69 - 3 * q^70 + 42 * q^71 - 3 * q^73 - 9 * q^74 + 6 * q^75 - 6 * q^76 + 24 * q^77 - 12 * q^78 - 39 * q^79 + 12 * q^82 + 15 * q^83 + 3 * q^84 - 9 * q^85 - 3 * q^86 + 9 * q^87 + 3 * q^88 + 3 * q^89 + 15 * q^91 - 3 * q^92 + 9 * q^93 + 42 * q^94 + 18 * q^95 - 6 * q^96 - 18 * q^97 - 3 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	−0.173648	+	0.984808i	−0.0708916	+	0.402046i
$7$	1.43969	−	2.49362i	0.544153	−	0.942500i	−0.454507	−	0.890743i	$-0.650185\pi$
$7$	1.43969	−	2.49362i	0.544153	−	0.942500i	0.998660	−	0.0517569i	$-0.0164821\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−0.939693	+	0.342020i	−0.297157	+	0.108156i
$11$	2.14543	+	3.71599i	0.646871	+	1.12041i	0.983866	+	0.178907i	$0.0572563\pi$
$11$	2.14543	+	3.71599i	0.646871	+	1.12041i	−0.336995	+	0.941507i	$0.609410\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.794263	+	4.50449i	−0.220289	+	1.24932i	0.651200	+	0.758906i	$0.274266\pi$
$13$	−0.794263	+	4.50449i	−0.220289	+	1.24932i	−0.871489	+	0.490415i	$0.836845\pi$
$14$	2.20574	−	1.85083i	0.589508	−	0.494656i
$15$	−0.766044	−	0.642788i	−0.197792	−	0.165967i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	5.08512	+	1.85083i	1.23332	+	0.448893i	0.874734	−	0.484603i	$-0.161036\pi$
$17$	5.08512	+	1.85083i	1.23332	+	0.448893i	0.358589	+	0.933496i	$0.383258\pi$
$18$	−1.00000			−0.235702
$19$	−3.79086	−	2.15160i	−0.869683	−	0.493611i
$19$	−3.79086	−	2.15160i	−0.869683	−	0.493611i
$20$	−1.00000			−0.223607
$21$	2.70574	+	0.984808i	0.590440	+	0.214903i
$22$	0.745100	+	4.22567i	0.158856	+	0.900916i
$23$	−0.0432332	−	0.0362770i	−0.00901475	−	0.00756428i	0.638269	−	0.769813i	$-0.279651\pi$
$23$	−0.0432332	−	0.0362770i	−0.00901475	−	0.00756428i	−0.647284	+	0.762249i	$0.724095\pi$
$24$	−0.766044	+	0.642788i	−0.156368	+	0.131208i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	−2.28699	+	3.96118i	−0.448515	+	0.776852i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	2.70574	−	0.984808i	0.511336	−	0.186111i
$29$	7.59879	−	2.76573i	1.41106	−	0.513584i	0.479619	−	0.877477i	$-0.340775\pi$
$29$	7.59879	−	2.76573i	1.41106	−	0.513584i	0.931441	+	0.363893i	$0.118552\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−1.88666	+	3.26779i	−0.338854	+	0.586912i	−0.984217	−	0.176963i	$-0.943373\pi$
$31$	−1.88666	+	3.26779i	−0.338854	+	0.586912i	0.645363	+	0.763876i	$0.276706\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−3.28699	+	2.75811i	−0.572191	+	0.480126i
$34$	4.14543	+	3.47843i	0.710935	+	0.596546i
$35$	0.500000	+	2.83564i	0.0845154	+	0.479311i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	−11.5963			−1.90641			−0.953207	−	0.302318i	$-0.902240\pi$
$37$	−11.5963			−1.90641			−0.953207	+	0.302318i	$0.902240\pi$
$38$	−2.82635	−	3.31839i	−0.458495	−	0.538315i
$39$	−4.57398			−0.732423
$40$	−0.939693	−	0.342020i	−0.148578	−	0.0540781i
$41$	−1.37686	−	7.80856i	−0.215029	−	1.21949i	−0.880856	−	0.473385i	$-0.843032\pi$
$41$	−1.37686	−	7.80856i	−0.215029	−	1.21949i	0.665826	−	0.746107i	$-0.268079\pi$
$42$	2.20574	+	1.85083i	0.340353	+	0.285590i
$43$	3.28106	−	2.75314i	0.500357	−	0.419849i	−0.357364	−	0.933965i	$-0.616324\pi$
$43$	3.28106	−	2.75314i	0.500357	−	0.419849i	0.857721	+	0.514116i	$0.171880\pi$
$44$	−0.745100	+	4.22567i	−0.112328	+	0.637044i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	−0.0282185	−	0.0488759i	−0.00416059	−	0.00720635i
$47$	−1.59967	+	0.582232i	−0.233336	+	0.0849273i	−0.456042	−	0.889958i	$-0.650733\pi$
$47$	−1.59967	+	0.582232i	−0.233336	+	0.0849273i	0.222706	+	0.974886i	$0.428511\pi$
$48$	−0.939693	+	0.342020i	−0.135633	+	0.0493664i
$49$	−0.645430	−	1.11792i	−0.0922042	−	0.159702i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−0.939693	+	5.32926i	−0.131583	+	0.746246i
$52$	−3.50387	+	2.94010i	−0.485899	+	0.407718i
$53$	−3.52094	−	2.95442i	−0.483639	−	0.405821i	0.368101	−	0.929786i	$-0.380008\pi$
$53$	−3.52094	−	2.95442i	−0.483639	−	0.405821i	−0.851740	+	0.523964i	$0.824452\pi$
$54$	−0.173648	−	0.984808i	−0.0236305	−	0.134015i
$55$	−4.03209	−	1.46756i	−0.543687	−	0.197886i
$56$	2.87939			0.384774
$57$	1.46064	−	4.10689i	0.193466	−	0.543971i
$58$	8.08647			1.06181
$59$	−5.13816	−	1.87014i	−0.668931	−	0.243471i	−0.0148434	−	0.999890i	$-0.504725\pi$
$59$	−5.13816	−	1.87014i	−0.668931	−	0.243471i	−0.654087	+	0.756419i	$0.726947\pi$
$60$	−0.173648	−	0.984808i	−0.0224179	−	0.127138i
$61$	7.67752	+	6.44220i	0.983006	+	0.824840i	0.984540	−	0.175159i	$-0.0560440\pi$
$61$	7.67752	+	6.44220i	0.983006	+	0.824840i	−0.00153459	+	0.999999i	$0.500488\pi$
$62$	−2.89053	+	2.42544i	−0.367098	+	0.308031i
$63$	−0.500000	+	2.83564i	−0.0629941	+	0.357257i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.28699	−	3.96118i	−0.283666	−	0.491324i
$66$	−4.03209	+	1.46756i	−0.496316	+	0.180644i
$67$	13.1814	−	4.79763i	1.61036	−	0.586124i	0.628851	−	0.777526i	$-0.283525\pi$
$67$	13.1814	−	4.79763i	1.61036	−	0.586124i	0.981512	+	0.191402i	$0.0613033\pi$
$68$	2.70574	+	4.68647i	0.328119	+	0.568318i
$69$	0.0282185	−	0.0488759i	0.00339711	−	0.00588396i
$70$	−0.500000	+	2.83564i	−0.0597614	+	0.338924i
$71$	8.98158	−	7.53644i	1.06592	−	0.894411i	0.0712413	−	0.997459i	$-0.477304\pi$
$71$	8.98158	−	7.53644i	1.06592	−	0.894411i	0.994676	+	0.103048i	$0.0328595\pi$
$72$	−0.766044	−	0.642788i	−0.0902792	−	0.0757532i
$73$	−2.79813	−	15.8690i	−0.327497	−	1.85733i	−0.491515	−	0.870869i	$-0.663557\pi$
$73$	−2.79813	−	15.8690i	−0.327497	−	1.85733i	0.164018	−	0.986457i	$-0.447554\pi$
$74$	−10.8969	−	3.96616i	−1.26674	−	0.461056i
$75$	1.00000			0.115470
$76$	−1.52094	−	4.08494i	−0.174464	−	0.468575i
$77$	12.3550			1.40799
$78$	−4.29813	−	1.56439i	−0.486668	−	0.177133i
$79$	0.0778483	+	0.441500i	0.00875862	+	0.0496726i	0.988874	−	0.148757i	$-0.0475271\pi$
$79$	0.0778483	+	0.441500i	0.00875862	+	0.0496726i	−0.980115	+	0.198429i	$0.936416\pi$
$80$	−0.766044	−	0.642788i	−0.0856464	−	0.0718658i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	1.37686	−	7.80856i	0.152049	−	0.862311i
$83$	7.82160	−	13.5474i	0.858533	−	1.48702i	−0.0147960	−	0.999891i	$-0.504710\pi$
$83$	7.82160	−	13.5474i	0.858533	−	1.48702i	0.873329	−	0.487132i	$-0.161957\pi$
$84$	1.43969	+	2.49362i	0.157083	+	0.272076i
$85$	−5.08512	+	1.85083i	−0.551559	+	0.200751i
$86$	4.02481	−	1.46491i	0.434007	−	0.157966i
$87$	4.04323	+	7.00309i	0.433480	+	0.750810i
$88$	−2.14543	+	3.71599i	−0.228704	+	0.396126i
$89$	−0.337496	+	1.91404i	−0.0357745	+	0.202887i	−0.997456	−	0.0712807i	$-0.977291\pi$
$89$	−0.337496	+	1.91404i	−0.0357745	+	0.202887i	0.961682	+	0.274168i	$0.0884025\pi$
$90$	0.766044	−	0.642788i	0.0807482	−	0.0677558i
$91$	10.0890	+	8.46567i	1.05761	+	0.887443i
$92$	−0.00980018	−	0.0555796i	−0.00102174	−	0.00579457i
$93$	−3.54576	−	1.29055i	−0.367678	−	0.133824i
$94$	−1.70233			−0.175582
$95$	4.28699	−	0.788496i	0.439836	−	0.0808980i
$96$	−1.00000			−0.102062
$97$	−11.1099	−	4.04369i	−1.12804	−	0.410574i	−0.290462	−	0.956887i	$-0.593809\pi$
$97$	−11.1099	−	4.04369i	−1.12804	−	0.410574i	−0.837581	+	0.546312i	$0.816031\pi$
$98$	−0.224155	−	1.27125i	−0.0226431	−	0.128415i
$99$	−3.28699	−	2.75811i	−0.330355	−	0.277201i
$100$	0.766044	−	0.642788i	0.0766044	−	0.0642788i
$101$	−3.31567	+	18.8041i	−0.329922	+	1.87108i	0.142628	+	0.989776i	$0.454445\pi$
$101$	−3.31567	+	18.8041i	−0.329922	+	1.87108i	−0.472550	+	0.881304i	$0.656666\pi$
$102$	−2.70574	+	4.68647i	−0.267908	+	0.464030i
$103$	−7.12701	−	12.3443i	−0.702245	−	1.21632i	−0.967677	−	0.252195i	$-0.918848\pi$
$103$	−7.12701	−	12.3443i	−0.702245	−	1.21632i	0.265431	−	0.964130i	$-0.414486\pi$
$104$	−4.29813	+	1.56439i	−0.421467	+	0.153401i
$105$	−2.70574	+	0.984808i	−0.264053	+	0.0961074i
$106$	−2.29813	−	3.98048i	−0.223214	−	0.386619i
$107$	0.0209445	−	0.0362770i	0.00202478	−	0.00350703i	−0.865011	−	0.501752i	$-0.832689\pi$
$107$	0.0209445	−	0.0362770i	0.00202478	−	0.00350703i	0.867036	+	0.498245i	$0.166022\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	−10.4855	+	8.79834i	−1.00432	+	0.842728i	−0.987578	−	0.157132i	$-0.949775\pi$
$109$	−10.4855	+	8.79834i	−1.00432	+	0.842728i	−0.0167465	+	0.999860i	$0.505331\pi$
$110$	−3.28699	−	2.75811i	−0.313402	−	0.262976i
$111$	−2.01367	−	11.4201i	−0.191129	−	1.08395i
$112$	2.70574	+	0.984808i	0.255668	+	0.0930556i
$113$	0.369585			0.0347676			0.0173838	−	0.999849i	$-0.494466\pi$
$113$	0.369585			0.0347676			0.0173838	+	0.999849i	$0.494466\pi$
$114$	2.77719	−	3.35965i	0.260108	−	0.314660i
$115$	0.0564370			0.00526278
$116$	7.59879	+	2.76573i	0.705530	+	0.256792i
$117$	−0.794263	−	4.50449i	−0.0734296	−	0.416440i
$118$	−4.18866	−	3.51471i	−0.385598	−	0.323555i
$119$	11.9363	−	10.0157i	1.09420	−	0.918141i
$120$	0.173648	−	0.984808i	0.0158518	−	0.0899002i
$121$	−3.70574	+	6.41852i	−0.336885	+	0.583502i
