LMFDB - Embedded newform 390.2.bb.b.361.2

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			361.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	390.361
Dual form			390.2.bb.b.121.2

$q$-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 $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$		−	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	−0.438182	−	0.898886i	$-0.644378\pi$
$11$	0.401924	−	0.232051i	0.121185	−	0.0699660i	0.559367	+	0.828920i	$0.311044\pi$
$12$	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	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$			1.00000i			0.235702i
$19$	−0.464102	−	0.267949i	−0.106472	−	0.0614718i	0.445818	−	0.895123i	$-0.352913\pi$
$19$	−0.464102	−	0.267949i	−0.106472	−	0.0614718i	−0.552291	+	0.833652i	$0.686246\pi$
$20$	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	0.851720	−	0.523998i	$-0.175560\pi$
$23$	−0.133975	−	0.232051i	−0.0279356	−	0.0483859i	−0.879655	+	0.475612i	$0.842227\pi$
$24$	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	0.639115	−	0.769111i	$-0.279301\pi$
$29$	−1.86603	−	3.23205i	−0.346512	−	0.600177i	−0.985627	+	0.168934i	$0.945967\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$			1.73205i			0.311086i	0.987829	+	0.155543i	$0.0497126\pi$
$31$			1.73205i			0.311086i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−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	−0.412427	−	0.910991i	$-0.635319\pi$
$37$	1.03590	−	0.598076i	0.170301	−	0.0983231i	0.582728	+	0.812668i	$0.301985\pi$
$38$	−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	−0.629115	−	0.777312i	$-0.716583\pi$
$41$	−1.73205	+	1.00000i	−0.270501	+	0.156174i	0.358614	+	0.933486i	$0.383249\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	0.964102	−	1.66987i	0.147024	−	0.254653i	−0.783102	−	0.621893i	$-0.786364\pi$
$43$	0.964102	−	1.66987i	0.147024	−	0.254653i	0.930126	+	0.367240i	$0.119697\pi$
$44$		−	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	$-0.723640\pi$
$47$		−	10.4641i		−	1.52635i	0.646194	−	0.763173i	$-0.276360\pi$
$48$	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	0.410911	−	0.911676i	$-0.365211\pi$
$59$	−1.33013	−	0.767949i	−0.173168	−	0.0999785i	−0.584079	+	0.811697i	$0.698544\pi$
$60$			1.00000i			0.129099i
$61$	−5.19615	+	9.00000i	−0.665299	+	1.15233i	0.313905	+	0.949454i	$0.398363\pi$
$61$	−5.19615	+	9.00000i	−0.665299	+	1.15233i	−0.979204	+	0.202878i	$0.934971\pi$
$62$	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	−0.240471	−	0.970656i	$-0.577302\pi$
$67$	3.92820	−	2.26795i	0.479906	−	0.277074i	0.720377	+	0.693582i	$0.243969\pi$
$68$	−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	0.00231747	−	0.999997i	$-0.499262\pi$
$71$	−7.26795	−	4.19615i	−0.862547	−	0.497992i	−0.864864	+	0.502006i	$0.832596\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	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	$-0.912821\pi$
$83$		−	4.92820i		−	0.540941i	0.962728	−	0.270470i	$-0.0871792\pi$
$84$	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	−0.116615	−	0.993177i	$-0.537205\pi$
$89$	6.46410	−	3.73205i	0.685193	−	0.395597i	0.801809	+	0.597581i	$0.203871\pi$
$90$	−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	0.134547	−	0.990907i	$-0.457042\pi$
$97$	−6.46410	−	3.73205i	−0.656330	−	0.378932i	−0.790877	+	0.611975i	$0.790375\pi$
$98$	−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	0.998688	+	0.0512163i	$0.0163098\pi$
