LMFDB - Embedded newform 390.2.i.g.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(61,390)]

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, 4]))

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

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

chi := DirichletCharacter("390.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$-0.780776 + 1.35234i$ of defining polynomial
Character	$\chi$	$=$	390.211
Dual form			390.2.i.g.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.280776 - 0.486319i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.280776 - 0.486319i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.06155 - 3.57071i) q^{11} +1.00000 q^{12} +(2.84233 - 2.21837i) q^{13} -0.561553 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.56155 - 2.70469i) q^{17} +1.00000 q^{18} +(-0.280776 + 0.486319i) q^{19} +(-0.500000 + 0.866025i) q^{20} -0.561553 q^{21} +(-2.06155 + 3.57071i) q^{22} +(-2.34233 - 4.05703i) q^{23} +(-0.500000 - 0.866025i) q^{24} +1.00000 q^{25} +(-3.34233 - 1.35234i) q^{26} +1.00000 q^{27} +(0.280776 + 0.486319i) q^{28} +(-1.21922 - 2.11176i) q^{29} +(-0.500000 + 0.866025i) q^{30} -6.68466 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.06155 + 3.57071i) q^{33} -3.12311 q^{34} +(0.280776 - 0.486319i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.06155 + 3.57071i) q^{37} +0.561553 q^{38} +(-3.34233 - 1.35234i) q^{39} +1.00000 q^{40} +(-6.12311 - 10.6055i) q^{41} +(0.280776 + 0.486319i) q^{42} +(-0.219224 + 0.379706i) q^{43} +4.12311 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-2.34233 + 4.05703i) q^{46} +7.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.34233 + 5.78908i) q^{49} +(-0.500000 - 0.866025i) q^{50} -3.12311 q^{51} +(0.500000 + 3.57071i) q^{52} +8.56155 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.06155 - 3.57071i) q^{55} +(0.280776 - 0.486319i) q^{56} +0.561553 q^{57} +(-1.21922 + 2.11176i) q^{58} +(-3.21922 + 5.57586i) q^{59} +1.00000 q^{60} +(-3.00000 + 5.19615i) q^{61} +(3.34233 + 5.78908i) q^{62} +(0.280776 + 0.486319i) q^{63} +1.00000 q^{64} +(2.84233 - 2.21837i) q^{65} +4.12311 q^{66} +(1.12311 + 1.94528i) q^{67} +(1.56155 + 2.70469i) q^{68} +(-2.34233 + 4.05703i) q^{69} -0.561553 q^{70} +(6.56155 - 11.3649i) q^{71} +(-0.500000 + 0.866025i) q^{72} +9.36932 q^{73} +(2.06155 - 3.57071i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-0.280776 - 0.486319i) q^{76} -2.31534 q^{77} +(0.500000 + 3.57071i) q^{78} +11.5616 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.12311 + 10.6055i) q^{82} -7.12311 q^{83} +(0.280776 - 0.486319i) q^{84} +(1.56155 - 2.70469i) q^{85} +0.438447 q^{86} +(-1.21922 + 2.11176i) q^{87} +(-2.06155 - 3.57071i) q^{88} +(9.40388 + 16.2880i) q^{89} +1.00000 q^{90} +(-0.280776 - 2.00514i) q^{91} +4.68466 q^{92} +(3.34233 + 5.78908i) q^{93} +(-3.50000 - 6.06218i) q^{94} +(-0.280776 + 0.486319i) q^{95} +1.00000 q^{96} +(3.56155 - 6.16879i) q^{97} +(3.34233 - 5.78908i) q^{98} +4.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 3 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 3 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 3 q^{7} + 4 q^{8} - 2 q^{9} - 2 q^{10} + 4 q^{12} - q^{13} + 6 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 4 q^{18} + 3 q^{19} - 2 q^{20} + 6 q^{21} + 3 q^{23} - 2 q^{24} + 4 q^{25} - q^{26} + 4 q^{27} - 3 q^{28} - 9 q^{29} - 2 q^{30} - 2 q^{31} - 2 q^{32} + 4 q^{34} - 3 q^{35} - 2 q^{36} - 6 q^{38} - q^{39} + 4 q^{40} - 8 q^{41} - 3 q^{42} - 5 q^{43} - 2 q^{45} + 3 q^{46} + 28 q^{47} - 2 q^{48} + q^{49} - 2 q^{50} + 4 q^{51} + 2 q^{52} + 26 q^{53} - 2 q^{54} - 3 q^{56} - 6 q^{57} - 9 q^{58} - 17 q^{59} + 4 q^{60} - 12 q^{61} + q^{62} - 3 q^{63} + 4 q^{64} - q^{65} - 12 q^{67} - 2 q^{68} + 3 q^{69} + 6 q^{70} + 18 q^{71} - 2 q^{72} - 12 q^{73} - 2 q^{75} + 3 q^{76} - 34 q^{77} + 2 q^{78} + 38 q^{79} - 2 q^{80} - 2 q^{81} - 8 q^{82} - 12 q^{83} - 3 q^{84} - 2 q^{85} + 10 q^{86} - 9 q^{87} + 17 q^{89} + 4 q^{90} + 3 q^{91} - 6 q^{92} + q^{93} - 14 q^{94} + 3 q^{95} + 4 q^{96} + 6 q^{97} + q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 3 * q^7 + 4 * q^8 - 2 * q^9 - 2 * q^10 + 4 * q^12 - q^13 + 6 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 4 * q^18 + 3 * q^19 - 2 * q^20 + 6 * q^21 + 3 * q^23 - 2 * q^24 + 4 * q^25 - q^26 + 4 * q^27 - 3 * q^28 - 9 * q^29 - 2 * q^30 - 2 * q^31 - 2 * q^32 + 4 * q^34 - 3 * q^35 - 2 * q^36 - 6 * q^38 - q^39 + 4 * q^40 - 8 * q^41 - 3 * q^42 - 5 * q^43 - 2 * q^45 + 3 * q^46 + 28 * q^47 - 2 * q^48 + q^49 - 2 * q^50 + 4 * q^51 + 2 * q^52 + 26 * q^53 - 2 * q^54 - 3 * q^56 - 6 * q^57 - 9 * q^58 - 17 * q^59 + 4 * q^60 - 12 * q^61 + q^62 - 3 * q^63 + 4 * q^64 - q^65 - 12 * q^67 - 2 * q^68 + 3 * q^69 + 6 * q^70 + 18 * q^71 - 2 * q^72 - 12 * q^73 - 2 * q^75 + 3 * q^76 - 34 * q^77 + 2 * q^78 + 38 * q^79 - 2 * q^80 - 2 * q^81 - 8 * q^82 - 12 * q^83 - 3 * q^84 - 2 * q^85 + 10 * q^86 - 9 * q^87 + 17 * q^89 + 4 * q^90 + 3 * q^91 - 6 * q^92 + q^93 - 14 * q^94 + 3 * q^95 + 4 * q^96 + 6 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−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
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	0.280776	−	0.486319i	0.106124	−	0.183811i	−0.808073	−	0.589082i	$-0.799489\pi$
$7$	0.280776	−	0.486319i	0.106124	−	0.183811i	0.914197	+	0.405271i	$0.132823\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−2.06155	−	3.57071i	−0.621582	−	1.07661i	−0.989191	−	0.146631i	$-0.953157\pi$
$11$	−2.06155	−	3.57071i	−0.621582	−	1.07661i	0.367610	−	0.929980i	$-0.380176\pi$
$12$	1.00000			0.288675
$13$	2.84233	−	2.21837i	0.788320	−	0.615265i
$13$	2.84233	−	2.21837i	0.788320	−	0.615265i
$14$	−0.561553			−0.150081
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.56155	−	2.70469i	0.378732	−	0.655983i	−0.612146	−	0.790745i	$-0.709693\pi$
$17$	1.56155	−	2.70469i	0.378732	−	0.655983i	0.990878	+	0.134761i	$0.0430268\pi$
$18$	1.00000			0.235702
$19$	−0.280776	+	0.486319i	−0.0644145	+	0.111569i	−0.896434	−	0.443177i	$-0.853851\pi$
$19$	−0.280776	+	0.486319i	−0.0644145	+	0.111569i	0.832020	+	0.554746i	$0.187185\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−0.561553			−0.122541
$22$	−2.06155	+	3.57071i	−0.439525	+	0.761279i
$23$	−2.34233	−	4.05703i	−0.488409	−	0.845950i	0.511502	−	0.859282i	$-0.329089\pi$
$23$	−2.34233	−	4.05703i	−0.488409	−	0.845950i	−0.999911	+	0.0133324i	$0.995756\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	1.00000			0.200000
$26$	−3.34233	−	1.35234i	−0.655485	−	0.265217i
$27$	1.00000			0.192450
$28$	0.280776	+	0.486319i	0.0530618	+	0.0919057i
$29$	−1.21922	−	2.11176i	−0.226404	−	0.392143i	0.730336	−	0.683088i	$-0.239364\pi$
$29$	−1.21922	−	2.11176i	−0.226404	−	0.392143i	−0.956740	+	0.290945i	$0.906030\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−6.68466			−1.20060			−0.600300	−	0.799775i	$-0.704952\pi$
$31$	−6.68466			−1.20060			−0.600300	+	0.799775i	$0.704952\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.06155	+	3.57071i	−0.358870	+	0.621582i