$122$	5.01114	+	8.67956i	0.453688	+	0.785810i
$123$	7.45084	−	2.71188i	0.671819	−	0.244522i
$124$	−3.54576	+	1.29055i	−0.318419	+	0.115895i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−1.43969	+	2.49362i	−0.128258	+	0.222149i
$127$	2.69072	−	15.2598i	0.238763	−	1.35409i	−0.595779	−	0.803148i	$-0.703157\pi$
$127$	2.69072	−	15.2598i	0.238763	−	1.35409i	0.834542	−	0.550944i	$-0.185732\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	3.28106	+	2.75314i	0.288881	+	0.242400i
$130$	−0.794263	−	4.50449i	−0.0696615	−	0.395070i
$131$	5.53209	+	2.01352i	0.483341	+	0.175922i	0.572186	−	0.820124i	$-0.306095\pi$
$131$	5.53209	+	2.01352i	0.483341	+	0.175922i	−0.0888453	+	0.996045i	$0.528318\pi$
$132$	−4.29086			−0.373471
$133$	−10.8229	+	6.35532i	−0.938469	+	0.551076i
$134$	14.0273			1.21178
$135$	0.939693	+	0.342020i	0.0808759	+	0.0294364i
$136$	0.939693	+	5.32926i	0.0805780	+	0.456980i
$137$	−2.51889	−	2.11360i	−0.215203	−	0.180577i	0.528813	−	0.848738i	$-0.322637\pi$
$137$	−2.51889	−	2.11360i	−0.215203	−	0.180577i	−0.744016	+	0.668161i	$0.767082\pi$
$138$	0.0432332	−	0.0362770i	0.00368026	−	0.00308810i
$139$	−1.93629	+	10.9812i	−0.164234	+	0.931417i	0.785617	+	0.618713i	$0.212346\pi$
$139$	−1.93629	+	10.9812i	−0.164234	+	0.931417i	−0.949851	+	0.312703i	$0.898765\pi$
$140$	−1.43969	+	2.49362i	−0.121676	+	0.210749i
$141$	−0.851167	−	1.47426i	−0.0716812	−	0.124155i
$142$	11.0175	−	4.01006i	0.924571	−	0.336517i
$143$	−18.4427	+	6.71259i	−1.54225	+	0.561335i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.04323	+	7.00309i	−0.335772	+	0.581575i
$146$	2.79813	−	15.8690i	0.231575	−	1.31333i
$147$	0.988856	−	0.829748i	0.0815594	−	0.0684365i
$148$	−8.88326	−	7.45394i	−0.730199	−	0.612710i
$149$	−1.51501	−	8.59208i	−0.124115	−	0.703890i	−0.981830	−	0.189764i	$-0.939228\pi$
$149$	−1.51501	−	8.59208i	−0.124115	−	0.703890i	0.857715	−	0.514126i	$-0.171884\pi$
$150$	0.939693	+	0.342020i	0.0767256	+	0.0279258i
$151$	7.83750			0.637806			0.318903	−	0.947787i	$-0.396686\pi$
$151$	7.83750			0.637806			0.318903	+	0.947787i	$0.396686\pi$
$152$	−0.0320889	−	4.35878i	−0.00260275	−	0.353544i
$153$	−5.41147			−0.437492
$154$	11.6099	+	4.22567i	0.935555	+	0.340514i
$155$	−0.655230	−	3.71599i	−0.0526293	−	0.298476i
$156$	−3.50387	−	2.94010i	−0.280534	−	0.235396i
$157$	−4.98886	+	4.18615i	−0.398154	+	0.334091i	−0.819780	−	0.572679i	$-0.805904\pi$
$157$	−4.98886	+	4.18615i	−0.398154	+	0.334091i	0.421626	+	0.906770i	$0.361460\pi$
$158$	−0.0778483	+	0.441500i	−0.00619328	+	0.0351238i
$159$	2.29813	−	3.98048i	0.182254	−	0.315673i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−0.152704	+	0.0555796i	−0.0120347	+	0.00438028i
$162$	0.939693	−	0.342020i	0.0738292	−	0.0268716i
$163$	−2.78446	−	4.82283i	−0.218096	−	0.377753i	0.736130	−	0.676840i	$-0.236651\pi$
$163$	−2.78446	−	4.82283i	−0.218096	−	0.377753i	−0.954226	+	0.299087i	$0.903318\pi$
$164$	3.96451	−	6.86673i	0.309576	−	0.536201i
$165$	0.745100	−	4.22567i	0.0580059	−	0.328968i
$166$	11.9834	−	10.0553i	0.930092	−	0.780440i
$167$	3.63950	+	3.05390i	0.281633	+	0.236318i	0.772651	−	0.634832i	$-0.218930\pi$
$167$	3.63950	+	3.05390i	0.281633	+	0.236318i	−0.491018	+	0.871150i	$0.663375\pi$
$168$	0.500000	+	2.83564i	0.0385758	+	0.218774i
$169$	−7.44356	−	2.70924i	−0.572582	−	0.208403i
$170$	−5.41147			−0.415041
$171$	4.29813	+	0.725293i	0.328686	+	0.0554645i
$172$	4.28312			0.326585
$173$	10.8576	+	3.95183i	0.825485	+	0.300452i	0.720005	−	0.693969i	$-0.244140\pi$
$173$	10.8576	+	3.95183i	0.825485	+	0.300452i	0.105481	+	0.994421i	$0.466362\pi$
$174$	1.40420	+	7.96361i	0.106452	+	0.603720i
$175$	−2.20574	−	1.85083i	−0.166738	−	0.139910i
$176$	−3.28699	+	2.75811i	−0.247766	+	0.207900i
$177$	0.949493	−	5.38484i	0.0713682	−	0.404749i
$178$	−0.971782	+	1.68317i	−0.0728381	+	0.126159i
$179$	−3.38919	−	5.87024i	−0.253320	−	0.438762i	0.711118	−	0.703073i	$-0.248189\pi$
$179$	−3.38919	−	5.87024i	−0.253320	−	0.438762i	−0.964438	+	0.264310i	$0.914856\pi$
$180$	0.939693	−	0.342020i	0.0700406	−	0.0254927i
$181$	−5.52481	+	2.01087i	−0.410656	+	0.149467i	−0.539084	−	0.842252i	$-0.681229\pi$
$181$	−5.52481	+	2.01087i	−0.410656	+	0.149467i	0.128427	+	0.991719i	$0.459007\pi$
$182$	6.58512	+	11.4058i	0.488122	+	0.845452i
$183$	−5.01114	+	8.67956i	−0.370434	+	0.641611i
$184$	0.00980018	−	0.0555796i	0.000722479	−	0.00409738i
$185$	8.88326	−	7.45394i	0.653110	−	0.548024i
$186$	−2.89053	−	2.42544i	−0.211944	−	0.177842i
$187$	4.03209	+	22.8671i	0.294856	+	1.67221i
$188$	−1.59967	−	0.582232i	−0.116668	−	0.0424637i
$189$	−2.87939			−0.209444
$190$	4.29813	+	0.725293i	0.311819	+	0.0526183i
$191$	6.43376			0.465531			0.232765	−	0.972533i	$-0.425223\pi$
$191$	6.43376			0.465531			0.232765	+	0.972533i	$0.425223\pi$
$192$	−0.939693	−	0.342020i	−0.0678165	−	0.0246832i
$193$	−2.80200	−	15.8910i	−0.201693	−	1.14386i	−0.902560	−	0.430564i	$-0.858315\pi$
$193$	−2.80200	−	15.8910i	−0.201693	−	1.14386i	0.700867	−	0.713292i	$-0.252796\pi$
$194$	−9.05690	−	7.59964i	−0.650248	−	0.545623i
$195$	3.50387	−	2.94010i	0.250917	−	0.210545i
$196$	0.224155	−	1.27125i	0.0160111	−	0.0908035i
$197$	−7.44222	+	12.8903i	−0.530236	+	0.918396i	0.469142	+	0.883123i	$0.344563\pi$
$197$	−7.44222	+	12.8903i	−0.530236	+	0.918396i	−0.999378	+	0.0352730i	$0.988770\pi$
$198$	−2.14543	−	3.71599i	−0.152469	−	0.264084i
$199$	−21.7738	+	7.92501i	−1.54350	+	0.561789i	−0.966882	−	0.255223i	$-0.917851\pi$
$199$	−21.7738	+	7.92501i	−1.54350	+	0.561789i	−0.576621	+	0.817012i	$0.695629\pi$
$200$	0.939693	−	0.342020i	0.0664463	−	0.0241845i
$201$	7.01367	+	12.1480i	0.494706	+	0.856856i
$202$	−9.54710	+	16.5361i	−0.671732	+	1.16347i
$203$	4.04323	−	22.9303i	0.283779	−	1.60939i
$204$	−4.14543	+	3.47843i	−0.290238	+	0.243539i
$205$	6.07398	+	5.09667i	0.424225	+	0.355967i
$206$	−2.47519	−	14.0375i	−0.172454	−	0.978037i
$207$	0.0530334	+	0.0193026i	0.00368608	+	0.00134162i
$208$	−4.57398			−0.317148
$209$	−0.137689	−	18.7029i	−0.00952414	−	1.29371i
$210$	−2.87939			−0.198696
$211$	1.94697	+	0.708638i	0.134035	+	0.0487846i	0.408167	−	0.912907i	$-0.366168\pi$
$211$	1.94697	+	0.708638i	0.134035	+	0.0487846i	−0.274132	+	0.961692i	$0.588390\pi$
$212$	−0.798133	−	4.52644i	−0.0548160	−	0.310877i
$213$	8.98158	+	7.53644i	0.615408	+	0.516388i
$214$	0.0320889	−	0.0269258i	0.00219355	−	0.00184061i
$215$	−0.743756	+	4.21805i	−0.0507237	+	0.287669i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	5.43242	+	9.40923i	0.368777	+	0.638740i
$218$	−12.8623	+	4.68150i	−0.871146	+	0.317071i
$219$	15.1420	−	5.51125i	1.02320	−	0.372416i
$220$	−2.14543	−	3.71599i	−0.144645	−	0.250532i
$221$	−12.3760	+	21.4358i	−0.832499	+	1.44193i
$222$	2.01367	−	11.4201i	0.135149	−	0.766466i
$223$	−14.2515	+	11.9584i	−0.954351	+	0.800795i	−0.980025	−	0.198875i	$-0.936271\pi$
$223$	−14.2515	+	11.9584i	−0.954351	+	0.800795i	0.0256741	+	0.999670i	$0.491827\pi$
$224$	2.20574	+	1.85083i	0.147377	+	0.123664i
$225$	0.173648	+	0.984808i	0.0115765	+	0.0656539i
$226$	0.347296	+	0.126406i	0.0231018	+	0.00840837i
$227$	4.51249			0.299504			0.149752	−	0.988724i	$-0.452152\pi$
$227$	4.51249			0.299504			0.149752	+	0.988724i	$0.452152\pi$
$228$	3.75877	−	2.20718i	0.248931	−	0.146174i
$229$	−2.44831			−0.161789			−0.0808945	−	0.996723i	$-0.525778\pi$
$229$	−2.44831			−0.161789			−0.0808945	+	0.996723i	$0.525778\pi$
$230$	0.0530334	+	0.0193026i	0.00349692	+	0.00127277i
$231$	2.14543	+	12.1673i	0.141159	+	0.800552i
$232$	6.19459	+	5.19788i	0.406695	+	0.341258i
$233$	−13.2344	+	11.1050i	−0.867016	+	0.727513i	−0.963468	−	0.267825i	$-0.913695\pi$
$233$	−13.2344	+	11.1050i	−0.867016	+	0.727513i	0.0964517	+	0.995338i	$0.469251\pi$
$234$	0.794263	−	4.50449i	0.0519226	−	0.294468i
$235$	0.851167	−	1.47426i	0.0555240	−	0.0961704i
$236$	−2.73396	−	4.73535i	−0.177965	−	0.308245i
$237$	−0.421274	+	0.153331i	−0.0273647	+	0.00995994i
$238$	14.6420	−	5.32926i	0.949102	−	0.345445i
$239$	8.27719	+	14.3365i	0.535407	+	0.927352i	0.999144	+	0.0413788i	$0.0131750\pi$
$239$	8.27719	+	14.3365i	0.535407	+	0.927352i	−0.463737	+	0.885973i	$0.653492\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	3.06670	−	17.3921i	0.197544	−	1.12033i	−0.711206	−	0.702984i	$-0.751851\pi$
$241$	3.06670	−	17.3921i	0.197544	−	1.12033i	0.908749	−	0.417342i	$-0.137038\pi$
$242$	−5.67752	+	4.76400i	−0.364965	+	0.306242i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	1.74035	+	9.87003i	0.111415	+	0.631864i
$245$	1.21301	+	0.441500i	0.0774964	+	0.0282064i
$246$	7.92902			0.505536
$247$	12.7028	−	15.3669i	0.808260	−	0.977775i
$248$	−3.77332			−0.239606
$249$	14.6998	+	5.35029i	0.931562	+	0.339061i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	13.2724	+	11.1369i	0.837749	+	0.702955i	0.957056	−	0.289902i	$-0.0936229\pi$