$101$	5.46410	+	9.46410i	0.543698	+	0.941713i	−0.454989	+	0.890497i	$0.650357\pi$
$102$	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	−0.722991	−	0.690858i	$-0.757233\pi$
$107$	−9.92820	−	17.1962i	−0.959796	−	1.66241i	−0.236805	−	0.971557i	$-0.576100\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$			11.8564i			1.13564i	0.823154	+	0.567819i	$0.192213\pi$
$109$			11.8564i			1.13564i	−0.823154	+	0.567819i	$0.807787\pi$
$110$	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	0.472896	+	0.881118i	$0.343209\pi$
$113$	−5.59808	+	9.69615i	−0.526623	+	0.912137i	−0.999519	+	0.0310191i	$0.990125\pi$
$114$	−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	0.597119	−	0.802153i	$-0.296312\pi$
$127$	−4.46410	−	7.73205i	−0.396125	−	0.686109i	−0.993244	+	0.116044i	$0.962979\pi$
$128$	−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	0.325676	−	0.945481i	$-0.394408\pi$
$137$	−3.86603	−	2.23205i	−0.330297	−	0.190697i	−0.655973	+	0.754784i	$0.727741\pi$
$138$		−	0.267949i		−	0.0228093i
$139$	−0.464102	+	0.803848i	−0.0393646	+	0.0681815i	−0.885036	−	0.465522i	$-0.845867\pi$
$139$	−0.464102	+	0.803848i	−0.0393646	+	0.0681815i	0.845672	+	0.533703i	$0.179200\pi$
$140$	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	0.998588	−	0.0531208i	$-0.0169168\pi$
$149$	17.7224	+	10.2321i	1.45188	+	0.838242i	0.453290	+	0.891363i	$0.350250\pi$
$150$	−0.866025	−	0.500000i	−0.0707107	−	0.0408248i
$151$			10.3923i			0.845714i	0.906196	+	0.422857i	$0.138973\pi$
$151$			10.3923i			0.845714i	−0.906196	+	0.422857i	$0.861027\pi$
$152$	−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	0.996877	+	0.0789748i	$0.0251647\pi$
$163$	19.9641	+	11.5263i	1.56371	+	0.902808i	0.566833	+	0.823833i	$0.308169\pi$
$164$			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	0.261191	−	0.965287i	$-0.415885\pi$
$167$	15.8660	−	9.16025i	1.22775	−	0.708842i	0.966559	+	0.256445i	$0.0825514\pi$
$168$	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	−0.804987	−	0.593293i	$-0.797828\pi$
$173$	1.46410	−	2.53590i	0.111314	−	0.192801i	0.916300	+	0.400492i	$0.131161\pi$
$174$		−	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	0.991576	+	0.129527i	$0.0413460\pi$
$179$	8.13397	+	14.0885i	0.607962	+	1.05302i	−0.383614	+	0.923494i	$0.625321\pi$
$180$	−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	0.473655	+	0.880711i	$0.342934\pi$
$191$	−7.26795	+	12.5885i	−0.525890	+	0.910869i	−0.999545	+	0.0301582i	$0.990399\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	20.1962	−	11.6603i	1.45375	−	0.839323i	0.455059	−	0.890461i	$-0.349618\pi$
$193$	20.1962	−	11.6603i	1.45375	−	0.839323i	0.998692	+	0.0511377i	$0.0162847\pi$
$194$	−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	0.0998228	−	0.995005i	$-0.468172\pi$
$197$	14.1962	−	8.19615i	1.01143	−	0.583952i	0.911611	+	0.411054i	$0.134839\pi$
$198$	0.232051	+	0.401924i	0.0164911	+	0.0285635i
$199$	9.46410	−	16.3923i	0.670892	−	1.16202i	−0.306759	−	0.951787i	$-0.599245\pi$
$199$	9.46410	−	16.3923i	0.670892	−	1.16202i	0.977651	−	0.210232i	$-0.0674221\pi$
$200$			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	−0.917816	−	0.397006i	$-0.870049\pi$
$211$	−11.6603	−	20.1962i	−0.802725	−	1.39036i	0.115091	−	0.993355i	$-0.463284\pi$
$212$	−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	0.599900	−	0.800075i	$-0.295207\pi$