$34$	−3.12311			−0.535608
$35$	0.280776	−	0.486319i	0.0474599	−	0.0822029i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.06155	+	3.57071i	0.338917	+	0.587022i	0.984229	−	0.176897i	$-0.0566060\pi$
$37$	2.06155	+	3.57071i	0.338917	+	0.587022i	−0.645312	+	0.763919i	$0.723273\pi$
$38$	0.561553			0.0910959
$39$	−3.34233	−	1.35234i	−0.535201	−	0.216548i
$40$	1.00000			0.158114
$41$	−6.12311	−	10.6055i	−0.956268	−	1.65631i	−0.731438	−	0.681908i	$-0.761151\pi$
$41$	−6.12311	−	10.6055i	−0.956268	−	1.65631i	−0.224830	−	0.974398i	$-0.572183\pi$
$42$	0.280776	+	0.486319i	0.0433247	+	0.0750407i
$43$	−0.219224	+	0.379706i	−0.0334313	+	0.0579047i	−0.882257	−	0.470768i	$-0.843977\pi$
$43$	−0.219224	+	0.379706i	−0.0334313	+	0.0579047i	0.848826	+	0.528673i	$0.177310\pi$
$44$	4.12311			0.621582
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−2.34233	+	4.05703i	−0.345358	+	0.598177i
$47$	7.00000			1.02105			0.510527	−	0.859861i	$-0.329450\pi$
$47$	7.00000			1.02105			0.510527	+	0.859861i	$0.329450\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	3.34233	+	5.78908i	0.477476	+	0.827012i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−3.12311			−0.437322
$52$	0.500000	+	3.57071i	0.0693375	+	0.495169i
$53$	8.56155			1.17602			0.588010	−	0.808854i	$-0.299912\pi$
$53$	8.56155			1.17602			0.588010	+	0.808854i	$0.299912\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−2.06155	−	3.57071i	−0.277980	−	0.481475i
$56$	0.280776	−	0.486319i	0.0375203	−	0.0649871i
$57$	0.561553			0.0743795
$58$	−1.21922	+	2.11176i	−0.160092	+	0.277287i
$59$	−3.21922	+	5.57586i	−0.419107	+	0.725915i	−0.995850	−	0.0910109i	$-0.970990\pi$
$59$	−3.21922	+	5.57586i	−0.419107	+	0.725915i	0.576743	+	0.816926i	$0.304324\pi$
$60$	1.00000			0.129099
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	3.34233	+	5.78908i	0.424476	+	0.735214i
$63$	0.280776	+	0.486319i	0.0353745	+	0.0612704i
$64$	1.00000			0.125000
$65$	2.84233	−	2.21837i	0.352548	−	0.275155i
$66$	4.12311			0.507519
$67$	1.12311	+	1.94528i	0.137209	+	0.237653i	0.926439	−	0.376444i	$-0.122853\pi$
$67$	1.12311	+	1.94528i	0.137209	+	0.237653i	−0.789230	+	0.614098i	$0.789520\pi$
$68$	1.56155	+	2.70469i	0.189366	+	0.327992i
$69$	−2.34233	+	4.05703i	−0.281983	+	0.488409i
$70$	−0.561553			−0.0671184
$71$	6.56155	−	11.3649i	0.778713	−	1.34877i	−0.153971	−	0.988075i	$-0.549206\pi$
$71$	6.56155	−	11.3649i	0.778713	−	1.34877i	0.932684	−	0.360695i	$-0.117461\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	9.36932			1.09660			0.548298	−	0.836283i	$-0.315276\pi$
$73$	9.36932			1.09660			0.548298	+	0.836283i	$0.315276\pi$
$74$	2.06155	−	3.57071i	0.239651	−	0.415087i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−0.280776	−	0.486319i	−0.0322073	−	0.0557846i
$77$	−2.31534			−0.263858
$78$	0.500000	+	3.57071i	0.0566139	+	0.404304i
$79$	11.5616			1.30078			0.650388	−	0.759602i	$-0.274606\pi$
$79$	11.5616			1.30078			0.650388	+	0.759602i	$0.274606\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.12311	+	10.6055i	−0.676184	+	1.17118i
$83$	−7.12311			−0.781862			−0.390931	−	0.920420i	$-0.627847\pi$
$83$	−7.12311			−0.781862			−0.390931	+	0.920420i	$0.627847\pi$
$84$	0.280776	−	0.486319i	0.0306352	−	0.0530618i
$85$	1.56155	−	2.70469i	0.169374	−	0.293365i
$86$	0.438447			0.0472790
$87$	−1.21922	+	2.11176i	−0.130714	+	0.226404i
$88$	−2.06155	−	3.57071i	−0.219762	−	0.380639i
$89$	9.40388	+	16.2880i	0.996810	+	1.72652i	0.567529	+	0.823354i	$0.307900\pi$
$89$	9.40388	+	16.2880i	0.996810	+	1.72652i	0.429281	+	0.903171i	$0.358767\pi$
$90$	1.00000			0.105409
$91$	−0.280776	−	2.00514i	−0.0294334	−	0.210196i
$92$	4.68466			0.488409
$93$	3.34233	+	5.78908i	0.346583	+	0.600300i
$94$	−3.50000	−	6.06218i	−0.360997	−	0.625266i
$95$	−0.280776	+	0.486319i	−0.0288071	+	0.0498953i
$96$	1.00000			0.102062
$97$	3.56155	−	6.16879i	0.361621	−	0.626346i	−0.626607	−	0.779335i	$-0.715557\pi$
$97$	3.56155	−	6.16879i	0.361621	−	0.626346i	0.988228	+	0.152990i	$0.0488901\pi$
$98$	3.34233	−	5.78908i	0.337626	−	0.584786i
$99$	4.12311			0.414388
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	4.43845	+	7.68762i	0.441642	+	0.764946i	0.997812	−	0.0661225i	$-0.0210628\pi$
$101$	4.43845	+	7.68762i	0.441642	+	0.764946i	−0.556170	+	0.831069i	$0.687729\pi$
$102$	1.56155	+	2.70469i	0.154617	+	0.267804i
$103$	4.56155			0.449463			0.224732	−	0.974421i	$-0.427849\pi$
$103$	4.56155			0.449463			0.224732	+	0.974421i	$0.427849\pi$
$104$	2.84233	−	2.21837i	0.278713	−	0.217529i
$105$	−0.561553			−0.0548019
$106$	−4.28078	−	7.41452i	−0.415786	−	0.720162i
$107$	−1.00000	−	1.73205i	−0.0966736	−	0.167444i	0.813632	−	0.581380i	$-0.197487\pi$
$107$	−1.00000	−	1.73205i	−0.0966736	−	0.167444i	−0.910306	+	0.413936i	$0.864154\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−3.75379			−0.359548			−0.179774	−	0.983708i	$-0.557537\pi$
$109$	−3.75379			−0.359548			−0.179774	+	0.983708i	$0.557537\pi$
$110$	−2.06155	+	3.57071i	−0.196561	+	0.340454i
$111$	2.06155	−	3.57071i	0.195674	−	0.338917i
$112$	−0.561553			−0.0530618
$113$	−4.34233	+	7.52113i	−0.408492	+	0.707529i	−0.994721	−	0.102617i	$-0.967279\pi$
$113$	−4.34233	+	7.52113i	−0.408492	+	0.707529i	0.586229	+	0.810145i	$0.300612\pi$
$114$	−0.280776	−	0.486319i	−0.0262971	−	0.0455479i
$115$	−2.34233	−	4.05703i	−0.218423	−	0.378320i
$116$	2.43845			0.226404
$117$	0.500000	+	3.57071i	0.0462250	+	0.330113i
$118$	6.43845			0.592707
$119$	−0.876894	−	1.51883i	−0.0803848	−	0.139231i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	−3.00000	+	5.19615i	−0.272727	+	0.472377i
$122$	6.00000			0.543214
$123$	−6.12311	+	10.6055i	−0.552102	+	0.956268i
$124$	3.34233	−	5.78908i	0.300150	−	0.519875i
$125$	1.00000			0.0894427
$126$	0.280776	−	0.486319i	0.0250136	−	0.0433247i
$127$	4.28078	+	7.41452i	0.379857	+	0.657932i	0.991041	−	0.133556i	$-0.0426397\pi$
$127$	4.28078	+	7.41452i	0.379857	+	0.657932i	−0.611184	+	0.791489i	$0.709306\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.438447			0.0386031
$130$	−3.34233	−	1.35234i	−0.293142	−	0.118608i
$131$	−2.12311			−0.185497			−0.0927483	−	0.995690i	$-0.529565\pi$
$131$	−2.12311			−0.185497			−0.0927483	+	0.995690i	$0.529565\pi$
$132$	−2.06155	−	3.57071i	−0.179435	−	0.310791i
$133$	0.157671	+	0.273094i	0.0136718	+	0.0236802i
$134$	1.12311	−	1.94528i	0.0970215	−	0.168046i
$135$	1.00000			0.0860663
$136$	1.56155	−	2.70469i	0.133902	−	0.231925i
$137$	−5.90388	+	10.2258i	−0.504403	+	0.873651i	0.495584	+	0.868560i	$0.334954\pi$
$137$	−5.90388	+	10.2258i	−0.504403	+	0.873651i	−0.999987	+	0.00509126i	$0.998379\pi$
$138$	4.68466			0.398785
$139$	−6.28078	+	10.8786i	−0.532729	+	0.922713i	0.466541	+	0.884500i	$0.345500\pi$
$139$	−6.28078	+	10.8786i	−0.532729	+	0.922713i	−0.999270	+	0.0382133i	$0.987833\pi$
$140$	0.280776	+	0.486319i	0.0237299	+	0.0411015i
$141$	−3.50000	−	6.06218i	−0.294753	−	0.510527i
$142$	−13.1231			−1.10127
$143$	−13.7808	−	5.57586i	−1.15241	−	0.466277i
$144$	1.00000			0.0833333