$251$	13.2724	+	11.1369i	0.837749	+	0.702955i	−0.119307	+	0.992857i	$0.538067\pi$
$252$	−2.20574	+	1.85083i	−0.138948	+	0.116592i
$253$	0.0420512	−	0.238484i	0.00264374	−	0.0149934i
$254$	7.74763	−	13.4193i	0.486129	−	0.842001i
$255$	−2.70574	−	4.68647i	−0.169440	−	0.293478i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−28.8282	+	10.4926i	−1.79825	+	0.654510i	−0.799718	+	0.600376i	$0.795018\pi$
$257$	−28.8282	+	10.4926i	−1.79825	+	0.654510i	−0.998534	+	0.0541338i	$0.982760\pi$
$258$	2.14156	+	3.70929i	0.133328	+	0.230930i
$259$	−16.6951	+	28.9167i	−1.03738	+	1.79680i
$260$	0.794263	−	4.50449i	0.0492581	−	0.279357i
$261$	−6.19459	+	5.19788i	−0.383436	+	0.321741i
$262$	4.50980	+	3.78417i	0.278616	+	0.233787i
$263$	0.0256923	+	0.145708i	0.00158425	+	0.00898475i	0.985590	−	0.169154i	$-0.0541035\pi$
$263$	0.0256923	+	0.145708i	0.00158425	+	0.00898475i	−0.984005	+	0.178139i	$0.942992\pi$
$264$	−4.03209	−	1.46756i	−0.248158	−	0.0903221i
$265$	4.59627			0.282346
$266$	−12.3439	+	2.27038i	−0.756853	+	0.139206i
$267$	−1.94356			−0.118944
$268$	13.1814	+	4.79763i	0.805181	+	0.293062i
$269$	−1.18567	−	6.72427i	−0.0722916	−	0.409986i	−0.999382	−	0.0351484i	$-0.988810\pi$
$269$	−1.18567	−	6.72427i	−0.0722916	−	0.409986i	0.927091	−	0.374837i	$-0.122301\pi$
$270$	0.766044	+	0.642788i	0.0466200	+	0.0391188i
$271$	3.36824	−	2.82629i	0.204606	−	0.171685i	−0.534727	−	0.845025i	$-0.679585\pi$
$271$	3.36824	−	2.82629i	0.204606	−	0.171685i	0.739333	+	0.673340i	$0.235141\pi$
$272$	−0.939693	+	5.32926i	−0.0569772	+	0.323134i
$273$	−6.58512	+	11.4058i	−0.398550	+	0.690308i
$274$	−1.64409	−	2.84764i	−0.0993228	−	0.172032i
$275$	4.03209	−	1.46756i	0.243144	−	0.0884972i
$276$	0.0530334	−	0.0193026i	0.00319224	−	0.00116188i
$277$	−9.68479	−	16.7746i	−0.581903	−	1.00789i	−0.995254	−	0.0973134i	$-0.968975\pi$
$277$	−9.68479	−	16.7746i	−0.581903	−	1.00789i	0.413351	−	0.910572i	$-0.364358\pi$
$278$	−5.57532	+	9.65674i	−0.334386	+	0.579173i
$279$	0.655230	−	3.71599i	0.0392276	−	0.222471i
$280$	−2.20574	+	1.85083i	−0.131818	+	0.110608i
$281$	24.5574	+	20.6061i	1.46497	+	1.22926i	0.920656	+	0.390374i	$0.127654\pi$
$281$	24.5574	+	20.6061i	1.46497	+	1.22926i	0.544313	+	0.838882i	$0.316790\pi$
$282$	−0.295607	−	1.67647i	−0.0176031	−	0.0998324i
$283$	19.2208	+	6.99578i	1.14256	+	0.415856i	0.842835	−	0.538171i	$-0.180885\pi$
$283$	19.2208	+	6.99578i	1.14256	+	0.415856i	0.299720	+	0.954027i	$0.403107\pi$
$284$	11.7246			0.695728
$285$	1.52094	+	4.08494i	0.0900930	+	0.241971i
$286$	−19.6263			−1.16053
$287$	−21.4538	−	7.80856i	−1.26638	−	0.460924i
$288$	−0.173648	−	0.984808i	−0.0102323	−	0.0580304i
$289$	9.41013	+	7.89604i	0.553537	+	0.464473i
$290$	−6.19459	+	5.19788i	−0.363759	+	0.305230i
$291$	2.05303	−	11.6433i	0.120351	−	0.682544i
$292$	8.05690	−	13.9550i	0.471495	−	0.816653i
$293$	4.76604	+	8.25503i	0.278435	+	0.482264i	0.970996	−	0.239095i	$-0.0768509\pi$
$293$	4.76604	+	8.25503i	0.278435	+	0.482264i	−0.692561	+	0.721360i	$0.743518\pi$
$294$	1.21301	−	0.441500i	0.0707442	−	0.0257488i
$295$	5.13816	−	1.87014i	0.299155	−	0.108884i
$296$	−5.79813	−	10.0427i	−0.337010	−	0.583718i
$297$	2.14543	−	3.71599i	0.124490	−	0.215624i
$298$	1.51501	−	8.59208i	0.0877624	−	0.497726i
$299$	0.197748	−	0.165930i	0.0114361	−	0.00959599i
$300$	0.766044	+	0.642788i	0.0442276	+	0.0371114i
$301$	−2.14156	−	12.1454i	−0.123437	−	0.700048i
$302$	7.36484	+	2.68058i	0.423799	+	0.154250i
$303$	−19.0942			−1.09693
$304$	1.46064	−	4.10689i	0.0837733	−	0.235546i
$305$	−10.0223			−0.573875
$306$	−5.08512	−	1.85083i	−0.290697	−	0.105805i
$307$	−3.74257	−	21.2252i	−0.213600	−	1.21139i	−0.883319	−	0.468771i	$-0.844697\pi$
$307$	−3.74257	−	21.2252i	−0.213600	−	1.21139i	0.669720	−	0.742614i	$-0.266414\pi$
$308$	9.46451	+	7.94166i	0.539290	+	0.452518i
$309$	10.9192	−	9.16231i	0.621172	−	0.521226i
$310$	0.655230	−	3.71599i	0.0372146	−	0.211054i
$311$	−1.46926	+	2.54482i	−0.0833138	+	0.144304i	−0.904671	−	0.426110i	$-0.859884\pi$
$311$	−1.46926	+	2.54482i	−0.0833138	+	0.144304i	0.821358	+	0.570414i	$0.193217\pi$
$312$	−2.28699	−	3.96118i	−0.129475	−	0.224258i
$313$	−8.06165	+	2.93420i	−0.455671	+	0.165851i	−0.559651	−	0.828729i	$-0.689065\pi$
$313$	−8.06165	+	2.93420i	−0.455671	+	0.165851i	0.103979	+	0.994579i	$0.466842\pi$
$314$	−6.11974	+	2.22740i	−0.345357	+	0.125700i
$315$	−1.43969	−	2.49362i	−0.0811175	−	0.140500i
$316$	−0.224155	+	0.388249i	−0.0126097	+	0.0218407i
$317$	−2.70439	+	15.3374i	−0.151894	+	0.861433i	0.809677	+	0.586876i	$0.199642\pi$
$317$	−2.70439	+	15.3374i	−0.151894	+	0.861433i	−0.961571	+	0.274557i	$0.911469\pi$
$318$	3.52094	−	2.95442i	0.197445	−	0.165676i
$319$	26.5801	+	22.3034i	1.48820	+	1.24875i
$320$	−0.173648	−	0.984808i	−0.00970723	−	0.0550524i
$321$	0.0393628	+	0.0143269i	0.00219702	+	0.000799650i
$322$	−0.162504			−0.00905598
$323$	−15.2947	−	17.9574i	−0.851022	−	0.999176i
$324$	1.00000			0.0555556
$325$	4.29813	+	1.56439i	0.238418	+	0.0867769i
$326$	−0.967034	−	5.48432i	−0.0535590	−	0.303748i
$327$	−10.4855	−	8.79834i	−0.579847	−	0.486549i
$328$	6.07398	−	5.09667i	0.335379	−	0.281417i
$329$	−0.851167	+	4.82721i	−0.0469263	+	0.266133i
$330$	2.14543	−	3.71599i	0.118102	−	0.204559i
$331$	−4.45677	−	7.71935i	−0.244966	−	0.424294i	0.717156	−	0.696913i	$-0.245443\pi$
$331$	−4.45677	−	7.71935i	−0.244966	−	0.424294i	−0.962122	+	0.272619i	$0.912110\pi$
$332$	14.6998	−	5.35029i	0.806757	−	0.293635i
$333$	10.8969	−	3.96616i	0.597148	−	0.217344i
$334$	2.37551	+	4.11451i	0.129982	+	0.225136i
$335$	−7.01367	+	12.1480i	−0.383198	+	0.663718i
$336$	−0.500000	+	2.83564i	−0.0272772	+	0.154697i
$337$	2.08647	−	1.75075i	0.113657	−	0.0953696i	−0.584188	−	0.811618i	$-0.698587\pi$
$337$	2.08647	−	1.75075i	0.113657	−	0.0953696i	0.697845	+	0.716249i	$0.254142\pi$
$338$	−6.06805	−	5.09170i	−0.330058	−	0.276952i
$339$	0.0641778	+	0.363970i	0.00348566	+	0.0197681i
$340$	−5.08512	−	1.85083i	−0.275779	−	0.100376i
$341$	−16.1908			−0.876780
$342$	3.79086	+	2.15160i	0.204986	+	0.116345i
$343$	16.4388			0.887613
$344$	4.02481	+	1.46491i	0.217003	+	0.0789828i
$345$	0.00980018	+	0.0555796i	0.000527624	+	0.00299230i
$346$	8.85117	+	7.42701i	0.475842	+	0.399279i
$347$	1.65657	−	1.39003i	0.0889296	−	0.0746208i	−0.597239	−	0.802063i	$-0.703736\pi$
$347$	1.65657	−	1.39003i	0.0889296	−	0.0746208i	0.686169	+	0.727443i	$0.259291\pi$
$348$	−1.40420	+	7.96361i	−0.0752730	+	0.426895i
$349$	1.16503	−	2.01789i	0.0623626	−	0.108015i	−0.833158	−	0.553034i	$-0.813470\pi$
$349$	1.16503	−	2.01789i	0.0623626	−	0.108015i	0.895521	+	0.445019i	$0.146803\pi$
$350$	−1.43969	−	2.49362i	−0.0769548	−	0.133290i
$351$	4.29813	−	1.56439i	0.229417	−	0.0835011i
$352$	−4.03209	+	1.46756i	−0.214911	+	0.0782212i
$353$	3.08647	+	5.34592i	0.164276	+	0.284534i	0.936398	−	0.350940i	$-0.114138\pi$
$353$	3.08647	+	5.34592i	0.164276	+	0.284534i	−0.772122	+	0.635474i	$0.780805\pi$
$354$	2.73396	−	4.73535i	0.145308	−	0.251681i
$355$	−2.03596	+	11.5465i	−0.108057	+	0.612825i
$356$	−1.48886	+	1.24930i	−0.0789092	+	0.0662127i
$357$	11.9363	+	10.0157i	0.631735	+	0.530089i
$358$	−1.17705	−	6.67539i	−0.0622091	−	0.352805i
$359$	11.8204	+	4.30228i	0.623858	+	0.227066i	0.634556	−	0.772877i	$-0.281183\pi$
$359$	11.8204	+	4.30228i	0.623858	+	0.227066i	−0.0106978	+	0.999943i	$0.503405\pi$
$360$	1.00000			0.0527046
$361$	9.74123	+	16.3128i	0.512696	+	0.858570i
$362$	−5.87939			−0.309014
$363$	−6.96451	−	2.53487i	−0.365542	−	0.133046i
$364$	2.28699	+	12.9702i	0.119871	+	0.679821i
$365$	12.3439	+	10.3578i	0.646109	+	0.542150i
$366$	−7.67752	+	6.44220i	−0.401310	+	0.336739i
$367$	−3.39275	+	19.2412i	−0.177100	+	1.00438i	0.758592	+	0.651566i	$0.225888\pi$
$367$	−3.39275	+	19.2412i	−0.177100	+	1.00438i	−0.935692	+	0.352819i	$0.885223\pi$
$368$	0.0282185	−	0.0488759i	0.00147099	−	0.00254783i
$369$	3.96451	+	6.86673i	0.206384	+	0.357468i
$370$	10.8969	−	3.96616i	0.566504	−	0.206191i
$371$	−12.4363	+	4.52644i	−0.645660	+	0.235001i
$372$	−1.88666	−	3.26779i	−0.0978187	−	0.169427i
$373$	−0.598326	+	1.03633i	−0.0309801	+	0.0536592i	−0.881100	−	0.472930i	$-0.843196\pi$
$373$	−0.598326	+	1.03633i	−0.0309801	+	0.0536592i	0.850120	+	0.526590i	$0.176530\pi$
$374$	−4.03209	+	22.8671i	−0.208494	+	1.18243i
$375$	−0.766044	+	0.642788i	−0.0395584	+	0.0331934i
$376$	−1.30406	−	1.09424i	−0.0672519	−	0.0564311i
$377$	6.42278	+	36.4254i	0.330790	+	1.87600i
$378$	−2.70574	−	0.984808i	−0.139168	−	0.0506530i
$379$	11.9213			0.612355			0.306177	−	0.951974i	$-0.400950\pi$
$379$	11.9213			0.612355			0.306177	+	0.951974i	$0.400950\pi$
$380$	3.79086	+	2.15160i	0.194467	+	0.110375i
$381$	15.4953			0.793846
$382$	6.04576	+	2.20048i	0.309328	+	0.112586i
$383$	−2.02317	−	11.4739i	−0.103379	−	0.586291i	−0.991855	−	0.127369i	$-0.959347\pi$
