LMFDB - Embedded newform 390.2.y.g.139.2

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			139.2
Root			$1.26217 - 1.18614i$ of defining polynomial
Character	$\chi$	$=$	390.139
Dual form			390.2.y.g.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 1.65831i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-3.73831 + 2.15831i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-3.73831 + 2.15831i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.12819 - 0.686141i) q^{10} +(3.15831 - 5.47036i) q^{11} -1.00000i q^{12} +(0.866025 - 3.50000i) q^{13} +4.31662 q^{14} +(2.12819 - 0.686141i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.61059 - 3.81662i) q^{17} -1.00000i q^{18} +(2.15831 + 3.73831i) q^{19} +(-2.18614 - 0.469882i) q^{20} +4.31662 q^{21} +(-5.47036 + 3.15831i) q^{22} +(-1.45785 - 0.841688i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 4.97494i) q^{25} +(-2.50000 + 2.59808i) q^{26} -1.00000i q^{27} +(-3.73831 - 2.15831i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-2.18614 - 0.469882i) q^{30} -4.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.47036 + 3.15831i) q^{33} -7.63325 q^{34} +(2.02830 - 9.43675i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(6.61059 + 3.81662i) q^{37} -4.31662i q^{38} +(-2.50000 + 2.59808i) q^{39} +(1.65831 + 1.50000i) q^{40} +(0.341688 - 0.591820i) q^{41} +(-3.73831 - 2.15831i) q^{42} +(2.00626 - 1.15831i) q^{43} +6.31662 q^{44} +(-2.18614 - 0.469882i) q^{45} +(0.841688 + 1.45785i) q^{46} +1.68338i q^{47} +(0.866025 - 0.500000i) q^{48} +(5.81662 - 10.0747i) q^{49} +(-2.05446 + 4.55842i) q^{50} -7.63325 q^{51} +(3.46410 - 1.00000i) q^{52} -4.68338i q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.33409 + 13.4430i) q^{55} +(2.15831 + 3.73831i) q^{56} -4.31662i q^{57} +(-2.59808 + 1.50000i) q^{58} +(-2.31662 - 4.01251i) q^{59} +(1.65831 + 1.50000i) q^{60} +(-0.341688 - 0.591820i) q^{61} +(3.46410 + 2.00000i) q^{62} +(-3.73831 - 2.15831i) q^{63} -1.00000 q^{64} +(4.50506 + 6.68614i) q^{65} +6.31662 q^{66} +(-6.01877 - 3.47494i) q^{67} +(6.61059 + 3.81662i) q^{68} +(0.841688 + 1.45785i) q^{69} +(-6.47494 + 7.15831i) q^{70} +(-4.15831 - 7.20241i) q^{71} +(0.866025 - 0.500000i) q^{72} -0.683375i q^{73} +(-3.81662 - 6.61059i) q^{74} +(-2.05446 + 4.55842i) q^{75} +(-2.15831 + 3.73831i) q^{76} +27.2665i q^{77} +(3.46410 - 1.00000i) q^{78} +4.00000 q^{79} +(-0.686141 - 2.12819i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.591820 + 0.341688i) q^{82} -8.31662i q^{83} +(2.15831 + 3.73831i) q^{84} +(-3.58673 + 16.6874i) q^{85} -2.31662 q^{86} +(-2.59808 + 1.50000i) q^{87} +(-5.47036 - 3.15831i) q^{88} +(-5.63325 + 9.75707i) q^{89} +(1.65831 + 1.50000i) q^{90} +(4.31662 + 14.9532i) q^{91} -1.68338i q^{92} +(3.46410 + 2.00000i) q^{93} +(0.841688 - 1.45785i) q^{94} +(-9.43675 - 2.02830i) q^{95} -1.00000 q^{96} +(5.19615 - 3.00000i) q^{97} +(-10.0747 + 5.81662i) q^{98} +6.31662 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 $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$7$	−3.73831	+	2.15831i	−1.41295	+	0.815765i	−0.995665	−	0.0930116i	$-0.970351\pi$
$7$	−3.73831	+	2.15831i	−1.41295	+	0.815765i	−0.417282	+	0.908777i	$0.637017\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.12819	−	0.686141i	0.672994	−	0.216977i
$11$	3.15831	−	5.47036i	0.952267	−	1.64937i	0.211765	−	0.977321i	$-0.432079\pi$
$11$	3.15831	−	5.47036i	0.952267	−	1.64937i	0.740502	−	0.672054i	$-0.234588\pi$
$12$		−	1.00000i		−	0.288675i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$14$	4.31662			1.15367
$15$	2.12819	−	0.686141i	0.549497	−	0.177161i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.61059	−	3.81662i	1.60330	−	0.925667i	0.612483	−	0.790484i	$-0.290171\pi$
$17$	6.61059	−	3.81662i	1.60330	−	0.925667i	0.990821	−	0.135183i	$-0.0431623\pi$
$18$		−	1.00000i		−	0.235702i
$19$	2.15831	+	3.73831i	0.495151	+	0.857626i	0.999984	−	0.00559033i	$-0.00177947\pi$
$19$	2.15831	+	3.73831i	0.495151	+	0.857626i	−0.504834	+	0.863217i	$0.668446\pi$
$20$	−2.18614	−	0.469882i	−0.488836	−	0.105069i
$21$	4.31662			0.941965
$22$	−5.47036	+	3.15831i	−1.16628	+	0.673354i
$23$	−1.45785	−	0.841688i	−0.303982	−	0.175504i	0.340248	−	0.940336i	$-0.389489\pi$
$23$	−1.45785	−	0.841688i	−0.303982	−	0.175504i	−0.644230	+	0.764832i	$0.722822\pi$
$24$	−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
$28$	−3.73831	−	2.15831i	−0.706474	−	0.407883i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$	−2.18614	−	0.469882i	−0.399133	−	0.0857883i
$31$	−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
$33$	−5.47036	+	3.15831i	−0.952267	+	0.549792i
$34$	−7.63325			−1.30909
$35$	2.02830	−	9.43675i	0.342846	−	1.59510i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	6.61059	+	3.81662i	1.08677	+	0.627449i	0.932716	−	0.360613i	$-0.117432\pi$
$37$	6.61059	+	3.81662i	1.08677	+	0.627449i	0.154058	+	0.988062i	$0.450766\pi$
$38$		−	4.31662i		−	0.700249i
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$	1.65831	+	1.50000i	0.262202	+	0.237171i
$41$	0.341688	−	0.591820i	0.0533626	−	0.0924268i	−0.838110	−	0.545501i	$-0.816339\pi$
$41$	0.341688	−	0.591820i	0.0533626	−	0.0924268i	0.891473	+	0.453074i	$0.149673\pi$
$42$	−3.73831	−	2.15831i	−0.576833	−	0.333035i
$43$	2.00626	−	1.15831i	0.305951	−	0.176641i	−0.339162	−	0.940728i	$-0.610144\pi$
$43$	2.00626	−	1.15831i	0.305951	−	0.176641i	0.645113	+	0.764087i	$0.276810\pi$
$44$	6.31662			0.952267
$45$	−2.18614	−	0.469882i	−0.325891	−	0.0700459i
$46$	0.841688	+	1.45785i	0.124100	+	0.214948i
$47$			1.68338i			0.245546i	0.992435	+	0.122773i	$0.0391786\pi$
$47$			1.68338i			0.245546i	−0.992435	+	0.122773i	$0.960821\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	5.81662	−	10.0747i	0.830946	−	1.43924i
$50$	−2.05446	+	4.55842i	−0.290544	+	0.644658i
$51$	−7.63325			−1.06887
$52$	3.46410	−	1.00000i	0.480384	−	0.138675i
$53$		−	4.68338i		−	0.643311i	−0.946857	−	0.321656i	$-0.895761\pi$
$53$		−	4.68338i		−	0.643311i	0.946857	−	0.321656i	$-0.104239\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	4.33409	+	13.4430i	0.584409	+	1.81265i
$56$	2.15831	+	3.73831i	0.288417	+	0.499552i
$57$		−	4.31662i		−	0.571751i
$58$	−2.59808	+	1.50000i	−0.341144	+	0.196960i
$59$	−2.31662	−	4.01251i	−0.301599	−	0.522385i	0.674899	−	0.737910i	$-0.264187\pi$
$59$	−2.31662	−	4.01251i	−0.301599	−	0.522385i	−0.976498	+	0.215525i	$0.930854\pi$
$60$	1.65831	+	1.50000i	0.214087	+	0.193649i
$61$	−0.341688	−	0.591820i	−0.0437486	−	0.0757748i	0.843322	−	0.537409i	$-0.180597\pi$
$61$	−0.341688	−	0.591820i	−0.0437486	−	0.0757748i	−0.887071	+	0.461634i	$0.847263\pi$
$62$	3.46410	+	2.00000i	0.439941	+	0.254000i
$63$	−3.73831	−	2.15831i	−0.470982	−	0.271922i
$64$	−1.00000			−0.125000
$65$	4.50506	+	6.68614i	0.558783	+	0.829314i
$66$	6.31662			0.777523
$67$	−6.01877	−	3.47494i	−0.735310	−	0.424531i	0.0850519	−	0.996377i	$-0.472894\pi$
$67$	−6.01877	−	3.47494i	−0.735310	−	0.424531i	−0.820361	+	0.571845i	$0.806228\pi$
$68$	6.61059	+	3.81662i	0.801652	+	0.462834i
$69$	0.841688	+	1.45785i	0.101327	+	0.175504i
$70$	−6.47494	+	7.15831i	−0.773903	+	0.855582i
$71$	−4.15831	−	7.20241i	−0.493501	−	0.854769i	0.506471	−	0.862257i	$-0.330950\pi$
$71$	−4.15831	−	7.20241i	−0.493501	−	0.854769i	−0.999972	+	0.00748834i	$0.997616\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		−	0.683375i		−	0.0799830i	−0.999200	−	0.0399915i	$-0.987267\pi$
$73$		−	0.683375i		−	0.0799830i	0.999200	−	0.0399915i	$-0.0127331\pi$
$74$	−3.81662	−	6.61059i	−0.443674	−	0.768465i
$75$	−2.05446	+	4.55842i	−0.237228	+	0.526361i
$76$	−2.15831	+	3.73831i	−0.247575	+	0.428813i
$77$			27.2665i			3.10731i
$78$	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	$0.427756\pi$
$80$	−0.686141	−	2.12819i	−0.0767129	−	0.237939i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.591820	+	0.341688i	−0.0653556	+	0.0377331i
$83$		−	8.31662i		−	0.912868i	−0.889757	−	0.456434i	$-0.849126\pi$
$83$		−	8.31662i		−	0.912868i	0.889757	−	0.456434i	$-0.150874\pi$
$84$	2.15831	+	3.73831i	0.235491	+	0.407883i
$85$	−3.58673	+	16.6874i	−0.389035	+	1.81000i
$86$	−2.31662			−0.249808
$87$	−2.59808	+	1.50000i	−0.278543	+	0.160817i
$88$	−5.47036	−	3.15831i	−0.583142	−	0.336677i
$89$	−5.63325	+	9.75707i	−0.597123	+	1.03425i	0.396120	+	0.918199i	$0.370356\pi$
$89$	−5.63325	+	9.75707i	−0.597123	+	1.03425i	−0.993243	+	0.116049i	$0.962977\pi$