$145$	−1.21922	−	2.11176i	−0.101251	−	0.175372i
$146$	−4.68466	−	8.11407i	−0.387705	−	0.671525i
$147$	3.34233	−	5.78908i	0.275671	−	0.477476i
$148$	−4.12311			−0.338917
$149$	1.09612	−	1.89853i	0.0897975	−	0.155534i	−0.817628	−	0.575747i	$-0.804711\pi$
$149$	1.09612	−	1.89853i	0.0897975	−	0.155534i	0.907425	+	0.420213i	$0.138045\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−15.3693			−1.25074			−0.625369	−	0.780329i	$-0.715051\pi$
$151$	−15.3693			−1.25074			−0.625369	+	0.780329i	$0.715051\pi$
$152$	−0.280776	+	0.486319i	−0.0227740	+	0.0394457i
$153$	1.56155	+	2.70469i	0.126244	+	0.218661i
$154$	1.15767	+	2.00514i	0.0932878	+	0.161579i
$155$	−6.68466			−0.536925
$156$	2.84233	−	2.21837i	0.227568	−	0.177612i
$157$	13.8769			1.10750			0.553748	−	0.832684i	$-0.313197\pi$
$157$	13.8769			1.10750			0.553748	+	0.832684i	$0.313197\pi$
$158$	−5.78078	−	10.0126i	−0.459894	−	0.796560i
$159$	−4.28078	−	7.41452i	−0.339488	−	0.588010i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−2.63068			−0.207327
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	7.21922	−	12.5041i	0.565453	−	0.979394i	−0.431554	−	0.902087i	$-0.642035\pi$
$163$	7.21922	−	12.5041i	0.565453	−	0.979394i	0.997007	−	0.0773067i	$-0.0246321\pi$
$164$	12.2462			0.956268
$165$	−2.06155	+	3.57071i	−0.160492	+	0.277980i
$166$	3.56155	+	6.16879i	0.276430	+	0.478791i
$167$	−2.18466	−	3.78394i	−0.169054	−	0.292810i	0.769034	−	0.639208i	$-0.220738\pi$
$167$	−2.18466	−	3.78394i	−0.169054	−	0.292810i	−0.938087	+	0.346398i	$0.887405\pi$
$168$	−0.561553			−0.0433247
$169$	3.15767	−	12.6107i	0.242898	−	0.970052i
$170$	−3.12311			−0.239531
$171$	−0.280776	−	0.486319i	−0.0214715	−	0.0371897i
$172$	−0.219224	−	0.379706i	−0.0167156	−	0.0289523i
$173$	−10.0885	+	17.4739i	−0.767018	+	1.32851i	0.172156	+	0.985070i	$0.444927\pi$
$173$	−10.0885	+	17.4739i	−0.767018	+	1.32851i	−0.939173	+	0.343444i	$0.888407\pi$
$174$	2.43845			0.184858
$175$	0.280776	−	0.486319i	0.0212247	−	0.0367623i
$176$	−2.06155	+	3.57071i	−0.155395	+	0.269153i
$177$	6.43845			0.483943
$178$	9.40388	−	16.2880i	0.704851	−	1.22084i
$179$	6.34233	+	10.9852i	0.474048	+	0.821075i	0.999559	−	0.0297120i	$-0.00945900\pi$
$179$	6.34233	+	10.9852i	0.474048	+	0.821075i	−0.525511	+	0.850787i	$0.676126\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	2.87689			0.213838			0.106919	−	0.994268i	$-0.465901\pi$
$181$	2.87689			0.213838			0.106919	+	0.994268i	$0.465901\pi$
$182$	−1.59612	+	1.24573i	−0.118312	+	0.0923398i
$183$	6.00000			0.443533
$184$	−2.34233	−	4.05703i	−0.172679	−	0.299088i
$185$	2.06155	+	3.57071i	0.151568	+	0.262524i
$186$	3.34233	−	5.78908i	0.245071	−	0.424476i
$187$	−12.8769			−0.941652
$188$	−3.50000	+	6.06218i	−0.255264	+	0.442130i
$189$	0.280776	−	0.486319i	0.0204235	−	0.0353745i
$190$	0.561553			0.0407393
$191$	−5.43845	+	9.41967i	−0.393512	+	0.681583i	−0.992910	−	0.118868i	$-0.962073\pi$
$191$	−5.43845	+	9.41967i	−0.393512	+	0.681583i	0.599398	+	0.800451i	$0.295407\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$193$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$194$	−7.12311			−0.511409
$195$	−3.34233	−	1.35234i	−0.239349	−	0.0968434i
$196$	−6.68466			−0.477476
$197$	−6.40388	−	11.0918i	−0.456258	−	0.790262i	0.542502	−	0.840055i	$-0.317477\pi$
$197$	−6.40388	−	11.0918i	−0.456258	−	0.790262i	−0.998760	+	0.0497931i	$0.984144\pi$
$198$	−2.06155	−	3.57071i	−0.146508	−	0.253760i
$199$	−1.43845	+	2.49146i	−0.101969	+	0.176615i	−0.912496	−	0.409086i	$-0.865848\pi$
$199$	−1.43845	+	2.49146i	−0.101969	+	0.176615i	0.810527	+	0.585701i	$0.199181\pi$
$200$	1.00000			0.0707107
$201$	1.12311	−	1.94528i	0.0792178	−	0.137209i
$202$	4.43845	−	7.68762i	0.312288	−	0.540899i
$203$	−1.36932			−0.0961072
$204$	1.56155	−	2.70469i	0.109331	−	0.189366i
$205$	−6.12311	−	10.6055i	−0.427656	−	0.740722i
$206$	−2.28078	−	3.95042i	−0.158909	−	0.275239i
$207$	4.68466			0.325606
$208$	−3.34233	−	1.35234i	−0.231749	−	0.0937682i
$209$	2.31534			0.160156
$210$	0.280776	+	0.486319i	0.0193754	+	0.0335592i
$211$	10.9654	+	18.9927i	0.754892	+	1.30751i	0.945428	+	0.325831i	$0.105644\pi$
$211$	10.9654	+	18.9927i	0.754892	+	1.30751i	−0.190536	+	0.981680i	$0.561023\pi$
$212$	−4.28078	+	7.41452i	−0.294005	+	0.509231i
$213$	−13.1231			−0.899180
$214$	−1.00000	+	1.73205i	−0.0683586	+	0.118401i
$215$	−0.219224	+	0.379706i	−0.0149509	+	0.0258958i
$216$	1.00000			0.0680414
$217$	−1.87689	+	3.25088i	−0.127412	+	0.220684i
$218$	1.87689	+	3.25088i	0.127119	+	0.220177i
$219$	−4.68466	−	8.11407i	−0.316560	−	0.548298i
$220$	4.12311			0.277980
$221$	−1.56155	−	11.1517i	−0.105041	−	0.750146i
$222$	−4.12311			−0.276725
$223$	−13.6501	−	23.6427i	−0.914078	−	1.58323i	−0.808246	−	0.588845i	$-0.799583\pi$
$223$	−13.6501	−	23.6427i	−0.914078	−	1.58323i	−0.105832	−	0.994384i	$-0.533751\pi$
$224$	0.280776	+	0.486319i	0.0187602	+	0.0324936i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	8.68466			0.577695
$227$	10.0000	−	17.3205i	0.663723	−	1.14960i	−0.315906	−	0.948790i	$-0.602309\pi$
$227$	10.0000	−	17.3205i	0.663723	−	1.14960i	0.979630	−	0.200812i	$-0.0643581\pi$
$228$	−0.280776	+	0.486319i	−0.0185949	+	0.0322073i
$229$	−24.2462			−1.60223			−0.801117	−	0.598507i	$-0.795761\pi$
$229$	−24.2462			−1.60223			−0.801117	+	0.598507i	$0.795761\pi$
$230$	−2.34233	+	4.05703i	−0.154449	+	0.267513i
$231$	1.15767	+	2.00514i	0.0761691	+	0.131929i
$232$	−1.21922	−	2.11176i	−0.0800460	−	0.138644i
$233$	−5.31534			−0.348220			−0.174110	−	0.984726i	$-0.555705\pi$
$233$	−5.31534			−0.348220			−0.174110	+	0.984726i	$0.555705\pi$
$234$	2.84233	−	2.21837i	0.185809	−	0.145019i
$235$	7.00000			0.456630
$236$	−3.21922	−	5.57586i	−0.209554	−	0.362957i
$237$	−5.78078	−	10.0126i	−0.375502	−	0.650388i
$238$	−0.876894	+	1.51883i	−0.0568406	+	0.0984508i
$239$	−11.3693			−0.735420			−0.367710	−	0.929941i	$-0.619858\pi$
$239$	−11.3693			−0.735420			−0.367710	+	0.929941i	$0.619858\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	14.0616	−	24.3553i	0.905784	−	1.56886i	0.0859232	−	0.996302i	$-0.472616\pi$
$241$	14.0616	−	24.3553i	0.905784	−	1.56886i	0.819861	−	0.572563i	$-0.194051\pi$
$242$	6.00000			0.385695
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−3.00000	−	5.19615i	−0.192055	−	0.332650i
$245$	3.34233	+	5.78908i	0.213534	+	0.369851i
$246$	12.2462			0.780790
$247$	0.280776	+	2.00514i	0.0178654	+	0.127584i
$248$	−6.68466			−0.424476
$249$	3.56155	+	6.16879i	0.225704	+	0.390931i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	4.06155	−	7.03482i	0.256363	−	0.444034i	−0.708902	−	0.705307i	$-0.750809\pi$
$251$	4.06155	−	7.03482i	0.256363	−	0.444034i	0.965265	+	0.261273i	$0.0841424\pi$
$252$	−0.561553			−0.0353745
$253$	−9.65767	+	16.7276i	−0.607173	+	1.05165i
$254$	4.28078	−	7.41452i	0.268600	−	0.465229i
$255$	−3.12311			−0.195576
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.78078	+	4.81645i	0.173460	+	0.300442i	0.939627	−	0.342200i	$-0.111172\pi$
$257$	2.78078	+	4.81645i	0.173460	+	0.300442i	−0.766167	+	0.642641i	$0.777839\pi$