$383$	−2.02317	−	11.4739i	−0.103379	−	0.586291i	0.888476	−	0.458922i	$-0.151764\pi$
$384$	−0.766044	−	0.642788i	−0.0390920	−	0.0328021i
$385$	−9.46451	+	7.94166i	−0.482356	+	0.404745i
$386$	2.80200	−	15.8910i	0.142618	−	0.808828i
$387$	−2.14156	+	3.70929i	−0.108862	+	0.188554i
$388$	−5.91147	−	10.2390i	−0.300110	−	0.519805i
$389$	17.3195	−	6.30380i	0.878136	−	0.319615i	0.136679	−	0.990615i	$-0.456357\pi$
$389$	17.3195	−	6.30380i	0.878136	−	0.319615i	0.741457	+	0.671000i	$0.234135\pi$
$390$	4.29813	−	1.56439i	0.217644	−	0.0792161i
$391$	−0.152704	−	0.264490i	−0.00772256	−	0.0133759i
$392$	0.645430	−	1.11792i	0.0325991	−	0.0564633i
$393$	−1.02229	+	5.79769i	−0.0515676	+	0.292455i
$394$	−11.4021	+	9.56753i	−0.574432	+	0.482005i
$395$	−0.343426	−	0.288169i	−0.0172796	−	0.0144993i
$396$	−0.745100	−	4.22567i	−0.0374427	−	0.212348i
$397$	−16.6557	−	6.06218i	−0.835925	−	0.304252i	−0.111637	−	0.993749i	$-0.535609\pi$
$397$	−16.6557	−	6.06218i	−0.835925	−	0.304252i	−0.724288	+	0.689497i	$0.757832\pi$
$398$	−23.1712			−1.16147
$399$	−8.13816	−	9.55493i	−0.407417	−	0.478345i
$400$	1.00000			0.0500000
$401$	−19.7087	−	7.17339i	−0.984207	−	0.358222i	−0.200733	−	0.979646i	$-0.564332\pi$
$401$	−19.7087	−	7.17339i	−0.984207	−	0.358222i	−0.783474	+	0.621424i	$0.786554\pi$
$402$	2.43582	+	13.8142i	0.121488	+	0.688991i
$403$	−13.2212	−	11.0939i	−0.658596	−	0.552628i
$404$	−14.6270	+	12.2735i	−0.727721	+	0.610630i
$405$	−0.173648	+	0.984808i	−0.00862865	+	0.0489355i
$406$	11.6420	−	20.1646i	0.577784	−	1.00075i
$407$	−24.8790	−	43.0916i	−1.23320	−	2.13597i
$408$	−5.08512	+	1.85083i	−0.251751	+	0.0916299i
$409$	−21.4354	+	7.80185i	−1.05991	+	0.385777i	−0.812396	−	0.583107i	$-0.801837\pi$
$409$	−21.4354	+	7.80185i	−1.05991	+	0.385777i	−0.247517	+	0.968883i	$0.579615\pi$
$410$	3.96451	+	6.86673i	0.195793	+	0.339124i
$411$	1.64409	−	2.84764i	0.0810968	−	0.140464i
$412$	2.47519	−	14.0375i	0.121944	−	0.691577i
$413$	−12.0608	+	10.1202i	−0.593472	+	0.497982i
$414$	0.0432332	+	0.0362770i	0.00212480	+	0.00178292i
$415$	2.71641	+	15.4056i	0.133344	+	0.756229i
$416$	−4.29813	−	1.56439i	−0.210733	−	0.0767007i
$417$	−11.1506			−0.546049
$418$	6.26739	−	17.6221i	0.306548	−	0.861924i
$419$	8.44150			0.412394			0.206197	−	0.978510i	$-0.433891\pi$
$419$	8.44150			0.412394			0.206197	+	0.978510i	$0.433891\pi$
$420$	−2.70574	−	0.984808i	−0.132026	−	0.0480537i
$421$	1.91013	+	10.8329i	0.0930940	+	0.527963i	0.995315	+	0.0966879i	$0.0308249\pi$
$421$	1.91013	+	10.8329i	0.0930940	+	0.527963i	−0.902221	+	0.431275i	$0.858064\pi$
$422$	1.58718	+	1.33180i	0.0772628	+	0.0648312i
$423$	1.30406	−	1.09424i	0.0634057	−	0.0532037i
$424$	0.798133	−	4.52644i	0.0387608	−	0.219823i
$425$	2.70574	−	4.68647i	0.131248	−	0.227327i
$426$	5.86231	+	10.1538i	0.284030	+	0.491954i
$427$	27.1177	−	9.87003i	1.31232	−	0.477644i
$428$	0.0393628	−	0.0143269i	0.00190267	−	0.000692517i
$429$	−9.81315	−	16.9969i	−0.473783	−	0.820617i
$430$	−2.14156	+	3.70929i	−0.103275	+	0.178878i
$431$	−5.58347	+	31.6655i	−0.268946	+	1.52527i	0.488610	+	0.872502i	$0.337504\pi$
$431$	−5.58347	+	31.6655i	−0.268946	+	1.52527i	−0.757557	+	0.652769i	$0.773607\pi$
$432$	0.766044	−	0.642788i	0.0368563	−	0.0309261i
$433$	29.4800	+	24.7366i	1.41672	+	1.18877i	0.953071	+	0.302747i	$0.0979039\pi$
$433$	29.4800	+	24.7366i	1.41672	+	1.18877i	0.463647	+	0.886020i	$0.346541\pi$
$434$	1.88666	+	10.6998i	0.0905625	+	0.513606i
$435$	−7.59879	−	2.76573i	−0.364334	−	0.132607i
$436$	−13.6878			−0.655526
$437$	0.0858375	+	0.230542i	0.00410617	+	0.0110283i
$438$	16.1138			0.769948
$439$	3.04664	+	1.10889i	0.145408	+	0.0529242i	0.413699	−	0.910414i	$-0.364237\pi$
$439$	3.04664	+	1.10889i	0.145408	+	0.0529242i	−0.268291	+	0.963338i	$0.586459\pi$
$440$	−0.745100	−	4.22567i	−0.0355212	−	0.201451i
$441$	0.988856	+	0.829748i	0.0470884	+	0.0395118i
$442$	−18.9611	+	15.9103i	−0.901888	+	0.756774i
$443$	−2.49454	+	14.1472i	−0.118519	+	0.672155i	0.866428	+	0.499301i	$0.166410\pi$
$443$	−2.49454	+	14.1472i	−0.118519	+	0.672155i	−0.984948	+	0.172854i	$0.944701\pi$
$444$	5.79813	−	10.0427i	0.275167	−	0.476604i
$445$	−0.971782	−	1.68317i	−0.0460669	−	0.0797901i
$446$	−17.4820	+	6.36295i	−0.827799	+	0.301294i
$447$	8.19846	−	2.98400i	0.387774	−	0.141138i
$448$	1.43969	+	2.49362i	0.0680191	+	0.117813i
$449$	−7.38800	+	12.7964i	−0.348661	+	0.603899i	−0.986012	−	0.166675i	$-0.946697\pi$
$449$	−7.38800	+	12.7964i	−0.348661	+	0.603899i	0.637351	+	0.770574i	$0.280030\pi$
$450$	−0.173648	+	0.984808i	−0.00818585	+	0.0464243i
$451$	26.0626	−	21.8691i	1.22724	−	1.02978i
$452$	0.283119	+	0.237565i	0.0133168	+	0.0111741i
$453$	1.36097	+	7.71843i	0.0639438	+	0.362643i
$454$	4.24035	+	1.54336i	0.199010	+	0.0724336i
$455$	−13.1702			−0.617431
$456$	4.28699	−	0.788496i	0.200757	−	0.0369247i
$457$	−1.82800			−0.0855103			−0.0427551	−	0.999086i	$-0.513614\pi$
$457$	−1.82800			−0.0855103			−0.0427551	+	0.999086i	$0.513614\pi$
$458$	−2.30066	−	0.837372i	−0.107503	−	0.0391278i
$459$	−0.939693	−	5.32926i	−0.0438611	−	0.248749i
$460$	0.0432332	+	0.0362770i	0.00201576	+	0.00169142i
$461$	−21.0514	+	17.6643i	−0.980463	+	0.822706i	−0.984159	−	0.177287i	$-0.943268\pi$
$461$	−21.0514	+	17.6643i	−0.980463	+	0.822706i	0.00369589	+	0.999993i	$0.498824\pi$
$462$	−2.14543	+	12.1673i	−0.0998144	+	0.566076i
$463$	19.6079	−	33.9618i	0.911255	−	1.57834i	0.0989622	−	0.995091i	$-0.468448\pi$
$463$	19.6079	−	33.9618i	0.911255	−	1.57834i	0.812293	−	0.583249i	$-0.198219\pi$
$464$	4.04323	+	7.00309i	0.187702	+	0.325110i
$465$	3.54576	−	1.29055i	0.164431	−	0.0598479i
$466$	−16.2344	+	5.90885i	−0.752045	+	0.273722i
$467$	12.8366	+	22.2337i	0.594008	+	1.02885i	0.993686	+	0.112196i	$0.0357885\pi$
$467$	12.8366	+	22.2337i	0.594008	+	1.02885i	−0.399678	+	0.916656i	$0.630878\pi$
$468$	2.28699	−	3.96118i	0.105716	−	0.183106i
$469$	7.01367	−	39.7765i	0.323861	−	1.83671i
$470$	1.30406	−	1.09424i	0.0601519	−	0.0504735i
$471$	−4.98886	−	4.18615i	−0.229874	−	0.192887i
$472$	−0.949493	−	5.38484i	−0.0437039	−	0.247857i
$473$	17.2699	+	6.28573i	0.794072	+	0.289018i
$474$	−0.448311			−0.0205916
$475$	−2.77719	+	3.35965i	−0.127426	+	0.154151i
$476$	15.5817			0.714187
$477$	4.31908	+	1.57202i	0.197757	+	0.0719777i
$478$	2.87464	+	16.3029i	0.131483	+	0.745676i
$479$	−18.9060	−	15.8640i	−0.863838	−	0.724846i	0.0989536	−	0.995092i	$-0.468450\pi$
$479$	−18.9060	−	15.8640i	−0.863838	−	0.724846i	−0.962791	+	0.270246i	$0.912895\pi$
$480$	0.766044	−	0.642788i	0.0349650	−	0.0293391i
$481$	9.21048	−	52.2353i	0.419962	−	2.38172i
$482$	8.83022	−	15.2944i	0.402206	−	0.696641i
$483$	−0.0812519	−	0.140732i	−0.00369709	−	0.00640355i
$484$	−6.96451	+	2.53487i	−0.316569	+	0.115222i
$485$	11.1099	−	4.04369i	0.504476	−	0.183614i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	5.51889	−	9.55899i	0.250085	−	0.433159i	−0.713464	−	0.700692i	$-0.752875\pi$
$487$	5.51889	−	9.55899i	0.250085	−	0.433159i	0.963549	+	0.267532i	$0.0862082\pi$
$488$	−1.74035	+	9.87003i	−0.0787820	+	0.446795i
$489$	4.26604	−	3.57964i	0.192917	−	0.161877i
$490$	0.988856	+	0.829748i	0.0446719	+	0.0374842i
$491$	−4.29726	−	24.3709i	−0.193932	−	1.09985i	−0.913931	−	0.405870i	$-0.866969\pi$
$491$	−4.29726	−	24.3709i	−0.193932	−	1.09985i	0.719998	−	0.693976i	$-0.244142\pi$
$492$	7.45084	+	2.71188i	0.335910	+	0.122261i
$493$	43.7597			1.97084
$494$	17.1925	−	10.0956i	0.773529	−	0.454222i
$495$	4.29086			0.192860
$496$	−3.54576	−	1.29055i	−0.159209	−	0.0579474i
$497$	−5.86231	−	33.2468i	−0.262961	−	1.49132i
$498$	11.9834	+	10.0553i	0.536989	+	0.450587i
$499$	15.5758	−	13.0696i	0.697268	−	0.585077i	−0.223727	−	0.974652i	$-0.571822\pi$
$499$	15.5758	−	13.0696i	0.697268	−	0.585077i	0.920995	+	0.389574i	$0.127378\pi$
$500$	−0.173648	+	0.984808i	−0.00776578	+	0.0440419i
$501$	−2.37551	+	4.11451i	−0.106130	+	0.183823i
$502$	8.66297	+	15.0047i	0.386647	+	0.669693i
$503$	5.63563	−	2.05120i	0.251280	−	0.0914585i	−0.213309	−	0.976985i	$-0.568424\pi$
$503$	5.63563	−	2.05120i	0.251280	−	0.0914585i	0.464589	+	0.885526i	$0.346202\pi$
$504$	−2.70574	+	0.984808i	−0.120523	+	0.0438668i
$505$	−9.54710	−	16.5361i	−0.424841	−	0.735845i
$506$	0.121082	−	0.209719i	0.00538273	−	0.00932317i
$507$	1.37551	−	7.80093i	0.0610888	−	0.346452i
$508$	11.8701	−	9.96016i	0.526648	−	0.441910i
$509$	−13.9290	−	11.6878i	−0.617393	−	0.518054i	0.279590	−	0.960119i	$-0.409801\pi$
$509$	−13.9290	−	11.6878i	−0.617393	−	0.518054i	−0.896983	+	0.442065i	$0.854246\pi$
$510$	−0.939693	−	5.32926i	−0.0416103	−	0.235984i
$511$	−43.5997	−	15.8690i	−1.92874	−	0.702003i
$512$	−1.00000			−0.0441942
$513$	0.0320889	+	4.35878i	0.00141676	+	0.192445i
$514$	−30.6783			−1.35316
$515$	13.3944	+	4.87516i	0.590228	+	0.214825i
