LMFDB - Embedded newform 390.2.bb.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(121,390)]

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, 0, 1]))

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

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

chi := DirichletCharacter("390.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bb (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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	390.121
Dual form			390.2.bb.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(0.866025 - 0.500000i) q^{6} +(1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(0.866025 - 0.500000i) q^{6} +(1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.401924 + 0.232051i) q^{11} +1.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} -1.00000i q^{18} +(-0.464102 + 0.267949i) q^{19} +(0.866025 - 0.500000i) q^{20} -2.00000i q^{21} +(0.232051 + 0.401924i) q^{22} +(-0.133975 + 0.232051i) q^{23} +(0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(2.59808 - 2.50000i) q^{26} -1.00000 q^{27} +(1.73205 + 1.00000i) q^{28} +(-1.86603 + 3.23205i) q^{29} +(-0.500000 - 0.866025i) q^{30} -1.73205i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.401924 - 0.232051i) q^{33} +4.00000i q^{34} +(-1.00000 - 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{36} +(1.03590 + 0.598076i) q^{37} -0.535898 q^{38} +(-2.50000 - 2.59808i) q^{39} +1.00000 q^{40} +(-1.73205 - 1.00000i) q^{41} +(1.00000 - 1.73205i) q^{42} +(0.964102 + 1.66987i) q^{43} +0.464102i q^{44} +(-0.866025 + 0.500000i) q^{45} +(-0.232051 + 0.133975i) q^{46} +10.4641i q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} +(-0.866025 - 0.500000i) q^{50} +4.00000 q^{51} +(3.50000 - 0.866025i) q^{52} -12.9282 q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.232051 - 0.401924i) q^{55} +(1.00000 + 1.73205i) q^{56} +0.535898i q^{57} +(-3.23205 + 1.86603i) q^{58} +(-1.33013 + 0.767949i) q^{59} -1.00000i q^{60} +(-5.19615 - 9.00000i) q^{61} +(0.866025 - 1.50000i) q^{62} +(-1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +(-3.46410 - 1.00000i) q^{65} +0.464102 q^{66} +(3.92820 + 2.26795i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(0.133975 + 0.232051i) q^{69} -2.00000i q^{70} +(-7.26795 + 4.19615i) q^{71} +(0.866025 - 0.500000i) q^{72} -2.00000i q^{73} +(0.598076 + 1.03590i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-0.464102 - 0.267949i) q^{76} +0.928203 q^{77} +(-0.866025 - 3.50000i) q^{78} -0.0717968 q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} +4.92820i q^{83} +(1.73205 - 1.00000i) q^{84} +(3.46410 - 2.00000i) q^{85} +1.92820i q^{86} +(1.86603 + 3.23205i) q^{87} +(-0.232051 + 0.401924i) q^{88} +(6.46410 + 3.73205i) q^{89} -1.00000 q^{90} +(-1.73205 - 7.00000i) q^{91} -0.267949 q^{92} +(-1.50000 - 0.866025i) q^{93} +(-5.23205 + 9.06218i) q^{94} +(0.267949 + 0.464102i) q^{95} +1.00000i q^{96} +(-6.46410 + 3.73205i) q^{97} +(-2.59808 + 1.50000i) q^{98} -0.464102i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} + 2 q^{10} + 12 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} - 2 q^{16} + 8 q^{17} + 12 q^{19} - 6 q^{22} - 4 q^{23} - 4 q^{25} - 4 q^{27} - 4 q^{29} - 2 q^{30} + 12 q^{33} - 4 q^{35} + 2 q^{36} + 18 q^{37} - 16 q^{38} - 10 q^{39} + 4 q^{40} + 4 q^{42} - 10 q^{43} + 6 q^{46} + 2 q^{48} - 6 q^{49} + 16 q^{51} + 14 q^{52} - 24 q^{53} - 6 q^{55} + 4 q^{56} - 6 q^{58} + 12 q^{59} - 4 q^{64} - 12 q^{66} - 12 q^{67} - 8 q^{68} + 4 q^{69} - 36 q^{71} - 8 q^{74} - 2 q^{75} + 12 q^{76} - 24 q^{77} - 28 q^{79} - 2 q^{81} - 4 q^{82} + 4 q^{87} + 6 q^{88} + 12 q^{89} - 4 q^{90} - 8 q^{92} - 6 q^{93} - 14 q^{94} + 8 q^{95} - 12 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 + 2 * q^10 + 12 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 - 2 * q^16 + 8 * q^17 + 12 * q^19 - 6 * q^22 - 4 * q^23 - 4 * q^25 - 4 * q^27 - 4 * q^29 - 2 * q^30 + 12 * q^33 - 4 * q^35 + 2 * q^36 + 18 * q^37 - 16 * q^38 - 10 * q^39 + 4 * q^40 + 4 * q^42 - 10 * q^43 + 6 * q^46 + 2 * q^48 - 6 * q^49 + 16 * q^51 + 14 * q^52 - 24 * q^53 - 6 * q^55 + 4 * q^56 - 6 * q^58 + 12 * q^59 - 4 * q^64 - 12 * q^66 - 12 * q^67 - 8 * q^68 + 4 * q^69 - 36 * q^71 - 8 * q^74 - 2 * q^75 + 12 * q^76 - 24 * q^77 - 28 * q^79 - 2 * q^81 - 4 * q^82 + 4 * q^87 + 6 * q^88 + 12 * q^89 - 4 * q^90 - 8 * q^92 - 6 * q^93 - 14 * q^94 + 8 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	1.73205	−	1.00000i	0.654654	−	0.377964i	−0.135583	−	0.990766i	$-0.543291\pi$
$7$	1.73205	−	1.00000i	0.654654	−	0.377964i	0.790237	+	0.612801i	$0.209957\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	0.401924	+	0.232051i	0.121185	+	0.0699660i	0.559367	−	0.828920i	$-0.311044\pi$
$11$	0.401924	+	0.232051i	0.121185	+	0.0699660i	−0.438182	+	0.898886i	$0.644378\pi$
$12$	1.00000			0.288675
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$	2.00000			0.534522
$15$	−0.866025	−	0.500000i	−0.223607	−	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−0.464102	+	0.267949i	−0.106472	+	0.0614718i	−0.552291	−	0.833652i	$-0.686246\pi$
$19$	−0.464102	+	0.267949i	−0.106472	+	0.0614718i	0.445818	+	0.895123i	$0.352913\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$		−	2.00000i		−	0.436436i
$22$	0.232051	+	0.401924i	0.0494734	+	0.0856904i
$23$	−0.133975	+	0.232051i	−0.0279356	+	0.0483859i	−0.879655	−	0.475612i	$-0.842227\pi$
$23$	−0.133975	+	0.232051i	−0.0279356	+	0.0483859i	0.851720	+	0.523998i	$0.175560\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−1.00000			−0.200000
$26$	2.59808	−	2.50000i	0.509525	−	0.490290i
$27$	−1.00000			−0.192450
$28$	1.73205	+	1.00000i	0.327327	+	0.188982i
$29$	−1.86603	+	3.23205i	−0.346512	+	0.600177i	−0.985627	−	0.168934i	$-0.945967\pi$
$29$	−1.86603	+	3.23205i	−0.346512	+	0.600177i	0.639115	+	0.769111i	$0.279301\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.401924	−	0.232051i	0.0699660	−	0.0403949i
$34$			4.00000i			0.685994i
$35$	−1.00000	−	1.73205i	−0.169031	−	0.292770i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	1.03590	+	0.598076i	0.170301	+	0.0983231i	0.582728	−	0.812668i	$-0.301985\pi$
$37$	1.03590	+	0.598076i	0.170301	+	0.0983231i	−0.412427	+	0.910991i	$0.635319\pi$
$38$	−0.535898			−0.0869342
$39$	−2.50000	−	2.59808i	−0.400320	−	0.416025i
$40$	1.00000			0.158114
$41$	−1.73205	−	1.00000i	−0.270501	−	0.156174i	0.358614	−	0.933486i	$-0.383249\pi$
$41$	−1.73205	−	1.00000i	−0.270501	−	0.156174i	−0.629115	+	0.777312i	$0.716583\pi$
$42$	1.00000	−	1.73205i	0.154303	−	0.267261i
$43$	0.964102	+	1.66987i	0.147024	+	0.254653i	0.930126	−	0.367240i	$-0.119697\pi$
$43$	0.964102	+	1.66987i	0.147024	+	0.254653i	−0.783102	+	0.621893i	$0.786364\pi$
$44$			0.464102i			0.0699660i
$45$	−0.866025	+	0.500000i	−0.129099	+	0.0745356i
$46$	−0.232051	+	0.133975i	−0.0342140	+	0.0197535i
$47$			10.4641i			1.52635i	0.646194	+	0.763173i	$0.276360\pi$