$258$	−0.219224	−	0.379706i	−0.0136483	−	0.0236395i
$259$	2.31534			0.143868
$260$	0.500000	+	3.57071i	0.0310087	+	0.221446i
$261$	2.43845			0.150936
$262$	1.06155	+	1.83866i	0.0655830	+	0.113593i
$263$	6.50000	+	11.2583i	0.400807	+	0.694218i	0.993824	−	0.110972i	$-0.0353964\pi$
$263$	6.50000	+	11.2583i	0.400807	+	0.694218i	−0.593016	+	0.805190i	$0.702063\pi$
$264$	−2.06155	+	3.57071i	−0.126880	+	0.219762i
$265$	8.56155			0.525932
$266$	0.157671	−	0.273094i	0.00966742	−	0.0167445i
$267$	9.40388	−	16.2880i	0.575508	−	0.996810i
$268$	−2.24621			−0.137209
$269$	−10.6847	+	18.5064i	−0.651455	+	1.12835i	0.331315	+	0.943520i	$0.392508\pi$
$269$	−10.6847	+	18.5064i	−0.651455	+	1.12835i	−0.982770	+	0.184833i	$0.940826\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	6.58854	+	11.4117i	0.400225	+	0.693211i	0.993753	−	0.111603i	$-0.0355985\pi$
$271$	6.58854	+	11.4117i	0.400225	+	0.693211i	−0.593528	+	0.804814i	$0.702265\pi$
$272$	−3.12311			−0.189366
$273$	−1.59612	+	1.24573i	−0.0966015	+	0.0753951i
$274$	11.8078			0.713333
$275$	−2.06155	−	3.57071i	−0.124316	−	0.215322i
$276$	−2.34233	−	4.05703i	−0.140992	−	0.244205i
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$	12.5616			0.753392
$279$	3.34233	−	5.78908i	0.200100	−	0.346583i
$280$	0.280776	−	0.486319i	0.0167796	−	0.0290631i
$281$	16.2462			0.969168			0.484584	−	0.874745i	$-0.338971\pi$
$281$	16.2462			0.969168			0.484584	+	0.874745i	$0.338971\pi$
$282$	−3.50000	+	6.06218i	−0.208422	+	0.360997i
$283$	−7.78078	−	13.4767i	−0.462519	−	0.801107i	0.536567	−	0.843858i	$-0.319721\pi$
$283$	−7.78078	−	13.4767i	−0.462519	−	0.801107i	−0.999086	+	0.0427513i	$0.986388\pi$
$284$	6.56155	+	11.3649i	0.389357	+	0.674385i
$285$	0.561553			0.0332635
$286$	2.06155	+	14.7224i	0.121902	+	0.870556i
$287$	−6.87689			−0.405930
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	3.62311	+	6.27540i	0.213124	+	0.369141i
$290$	−1.21922	+	2.11176i	−0.0715953	+	0.124007i
$291$	−7.12311			−0.417564
$292$	−4.68466	+	8.11407i	−0.274149	+	0.474840i
$293$	−1.96543	+	3.40423i	−0.114822	+	0.198877i	−0.917709	−	0.397254i	$-0.869963\pi$
$293$	−1.96543	+	3.40423i	−0.114822	+	0.198877i	0.802887	+	0.596132i	$0.203296\pi$
$294$	−6.68466			−0.389857
$295$	−3.21922	+	5.57586i	−0.187430	+	0.324639i
$296$	2.06155	+	3.57071i	0.119825	+	0.207544i
$297$	−2.06155	−	3.57071i	−0.119623	−	0.207194i
$298$	−2.19224			−0.126993
$299$	−15.6577	−	6.33527i	−0.905506	−	0.366378i
$300$	1.00000			0.0577350
$301$	0.123106	+	0.213225i	0.00709569	+	0.0122901i
$302$	7.68466	+	13.3102i	0.442202	+	0.765917i
$303$	4.43845	−	7.68762i	0.254982	−	0.441642i
$304$	0.561553			0.0322073
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$	1.56155	−	2.70469i	0.0892680	−	0.154617i
$307$	25.6155			1.46196			0.730978	−	0.682401i	$-0.239064\pi$
$307$	25.6155			1.46196			0.730978	+	0.682401i	$0.239064\pi$
$308$	1.15767	−	2.00514i	0.0659644	−	0.114254i
$309$	−2.28078	−	3.95042i	−0.129749	−	0.224732i
$310$	3.34233	+	5.78908i	0.189832	+	0.328798i
$311$	30.7386			1.74303			0.871514	−	0.490371i	$-0.163139\pi$
$311$	30.7386			1.74303			0.871514	+	0.490371i	$0.163139\pi$
$312$	−3.34233	−	1.35234i	−0.189222	−	0.0765614i
$313$	31.3693			1.77310			0.886549	−	0.462634i	$-0.153096\pi$
$313$	31.3693			1.77310			0.886549	+	0.462634i	$0.153096\pi$
$314$	−6.93845	−	12.0177i	−0.391559	−	0.678200i
$315$	0.280776	+	0.486319i	0.0158200	+	0.0274010i
$316$	−5.78078	+	10.0126i	−0.325194	+	0.563253i
$317$	−24.8078			−1.39334			−0.696671	−	0.717390i	$-0.745336\pi$
$317$	−24.8078			−1.39334			−0.696671	+	0.717390i	$0.745336\pi$
$318$	−4.28078	+	7.41452i	−0.240054	+	0.415786i
$319$	−5.02699	+	8.70700i	−0.281457	+	0.487498i
$320$	1.00000			0.0559017
$321$	−1.00000	+	1.73205i	−0.0558146	+	0.0966736i
$322$	1.31534	+	2.27824i	0.0733011	+	0.126961i
$323$	0.876894	+	1.51883i	0.0487917	+	0.0845097i
$324$	1.00000			0.0555556
$325$	2.84233	−	2.21837i	0.157664	−	0.123053i
$326$	−14.4384			−0.799672
$327$	1.87689	+	3.25088i	0.103792	+	0.179774i
$328$	−6.12311	−	10.6055i	−0.338092	−	0.585592i
$329$	1.96543	−	3.40423i	0.108358	−	0.187681i
$330$	4.12311			0.226969
$331$	−15.3693	+	26.6204i	−0.844774	+	1.46319i	0.0410432	+	0.999157i	$0.486932\pi$
$331$	−15.3693	+	26.6204i	−0.844774	+	1.46319i	−0.885817	+	0.464034i	$0.846401\pi$
$332$	3.56155	−	6.16879i	0.195466	−	0.338556i
$333$	−4.12311			−0.225945
$334$	−2.18466	+	3.78394i	−0.119539	+	0.207048i
$335$	1.12311	+	1.94528i	0.0613618	+	0.106282i
$336$	0.280776	+	0.486319i	0.0153176	+	0.0265309i
$337$	−6.00000			−0.326841			−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000			−0.326841			−0.163420	+	0.986557i	$0.552253\pi$
$338$	−12.5000	+	3.57071i	−0.679910	+	0.194221i
$339$	8.68466			0.471686
$340$	1.56155	+	2.70469i	0.0846871	+	0.146682i
$341$	13.7808	+	23.8690i	0.746271	+	1.29258i
$342$	−0.280776	+	0.486319i	−0.0151826	+	0.0262971i
$343$	7.68466			0.414933
$344$	−0.219224	+	0.379706i	−0.0118197	+	0.0204724i
$345$	−2.34233	+	4.05703i	−0.126107	+	0.218423i
$346$	20.1771			1.08473
$347$	−0.438447	+	0.759413i	−0.0235371	+	0.0407674i	−0.877554	−	0.479478i	$-0.840826\pi$
$347$	−0.438447	+	0.759413i	−0.0235371	+	0.0407674i	0.854017	+	0.520245i	$0.174159\pi$
$348$	−1.21922	−	2.11176i	−0.0653572	−	0.113202i
$349$	−4.24621	−	7.35465i	−0.227294	−	0.393686i	0.729711	−	0.683756i	$-0.239655\pi$
$349$	−4.24621	−	7.35465i	−0.227294	−	0.393686i	−0.957005	+	0.290070i	$0.906321\pi$
$350$	−0.561553			−0.0300163
$351$	2.84233	−	2.21837i	0.151712	−	0.118408i
$352$	4.12311			0.219762
$353$	12.9309	+	22.3969i	0.688241	+	1.19207i	0.972407	+	0.233293i	$0.0749501\pi$
$353$	12.9309	+	22.3969i	0.688241	+	1.19207i	−0.284166	+	0.958775i	$0.591717\pi$
$354$	−3.21922	−	5.57586i	−0.171100	−	0.296354i
$355$	6.56155	−	11.3649i	0.348251	−	0.603189i
$356$	−18.8078			−0.996810
$357$	−0.876894	+	1.51883i	−0.0464102	+	0.0803848i
$358$	6.34233	−	10.9852i	0.335203	−	0.580588i
$359$	13.1231			0.692611			0.346306	−	0.938122i	$-0.387436\pi$
$359$	13.1231			0.692611			0.346306	+	0.938122i	$0.387436\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	9.34233	+	16.1814i	0.491702	+	0.851652i
$362$	−1.43845	−	2.49146i	−0.0756031	−	0.130948i
$363$	6.00000			0.314918
$364$	1.87689	+	0.759413i	0.0983760	+	0.0398040i
$365$	9.36932			0.490412
$366$	−3.00000	−	5.19615i	−0.156813	−	0.271607i
$367$	−6.24621	−	10.8188i	−0.326050	−	0.564734i	0.655675	−	0.755044i	$-0.272384\pi$
$367$	−6.24621	−	10.8188i	−0.326050	−	0.564734i	−0.981724	+	0.190309i	$0.939051\pi$
$368$	−2.34233	+	4.05703i	−0.122102	+	0.211487i
$369$	12.2462			0.637512
$370$	2.06155	−	3.57071i	0.107175	−	0.185633i
$371$	2.40388	−	4.16365i	0.124803	−	0.216166i
$372$	−6.68466			−0.346583
$373$	12.9039	−	22.3502i	0.668138	−	1.15725i	−0.310287	−	0.950643i	$-0.600425\pi$
$373$	12.9039	−	22.3502i	0.668138	−	1.15725i	0.978424	−	0.206605i	$-0.0662416\pi$
$374$	6.43845	+	11.1517i	0.332924	+	0.576642i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	7.00000			0.360997
$377$	−8.15009	−	3.29762i	−0.419751	−	0.169836i