$90$	1.65831	+	1.50000i	0.174801	+	0.158114i
$91$	4.31662	+	14.9532i	0.452505	+	1.56752i
$92$		−	1.68338i		−	0.175504i
$93$	3.46410	+	2.00000i	0.359211	+	0.207390i
$94$	0.841688	−	1.45785i	0.0868134	−	0.150365i
$95$	−9.43675	−	2.02830i	−0.968190	−	0.208100i
$96$	−1.00000			−0.102062
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	−0.212445	−	0.977173i	$-0.568143\pi$
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	0.740034	+	0.672569i	$0.234809\pi$
$98$	−10.0747	+	5.81662i	−1.01770	+	0.587568i
$99$	6.31662			0.634845
$100$	4.05842	−	2.92048i	0.405842	−	0.292048i
$101$	0.183375	−	0.317615i	0.0182465	−	0.0316039i	−0.856758	−	0.515719i	$-0.827525\pi$
$101$	0.183375	−	0.317615i	0.0182465	−	0.0316039i	0.875004	+	0.484115i	$0.160858\pi$
$102$	6.61059	+	3.81662i	0.654546	+	0.377902i
$103$		−	8.31662i		−	0.819461i	−0.912207	−	0.409731i	$-0.865623\pi$
$103$		−	8.31662i		−	0.819461i	0.912207	−	0.409731i	$-0.134377\pi$
$104$	−3.50000	−	0.866025i	−0.343203	−	0.0849208i
$105$	−6.47494	+	7.15831i	−0.631889	+	0.698580i
$106$	−2.34169	+	4.05592i	−0.227445	+	0.393946i
$107$	10.1181	+	5.84169i	0.978154	+	0.564737i	0.901712	−	0.432337i	$-0.142311\pi$
$107$	10.1181	+	5.84169i	0.978154	+	0.564737i	0.0764414	+	0.997074i	$0.475644\pi$
$108$	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	$0.407226\pi$
$110$	2.96807	−	13.8090i	0.282994	−	1.31664i
$111$	−3.81662	−	6.61059i	−0.362258	−	0.627449i
$112$		−	4.31662i		−	0.407883i
$113$	14.0872	−	8.13325i	1.32521	−	0.765112i	0.340657	−	0.940187i	$-0.389350\pi$
$113$	14.0872	−	8.13325i	1.32521	−	0.765112i	0.984555	+	0.175076i	$0.0560170\pi$
$114$	−2.15831	+	3.73831i	−0.202144	+	0.350125i
$115$	3.58255	−	1.15503i	0.334074	−	0.107707i
$116$	3.00000			0.278543
$117$	3.46410	−	1.00000i	0.320256	−	0.0924500i
$118$			4.63325i			0.426525i
$119$	−16.4749	+	28.5354i	−1.51026	+	2.61584i
$120$	−0.686141	−	2.12819i	−0.0626358	−	0.194277i
$121$	−14.4499	−	25.0279i	−1.31362	−	2.27527i
$122$			0.683375i			0.0618699i
$123$	−0.591820	+	0.341688i	−0.0533626	+	0.0308089i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	9.00000	+	6.63325i	0.804984	+	0.593296i
$126$	2.15831	+	3.73831i	0.192278	+	0.333035i
$127$	−3.46410	−	2.00000i	−0.307389	−	0.177471i	0.338368	−	0.941014i	$-0.390125\pi$
$127$	−3.46410	−	2.00000i	−0.307389	−	0.177471i	−0.645758	+	0.763542i	$0.723458\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−2.31662			−0.203967
$130$	−0.558422	−	8.04290i	−0.0489768	−	0.705409i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−5.47036	−	3.15831i	−0.476134	−	0.274896i
$133$	−16.1369	−	9.31662i	−1.39924	−	0.807854i
$134$	3.47494	+	6.01877i	0.300189	+	0.519942i
$135$	1.65831	+	1.50000i	0.142725	+	0.129099i
$136$	−3.81662	−	6.61059i	−0.327273	−	0.566853i
$137$	4.87854	−	2.81662i	0.416802	−	0.240640i	−0.276906	−	0.960897i	$-0.589309\pi$
$137$	4.87854	−	2.81662i	0.416802	−	0.240640i	0.693708	+	0.720256i	$0.255976\pi$
$138$		−	1.68338i		−	0.143298i
$139$	2.63325	+	4.56092i	0.223349	+	0.386852i	0.955823	−	0.293943i	$-0.0949676\pi$
$139$	2.63325	+	4.56092i	0.223349	+	0.386852i	−0.732474	+	0.680795i	$0.761634\pi$
$140$	9.18662	−	2.96181i	0.776411	−	0.250319i
$141$	0.841688	−	1.45785i	0.0708829	−	0.122773i
$142$			8.31662i			0.697916i
$143$	−16.4111	−	15.7916i	−1.37236	−	1.32056i
$144$	−1.00000			−0.0833333
$145$	2.05842	+	6.38458i	0.170943	+	0.530211i
$146$	−0.341688	+	0.591820i	−0.0282783	+	0.0489794i
$147$	−10.0747	+	5.81662i	−0.830946	+	0.479747i
$148$			7.63325i			0.627449i
$149$	−1.81662	−	3.14649i	−0.148824	−	0.257770i	0.781969	−	0.623317i	$-0.214215\pi$
$149$	−1.81662	−	3.14649i	−0.148824	−	0.257770i	−0.930793	+	0.365547i	$0.880882\pi$
$150$	4.05842	−	2.92048i	0.331369	−	0.238456i
$151$	6.94987			0.565573			0.282786	−	0.959183i	$-0.408741\pi$
$151$	6.94987			0.565573			0.282786	+	0.959183i	$0.408741\pi$
$152$	3.73831	−	2.15831i	0.303217	−	0.175062i
$153$	6.61059	+	3.81662i	0.534434	+	0.308556i
$154$	13.6332	−	23.6135i	1.09860	−	1.90283i
$155$	6.00000	−	6.63325i	0.481932	−	0.532795i
$156$	−3.50000	−	0.866025i	−0.280224	−	0.0693375i
$157$			14.2665i			1.13859i	0.822133	+	0.569295i	$0.192784\pi$
$157$			14.2665i			1.13859i	−0.822133	+	0.569295i	$0.807216\pi$
$158$	−3.46410	−	2.00000i	−0.275589	−	0.159111i
$159$	−2.34169	+	4.05592i	−0.185708	+	0.321656i
$160$	−0.469882	+	2.18614i	−0.0371474	+	0.172830i
$161$	7.26650			0.572680
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−7.47661	+	4.31662i	−0.585614	+	0.338104i	−0.763361	−	0.645972i	$-0.776452\pi$
$163$	−7.47661	+	4.31662i	−0.585614	+	0.338104i	0.177748	+	0.984076i	$0.443119\pi$
$164$	0.683375			0.0533626
$165$	2.96807	−	13.8090i	0.231064	−	1.07503i
$166$	−4.15831	+	7.20241i	−0.322748	+	0.559015i
$167$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$167$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$168$		−	4.31662i		−	0.333035i
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$	11.4499	−	12.6583i	0.878165	−	0.970848i
$171$	−2.15831	+	3.73831i	−0.165050	+	0.285875i
$172$	2.00626	+	1.15831i	0.152976	+	0.0883205i
$173$	−13.2212	+	7.63325i	−1.00519	+	0.580345i	−0.909779	−	0.415093i	$-0.863749\pi$
$173$	−13.2212	+	7.63325i	−1.00519	+	0.580345i	−0.0954084	+	0.995438i	$0.530416\pi$
$174$	3.00000			0.227429
$175$	12.6066	+	17.5187i	0.952971	+	1.32429i
$176$	3.15831	+	5.47036i	0.238067	+	0.412344i
$177$			4.63325i			0.348256i
$178$	9.75707	−	5.63325i	0.731324	−	0.422230i
$179$	3.79156	−	6.56718i	0.283395	−	0.490854i	−0.688824	−	0.724929i	$-0.741873\pi$
$179$	3.79156	−	6.56718i	0.283395	−	0.490854i	0.972219	+	0.234075i	$0.0752060\pi$
$180$	−0.686141	−	2.12819i	−0.0511419	−	0.158626i
$181$	19.9499			1.48286			0.741431	−	0.671029i	$-0.234147\pi$
$181$	19.9499			1.48286			0.741431	+	0.671029i	$0.234147\pi$
$182$	3.73831	−	15.1082i	0.277102	−	1.11989i
$183$			0.683375i			0.0505165i
$184$	−0.841688	+	1.45785i	−0.0620500	+	0.107474i
$185$	−16.2450	+	5.23748i	−1.19436	+	0.385067i
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$		−	48.2164i		−	3.52593i
$188$	−1.45785	+	0.841688i	−0.106324	+	0.0613864i
$189$	2.15831	+	3.73831i	0.156994	+	0.271922i
$190$	7.15831	+	6.47494i	0.519319	+	0.469741i
$191$	−6.31662	−	10.9407i	−0.457055	−	0.791642i	0.541749	−	0.840540i	$-0.317762\pi$
$191$	−6.31662	−	10.9407i	−0.457055	−	0.791642i	−0.998804	+	0.0488981i	$0.984429\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	3.42069	+	1.97494i	0.246227	+	0.142159i	0.618035	−	0.786150i	$-0.287929\pi$
$193$	3.42069	+	1.97494i	0.246227	+	0.142159i	−0.371809	+	0.928309i	$0.621262\pi$
$194$	−6.00000			−0.430775
$195$	−0.558422	−	8.04290i	−0.0399894	−	0.575964i
$196$	11.6332			0.830946
$197$	−11.4891	−	6.63325i	−0.818566	−	0.472599i	0.0313555	−	0.999508i	$-0.490018\pi$
$197$	−11.4891	−	6.63325i	−0.818566	−	0.472599i	−0.849922	+	0.526909i	$0.823351\pi$
$198$	−5.47036	−	3.15831i	−0.388761	−	0.224451i
$199$	−11.1583	−	19.3268i	−0.790992	−	1.37004i	−0.925353	−	0.379106i	$-0.876232\pi$
$199$	−11.1583	−	19.3268i	−0.790992	−	1.37004i	0.134362	−	0.990932i	$-0.457102\pi$
$200$	−4.97494	+	0.500000i	−0.351781	+	0.0353553i
$201$	3.47494	+	6.01877i	0.245103	+	0.424531i
$202$	−0.317615	+	0.183375i	−0.0223473	+	0.0129022i
$203$			12.9499i			0.908903i
$204$	−3.81662	−	6.61059i	−0.267217	−	0.462834i
$205$	0.468892	+	1.45436i	0.0327488	+	0.101577i
$206$	−4.15831	+	7.20241i	−0.289723	+	0.501816i
$207$		−	1.68338i		−	0.117003i
$208$	2.59808	+	2.50000i	0.180144	+	0.173344i
$209$	27.2665			1.88606
$210$	9.18662	−	2.96181i	0.633937	−	0.204384i
$211$	−4.31662	+	7.47661i	−0.297169	+	0.514711i	−0.975487	−	0.220057i	$-0.929376\pi$
$211$	−4.31662	+	7.47661i	−0.297169	+	0.514711i	0.678318	+	0.734768i	$0.262709\pi$
$212$	4.05592	−	2.34169i	0.278562	−	0.160828i
$213$			8.31662i			0.569846i
$214$	−5.84169	−	10.1181i	−0.399330	−	0.691659i
$215$	−1.08854	+	5.06447i	−0.0742378	+	0.345394i
$216$	−1.00000			−0.0680414
$217$	14.9532	−	8.63325i	1.01509	−	0.586063i
$218$	−5.19615	−	3.00000i	−0.351928	−	0.203186i
$219$	−0.341688	+	0.591820i	−0.0230891	+	0.0399915i
$220$	−9.47494	+	10.4749i	−0.638800	+	0.706220i
$221$	−7.63325	−	26.4424i	−0.513468	−	1.77871i
$222$			7.63325i			0.512310i
$223$	6.37979	+	3.68338i	0.427223	+	0.246657i	0.698163	−	0.715939i	$-0.254001\pi$
$223$	6.37979	+	3.68338i	0.427223	+	0.246657i	−0.270940	+	0.962596i	$0.587335\pi$