$516$	0.743756	+	4.21805i	0.0327420	+	0.185689i
$517$	−5.59555	−	4.69523i	−0.246092	−	0.206496i
$518$	−25.5783	+	21.4628i	−1.12385	+	0.943019i
$519$	−2.00640	+	11.3788i	−0.0880710	+	0.499476i
$520$	2.28699	−	3.96118i	0.100291	−	0.173709i
$521$	−10.2365	−	17.7301i	−0.448468	−	0.776770i	0.549818	−	0.835284i	$-0.314697\pi$
$521$	−10.2365	−	17.7301i	−0.448468	−	0.776770i	−0.998287	+	0.0585143i	$0.981364\pi$
$522$	−7.59879	+	2.76573i	−0.332590	+	0.121053i
$523$	−22.0091	+	8.01065i	−0.962390	+	0.350281i	−0.774970	−	0.631998i	$-0.782235\pi$
$523$	−22.0091	+	8.01065i	−0.962390	+	0.350281i	−0.187420	+	0.982280i	$0.560013\pi$
$524$	2.94356	+	5.09840i	0.128590	+	0.222725i
$525$	1.43969	−	2.49362i	0.0628333	−	0.108831i
$526$	−0.0256923	+	0.145708i	−0.00112024	+	0.00635318i
$527$	−15.6420	+	13.1252i	−0.681377	+	0.571743i
$528$	−3.28699	−	2.75811i	−0.143048	−	0.120031i
$529$	−3.99335	−	22.6474i	−0.173624	−	0.984671i
$530$	4.31908	+	1.57202i	0.187609	+	0.0682840i
$531$	5.46791			0.237287
$532$	−12.3760	−	2.08840i	−0.536567	−	0.0905435i
$533$	36.2671			1.57090
$534$	−1.82635	−	0.664738i	−0.0790340	−	0.0287660i
$535$	0.00727396	+	0.0412527i	0.000314481	+	0.00178351i
$536$	10.7456	+	9.01660i	0.464138	+	0.389458i
$537$	5.19253	−	4.35705i	0.224074	−	0.188021i
$538$	1.18567	−	6.72427i	0.0511179	−	0.289904i
$539$	2.76945	−	4.79682i	0.119289	−	0.206614i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	−5.53374	+	2.01412i	−0.237914	+	0.0865936i	−0.458226	−	0.888836i	$-0.651515\pi$
$541$	−5.53374	+	2.01412i	−0.237914	+	0.0865936i	0.220312	+	0.975430i	$0.429293\pi$
$542$	4.13176	−	1.50384i	0.177474	−	0.0645953i
$543$	−2.93969	−	5.09170i	−0.126154	−	0.218506i
$544$	−2.70574	+	4.68647i	−0.116008	+	0.200931i
$545$	2.37686	−	13.4798i	0.101813	−	0.577413i
$546$	−10.0890	+	8.46567i	−0.431769	+	0.362297i
$547$	6.99273	+	5.86759i	0.298987	+	0.250880i	0.779923	−	0.625876i	$-0.215258\pi$
$547$	6.99273	+	5.86759i	0.298987	+	0.250880i	−0.480935	+	0.876756i	$0.659703\pi$
$548$	−0.570985	−	3.23822i	−0.0243913	−	0.138330i
$549$	−9.41787	−	3.42782i	−0.401945	−	0.146296i
$550$	4.29086			0.182963
$551$	−34.7567	−	5.86506i	−1.48069	−	0.249860i
$552$	0.0564370			0.00240212
$553$	1.21301	+	0.441500i	0.0515825	+	0.0187745i
$554$	−3.36349	−	19.0753i	−0.142901	−	0.810433i
$555$	8.88326	+	7.45394i	0.377073	+	0.316402i
$556$	−8.54189	+	7.16750i	−0.362257	+	0.303970i
$557$	7.01249	−	39.7698i	0.297129	−	1.68510i	−0.361294	−	0.932452i	$-0.617665\pi$
$557$	7.01249	−	39.7698i	0.297129	−	1.68510i	0.658423	−	0.752648i	$-0.271224\pi$
$558$	1.88666	−	3.26779i	0.0798687	−	0.138337i
$559$	9.79544	+	16.9662i	0.414303	+	0.717594i
$560$	−2.70574	+	0.984808i	−0.114338	+	0.0416157i
$561$	−21.8195	+	7.94166i	−0.921222	+	0.335297i
$562$	16.0287	+	27.7625i	0.676129	+	1.17109i
$563$	8.94996	−	15.5018i	0.377196	−	0.653322i	−0.613457	−	0.789728i	$-0.710222\pi$
$563$	8.94996	−	15.5018i	0.377196	−	0.653322i	0.990653	+	0.136406i	$0.0435550\pi$
$564$	0.295607	−	1.67647i	0.0124473	−	0.0705922i
$565$	−0.283119	+	0.237565i	−0.0119109	+	0.00999442i
$566$	15.6689	+	13.1478i	0.658613	+	0.552642i
$567$	−0.500000	−	2.83564i	−0.0209980	−	0.119086i
$568$	11.0175	+	4.01006i	0.462286	+	0.168258i
$569$	−18.2344			−0.764427			−0.382213	−	0.924074i	$-0.624838\pi$
$569$	−18.2344			−0.764427			−0.382213	+	0.924074i	$0.624838\pi$
$570$	0.0320889	+	4.35878i	0.00134406	+	0.182569i
$571$	40.3259			1.68759			0.843794	−	0.536667i	$-0.180317\pi$
$571$	40.3259			1.68759			0.843794	+	0.536667i	$0.180317\pi$
$572$	−18.4427	−	6.71259i	−0.771127	−	0.280667i
$573$	1.11721	+	6.33602i	0.0466722	+	0.264691i
$574$	−17.4893	−	14.6753i	−0.729990	−	0.612535i
$575$	−0.0432332	+	0.0362770i	−0.00180295	+	0.00151286i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	−1.72621	+	2.98989i	−0.0718633	+	0.124471i	−0.899718	−	0.436472i	$-0.856228\pi$
$577$	−1.72621	+	2.98989i	−0.0718633	+	0.124471i	0.827855	+	0.560943i	$0.189561\pi$
$578$	6.14203	+	10.6383i	0.255475	+	0.442495i
$579$	15.1630	−	5.51887i	0.630152	−	0.229356i
$580$	−7.59879	+	2.76573i	−0.315523	+	0.114841i
$581$	−22.5214	−	39.0082i	−0.934346	−	1.61833i
$582$	5.91147	−	10.2390i	0.245038	−	0.424419i
$583$	3.42468	−	19.4223i	0.141836	−	0.804390i
$584$	12.3439	−	10.3578i	0.510794	−	0.428607i
$585$	3.50387	+	2.94010i	0.144867	+	0.121558i
$586$	1.65523	+	9.38728i	0.0683769	+	0.387785i
$587$	−39.4984	−	14.3762i	−1.63027	−	0.593371i	−0.644974	−	0.764205i	$-0.723132\pi$
$587$	−39.4984	−	14.3762i	−1.63027	−	0.593371i	−0.985300	+	0.170834i	$0.945354\pi$
$588$	1.29086			0.0532341
$589$	14.1830	−	8.32839i	0.584402	−	0.343165i
$590$	5.46791			0.225110
$591$	−13.9868	−	5.09078i	−0.575340	−	0.209407i
$592$	−2.01367	−	11.4201i	−0.0827614	−	0.469363i
$593$	24.5239	+	20.5780i	1.00708	+	0.845038i	0.987949	−	0.154779i	$-0.0494665\pi$
$593$	24.5239	+	20.5780i	1.00708	+	0.845038i	0.0191283	+	0.999817i	$0.493911\pi$
$594$	3.28699	−	2.75811i	0.134867	−	0.113167i
$595$	−2.70574	+	15.3450i	−0.110924	+	0.629084i
$596$	4.36231	−	7.55574i	0.178687	−	0.309495i
$597$	−11.5856	−	20.0668i	−0.474167	−	0.821281i
$598$	0.242574	−	0.0882896i	0.00991958	−	0.00361043i
$599$	1.01114	−	0.368026i	0.0413142	−	0.0150372i	−0.321280	−	0.946984i	$-0.604113\pi$
$599$	1.01114	−	0.368026i	0.0413142	−	0.0150372i	0.362595	+	0.931947i	$0.381891\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−17.9971	+	31.1718i	−0.734116	+	1.27153i	0.220995	+	0.975275i	$0.429070\pi$
$601$	−17.9971	+	31.1718i	−0.734116	+	1.27153i	−0.955110	+	0.296250i	$0.904264\pi$
$602$	2.14156	−	12.1454i	0.0872834	−	0.495009i
$603$	−10.7456	+	9.01660i	−0.437593	+	0.367184i
$604$	6.00387	+	5.03785i	0.244294	+	0.204987i
$605$	−1.28699	−	7.29888i	−0.0523235	−	0.296742i
$606$	−17.9427	−	6.53060i	−0.728872	−	0.265288i
$607$	−14.9956			−0.608651			−0.304325	−	0.952568i	$-0.598431\pi$
$607$	−14.9956			−0.608651			−0.304325	+	0.952568i	$0.598431\pi$
$608$	2.77719	−	3.35965i	0.112630	−	0.136252i
$609$	23.2841			0.943517
$610$	−9.41787	−	3.42782i	−0.381318	−	0.138789i
$611$	−1.35210	−	7.66814i	−0.0547001	−	0.310220i
$612$	−4.14543	−	3.47843i	−0.167569	−	0.140607i
$613$	−14.0255	+	11.7688i	−0.566486	+	0.475338i	−0.880478	−	0.474088i	$-0.842778\pi$
$613$	−14.0255	+	11.7688i	−0.566486	+	0.475338i	0.313992	+	0.949426i	$0.398334\pi$
$614$	3.74257	−	21.2252i	0.151038	−	0.856579i
$615$	−3.96451	+	6.86673i	−0.159864	+	0.276893i
$616$	6.17752	+	10.6998i	0.248899	+	0.431106i
$617$	33.7019	−	12.2665i	1.35679	−	0.493831i	0.441729	−	0.897149i	$-0.354365\pi$
$617$	33.7019	−	12.2665i	1.35679	−	0.493831i	0.915060	+	0.403318i	$0.132143\pi$
$618$	13.3944	−	4.87516i	0.538802	−	0.196108i
$619$	10.9979	+	19.0490i	0.442045	+	0.765644i	0.997841	−	0.0656747i	$-0.0209200\pi$
$619$	10.9979	+	19.0490i	0.442045	+	0.765644i	−0.555797	+	0.831318i	$0.687587\pi$
$620$	1.88666	−	3.26779i	0.0757701	−	0.131238i
$621$	−0.00980018	+	0.0555796i	−0.000393268	+	0.00223033i
$622$	−2.25103	+	1.88884i	−0.0902581	+	0.0757355i
$623$	4.28699	+	3.59721i	0.171755	+	0.144119i
$624$	−0.794263	−	4.50449i	−0.0317960	−	0.180324i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−8.57903			−0.342887
$627$	18.3949	−	3.38332i	0.734620	−	0.135117i
$628$	−6.51249			−0.259877
$629$	−58.9684	−	21.4628i	−2.35123	−	0.855776i
$630$	−0.500000	−	2.83564i	−0.0199205	−	0.112975i
$631$	−8.30974	−	6.97270i	−0.330806	−	0.277579i	0.462222	−	0.886764i	$-0.347052\pi$
$631$	−8.30974	−	6.97270i	−0.330806	−	0.277579i	−0.793028	+	0.609185i	$0.791497\pi$
$632$	−0.343426	+	0.288169i	−0.0136608	+	0.0114627i
$633$	−0.359785	+	2.04044i	−0.0143002	+	0.0811003i
$634$	−7.78699	+	13.4875i	−0.309261	+	0.535655i
$635$	7.74763	+	13.4193i	0.307455	+	0.532528i
$636$	4.31908	−	1.57202i	0.171263	−	0.0623345i
$637$	5.54829	−	2.01941i	0.219831	−	0.0800120i
$638$	17.3489	+	30.0493i	0.686851	+	1.18966i
$639$	−5.86231	+	10.1538i	−0.231909	+	0.401679i
$640$	0.173648	−	0.984808i	0.00686405	−	0.0389279i
$641$	9.11515	−	7.64852i	0.360027	−	0.302098i	−0.444775	−	0.895643i	$-0.646716\pi$
$641$	9.11515	−	7.64852i	0.360027	−	0.302098i	0.804801	+	0.593544i	$0.202272\pi$
$642$	0.0320889	+	0.0269258i	0.00126645	+	0.00106268i
$643$	1.16069	+	6.58262i	0.0457733	+	0.259593i	0.999103	−	0.0423368i	$-0.0134803\pi$
$643$	1.16069	+	6.58262i	0.0457733	+	0.259593i	−0.953330	+	0.301930i	$0.902369\pi$
$644$	−0.152704	−	0.0555796i	−0.00601737	−	0.00219014i
$645$	−4.28312			−0.168648
$646$	−8.23055	−	22.1055i	−0.323827	−	0.869731i
$647$	−32.4561			−1.27598			−0.637990	−	0.770045i	$-0.720234\pi$
$647$	−32.4561			−1.27598			−0.637990	+	0.770045i	$0.720234\pi$
$648$	0.939693	+	0.342020i	0.0369146	+	0.0134358i
$649$	−4.07414	−	23.1056i	−0.159924	−	0.906974i
$650$	3.50387	+	2.94010i	0.137433	+	0.115320i
$651$	−8.32295	+	6.98378i	−0.326202	+	0.273716i