$47$			10.4641i			1.52635i	−0.646194	+	0.763173i	$0.723640\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	4.00000			0.560112
$52$	3.50000	−	0.866025i	0.485363	−	0.120096i
$53$	−12.9282			−1.77583			−0.887913	−	0.460012i	$-0.847845\pi$
$53$	−12.9282			−1.77583			−0.887913	+	0.460012i	$0.847845\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	0.232051	−	0.401924i	0.0312897	−	0.0541954i
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$			0.535898i			0.0709815i
$58$	−3.23205	+	1.86603i	−0.424389	+	0.245021i
$59$	−1.33013	+	0.767949i	−0.173168	+	0.0999785i	−0.584079	−	0.811697i	$-0.698544\pi$
$59$	−1.33013	+	0.767949i	−0.173168	+	0.0999785i	0.410911	+	0.911676i	$0.365211\pi$
$60$		−	1.00000i		−	0.129099i
$61$	−5.19615	−	9.00000i	−0.665299	−	1.15233i	−0.979204	−	0.202878i	$-0.934971\pi$
$61$	−5.19615	−	9.00000i	−0.665299	−	1.15233i	0.313905	−	0.949454i	$-0.398363\pi$
$62$	0.866025	−	1.50000i	0.109985	−	0.190500i
$63$	−1.73205	−	1.00000i	−0.218218	−	0.125988i
$64$	−1.00000			−0.125000
$65$	−3.46410	−	1.00000i	−0.429669	−	0.124035i
$66$	0.464102			0.0571270
$67$	3.92820	+	2.26795i	0.479906	+	0.277074i	0.720377	−	0.693582i	$-0.243969\pi$
$67$	3.92820	+	2.26795i	0.479906	+	0.277074i	−0.240471	+	0.970656i	$0.577302\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	0.133975	+	0.232051i	0.0161286	+	0.0279356i
$70$		−	2.00000i		−	0.239046i
$71$	−7.26795	+	4.19615i	−0.862547	+	0.497992i	−0.864864	−	0.502006i	$-0.832596\pi$
$71$	−7.26795	+	4.19615i	−0.862547	+	0.497992i	0.00231747	+	0.999997i	$0.499262\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		−	2.00000i		−	0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$		−	2.00000i		−	0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$	0.598076	+	1.03590i	0.0695249	+	0.120421i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−0.464102	−	0.267949i	−0.0532361	−	0.0307359i
$77$	0.928203			0.105779
$78$	−0.866025	−	3.50000i	−0.0980581	−	0.396297i
$79$	−0.0717968			−0.00807777			−0.00403888	−	0.999992i	$-0.501286\pi$
$79$	−0.0717968			−0.00807777			−0.00403888	+	0.999992i	$0.501286\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$			4.92820i			0.540941i	0.962728	+	0.270470i	$0.0871792\pi$
$83$			4.92820i			0.540941i	−0.962728	+	0.270470i	$0.912821\pi$
$84$	1.73205	−	1.00000i	0.188982	−	0.109109i
$85$	3.46410	−	2.00000i	0.375735	−	0.216930i
$86$			1.92820i			0.207924i
$87$	1.86603	+	3.23205i	0.200059	+	0.346512i
$88$	−0.232051	+	0.401924i	−0.0247367	+	0.0428452i
$89$	6.46410	+	3.73205i	0.685193	+	0.395597i	0.801809	−	0.597581i	$-0.203871\pi$
$89$	6.46410	+	3.73205i	0.685193	+	0.395597i	−0.116615	+	0.993177i	$0.537205\pi$
$90$	−1.00000			−0.105409
$91$	−1.73205	−	7.00000i	−0.181568	−	0.733799i
$92$	−0.267949			−0.0279356
$93$	−1.50000	−	0.866025i	−0.155543	−	0.0898027i
$94$	−5.23205	+	9.06218i	−0.539645	+	0.934692i
$95$	0.267949	+	0.464102i	0.0274910	+	0.0476158i
$96$			1.00000i			0.102062i
$97$	−6.46410	+	3.73205i	−0.656330	+	0.378932i	−0.790877	−	0.611975i	$-0.790375\pi$
$97$	−6.46410	+	3.73205i	−0.656330	+	0.378932i	0.134547	+	0.990907i	$0.457042\pi$
$98$	−2.59808	+	1.50000i	−0.262445	+	0.151523i
$99$		−	0.464102i		−	0.0466440i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	5.46410	−	9.46410i	0.543698	−	0.941713i	−0.454989	−	0.890497i	$-0.650357\pi$
$101$	5.46410	−	9.46410i	0.543698	−	0.941713i	0.998688	−	0.0512163i	$-0.0163098\pi$
$102$	3.46410	+	2.00000i	0.342997	+	0.198030i
$103$	15.8564			1.56238			0.781189	−	0.624295i	$-0.214613\pi$
$103$	15.8564			1.56238			0.781189	+	0.624295i	$0.214613\pi$
$104$	3.46410	+	1.00000i	0.339683	+	0.0980581i
$105$	−2.00000			−0.195180
$106$	−11.1962	−	6.46410i	−1.08747	−	0.627849i
$107$	−9.92820	+	17.1962i	−0.959796	+	1.66241i	−0.236805	+	0.971557i	$0.576100\pi$
$107$	−9.92820	+	17.1962i	−0.959796	+	1.66241i	−0.722991	+	0.690858i	$0.757233\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$		−	11.8564i		−	1.13564i	−0.823154	−	0.567819i	$-0.807787\pi$
$109$		−	11.8564i		−	1.13564i	0.823154	−	0.567819i	$-0.192213\pi$
$110$	0.401924	−	0.232051i	0.0383219	−	0.0221252i
$111$	1.03590	−	0.598076i	0.0983231	−	0.0567669i
$112$			2.00000i			0.188982i
$113$	−5.59808	−	9.69615i	−0.526623	−	0.912137i	−0.999519	−	0.0310191i	$-0.990125\pi$
$113$	−5.59808	−	9.69615i	−0.526623	−	0.912137i	0.472896	−	0.881118i	$-0.343209\pi$
$114$	−0.267949	+	0.464102i	−0.0250957	+	0.0434671i
$115$	0.232051	+	0.133975i	0.0216388	+	0.0124932i
$116$	−3.73205			−0.346512
$117$	−3.50000	+	0.866025i	−0.323575	+	0.0800641i
$118$	−1.53590			−0.141391
$119$	6.92820	+	4.00000i	0.635107	+	0.366679i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−5.39230	−	9.33975i	−0.490210	−	0.849068i
$122$		−	10.3923i		−	0.940875i
$123$	−1.73205	+	1.00000i	−0.156174	+	0.0901670i
$124$	1.50000	−	0.866025i	0.134704	−	0.0777714i
$125$			1.00000i			0.0894427i
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	−4.46410	+	7.73205i	−0.396125	+	0.686109i	−0.993244	−	0.116044i	$-0.962979\pi$
$127$	−4.46410	+	7.73205i	−0.396125	+	0.686109i	0.597119	+	0.802153i	$0.296312\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	1.92820			0.169769
$130$	−2.50000	−	2.59808i	−0.219265	−	0.227866i
$131$	−1.33975			−0.117054			−0.0585271	−	0.998286i	$-0.518640\pi$
$131$	−1.33975			−0.117054			−0.0585271	+	0.998286i	$0.518640\pi$
$132$	0.401924	+	0.232051i	0.0349830	+	0.0201974i
$133$	−0.535898	+	0.928203i	−0.0464683	+	0.0804854i
$134$	2.26795	+	3.92820i	0.195921	+	0.339345i
$135$			1.00000i			0.0860663i
$136$	−3.46410	+	2.00000i	−0.297044	+	0.171499i
$137$	−3.86603	+	2.23205i	−0.330297	+	0.190697i	−0.655973	−	0.754784i	$-0.727741\pi$
$137$	−3.86603	+	2.23205i	−0.330297	+	0.190697i	0.325676	+	0.945481i	$0.394408\pi$
$138$			0.267949i			0.0228093i
$139$	−0.464102	−	0.803848i	−0.0393646	−	0.0681815i	0.845672	−	0.533703i	$-0.179200\pi$
$139$	−0.464102	−	0.803848i	−0.0393646	−	0.0681815i	−0.885036	+	0.465522i	$0.845867\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$	9.06218	+	5.23205i	0.763173	+	0.440618i
$142$	−8.39230			−0.704267
$143$	1.20577	−	1.16025i	0.100832	−	0.0970253i
$144$	1.00000			0.0833333
$145$	3.23205	+	1.86603i	0.268407	+	0.154965i
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$	1.50000	+	2.59808i	0.123718	+	0.214286i
$148$			1.19615i			0.0983231i
$149$	17.7224	−	10.2321i	1.45188	−	0.838242i	0.453290	−	0.891363i	$-0.350250\pi$
$149$	17.7224	−	10.2321i	1.45188	−	0.838242i	0.998588	+	0.0531208i	$0.0169168\pi$
$150$	−0.866025	+	0.500000i	−0.0707107	+	0.0408248i
$151$		−	10.3923i		−	0.845714i	−0.906196	−	0.422857i	$-0.861027\pi$
$151$		−	10.3923i		−	0.845714i	0.906196	−	0.422857i	$-0.138973\pi$
$152$	−0.267949	−	0.464102i	−0.0217335	−	0.0376436i
$153$	2.00000	−	3.46410i	0.161690	−	0.280056i
$154$	0.803848	+	0.464102i	0.0647759	+	0.0373984i
$155$	−1.73205			−0.139122
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$	−5.00000			−0.399043			−0.199522	−	0.979893i	$-0.563939\pi$
