LMFDB - Embedded newform 390.2.y.g.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(139,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("390.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.y (of order $6$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.2
Root			$-0.396143 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	390.289
Dual form			390.2.y.g.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 1.65831i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.00626 + 1.15831i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 1.65831i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.00626 + 1.15831i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.469882 - 2.18614i) q^{10} +(-0.158312 - 0.274205i) q^{11} +1.00000i q^{12} +(0.866025 + 3.50000i) q^{13} -2.31662 q^{14} +(0.469882 - 2.18614i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.87854 - 2.81662i) q^{17} +1.00000i q^{18} +(-1.15831 + 2.00626i) q^{19} +(0.686141 + 2.12819i) q^{20} -2.31662 q^{21} +(0.274205 + 0.158312i) q^{22} +(-7.20241 + 4.15831i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 4.97494i) q^{25} +(-2.50000 - 2.59808i) q^{26} +1.00000i q^{27} +(2.00626 - 1.15831i) q^{28} +(1.50000 + 2.59808i) q^{29} +(0.686141 + 2.12819i) q^{30} -4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(0.274205 + 0.158312i) q^{33} +5.63325 q^{34} +(-4.93023 + 1.58953i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.87854 + 2.81662i) q^{37} -2.31662i q^{38} +(-2.50000 - 2.59808i) q^{39} +(-1.65831 - 1.50000i) q^{40} +(3.65831 + 6.33638i) q^{41} +(2.00626 - 1.15831i) q^{42} +(-3.73831 - 2.15831i) q^{43} -0.316625 q^{44} +(0.686141 + 2.12819i) q^{45} +(4.15831 - 7.20241i) q^{46} -8.31662i q^{47} +(0.866025 + 0.500000i) q^{48} +(-0.816625 - 1.41444i) q^{49} +(2.92048 + 4.05842i) q^{50} +5.63325 q^{51} +(3.46410 + 1.00000i) q^{52} +11.3166i q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.692186 + 0.148776i) q^{55} +(-1.15831 + 2.00626i) q^{56} -2.31662i q^{57} +(-2.59808 - 1.50000i) q^{58} +(4.31662 - 7.47661i) q^{59} +(-1.65831 - 1.50000i) q^{60} +(-3.65831 + 6.33638i) q^{61} +(3.46410 - 2.00000i) q^{62} +(2.00626 - 1.15831i) q^{63} -1.00000 q^{64} +(-7.10313 - 3.81386i) q^{65} -0.316625 q^{66} +(11.2149 - 6.47494i) q^{67} +(-4.87854 + 2.81662i) q^{68} +(4.15831 - 7.20241i) q^{69} +(3.47494 - 3.84169i) q^{70} +(-0.841688 + 1.45785i) q^{71} +(0.866025 + 0.500000i) q^{72} +7.31662i q^{73} +(2.81662 - 4.87854i) q^{74} +(2.92048 + 4.05842i) q^{75} +(1.15831 + 2.00626i) q^{76} -0.733501i q^{77} +(3.46410 + 1.00000i) q^{78} +4.00000 q^{79} +(2.18614 + 0.469882i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.33638 - 3.65831i) q^{82} +1.68338i q^{83} +(-1.15831 + 2.00626i) q^{84} +(11.9886 - 3.86520i) q^{85} +4.31662 q^{86} +(-2.59808 - 1.50000i) q^{87} +(0.274205 - 0.158312i) q^{88} +(7.63325 + 13.2212i) q^{89} +(-1.65831 - 1.50000i) q^{90} +(-2.31662 + 8.02502i) q^{91} +8.31662i q^{92} +(3.46410 - 2.00000i) q^{93} +(4.15831 + 7.20241i) q^{94} +(-1.58953 - 4.93023i) q^{95} -1.00000 q^{96} +(5.19615 + 3.00000i) q^{97} +(1.41444 + 0.816625i) q^{98} -0.316625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 12 q^{5} + 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 12 * q^5 + 4 * q^6 + 4 * q^9	$ 8 q + 4 q^{4} - 12 q^{5} + 4 q^{6} + 4 q^{9} + 12 q^{11} + 8 q^{14} - 4 q^{16} + 4 q^{19} - 6 q^{20} + 8 q^{21} - 4 q^{24} - 4 q^{25} - 20 q^{26} + 12 q^{29} - 6 q^{30} - 32 q^{31} - 8 q^{34} - 22 q^{35} - 4 q^{36} - 20 q^{39} + 16 q^{41} + 24 q^{44} - 6 q^{45} + 20 q^{46} + 20 q^{49} - 8 q^{51} - 4 q^{54} - 18 q^{55} + 4 q^{56} + 8 q^{59} - 16 q^{61} - 8 q^{64} + 24 q^{66} + 20 q^{69} - 12 q^{70} - 20 q^{71} - 4 q^{74} - 4 q^{76} + 32 q^{79} + 6 q^{80} - 4 q^{81} + 4 q^{84} + 44 q^{85} + 8 q^{86} + 8 q^{89} + 8 q^{91} + 20 q^{94} - 6 q^{95} - 8 q^{96} + 24 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 12 * q^5 + 4 * q^6 + 4 * q^9 + 12 * q^11 + 8 * q^14 - 4 * q^16 + 4 * q^19 - 6 * q^20 + 8 * q^21 - 4 * q^24 - 4 * q^25 - 20 * q^26 + 12 * q^29 - 6 * q^30 - 32 * q^31 - 8 * q^34 - 22 * q^35 - 4 * q^36 - 20 * q^39 + 16 * q^41 + 24 * q^44 - 6 * q^45 + 20 * q^46 + 20 * q^49 - 8 * q^51 - 4 * q^54 - 18 * q^55 + 4 * q^56 + 8 * q^59 - 16 * q^61 - 8 * q^64 + 24 * q^66 + 20 * q^69 - 12 * q^70 - 20 * q^71 - 4 * q^74 - 4 * q^76 + 32 * q^79 + 6 * q^80 - 4 * q^81 + 4 * q^84 + 44 * q^85 + 8 * q^86 + 8 * q^89 + 8 * q^91 + 20 * q^94 - 6 * q^95 - 8 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.50000	+	1.65831i	−0.670820	+	0.741620i
$5$	−1.50000	+	1.65831i	−0.670820	+	0.741620i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	2.00626	+	1.15831i	0.758293	+	0.437801i	0.828683	−	0.559719i	$-0.189091\pi$
$7$	2.00626	+	1.15831i	0.758293	+	0.437801i	−0.0703892	+	0.997520i	$0.522424\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.469882	−	2.18614i	0.148590	−	0.691318i
$11$	−0.158312	−	0.274205i	−0.0477330	−	0.0826760i	0.841172	−	0.540768i	$-0.181866\pi$
$11$	−0.158312	−	0.274205i	−0.0477330	−	0.0826760i	−0.888905	+	0.458092i	$0.848533\pi$
$12$			1.00000i			0.288675i
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$14$	−2.31662			−0.619144
$15$	0.469882	−	2.18614i	0.121323	−	0.564459i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.87854	−	2.81662i	−1.18322	−	0.683132i	−0.226462	−	0.974020i	$-0.572716\pi$
$17$	−4.87854	−	2.81662i	−1.18322	−	0.683132i	−0.956757	+	0.290888i	$0.906049\pi$
$18$			1.00000i			0.235702i
$19$	−1.15831	+	2.00626i	−0.265735	+	0.460267i	−0.967756	−	0.251890i	$-0.918948\pi$
$19$	−1.15831	+	2.00626i	−0.265735	+	0.460267i	0.702021	+	0.712156i	$0.252281\pi$
$20$	0.686141	+	2.12819i	0.153426	+	0.475879i
$21$	−2.31662			−0.505529
$22$	0.274205	+	0.158312i	0.0584607	+	0.0337523i
$23$	−7.20241	+	4.15831i	−1.50181	+	0.867068i	−0.501808	+	0.864979i	$0.667332\pi$
$23$	−7.20241	+	4.15831i	−1.50181	+	0.867068i	−0.999998	+	0.00208912i	$0.999335\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	−	4.97494i	−0.100000	−	0.994987i
$26$	−2.50000	−	2.59808i	−0.490290	−	0.509525i
$27$			1.00000i			0.192450i
$28$	2.00626	−	1.15831i	0.379147	−	0.218900i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	0.686141	+	2.12819i	0.125272	+	0.388553i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.274205	+	0.158312i	0.0477330	+	0.0275587i
$34$	5.63325			0.966094
$35$	−4.93023	+	1.58953i	−0.833361	+	0.268680i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−4.87854	+	2.81662i	−0.802027	+	0.463050i	−0.844179	−	0.536061i	$-0.819912\pi$
$37$	−4.87854	+	2.81662i	−0.802027	+	0.463050i	0.0421527	+	0.999111i	$0.486578\pi$
$38$		−	2.31662i		−	0.375806i
$39$	−2.50000	−	2.59808i	−0.400320	−	0.416025i
$40$	−1.65831	−	1.50000i	−0.262202	−	0.237171i
$41$	3.65831	+	6.33638i	0.571332	+	0.989577i	0.996429	+	0.0844290i	$0.0269066\pi$
$41$	3.65831	+	6.33638i	0.571332	+	0.989577i	−0.425097	+	0.905148i	$0.639760\pi$
$42$	2.00626	−	1.15831i	0.309572	−	0.178731i
$43$	−3.73831	−	2.15831i	−0.570086	−	0.329140i	0.187097	−	0.982341i	$-0.440092\pi$
$43$	−3.73831	−	2.15831i	−0.570086	−	0.329140i	−0.757184	+	0.653202i	$0.773425\pi$
$44$	−0.316625			−0.0477330
$45$	0.686141	+	2.12819i	0.102284	+	0.317252i
$46$	4.15831	−	7.20241i	0.613110	−	1.06194i
$47$		−	8.31662i		−	1.21310i	−0.795044	−	0.606552i	$-0.792552\pi$
$47$		−	8.31662i		−	1.21310i	0.795044	−	0.606552i	$-0.207448\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−0.816625	−	1.41444i	−0.116661	−	0.202062i
$50$	2.92048	+	4.05842i	0.413018	+	0.573948i
$51$	5.63325			0.788813
$52$	3.46410	+	1.00000i	0.480384	+	0.138675i
$53$			11.3166i			1.55446i	0.629218	+	0.777229i	$0.283375\pi$
$53$			11.3166i			1.55446i	−0.629218	+	0.777229i	$0.716625\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	0.692186	+	0.148776i	0.0933344	+	0.0200610i
$56$	−1.15831	+	2.00626i	−0.154786	+	0.268097i
$57$		−	2.31662i		−	0.306844i
$58$	−2.59808	−	1.50000i	−0.341144	−	0.196960i
$59$	4.31662	−	7.47661i	0.561977	−	0.973372i	−0.435347	−	0.900263i	$-0.643374\pi$
$59$	4.31662	−	7.47661i	0.561977	−	0.973372i	0.997324	−	0.0731095i	$-0.0232923\pi$
$60$	−1.65831	−	1.50000i	−0.214087	−	0.193649i
$61$	−3.65831	+	6.33638i	−0.468399	+	0.811291i	−0.999348	−	0.0361132i	$-0.988502\pi$
$61$	−3.65831	+	6.33638i	−0.468399	+	0.811291i	0.530949	+	0.847404i	$0.321836\pi$
$62$	3.46410	−	2.00000i	0.439941	−	0.254000i
$63$	2.00626	−	1.15831i	0.252764	−	0.145934i
$64$	−1.00000			−0.125000
$65$	−7.10313	−	3.81386i	−0.881035	−	0.473051i
$66$	−0.316625			−0.0389738
$67$	11.2149	−	6.47494i	1.37012	−	0.791039i	0.379178	−	0.925324i	$-0.376207\pi$
$67$	11.2149	−	6.47494i	1.37012	−	0.791039i	0.990943	+	0.134284i	$0.0428736\pi$
$68$	−4.87854	+	2.81662i	−0.591610	+	0.341566i
$69$	4.15831	−	7.20241i	0.500602	−	0.867068i
