LMFDB - Embedded newform 418.2.e.a.353.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(45,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("418.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.e (of order $3$, degree $2$, 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:	$3.33774680449$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			353.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	418.353
Dual form			418.2.e.a.45.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} -1.00000 q^{11} +2.00000 q^{12} +(-2.00000 - 3.46410i) q^{13} +(1.50000 - 2.59808i) q^{14} +(-1.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +1.00000 q^{18} +(-0.500000 + 4.33013i) q^{19} +1.00000 q^{20} +(3.00000 - 5.19615i) q^{21} +(0.500000 - 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(2.00000 + 3.46410i) q^{25} +4.00000 q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(-5.00000 - 8.66025i) q^{29} +2.00000 q^{30} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} +(2.00000 + 3.46410i) q^{34} +(1.50000 - 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +3.00000 q^{37} +(-3.50000 - 2.59808i) q^{38} +8.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(3.00000 + 5.19615i) q^{42} +(2.00000 - 3.46410i) q^{43} +(0.500000 + 0.866025i) q^{44} +1.00000 q^{45} +4.00000 q^{46} +(-3.00000 - 5.19615i) q^{47} +(-1.00000 - 1.73205i) q^{48} +2.00000 q^{49} -4.00000 q^{50} +(4.00000 + 6.92820i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(0.500000 + 0.866025i) q^{53} +(2.00000 - 3.46410i) q^{54} +(0.500000 - 0.866025i) q^{55} -3.00000 q^{56} +(-7.00000 - 5.19615i) q^{57} +10.0000 q^{58} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(-6.00000 - 10.3923i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +4.00000 q^{65} +(1.00000 + 1.73205i) q^{66} +(-6.00000 - 10.3923i) q^{67} -4.00000 q^{68} +8.00000 q^{69} +(1.50000 + 2.59808i) q^{70} +(-7.00000 + 12.1244i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-3.00000 + 5.19615i) q^{73} +(-1.50000 + 2.59808i) q^{74} -8.00000 q^{75} +(4.00000 - 1.73205i) q^{76} +3.00000 q^{77} +(-4.00000 + 6.92820i) q^{78} +(-8.50000 + 14.7224i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-3.00000 - 5.19615i) q^{82} -13.0000 q^{83} -6.00000 q^{84} +(2.00000 + 3.46410i) q^{85} +(2.00000 + 3.46410i) q^{86} +20.0000 q^{87} -1.00000 q^{88} +(1.00000 + 1.73205i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(6.00000 + 10.3923i) q^{91} +(-2.00000 + 3.46410i) q^{92} +(-4.00000 + 6.92820i) q^{93} +6.00000 q^{94} +(-3.50000 - 2.59808i) q^{95} +2.00000 q^{96} +(-2.50000 + 4.33013i) q^{97} +(-1.00000 + 1.73205i) q^{98} +(0.500000 + 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} - 6 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 - q^5 - 2 * q^6 - 6 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} - 6 q^{7} + 2 q^{8} - q^{9} - q^{10} - 2 q^{11} + 4 q^{12} - 4 q^{13} + 3 q^{14} - 2 q^{15} - q^{16} + 4 q^{17} + 2 q^{18} - q^{19} + 2 q^{20} + 6 q^{21} + q^{22} - 4 q^{23} - 2 q^{24} + 4 q^{25} + 8 q^{26} - 8 q^{27} + 3 q^{28} - 10 q^{29} + 4 q^{30} + 8 q^{31} - q^{32} + 2 q^{33} + 4 q^{34} + 3 q^{35} - q^{36} + 6 q^{37} - 7 q^{38} + 16 q^{39} - q^{40} - 6 q^{41} + 6 q^{42} + 4 q^{43} + q^{44} + 2 q^{45} + 8 q^{46} - 6 q^{47} - 2 q^{48} + 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{52} + q^{53} + 4 q^{54} + q^{55} - 6 q^{56} - 14 q^{57} + 20 q^{58} - 12 q^{59} - 2 q^{60} - 12 q^{61} - 4 q^{62} + 3 q^{63} + 2 q^{64} + 8 q^{65} + 2 q^{66} - 12 q^{67} - 8 q^{68} + 16 q^{69} + 3 q^{70} - 14 q^{71} - q^{72} - 6 q^{73} - 3 q^{74} - 16 q^{75} + 8 q^{76} + 6 q^{77} - 8 q^{78} - 17 q^{79} - q^{80} + 11 q^{81} - 6 q^{82} - 26 q^{83} - 12 q^{84} + 4 q^{85} + 4 q^{86} + 40 q^{87} - 2 q^{88} + 2 q^{89} - q^{90} + 12 q^{91} - 4 q^{92} - 8 q^{93} + 12 q^{94} - 7 q^{95} + 4 q^{96} - 5 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 - q^5 - 2 * q^6 - 6 * q^7 + 2 * q^8 - q^9 - q^10 - 2 * q^11 + 4 * q^12 - 4 * q^13 + 3 * q^14 - 2 * q^15 - q^16 + 4 * q^17 + 2 * q^18 - q^19 + 2 * q^20 + 6 * q^21 + q^22 - 4 * q^23 - 2 * q^24 + 4 * q^25 + 8 * q^26 - 8 * q^27 + 3 * q^28 - 10 * q^29 + 4 * q^30 + 8 * q^31 - q^32 + 2 * q^33 + 4 * q^34 + 3 * q^35 - q^36 + 6 * q^37 - 7 * q^38 + 16 * q^39 - q^40 - 6 * q^41 + 6 * q^42 + 4 * q^43 + q^44 + 2 * q^45 + 8 * q^46 - 6 * q^47 - 2 * q^48 + 4 * q^49 - 8 * q^50 + 8 * q^51 - 4 * q^52 + q^53 + 4 * q^54 + q^55 - 6 * q^56 - 14 * q^57 + 20 * q^58 - 12 * q^59 - 2 * q^60 - 12 * q^61 - 4 * q^62 + 3 * q^63 + 2 * q^64 + 8 * q^65 + 2 * q^66 - 12 * q^67 - 8 * q^68 + 16 * q^69 + 3 * q^70 - 14 * q^71 - q^72 - 6 * q^73 - 3 * q^74 - 16 * q^75 + 8 * q^76 + 6 * q^77 - 8 * q^78 - 17 * q^79 - q^80 + 11 * q^81 - 6 * q^82 - 26 * q^83 - 12 * q^84 + 4 * q^85 + 4 * q^86 + 40 * q^87 - 2 * q^88 + 2 * q^89 - q^90 + 12 * q^91 - 4 * q^92 - 8 * q^93 + 12 * q^94 - 7 * q^95 + 4 * q^96 - 5 * q^97 - 2 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	−1.00000	−	1.73205i	−0.408248	−	0.707107i
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	2.00000			0.577350
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$	1.50000	−	2.59808i	0.400892	−	0.694365i
$15$	−1.00000	−	1.73205i	−0.258199	−	0.447214i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$	1.00000			0.235702
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$20$	1.00000			0.223607
$21$	3.00000	−	5.19615i	0.654654	−	1.13389i
$22$	0.500000	−	0.866025i	0.106600	−	0.184637i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	−1.00000	+	1.73205i	−0.204124	+	0.353553i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	4.00000			0.784465
$27$	−4.00000			−0.769800
$28$	1.50000	+	2.59808i	0.283473	+	0.490990i
$29$	−5.00000	−	8.66025i	−0.928477	−	1.60817i	−0.785872	−	0.618389i	$-0.787786\pi$
$29$	−5.00000	−	8.66025i	−0.928477	−	1.60817i	−0.142605	−	0.989780i	$-0.545548\pi$
$30$	2.00000			0.365148
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.00000	−	1.73205i	0.174078	−	0.301511i
$34$	2.00000	+	3.46410i	0.342997	+	0.594089i
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	−3.50000	−	2.59808i	−0.567775	−	0.421464i
$39$	8.00000			1.28103
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$	3.00000	+	5.19615i	0.462910	+	0.801784i
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	1.00000			0.149071
$46$	4.00000			0.589768
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$	−1.00000	−	1.73205i	−0.144338	−	0.250000i
$49$	2.00000			0.285714
$50$	−4.00000			−0.565685
$51$	4.00000	+	6.92820i	0.560112	+	0.970143i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	0.898321	−	0.439340i	$-0.144788\pi$
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	−0.829640	+	0.558298i	$0.811454\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$	0.500000	−	0.866025i	0.0674200	−	0.116775i
$56$	−3.00000			−0.400892
$57$	−7.00000	−	5.19615i	−0.927173	−	0.688247i
$58$	10.0000			1.31306
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$	−1.00000	+	1.73205i	−0.129099	+	0.223607i
$61$	−6.00000	−	10.3923i	−0.768221	−	1.33060i	−0.938527	−	0.345207i	$-0.887809\pi$
$61$	−6.00000	−	10.3923i	−0.768221	−	1.33060i	0.170305	−	0.985391i	$-0.445525\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	1.50000	+	2.59808i	0.188982	+	0.327327i
$64$	1.00000			0.125000
$65$	4.00000			0.496139
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$	−4.00000			−0.485071
$69$	8.00000			0.963087
$70$	1.50000	+	2.59808i	0.179284	+	0.310530i
$71$	−7.00000	+	12.1244i	−0.830747	+	1.43890i	0.0666994	+	0.997773i	$0.478753\pi$
$71$	−7.00000	+	12.1244i	−0.830747	+	1.43890i	−0.897447	+	0.441123i	$0.854580\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	0.635323	+	0.772246i	$0.280867\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$	−8.00000			−0.923760
$76$	4.00000	−	1.73205i	0.458831	−	0.198680i
$77$	3.00000			0.341882
$78$	−4.00000	+	6.92820i	−0.452911	+	0.784465i