$157$	−5.00000			−0.399043			−0.199522	+	0.979893i	$0.563939\pi$
$158$	−0.0621778	−	0.0358984i	−0.00494660	−	0.00285592i
$159$	−6.46410	+	11.1962i	−0.512637	+	0.887913i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$			0.535898i			0.0422347i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	19.9641	−	11.5263i	1.56371	−	0.902808i	0.566833	−	0.823833i	$-0.308169\pi$
$163$	19.9641	−	11.5263i	1.56371	−	0.902808i	0.996877	−	0.0789748i	$-0.0251647\pi$
$164$		−	2.00000i		−	0.156174i
$165$	−0.232051	−	0.401924i	−0.0180651	−	0.0312897i
$166$	−2.46410	+	4.26795i	−0.191251	+	0.331257i
$167$	15.8660	+	9.16025i	1.22775	+	0.708842i	0.966559	−	0.256445i	$-0.0825514\pi$
$167$	15.8660	+	9.16025i	1.22775	+	0.708842i	0.261191	+	0.965287i	$0.415885\pi$
$168$	2.00000			0.154303
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	4.00000			0.306786
$171$	0.464102	+	0.267949i	0.0354907	+	0.0204906i
$172$	−0.964102	+	1.66987i	−0.0735121	+	0.127327i
$173$	1.46410	+	2.53590i	0.111314	+	0.192801i	0.916300	−	0.400492i	$-0.131161\pi$
$173$	1.46410	+	2.53590i	0.111314	+	0.192801i	−0.804987	+	0.593293i	$0.797828\pi$
$174$			3.73205i			0.282926i
$175$	−1.73205	+	1.00000i	−0.130931	+	0.0755929i
$176$	−0.401924	+	0.232051i	−0.0302961	+	0.0174915i
$177$			1.53590i			0.115445i
$178$	3.73205	+	6.46410i	0.279729	+	0.484505i
$179$	8.13397	−	14.0885i	0.607962	−	1.05302i	−0.383614	−	0.923494i	$-0.625321\pi$
$179$	8.13397	−	14.0885i	0.607962	−	1.05302i	0.991576	−	0.129527i	$-0.0413460\pi$
$180$	−0.866025	−	0.500000i	−0.0645497	−	0.0372678i
$181$	10.9282			0.812287			0.406143	−	0.913809i	$-0.366873\pi$
$181$	10.9282			0.812287			0.406143	+	0.913809i	$0.366873\pi$
$182$	2.00000	−	6.92820i	0.148250	−	0.513553i
$183$	−10.3923			−0.768221
$184$	−0.232051	−	0.133975i	−0.0171070	−	0.00987674i
$185$	0.598076	−	1.03590i	0.0439714	−	0.0761608i
$186$	−0.866025	−	1.50000i	−0.0635001	−	0.109985i
$187$			1.85641i			0.135754i
$188$	−9.06218	+	5.23205i	−0.660927	+	0.381587i
$189$	−1.73205	+	1.00000i	−0.125988	+	0.0727393i
$190$			0.535898i			0.0388782i
$191$	−7.26795	−	12.5885i	−0.525890	−	0.910869i	−0.999545	−	0.0301582i	$-0.990399\pi$
$191$	−7.26795	−	12.5885i	−0.525890	−	0.910869i	0.473655	−	0.880711i	$-0.342934\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	20.1962	+	11.6603i	1.45375	+	0.839323i	0.998692	−	0.0511377i	$-0.0162847\pi$
$193$	20.1962	+	11.6603i	1.45375	+	0.839323i	0.455059	+	0.890461i	$0.349618\pi$
$194$	−7.46410			−0.535891
$195$	−2.59808	+	2.50000i	−0.186052	+	0.179029i
$196$	−3.00000			−0.214286
$197$	14.1962	+	8.19615i	1.01143	+	0.583952i	0.911611	−	0.411054i	$-0.134839\pi$
$197$	14.1962	+	8.19615i	1.01143	+	0.583952i	0.0998228	+	0.995005i	$0.468172\pi$
$198$	0.232051	−	0.401924i	0.0164911	−	0.0285635i
$199$	9.46410	+	16.3923i	0.670892	+	1.16202i	0.977651	+	0.210232i	$0.0674221\pi$
$199$	9.46410	+	16.3923i	0.670892	+	1.16202i	−0.306759	+	0.951787i	$0.599245\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	3.92820	−	2.26795i	0.277074	−	0.159969i
$202$	9.46410	−	5.46410i	0.665892	−	0.384453i
$203$			7.46410i			0.523877i
$204$	2.00000	+	3.46410i	0.140028	+	0.242536i
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	13.7321	+	7.92820i	0.956757	+	0.552384i
$207$	0.267949			0.0186238
$208$	2.50000	+	2.59808i	0.173344	+	0.180144i
$209$	−0.248711			−0.0172037
$210$	−1.73205	−	1.00000i	−0.119523	−	0.0690066i
$211$	−11.6603	+	20.1962i	−0.802725	+	1.39036i	0.115091	+	0.993355i	$0.463284\pi$
$211$	−11.6603	+	20.1962i	−0.802725	+	1.39036i	−0.917816	+	0.397006i	$0.870049\pi$
$212$	−6.46410	−	11.1962i	−0.443956	−	0.768955i
$213$			8.39230i			0.575031i
$214$	−17.1962	+	9.92820i	−1.17550	+	0.678678i
$215$	1.66987	−	0.964102i	0.113884	−	0.0657512i
$216$		−	1.00000i		−	0.0680414i
$217$	−1.73205	−	3.00000i	−0.117579	−	0.203653i
$218$	5.92820	−	10.2679i	0.401509	−	0.695433i
$219$	−1.73205	−	1.00000i	−0.117041	−	0.0675737i
$220$	0.464102			0.0312897
$221$	14.0000	−	3.46410i	0.941742	−	0.233021i
$222$	1.19615			0.0802805
$223$	23.7846	+	13.7321i	1.59274	+	0.919566i	0.992835	+	0.119491i	$0.0381263\pi$
$223$	23.7846	+	13.7321i	1.59274	+	0.919566i	0.599900	+	0.800075i	$0.295207\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$		−	11.1962i		−	0.744757i
$227$	−3.80385	+	2.19615i	−0.252470	+	0.145764i	−0.620895	−	0.783894i	$-0.713231\pi$
$227$	−3.80385	+	2.19615i	−0.252470	+	0.145764i	0.368425	+	0.929658i	$0.379897\pi$
$228$	−0.464102	+	0.267949i	−0.0307359	+	0.0177454i
$229$		−	19.8564i		−	1.31215i	−0.754696	−	0.656074i	$-0.772216\pi$
$229$		−	19.8564i		−	1.31215i	0.754696	−	0.656074i	$-0.227784\pi$
$230$	0.133975	+	0.232051i	0.00883402	+	0.0153010i
$231$	0.464102	−	0.803848i	0.0305356	−	0.0528893i
$232$	−3.23205	−	1.86603i	−0.212195	−	0.122511i
$233$	−18.1244			−1.18737			−0.593683	−	0.804699i	$-0.702327\pi$
$233$	−18.1244			−1.18737			−0.593683	+	0.804699i	$0.702327\pi$
$234$	−3.46410	−	1.00000i	−0.226455	−	0.0653720i
$235$	10.4641			0.682603
$236$	−1.33013	−	0.767949i	−0.0865839	−	0.0499892i
$237$	−0.0358984	+	0.0621778i	−0.00233185	+	0.00403888i
$238$	4.00000	+	6.92820i	0.259281	+	0.449089i
$239$		−	4.39230i		−	0.284115i	−0.989858	−	0.142057i	$-0.954628\pi$
$239$		−	4.39230i		−	0.284115i	0.989858	−	0.142057i	$-0.0453717\pi$
$240$	0.866025	−	0.500000i	0.0559017	−	0.0322749i
$241$	−12.3564	+	7.13397i	−0.795946	+	0.459540i	−0.842052	−	0.539397i	$-0.818652\pi$
$241$	−12.3564	+	7.13397i	−0.795946	+	0.459540i	0.0461056	+	0.998937i	$0.485319\pi$
$242$		−	10.7846i		−	0.693261i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	5.19615	−	9.00000i	0.332650	−	0.576166i
$245$	2.59808	+	1.50000i	0.165985	+	0.0958315i
$246$	−2.00000			−0.127515
$247$	0.464102	+	1.87564i	0.0295301	+	0.119344i
$248$	1.73205			0.109985
$249$	4.26795	+	2.46410i	0.270470	+	0.156156i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−6.13397	−	10.6244i	−0.387173	−	0.670603i	0.604895	−	0.796305i	$-0.293215\pi$
$251$	−6.13397	−	10.6244i	−0.387173	−	0.670603i	−0.992068	+	0.125702i	$0.959882\pi$
$252$		−	2.00000i		−	0.125988i
$253$	−0.107695	+	0.0621778i	−0.00677074	+	0.00390909i
$254$	−7.73205	+	4.46410i	−0.485152	+	0.280103i
$255$		−	4.00000i		−	0.250490i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.3301	−	19.6244i	0.706754	−	1.22413i	−0.259301	−	0.965797i	$-0.583492\pi$
$257$	11.3301	−	19.6244i	0.706754	−	1.22413i	0.966055	−	0.258337i	$-0.0831745\pi$
$258$	1.66987	+	0.964102i	0.103962	+	0.0600223i
$259$	2.39230			0.148651
$260$	−0.866025	−	3.50000i	−0.0537086	−	0.217061i
$261$	3.73205			0.231008
$262$	−1.16025	−	0.669873i	−0.0716807	−	0.0413849i
$263$	9.06218	−	15.6962i	0.558798	−	0.967866i	−0.438799	−	0.898585i	$-0.644596\pi$
$263$	9.06218	−	15.6962i	0.558798	−	0.967866i	0.997597	−	0.0692812i	$-0.0220706\pi$
$264$	0.232051	+	0.401924i	0.0142817	+	0.0247367i
$265$			12.9282i			0.794173i
$266$	−0.928203	+	0.535898i	−0.0569118	+	0.0328580i