$652$	0.967034	−	5.48432i	0.0378720	−	0.214783i
$653$	−2.30272	+	3.98843i	−0.0901124	+	0.156079i	−0.907558	−	0.419926i	$-0.862056\pi$
$653$	−2.30272	+	3.98843i	−0.0901124	+	0.156079i	0.817446	+	0.576005i	$0.195389\pi$
$654$	−6.84389	−	11.8540i	−0.267617	−	0.463527i
$655$	−5.53209	+	2.01352i	−0.216157	+	0.0786746i
$656$	7.45084	−	2.71188i	0.290906	−	0.105881i
$657$	8.05690	+	13.9550i	0.314330	+	0.544435i
$658$	−2.45084	+	4.24497i	−0.0955436	+	0.165486i
$659$	−1.79086	+	10.1565i	−0.0697620	+	0.395640i	0.929854	+	0.367929i	$0.119933\pi$
$659$	−1.79086	+	10.1565i	−0.0697620	+	0.395640i	−0.999616	+	0.0277111i	$0.991178\pi$
$660$	3.28699	−	2.75811i	0.127946	−	0.107359i
$661$	−16.7044	−	14.0166i	−0.649726	−	0.545184i	0.257262	−	0.966342i	$-0.417180\pi$
$661$	−16.7044	−	14.0166i	−0.649726	−	0.545184i	−0.906988	+	0.421157i	$0.861624\pi$
$662$	−1.54782	−	8.77812i	−0.0601577	−	0.341171i
$663$	−23.2592	−	8.46567i	−0.903314	−	0.328779i
$664$	15.6432			0.607074
$665$	4.20574	−	11.8253i	0.163091	−	0.458566i
$666$	11.5963			0.449346
$667$	−0.428853	−	0.156090i	−0.0166053	−	0.00604382i
$668$	0.825008	+	4.67885i	0.0319205	+	0.181030i
$669$	−14.2515	−	11.9584i	−0.550995	−	0.462339i
$670$	−10.7456	+	9.01660i	−0.415137	+	0.348342i
$671$	−7.46761	+	42.3509i	−0.288284	+	1.63494i
$672$	−1.43969	+	2.49362i	−0.0555373	+	0.0961935i
$673$	−22.7310	−	39.3713i	−0.876216	−	1.51765i	−0.855461	−	0.517867i	$-0.826726\pi$
$673$	−22.7310	−	39.3713i	−0.876216	−	1.51765i	−0.0207551	−	0.999785i	$-0.506607\pi$
$674$	2.55943	−	0.931556i	0.0985856	−	0.0358822i
$675$	−0.939693	+	0.342020i	−0.0361688	+	0.0131644i
$676$	−3.96064	−	6.86002i	−0.152332	−	0.263847i
$677$	17.9846	−	31.1502i	0.691203	−	1.19720i	−0.280241	−	0.959930i	$-0.590414\pi$
$677$	17.9846	−	31.1502i	0.691203	−	1.19720i	0.971444	−	0.237270i	$-0.0762524\pi$
$678$	−0.0641778	+	0.363970i	−0.00246473	+	0.0139782i
$679$	−26.0783	+	21.8823i	−1.00079	+	0.839766i
$680$	−4.14543	−	3.47843i	−0.158970	−	0.133392i
$681$	0.783585	+	4.44393i	0.0300271	+	0.170292i
$682$	−15.2144	−	5.53757i	−0.582588	−	0.212045i
$683$	24.6186			0.942003			0.471001	−	0.882132i	$-0.343893\pi$
$683$	24.6186			0.942003			0.471001	+	0.882132i	$0.343893\pi$
$684$	2.82635	+	3.31839i	0.108068	+	0.126882i
$685$	3.28817			0.125635
$686$	15.4474	+	5.62241i	0.589786	+	0.214664i
$687$	−0.425145	−	2.41112i	−0.0162203	−	0.0919898i
$688$	3.28106	+	2.75314i	0.125089	+	0.104962i
$689$	16.1047	−	13.5135i	0.613541	−	0.514822i
$690$	−0.00980018	+	0.0555796i	−0.000373086	+	0.00211588i
$691$	6.13862	−	10.6324i	0.233524	−	0.404476i	−0.725319	−	0.688413i	$-0.758308\pi$
$691$	6.13862	−	10.6324i	0.233524	−	0.404476i	0.958843	+	0.283938i	$0.0916409\pi$
$692$	5.77719	+	10.0064i	0.219616	+	0.380386i
$693$	−11.6099	+	4.22567i	−0.441025	+	0.160520i
$694$	2.03209	−	0.739620i	0.0771370	−	0.0280756i
$695$	−5.57532	−	9.65674i	−0.211484	−	0.366301i
$696$	−4.04323	+	7.00309i	−0.153258	+	0.265451i
$697$	7.45084	−	42.2558i	0.282221	−	1.60055i
$698$	1.78493	−	1.49773i	0.0675606	−	0.0566901i
$699$	−13.2344	−	11.1050i	−0.500572	−	0.420030i
$700$	−0.500000	−	2.83564i	−0.0188982	−	0.107177i
$701$	24.7361	+	9.00319i	0.934269	+	0.340046i	0.763900	−	0.645335i	$-0.223282\pi$
$701$	24.7361	+	9.00319i	0.934269	+	0.340046i	0.170368	+	0.985380i	$0.445504\pi$
$702$	4.57398			0.172634
$703$	43.9598	+	24.9505i	1.65798	+	0.941027i
$704$	−4.29086			−0.161718
$705$	1.59967	+	0.582232i	0.0602471	+	0.0219281i
$706$	1.07192	+	6.07915i	0.0403422	+	0.228792i
$707$	42.1168	+	35.3402i	1.58397	+	1.32910i
$708$	4.18866	−	3.51471i	0.157420	−	0.132091i
$709$	−8.15002	+	46.2210i	−0.306080	+	1.73587i	0.312296	+	0.949985i	$0.398902\pi$
$709$	−8.15002	+	46.2210i	−0.306080	+	1.73587i	−0.618376	+	0.785882i	$0.712209\pi$
$710$	−5.86231	+	10.1538i	−0.220009	+	0.381066i
$711$	−0.224155	−	0.388249i	−0.00840648	−	0.0145605i
$712$	−1.82635	+	0.664738i	−0.0684454	+	0.0249121i
$713$	0.200112	−	0.0728348i	0.00749425	−	0.00272768i
$714$	7.79086	+	13.4942i	0.291566	+	0.505006i
$715$	9.81315	−	16.9969i	0.366991	−	0.635647i
$716$	1.17705	−	6.67539i	0.0439885	−	0.249471i
$717$	−12.6814	+	10.6409i	−0.473595	+	0.397394i
$718$	9.63610	+	8.08564i	0.359616	+	0.301754i
$719$	−6.39676	−	36.2779i	−0.238559	−	1.35294i	−0.834987	−	0.550269i	$-0.814525\pi$
$719$	−6.39676	−	36.2779i	−0.238559	−	1.35294i	0.596428	−	0.802666i	$-0.296586\pi$
$720$	0.939693	+	0.342020i	0.0350203	+	0.0127463i
$721$	−41.0428			−1.52851
$722$	3.57444	+	18.6607i	0.133027	+	0.694481i
$723$	17.6604			0.656799
$724$	−5.52481	−	2.01087i	−0.205328	−	0.0747333i
$725$	−1.40420	−	7.96361i	−0.0521507	−	0.295761i
$726$	−5.67752	−	4.76400i	−0.210712	−	0.176809i
$727$	−20.2114	+	16.9594i	−0.749600	+	0.628989i	−0.935397	−	0.353599i	$-0.884958\pi$
$727$	−20.2114	+	16.9594i	−0.749600	+	0.628989i	0.185797	+	0.982588i	$0.440513\pi$
$728$	−2.28699	+	12.9702i	−0.0847615	+	0.480706i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	8.05690	+	13.9550i	0.298199	+	0.516496i
$731$	21.7802	−	7.92734i	0.805569	−	0.293203i
$732$	−9.41787	+	3.42782i	−0.348095	+	0.126696i
$733$	−10.2785	−	17.8029i	−0.379646	−	0.657567i	0.611364	−	0.791349i	$-0.290621\pi$
$733$	−10.2785	−	17.8029i	−0.379646	−	0.657567i	−0.991011	+	0.133783i	$0.957288\pi$
$734$	−9.76904	+	16.9205i	−0.360582	+	0.624546i
$735$	−0.224155	+	1.27125i	−0.00826810	+	0.0468907i
$736$	0.0432332	−	0.0362770i	0.00159360	−	0.00133719i
$737$	46.1077	+	38.6890i	1.69840	+	1.42513i
$738$	1.37686	+	7.80856i	0.0506829	+	0.287437i
$739$	−5.86736	−	2.13555i	−0.215834	−	0.0785573i	0.231840	−	0.972754i	$-0.425525\pi$
$739$	−5.86736	−	2.13555i	−0.215834	−	0.0785573i	−0.447674	+	0.894197i	$0.647748\pi$
$740$	11.5963			0.426287
$741$	17.3393	+	9.84137i	0.636975	+	0.361532i
$742$	−13.2344			−0.485851
$743$	10.6004	+	3.85825i	0.388892	+	0.141545i	0.529064	−	0.848582i	$-0.322543\pi$
$743$	10.6004	+	3.85825i	0.388892	+	0.141545i	−0.140171	+	0.990127i	$0.544765\pi$
$744$	−0.655230	−	3.71599i	−0.0240219	−	0.136235i
$745$	6.68345	+	5.60808i	0.244863	+	0.205464i
$746$	−0.916689	+	0.769193i	−0.0335624	+	0.0281622i
$747$	−2.71641	+	15.4056i	−0.0993884	+	0.563660i
$748$	−11.6099	+	20.1090i	−0.424501	+	0.735258i
$749$	−0.0603074	−	0.104455i	−0.00220358	−	0.00381672i
$750$	−0.939693	+	0.342020i	−0.0343127	+	0.0124888i
$751$	31.0244	−	11.2920i	1.13210	−	0.412049i	0.293044	−	0.956099i	$-0.405332\pi$
$751$	31.0244	−	11.2920i	1.13210	−	0.412049i	0.839053	+	0.544050i	$0.183110\pi$
$752$	−0.851167	−	1.47426i	−0.0310389	−	0.0537609i
$753$	−8.66297	+	15.0047i	−0.315696	+	0.546802i
$754$	−6.42278	+	36.4254i	−0.233904	+	1.32653i
$755$	−6.00387	+	5.03785i	−0.218503	+	0.183346i
$756$	−2.20574	−	1.85083i	−0.0802219	−	0.0673142i
$757$	1.93464	+	10.9719i	0.0703157	+	0.398780i	0.999570	+	0.0293383i	$0.00934000\pi$
$757$	1.93464	+	10.9719i	0.0703157	+	0.398780i	−0.929254	+	0.369442i	$0.879549\pi$
$758$	11.2023	+	4.07732i	0.406887	+	0.148095i
$759$	0.242163			0.00878997
$760$	2.82635	+	3.31839i	0.102523	+	0.120371i
$761$	29.9691			1.08638			0.543190	−	0.839610i	$-0.317216\pi$
$761$	29.9691			1.08638			0.543190	+	0.839610i	$0.317216\pi$
$762$	14.5608	+	5.29969i	0.527481	+	0.191987i
$763$	6.84389	+	38.8136i	0.247766	+	1.40515i
$764$	4.92855	+	4.13554i	0.178309	+	0.149619i
$765$	4.14543	−	3.47843i	0.149878	−	0.125763i
$766$	2.02317	−	11.4739i	0.0731000	−	0.414570i
$767$	12.5051	−	21.6594i	0.451531	−	0.782075i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	10.8816	−	3.96058i	0.392401	−	0.142822i	−0.138282	−	0.990393i	$-0.544158\pi$
$769$	10.8816	−	3.96058i	0.392401	−	0.142822i	0.530682	+	0.847571i	$0.321936\pi$
$770$	−11.6099	+	4.22567i	−0.418393	+	0.152283i
$771$	−15.3391	−	26.5682i	−0.552426	−	0.956830i
$772$	8.06805	−	13.9743i	0.290375	−	0.502945i
$773$	−9.25624	+	52.4948i	−0.332924	+	1.88811i	0.113914	+	0.993491i	$0.463661\pi$
$773$	−9.25624	+	52.4948i	−0.332924	+	1.88811i	−0.446838	+	0.894615i	$0.647450\pi$
$774$	−3.28106	+	2.75314i	−0.117935	+	0.0989594i
$775$	2.89053	+	2.42544i	0.103831	+	0.0871245i
$776$	−2.05303	−	11.6433i	−0.0736996	−	0.417971i
$777$	−31.3764	−	11.4201i	−1.12562	−	0.409694i
$778$	18.4311			0.660786
$779$	−11.5814	+	32.5636i	−0.414947	+	1.16671i
$780$	4.57398			0.163775
$781$	47.2747	+	17.2066i	1.69162	+	0.615700i
$782$	−0.0530334	−	0.300767i	−0.00189647	−	0.0107554i
$783$	−6.19459	−	5.19788i	−0.221377	−	0.185757i
$784$	0.988856	−	0.829748i	0.0353163	−	0.0296339i
$785$	1.13088	−	6.41355i	0.0403629	−	0.228909i
$786$	−2.94356	+	5.09840i	−0.104993	+	0.181854i
$787$	10.5753	+	18.3170i	0.376970	+	0.652930i	0.990620	−	0.136648i	$-0.0436328\pi$
$787$	10.5753	+	18.3170i	0.376970	+	0.652930i	−0.613650	+	0.789578i	$0.710299\pi$
$788$	−13.9868	+	5.09078i	−0.498259	+	0.181351i