$79$	−8.50000	+	14.7224i	−0.956325	+	1.65640i	−0.225018	+	0.974355i	$0.572244\pi$
$79$	−8.50000	+	14.7224i	−0.956325	+	1.65640i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	−13.0000			−1.42694			−0.713468	−	0.700688i	$-0.752876\pi$
$83$	−13.0000			−1.42694			−0.713468	+	0.700688i	$0.752876\pi$
$84$	−6.00000			−0.654654
$85$	2.00000	+	3.46410i	0.216930	+	0.375735i
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$	20.0000			2.14423
$88$	−1.00000			−0.106600
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	6.00000	+	10.3923i	0.628971	+	1.08941i
$92$	−2.00000	+	3.46410i	−0.208514	+	0.361158i
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$	6.00000			0.618853
$95$	−3.50000	−	2.59808i	−0.359092	−	0.266557i
$96$	2.00000			0.204124
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	0.710742	+	0.703452i	$0.248359\pi$
$98$	−1.00000	+	1.73205i	−0.101015	+	0.174964i
$99$	0.500000	+	0.866025i	0.0502519	+	0.0870388i
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	−8.00000			−0.792118
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−2.00000	−	3.46410i	−0.196116	−	0.339683i
$105$	3.00000	+	5.19615i	0.292770	+	0.507093i
$106$	−1.00000			−0.0971286
$107$	−7.00000			−0.676716			−0.338358	−	0.941018i	$-0.609871\pi$
$107$	−7.00000			−0.676716			−0.338358	+	0.941018i	$0.609871\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	−0.754204	−	0.656640i	$-0.771977\pi$
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	0.945769	+	0.324840i	$0.105310\pi$
$110$	0.500000	+	0.866025i	0.0476731	+	0.0825723i
$111$	−3.00000	+	5.19615i	−0.284747	+	0.493197i
$112$	1.50000	−	2.59808i	0.141737	−	0.245495i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	8.00000	−	3.46410i	0.749269	−	0.324443i
$115$	4.00000			0.373002
$116$	−5.00000	+	8.66025i	−0.464238	+	0.804084i
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$	−6.00000	−	10.3923i	−0.552345	−	0.956689i
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	1.00000			0.0909091
$122$	12.0000			1.08643
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	−9.00000			−0.804984
$126$	−3.00000			−0.267261
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	0.987108	−	0.160055i	$-0.0511671\pi$
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	−0.632166	+	0.774833i	$0.717834\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$	−2.00000	+	3.46410i	−0.175412	+	0.303822i
$131$	8.00000	−	13.8564i	0.698963	−	1.21064i	−0.269863	−	0.962899i	$-0.586978\pi$
$131$	8.00000	−	13.8564i	0.698963	−	1.21064i	0.968826	−	0.247741i	$-0.0796882\pi$
$132$	−2.00000			−0.174078
$133$	1.50000	−	12.9904i	0.130066	−	1.12641i
$134$	12.0000			1.03664
$135$	2.00000	−	3.46410i	0.172133	−	0.298142i
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	−0.500000	−	0.866025i	−0.0427179	−	0.0739895i	0.843876	−	0.536538i	$-0.180268\pi$
$137$	−0.500000	−	0.866025i	−0.0427179	−	0.0739895i	−0.886594	+	0.462549i	$0.846935\pi$
$138$	−4.00000	+	6.92820i	−0.340503	+	0.589768i
$139$	8.50000	+	14.7224i	0.720961	+	1.24874i	0.960615	+	0.277882i	$0.0896325\pi$
$139$	8.50000	+	14.7224i	0.720961	+	1.24874i	−0.239655	+	0.970858i	$0.577034\pi$
$140$	−3.00000			−0.253546
$141$	12.0000			1.01058
$142$	−7.00000	−	12.1244i	−0.587427	−	1.01745i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$	1.00000			0.0833333
$145$	10.0000			0.830455
$146$	−3.00000	−	5.19615i	−0.248282	−	0.430037i
$147$	−2.00000	+	3.46410i	−0.164957	+	0.285714i
$148$	−1.50000	−	2.59808i	−0.123299	−	0.213561i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	4.00000	−	6.92820i	0.326599	−	0.565685i
$151$	15.0000			1.22068			0.610341	−	0.792139i	$-0.291032\pi$
$151$	15.0000			1.22068			0.610341	+	0.792139i	$0.291032\pi$
$152$	−0.500000	+	4.33013i	−0.0405554	+	0.351220i
$153$	−4.00000			−0.323381
$154$	−1.50000	+	2.59808i	−0.120873	+	0.209359i
$155$	−2.00000	+	3.46410i	−0.160644	+	0.278243i
$156$	−4.00000	−	6.92820i	−0.320256	−	0.554700i
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	−0.948373	−	0.317156i	$-0.897272\pi$
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	0.748852	+	0.662738i	$0.230606\pi$
$158$	−8.50000	−	14.7224i	−0.676224	−	1.17125i
$159$	−2.00000			−0.158610
$160$	1.00000			0.0790569
$161$	6.00000	+	10.3923i	0.472866	+	0.819028i
$162$	5.50000	+	9.52628i	0.432121	+	0.748455i
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	6.00000			0.468521
$165$	1.00000	+	1.73205i	0.0778499	+	0.134840i
$166$	6.50000	−	11.2583i	0.504498	−	0.873816i
$167$	−8.50000	−	14.7224i	−0.657750	−	1.13926i	−0.981197	−	0.193010i	$-0.938175\pi$
$167$	−8.50000	−	14.7224i	−0.657750	−	1.13926i	0.323447	−	0.946246i	$-0.395158\pi$
$168$	3.00000	−	5.19615i	0.231455	−	0.400892i
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	−4.00000			−0.306786
$171$	4.00000	−	1.73205i	0.305888	−	0.132453i
$172$	−4.00000			−0.304997
$173$	2.00000	−	3.46410i	0.152057	−	0.263371i	−0.779926	−	0.625871i	$-0.784744\pi$
$173$	2.00000	−	3.46410i	0.152057	−	0.263371i	0.931984	+	0.362500i	$0.118077\pi$
$174$	−10.0000	+	17.3205i	−0.758098	+	1.31306i
$175$	−6.00000	−	10.3923i	−0.453557	−	0.785584i
$176$	0.500000	−	0.866025i	0.0376889	−	0.0652791i
$177$	−12.0000	−	20.7846i	−0.901975	−	1.56227i
$178$	−2.00000			−0.149906
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	8.50000	+	14.7224i	0.631800	+	1.09431i	0.987184	+	0.159589i	$0.0510169\pi$
$181$	8.50000	+	14.7224i	0.631800	+	1.09431i	−0.355383	+	0.934721i	$0.615650\pi$
$182$	−12.0000			−0.889499
$183$	24.0000			1.77413
$184$	−2.00000	−	3.46410i	−0.147442	−	0.255377i
$185$	−1.50000	+	2.59808i	−0.110282	+	0.191014i
$186$	−4.00000	−	6.92820i	−0.293294	−	0.508001i
$187$	−2.00000	+	3.46410i	−0.146254	+	0.253320i
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$	12.0000			0.872872
$190$	4.00000	−	1.73205i	0.290191	−	0.125656i
$191$	18.0000			1.30243			0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000			1.30243			0.651217	+	0.758891i	$0.274259\pi$
$192$	−1.00000	+	1.73205i	−0.0721688	+	0.125000i
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	−2.50000	−	4.33013i	−0.179490	−	0.310885i
$195$	−4.00000	+	6.92820i	−0.286446	+	0.496139i
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	−1.00000			−0.0710669
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	24.0000			1.69283
$202$		0			0
$203$	15.0000	+	25.9808i	1.05279	+	1.82349i
$204$	4.00000	−	6.92820i	0.280056	−	0.485071i
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$		0			0
$207$	−2.00000	+	3.46410i	−0.139010	+	0.240772i
$208$	4.00000			0.277350
$209$	0.500000	−	4.33013i	0.0345857	−	0.299521i
$210$	−6.00000			−0.414039
$211$	11.5000	−	19.9186i	0.791693	−	1.37125i	−0.133226	−	0.991086i	$-0.542533\pi$
$211$	11.5000	−	19.9186i	0.791693	−	1.37125i	0.924918	−	0.380166i	$-0.124133\pi$
$212$	0.500000	−	0.866025i	0.0343401	−	0.0594789i
$213$	−14.0000	−	24.2487i	−0.959264	−	1.66149i
$214$	3.50000	−	6.06218i	0.239255	−	0.414402i
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$	−4.00000			−0.272166
$217$	−12.0000			−0.814613
$218$	2.00000	+	3.46410i	0.135457	+	0.234619i
$219$	−6.00000	−	10.3923i	−0.405442	−	0.702247i
$220$	−1.00000			−0.0674200
$221$	−16.0000			−1.07628
$222$	−3.00000	−	5.19615i	−0.201347	−	0.348743i
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	0.463409	+	0.886145i	$0.346626\pi$
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	−0.999128	+	0.0417488i	$0.986707\pi$
$224$	1.50000	+	2.59808i	0.100223	+	0.173591i
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	−3.00000			−0.199117			−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000			−0.199117			−0.0995585	+	0.995032i	$0.531743\pi$
$228$	−1.00000	+	8.66025i	−0.0662266	+	0.573539i
$229$	−13.0000			−0.859064			−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000			−0.859064			−0.429532	+	0.903052i	$0.641321\pi$
$230$	−2.00000	+	3.46410i	−0.131876	+	0.228416i