$70$	3.47494	−	3.84169i	0.415334	−	0.459169i
$71$	−0.841688	+	1.45785i	−0.0998899	+	0.173014i	−0.911639	−	0.410992i	$-0.865182\pi$
$71$	−0.841688	+	1.45785i	−0.0998899	+	0.173014i	0.811749	+	0.584006i	$0.198516\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			7.31662i			0.856346i	0.903697	+	0.428173i	$0.140843\pi$
$73$			7.31662i			0.856346i	−0.903697	+	0.428173i	$0.859157\pi$
$74$	2.81662	−	4.87854i	0.327426	−	0.567118i
$75$	2.92048	+	4.05842i	0.337228	+	0.468626i
$76$	1.15831	+	2.00626i	0.132868	+	0.230133i
$77$		−	0.733501i		−	0.0835902i
$78$	3.46410	+	1.00000i	0.392232	+	0.113228i
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	2.18614	+	0.469882i	0.244418	+	0.0525344i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.33638	−	3.65831i	−0.699736	−	0.403993i
$83$			1.68338i			0.184774i	0.995723	+	0.0923872i	$0.0294498\pi$
$83$			1.68338i			0.184774i	−0.995723	+	0.0923872i	$0.970550\pi$
$84$	−1.15831	+	2.00626i	−0.126382	+	0.218900i
$85$	11.9886	−	3.86520i	1.30035	−	0.419240i
$86$	4.31662			0.465474
$87$	−2.59808	−	1.50000i	−0.278543	−	0.160817i
$88$	0.274205	−	0.158312i	0.0292304	−	0.0168762i
$89$	7.63325	+	13.2212i	0.809123	+	1.40144i	0.913472	+	0.406901i	$0.133391\pi$
$89$	7.63325	+	13.2212i	0.809123	+	1.40144i	−0.104349	+	0.994541i	$0.533276\pi$
$90$	−1.65831	−	1.50000i	−0.174801	−	0.158114i
$91$	−2.31662	+	8.02502i	−0.242848	+	0.841251i
$92$			8.31662i			0.867068i
$93$	3.46410	−	2.00000i	0.359211	−	0.207390i
$94$	4.15831	+	7.20241i	0.428897	+	0.742872i
$95$	−1.58953	−	4.93023i	−0.163082	−	0.505831i
$96$	−1.00000			−0.102062
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	0.740034	−	0.672569i	$-0.234809\pi$
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	−0.212445	+	0.977173i	$0.568143\pi$
$98$	1.41444	+	0.816625i	0.142880	+	0.0824916i
$99$	−0.316625			−0.0318220
$100$	−4.55842	−	2.05446i	−0.455842	−	0.205446i
$101$	6.81662	+	11.8067i	0.678280	+	1.17481i	0.975499	+	0.220005i	$0.0706075\pi$
$101$	6.81662	+	11.8067i	0.678280	+	1.17481i	−0.297219	+	0.954809i	$0.596059\pi$
$102$	−4.87854	+	2.81662i	−0.483047	+	0.278887i
$103$			1.68338i			0.165868i	0.996555	+	0.0829339i	$0.0264291\pi$
$103$			1.68338i			0.165868i	−0.996555	+	0.0829339i	$0.973571\pi$
$104$	−3.50000	+	0.866025i	−0.343203	+	0.0849208i
$105$	3.47494	−	3.84169i	0.339119	−	0.374910i
$106$	−5.65831	−	9.80048i	−0.549584	−	0.951907i
$107$	15.8627	−	9.15831i	1.53350	−	0.885367i	0.534305	−	0.845292i	$-0.320573\pi$
$107$	15.8627	−	9.15831i	1.53350	−	0.885367i	0.999197	−	0.0400756i	$-0.0127599\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$	−0.673839	+	0.217249i	−0.0642480	+	0.0207139i
$111$	2.81662	−	4.87854i	0.267342	−	0.463050i
$112$		−	2.31662i		−	0.218900i
$113$	−8.89105	−	5.13325i	−0.836400	−	0.482896i	0.0196392	−	0.999807i	$-0.493748\pi$
$113$	−8.89105	−	5.13325i	−0.836400	−	0.482896i	−0.856039	+	0.516912i	$0.827082\pi$
$114$	1.15831	+	2.00626i	0.108486	+	0.187903i
$115$	3.90783	−	18.1813i	0.364407	−	1.69542i
$116$	3.00000			0.278543
$117$	3.46410	+	1.00000i	0.320256	+	0.0924500i
$118$			8.63325i			0.794755i
$119$	−6.52506	−	11.3017i	−0.598152	−	1.03603i
$120$	2.18614	+	0.469882i	0.199566	+	0.0428942i
$121$	5.44987	−	9.43946i	0.495443	−	0.858133i
$122$		−	7.31662i		−	0.662416i
$123$	−6.33638	−	3.65831i	−0.571332	−	0.329859i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	9.00000	+	6.63325i	0.804984	+	0.593296i
$126$	−1.15831	+	2.00626i	−0.103191	+	0.178731i
$127$	−3.46410	+	2.00000i	−0.307389	+	0.177471i	−0.645758	−	0.763542i	$-0.723458\pi$
$127$	−3.46410	+	2.00000i	−0.307389	+	0.177471i	0.338368	+	0.941014i	$0.390125\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	4.31662			0.380058
$130$	8.05842	−	0.248667i	0.706770	−	0.0218095i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	0.274205	−	0.158312i	0.0238665	−	0.0137793i
$133$	−4.64774	+	2.68338i	−0.403010	+	0.232678i
$134$	−6.47494	+	11.2149i	−0.559349	+	0.968822i
$135$	−1.65831	−	1.50000i	−0.142725	−	0.129099i
$136$	2.81662	−	4.87854i	0.241524	−	0.418331i
$137$	−6.61059	−	3.81662i	−0.564781	−	0.326076i	0.190281	−	0.981730i	$-0.439060\pi$
$137$	−6.61059	−	3.81662i	−0.564781	−	0.326076i	−0.755062	+	0.655653i	$0.772393\pi$
$138$			8.31662i			0.707958i
$139$	−10.6332	+	18.4173i	−0.901900	+	1.56214i	−0.0768758	+	0.997041i	$0.524494\pi$
$139$	−10.6332	+	18.4173i	−0.901900	+	1.56214i	−0.825025	+	0.565097i	$0.808839\pi$
$140$	−1.08854	+	5.06447i	−0.0919984	+	0.428026i
$141$	4.15831	+	7.20241i	0.350193	+	0.606552i
$142$		−	1.68338i		−	0.141266i
$143$	0.822615	−	0.791562i	0.0687906	−	0.0661937i
$144$	−1.00000			−0.0833333
$145$	−6.55842	−	1.40965i	−0.544647	−	0.117065i
$146$	−3.65831	−	6.33638i	−0.302764	−	0.524403i
$147$	1.41444	+	0.816625i	0.116661	+	0.0673541i
$148$			5.63325i			0.463050i
$149$	4.81662	−	8.34264i	0.394593	−	0.683456i	−0.598456	−	0.801156i	$-0.704219\pi$
$149$	4.81662	−	8.34264i	0.394593	−	0.683456i	0.993049	+	0.117700i	$0.0375522\pi$
$150$	−4.55842	−	2.05446i	−0.372194	−	0.167746i
$151$	−12.9499			−1.05385			−0.526923	−	0.849913i	$-0.676654\pi$
$151$	−12.9499			−1.05385			−0.526923	+	0.849913i	$0.676654\pi$
$152$	−2.00626	−	1.15831i	−0.162729	−	0.0939515i
$153$	−4.87854	+	2.81662i	−0.394406	+	0.227711i
$154$	0.366750	+	0.635230i	0.0295536	+	0.0511883i
$155$	6.00000	−	6.63325i	0.481932	−	0.532795i
$156$	−3.50000	+	0.866025i	−0.280224	+	0.0693375i
$157$			12.2665i			0.978973i	0.872011	+	0.489487i	$0.162816\pi$
$157$			12.2665i			0.978973i	−0.872011	+	0.489487i	$0.837184\pi$
$158$	−3.46410	+	2.00000i	−0.275589	+	0.159111i
$159$	−5.65831	−	9.80048i	−0.448733	−	0.777229i
$160$	−2.12819	+	0.686141i	−0.168249	+	0.0542442i
$161$	−19.2665			−1.51841
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	4.01251	+	2.31662i	0.314284	+	0.181452i	0.648842	−	0.760923i	$-0.275254\pi$
$163$	4.01251	+	2.31662i	0.314284	+	0.181452i	−0.334558	+	0.942375i	$0.608587\pi$
$164$	7.31662			0.571332
$165$	−0.673839	+	0.217249i	−0.0524583	+	0.0169128i
$166$	−0.841688	−	1.45785i	−0.0653276	−	0.113151i
$167$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$167$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$168$		−	2.31662i		−	0.178731i
$169$	−11.5000	+	6.06218i	−0.884615	+	0.466321i
$170$	−8.44987	+	9.34169i	−0.648076	+	0.716475i
$171$	1.15831	+	2.00626i	0.0885784	+	0.153422i
$172$	−3.73831	+	2.15831i	−0.285043	+	0.164570i
$173$	9.75707	+	5.63325i	0.741817	+	0.428288i	0.822729	−	0.568433i	$-0.192450\pi$
$173$	9.75707	+	5.63325i	0.741817	+	0.428288i	−0.0809128	+	0.996721i	$0.525784\pi$
$174$	3.00000			0.227429
$175$	4.75940	−	10.5602i	0.359777	−	0.798273i
$176$	−0.158312	+	0.274205i	−0.0119332	+	0.0206690i
$177$			8.63325i			0.648915i
$178$	−13.2212	−	7.63325i	−0.990969	−	0.572136i
$179$	−12.7916	−	22.1556i	−0.956086	−	1.65599i	−0.731863	−	0.681452i	$-0.761349\pi$
$179$	−12.7916	−	22.1556i	−0.956086	−	1.65599i	−0.224224	−	0.974538i	$-0.571985\pi$
$180$	2.18614	+	0.469882i	0.162945	+	0.0350229i
$181$	0.0501256			0.00372581			0.00186290	−	0.999998i	$-0.499407\pi$
$181$	0.0501256			0.00372581			0.00186290	+	0.999998i	$0.499407\pi$
$182$	−2.00626	−	8.10819i	−0.148714	−	0.601019i
$183$		−	7.31662i		−	0.540860i
$184$	−4.15831	−	7.20241i	−0.306555	−	0.530969i
$185$	2.64696	−	12.3151i	0.194609	−	0.905422i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$			1.78363i			0.130432i
$188$	−7.20241	−	4.15831i	−0.525290	−	0.303276i
$189$	−1.15831	+	2.00626i	−0.0842548	+	0.145934i
$190$	3.84169	+	3.47494i	0.278705	+	0.252098i
$191$	0.316625	−	0.548410i	0.0229102	−	0.0396816i	−0.854343	−	0.519710i	$-0.826040\pi$
$191$	0.316625	−	0.548410i	0.0229102	−	0.0396816i	0.877253	+	0.480028i	$0.159373\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−13.8130	+	7.97494i	−0.994281	+	0.574049i	−0.906551	−	0.422096i	$-0.861295\pi$
$193$	−13.8130	+	7.97494i	−0.994281	+	0.574049i	−0.0877300	+	0.996144i	$0.527961\pi$
$194$	−6.00000			−0.430775
$195$	8.05842	−	0.248667i	0.577076	−	0.0178074i
$196$	−1.63325			−0.116661
$197$	11.4891	−	6.63325i	0.818566	−	0.472599i	−0.0313555	−	0.999508i	$-0.509982\pi$
$197$	11.4891	−	6.63325i	0.818566	−	0.472599i	0.849922	+	0.526909i	$0.176649\pi$
$198$	0.274205	−	0.158312i	0.0194869	−	0.0112508i
$199$	−7.84169	+	13.5822i	−0.555882	+	0.962817i	0.441952	+	0.897039i	$0.354286\pi$
$199$	−7.84169	+	13.5822i	−0.555882	+	0.962817i	−0.997834	+	0.0657779i	$0.979047\pi$
$200$	4.97494	−	0.500000i	0.351781	−	0.0353553i
$201$	−6.47494	+	11.2149i	−0.456707	+	0.791039i
$202$	−11.8067	−	6.81662i	−0.830719	−	0.479616i
$203$			6.94987i			0.487786i
$204$	2.81662	−	4.87854i	0.197203	−	0.341566i
$205$	−15.9952	−	3.43795i	−1.11715	−	0.240117i
$206$	−0.841688	−	1.45785i	−0.0586432	−	0.101573i
$207$			8.31662i			0.578045i