$224$	−2.15831	+	3.73831i	−0.144208	+	0.249776i
$225$	4.05842	−	2.92048i	0.270561	−	0.194699i
$226$	−16.2665			−1.08203
$227$	−25.6197	+	14.7916i	−1.70044	+	0.981750i	−0.755134	+	0.655571i	$0.772428\pi$
$227$	−25.6197	+	14.7916i	−1.70044	+	0.981750i	−0.945308	+	0.326180i	$0.894238\pi$
$228$	3.73831	−	2.15831i	0.247575	−	0.142938i
$229$	12.0000			0.792982			0.396491	−	0.918039i	$-0.370228\pi$
$229$	12.0000			0.792982			0.396491	+	0.918039i	$0.370228\pi$
$230$	−3.68009	−	0.790988i	−0.242658	−	0.0521562i
$231$	13.6332	−	23.6135i	0.897002	−	1.55365i
$232$	−2.59808	−	1.50000i	−0.170572	−	0.0984798i
$233$		−	11.3668i		−	0.744661i	−0.928100	−	0.372330i	$-0.878559\pi$
$233$		−	11.3668i		−	0.744661i	0.928100	−	0.372330i	$-0.121441\pi$
$234$	−3.50000	−	0.866025i	−0.228802	−	0.0566139i
$235$	−2.79156	−	2.52506i	−0.182101	−	0.164717i
$236$	2.31662	−	4.01251i	0.150799	−	0.261192i
$237$	−3.46410	−	2.00000i	−0.225018	−	0.129914i
$238$	28.5354	−	16.4749i	1.84968	−	1.06791i
$239$	−8.31662			−0.537958			−0.268979	−	0.963146i	$-0.586686\pi$
$239$	−8.31662			−0.537958			−0.268979	+	0.963146i	$0.586686\pi$
$240$	−0.469882	+	2.18614i	−0.0303307	+	0.141115i
$241$	12.8166	+	22.1990i	0.825591	+	1.42997i	0.901466	+	0.432849i	$0.142492\pi$
$241$	12.8166	+	22.1990i	0.825591	+	1.42997i	−0.0758751	+	0.997117i	$0.524175\pi$
$242$			28.8997i			1.85775i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	0.341688	−	0.591820i	0.0218743	−	0.0378874i
$245$	7.98205	+	24.7578i	0.509954	+	1.58172i
$246$	0.683375			0.0435704
$247$	14.9532	−	4.31662i	0.951451	−	0.274660i
$248$			4.00000i			0.254000i
$249$	−4.15831	+	7.20241i	−0.263522	+	0.456434i
$250$	−4.47760	−	10.2446i	−0.283189	−	0.647923i
$251$	12.9499	+	22.4298i	0.817389	+	1.41576i	0.907600	+	0.419836i	$0.137913\pi$
$251$	12.9499	+	22.4298i	0.817389	+	1.41576i	−0.0902110	+	0.995923i	$0.528754\pi$
$252$		−	4.31662i		−	0.271922i
$253$	−9.20866	+	5.31662i	−0.578944	+	0.334253i
$254$	2.00000	+	3.46410i	0.125491	+	0.217357i
$255$	11.4499	−	12.6583i	0.717019	−	0.792694i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−19.2834	−	11.1332i	−1.20286	−	0.694473i	−0.241672	−	0.970358i	$-0.577696\pi$
$257$	−19.2834	−	11.1332i	−1.20286	−	0.694473i	−0.961191	+	0.275885i	$0.911029\pi$
$258$	2.00626	+	1.15831i	0.124904	+	0.0721134i
$259$	−32.9499			−2.04741
$260$	−3.53784	+	7.24456i	−0.219408	+	0.449289i
$261$	3.00000			0.185695
$262$		0			0
$263$	−13.4954	−	7.79156i	−0.832161	−	0.480448i	0.0224311	−	0.999748i	$-0.492859\pi$
$263$	−13.4954	−	7.79156i	−0.832161	−	0.480448i	−0.854592	+	0.519300i	$0.826193\pi$
$264$	3.15831	+	5.47036i	0.194381	+	0.336677i
$265$	7.76650	+	7.02506i	0.477092	+	0.431546i
$266$	9.31662	+	16.1369i	0.571239	+	0.989415i
$267$	9.75707	−	5.63325i	0.597123	−	0.344749i
$268$		−	6.94987i		−	0.424531i
$269$	6.31662	+	10.9407i	0.385131	+	0.667067i	0.991787	−	0.127897i	$-0.0408228\pi$
$269$	6.31662	+	10.9407i	0.385131	+	0.667067i	−0.606656	+	0.794964i	$0.707489\pi$
$270$	−0.686141	−	2.12819i	−0.0417572	−	0.129518i
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$			7.63325i			0.462834i
$273$	3.73831	−	15.1082i	0.226253	−	0.914389i
$274$	−5.63325			−0.340317
$275$	−28.7938	−	12.9772i	−1.73633	−	0.782556i
$276$	−0.841688	+	1.45785i	−0.0506636	+	0.0877520i
$277$	−23.3827	+	13.5000i	−1.40493	+	0.811136i	−0.994893	−	0.100933i	$-0.967817\pi$
$277$	−23.3827	+	13.5000i	−1.40493	+	0.811136i	−0.410036	+	0.912069i	$0.634484\pi$
$278$		−	5.26650i		−	0.315864i
$279$	−2.00000	−	3.46410i	−0.119737	−	0.207390i
$280$	−9.43675	−	2.02830i	−0.563954	−	0.121214i
$281$	−27.2164			−1.62359			−0.811796	−	0.583941i	$-0.801510\pi$
$281$	−27.2164			−1.62359			−0.811796	+	0.583941i	$0.801510\pi$
$282$	−1.45785	+	0.841688i	−0.0868134	+	0.0501218i
$283$	19.8752	+	11.4749i	1.18146	+	0.682114i	0.956351	−	0.292220i	$-0.0943940\pi$
$283$	19.8752	+	11.4749i	1.18146	+	0.682114i	0.225105	+	0.974334i	$0.427727\pi$
$284$	4.15831	−	7.20241i	0.246750	−	0.427384i
$285$	7.15831	+	6.47494i	0.424022	+	0.383542i
$286$	6.31662	+	21.8814i	0.373510	+	1.29388i
$287$			2.94987i			0.174126i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	20.6332	−	35.7378i	1.21372	−	2.10223i
$290$	1.40965	−	6.55842i	0.0827772	−	0.385124i
$291$	−6.00000			−0.351726
$292$	0.591820	−	0.341688i	0.0346337	−	0.0199958i
$293$	18.4607	−	10.6583i	1.07849	−	0.622665i	0.148000	−	0.988987i	$-0.452717\pi$
$293$	18.4607	−	10.6583i	1.07849	−	0.622665i	0.930488	+	0.366322i	$0.119383\pi$
$294$	11.6332			0.678465
$295$	10.1289	+	2.17708i	0.589729	+	0.126755i
$296$	3.81662	−	6.61059i	0.221837	−	0.384233i
$297$	−5.47036	−	3.15831i	−0.317422	−	0.183264i
$298$			3.63325i			0.210468i
$299$	−4.20844	+	4.37354i	−0.243380	+	0.252928i
$300$	−4.97494	+	0.500000i	−0.287228	+	0.0288675i
$301$	−5.00000	+	8.66025i	−0.288195	+	0.499169i
$302$	−6.01877	−	3.47494i	−0.346341	−	0.199960i
$303$	−0.317615	+	0.183375i	−0.0182465	+	0.0105346i
$304$	−4.31662			−0.247575
$305$	1.49395	+	0.321106i	0.0855436	+	0.0183865i
$306$	−3.81662	−	6.61059i	−0.218182	−	0.377902i
$307$			16.2164i			0.925517i	0.886484	+	0.462759i	$0.153140\pi$
$307$			16.2164i			0.925517i	−0.886484	+	0.462759i	$0.846860\pi$
$308$	−23.6135	+	13.6332i	−1.34550	+	0.776826i
$309$	−4.15831	+	7.20241i	−0.236558	+	0.409731i
$310$	−8.51278	+	2.74456i	−0.483493	+	0.155881i
$311$	12.3166			0.698412			0.349206	−	0.937046i	$-0.386451\pi$
$311$	12.3166			0.698412			0.349206	+	0.937046i	$0.386451\pi$
$312$	2.59808	+	2.50000i	0.147087	+	0.141535i
$313$			30.0000i			1.69570i	0.530236	+	0.847850i	$0.322103\pi$
$313$			30.0000i			1.69570i	−0.530236	+	0.847850i	$0.677897\pi$
$314$	7.13325	−	12.3552i	0.402553	−	0.697241i
$315$	9.18662	−	2.96181i	0.517607	−	0.166879i
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$			3.94987i			0.221847i	0.993829	+	0.110924i	$0.0353809\pi$
$317$			3.94987i			0.221847i	−0.993829	+	0.110924i	$0.964619\pi$
$318$	4.05592	−	2.34169i	0.227445	−	0.131315i
$319$	−9.47494	−	16.4111i	−0.530495	−	0.918844i
$320$	1.50000	−	1.65831i	0.0838525	−	0.0927025i
$321$	−5.84169	−	10.1181i	−0.326051	−	0.564737i
$322$	−6.29297	−	3.63325i	−0.350694	−	0.202473i
$323$	28.5354	+	16.4749i	1.58775	+	0.916690i
$324$	−1.00000			−0.0555556
$325$	−17.8453	−	2.55842i	−0.989879	−	0.141916i
$326$	8.63325			0.478151
$327$	−5.19615	−	3.00000i	−0.287348	−	0.165900i
$328$	−0.591820	−	0.341688i	−0.0326778	−	0.0188665i
$329$	−3.63325	−	6.29297i	−0.200308	−	0.346943i
$330$	−9.47494	+	10.4749i	−0.521578	+	0.576626i
$331$	−2.63325	−	4.56092i	−0.144736	−	0.250691i	0.784538	−	0.620081i	$-0.212900\pi$
$331$	−2.63325	−	4.56092i	−0.144736	−	0.250691i	−0.929275	+	0.369390i	$0.879567\pi$
$332$	7.20241	−	4.15831i	0.395284	−	0.228217i
$333$			7.63325i			0.418300i
$334$		0			0
$335$	14.7907	−	4.76859i	0.808101	−	0.260536i
$336$	−2.15831	+	3.73831i	−0.117746	+	0.203941i
$337$			4.68338i			0.255120i	0.991831	+	0.127560i	$0.0407145\pi$
$337$			4.68338i			0.255120i	−0.991831	+	0.127560i	$0.959286\pi$
$338$	6.92820	+	11.0000i	0.376845	+	0.598321i
$339$	−16.2665			−0.883475
$340$	−16.2450	+	5.23748i	−0.881011	+	0.284042i
$341$	−12.6332	+	21.8814i	−0.684129	+	1.18495i
$342$	3.73831	−	2.15831i	0.202144	−	0.116708i
$343$			20.0000i			1.07990i
$344$	−1.15831	−	2.00626i	−0.0624520	−	0.108170i
$345$	−3.68009	−	0.790988i	−0.198130	−	0.0425853i
$346$	15.2665			0.820732
$347$	1.37103	−	0.791562i	0.0736005	−	0.0424933i	−0.462748	−	0.886490i	$-0.653137\pi$
$347$	1.37103	−	0.791562i	0.0736005	−	0.0424933i	0.536349	+	0.843997i	$0.319803\pi$
$348$	−2.59808	−	1.50000i	−0.139272	−	0.0804084i
$349$	0.366750	−	0.635230i	0.0196317	−	0.0340031i	−0.856043	−	0.516905i	$-0.827084\pi$
$349$	0.366750	−	0.635230i	0.0196317	−	0.0340031i	0.875674	+	0.482902i	$0.160417\pi$
$350$	−2.15831	−	21.4749i	−0.115367	−	1.14788i
$351$	−3.50000	−	0.866025i	−0.186816	−	0.0462250i
$352$		−	6.31662i		−	0.336677i
$353$	17.6381	+	10.1834i	0.938783	+	0.542006i	0.889578	−	0.456782i	$-0.150998\pi$
$353$	17.6381	+	10.1834i	0.938783	+	0.542006i	0.0492041	+	0.998789i	$0.484332\pi$
$354$	2.31662	−	4.01251i	0.123127	−	0.213263i
$355$	18.1813	+	3.90783i	0.964964	+	0.207406i
$356$	−11.2665			−0.597123
$357$	28.5354	−	16.4749i	1.51026	−	0.871946i
$358$	−6.56718	+	3.79156i	−0.347086	+	0.200390i
$359$	16.3166			0.861159			0.430579	−	0.902553i	$-0.358309\pi$
$359$	16.3166			0.861159			0.430579	+	0.902553i	$0.358309\pi$