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$	−5.00000	−	8.66025i	−0.328266	−	0.568574i
$233$	8.00000	−	13.8564i	0.524097	−	0.907763i	−0.475509	−	0.879711i	$-0.657736\pi$
$233$	8.00000	−	13.8564i	0.524097	−	0.907763i	0.999606	−	0.0280525i	$-0.00893057\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	6.00000			0.391397
$236$	12.0000			0.781133
$237$	−17.0000	−	29.4449i	−1.10427	−	1.91265i
$238$	−6.00000	−	10.3923i	−0.388922	−	0.673633i
$239$	−5.00000			−0.323423			−0.161712	−	0.986838i	$-0.551701\pi$
$239$	−5.00000			−0.323423			−0.161712	+	0.986838i	$0.551701\pi$
$240$	2.00000			0.129099
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	−6.00000	+	10.3923i	−0.384111	+	0.665299i
$245$	−1.00000	+	1.73205i	−0.0638877	+	0.110657i
$246$	12.0000			0.765092
$247$	16.0000	−	6.92820i	1.01806	−	0.440831i
$248$	4.00000			0.254000
$249$	13.0000	−	22.5167i	0.823842	−	1.42694i
$250$	4.50000	−	7.79423i	0.284605	−	0.492950i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$	1.50000	−	2.59808i	0.0944911	−	0.163663i
$253$	2.00000	+	3.46410i	0.125739	+	0.217786i
$254$	−8.00000			−0.501965
$255$	−8.00000			−0.500979
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.500000	+	0.866025i	0.0311891	+	0.0540212i	0.881199	−	0.472746i	$-0.156737\pi$
$257$	0.500000	+	0.866025i	0.0311891	+	0.0540212i	−0.850010	+	0.526767i	$0.823404\pi$
$258$	−8.00000			−0.498058
$259$	−9.00000			−0.559233
$260$	−2.00000	−	3.46410i	−0.124035	−	0.214834i
$261$	−5.00000	+	8.66025i	−0.309492	+	0.536056i
$262$	8.00000	+	13.8564i	0.494242	+	0.856052i
$263$	11.5000	−	19.9186i	0.709120	−	1.22823i	−0.256063	−	0.966660i	$-0.582426\pi$
$263$	11.5000	−	19.9186i	0.709120	−	1.22823i	0.965184	−	0.261573i	$-0.0842411\pi$
$264$	1.00000	−	1.73205i	0.0615457	−	0.106600i
$265$	−1.00000			−0.0614295
$266$	10.5000	+	7.79423i	0.643796	+	0.477895i
$267$	−4.00000			−0.244796
$268$	−6.00000	+	10.3923i	−0.366508	+	0.634811i
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	−0.998816	−	0.0486418i	$-0.984511\pi$
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	0.541533	+	0.840679i	$0.317844\pi$
$270$	2.00000	+	3.46410i	0.121716	+	0.210819i
$271$	10.5000	−	18.1865i	0.637830	−	1.10475i	−0.348079	−	0.937465i	$-0.613166\pi$
$271$	10.5000	−	18.1865i	0.637830	−	1.10475i	0.985908	−	0.167288i	$-0.0535009\pi$
$272$	2.00000	+	3.46410i	0.121268	+	0.210042i
$273$	−24.0000			−1.45255
$274$	1.00000			0.0604122
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	−4.00000			−0.240337			−0.120168	−	0.992754i	$-0.538343\pi$
$277$	−4.00000			−0.240337			−0.120168	+	0.992754i	$0.538343\pi$
$278$	−17.0000			−1.01959
$279$	−2.00000	−	3.46410i	−0.119737	−	0.207390i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	−2.00000	−	3.46410i	−0.119310	−	0.206651i	0.800184	−	0.599754i	$-0.204735\pi$
$281$	−2.00000	−	3.46410i	−0.119310	−	0.206651i	−0.919494	+	0.393103i	$0.871402\pi$
$282$	−6.00000	+	10.3923i	−0.357295	+	0.618853i
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	−0.991960	−	0.126550i	$-0.959610\pi$
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	0.605575	+	0.795788i	$0.292943\pi$
$284$	14.0000			0.830747
$285$	8.00000	−	3.46410i	0.473879	−	0.205196i
$286$	−4.00000			−0.236525
$287$	9.00000	−	15.5885i	0.531253	−	0.920158i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−5.00000	+	8.66025i	−0.293610	+	0.508548i
$291$	−5.00000	−	8.66025i	−0.293105	−	0.507673i
$292$	6.00000			0.351123
$293$	30.0000			1.75262			0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000			1.75262			0.876309	+	0.481749i	$0.159998\pi$
$294$	−2.00000	−	3.46410i	−0.116642	−	0.202031i
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$	3.00000			0.174371
$297$	4.00000			0.232104
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	−8.00000	+	13.8564i	−0.462652	+	0.801337i
$300$	4.00000	+	6.92820i	0.230940	+	0.400000i
$301$	−6.00000	+	10.3923i	−0.345834	+	0.599002i
$302$	−7.50000	+	12.9904i	−0.431577	+	0.747512i
$303$		0			0
$304$	−3.50000	−	2.59808i	−0.200739	−	0.149010i
$305$	12.0000			0.687118
$306$	2.00000	−	3.46410i	0.114332	−	0.198030i
$307$	−14.5000	+	25.1147i	−0.827559	+	1.43337i	0.0723893	+	0.997376i	$0.476938\pi$
$307$	−14.5000	+	25.1147i	−0.827559	+	1.43337i	−0.899948	+	0.435997i	$0.856396\pi$
$308$	−1.50000	−	2.59808i	−0.0854704	−	0.148039i
$309$		0			0
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$	8.00000			0.452911
$313$	4.50000	+	7.79423i	0.254355	+	0.440556i	0.964720	−	0.263278i	$-0.0848035\pi$
$313$	4.50000	+	7.79423i	0.254355	+	0.440556i	−0.710365	+	0.703833i	$0.751470\pi$
$314$	−2.50000	−	4.33013i	−0.141083	−	0.244363i
$315$	−3.00000			−0.169031
$316$	17.0000			0.956325
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$	1.00000	−	1.73205i	0.0560772	−	0.0971286i
$319$	5.00000	+	8.66025i	0.279946	+	0.484881i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	7.00000	−	12.1244i	0.390702	−	0.676716i
$322$	−12.0000			−0.668734
$323$	14.0000	+	10.3923i	0.778981	+	0.578243i
$324$	−11.0000			−0.611111
$325$	8.00000	−	13.8564i	0.443760	−	0.768615i
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$	4.00000	+	6.92820i	0.221201	+	0.383131i
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	9.00000	+	15.5885i	0.496186	+	0.859419i
$330$	−2.00000			−0.110096
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	6.50000	+	11.2583i	0.356734	+	0.617881i
$333$	−1.50000	−	2.59808i	−0.0821995	−	0.142374i
$334$	17.0000			0.930199
$335$	12.0000			0.655630
$336$	3.00000	+	5.19615i	0.163663	+	0.283473i
$337$	−14.0000	+	24.2487i	−0.762629	+	1.32091i	0.178863	+	0.983874i	$0.442758\pi$
$337$	−14.0000	+	24.2487i	−0.762629	+	1.32091i	−0.941491	+	0.337037i	$0.890575\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$	6.00000	−	10.3923i	0.325875	−	0.564433i
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	−4.00000			−0.216612
$342$	−0.500000	+	4.33013i	−0.0270369	+	0.234146i
$343$	15.0000			0.809924
$344$	2.00000	−	3.46410i	0.107833	−	0.186772i
$345$	−4.00000	+	6.92820i	−0.215353	+	0.373002i
$346$	2.00000	+	3.46410i	0.107521	+	0.186231i
$347$	−6.50000	+	11.2583i	−0.348938	+	0.604379i	−0.986061	−	0.166383i	$-0.946791\pi$
$347$	−6.50000	+	11.2583i	−0.348938	+	0.604379i	0.637123	+	0.770762i	$0.280124\pi$
$348$	−10.0000	−	17.3205i	−0.536056	−	0.928477i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$	12.0000			0.641427
$351$	8.00000	+	13.8564i	0.427008	+	0.739600i
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	19.0000			1.01127			0.505634	−	0.862748i	$-0.331259\pi$
$353$	19.0000			1.01127			0.505634	+	0.862748i	$0.331259\pi$
$354$	24.0000			1.27559
$355$	−7.00000	−	12.1244i	−0.371521	−	0.643494i
$356$	1.00000	−	1.73205i	0.0529999	−	0.0917985i
$357$	−12.0000	−	20.7846i	−0.635107	−	1.10004i
$358$	10.0000	−	17.3205i	0.528516	−	0.915417i
$359$	−3.50000	+	6.06218i	−0.184723	+	0.319950i	−0.943483	−	0.331421i	$-0.892472\pi$
$359$	−3.50000	+	6.06218i	−0.184723	+	0.319950i	0.758760	+	0.651370i	$0.225805\pi$
$360$	1.00000			0.0527046
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$	−17.0000			−0.893500
$363$	−1.00000	+	1.73205i	−0.0524864	+	0.0909091i
$364$	6.00000	−	10.3923i	0.314485	−	0.544705i
$365$	−3.00000	−	5.19615i	−0.157027	−	0.271979i
$366$	−12.0000	+	20.7846i	−0.627250	+	1.08643i
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$	4.00000			0.208514
$369$	6.00000			0.312348
$370$	−1.50000	−	2.59808i	−0.0779813	−	0.135068i
$371$	−1.50000	−	2.59808i	−0.0778761	−	0.134885i
$372$	8.00000			0.414781
$373$	−28.0000			−1.44979			−0.724893	−	0.688862i	$-0.758111\pi$
$373$	−28.0000			−1.44979			−0.724893	+	0.688862i	$0.758111\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$	9.00000	−	15.5885i	0.464758	−	0.804984i
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	−20.0000	+	34.6410i	−1.03005	+	1.78410i
$378$	−6.00000	+	10.3923i	−0.308607	+	0.534522i
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$	−0.500000	+	4.33013i	−0.0256495	+	0.222131i