$208$	2.59808	−	2.50000i	0.180144	−	0.173344i
$209$	0.733501			0.0507373
$210$	−1.08854	+	5.06447i	−0.0751164	+	0.349481i
$211$	2.31662	+	4.01251i	0.159483	+	0.276233i	0.934682	−	0.355484i	$-0.115684\pi$
$211$	2.31662	+	4.01251i	0.159483	+	0.276233i	−0.775199	+	0.631717i	$0.782351\pi$
$212$	9.80048	+	5.65831i	0.673100	+	0.388614i
$213$		−	1.68338i		−	0.115343i
$214$	−9.15831	+	15.8627i	−0.626049	+	1.08435i
$215$	9.18662	−	2.96181i	0.626522	−	0.201994i
$216$	−1.00000			−0.0680414
$217$	−8.02502	−	4.63325i	−0.544774	−	0.314525i
$218$	−5.19615	+	3.00000i	−0.351928	+	0.203186i
$219$	−3.65831	−	6.33638i	−0.247206	−	0.428173i
$220$	0.474937	−	0.525063i	0.0320203	−	0.0353997i
$221$	5.63325	−	19.5141i	0.378933	−	1.31266i
$222$			5.63325i			0.378079i
$223$	17.8689	−	10.3166i	1.19659	−	0.690852i	0.236798	−	0.971559i	$-0.423902\pi$
$223$	17.8689	−	10.3166i	1.19659	−	0.690852i	0.959794	+	0.280707i	$0.0905688\pi$
$224$	1.15831	+	2.00626i	0.0773930	+	0.134049i
$225$	−4.55842	−	2.05446i	−0.303895	−	0.136964i
$226$	10.2665			0.682917
$227$	3.10308	+	1.79156i	0.205958	+	0.118910i	0.599432	−	0.800426i	$-0.295393\pi$
$227$	3.10308	+	1.79156i	0.205958	+	0.118910i	−0.393473	+	0.919336i	$0.628727\pi$
$228$	−2.00626	−	1.15831i	−0.132868	−	0.0767111i
$229$	12.0000			0.792982			0.396491	−	0.918039i	$-0.370228\pi$
$229$	12.0000			0.792982			0.396491	+	0.918039i	$0.370228\pi$
$230$	5.70637	+	17.6994i	0.376267	+	1.16706i
$231$	0.366750	+	0.635230i	0.0241304	+	0.0417951i
$232$	−2.59808	+	1.50000i	−0.170572	+	0.0984798i
$233$			24.6332i			1.61378i	0.590703	+	0.806889i	$0.298850\pi$
$233$			24.6332i			1.61378i	−0.590703	+	0.806889i	$0.701150\pi$
$234$	−3.50000	+	0.866025i	−0.228802	+	0.0566139i
$235$	13.7916	+	12.4749i	0.899662	+	0.813775i
$236$	−4.31662	−	7.47661i	−0.280988	−	0.486686i
$237$	−3.46410	+	2.00000i	−0.225018	+	0.129914i
$238$	11.3017	+	6.52506i	0.732583	+	0.422957i
$239$	−1.68338			−0.108888			−0.0544442	−	0.998517i	$-0.517339\pi$
$239$	−1.68338			−0.108888			−0.0544442	+	0.998517i	$0.517339\pi$
$240$	−2.12819	+	0.686141i	−0.137374	+	0.0442902i
$241$	6.18338	−	10.7099i	0.398306	−	0.689887i	−0.595211	−	0.803570i	$-0.702931\pi$
$241$	6.18338	−	10.7099i	0.398306	−	0.689887i	0.993517	+	0.113683i	$0.0362648\pi$
$242$			10.8997i			0.700662i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	3.65831	+	6.33638i	0.234199	+	0.405645i
$245$	3.57051	+	0.767434i	0.228112	+	0.0490296i
$246$	7.31662			0.466491
$247$	−8.02502	−	2.31662i	−0.510620	−	0.147403i
$248$		−	4.00000i		−	0.254000i
$249$	−0.841688	−	1.45785i	−0.0533398	−	0.0923872i
$250$	−11.1109	−	1.24456i	−0.702712	−	0.0787131i
$251$	−6.94987	+	12.0375i	−0.438672	+	0.759803i	−0.997587	−	0.0694223i	$-0.977884\pi$
$251$	−6.94987	+	12.0375i	−0.438672	+	0.759803i	0.558915	+	0.829225i	$0.311218\pi$
$252$		−	2.31662i		−	0.145934i
$253$	2.28046	+	1.31662i	0.143371	+	0.0827755i
$254$	2.00000	−	3.46410i	0.125491	−	0.217357i
$255$	−8.44987	+	9.34169i	−0.529152	+	0.584999i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.69490	−	2.13325i	0.230481	−	0.133068i	−0.380313	−	0.924858i	$-0.624184\pi$
$257$	3.69490	−	2.13325i	0.230481	−	0.133068i	0.610794	+	0.791789i	$0.290850\pi$
$258$	−3.73831	+	2.15831i	−0.232737	+	0.134371i
$259$	−13.0501			−0.810895
$260$	−6.85446	+	4.24456i	−0.425096	+	0.263237i
$261$	3.00000			0.185695
$262$		0			0
$263$	15.2274	−	8.79156i	0.938964	−	0.542111i	0.0493284	−	0.998783i	$-0.484292\pi$
$263$	15.2274	−	8.79156i	0.938964	−	0.542111i	0.889635	+	0.456672i	$0.150959\pi$
$264$	−0.158312	+	0.274205i	−0.00974345	+	0.0168762i
$265$	−18.7665	−	16.9749i	−1.15282	−	1.04276i
$266$	2.68338	−	4.64774i	0.164528	−	0.284971i
$267$	−13.2212	−	7.63325i	−0.809123	−	0.467147i
$268$		−	12.9499i		−	0.791039i
$269$	−0.316625	+	0.548410i	−0.0193050	+	0.0334372i	−0.875516	−	0.483188i	$-0.839479\pi$
$269$	−0.316625	+	0.548410i	−0.0193050	+	0.0334372i	0.856212	+	0.516625i	$0.172812\pi$
$270$	2.18614	+	0.469882i	0.133044	+	0.0285961i
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$			5.63325i			0.341566i
$273$	−2.00626	−	8.10819i	−0.121424	−	0.490730i
$274$	7.63325			0.461141
$275$	−1.28500	+	0.924697i	−0.0774882	+	0.0557613i
$276$	−4.15831	−	7.20241i	−0.250301	−	0.433534i
$277$	−23.3827	−	13.5000i	−1.40493	−	0.811136i	−0.410036	−	0.912069i	$-0.634484\pi$
$277$	−23.3827	−	13.5000i	−1.40493	−	0.811136i	−0.994893	+	0.100933i	$0.967817\pi$
$278$		−	21.2665i		−	1.27548i
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$	−1.58953	−	4.93023i	−0.0949926	−	0.294637i
$281$	19.2164			1.14635			0.573176	−	0.819432i	$-0.305711\pi$
$281$	19.2164			1.14635			0.573176	+	0.819432i	$0.305711\pi$
$282$	−7.20241	−	4.15831i	−0.428897	−	0.247624i
$283$	2.64149	−	1.52506i	0.157020	−	0.0906556i	−0.419431	−	0.907787i	$-0.637770\pi$
$283$	2.64149	−	1.52506i	0.157020	−	0.0906556i	0.576451	+	0.817132i	$0.304437\pi$
$284$	0.841688	+	1.45785i	0.0499450	+	0.0865072i
$285$	3.84169	+	3.47494i	0.227562	+	0.205838i
$286$	−0.316625	+	1.09682i	−0.0187224	+	0.0648564i
$287$			16.9499i			1.00052i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	7.36675	+	12.7596i	0.433338	+	0.750564i
$290$	6.38458	−	2.05842i	0.374916	−	0.120875i
$291$	−6.00000			−0.351726
$292$	6.33638	+	3.65831i	0.370809	+	0.214087i
$293$	12.7162	+	7.34169i	0.742887	+	0.428906i	0.823118	−	0.567870i	$-0.192232\pi$
$293$	12.7162	+	7.34169i	0.742887	+	0.428906i	−0.0802311	+	0.996776i	$0.525566\pi$
$294$	−1.63325			−0.0952530
$295$	5.92362	+	18.3732i	0.344887	+	1.06973i
$296$	−2.81662	−	4.87854i	−0.163713	−	0.283559i
$297$	0.274205	−	0.158312i	0.0159110	−	0.00918622i
$298$			9.63325i			0.558039i
$299$	−20.7916	−	21.6072i	−1.20241	−	1.24958i
$300$	4.97494	−	0.500000i	0.287228	−	0.0288675i
$301$	−5.00000	−	8.66025i	−0.288195	−	0.499169i
$302$	11.2149	−	6.47494i	0.645346	−	0.372591i
$303$	−11.8067	−	6.81662i	−0.678280	−	0.391605i
$304$	2.31662			0.132868
$305$	−5.02023	−	15.5712i	−0.287458	−	0.891604i
$306$	2.81662	−	4.87854i	0.161016	−	0.278887i
$307$			30.2164i			1.72454i	0.506449	+	0.862270i	$0.330958\pi$
$307$			30.2164i			1.72454i	−0.506449	+	0.862270i	$0.669042\pi$
$308$	−0.635230	−	0.366750i	−0.0361956	−	0.0208975i
$309$	−0.841688	−	1.45785i	−0.0478819	−	0.0829339i
$310$	−1.87953	+	8.74456i	−0.106750	+	0.496658i
$311$	5.68338			0.322275			0.161137	−	0.986932i	$-0.448484\pi$
$311$	5.68338			0.322275			0.161137	+	0.986932i	$0.448484\pi$
$312$	2.59808	−	2.50000i	0.147087	−	0.141535i
$313$		−	30.0000i		−	1.69570i	−0.530236	−	0.847850i	$-0.677897\pi$
$313$		−	30.0000i		−	1.69570i	0.530236	−	0.847850i	$-0.322103\pi$
$314$	−6.13325	−	10.6231i	−0.346119	−	0.599496i
$315$	−1.08854	+	5.06447i	−0.0613323	+	0.285350i
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$			15.9499i			0.895834i	0.894075	+	0.447917i	$0.147834\pi$
$317$			15.9499i			0.895834i	−0.894075	+	0.447917i	$0.852166\pi$
$318$	9.80048	+	5.65831i	0.549584	+	0.317302i
$319$	0.474937	−	0.822615i	0.0265914	−	0.0460576i
$320$	1.50000	−	1.65831i	0.0838525	−	0.0927025i
$321$	−9.15831	+	15.8627i	−0.511167	+	0.885367i
$322$	16.6853	−	9.63325i	0.929834	−	0.536840i
$323$	11.3017	−	6.52506i	0.628846	−	0.363064i
$324$	−1.00000			−0.0555556
$325$	16.9793	−	6.05842i	0.941840	−	0.336061i
$326$	−4.63325			−0.256612
$327$	−5.19615	+	3.00000i	−0.287348	+	0.165900i
$328$	−6.33638	+	3.65831i	−0.349868	+	0.201997i
$329$	9.63325	−	16.6853i	0.531098	−	0.919889i
$330$	0.474937	−	0.525063i	0.0261444	−	0.0289038i
$331$	10.6332	−	18.4173i	0.584456	−	1.01231i	−0.410487	−	0.911867i	$-0.634641\pi$
$331$	10.6332	−	18.4173i	0.584456	−	1.01231i	0.994943	−	0.100441i	$-0.0320255\pi$
$332$	1.45785	+	0.841688i	0.0800097	+	0.0461936i
$333$			5.63325i			0.308700i
$334$		0			0
$335$	−6.08491	+	28.3102i	−0.332454	+	1.54675i
$336$	1.15831	+	2.00626i	0.0631911	+	0.109450i
$337$		−	11.3166i		−	0.616456i	−0.951313	−	0.308228i	$-0.900264\pi$
$337$		−	11.3166i		−	0.616456i	0.951313	−	0.308228i	$-0.0997359\pi$
$338$	6.92820	−	11.0000i	0.376845	−	0.598321i
$339$	10.2665			0.557600
$340$	2.64696	−	12.3151i	0.143552	−	0.667879i
$341$	0.633250	+	1.09682i	0.0342924	+	0.0593962i
$342$	−2.00626	−	1.15831i	−0.108486	−	0.0626344i
$343$		−	20.0000i		−	1.07990i
$344$	2.15831	−	3.73831i	0.116368	−	0.201556i
$345$	5.70637	+	17.6994i	0.307221	+	0.952903i
$346$	−11.2665			−0.605691
$347$	−27.3518	−	15.7916i	−1.46832	−	0.847735i	−0.468951	−	0.883224i	$-0.655368\pi$
$347$	−27.3518	−	15.7916i	−1.46832	−	0.847735i	−0.999370	+	0.0354888i	$0.988701\pi$
$348$	−2.59808	+	1.50000i	−0.139272	+	0.0804084i
$349$	13.6332	+	23.6135i	0.729771	+	1.26400i	0.956980	+	0.290155i	$0.0937067\pi$
$349$	13.6332	+	23.6135i	0.729771	+	1.26400i	−0.227209	+	0.973846i	$0.572960\pi$
$350$	1.15831	+	11.5251i	0.0619144	+	0.616041i
$351$	−3.50000	+	0.866025i	−0.186816	+	0.0462250i