$360$	−0.469882	+	2.18614i	−0.0247650	+	0.115220i
$361$	0.183375	−	0.317615i	0.00965133	−	0.0167166i
$362$	−17.2771	−	9.97494i	−0.908064	−	0.524271i
$363$			28.8997i			1.51684i
$364$	−10.7916	+	11.2149i	−0.565632	+	0.587822i
$365$	1.13325	+	1.02506i	0.0593170	+	0.0536542i
$366$	0.341688	−	0.591820i	0.0178603	−	0.0309349i
$367$	17.0463	+	9.84169i	0.889810	+	0.513732i	0.873880	−	0.486141i	$-0.161596\pi$
$367$	17.0463	+	9.84169i	0.889810	+	0.513732i	0.0159295	+	0.999873i	$0.494929\pi$
$368$	1.45785	−	0.841688i	0.0759955	−	0.0438760i
$369$	0.683375			0.0355751
$370$	16.6874	+	3.58673i	0.867534	+	0.186465i
$371$	10.1082	+	17.5079i	0.524791	+	0.908965i
$372$			4.00000i			0.207390i
$373$	−0.866025	+	0.500000i	−0.0448411	+	0.0258890i	−0.522253	−	0.852791i	$-0.674908\pi$
$373$	−0.866025	+	0.500000i	−0.0448411	+	0.0258890i	0.477412	+	0.878680i	$0.341575\pi$
$374$	−24.1082	+	41.7566i	−1.24660	+	2.15918i
$375$	−4.47760	−	10.2446i	−0.231222	−	0.529027i
$376$	1.68338			0.0868134
$377$	−7.79423	−	7.50000i	−0.401423	−	0.386270i
$378$		−	4.31662i		−	0.222023i
$379$	−6.94987	+	12.0375i	−0.356991	+	0.618327i	−0.987457	−	0.157891i	$-0.949531\pi$
$379$	−6.94987	+	12.0375i	−0.356991	+	0.618327i	0.630466	+	0.776217i	$0.282864\pi$
$380$	−2.96181	−	9.18662i	−0.151938	−	0.471263i
$381$	2.00000	+	3.46410i	0.102463	+	0.177471i
$382$			12.6332i			0.646373i
$383$	−5.83138	+	3.36675i	−0.297970	+	0.172033i	−0.641530	−	0.767098i	$-0.721700\pi$
$383$	−5.83138	+	3.36675i	−0.297970	+	0.172033i	0.343561	+	0.939130i	$0.388367\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−45.2164	−	40.8997i	−2.30444	−	2.08444i
$386$	−1.97494	−	3.42069i	−0.100522	−	0.174109i
$387$	2.00626	+	1.15831i	0.101984	+	0.0588803i
$388$	5.19615	+	3.00000i	0.263795	+	0.152302i
$389$	15.6332			0.792637			0.396319	−	0.918113i	$-0.370288\pi$
$389$	15.6332			0.792637			0.396319	+	0.918113i	$0.370288\pi$
$390$	−3.53784	+	7.24456i	−0.179145	+	0.366843i
$391$	−12.8496			−0.649833
$392$	−10.0747	−	5.81662i	−0.508849	−	0.293784i
$393$		0			0
$394$	6.63325	+	11.4891i	0.334178	+	0.578814i
$395$	−6.00000	+	6.63325i	−0.301893	+	0.333755i
$396$	3.15831	+	5.47036i	0.158711	+	0.274896i
$397$	−15.5016	+	8.94987i	−0.778005	+	0.449181i	−0.835723	−	0.549152i	$-0.814951\pi$
$397$	−15.5016	+	8.94987i	−0.778005	+	0.449181i	0.0577179	+	0.998333i	$0.481618\pi$
$398$			22.3166i			1.11863i
$399$	9.31662	+	16.1369i	0.466415	+	0.807854i
$400$	4.55842	+	2.05446i	0.227921	+	0.102723i
$401$	5.34169	−	9.25207i	0.266751	−	0.462027i	−0.701270	−	0.712896i	$-0.747383\pi$
$401$	5.34169	−	9.25207i	0.266751	−	0.462027i	0.968021	+	0.250869i	$0.0807165\pi$
$402$		−	6.94987i		−	0.346628i
$403$	−3.46410	+	14.0000i	−0.172559	+	0.697390i
$404$	0.366750			0.0182465
$405$	−0.686141	−	2.12819i	−0.0340946	−	0.105751i
$406$	6.47494	−	11.2149i	0.321346	−	0.556587i
$407$	41.7566	−	24.1082i	2.06980	−	1.19500i
$408$			7.63325i			0.377902i
$409$	−10.5000	−	18.1865i	−0.519192	−	0.899266i	−0.999751	−	0.0223042i	$-0.992900\pi$
$409$	−10.5000	−	18.1865i	−0.519192	−	0.899266i	0.480560	−	0.876962i	$-0.340434\pi$
$410$	0.321106	−	1.49395i	0.0158583	−	0.0737811i
$411$	−5.63325			−0.277868
$412$	7.20241	−	4.15831i	0.354837	−	0.204865i
$413$	17.3205	+	10.0000i	0.852286	+	0.492068i
$414$	−0.841688	+	1.45785i	−0.0413667	+	0.0716492i
$415$	13.7916	+	12.4749i	0.677001	+	0.612371i
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$		−	5.26650i		−	0.257902i
$418$	−23.6135	−	13.6332i	−1.15497	−	0.666824i
$419$	−19.5831	+	33.9190i	−0.956698	+	1.65705i	−0.226265	+	0.974066i	$0.572652\pi$
$419$	−19.5831	+	33.9190i	−0.956698	+	1.65705i	−0.730433	+	0.682984i	$0.760682\pi$
$420$	−9.43675	−	2.02830i	−0.460466	−	0.0989711i
$421$	−37.9499			−1.84956			−0.924782	−	0.380498i	$-0.875753\pi$
$421$	−37.9499			−1.84956			−0.924782	+	0.380498i	$0.875753\pi$
$422$	7.47661	−	4.31662i	0.363956	−	0.210130i
$423$	−1.45785	+	0.841688i	−0.0708829	+	0.0409243i
$424$	−4.68338			−0.227445
$425$	−22.2928	−	30.9789i	−1.08136	−	1.50270i
$426$	4.15831	−	7.20241i	0.201471	−	0.348958i
$427$	2.55467	+	1.47494i	0.123629	+	0.0713772i
$428$			11.6834i			0.564737i
$429$	6.31662	+	21.8814i	0.304970	+	1.05645i
$430$	3.47494	−	3.84169i	0.167576	−	0.185263i
$431$	6.47494	−	11.2149i	0.311887	−	0.540204i	−0.666884	−	0.745161i	$-0.732372\pi$
$431$	6.47494	−	11.2149i	0.311887	−	0.540204i	0.978771	+	0.204958i	$0.0657057\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	7.43320	−	4.29156i	0.357217	−	0.206239i	−0.310642	−	0.950527i	$-0.600544\pi$
$433$	7.43320	−	4.29156i	0.357217	−	0.206239i	0.667859	+	0.744288i	$0.267211\pi$
$434$	−17.2665			−0.828818
$435$	1.40965	−	6.55842i	0.0675873	−	0.314452i
$436$	3.00000	+	5.19615i	0.143674	+	0.248851i
$437$		−	7.26650i		−	0.347604i
$438$	0.591820	−	0.341688i	0.0282783	−	0.0163265i
$439$	−19.1583	+	33.1832i	−0.914376	+	1.58375i	−0.106565	+	0.994306i	$0.533985\pi$
$439$	−19.1583	+	33.1832i	−0.914376	+	1.58375i	−0.807812	+	0.589441i	$0.799348\pi$
$440$	13.4430	−	4.33409i	0.640870	−	0.206620i
$441$	11.6332			0.553964
$442$	−6.61059	+	26.7164i	−0.314434	+	1.27077i
$443$			13.2665i			0.630310i	0.949040	+	0.315155i	$0.102057\pi$
$443$			13.2665i			0.630310i	−0.949040	+	0.315155i	$0.897943\pi$
$444$	3.81662	−	6.61059i	0.181129	−	0.313725i
$445$	−7.73040	−	23.9773i	−0.366456	−	1.13663i
$446$	−3.68338	−	6.37979i	−0.174413	−	0.302092i
$447$			3.63325i			0.171847i
$448$	3.73831	−	2.15831i	0.176618	−	0.101971i
$449$	8.26650	+	14.3180i	0.390120	+	0.675708i	0.992465	−	0.122528i	$-0.0391001\pi$
$449$	8.26650	+	14.3180i	0.390120	+	0.675708i	−0.602345	+	0.798236i	$0.705767\pi$
$450$	−4.97494	+	0.500000i	−0.234521	+	0.0235702i
$451$	−2.15831	−	3.73831i	−0.101631	−	0.176030i
$452$	14.0872	+	8.13325i	0.662606	+	0.382556i
$453$	−6.01877	−	3.47494i	−0.282786	−	0.163267i
$454$	29.5831			1.38840
$455$	−31.2721	−	15.2715i	−1.46606	−	0.715940i
$456$	−4.31662			−0.202144
$457$	−13.8130	−	7.97494i	−0.646145	−	0.373052i	0.140833	−	0.990033i	$-0.455022\pi$
$457$	−13.8130	−	7.97494i	−0.646145	−	0.373052i	−0.786978	+	0.616982i	$0.788355\pi$
$458$	−10.3923	−	6.00000i	−0.485601	−	0.280362i
$459$	−3.81662	−	6.61059i	−0.178145	−	0.308556i
$460$	2.79156	+	2.52506i	0.130157	+	0.117732i
$461$	−4.81662	−	8.34264i	−0.224333	−	0.388555i	0.731786	−	0.681534i	$-0.238687\pi$
$461$	−4.81662	−	8.34264i	−0.224333	−	0.388555i	−0.956119	+	0.292979i	$0.905354\pi$
$462$	−23.6135	+	13.6332i	−1.09860	+	0.634276i
$463$		−	8.94987i		−	0.415936i	−0.978136	−	0.207968i	$-0.933315\pi$
$463$		−	8.94987i		−	0.415936i	0.978136	−	0.207968i	$-0.0666850\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$	−8.51278	+	2.74456i	−0.394771	+	0.127276i
$466$	−5.68338	+	9.84389i	−0.263277	+	0.456010i
$467$		−	33.5831i		−	1.55404i	−0.629475	−	0.777021i	$-0.716730\pi$
$467$		−	33.5831i		−	1.55404i	0.629475	−	0.777021i	$-0.283270\pi$
$468$	2.59808	+	2.50000i	0.120096	+	0.115563i
$469$	30.0000			1.38527
$470$	1.15503	+	3.58255i	0.0532777	+	0.165251i
$471$	7.13325	−	12.3552i	0.328683	−	0.569295i
$472$	−4.01251	+	2.31662i	−0.184691	+	0.106631i
$473$		−	14.6332i		−	0.672838i
$474$	2.00000	+	3.46410i	0.0918630	+	0.159111i
$475$	17.5187	−	12.6066i	0.803812	−	0.578431i
$476$	−32.9499			−1.51026
$477$	4.05592	−	2.34169i	0.185708	−	0.107219i
$478$	7.20241	+	4.15831i	0.329430	+	0.190197i
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	1.50000	−	1.65831i	0.0684653	−	0.0756913i
$481$	19.0831	−	19.8318i	0.870116	−	0.904251i
$482$		−	25.6332i		−	1.16756i
$483$	−6.29297	−	3.63325i	−0.286340	−	0.165319i
$484$	14.4499	−	25.0279i	0.656812	−	1.13763i
$485$	−2.81929	+	13.1168i	−0.128017	+	0.595605i
$486$	−1.00000			−0.0453609
$487$	−3.73831	+	2.15831i	−0.169399	+	0.0978025i	−0.582302	−	0.812972i	$-0.697848\pi$
$487$	−3.73831	+	2.15831i	−0.169399	+	0.0978025i	0.412903	+	0.910775i	$0.364515\pi$
$488$	−0.591820	+	0.341688i	−0.0267904	+	0.0154675i
$489$	8.63325			0.390409
$490$	5.46625	−	25.4319i	0.246940	−	1.14890i
$491$	19.7916	−	34.2800i	0.893181	−	1.54703i	0.0571405	−	0.998366i	$-0.481802\pi$
$491$	19.7916	−	34.2800i	0.893181	−	1.54703i	0.836040	−	0.548668i	$-0.184865\pi$
$492$	−0.591820	−	0.341688i	−0.0266813	−	0.0154045i
$493$		−	22.8997i		−	1.03135i
$494$	−15.1082	−	3.73831i	−0.679749	−	0.168194i
$495$	−9.47494	+	10.4749i	−0.425867	+	0.470813i
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	31.0901	+	17.9499i	1.39458	+	0.805162i