$223$	23.7846	−	13.7321i	1.59274	−	0.919566i	0.992835	−	0.119491i	$-0.0381263\pi$
$224$	−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	0.368425	−	0.929658i	$-0.379897\pi$
$227$	−3.80385	−	2.19615i	−0.252470	−	0.145764i	−0.620895	+	0.783894i	$0.713231\pi$
$228$	−0.464102	−	0.267949i	−0.0307359	−	0.0177454i
$229$			19.8564i			1.31215i	0.754696	+	0.656074i	$0.227784\pi$
$229$			19.8564i			1.31215i	−0.754696	+	0.656074i	$0.772216\pi$
$230$	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	$0.0453717\pi$
$239$			4.39230i			0.284115i	−0.989858	+	0.142057i	$0.954628\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	−12.3564	−	7.13397i	−0.795946	−	0.459540i	0.0461056	−	0.998937i	$-0.485319\pi$
$241$	−12.3564	−	7.13397i	−0.795946	−	0.459540i	−0.842052	+	0.539397i	$0.818652\pi$
$242$			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	−0.992068	−	0.125702i	$-0.959882\pi$
$251$	−6.13397	+	10.6244i	−0.387173	+	0.670603i	0.604895	+	0.796305i	$0.293215\pi$
$252$			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	0.966055	+	0.258337i	$0.0831745\pi$
$257$	11.3301	+	19.6244i	0.706754	+	1.22413i	−0.259301	+	0.965797i	$0.583492\pi$
$258$	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	0.997597	+	0.0692812i	$0.0220706\pi$
$263$	9.06218	+	15.6962i	0.558798	+	0.967866i	−0.438799	+	0.898585i	$0.644596\pi$
$264$	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	−0.988908	−	0.148527i	$-0.952547\pi$
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	0.623082	+	0.782157i	$0.285880\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	7.96410	−	4.59808i	0.483785	−	0.279313i	−0.238208	−	0.971214i	$-0.576560\pi$
$271$	7.96410	−	4.59808i	0.483785	−	0.279313i	0.721992	+	0.691901i	$0.243227\pi$
$272$	−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	−0.975739	−	0.218938i	$-0.929741\pi$
$277$	−4.96410	+	8.59808i	−0.298264	+	0.516608i	0.677475	+	0.735546i	$0.263074\pi$
$278$			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	$0.0469604\pi$
$281$			4.92820i			0.293992i	−0.989137	+	0.146996i	$0.953040\pi$
$282$	5.23205	−	9.06218i	0.311564	−	0.539645i
$283$	−1.96410	−	3.40192i	−0.116754	−	0.202223i	0.801726	−	0.597692i	$-0.203915\pi$
$283$	−1.96410	−	3.40192i	−0.116754	−	0.202223i	−0.918479	+	0.395469i	$0.870582\pi$
$284$	−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	0.601144	−	0.799141i	$-0.294712\pi$
$293$	3.58846	+	2.07180i	0.209640	+	0.121036i	−0.391504	+	0.920176i	$0.628045\pi$
$294$		−	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	$0.116449\pi$
$307$			12.5359i			0.715462i	−0.933825	+	0.357731i	$0.883551\pi$
$308$	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	$0.205937\pi$
$317$			21.4641i			1.20554i	−0.797913	+	0.602772i	$0.794063\pi$
$318$	−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	−0.223812	−	0.974632i	$-0.571850\pi$
$331$	−21.4641	−	12.3923i	−1.17977	−	0.681143i	−0.955962	+	0.293490i	$0.905183\pi$
$332$	−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	0.391623	+	0.920126i	$0.371914\pi$
$347$	−11.1962	+	19.3923i	−0.601041	+	1.04103i	−0.992664	+	0.120908i	$0.961420\pi$
$348$	−1.86603	−	3.23205i	−0.100029	−	0.173256i
$349$	−12.5885	+	7.26795i	−0.673845	+	0.389044i	−0.797532	−	0.603277i	$-0.793861\pi$
$349$	−12.5885	+	7.26795i	−0.673845	+	0.389044i	0.123687	+	0.992321i	$0.460528\pi$
$350$	−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	−0.545385	−	0.838186i	$-0.683617\pi$