$267$	6.46410	−	3.73205i	0.395597	−	0.228398i
$268$			4.53590i			0.277074i
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	0.623082	−	0.782157i	$-0.285880\pi$
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	−0.988908	+	0.148527i	$0.952547\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	7.96410	+	4.59808i	0.483785	+	0.279313i	0.721992	−	0.691901i	$-0.243227\pi$
$271$	7.96410	+	4.59808i	0.483785	+	0.279313i	−0.238208	+	0.971214i	$0.576560\pi$
$272$	−4.00000			−0.242536
$273$	−6.92820	−	2.00000i	−0.419314	−	0.121046i
$274$	−4.46410			−0.269686
$275$	−0.401924	−	0.232051i	−0.0242369	−	0.0139932i
$276$	−0.133975	+	0.232051i	−0.00806432	+	0.0139678i
$277$	−4.96410	−	8.59808i	−0.298264	−	0.516608i	0.677475	−	0.735546i	$-0.263074\pi$
$277$	−4.96410	−	8.59808i	−0.298264	−	0.516608i	−0.975739	+	0.218938i	$0.929741\pi$
$278$		−	0.928203i		−	0.0556699i
$279$	−1.50000	+	0.866025i	−0.0898027	+	0.0518476i
$280$	1.73205	−	1.00000i	0.103510	−	0.0597614i
$281$		−	4.92820i		−	0.293992i	−0.989137	−	0.146996i	$-0.953040\pi$
$281$		−	4.92820i		−	0.293992i	0.989137	−	0.146996i	$-0.0469604\pi$
$282$	5.23205	+	9.06218i	0.311564	+	0.539645i
$283$	−1.96410	+	3.40192i	−0.116754	+	0.202223i	−0.918479	−	0.395469i	$-0.870582\pi$
$283$	−1.96410	+	3.40192i	−0.116754	+	0.202223i	0.801726	+	0.597692i	$0.203915\pi$
$284$	−7.26795	−	4.19615i	−0.431273	−	0.248996i
$285$	0.535898			0.0317439
$286$	1.62436	−	0.401924i	0.0960502	−	0.0237663i
$287$	−4.00000			−0.236113
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	1.86603	+	3.23205i	0.109577	+	0.189793i
$291$			7.46410i			0.437553i
$292$	1.73205	−	1.00000i	0.101361	−	0.0585206i
$293$	3.58846	−	2.07180i	0.209640	−	0.121036i	−0.391504	−	0.920176i	$-0.628045\pi$
$293$	3.58846	−	2.07180i	0.209640	−	0.121036i	0.601144	+	0.799141i	$0.294712\pi$
$294$			3.00000i			0.174964i
$295$	0.767949	+	1.33013i	0.0447117	+	0.0774430i
$296$	−0.598076	+	1.03590i	−0.0347625	+	0.0602104i
$297$	−0.401924	−	0.232051i	−0.0233220	−	0.0134650i
$298$	20.4641			1.18545
$299$	0.669873	+	0.696152i	0.0387398	+	0.0402595i
$300$	−1.00000			−0.0577350
$301$	3.33975	+	1.92820i	0.192500	+	0.111140i
$302$	5.19615	−	9.00000i	0.299005	−	0.517892i
$303$	−5.46410	−	9.46410i	−0.313904	−	0.543698i
$304$		−	0.535898i		−	0.0307359i
$305$	−9.00000	+	5.19615i	−0.515339	+	0.297531i
$306$	3.46410	−	2.00000i	0.198030	−	0.114332i
$307$		−	12.5359i		−	0.715462i	−0.933825	−	0.357731i	$-0.883551\pi$
$307$		−	12.5359i		−	0.715462i	0.933825	−	0.357731i	$-0.116449\pi$
$308$	0.464102	+	0.803848i	0.0264446	+	0.0458035i
$309$	7.92820	−	13.7321i	0.451020	−	0.781189i
$310$	−1.50000	−	0.866025i	−0.0851943	−	0.0491869i
$311$	−7.60770			−0.431393			−0.215696	−	0.976460i	$-0.569202\pi$
$311$	−7.60770			−0.431393			−0.215696	+	0.976460i	$0.569202\pi$
$312$	2.59808	−	2.50000i	0.147087	−	0.141535i
$313$	−28.0000			−1.58265			−0.791327	−	0.611393i	$-0.790609\pi$
$313$	−28.0000			−1.58265			−0.791327	+	0.611393i	$0.790609\pi$
$314$	−4.33013	−	2.50000i	−0.244363	−	0.141083i
$315$	−1.00000	+	1.73205i	−0.0563436	+	0.0975900i
$316$	−0.0358984	−	0.0621778i	−0.00201944	−	0.00349778i
$317$		−	21.4641i		−	1.20554i	−0.797913	−	0.602772i	$-0.794063\pi$
$317$		−	21.4641i		−	1.20554i	0.797913	−	0.602772i	$-0.205937\pi$
$318$	−11.1962	+	6.46410i	−0.627849	+	0.362489i
$319$	−1.50000	+	0.866025i	−0.0839839	+	0.0484881i
$320$			1.00000i			0.0559017i
$321$	9.92820	+	17.1962i	0.554138	+	0.959796i
$322$	−0.267949	+	0.464102i	−0.0149322	+	0.0258634i
$323$	−1.85641	−	1.07180i	−0.103293	−	0.0596364i
$324$	−1.00000			−0.0555556
$325$	−1.00000	+	3.46410i	−0.0554700	+	0.192154i
$326$	23.0526			1.27676
$327$	−10.2679	−	5.92820i	−0.567819	−	0.327830i
$328$	1.00000	−	1.73205i	0.0552158	−	0.0956365i
$329$	10.4641	+	18.1244i	0.576905	+	0.999228i
$330$		−	0.464102i		−	0.0255480i
$331$	−21.4641	+	12.3923i	−1.17977	+	0.681143i	−0.955962	−	0.293490i	$-0.905183\pi$
$331$	−21.4641	+	12.3923i	−1.17977	+	0.681143i	−0.223812	+	0.974632i	$0.571850\pi$
$332$	−4.26795	+	2.46410i	−0.234234	+	0.135235i
$333$		−	1.19615i		−	0.0655487i
$334$	9.16025	+	15.8660i	0.501227	+	0.868150i
$335$	2.26795	−	3.92820i	0.123911	−	0.214621i
$336$	1.73205	+	1.00000i	0.0944911	+	0.0545545i
$337$	−25.3205			−1.37930			−0.689648	−	0.724145i	$-0.742235\pi$
$337$	−25.3205			−1.37930			−0.689648	+	0.724145i	$0.742235\pi$
$338$	−6.06218	−	11.5000i	−0.329739	−	0.625518i
$339$	−11.1962			−0.608092
$340$	3.46410	+	2.00000i	0.187867	+	0.108465i
$341$	0.401924	−	0.696152i	0.0217654	−	0.0376988i
$342$	0.267949	+	0.464102i	0.0144890	+	0.0250957i
$343$			20.0000i			1.07990i
$344$	−1.66987	+	0.964102i	−0.0900335	+	0.0519809i
$345$	0.232051	−	0.133975i	0.0124932	−	0.00721295i
$346$			2.92820i			0.157421i
$347$	−11.1962	−	19.3923i	−0.601041	−	1.04103i	−0.992664	−	0.120908i	$-0.961420\pi$
$347$	−11.1962	−	19.3923i	−0.601041	−	1.04103i	0.391623	−	0.920126i	$-0.371914\pi$
$348$	−1.86603	+	3.23205i	−0.100029	+	0.173256i
$349$	−12.5885	−	7.26795i	−0.673845	−	0.389044i	0.123687	−	0.992321i	$-0.460528\pi$
$349$	−12.5885	−	7.26795i	−0.673845	−	0.389044i	−0.797532	+	0.603277i	$0.793861\pi$
$350$	−2.00000			−0.106904
$351$	−1.00000	+	3.46410i	−0.0533761	+	0.184900i
$352$	−0.464102			−0.0247367
$353$	−1.73205	−	1.00000i	−0.0921878	−	0.0532246i	0.453197	−	0.891410i	$-0.350283\pi$
$353$	−1.73205	−	1.00000i	−0.0921878	−	0.0532246i	−0.545385	+	0.838186i	$0.683617\pi$
$354$	−0.767949	+	1.33013i	−0.0408160	+	0.0706955i
$355$	4.19615	+	7.26795i	0.222709	+	0.385743i
$356$			7.46410i			0.395597i
$357$	6.92820	−	4.00000i	0.366679	−	0.211702i
$358$	14.0885	−	8.13397i	0.744598	−	0.429894i
$359$		−	18.9282i		−	0.998992i	−0.866316	−	0.499496i	$-0.833518\pi$
$359$		−	18.9282i		−	0.998992i	0.866316	−	0.499496i	$-0.166482\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	−9.35641	+	16.2058i	−0.492442	+	0.852935i
$362$	9.46410	+	5.46410i	0.497422	+	0.287187i
$363$	−10.7846			−0.566045
$364$	5.19615	−	5.00000i	0.272352	−	0.262071i
$365$	−2.00000			−0.104685
$366$	−9.00000	−	5.19615i	−0.470438	−	0.271607i
$367$	−18.1962	+	31.5167i	−0.949831	+	1.64516i	−0.204056	+	0.978959i	$0.565412\pi$
$367$	−18.1962	+	31.5167i	−0.949831	+	1.64516i	−0.745776	+	0.666197i	$0.767921\pi$
$368$	−0.133975	−	0.232051i	−0.00698391	−	0.0120965i
$369$			2.00000i			0.104116i
$370$	1.03590	−	0.598076i	0.0538538	−	0.0310925i
$371$	−22.3923	+	12.9282i	−1.16255	+	0.671199i
$372$		−	1.73205i		−	0.0898027i
$373$	−12.8923	−	22.3301i	−0.667538	−	1.15621i	−0.978590	−	0.205817i	$-0.934015\pi$
$373$	−12.8923	−	22.3301i	−0.667538	−	1.15621i	0.311052	−	0.950393i	$-0.399319\pi$
$374$	−0.928203	+	1.60770i	−0.0479962	+	0.0831319i
$375$	0.866025	+	0.500000i	0.0447214	+	0.0258199i
$376$	−10.4641			−0.539645
$377$	9.33013	+	9.69615i	0.480526	+	0.499377i
$378$	−2.00000			−0.102869
$379$	−0.124356	−	0.0717968i	−0.00638772	−	0.00368795i	0.496803	−	0.867863i	$-0.334507\pi$