$498$	7.20241	−	4.15831i	0.322748	−	0.186338i
$499$	41.8997			1.87569			0.937845	−	0.347054i	$-0.112818\pi$
$499$	41.8997			1.87569			0.937845	+	0.347054i	$0.112818\pi$
$500$	−1.24456	+	11.1109i	−0.0556585	+	0.496892i
$501$		0			0
$502$		−	25.8997i		−	1.15596i
$503$	15.8627	−	9.15831i	0.707281	−	0.408349i	−0.102772	−	0.994705i	$-0.532771\pi$
$503$	15.8627	−	9.15831i	0.707281	−	0.408349i	0.810054	+	0.586356i	$0.199438\pi$
$504$	−2.15831	+	3.73831i	−0.0961389	+	0.166517i
$505$	0.251642	+	0.780516i	0.0111979	+	0.0347325i
$506$	10.6332			0.472706
$507$	6.92820	+	11.0000i	0.307692	+	0.488527i
$508$		−	4.00000i		−	0.177471i
$509$	18.0831	−	31.3209i	0.801520	−	1.38827i	−0.117095	−	0.993121i	$-0.537358\pi$
$509$	18.0831	−	31.3209i	0.801520	−	1.38827i	0.918615	−	0.395153i	$-0.129309\pi$
$510$	−16.2450	+	5.23748i	−0.719342	+	0.231920i
$511$	1.47494	+	2.55467i	0.0652474	+	0.113012i
$512$			1.00000i			0.0441942i
$513$	3.73831	−	2.15831i	0.165050	−	0.0952918i
$514$	11.1332	+	19.2834i	0.491067	+	0.850552i
$515$	13.7916	+	12.4749i	0.607729	+	0.549711i
$516$	−1.15831	−	2.00626i	−0.0509919	−	0.0883205i
$517$	9.20866	+	5.31662i	0.404997	+	0.233825i
$518$	28.5354	+	16.4749i	1.25377	+	0.723867i
$519$	15.2665			0.670125
$520$	6.68614	−	4.50506i	0.293207	−	0.197560i
$521$	−20.0501			−0.878412			−0.439206	−	0.898386i	$-0.644740\pi$
$521$	−20.0501			−0.878412			−0.439206	+	0.898386i	$0.644740\pi$
$522$	−2.59808	−	1.50000i	−0.113715	−	0.0656532i
$523$	21.5204	+	12.4248i	0.941022	+	0.543299i	0.890280	−	0.455413i	$-0.150508\pi$
$523$	21.5204	+	12.4248i	0.941022	+	0.543299i	0.0507412	+	0.998712i	$0.483842\pi$
$524$		0			0
$525$	−2.15831	−	21.4749i	−0.0941965	−	0.937243i
$526$	7.79156	+	13.4954i	0.339728	+	0.588427i
$527$	−26.4424	+	15.2665i	−1.15185	+	0.665019i
$528$		−	6.31662i		−	0.274896i
$529$	−10.0831	−	17.4645i	−0.438397	−	0.759325i
$530$	−3.21345	−	9.96713i	−0.139584	−	0.432945i
$531$	2.31662	−	4.01251i	0.100533	−	0.174128i
$532$		−	18.6332i		−	0.807854i
$533$	−1.77546	−	1.70844i	−0.0769037	−	0.0740007i
$534$	−11.2665			−0.487549
$535$	−24.8645	+	8.01644i	−1.07499	+	0.346581i
$536$	−3.47494	+	6.01877i	−0.150094	+	0.259971i
$537$	−6.56718	+	3.79156i	−0.283395	+	0.163618i
$538$		−	12.6332i		−	0.544658i
$539$	−36.7414	−	63.6380i	−1.58257	−	2.74108i
$540$	−0.469882	+	2.18614i	−0.0202205	+	0.0940765i
$541$	25.2164			1.08414			0.542068	−	0.840334i	$-0.317641\pi$
$541$	25.2164			1.08414			0.542068	+	0.840334i	$0.317641\pi$
$542$	−13.8564	+	8.00000i	−0.595184	+	0.343629i
$543$	−17.2771	−	9.97494i	−0.741431	−	0.428066i
$544$	3.81662	−	6.61059i	0.163636	−	0.283427i
$545$	−9.00000	+	9.94987i	−0.385518	+	0.426206i
$546$	−10.7916	+	11.2149i	−0.461836	+	0.479954i
$547$			30.9499i			1.32332i	0.749804	+	0.661661i	$0.230148\pi$
$547$			30.9499i			1.32332i	−0.749804	+	0.661661i	$0.769852\pi$
$548$	4.87854	+	2.81662i	0.208401	+	0.120320i
$549$	0.341688	−	0.591820i	0.0145829	−	0.0252583i
$550$	18.4476	+	25.6355i	0.786608	+	1.09310i
$551$	12.9499			0.551683
$552$	1.45785	−	0.841688i	0.0620500	−	0.0358246i
$553$	−14.9532	+	8.63325i	−0.635876	+	0.367123i
$554$	27.0000			1.14712
$555$	16.6874	+	3.58673i	0.708339	+	0.152248i
$556$	−2.63325	+	4.56092i	−0.111675	+	0.193426i
$557$	−34.0492	−	19.6583i	−1.44271	−	0.832949i	−0.444681	−	0.895689i	$-0.646683\pi$
$557$	−34.0492	−	19.6583i	−1.44271	−	0.832949i	−0.998030	+	0.0627397i	$0.980016\pi$
$558$			4.00000i			0.169334i
$559$	−2.31662	−	8.02502i	−0.0979828	−	0.339422i
$560$	7.15831	+	6.47494i	0.302494	+	0.273616i
$561$	−24.1082	+	41.7566i	−1.01785	+	1.76297i
$562$	23.5701	+	13.6082i	0.994243	+	0.574027i
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$	1.68338			0.0708829
$565$	−7.64333	+	35.5609i	−0.321557	+	1.49606i
$566$	−11.4749	−	19.8752i	−0.482328	−	0.835416i
$567$		−	4.31662i		−	0.181281i
$568$	−7.20241	+	4.15831i	−0.302206	+	0.174479i
$569$	−21.2665	+	36.8347i	−0.891538	+	1.54419i	−0.0535064	+	0.998568i	$0.517040\pi$
$569$	−21.2665	+	36.8347i	−0.891538	+	1.54419i	−0.838032	+	0.545622i	$0.816294\pi$
$570$	−2.96181	−	9.18662i	−0.124057	−	0.384785i
$571$	−28.9499			−1.21151			−0.605757	−	0.795650i	$-0.707130\pi$
$571$	−28.9499			−1.21151			−0.605757	+	0.795650i	$0.707130\pi$
$572$	5.47036	−	22.1082i	0.228727	−	0.924390i
$573$			12.6332i			0.527762i
$574$	1.47494	−	2.55467i	0.0615627	−	0.106630i
$575$	−3.45842	+	7.67353i	−0.144226	+	0.320009i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	24.0501i		−	1.00122i	−0.865673	−	0.500610i	$-0.833109\pi$
$577$		−	24.0501i		−	1.00122i	0.865673	−	0.500610i	$-0.166891\pi$
$578$	−35.7378	+	20.6332i	−1.48650	+	0.858230i
$579$	−1.97494	−	3.42069i	−0.0820756	−	0.142159i
$580$	−4.50000	+	4.97494i	−0.186852	+	0.206573i
$581$	17.9499	+	31.0901i	0.744686	+	1.28983i
$582$	5.19615	+	3.00000i	0.215387	+	0.124354i
$583$	−25.6197	−	14.7916i	−1.06106	−	0.612604i
$584$	−0.683375			−0.0282783
$585$	−3.53784	+	7.24456i	−0.146272	+	0.299526i
$586$	−21.3166			−0.880582
$587$	16.0500	+	9.26650i	0.662456	+	0.382469i	0.793212	−	0.608945i	$-0.208407\pi$
$587$	16.0500	+	9.26650i	0.662456	+	0.382469i	−0.130756	+	0.991415i	$0.541740\pi$
$588$	−10.0747	−	5.81662i	−0.415473	−	0.239874i
$589$	−8.63325	−	14.9532i	−0.355727	−	0.616137i
$590$	−7.68338	−	6.94987i	−0.316320	−	0.286122i
$591$	6.63325	+	11.4891i	0.272855	+	0.472599i
$592$	−6.61059	+	3.81662i	−0.271693	+	0.156862i
$593$			4.36675i			0.179321i	0.995972	+	0.0896605i	$0.0285782\pi$
$593$			4.36675i			0.179321i	−0.995972	+	0.0896605i	$0.971422\pi$
$594$	3.15831	+	5.47036i	0.129587	+	0.224451i
$595$	−22.6082	−	70.1237i	−0.926848	−	2.87479i
$596$	1.81662	−	3.14649i	0.0744119	−	0.128885i
$597$			22.3166i			0.913359i
$598$	5.83138	−	1.68338i	0.238463	−	0.0688383i
$599$	25.2665			1.03236			0.516181	−	0.856480i	$-0.327353\pi$
$599$	25.2665			1.03236			0.516181	+	0.856480i	$0.327353\pi$
$600$	4.55842	+	2.05446i	0.186097	+	0.0838728i
$601$	−16.5000	+	28.5788i	−0.673049	+	1.16576i	0.303986	+	0.952676i	$0.401682\pi$
$601$	−16.5000	+	28.5788i	−0.673049	+	1.16576i	−0.977035	+	0.213079i	$0.931651\pi$
$602$	8.66025	−	5.00000i	0.352966	−	0.203785i
$603$		−	6.94987i		−	0.283021i
$604$	3.47494	+	6.01877i	0.141393	+	0.244900i
$605$	63.1789	+	13.5795i	2.56859	+	0.552084i
$606$	0.366750			0.0148982
$607$	−22.4298	+	12.9499i	−0.910399	+	0.525619i	−0.880560	−	0.473936i	$-0.842833\pi$
$607$	−22.4298	+	12.9499i	−0.910399	+	0.525619i	−0.0298396	+	0.999555i	$0.509500\pi$
$608$	3.73831	+	2.15831i	0.151608	+	0.0875311i
$609$	6.47494	−	11.2149i	0.262378	−	0.454451i
$610$	−1.13325	−	1.02506i	−0.0458839	−	0.0415036i
$611$	5.89181	+	1.45785i	0.238357	+	0.0589781i
$612$			7.63325i			0.308556i
$613$	30.2241	+	17.4499i	1.22074	+	0.704794i	0.965075	−	0.261972i	$-0.0843729\pi$
$613$	30.2241	+	17.4499i	1.22074	+	0.704794i	0.255663	+	0.966766i	$0.417706\pi$
$614$	8.10819	−	14.0438i	0.327220	−	0.566761i
$615$	0.321106	−	1.49395i	0.0129482	−	0.0602421i
$616$	27.2665			1.09860
$617$	3.69490	−	2.13325i	0.148751	−	0.0858814i	−0.423777	−	0.905766i	$-0.639296\pi$
$617$	3.69490	−	2.13325i	0.148751	−	0.0858814i	0.572528	+	0.819885i	$0.305963\pi$
$618$	7.20241	−	4.15831i	0.289723	−	0.167272i
$619$	35.1662			1.41345			0.706725	−	0.707488i	$-0.250172\pi$
$619$	35.1662			1.41345			0.706725	+	0.707488i	$0.250172\pi$
$620$	8.74456	+	1.87953i	0.351190	+	0.0754836i
$621$	−0.841688	+	1.45785i	−0.0337758	+	0.0585013i
$622$	−10.6665	−	6.15831i	−0.427688	−	0.246926i
$623$		−	48.6332i		−	1.94845i
$624$	−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
$627$	−23.6135	−	13.6332i	−0.943032	−	0.544460i
$628$	−12.3552	+	7.13325i	−0.493024	+	0.284648i
$629$	58.2665			2.32324
$630$	−9.43675	−	2.02830i	−0.375969	−	0.0808096i
$631$	10.0000	+	17.3205i	0.398094	+	0.689519i	0.993491	−	0.113913i	$-0.0363385\pi$
$631$	10.0000	+	17.3205i	0.398094	+	0.689519i	−0.595397	+	0.803432i	$0.703005\pi$
$632$		−	4.00000i		−	0.159111i
$633$	7.47661	−	4.31662i	0.297169	−	0.171570i
$634$	1.97494	−	3.42069i	0.0784348	−	0.135853i
$635$	8.51278	−	2.74456i	0.337819	−	0.108915i
$636$	−4.68338			−0.185708
$637$	−30.2241	−	29.0831i	−1.19752	−	1.15232i
$638$			18.9499i			0.750233i
$639$	4.15831	−	7.20241i	0.164500	−	0.284923i
$640$	−2.12819	+	0.686141i	−0.0841243	+	0.0271221i
$641$	−6.60819	−	11.4457i	−0.261008	−	0.452079i	0.705502	−	0.708708i	$-0.250721\pi$