$353$	−1.73205	+	1.00000i	−0.0921878	+	0.0532246i	0.453197	+	0.891410i	$0.350283\pi$
$354$	−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	$0.166482\pi$
$359$			18.9282i			0.998992i	−0.866316	+	0.499496i	$0.833518\pi$
$360$	−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	−0.745776	−	0.666197i	$-0.767921\pi$
$367$	−18.1962	−	31.5167i	−0.949831	−	1.64516i	−0.204056	−	0.978959i	$-0.565412\pi$
$368$	−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	0.311052	+	0.950393i	$0.399319\pi$
$373$	−12.8923	+	22.3301i	−0.667538	+	1.15621i	−0.978590	+	0.205817i	$0.934015\pi$
$374$	−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	−0.503190	−	0.864176i	$-0.667841\pi$
$379$	−0.124356	+	0.0717968i	−0.00638772	+	0.00368795i	0.496803	+	0.867863i	$0.334507\pi$
$380$	−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	0.394574	−	0.918864i	$-0.370892\pi$
$383$	−3.99038	−	2.30385i	−0.203899	−	0.117721i	−0.598473	+	0.801143i	$0.704226\pi$
$384$	−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	0.739786	−	0.672843i	$-0.234927\pi$
$397$	10.5000	+	6.06218i	0.526980	+	0.304252i	−0.212806	+	0.977095i	$0.568260\pi$
$398$		−	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	0.391292	−	0.920267i	$-0.372028\pi$
$401$	27.7128	−	16.0000i	1.38391	−	0.799002i	0.992620	+	0.121265i	$0.0386950\pi$
$402$	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	0.411905	−	0.911227i	$-0.364864\pi$
$409$	−3.46410	−	2.00000i	−0.171289	−	0.0988936i	−0.583193	+	0.812333i	$0.698197\pi$
$410$	−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	0.845722	−	0.533624i	$-0.179170\pi$
$419$	−0.803848	−	1.39230i	−0.0392705	−	0.0680185i	−0.884993	+	0.465605i	$0.845837\pi$
$420$	−1.00000	+	1.73205i	−0.0487950	+	0.0845154i
$421$		−	16.3923i		−	0.798912i	−0.916752	−	0.399456i	$-0.869199\pi$
$421$		−	16.3923i		−	0.798912i	0.916752	−	0.399456i	$-0.130801\pi$
$422$	−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	−0.650213	−	0.759752i	$-0.725320\pi$
$431$	−6.58846	+	3.80385i	−0.317355	+	0.183225i	0.332858	+	0.942977i	$0.391987\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	7.66025	−	13.2679i	0.368128	−	0.637617i	−0.621145	−	0.783696i	$-0.713332\pi$
$433$	7.66025	−	13.2679i	0.368128	−	0.637617i	0.989273	+	0.146079i	$0.0466654\pi$
$434$			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	0.724123	−	0.689670i	$-0.242245\pi$
$439$	−4.92820	−	8.53590i	−0.235210	−	0.407396i	−0.959334	+	0.282274i	$0.908911\pi$
$440$	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	−0.986092	−	0.166203i	$-0.946849\pi$
$449$	−34.3923	−	19.8564i	−1.62307	−	0.937082i	−0.636982	−	0.770879i	$-0.719817\pi$
$450$		−	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	−0.975858	−	0.218407i	$-0.929914\pi$
$457$	−27.2487	+	15.7321i	−1.27464	+	0.735914i	−0.298783	+	0.954321i	$0.596581\pi$
$458$	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	0.624667	−	0.780891i	$-0.285235\pi$
$461$	5.59808	+	3.23205i	0.260728	+	0.150532i	−0.363938	+	0.931423i	$0.618568\pi$
$462$	0.803848	+	0.464102i	0.0373984	+	0.0215920i
$463$			20.9282i			0.972616i	0.873787	+	0.486308i	$0.161657\pi$
$463$			20.9282i			0.972616i	−0.873787	+	0.486308i	$0.838343\pi$
$464$	−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	−0.470753	−	0.882265i	$-0.656018\pi$
$479$	1.26795	−	0.732051i	0.0579341	−	0.0334483i	0.528687	+	0.848817i	$0.322684\pi$