$789$	−0.139033	+	0.0506039i	−0.00494971	+	0.00180155i
$790$	−0.224155	−	0.388249i	−0.00797509	−	0.0138133i
$791$	0.532089	−	0.921605i	0.0189189	−	0.0327685i
$792$	0.745100	−	4.22567i	0.0264760	−	0.150153i
$793$	−35.1168	+	29.4665i	−1.24703	+	1.04639i
$794$	−13.5778	−	11.3932i	−0.481860	−	0.404328i
$795$	0.798133	+	4.52644i	0.0283069	+	0.160536i
$796$	−21.7738	−	7.92501i	−0.771751	−	0.280895i
$797$	−26.7674			−0.948152			−0.474076	−	0.880484i	$-0.657218\pi$
$797$	−26.7674			−0.948152			−0.474076	+	0.880484i	$0.657218\pi$
$798$	−4.37939	−	11.7621i	−0.155029	−	0.416374i
$799$	−9.21213			−0.325902
$800$	0.939693	+	0.342020i	0.0332232	+	0.0120922i
$801$	−0.337496	−	1.91404i	−0.0119248	−	0.0676291i
$802$	−16.0667	−	13.4816i	−0.567335	−	0.476051i
$803$	52.9659	−	44.4437i	1.86913	−	1.56838i
$804$	−2.43582	+	13.8142i	−0.0859048	+	0.487190i
$805$	0.0812519	−	0.140732i	0.00286375	−	0.00496017i
$806$	−8.62954	−	14.9468i	−0.303962	−	0.526478i
$807$	6.41622	−	2.33531i	0.225862	−	0.0822069i
$808$	−17.9427	+	6.53060i	−0.631221	+	0.229746i
$809$	8.95084	+	15.5033i	0.314695	+	0.545067i	0.979373	−	0.202063i	$-0.0647645\pi$
$809$	8.95084	+	15.5033i	0.314695	+	0.545067i	−0.664678	+	0.747130i	$0.731431\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	0.452181	−	2.56445i	0.0158782	−	0.0900499i	−0.975839	−	0.218492i	$-0.929886\pi$
$811$	0.452181	−	2.56445i	0.0158782	−	0.0900499i	0.991717	+	0.128442i	$0.0409975\pi$
$812$	17.8366	−	14.9667i	0.625943	−	0.525228i
$813$	3.36824	+	2.82629i	0.118129	+	0.0991223i
$814$	−8.64038	−	49.0020i	−0.302845	−	1.71752i
$815$	5.23308	+	1.90468i	0.183307	+	0.0667182i
$816$	−5.41147			−0.189439
$817$	−18.3617	+	3.37722i	−0.642394	+	0.118154i
$818$	−22.8111			−0.797571
$819$	−12.3760	−	4.50449i	−0.432452	−	0.157400i
$820$	1.37686	+	7.80856i	0.0480820	+	0.272687i
$821$	−19.5503	−	16.4047i	−0.682312	−	0.572528i	0.234369	−	0.972148i	$-0.424698\pi$
$821$	−19.5503	−	16.4047i	−0.682312	−	0.572528i	−0.916681	+	0.399620i	$0.869142\pi$
$822$	2.51889	−	2.11360i	0.0878562	−	0.0737201i
$823$	3.40925	−	19.3348i	0.118839	−	0.673970i	−0.865938	−	0.500151i	$-0.833278\pi$
$823$	3.40925	−	19.3348i	0.118839	−	0.673970i	0.984778	−	0.173819i	$-0.0556109\pi$
$824$	7.12701	−	12.3443i	0.248281	−	0.430036i
$825$	2.14543	+	3.71599i	0.0746943	+	0.129374i
$826$	−14.7947	+	5.38484i	−0.514774	+	0.187363i
$827$	−40.3448	+	14.6843i	−1.40293	+	0.510624i	−0.929046	−	0.369965i	$-0.879370\pi$
$827$	−40.3448	+	14.6843i	−1.40293	+	0.510624i	−0.473881	+	0.880589i	$0.657147\pi$
$828$	0.0282185	+	0.0488759i	0.000980660	+	0.00169855i
$829$	−12.3259	+	21.3492i	−0.428098	+	0.741487i	−0.996704	−	0.0811228i	$-0.974149\pi$
$829$	−12.3259	+	21.3492i	−0.428098	+	0.741487i	0.568606	+	0.822610i	$0.307483\pi$
$830$	−2.71641	+	15.4056i	−0.0942881	+	0.534735i
$831$	14.8380	−	12.4505i	0.514723	−	0.431904i
$832$	−3.50387	−	2.94010i	−0.121475	−	0.101930i
$833$	−1.21301	−	6.87933i	−0.0420283	−	0.238355i
$834$	−10.4782	−	3.81374i	−0.362830	−	0.132059i
$835$	−4.75103			−0.164416
$836$	11.9165	−	14.4158i	0.412142	−	0.498580i
$837$	3.77332			0.130425
$838$	7.93242	+	2.88716i	0.274021	+	0.0997354i
$839$	0.340327	+	1.93009i	0.0117494	+	0.0666341i	0.990119	−	0.140232i	$-0.0447847\pi$
$839$	0.340327	+	1.93009i	0.0117494	+	0.0666341i	−0.978369	+	0.206866i	$0.933674\pi$
$840$	−2.20574	−	1.85083i	−0.0761052	−	0.0638598i
$841$	27.8771	−	23.3916i	0.961279	−	0.806608i
$842$	−1.91013	+	10.8329i	−0.0658274	+	0.373326i
$843$	−16.0287	+	27.7625i	−0.552057	+	0.956191i
$844$	1.03596	+	1.79433i	0.0356592	+	0.0617635i
$845$	7.44356	−	2.70924i	0.256066	−	0.0932005i
$846$	1.59967	−	0.582232i	0.0549978	−	0.0200176i
$847$	10.6702	+	18.4814i	0.366634	+	0.635029i
$848$	2.29813	−	3.98048i	0.0789182	−	0.136690i
$849$	−3.55185	+	20.1436i	−0.121899	+	0.691325i
$850$	4.14543	−	3.47843i	0.142187	−	0.119309i
$851$	0.501344	+	0.420678i	0.0171859	+	0.0144206i
$852$	2.03596	+	11.5465i	0.0697508	+	0.395577i
$853$	−15.9572	−	5.80796i	−0.546365	−	0.198861i	0.0540656	−	0.998537i	$-0.482782\pi$
$853$	−15.9572	−	5.80796i	−0.546365	−	0.198861i	−0.600431	+	0.799677i	$0.705004\pi$
$854$	28.8580			0.987501
$855$	−3.75877	+	2.20718i	−0.128547	+	0.0754840i
$856$	0.0418891			0.00143174
$857$	37.9334	+	13.8066i	1.29578	+	0.471625i	0.895620	−	0.444821i	$-0.146733\pi$
$857$	37.9334	+	13.8066i	1.29578	+	0.471625i	0.400159	+	0.916446i	$0.368955\pi$
$858$	−3.40807	−	19.3281i	−0.116350	−	0.659851i
$859$	−1.44949	−	1.21627i	−0.0494561	−	0.0414986i	0.617725	−	0.786395i	$-0.288055\pi$
$859$	−1.44949	−	1.21627i	−0.0494561	−	0.0414986i	−0.667181	+	0.744896i	$0.732499\pi$
$860$	−3.28106	+	2.75314i	−0.111883	+	0.0938811i
$861$	3.96451	−	22.4838i	0.135110	−	0.766247i
$862$	−16.0770	+	27.8461i	−0.547584	+	0.948443i
$863$	3.96585	+	6.86906i	0.134999	+	0.233825i	0.925597	−	0.378510i	$-0.123563\pi$
$863$	3.96585	+	6.86906i	0.134999	+	0.233825i	−0.790598	+	0.612336i	$0.790230\pi$
$864$	0.939693	−	0.342020i	0.0319690	−	0.0116358i
$865$	−10.8576	+	3.95183i	−0.369168	+	0.134366i
$866$	19.2417	+	33.3276i	0.653859	+	1.13252i
$867$	−6.14203	+	10.6383i	−0.208594	+	0.361296i
$868$	−1.88666	+	10.6998i	−0.0640374	+	0.363174i
$869$	−1.47359	+	1.23649i	−0.0499882	+	0.0419451i
$870$	−6.19459	−	5.19788i	−0.210016	−	0.176225i
$871$	11.1414	+	63.1860i	0.377512	+	2.14098i
$872$	−12.8623	−	4.68150i	−0.435573	−	0.158536i
$873$	11.8229			0.400146
$874$	0.00181100	+	0.245996i	6.12580e−5	+	0.00832095i
$875$	2.87939			0.0973410
$876$	15.1420	+	5.51125i	0.511602	+	0.186208i
$877$	7.54829	+	42.8085i	0.254887	+	1.44554i	0.796361	+	0.604821i	$0.206755\pi$
$877$	7.54829	+	42.8085i	0.254887	+	1.44554i	−0.541474	+	0.840718i	$0.682133\pi$
$878$	2.48364	+	2.08402i	0.0838188	+	0.0703323i
$879$	−7.30200	+	6.12711i	−0.246290	+	0.206662i
$880$	0.745100	−	4.22567i	0.0251173	−	0.142447i
$881$	−0.534148	+	0.925172i	−0.0179959	+	0.0311698i	−0.874883	−	0.484334i	$-0.839062\pi$
$881$	−0.534148	+	0.925172i	−0.0179959	+	0.0311698i	0.856887	+	0.515504i	$0.172395\pi$
$882$	0.645430	+	1.11792i	0.0217327	+	0.0376422i
$883$	21.9957	−	8.00579i	0.740215	−	0.269416i	0.0557327	−	0.998446i	$-0.482251\pi$
$883$	21.9957	−	8.00579i	0.740215	−	0.269416i	0.684482	+	0.729030i	$0.260028\pi$
$884$	−23.2592	+	8.46567i	−0.782293	+	0.284731i
$885$	2.73396	+	4.73535i	0.0919009	+	0.159177i
$886$	−7.18273	+	12.4409i	−0.241309	+	0.417959i
$887$	−4.65152	+	26.3801i	−0.156183	+	0.885757i	0.801514	+	0.597976i	$0.204028\pi$
$887$	−4.65152	+	26.3801i	−0.156183	+	0.885757i	−0.957696	+	0.287780i	$0.907083\pi$
$888$	8.88326	−	7.45394i	0.298103	−	0.250138i
$889$	−34.1785	−	28.6791i	−1.14631	−	0.961867i
$890$	−0.337496	−	1.91404i	−0.0113129	−	0.0641586i
$891$	4.03209	+	1.46756i	0.135080	+	0.0491651i
$892$	−18.6040			−0.622908
$893$	7.31686	+	1.23469i	0.244849	+	0.0413173i
$894$	8.72462			0.291795
$895$	6.36959	+	2.31834i	0.212912	+	0.0774935i
$896$	0.500000	+	2.83564i	0.0167038	+	0.0947321i
$897$	0.197748	+	0.165930i	0.00660261	+	0.00554025i
$898$	−11.3191	+	9.49783i	−0.377723	+	0.316947i
$899$	−5.29849	+	30.0493i	−0.176715	+	1.00220i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−12.4363	−	21.5403i	−0.414313	−	0.717611i
$902$	31.9705	−	11.6363i	1.06450	−	0.387447i
$903$	11.5890	−	4.21805i	0.385658	−	0.140368i
$904$	0.184793	+	0.320070i	0.00614611	+	0.0106454i
$905$	2.93969	−	5.09170i	0.0977187	−	0.169254i
$906$	−1.36097	+	7.71843i	−0.0452151	+	0.256428i
$907$	−41.4745	+	34.8013i	−1.37714	+	1.15556i	−0.406882	+	0.913481i	$0.633384\pi$
$907$	−41.4745	+	34.8013i	−1.37714	+	1.15556i	−0.970257	+	0.242076i	$0.922172\pi$
$908$	3.45677	+	2.90057i	0.114717	+	0.0962589i
$909$	−3.31567	−	18.8041i	−0.109974	−	0.623693i
$910$	−12.3760	−	4.50449i	−0.410260	−	0.149322i
$911$	−35.3806			−1.17221			−0.586106	−	0.810234i	$-0.699340\pi$
$911$	−35.3806			−1.17221			−0.586106	+	0.810234i	$0.699340\pi$
$912$	4.29813	+	0.725293i	0.142325	+	0.0240168i
$913$	67.1228			2.22144
$914$	−1.71776	−	0.625213i	−0.0568184	−	0.0206802i
$915$	−1.74035	−	9.87003i	−0.0575343	−	0.326293i
$916$	−1.87551	−	1.57374i	−0.0619688	−	0.0519980i
$917$	12.9855	−	10.8961i	0.428817	−	0.359821i
$918$	0.939693	−	5.32926i	0.0310145	−	0.175892i
$919$	−29.5758	+	51.2268i	−0.975615	+	1.68982i	−0.297726	+	0.954651i	$0.596228\pi$
$919$	−29.5758	+	51.2268i	−0.975615	+	1.68982i	−0.677890	+	0.735164i	$0.737105\pi$
$920$	0.0282185	+	0.0488759i	0.000930336	+	0.00161139i
$921$	20.2528	−	7.37143i	0.667354	−	0.242897i
$922$	−25.8234	+	9.39895i	−0.850449	+	0.309538i
$923$	26.8141	+	46.4434i	0.882596	+	1.52870i
$924$	−6.17752	+	10.6998i	−0.203225	+	0.351997i
$925$	−2.01367	+	11.4201i	−0.0662091	+	0.375490i
$926$	30.0410	−	25.2074i	0.987209	−	0.828367i
$927$	10.9192	+	9.16231i	0.358634	+	0.300930i
$928$	1.40420	+	7.96361i	0.0460951	+	0.261418i