$381$	−16.0000			−0.819705
$382$	−9.00000	+	15.5885i	−0.460480	+	0.797575i
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	−0.949938	−	0.312437i	$-0.898855\pi$
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	0.745548	+	0.666452i	$0.232188\pi$
$384$	−1.00000	−	1.73205i	−0.0510310	−	0.0883883i
$385$	−1.50000	+	2.59808i	−0.0764471	+	0.132410i
$386$	5.00000	+	8.66025i	0.254493	+	0.440795i
$387$	−4.00000			−0.203331
$388$	5.00000			0.253837
$389$	−10.5000	−	18.1865i	−0.532371	−	0.922094i	−0.999286	−	0.0377914i	$-0.987968\pi$
$389$	−10.5000	−	18.1865i	−0.532371	−	0.922094i	0.466915	−	0.884302i	$-0.345366\pi$
$390$	−4.00000	−	6.92820i	−0.202548	−	0.350823i
$391$	−16.0000			−0.809155
$392$	2.00000			0.101015
$393$	16.0000	+	27.7128i	0.807093	+	1.39793i
$394$	6.00000	−	10.3923i	0.302276	−	0.523557i
$395$	−8.50000	−	14.7224i	−0.427681	−	0.740766i
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	−12.5000	+	21.6506i	−0.627357	+	1.08661i	0.360723	+	0.932673i	$0.382530\pi$
$397$	−12.5000	+	21.6506i	−0.627357	+	1.08661i	−0.988080	+	0.153941i	$0.950803\pi$
$398$	−10.0000			−0.501255
$399$	21.0000	+	15.5885i	1.05131	+	0.780399i
$400$	−4.00000			−0.200000
$401$	−5.00000	+	8.66025i	−0.249688	+	0.432472i	−0.963439	−	0.267927i	$-0.913661\pi$
$401$	−5.00000	+	8.66025i	−0.249688	+	0.432472i	0.713751	+	0.700399i	$0.246995\pi$
$402$	−12.0000	+	20.7846i	−0.598506	+	1.03664i
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$		0			0
$405$	5.50000	+	9.52628i	0.273297	+	0.473365i
$406$	−30.0000			−1.48888
$407$	−3.00000			−0.148704
$408$	4.00000	+	6.92820i	0.198030	+	0.342997i
$409$	10.0000	+	17.3205i	0.494468	+	0.856444i	0.999980	−	0.00637586i	$-0.00202951\pi$
$409$	10.0000	+	17.3205i	0.494468	+	0.856444i	−0.505511	+	0.862820i	$0.668696\pi$
$410$	6.00000			0.296319
$411$	2.00000			0.0986527
$412$		0			0
$413$	18.0000	−	31.1769i	0.885722	−	1.53412i
$414$	−2.00000	−	3.46410i	−0.0982946	−	0.170251i
$415$	6.50000	−	11.2583i	0.319072	−	0.552650i
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	−34.0000			−1.66499
$418$	3.50000	+	2.59808i	0.171191	+	0.127076i
$419$	−38.0000			−1.85642			−0.928211	−	0.372055i	$-0.878653\pi$
$419$	−38.0000			−1.85642			−0.928211	+	0.372055i	$0.878653\pi$
$420$	3.00000	−	5.19615i	0.146385	−	0.253546i
$421$	1.50000	−	2.59808i	0.0731055	−	0.126622i	−0.827155	−	0.561973i	$-0.810042\pi$
$421$	1.50000	−	2.59808i	0.0731055	−	0.126622i	0.900261	+	0.435351i	$0.143376\pi$
$422$	11.5000	+	19.9186i	0.559811	+	0.969622i
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$	0.500000	+	0.866025i	0.0242821	+	0.0420579i
$425$	16.0000			0.776114
$426$	28.0000			1.35660
$427$	18.0000	+	31.1769i	0.871081	+	1.50876i
$428$	3.50000	+	6.06218i	0.169179	+	0.293026i
$429$	−8.00000			−0.386244
$430$	−4.00000			−0.192897
$431$	−6.50000	−	11.2583i	−0.313094	−	0.542295i	0.665937	−	0.746008i	$-0.268032\pi$
$431$	−6.50000	−	11.2583i	−0.313094	−	0.542295i	−0.979030	+	0.203714i	$0.934699\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	9.00000	+	15.5885i	0.432512	+	0.749133i	0.997089	−	0.0762473i	$-0.0242938\pi$
$433$	9.00000	+	15.5885i	0.432512	+	0.749133i	−0.564577	+	0.825381i	$0.690961\pi$
$434$	6.00000	−	10.3923i	0.288009	−	0.498847i
$435$	−10.0000	+	17.3205i	−0.479463	+	0.830455i
$436$	−4.00000			−0.191565
$437$	16.0000	−	6.92820i	0.765384	−	0.331421i
$438$	12.0000			0.573382
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	−0.877711	−	0.479191i	$-0.840930\pi$
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	0.853847	+	0.520524i	$0.174263\pi$
$440$	0.500000	−	0.866025i	0.0238366	−	0.0412861i
$441$	−1.00000	−	1.73205i	−0.0476190	−	0.0824786i
$442$	8.00000	−	13.8564i	0.380521	−	0.659082i
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$	6.00000			0.284747
$445$	−2.00000			−0.0948091
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$	6.00000	+	10.3923i	0.283790	+	0.491539i
$448$	−3.00000			−0.141737
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$	2.00000	+	3.46410i	0.0942809	+	0.163299i
$451$	3.00000	−	5.19615i	0.141264	−	0.244677i
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	−15.0000	+	25.9808i	−0.704761	+	1.22068i
$454$	1.50000	−	2.59808i	0.0703985	−	0.121934i
$455$	−12.0000			−0.562569
$456$	−7.00000	−	5.19615i	−0.327805	−	0.243332i
$457$	38.0000			1.77757			0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000			1.77757			0.888783	+	0.458329i	$0.151552\pi$
$458$	6.50000	−	11.2583i	0.303725	−	0.526067i
$459$	−8.00000	+	13.8564i	−0.373408	+	0.646762i
$460$	−2.00000	−	3.46410i	−0.0932505	−	0.161515i
$461$	1.00000	−	1.73205i	0.0465746	−	0.0806696i	−0.841798	−	0.539792i	$-0.818503\pi$
$461$	1.00000	−	1.73205i	0.0465746	−	0.0806696i	0.888373	+	0.459123i	$0.151836\pi$
$462$	−3.00000	−	5.19615i	−0.139573	−	0.241747i
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	10.0000			0.464238
$465$	−4.00000	−	6.92820i	−0.185496	−	0.321288i
$466$	8.00000	+	13.8564i	0.370593	+	0.641886i
$467$	14.0000			0.647843			0.323921	−	0.946084i	$-0.394999\pi$
$467$	14.0000			0.647843			0.323921	+	0.946084i	$0.394999\pi$
$468$	4.00000			0.184900
$469$	18.0000	+	31.1769i	0.831163	+	1.43962i
$470$	−3.00000	+	5.19615i	−0.138380	+	0.239681i
$471$	−5.00000	−	8.66025i	−0.230388	−	0.399043i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	−2.00000	+	3.46410i	−0.0919601	+	0.159280i
$474$	34.0000			1.56167
$475$	−16.0000	+	6.92820i	−0.734130	+	0.317888i
$476$	12.0000			0.550019
$477$	0.500000	−	0.866025i	0.0228934	−	0.0396526i
$478$	2.50000	−	4.33013i	0.114347	−	0.198055i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	−1.00000	+	1.73205i	−0.0456435	+	0.0790569i
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	−10.0000			−0.455488
$483$	−24.0000			−1.09204
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	−2.50000	−	4.33013i	−0.113519	−	0.196621i
$486$	−10.0000			−0.453609
$487$	18.0000			0.815658			0.407829	−	0.913058i	$-0.366286\pi$
$487$	18.0000			0.815658			0.407829	+	0.913058i	$0.366286\pi$
$488$	−6.00000	−	10.3923i	−0.271607	−	0.470438i
$489$	−4.00000	+	6.92820i	−0.180886	+	0.313304i
$490$	−1.00000	−	1.73205i	−0.0451754	−	0.0782461i
$491$	−0.500000	+	0.866025i	−0.0225647	+	0.0390832i	−0.877087	−	0.480331i	$-0.840517\pi$
$491$	−0.500000	+	0.866025i	−0.0225647	+	0.0390832i	0.854523	+	0.519414i	$0.173850\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$	−40.0000			−1.80151
$494$	−2.00000	+	17.3205i	−0.0899843	+	0.779287i
$495$	−1.00000			−0.0449467
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	21.0000	−	36.3731i	0.941979	−	1.63156i
$498$	13.0000	+	22.5167i	0.582544	+	1.00900i
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.0619186	−	0.998081i	$-0.480278\pi$
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.833404	−	0.552664i	$-0.186389\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$	34.0000			1.51901
$502$		0			0
$503$	−4.00000	−	6.92820i	−0.178351	−	0.308913i	0.762965	−	0.646440i	$-0.223743\pi$
$503$	−4.00000	−	6.92820i	−0.178351	−	0.308913i	−0.941316	+	0.337527i	$0.890410\pi$
$504$	1.50000	+	2.59808i	0.0668153	+	0.115728i
$505$		0			0
$506$	−4.00000			−0.177822
$507$	−3.00000	−	5.19615i	−0.133235	−	0.230769i
$508$	4.00000	−	6.92820i	0.177471	−	0.307389i
$509$	6.50000	+	11.2583i	0.288107	+	0.499017i	0.973358	−	0.229291i	$-0.0736406\pi$
$509$	6.50000	+	11.2583i	0.288107	+	0.499017i	−0.685251	+	0.728307i	$0.740307\pi$
$510$	4.00000	−	6.92820i	0.177123	−	0.306786i
$511$	9.00000	−	15.5885i	0.398137	−	0.689593i
$512$	1.00000			0.0441942
$513$	2.00000	−	17.3205i	0.0883022	−	0.764719i
$514$	−1.00000			−0.0441081
$515$		0			0
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$	3.00000	+	5.19615i	0.131940	+	0.228527i
$518$	4.50000	−	7.79423i	0.197719	−	0.342459i
$519$	4.00000	+	6.92820i	0.175581	+	0.304114i
$520$	4.00000			0.175412
$521$	25.0000			1.09527			0.547635	−	0.836717i	$-0.315528\pi$