$352$		−	0.316625i		−	0.0168762i
$353$	29.1272	−	16.8166i	1.55029	−	0.895059i	0.552169	−	0.833732i	$-0.313800\pi$
$353$	29.1272	−	16.8166i	1.55029	−	0.895059i	0.998118	−	0.0613266i	$-0.0195331\pi$
$354$	−4.31662	−	7.47661i	−0.229426	−	0.397378i
$355$	−1.15503	−	3.58255i	−0.0613027	−	0.190142i
$356$	15.2665			0.809123
$357$	11.3017	+	6.52506i	0.598152	+	0.345343i
$358$	22.1556	+	12.7916i	1.17096	+	0.676055i
$359$	9.68338			0.511069			0.255534	−	0.966800i	$-0.417749\pi$
$359$	9.68338			0.511069			0.255534	+	0.966800i	$0.417749\pi$
$360$	−2.12819	+	0.686141i	−0.112166	+	0.0361628i
$361$	6.81662	+	11.8067i	0.358770	+	0.621407i
$362$	−0.0434101	+	0.0250628i	−0.00228158	+	0.00131727i
$363$			10.8997i			0.572088i
$364$	5.79156	+	6.01877i	0.303560	+	0.315469i
$365$	−12.1332	−	10.9749i	−0.635083	−	0.574454i
$366$	3.65831	+	6.33638i	0.191223	+	0.331208i
$367$	22.7909	−	13.1583i	1.18967	−	0.686858i	0.231441	−	0.972849i	$-0.425656\pi$
$367$	22.7909	−	13.1583i	1.18967	−	0.686858i	0.958232	+	0.285991i	$0.0923226\pi$
$368$	7.20241	+	4.15831i	0.375451	+	0.216767i
$369$	7.31662			0.380888
$370$	3.86520	+	11.9886i	0.200942	+	0.623260i
$371$	−13.1082	+	22.7040i	−0.680543	+	1.17874i
$372$		−	4.00000i		−	0.207390i
$373$	−0.866025	−	0.500000i	−0.0448411	−	0.0258890i	0.477412	−	0.878680i	$-0.341575\pi$
$373$	−0.866025	−	0.500000i	−0.0448411	−	0.0258890i	−0.522253	+	0.852791i	$0.674908\pi$
$374$	−0.891813	−	1.54467i	−0.0461146	−	0.0798728i
$375$	−11.1109	−	1.24456i	−0.573762	−	0.0642689i
$376$	8.31662			0.428897
$377$	−7.79423	+	7.50000i	−0.401423	+	0.386270i
$378$		−	2.31662i		−	0.119154i
$379$	12.9499	+	22.4298i	0.665190	+	1.15214i	0.979234	+	0.202735i	$0.0649830\pi$
$379$	12.9499	+	22.4298i	0.665190	+	1.15214i	−0.314043	+	0.949409i	$0.601684\pi$
$380$	−5.06447	−	1.08854i	−0.259802	−	0.0558409i
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$			0.633250i			0.0323999i
$383$	−28.8096	−	16.6332i	−1.47210	−	0.849919i	−0.472595	−	0.881280i	$-0.656683\pi$
$383$	−28.8096	−	16.6332i	−1.47210	−	0.849919i	−0.999508	+	0.0313602i	$0.990016\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	1.21637	+	1.10025i	0.0619921	+	0.0560740i
$386$	7.97494	−	13.8130i	0.405914	−	0.703063i
$387$	−3.73831	+	2.15831i	−0.190029	+	0.109713i
$388$	5.19615	−	3.00000i	0.263795	−	0.152302i
$389$	2.36675			0.119999			0.0599995	−	0.998198i	$-0.480890\pi$
$389$	2.36675			0.119999			0.0599995	+	0.998198i	$0.480890\pi$
$390$	−6.85446	+	4.24456i	−0.347089	+	0.214932i
$391$	46.8496			2.36929
$392$	1.41444	−	0.816625i	0.0714398	−	0.0412458i
$393$		0			0
$394$	−6.63325	+	11.4891i	−0.334178	+	0.578814i
$395$	−6.00000	+	6.63325i	−0.301893	+	0.333755i
$396$	−0.158312	+	0.274205i	−0.00795550	+	0.0137793i
$397$	18.9657	+	10.9499i	0.951863	+	0.549558i	0.893659	−	0.448746i	$-0.148129\pi$
$397$	18.9657	+	10.9499i	0.951863	+	0.549558i	0.0582039	+	0.998305i	$0.481463\pi$
$398$		−	15.6834i		−	0.786137i
$399$	2.68338	−	4.64774i	0.134337	−	0.232678i
$400$	−4.05842	+	2.92048i	−0.202921	+	0.146024i
$401$	8.65831	+	14.9966i	0.432375	+	0.748896i	0.997077	−	0.0763987i	$-0.0243422\pi$
$401$	8.65831	+	14.9966i	0.432375	+	0.748896i	−0.564702	+	0.825295i	$0.691009\pi$
$402$		−	12.9499i		−	0.645881i
$403$	−3.46410	−	14.0000i	−0.172559	−	0.697390i
$404$	13.6332			0.678280
$405$	2.18614	+	0.469882i	0.108630	+	0.0233486i
$406$	−3.47494	−	6.01877i	−0.172458	−	0.298706i
$407$	1.54467	+	0.891813i	0.0765662	+	0.0442055i
$408$			5.63325i			0.278887i
$409$	−10.5000	+	18.1865i	−0.519192	+	0.899266i	0.480560	+	0.876962i	$0.340434\pi$
$409$	−10.5000	+	18.1865i	−0.519192	+	0.899266i	−0.999751	+	0.0223042i	$0.992900\pi$
$410$	15.5712	−	5.02023i	0.769007	−	0.247932i
$411$	7.63325			0.376520
$412$	1.45785	+	0.841688i	0.0718229	+	0.0414670i
$413$	17.3205	−	10.0000i	0.852286	−	0.492068i
$414$	−4.15831	−	7.20241i	−0.204370	−	0.353979i
$415$	−2.79156	−	2.52506i	−0.137032	−	0.123950i
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$		−	21.2665i		−	1.04142i
$418$	−0.635230	+	0.366750i	−0.0310701	+	0.0179383i
$419$	13.5831	+	23.5267i	0.663579	+	1.14935i	0.979668	+	0.200623i	$0.0642967\pi$
$419$	13.5831	+	23.5267i	0.663579	+	1.14935i	−0.316089	+	0.948729i	$0.602370\pi$
$420$	−1.58953	−	4.93023i	−0.0775611	−	0.240570i
$421$	−18.0501			−0.879709			−0.439855	−	0.898069i	$-0.644970\pi$
$421$	−18.0501			−0.879709			−0.439855	+	0.898069i	$0.644970\pi$
$422$	−4.01251	−	2.31662i	−0.195326	−	0.112772i
$423$	−7.20241	−	4.15831i	−0.350193	−	0.202184i
$424$	−11.3166			−0.549584
$425$	−11.5733	+	25.6787i	−0.561386	+	1.24560i
$426$	0.841688	+	1.45785i	0.0407799	+	0.0706329i
$427$	−14.6790	+	8.47494i	−0.710368	+	0.410131i
$428$		−	18.3166i		−	0.885367i
$429$	−0.316625	+	1.09682i	−0.0152868	+	0.0529550i
$430$	−6.47494	+	7.15831i	−0.312249	+	0.345204i
$431$	−3.47494	−	6.01877i	−0.167382	−	0.289914i	0.770117	−	0.637903i	$-0.220198\pi$
$431$	−3.47494	−	6.01877i	−0.167382	−	0.289914i	−0.937499	+	0.347989i	$0.886865\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−21.2896	−	12.2916i	−1.02311	−	0.590695i	−0.108109	−	0.994139i	$-0.534480\pi$
$433$	−21.2896	−	12.2916i	−1.02311	−	0.590695i	−0.915004	+	0.403444i	$0.867813\pi$
$434$	9.26650			0.444806
$435$	6.38458	−	2.05842i	0.306117	−	0.0986938i
$436$	3.00000	−	5.19615i	0.143674	−	0.248851i
$437$		−	19.2665i		−	0.921642i
$438$	6.33638	+	3.65831i	0.302764	+	0.174801i
$439$	−15.8417	−	27.4386i	−0.756082	−	1.30957i	−0.944834	−	0.327548i	$-0.893778\pi$
$439$	−15.8417	−	27.4386i	−0.756082	−	1.30957i	0.188752	−	0.982025i	$-0.439556\pi$
$440$	−0.148776	+	0.692186i	−0.00709263	+	0.0329987i
$441$	−1.63325			−0.0777738
$442$	4.87854	+	19.7164i	0.232048	+	0.937812i
$443$			13.2665i			0.630310i	0.949040	+	0.315155i	$0.102057\pi$
$443$			13.2665i			0.630310i	−0.949040	+	0.315155i	$0.897943\pi$
$444$	−2.81662	−	4.87854i	−0.133671	−	0.231525i
$445$	−33.3747	−	7.17345i	−1.58211	−	0.340054i
$446$	−10.3166	+	17.8689i	−0.488506	+	0.846118i
$447$			9.63325i			0.455637i
$448$	−2.00626	−	1.15831i	−0.0947867	−	0.0547251i
$449$	−18.2665	+	31.6385i	−0.862049	+	1.49311i	0.00789800	+	0.999969i	$0.497486\pi$
$449$	−18.2665	+	31.6385i	−0.862049	+	1.49311i	−0.869947	+	0.493145i	$0.835847\pi$
$450$	4.97494	−	0.500000i	0.234521	−	0.0235702i
$451$	1.15831	−	2.00626i	0.0545428	−	0.0944709i
$452$	−8.89105	+	5.13325i	−0.418200	+	0.241448i
$453$	11.2149	−	6.47494i	0.526923	−	0.304219i
$454$	−3.58312			−0.168164
$455$	−9.83306	−	15.8792i	−0.460981	−	0.744429i
$456$	2.31662			0.108486
$457$	3.42069	−	1.97494i	0.160013	−	0.0923837i	−0.417855	−	0.908514i	$-0.637218\pi$
$457$	3.42069	−	1.97494i	0.160013	−	0.0923837i	0.577868	+	0.816130i	$0.303885\pi$
$458$	−10.3923	+	6.00000i	−0.485601	+	0.280362i
$459$	2.81662	−	4.87854i	0.131469	−	0.227711i
$460$	−13.7916	−	12.4749i	−0.643035	−	0.581647i
$461$	1.81662	−	3.14649i	0.0846087	−	0.146546i	−0.820616	−	0.571480i	$-0.806369\pi$
$461$	1.81662	−	3.14649i	0.0846087	−	0.146546i	0.905224	+	0.424934i	$0.139703\pi$
$462$	−0.635230	−	0.366750i	−0.0295536	−	0.0170628i
$463$		−	10.9499i		−	0.508884i	−0.967088	−	0.254442i	$-0.918108\pi$
$463$		−	10.9499i		−	0.508884i	0.967088	−	0.254442i	$-0.0818918\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$	−1.87953	+	8.74456i	−0.0871610	+	0.405519i
$466$	−12.3166	−	21.3330i	−0.570557	−	0.988233i
$467$			0.416876i			0.0192907i	0.999953	+	0.00964536i	$0.00307026\pi$
$467$			0.416876i			0.0192907i	−0.999953	+	0.00964536i	$0.996930\pi$
$468$	2.59808	−	2.50000i	0.120096	−	0.115563i
$469$	30.0000			1.38527
$470$	−18.1813	−	3.90783i	−0.838641	−	0.180255i
$471$	−6.13325	−	10.6231i	−0.282605	−	0.489487i
$472$	7.47661	+	4.31662i	0.344139	+	0.198689i
$473$			1.36675i			0.0628433i
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$	10.5602	+	4.75940i	0.484533	+	0.218376i
$476$	−13.0501			−0.598152
$477$	9.80048	+	5.65831i	0.448733	+	0.259076i
$478$	1.45785	−	0.841688i	0.0666803	−	0.0384979i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	1.50000	−	1.65831i	0.0684653	−	0.0756913i
$481$	−14.0831	−	14.6356i	−0.642135	−	0.667326i
$482$			12.3668i			0.563290i
$483$	16.6853	−	9.63325i	0.759206	−	0.438328i
$484$	−5.44987	−	9.43946i	−0.247722	−	0.429066i
$485$	−12.7692	+	4.11684i	−0.579818	+	0.186936i
$486$	−1.00000			−0.0453609
$487$	2.00626	+	1.15831i	0.0909121	+	0.0524881i	0.544767	−	0.838588i	$-0.316618\pi$
$487$	2.00626	+	1.15831i	0.0909121	+	0.0524881i	−0.453855	+	0.891076i	$0.649951\pi$
$488$	−6.33638	−	3.65831i	−0.286835	−	0.165604i
$489$	−4.63325			−0.209523
$490$	−3.47587	+	1.12064i	−0.157024	+	0.0506253i
$491$	3.20844	+	5.55718i	0.144795	+	0.250792i	0.929296	−	0.369335i	$-0.120414\pi$
$491$	3.20844	+	5.55718i	0.144795	+	0.250792i	−0.784502	+	0.620127i	$0.787081\pi$
$492$	−6.33638	+	3.65831i	−0.285666	+	0.164929i