$378$	−0.561553			−0.0288832
$379$	8.84233	+	15.3154i	0.454200	+	0.786697i	0.998642	−	0.0521012i	$-0.0165918\pi$
$379$	8.84233	+	15.3154i	0.454200	+	0.786697i	−0.544442	+	0.838799i	$0.683259\pi$
$380$	−0.280776	−	0.486319i	−0.0144035	−	0.0249476i
$381$	4.28078	−	7.41452i	0.219311	−	0.379857i
$382$	10.8769			0.556510
$383$	−0.0961180	+	0.166481i	−0.00491140	+	0.00850679i	−0.868471	−	0.495741i	$-0.834897\pi$
$383$	−0.0961180	+	0.166481i	−0.00491140	+	0.00850679i	0.863559	+	0.504247i	$0.168230\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−2.31534			−0.118001
$386$		0			0
$387$	−0.219224	−	0.379706i	−0.0111438	−	0.0193016i
$388$	3.56155	+	6.16879i	0.180810	+	0.313173i
$389$	−18.0540			−0.915373			−0.457686	−	0.889114i	$-0.651322\pi$
$389$	−18.0540			−0.915373			−0.457686	+	0.889114i	$0.651322\pi$
$390$	0.500000	+	3.57071i	0.0253185	+	0.180810i
$391$	−14.6307			−0.739905
$392$	3.34233	+	5.78908i	0.168813	+	0.292393i
$393$	1.06155	+	1.83866i	0.0535483	+	0.0927483i
$394$	−6.40388	+	11.0918i	−0.322623	+	0.558799i
$395$	11.5616			0.581725
$396$	−2.06155	+	3.57071i	−0.103597	+	0.179435i
$397$	10.0616	−	17.4271i	0.504975	−	0.874642i	−0.495009	−	0.868888i	$-0.664835\pi$
$397$	10.0616	−	17.4271i	0.504975	−	0.874642i	0.999983	−	0.00575403i	$-0.00183158\pi$
$398$	2.87689			0.144206
$399$	0.157671	−	0.273094i	0.00789341	−	0.0136718i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−0.157671	−	0.273094i	−0.00787370	−	0.0136377i	0.862062	−	0.506803i	$-0.169173\pi$
$401$	−0.157671	−	0.273094i	−0.00787370	−	0.0136377i	−0.869935	+	0.493166i	$0.835840\pi$
$402$	−2.24621			−0.112031
$403$	−19.0000	+	14.8290i	−0.946457	+	0.738687i
$404$	−8.87689			−0.441642
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	0.684658	+	1.18586i	0.0339790	+	0.0588534i
$407$	8.50000	−	14.7224i	0.421329	−	0.729764i
$408$	−3.12311			−0.154617
$409$	9.40388	−	16.2880i	0.464992	−	0.805390i	−0.534209	−	0.845352i	$-0.679391\pi$
$409$	9.40388	−	16.2880i	0.464992	−	0.805390i	0.999201	+	0.0399625i	$0.0127239\pi$
$410$	−6.12311	+	10.6055i	−0.302399	+	0.523770i
$411$	11.8078			0.582434
$412$	−2.28078	+	3.95042i	−0.112366	+	0.194623i
$413$	1.80776	+	3.13114i	0.0889543	+	0.154073i
$414$	−2.34233	−	4.05703i	−0.115119	−	0.199392i
$415$	−7.12311			−0.349660
$416$	0.500000	+	3.57071i	0.0245145	+	0.175069i
$417$	12.5616			0.615142
$418$	−1.15767	−	2.00514i	−0.0566235	−	0.0980748i
$419$	−16.2462	−	28.1393i	−0.793679	−	1.37469i	−0.923674	−	0.383178i	$-0.874829\pi$
$419$	−16.2462	−	28.1393i	−0.793679	−	1.37469i	0.129995	−	0.991515i	$-0.458504\pi$
$420$	0.280776	−	0.486319i	0.0137005	−	0.0237299i
$421$	−32.4924			−1.58358			−0.791792	−	0.610791i	$-0.790852\pi$
$421$	−32.4924			−1.58358			−0.791792	+	0.610791i	$0.790852\pi$
$422$	10.9654	−	18.9927i	0.533789	−	0.924550i
$423$	−3.50000	+	6.06218i	−0.170176	+	0.294753i
$424$	8.56155			0.415786
$425$	1.56155	−	2.70469i	0.0757464	−	0.131197i
$426$	6.56155	+	11.3649i	0.317908	+	0.550633i
$427$	1.68466	+	2.91791i	0.0815263	+	0.141208i
$428$	2.00000			0.0966736
$429$	2.06155	+	14.7224i	0.0995327	+	0.710806i
$430$	0.438447			0.0211438
$431$	11.3693	+	19.6922i	0.547641	+	0.948542i	0.998436	+	0.0559140i	$0.0178073\pi$
$431$	11.3693	+	19.6922i	0.547641	+	0.948542i	−0.450795	+	0.892628i	$0.648859\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	9.36932	−	16.2281i	0.450261	−	0.779874i	−0.548141	−	0.836386i	$-0.684664\pi$
$433$	9.36932	−	16.2281i	0.450261	−	0.779874i	0.998402	+	0.0565114i	$0.0179977\pi$
$434$	3.75379			0.180188
$435$	−1.21922	+	2.11176i	−0.0584573	+	0.101251i
$436$	1.87689	−	3.25088i	0.0898869	−	0.155689i
$437$	2.63068			0.125843
$438$	−4.68466	+	8.11407i	−0.223842	+	0.387705i
$439$	−12.5616	−	21.7572i	−0.599530	−	1.03842i	−0.992890	−	0.119032i	$-0.962021\pi$
$439$	−12.5616	−	21.7572i	−0.599530	−	1.03842i	0.393360	−	0.919384i	$-0.371313\pi$
$440$	−2.06155	−	3.57071i	−0.0982807	−	0.170227i
$441$	−6.68466			−0.318317
$442$	−8.87689	+	6.92820i	−0.422231	+	0.329541i
$443$	−13.1231			−0.623498			−0.311749	−	0.950165i	$-0.600915\pi$
$443$	−13.1231			−0.623498			−0.311749	+	0.950165i	$0.600915\pi$
$444$	2.06155	+	3.57071i	0.0978370	+	0.169459i
$445$	9.40388	+	16.2880i	0.445787	+	0.772125i
$446$	−13.6501	+	23.6427i	−0.646351	+	1.11951i
$447$	−2.19224			−0.103689
$448$	0.280776	−	0.486319i	0.0132654	−	0.0229764i
$449$	10.0885	−	17.4739i	0.476108	−	0.824643i	−0.523518	−	0.852015i	$-0.675381\pi$
$449$	10.0885	−	17.4739i	0.476108	−	0.824643i	0.999625	+	0.0273722i	$0.00871392\pi$
$450$	1.00000			0.0471405
$451$	−25.2462	+	43.7277i	−1.18880	+	2.05906i
$452$	−4.34233	−	7.52113i	−0.204246	−	0.353764i
$453$	7.68466	+	13.3102i	0.361057	+	0.625369i
$454$	−20.0000			−0.938647
$455$	−0.280776	−	2.00514i	−0.0131630	−	0.0940026i
$456$	0.561553			0.0262971
$457$	−10.1231	−	17.5337i	−0.473539	−	0.820193i	0.526002	−	0.850483i	$-0.323690\pi$
$457$	−10.1231	−	17.5337i	−0.473539	−	0.820193i	−0.999541	+	0.0302897i	$0.990357\pi$
$458$	12.1231	+	20.9978i	0.566476	+	0.981164i
$459$	1.56155	−	2.70469i	0.0728870	−	0.126244i
$460$	4.68466			0.218423
$461$	15.0270	−	26.0275i	0.699877	−	1.21222i	−0.268632	−	0.963243i	$-0.586572\pi$
$461$	15.0270	−	26.0275i	0.699877	−	1.21222i	0.968509	−	0.248979i	$-0.0800950\pi$
$462$	1.15767	−	2.00514i	0.0538597	−	0.0932878i
$463$	−7.61553			−0.353924			−0.176962	−	0.984218i	$-0.556627\pi$
$463$	−7.61553			−0.353924			−0.176962	+	0.984218i	$0.556627\pi$
$464$	−1.21922	+	2.11176i	−0.0566010	+	0.0980359i
$465$	3.34233	+	5.78908i	0.154997	+	0.268462i
$466$	2.65767	+	4.60322i	0.123114	+	0.213240i
$467$	−17.8617			−0.826543			−0.413271	−	0.910608i	$-0.635614\pi$
$467$	−17.8617			−0.826543			−0.413271	+	0.910608i	$0.635614\pi$
$468$	−3.34233	−	1.35234i	−0.154499	−	0.0625121i
$469$	1.26137			0.0582445
$470$	−3.50000	−	6.06218i	−0.161443	−	0.279627i
$471$	−6.93845	−	12.0177i	−0.319707	−	0.553748i
$472$	−3.21922	+	5.57586i	−0.148177	+	0.256650i
$473$	1.80776			0.0831211
$474$	−5.78078	+	10.0126i	−0.265520	+	0.459894i
$475$	−0.280776	+	0.486319i	−0.0128829	+	0.0223138i
$476$	1.75379			0.0803848
$477$	−4.28078	+	7.41452i	−0.196003	+	0.339488i
$478$	5.68466	+	9.84612i	0.260010	+	0.450351i
$479$	19.1231	+	33.1222i	0.873757	+	1.51339i	0.858081	+	0.513514i	$0.171657\pi$
$479$	19.1231	+	33.1222i	0.873757	+	1.51339i	0.0156760	+	0.999877i	$0.495010\pi$
$480$	1.00000			0.0456435
$481$	13.7808	+	5.57586i	0.628349	+	0.254237i
$482$	−28.1231			−1.28097
$483$	1.31534	+	2.27824i	0.0598501	+	0.103663i
$484$	−3.00000	−	5.19615i	−0.136364	−	0.236189i
$485$	3.56155	−	6.16879i	0.161722	−	0.280110i
$486$	1.00000			0.0453609
$487$	−6.52699	+	11.3051i	−0.295766	+	0.512282i	−0.975163	−	0.221489i	$-0.928908\pi$
$487$	−6.52699	+	11.3051i	−0.295766	+	0.512282i	0.679397	+	0.733771i	$0.262242\pi$
$488$	−3.00000	+	5.19615i	−0.135804	+	0.235219i
$489$	−14.4384			−0.652929
$490$	3.34233	−	5.78908i	0.150991	−	0.261524i
$491$	8.71922	+	15.1021i	0.393493	+	0.681550i	0.992908	−	0.118889i	$-0.0379332\pi$