$521$	25.0000			1.09527			0.547635	+	0.836717i	$0.315528\pi$
$522$	−5.00000	−	8.66025i	−0.218844	−	0.379049i
$523$	−4.50000	−	7.79423i	−0.196771	−	0.340818i	0.750708	−	0.660634i	$-0.229712\pi$
$523$	−4.50000	−	7.79423i	−0.196771	−	0.340818i	−0.947480	+	0.319816i	$0.896379\pi$
$524$	−16.0000			−0.698963
$525$	24.0000			1.04745
$526$	11.5000	+	19.9186i	0.501424	+	0.868492i
$527$	8.00000	−	13.8564i	0.348485	−	0.603595i
$528$	1.00000	+	1.73205i	0.0435194	+	0.0753778i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	0.500000	−	0.866025i	0.0217186	−	0.0376177i
$531$	12.0000			0.520756
$532$	−12.0000	+	5.19615i	−0.520266	+	0.225282i
$533$	24.0000			1.03956
$534$	2.00000	−	3.46410i	0.0865485	−	0.149906i
$535$	3.50000	−	6.06218i	0.151318	−	0.262091i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	20.0000	−	34.6410i	0.863064	−	1.49487i
$538$	−7.50000	−	12.9904i	−0.323348	−	0.560055i
$539$	−2.00000			−0.0861461
$540$	−4.00000			−0.172133
$541$	11.0000	+	19.0526i	0.472927	+	0.819133i	0.999520	−	0.0309841i	$-0.00986412\pi$
$541$	11.0000	+	19.0526i	0.472927	+	0.819133i	−0.526593	+	0.850118i	$0.676531\pi$
$542$	10.5000	+	18.1865i	0.451014	+	0.781179i
$543$	−34.0000			−1.45908
$544$	−4.00000			−0.171499
$545$	2.00000	+	3.46410i	0.0856706	+	0.148386i
$546$	12.0000	−	20.7846i	0.513553	−	0.889499i
$547$	−17.5000	−	30.3109i	−0.748246	−	1.29600i	−0.948663	−	0.316289i	$-0.897563\pi$
$547$	−17.5000	−	30.3109i	−0.748246	−	1.29600i	0.200417	−	0.979711i	$-0.435770\pi$
$548$	−0.500000	+	0.866025i	−0.0213589	+	0.0369948i
$549$	−6.00000	+	10.3923i	−0.256074	+	0.443533i
$550$	4.00000			0.170561
$551$	40.0000	−	17.3205i	1.70406	−	0.737878i
$552$	8.00000			0.340503
$553$	25.5000	−	44.1673i	1.08437	−	1.87818i
$554$	2.00000	−	3.46410i	0.0849719	−	0.147176i
$555$	−3.00000	−	5.19615i	−0.127343	−	0.220564i
$556$	8.50000	−	14.7224i	0.360480	−	0.624370i
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	0.964686	−	0.263404i	$-0.0848453\pi$
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	−0.710457	+	0.703740i	$0.751512\pi$
$558$	4.00000			0.169334
$559$	−16.0000			−0.676728
$560$	1.50000	+	2.59808i	0.0633866	+	0.109789i
$561$	−4.00000	−	6.92820i	−0.168880	−	0.292509i
$562$	4.00000			0.168730
$563$	−33.0000			−1.39078			−0.695392	−	0.718631i	$-0.744769\pi$
$563$	−33.0000			−1.39078			−0.695392	+	0.718631i	$0.744769\pi$
$564$	−6.00000	−	10.3923i	−0.252646	−	0.437595i
$565$	3.00000	−	5.19615i	0.126211	−	0.218604i
$566$	−6.50000	−	11.2583i	−0.273215	−	0.473223i
$567$	−16.5000	+	28.5788i	−0.692935	+	1.20020i
$568$	−7.00000	+	12.1244i	−0.293713	+	0.508727i
$569$	−36.0000			−1.50920			−0.754599	−	0.656186i	$-0.772169\pi$
$569$	−36.0000			−1.50920			−0.754599	+	0.656186i	$0.772169\pi$
$570$	−1.00000	+	8.66025i	−0.0418854	+	0.362738i
$571$	19.0000			0.795125			0.397563	−	0.917575i	$-0.369856\pi$
$571$	19.0000			0.795125			0.397563	+	0.917575i	$0.369856\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	−18.0000	+	31.1769i	−0.751961	+	1.30243i
$574$	9.00000	+	15.5885i	0.375653	+	0.650650i
$575$	8.00000	−	13.8564i	0.333623	−	0.577852i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	17.0000			0.707719			0.353860	−	0.935299i	$-0.384869\pi$
$577$	17.0000			0.707719			0.353860	+	0.935299i	$0.384869\pi$
$578$	−1.00000			−0.0415945
$579$	10.0000	+	17.3205i	0.415586	+	0.719816i
$580$	−5.00000	−	8.66025i	−0.207614	−	0.359597i
$581$	39.0000			1.61799
$582$	10.0000			0.414513
$583$	−0.500000	−	0.866025i	−0.0207079	−	0.0358671i
$584$	−3.00000	+	5.19615i	−0.124141	+	0.215018i
$585$	−2.00000	−	3.46410i	−0.0826898	−	0.143223i
$586$	−15.0000	+	25.9808i	−0.619644	+	1.07326i
$587$	−12.0000	+	20.7846i	−0.495293	+	0.857873i	−0.999985	−	0.00542667i	$-0.998273\pi$
$587$	−12.0000	+	20.7846i	−0.495293	+	0.857873i	0.504692	+	0.863299i	$0.331606\pi$
$588$	4.00000			0.164957
$589$	−2.00000	+	17.3205i	−0.0824086	+	0.713679i
$590$	12.0000			0.494032
$591$	12.0000	−	20.7846i	0.493614	−	0.854965i
$592$	−1.50000	+	2.59808i	−0.0616496	+	0.106780i
$593$	6.00000	+	10.3923i	0.246390	+	0.426761i	0.962522	−	0.271205i	$-0.0874221\pi$
$593$	6.00000	+	10.3923i	0.246390	+	0.426761i	−0.716131	+	0.697966i	$0.754089\pi$
$594$	−2.00000	+	3.46410i	−0.0820610	+	0.142134i
$595$	−6.00000	−	10.3923i	−0.245976	−	0.426043i
$596$	−6.00000			−0.245770
$597$	−20.0000			−0.818546
$598$	−8.00000	−	13.8564i	−0.327144	−	0.566631i
$599$	−16.0000	−	27.7128i	−0.653742	−	1.13231i	−0.982208	−	0.187799i	$-0.939865\pi$
$599$	−16.0000	−	27.7128i	−0.653742	−	1.13231i	0.328465	−	0.944516i	$-0.393469\pi$
$600$	−8.00000			−0.326599
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	−6.00000	−	10.3923i	−0.244542	−	0.423559i
$603$	−6.00000	+	10.3923i	−0.244339	+	0.423207i
$604$	−7.50000	−	12.9904i	−0.305171	−	0.528571i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$		0			0
$607$	−40.0000			−1.62355			−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000			−1.62355			−0.811775	+	0.583970i	$0.801498\pi$
$608$	4.00000	−	1.73205i	0.162221	−	0.0702439i
$609$	−60.0000			−2.43132
$610$	−6.00000	+	10.3923i	−0.242933	+	0.420772i
$611$	−12.0000	+	20.7846i	−0.485468	+	0.840855i
$612$	2.00000	+	3.46410i	0.0808452	+	0.140028i
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	−0.658012	−	0.753007i	$-0.728603\pi$
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	0.981129	+	0.193352i	$0.0619359\pi$
$614$	−14.5000	−	25.1147i	−0.585172	−	1.01355i
$615$	12.0000			0.483887
$616$	3.00000			0.120873
$617$	−16.5000	−	28.5788i	−0.664265	−	1.15054i	−0.979484	−	0.201522i	$-0.935411\pi$
$617$	−16.5000	−	28.5788i	−0.664265	−	1.15054i	0.315219	−	0.949019i	$-0.397922\pi$
$618$		0			0
$619$	−32.0000			−1.28619			−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000			−1.28619			−0.643094	+	0.765787i	$0.722350\pi$
$620$	4.00000			0.160644
$621$	8.00000	+	13.8564i	0.321029	+	0.556038i
$622$	9.00000	−	15.5885i	0.360867	−	0.625040i
$623$	−3.00000	−	5.19615i	−0.120192	−	0.208179i
$624$	−4.00000	+	6.92820i	−0.160128	+	0.277350i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−9.00000			−0.359712
$627$	7.00000	+	5.19615i	0.279553	+	0.207514i
$628$	5.00000			0.199522
$629$	6.00000	−	10.3923i	0.239236	−	0.414368i
$630$	1.50000	−	2.59808i	0.0597614	−	0.103510i
$631$	−20.0000	−	34.6410i	−0.796187	−	1.37904i	−0.922082	−	0.386994i	$-0.873514\pi$
$631$	−20.0000	−	34.6410i	−0.796187	−	1.37904i	0.125895	−	0.992044i	$-0.459820\pi$
$632$	−8.50000	+	14.7224i	−0.338112	+	0.585627i
$633$	23.0000	+	39.8372i	0.914168	+	1.58339i
$634$	−18.0000			−0.714871
$635$	−8.00000			−0.317470
$636$	1.00000	+	1.73205i	0.0396526	+	0.0686803i
$637$	−4.00000	−	6.92820i	−0.158486	−	0.274505i
$638$	−10.0000			−0.395904
$639$	14.0000			0.553831
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	20.5000	−	35.5070i	0.809701	−	1.40244i	−0.103370	−	0.994643i	$-0.532962\pi$
$641$	20.5000	−	35.5070i	0.809701	−	1.40244i	0.913071	−	0.407801i	$-0.133704\pi$
$642$	7.00000	+	12.1244i	0.276268	+	0.478510i
$643$	13.0000	−	22.5167i	0.512670	−	0.887970i	−0.487222	−	0.873278i	$-0.661990\pi$
$643$	13.0000	−	22.5167i	0.512670	−	0.887970i	0.999892	−	0.0146923i	$-0.00467688\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$	−8.00000			−0.315000
$646$	−16.0000	+	6.92820i	−0.629512	+	0.272587i
$647$	42.0000			1.65119			0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000			1.65119			0.825595	+	0.564263i	$0.190840\pi$
$648$	5.50000	−	9.52628i	0.216060	−	0.374228i
$649$	6.00000	−	10.3923i	0.235521	−	0.407934i
$650$	8.00000	+	13.8564i	0.313786	+	0.543493i
$651$	12.0000	−	20.7846i	0.470317	−	0.814613i
$652$	−2.00000	−	3.46410i	−0.0783260	−	0.135665i
$653$	10.0000			0.391330			0.195665	−	0.980671i	$-0.437313\pi$
$653$	10.0000			0.391330			0.195665	+	0.980671i	$0.437313\pi$
$654$	−8.00000			−0.312825
$655$	8.00000	+	13.8564i	0.312586	+	0.541415i
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	6.00000			0.234082