$379$	−0.124356	−	0.0717968i	−0.00638772	−	0.00368795i	−0.503190	+	0.864176i	$0.667841\pi$
$380$	−0.267949	+	0.464102i	−0.0137455	+	0.0238079i
$381$	4.46410	+	7.73205i	0.228703	+	0.396125i
$382$		−	14.5359i		−	0.743721i
$383$	−3.99038	+	2.30385i	−0.203899	+	0.117721i	−0.598473	−	0.801143i	$-0.704226\pi$
$383$	−3.99038	+	2.30385i	−0.203899	+	0.117721i	0.394574	+	0.918864i	$0.370892\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		−	0.928203i		−	0.0473056i
$386$	11.6603	+	20.1962i	0.593491	+	1.02796i
$387$	0.964102	−	1.66987i	0.0490080	−	0.0848844i
$388$	−6.46410	−	3.73205i	−0.328165	−	0.189466i
$389$	−20.2679			−1.02763			−0.513813	−	0.857902i	$-0.671767\pi$
$389$	−20.2679			−1.02763			−0.513813	+	0.857902i	$0.671767\pi$
$390$	−3.50000	+	0.866025i	−0.177229	+	0.0438529i
$391$	−1.07180			−0.0542031
$392$	−2.59808	−	1.50000i	−0.131223	−	0.0757614i
$393$	−0.669873	+	1.16025i	−0.0337906	+	0.0585271i
$394$	8.19615	+	14.1962i	0.412916	+	0.715192i
$395$			0.0717968i			0.00361249i
$396$	0.401924	−	0.232051i	0.0201974	−	0.0116610i
$397$	10.5000	−	6.06218i	0.526980	−	0.304252i	−0.212806	−	0.977095i	$-0.568260\pi$
$397$	10.5000	−	6.06218i	0.526980	−	0.304252i	0.739786	+	0.672843i	$0.234927\pi$
$398$			18.9282i			0.948785i
$399$	0.535898	+	0.928203i	0.0268285	+	0.0464683i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	27.7128	+	16.0000i	1.38391	+	0.799002i	0.992620	−	0.121265i	$-0.0386950\pi$
$401$	27.7128	+	16.0000i	1.38391	+	0.799002i	0.391292	+	0.920267i	$0.372028\pi$
$402$	4.53590			0.226230
$403$	−6.00000	−	1.73205i	−0.298881	−	0.0862796i
$404$	10.9282			0.543698
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$	−3.73205	+	6.46410i	−0.185219	+	0.320808i
$407$	0.277568	+	0.480762i	0.0137585	+	0.0238305i
$408$			4.00000i			0.198030i
$409$	−3.46410	+	2.00000i	−0.171289	+	0.0988936i	−0.583193	−	0.812333i	$-0.698197\pi$
$409$	−3.46410	+	2.00000i	−0.171289	+	0.0988936i	0.411905	+	0.911227i	$0.364864\pi$
$410$	−1.73205	+	1.00000i	−0.0855399	+	0.0493865i
$411$			4.46410i			0.220198i
$412$	7.92820	+	13.7321i	0.390595	+	0.676530i
$413$	−1.53590	+	2.66025i	−0.0755766	+	0.130903i
$414$	0.232051	+	0.133975i	0.0114047	+	0.00658449i
$415$	4.92820			0.241916
$416$	0.866025	+	3.50000i	0.0424604	+	0.171602i
$417$	−0.928203			−0.0454543
$418$	−0.215390	−	0.124356i	−0.0105351	−	0.00608243i
$419$	−0.803848	+	1.39230i	−0.0392705	+	0.0680185i	−0.884993	−	0.465605i	$-0.845837\pi$
$419$	−0.803848	+	1.39230i	−0.0392705	+	0.0680185i	0.845722	+	0.533624i	$0.179170\pi$
$420$	−1.00000	−	1.73205i	−0.0487950	−	0.0845154i
$421$			16.3923i			0.798912i	0.916752	+	0.399456i	$0.130801\pi$
$421$			16.3923i			0.798912i	−0.916752	+	0.399456i	$0.869199\pi$
$422$	−20.1962	+	11.6603i	−0.983133	+	0.567612i
$423$	9.06218	−	5.23205i	0.440618	−	0.254391i
$424$		−	12.9282i		−	0.627849i
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$	−4.19615	+	7.26795i	−0.203304	+	0.352133i
$427$	−18.0000	−	10.3923i	−0.871081	−	0.502919i
$428$	−19.8564			−0.959796
$429$	−0.401924	−	1.62436i	−0.0194051	−	0.0784246i
$430$	1.92820			0.0929862
$431$	−6.58846	−	3.80385i	−0.317355	−	0.183225i	0.332858	−	0.942977i	$-0.391987\pi$
$431$	−6.58846	−	3.80385i	−0.317355	−	0.183225i	−0.650213	+	0.759752i	$0.725320\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	7.66025	+	13.2679i	0.368128	+	0.637617i	0.989273	−	0.146079i	$-0.0466654\pi$
$433$	7.66025	+	13.2679i	0.368128	+	0.637617i	−0.621145	+	0.783696i	$0.713332\pi$
$434$		−	3.46410i		−	0.166282i
$435$	3.23205	−	1.86603i	0.154965	−	0.0894691i
$436$	10.2679	−	5.92820i	0.491746	−	0.283909i
$437$		−	0.143594i		−	0.00686901i
$438$	−1.00000	−	1.73205i	−0.0477818	−	0.0827606i
$439$	−4.92820	+	8.53590i	−0.235210	+	0.407396i	−0.959334	−	0.282274i	$-0.908911\pi$
$439$	−4.92820	+	8.53590i	−0.235210	+	0.407396i	0.724123	+	0.689670i	$0.242245\pi$
$440$	0.401924	+	0.232051i	0.0191610	+	0.0110626i
$441$	3.00000			0.142857
$442$	13.8564	+	4.00000i	0.659082	+	0.190261i
$443$	−4.39230			−0.208685			−0.104342	−	0.994541i	$-0.533274\pi$
$443$	−4.39230			−0.208685			−0.104342	+	0.994541i	$0.533274\pi$
$444$	1.03590	+	0.598076i	0.0491616	+	0.0283834i
$445$	3.73205	−	6.46410i	0.176916	−	0.306428i
$446$	13.7321	+	23.7846i	0.650231	+	1.12623i
$447$		−	20.4641i		−	0.967919i
$448$	−1.73205	+	1.00000i	−0.0818317	+	0.0472456i
$449$	−34.3923	+	19.8564i	−1.62307	+	0.937082i	−0.636982	+	0.770879i	$0.719817\pi$
$449$	−34.3923	+	19.8564i	−1.62307	+	0.937082i	−0.986092	+	0.166203i	$0.946849\pi$
$450$			1.00000i			0.0471405i
$451$	−0.464102	−	0.803848i	−0.0218537	−	0.0378517i
$452$	5.59808	−	9.69615i	0.263311	−	0.456069i
$453$	−9.00000	−	5.19615i	−0.422857	−	0.244137i
$454$	−4.39230			−0.206141
$455$	−7.00000	+	1.73205i	−0.328165	+	0.0811998i
$456$	−0.535898			−0.0250957
$457$	−27.2487	−	15.7321i	−1.27464	−	0.735914i	−0.298783	−	0.954321i	$-0.596581\pi$
$457$	−27.2487	−	15.7321i	−1.27464	−	0.735914i	−0.975858	+	0.218407i	$0.929914\pi$
$458$	9.92820	−	17.1962i	0.463914	−	0.803523i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$			0.267949i			0.0124932i
$461$	5.59808	−	3.23205i	0.260728	−	0.150532i	−0.363938	−	0.931423i	$-0.618568\pi$
$461$	5.59808	−	3.23205i	0.260728	−	0.150532i	0.624667	+	0.780891i	$0.285235\pi$
$462$	0.803848	−	0.464102i	0.0373984	−	0.0215920i
$463$		−	20.9282i		−	0.972616i	−0.873787	−	0.486308i	$-0.838343\pi$
$463$		−	20.9282i		−	0.972616i	0.873787	−	0.486308i	$-0.161657\pi$
$464$	−1.86603	−	3.23205i	−0.0866281	−	0.150044i
$465$	−0.866025	+	1.50000i	−0.0401610	+	0.0695608i
$466$	−15.6962	−	9.06218i	−0.727110	−	0.419797i
$467$	11.8564			0.548649			0.274325	−	0.961637i	$-0.411546\pi$
$467$	11.8564			0.548649			0.274325	+	0.961637i	$0.411546\pi$
$468$	−2.50000	−	2.59808i	−0.115563	−	0.120096i
$469$	9.07180			0.418897
$470$	9.06218	+	5.23205i	0.418007	+	0.241337i
$471$	−2.50000	+	4.33013i	−0.115194	+	0.199522i
$472$	−0.767949	−	1.33013i	−0.0353477	−	0.0612241i
$473$			0.894882i			0.0411467i
$474$	−0.0621778	+	0.0358984i	−0.00285592	+	0.00164887i
$475$	0.464102	−	0.267949i	0.0212944	−	0.0122944i
$476$			8.00000i			0.366679i
$477$	6.46410	+	11.1962i	0.295971	+	0.512637i
$478$	2.19615	−	3.80385i	0.100450	−	0.173984i
$479$	1.26795	+	0.732051i	0.0579341	+	0.0334483i	0.528687	−	0.848817i	$-0.322684\pi$
$479$	1.26795	+	0.732051i	0.0579341	+	0.0334483i	−0.470753	+	0.882265i	$0.656018\pi$
$480$	1.00000			0.0456435
$481$	3.10770	−	2.99038i	0.141699	−	0.136350i
$482$	−14.2679			−0.649887
$483$	0.464102	+	0.267949i	0.0211174	+	0.0121921i
$484$	5.39230	−	9.33975i	0.245105	−	0.424534i
$485$	3.73205	+	6.46410i	0.169464	+	0.293520i
$486$			1.00000i			0.0453609i
$487$	33.9282	−	19.5885i	1.53743	−	0.887638i	0.538446	−	0.842660i	$-0.319012\pi$
$487$	33.9282	−	19.5885i	1.53743	−	0.887638i	0.998988	−	0.0449775i	$-0.0143216\pi$
$488$	9.00000	−	5.19615i	0.407411	−	0.235219i
$489$		−	23.0526i		−	1.04247i
$490$	1.50000	+	2.59808i	0.0677631	+	0.117369i