$491$	8.71922	+	15.1021i	0.393493	+	0.681550i	−0.599415	+	0.800439i	$0.704600\pi$
$492$	−6.12311	−	10.6055i	−0.276051	−	0.478134i
$493$	−7.61553			−0.342986
$494$	1.59612	−	1.24573i	0.0718127	−	0.0560481i
$495$	4.12311			0.185320
$496$	3.34233	+	5.78908i	0.150075	+	0.259938i
$497$	−3.68466	−	6.38202i	−0.165280	−	0.286273i
$498$	3.56155	−	6.16879i	0.159597	−	0.276430i
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−2.18466	+	3.78394i	−0.0976033	+	0.169054i
$502$	−8.12311			−0.362552
$503$	21.5270	−	37.2858i	0.959841	−	1.66249i	0.236962	−	0.971519i	$-0.423848\pi$
$503$	21.5270	−	37.2858i	0.959841	−	1.66249i	0.722879	−	0.690974i	$-0.242818\pi$
$504$	0.280776	+	0.486319i	0.0125068	+	0.0216624i
$505$	4.43845	+	7.68762i	0.197508	+	0.342094i
$506$	19.3153			0.858672
$507$	−12.5000	+	3.57071i	−0.555144	+	0.158581i
$508$	−8.56155			−0.379857
$509$	−20.2732	−	35.1142i	−0.898594	−	1.55641i	−0.829293	−	0.558814i	$-0.811256\pi$
$509$	−20.2732	−	35.1142i	−0.898594	−	1.55641i	−0.0693009	−	0.997596i	$-0.522077\pi$
$510$	1.56155	+	2.70469i	0.0691467	+	0.119766i
$511$	2.63068	−	4.55648i	0.116375	−	0.201567i
$512$	1.00000			0.0441942
$513$	−0.280776	+	0.486319i	−0.0123966	+	0.0214715i
$514$	2.78078	−	4.81645i	0.122655	−	0.212444i
$515$	4.56155			0.201006
$516$	−0.219224	+	0.379706i	−0.00965078	+	0.0167156i
$517$	−14.4309	−	24.9950i	−0.634669	−	1.09928i
$518$	−1.15767	−	2.00514i	−0.0508651	−	0.0881010i
$519$	20.1771			0.885676
$520$	2.84233	−	2.21837i	0.124644	−	0.0972820i
$521$	−6.31534			−0.276680			−0.138340	−	0.990385i	$-0.544177\pi$
$521$	−6.31534			−0.276680			−0.138340	+	0.990385i	$0.544177\pi$
$522$	−1.21922	−	2.11176i	−0.0533640	−	0.0924291i
$523$	14.9039	+	25.8143i	0.651701	+	1.12878i	0.982710	+	0.185152i	$0.0592777\pi$
$523$	14.9039	+	25.8143i	0.651701	+	1.12878i	−0.331009	+	0.943628i	$0.607389\pi$
$524$	1.06155	−	1.83866i	0.0463741	−	0.0803224i
$525$	−0.561553			−0.0245082
$526$	6.50000	−	11.2583i	0.283413	−	0.490887i
$527$	−10.4384	+	18.0799i	−0.454706	+	0.787574i
$528$	4.12311			0.179435
$529$	0.526988	−	0.912769i	0.0229125	−	0.0396856i
$530$	−4.28078	−	7.41452i	−0.185945	−	0.322066i
$531$	−3.21922	−	5.57586i	−0.139702	−	0.241972i
$532$	−0.315342			−0.0136718
$533$	−40.9309	−	16.5611i	−1.77291	−	0.717341i
$534$	−18.8078			−0.813892
$535$	−1.00000	−	1.73205i	−0.0432338	−	0.0748831i
$536$	1.12311	+	1.94528i	0.0485108	+	0.0840231i
$537$	6.34233	−	10.9852i	0.273692	−	0.474048i
$538$	21.3693			0.921297
$539$	13.7808	−	23.8690i	0.593580	−	1.02811i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−27.3693			−1.17670			−0.588349	−	0.808607i	$-0.700222\pi$
$541$	−27.3693			−1.17670			−0.588349	+	0.808607i	$0.700222\pi$
$542$	6.58854	−	11.4117i	0.283002	−	0.490174i
$543$	−1.43845	−	2.49146i	−0.0617297	−	0.106919i
$544$	1.56155	+	2.70469i	0.0669510	+	0.115963i
$545$	−3.75379			−0.160795
$546$	1.87689	+	0.759413i	0.0803237	+	0.0324999i
$547$	−5.61553			−0.240103			−0.120051	−	0.992768i	$-0.538306\pi$
$547$	−5.61553			−0.240103			−0.120051	+	0.992768i	$0.538306\pi$
$548$	−5.90388	−	10.2258i	−0.252201	−	0.436826i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$	−2.06155	+	3.57071i	−0.0879049	+	0.152256i
$551$	1.36932			0.0583349
$552$	−2.34233	+	4.05703i	−0.0996962	+	0.172679i
$553$	3.24621	−	5.62260i	0.138043	−	0.239097i
$554$	−1.00000			−0.0424859
$555$	2.06155	−	3.57071i	0.0875080	−	0.151568i
$556$	−6.28078	−	10.8786i	−0.266364	−	0.461356i
$557$	4.28078	+	7.41452i	0.181382	+	0.314163i	0.942352	−	0.334625i	$-0.108610\pi$
$557$	4.28078	+	7.41452i	0.181382	+	0.314163i	−0.760969	+	0.648788i	$0.775276\pi$
$558$	−6.68466			−0.282984
$559$	0.219224	+	1.56557i	0.00927217	+	0.0662165i
$560$	−0.561553			−0.0237299
$561$	6.43845	+	11.1517i	0.271831	+	0.470826i
$562$	−8.12311	−	14.0696i	−0.342653	−	0.593492i
$563$	16.4924	−	28.5657i	0.695073	−	1.20390i	−0.275083	−	0.961420i	$-0.588705\pi$
$563$	16.4924	−	28.5657i	0.695073	−	1.20390i	0.970156	−	0.242481i	$-0.0779612\pi$
$564$	7.00000			0.294753
$565$	−4.34233	+	7.52113i	−0.182683	+	0.316417i
$566$	−7.78078	+	13.4767i	−0.327050	+	0.566468i
$567$	−0.561553			−0.0235830
$568$	6.56155	−	11.3649i	0.275317	−	0.476862i
$569$	−13.0885	−	22.6700i	−0.548700	−	0.950377i	−0.998364	−	0.0571787i	$-0.981790\pi$
$569$	−13.0885	−	22.6700i	−0.548700	−	0.950377i	0.449664	−	0.893198i	$-0.351544\pi$
$570$	−0.280776	−	0.486319i	−0.0117604	−	0.0203697i
$571$	23.6847			0.991172			0.495586	−	0.868559i	$-0.334953\pi$
$571$	23.6847			0.991172			0.495586	+	0.868559i	$0.334953\pi$
$572$	11.7192	−	9.14657i	0.490005	−	0.382437i
$573$	10.8769			0.454389
$574$	3.43845	+	5.95557i	0.143518	+	0.248580i
$575$	−2.34233	−	4.05703i	−0.0976819	−	0.169190i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−40.7386			−1.69597			−0.847986	−	0.530019i	$-0.822185\pi$
$577$	−40.7386			−1.69597			−0.847986	+	0.530019i	$0.822185\pi$
$578$	3.62311	−	6.27540i	0.150701	−	0.261022i
$579$		0			0
$580$	2.43845			0.101251
$581$	−2.00000	+	3.46410i	−0.0829740	+	0.143715i
$582$	3.56155	+	6.16879i	0.147631	+	0.255705i
$583$	−17.6501	−	30.5709i	−0.730992	−	1.26612i
$584$	9.36932			0.387705
$585$	0.500000	+	3.57071i	0.0206725	+	0.147631i
$586$	3.93087			0.162383
$587$	20.1231	+	34.8542i	0.830569	+	1.43859i	0.897587	+	0.440837i	$0.145318\pi$
$587$	20.1231	+	34.8542i	0.830569	+	1.43859i	−0.0670179	+	0.997752i	$0.521348\pi$
$588$	3.34233	+	5.78908i	0.137835	+	0.238738i
$589$	1.87689	−	3.25088i	0.0773361	−	0.133950i
$590$	6.43845			0.265067
$591$	−6.40388	+	11.0918i	−0.263421	+	0.456258i
$592$	2.06155	−	3.57071i	0.0847293	−	0.146755i
$593$	33.1771			1.36242			0.681210	−	0.732088i	$-0.261454\pi$
$593$	33.1771			1.36242			0.681210	+	0.732088i	$0.261454\pi$
$594$	−2.06155	+	3.57071i	−0.0845865	+	0.146508i
$595$	−0.876894	−	1.51883i	−0.0359492	−	0.0622658i
$596$	1.09612	+	1.89853i	0.0448987	+	0.0777669i
$597$	2.87689			0.117743
$598$	2.34233	+	16.7276i	0.0957850	+	0.684041i
$599$	−14.0000			−0.572024			−0.286012	−	0.958226i	$-0.592330\pi$
$599$	−14.0000			−0.572024			−0.286012	+	0.958226i	$0.592330\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	−14.9924	−	25.9676i	−0.611554	−	1.05924i	−0.990979	−	0.134020i	$-0.957212\pi$
$601$	−14.9924	−	25.9676i	−0.611554	−	1.05924i	0.379425	−	0.925222i	$-0.376122\pi$
$602$	0.123106	−	0.213225i	0.00501741	−	0.00869041i
$603$	−2.24621			−0.0914728
$604$	7.68466	−	13.3102i	0.312684	−	0.541585i
$605$	−3.00000	+	5.19615i	−0.121967	+	0.211254i
$606$	−8.87689			−0.360599
$607$	−16.2116	+	28.0794i	−0.658010	+	1.13971i	0.323120	+	0.946358i	$0.395268\pi$
$607$	−16.2116	+	28.0794i	−0.658010	+	1.13971i	−0.981130	+	0.193349i	$0.938065\pi$
$608$	−0.280776	−	0.486319i	−0.0113870	−	0.0197228i
$609$	0.684658	+	1.18586i	0.0277438	+	0.0480536i
$610$	6.00000			0.242933
$611$	19.8963	−	15.5286i	0.804918	−	0.628219i
$612$	−3.12311			−0.126244
$613$	−9.93845	−	17.2139i	−0.401410	−	0.695263i	0.592486	−	0.805581i	$-0.298146\pi$
$613$	−9.93845	−	17.2139i	−0.401410	−	0.695263i	−0.993896	+	0.110318i	$0.964813\pi$