$658$	−18.0000			−0.701713
$659$	15.5000	+	26.8468i	0.603794	+	1.04580i	0.992241	+	0.124331i	$0.0396785\pi$
$659$	15.5000	+	26.8468i	0.603794	+	1.04580i	−0.388447	+	0.921471i	$0.626988\pi$
$660$	1.00000	−	1.73205i	0.0389249	−	0.0674200i
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$	−10.0000	+	17.3205i	−0.388661	+	0.673181i
$663$	16.0000	−	27.7128i	0.621389	−	1.07628i
$664$	−13.0000			−0.504498
$665$	10.5000	+	7.79423i	0.407173	+	0.302247i
$666$	3.00000			0.116248
$667$	−20.0000	+	34.6410i	−0.774403	+	1.34131i
$668$	−8.50000	+	14.7224i	−0.328875	+	0.569628i
$669$	−16.0000	−	27.7128i	−0.618596	−	1.07144i
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	6.00000	+	10.3923i	0.231627	+	0.401190i
$672$	−6.00000			−0.231455
$673$	−42.0000			−1.61898			−0.809491	−	0.587133i	$-0.800257\pi$
$673$	−42.0000			−1.61898			−0.809491	+	0.587133i	$0.800257\pi$
$674$	−14.0000	−	24.2487i	−0.539260	−	0.934025i
$675$	−8.00000	−	13.8564i	−0.307920	−	0.533333i
$676$	3.00000			0.115385
$677$	−38.0000			−1.46046			−0.730229	−	0.683202i	$-0.760587\pi$
$677$	−38.0000			−1.46046			−0.730229	+	0.683202i	$0.760587\pi$
$678$	6.00000	+	10.3923i	0.230429	+	0.399114i
$679$	7.50000	−	12.9904i	0.287824	−	0.498525i
$680$	2.00000	+	3.46410i	0.0766965	+	0.132842i
$681$	3.00000	−	5.19615i	0.114960	−	0.199117i
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	−2.00000			−0.0765279			−0.0382639	−	0.999268i	$-0.512183\pi$
$683$	−2.00000			−0.0765279			−0.0382639	+	0.999268i	$0.512183\pi$
$684$	−3.50000	−	2.59808i	−0.133826	−	0.0993399i
$685$	1.00000			0.0382080
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$	13.0000	−	22.5167i	0.495981	−	0.859064i
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	2.00000	−	3.46410i	0.0761939	−	0.131972i
$690$	−4.00000	−	6.92820i	−0.152277	−	0.263752i
$691$	16.0000			0.608669			0.304334	−	0.952565i	$-0.401566\pi$
$691$	16.0000			0.608669			0.304334	+	0.952565i	$0.401566\pi$
$692$	−4.00000			−0.152057
$693$	−1.50000	−	2.59808i	−0.0569803	−	0.0986928i
$694$	−6.50000	−	11.2583i	−0.246737	−	0.427360i
$695$	−17.0000			−0.644847
$696$	20.0000			0.758098
$697$	12.0000	+	20.7846i	0.454532	+	0.787273i
$698$	13.0000	−	22.5167i	0.492057	−	0.852268i
$699$	16.0000	+	27.7128i	0.605176	+	1.04819i
$700$	−6.00000	+	10.3923i	−0.226779	+	0.392792i
$701$	−6.00000	+	10.3923i	−0.226617	+	0.392512i	−0.956803	−	0.290736i	$-0.906100\pi$
$701$	−6.00000	+	10.3923i	−0.226617	+	0.392512i	0.730186	+	0.683248i	$0.239433\pi$
$702$	−16.0000			−0.603881
$703$	−1.50000	+	12.9904i	−0.0565736	+	0.489942i
$704$	−1.00000			−0.0376889
$705$	−6.00000	+	10.3923i	−0.225973	+	0.391397i
$706$	−9.50000	+	16.4545i	−0.357537	+	0.619273i
$707$		0			0
$708$	−12.0000	+	20.7846i	−0.450988	+	0.781133i
$709$	−9.50000	−	16.4545i	−0.356780	−	0.617961i	0.630641	−	0.776075i	$-0.282792\pi$
$709$	−9.50000	−	16.4545i	−0.356780	−	0.617961i	−0.987421	+	0.158114i	$0.949459\pi$
$710$	14.0000			0.525411
$711$	17.0000			0.637550
$712$	1.00000	+	1.73205i	0.0374766	+	0.0649113i
$713$	−8.00000	−	13.8564i	−0.299602	−	0.518927i
$714$	24.0000			0.898177
$715$	−4.00000			−0.149592
$716$	10.0000	+	17.3205i	0.373718	+	0.647298i
$717$	5.00000	−	8.66025i	0.186728	−	0.323423i
$718$	−3.50000	−	6.06218i	−0.130619	−	0.226238i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$		0			0
$722$	13.0000	−	13.8564i	0.483810	−	0.515682i
$723$	−20.0000			−0.743808
$724$	8.50000	−	14.7224i	0.315900	−	0.547155i
$725$	20.0000	−	34.6410i	0.742781	−	1.28654i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	−7.00000	+	12.1244i	−0.259616	+	0.449667i	−0.966139	−	0.258022i	$-0.916929\pi$
$727$	−7.00000	+	12.1244i	−0.259616	+	0.449667i	0.706523	+	0.707690i	$0.250263\pi$
$728$	6.00000	+	10.3923i	0.222375	+	0.385164i
$729$	13.0000			0.481481
$730$	6.00000			0.222070
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$	−12.0000	−	20.7846i	−0.443533	−	0.768221i
$733$	−32.0000			−1.18195			−0.590973	−	0.806691i	$-0.701256\pi$
$733$	−32.0000			−1.18195			−0.590973	+	0.806691i	$0.701256\pi$
$734$	16.0000			0.590571
$735$	−2.00000	−	3.46410i	−0.0737711	−	0.127775i
$736$	−2.00000	+	3.46410i	−0.0737210	+	0.127688i
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	2.00000	−	3.46410i	0.0735712	−	0.127429i	−0.826893	−	0.562360i	$-0.809894\pi$
$739$	2.00000	−	3.46410i	0.0735712	−	0.127429i	0.900464	+	0.434930i	$0.143227\pi$
$740$	3.00000			0.110282
$741$	−4.00000	+	34.6410i	−0.146944	+	1.27257i
$742$	3.00000			0.110133
$743$	−4.50000	+	7.79423i	−0.165089	+	0.285943i	−0.936687	−	0.350168i	$-0.886124\pi$
$743$	−4.50000	+	7.79423i	−0.165089	+	0.285943i	0.771598	+	0.636111i	$0.219458\pi$
$744$	−4.00000	+	6.92820i	−0.146647	+	0.254000i
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$	14.0000	−	24.2487i	0.512576	−	0.887808i
$747$	6.50000	+	11.2583i	0.237823	+	0.411921i
$748$	4.00000			0.146254
$749$	21.0000			0.767323
$750$	9.00000	+	15.5885i	0.328634	+	0.569210i
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	0.760263	−	0.649616i	$-0.225070\pi$
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	−0.942715	+	0.333599i	$0.891737\pi$
$752$	6.00000			0.218797
$753$		0			0
$754$	−20.0000	−	34.6410i	−0.728357	−	1.26155i
$755$	−7.50000	+	12.9904i	−0.272953	+	0.472768i
$756$	−6.00000	−	10.3923i	−0.218218	−	0.377964i
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	−0.593899	−	0.804539i	$-0.702412\pi$
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	0.993701	+	0.112062i	$0.0357456\pi$
$758$	−2.00000	+	3.46410i	−0.0726433	+	0.125822i
$759$	−8.00000			−0.290382
$760$	−3.50000	−	2.59808i	−0.126958	−	0.0942421i
$761$	22.0000			0.797499			0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000			0.797499			0.398750	+	0.917060i	$0.369444\pi$
$762$	8.00000	−	13.8564i	0.289809	−	0.501965i
$763$	−6.00000	+	10.3923i	−0.217215	+	0.376227i
$764$	−9.00000	−	15.5885i	−0.325609	−	0.563971i
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$	−4.00000	−	6.92820i	−0.144526	−	0.250326i
$767$	48.0000			1.73318
$768$	2.00000			0.0721688
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	0.990726	+	0.135877i	$0.0433852\pi$
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	−0.377690	+	0.925932i	$0.623282\pi$
$770$	−1.50000	−	2.59808i	−0.0540562	−	0.0936282i
$771$	−2.00000			−0.0720282
$772$	−10.0000			−0.359908
$773$	13.0000	+	22.5167i	0.467578	+	0.809868i	0.999314	−	0.0370420i	$-0.0117935\pi$
$773$	13.0000	+	22.5167i	0.467578	+	0.809868i	−0.531736	+	0.846910i	$0.678460\pi$
$774$	2.00000	−	3.46410i	0.0718885	−	0.124515i
$775$	8.00000	+	13.8564i	0.287368	+	0.497737i
$776$	−2.50000	+	4.33013i	−0.0897448	+	0.155443i
$777$	9.00000	−	15.5885i	0.322873	−	0.559233i
$778$	21.0000			0.752886
$779$	−21.0000	−	15.5885i	−0.752403	−	0.558514i
$780$	8.00000			0.286446
$781$	7.00000	−	12.1244i	0.250480	−	0.433844i
$782$	8.00000	−	13.8564i	0.286079	−	0.495504i
$783$	20.0000	+	34.6410i	0.714742	+	1.23797i
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$	−2.50000	−	4.33013i	−0.0892288	−	0.154549i
$786$	−32.0000			−1.14140
$787$	7.00000			0.249523			0.124762	−	0.992187i	$-0.460183\pi$
$787$	7.00000			0.249523			0.124762	+	0.992187i	$0.460183\pi$
$788$	6.00000	+	10.3923i	0.213741	+	0.370211i
$789$	23.0000	+	39.8372i	0.818822	+	1.41824i
$790$	17.0000			0.604833
$791$	18.0000			0.640006
$792$	0.500000	+	0.866025i	0.0177667	+	0.0307729i
$793$	−24.0000	+	41.5692i	−0.852265	+	1.47617i
$794$	−12.5000	−	21.6506i	−0.443608	−	0.768352i
$795$	1.00000	−	1.73205i	0.0354663	−	0.0614295i
$796$	5.00000	−	8.66025i	0.177220	−	0.306955i
$797$	37.0000			1.31061			0.655304	−	0.755366i	$-0.272541\pi$
$797$	37.0000			1.31061			0.655304	+	0.755366i	$0.272541\pi$
$798$	−24.0000	+	10.3923i	−0.849591	+	0.367884i
$799$	−24.0000			−0.849059
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	1.00000	−	1.73205i	0.0353333	−	0.0611990i
$802$	−5.00000	−	8.66025i	−0.176556	−	0.305804i