$491$	−8.66025	+	15.0000i	−0.390832	+	0.676941i	−0.992559	−	0.121761i	$-0.961146\pi$
$491$	−8.66025	+	15.0000i	−0.390832	+	0.676941i	0.601728	+	0.798701i	$0.294479\pi$
$492$	−1.73205	−	1.00000i	−0.0780869	−	0.0450835i
$493$	−14.9282			−0.672332
$494$	−0.535898	+	1.85641i	−0.0241112	+	0.0835237i
$495$	−0.464102			−0.0208598
$496$	1.50000	+	0.866025i	0.0673520	+	0.0388857i
$497$	−8.39230	+	14.5359i	−0.376446	+	0.652024i
$498$	2.46410	+	4.26795i	0.110419	+	0.191251i
$499$		−	13.4641i		−	0.602736i	−0.953508	−	0.301368i	$-0.902557\pi$
$499$		−	13.4641i		−	0.602736i	0.953508	−	0.301368i	$-0.0974433\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	15.8660	−	9.16025i	0.708842	−	0.409250i
$502$		−	12.2679i		−	0.547545i
$503$	−15.5885	−	27.0000i	−0.695055	−	1.20387i	−0.970162	−	0.242457i	$-0.922047\pi$
$503$	−15.5885	−	27.0000i	−0.695055	−	1.20387i	0.275107	−	0.961414i	$-0.411287\pi$
$504$	1.00000	−	1.73205i	0.0445435	−	0.0771517i
$505$	−9.46410	−	5.46410i	−0.421147	−	0.243149i
$506$	−0.124356			−0.00552828
$507$	−11.5000	+	6.06218i	−0.510733	+	0.269231i
$508$	−8.92820			−0.396125
$509$	16.7942	+	9.69615i	0.744391	+	0.429774i	0.823664	−	0.567079i	$-0.191926\pi$
$509$	16.7942	+	9.69615i	0.744391	+	0.429774i	−0.0792726	+	0.996853i	$0.525260\pi$
$510$	2.00000	−	3.46410i	0.0885615	−	0.153393i
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$		−	1.00000i		−	0.0441942i
$513$	0.464102	−	0.267949i	0.0204906	−	0.0118302i
$514$	19.6244	−	11.3301i	0.865593	−	0.499750i
$515$		−	15.8564i		−	0.698717i
$516$	0.964102	+	1.66987i	0.0424422	+	0.0735121i
$517$	−2.42820	+	4.20577i	−0.106792	+	0.184970i
$518$	2.07180	+	1.19615i	0.0910295	+	0.0525559i
$519$	2.92820			0.128534
$520$	1.00000	−	3.46410i	0.0438529	−	0.151911i
$521$	17.3205			0.758825			0.379413	−	0.925228i	$-0.376126\pi$
$521$	17.3205			0.758825			0.379413	+	0.925228i	$0.376126\pi$
$522$	3.23205	+	1.86603i	0.141463	+	0.0816737i
$523$	14.8923	−	25.7942i	0.651195	−	1.12790i	−0.331638	−	0.943407i	$-0.607601\pi$
$523$	14.8923	−	25.7942i	0.651195	−	1.12790i	0.982833	−	0.184496i	$-0.0590653\pi$
$524$	−0.669873	−	1.16025i	−0.0292635	−	0.0506859i
$525$			2.00000i			0.0872872i
$526$	15.6962	−	9.06218i	0.684385	−	0.395130i
$527$	6.00000	−	3.46410i	0.261364	−	0.150899i
$528$			0.464102i			0.0201974i
$529$	11.4641	+	19.8564i	0.498439	+	0.863322i
$530$	−6.46410	+	11.1962i	−0.280783	+	0.486330i
$531$	1.33013	+	0.767949i	0.0577226	+	0.0333262i
$532$	−1.07180			−0.0464683
$533$	−5.19615	+	5.00000i	−0.225070	+	0.216574i
$534$	7.46410			0.323003
$535$	17.1962	+	9.92820i	0.743455	+	0.429234i
$536$	−2.26795	+	3.92820i	−0.0979605	+	0.169673i
$537$	−8.13397	−	14.0885i	−0.351007	−	0.607962i
$538$		−	12.0000i		−	0.517357i
$539$	−1.20577	+	0.696152i	−0.0519362	+	0.0299854i
$540$	−0.866025	+	0.500000i	−0.0372678	+	0.0215166i
$541$		−	13.0718i		−	0.562000i	−0.959708	−	0.281000i	$-0.909334\pi$
$541$		−	13.0718i		−	0.562000i	0.959708	−	0.281000i	$-0.0906662\pi$
$542$	4.59808	+	7.96410i	0.197504	+	0.342087i
$543$	5.46410	−	9.46410i	0.234487	−	0.406143i
$544$	−3.46410	−	2.00000i	−0.148522	−	0.0857493i
$545$	−11.8564			−0.507873
$546$	−5.00000	−	5.19615i	−0.213980	−	0.222375i
$547$	9.07180			0.387882			0.193941	−	0.981013i	$-0.437873\pi$
$547$	9.07180			0.387882			0.193941	+	0.981013i	$0.437873\pi$
$548$	−3.86603	−	2.23205i	−0.165148	−	0.0953485i
$549$	−5.19615	+	9.00000i	−0.221766	+	0.384111i
$550$	−0.232051	−	0.401924i	−0.00989468	−	0.0171381i
$551$		−	2.00000i		−	0.0852029i
$552$	−0.232051	+	0.133975i	−0.00987674	+	0.00570234i
$553$	−0.124356	+	0.0717968i	−0.00528814	+	0.00305311i
$554$		−	9.92820i		−	0.421809i
$555$	−0.598076	−	1.03590i	−0.0253869	−	0.0439714i
$556$	0.464102	−	0.803848i	0.0196823	−	0.0340907i
$557$	32.6603	+	18.8564i	1.38386	+	0.798972i	0.992614	−	0.121315i	$-0.0387111\pi$
$557$	32.6603	+	18.8564i	1.38386	+	0.798972i	0.391245	+	0.920286i	$0.372044\pi$
$558$	−1.73205			−0.0733236
$559$	6.74871	−	1.66987i	0.285440	−	0.0706281i
$560$	2.00000			0.0845154
$561$	1.60770	+	0.928203i	0.0678769	+	0.0391888i
$562$	2.46410	−	4.26795i	0.103942	−	0.180033i
$563$	19.6603	+	34.0526i	0.828581	+	1.43514i	0.899152	+	0.437637i	$0.144185\pi$
$563$	19.6603	+	34.0526i	0.828581	+	1.43514i	−0.0705706	+	0.997507i	$0.522482\pi$
$564$			10.4641i			0.440618i
$565$	−9.69615	+	5.59808i	−0.407920	+	0.235513i
$566$	−3.40192	+	1.96410i	−0.142994	+	0.0825573i
$567$			2.00000i			0.0839921i
$568$	−4.19615	−	7.26795i	−0.176067	−	0.304956i
$569$	2.66025	−	4.60770i	0.111524	−	0.193165i	−0.804861	−	0.593463i	$-0.797760\pi$
$569$	2.66025	−	4.60770i	0.111524	−	0.193165i	0.916385	+	0.400299i	$0.131094\pi$
$570$	0.464102	+	0.267949i	0.0194391	+	0.0112232i
$571$	45.1769			1.89060			0.945298	−	0.326209i	$-0.105771\pi$
$571$	45.1769			1.89060			0.945298	+	0.326209i	$0.105771\pi$
$572$	1.60770	+	0.464102i	0.0672211	+	0.0194051i
$573$	−14.5359			−0.607246
$574$	−3.46410	−	2.00000i	−0.144589	−	0.0834784i
$575$	0.133975	−	0.232051i	0.00558713	−	0.00967719i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			10.0000i			0.416305i	0.978096	+	0.208153i	$0.0667451\pi$
$577$			10.0000i			0.416305i	−0.978096	+	0.208153i	$0.933255\pi$
$578$	0.866025	−	0.500000i	0.0360219	−	0.0207973i
$579$	20.1962	−	11.6603i	0.839323	−	0.484584i
$580$			3.73205i			0.154965i
$581$	4.92820	+	8.53590i	0.204456	+	0.354129i
$582$	−3.73205	+	6.46410i	−0.154698	+	0.267946i
$583$	−5.19615	−	3.00000i	−0.215203	−	0.124247i
$584$	2.00000			0.0827606
$585$	0.866025	+	3.50000i	0.0358057	+	0.144707i
$586$	4.14359			0.171170
$587$	−15.9282	−	9.19615i	−0.657427	−	0.379566i	0.133869	−	0.990999i	$-0.457260\pi$
$587$	−15.9282	−	9.19615i	−0.657427	−	0.379566i	−0.791296	+	0.611433i	$0.790593\pi$
$588$	−1.50000	+	2.59808i	−0.0618590	+	0.107143i
$589$	0.464102	+	0.803848i	0.0191230	+	0.0331220i
$590$			1.53590i			0.0632319i
$591$	14.1962	−	8.19615i	0.583952	−	0.337145i
$592$	−1.03590	+	0.598076i	−0.0425752	+	0.0245808i
$593$			31.1051i			1.27733i	0.769483	+	0.638667i	$0.220514\pi$
$593$			31.1051i			1.27733i	−0.769483	+	0.638667i	$0.779486\pi$
$594$	−0.232051	−	0.401924i	−0.00952116	−	0.0164911i
$595$	4.00000	−	6.92820i	0.163984	−	0.284029i
$596$	17.7224	+	10.2321i	0.725939	+	0.419121i
$597$	18.9282			0.774680
$598$	0.232051	+	0.937822i	0.00948926	+	0.0383504i
$599$	10.3923			0.424618			0.212309	−	0.977203i	$-0.431902\pi$
$599$	10.3923			0.424618			0.212309	+	0.977203i	$0.431902\pi$
$600$	−0.866025	−	0.500000i	−0.0353553	−	0.0204124i
$601$	−10.8923	+	18.8660i	−0.444306	+	0.769561i	−0.998004	−	0.0631568i	$-0.979883\pi$
$601$	−10.8923	+	18.8660i	−0.444306	+	0.769561i	0.553697	+	0.832718i	$0.313216\pi$
$602$	1.92820	+	3.33975i	0.0785877	+	0.136118i
$603$		−	4.53590i		−	0.184716i
$604$	9.00000	−	5.19615i	0.366205	−	0.211428i
$605$	−9.33975	+	5.39230i	−0.379715	+	0.219228i
$606$		−	10.9282i		−	0.443928i
$607$	−21.5885	−	37.3923i	−0.876248	−	1.51771i	−0.855427	−	0.517924i	$-0.826705\pi$