$614$	−12.8078	−	22.1837i	−0.516879	−	0.895261i
$615$	−6.12311	+	10.6055i	−0.246907	+	0.427656i
$616$	−2.31534			−0.0932878
$617$	14.6577	−	25.3878i	0.590096	−	1.02208i	−0.404123	−	0.914704i	$-0.632423\pi$
$617$	14.6577	−	25.3878i	0.590096	−	1.02208i	0.994219	−	0.107371i	$-0.0342433\pi$
$618$	−2.28078	+	3.95042i	−0.0917463	+	0.158909i
$619$	−20.5616			−0.826439			−0.413219	−	0.910632i	$-0.635596\pi$
$619$	−20.5616			−0.826439			−0.413219	+	0.910632i	$0.635596\pi$
$620$	3.34233	−	5.78908i	0.134231	−	0.232495i
$621$	−2.34233	−	4.05703i	−0.0939944	−	0.162803i
$622$	−15.3693	−	26.6204i	−0.616253	−	1.06738i
$623$	10.5616			0.423140
$624$	0.500000	+	3.57071i	0.0200160	+	0.142943i
$625$	1.00000			0.0400000
$626$	−15.6847	−	27.1666i	−0.626885	−	1.08580i
$627$	−1.15767	−	2.00514i	−0.0462329	−	0.0800778i
$628$	−6.93845	+	12.0177i	−0.276874	+	0.479560i
$629$	12.8769			0.513435
$630$	0.280776	−	0.486319i	0.0111864	−	0.0193754i
$631$	6.87689	−	11.9111i	0.273765	−	0.474175i	−0.696058	−	0.717986i	$-0.745064\pi$
$631$	6.87689	−	11.9111i	0.273765	−	0.474175i	0.969823	+	0.243811i	$0.0783977\pi$
$632$	11.5616			0.459894
$633$	10.9654	−	18.9927i	0.435837	−	0.754892i
$634$	12.4039	+	21.4842i	0.492621	+	0.853245i
$635$	4.28078	+	7.41452i	0.169877	+	0.294236i
$636$	8.56155			0.339488
$637$	22.3423	+	9.03996i	0.885235	+	0.358176i
$638$	10.0540			0.398041
$639$	6.56155	+	11.3649i	0.259571	+	0.449590i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	5.71922	−	9.90599i	0.225896	−	0.391263i	−0.730692	−	0.682707i	$-0.760802\pi$
$641$	5.71922	−	9.90599i	0.225896	−	0.391263i	0.956588	+	0.291444i	$0.0941358\pi$
$642$	2.00000			0.0789337
$643$	−10.8769	+	18.8393i	−0.428943	+	0.742951i	−0.996780	−	0.0801904i	$-0.974447\pi$
$643$	−10.8769	+	18.8393i	−0.428943	+	0.742951i	0.567837	+	0.823141i	$0.307780\pi$
$644$	1.31534	−	2.27824i	0.0518317	−	0.0897752i
$645$	0.438447			0.0172638
$646$	0.876894	−	1.51883i	0.0345009	−	0.0597574i
$647$	−17.5270	−	30.3576i	−0.689057	−	1.19348i	−0.972143	−	0.234387i	$-0.924692\pi$
$647$	−17.5270	−	30.3576i	−0.689057	−	1.19348i	0.283086	−	0.959094i	$-0.408642\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	26.5464			1.04204
$650$	−3.34233	−	1.35234i	−0.131097	−	0.0530433i
$651$	3.75379			0.147123
$652$	7.21922	+	12.5041i	0.282727	+	0.489697i
$653$	22.2808	+	38.5914i	0.871914	+	1.51020i	0.860014	+	0.510270i	$0.170455\pi$
$653$	22.2808	+	38.5914i	0.871914	+	1.51020i	0.0119002	+	0.999929i	$0.496212\pi$
$654$	1.87689	−	3.25088i	0.0733924	−	0.127119i
$655$	−2.12311			−0.0829566
$656$	−6.12311	+	10.6055i	−0.239067	+	0.414076i
$657$	−4.68466	+	8.11407i	−0.182766	+	0.316560i
$658$	−3.93087			−0.153241
$659$	3.02699	−	5.24290i	0.117915	−	0.204234i	−0.801026	−	0.598629i	$-0.795712\pi$
$659$	3.02699	−	5.24290i	0.117915	−	0.204234i	0.918941	+	0.394395i	$0.129046\pi$
$660$	−2.06155	−	3.57071i	−0.0802458	−	0.138990i
$661$	−14.8078	−	25.6478i	−0.575955	−	0.997584i	−0.995937	−	0.0900513i	$-0.971297\pi$
$661$	−14.8078	−	25.6478i	−0.575955	−	0.997584i	0.419982	−	0.907532i	$-0.362036\pi$
$662$	30.7386			1.19469
$663$	−8.87689	+	6.92820i	−0.344750	+	0.269069i
$664$	−7.12311			−0.276430
$665$	0.157671	+	0.273094i	0.00611421	+	0.0105901i
$666$	2.06155	+	3.57071i	0.0798835	+	0.138362i
$667$	−5.71165	+	9.89286i	−0.221156	+	0.383053i
$668$	4.36932			0.169054
$669$	−13.6501	+	23.6427i	−0.527743	+	0.914078i
$670$	1.12311	−	1.94528i	0.0433894	−	0.0751526i
$671$	24.7386			0.955024
$672$	0.280776	−	0.486319i	0.0108312	−	0.0187602i
$673$	−12.8769	−	22.3034i	−0.496368	−	0.859734i	0.503623	−	0.863923i	$-0.332000\pi$
$673$	−12.8769	−	22.3034i	−0.496368	−	0.859734i	−0.999991	+	0.00418904i	$0.998667\pi$
$674$	3.00000	+	5.19615i	0.115556	+	0.200148i
$675$	1.00000			0.0384900
$676$	9.34233	+	9.03996i	0.359320	+	0.347691i
$677$	−37.1231			−1.42676			−0.713378	−	0.700779i	$-0.752836\pi$
$677$	−37.1231			−1.42676			−0.713378	+	0.700779i	$0.752836\pi$
$678$	−4.34233	−	7.52113i	−0.166766	−	0.288847i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$	1.56155	−	2.70469i	0.0598828	−	0.103720i
$681$	−20.0000			−0.766402
$682$	13.7808	−	23.8690i	0.527693	−	0.913991i
$683$	−8.56155	+	14.8290i	−0.327599	+	0.567418i	−0.982035	−	0.188700i	$-0.939573\pi$
$683$	−8.56155	+	14.8290i	−0.327599	+	0.567418i	0.654436	+	0.756117i	$0.272906\pi$
$684$	0.561553			0.0214715
$685$	−5.90388	+	10.2258i	−0.225576	+	0.390709i
$686$	−3.84233	−	6.65511i	−0.146701	−	0.254093i
$687$	12.1231	+	20.9978i	0.462525	+	0.801117i
$688$	0.438447			0.0167156
$689$	24.3348	−	18.9927i	0.927080	−	0.723564i
$690$	4.68466			0.178342
$691$	10.2808	+	17.8068i	0.391099	+	0.677404i	0.992595	−	0.121472i	$-0.0387616\pi$
$691$	10.2808	+	17.8068i	0.391099	+	0.677404i	−0.601496	+	0.798876i	$0.705428\pi$
$692$	−10.0885	−	17.4739i	−0.383509	−	0.664257i
$693$	1.15767	−	2.00514i	0.0439763	−	0.0761691i
$694$	0.876894			0.0332865
$695$	−6.28078	+	10.8786i	−0.238243	+	0.412650i
$696$	−1.21922	+	2.11176i	−0.0462146	+	0.0800460i
$697$	−38.2462			−1.44868
$698$	−4.24621	+	7.35465i	−0.160721	+	0.278378i
$699$	2.65767	+	4.60322i	0.100522	+	0.174110i
$700$	0.280776	+	0.486319i	0.0106124	+	0.0183811i
$701$	−36.3002			−1.37104			−0.685520	−	0.728054i	$-0.740425\pi$
$701$	−36.3002			−1.37104			−0.685520	+	0.728054i	$0.740425\pi$
$702$	−3.34233	−	1.35234i	−0.126148	−	0.0510410i
$703$	−2.31534			−0.0873248
$704$	−2.06155	−	3.57071i	−0.0776977	−	0.134576i
$705$	−3.50000	−	6.06218i	−0.131818	−	0.228315i
$706$	12.9309	−	22.3969i	0.486660	−	0.842919i
$707$	4.98485			0.187474
$708$	−3.21922	+	5.57586i	−0.120986	+	0.209554i
$709$	−17.1231	+	29.6581i	−0.643072	+	1.11383i	0.341672	+	0.939819i	$0.389007\pi$
$709$	−17.1231	+	29.6581i	−0.643072	+	1.11383i	−0.984743	+	0.174013i	$0.944326\pi$
$710$	−13.1231			−0.492501
$711$	−5.78078	+	10.0126i	−0.216796	+	0.375502i
$712$	9.40388	+	16.2880i	0.352425	+	0.610419i
$713$	15.6577	+	27.1199i	0.586384	+	1.01565i
$714$	1.75379			0.0656339
$715$	−13.7808	−	5.57586i	−0.515372	−	0.208525i
$716$	−12.6847			−0.474048
$717$	5.68466	+	9.84612i	0.212297	+	0.367710i
$718$	−6.56155	−	11.3649i	−0.244875	−	0.424136i
$719$	−22.4924	+	38.9580i	−0.838826	+	1.45289i	0.0520512	+	0.998644i	$0.483424\pi$
$719$	−22.4924	+	38.9580i	−0.838826	+	1.45289i	−0.890877	+	0.454245i	$0.849909\pi$
$720$	1.00000			0.0372678
$721$	1.28078	−	2.21837i	0.0476986	−	0.0826164i
$722$	9.34233	−	16.1814i	0.347685	−	0.602209i
$723$	−28.1231			−1.04591
$724$	−1.43845	+	2.49146i	−0.0534595	+	0.0925945i
$725$	−1.21922	−	2.11176i	−0.0452808	−	0.0784287i
$726$	−3.00000	−	5.19615i	−0.111340	−	0.192847i
$727$	38.4233			1.42504			0.712521	−	0.701651i	$-0.247554\pi$
$727$	38.4233			1.42504			0.712521	+	0.701651i	$0.247554\pi$
$728$	−0.280776	−	2.00514i	−0.0104063	−	0.0743156i
$729$	1.00000			0.0370370
$730$	−4.68466	−	8.11407i	−0.173387	−	0.300315i
$731$	0.684658	+	1.18586i	0.0253230	+	0.0438607i
$732$	−3.00000	+	5.19615i	−0.110883	+	0.192055i
$733$	20.0691			0.741270			0.370635	−	0.928779i	$-0.379140\pi$