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$	−12.0000	−	20.7846i	−0.423207	−	0.733017i
$805$	−12.0000			−0.422944
$806$	16.0000			0.563576
$807$	−15.0000	−	25.9808i	−0.528025	−	0.914566i
$808$		0			0
$809$	−28.0000			−0.984428			−0.492214	−	0.870474i	$-0.663812\pi$
$809$	−28.0000			−0.984428			−0.492214	+	0.870474i	$0.663812\pi$
$810$	−11.0000			−0.386501
$811$	−17.5000	−	30.3109i	−0.614508	−	1.06436i	−0.990471	−	0.137724i	$-0.956021\pi$
$811$	−17.5000	−	30.3109i	−0.614508	−	1.06436i	0.375962	−	0.926635i	$-0.377312\pi$
$812$	15.0000	−	25.9808i	0.526397	−	0.911746i
$813$	21.0000	+	36.3731i	0.736502	+	1.27566i
$814$	1.50000	−	2.59808i	0.0525750	−	0.0910625i
$815$	−2.00000	+	3.46410i	−0.0700569	+	0.121342i
$816$	−8.00000			−0.280056
$817$	14.0000	+	10.3923i	0.489798	+	0.363581i
$818$	−20.0000			−0.699284
$819$	6.00000	−	10.3923i	0.209657	−	0.363137i
$820$	−3.00000	+	5.19615i	−0.104765	+	0.181458i
$821$	26.0000	+	45.0333i	0.907406	+	1.57167i	0.817654	+	0.575710i	$0.195274\pi$
$821$	26.0000	+	45.0333i	0.907406	+	1.57167i	0.0897520	+	0.995964i	$0.471393\pi$
$822$	−1.00000	+	1.73205i	−0.0348790	+	0.0604122i
$823$	−1.00000	−	1.73205i	−0.0348578	−	0.0603755i	0.848070	−	0.529884i	$-0.177765\pi$
$823$	−1.00000	−	1.73205i	−0.0348578	−	0.0603755i	−0.882928	+	0.469508i	$0.844431\pi$
$824$		0			0
$825$	8.00000			0.278524
$826$	18.0000	+	31.1769i	0.626300	+	1.08478i
$827$	22.0000	+	38.1051i	0.765015	+	1.32504i	0.940239	+	0.340516i	$0.110602\pi$
$827$	22.0000	+	38.1051i	0.765015	+	1.32504i	−0.175224	+	0.984529i	$0.556065\pi$
$828$	4.00000			0.139010
$829$	46.0000			1.59765			0.798823	−	0.601566i	$-0.205456\pi$
$829$	46.0000			1.59765			0.798823	+	0.601566i	$0.205456\pi$
$830$	6.50000	+	11.2583i	0.225618	+	0.390782i
$831$	4.00000	−	6.92820i	0.138758	−	0.240337i
$832$	−2.00000	−	3.46410i	−0.0693375	−	0.120096i
$833$	4.00000	−	6.92820i	0.138592	−	0.240048i
$834$	17.0000	−	29.4449i	0.588662	−	1.01959i
$835$	17.0000			0.588309
$836$	−4.00000	+	1.73205i	−0.138343	+	0.0599042i
$837$	−16.0000			−0.553041
$838$	19.0000	−	32.9090i	0.656344	−	1.13682i
$839$	28.0000	−	48.4974i	0.966667	−	1.67432i	0.261600	−	0.965176i	$-0.415750\pi$
$839$	28.0000	−	48.4974i	0.966667	−	1.67432i	0.705067	−	0.709141i	$-0.250917\pi$
$840$	3.00000	+	5.19615i	0.103510	+	0.179284i
$841$	−35.5000	+	61.4878i	−1.22414	+	2.12027i
$842$	1.50000	+	2.59808i	0.0516934	+	0.0895356i
$843$	8.00000			0.275535
$844$	−23.0000			−0.791693
$845$	−1.50000	−	2.59808i	−0.0516016	−	0.0893765i
$846$	−3.00000	−	5.19615i	−0.103142	−	0.178647i
$847$	−3.00000			−0.103081
$848$	−1.00000			−0.0343401
$849$	−13.0000	−	22.5167i	−0.446159	−	0.772770i
$850$	−8.00000	+	13.8564i	−0.274398	+	0.475271i
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$	−14.0000	+	24.2487i	−0.479632	+	0.830747i
$853$	−21.0000	+	36.3731i	−0.719026	+	1.24539i	0.242360	+	0.970186i	$0.422079\pi$
$853$	−21.0000	+	36.3731i	−0.719026	+	1.24539i	−0.961386	+	0.275204i	$0.911255\pi$
$854$	−36.0000			−1.23189
$855$	−0.500000	+	4.33013i	−0.0170996	+	0.148087i
$856$	−7.00000			−0.239255
$857$	−24.0000	+	41.5692i	−0.819824	+	1.41998i	0.0859870	+	0.996296i	$0.472596\pi$
$857$	−24.0000	+	41.5692i	−0.819824	+	1.41998i	−0.905811	+	0.423681i	$0.860738\pi$
$858$	4.00000	−	6.92820i	0.136558	−	0.236525i
$859$	3.00000	+	5.19615i	0.102359	+	0.177290i	0.912656	−	0.408729i	$-0.134028\pi$
$859$	3.00000	+	5.19615i	0.102359	+	0.177290i	−0.810297	+	0.586019i	$0.800694\pi$
$860$	2.00000	−	3.46410i	0.0681994	−	0.118125i
$861$	18.0000	+	31.1769i	0.613438	+	1.06251i
$862$	13.0000			0.442782
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$	2.00000	+	3.46410i	0.0680414	+	0.117851i
$865$	2.00000	+	3.46410i	0.0680020	+	0.117783i
$866$	−18.0000			−0.611665
$867$	−2.00000			−0.0679236
$868$	6.00000	+	10.3923i	0.203653	+	0.352738i
$869$	8.50000	−	14.7224i	0.288343	−	0.499424i
$870$	−10.0000	−	17.3205i	−0.339032	−	0.587220i
$871$	−24.0000	+	41.5692i	−0.813209	+	1.40852i
$872$	2.00000	−	3.46410i	0.0677285	−	0.117309i
$873$	5.00000			0.169224
$874$	−2.00000	+	17.3205i	−0.0676510	+	0.585875i
$875$	27.0000			0.912767
$876$	−6.00000	+	10.3923i	−0.202721	+	0.351123i
$877$	6.00000	−	10.3923i	0.202606	−	0.350923i	−0.746762	−	0.665092i	$-0.768392\pi$
$877$	6.00000	−	10.3923i	0.202606	−	0.350923i	0.949367	+	0.314169i	$0.101726\pi$
$878$	−0.500000	−	0.866025i	−0.0168742	−	0.0292269i
$879$	−30.0000	+	51.9615i	−1.01187	+	1.75262i
$880$	0.500000	+	0.866025i	0.0168550	+	0.0291937i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$	2.00000			0.0673435
$883$	13.0000	+	22.5167i	0.437485	+	0.757746i	0.997495	−	0.0707399i	$-0.0225360\pi$
$883$	13.0000	+	22.5167i	0.437485	+	0.757746i	−0.560010	+	0.828486i	$0.689203\pi$
$884$	8.00000	+	13.8564i	0.269069	+	0.466041i
$885$	24.0000			0.806751
$886$	24.0000			0.806296
$887$	−14.5000	−	25.1147i	−0.486862	−	0.843270i	0.513024	−	0.858375i	$-0.328525\pi$
$887$	−14.5000	−	25.1147i	−0.486862	−	0.843270i	−0.999886	+	0.0151042i	$0.995192\pi$
$888$	−3.00000	+	5.19615i	−0.100673	+	0.174371i
$889$	−12.0000	−	20.7846i	−0.402467	−	0.697093i
$890$	1.00000	−	1.73205i	0.0335201	−	0.0580585i
$891$	−5.50000	+	9.52628i	−0.184257	+	0.319142i
$892$	16.0000			0.535720
$893$	24.0000	−	10.3923i	0.803129	−	0.347765i
$894$	−12.0000			−0.401340
$895$	10.0000	−	17.3205i	0.334263	−	0.578961i
$896$	1.50000	−	2.59808i	0.0501115	−	0.0867956i
$897$	−16.0000	−	27.7128i	−0.534224	−	0.925304i
$898$	16.5000	−	28.5788i	0.550612	−	0.953688i
$899$	−20.0000	−	34.6410i	−0.667037	−	1.15534i
$900$	−4.00000			−0.133333
$901$	4.00000			0.133259
$902$	3.00000	+	5.19615i	0.0998891	+	0.173013i
$903$	−12.0000	−	20.7846i	−0.399335	−	0.691669i
$904$	−6.00000			−0.199557
$905$	−17.0000			−0.565099
$906$	−15.0000	−	25.9808i	−0.498342	−	0.863153i
$907$	1.00000	−	1.73205i	0.0332045	−	0.0575118i	−0.848946	−	0.528480i	$-0.822762\pi$
$907$	1.00000	−	1.73205i	0.0332045	−	0.0575118i	0.882150	+	0.470968i	$0.156095\pi$
$908$	1.50000	+	2.59808i	0.0497792	+	0.0862202i
$909$		0			0
$910$	6.00000	−	10.3923i	0.198898	−	0.344502i
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	8.00000	−	3.46410i	0.264906	−	0.114708i
$913$	13.0000			0.430237
$914$	−19.0000	+	32.9090i	−0.628464	+	1.08853i
$915$	−12.0000	+	20.7846i	−0.396708	+	0.687118i
$916$	6.50000	+	11.2583i	0.214766	+	0.371986i
$917$	−24.0000	+	41.5692i	−0.792550	+	1.37274i
$918$	−8.00000	−	13.8564i	−0.264039	−	0.457330i
$919$	45.0000			1.48441			0.742207	−	0.670171i	$-0.233779\pi$
$919$	45.0000			1.48441			0.742207	+	0.670171i	$0.233779\pi$
$920$	4.00000			0.131876
$921$	−29.0000	−	50.2295i	−0.955582	−	1.65512i
$922$	1.00000	+	1.73205i	0.0329332	+	0.0570421i
$923$	56.0000			1.84326
$924$	6.00000			0.197386
$925$	6.00000	+	10.3923i	0.197279	+	0.341697i
$926$	−2.00000	+	3.46410i	−0.0657241	+	0.113837i
$927$		0			0
$928$	−5.00000	+	8.66025i	−0.164133	+	0.284287i
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	−0.957708	−	0.287742i	$-0.907096\pi$
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	0.728046	+	0.685529i	$0.240429\pi$
$930$	8.00000			0.262330
$931$	−1.00000	+	8.66025i	−0.0327737	+	0.283828i
$932$	−16.0000			−0.524097
$933$	18.0000	−	31.1769i	0.589294	−	1.02069i
$934$	−7.00000	+	12.1244i	−0.229047	+	0.396721i
$935$	−2.00000	−	3.46410i	−0.0654070	−	0.113288i
$936$	−2.00000	+	3.46410i	−0.0653720	+	0.113228i
$937$	19.0000	+	32.9090i	0.620703	+	1.07509i	0.989355	+	0.145522i	$0.0464860\pi$
$937$	19.0000	+	32.9090i	0.620703	+	1.07509i	−0.368652	+	0.929567i	$0.620181\pi$
$938$	−36.0000			−1.17544
$939$	−18.0000			−0.587408
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	0.992607	−	0.121376i	$-0.0387306\pi$
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	−0.601418	+	0.798935i	$0.705397\pi$
$942$	10.0000			0.325818
$943$	24.0000			0.781548
$944$	−6.00000	−	10.3923i	−0.195283	−	0.338241i
$945$	−6.00000	+	10.3923i	−0.195180	+	0.338062i