$607$	−21.5885	−	37.3923i	−0.876248	−	1.51771i	−0.0208216	−	0.999783i	$-0.506628\pi$
$608$	0.267949	−	0.464102i	0.0108668	−	0.0188218i
$609$	6.46410	+	3.73205i	0.261939	+	0.151230i
$610$	−10.3923			−0.420772
$611$	36.2487	+	10.4641i	1.46647	+	0.423332i
$612$	4.00000			0.161690
$613$	0.820508	+	0.473721i	0.0331400	+	0.0191334i	0.516478	−	0.856300i	$-0.327243\pi$
$613$	0.820508	+	0.473721i	0.0331400	+	0.0191334i	−0.483338	+	0.875434i	$0.660576\pi$
$614$	6.26795	−	10.8564i	0.252954	−	0.438129i
$615$	1.00000	+	1.73205i	0.0403239	+	0.0698430i
$616$			0.928203i			0.0373984i
$617$	13.4545	−	7.76795i	0.541657	−	0.312726i	−0.204093	−	0.978951i	$-0.565425\pi$
$617$	13.4545	−	7.76795i	0.541657	−	0.312726i	0.745750	+	0.666226i	$0.232091\pi$
$618$	13.7321	−	7.92820i	0.552384	−	0.318919i
$619$		−	24.2487i		−	0.974638i	−0.873224	−	0.487319i	$-0.837975\pi$
$619$		−	24.2487i		−	0.974638i	0.873224	−	0.487319i	$-0.162025\pi$
$620$	−0.866025	−	1.50000i	−0.0347804	−	0.0602414i
$621$	0.133975	−	0.232051i	0.00537622	−	0.00931188i
$622$	−6.58846	−	3.80385i	−0.264173	−	0.152520i
$623$	14.9282			0.598086
$624$	3.50000	−	0.866025i	0.140112	−	0.0346688i
$625$	1.00000			0.0400000
$626$	−24.2487	−	14.0000i	−0.969173	−	0.559553i
$627$	−0.124356	+	0.215390i	−0.00496629	+	0.00860186i
$628$	−2.50000	−	4.33013i	−0.0997609	−	0.172791i
$629$			4.78461i			0.190775i
$630$	−1.73205	+	1.00000i	−0.0690066	+	0.0398410i
$631$	−21.2487	+	12.2679i	−0.845898	+	0.488379i	−0.859265	−	0.511531i	$-0.829078\pi$
$631$	−21.2487	+	12.2679i	−0.845898	+	0.488379i	0.0133668	+	0.999911i	$0.495745\pi$
$632$		−	0.0717968i		−	0.00285592i
$633$	11.6603	+	20.1962i	0.463453	+	0.802725i
$634$	10.7321	−	18.5885i	0.426224	−	0.738242i
$635$	7.73205	+	4.46410i	0.306837	+	0.177152i
$636$	−12.9282			−0.512637
$637$	7.50000	+	7.79423i	0.297161	+	0.308819i
$638$	−1.73205			−0.0685725
$639$	7.26795	+	4.19615i	0.287516	+	0.165997i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−13.9282	−	24.1244i	−0.550131	−	0.952855i	−0.998265	−	0.0588882i	$-0.981244\pi$
$641$	−13.9282	−	24.1244i	−0.550131	−	0.952855i	0.448134	−	0.893967i	$-0.352089\pi$
$642$			19.8564i			0.783670i
$643$	23.7846	−	13.7321i	0.937973	−	0.541539i	0.0486490	−	0.998816i	$-0.484508\pi$
$643$	23.7846	−	13.7321i	0.937973	−	0.541539i	0.889324	+	0.457277i	$0.151175\pi$
$644$	−0.464102	+	0.267949i	−0.0182882	+	0.0105587i
$645$		−	1.92820i		−	0.0759229i
$646$	−1.07180	−	1.85641i	−0.0421693	−	0.0730393i
$647$	−10.6603	+	18.4641i	−0.419098	+	0.725899i	−0.995849	−	0.0910212i	$-0.970987\pi$
$647$	−10.6603	+	18.4641i	−0.419098	+	0.725899i	0.576751	+	0.816920i	$0.304320\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−0.712813			−0.0279804
$650$	−2.59808	+	2.50000i	−0.101905	+	0.0980581i
$651$	−3.46410			−0.135769
$652$	19.9641	+	11.5263i	0.781855	+	0.451404i
$653$	22.1244	−	38.3205i	0.865793	−	1.49960i	−0.000464739	−	1.00000i	$-0.500148\pi$
$653$	22.1244	−	38.3205i	0.865793	−	1.49960i	0.866258	−	0.499597i	$-0.166519\pi$
$654$	−5.92820	−	10.2679i	−0.231811	−	0.401509i
$655$			1.33975i			0.0523482i
$656$	1.73205	−	1.00000i	0.0676252	−	0.0390434i
$657$	−1.73205	+	1.00000i	−0.0675737	+	0.0390137i
$658$			20.9282i			0.815866i
$659$	1.86603	+	3.23205i	0.0726900	+	0.125903i	0.900079	−	0.435726i	$-0.143508\pi$
$659$	1.86603	+	3.23205i	0.0726900	+	0.125903i	−0.827389	+	0.561629i	$0.810175\pi$
$660$	0.232051	−	0.401924i	0.00903257	−	0.0156449i
$661$	37.5167	+	21.6603i	1.45923	+	0.842486i	0.998973	−	0.0453002i	$-0.0144244\pi$
$661$	37.5167	+	21.6603i	1.45923	+	0.842486i	0.460256	+	0.887786i	$0.347758\pi$
$662$	−24.7846			−0.963281
$663$	4.00000	−	13.8564i	0.155347	−	0.538138i
$664$	−4.92820			−0.191251
$665$	0.928203	+	0.535898i	0.0359942	+	0.0207812i
$666$	0.598076	−	1.03590i	0.0231750	−	0.0401402i
$667$	−0.500000	−	0.866025i	−0.0193601	−	0.0335326i
$668$			18.3205i			0.708842i
$669$	23.7846	−	13.7321i	0.919566	−	0.530912i
$670$	3.92820	−	2.26795i	0.151760	−	0.0876185i
$671$		−	4.82309i		−	0.186193i
$672$	1.00000	+	1.73205i	0.0385758	+	0.0668153i
$673$	−16.0000	+	27.7128i	−0.616755	+	1.06825i	0.373319	+	0.927703i	$0.378220\pi$
$673$	−16.0000	+	27.7128i	−0.616755	+	1.06825i	−0.990074	+	0.140548i	$0.955114\pi$
$674$	−21.9282	−	12.6603i	−0.844643	−	0.487655i
$675$	1.00000			0.0384900
$676$	0.500000	−	12.9904i	0.0192308	−	0.499630i
$677$	11.6077			0.446120			0.223060	−	0.974805i	$-0.428395\pi$
$677$	11.6077			0.446120			0.223060	+	0.974805i	$0.428395\pi$
$678$	−9.69615	−	5.59808i	−0.372378	−	0.214993i
$679$	−7.46410	+	12.9282i	−0.286446	+	0.496139i
$680$	2.00000	+	3.46410i	0.0766965	+	0.132842i
$681$			4.39230i			0.168313i
$682$	0.696152	−	0.401924i	0.0266571	−	0.0153905i
$683$	−0.679492	+	0.392305i	−0.0260000	+	0.0150111i	−0.512944	−	0.858422i	$-0.671445\pi$
$683$	−0.679492	+	0.392305i	−0.0260000	+	0.0150111i	0.486944	+	0.873433i	$0.338112\pi$
$684$			0.535898i			0.0204906i
$685$	2.23205	+	3.86603i	0.0852823	+	0.147713i
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	−17.1962	−	9.92820i	−0.656074	−	0.378785i
$688$	−1.92820			−0.0735121
$689$	−12.9282	+	44.7846i	−0.492525	+	1.70616i
$690$	0.267949			0.0102007
$691$	−30.4641	−	17.5885i	−1.15891	−	0.669096i	−0.207867	−	0.978157i	$-0.566652\pi$
$691$	−30.4641	−	17.5885i	−1.15891	−	0.669096i	−0.951042	+	0.309061i	$0.899985\pi$
$692$	−1.46410	+	2.53590i	−0.0556568	+	0.0964004i
$693$	−0.464102	−	0.803848i	−0.0176298	−	0.0305356i
$694$		−	22.3923i		−	0.850000i
$695$	−0.803848	+	0.464102i	−0.0304917	+	0.0176044i
$696$	−3.23205	+	1.86603i	−0.122511	+	0.0707315i
$697$		−	8.00000i		−	0.303022i
$698$	−7.26795	−	12.5885i	−0.275096	−	0.476480i
$699$	−9.06218	+	15.6962i	−0.342763	+	0.593683i
$700$	−1.73205	−	1.00000i	−0.0654654	−	0.0377964i
$701$	−3.73205			−0.140958			−0.0704788	−	0.997513i	$-0.522453\pi$
$701$	−3.73205			−0.140958			−0.0704788	+	0.997513i	$0.522453\pi$
$702$	−2.59808	+	2.50000i	−0.0980581	+	0.0943564i
$703$	−0.641016			−0.0241764
$704$	−0.401924	−	0.232051i	−0.0151481	−	0.00874574i
$705$	5.23205	−	9.06218i	0.197050	−	0.341301i
$706$	−1.00000	−	1.73205i	−0.0376355	−	0.0651866i
$707$		−	21.8564i		−	0.821995i
$708$	−1.33013	+	0.767949i	−0.0499892	+	0.0288613i
$709$	7.85641	−	4.53590i	0.295054	−	0.170349i	−0.345165	−	0.938542i	$-0.612177\pi$
$709$	7.85641	−	4.53590i	0.295054	−	0.170349i	0.640219	+	0.768193i	$0.278844\pi$
$710$			8.39230i			0.314958i
$711$	0.0358984	+	0.0621778i	0.00134629	+	0.00233185i
$712$	−3.73205	+	6.46410i	−0.139865	+	0.242252i
$713$	0.401924	+	0.232051i	0.0150522	+	0.00869037i
$714$	8.00000			0.299392
$715$	−1.16025	−	1.20577i	−0.0433910	−	0.0450933i
$716$	16.2679			0.607962
$717$	−3.80385	−	2.19615i	−0.142057	−	0.0820168i
$718$	9.46410	−	16.3923i	0.353197	−	0.611755i
$719$	−17.3205	−	30.0000i	−0.645946	−	1.11881i	−0.984082	−	0.177714i	$-0.943130\pi$
$719$	−17.3205	−	30.0000i	−0.645946	−	1.11881i	0.338136	−	0.941097i	$-0.390204\pi$
$720$		−	1.00000i		−	0.0372678i