$493$		−	16.8997i		−	0.761126i
$494$	8.10819	−	2.00626i	0.364805	−	0.0902657i
$495$	0.474937	−	0.525063i	0.0213468	−	0.0235998i
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−3.37728	+	1.94987i	−0.151492	+	0.0874638i
$498$	1.45785	+	0.841688i	0.0653276	+	0.0377169i
$499$	2.10025			0.0940202			0.0470101	−	0.998894i	$-0.485031\pi$
$499$	2.10025			0.0940202			0.0470101	+	0.998894i	$0.485031\pi$
$500$	10.2446	−	4.47760i	0.458151	−	0.200245i
$501$		0			0
$502$		−	13.8997i		−	0.620376i
$503$	10.1181	+	5.84169i	0.451144	+	0.260468i	0.708313	−	0.705898i	$-0.249456\pi$
$503$	10.1181	+	5.84169i	0.451144	+	0.260468i	−0.257169	+	0.966366i	$0.582790\pi$
$504$	1.15831	+	2.00626i	0.0515953	+	0.0893657i
$505$	−29.8042	−	6.40602i	−1.32627	−	0.285064i
$506$	−2.63325			−0.117062
$507$	6.92820	−	11.0000i	0.307692	−	0.488527i
$508$			4.00000i			0.177471i
$509$	−15.0831	−	26.1247i	−0.668548	−	1.15796i	−0.978310	−	0.207145i	$-0.933583\pi$
$509$	−15.0831	−	26.1247i	−0.668548	−	1.15796i	0.309763	−	0.950814i	$-0.399750\pi$
$510$	2.64696	−	12.3151i	0.117209	−	0.545321i
$511$	−8.47494	+	14.6790i	−0.374909	+	0.649362i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.00626	−	1.15831i	−0.0885784	−	0.0511407i
$514$	−2.13325	+	3.69490i	−0.0940936	+	0.162975i
$515$	−2.79156	−	2.52506i	−0.123011	−	0.111268i
$516$	2.15831	−	3.73831i	0.0950144	−	0.164570i
$517$	−2.28046	+	1.31662i	−0.100295	+	0.0579051i
$518$	11.3017	−	6.52506i	0.496570	−	0.286695i
$519$	−11.2665			−0.494544
$520$	3.81386	−	7.10313i	0.167249	−	0.311493i
$521$	−39.9499			−1.75024			−0.875118	−	0.483910i	$-0.839216\pi$
$521$	−39.9499			−1.75024			−0.875118	+	0.483910i	$0.839216\pi$
$522$	−2.59808	+	1.50000i	−0.113715	+	0.0656532i
$523$	−30.1807	+	17.4248i	−1.31971	+	0.761934i	−0.983681	−	0.179919i	$-0.942417\pi$
$523$	−30.1807	+	17.4248i	−1.31971	+	0.761934i	−0.336027	+	0.941853i	$0.609083\pi$
$524$		0			0
$525$	1.15831	+	11.5251i	0.0505529	+	0.502995i
$526$	−8.79156	+	15.2274i	−0.383330	+	0.663948i
$527$	19.5141	+	11.2665i	0.850050	+	0.490776i
$528$		−	0.316625i		−	0.0137793i
$529$	23.0831	−	39.9811i	1.00361	−	1.73831i
$530$	24.7397	+	5.31748i	1.07463	+	0.230976i
$531$	−4.31662	−	7.47661i	−0.187326	−	0.324457i
$532$			5.36675i			0.232678i
$533$	−19.0091	+	18.2916i	−0.823378	+	0.792295i
$534$	15.2665			0.660646
$535$	−8.60665	+	40.0427i	−0.372098	+	1.73120i
$536$	6.47494	+	11.2149i	0.279675	+	0.484411i
$537$	22.1556	+	12.7916i	0.956086	+	0.551997i
$538$		−	0.633250i		−	0.0273013i
$539$	−0.258564	+	0.447845i	−0.0111371	+	0.0192901i
$540$	−2.12819	+	0.686141i	−0.0915829	+	0.0295268i
$541$	−21.2164			−0.912163			−0.456082	−	0.889938i	$-0.650747\pi$
$541$	−21.2164			−0.912163			−0.456082	+	0.889938i	$0.650747\pi$
$542$	−13.8564	−	8.00000i	−0.595184	−	0.343629i
$543$	−0.0434101	+	0.0250628i	−0.00186290	+	0.00107555i
$544$	−2.81662	−	4.87854i	−0.120762	−	0.209166i
$545$	−9.00000	+	9.94987i	−0.385518	+	0.426206i
$546$	5.79156	+	6.01877i	0.247856	+	0.257579i
$547$		−	11.0501i		−	0.472469i	−0.971696	−	0.236235i	$-0.924087\pi$
$547$		−	11.0501i		−	0.472469i	0.971696	−	0.236235i	$-0.0759134\pi$
$548$	−6.61059	+	3.81662i	−0.282390	+	0.163038i
$549$	3.65831	+	6.33638i	0.156133	+	0.270430i
$550$	0.650492	−	1.44331i	0.0277371	−	0.0615429i
$551$	−6.94987			−0.296075
$552$	7.20241	+	4.15831i	0.306555	+	0.176990i
$553$	8.02502	+	4.63325i	0.341259	+	0.197026i
$554$	27.0000			1.14712
$555$	3.86520	+	11.9886i	0.164069	+	0.508890i
$556$	10.6332	+	18.4173i	0.450950	+	0.781069i
$557$	−28.3046	+	16.3417i	−1.19931	+	0.692420i	−0.960400	−	0.278623i	$-0.910122\pi$
$557$	−28.3046	+	16.3417i	−1.19931	+	0.692420i	−0.238905	+	0.971043i	$0.576789\pi$
$558$		−	4.00000i		−	0.169334i
$559$	4.31662	−	14.9532i	0.182574	−	0.632454i
$560$	3.84169	+	3.47494i	0.162341	+	0.146843i
$561$	−0.891813	−	1.54467i	−0.0376524	−	0.0652158i
$562$	−16.6419	+	9.60819i	−0.701995	+	0.405297i
$563$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$563$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$564$	8.31662			0.350193
$565$	21.8491	−	7.04426i	0.919199	−	0.296354i
$566$	−1.52506	+	2.64149i	−0.0641032	+	0.111030i
$567$		−	2.31662i		−	0.0972891i
$568$	−1.45785	−	0.841688i	−0.0611698	−	0.0353164i
$569$	5.26650	+	9.12184i	0.220783	+	0.382408i	0.955046	−	0.296458i	$-0.0958054\pi$
$569$	5.26650	+	9.12184i	0.220783	+	0.382408i	−0.734263	+	0.678865i	$0.762472\pi$
$570$	−5.06447	−	1.08854i	−0.212127	−	0.0455939i
$571$	−9.05013			−0.378736			−0.189368	−	0.981906i	$-0.560644\pi$
$571$	−9.05013			−0.378736			−0.189368	+	0.981906i	$0.560644\pi$
$572$	−0.274205	−	1.10819i	−0.0114651	−	0.0463356i
$573$			0.633250i			0.0264544i
$574$	−8.47494	−	14.6790i	−0.353737	−	0.612691i
$575$	24.2885	+	33.7524i	1.01290	+	1.40757i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$			43.9499i			1.82966i	0.403842	+	0.914829i	$0.367674\pi$
$577$			43.9499i			1.82966i	−0.403842	+	0.914829i	$0.632326\pi$
$578$	−12.7596	−	7.36675i	−0.530729	−	0.306416i
$579$	7.97494	−	13.8130i	0.331427	−	0.574049i
$580$	−4.50000	+	4.97494i	−0.186852	+	0.206573i
$581$	−1.94987	+	3.37728i	−0.0808944	+	0.140113i
$582$	5.19615	−	3.00000i	0.215387	−	0.124354i
$583$	3.10308	−	1.79156i	0.128516	−	0.0741989i
$584$	−7.31662			−0.302764
$585$	−6.85446	+	4.24456i	−0.283397	+	0.175491i
$586$	−14.6834			−0.606565
$587$	−29.9065	+	17.2665i	−1.23437	+	0.712665i	−0.967938	−	0.251189i	$-0.919179\pi$
$587$	−29.9065	+	17.2665i	−1.23437	+	0.712665i	−0.266433	+	0.963853i	$0.585845\pi$
$588$	1.41444	−	0.816625i	0.0583303	−	0.0336770i
$589$	4.63325	−	8.02502i	0.190910	−	0.330665i
$590$	−14.3166	−	12.9499i	−0.589406	−	0.533138i
$591$	−6.63325	+	11.4891i	−0.272855	+	0.472599i
$592$	4.87854	+	2.81662i	0.200507	+	0.115763i
$593$		−	17.6332i		−	0.724111i	−0.932157	−	0.362055i	$-0.882075\pi$
$593$		−	17.6332i		−	0.724111i	0.932157	−	0.362055i	$-0.117925\pi$
$594$	−0.158312	+	0.274205i	−0.00649564	+	0.0112508i
$595$	28.5294	+	6.13202i	1.16959	+	0.251388i
$596$	−4.81662	−	8.34264i	−0.197297	−	0.341728i
$597$		−	15.6834i		−	0.641878i
$598$	28.8096	+	8.31662i	1.17811	+	0.340092i
$599$	−1.26650			−0.0517478			−0.0258739	−	0.999665i	$-0.508237\pi$
$599$	−1.26650			−0.0517478			−0.0258739	+	0.999665i	$0.508237\pi$
$600$	−4.05842	+	2.92048i	−0.165684	+	0.119228i
$601$	−16.5000	−	28.5788i	−0.673049	−	1.16576i	−0.977035	−	0.213079i	$-0.931651\pi$
$601$	−16.5000	−	28.5788i	−0.673049	−	1.16576i	0.303986	−	0.952676i	$-0.401682\pi$
$602$	8.66025	+	5.00000i	0.352966	+	0.203785i
$603$		−	12.9499i		−	0.527360i
$604$	−6.47494	+	11.2149i	−0.263461	+	0.456329i
$605$	7.47876	+	23.1968i	0.304055	+	0.943083i
$606$	13.6332			0.553813
$607$	12.0375	+	6.94987i	0.488588	+	0.282087i	0.723989	−	0.689812i	$-0.242307\pi$
$607$	12.0375	+	6.94987i	0.488588	+	0.282087i	−0.235400	+	0.971899i	$0.575640\pi$
$608$	−2.00626	+	1.15831i	−0.0813644	+	0.0469758i
$609$	−3.47494	−	6.01877i	−0.140812	−	0.243893i
$610$	12.1332	+	10.9749i	0.491261	+	0.444362i
$611$	29.1082	−	7.20241i	1.17759	−	0.291378i
$612$			5.63325i			0.227711i
$613$	−4.24331	+	2.44987i	−0.171386	+	0.0989495i	−0.583239	−	0.812301i	$-0.698215\pi$
$613$	−4.24331	+	2.44987i	−0.171386	+	0.0989495i	0.411853	+	0.911250i	$0.364882\pi$
$614$	−15.1082	−	26.1681i	−0.609717	−	1.05606i
$615$	15.5712	−	5.02023i	0.627891	−	0.202435i
$616$	0.733501			0.0295536
$617$	−19.2834	−	11.1332i	−0.776319	−	0.448208i	0.0588054	−	0.998269i	$-0.481271\pi$
$617$	−19.2834	−	11.1332i	−0.776319	−	0.448208i	−0.835124	+	0.550062i	$0.814604\pi$
$618$	1.45785	+	0.841688i	0.0586432	+	0.0338576i
$619$	−31.1662			−1.25268			−0.626339	−	0.779551i	$-0.715447\pi$
$619$	−31.1662			−1.25268			−0.626339	+	0.779551i	$0.715447\pi$
$620$	−2.74456	−	8.51278i	−0.110224	−	0.341881i
$621$	−4.15831	−	7.20241i	−0.166867	−	0.289023i
$622$	−4.92195	+	2.84169i	−0.197352	+	0.113941i
$623$			35.3668i			1.41694i
$624$	−1.00000	+	3.46410i	−0.0400320	+	0.138675i
$625$	−24.5000	+	4.97494i	−0.980000	+	0.198997i
$626$	15.0000	+	25.9808i	0.599521	+	1.03840i
$627$	−0.635230	+	0.366750i	−0.0253687	+	0.0146466i
$628$	10.6231	+	6.13325i	0.423908	+	0.244743i
$629$	31.7335			1.26530
$630$	−1.58953	−	4.93023i	−0.0633284	−	0.196425i
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	−0.595397	−	0.803432i	$-0.703005\pi$
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	0.993491	+	0.113913i	$0.0363385\pi$
$632$			4.00000i			0.159111i
$633$	−4.01251	−	2.31662i	−0.159483	−	0.0920776i
$634$	−7.97494	−	13.8130i	−0.316725	−	0.548584i
$635$	1.87953	−	8.74456i	0.0745868	−	0.347017i
$636$	−11.3166			−0.448733
$637$	4.24331	−	4.08312i	0.168126	−	0.161779i
$638$			0.949874i			0.0376059i
$639$	0.841688	+	1.45785i	0.0332966	+	0.0576715i
$640$	−0.469882	+	2.18614i	−0.0185737	+	0.0864148i
$641$	16.6082	−	28.7662i	0.655984	−	1.13620i	−0.325662	−	0.945486i	$-0.605587\pi$