$946$	−2.00000	−	3.46410i	−0.0650256	−	0.112628i
$947$	15.0000	−	25.9808i	0.487435	−	0.844261i	−0.512461	−	0.858710i	$-0.671266\pi$
$947$	15.0000	−	25.9808i	0.487435	−	0.844261i	0.999896	+	0.0144491i	$0.00459946\pi$
$948$	−17.0000	+	29.4449i	−0.552134	+	0.956325i
$949$	24.0000			0.779073
$950$	2.00000	−	17.3205i	0.0648886	−	0.561951i
$951$	−36.0000			−1.16738
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$953$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$954$	0.500000	+	0.866025i	0.0161881	+	0.0280386i
$955$	−9.00000	+	15.5885i	−0.291233	+	0.504431i
$956$	2.50000	+	4.33013i	0.0808558	+	0.140046i
$957$	−20.0000			−0.646508
$958$		0			0
$959$	1.50000	+	2.59808i	0.0484375	+	0.0838963i
$960$	−1.00000	−	1.73205i	−0.0322749	−	0.0559017i
$961$	−15.0000			−0.483871
$962$	12.0000			0.386896
$963$	3.50000	+	6.06218i	0.112786	+	0.195351i
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	5.00000	+	8.66025i	0.160956	+	0.278783i
$966$	12.0000	−	20.7846i	0.386094	−	0.668734i
$967$	18.5000	−	32.0429i	0.594920	−	1.03043i	−0.398638	−	0.917108i	$-0.630517\pi$
$967$	18.5000	−	32.0429i	0.594920	−	1.03043i	0.993558	−	0.113323i	$-0.0361496\pi$
$968$	1.00000			0.0321412
$969$	−32.0000	+	13.8564i	−1.02799	+	0.445132i
$970$	5.00000			0.160540
$971$	25.0000	−	43.3013i	0.802288	−	1.38960i	−0.115818	−	0.993270i	$-0.536949\pi$
$971$	25.0000	−	43.3013i	0.802288	−	1.38960i	0.918107	−	0.396333i	$-0.129718\pi$
$972$	5.00000	−	8.66025i	0.160375	−	0.277778i
$973$	−25.5000	−	44.1673i	−0.817492	−	1.41594i
$974$	−9.00000	+	15.5885i	−0.288379	+	0.499486i
$975$	16.0000	+	27.7128i	0.512410	+	0.887520i
$976$	12.0000			0.384111
$977$	9.00000			0.287936			0.143968	−	0.989582i	$-0.454014\pi$
$977$	9.00000			0.287936			0.143968	+	0.989582i	$0.454014\pi$
$978$	−4.00000	−	6.92820i	−0.127906	−	0.221540i
$979$	−1.00000	−	1.73205i	−0.0319601	−	0.0553566i
$980$	2.00000			0.0638877
$981$	−4.00000			−0.127710
$982$	−0.500000	−	0.866025i	−0.0159556	−	0.0276360i
$983$	−19.0000	+	32.9090i	−0.606006	+	1.04963i	0.385886	+	0.922547i	$0.373896\pi$
$983$	−19.0000	+	32.9090i	−0.606006	+	1.04963i	−0.991892	+	0.127086i	$0.959437\pi$
$984$	−6.00000	−	10.3923i	−0.191273	−	0.331295i
$985$	6.00000	−	10.3923i	0.191176	−	0.331126i
$986$	20.0000	−	34.6410i	0.636930	−	1.10319i
$987$	−36.0000			−1.14589
$988$	−14.0000	−	10.3923i	−0.445399	−	0.330623i
$989$	−16.0000			−0.508770
$990$	0.500000	−	0.866025i	0.0158910	−	0.0275241i
$991$	−19.0000	+	32.9090i	−0.603555	+	1.04539i	0.388723	+	0.921355i	$0.372916\pi$
$991$	−19.0000	+	32.9090i	−0.603555	+	1.04539i	−0.992278	+	0.124033i	$0.960417\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	−20.0000	+	34.6410i	−0.634681	+	1.09930i
$994$	21.0000	+	36.3731i	0.666080	+	1.15368i
$995$	−10.0000			−0.317021
$996$	−26.0000			−0.823842
$997$	−22.0000	−	38.1051i	−0.696747	−	1.20680i	−0.969588	−	0.244742i	$-0.921297\pi$
$997$	−22.0000	−	38.1051i	−0.696747	−	1.20680i	0.272841	−	0.962059i	$-0.412037\pi$
$998$	20.0000	+	34.6410i	0.633089	+	1.09654i
$999$	−12.0000			−0.379663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.e.a.353.1	yes	2
19.7	even	3	inner	418.2.e.a.45.1	✓	2
19.8	odd	6		7942.2.a.c.1.1		1
19.11	even	3		7942.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.e.a.45.1	✓	2	19.7	even	3	inner
418.2.e.a.353.1	yes	2	1.1	even	1	trivial
7942.2.a.c.1.1		1	19.8	odd	6
7942.2.a.s.1.1		1	19.11	even	3

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} -1.00000 q^{11} +2.00000 q^{12} +(-2.00000 - 3.46410i) q^{13} +(1.50000 - 2.59808i) q^{14} +(-1.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +1.00000 q^{18} +(-0.500000 + 4.33013i) q^{19} +1.00000 q^{20} +(3.00000 - 5.19615i) q^{21} +(0.500000 - 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(2.00000 + 3.46410i) q^{25} +4.00000 q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(-5.00000 - 8.66025i) q^{29} +2.00000 q^{30} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} +(2.00000 + 3.46410i) q^{34} +(1.50000 - 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +3.00000 q^{37} +(-3.50000 - 2.59808i) q^{38} +8.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(3.00000 + 5.19615i) q^{42} +(2.00000 - 3.46410i) q^{43} +(0.500000 + 0.866025i) q^{44} +1.00000 q^{45} +4.00000 q^{46} +(-3.00000 - 5.19615i) q^{47} +(-1.00000 - 1.73205i) q^{48} +2.00000 q^{49} -4.00000 q^{50} +(4.00000 + 6.92820i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(0.500000 + 0.866025i) q^{53} +(2.00000 - 3.46410i) q^{54} +(0.500000 - 0.866025i) q^{55} -3.00000 q^{56} +(-7.00000 - 5.19615i) q^{57} +10.0000 q^{58} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(-6.00000 - 10.3923i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +4.00000 q^{65} +(1.00000 + 1.73205i) q^{66} +(-6.00000 - 10.3923i) q^{67} -4.00000 q^{68} +8.00000 q^{69} +(1.50000 + 2.59808i) q^{70} +(-7.00000 + 12.1244i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-3.00000 + 5.19615i) q^{73} +(-1.50000 + 2.59808i) q^{74} -8.00000 q^{75} +(4.00000 - 1.73205i) q^{76} +3.00000 q^{77} +(-4.00000 + 6.92820i) q^{78} +(-8.50000 + 14.7224i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-3.00000 - 5.19615i) q^{82} -13.0000 q^{83} -6.00000 q^{84} +(2.00000 + 3.46410i) q^{85} +(2.00000 + 3.46410i) q^{86} +20.0000 q^{87} -1.00000 q^{88} +(1.00000 + 1.73205i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(6.00000 + 10.3923i) q^{91} +(-2.00000 + 3.46410i) q^{92} +(-4.00000 + 6.92820i) q^{93} +6.00000 q^{94} +(-3.50000 - 2.59808i) q^{95} +2.00000 q^{96} +(-2.50000 + 4.33013i) q^{97} +(-1.00000 + 1.73205i) q^{98} +(0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} - 6 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 - q^5 - 2 * q^6 - 6 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} - 6 q^{7} + 2 q^{8} - q^{9} - q^{10} - 2 q^{11} + 4 q^{12} - 4 q^{13} + 3 q^{14} - 2 q^{15} - q^{16} + 4 q^{17} + 2 q^{18} - q^{19} + 2 q^{20} + 6 q^{21} + q^{22} - 4 q^{23} - 2 q^{24} + 4 q^{25} + 8 q^{26} - 8 q^{27} + 3 q^{28} - 10 q^{29} + 4 q^{30} + 8 q^{31} - q^{32} + 2 q^{33} + 4 q^{34} + 3 q^{35} - q^{36} + 6 q^{37} - 7 q^{38} + 16 q^{39} - q^{40} - 6 q^{41} + 6 q^{42} + 4 q^{43} + q^{44} + 2 q^{45} + 8 q^{46} - 6 q^{47} - 2 q^{48} + 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{52} + q^{53} + 4 q^{54} + q^{55} - 6 q^{56} - 14 q^{57} + 20 q^{58} - 12 q^{59} - 2 q^{60} - 12 q^{61} - 4 q^{62} + 3 q^{63} + 2 q^{64} + 8 q^{65} + 2 q^{66} - 12 q^{67} - 8 q^{68} + 16 q^{69} + 3 q^{70} - 14 q^{71} - q^{72} - 6 q^{73} - 3 q^{74} - 16 q^{75} + 8 q^{76} + 6 q^{77} - 8 q^{78} - 17 q^{79} - q^{80} + 11 q^{81} - 6 q^{82} - 26 q^{83} - 12 q^{84} + 4 q^{85} + 4 q^{86} + 40 q^{87} - 2 q^{88} + 2 q^{89} - q^{90} + 12 q^{91} - 4 q^{92} - 8 q^{93} + 12 q^{94} - 7 q^{95} + 4 q^{96} - 5 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 - q^5 - 2 * q^6 - 6 * q^7 + 2 * q^8 - q^9 - q^10 - 2 * q^11 + 4 * q^12 - 4 * q^13 + 3 * q^14 - 2 * q^15 - q^16 + 4 * q^17 + 2 * q^18 - q^19 + 2 * q^20 + 6 * q^21 + q^22 - 4 * q^23 - 2 * q^24 + 4 * q^25 + 8 * q^26 - 8 * q^27 + 3 * q^28 - 10 * q^29 + 4 * q^30 + 8 * q^31 - q^32 + 2 * q^33 + 4 * q^34 + 3 * q^35 - q^36 + 6 * q^37 - 7 * q^38 + 16 * q^39 - q^40 - 6 * q^41 + 6 * q^42 + 4 * q^43 + q^44 + 2 * q^45 + 8 * q^46 - 6 * q^47 - 2 * q^48 + 4 * q^49 - 8 * q^50 + 8 * q^51 - 4 * q^52 + q^53 + 4 * q^54 + q^55 - 6 * q^56 - 14 * q^57 + 20 * q^58 - 12 * q^59 - 2 * q^60 - 12 * q^61 - 4 * q^62 + 3 * q^63 + 2 * q^64 + 8 * q^65 + 2 * q^66 - 12 * q^67 - 8 * q^68 + 16 * q^69 + 3 * q^70 - 14 * q^71 - q^72 - 6 * q^73 - 3 * q^74 - 16 * q^75 + 8 * q^76 + 6 * q^77 - 8 * q^78 - 17 * q^79 - q^80 + 11 * q^81 - 6 * q^82 - 26 * q^83 - 12 * q^84 + 4 * q^85 + 4 * q^86 + 40 * q^87 - 2 * q^88 + 2 * q^89 - q^90 + 12 * q^91 - 4 * q^92 - 8 * q^93 + 12 * q^94 - 7 * q^95 + 4 * q^96 - 5 * q^97 - 2 * q^98 + q^99

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