$641$	−6.60819	−	11.4457i	−0.261008	−	0.452079i	−0.966510	+	0.256629i	$0.917388\pi$
$642$			11.6834i			0.461106i
$643$	12.7596	−	7.36675i	0.503189	−	0.290516i	−0.226841	−	0.973932i	$-0.572840\pi$
$643$	12.7596	−	7.36675i	0.503189	−	0.290516i	0.730030	+	0.683416i	$0.239506\pi$
$644$	3.63325	+	6.29297i	0.143170	+	0.247978i
$645$	3.47494	−	3.84169i	0.136826	−	0.151266i
$646$	−16.4749	−	28.5354i	−0.648198	−	1.12271i
$647$	32.8221	+	18.9499i	1.29037	+	0.744996i	0.978720	−	0.205200i	$-0.0657845\pi$
$647$	32.8221	+	18.9499i	1.29037	+	0.744996i	0.311652	+	0.950196i	$0.399118\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−29.2665			−1.14881
$650$	14.1753	+	11.1383i	0.556000	+	0.436880i
$651$	−17.2665			−0.676727
$652$	−7.47661	−	4.31662i	−0.292807	−	0.169052i
$653$	23.6135	+	13.6332i	0.924067	+	0.533510i	0.884930	−	0.465724i	$-0.154206\pi$
$653$	23.6135	+	13.6332i	0.924067	+	0.533510i	0.0391367	+	0.999234i	$0.487539\pi$
$654$	3.00000	+	5.19615i	0.117309	+	0.203186i
$655$		0			0
$656$	0.341688	+	0.591820i	0.0133407	+	0.0231067i
$657$	0.591820	−	0.341688i	0.0230891	−	0.0133305i
$658$			7.26650i			0.283278i
$659$	14.3166	+	24.7971i	0.557697	+	0.965959i	0.997688	+	0.0679569i	$0.0216480\pi$
$659$	14.3166	+	24.7971i	0.557697	+	0.965959i	−0.439992	+	0.898002i	$0.645019\pi$
$660$	13.4430	−	4.33409i	0.523268	−	0.168704i
$661$	5.97494	−	10.3489i	0.232398	−	0.402525i	−0.726115	−	0.687573i	$-0.758676\pi$
$661$	5.97494	−	10.3489i	0.232398	−	0.402525i	0.958513	+	0.285048i	$0.0920094\pi$
$662$			5.26650i			0.204688i
$663$	−6.61059	+	26.7164i	−0.256734	+	1.03758i
$664$	−8.31662			−0.322748
$665$	39.6552	−	12.7850i	1.53776	−	0.495782i
$666$	3.81662	−	6.61059i	0.147891	−	0.256155i
$667$	−4.37354	+	2.52506i	−0.169344	+	0.0977708i
$668$		0			0
$669$	−3.68338	−	6.37979i	−0.142408	−	0.246657i
$670$	−15.1934	−	3.26562i	−0.586972	−	0.126162i
$671$	−4.31662			−0.166641
$672$	3.73831	−	2.15831i	0.144208	−	0.0832587i
$673$	−32.7787	−	18.9248i	−1.26353	−	0.729498i	−0.289772	−	0.957096i	$-0.593580\pi$
$673$	−32.7787	−	18.9248i	−1.26353	−	0.729498i	−0.973755	+	0.227598i	$0.926913\pi$
$674$	2.34169	−	4.05592i	0.0901984	−	0.156228i
$675$	−4.97494	+	0.500000i	−0.191485	+	0.0192450i
$676$	−0.500000	−	12.9904i	−0.0192308	−	0.499630i
$677$		−	27.2665i		−	1.04794i	−0.851738	−	0.523968i	$-0.824451\pi$
$677$		−	27.2665i		−	1.04794i	0.851738	−	0.523968i	$-0.175549\pi$
$678$	14.0872	+	8.13325i	0.541016	+	0.312356i
$679$	−12.9499	+	22.4298i	−0.496971	+	0.860778i
$680$	16.6874	+	3.58673i	0.639931	+	0.137545i
$681$	29.5831			1.13363
$682$	21.8814	−	12.6332i	0.837883	−	0.483752i
$683$	1.09682	−	0.633250i	0.0419687	−	0.0242306i	−0.478869	−	0.877886i	$-0.658953\pi$
$683$	1.09682	−	0.633250i	0.0419687	−	0.0242306i	0.520838	+	0.853656i	$0.325620\pi$
$684$	−4.31662			−0.165050
$685$	−2.64696	+	12.3151i	−0.101135	+	0.470535i
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	−10.3923	−	6.00000i	−0.396491	−	0.228914i
$688$			2.31662i			0.0883205i
$689$	−16.3918	−	4.05592i	−0.624478	−	0.154518i
$690$	2.79156	+	2.52506i	0.106273	+	0.0961275i
$691$	17.4248	−	30.1807i	0.662871	−	1.14813i	−0.316987	−	0.948430i	$-0.602671\pi$
$691$	17.4248	−	30.1807i	0.662871	−	1.14813i	0.979858	−	0.199696i	$-0.0639956\pi$
$692$	−13.2212	−	7.63325i	−0.502594	−	0.290173i
$693$	−23.6135	+	13.6332i	−0.897002	+	0.517884i
$694$	−1.58312			−0.0600946
$695$	−11.5133	−	2.47463i	−0.436725	−	0.0938682i
$696$	1.50000	+	2.59808i	0.0568574	+	0.0984798i
$697$		−	5.21637i		−	0.197584i
$698$	−0.635230	+	0.366750i	−0.0240438	+	0.0138817i
$699$	−5.68338	+	9.84389i	−0.214965	+	0.372330i
$700$	−8.86832	+	19.6770i	−0.335191	+	0.743721i
$701$	−15.3668			−0.580394			−0.290197	−	0.956967i	$-0.593721\pi$
$701$	−15.3668			−0.580394			−0.290197	+	0.956967i	$0.593721\pi$
$702$	2.59808	+	2.50000i	0.0980581	+	0.0943564i
$703$			32.9499i			1.24273i
$704$	−3.15831	+	5.47036i	−0.119033	+	0.206172i
$705$	1.15503	+	3.58255i	0.0435010	+	0.134927i
$706$	−10.1834	−	17.6381i	−0.383256	−	0.663820i
$707$			1.58312i			0.0595395i
$708$	−4.01251	+	2.31662i	−0.150799	+	0.0870641i
$709$	−0.974937	−	1.68864i	−0.0366145	−	0.0634182i	0.847137	−	0.531374i	$-0.178324\pi$
$709$	−0.974937	−	1.68864i	−0.0366145	−	0.0634182i	−0.883752	+	0.467956i	$0.844991\pi$
$710$	−13.7916	−	12.4749i	−0.517588	−	0.468176i
$711$	2.00000	+	3.46410i	0.0750059	+	0.129914i
$712$	9.75707	+	5.63325i	0.365662	+	0.211115i
$713$	5.83138	+	3.36675i	0.218387	+	0.126086i
$714$	−32.9499			−1.23312
$715$	50.8040	−	3.52734i	1.89996	−	0.131915i
$716$	7.58312			0.283395
$717$	7.20241	+	4.15831i	0.268979	+	0.155295i
$718$	−14.1306	−	8.15831i	−0.527350	−	0.304466i
$719$	−12.3166	−	21.3330i	−0.459333	−	0.795587i	0.539593	−	0.841926i	$-0.318578\pi$
$719$	−12.3166	−	21.3330i	−0.459333	−	0.795587i	−0.998926	+	0.0463385i	$0.985245\pi$
$720$	1.50000	−	1.65831i	0.0559017	−	0.0618017i
$721$	17.9499	+	31.0901i	0.668488	+	1.15786i
$722$	−0.317615	+	0.183375i	−0.0118204	+	0.00682452i
$723$		−	25.6332i		−	0.953311i
$724$	9.97494	+	17.2771i	0.370716	+	0.642098i
$725$	−13.6753	−	6.16337i	−0.507887	−	0.228902i
$726$	14.4499	−	25.0279i	0.536285	−	0.928873i
$727$		−	14.8496i		−	0.550742i	−0.961338	−	0.275371i	$-0.911199\pi$
$727$		−	14.8496i		−	0.550742i	0.961338	−	0.275371i	$-0.0888007\pi$
$728$	14.9532	−	4.31662i	0.554203	−	0.159985i
$729$	−1.00000			−0.0370370
$730$	−0.468892	−	1.45436i	−0.0173545	−	0.0538281i
$731$	8.84169	−	15.3143i	0.327022	−	0.566418i
$732$	−0.591820	+	0.341688i	−0.0218743	+	0.0126291i
$733$		−	1.00000i		−	0.0369358i	−0.999829	−	0.0184679i	$-0.994121\pi$
$733$		−	1.00000i		−	0.0369358i	0.999829	−	0.0184679i	$-0.00587886\pi$
$734$	−9.84169	−	17.0463i	−0.363263	−	0.629191i
$735$	5.46625	−	25.4319i	0.201626	−	0.938070i
$736$	−1.68338			−0.0620500
$737$	−38.0183	+	21.9499i	−1.40042	+	0.808534i
$738$	−0.591820	−	0.341688i	−0.0217852	−	0.0125777i
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	−0.974818	−	0.223001i	$-0.928415\pi$
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	0.680534	+	0.732717i	$0.261748\pi$
$740$	−12.6583	−	11.4499i	−0.465329	−	0.420906i
$741$	−15.1082	−	3.73831i	−0.555013	−	0.137330i
$742$		−	20.2164i		−	0.742166i
$743$	0.548410	+	0.316625i	0.0201192	+	0.0116158i	0.510026	−	0.860159i	$-0.329636\pi$
$743$	0.548410	+	0.316625i	0.0201192	+	0.0116158i	−0.489907	+	0.871775i	$0.662969\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$	7.94279	+	1.70720i	0.291001	+	0.0625469i
$746$	1.00000			0.0366126
$747$	7.20241	−	4.15831i	0.263522	−	0.152145i
$748$	41.7566	−	24.1082i	1.52677	−	0.881483i
$749$	−50.4327			−1.84277
$750$	−1.24456	+	11.1109i	−0.0454450	+	0.405711i
$751$	−12.4248	+	21.5204i	−0.453388	+	0.785291i	−0.998594	−	0.0530113i	$-0.983118\pi$
$751$	−12.4248	+	21.5204i	−0.453388	+	0.785291i	0.545206	+	0.838302i	$0.316451\pi$
$752$	−1.45785	−	0.841688i	−0.0531622	−	0.0306932i
$753$		−	25.8997i		−	0.943839i
$754$	3.00000	+	10.3923i	0.109254	+	0.378465i
$755$	−10.4248	+	11.5251i	−0.379398	+	0.419440i
$756$	−2.15831	+	3.73831i	−0.0784971	+	0.135961i
$757$	1.81887	+	1.05013i	0.0661080	+	0.0381675i	0.532690	−	0.846311i	$-0.321181\pi$
$757$	1.81887	+	1.05013i	0.0661080	+	0.0381675i	−0.466582	+	0.884478i	$0.654515\pi$
$758$	12.0375	−	6.94987i	0.437223	−	0.252431i
$759$	10.6332			0.385963
$760$	−2.02830	+	9.43675i	−0.0735743	+	0.342307i
$761$	−9.63325	−	16.6853i	−0.349205	−	0.604841i	0.636903	−	0.770944i	$-0.280215\pi$
$761$	−9.63325	−	16.6853i	−0.349205	−	0.604841i	−0.986108	+	0.166103i	$0.946882\pi$
$762$		−	4.00000i		−	0.144905i
$763$	−22.4298	+	12.9499i	−0.812015	+	0.468817i
$764$	6.31662	−	10.9407i	0.228527	−	0.395821i
$765$	−16.2450	+	5.23748i	−0.587341	+	0.189362i
$766$	6.73350			0.243291
$767$	−16.0500	+	4.63325i	−0.579534	+	0.167297i
$768$			1.00000i			0.0360844i
$769$	−4.94987	+	8.57343i	−0.178497	+	0.309166i	−0.941366	−	0.337387i	$-0.890457\pi$
$769$	−4.94987	+	8.57343i	−0.178497	+	0.309166i	0.762869	+	0.646553i	$0.223790\pi$
$770$	18.7087	+	58.0284i	0.674213	+	2.09120i
$771$	11.1332	+	19.2834i	0.400954	+	0.694473i
$772$			3.94987i			0.142159i
$773$	−16.6853	+	9.63325i	−0.600128	+	0.346484i	−0.769092	−	0.639138i	$-0.779291\pi$
$773$	−16.6853	+	9.63325i	−0.600128	+	0.346484i	0.168964	+	0.985622i	$0.445958\pi$
$774$	−1.15831	−	2.00626i	−0.0416347	−	0.0721134i
$775$	2.00000	+	19.8997i	0.0718421	+	0.714820i