$641$	16.6082	−	28.7662i	0.655984	−	1.13620i	0.981646	−	0.190711i	$-0.0610794\pi$
$642$		−	18.3166i		−	0.722900i
$643$	35.7378	+	20.6332i	1.40936	+	0.813696i	0.995327	−	0.0965646i	$-0.0307854\pi$
$643$	35.7378	+	20.6332i	1.40936	+	0.813696i	0.414036	+	0.910261i	$0.364119\pi$
$644$	−9.63325	+	16.6853i	−0.379603	+	0.657492i
$645$	−6.47494	+	7.15831i	−0.254950	+	0.281858i
$646$	−6.52506	+	11.3017i	−0.256725	+	0.444661i
$647$	−1.64523	+	0.949874i	−0.0646807	+	0.0373434i	−0.531992	−	0.846750i	$-0.678556\pi$
$647$	−1.64523	+	0.949874i	−0.0646807	+	0.0373434i	0.467311	+	0.884093i	$0.345223\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−2.73350			−0.107299
$650$	−11.6753	+	13.7364i	−0.457942	+	0.538785i
$651$	9.26650			0.363183
$652$	4.01251	−	2.31662i	0.157142	−	0.0907260i
$653$	0.635230	−	0.366750i	0.0248585	−	0.0143521i	−0.487519	−	0.873112i	$-0.662098\pi$
$653$	0.635230	−	0.366750i	0.0248585	−	0.0143521i	0.512378	+	0.858760i	$0.328765\pi$
$654$	3.00000	−	5.19615i	0.117309	−	0.203186i
$655$		0			0
$656$	3.65831	−	6.33638i	0.142833	−	0.247394i
$657$	6.33638	+	3.65831i	0.247206	+	0.142724i
$658$			19.2665i			0.751086i
$659$	7.68338	−	13.3080i	0.299302	−	0.518406i	−0.676675	−	0.736282i	$-0.736580\pi$
$659$	7.68338	−	13.3080i	0.299302	−	0.518406i	0.975976	+	0.217876i	$0.0699129\pi$
$660$	−0.148776	+	0.692186i	−0.00579111	+	0.0269433i
$661$	−3.97494	−	6.88479i	−0.154607	−	0.267787i	0.778309	−	0.627882i	$-0.216078\pi$
$661$	−3.97494	−	6.88479i	−0.154607	−	0.267787i	−0.932916	+	0.360094i	$0.882745\pi$
$662$			21.2665i			0.826546i
$663$	4.87854	+	19.7164i	0.189467	+	0.765720i
$664$	−1.68338			−0.0653276
$665$	2.52174	−	11.7325i	0.0977888	−	0.454966i
$666$	−2.81662	−	4.87854i	−0.109142	−	0.189039i
$667$	−21.6072	−	12.4749i	−0.836635	−	0.483031i
$668$		0			0
$669$	−10.3166	+	17.8689i	−0.398864	+	0.690852i
$670$	−8.88544	−	27.5598i	−0.343274	−	1.06473i
$671$	2.31662			0.0894323
$672$	−2.00626	−	1.15831i	−0.0773930	−	0.0446829i
$673$	18.9223	−	10.9248i	0.729402	−	0.421121i	−0.0888013	−	0.996049i	$-0.528304\pi$
$673$	18.9223	−	10.9248i	0.729402	−	0.421121i	0.818203	+	0.574929i	$0.194970\pi$
$674$	5.65831	+	9.80048i	0.217950	+	0.377501i
$675$	4.97494	−	0.500000i	0.191485	−	0.0192450i
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$			0.733501i			0.0281907i	0.999901	+	0.0140954i	$0.00448684\pi$
$677$			0.733501i			0.0281907i	−0.999901	+	0.0140954i	$0.995513\pi$
$678$	−8.89105	+	5.13325i	−0.341459	+	0.197141i
$679$	6.94987	+	12.0375i	0.266712	+	0.461958i
$680$	3.86520	+	11.9886i	0.148224	+	0.459744i
$681$	−3.58312			−0.137306
$682$	−1.09682	−	0.633250i	−0.0419994	−	0.0242484i
$683$	−21.8814	−	12.6332i	−0.837270	−	0.483398i	0.0190656	−	0.999818i	$-0.493931\pi$
$683$	−21.8814	−	12.6332i	−0.837270	−	0.483398i	−0.856335	+	0.516420i	$0.827264\pi$
$684$	2.31662			0.0885784
$685$	16.2450	−	5.23748i	0.620691	−	0.200114i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	−10.3923	+	6.00000i	−0.396491	+	0.228914i
$688$			4.31662i			0.164570i
$689$	−39.6082	+	9.80048i	−1.50895	+	0.373369i
$690$	−13.7916	−	12.4749i	−0.525036	−	0.474913i
$691$	−12.4248	−	21.5204i	−0.472662	−	0.818675i	0.526848	−	0.849959i	$-0.323374\pi$
$691$	−12.4248	−	21.5204i	−0.472662	−	0.818675i	−0.999511	+	0.0312845i	$0.990040\pi$
$692$	9.75707	−	5.63325i	0.370908	−	0.214144i
$693$	−0.635230	−	0.366750i	−0.0241304	−	0.0139317i
$694$	31.5831			1.19888
$695$	−14.5918	−	45.2592i	−0.553499	−	1.71678i
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$		−	41.2164i		−	1.56118i
$698$	−23.6135	−	13.6332i	−0.893783	−	0.516026i
$699$	−12.3166	−	21.3330i	−0.465858	−	0.806889i
$700$	−6.76566	−	9.40184i	−0.255718	−	0.355356i
$701$	−28.6332			−1.08146			−0.540731	−	0.841195i	$-0.681852\pi$
$701$	−28.6332			−1.08146			−0.540731	+	0.841195i	$0.681852\pi$
$702$	2.59808	−	2.50000i	0.0980581	−	0.0943564i
$703$		−	13.0501i		−	0.492195i
$704$	0.158312	+	0.274205i	0.00596662	+	0.0103345i
$705$	−18.1813	−	3.90783i	−0.684748	−	0.147177i
$706$	−16.8166	+	29.1272i	−0.632902	+	1.09622i
$707$			31.5831i			1.18781i
$708$	7.47661	+	4.31662i	0.280988	+	0.162229i
$709$	8.97494	−	15.5450i	0.337061	−	0.583807i	−0.646818	−	0.762645i	$-0.723901\pi$
$709$	8.97494	−	15.5450i	0.337061	−	0.583807i	0.983879	+	0.178838i	$0.0572339\pi$
$710$	2.79156	+	2.52506i	0.104765	+	0.0947639i
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	−13.2212	+	7.63325i	−0.495485	+	0.286068i
$713$	28.8096	−	16.6332i	1.07893	−	0.622920i
$714$	−13.0501			−0.488389
$715$	0.0787340	+	2.55150i	0.00294449	+	0.0954205i
$716$	−25.5831			−0.956086
$717$	1.45785	−	0.841688i	0.0544442	−	0.0314334i
$718$	−8.38605	+	4.84169i	−0.312965	+	0.180690i
$719$	−5.68338	+	9.84389i	−0.211954	+	0.367115i	−0.952326	−	0.305082i	$-0.901316\pi$
$719$	−5.68338	+	9.84389i	−0.211954	+	0.367115i	0.740372	+	0.672197i	$0.234649\pi$
$720$	1.50000	−	1.65831i	0.0559017	−	0.0618017i
$721$	−1.94987	+	3.37728i	−0.0726171	+	0.125777i
$722$	−11.8067	−	6.81662i	−0.439401	−	0.253689i
$723$			12.3668i			0.459924i
$724$	0.0250628	−	0.0434101i	0.000931452	−	0.00161332i
$725$	12.1753	−	8.76144i	0.452178	−	0.325392i
$726$	−5.44987	−	9.43946i	−0.202264	−	0.350331i
$727$		−	44.8496i		−	1.66338i	−0.555240	−	0.831690i	$-0.687374\pi$
$727$		−	44.8496i		−	1.66338i	0.555240	−	0.831690i	$-0.312626\pi$
$728$	−8.02502	−	2.31662i	−0.297427	−	0.0858598i
$729$	−1.00000			−0.0370370
$730$	15.9952	+	3.43795i	0.592008	+	0.127244i
$731$	12.1583	+	21.0588i	0.449691	+	0.778888i
$732$	−6.33638	−	3.65831i	−0.234199	−	0.135215i
$733$			1.00000i			0.0369358i	0.999829	+	0.0184679i	$0.00587886\pi$
$733$			1.00000i			0.0369358i	−0.999829	+	0.0184679i	$0.994121\pi$
$734$	−13.1583	+	22.7909i	−0.485682	+	0.841226i
$735$	−3.47587	+	1.12064i	−0.128209	+	0.0413354i
$736$	−8.31662			−0.306555
$737$	−3.55092	−	2.05013i	−0.130800	−	0.0755173i
$738$	−6.33638	+	3.65831i	−0.233245	+	0.134664i
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$	−9.34169	−	8.44987i	−0.343407	−	0.310624i
$741$	8.10819	−	2.00626i	0.297862	−	0.0737017i
$742$		−	26.2164i		−	0.962433i
$743$	−10.9407	+	6.31662i	−0.401376	+	0.231734i	−0.687077	−	0.726584i	$-0.741107\pi$
$743$	−10.9407	+	6.31662i	−0.401376	+	0.231734i	0.285702	+	0.958319i	$0.407773\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	6.60976	+	20.5014i	0.242163	+	0.751114i
$746$	1.00000			0.0366126
$747$	1.45785	+	0.841688i	0.0533398	+	0.0307957i
$748$	1.54467	+	0.891813i	0.0564786	+	0.0326079i
$749$	42.4327			1.55046
$750$	10.2446	−	4.47760i	0.374079	−	0.163499i
$751$	17.4248	+	30.1807i	0.635840	+	1.10131i	0.986336	+	0.164744i	$0.0526797\pi$
$751$	17.4248	+	30.1807i	0.635840	+	1.10131i	−0.350496	+	0.936564i	$0.613987\pi$
$752$	−7.20241	+	4.15831i	−0.262645	+	0.151638i
$753$		−	13.8997i		−	0.506535i
$754$	3.00000	−	10.3923i	0.109254	−	0.378465i
$755$	19.4248	−	21.4749i	0.706941	−	0.781553i
$756$	1.15831	+	2.00626i	0.0421274	+	0.0729668i
$757$	36.2862	−	20.9499i	1.31885	−	0.761436i	0.335303	−	0.942110i	$-0.391161\pi$
$757$	36.2862	−	20.9499i	1.31885	−	0.761436i	0.983543	+	0.180674i	$0.0578280\pi$
$758$	−22.4298	−	12.9499i	−0.814688	−	0.470361i
$759$	−2.63325			−0.0955809
$760$	4.93023	−	1.58953i	0.178838	−	0.0576583i
$761$	3.63325	−	6.29297i	0.131705	−	0.228120i	−0.792629	−	0.609705i	$-0.791288\pi$
$761$	3.63325	−	6.29297i	0.131705	−	0.228120i	0.924334	+	0.381584i	$0.124621\pi$
$762$			4.00000i			0.144905i
$763$	12.0375	+	6.94987i	0.435788	+	0.251602i
$764$	−0.316625	−	0.548410i	−0.0114551	−	0.0198408i
$765$	2.64696	−	12.3151i	0.0957011	−	0.445253i
$766$	33.2665			1.20197
$767$	29.9065	+	8.63325i	1.07986	+	0.311729i
$768$		−	1.00000i		−	0.0360844i
$769$	14.9499	+	25.8939i	0.539106	+	0.933759i	0.998952	+	0.0457608i	$0.0145712\pi$
$769$	14.9499	+	25.8939i	0.539106	+	0.933759i	−0.459846	+	0.887999i	$0.652095\pi$
$770$	−1.60354	−	0.344659i	−0.0577874	−	0.0124206i
$771$	−2.13325	+	3.69490i	−0.0768271	+	0.133068i
$772$			15.9499i			0.574049i
$773$	6.29297	+	3.63325i	0.226343	+	0.130679i	0.608884	−	0.793260i	$-0.291618\pi$
$773$	6.29297	+	3.63325i	0.226343	+	0.130679i	−0.382541	+	0.923938i	$0.624951\pi$
$774$	2.15831	−	3.73831i	0.0775789	−	0.134371i
$775$	2.00000	+	19.8997i	0.0718421	+	0.714820i
$776$	−3.00000	+	5.19615i	−0.107694	+	0.186531i
$777$	11.3017	−	6.52506i	0.405448	−	0.234085i
$778$	−2.04967	+	1.18338i	−0.0734841	+	0.0424261i
$779$	−16.9499			−0.607292
$780$	3.81386	−	7.10313i	0.136558	−	0.254333i
$781$	0.532998			0.0190722
$782$	−40.5730	+	23.4248i	−1.45089	+	0.837670i
$783$	−2.59808	+	1.50000i	−0.0928477	+	0.0536056i
$784$	−0.816625	+	1.41444i	−0.0291652	+	0.0505156i
$785$	−20.3417	−	18.3997i	−0.726026	−	0.656715i
$786$		0			0
$787$	−17.8689	−	10.3166i	−0.636958	−	0.367748i	0.146484	−	0.989213i	$-0.453204\pi$