$480$	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	0.998988	+	0.0449775i	$0.0143216\pi$
$487$	33.9282	+	19.5885i	1.53743	+	0.887638i	0.538446	+	0.842660i	$0.319012\pi$
$488$	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	0.601728	−	0.798701i	$-0.294479\pi$
$491$	−8.66025	−	15.0000i	−0.390832	−	0.676941i	−0.992559	+	0.121761i	$0.961146\pi$
$492$	−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	$0.0974433\pi$
$499$			13.4641i			0.602736i	−0.953508	+	0.301368i	$0.902557\pi$
$500$	−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	0.275107	+	0.961414i	$0.411287\pi$
$503$	−15.5885	+	27.0000i	−0.695055	+	1.20387i	−0.970162	+	0.242457i	$0.922047\pi$
$504$	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	−0.0792726	−	0.996853i	$-0.525260\pi$
$509$	16.7942	−	9.69615i	0.744391	−	0.429774i	0.823664	+	0.567079i	$0.191926\pi$
$510$	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	0.982833	+	0.184496i	$0.0590653\pi$
$523$	14.8923	+	25.7942i	0.651195	+	1.12790i	−0.331638	+	0.943407i	$0.607601\pi$
$524$	−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	$0.0906662\pi$
$541$			13.0718i			0.562000i	−0.959708	+	0.281000i	$0.909334\pi$
$542$	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	0.391245	−	0.920286i	$-0.372044\pi$
$557$	32.6603	−	18.8564i	1.38386	−	0.798972i	0.992614	+	0.121315i	$0.0387111\pi$
$558$	−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	−0.0705706	−	0.997507i	$-0.522482\pi$
$563$	19.6603	−	34.0526i	0.828581	−	1.43514i	0.899152	−	0.437637i	$-0.144185\pi$
$564$		−	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	0.916385	−	0.400299i	$-0.131094\pi$
$569$	2.66025	+	4.60770i	0.111524	+	0.193165i	−0.804861	+	0.593463i	$0.797760\pi$
$570$	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	$-0.933255\pi$
$577$		−	10.0000i		−	0.416305i	0.978096	−	0.208153i	$-0.0667451\pi$
$578$	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	−0.791296	−	0.611433i	$-0.790593\pi$
$587$	−15.9282	+	9.19615i	−0.657427	+	0.379566i	0.133869	+	0.990999i	$0.457260\pi$
$588$	−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	$-0.779486\pi$
$593$		−	31.1051i		−	1.27733i	0.769483	−	0.638667i	$-0.220514\pi$
$594$	−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	0.553697	−	0.832718i	$-0.313216\pi$
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	−0.998004	+	0.0631568i	$0.979883\pi$
$602$	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	−0.0208216	+	0.999783i	$0.506628\pi$
$607$	−21.5885	+	37.3923i	−0.876248	+	1.51771i	−0.855427	+	0.517924i	$0.826705\pi$
$608$	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	−0.483338	−	0.875434i	$-0.660576\pi$
$613$	0.820508	−	0.473721i	0.0331400	−	0.0191334i	0.516478	+	0.856300i	$0.327243\pi$
$614$	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	0.745750	−	0.666226i	$-0.232091\pi$
$617$	13.4545	+	7.76795i	0.541657	+	0.312726i	−0.204093	+	0.978951i	$0.565425\pi$
$618$	13.7321	+	7.92820i	0.552384	+	0.318919i
$619$			24.2487i			0.974638i	0.873224	+	0.487319i	$0.162025\pi$
$619$			24.2487i			0.974638i	−0.873224	+	0.487319i	$0.837975\pi$
$620$	−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	0.0133668	−	0.999911i	$-0.495745\pi$
$631$	−21.2487	−	12.2679i	−0.845898	−	0.488379i	−0.859265	+	0.511531i	$0.829078\pi$
$632$			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	0.448134	+	0.893967i	$0.352089\pi$