$929$	44.2147	+	16.0928i	1.45064	+	0.527989i	0.942769	−	0.333446i	$-0.108211\pi$
$929$	44.2147	+	16.0928i	1.45064	+	0.527989i	0.507868	+	0.861435i	$0.330434\pi$
$930$	3.77332			0.123732
$931$	0.0414222	+	5.62657i	0.00135756	+	0.184403i
$932$	−17.2763			−0.565904
$933$	−2.76130	−	1.00503i	−0.0904008	−	0.0329032i
$934$	4.45811	+	25.2832i	0.145874	+	0.827292i
$935$	−17.7875	−	14.9254i	−0.581712	−	0.488114i
$936$	3.50387	−	2.94010i	0.114528	−	0.0961001i
$937$	0.183448	−	1.04039i	0.00599300	−	0.0339880i	−0.981665	−	0.190616i	$-0.938951\pi$
$937$	0.183448	−	1.04039i	0.00599300	−	0.0339880i	0.987658	+	0.156628i	$0.0500625\pi$
$938$	20.1951	−	34.9789i	0.659392	−	1.14210i
$939$	−4.28952	−	7.42966i	−0.139983	−	0.242458i
$940$	1.59967	−	0.582232i	0.0521755	−	0.0189903i
$941$	9.71126	−	3.53461i	0.316578	−	0.115225i	−0.178844	−	0.983877i	$-0.557236\pi$
$941$	9.71126	−	3.53461i	0.316578	−	0.115225i	0.495422	+	0.868653i	$0.335013\pi$
$942$	−3.25624	−	5.63998i	−0.106094	−	0.183760i
$943$	−0.223745	+	0.387537i	−0.00728614	+	0.0126200i
$944$	0.949493	−	5.38484i	0.0309034	−	0.175262i
$945$	2.20574	−	1.85083i	0.0717526	−	0.0602076i
$946$	14.0786	+	11.8133i	0.457734	+	0.384084i
$947$	−8.25775	−	46.8320i	−0.268341	−	1.52184i	−0.759350	−	0.650682i	$-0.774483\pi$
$947$	−8.25775	−	46.8320i	−0.268341	−	1.52184i	0.491009	−	0.871154i	$-0.336628\pi$
$948$	−0.421274	−	0.153331i	−0.0136824	−	0.00497997i
$949$	73.7042			2.39254
$950$	−3.75877	+	2.20718i	−0.121951	+	0.0716104i
$951$	−15.5740			−0.505021
$952$	14.6420	+	5.32926i	0.474551	+	0.172722i
$953$	−0.985290	−	5.58786i	−0.0319167	−	0.181008i	0.964682	−	0.263418i	$-0.0848497\pi$
$953$	−0.985290	−	5.58786i	−0.0319167	−	0.181008i	−0.996599	+	0.0824091i	$0.973739\pi$
$954$	3.52094	+	2.95442i	0.113995	+	0.0956530i
$955$	−4.92855	+	4.13554i	−0.159484	+	0.133823i
$956$	−2.87464	+	16.3029i	−0.0929724	+	0.527273i
$957$	−17.3489	+	30.0493i	−0.560812	+	0.971354i
$958$	−12.3400	−	21.3735i	−0.398688	−	0.690548i
$959$	−8.89693	+	3.23822i	−0.287297	+	0.104567i
$960$	0.939693	−	0.342020i	0.0303284	−	0.0110387i
$961$	8.38103	+	14.5164i	0.270356	+	0.468270i
$962$	26.5205	−	45.9349i	0.855056	−	1.48100i
$963$	−0.00727396	+	0.0412527i	−0.000234400	+	0.00132935i
$964$	13.5287	−	11.3519i	0.435730	−	0.365621i
$965$	12.3610	+	10.3721i	0.397914	+	0.333889i
$966$	−0.0282185	−	0.160035i	−0.000907915	−	0.00514904i
$967$	−3.82130	−	1.39084i	−0.122885	−	0.0447264i	0.279846	−	0.960045i	$-0.409717\pi$
$967$	−3.82130	−	1.39084i	−0.122885	−	0.0447264i	−0.402731	+	0.915319i	$0.631939\pi$
$968$	−7.41147			−0.238214
$969$	15.0287	−	18.1806i	0.482791	−	0.584046i
$970$	11.8229			0.379612
$971$	−38.8974	−	14.1575i	−1.24828	−	0.454336i	−0.368458	−	0.929644i	$-0.620114\pi$
$971$	−38.8974	−	14.1575i	−1.24828	−	0.454336i	−0.879819	+	0.475309i	$0.842336\pi$
$972$	0.173648	+	0.984808i	0.00556977	+	0.0315877i
$973$	24.5954	+	20.6380i	0.788492	+	0.661623i
$974$	8.45542	−	7.09494i	0.270929	−	0.227337i
$975$	−0.794263	+	4.50449i	−0.0254368	+	0.144259i
$976$	−5.01114	+	8.67956i	−0.160403	+	0.277826i
$977$	−7.80587	−	13.5202i	−0.249732	−	0.432549i	0.713719	−	0.700432i	$-0.247009\pi$
$977$	−7.80587	−	13.5202i	−0.249732	−	0.432549i	−0.963451	+	0.267883i	$0.913676\pi$
$978$	5.23308	−	1.90468i	0.167335	−	0.0609051i
$979$	−7.83662	+	2.85230i	−0.250459	+	0.0911598i
$980$	0.645430	+	1.11792i	0.0206175	+	0.0357105i
$981$	6.84389	−	11.8540i	0.218509	−	0.378468i
$982$	4.29726	−	24.3709i	0.137131	−	0.777708i
$983$	−5.74170	+	4.81786i	−0.183132	+	0.153666i	−0.729745	−	0.683719i	$-0.760361\pi$
$983$	−5.74170	+	4.81786i	−0.183132	+	0.153666i	0.546613	+	0.837385i	$0.315917\pi$
$984$	6.07398	+	5.09667i	0.193631	+	0.162476i
$985$	−2.58466	−	14.6583i	−0.0823540	−	0.467053i
$986$	41.1207	+	14.9667i	1.30955	+	0.476637i
$987$	−4.90167			−0.156022
$988$	19.6086	−	3.60656i	0.623832	−	0.114740i
$989$	−0.241726			−0.00768645
$990$	4.03209	+	1.46756i	0.128148	+	0.0466421i
$991$	−9.72487	−	55.1525i	−0.308921	−	1.75198i	−0.604450	−	0.796643i	$-0.706607\pi$
$991$	−9.72487	−	55.1525i	−0.308921	−	1.75198i	0.295530	−	0.955334i	$-0.404504\pi$
$992$	−2.89053	−	2.42544i	−0.0917744	−	0.0770079i
$993$	6.82816	−	5.72951i	0.216685	−	0.181820i
$994$	5.86231	−	33.2468i	0.185941	−	1.05453i
$995$	11.5856	−	20.0668i	0.367288	−	0.636161i
$996$	7.82160	+	13.5474i	0.247837	+	0.429266i
$997$	31.8161	−	11.5801i	1.00763	−	0.366746i	0.215106	−	0.976591i	$-0.430990\pi$
$997$	31.8161	−	11.5801i	1.00763	−	0.366746i	0.792521	+	0.609844i	$0.208768\pi$
$998$	19.1065	−	6.95421i	0.604807	−	0.220132i
$999$	5.79813	+	10.0427i	0.183445	+	0.317736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.f.61.1	✓	6
19.5	even	9	inner	570.2.u.f.271.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.f.61.1	✓	6	1.1	even	1	trivial
570.2.u.f.271.1	yes	6	19.5	even	9	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(1.43969 - 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(2.14543 + 3.71599i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.794263 + 4.50449i) q^{13} +(2.20574 - 1.85083i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(5.08512 + 1.85083i) q^{17} -1.00000 q^{18} +(-3.79086 - 2.15160i) q^{19} -1.00000 q^{20} +(2.70574 + 0.984808i) q^{21} +(0.745100 + 4.22567i) q^{22} +(-0.0432332 - 0.0362770i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-2.28699 + 3.96118i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(2.70574 - 0.984808i) q^{28} +(7.59879 - 2.76573i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-1.88666 + 3.26779i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-3.28699 + 2.75811i) q^{33} +(4.14543 + 3.47843i) q^{34} +(0.500000 + 2.83564i) q^{35} +(-0.939693 - 0.342020i) q^{36} -11.5963 q^{37} +(-2.82635 - 3.31839i) q^{38} -4.57398 q^{39} +(-0.939693 - 0.342020i) q^{40} +(-1.37686 - 7.80856i) q^{41} +(2.20574 + 1.85083i) q^{42} +(3.28106 - 2.75314i) q^{43} +(-0.745100 + 4.22567i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-0.0282185 - 0.0488759i) q^{46} +(-1.59967 + 0.582232i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.939693 + 5.32926i) q^{51} +(-3.50387 + 2.94010i) q^{52} +(-3.52094 - 2.95442i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(-4.03209 - 1.46756i) q^{55} +2.87939 q^{56} +(1.46064 - 4.10689i) q^{57} +8.08647 q^{58} +(-5.13816 - 1.87014i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(7.67752 + 6.44220i) q^{61} +(-2.89053 + 2.42544i) q^{62} +(-0.500000 + 2.83564i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.28699 - 3.96118i) q^{65} +(-4.03209 + 1.46756i) q^{66} +(13.1814 - 4.79763i) q^{67} +(2.70574 + 4.68647i) q^{68} +(0.0282185 - 0.0488759i) q^{69} +(-0.500000 + 2.83564i) q^{70} +(8.98158 - 7.53644i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-2.79813 - 15.8690i) q^{73} +(-10.8969 - 3.96616i) q^{74} +1.00000 q^{75} +(-1.52094 - 4.08494i) q^{76} +12.3550 q^{77} +(-4.29813 - 1.56439i) q^{78} +(0.0778483 + 0.441500i) q^{79} +(-0.766044 - 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(1.37686 - 7.80856i) q^{82} +(7.82160 - 13.5474i) q^{83} +(1.43969 + 2.49362i) q^{84} +(-5.08512 + 1.85083i) q^{85} +(4.02481 - 1.46491i) q^{86} +(4.04323 + 7.00309i) q^{87} +(-2.14543 + 3.71599i) q^{88} +(-0.337496 + 1.91404i) q^{89} +(0.766044 - 0.642788i) q^{90} +(10.0890 + 8.46567i) q^{91} +(-0.00980018 - 0.0555796i) q^{92} +(-3.54576 - 1.29055i) q^{93} -1.70233 q^{94} +(4.28699 - 0.788496i) q^{95} -1.00000 q^{96} +(-11.1099 - 4.04369i) q^{97} +(-0.224155 - 1.27125i) q^{98} +(-3.28699 - 2.75811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 15 q^{13} + 3 q^{14} + 9 q^{17} - 6 q^{18} + 9 q^{19} - 6 q^{20} + 6 q^{21} + 3 q^{22} + 15 q^{23} - 6 q^{26} - 3 q^{27} + 6 q^{28} + 3 q^{29} - 3 q^{30}+ \cdots - 12 q^{99}+O(q^{100}) \) 6 * q + 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 15 * q^13 + 3 * q^14 + 9 * q^17 - 6 * q^18 + 9 * q^19 - 6 * q^20 + 6 * q^21 + 3 * q^22 + 15 * q^23 - 6 * q^26 - 3 * q^27 + 6 * q^28 + 3 * q^29 - 3 * q^30 - 18 * q^31 - 12 * q^33 + 9 * q^34 + 3 * q^35 - 42 * q^37 - 18 * q^38 - 12 * q^39 - 12 * q^41 + 3 * q^42 - 15 * q^43 - 3 * q^44 + 3 * q^45 - 15 * q^46 - 24 * q^47 + 12 * q^49 + 3 * q^50 + 3 * q^52 - 18 * q^53 - 15 * q^55 + 6 * q^56 + 18 * q^58 + 3 * q^59 + 21 * q^61 - 3 * q^63 - 3 * q^64 - 6 * q^65 - 15 * q^66 + 30 * q^67 + 6 * q^68 + 15 * q^69 - 3 * q^70 + 42 * q^71 - 3 * q^73 - 9 * q^74 + 6 * q^75 - 6 * q^76 + 24 * q^77 - 12 * q^78 - 39 * q^79 + 12 * q^82 + 15 * q^83 + 3 * q^84 - 9 * q^85 - 3 * q^86 + 9 * q^87 + 3 * q^88 + 3 * q^89 + 15 * q^91 - 3 * q^92 + 9 * q^93 + 42 * q^94 + 18 * q^95 - 6 * q^96 - 18 * q^97 - 3 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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