$733$	20.0691			0.741270			0.370635	+	0.928779i	$0.379140\pi$
$734$	−6.24621	+	10.8188i	−0.230552	+	0.399328i
$735$	3.34233	−	5.78908i	0.123284	−	0.213534i
$736$	4.68466			0.172679
$737$	4.63068	−	8.02058i	0.170573	−	0.295442i
$738$	−6.12311	−	10.6055i	−0.225395	−	0.390395i
$739$	13.7732	+	23.8559i	0.506655	+	0.877553i	0.999970	+	0.00770202i	$0.00245165\pi$
$739$	13.7732	+	23.8559i	0.506655	+	0.877553i	−0.493315	+	0.869851i	$0.664215\pi$
$740$	−4.12311			−0.151568
$741$	1.59612	−	1.24573i	0.0586349	−	0.0457631i
$742$	−4.80776			−0.176499
$743$	−6.58854	−	11.4117i	−0.241710	−	0.418654i	0.719491	−	0.694501i	$-0.244375\pi$
$743$	−6.58854	−	11.4117i	−0.241710	−	0.418654i	−0.961202	+	0.275847i	$0.911042\pi$
$744$	3.34233	+	5.78908i	0.122536	+	0.212238i
$745$	1.09612	−	1.89853i	0.0401587	−	0.0695568i
$746$	−25.8078			−0.944889
$747$	3.56155	−	6.16879i	0.130310	−	0.225704i
$748$	6.43845	−	11.1517i	0.235413	−	0.407747i
$749$	−1.12311			−0.0410374
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	11.9039	+	20.6181i	0.434379	+	0.752366i	0.997245	−	0.0741820i	$-0.0236346\pi$
$751$	11.9039	+	20.6181i	0.434379	+	0.752366i	−0.562866	+	0.826548i	$0.690301\pi$
$752$	−3.50000	−	6.06218i	−0.127632	−	0.221065i
$753$	−8.12311			−0.296022
$754$	1.21922	+	8.70700i	0.0444015	+	0.317090i
$755$	−15.3693			−0.559347
$756$	0.280776	+	0.486319i	0.0102117	+	0.0176873i
$757$	14.2116	+	24.6153i	0.516531	+	0.894658i	0.999816	+	0.0191948i	$0.00611027\pi$
$757$	14.2116	+	24.6153i	0.516531	+	0.894658i	−0.483285	+	0.875463i	$0.660556\pi$
$758$	8.84233	−	15.3154i	0.321168	−	0.556279i
$759$	19.3153			0.701102
$760$	−0.280776	+	0.486319i	−0.0101848	+	0.0176406i
$761$	8.96543	−	15.5286i	0.324997	−	0.562911i	−0.656515	−	0.754313i	$-0.727970\pi$
$761$	8.96543	−	15.5286i	0.324997	−	0.562911i	0.981512	+	0.191402i	$0.0613035\pi$
$762$	−8.56155			−0.310152
$763$	−1.05398	+	1.82554i	−0.0381565	+	0.0660889i
$764$	−5.43845	−	9.41967i	−0.196756	−	0.340792i
$765$	1.56155	+	2.70469i	0.0564581	+	0.0977882i
$766$	0.192236			0.00694577
$767$	3.21922	+	22.9899i	0.116239	+	0.830116i
$768$	1.00000			0.0360844
$769$	16.6577	+	28.8519i	0.600691	+	1.04043i	0.992717	+	0.120473i	$0.0384411\pi$
$769$	16.6577	+	28.8519i	0.600691	+	1.04043i	−0.392026	+	0.919954i	$0.628226\pi$
$770$	1.15767	+	2.00514i	0.0417196	+	0.0722604i
$771$	2.78078	−	4.81645i	0.100147	−	0.173460i
$772$

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.280776 - 0.486319i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.280776 - 0.486319i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.06155 - 3.57071i) q^{11} +1.00000 q^{12} +(2.84233 - 2.21837i) q^{13} -0.561553 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.56155 - 2.70469i) q^{17} +1.00000 q^{18} +(-0.280776 + 0.486319i) q^{19} +(-0.500000 + 0.866025i) q^{20} -0.561553 q^{21} +(-2.06155 + 3.57071i) q^{22} +(-2.34233 - 4.05703i) q^{23} +(-0.500000 - 0.866025i) q^{24} +1.00000 q^{25} +(-3.34233 - 1.35234i) q^{26} +1.00000 q^{27} +(0.280776 + 0.486319i) q^{28} +(-1.21922 - 2.11176i) q^{29} +(-0.500000 + 0.866025i) q^{30} -6.68466 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.06155 + 3.57071i) q^{33} -3.12311 q^{34} +(0.280776 - 0.486319i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.06155 + 3.57071i) q^{37} +0.561553 q^{38} +(-3.34233 - 1.35234i) q^{39} +1.00000 q^{40} +(-6.12311 - 10.6055i) q^{41} +(0.280776 + 0.486319i) q^{42} +(-0.219224 + 0.379706i) q^{43} +4.12311 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-2.34233 + 4.05703i) q^{46} +7.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.34233 + 5.78908i) q^{49} +(-0.500000 - 0.866025i) q^{50} -3.12311 q^{51} +(0.500000 + 3.57071i) q^{52} +8.56155 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.06155 - 3.57071i) q^{55} +(0.280776 - 0.486319i) q^{56} +0.561553 q^{57} +(-1.21922 + 2.11176i) q^{58} +(-3.21922 + 5.57586i) q^{59} +1.00000 q^{60} +(-3.00000 + 5.19615i) q^{61} +(3.34233 + 5.78908i) q^{62} +(0.280776 + 0.486319i) q^{63} +1.00000 q^{64} +(2.84233 - 2.21837i) q^{65} +4.12311 q^{66} +(1.12311 + 1.94528i) q^{67} +(1.56155 + 2.70469i) q^{68} +(-2.34233 + 4.05703i) q^{69} -0.561553 q^{70} +(6.56155 - 11.3649i) q^{71} +(-0.500000 + 0.866025i) q^{72} +9.36932 q^{73} +(2.06155 - 3.57071i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-0.280776 - 0.486319i) q^{76} -2.31534 q^{77} +(0.500000 + 3.57071i) q^{78} +11.5616 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.12311 + 10.6055i) q^{82} -7.12311 q^{83} +(0.280776 - 0.486319i) q^{84} +(1.56155 - 2.70469i) q^{85} +0.438447 q^{86} +(-1.21922 + 2.11176i) q^{87} +(-2.06155 - 3.57071i) q^{88} +(9.40388 + 16.2880i) q^{89} +1.00000 q^{90} +(-0.280776 - 2.00514i) q^{91} +4.68466 q^{92} +(3.34233 + 5.78908i) q^{93} +(-3.50000 - 6.06218i) q^{94} +(-0.280776 + 0.486319i) q^{95} +1.00000 q^{96} +(3.56155 - 6.16879i) q^{97} +(3.34233 - 5.78908i) q^{98} +4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 3 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 3 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 3 q^{7} + 4 q^{8} - 2 q^{9} - 2 q^{10} + 4 q^{12} - q^{13} + 6 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 4 q^{18} + 3 q^{19} - 2 q^{20} + 6 q^{21} + 3 q^{23} - 2 q^{24} + 4 q^{25} - q^{26} + 4 q^{27} - 3 q^{28} - 9 q^{29} - 2 q^{30} - 2 q^{31} - 2 q^{32} + 4 q^{34} - 3 q^{35} - 2 q^{36} - 6 q^{38} - q^{39} + 4 q^{40} - 8 q^{41} - 3 q^{42} - 5 q^{43} - 2 q^{45} + 3 q^{46} + 28 q^{47} - 2 q^{48} + q^{49} - 2 q^{50} + 4 q^{51} + 2 q^{52} + 26 q^{53} - 2 q^{54} - 3 q^{56} - 6 q^{57} - 9 q^{58} - 17 q^{59} + 4 q^{60} - 12 q^{61} + q^{62} - 3 q^{63} + 4 q^{64} - q^{65} - 12 q^{67} - 2 q^{68} + 3 q^{69} + 6 q^{70} + 18 q^{71} - 2 q^{72} - 12 q^{73} - 2 q^{75} + 3 q^{76} - 34 q^{77} + 2 q^{78} + 38 q^{79} - 2 q^{80} - 2 q^{81} - 8 q^{82} - 12 q^{83} - 3 q^{84} - 2 q^{85} + 10 q^{86} - 9 q^{87} + 17 q^{89} + 4 q^{90} + 3 q^{91} - 6 q^{92} + q^{93} - 14 q^{94} + 3 q^{95} + 4 q^{96} + 6 q^{97} + q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 3 * q^7 + 4 * q^8 - 2 * q^9 - 2 * q^10 + 4 * q^12 - q^13 + 6 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 4 * q^18 + 3 * q^19 - 2 * q^20 + 6 * q^21 + 3 * q^23 - 2 * q^24 + 4 * q^25 - q^26 + 4 * q^27 - 3 * q^28 - 9 * q^29 - 2 * q^30 - 2 * q^31 - 2 * q^32 + 4 * q^34 - 3 * q^35 - 2 * q^36 - 6 * q^38 - q^39 + 4 * q^40 - 8 * q^41 - 3 * q^42 - 5 * q^43 - 2 * q^45 + 3 * q^46 + 28 * q^47 - 2 * q^48 + q^49 - 2 * q^50 + 4 * q^51 + 2 * q^52 + 26 * q^53 - 2 * q^54 - 3 * q^56 - 6 * q^57 - 9 * q^58 - 17 * q^59 + 4 * q^60 - 12 * q^61 + q^62 - 3 * q^63 + 4 * q^64 - q^65 - 12 * q^67 - 2 * q^68 + 3 * q^69 + 6 * q^70 + 18 * q^71 - 2 * q^72 - 12 * q^73 - 2 * q^75 + 3 * q^76 - 34 * q^77 + 2 * q^78 + 38 * q^79 - 2 * q^80 - 2 * q^81 - 8 * q^82 - 12 * q^83 - 3 * q^84 - 2 * q^85 + 10 * q^86 - 9 * q^87 + 17 * q^89 + 4 * q^90 + 3 * q^91 - 6 * q^92 + q^93 - 14 * q^94 + 3 * q^95 + 4 * q^96 + 6 * q^97 + q^98

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