$787$	−17.8689	−	10.3166i	−0.636958	−	0.367748i	−0.783442	+	0.621465i	$0.786538\pi$
$788$		−	13.2665i		−	0.472599i
$789$	−8.79156	+	15.2274i	−0.312988	+	0.542111i
$790$	1.87953	−	8.74456i	0.0668706	−	0.311118i
$791$	−11.8918	−	20.5972i	−0.422824	−	0.732353i
$792$		−	0.316625i		−	0.0112508i
$793$	−25.3455	−	7.31662i	−0.900046	−	0.259821i
$794$	−21.8997			−0.777193
$795$	24.7397	+	5.31748i	0.877428	+	0.188591i
$796$	7.84169	+	13.5822i	0.277941	+	0.481408i
$797$	12.5859	+	7.26650i	0.445817	+	0.257393i	0.706062	−	0.708150i	$-0.250470\pi$
$797$	12.5859	+	7.26650i	0.445817	+	0.257393i	−0.260245	+	0.965543i	$0.583803\pi$
$798$			5.36675i			0.189981i
$799$	−23.4248	+	40.5730i	−0.828710	+	1.43537i
$800$	2.05446	−	4.55842i	0.0726360	−	0.161165i
$801$	15.2665			0.539415
$802$	−14.9966	−	8.65831i	−0.529550	−	0.305736i
$803$	2.00626	−	1.15831i	0.0707992	−	0.0408760i
$804$	6.47494	+	11.2149i	0.228353	+	0.395520i
$805$	28.8997	−	31.9499i	1.01858	−	1.12609i
$806$	10.0000	+	10.3923i	0.352235	+	0.366053i
$807$		−	0.633250i		−	0.0222914i
$808$	−11.8067	+	6.81662i	−0.415360	+	0.239808i
$809$	20.2916	+	35.1460i	0.713413	+	1.23567i	0.963568	+	0.267462i	$0.0861851\pi$
$809$	20.2916	+	35.1460i	0.713413	+	1.23567i	−0.250155	+	0.968206i	$0.580482\pi$
$810$	−2.12819	+	0.686141i	−0.0747771	+	0.0241085i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	6.01877	+	3.47494i	0.211217	+	0.121946i
$813$	−13.8564	−	8.00000i	−0.485965	−	0.280572i
$814$	−1.78363			−0.0625161
$815$	−9.86046	+	3.17906i	−0.345397	+	0.111358i
$816$	−2.81662	−	4.87854i	−0.0986016	−	0.170783i
$817$	8.66025	−	5.00000i	0.302984	−	0.174928i
$818$		−	21.0000i		−	0.734248i
$819$	5.79156	+	6.01877i	0.202374	+	0.210313i
$820$	−10.9749	+	12.1332i	−0.383261	+	0.423711i
$821$	17.5831	+	30.4549i	0.613655	+	1.06288i	0.990619	+	0.136654i	$0.0436349\pi$
$821$	17.5831	+	30.4549i	0.613655	+	1.06288i	−0.376964	+	0.926228i	$0.623032\pi$
$822$	−6.61059	+	3.81662i	−0.230571	+	0.133120i
$823$	39.7503	+	22.9499i	1.38561	+	0.799982i	0.992817	−	0.119644i	$-0.0381755\pi$
$823$	39.7503	+	22.9499i	1.38561	+	0.799982i	0.392793	+	0.919627i	$0.371509\pi$
$824$	−1.68338			−0.0586432
$825$	0.650492	−	1.44331i	0.0226472	−	0.0502496i
$826$	−10.0000	+	17.3205i	−0.347945	+	0.602658i
$827$		−	25.2665i		−	0.878602i	−0.898340	−	0.439301i	$-0.855226\pi$
$827$		−	25.2665i		−	0.878602i	0.898340	−	0.439301i	$-0.144774\pi$
$828$	7.20241	+	4.15831i	0.250301	+	0.144511i
$829$	−14.3417	−	24.8405i	−0.498107	−	0.862747i	0.501890	−	0.864931i	$-0.332638\pi$
$829$	−14.3417	−	24.8405i	−0.498107	−	0.862747i	−0.999998	+	0.00218401i	$0.999305\pi$
$830$	3.68009	+	0.790988i	0.127738	+	0.0274556i
$831$	27.0000			0.936620
$832$	−0.866025	−	3.50000i	−0.0300240	−	0.121341i
$833$			9.20050i			0.318779i
$834$	10.6332	+	18.4173i	0.368199	+	0.637740i
$835$		0			0
$836$	0.366750	−	0.635230i	0.0126843	−	0.0219699i
$837$		−	4.00000i		−	0.138260i
$838$	−23.5267	−	13.5831i	−0.812715	−	0.469221i
$839$	−20.3166	+	35.1894i	−0.701408	+	1.21487i	0.266565	+	0.963817i	$0.414111\pi$
$839$	−20.3166	+	35.1894i	−0.701408	+	1.21487i	−0.967972	+	0.251057i	$0.919222\pi$
$840$	3.84169	+	3.47494i	0.132551	+	0.119897i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	15.6319	−	9.02506i	0.538710	−	0.311024i
$843$	−16.6419	+	9.60819i	−0.573176	+	0.330924i
$844$	4.63325			0.159483
$845$	7.19702	−	28.1639i	0.247585	−	0.968866i
$846$	8.31662			0.285931
$847$	21.8677	−	12.6253i	0.751383	−	0.433811i
$848$	9.80048	−	5.65831i	0.336550	−	0.194307i
$849$	−1.52506	+	2.64149i	−0.0523400	+	0.0906556i
$850$	−2.81662	−	28.0251i	−0.0966094	−	0.961252i
$851$	23.4248	−	40.5730i	0.802992	−	1.39082i
$852$	−1.45785	−	0.841688i	−0.0499450	−	0.0288357i
$853$		−	5.10025i		−	0.174629i	−0.996181	−	0.0873146i	$-0.972171\pi$
$853$		−	5.10025i		−	0.174629i	0.996181	−	0.0873146i	$-0.0278285\pi$
$854$	8.47494	−	14.6790i	0.290006	−	0.502306i
$855$	−5.06447	−	1.08854i	−0.173201	−	0.0372273i
$856$	9.15831	+	15.8627i	0.313025	+	0.542175i
$857$		−	26.2665i		−	0.897247i	−0.893721	−	0.448623i	$-0.851915\pi$
$857$		−	26.2665i		−	0.897247i	0.893721	−	0.448623i	$-0.148085\pi$
$858$	−0.274205	−	1.10819i	−0.00936121	−	0.0378329i
$859$	32.8496			1.12081			0.560407	−	0.828217i	$-0.310645\pi$
$859$	32.8496			1.12081			0.560407	+	0.828217i	$0.310645\pi$
$860$	2.02830	−	9.43675i	0.0691646	−	0.321790i
$861$	−8.47494	−	14.6790i	−0.288825	−	0.500260i
$862$	6.01877	+	3.47494i	0.205000	+	0.118357i
$863$			39.4829i			1.34401i	0.740545	+	0.672006i	$0.234567\pi$
$863$			39.4829i			1.34401i	−0.740545	+	0.672006i	$0.765433\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−23.9773	+	7.73040i	−0.815253	+	0.262842i
$866$	24.5831			0.835369
$867$	−12.7596	−	7.36675i	−0.433338	−	0.250188i
$868$	−8.02502	+	4.63325i	−0.272387	+	0.157263i
$869$	−0.633250	−	1.09682i	−0.0214815	−	0.0372071i
$870$	−4.50000	+	4.97494i	−0.152564	+	0.168666i
$871$	32.3747	+	33.6448i	1.09697	+	1.14001i
$872$			6.00000i			0.203186i
$873$	5.19615	−	3.00000i	0.175863	−	0.101535i
$874$	9.63325	+	16.6853i	0.325850	+	0.564388i
$875$	10.3729	+	23.7328i	0.350669	+	0.802315i
$876$	−7.31662			−0.247206
$877$	10.1615	+	5.86675i	0.343130	+	0.198106i	0.661655	−	0.749808i	$-0.269854\pi$
$877$	10.1615	+	5.86675i	0.343130	+	0.198106i	−0.318525	+	0.947914i	$0.603188\pi$
$878$	27.4386	+	15.8417i	0.926008	+	0.534631i
$879$	−14.6834			−0.495258
$880$	−0.217249	−	0.673839i	−0.00732347	−	0.0227151i
$881$	−19.3417	−	33.5008i	−0.651638	−	1.12867i	−0.982725	−	0.185070i	$-0.940749\pi$
$881$	−19.3417	−	33.5008i	−0.651638	−	1.12867i	0.331087	−	0.943600i	$-0.392585\pi$
$882$	1.41444	−	0.816625i	0.0476265	−	0.0274972i
$883$			40.6332i			1.36742i	0.729755	+	0.683709i	$0.239634\pi$
$883$			40.6332i			1.36742i	−0.729755	+	0.683709i	$0.760366\pi$
$884$	−14.0831	−	14.6356i	−0.473667	−	0.492249i
$885$	−14.3166	−	12.9499i	−0.481248	−	0.435305i
$886$	−6.63325	−	11.4891i	−0.222848	−	0.385985i
$887$	12.7596	−	7.36675i	0.428425	−	0.247351i	−0.270250	−	0.962790i	$-0.587107\pi$
$887$	12.7596	−	7.36675i	0.428425	−	0.247351i	0.698675	+	0.715439i	$0.253773\pi$
$888$	4.87854	+	2.81662i	0.163713	+	0.0945197i
$889$	−9.26650			−0.310788
$890$	32.4901	−	10.4750i	1.08907	−	0.351122i
$891$	−0.158312	+	0.274205i	−0.00530366	+	0.00918622i
$892$		−	20.6332i		−	0.690852i
$893$	16.6853	+	9.63325i	0.558352	+	0.322364i
$894$	−4.81662	−	8.34264i	−0.161092	−	0.279020i
$895$	55.9283	+	12.0210i	1.86948	+	0.401819i
$896$	2.31662			0.0773930
$897$	28.8096	+	8.31662i	0.961926	+	0.277684i
$898$		−	36.5330i		−	1.21912i
$899$	−6.00000	−	10.3923i	−0.200111	−	0.346603i
$900$	−4.05842	+	2.92048i	−0.135281	+	0.0973494i
$901$	31.8747	−	55.2086i	1.06190	−	1.83926i
$902$			2.31662i			0.0771352i
$903$	8.66025	+	5.00000i	0.288195	+	0.166390i
$904$	5.13325	−	8.89105i	0.170729	−	0.295712i
$905$	−0.0751884	+	0.0831240i	−0.00249935	+	0.00276313i
$906$	−6.47494	+	11.2149i	−0.215115	+	0.372591i
$907$	−46.1301	+	26.6332i	−1.53173	+	0.884343i	−0.532444	+	0.846465i	$0.678726\pi$
$907$	−46.1301	+	26.6332i	−1.53173	+	0.884343i	−0.999282	+	0.0378772i	$0.987940\pi$
$908$	3.10308	−	1.79156i	0.102979	−	0.0594551i
$909$	13.6332			0.452186
$910$	16.4553	+	8.83528i	0.545488	+	0.292887i
$911$	−47.1662			−1.56269			−0.781344	−	0.624101i	$-0.785465\pi$
$911$	−47.1662			−1.56269			−0.781344	+	0.624101i	$0.785465\pi$
$912$	−2.00626	+	1.15831i	−0.0664338	+	0.0383556i
$913$	0.461590	−	0.266499i	0.0152764	−	0.00881983i
$914$	−1.97494	+	3.42069i	−0.0653251	+	0.113146i
$915$	12.1332	+	10.9749i	0.401113	+	0.362820i
$916$	6.00000	−	10.3923i	0.198246	−	0.343371i
$917$		0			0
$918$			5.63325i			0.185925i
$919$	24.9499	−	43.2145i	0.823020	−	1.42551i	−0.0804024	−	0.996762i	$-0.525621\pi$
$919$	24.9499	−	43.2145i	0.823020	−	1.42551i	0.903423	−	0.428751i	$-0.141046\pi$
$920$	18.1813	+	3.90783i	0.599420	+	0.128837i
$921$	−15.1082	−	26.1681i	−0.497832	−	0.862270i
$922$			3.63325i			0.119655i
$923$	−5.83138	−	1.68338i	−0.191942	−	0.0554090i
$924$	0.733501			0.0241304
$925$	16.4518	+	22.8621i	0.540932	+	0.751701i
$926$	5.47494	+	9.48287i	0.179918	+	0.311626i
$927$	1.45785	+	0.841688i	0.0478819	+	0.0276446i
$928$			3.00000i			0.0984798i
$929$	−24.2916	+	42.0742i	−0.796980	+	1.38041i	0.124594	+	0.992208i	$0.460237\pi$
$929$	−24.2916	+	42.0742i	−0.796980	+	1.38041i	−0.921574	+	0.388203i	$0.873096\pi$
$930$	−2.74456	−	8.51278i	−0.0899978	−	0.279145i
$931$	3.78363			0.124003
$932$	21.3330	+	12.3166i	0.698786	+	0.403444i
$933$	−4.92195	+	2.84169i	−0.161137	+	0.0930327i
$934$	−0.208438	−	0.361025i	−0.00682030	−	0.0118131i
$935$	−2.95781	−	2.67544i	−0.0967307	−	0.0874962i
$936$	−1.00000	+	3.46410i	−0.0326860	+	0.113228i
$937$		−	33.2164i		−	1.08513i	−0.840013	−	0.542566i	$-0.817453\pi$
$937$		−	33.2164i		−	1.08513i	0.840013	−	0.542566i	$-0.182547\pi$