$721$	27.4641	−	15.8564i	1.02282	−	0.590523i
$722$	−16.2058	+	9.35641i	−0.603116	+	0.348209i
$723$			14.2679i			0.530631i
$724$	5.46410	+	9.46410i	0.203072	+	0.351731i
$725$	1.86603	−	3.23205i	0.0693024	−	0.120035i
$726$	−9.33975	−	5.39230i	−0.346630	−	0.200127i
$727$	23.7128			0.879460			0.439730	−	0.898130i	$-0.355074\pi$
$727$	23.7128			0.879460			0.439730	+	0.898130i	$0.355074\pi$
$728$	7.00000	−	1.73205i	0.259437	−	0.0641941i
$729$	1.00000			0.0370370
$730$	−1.73205	−	1.00000i	−0.0641061	−	0.0370117i
$731$	−3.85641	+	6.67949i	−0.142634	+	0.247050i
$732$	−5.19615	−	9.00000i	−0.192055	−	0.332650i
$733$			37.0718i			1.36928i	0.728882	+	0.684639i	$0.240040\pi$
$733$			37.0718i			1.36928i	−0.728882	+	0.684639i	$0.759960\pi$
$734$	−31.5167	+	18.1962i	−1.16330	+	0.671632i
$735$	2.59808	−	1.50000i	0.0958315	−	0.0553283i
$736$		−	0.267949i		−	0.00987674i
$737$	1.05256	+	1.82309i	0.0387715	+	0.0671542i
$738$	−1.00000	+	1.73205i	−0.0368105	+	0.0637577i
$739$	−13.2679	−	7.66025i	−0.488069	−	0.281787i	0.235704	−	0.971825i	$-0.424260\pi$
$739$	−13.2679	−	7.66025i	−0.488069	−	0.281787i	−0.723773	+	0.690038i	$0.757594\pi$
$740$	1.19615			0.0439714
$741$	1.85641	+	0.535898i	0.0681968	+	0.0196867i
$742$	−25.8564			−0.949219
$743$	29.0429	+	16.7679i	1.06548	+	0.615156i	0.926944	−	0.375201i	$-0.122426\pi$
$743$	29.0429	+	16.7679i	1.06548	+	0.615156i	0.138539	+	0.990357i	$0.455760\pi$
$744$	0.866025	−	1.50000i	0.0317500	−	0.0549927i
$745$	−10.2321	−	17.7224i	−0.374873	−	0.649300i
$746$		−	25.7846i		−	0.944042i
$747$	4.26795	−	2.46410i	0.156156	−	0.0901568i
$748$	−1.60770	+	0.928203i	−0.0587832	+	0.0339385i
$749$			39.7128i			1.45107i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	−13.9641	+	24.1865i	−0.509557	+	0.882579i	0.490381	+	0.871508i	$0.336857\pi$
$751$	−13.9641	+	24.1865i	−0.509557	+	0.882579i	−0.999939	+	0.0110712i	$0.996476\pi$
$752$	−9.06218	−	5.23205i	−0.330464	−	0.190793i
$753$	−12.2679			−0.447069
$754$	3.23205	+	13.0622i	0.117704	+	0.475696i
$755$	−10.3923			−0.378215
$756$	−1.73205	−	1.00000i	−0.0629941	−	0.0363696i
$757$	9.00000	−	15.5885i	0.327111	−	0.566572i	−0.654827	−	0.755779i	$-0.727258\pi$
$757$	9.00000	−	15.5885i	0.327111	−	0.566572i	0.981937	+	0.189207i	$0.0605917\pi$
$758$	−0.0717968	−	0.124356i	−0.00260778	−	0.00451680i
$759$			0.124356i			0.00451382i
$760$	−0.464102	+	0.267949i	−0.0168347	+	0.00971954i
$761$	−16.3923	+	9.46410i	−0.594221	+	0.343073i	−0.766765	−	0.641928i	$-0.778135\pi$
$761$	−16.3923	+	9.46410i	−0.594221	+	0.343073i	0.172544	+	0.985002i	$0.444801\pi$
$762$			8.92820i			0.323435i
$763$	−11.8564	−	20.5359i	−0.429231	−	0.743449i
$764$	7.26795	−	12.5885i	0.262945	−	0.455434i
$765$	−3.46410	−	2.00000i	−0.125245	−	0.0723102i
$766$	−4.60770			−0.166483
$767$	1.33013	+	5.37564i	0.0480281	+	0.194103i
$768$	−1.00000			−0.0360844
$769$	−16.9641	−	9.79423i	−0.611741	−	0.353189i	0.161905

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.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(0.866025 - 0.500000i) q^{6} +(1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(0.866025 - 0.500000i) q^{6} +(1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.401924 + 0.232051i) q^{11} +1.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} -1.00000i q^{18} +(-0.464102 + 0.267949i) q^{19} +(0.866025 - 0.500000i) q^{20} -2.00000i q^{21} +(0.232051 + 0.401924i) q^{22} +(-0.133975 + 0.232051i) q^{23} +(0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(2.59808 - 2.50000i) q^{26} -1.00000 q^{27} +(1.73205 + 1.00000i) q^{28} +(-1.86603 + 3.23205i) q^{29} +(-0.500000 - 0.866025i) q^{30} -1.73205i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.401924 - 0.232051i) q^{33} +4.00000i q^{34} +(-1.00000 - 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{36} +(1.03590 + 0.598076i) q^{37} -0.535898 q^{38} +(-2.50000 - 2.59808i) q^{39} +1.00000 q^{40} +(-1.73205 - 1.00000i) q^{41} +(1.00000 - 1.73205i) q^{42} +(0.964102 + 1.66987i) q^{43} +0.464102i q^{44} +(-0.866025 + 0.500000i) q^{45} +(-0.232051 + 0.133975i) q^{46} +10.4641i q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} +(-0.866025 - 0.500000i) q^{50} +4.00000 q^{51} +(3.50000 - 0.866025i) q^{52} -12.9282 q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.232051 - 0.401924i) q^{55} +(1.00000 + 1.73205i) q^{56} +0.535898i q^{57} +(-3.23205 + 1.86603i) q^{58} +(-1.33013 + 0.767949i) q^{59} -1.00000i q^{60} +(-5.19615 - 9.00000i) q^{61} +(0.866025 - 1.50000i) q^{62} +(-1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +(-3.46410 - 1.00000i) q^{65} +0.464102 q^{66} +(3.92820 + 2.26795i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(0.133975 + 0.232051i) q^{69} -2.00000i q^{70} +(-7.26795 + 4.19615i) q^{71} +(0.866025 - 0.500000i) q^{72} -2.00000i q^{73} +(0.598076 + 1.03590i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-0.464102 - 0.267949i) q^{76} +0.928203 q^{77} +(-0.866025 - 3.50000i) q^{78} -0.0717968 q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} +4.92820i q^{83} +(1.73205 - 1.00000i) q^{84} +(3.46410 - 2.00000i) q^{85} +1.92820i q^{86} +(1.86603 + 3.23205i) q^{87} +(-0.232051 + 0.401924i) q^{88} +(6.46410 + 3.73205i) q^{89} -1.00000 q^{90} +(-1.73205 - 7.00000i) q^{91} -0.267949 q^{92} +(-1.50000 - 0.866025i) q^{93} +(-5.23205 + 9.06218i) q^{94} +(0.267949 + 0.464102i) q^{95} +1.00000i q^{96} +(-6.46410 + 3.73205i) q^{97} +(-2.59808 + 1.50000i) q^{98} -0.464102i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} + 2 q^{10} + 12 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} - 2 q^{16} + 8 q^{17} + 12 q^{19} - 6 q^{22} - 4 q^{23} - 4 q^{25} - 4 q^{27} - 4 q^{29} - 2 q^{30} + 12 q^{33} - 4 q^{35} + 2 q^{36} + 18 q^{37} - 16 q^{38} - 10 q^{39} + 4 q^{40} + 4 q^{42} - 10 q^{43} + 6 q^{46} + 2 q^{48} - 6 q^{49} + 16 q^{51} + 14 q^{52} - 24 q^{53} - 6 q^{55} + 4 q^{56} - 6 q^{58} + 12 q^{59} - 4 q^{64} - 12 q^{66} - 12 q^{67} - 8 q^{68} + 4 q^{69} - 36 q^{71} - 8 q^{74} - 2 q^{75} + 12 q^{76} - 24 q^{77} - 28 q^{79} - 2 q^{81} - 4 q^{82} + 4 q^{87} + 6 q^{88} + 12 q^{89} - 4 q^{90} - 8 q^{92} - 6 q^{93} - 14 q^{94} + 8 q^{95} - 12 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 + 2 * q^10 + 12 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 - 2 * q^16 + 8 * q^17 + 12 * q^19 - 6 * q^22 - 4 * q^23 - 4 * q^25 - 4 * q^27 - 4 * q^29 - 2 * q^30 + 12 * q^33 - 4 * q^35 + 2 * q^36 + 18 * q^37 - 16 * q^38 - 10 * q^39 + 4 * q^40 + 4 * q^42 - 10 * q^43 + 6 * q^46 + 2 * q^48 - 6 * q^49 + 16 * q^51 + 14 * q^52 - 24 * q^53 - 6 * q^55 + 4 * q^56 - 6 * q^58 + 12 * q^59 - 4 * q^64 - 12 * q^66 - 12 * q^67 - 8 * q^68 + 4 * q^69 - 36 * q^71 - 8 * q^74 - 2 * q^75 + 12 * q^76 - 24 * q^77 - 28 * q^79 - 2 * q^81 - 4 * q^82 + 4 * q^87 + 6 * q^88 + 12 * q^89 - 4 * q^90 - 8 * q^92 - 6 * q^93 - 14 * q^94 + 8 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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