$776$	−3.00000	−	5.19615i	−0.107694	−	0.186531i
$777$	28.5354	+	16.4749i	1.02370	+	0.591035i
$778$	−13.5388	−	7.81662i	−0.485389	−	0.280240i
$779$	2.94987			0.105690
$780$	6.68614	−	4.50506i	0.239402	−	0.161307i
$781$	−52.5330			−1.87978
$782$	11.1281	+	6.42481i	0.397940	+	0.229751i
$783$	−2.59808	−	1.50000i	−0.0928477	−	0.0536056i
$784$	5.81662	+	10.0747i	0.207737	+	0.359810i
$785$	−23.6583	−	21.3997i	−0.844401	−	0.763790i
$786$		0			0
$787$	−6.37979	+	3.68338i	−0.227415	+	0.131298i	−0.609379	−	0.792879i	$-0.708581\pi$
$787$	−6.37979	+	3.68338i	−0.227415	+	0.131298i	0.381964	+	0.924177i	$0.375248\pi$
$788$		−	13.2665i		−	0.472599i
$789$	7.79156	+	13.4954i	0.277387	+	0.480448i
$790$	8.51278	−	2.74456i	0.302871	−	0.0976472i
$791$	−35.1082	+	60.8092i	−1.24830	+	2.16212i
$792$		−	6.31662i		−	0.224451i
$793$	−2.36728	+	0.683375i	−0.0840646	+	0.0242674i
$794$	17.8997			0.635238
$795$	−3.21345	−	9.96713i	−0.113969	−	0.353498i
$796$	11.1583	−	19.3268i	0.395496	−	0.685019i
$797$	−33.3706	+	19.2665i	−1.18205	+	0.682454i	−0.956487	−	0.291775i	$-0.905754\pi$
$797$	−33.3706	+	19.2665i	−1.18205	+	0.682454i	−0.225559	+	0.974230i	$0.572421\pi$
$798$		−	18.6332i		−	0.659610i
$799$	6.42481	+	11.1281i	0.227293	+	0.393684i
$800$	−2.92048	−	4.05842i	−0.103255	−	0.143487i
$801$	−11.2665			−0.398082
$802$	−9.25207	+	5.34169i	−0.326702	+	0.188622i
$803$	−3.73831	−	2.15831i	−0.131922	−	0.0761652i
$804$	−3.47494	+	6.01877i	−0.122552	+	0.212266i
$805$	−10.8997	+	12.0501i	−0.384166	+	0.424711i
$806$	10.0000	−	10.3923i	0.352235	−	0.366053i
$807$		−	12.6332i		−	0.444711i
$808$	−0.317615	−	0.183375i	−0.0111737	−	0.00645112i
$809$	3.70844	−	6.42320i	0.130382	−	0.225828i	−0.793442	−	0.608646i	$-0.791713\pi$
$809$	3.70844	−	6.42320i	0.130382	−	0.225828i	0.923824	+	0.382818i	$0.125046\pi$
$810$	−0.469882	+	2.18614i	−0.0165100	+	0.0768132i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−11.2149	+	6.47494i	−0.393567	+	0.227226i
$813$	−13.8564	+	8.00000i	−0.485965	+	0.280572i
$814$	−48.2164			−1.68998
$815$	4.05661	−	18.8735i	0.142097	−	0.661110i
$816$	3.81662	−	6.61059i	0.133609	−	0.231417i
$817$	8.66025	+	5.00000i	0.302984	+	0.174928i
$818$			21.0000i			0.734248i
$819$	−10.7916	+	11.2149i	−0.377088	+	0.391881i
$820$	−1.02506	+	1.13325i	−0.0357967	+	0.0395748i
$821$	−15.5831	+	26.9908i	−0.543855	+	0.941984i	0.454823	+	0.890582i	$0.349702\pi$
$821$	−15.5831	+	26.9908i	−0.543855	+	0.941984i	−0.998678	+	0.0514024i	$0.983631\pi$
$822$	4.87854	+	2.81662i	0.170159	+	0.0982411i
$823$	5.28297	−	3.05013i	0.184153	−	0.106321i	−0.405090	−	0.914277i	$-0.632760\pi$
$823$	5.28297	−	3.05013i	0.184153	−	0.106321i	0.589242	+	0.807956i	$0.299426\pi$
$824$	−8.31662			−0.289723
$825$	18.4476	+	25.6355i	0.642262	+	0.892515i
$826$	−10.0000	−	17.3205i	−0.347945	−	0.602658i
$827$		−	1.26650i		−	0.0440405i	−0.999758	−	0.0220202i	$-0.992990\pi$
$827$		−	1.26650i		−	0.0440405i	0.999758	−	0.0220202i	$-0.00700983\pi$
$828$	1.45785	−	0.841688i	0.0506636	−	0.0292507i
$829$	−17.6583	+	30.5851i	−0.613299	+	1.06226i	0.377382	+	0.926058i	$0.376824\pi$
$829$	−17.6583	+	30.5851i	−0.613299	+	1.06226i	−0.990680	+	0.136207i	$0.956509\pi$
$830$	−5.70637	−	17.6994i	−0.198071	−	0.614355i
$831$	27.0000			0.936620
$832$	−0.866025	+	3.50000i	−0.0300240	+	0.121341i
$833$		−	88.7995i		−	3.07672i
$834$	−2.63325	+	4.56092i	−0.0911820	+	0.157932i
$835$		0			0
$836$	13.6332	+	23.6135i	0.471516	+	0.816689i
$837$			4.00000i			0.138260i
$838$	33.9190	−	19.5831i	1.17171	−	0.676488i
$839$	−13.6834	−	23.7003i	−0.472403	−	0.818225i	0.527099	−	0.849804i	$-0.323280\pi$
$839$	−13.6834	−	23.7003i	−0.472403	−	0.818225i	−0.999501	+	0.0315788i	$0.989946\pi$
$840$	7.15831	+	6.47494i	0.246985	+	0.223407i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	32.8656	+	18.9749i	1.13262	+	0.653920i
$843$	23.5701	+	13.6082i	0.811796	+	0.468691i
$844$	−8.63325			−0.297169
$845$	27.3030	−	9.97733i	0.939251	−	0.343230i
$846$	1.68338			0.0578756
$847$	108.036	+	62.3747i	3.71217	+	2.14322i
$848$	4.05592	+	2.34169i	0.139281	+	0.0804139i
$849$	−11.4749	−	19.8752i	−0.393819	−	0.682114i
$850$	3.81662	+	37.9749i	0.130909	+	1.30253i
$851$	−6.42481	−	11.1281i	−0.220240	−	0.381466i
$852$	−7.20241	+	4.15831i	−0.246750	+	0.142461i
$853$			44.8997i			1.53734i	0.639647	+	0.768669i	$0.279081\pi$
$853$			44.8997i			1.53734i	−0.639647	+	0.768669i	$0.720919\pi$
$854$	−1.47494	−	2.55467i	−0.0504713	−	0.0874189i
$855$	−2.96181	−	9.18662i	−0.101292	−	0.314176i
$856$	5.84169	−	10.1181i	0.199665	−	0.345830i
$857$		−	0.266499i		−	0.00910344i	−0.999990	−	0.00455172i	$-0.998551\pi$
$857$		−	0.266499i		−	0.00910344i	0.999990	−	0.00455172i	$-0.00144886\pi$
$858$	5.47036	−	22.1082i	0.186755	−	0.754761i
$859$	−26.8496			−0.916097			−0.458049	−	0.888927i	$-0.651451\pi$
$859$	−26.8496			−0.916097			−0.458049	+	0.888927i	$0.651451\pi$
$860$	−4.93023	+	1.58953i	−0.168119	+	0.0542025i
$861$	1.47494	−	2.55467i	0.0502657	−	0.0870628i
$862$	−11.2149	+	6.47494i	−0.381982	+	0.220537i
$863$			33.4829i			1.13977i	0.821724	+	0.569885i	$0.193012\pi$
$863$			33.4829i			1.13977i	−0.821724	+	0.569885i	$0.806988\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	7.17345	−	33.3747i	0.243905	−	1.13477i
$866$	−8.58312			−0.291666
$867$	−35.7378	+	20.6332i	−1.21372	+	0.700742i
$868$	14.9532	+	8.63325i	0.507546	+	0.293032i
$869$	12.6332	−	21.8814i	0.428554	−	0.742277i
$870$	−4.50000	+	4.97494i	−0.152564	+	0.168666i
$871$	−17.3747	+	18.0563i	−0.588719	+	0.611814i
$872$		−	6.00000i		−	0.203186i
$873$	5.19615	+	3.00000i	0.175863	+	0.101535i
$874$	−3.63325	+	6.29297i	−0.122897	+	0.212863i
$875$	−47.9614	−	5.37231i	−1.62139	−	0.181617i
$876$	−0.683375			−0.0230891
$877$	33.1398	−	19.1332i	1.11905	−	0.646084i	0.177892	−	0.984050i	$-0.443072\pi$
$877$	33.1398	−	19.1332i	1.11905	−	0.646084i	0.941158	+	0.337966i	$0.109739\pi$
$878$	33.1832	−	19.1583i	1.11988	−	0.646562i
$879$	−21.3166			−0.718992
$880$	−13.8090	−	2.96807i	−0.465502	−	0.100054i
$881$	−22.6583	+	39.2453i	−0.763378	+	1.32221i	0.177722	+	0.984081i	$0.443127\pi$
$881$	−22.6583	+	39.2453i	−0.763378	+	1.32221i	−0.941100	+	0.338129i	$0.890206\pi$
$882$	−10.0747	−	5.81662i	−0.339232	−	0.195856i
$883$		−	27.3668i		−	0.920964i	−0.887669	−	0.460482i	$-0.847677\pi$
$883$		−	27.3668i		−	0.920964i	0.887669	−	0.460482i	$-0.152323\pi$
$884$	19.0831	−	19.8318i	0.641835	−	0.667014i
$885$	−7.68338	−	6.94987i	−0.258274	−	0.233617i
$886$	6.63325	−	11.4891i	0.222848	−	0.385985i
$887$	35.7378	+	20.6332i	1.19996	+	0.692797i	0.960546	−	0.278121i	$-0.0897116\pi$
$887$	35.7378	+	20.6332i	1.19996	+	0.692797i	0.239413	+	0.970918i	$0.423045\pi$
$888$	−6.61059	+	3.81662i	−0.221837	+	0.128078i
$889$	17.2665			0.579100
$890$	−5.29392	+	24.6302i	−0.177453	+	0.825605i
$891$	3.15831	+	5.47036i	0.105807	+	0.183264i
$892$			7.36675i			0.246657i
$893$	−6.29297	+	3.63325i	−0.210586	+	0.121582i
$894$	1.81662	−	3.14649i	0.0607570	−	0.105234i
$895$	5.20309	+	16.1384i	0.173920	+	0.539446i
$896$	−4.31662			−0.144208
$897$	5.83138	−	1.68338i	0.194704	−	0.0562063i
$898$		−	16.5330i		−	0.551713i
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$	4.55842	+	2.05446i	0.151947	+	0.0684819i
$901$	−17.8747	−	30.9599i	−0.595492	−	1.03142i
$902$			4.31662i			0.143728i
$903$	8.66025	−	5.00000i	0.288195	−	0.166390i
$904$	−8.13325	−	14.0872i	−0.270508	−	0.468533i
$905$	−29.9248	+	33.0831i	−0.994734	+	1.09972i
$906$	3.47494	+	6.01877i	0.115447	+	0.199960i
$907$	−23.1519	−	13.3668i	−0.768746	−	0.443836i	0.0636811	−	0.997970i	$-0.479716\pi$
$907$	−23.1519	−	13.3668i	−0.768746	−	0.443836i	−0.832427	+	0.554135i	$0.813049\pi$
$908$	−25.6197	−	14.7916i	−0.850221	−	0.490875i
$909$	0.366750			0.0121643
$910$	19.4466	+	28.8616i	0.644650	+	0.956751i
$911$	19.1662			0.635006			0.317503	−	0.948257i	$-0.397156\pi$
$911$	19.1662			0.635006			0.317503	+	0.948257i	$0.397156\pi$
$912$	3.73831	+	2.15831i	0.123788	+	0.0714689i
$913$	−45.4949	−	26.2665i	−1.50566	−	0.869294i
$914$	7.97494	+	13.8130i	0.263787	+	0.456893i
$915$	−1.13325	−	1.02506i	−0.0374641	−	0.0338875i
$916$	6.00000	+	10.3923i	0.198246	+	0.343371i
$917$		0			0
$918$			7.63325i			0.251935i
$919$	5.05013	+	8.74707i	0.166588	+	0.288539i	0.937218	−	0.348744i	$-0.113392\pi$
$919$	5.05013	+	8.74707i	0.166588	+	0.288539i	−0.770630	+	0.637283i	$0.780058\pi$
$920$	−1.15503	−	3.58255i	−0.0380803	−	0.118113i