$641$	−13.9282	+	24.1244i	−0.550131	+	0.952855i	−0.998265	+	0.0588882i	$0.981244\pi$
$642$		−	19.8564i		−	0.783670i
$643$	23.7846	+	13.7321i	0.937973	+	0.541539i	0.889324	−	0.457277i	$-0.151175\pi$
$643$	23.7846	+	13.7321i	0.937973	+	0.541539i	0.0486490	+	0.998816i	$0.484508\pi$
$644$	−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	0.576751	−	0.816920i	$-0.304320\pi$
$647$	−10.6603	−	18.4641i	−0.419098	−	0.725899i	−0.995849	+	0.0910212i	$0.970987\pi$
$648$	−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	0.866258	+	0.499597i	$0.166519\pi$
$653$	22.1244	+	38.3205i	0.865793	+	1.49960i	−0.000464739		1.00000i	$0.500148\pi$
$654$	−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	−0.827389	−	0.561629i	$-0.810175\pi$
$659$	1.86603	−	3.23205i	0.0726900	−	0.125903i	0.900079	+	0.435726i	$0.143508\pi$
$660$	0.232051	+	0.401924i	0.00903257	+	0.0156449i
$661$	37.5167	−	21.6603i	1.45923	−	0.842486i	0.460256	−	0.887786i	$-0.347758\pi$
$661$	37.5167	−	21.6603i	1.45923	−	0.842486i	0.998973	+	0.0453002i	$0.0144244\pi$
$662$	−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	−0.990074	−	0.140548i	$-0.955114\pi$
$673$	−16.0000	−	27.7128i	−0.616755	−	1.06825i	0.373319	−	0.927703i	$-0.378220\pi$
$674$	−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	0.486944	−	0.873433i	$-0.338112\pi$
$683$	−0.679492	−	0.392305i	−0.0260000	−	0.0150111i	−0.512944	+	0.858422i	$0.671445\pi$
$684$		−	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	−0.951042	−	0.309061i	$-0.899985\pi$
$691$	−30.4641	+	17.5885i	−1.15891	+	0.669096i	−0.207867	+	0.978157i	$0.566652\pi$
$692$	−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	0.640219	−	0.768193i	$-0.278844\pi$
$709$	7.85641	+	4.53590i	0.295054	+	0.170349i	−0.345165	+	0.938542i	$0.612177\pi$
$710$		−	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	0.338136	+	0.941097i	$0.390204\pi$
$719$	−17.3205	+	30.0000i	−0.645946	+	1.11881i	−0.984082	+	0.177714i	$0.943130\pi$
$720$			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	$-0.759960\pi$
$733$		−	37.0718i		−	1.36928i	0.728882	−	0.684639i	$-0.240040\pi$
$734$	−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	−0.723773	−	0.690038i	$-0.757594\pi$
$739$	−13.2679	+	7.66025i	−0.488069	+	0.281787i	0.235704	+	0.971825i	$0.424260\pi$
$740$	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	0.138539	−	0.990357i	$-0.455760\pi$
$743$	29.0429	−	16.7679i	1.06548	−	0.615156i	0.926944	+	0.375201i	$0.122426\pi$
$744$	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	−0.999939	−	0.0110712i	$-0.996476\pi$
$751$	−13.9641	−	24.1865i	−0.509557	−	0.882579i	0.490381	−	0.871508i	$-0.336857\pi$
$752$	−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	0.981937	−	0.189207i	$-0.0605917\pi$
$757$	9.00000	+	15.5885i	0.327111	+	0.566572i	−0.654827	+	0.755779i	$0.727258\pi$
$758$	−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	0.172544	−	0.985002i	$-0.444801\pi$
$761$	−16.3923	−	9.46410i	−0.594221	−	0.343073i	−0.766765	+	0.641928i	$0.778135\pi$
$762$		−	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	−0.773647	−	0.633617i	$-0.781569\pi$
$769$	−16.9641	+	9.79423i	−0.611741	+	0.353189i	0.161905	+	0.986806i	$0.448236\pi$
$770$	0.464102	+

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

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Representations

Groups

Database

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