$938$	−25.9808	+	15.0000i	−0.848302	+	0.489767i
$939$	15.0000	+	25.9808i	0.489506	+	0.847850i
$940$	17.6994	−	5.70637i	0.577291	−	0.186121i
$941$	23.3668			0.761734			0.380867	−	0.924630i	$-0.375626\pi$
$941$	23.3668			0.761734			0.380867	+	0.924630i	$0.375626\pi$
$942$	10.6231	+	6.13325i	0.346119	+	0.199832i
$943$	−52.6973	−	30.4248i	−1.71606	−	0.990768i
$944$	−8.63325			−0.280988
$945$	−1.58953	−	4.93023i	−0.0517074	−	0.160380i
$946$	−0.683375	−	1.18364i	−0.0222184	−	0.0384835i
$947$	50.6911	−	29.2665i	1.64724	−	0.951033i	0.669075	−	0.743195i	$-0.266690\pi$
$947$	50.6911	−	29.2665i	1.64724	−	0.951033i	0.978163	−	0.207839i	$-0.0666429\pi$
$948$			4.00000i			0.129914i
$949$	−25.6082	+	6.33638i	−0.831277	+	0.205688i
$950$	−11.5251	+	1.15831i	−0.373922	+	0.0375806i
$951$	−7.97494	−	13.8130i	−0.258605	−	0.447917i
$952$	11.3017	−	6.52506i	0.366292	−	0.211479i
$953$	−5.19615	−	3.00000i	−0.168320	−	0.0971795i	0.413473	−	0.910516i	$-0.364315\pi$
$953$	−5.19615	−	3.00000i	−0.168320	−	0.0971795i	−0.581793	+	0.813337i	$0.697649\pi$
$954$	−11.3166			−0.366389
$955$	0.434498	+	1.34768i	0.0140600	+	0.0436098i
$956$	−0.841688	+	1.45785i	−0.0272221	+	0.0471501i
$957$			0.949874i			0.0307051i
$958$		0			0
$959$	−8.84169	−	15.3143i	−0.285513	−	0.494523i
$960$	−0.469882	+	2.18614i	−0.0151654	+	0.0705574i
$961$	−15.0000			−0.483871
$962$	19.5141	+	5.63325i	0.629161	+	0.181623i
$963$		−	18.3166i		−	0.590245i
$964$	−6.18338	−	10.7099i	−0.199153	−	0.344943i
$965$	7.49456	−	34.8687i	0.241258	−	1.12246i
$966$	−9.63325	+	16.6853i	−0.309945	+	0.536840i
$967$			36.8496i			1.18500i	0.805569	+	0.592502i	$0.201860\pi$
$967$			36.8496i			1.18500i	−0.805569	+	0.592502i	$0.798140\pi$
$968$	9.43946	+	5.44987i	0.303396	+	0.175166i
$969$	−6.52506	+	11.3017i	−0.209615	+	0.363064i
$970$	9.00000	−	9.94987i	0.288973	−	0.319471i
$971$	18.6332	−	32.2737i	0.597969	−	1.03571i	−0.395151	−	0.918616i	$-0.629308\pi$
$971$	18.6332	−	32.2737i	0.597969	−	1.03571i	0.993120	−	0.117097i	$-0.0373589\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	−42.6660	+	24.6332i	−1.36781	+	0.789706i
$974$	−2.31662			−0.0742294
$975$	−11.6753	+	13.7364i	−0.373908	+	0.439916i
$976$	7.31662			0.234199
$977$	−44.7157	+	25.8166i	−1.43058	+	0.825947i	−0.997165	−	0.0752464i	$-0.976026\pi$
$977$	−44.7157	+	25.8166i	−1.43058	+	0.825947i	−0.433417	+	0.901193i	$0.642692\pi$
$978$	4.01251	−	2.31662i	0.128306	−	0.0740775i
$979$	2.41688	−	4.18615i	0.0772437	−	0.133790i
$980$	2.44987	−	2.70844i	0.0782584	−	0.0865179i
$981$	3.00000	−	5.19615i	0.0957826	−	0.165900i
$982$	−5.55718	−	3.20844i	−0.177337	−	0.102385i
$983$			36.0000i			1.14822i	0.818778	+	0.574111i	$0.194652\pi$
$983$			36.0000i			1.14822i	−0.818778	+	0.574111i	$0.805348\pi$
$984$	3.65831	−	6.33638i	0.116623	−	0.201997i
$985$	−6.23369	+	29.0024i	−0.198622	+	0.924094i
$986$	8.44987	+	14.6356i	0.269099	+	0.466093i
$987$			19.2665i			0.613259i
$988$	−6.01877	+	5.79156i	−0.191483	+	0.184254i
$989$	35.8997			1.14155
$990$	−0.148776	+	0.692186i	−0.00472842	+	0.0219991i
$991$	−1.84169	−	3.18990i	−0.0585031	−	0.101330i	0.835291	−	0.549809i	$-0.185299\pi$
$991$	−1.84169	−	3.18990i	−0.0585031	−	0.101330i	−0.893794	+	0.448478i	$0.851966\pi$
$992$	−3.46410	−	2.00000i	−0.109985	−	0.0635001i
$993$			21.2665i			0.674872i
$994$	1.94987	−	3.37728i	0.0618463	−	0.107121i
$995$	−10.7610	−	33.3773i	−0.341147	−	1.05813i
$996$	−1.68338			−0.0533398
$997$	37.7875	+	21.8166i	1.19674	+	0.690939i	0.959827	−	0.280591i	$-0.0905304\pi$
$997$	37.7875	+	21.8166i	1.19674	+	0.690939i	0.236915	+	0.971530i	$0.423864\pi$
$998$	−1.81887	+	1.05013i	−0.0575754	+	0.0332411i
$999$	−2.81662	−	4.87854i	−0.0891141	−	0.154350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.y.g.289.2	yes	8
3.2	odd	2		1170.2.bp.g.289.3		8
5.2	odd	4		1950.2.i.bb.601.1		4
5.3	odd	4		1950.2.i.be.601.2		4
5.4	even	2	inner	390.2.y.g.289.3	yes	8
13.9	even	3	inner	390.2.y.g.139.4	yes	8
15.14	odd	2		1170.2.bp.g.289.2		8
39.35	odd	6		1170.2.bp.g.919.1		8
65.9	even	6	inner	390.2.y.g.139.1	✓	8
65.22	odd	12		1950.2.i.bb.451.1		4
65.48	odd	12		1950.2.i.be.451.2		4
195.74	odd	6		1170.2.bp.g.919.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.g.139.1	✓	8	65.9	even	6	inner
390.2.y.g.139.4	yes	8	13.9	even	3	inner
390.2.y.g.289.2	yes	8	1.1	even	1	trivial
390.2.y.g.289.3	yes	8	5.4	even	2	inner
1170.2.bp.g.289.2		8	15.14	odd	2
1170.2.bp.g.289.3		8	3.2	odd	2
1170.2.bp.g.919.1		8	39.35	odd	6
1170.2.bp.g.919.4		8	195.74	odd	6
1950.2.i.bb.451.1		4	65.22	odd	12
1950.2.i.bb.601.1		4	5.2	odd	4
1950.2.i.be.451.2		4	65.48	odd	12
1950.2.i.be.601.2		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 1.65831i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.00626 + 1.15831i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 1.65831i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.00626 + 1.15831i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.469882 - 2.18614i) q^{10} +(-0.158312 - 0.274205i) q^{11} +1.00000i q^{12} +(0.866025 + 3.50000i) q^{13} -2.31662 q^{14} +(0.469882 - 2.18614i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.87854 - 2.81662i) q^{17} +1.00000i q^{18} +(-1.15831 + 2.00626i) q^{19} +(0.686141 + 2.12819i) q^{20} -2.31662 q^{21} +(0.274205 + 0.158312i) q^{22} +(-7.20241 + 4.15831i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 4.97494i) q^{25} +(-2.50000 - 2.59808i) q^{26} +1.00000i q^{27} +(2.00626 - 1.15831i) q^{28} +(1.50000 + 2.59808i) q^{29} +(0.686141 + 2.12819i) q^{30} -4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(0.274205 + 0.158312i) q^{33} +5.63325 q^{34} +(-4.93023 + 1.58953i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.87854 + 2.81662i) q^{37} -2.31662i q^{38} +(-2.50000 - 2.59808i) q^{39} +(-1.65831 - 1.50000i) q^{40} +(3.65831 + 6.33638i) q^{41} +(2.00626 - 1.15831i) q^{42} +(-3.73831 - 2.15831i) q^{43} -0.316625 q^{44} +(0.686141 + 2.12819i) q^{45} +(4.15831 - 7.20241i) q^{46} -8.31662i q^{47} +(0.866025 + 0.500000i) q^{48} +(-0.816625 - 1.41444i) q^{49} +(2.92048 + 4.05842i) q^{50} +5.63325 q^{51} +(3.46410 + 1.00000i) q^{52} +11.3166i q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.692186 + 0.148776i) q^{55} +(-1.15831 + 2.00626i) q^{56} -2.31662i q^{57} +(-2.59808 - 1.50000i) q^{58} +(4.31662 - 7.47661i) q^{59} +(-1.65831 - 1.50000i) q^{60} +(-3.65831 + 6.33638i) q^{61} +(3.46410 - 2.00000i) q^{62} +(2.00626 - 1.15831i) q^{63} -1.00000 q^{64} +(-7.10313 - 3.81386i) q^{65} -0.316625 q^{66} +(11.2149 - 6.47494i) q^{67} +(-4.87854 + 2.81662i) q^{68} +(4.15831 - 7.20241i) q^{69} +(3.47494 - 3.84169i) q^{70} +(-0.841688 + 1.45785i) q^{71} +(0.866025 + 0.500000i) q^{72} +7.31662i q^{73} +(2.81662 - 4.87854i) q^{74} +(2.92048 + 4.05842i) q^{75} +(1.15831 + 2.00626i) q^{76} -0.733501i q^{77} +(3.46410 + 1.00000i) q^{78} +4.00000 q^{79} +(2.18614 + 0.469882i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.33638 - 3.65831i) q^{82} +1.68338i q^{83} +(-1.15831 + 2.00626i) q^{84} +(11.9886 - 3.86520i) q^{85} +4.31662 q^{86} +(-2.59808 - 1.50000i) q^{87} +(0.274205 - 0.158312i) q^{88} +(7.63325 + 13.2212i) q^{89} +(-1.65831 - 1.50000i) q^{90} +(-2.31662 + 8.02502i) q^{91} +8.31662i q^{92} +(3.46410 - 2.00000i) q^{93} +(4.15831 + 7.20241i) q^{94} +(-1.58953 - 4.93023i) q^{95} -1.00000 q^{96} +(5.19615 + 3.00000i) q^{97} +(1.41444 + 0.816625i) q^{98} -0.316625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 12 q^{5} + 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 12 * q^5 + 4 * q^6 + 4 * q^9	\( 8 q + 4 q^{4} - 12 q^{5} + 4 q^{6} + 4 q^{9} + 12 q^{11} + 8 q^{14} - 4 q^{16} + 4 q^{19} - 6 q^{20} + 8 q^{21} - 4 q^{24} - 4 q^{25} - 20 q^{26} + 12 q^{29} - 6 q^{30} - 32 q^{31} - 8 q^{34} - 22 q^{35} - 4 q^{36} - 20 q^{39} + 16 q^{41} + 24 q^{44} - 6 q^{45} + 20 q^{46} + 20 q^{49} - 8 q^{51} - 4 q^{54} - 18 q^{55} + 4 q^{56} + 8 q^{59} - 16 q^{61} - 8 q^{64} + 24 q^{66} + 20 q^{69} - 12 q^{70} - 20 q^{71} - 4 q^{74} - 4 q^{76} + 32 q^{79} + 6 q^{80} - 4 q^{81} + 4 q^{84} + 44 q^{85} + 8 q^{86} + 8 q^{89} + 8 q^{91} + 20 q^{94} - 6 q^{95} - 8 q^{96} + 24 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 12 * q^5 + 4 * q^6 + 4 * q^9 + 12 * q^11 + 8 * q^14 - 4 * q^16 + 4 * q^19 - 6 * q^20 + 8 * q^21 - 4 * q^24 - 4 * q^25 - 20 * q^26 + 12 * q^29 - 6 * q^30 - 32 * q^31 - 8 * q^34 - 22 * q^35 - 4 * q^36 - 20 * q^39 + 16 * q^41 + 24 * q^44 - 6 * q^45 + 20 * q^46 + 20 * q^49 - 8 * q^51 - 4 * q^54 - 18 * q^55 + 4 * q^56 + 8 * q^59 - 16 * q^61 - 8 * q^64 + 24 * q^66 + 20 * q^69 - 12 * q^70 - 20 * q^71 - 4 * q^74 - 4 * q^76 + 32 * q^79 + 6 * q^80 - 4 * q^81 + 4 * q^84 + 44 * q^85 + 8 * q^86 + 8 * q^89 + 8 * q^91 + 20 * q^94 - 6 * q^95 - 8 * q^96 + 24 * q^99

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