$921$	8.10819	−	14.0438i	0.267174	−	0.462759i
$922$			9.63325i			0.317254i
$923$	−28.8096	+	8.31662i	−0.948281	+	0.273745i
$924$	27.2665			0.897002
$925$	15.6822	−	34.7956i	0.515627	−	1.14407i
$926$	−4.47494	+	7.75082i	−0.147056	+	0.254708i
$927$	7.20241	−	4.15831i	0.236558	−	0.136577i
$928$		−	3.00000i		−	0.0984798i
$929$	−7.70844	−	13.3514i	−0.252906	−	0.438045i	0.711419	−	0.702768i	$-0.248053\pi$
$929$	−7.70844	−	13.3514i	−0.252906	−	0.438045i	−0.964325	+	0.264723i	$0.914720\pi$
$930$	8.74456	+	1.87953i	0.286746	+	0.0616321i
$931$	50.2164			1.64578
$932$	9.84389	−	5.68338i	0.322447	−	0.186165i
$933$	−10.6665	−	6.15831i	−0.349206	−	0.201614i
$934$	−16.7916	+	29.0838i	−0.549437	+	0.951652i
$935$	79.9578	+	72.3246i	2.61490	+	2.36527i
$936$	−1.00000	−	3.46410i	−0.0326860	−	0.113228i
$937$		−	13.2164i		−	0.431760i	−0.976420	−	0.215880i	$-0.930738\pi$
$937$		−	13.2164i		−	0.431760i	0.976420	−	0.215880i	$-0.0692620\pi$
$938$	−25.9808	−	15.0000i	−0.848302	−	0.489767i
$939$	15.0000	−	25.9808i	0.489506	−	0.847850i
$940$	0.790988	−	3.68009i	0.0257992	−	0.120031i
$941$	36.6332			1.19421			0.597105	−	0.802163i	$-0.296318\pi$
$941$	36.6332			1.19421			0.597105	+	0.802163i	$0.296318\pi$
$942$	−12.3552	+	7.13325i	−0.402553	+	0.232414i
$943$	−0.996256	+	0.575188i	−0.0324425	+	0.0187307i
$944$	4.63325			0.150799
$945$	−9.43675	−	2.02830i	−0.306977	−	0.0659807i
$946$	−7.31662	+	12.6728i	−0.237884	+	0.412027i
$947$	4.73456	+	2.73350i	0.153853	+	0.0888268i	0.574950	−	0.818189i	$-0.305022\pi$
$947$	4.73456	+	2.73350i	0.153853	+	0.0888268i	−0.421097	+	0.907015i	$0.638355\pi$
$948$		−	4.00000i		−	0.129914i
$949$	−2.39181	−	0.591820i	−0.0776415	−	0.0192113i
$950$	−21.4749	+	2.15831i	−0.696739	+	0.0700249i
$951$	1.97494	−	3.42069i	0.0640417	−	0.110924i
$952$	28.5354	+	16.4749i	0.924839	+	0.533956i
$953$	−5.19615	+	3.00000i	−0.168320	+	0.0971795i	−0.581793	−	0.813337i	$-0.697649\pi$
$953$	−5.19615	+	3.00000i	−0.168320	+	0.0971795i	0.413473	+	0.910516i	$0.364315\pi$
$954$	−4.68338			−0.151630
$955$	27.6181	+	5.93614i	0.893699	+	0.192089i
$956$	−4.15831	−	7.20241i	−0.134489	−	0.232943i
$957$			18.9499i			0.612562i
$958$		0			0
$959$	−12.1583	+	21.0588i	−0.392612	+	0.680025i
$960$	−2.12819	+	0.686141i	−0.0686872	+	0.0221451i
$961$	−15.0000			−0.483871
$962$	−26.4424	+	7.63325i	−0.852536	+	0.246106i
$963$			11.6834i			0.376492i
$964$	−12.8166	+	22.1990i	−0.412796	+	0.714983i
$965$	−8.40610	+	2.71017i	−0.270602	+	0.0872434i
$966$	3.63325	+	6.29297i	0.116898	+	0.202473i
$967$			22.8496i			0.734794i	0.930064	+	0.367397i	$0.119751\pi$
$967$			22.8496i			0.734794i	−0.930064	+	0.367397i	$0.880249\pi$
$968$	−25.0279	+	14.4499i	−0.804428	+	0.464437i
$969$	−16.4749	−	28.5354i	−0.529251	−	0.916690i
$970$	9.00000	−	9.94987i	0.288973	−	0.319471i
$971$	5.36675	+	9.29548i	0.172227	+	0.298306i	0.939198	−	0.343375i	$-0.111570\pi$
$971$	5.36675	+	9.29548i	0.172227	+	0.298306i	−0.766971	+	0.641682i	$0.778237\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	−19.6878	−	11.3668i	−0.631162	−	0.364401i
$974$	4.31662			0.138314
$975$	14.1753	+	11.1383i	0.453972	+	0.356711i
$976$	0.683375			0.0218743
$977$	−33.2266	−	19.1834i	−1.06301	−	0.613731i	−0.136748	−	0.990606i	$-0.543665\pi$
$977$	−33.2266	−	19.1834i	−1.06301	−	0.613731i	−0.926264	+	0.376875i	$0.876999\pi$
$978$	−7.47661	−	4.31662i	−0.239076	−	0.138030i
$979$	35.5831	+	61.6318i	1.13724	+	1.96976i
$980$	−17.4499	+	19.2916i	−0.557416	+	0.616246i
$981$	3.00000	+	5.19615i	0.0957826	+	0.165900i
$982$	−34.2800	+	19.7916i	−1.09392	+	0.631574i
$983$		−	36.0000i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$		−	36.0000i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$	0.341688	+	0.591820i	0.0108926	+	0.0188665i
$985$	28.2337	−	9.10268i	0.899600	−	0.290036i
$986$	−11.4499	+	19.8318i	−0.364638	+	0.631572i
$987$			7.26650i			0.231295i
$988$	11.2149	+	10.7916i	0.356794	+	0.343325i
$989$	−3.89975			−0.124005
$990$	13.4430	−	4.33409i	0.427247	−	0.137747i
$991$	−5.15831	+	8.93446i	−0.163859	+	0.283812i	−0.936250	−	0.351336i	$-0.885728\pi$
$991$	−5.15831	+	8.93446i	−0.163859	+	0.283812i	0.772390	+	0.635148i	$0.219061\pi$
$992$	−3.46410	+	2.00000i	−0.109985	+	0.0635001i
$993$			5.26650i			0.167127i
$994$	−17.9499	−	31.0901i	−0.569335	−	0.986118i
$995$	48.7873	+	10.4862i	1.54666	+	0.332434i
$996$	−8.31662			−0.263522
$997$	26.2984	−	15.1834i	0.832878	−	0.480862i	−0.0219591	−	0.999759i	$-0.506990\pi$
$997$	26.2984	−	15.1834i	0.832878	−	0.480862i	0.854837	+	0.518897i	$0.173657\pi$
$998$	−36.2862	−	20.9499i	−1.14862	−	0.663157i
$999$	3.81662	−	6.61059i	0.120753	−	0.209150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.y.g.139.2	✓	8
3.2	odd	2		1170.2.bp.g.919.3		8
5.2	odd	4		1950.2.i.be.451.1		4
5.3	odd	4		1950.2.i.bb.451.2		4
5.4	even	2	inner	390.2.y.g.139.3	yes	8
13.3	even	3	inner	390.2.y.g.289.4	yes	8
15.14	odd	2		1170.2.bp.g.919.2		8
39.29	odd	6		1170.2.bp.g.289.1		8
65.3	odd	12		1950.2.i.bb.601.2		4
65.29	even	6	inner	390.2.y.g.289.1	yes	8
65.42	odd	12		1950.2.i.be.601.1		4
195.29	odd	6		1170.2.bp.g.289.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.g.139.2	✓	8	1.1	even	1	trivial
390.2.y.g.139.3	yes	8	5.4	even	2	inner
390.2.y.g.289.1	yes	8	65.29	even	6	inner
390.2.y.g.289.4	yes	8	13.3	even	3	inner
1170.2.bp.g.289.1		8	39.29	odd	6
1170.2.bp.g.289.4		8	195.29	odd	6
1170.2.bp.g.919.2		8	15.14	odd	2
1170.2.bp.g.919.3		8	3.2	odd	2
1950.2.i.bb.451.2		4	5.3	odd	4
1950.2.i.bb.601.2		4	65.3	odd	12
1950.2.i.be.451.1		4	5.2	odd	4
1950.2.i.be.601.1		4	65.42	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 1.65831i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-3.73831 + 2.15831i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-3.73831 + 2.15831i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.12819 - 0.686141i) q^{10} +(3.15831 - 5.47036i) q^{11} -1.00000i q^{12} +(0.866025 - 3.50000i) q^{13} +4.31662 q^{14} +(2.12819 - 0.686141i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.61059 - 3.81662i) q^{17} -1.00000i q^{18} +(2.15831 + 3.73831i) q^{19} +(-2.18614 - 0.469882i) q^{20} +4.31662 q^{21} +(-5.47036 + 3.15831i) q^{22} +(-1.45785 - 0.841688i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 4.97494i) q^{25} +(-2.50000 + 2.59808i) q^{26} -1.00000i q^{27} +(-3.73831 - 2.15831i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-2.18614 - 0.469882i) q^{30} -4.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.47036 + 3.15831i) q^{33} -7.63325 q^{34} +(2.02830 - 9.43675i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(6.61059 + 3.81662i) q^{37} -4.31662i q^{38} +(-2.50000 + 2.59808i) q^{39} +(1.65831 + 1.50000i) q^{40} +(0.341688 - 0.591820i) q^{41} +(-3.73831 - 2.15831i) q^{42} +(2.00626 - 1.15831i) q^{43} +6.31662 q^{44} +(-2.18614 - 0.469882i) q^{45} +(0.841688 + 1.45785i) q^{46} +1.68338i q^{47} +(0.866025 - 0.500000i) q^{48} +(5.81662 - 10.0747i) q^{49} +(-2.05446 + 4.55842i) q^{50} -7.63325 q^{51} +(3.46410 - 1.00000i) q^{52} -4.68338i q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.33409 + 13.4430i) q^{55} +(2.15831 + 3.73831i) q^{56} -4.31662i q^{57} +(-2.59808 + 1.50000i) q^{58} +(-2.31662 - 4.01251i) q^{59} +(1.65831 + 1.50000i) q^{60} +(-0.341688 - 0.591820i) q^{61} +(3.46410 + 2.00000i) q^{62} +(-3.73831 - 2.15831i) q^{63} -1.00000 q^{64} +(4.50506 + 6.68614i) q^{65} +6.31662 q^{66} +(-6.01877 - 3.47494i) q^{67} +(6.61059 + 3.81662i) q^{68} +(0.841688 + 1.45785i) q^{69} +(-6.47494 + 7.15831i) q^{70} +(-4.15831 - 7.20241i) q^{71} +(0.866025 - 0.500000i) q^{72} -0.683375i q^{73} +(-3.81662 - 6.61059i) q^{74} +(-2.05446 + 4.55842i) q^{75} +(-2.15831 + 3.73831i) q^{76} +27.2665i q^{77} +(3.46410 - 1.00000i) q^{78} +4.00000 q^{79} +(-0.686141 - 2.12819i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.591820 + 0.341688i) q^{82} -8.31662i q^{83} +(2.15831 + 3.73831i) q^{84} +(-3.58673 + 16.6874i) q^{85} -2.31662 q^{86} +(-2.59808 + 1.50000i) q^{87} +(-5.47036 - 3.15831i) q^{88} +(-5.63325 + 9.75707i) q^{89} +(1.65831 + 1.50000i) q^{90} +(4.31662 + 14.9532i) q^{91} -1.68338i q^{92} +(3.46410 + 2.00000i) q^{93} +(0.841688 - 1.45785i) q^{94} +(-9.43675 - 2.02830i) q^{95} -1.00000 q^{96} +(5.19615 - 3.00000i) q^{97} +(-10.0747 + 5.81662i) q^{98} +6.31662 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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